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A biomechanical investigation of blood flow occlusion achieved with the use of surgical pneumatic tourniquets Breault, Martine 1989

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A BIOMECHANICAL INVESTIGATION OF BLOOD FLOW OCCLUSION ACHIEVED WITH THE USE OF SURGICAL PNEUMATIC TOURNIQUETS by Martine Breault B.A.Sc, McGill University, Montreal, 1985  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Mechanical Engineering  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA October 1988 © Martine Breault, 1988  In presenting  this thesis in partial fulfilment of the  degree at the  and  study. I further agree that permission for extensive  copying of this thesis for scholarly purposes may or  by  his or  her  representatives.  be  permission.  Department The University of British Columbia Vancouver, Canada  DE-6  (2/88)  ft/nrZZ.  granted by  It is understood  publication of this thesis for financial gain shall not be  Date  advanced  University of British Columbia, I agree that the Library shall make it  freely available for reference department  requirements for an  the head of  my  that  or  copying  allowed without my  written  "Operating on a hand without a tourniquet is like trying to fix a watch in a bottle of ink." - S.Bunnell  ABSTRACT  The use of the modern pneumatic surgical tourniquet has greatly facilitated orthopaedic limb surgery since its introduction. Overly high inflation pressures and improper application procedures have, however, resulted in occasional cutaneous, vascular and neuromuscular injuries. The present research models the mechanism of blood flow occlusion produced by a pneumatic cuff to determine safer inflation pressures and efficacious application procedures. A computerized data acquisition system using a biomedical pneumatic pressure sensor was utilized to measure surface and internal soft tissue pressures. Minimal occlusive cuff inflation pressures were determined by a series of pressure measurements on exsanguinated and non-exsanguinated limbs of normotensive subjects and patients. It was found that occlusion was achievable near patient diastolic pressure providing the cuff width was equal to or greater than the limb circumference. Analytical models were developed to understand the mechanism causing arrest of blood flow. To illustrate the application of the model and analytic techniques, two commercial tourniquet cuffs were analysed and tested to improve their design. Wider, thinner, softer and shape-matching cuff designs were suggested for future manufacture.  iv  TABLE OF CONTENTS Abstract Table of Contents List of Tables List of Figures Nomenclature . Terminology Acknowledgments  iii iv viii ix xvii xx xxii  CHAPTER 1 - INTRODUCTION  1  1.1 Historical Development of the Tourniquet  2  1.2 Injuries Caused by Tourniquet Use  3  1.3 Problem Definition 1.3.1 Research Objectives  4 5  CHAPTER 2 - REVIEW OF LITERATURE 2.1 Studies Investigating Soft Tissue Compression Patterns 2.1.1 2.1.2 2.1.3 2.1.4  Studies Studies Studies Studies  with Limb Models with Animals with Cadavers with Humans  2.2 Studies Investigating Blood Flow Occlusion CHAPTER 3 - E X P E R I M E N T A L INVESTIGATION 3.1 Experiments to Investigate the Pressure Distribution in the Soft Tissues beneath the Tourniquet Cuff  9 ,  9 10 11 13 15 16 18 19  3.1.1 Procedure and Apparatus 3.1.1.1 Biomedical Pressure Sensor 3.1.1.2 Pressure Data Acquisition System  19 20 22  3.1.2 Experiments to Determine the Surface Pressure Distribution 3.1.2.1 Surface Pressure Measurements and Results 3.1.2.2 Surface Pressure Analysis  24 24 26  3.1.3 Experiments to Determine Internal Pressure Distribution 3.1.3.1 Internal Pressure Measurements and Results 3.1.3.2 Internal Pressure Analysis  27 28 30  3.2 Experiments to Investigate the Occlusion Pressure 3.2.1 Laboratory Experiments  32 32  V  3.2.1.1 Detection of Blood Flow 3.2.1.2 Experimental Procedure 3.2.1.3 Experimental Results  33 34 34  3.2.1 Clinical Experiments 3.2.2.1 Clinical Experiment Procedure 3.2.2.2 Clinical Experiment Results  36 36 36  3.2.3 Correlation of Experimental Data 3.2.3.1 Correlation with Blood Pressure 3.2.3.2 Curve Fitting  38 38 39  CHAPTER 4 - ANALYTICAL MODEL 4.1 Model Assumptions  41 41  4.1.1 Assumptions Pertaining to the Limb 4.1.2 Assumptions Pertaining to the Main Artery of the Limb  42 42  4.1.3 Assumptions Pertaining to the Main Nerves  43  4.2 Soft Tissue Compression Model  43  4.2.1 Isotropic Material Model  44  4.2.2 Orthotropic Material Model 4.2.2.1 Plane Stress Condition  46 46  4.2.2.2 Plane Strain Condition  46  4.3 Blood Flow Occlusion Models  47  4.3.1 Fluid Dynamic Approach  48  4.3.2 Elasticity Approach 4.3.2.1 Collapsible Tube Approach 4.3.2.2 Flexible Strip Beam Approach  51 51 53  CHAPTER 5 - CLINICAL EVALUATION OF OCCLUSIVE CUFFS 5.1 Physiological Effects in Blood Flow Occlusion 5.1.1 Variation of Biological Tissues 5.1.1.1 Evaluation of Soft Tissue Composition 5.1.2 Variation of Arterial System 5.1.2.1 Effect of Anaesthetics in the Blood Stream 5.1.3 Consideration of Ischaemia and Compression as Cause of Neural Damage 5.2 Characterization of Pneumatic Cuffs 5.2.1 Evaluation of Cuff Designs  57 58 58 59 60 61 62 64 65  vi  5.2.1.1 Shape and Dimensions of Occlusive Cuffs  65  5.2.2 Adjustment of Cuff to the Limbs  66  5.2.2.1 Characterization of Limbs  66  5.2.3 Transmission of the Cuff Pressure to the Limb  68  5.2.3.1 Evaluation of Cuff Designs 5.2.3.2 Evaluation of Snugness during Cuff Application 5.2.3.3 Application of an Interfacing Layer between the Cuff and the Limb  69 70 73  75  CHAPTER 6 -CONCLUSIONS AND RECOMMENDATIONS 6.1 Conclusions  75  6.1.1 General Conclusions Resulting from Present Research  75  6.1.2 Specific Conclusions on Clinical Use of Pneumatic Tourniquet Cuffs . .  77  6.2 Recommendations for Clinical Use  79  6.2.1 Proper Selection and Use of Cuffs 6.2.2 Snugness of Cuff Application 6.2.3 Use of Protective Interface 6.2.4 Cuff Inflation Pressure Setting 6.3 Recommendations for the Design of Future Pneumatic Cuffs  80 81 82 82 83  6.3.1 Shape of Cuffs 6.3.2 Incorporation of Snugness Bladder 6.3.3 Material of Fabrication 6.4 Recommendations for Further Investigation 6.4.1 Pressure Profile Experiments 6.4.2 Blood Flow Occlusion Experiments References Tables Figures  APPENDICES  ,  83 85 85 86 86 87 89 97 102  198  A. Periodic Transducer Calibration  198  B. Control Software  200  C. Protocols  205  C. 1 Surface Pressure Measurements C.2 Internal Pressure Measurements C.3 Limb-Cuff Interface Tests  205 206 207  v i i  C.4 Occlusion Pressure Tests C.5 Clinical Trials for Occlusion Pressure Measurements C.6 Exsanguination Tests C.7 Physical Evaluation of Standards Cuffs C. 8 Snugness Tests D. Thick Walled Cylinder Derivation D. 1 Limb Made of Isotropic Material  E.  F.  208 209 210 211 211 212 212  D. 2 Limb Made of Orthotropic Material  214  Collapsible Tube Derivation  215  E. l Work Done E.2 Stored Elastic Energy  215 217  E. 3 Critical Load  218  Beam Deflection Solutions  220  F. l Deflection due to Internal Pressure F.2 Deflection due to External Load F.3 Superposition of Deflections G. Cuff Drawings  220 221 226 227  viii  LIST OF TABLES Table Number  Page  1  List of Instrumentation and Specifications  97  2  Model Parameter Values  98  3  Occlusion Pressure Data for Similar Systolic Blood Pressures  99  4  Occlusion Pressure Data for Similar Systolic and Diastolic Blood Pressures Occlusion Pressure Data for Similar Diastolic Blood Pressures  5  100 101  ix  LIST OF FIGURES Figure . . Number  Page  2.1  Longitudinal View of Dahlin's Limb Model Showing the Slit Catheter Positions  2.2  (a) (b)  102  Griffiths' and Heywood's Limb Models Made of a Core Surrounded by Fluid Tissue Model Made of a Core Surrounded by Elastic Solid Tissue  102 102  2.3  Variation of Stresses Sustained by a Fluid Element and a Solid Element....  2.4  Element Subjected to Principal Stresses  103  2.5  Canine Thigh with the Tourniquet in Place Showing the Withdrawal of the Slit Catheter  104  2.6  (a) (b)  2.7  (a) (b)  103  Longitudinal View of the Thigh Showing the Five Positions of the Catheter Cross Section of the Thigh Showing the Three Planes of Pressure Measurement  104  Tissue Pressure Distribution under the Pneumatic Tourniquet Inflated to 200 mmHg Tissue Pressure Distribution under the Esmarch Bandage tourniquet Wrapped Six Times around the Limb  105  104  105  2.8  Subcutaneous Tissue Pressure versus Position under the Pneumatic Tourniquet and the Esmarch Bandage Tourniquet  105  2.9  Pressure Probe used by Shaw and Murray to Measure Soft Tissue Pressures beneath a Pneumatic Tourniquet  106  2.10  Schematic Representation of Shaw and Murray's Experimental Configuration  2.11  Positions of Slit Catheter Used by Hargens et al. in Disarticulated Upper and Lower Limbs  108  2.12  Pressure Profiles for the Arm and the Thigh under the Pneumatic Tourniquet Inflated to 300 mmHg  109  2.13  Correlation between Longitudinal and Radial Pressure Profiles  2.14  Special Clamp Used by Parkes to Apply Selective Pneumatic Pressure to the Limb  2.15 2.16  107  109 .  10  1  Nomogram Relating Tourniquet Pressure to Underlying Soft Tissue Pressure and Leg Circumference  Ill  Graph of the Doppler Occlusion Pressure as a Function of Cuff Width  Ill  X  3.1  Pneumatic Pressure Sensor Operation  3.2  Sketch of the Electrical Circuit Printed onto Mylar with Conductive Ink . . . .  3.3  Sketch Showing the Relative Length of the Pneumatic Pressure Sensor  112 113  to Cuff Width  114  3.4  Sketch of the Pneumatic Pressure Sensor  114  3.5  Sketch of the Pneumatic Pressure Sensor Plastic Reinforcements  115  3.6  Position of the Pneumatic Pressure Sensor Relative to the Tourniquet Cuff Applied on the Limb  115  3.7  Pneumatic System Used to Individually Calibrate the Pressure Sensors . . . .  116  3.8  Data Acquisition System Used to Measure Surface and Internal Soft Tissue Pressure  3.9  Block Diagram of the Double Feedback Loop Control Software  3.10  (a)  3.11 3.12 3.13  3.14  Algorithm of the Program "DATA"; Inflation and Deflation Control of the Pressure Sensor and the Cuff (b) Status Check Control of the Pneumatic Pressure Sensor Electrical Contacts ' Plexiglass Models Representing the Upper and Lower Limbs Sketch of the Foam Addition on Opposite Sides of the Cylinder to Simulate the Oval Shape of the Upper Limb (a) Preparation of Limb Models; Bare Plexiglass Cylinder Wrapped twice with the Aspen Cuff (b) Cylinder Coated with one Layer of Foam (c) Cylinder Coated with One Half Width Layer of Foam and Full Width Layer of Foam  117 118 119 120 121 122 23 123  1  123  Typical Pressure Distribution underneath the Pneumatic Tourniquet Cuff  1 2 4  3.15  Pressure Sensor Placement Locations around the Limb  125  3.16  Anterior Surface Pressure Profile  126  3.17  Medial Surface Pressure Profile  1 2 6  3.18  Posterior Surface Pressure Profile  1 2 7  3.19  Lateral Surface Pressure Profile  1 2 7  3.20  Example of Surface Pressure Measurement  xi  3.21  Repetition of the Previous Pressure Measurement Following a Recovery Period  128  3.22  Second Example of Surface Pressure Measurement  ^ 9  3.23  Repetition of the Previous Pressure Measurement without a Recovery Period  ^ 9  3.24  Pressure Profile Comparison to McLaren' s Results  3.25  Three-Dimensional View of the Pressure Distribution on the Upper Limb Produced by the 24" Freeman Tourniquet Cuff  3.26  Sketch of the Gap Created by the Overlapping of a Thick Cuff  3.27  Three-Dimensional View of the Pressure Distribution on the Upper Limb Produced by the 24" Aspen Tourniquet Cuff  3.28  Surface Pressure Distribution Discontinuity at Location #3  3.29  Three-Dimensional View of the Pressure Distribution on the Lower  ^1 232  133  Limb Encircled by the 34" Aspen Tourniquet Cuff  134  3.30  Surface Pressure Distribution Discontinuity at Location #5  134  3.31  Sketch Showing the Location of the Median Nerve in the Upper Limb of a Cadaver Sketch Showing the Location of the Radial Nerve in the Upper Limb of a Cadaver  135  3.33  Sketch Showing the Location of the Sciatic Nerve in the Lower Limb of a Cadaver  135  3.34  Sketch Showing the Location of the Saphenous Nerve and the Femoral Artery in the Lower Limb of a Cadaver  137  Internal Pressure Distribution in the Right and Left Upper Limbs of Cadaver #1  138  Internal Pressure Distribution in the Right and Left Lower Limbs of Cadaver #1  138  Distribution of the Averaged Internal Pressures in the Upper Limbs of Cadaver #3  139  Distribution of the Averaged Internal Pressures in the Lower Limbs of Cadaver #3  139  Internal Pressure Profiles for Three Different Cuff Inflation Pressures in the Upper Limb  140  Averaged Pressure Profiles in the Upper Limb Three Different Cuff Inflation Pressures  140  3.32  3.35 3.36 3.37 3.38 3.39 3.40  135  xii  3.41  Variation of Internal Soft Tissue Pressure in Cadaver #2 Caused by Oedema  141  3.42  Averaged Pressure Distribution for the Upper Limbs of Three Cadavers . . . .  142  3.43  Averaged Pressure Distribution for the Lower Limbs of Three Cadavers  143  3.44  Longitudinal Cross-Section of the Limb Showing the Pressure Distribution on the Main Artery and Nerves  I  3.45  Comparison of the Pressure Outputs between the Laser and Ultrasonic Dopplers  I  3.46  Plot of Occlusion Pressure versus the Ratio of Cuff Width to Limb Circumference for the Upper Limb . . .  I -*  4 4  4 4  4  3.47  Plot of Occlusion Pressure versus the Ratio of Cuff Width to Limb Circumference for the Lower Limb  3.48  Plot of Occlusion Pressure as a Function of the Ratio of Cuff Width to Limb Circumference for Upper and Lower Limbs  3.49  Graph of the Averaged Occlusion Pressure as a Function of Cuff Width for the Upper Limbs of Normotensive Subjects  3.50  Graph of Occlusion Pressure as a Function of the Pre-Occlusive Proximal Cuff Pressure when Utilizing Two Cuffs  3.51  Plot of Occlusion Pressure versus Cuff Width to Limb Circumference Ratio Obtained from Clinical Data  3.52  Plot of Occlusion Pressure versus Cuff Width to Limb Circumference Ratio for Exsanguinated Limbs  .-  3.53  Plots of the Difference in Occlusion and Blood Pressures versus Cuff Width to Limb Circumference Ratio  .- -  3.54  Plot of the Difference in Occlusion and Diastolic Pressures versus Cuff Width to Limb Circumference Ratio for the Upper Limb  .  3.55  Plot of the Difference between Occlusion and Diastolic Pressures versus Cuff Width to Limb Circumference Ratio for the Lower Limb  3.56  Plot of the Difference between Occlusion and Diastolic Pressures versus Cuff Width to Limb Circumference Ratio for Upper and Lower Limbs  ^^  3.57  Plot of the Difference between Occlusion and Diastolic Pressures versus Cuff Width to Limb Circumference Ratio Obtained from the Clinical Data  ^  148  n  ^3  xiii  3.58  Superposition of the Clinical and Experimental Data Plots of the Difference between Occlusion and Diastolic Pressures versus Cuff Width to Limb Circumference Ratio  155  Plot of the Difference between Occlusion and Diastolic Pressures versus Cuff Width to Limb Circumference Ratio  156  3.60  Plot of Nondimensional Pressure versus Cuff Width to Limb Circumference Ratio for Experimental and Clinical Data  157  3.61  Plot of Nondimensional Pressure versus Cuff Width to Limb Circumference Ratio for Exsanguinated Limbs  158  3.62  Mathematical Correlation of Experimental Occlusion Pressure Data  158  3.63  Mathematical Correlations of Experimental and Clinical Occlusion Pressure Data  159  3.64  Mathematical Correlations of Nondimensionalized Experimental and Clinical Occlusion Pressure Data  160  4.1  Arterial Tree of the Upper Limb Showing the Region of Compression  161  4.2  Longitudinal and Cross-Section Views of the Thick Walled Cylinder Showing an Infinitesimal Element ,  162  4.3  (a)  3.59  (b) 4.4  Graph of Radial Pressure Change as Function of Poisson's Ratio for an Upper Limb Graph of Radial Pressure Change as Function of Poisson's Ratio for an Upper Limb  163 164  Schematic of a Stenosis in an Artery Causing a Differential in Pressure from the Inlet to the Outlet of the Vessel  165  4.5  Sketch Showing the Pressure Loss along the Tube Caused by a Stenosis . . . .  165  4.6  Effect of the Stenosis Radius on the Pressure Loss  166  4.7  Effect the Stenosis Radius on the Flow and the Pressure Loss  166  4.8 4.9  Section of an Artery Combined Effect of Fluid Friction and Vessel Constriction on Hemostasis  167 167  4.10  (a) (b) (c)  168 168 168  4.11  Structural Model of the Artery Showing a Beam Element Removed from the Cylinder  169  Initial and Final States of the Cylinder Divided into Beam Elements Showing One Deflected Element in the Final State  169  4.12  Collapsible Tube Structural Model of a Artery; Open Vessel. . . . . . . Partially Collapsed Vessel Collapsed Vessel  xiv  4.13  Lateral V i e w of the Beam with Loads Applied it and the Resulting Deflection  159  4.14  Plot of the Occlusion to Diastolic Pressure Ratio versus C u f f Width for Various Loads A p p l i e d on the Beam  170  Plot of the Occlusion to B l o o d Pressure Ratio versus C u f f Width for Various Loads A p p l i e d on the Beam  171  5.1  Displacement of Tissue Layers Compression  172  5.2  Graph of Occlusion Pressure as a Function of L i m b Circumference  172  5.3  Details of the Peripheral Nerve Showing the Invagination of a Paranode by an Adjacent One from Right to Left  173  5.4  L o w Power Electron Micrograph of Abnormal Myelinated Fiber Showing the Indentation at Schwann C e l l Junction  173  5.5  Schematic of the Displacement of the Nodes of Ranvier beneath the  4.15  through Interlayer Slippage  and  Edges of the Tourniquet C u f f  174  5.6  Progressive Stages of Nerve Delamination and Conduction Blockage  174  5.7  Cross-Section Area of a L i m b Encircled by an Inflated Cuff  175  5.8  Normalized L i m b Circumference Distributions for the Upper and L o w e r Limbs (a) Normal Distributions of the Difference between L i m b Circumference at the Proximal and Distal Ends of the Cuffs for the Upper and L o w e r Limbs (b) Normal Distribution of the Curvature Angle Combining Upper and L o w e r L i m b Data  5.9  5.10  176 177 177  Comparison between the Pressure Profiles of the Tourniquet and the B l o o d Pressure Cuffs  178  5.11  Pressure Profile on a Tapered L i m b Produced by a B l o o d Pressure C u f f . . . .  179  5.12  Pressure Profile on a Cylindrical L i m b Produced by the Freeman C u f f  180  5.13  Pressure Profile on a Tapered L i m b Produced by the Freeman C u f f  181  5.14  Pressure Profile on a Cylindrical L i m b Produced by the Aspen C u f f  182  5.15  Pressure Profile on a Tapered L i m b Encircled by the Aspen C u f f  183  5.16  Pressure Profile on a Stepped Cylindrical L i m b M o d e l Produced by the Aspen C u f f  184  Schematic Showing a Proper and an Improper C u f f Fit on the L i m b  185  5.17  XV  5.18  Variation in Pressure Profiles Due to a Small Displacement of the Cuff. . . .  186  5.19 Pressure Distribution on a Limb Produced by the Freeman Cuff Showing the Degree of Snugness for Loose, Medium-Loose, Medium, and Tight Cuff Fits  187  5.20 Pressure Distribution on a Limb Produced by the Aspen Cuff Showing the Degree of Snugness for Loose, Medium-Loose, Medium, and Tight Cuff Fits.  188  5.21 Experimental Configuration for the Cuff Snugness Test  188  5.22 Calibration Curve for the Five Bladders Used inside the Tourniquet Cuffs 5.23 Plot of Cuff Pressure versus Volume Generated from the Snugness Test on the Upper Limb 5.24 Plot of Cuff Pressure versus Volume Generated from the Snugness Test on the Lower Limb 5.25  189 190 190  Typical Graph for Clinical Use Showing the Three Levels of Snugness . . . .  191  5.26 Plot of Cuff Pressure versus Volume for the Upper and Lower Limbs 5.27 Pressure Distributions underneath the 24" Aspen Cuff with Different Interfacial Materials  192 193  5.28 Pressure Distributions underneath the 34" Aspen Cuff with Different Interfacial Materials  194  6.1  Plot of Occlusion to Diastolic Pressure Ratio versus Cuff Width Showing the 99% Confidence Limit of the Theoretical Curve  195  6.2  Normal Distribution Curve of the Limb Curvature Angle Showing Five Recommended Cuff Designs  196  6.3  Sketch of the Most Desirable Pressure Distribution for Future Cuff Designs A. 1 Graph of Pressure versus Transducer Voltage Output  197 199  A.2  Graph of Cuff Pressure versus Pressure Transferred to the Surface  199  E. 1  Segment of a Ring Distorted to an Ellipse from a Circle .  219  E.2  Inextensible Ring Deformation  219  G.1  Sketch of the 24" Freeman Cuff  G.2  Sketch of the 24" Dual Freeman Cuff  227  G.3  Sketch of the 24" Aspen Cuff  228  .  227  xvi  G.4  Sketch of the 24" Dual Aspen Cuff  228  G.5  Sketch of the 24" Banana Aspen Cuff  229  NOMENCLATURE A  cross-section area of the artery [m ]  b  width of the beam element [m]  CIRC  limb circumference [m]  DOP  doppler occlusion pressure [Pa]  e  radial strain  et  tangential strain  e  axial strain  2  r  z  E  Young's modulus [Pa]  E  r  radial Young's modulus of muscle [Pa]  E  t  tangential Young's modulus of muscle [Pa]  Eb  Young's modulus of bone [Pa]  F  shear force [N]  Fr  radial force [N]  h  wall thickness of the artery [m]  I  moment of inertia [m4]  /'  difference between beam length and half cuff width [m]  I  half cuff width [m]  L  cuff width [m]  M  bending moment [N-m]  n  limb radius to bone radius ratio  P  pressure [Pa]  Pc  contracting pressure [Pa]  Pcuff  cuff pressure [Pa]  Pcrit  critical collapsible pressure [Pa]  Pdia  diastolic blood pressure [Pa]  x v i i i  expanding pressure [Pa] Pi  inner pressure [Pa]  Pext  external pressure applied on the limb by the cuff [Pa]  Pi  laminar pressure [Pa]  Pmean  arterial blood pressure [Pa]  Po  outer pressure [Pa]  Pocc  occlusion pressure [Pa]  Ps  symmetrical pressure [Pa]  Psys  systolic blood pressure [Pa]  Pt  turbulent pressure [Pa]  Pu  unsteady pressure [Pa]  r  radius [m]  Rb  bone radius [m]  Ri  inner radius [m]  Ro  outer radius [m]  s#  cell position along pneumatic pressure sensor  So  hoop stress [Pa]  Sr  radial stress [Pa]  S  shear stress [Pa]  s  St  tangential stress [Pa]  t  time [s]  u  soft tissue displacement [m]  U  elastic stored energy [J]  V  mean blood velocity [m/s]  VOL  volume [m3]  W  work of deformation [J]  X  cuff width to limb circumference ratio  xix  Y  difference between occlusion pressure and diastolic blood pressure [Pa]  GREEK SYMBOLS  a  angle between planes and principal stresses [radians]  8  standard deviation  r\  blood viscosity [cP]  JJ.  dynamic viscosity [kg/ms]  TC  3.1416  0  angle [radians]  p  blood density [kg/m ]  x  3  w  wall tension [Pa]  D  Poisson's ratio of muscle  Db  Poisson' s ratio of bone  co  external load distribution [Pa]  XX  TERMINOLOGY Acidosis: an abnormal state of reduced alkalinity (measured acidity) of the blood and of the body tissues. Aneurysm: a permanent abnormal blood-filled dilatation of a blood vessel resulting from disease of the vessel wall. Atherosclerotic vascular disease (atherosclerosis): disease characterized by the deposition of fatty substances in the arteries and fibrosis of the inner layer of the vessels. Carpal syndrome: symptom characterizing abnormality of the wrist bones. Catheter: tubular medical device for insertion into canals, vessels, passageways of body cavities usually to permit injection or withdrawal of fluids or to keep a passage open. Diastolic Pressure: pressure associated with the period of dilatation of the heart, especially of the ventricles. Dysplasia: abnormal growth. Embolus: an abnormal particle circulating in the blood. Exsanguination: action of draining blood out of a limb. Fibrinolytic activity: enzymatic breakdown of fibrin, a fibrous protein necessary for the clotting of blood. Gangrene: local death of soft tissues due to loss of blood supply. Hemodynamics: mechanisms involved in the circulation of blood. Hemostasis: cessation of blood flow. Intravenous regional anaesthesia (IVR): local anaesthesia using a double tourniquet. The proximal cuff is inflated during the anaesthetic injection. It is then deflated while the distal cuff if inflated over the portion of the limb already anaesthetized. Ischaemia: local deficiency in red blood cells, in hemoglobin, or in total blood volume. Lumen: the cavity of a tubular organ. Morphine: a bitter crystalline addictive narcotic base that is used in the form of a soluble salt as an analgesic and sedative. Necrosis: localized death of tissues. Normotensive patient: patient that has a systolic blood pressure ranging from 110 mmHg to 135 mmHg. Occlusion pressure: tourniquet pressure necessary to cause the cessation of blood flow.  xxi Oedema: abnormal excess accumulation of serous fluid in connective tissue or i n serous cavity. Paresthesia: a sensation of pricking, tingling, or creeping on the skin. Radiopaque dye: fluid being opaque to various forms of radiation such as x-rays. Sclerosis: pathological hardening of tissue from overgrowth of fibrous tissue or increase of interstitial tissue. Slit catheter: diagnostic device for compartmental syndrome to determine whether or not surgery is necessary. Stenosis: a narrowing or constriction of the diameter of a bodily passage or orifice. Stereotactic technique: non-invasive technique using an auditive device to detect the onset of blood flow. Strangulation: pathological constriction from excessive compression of the main blood vessels interrupting the flow. Systolic Pressure: pressure associated with the period of contraction of the heart, especially that of the ventricles during which blood is forced into the aorta and the pulmonary trunk. Thrombus: a clot of blood formed within a blood vessel and remaining attached to its place of origin. Trophic disorder: deregulation of the system because of malnutrition or poor blood supply. Turgor: the normal state of turgidity and tension i n living cells. Volkmann: ischaemic necrosis causing fibrosis and shortening of muscles. It is caused by the compression of muscle or vascular disease.  xxii  ACKNOWLEGMENTS I wish to thank the Science Council of British Columbia for the financial aid that permitted the realization of this project. The assistance and support throughout the project of Dr. D. P. Romilly is greatly appreciated. A special thanks is given to Dr. J. McEwen for his energetic supervision and many constructive suggestions to this research. Special attention to R. MacNeil for his great help in debugging my computer programs. Additional thanks are due to the staff of the Research Institute of Vancouver General Hospital for allowing me the use of their laboratory facilities and tolerating me for two years. I wish to express my appreciation to Drs. R. McGraw and B. Graham for their orthopaedic expertise. Thanks are extended to Drs. P. Gropper and Landells for letting me use my experimental cuff during actual surgery. A special thank you is given to all the brave subjects that volunteered to my experiments. A final thank to Ian Chang, my regular subject, who helped me considerably in the development of my thesis.  1  CHAPTER 1 - INTRODUCTION The tourniquet is commonly known as a first aid measure to control bleeding. It was originally designed as a surgical device used to provide a bloodless field in limb surgery [1,2].  The use of a tourniquet facilitates and accelerates the operation and allows the  orthopaedic surgeon to perform accurate surgery. The tourniquet accomplishes hemostasis by applying an external pressure to the limb to constrict the underlying blood vessels, thereby preventing blood from flowing to the extremities of the limb. The current design of a tourniquet consists of a pneumatic cuff inflated by a pressure controller. Most surgeons make their decisions regarding inflation pressure level and duration of use predominantly based on their skill and experience due to the lack of available scientific information about safe tourniquet use. At present, surgical tourniquets are rarely set at the minimum effective pressure, i.e. the minimum pressure required to safely occlude blood flow distal to the cuff for the duration of a surgical procedure. Insufficient cuff pressures allow flooding of the surgical site causing the surgeon difficulty in performing the operation while excessive tourniquet pressures can severely compress the soft tissues and lead to cutaneous, vascular, muscular, and neurological injuries [3]. Specifically, the walls of blood vessels are easily damaged by high external pressures causing vascular problems. The mechanical compression of peripheral nerves can lead to functional neuromuscular impairments by disruption of the axon [4]. There is evidence that the likelihood and severity of such injuries may increase with higher cuff pressure [5]. Generally, because of a lack of sufficient information, pressure levels are set far above what is needed to occlude blood vessels and attain a perfectly dry surgical field. Thus, there is a need to determine guidelines for proper use of a tourniquet, implying the study of the mechanisms governing blood flow and the investigation of injuries associated with the prolonged or excessive inflation. The goal of this investigation was to  2  ascertain safe levels of cuff inflation pressure which will efficaciously arrest blood flow while avoiding unnecessary injuries caused by overpressurization. In this chapter, the development of the tourniquet is reviewed; injuries related to cuff use are considered. Finally, the scope and objectives of this research are defined.  1.1 Historical Development of the Tourniquet The historical development of occlusive devices has taken place over many centuries. Roman surgeons used constrictive devices to control hemorrhage while performing amputations [6]. Archigenes and Heliodorus, around 100 A.D., used narrow bands knotted around limbs above and below the surgical site to control venous bleeding [7,8]. A refinement was introduced in 1653 by William Fabry of Hilden used sticks to twist and tighten or loosen the constrictive bandage [7-9]. Morell in 1674 used the paddled Spanish windlass, usually employed for strangulation, to achieve hemostasis [79]. In 1700, Ambroise Pare used a wider bandage above the amputation site to effect occlusion [2,7,8]. In 1718, the French surgeon Jean Louis Petit made a device with considerable advancement over the previous occlusive bandage [7,8,11]. He invented a screw mechanism to tighten the cloth bandage wrapped around the limb. The screw was mounted on a curved support applied over the strap to maintain the pressure over the main blood vessels. The occlusive device took the name "tourniquet" from the word "tourner" meaning to turn. The Petit tourniquet remained in use until the end of the 18th century. In 1864, Joseph Lister exsanguinated the limb before using the tourniquet by elevating the limb for four minutes [2,7,8]. A few years later, exsanguination was achieved by using a rubber bandage for strapping the limb. Nicoise and GrandessoSylvestri improved later on the exsanguination technique [8,12]. In 1873, a strapping method replaced the use of a tourniquet. Johann Friederich August von Esmarch used a  3  two inch wide elastic rubber tube to constrict the limb and stop blood flow [7,8]. The advantage of an Esmarch bandage over a Petit tourniquet was that pressure applied on the limb was preserved over the duration of the surgical procedure while the Petit tourniquet typically became loose during the course of the operation. It was not until 1881 that Volkmann recognized that there was an increased risk of nerve injury and paralysis associated with the Esmarch bandage [11]. In 1904 Harvey Cushing improved the occlusive techniques by using a pneumatic tourniquet [6,7,10]. The original design consisted of a cylindrical bladder inflatable by a bicycle pump [13]. A manometer was then connected to a tank of compressed air to monitor the pressure in the bladder [14]. The pneumatic tourniquet considerably reduced the probability of nerve injuries. Shortly after, in 1908, August Bier used two adjacent tourniquets to administer local anaesthesia. Only the proximal tourniquet was inflated during the injection of the anaesthetics. The distal cuff was then inflated followed by the deflation of the proximal cuff once the drugs were absorbed by the soft tissues. This helped to minimize the pain imparted by the tourniquet as the inflated cuff was applied over an anesthetized area. In 1963, Holmes introduced a tourniquet made of two adjacent bladders (dual tourniquet) for intravenous anaesthesia. An automated microprocessor-controlled tourniquet system is generally used for limb surgery today. This tourniquet was designed by J. A. McEwen and R. W. McGraw in 1982 [15]. The automated tourniquet system provides much better regulation of the cuff pressure than the previous tourniquet systems.  1.2 Injuries Caused by Tourniquet Use The use of an inflatable cuff to arrest blood flow has been made safer with the automated microprocessor-controlled tourniquet but is not without problems. The high cuff pressures used can cause soft tissue injuries and ultimately cause damage to the more deeply embedded blood vessels and peripheral nerves.  4  The occlusion of blood flow in a limb has been reported to damage both soft and hard tissues by ischaemia and mechanical compression [15,19]. The level of pressure and the time of application of the tourniquet have been shown to be contributing factors in defining the severity of the lesions [18]. Cutaneous [6], vascular [20], muscular [21], and neurological [22] injuries have been reported. The tourniquet cuff can cause skin necrosis [23], damages to subcutaneous tissues [24], and can lead to modification of the compliance of the arterial walls [25]. An abnormal swelling of the limb subsequent to tourniquet release has been observed [26] as a vascular reaction to excessive inflation pressure [27]. Cuff over-inflation has been found to induce serious vascular problems: deep vein thrombosis [27,28], an increase in fibrinolytic activity [29], acidosis [30], deregulation of the systemic circulation [31], hypertension [32], and circulatory stasis [30]. Most of these problems are caused by the mechanical compression caused by the tourniquet [33-35]. In the literature cases of acute degeneration in striated muscles [20] and ultrastructural alterations in injured motor nerve muscles have been reported [16]. Functional and morphological changes in the peripheral nervous system can occur; conduction blocks [36,37] which result in paraesthesia [38] and nerve paralysis have been seen in cases [39]. In extreme cases, even bone marrow has been noted to undergo structural change under external compression [40]. There is clearly a need to see injuries associated with the use of a pneumatic tourniquet reduced. A safe and efficacious way to arrest blood flow must be devised to reduce theriskof injuries.  1.3 Problem Definition The proper use of the tourniquet remains at present a very subjective matter [24]. Hospitals and cuff manufacturers recommend cuff inflation pressure guidelines based on limited published research work. Surgeons choose the cuff pressure and inflation time  5  depending on the previous history and on the pre-operative blood pressure of the patient. The decision is based on skill, experience, personal preference, and personal interpretation of the literature results [24]. Generally, high tourniquet inflation pressures are used in order to guarantee a bloodless operating field. The main aim of this project was to attempt to minimize the necessary compression pressure and hence injury due to the over-inflation of the tourniquet cuff without reducing efficacy of occlusion.  1.3.1 Research Objectives The intent of this biomechanical research was to investigate and model the mechanisms of blood flow occlusion in a limb subjected to a surgical pneumatic tourniquet cuff. The model attempted to quantify the minimum inflation pressure required to ensure a bloodless surgical field and correspondingly minimize the risk of cuff related injuries. Furthermore, it was intended to propose an improved clinical technique to reduce the incidence of injuries related to tourniquet selection and application. To accomplish this, six specific objectives were defined.  I • To perforin a literature search and critically review previous research related to the development and use of surgical pneumatic tourniquet cuffs. Previous experimental and clinical research work related to the use of surgical tourniquet cuffs to achieve blood flow occlusion were collected and studied to act as a basis for this work. There was particularly reference to work done on the distribution of pressure in the underlying soft tissues of a limb as well as work detailing parameters related to blood flow occlusion. This literature review is presented in Chapter 2.  II • To experimentally determine the pressure distribution on the surface and within the limb as developed under a pneumatic tourniquet cuff.  6  Experimental measurements of the soft tissue pressure distribution over the surface of the limb under the tourniquet cuff were obtained as a function of limb position and inflation pressure. This was done to better understand the transmission of applied pressure from the cuff to the limb. Measurements of the pressure distribution inside the limb were then obtained to quantify the transmission of pressure through the soft tissues to the principle arteries. This information allowed the development of an empirical model of the full pressure distribution within the portion of the limb encircled by the occlusive cuff. This work is discussed in Chapter 3, Section 3.1.  Ill •  To experimentally determine the effect of variations in tourniquet and  patient parameters on the cuff inflation pressure required to occlude blood flow.  The tourniquet inflation pressure required to occlude blood flow was measured using various cuff designs on a variety of normotensive patients. The effects of changes in tourniquet dimensions, blood pressure and limb circumference were then quantified. These effects were also clinically evaluated on patients in surgery. This experimentation was performed to determine the minimum cuff inflation pressure necessary to cause hemostasis. This work is discussed in Chapter 3, Section 3.2.  TV • To develop analytical models to explain and allow predictions of the pressure distribution in the limb under the cuff.  Analytical models related to the compression of surface and internal soft tissues were developed using concepts based on the theory of elasticity. In this analysis, the limb was basically assumed to be a cylinder made of elastic material, compressed externally by the pneumatic cuff. These models were then compared with the pressure measurements both on the surface and within the limb. This work is presented in Chapter 4, Section 4.2.  7  V •  To develop analytical models to explain and allow predictions of the  mechanism by which occlusion occurs in the artery. Analytical models related to the arrest of arterial flow were investigated to explain the observed arrest of blood flow due to compression of the limb. The blood flow occlusion was first considered as a fluid dynamic problem, and then as an elasticity problem. Two mechanisms were considered for this last problem. Bloodflowocclusion was initially assumed to be caused by collapse of the vessel and second by the gradual constriction of the artery. These analytical models are presented in Chapter 4, Section 4.3.  VI •  To utilize the experimental and analytical models to evaluate current  pneumatic cuff designs and to improve clinical application techniques. Physiological parameters affecting blood flow occlusion were first evaluated to determine their effect on cuff inflation pressure. Pneumatic cuffs were then clinically evaluated for safety and efficacy. The physiology of a compressed limb and the clinical characterization of cuffs are presented in Chapter 5.  General conclusions made from the experimental, analytical, and clinical research work are presented in Chapter 6, Section 6.1. These are followed by more specific conclusions for clinical use of the tourniquet. Clinical recommendations are also presented for improved tourniquet cuff design based on the experimental and analytical results of this research. Application techniques are suggested to minimize the cuff inflation pressure while ensuring safe limb compression in view of protecting structures and tissues. The recommended improvements in cuff design and application technique are discussed in Sections 6.2 and 6.3. Further investigatory work is proposed in Section 6.4 to clarify injuries related to tourniquet application.  8  The following chapter provides the pertinent background information necessary to a comprehensive understanding of the current problem associated with pneumatic cuffs. The research which has been conducted to investigate the problems is first presented.  9  CHAPTER 2 - REVIEW OF LITERATURE  The surgical pneumatic tourniquet has undergone many design improvements since its introduction in 1904. The automated version used routinely in orthopaedic surgery today still appears to occasionally cause compression related injuries. Other injuries, related to tourniquet application, have also been recognized. Previous attempts have been made to understand the mechanisms of blood flow occlusion to avoid subsequent neuromuscular impairment. To this end, the limb portion beneath the pneumatic cuff has been investigated both analytically and experimentally. These previous investigations have been primarily of two types. In the first type compression patterns in the limb produced by the tourniquet were developed. These soft tissue compression patterns were then evaluated in an attempt to understand the mechanisms causing nerve and muscle injuries. Experiments were performed on limb models, animal specimens, fresh human cadavers, and human subjects to obtain a representative pressure distribution caused by the inflated tourniquet cuff. The second type of investigation dealt with the direct measurement of blood flow during limb compression. This allowed determination of the exact cuff pressure at which occlusion occurred. The possibility of occluding blood flow at cuff inflation pressures lower than the currently accepted pressures has also been investigated. Recent research papers investigating the compression patterns and the possibility of lowering occlusion pressures are considered and are discussed in this chapter.  2.1 Studies Investigating Soft Tissue Compression Patterns Many authors have acknowledged the hazards associated with the use of the compressive occlusive device. In particular, Solonen [41] in 1968 showed that ischaemia associated with the use of a tourniquet caused morphological changes in muscles. Ochoa et al. [29] in 1972 observed that anatomical lesions occurred in peripheral nerves due to  10  the compression of the tourniquet. Investigators discussed in detail whether tourniquet related injuries are caused by a vascular or structural disorder. Generally, overcompression has been accepted as the primary cause of injuries while ischaemia has been considered to be a secondary cause [18-40]. The available literature regarding soft tissue pressure measurements is reported below.  2.1.1 Studies with Artificial Limb Models Limb models have been used in an attempt to measure the transmission of tourniquet cuff pressure to the underlying tissues. Dahlin wrapped the standard pneumatic cuff around limb models made of Swedish sausages without bones [42]. Figure 2.1 shows the three positions in the limb model where the slit catheter was inserted to measure soft tissue pressure while the cuff was inflated at 300 mmHg. Dahlin found that the soft tissue surface pressures were highest in the central region beneath the cuff midpoint and decreased symmetrically to the edges of the cuff. Previous studies by other investigators had shown that neuromuscular injuries occurred primarily under the edges of the cuffs [35-38] rather than in the center of the cuff. For this reason, the measurements taken by Dahlin did not seem to help explain why nerve injuries occur predominantly at the cuff edges. More investigations were, however, done with limb models. To understand the mechanisms of nerve damage related to cuff application, Griffiths and Heywood [44] developed a biomechanical model of the limb. In the development of this model, they made the assumption that nerve tissue was tolerant of simple ischaemia over prolonged periods. They also assumed that high cuff pressure applied over a short time was more likely to produce irreversible damage than low cuff pressure applied over a longer period. Griffiths and Heywood developed two variations of their model: a rigid core surrounded by fluid tissue and a rigid core surrounded by elastic solid tissue. Figure 2.2 shows the two variations of the model with the corresponding radial and hoop stress distributions.  11  It is known that afluidmaterial resists and sustains direct pressure but does not sustain shearing forces (Figure 2.3). Therefore, the results of the first model showed that pressure is transmitted uniformly through the tissues. This led to the suggestion that the arterial pressure is equal to the cuff pressure for blood pressure measurement. The model also led to the conclusion that all nerves within the limb are equally susceptible to injury. The results of the second model, however, did not lead to the same conclusions. The second model showed that the pressure was not uniform, but increased from the limb surface to the bone. This suggested that the deeply embedded nerves are more susceptible to injury because of high radial stresses and generated shear stresses (Figure 2.4). The second model also suggested that arterial pressure must be greater than the cuff pressure leading to an overestimation of blood pressure measurement. Since in neither of the limb model variations could they simultaneously predict nerve injury and measure blood pressure, Griffith and Heywood developed a two-phase compression theory. They first stipulated that the limb initially behaves with fluid properties as the compression of the tourniquet cuff forces the fluid away from the region underneath the cuff. They then stipulated that the limb exhibits properties of an elastic solid material when it is further compressed. The first stage of the limb compression led to an adequate blood pressure measurement while the second stage explained nerve injuries as a result of long compression. The model, however, did not explain the experimental internal tissue compression patterns determined experimentally by other investigators.  2.1.2 Studies with Animals McLaren and Rorabeck [45] measured the internal pressure distribution in the hind limbs of anesthetized mongrel dogs to investigate the cause of injuries. Figure 2.5 shows a canine thigh with a slit catheter coupled with a transducer to measure the soft tissue pressure. The limbs were compressed by a standard 8.5 cm wide surgical pneumatic  12  tourniquet inflated to 200 mmHg and later by a 10 cm wide Esmarch bandage wrapped three to seven times. Figure 2.6a shows the five slit catheter paths in the limb used to generate the pressure distributions. The stars on this figure represent the entry points while the black circles indicate the location of the pressure measurements. Figure 2.6b shows the three longitudinal planes in which the pressure measurements were obtained. Based on the measurements obtained using the pneumatic tourniquet, McLaren and Rorabeck reported a decrease in the surface pressure from the midpoint to the edges of the cuff but no decrease in the radial pressure from the surface to the bone (Figure 2.7a). However, in the case of the Esmarch bandage they found a radial pressure increase (Figure 2.7b). The bell-shaped pressure profile obtained using the pneumatic cuff is superimposed on the flat profile of the Esmarch bandage in Figure 2.8 for comparison. From the experimental pressure profiles, McLaren and Rorabeck concluded that neuromuscular injuries were caused by the concentration of pressure on the limb rather than the cuff inflation pressure per se. It was concluded that the Esmarch bandage was more prone to cause nerve injury than the pneumatic cuff because it generated an internal pressure higher than the surface pressure. Since the Esmarch bandage is only used for a few minutes to exsanguinate the limb prior to cuff application, the findings of McLaren and Rorabeck seemed to be incomplete with regards to tourniquet related injuries. Further tests by Ochoa and al. [29] proved that neuromuscular injuries were caused by the generation of internal shear stresses displacing the soft tissues towards the edges of the tourniquet cuff. Ochoa and al. performed an experiment on baboons to determine the relative effect of ischaemia and mechanical compression on nerves during compression of the limb using a pneumatic tourniquet cuff. More information on the experiment is presented in section 5.1.3. Further experiments were performed with the tourniquet cuff to clarify the mechanisms of nerve injuries. Pedowitz et al. [46] measured the soft tissue pressure in the hind limbs of six white rabbits. A curved tourniquet with a stiff exterior shell was  13  specially designed to fit the conical limb geometry of the rabbits. In this investigation the tourniquet was inflated up to 350 mmHg while two pressure catheters were positioned in the limb: one located in the subcutaneous tissues and the other placed next to the sciatic nerve. A symmetrical pressure distribution was obtained in the longitudinal plane with a considerable decrease in pressure in the radial direction from the skin to the bone. From this data Pedowitz et al. attributed soft tissue damage to tissue displacement at the edges of the cuff caused by induced shear stresses and therefore supported the theory of Ochoa et al [29].  2.1.3 Studies with Cadavers The animal experiments were a first step in the investigation of tourniquet related injuries. The second step involved human limb experiments. The practical impossibility of measuring the pressure distribution inside a patient's limb led to the use of cadaver limbs. This technique has proven to be a definite improvement over previous studies of limb models and animal limbs. Shaw and Murray [47] measured the softtissuepressure in four fresh cadaver legs in order to validate pressure patterns obtained in the animal limbs. Figure 2.9 shows the complex rigid stainless-steel probe inserted in the limbs to take these pressure measurements. The pressure probe was positioned parallel to the femur, at five locations within the thigh directly beneath the cuff. The measurements were performed using a standard tourniquet cuff inflated to 300 mmHg. The experimental set-up is shown on Figure 2.10. The three pressure measurements in the muscle were found to be similar while the surface and the bone pressure measurements were found to be significantly different. Radial pressure decreases of 5% and 32% were measured from the subcutaneous soft tissues to the bone in legs of small and large circumference respectively. Unfortunately, the pressure profiles were found to be affected by the large size of the sensing probe therefore casting doubt on the accuracy of the data. Moreover,  14  the experiments were performed on disarticulated limbs which reduced the tension in the soft tissues and caused further experimental errors. Hargens et al. [48] also measured the soft tissue pressure in disarticulated limbs but with 100 cm long slit catheters to reduce the volume of the instrument. Figure 2.11 shows the four tissue depths which the slit catheters were inserted. The measurements were taken in six upper and lower human limbs using a standard Kidde 8 cm wide pneumatic tourniquet inflated to pressures varying from 100 to 500 mmHg. The soft tissue pressure was found to decrease radially from the subcutaneous to the bone locations to a value of 97.6% of the cuff pressure in the upper limbs and 92.7% in the lower limbs. Figure 2.12 shows these results and the steep pressure gradients in the longitudinal direction close to the edges of the cuff. Figure 2.13 shows the correlation between the longitudinal and radial pressure profiles for cuff pressures of 150 mmHg and 300 mmHg. Hargens et al. attributed nerve lesions to the substantial soft tissue deformation caused by the observed high compressive pressure. By applying these recommendations, they recommended using a cuff wider than the standard cuff and lowering the cuff inflation pressure. They were able to maintain hemostasis and reduce theriskof injuries. Unfortunately the insertion of a rigid probe or slit catheter into the limb (as was used in many of the studies previously reported for measurement of internal compression patterns) either pre-compressed or injected fluid to the tissues to compensate for the tissue disturbance. Because of these effects, the pressure patterns obtained did not accurately reflect the typical compression patterns in a limb under a pneumatic cuff. Recognition of this problem has subsequently led to the development of a new pressure sensor (refer to section 3.1.1.1) which will significantly reduce these effects.  2.1.4 Studies with Humans Although actual pressure measurements are not possible in patients' limbs, a clinical investigation of the tourniquet compression may lead to clarifying information on  15  injuries. Parkes studied the clinical effect of soft tissue compression by varying the applied tourniquet cuff pressure on the upper limb of human subjects [49]. Three series of tests were performed using cuff pressures varying from 70 mmHg to 300 mmHg. During the first series of tests, discomfort was experienced 30 minutes after the inflation of the cuff at 300 mmHg because of the loss of sensory and motor function of fingertips, hand, and forearm. While these symptoms are known to be caused by ischaemia, the maximum inflation time necessary to cause permanent damage was unknown. Parkes attributed post-operative tourniquet palsies to compression lesions rather than to the ischaemic effect of cuff inflation [50]. For the second series of tests, the inflation of the pneumatic cuff to a low pressure of 70 mmHg caused the venous pressure to rise but did not arrest the arterial circulation. Oedema due to fluid collection was observed distal to the cuff but there were no signs of lesions as long as the vessels were not occluded. Venous occlusion occurred only when the diastolic pressure of the subject fell below the cuff inflation pressure. It was also observed that after a long period of time, venous occlusion could lead to ischaemic lesions. For the third series of tests, a special clamp was used in combination with the tourniquet cuff inflated at 70 mmHg. Figure 2.14 shows the clamp that allowed blood to escape via the superficial vein in order to avoid an increase in venous or capillary pressure. This allowed normal circulation to continue except in the compressed veins and capillaries and therefore avoided venous congestion. Based on this work, Parkes recommended applying the tourniquet for the shortest possible period of time while still allowing surgery to be performed. He suggested that the cuff inflation pressure was not to exceed 300 mmHg to avoid permanent nerve damage and minimize tissue injuries.  16  2.2 Studies Investigating Blood Flow Occlusion Many studies have been performed to relate cuff inflation pressure to occlusion pressure. Shaw and Murray plotted a nomogram in an attempt to select the proper inflation pressure for a particular surgical procedure (Figure 2.15). This plot relates the tourniquet cuff inflation pressure to the underlying tissue pressure and thigh circumference. A cuff inflation pressure 70 mmHg to 100 mmHg higher than the systolic blood pressure measured at the time of the injection of the anesthetics was recommended to allow for fluctuations in blood pressure during the operation. An even greater increase in the inflation pressure value was recommended for occluding limbs of obese patients in which there is a greater drop in pressure from subcutaneoustissuesto the bone. There was, however, no quantitative recommendation concerning cuff inflation pressure for obese patients. Moore et al. [51] investigated the effect of variations in cuff width on the pressure required to arrest blood flow in the upper extremities. Blood flow was occluded with three tourniquet sizes on ten normal subjects and was monitored by an ultrasonic doppler flowmeter. Hemostasis was obtained by inflation of the wide cuff at pressures lower than the pressures currently set above the pre-operative systolic pressure of the patient. A 15.5 cm cuff occluded blood flow at subsystolic pressures while a 4.5 cm cuff occluded flow at suprasystolic value. The doppler occlusion pressure (DOP) has been plotted as a function of cuff width (L) in Figure 2.16. The dotted lines on this figure denote the data points obtained for each of the ten subjects while the upper and lower solid lines represent linear plots for arm circumferences (CIRC) of 30 and 25 cm respectively obtained by a least square multiple linear regression analysis performed on the experimental data. The resulting equation related the doppler occlusion pressure to cuff width and limb circumference. It was found that the occlusion pressure was not significantly affected by blood pressure variation and was therefore eliminated from the equation.  17  DOP = 86.14 - 3.94 (L) + 2.6 (CIRC)  (1)  The equation was developed to predict the occlusion pressure using a specific surgical tourniquet for a given limb circumference. The cuff width necessary to occlude blood flow at subsystolic pressure was also determined. The pressure transmitted by the tourniquet to the underlying soft tissues was determined to be responsible for the variations in occlusion pressure observed with the different cuff widths. Moore et al. stated that the parabolic pressure profile of the narrow cuff caused a greater axial tissue displacement than the flat pressure profile of the wide cuff. For this reason, higher occlusion pressures were associated with the narrow cuff for similar inflation pressures. They concluded that the deformation of the artery paralleled the pressure profile applied to the limb. Regarding the edge effects of the cuff, they stipulated that an accumulation of frictional resistance may be responsible for hemostasis without complete closure of the blood vessels. They further explained that nerve injuries primarily occurred beneath the edges of the cuff because these were the regions of highest shear stress and tissue deformation. To reduce the incidence of nerve damage, they proposed the use of wider tourniquet cuffs to reduce the occlusion pressure and consequently decrease the pressure gradient at the edges of the cuff. Based on the information obtained from the aforementioned investigations, an experimental program was designed to investigate the pressure delivered by the pneumatic tourniquet cuff on and inside the limb and measure the cuff pressure necessary to arrest arterial flow. This experimental program is described in the following chapter.  18  CHAPTER 3 - EXPERIMENTAL  INVESTIGATION  An experimental investigation of the limb encircled by a pneumatic tourniquet cuff was performed to improve the understanding of the mechanisms of blood flow occlusion. The experiments during this investigation fell into two categories: those related to the compression of soft tissues of the limb, and those related to the dynamics of blood flow occlusion. The experiments in the first category were performed to investigate the causes of injuries of surface tissues and internal structures in the compressed portion of the limb. The application of a pneumatic tourniquet cuff on a limb compresses the muscles and ultimately the arteries which stop the flow of blood distally to the cuff. Direct measurements of pressure in the soft tissues were undertaken to study the compressive phenomenon. To obtain these measurements, an automated data acquisition system was designed along with the adaptation of a pneumatic pressure sensor. The compression patterns beneath the inflated cuff were used to map and obtain a three-dimensional profile of the pressure distribution on the surface and inside the limb. The experiments in the second category were performed to investigate the effect of inflation pressure and cuff geometry on the dynamics of bloodflow.The occlusion of arterial flow is known to be related to the cuff inflation pressure. To determine this relationship, inflation pressures were directly measured at the moment of the cessation of blood flow which was detected acoustically with ultrasound. Occlusion pressure data were collected on normotensive subjects and patients. This data was then utilized to predict the minimal cuff inflation necessary to obtain hemostasis in other subjects.  19  3.1 Experiments to Investigate the Pressure Distribution in the Soft Tissues beneath the Tourniquet Cuff The soft tissue pressure measurements were used to map the pressure distribution in the limb encircled by an inflated pneumatic cuff. This pressure distribution map was used to understand the transmission of cuff inflation pressures to the surface and the underlying tissues of the limb through visualization of the compression patterns. Such visualization helps to identify the anatomical regions and structures susceptible to injury due to overcompression. These compression patterns also provide information useful in developing the physiological mechanism of blood flow occlusion. In order to study the compression of soft tissues and ultimately the blood vessels of the limb, two experiments were performed. The first consisted of measuring the pressure on the surface of the limb to determine the actual pressure pattern applied to the limb surface by the tourniquet for a given tourniquet pressure. In the second, the pressure within the muscles was measured to evaluate the transmission of pressure from the surface of the limb to the underlying soft tissues. Because of limitations associated with measuring softtissuepressure using previous experimental techniques, a data acquisition system was designed along with the adaptation and development of a pneumatic pressure sensor. The new pressure sensor eliminated fluid injection and reduced the volume of the device in the limb. This apparatus was used for both the surface and internal pressure measurements and is described in the following section.  3.1.1 Procedure and Apparatus The automated system directly measured the pressure underneath a tourniquet cuff. This system facilitated the acquisition of pressure data and assisted in the processing of the data. A pneumatic pressure transducer was incorporated into the design of the  20  pressure data acquisition system. Details of the data acquisition system, fabrication and use of the pressure sensor are presented below.  3.1.1.1 Biomedical Pressure Sensor A better method of measuring soft tissue pressure was deemed necessary to avoid the problems associated with the two previously reported methods of pressure measurement. A novel biomedical tissue pressure sensor, developed previously in Vancouver, was employed in all of the studies described in this thesis. This sensor was chosen because its characteristics were particularly well suited to measuring pressures applied to tissues beneath a tourniquet cuff at multiple locations without substantially disturbing the soft tissues [52]. This novel pneumatic pressure sensor is thin, flexible, and lightweight and has the advantage of being radiopaque ensuring proper positioning inside the limb tissues [53,54]. This is a significant improvement over a slit catheter [45] and a rigid probe sensor [47], both of which had disadvantages such as fluid injection into the limb during the pressure measurement and pre-compression of the soft tissues. The pressure sensor consists of two thin flexible strips bonded at the edges forming an air channel. Electrical contacts located on the two opposite sides form a switch. If the externally applied pressure is greater than the measured internal pressure, the channel sides collapse and the contacts close. Conversely, if the externally applied pressure is less than the measured internal pressure, the channel sides are separated to open the electrical contacts. Thus, external pressure is measured by determining the state of the electrical contacts and measuring the internal pressure (Figure 3.1). Fabrication of the sensor consisted of assembling two strips of mylar (3 to 5 mil thick). The use of mylar provided good flexibility and durability. An electrical circuit was printed on the strips with conductive silver ink. The circuit was printed on one strip of mylar and a corresponding array of five pressure cells was printed on the other sheet of mylar as shown in Figure 3.2. Two complete patterns (7.2 cm and 10.0 cm long) were  21  printed on the mylar to cover the entire width of the two standard tourniquet cuffs (Figure 3.3). The two pieces of mylar were then heat sealed together at the edges with the printed faces touching each other leaving a 1.4 cm wide inner channel to form inflatable air pockets. To finish the pressure sensor, an electrical connector was crimped onto the end of the sensor to allow connection to a Cobe pressure transducer. A pneumatic fitting was the glued onto the mylar sheet to allow for inflation (Figure 3.4). The Cobe transducer is a precalibrated piezoresistive pressure measuring device that was chosen because of its compatibility with popular blood pressure monitoring systems. The pressure sensor required careful handling to avoid disconnection of the pneumatic fitting, breakage of the electrical connector, or damage to the printed circuit. The pressure sensor remains a fragile device. The life of the sensor was extended by adding two plastic reinforcements screwed together on the end of the sensor to protect the proximal end of the sensor while providing arigidsection suitable for handling the sensor (Figure 3.5). The addition of coating layers of mylar made the sensor more resistant and forced the sensor to remain straight during application on the skin or between layers of muscle. The mylar coating also offered additional protection for the circuitry and contributed to the durability of the sensor. The pneumatic pressure sensor was placed underneath the cuff leaving the electrical fitting and the pneumatic connector outside the cuff region (Figure 3.6). With this sensor, the externally applied pressure at the location of the individual contact switches could be made by systematically varying the measured internal pressure and noting the internal pressure when the switch condition changed. The occurrence of a change would indicate that either rising internal pressure had just exceeded the external pressure or a falling internal pressure had just fallen below the external pressure. Thus, with five separate contact points per sensor, the pressure at five known locations could be measured thereby creating a set of ten pressure data points for every inflation-deflation cycle of internal pressure.  22  To ensure reliability, each pneumatic pressure sensor was carefully calibrated before every test. In order to calibrate the pressure sensor, a known uniform pressure was applied over the exterior of the sensor. The bladder confined in a wooden frame shown in Figure 3.7 was used to provide the uniform external pressure. The sensor was inserted into this secondary bladder. A second pressure source was used to inflate the pressure sensor. The pressure provided to the sensor was monitored using a manometer and compared to the known pressure applied by the bladder. The incorporation of a calibration subroutine in the software permitted frequent calibration of the biomedical pressure transducer to ensure consistent pressure data (Appendix A). The reduced size and flexible nature of the pressure sensor facilitated its insertion between the cuff and the skin, and between muscle layers. Its flexibility also allowed it to easily contour to any limb geometry or anatomical structure shape. Preliminary testing indicated the best way to use the equipment and handle the pressure sensor to obtain accurate and reliable pressure measurements. The pressure sensor was used in a flat position (it was not bent or twisted) in order to allow smooth air flow in the inner channel during inflation and deflation. Overall, the pneumatic pressure sensor was found to have considerable advantages: it was reliable, accurate and highly adaptable to the system being measured; it was easily sterilized for reuse or could be disposed of after use without significant expense.  3.1.1.2  Pressure Data Acquisition System  An automated system was designed around the pneumatic sensor to accelerate and facilitate the acquisition and processing of the pressure data. The system was used for measuring both surface and internal pressure profiles. The hardware of the system consisted primarily of an interface board connecting the pressure sensor to an analog/digital board (Tecmar LabTender) in a personal computer (Figure 3.8). Two Cobe transducers, three Clippard valves, and the five pressure cells  23  were connected to the interface board along with a power supply. The Clippard valves are electrical valves that open with +5 volts. A connecting board provided access to the various A/D and D/A channels. An Aspen pressure source, A.T.S. 500 [55-58], controlled the air pressure available from the standard hospital wall outlets. Two reservoir-bladders were added to the hardware to minimize pressure surges from the hospital compressed air distribution system. The first bladder was placed at the outlet of the pressure source while a second smaller bladder was placed in the supply line just before the sensor. A mechanical valve was used at the outlet of the pressure sensor valve to control the air flow during deflation. Table 1 lists the equipment used in this apparatus. Customized software was written to calibrate the pressure sensor, initiate the valves, control the rate of inflation and deflation of the pressure sensor, monitor the status of the sensor contacts, and convert transducer output voltage into pressure data. The control software was based on a double loop feedback system (Figure 3.9). The sensor valve was periodically turned off during inflation and deflation to control the rate of change of pressure in the sensor and improve the accuracy of the measurements. A first software program used an iterative approach to successively inflate and deflate the pneumatic cuff until a preselected soft tissue pressure was reached. A second program was then employed to accelerate the pressure measurement rate by eliminating the feedback loop. A block diagram of this program is shown in Figures 3.10a and 3.10b. Appendix B lists the second control software called "data" used in most of the experiments. After initialization the software required two sets of pressure data, one set during inflation and one set during deflation of the pressure sensor. These pressure values were averaged and a calculation of the hysteresis was performed. The pressure measurements were then scaled to produce pressure values in mmHg which were displayed on the monitor in both graphical and numerical form. Once processed, the information was stored on a floppy diskette. The program was then rerun if required. At the end of the measurements, all the valves were opened to depressurize the sensor. At this point, an  24  automatic non-invasive arterial blood pressure monitor (Dinamap 845) was used to measure the patient's blood pressure.  3.1.2 Experiments to Determine the Surface Pressure Distribution The first step in the development of the experimental model was to determine the surface pressure distribution beneath the tourniquet cuff. This distribution was generated based on the soft tissue pressure data collected at positions located longitudinally and circumferentially about the limb. To acquire this data, the five cells of the pressure sensor were first positioned along the axis of the limb and centered accurately beneath the cuff. Axial pressure profiles were then measured at the eight locations around the circumference of the limb. The resulting matrix of 40 pressure points was deemed sufficient to represent the surface compression patterns of limbs having a circumference in the range from 25 cm to 55 cm. These pressure measurements were obtained from both limb models and limbs of healthy normotensive subjects using three standard tourniquet cuffs: the 24" Freeman, 24" Aspen, and 34" Aspen cuffs (available from Aspen Laboratories Inc., Greenwood Village, CO.).  3.1.2.1 Surface Pressure Measurements and Results The first series of tests were performed on limb models to simplify the application of the pneumatic sensor and to become proficient with the pressure data acquisition system. Plexiglass cylinders of 9 and 18 cm diameters were used to represent the upper and lower limbs respectively [59] (Figure 3.11). A 1 cm thick layer of soft foam was used to cover the limb model to simulate the biological soft tissues. Additional pieces of foam were used to obtain an oval cross-section representative of the limb geometry (Figure 3.12). A second layer of foam, covering only half the width, was wrapped over the first layer to simulate the conical shaped portion of the limb. Two cylinders with different diameters  25  were used in order to study the effect of the overlying wraps of the cuff on the transmission of applied pressure. Figure 3.13 shows the one, one and three quarters, and two wraps that were evaluated during these experiments. Longitudinal and circumferential pressure measurements were obtained on the plexiglass cylinder by successively displacing the pressure sensor circumferentially around the pre-marked cylinders. The pressure sensors were also marked to ensure repeatable central positioning beneath the cuff during the successive placements of the pressure sensor at the defined positions around the cylinder. The use of the automated data acquisition system with the biomedical transducer allowed repeatable pressure measurements to be obtained. A parabolic longitudinal pressure distribution, shown in Figure 3.14, was obtained as the basic pattern of surface soft tissue pressure profile. The tourniquet cuff pressure of 200 mmHg was entirely transmitted to the surface of the limb in positions #3 and #4 (inflation values). Further measurements were taken on limbs of normotensive subjects in an attempt to reproduce the pressure data found in the literature. The tests published by McLaren [45] were of particular interest. Soft tissue pressure distributions were measured on the upper and lower limbs of 13 volunteers in age ranging from 21 to 56 years. The test procedure employed was similar to that previously outlined for the limb model measurements. The circumference of the limb was first measured and divided into eight equal segments (Figure 3.15). The pressure sensor was then inserted between the skin and the cuff at each position to obtain the pressure profile around the limb circumference. The protocol of the test is listed in Appendix C. Examples of the circumferential surface pressure profiles are shown on Figures 3.16 to 3.19. The four histograms represent the axial pressure profiles when the sensor was displaced in a clockwise direction on the left arm of the subject at the anterior, medial, posterior, and lateral positions. It is noted that the pressure profiles are not consistently symmetrical around the limb with the peak values varying from 187.3 to 169.8 mmHg for a similar maximum cuff inflation level.  26  Pressure measurements were repeatable within 4 mmHg when a recovery period was allowed between the pressure measurements (Figures 3.20 and 3.21). When the surface pressure measurements were successively taken without a recovery period, a difference of 7 mmHg was obtained between the pressure profiles (Figures 3.22 and 3.23). This difference in pressure is believed to be associated with the displacement of soft tissues away from the compressed section of the limb. The reduction of limb diameter caused an apparent decrease in the soft tissue pressure as the cuff became loose. In the case of a second set of pressure measurements taken after a recovery period, the elastic soft tissues were seen to displace to their initial position after compression of the limb and the second set of compression patterns were similar. Slow recovery of the muscle tissue was observed in both upper and lower limbs, therefore a minimum of three to five minutes was necessary between trials. The resulting axial pressure profiles obtained by averaging the experimental pressure data from all the subjects were compared to the profiles obtained by McLaren. For similar cuff inflation pressure, the peak pressure was found to be within 2% for the two distributions (Figure 3.24). However, McLaren's pressure profile is more of a bell curve, offset at 45% of the cuff length, in contrast to the parabolic pressure profile centered about the middle of the cuff obtained in this study.  3.1.2.2 Surface Pressure Analysis The first part of the experimental model was developed after collection of the surface soft tissue pressure measurements. The program "DISSPLA" was used to generate the three-dimensional plots of the softtissuesurface pressure distributions. Figure 3.25 shows the surface pressure profile of a limb encircled by the 24" Freeman cuff inflated to 200 mmHg. The peak pressure value in the center of the cuff reached values of 190 mmHg while the pressures at the edges of the cuff decreased to 42 mmHg. A sudden drop in pressure occurs at position #6 on the cuff where the pressure was evaluated at 68  27  mmHg. This local surface pressure drop is believed to be caused by the formation of a small gap created by the overlap of the thick cuff and the limb (Figure 3.26a). The pressure sensor positioned in this gap was therefore allowed to inflate freely causing the electrical switches to prematurely break open. Figure 3.27 shows the surface pressure distribution measured under the 24" Aspen cuff inflated to 200 mmHg. The peak pressure reached a value of 197 mmHg and decreased towards a minimum value of 38 mmHg. Position #3 showed a sudden drop of pressure in the middle of the cuff estimated at 135 mmHg (Figure 3.28). This loss of surface pressure was also associated with the formation of a gap on the surface of the limb. The pressure loss in the case of the Aspen was smaller than in the case of the Freeman because of the presence of a seam around the pneumatic cuff reducing the gap to the limb. The surface pressure distribution was also obtained under a 34" Aspen cuff, typically used for limbs of larger circumference. Figure 3.29 shows the resulting plots. In these measurements the peak pressure reached a value of 196 mmHg at the center of the cuff when inflated to 200 mmHg. Figure 3.30 shows the change in the pressure distribution around the limb at position #5 where the pressure decreased to 105 mmHg due to the edge of the cuff. The number of wraps around the limb was not an appreciable factor controlling the pressure profiles. The snugness of the cuff application, however, seemed to be an important parameter in determining the pressure delivered to the surface of the limb as low pressure readings were associated with a cuff loosely applied on the limb.  3.1.3 Experiments to Determine the Internal Pressure Distribution The effect of limb compression by a pneumatic cuff cannot be fully explained by surface pressure profiles. The transmission of the surface pressure in order to the  28  underlying internal soft tissues needed to be considered to understand the mechanisms of blood flow occlusion and nerve damage. The experimental model was completed through the mapping of the pressure distribution within the limb. Presented below are experiments in which the internal pressure profiles were measured in two main nerve locations of the upper and lower limbs. The internal pressure distribution was then compared to surface pressure measurements to evaluate the radial pressure change.  3.1.3.1 Internal Pressure Measurements and Results One female and three male cadavers were made available for internal pressure measurements. The age of these cadavers ranged from approximately 40 to 70 years old. Tests were performed on all sixteen limbs of the four cadavers as none of the limbs showed any sign of abnormality or disease. The same experimental apparatus as previously discussed was used to take the internal pressure measurements. Longitudinal incisions were carefully made in order to protect the soft tissues and minimize the displacement of the other internal structures. The limbs were left attached to the bodies in order to keep the muscular turgor as normal as possible. The radial and the median nerves (the two main nerves of the upper limb) were exposed in order to position the pressure sensors along them (Figures 3.31 and 3.32). The electrical fittings and pneumatic connectors were left outside the limb. The main subcutaneous and cutaneous tissue layers were then carefully sewn back together. The fibrous nature of the tissues attached to the bone made it impossible to place a sensor directly on the humerus. Two pressure sensors were also inserted in a similar positions in the lower limb. Figures 3.33 and 3.34 show the surgical incisions exposing the sciatic and the saphenous nerves (i.e. the main nerves of the lower extremity). Again, the fibrous nature of the tissues attached to the femur did not allow the positioning of a sensor directly on the bone.  29  Use of the pneumatic pressure sensor did not disturb the anatomical integrity of the cadaver limbs. This allowed internal soft tissue pressure measurements to be obtained which were representative of clinical cases. Some difficulties arose with the positioning of the pressure sensors. It was difficult to place the pneumatic sensor in a flat position along the main nerves due to their curved anatomy. Since the width of the sensor is much wider than the diameter of the nerves, the measured pressure was actually an average pressure acting over the region surrounding the nerves. The natural curvature of the radial nerve around the humerus forced the position of the sensor to be slightly twisted. This caused an obstruction of the air flow during inflation of the sensor and errors in the pressure readings. The pressure at the saphenous nerve location was also difficult to measure. The presence of a canal in which the nerve is located caused the electrical contacts of the sensor to break open quickly leading to low pressure readings. Once the sensors were placed as accurately as possible, the 24" and 34" Aspen tourniquet cuffs were wrapped around the upper and lower limbs respectively. The control program was then initiated and measurements were taken at an inflation pressure of 200 mmHg. A statistical comparison of these pressure measurements showed no difference between the left and right limbs of the first cadaver (Figures 3.35 and 3.36). Right and left limb internal pressure measurements of each cadaver were therefore combined. It was also determined that there was no statistical difference between the pressure in the two nerve locations of a limb. For this reason, the pressure measurements at the radial and median nerve locations were averaged. The pressure measurements at the sciatic and saphenous nerve locations were also analyzed together. Upper and lower limb pressure data were, however, analyzed individually due to the large variation in circumference and the anatomical differences between the arms and legs. Figures 3.37 and 3.38 show plots of the three curves for the averaged pressure distributions from the third specimen with an applied cuff inflation pressure of 200 mmHg. In this test, the peak pressure reached average values of 187.6 mmHg in the  30  upper limb and 174.5 mmHg in the lower limb. Pressure measurements at the surface of the limb indicated pressures of 186.1 mmHg and 183.8 mmHg for the arm and the leg respectively. Soft tissue profiles were also obtained for the upper limb of the third cadaver for three cuff inflation pressures: 100 mmHg, 200 mmHg, and 300 mmHg. Figure 3.39 show the parabolic profiles superimposed on the same graph for comparison. Parabolic pressure profiles were obtained over the entire width of the cuff in all cases. The pressure measurements were averaged for the three inflation pressures in order to plot three curves and evaluate the peak pressure for the various inflation levels. Figure 3.40 shows the average peak pressure values (position #3) of 97 mmHg, 194 mmHg, and 296 mmHg for the three sets of pressure profiles. This indicates that the pressure loss is independent of the inflation pressure. The measurements taken from the second cadaver were not very repeatable. Figure 3.41 shows the great variation in soft tissue pressure profiles. A variation of 20 mmHg in the pressure measurements was obtained attributed to the significant oedema of the limbs. This shows that the elasticity of dead soft tissues is not completely representative of living tissues.  3.1.3.2 Internal Pressure Analysis Pressure readings obtained from the four limbs of the three first cadavers were averaged to evaluate the compressive effect of the pneumatic cuff on limbs. Figures 3.42 and 3.43 show the two curves obtained for the upper and lower limbs. In the case of the upper limb, the surface pressure reached a value of 186.1 mmHg and the internal pressures reached values of 186.0 mmHg and 189.2 mmHg for the radial and median nerve locations respectively. It was determined that the radial pressure decrease (0.8% radial pressure decrease) was not statistically different [60-63]. In the case of the lower limb, the surface pressure reached a value of 183.8 mmHg and the  31  internal pressures reached values of 182.0 mmHg and 167.0 mmHg for the sciatic and saphenous nerve locations respectively. The pressures obtained for the sciatic and saphenous nerve positions were determined to be statistically similar so that they could be analyzed together. This led to a 4.6% decrease from the surface of the limb to the bone. This radial soft tissue pressure decrease is believed to be associated with a great lateral tissue displacement. Figure 3.44 shows the longitudinal cross-section of the limb including the relative positions of the main nutrient artery and the large nerves. The parabolic pressure distribution of the skin flattens out with radial depth because of changes in axial tissue displacement. Since the peak pressure is a direct function of the axialtissuedisplacement one would expect a lower peak pressure in the case of a fatty leg in comparison with a muscular arm subjected to the same external applied load. Further tests to evaluate the effect of tissue composition on occlusion pressure were later performed and are presented in Chapter 4. The measured radial pressure decrease (0.75%) found from the upper limb measurements is less than the 5% pressure difference obtained by Shaw and Murray. In in the case of the lower limb, Shaw and Murray found a 32% radial decrease of applied cuff pressure which is considerably higher than the measured radial pressure decrease (4.6%) of the present testing. Hargens et al. measured radial pressure decreases much larger than the present ones in both the upper and lower limbs. They measured 21.5% and 54.5% pressure decrease from the cuff pressure to the pressure measured near the bone of the upper and lower limbs respectively. The higher radial pressure change found by the previous investigators may be associated with their measuring technique and the condition of their specimens.  32  3.2 Experiments to Investigate Occlusion Pressure Even though over-inflation of the cuff is one of the main causes of nerve problems associated with the use of the orthopaedic surgical tourniquets, the minimum required level of cuff inflation pressures to obtain hemostasis has not been fully investigated. Some surgeons inflate the standard tourniquet cuff to a pressure ranging from 250 mmHg to 300 mmHg for arms and from 300 mmHg to 400 mmHg for legs [9]. Other surgeons inflate the tourniquet pressure to a value of 70 mmHg above the pre-operative systolic blood pressure of the patient for the upper limb and to a value equal to twice the systolic blood pressure for the lower limb [12]. During this research, blood flow occlusion was shown to be possible using pneumatic cuffs inflated at lower pressures than currently employed. Experimental tests were performed to accurately determine the minimum cuff inflation pressure necessary to ensure hemostasis in all surgical cases. Experiments to investigate the required pressure to ensure the cessation of blood flow for variations in tourniquet parameters were also performed and are described below. Using these results, the occlusion pressure was then related to parameters such as cuff width, limb circumference, and blood pressure. In the experiments, different pneumatic cuffs were used on normotensive subjects. Occlusion pressures were determined by slowly decreasing the cuff inflation pressure until blood flow was detected past the cuff. In the laboratory tests, the onset of blood flow was detected using an ultrasonic doppler flowmeter while in the operating room testsfloodingof the surgical site was used to indicate the onset of bloodflow.The procedure and results of these are discussed below.  3.2.1 Laboratory Experiments Three series of experiments were carried out to study the mechanisms of blood flow cessation. The first series of tests consisted of measuring occlusion pressure in the  33  laboratory on limbs of normotensive subjects free of vascular disease. Seven and nine types of pneumatic cuffs were tested on upper and lower limb respectively of 34 subjects. A total of 148 occlusion pressure data points were obtained. The second series of occlusion pressure measurements were performed on patients in the operating room. Finally, the third series of occlusion pressure measurements were performed on exsanguinated limbs of normotensive subjects in the laboratory in order to correlate occlusion pressure data with data obtained in the previous two experiments.  3.2.1.1 Detection of Blood Flow The ultrasonic doppler flowmeter was compared to a Perimed laser doppler in order to evaluate the accuracy of the instrument in detecting blood flow. Ultrasound has been shown to travel with minimal loss of intensity for long distances. It travels well in aqueous media like body fluids and muscle [52] compared to the Perimed doppler. Successive tests were performed by placing the sensing probe at the same location on the elbow. The occlusion pressure measurements obtained using the ultrasonic doppler were found to be lower than the corresponding measurements using the Perimed laser doppler (Figure 3.45). This was predominantly due to the needle style indicator of the Perimed device which was very sensitive to arm motions and other artifacts that could be misinterpreted as flow-induced events. The analog display was also more difficult to use than the ultrasonic doppler due to the difficulty of reading an unsteady indicator needle. The ultrasonic doppler flowmeter was therefore chosen due to its better suitability and its availability. Using the ultrasonic doppler, occlusion pressure data were found to be repeatable up to 5 mmHg for successive measurements.  34  3.2.1.2 Experimental Procedure Each subject was placed in a supine position for the entire test. First, the blood pressure of the subject was taken on the left limb using a non-invasive arterial blood pressure monitor (Dinamap 845). The surgical tourniquet was then applied on the right arm in a manner snug enough so that one finger could be easily inserted between the cuff and the skin but three fingers could not be inserted at all. The tourniquet cuff was then connected to a tourniquet system (A.T.S. 1000) which inflated the cuff up to 200 mmHg. The ultrasonic doppler flowmeter (Doppler 801-A) was used to detect the onset of blood flow in the brachial artery at the level of the elbow or the wrist. Conductive ultrasonic gel was used to improve the contact of the sensing element with the skin and to facilitate the transmission of the ultrasonic waves. The cuff was slowly deflated until a signal was detected at which time the cuff inflation pressure (the occlusion pressure) was recorded. The measurement was then repeated to ensure its validity. The blood pressure of the patient was also taken at the end of the test, and the circumference of the limb at the midpoint the cuff was recorded. The protocol of the test is listed in Appendix C.  3.2.1.3 Experimental Results The occlusion pressure data collected from the experimental tests were related to the width of the cuff. Figures 3.46 and 3.47 show the occlusion pressure data for left and right limbs plotted together as they showed no significant differences in their levels. Upper and lower limb data were combined on the same graph because the initial plots showed signs of continuity in the pressure data patterns (Figure 3.48). In fact, the data points were confined within a narrow band only 20 mmHg wide.  35  The following observations were made indicating that the width of the cuff is an important parameter in determining the minimum cuff pressure needed to occlude arterial flows: 1) The occlusion pressure data became asymptotic when the limb circumference reached a size ten times greater than the cuff width. This indicates that for very narrow cuffs, extremely high cuff inflation pressures are necessary to ensure arrest of blood flow [62,63]. 2) The occlusion pressure measurements became nearly constant once the cuff width to limb circumference ratio exceeded unity. 3) As cuff width increased, the occlusion pressures appeared to approach an average pressure value near diastolic blood pressure of the subject. 4) Curves of occlusion pressure versus cuff width based on the upper limb measurements (Figure 3.49) showed a decrease of occlusion pressure with increase of cuff width. These resulting curves showed similarity with the graphs from previous researchers [51,64]. A second test was performed in order to study the effect of cuff width on occlusion pressure. Two tourniquet cuffs were used in tandem on the limb to determine the effect of pre-occlusion. The first cuff was placed on the upper part of the arm above the elbow, and the second one was placed on the forearm. The proximal cuff was inflated to a fixed pressure while the occlusion pressure was measured with the distal cuff using the ultrasonic doppler flowmeter. The proximal cuff was successively inflated to pressures varying from 0 mmHg to 100 mmHg in steps of 10 mmHg. Inflation of the proximal cuff caused a linear decrease in the occlusion pressures seen in the distal cuff (Figure 3.50). Based on these findings, it is believed that the cuff width has a damping effect on the arterial pressure as the pulses of the arterial flow  36  gradually decreased in amplitude beneath the proximal cuff so that the flow became steady beneath the distal cuff thus requiring less external pressure to occlude the blood flow.  3.2.2 Clinical Experiments Occlusion pressures were also measured clinically to verify the validity of the experimental occlusion pressure data obtained with the ultrasonic doppler. The determination of the onset of blood flow was done by noting when blood entered the surgical site. These measurements were obtained from 23 patients undergoing hand surgery.  3.2.2.1 Clinical Experiment Procedure Shortly after each patient was put under general anaesthesia, a 19 cm wide tourniquet cuff was applied on the upper part of the limb undergoing surgery. The limb was then elevated and an Esmarch bandage applied to exsanguinate the limb. The cuff was inflated to 200 mmHg and the bandage removed. The surgical procedure was then performed. Upon completion of the surgery, but with the site still open, the cuff was slowly deflated at the rate of 1 mmHg per second. The occlusion pressure was recorded as being the tourniquet pressure from the tourniquet system (A.T.S. 1000) at the first appearance of blood in the surgical site. The patient's blood pressure was recorded at the beginning of the operation, at the moment of cuff deflation, and at the first sign of blood in the surgical field.  3.2.2.2 Clinical Experiment Results Figure 3.51 shows the plot of occlusion pressures for the 23 tested patients. The occlusion pressures measured in the operating room were found to be 1.0 mmHg to 58.5  37  mmHg lower than the pressures measured in laboratory to give an average decrease in occlusion pressure of 27.1 mmHg. Patients undergoing hand surgery had their limb elevated and wrapped with an Esmarch bandage prior to the operation in order to flush the blood away from the surgical site. It was hypothesized that this discrepancy between the experimental and clinical occlusion pressure measurements was associated with this practice of limb exsanguination. This hypothesis was verified experimentally by performing exsanguination tests which indicated that the observed differences in measured occlusion pressure were not caused by the different methods used to determine the onset of blood flow. This test consisted of measuring the cuff inflation pressure necessary to cause cessation of blood flow in exsanguinated limbs. Exsanguination consists of draining the blood out of the limb prior to cuff inflation. In this test, occlusion pressures were measured with the standard 24" Aspen tourniquet cuff using an ultrasonic doppler. Tests were performed on eight normotensive subjects and compared the following five different methods to exsanguinate the limbs: 1) no exsanguination; 2) exsanguination by a five minute elevation; 3) exsanguination using a pneumatic sleeve inflated up to 75 mmHg; 4) exsanguination using a pneumatic sleeve inflated up to 125 mmHg; 5) exsanguination using an Esmarch bandage. Figures 3.52 shows the results of the exsanguination experiment. The occlusion pressure data agreed with the clinical experimental results, in that all the occlusion pressure points obtained with exsanguination were lower than those without exsanguination by a difference varying from 8.0 mmHg to 42.25 mmHg. This indicates that the procedures of exsanguinating the limb prior to cuff inflation in the laboratory tests were effectively reproducing the conditions found in the operating room.  38  3.2.3 Correlation of Experimental Data The second part of the experimental model was completed through a numerical analysis of experimental occlusion pressure data. Mathematical correlations between occlusion pressure and independent variables such as cuff width, limb circumference, and subject's blood pressure were developed. The developed correlation between these variables allowed for increased accuracy in prediction of the occlusion pressure required in a prospective patient and hence the determination of the desirable cuff inflation pressure.  3.2.3.1 Correlation with Blood Pressure Normalized pressure ratios based on various blood pressure parameters were considered during this analysis. These parameters were mean arterial pressure, systolic pressure and diastolic pressure. To account for individual differences in these values, the normalized ratios used were based only on the inflation pressure increase above the patient's blood pressure required to occlude flow. The patient's blood pressure value was therefore subtracted from the occlusion pressure value before normalizing. Figure 3.53 show averaged curves of normalized pressure ratios (using the three blood pressure parameters) versus cuff width to limb circumference ratio for the 14 tourniquets tested. The points calculated by taking the difference between the occlusion pressure and the diastolic blood pressure converged on the abscissa as cuff width increased. A more detailed analysis was then performed by correlating all previous occlusion pressure with the diastolic blood pressure of the patient. Figures 3.54 and 3.55 graph the occlusion pressure increase over diastolic pressure for both the upper and lower limbs respectively. Figure 3.56 combines all the data on the same graph showing a single relationship. The occlusion pressure data obtained clinically were also related to the patients blood pressure and plotted in Figure 3.57. Figure 3.58 shows this clinical data and the previous  39  experimental occlusion pressure data combined on the same graph to clearly illustrate the effect of exsanguination on the arrest of blood flow. Finally, the occlusion pressure data from the exsanguination tests was related to blood pressure and plotted in Figure 3.59. All graphs were normalized by dividing the difference between the occlusion pressure and diastolic blood pressure by the difference between the systolic and diastolic blood pressures (Figures 3.60 and 3.61). Unfortunately, normalizing the occlusion pressures did not significantly improve correlation of the data. However, the diastolic pressure level appears to be the dominant parameter in the determination of the pressure at which blood flow resumes as it is the main resting state of the blood pressure.  3.2.3.2 Curve Fitting Various mathematical functions were explored to determine the relationship of the experimental and clinical occlusion pressure data. A simple inverse relationship provided the best correlation of the experimental data. Neither a multiple linear regression analysis, a polynomial fit up to the fourth degree, logarithmic or exponential functions with various coefficients represented the trend of experimental points. The resulting relationships fitting the laboratory and clinical occlusion pressure points are described below. Figure 3.62 shows the experimental occlusion pressure points measured in the laboratory and an inverse curve superimposed over the points. The simplest function which correlated with the laboratory experimental data was defined as: (1) Pocc - Pdia =16 (Limb Circ)/ (Cuff Width) where Pocc is the occlusion pressure while Pdia is the diastolic pressure of the subject at the time of occlusion. This mathematical relationship derived from the experimental occlusion pressure data is of no practical use as the predicted occlusion pressure is higher than that found to be necessary clinically. Figure 3.63 shows a curve fitting the clinical  40  occlusion pressure data. The mathematical relationship of this second curve is the following: (2)  Pocc - Pdia =8 (Limb Circ)/ (Cuff Width) The difference between occlusion pressure and diastolic pressure obtained in the operation room decreased up to 50 mmHg of the value obtained in the laboratory tests. Nondimensionalizing the data did not significantly change the correlation (Figure 3.64). Correlation of experimental data was the first step in identifying important parameters affecting blood flow occlusion by the inflation of a pneumatic tourniquet cuff around a limb. The next step was to develop analytical models to explain the mechanism by which occlusion occurs. This is discussed in Chapter 4.  41  CHAPTER 4 - ANALYTICAL MODELS  Mathematical correlations of the experimental results of soft tissue and occlusion pressures were presented in the previous chapter. Analytical and numerical models are considered in this chapter. The main objectives of this phase were to explain the mechanisms of blood flow occlusion in a limb encircled by an inflated pneumatic tourniquet cuff and to investigate the causes of injuries associated with the use of an occlusive device. The analytical models of compression of soft tissues and the occlusion of bloodflowwere treated in two separate stages. In the first stage, the inflation of the tourniquet cuff causing compression of the surface and internal soft tissues of the limb was considered. The compression of the muscle tissue was modelled based on elasticity theory applied to a limb made of isotropic or orthotropic material. In the second stage, the compression of blood vessels was considered. The dynamics of blood flow occlusion was modelled using two approaches. The first approach hypothesized that occlusion occurs because of fluid resistance in a partly constricted blood vessel. In this case the decrease influidpressure was evaluated along a stenosis of the artery. The second approach considered that bloodflowocclusion occurs by complete constriction of the blood vessels. The closure of the blood vessels was modelled using the theory of collapsible tubes and the theory of beam deflection.  4.1 Model Assumptions Compression of a limb and the arrest of blood flow are physiological phenomena that must be simplified for mathematical modelling. The following assumptions were made in this analysis pertaining to the properties of the limb, the main blood vessel, and the main nerves. The assumptions were used for developing both the soft tissue compression model and the blood flow occlusion model.  42  4.1.1 Assumptions Pertaining to the Limb 1)  The limb is a circular cylinder.  2)  The limb is made of three superimposed layers of tissues: cutaneous tissues (skin and fat), soft tissues (muscles, ligaments and tendons), and hard tissue (bone).  3)  Each layer of the limb is made of elastic material.  4)  The limb is assumed to be infinitely long. The end faces are free from any load (plane stress condition).  5)  External surface forces are evenly distributed around the limb and are symmetrical with respect to the midpoint of the cuff.  6)  The bone is located in the center of the limb.  4.1.2 Assumptions Pertaining to the Main Artery of the Limb 1)  The main artery runs axially along the limb.  2)  The main artery is a straight tube of constant circular cross-section.  3)  The artery wall is made of a homogeneous, isotropic, elastic material.  4)  The blood flow is quasilaminar.  5)  Blood is considered to be a Newtonian, homogeneous, incompressible fluid.  6)  Blood has a constant fluid density.  7)  There is no fluid entry effect.  8)  The flow is pulsating from systolic to diastolic blood pressure levels.  9)  The artery walls expand and contract under the blood pressure waves.  10)  The brachial artery is the biggest artery over the part of the upper limb where the cuff is applied. It is the only one of concern in the determination of occlusion pressure (Figure 4.1).  11)  The femoral artery is the main artery in the lower limb where the cuff is applied. It is the only one of concern in the determination of occlusion pressure.  43  4.1.3 Assumptions Pertaining to the Main Nerves 1)  Nerve axons are small circular cylinders (the axon) covered with a sheath of uniform thickness, the myelin.  2)  The axon is of constant diameter.  3)  The axon sheath is non-resistant to shear forces.  4.2 Soft Tissue Compression Model The experimental measurements of soft tissue pressure in cadaver limbs encircled by inflated pneumatic cuffs presented in the previous chapter showed a radial decrease of pressure from the surface of the limb to the important peripheral nerves. The average radial pressure decrease was estimated to be negligible in the case of the upper limb and 4.6% of the cuff pressure in the case of the lower limb. The 99% upper and lower confidence limits of the average radial pressure change for the upper limb were found to be a decrease of 5.4% and 6.8% of the cuff inflation pressure respectively. Likewise, for the lower limb, the upper and lower limits of the 99% confidence range were calculated as an increase of 2.4% and a decrease of 11.8% of the cuff inflation pressure. It is important to be able to predict the radial pressure gradient in order to determine the perineural and periarterial pressures. Knowledge of these pressures was required to determine cuff inflation pressures sufficient to achieve hemostasis. An analytical model of the soft tissue compression has therefore been developed to allow prediction of this radial pressure gradient. The experimental data previously presented in Section 3.1.3 was used to verify the accuracy of this model. In this analysis the limb was modelled as a thick walled cylinder of elastic material. An external load was applied radially over a finite length of the cylinder to simulate the cuff inflation pressure on the limb. The bone of the limb was represented as a rigid core, located at the center of the thick walled cylinder. The inner radius Ri of the softtissuesis equivalent to the bone radius and the outer radius R of the cylinder is the limb radius. Q  44  No relative displacement occurs at this interface. These radii are the two boundary values necessary to determine mathematically the radial pressure distribution in the soft tissues. Po and Pi represent the outer pressure applied on the cylinder and the inner pressure at the interface between the bone and soft tissues respectively. Elasticity theory was used to obtain an equation describing the radial pressure distribution in the limb soft tissues. The elasticity equations were solved in cylindrical coordinates based on two different assumptions. The first case assumes that the limb consists of a homogeneous isotropic material while the second case assumes that the limb can be modelled as an orthotropic material. The model, based on these assumptions, was developed as outlined in the following sections.  4.2.1 Isotropic Material Model To develop the radial pressure distribution equation, the theory of elasticity was applied on an infinitesimal element of a thick-walled cylinder made of isotropic material [65-67] (Figure 4.2). The end faces of the cylinder were assumed to be free from applied loads while all external surface forces were assumed evenly distributed around the cylinder and symmetric about the midpoint. Limiting cases for the radial pressure distributions were calculated for both the upper and lower limbs by assuming alternately plane stress and plane strain conditions. The plane stress condition assumes that there is no axial stress applied on the limb tissues. The equations to determine the internal soft tissue pressure were derived from static equilibrium. The solution provided an expression for the radial displacement of the soft tissues at any radial location in the limb from the surface to the bone. Simplified general equations for the radial and tangential stresses at any point of an elastic cylinder were then obtained by substituting the radial displacement expression and its derivative in the principal stress equations (Appendix D.l).  45  Using the known external pressure P applied on the limb, the inner pressure Pi was 0  evaluated by equating the displacement of the softtissuesand the displacement of the bone at the interface. Under the external pressure, the displacement of the bone is small relative to the displacement of the muscle. The mechanical properties of muscle are, however, not as well defined as those of bonetissue.For this reason, the equations were solved for a range of Poisson's ratio varying from 0.3 to 0.5 as documented by Fung [68]. An iterative solution of the internal pressure at the bone and soft tissue interface was obtained using the program "T-K Solver". The pressure was then calculated at the nerve location. Radial pressure increases of 63.1% to 39.8% were calculated for the upper limb while pressure increases of 76.0% to 45.4% were calculated for the lower limb. An assumption of plane strain conditions represents the limiting case accounting for the generation of both axial and radial forces due to the curvature of the inflated cuff on the limb and the restraint resulting from muscle connection to the bone. The same equations of elasticity were used to calculate the internal pressure with the exception of the coefficient of the first term of the equation of the soft tissue displacement (Appendix D.l). The percentage change in radial pressure ranged from an increase of 47.4% to a decrease of 0.4% of the cuff inflation pressure for the upper limb. The percentage change of the radial pressure ranged from an increase of 56.7% to a decrease of 0.5% of the cuff pressure calculated for the lower limb. As can be seen in Figure 4.3a and 4.3b, neither the limiting plane stress nor the plane strain solutions correlated well with the experimental pressure data. It is possible that the cause of the discrepancies between the numerical and experimental results he in the fact that muscle tissue cannot be accurately represented as an isotropic material. This can be understood in view of the fact that muscle tissue primarily consists of directional fibres lying parallel to the bone.  46  4.2.2 Orthotropic Material Model The model of a limb assuming an isotropic material did not evaluate the radial pressure distribution satisfactorily when compared to the experimental pressure distribution. For this reason, it was decided to hypothesize that the limb was made of orthotropic material. Since the muscles run in a longitudinal direction in the limb, it was assumed that the properties of the material were similar in the radial and tangential directions but different in the longitudinal direction [68]. As before, the derivation of the orthotropic limb model was performed for the limiting plane stress and plane strain conditions.  4.2.2.1  Plane Stress Condition  Static equilibrium was still assumed in the model to allow derivation of the equations necessary to evaluate the internal pressure at the location of the bone and soft tissue interface. New elastic equations for an orthotropic material were used to calculate the internal pressure (Appendix D.2). Poisson's ratio was varied from 0.3 to 0.5. Radial pressure increases ranging from 19.6% to 4.0% of the cuff pressure were calculated for the upper limb. Radial pressure increases ranging from 27.3% to a 8.2% of the cuff pressure were calculated for the lower limb. These pressures represented the upper limits since the model assumed axial movement of the tissues. To consider the case of limited axial movement of the tissues, a plane strain condition was also considered.  4.2.2.2  Plane Strain Condition  The soft tissue internal pressure of the limb was also evaluated based on the assumption of plane strain condition. In this case a radial pressure increase of 6.0% to a radial pressure decrease of 31.0% were calculated from the surface of the upper limb to  47 the tissue/bone interface. A radial pressure ranging from an increase of 10.8% to a decrease of 34.7% was calculated for the lower limb. It is recognized that the plane stress or plane strain conditions assumed here represent bounding solutions to the real case. In reality, the axial condition varies as a function of radial position due to variations in applied loading, material properties and constraint conditions. At the limb surface, a position varying applied axial stress occurs due to the applied pressure at the cuff. The axial stress beneath the limb surface varies as a function of both radial pressure and the anatomical variations in limb stiffness. At positions close to the bone, the soft tissues experience constraint due to fiber attachment to the much stiffer bone structure creating a more displacement controlled system. This analysis has not attempted to evaluate this complex variation but rather to provide a simple model to better understand and predict the radial pressure distribution across the limb section. Based on a range of Poisson's ratio between 0.4 and 0.48 (Figure 4.3a and 4.3b), the numerical data for the conditions of plane stress and strain for an orthotropic limb material lies within the limits of the experimental data. This model appears to give an adequate prediction for the radial pressure gradient in both the upper and lower limbs.  4.3 Blood Flow Occlusion Models On a gross scale, sufficient compression of a limb using a pneumatic cuff results in the occlusion of arterial flow. On a much smaller scale, it is the main artery of the limb that is of primary concern and ultimately constricted due to external pressurization of the limb and pressure transmission through the softtissues.Two mechanisms are believed to contribute to the arrest of blood flow upon constriction of the artery. The first mechanism is a result of fluid dynamics in a constricted tube. The second mechanism is associated with the elastic stiffness properties of the blood vessels. These two mechanisms are outlined in the following section.  48  4.3.1 Fluid Dynamics Approach This approach was considered to address the possibility of blood flow arrest without complete constriction of the vessels. The occlusion of blood flow was considered to primarily be a fluid dynamic phenomenon. Basic thermodynamic andfluidprinciples were therefore applied to analyze the cessation of flow in the artery. Although complete numerical solutions could not be carried out due to insufficient information, the development of the equations for this mechanism are presented here for completeness. The constriction of a blood vessel due to the compression of the soft tissues is equivalent to the occurrence of a stenosis in the vessel (Figure 4.4) where the length of the stenosis is equal to the width of the cuff [69-74]. The decrease in occlusion pressure associated with an increase in cuff width is believed to be caused by a pressure loss of the fluid in the constricted vessel. This pressure drop is associated with increase in frictional resistance and flow velocity. In vascular surgery, a critical stenosis is defined as the degree of arterial narrowing necessary to produce a measurable reduction in blood pressure and flow. Blood flow in an elastic tube has been previously formulated mathematically assuming laminar flow [75-78] or turbulent flow [79-81]. Previous hemodynamic analysis also considered steady [75,76] and pulsatile [77-81] flows. While passing through the stenosis, the bloodflowloses pressure through three different mechanisms: viscous losses (or laminar pressure loss AP ), inertial losses (or turbulent pressure loss ;  AP ), and unsteady losses (AP ). The viscous losses occur because of the shear stress at t  U  the wall of the artery. The inertial losses occur in the divergent section downstream of the stenosis. The unsteady fluid losses are due to the pulsatileflowcaused by the systole and diastole. Some pressure is also converted into wall distension according to Laplace [82,83]. The total pressure loss was expressed by Young [70] as follows: (1) AP = x + Pi -P w  0  49  (2) (AP  / +  AP + AP ) = T + P i - P o t  u  w  The equation was then expanded mathematically as follows: (3) [8LT|/r ] + 1/2 [p(A /A -)2V2] + [pL dV/dt] = PR/h + P - P 2  1  2  {  0  The total pressure drop was also represented by the sum of three components related to the geometry of the blood vessel [25]. AP occurs along the contracting portion of the C  vessel, A P occurs across the symmetrical portion of the vessel, and A P occurs along S  e  the expanding portion of the vessel. The total pressure loss was therefore expressed as: (4) AP = AP + AP + A P S  C  e  Accounting for the various stenosis configurations, the equation was further developed as follows: (5) AP = [(Aj/A2) V i (8D/R, ) L] + [(Ai/A )3/2 V i (4.8D/R,)] + [p V , ( A i / A ) ] 2  2  2  2  2  2  The equation cannot be evaluated in this analysis because the area of the constriction is unknown. Strandness and Sumner [25], however, performed experiments to evaluate the pressure losses across a number of stenoses. They used a 1 cm long symmetrical stenosis in a tube to study the effect of lumen reduction on the pressure loss. The pressure losses were found to be mainly due to the entry and exit effects. Figure 4.5 shows these kinetic energy losses causing the bulk of the decrease in pressure and flow. The reduction of the stenosis diameter from 0.5 cm to 0.0 cm showed that high velocity flow has a greater pressure loss than low velocity flow for an equivalent stenosis radius (Figure 4.6). Figure 4.7 shows the decrease in flow related to the increase in pressure gradient. The results of Strandness and Sumner show that a 50% decrease in the arterial lumen is necessary to affect the flow. Flanigran [84] found that a significant decrease in the flow occurred only at 80% of lumen reduction. Most importantly, these  50  authors found that blood flow arrest is possible without the complete closure of the artery. Figure 4.8 shows a part of an artery with sections 1 and 2 representing the inlet and the outlet respectively. The length of the stenosis was assumed equivalent to the cuff width. From Bernoulli's equation : (6)  (0.5 p V^) + Pi = (0.5 p V 2) + P + AP 2  2  where AP was calculated previously. Using the equation of continuity Vj Ai = V 2 A 2 , the pressure difference was determined as: (7) P1-P2 = 0.5 pV 2 [(Ai/A )2 -1] + { [(Ai/A )2 Vi (8 D / R ^ ) L] x  2  2  + [(Ai/A )3/2 Vi (4.8 u/Ri)] + [pV 2 (Ai/A )2] } 2  t  2  The variables Pi, P , Ai, p, Vj, D, L are known in equation (7). The reduction of the 2  artery, A , is unknown and dependent on the external pressure. The reduced radius of the 2  artery at the end of the cuff was calculated for an inlet pressure of 120 mmHg, an outlet pressure of 80 mmHg, and a cuff width of 8.5 cm. The artery was found to decrease to 0.104 cm which is half the size of the original artery radius. It is speculated that blood could be arrested without complete constriction of the vessel because of its non-Newtonian characteristic, as it is made of plasma and suspended corpuscles. When the lumen of the artery decreases in size, the diameter of the blood cells approaches the diameter of the artery. When this occurs, the corpuscles of blood likely move in an orderly fashion [77] at a very low velocity. A small increase in external pressure on the artery causing further lumen decrease may cause blood flow arrest without complete constriction (Figure 4.9). Unfortunately, tests with radiopaque dye injected intravenously in combination with photographic imaging or another suitable technique would have to be used to confirm this hypothesis of the mechanism of hemostasis.  51  4.3.2 Elasticity Approach The application of pressure on the limb has the ultimate effect of applying external pressure on the blood vessels. In the previous approach it was assumed that partial constriction occurred as a result of generated soft tissue pressures. In this analysis, the external pressure was assumed to be sufficient to completely close the arterial vessels. Two approaches were developed to predict the pressure required to close the vessel. The arteries werefirstmodelled as collapsible tubes externally loaded over a finite length. The second approach assumed that a strip of the artery wall subjected to a net external pressure behaves as a beam with fixed supports at the ends.  4.3.2.1 Collapsible Tube Approach Using this approach, the blood vessel was modelled as an elastic tube subjected to an internal pressure (the systemic blood pressure) and an external pressure (tourniquet cuff pressure). The difference between the opposing pressures governs the behavior of the vessel. In the theory of buckling, a tube suddenly collapses under load when a critical stress is achieved [85,86]. The minimum pressure necessary to cause a tube to collapse is denoted as the critical closing pressure [87-91]. This critical load varies with the geometry of the tube, the wall resistance, and the transmural pressure. When the transmural pressure acting on the tube is smaller than the critical pressure, the tube remains fully open (Figure 4.10 a). When the transmural pressure approaches the critical closing pressure, the tube wall is in a state of instability, and may buckle or collapse at any time (Figure 4.10 b). The tube completely collapses when the transmural pressure is greater than the critical pressure (Figure 4.10 c). Von Mises [92] found that the critical transmural pressure necessary to uniformly collapse a cylinder is a function of Young's modulus, tube wall thickness, tube length, tube radius, Poisson's ratio, and the number of  52  circular lobes. Figure 4.10 shows a sketch of a two-lobe tube. The critical pressure was predicted as follows: (8) -Pcrit- [l/(l+(nL/7tr) )] [(Eh3/12r3) (2n2-l-u/l-<u2) + (Eh/r(n2-l)] 2  + [Eh3 (n2-l)] / [12r3 (1-TJ2)] If the length to radius ratio is sufficiently large, as in the case of an artery, the second term of the equation becomes small and can be neglected. For a two-lobe problem, the equation of the critical pressure then reduces to: (9) -P t = Eh3/[4r3 (1-0)2)] cri  This equation allows the calculation of a critical point load necessary to cause closure of the blood vessel. In the case of an artery, the internal pressure varies from diastolic to systolic. The critical closing pressure was calculated for a typical normotensive patient with a blood pressure equivalent to 120/80 using a point load on a typical artery (parameter values are listed in Table 2). The closing pressure was calculated to be 17.3 mmHg. For the same conditions, the calculated value was significantly lower than the experimentally measured transmural pressure of 86.3 mmHg. This variation suggested that a simpler point load assumption did not sufficiently represent the true load distribution. To improve the prediction of the critical closing pressure, the applied cuff/pressure length was incorporated into the equation. This equation was derived from the principle of the conservation of energy applied to a collapsible tube [93] (Appendix E). The following equation represents the equation for a continuous critical load: (10) - o/  L / 2  P(x) dx = E h3 L /8(1-1)2) r3  When the critical load was calculated for a continuous load (with a ramp linear function), the transmural value increased to 107.8 mmHg above the blood pressure. For a parabolic pressure profile, a value of 197.0 mmHg was obtained. These calculated values  53  were significantly larger than the experimentally measured occlusion pressure values suggesting that this approach did not adequately model the mechanism of hemostasis. As occlusion occurs prior to these values, sudden collapse is unlikely. Constriction of the vessel is more apt to occur gradually. In view of this, a flexible strip beam approach was considered in an attempt to model the occlusion of blood flow.  4.3.2.2 Flexible Strip Beam Approach In this model, hemostasis was considered to be caused by the gradual constriction of the blood vessels. To model this mechanism, the artery was treated as a series of longitudinal strips arranged in a circle of diameter equal to the vessel diameter (Figure 4.11). Each individual strip of artery was modelled as a beam element. The element located at the top of the artery is shown in Figure 4.12. In this element, the hoop stresses and curvature effects were assumed to be negligible. Stiffness was therefore only developed in the longitudinal direction. Upon application of the assumed axisymmetrical soft tissue pressure load, all of the vessel beam elements deflect in a similar fashion meeting at a central point resulting in blood flow arrest. An external load was applied over a length equivalent to the cuff width to properly simulate deflection of the flexible strip element. An internal load was also applied on the bottom of the entire length of the strip to simulate the blood pressure in the vessel. The solution to the beam deflection problem was obtained by using only half of the beam due to symmetry (Figure 4.13) [93]. Occlusion was assumed to be achieved when the beam deflects an amount equal to the radius of the artery. This represents the maximum achievable deflection of the artery strips thereby causing the blood vessel to be fully constricted. The deflection of the vessel element was first evaluated assuming an external uniform distributed load to obtain an initial approximation of the required cuff inflation  54  pressure P necessary to cause occlusion. The uniform continuous load was applied over c  a length equal to the cuff width. The equation for element deflection is therefore: (11) - CO (x) = -P <x-/'>0 c  An internal pressure equivalent to the diastolic blood pressure was applied over the bottom of the element. The cuff inflation pressure P was calculated by solving equation c  (11) for a deflection equal to the artery radius. The detailed solution of the strip/beam deflection with uniform load is given in Appendix F. The occlusion pressure was calculated for a cuff width varying from 1 cm to 20 cm. The results are shown in Figure 4.14. The occlusion pressure (cuff inflation pressure) was nondimensionalized by dividing by the systolic pressure and then plotted as a function of cuff width. An inverse non-linear relationship similar to the experimental occlusion pressure data was obtained. To improve the accuracy of this model, the occlusion pressure was also systematically calculated assuming applied pressure distributions which more accurately represent those obtained from the soft tissue measurements. In particular, the deflection of the beam element caused by a linear ramp distribution and an offset cosine distribution was calculated as these functions are easily integrated and approximate the pressure distribution of the cuff more so than the previously assumed uniform load distribution. The linear ramp distribution used is the following: (12) - co (x) = - 0.9807 P (<x-/'>l / (L-F)) c  The offset cosine function load used is the following: (13) - co (x) = - 0.3277 P [1 - COS(TC <x-/'> / (L-f)) ] 1  c  The results are shown in Figure 4.14. Upon comparison of these results (Figure 4.14), it was readily apparent that the calculated occlusion pressure became more closely correlated with the experimental data  55  as more accurate soft tissue pressure distributions were utilized. In view of this, the experimental pressure distribution was curve fitted to obtain the best possible external load function to be used in predicting the occlusion pressure. A Taylor expansion series utilizing three terms was obtained as the best fit for the experimental pressure distribution produced by the cuff. (14) - co (x) = - 0.4904 P<x-/'>0 { [TC/(L-/') (x-/)] 12 2  c  [7C/(L-/')(x-/')] /24 + [7t/(L-/') (x-/')] /720} 4  6  The cuff inflation pressure was then calculated for the Taylor expansion series both with and without an offset. This was done to verify the effect of sharp pressure discontinuity at the edge of the cuff. The pressure ratios obtained with the Taylor series pressure distribution with an offset were lower than the ratios obtained with the Taylor series pressure distribution without an offset. Figure 4.14 shows a plot of the occlusion to diastolic pressure ratio calculated with all the pressure distributions shown previously as a function of the cuff width. The pressure data obtained from the uniform and cosine pressure distributions were not verified by the experimental pressure ratio for cuff widths smaller than 8 cm. The uniform and cosine load distributions predicted occlusion with average accuracies of 38.7% and 26.2% respectively (sample standard deviations of 2.3 and 1.5). The loading of the beam strip with a Taylor series pressure distribution with offset predicted occlusion with an average accuracy of 13.9%. The pressure ratios calculated from the ramp linear and Taylor series pressure distributions predicted the experimental pressure ratios for all the range of cuff width with average accuracies of 5.8% and 7.7% respectively (sample standard deviations of 4.9 and 3.6). In view of further improving the accuracy of the beam strip model, the experimental surface pressure profiles produced by the cuff were curved fitted. The pressure profile obtained by McLaren [45] was also curve fitted for the cuff pressure profile for  56  comparison purposes. Figure 4.15 shows the resulting plots generated from the loading of the beam strip by the curved fitted cuff pressure profiles. The analytical curves were verified by the experimental occlusion to diastolic pressure ratios with an accuracy of 4.9% for the profile of McLaren and with an average accuracy of 5.2% for the present pressure profile. The correlation obtained between the predicted cuff pressure required to occlude arterial flow and the occlusion pressure measurements strongly supports the use of this analytical model in the prediction of blood flow occlusion. It also supports the hypothesis that hemostasis occurs as a result of elastic constriction of the blood vessels over a finite length of the limb and occurs more readily with increased cuff length approaching a diastolic pressure threshold.  57  CHAPTER 5 - CLINICAL EVALUATION OF OCCLUSIVE CUFFS Experimental and analytical work is usually sufficient in an engineering project in order to produce a prototype and go on to production. In medicine, a product must be tested clinically before being used. Similarly in the present biomechanical engineering cuff evaluation, a clinical testing phase has been performed to assess the safety and efficacy of currently used occlusive cuffs and to illustrate the application of the model and analytic techniques. Further objectives of this clinical evaluation were to optimize the use of the tourniquet cuffs and identify possible cuff design improvements. This was performed with the intent of reducing future cuff related injuries. To obtain a complete understanding of the clinical usage of a tourniquet cuff, two series of tests were performed. The first series entailed analyzing the physical features of the cuff and the biological features of the limb. This was done in view of improving ways to predict the lowest cuff inflation pressure required to arrest arterial flow. The natural variation of biological soft tissues and arterial systems among patients were considered in combination with differences in the methods of exsanguination and the injection of anaesthetics. The occurrence of nerve injuries of various degrees was also analyzed as a direct consequence of tissue compression under the pneumatic cuff. During the second series of tests, pneumatic occlusive cuffs were evaluated in order to assess the safety and efficacy in the use of these devices to achieve blood flow occlusion. The current cuff designs were then evaluated with regards to proper fit on the limb. Tourniquet cuffs were also evaluated according to the pressure profile they deliver on the surface of the limb. The snugness of cuff application was particularly considered as an important parameter affecting the cuff pressure delivery on the limb. Finally, the effect of adding an interfacing layer between the cuff and the limb was considered in the delivery of cuff pressure to the limb.  58  5.1 Physiological Effects in Blood Flow Occlusion Physiological concepts were used in this section to analyze the compression of a limb by a surgical tourniquet. Mechanical models assumed constant properties for blood and soft tissues as it is traditionally done for elastic engineering materials [68,94,95]. However, it is know that biological tissues exhibit complex behavior that can change as result of chemical, nervous, or mechanical disorder. It was also assumed that only one main artery had to be occluded although the arterial system is very complex. Since the limb is part of a larger physiological system, the local compression of the limb directly and indirectly affects the skeletal, muscular, neurological, and vascular systems [96]. High cuff inflation pressures appear to be necessary to constrict the deeply embodied arteries in the limb making the peripheral nerves vulnerable to injuries. Nerve injuries were shown to be primarily caused by compression rather than ischaemia [29]. The determination of the exact occlusion pressure would allow a surgeon to lower the cuff inflation pressure and reduce the incidence of injuries. Two physiological effects were considered to be related to occlusion pressure: the variation of biological tissues and the variation of arterial systems.  5.1.1 Variation of Biological Tissues The ease at which arterial flow can be occluded in a limb depends on the compressibility of the soft tissues. The cadaver test results indicated that 90.1% to 97.5% of the externally applied pressure was transmitted from the cutaneous layers to the center of limbs of small circumference. In the case of larger size limbs, as for thighs, 80.4% to 94.1% of the surface soft tissue pressure was transmitted to the deeper tissues. The soft tissue measurements on cadavers indicated that the living tissue is more elastic and has greater turgor than the deadtissue.This was qualitatively shown with the application of the cuff in a snug way on the specimen showing oedema. In this case, the application of  the cuff on a limb compressed the soft tissues by expelling the fluid awayfromthe compressed region. The limb may be modelled by a superposition of soft tissue layers. During the inflation of the cuff, the compressive forces remain normal to the surface of the cuff and radial and shear stresses are generated in the underlying tissues due to the cuff curvature. If the tissue is assumed to be elastic, the radial cuff inflation pressure partially reduces as a result of this axial stress pushing away from the center of the cuff. The generation of shear stresses causes an axial tissue displacement since the internal tissues are not restricted on either side of the cuff. The degree of axial displacement depends on both the pressure profile and the amplitude of the peak pressure applied to the limb. Under external compression, each layer of tissue deforms differently because of interlayer slippage (Figure 5.1). The resulting pressure profile at the center of the limb is therefore of smaller amplitude and larger span.  5.1.1.1 Evaluation of Soft Tissue Composition Two limbs of similar circumference can have significantly different tissue composition. The bone diameter to limb diameter ratio and the ratio between muscular and fatty tissues vary among patients. As a direct consequence of the consistency of a limb, a variation in the vascularization of the limb is expected as well as a variation in the size of the main blood vessels. It is therefore expected that a limb having large blood vessels and a high ratio of muscular tissue with respect to fat requires a higher occlusion pressure than a limb having smaller blood vessels and a smaller ratio of muscle to fat. In order to compare the compressibility of various tissue composition, occlusion pressures measured on limbs of similar circumference. Figure 5.2 shows these results. A variation in occlusion pressure of 55 mmHg and 85 mmHg were measured for the upper and lower limbs respectively.  60  Atissuecomposition evaluation was initiated to explain the apparent difference in occlusion pressure between fatty and muscular limbs. To detenriine the compliance of soft tissues a device measuring the pressure applied on the limb as function of the tissue displacement at the surface of the limb was used. The resolution of the instrument did not, however, allow measurement of the soft tissue displacement caused by a small pressure. The device was therefore incapable of giving adequate information of tissue composition in view of predicting occlusion pressure. The evaluation of occlusion pressure for similar limbs remains a subjective matter since blood pressure is a parameter to be considered. There is no current technique to assess quantitatively the proportion of muscles with respect to fat. At the present time, the only way to estimate qualitatively the fat/muscle composition of a limb is by pinching the skin. To quantitatively assess the nature of the soft tissues it is recommended that a strain gauge be attached to the pinching instrument. This will provide a repeatable way of measuring the soft tissue composition therefore allowing a comparison of the occlusion pressure between limbs of similar circumference to be performed.  5.1.2 Variation of Arterial Systems Application of basic hemodynamic principles provides important information on occlusion pressure. The heart is basically a complex mechanical pump with feedback control that regulates the circulatory flow. Abnormalities in arterial flow are regulated and blood flow is redirected to secondary routes. This increased flow forces an expansion in the diameter of adjacent arteries and a corresponding reduction in the volume of blood sent to the obstructed region [97-101]. The occlusion pressure is directly related to the physiological properties of the arterial system. Physical parameters such as blood viscosity, peripheral resistance, and size of the arteries directly affect the pressure required to close the arteries. Higher cuff inflation pressures are required to constrict calcified arteries [101], large or inelastic  61  vessels [102,103]. Such high cuff pressures expose the patient to a higher risk of damage to the peripheral nerves [101]. Physiological parameters such as arterial systemic volume, cardiac output, and blood pressure also affect the occlusion pressure. Hypertensive patients require higher cuff inflation pressures whereas hypotensive patients require lower cuff pressures than normotensive patients to ensure arrest of blood flow. In this research, blood flow occlusion pressures were measured in young healthy normotensive subjects. For this reason, prediction of blood flow occlusion from the experimental model should be restricted to normotensive patients (110 mmHg < Psys < 135 mmHg). Overall, the use of a pneumatic tourniquet cuff has been shown to have important physiological consequences. The arrest of blood flow has been reported to lead to vascular complications such as swelling [26], deep-vein thrombosis [27], pulmonary embolism [28], and hypertension [32]. This emphasizes the need to reduce the inflation pressure and the time of application.  5.1.2.1 Effects of Anaesthetics in the Blood Stream Toxins, drugs, nervous stimuli, and anaesthetic agents can cause important cardiovascular changes [104-106] which may also lead to significant changes in the occlusion pressure. A 14% decrease in arterial pressure and a 17% decrease in peripheral pressure have been reported as a result of the administration of narcotics [107,108]. This could lead to decreases in the cuff inflation pressures required to ensure cessation of blood flow. The effect of anaesthetic agents in the blood stream of the patient was considered in order to compare experimental and clinical occlusion pressure data. In the various clinical trials, the occlusion pressures were obtained from patients anesthetized using general anaesthetics which were nonselective analgesics; i.e. they affected the central nervous system. The anaesthesia was administered via inhalation and intravenous  62 injection. Premedication with morphine (Demerol) was given to the patient followed by administration of a mixture of nitrous oxide, oxygen, and halothane plus an injection of pentothal and fentanyl throughout the surgery. In all 23 patients tested, the systolic pressure dropped an average of 35.5 mmHg and the diastolic pressure dropped by 25.8 mmHg. For a particular cuff and patient, this decrease would directly translate to a reduction in the pressure required for blood occlusion. Unfortunately, the occlusion pressure could only be measured at the end of the procedure as deflation of the tourniquet cuff would lead to flooding of the surgical site. The data nevertheless showed that a gradual decrease in cuff pressure would be safe in providing hemostasis. The barbiturates and narcotics used during anaesthesia have a relaxing effect on the smooth muscles [109]. The vasodilatation of blood vessels and the relaxation of muscles reduce the cuff inflation pressure required to occlude blood flow. Nevertheless, the possibility of increases in blood pressure due to a vascular reaction to the anaesthetic agents should be considered. This would cause the blood pressure to rise and consequendy the occlusion pressure to increase. The cuff pressure could be decreased after stabilization of the blood pressure i.e. with no sign of vascular reaction.  5.1.3 Consideration of Ischaemia and Compression as Cause of Neural Damage One of the main concerns in using high pressures to inflate the tourniquet cuff is the potential of damaging the peripheral nerves. Nerve injuries are caused by two main mechanisms. The first mechanism consists of diffuse loss of blood causing starvation of oxygen while the second mechanism consists of a definite disruption of the neural structure causing interruption of neural transmission. An experiment on baboons was carried out by Ochoa et al. [29] to determine the relative effect of ischaemia and mechanical compression on nerves during the use of a pneumatic tourniquet. Under both conditions, samples of damaged tissues were analyzed;  63  results suggested that the local conduction block was caused mainly by the structural damage rather than the ischaemia (Figure 5.3). At the proximal edge of the cuff, 15% of the neural fibres were found to be histologically abnormal. Seven to fourteen days after chronic compression, the damaged paranodal myelin underwent degeneration. Even after shorter time periods, the myelin damage impaired neural conduction by reducing the current flow at the node of Ranvier and thereby delaying the activation of adjacent nodes. The study concluded that the mechanical compression was responsible to the injuries. Neurons are typically covered by a concentric insulating material, the myelin, and further surrounded by a thin outer insulating layer, the neurilemma. The myelin is interrupted in short segments to form the nodes of Ranvier. Figure 5.4 shows the Schwann cells enclosed in the nodes with pseudopodia reaching out to embrace the neighboring unmyelinated fibres [29]. As an extreme external pressure was applied on the limb or as a pressure differential was applied between one part of the nerve and another, a progressive demyelination was seen to occur in the region of high shear stress accompanied with the displacement of the nodes of Ranvier [29]. The displacement was maximal under the edges of the compressive cuff with relative or complete sparing under its center (Figure 5.5). The nodes of Ranvier were displaced towards the incompressed tissues. Tourniquets applied over a long period of time or at high pressure are likely to cause nerve damage since the incidence of demyelination increases with presence of localized pressure. The consequences of mechanical compressive nerve damage are numerous: muscle atrophy, loss of cutaneous deep sensitivity, reflex and vasomotor inactivity, trophic disorder, pain and functional palsies, development of gangrene, aneurysm formation, tendon and muscle injuries, contractures and paralysis, and ankylosis [32-40]. Depending on the severity of the lesion, damaged tissues may or may not regenerate resulting in either partial or complete recovery of the nerve. An acute compression typically leads to a temporary paralysis while the case of chronic compression usually causes irreversible damage. Nerve damage caused by mechanical  64 compression occurs in various degrees. As the pressure is increased and the nerve is compressed, the axon is deformed gradually into irregular patterns. Initially, there is no gross apparent break in the continuity of the structures (Figure 5.6.1) but the axons are injured and Wallerian degeneration begins to occur (Figure 5.6.2). In the worst case, the axon is destroyed and the degeneration persists (Figure 5.6.3). In this case there is loss of motor and sympathetic function and persistent sensory deficit. The funiculi of the nerves trunk get disrupted and disorganized (Figure 5.6.4). The axon has the capability to regenerate into the interfunicular connective tissues. The cross-sectional area of the distal stump shrinks and the fibers undergo distortion (Figure 5.6.5). There is complete disorganization and total loss of function with negligible recovery. Nerves are therefore very susceptible to damage as a result of externally applied pressures. Although it has been reported that a uniformly distributed pressure over a nerve is unlikely to cause damage, neurons of the peripheral nervous system have been shown to be vulnerable to shear forces generated from the inflation of the cuff [110-113]. Nerves can also be injured by manipulation of the limb. During an operation, the surgeon may strain the limb by pulling, bending, of twisting the limb. The large displacement of the limb may cause generation of stresses that can damage the deeper structures. The normal combination of limb manipulation, cuff over-inflation and the surgical procedure itself makes it difficult to determine precisely the cause of permanent nerve damage.  5.2 Characterization of Pneumatic Cuffs Three series of clinical tests were conducted with five representative in types and sizes of tourniquet cuffs to characterize design and performance parameters. The first series of tests were performed in attempt to geometrically characterize limbs; the second series of tests were performed to evaluate the current cuff designs; and the third series of tests were done to assess the match of the cuff with respect to the limbs.  65  5.2.1 Evaluation of Cuff Designs A number of concerns have been expressed about current cuff designs. The specific cuff design determines the pressure distribution generated on the soft tissues when inflated. This distribution of pressure directly affects the direction and magnitude of the deformation of the soft tissues and consequently of blood vessels and nerves. The dimensions and curvature of the cuff dictating the pressure distribution were investigated. The effect of using a reinforcing material inside the cuff on the pressure distribution was also investigated. Lastly, the material used for the fabrication in current tourniquet cuffs was examined.  5.2.1.1 Shape and Dimensions of Occlusive Cuffs To evaluate the relationship of shapes and sizes to occlusive effect, a comparative analysis was carried out between two typical tourniquet cuffs: the Aspen and Freeman tourniquet cuffs. The Aspen style tourniquets are newer designs where the manufacturer attempted to improve the Freeman cuff design. Of first concern to the surgeon is the selection of a cuff that does not obstruct or interfere with the surgical site. The selection of a specific cuff width directiy affects the occlusion pressure as the ratio of cuff width to limb circumference has been shown to be an important parameter. Five tourniquets cuffs were evaluated and compared: 1) 2) 3) 4) 5)  24" single Freeman, 24" single Aspen, 24" Aspen, banana type, 24" dual Freeman, and 24" dual Aspen. Width, length, thickness, and curvature of the cuffs were measured with the bladders  deflated and the cuffs lying flat rather than encircling a limb. The same measurements were repeated after inflation to 200 mmHg (Appendix G).  66  The widths of the deflated bladders were found to be similar for the 24" single Freeman, Aspen, and banana Aspen cuffs, and decreased by 24.1% upon inflation. This reduction of the bladder width upon inflation may be of concern during clinical application because the reduced width may transmit pressure over a narrower band on the limb. This pressure may ultimately compress the muscles, blood vessel, and nerves more severely. Hence a greater pressure may thus required with increased risk of injury. The curvature of each cuff was evaluated for its ability to fit the limbs. The Freeman cuff forms a right angle cylinder when wrapped around itself. The Aspen cuff has a curved contour designed to fit conical limb shapes. The difference between the proximal and distal circumferences of the single Aspen tourniquet cuff varies from 1.8 cm to 2.2 cm. The two designs of tourniquet cuffs are reinforced by a stiffener placed on the external wall of the bladder, forcing the cuff to curve inward when inflated (Figure 5.7). The shape and rigidity of the stiffeners are important variables with respect to underlying pressure distribution.  5.2.2 Adjustment of Cuff to the Limb The adjustment of a tourniquet cuff is the first step in reducing the incidence of injuries. Tests were conducted to obtain standard measurements of upper and lower limbs in order to evaluate the application of tourniquet cuffs and to consider improvements for future designs.  5.2.2.1 Characterization of Limbs A tourniquet cuff should cover the surface of the limb beneath the cuff perfectly in order to have optimal performance in occluding blood flow. The geometry and size of limbs, however, vary greatly from patient to patient. Two tests were performed to  67  evaluate the biological variation of limbs and obtain reference values for future cuff design. The first test measured the circumference of the limb at the midpoint of the cuff. The second test measured the circumference of the limb at the distal and proximal edges of the cuff to evaluate the difference in circumference as an indication of limb curvature. Normal distribution curves were then generated from normotensive patients and subjects for use in evaluating standard cuff designs. Limb circumferences were measured on 54 normotensive subjects and patients in order to generate normal distribution curves. The curves were generated from the measured data based on the following relationship: [-l/2(x-x)/82] 2  /to -[1/(8 27t)]  e  where x is the limb circumference, % is the mean value, and 8 is the standard deviation. Figure 5.8 shows the distribution curves. The mean circumference of arms was 27.0 cm with a standard deviation of 2.6 cm. The mean circumference of legs was 49.2 cm with a standard deviation of 6.6 cm. The American Humanscale [118] tabulated the following limb circumferences: arm (cm)  leg (cm)  Female Male F & M average  26.39 31.10 28.75  43.98 53.40 48.69  Experimental  27.00  49.20  The present experimental circumference values were found to be within 6.5% of the average circumference values of the American standard for both upper and lower extremities. The shape of the limb was also evaluated by conical or cylindrical characterization. Proximal and distal limb circumferences at the edges of the cuff were measured on both upper limbs and lower limbs. Even after a few minutes, a cuff when applied directly on  68  the skin, leaves a temporary imprint on the limb. This imprint made it easy to measure the proximal and distal limb circumferences located directly underneath the edges of the cuff once removed. Figure 5.9 a shows the resulting normal curves for upper and lower limbs. The circumference proximal to distal difference for both the upper and lower limbs reached a mean of 1.25 cm over the 8.5 cm wide cuff. Standard deviations were evaluated to 1.11 cm and 1.01 cm for the upper and lower limbs respectively. Limb circumference differences between the proximal and distal edges of the cuff were measured and compared to the actual degree of curvature of the Aspen tourniquet cuff. The difference in circumference between the proximal and distal edges of the 24" Aspen tourniquet was evaluated at 2.0 cm ± 2 cm for both the upper and lower limbs while the 24" Freeman tourniquet was evaluated at 0 cm. Figure 5.9 a shows the circumference difference measurements of the two cuff designs superimposed on the normal curves. Based on the circumference difference measurements, the Aspen cuff was evaluated to be 60.5% and 59.7% too tapered for upper and lower limbs respectively. The curvature of the limb was further described in terms of angles in order to incorporate the cuff width. Figure 5.9 b shows the average normal distribution curve combining data from upper and lower limbs. Again, the curvature of the Freeman and Aspen cuffs are shown in the figure. The effect of an improper cuff fitting on the limb is analyzed in the following section.  5.2.3 Transmission of the Cuff Pressure to the Limb Three dominant factors were found to affect the transmission of cuff pressure and its effectiveness to cause blood flow occlusion. The first factor was the effect of tourniquet design itself on pressure delivered to the limb. The second factor was the effect of cuff snugness on pressure delivery. Finally, the third factor was the effect of applying an interface between the cuff and the limb.  69  In order to evaluate the effect of theses influences, the pressure distributed on the limb was evaluated for currently used tourniquet and blood pressure cuffs. Surface pressure patterns were measured with the pneumatic pressure sensor using both limb models and human limbs. A comparative analysis was also carried out between the occlusive cuffs to determine their potential in causing limb damage, in particular nerve injuries.  5.2.3.1 Evaluation of Cuff Designs The effect of tourniquet design was analyzed first. Two main differences exist between the tourniquet cuff and the blood pressure cuff: the width of the cuff and the presence of stiffener inside the cuff. These physical elements affect the surface pressure profile delivered on the limb leading to the recognition that the two types of cuffs are used for different applications. The pressure delivery of two basic tourniquet cuff designs were considered. Figure 5.10 shows the two pressure distribution graphs. The bottom graph shows the parabolic pressure distribution obtained using the standard Freeman surgical tourniquet cuff. In this case the peak pressure reached the inflation pressure of 200 mmHg at the center of the cuff while the pressure at the edges of the cuff dropped to 90 mmHg. The top graph was obtained by using a standard blood pressure cuff (Baumanometer V-LOK) applied on an upper limb. With the cuff inflated to a pressure of 200 mmHg, the plot shows a central plateau at 189 mmHg that covers most of the cuff width. In comparison, the blood pressure cuff transmitted a more uniform pressure distribution onto the limb. The large plateau covered over two thirds of the cuff width. When the blood pressure cuff was applied on a tapered limb, the proximal portion of the limb underneath the cuff was more compressed and a non-symmetrical pressure profile was obtained (Figure 5.11). A high pressure gradient was found at the edges of the cuff. The blood pressure cuff is thus  70  considered to be more hazardous than the tourniquet cuff for equivalent cuff widths and inflation pressure. A comparison was also made between the Freeman and Aspen tourniquet cuffs. The Freeman cuff has a fixed contour. Figure 5.12 shows a symmetrical pressure distribution about the midpoint of the cuff produced by the Freeman cuff applied on a cylinder. Figure 5.13 shows the pressure distribution produced by the same Freeman cuff applied on a very tapered limb. The peak pressure was shifted towards the proximal edge of the cuff due to increased compression of the section of the limb having a larger circumference. Figure 5.14 shows the pressure distribution when the Aspen tourniquet cuff was applied on a straight limb. The peak pressure distribution was shifted to the distal part of the cuff due to its curved contour. Applied on a tapered limb, the Aspen tourniquet cuff showed a symmetrical pressure distribution about the midpoint of the cuff (Figure 5.15). Figure 5.16 shows the same symmetrical surface pressure distribution obtained on a conical limb model. A perfectly symmetrical pressure distribution was obtained only in the cases where the limb shape corresponded exactiy to the curvature of the cuff. Uneven application of pressure on the surface of the limb or a high pressure gradient at the edges of the cuff generates high shear stresses. The discrepancy in cuff and limb geometry caused a surface pressure decrease of 47.6 mmHg to 115.4 mmHg depending on the difference in circumference between the limb and the cuff. An average of 55.5 mmHg per centimeter of circumference was evaluated for all the tested limb/cuff combinations. This results in displacement of the underlying softtissuescausing slippage of the protecting sheath of the peripheral nerves and resulting damage as shown by the sketch of Figure 5.17.  5.2.3.2 Evaluation of Snugness during Cuff Application The snugness during cuff application was evaluated in order to determine the effect it has on pressure delivery. A small rotation of the cuff around the limb or lateral  71  displacement along the limb affects the surface pressure distribution. Figure 5.18 shows the pressure profiles from a cuff inflated at 200 mmHg. The pressure drop is shown to be directly related to the degree of snugness of the cuff. The snugness of tourniquet cuffs at the time of application prior to cuff inflation is an important parameter in the prediction of blood flow occlusion. It was desirable to develop a method to control the snugness variable so that the cuff inflation pressure is fully transmitted to the soft tissues. So far, the "1-2-3 finger" method has been used as an indication of cuff snugness. This method stipulates that at the time of cuff application, one finger can be inserted between the cuff and the skin with no difficulty but that three fingers cannot be inserted easily. This is a commonly used but subjective method. A technique and apparatus for assuring consistency in snugness of cuff application, independent of the cuff or the user, which had been developed previously [57,119] was used to evaluate the effect of variation in snugness on pressure actually applied to the limb. Two series of tests were performed to quantitatively determine the snugness of application of a tourniquet cuff. The first snugness test consisted of measuring the pressure on the limb with the pneumatic pressure sensor prior to cuff inflation. The second test used a secondary bladder to assess snugness. This test bladder was inserted between the tourniquet cuff bladder and the limb and was inflated prior to cuff inflation to determine the degree of snugness. For the first test, measurements were done with Freeman and Aspen (18" and 24") child and adult cuffs of the single and dual cuff types. Four degrees of snugness were applied on the limb by inserting three, two, one, and no fingers between the cuff and the limb. These snugness degrees were referred to as loose, medium-loose, medium, and tight. The protocol of the test is listed in Appendix C. Figures 5.19 and 5.20 show the resulting pressure profiles from the Freeman and Aspen cuffs respectively. For the single and dual tourniquet cuffs, the peak pressures gradually decreased from the tight fit to the loose fit. A small variation in the snugness was found to cause a significant pressure difference on the order of 50 mmHg.  72  The snugness was not completely assessed with the first test as a large degree of subjectivity was still required in the generation of pressure profiles. Although it is known that soft tissue pressure at the surface of the limb decreases with loosening of the cuff, there is still no information available to apply a cuff in a repeatable manner. As noted above, the technique and apparatus for quantitatively assessing snugness, which had been developed previously and independenfly, was utilized in the thesis research to assess the variation in occlusion pressure associated with variation in cuff snugness, and to assure uniform snugness of cuff application when desired. To conveniently employ this snugness-measuring technique and apparatus, a secondary bladder was attached to a tourniquet cuff. This secondary snugness sensing bladder was attached to the cuff between the tourniquet bladder and the stiffener (Figure 5.21). Six bladders of different sizes were available to perform evaluation tests. Calibration curves were generated (Figure 5.22) in order to determine the range of operation of the bladder and select a bladder appropriate for a specific cuff. The snugness bladder was chosen so that its width was equal to one third of the width of the cuff bladder. Monitoring the pressure and volume in the secondary bladder, separately inflated, provides a way to control the degree of snugness of the cuff. A 60 cm3 syringe was used to measure the volume of air required to inflate the secondary bladder while a 300 mmHg manometer monitored the internal pressure. Inflation volumes of 10 cm3, 20 cm3, 30 cm3 and 40 cm3 were chosen to represent the four degrees of snugness previously studied. Tests were performed on 12 limbs of normal subjects. Graphs of bladder pressure as a function of cuff inflation volume were generated for upper and lower limbs (Figures 5.23 and 5.24). For each level of snugness the data points follow a linear pattern in a parallel fashion (Figure 5.25). The three basic degrees of snugness could be marked directly on the syringe or the manometer. The pressure measured for an inflation volume of 30 cm3 in the case of the upper limb was found to be equivalent to the pressure obtained by inflating the cuff of the lower  73  limb up to a volume of 40 cm . Snugness pressure data from the upper and lower limbs 3  were combined together on the same graph (Figure 5.26). For set inflation volumes of 30 cm3 and 40 cm3 in the snugness bladder, a pressure varying from 280 mmHg to 300 mmHg indicates the normal range of cuff application. A measured pressure higher than 300 mmHg or lower than 180 mmHg indicates the need to readjust the cuff on the limb. The developed technique and apparatus for quantitatively assessing snugness, employed as described above, was found to eliminate subjectivity in the application of a tourniquet cuff. It was possible to apply the tourniquet cuff on any limb in a repeatable way with a predictable application of pressure to the underlying soft tissues.  5.2.3.3 Application of an Interfacing Layer between the Cuff and the Limb The effect of placing an interfacing material between the limb and the cuff was considered in terms of transmission of the applied pressure to the soft tissues. The materials used in fabrication of the pneumatic cuff were also evaluated in order to determine whether or not they might increase the risk of tissue damage. The Freeman and the Aspen were the only cuffs utilized in this phase of the clinical study. The Freeman cuff is constructed using aflexiblecotton material which is resistant to pressure but sufficiently compliant and soft enough to avoid skin lesions. However, this material has two disadvantages: it absorbs the preparation solution applied on the limb prior to surgery and it shrinks when washed in hot water. The Aspen tourniquet cuff is made of urethane coated nylon and is very resistant to wear. This material does not absorb the preparation solution but can cause bruising, pinching, and reddening of the skin. It cannot sustain high temperature and must be cleaned with an alkaline detergent and water [120]. The need for a protecting soft bandage underneath the tourniquet for the comfort of the patients was recognized by the nursing department of the Vancouver General Hospital. To examine the effects of a soft bandage, a test was designed to measure the  74  pressure delivered to the limb by the cuff when several soft interfacing layers were used. The objective of the test was to determine the effect of the bandage on the soft tissue pressure distribution over the surface of the limb. Tests were performed using the 24" and 34" Aspen cuffs. The pneumatic pressure sensor was used to obtain the pressure profile along the skin beneath the tourniquet cuff. The sensor was placed direcdy on the skin and was maintained in the same position for all the tests. The first test was done without the bandage to obtain a pressure profile for reference. In the following tests, various protecting fabrics were applied on the skin and the delivered pressure evaluated. The following interfacing options were investigated: 1)  no interfacing layer,  2)  soft bandage of type Webril (1 and 2 layers),  3)  thin foam of thickness 0.3 cm (1 and 2 layers), and  4)  thick foam of thickness 1.0 cm.  The pressure profiles across the width of the tourniquet cuff were measured on five volunteers. The pressure data were averaged for the upper and lower limb to obtain general pressure distributions. Figures 5.27 and 5.28 show that the resulting pressure profiles are similar for all the tests. The pressure distribution delivered on the limb by the tourniquet cuff was not significantly affected by the presence of an underlying bandage. In the case of the upper limb, there was a variation of 20 mmHg measured in the peak pressures. That pressure variation increased to 30 mmHg in the case of the lower limb pressure patterns. The application of interfacing layer between the cuff and the limb therefore has no significant consequence on the pressure distribution and should be used to protect the surface of the limb from cutaneous injury.  75  CHAPTER 6 - CONCLUSIONS AND RECOMMENDATIONS  This research project considered the mechanisms of blood flow occlusion in a limb encircled by a tourniquet cuff, in view of reducing the incidence of injuries that occur due to over-inflation. In this chapter, conclusions resulting from the experimental, analytical, and clinical investigations are presented. Recommendations concerning the clinical use and design of future tourniquets follow. Finally, ideas for further work important in study of bloodflowocclusion are suggested.  6.1 Conclusions Experimental and clinical tests were performed in order to produce hemostasis in the distal part of the limb in a safe and efficacious way. Analytical models were developed and validated by the experimental results. These analytical models were used to make clinical predictions and explain the mechanisms of soft tissue compression and blood flow occlusion. Conclusions drawn from the investigations are presented in two sections. General conclusions drawn from the experimental and analytical investigations are presented in the first section. More specific conclusions based on the clinical use of the pneumatic tourniquet are presented in the second section. 6.1.1 General Conclusions Resulting from the Present Research General conclusions were drawn from the experimental and analytical investigations which provided the necessary information essential for a better understanding of blood flow occlusion in a limb encircled by a surgical tourniquet. A discussion follows each conclusion. • Blood flow can be occluded at cuff inflation pressures significantly lower than pressures currently being employed in clinical practice. Surgical tourniquet cuffs  76 are generally over-inflated to ensure arterial flow occlusion. The measurement of internal soft tissue pressure in the lower limbs of cadavers showed a radial pressure decrease of 4.6% from the surface to the bone. There was a negligible radial decrease of pressure in the arm. This was contrary to results from other investigators, who found both pressure increases and decreases [47,48]. The values obtained in this study are more representative of the actual pressure distribution than the pressure gradients measured previously due to the use of a thin and flexible pneumatic sensor capable of measuring perineural soft tissue pressure in non-disarticulated limbs. The occlusion pressures measured on subjects with an ultrasonic doppler showed that the occlusion pressure is inversely proportional to the ratio of cuff width and limb circumference. • Occlusion pressure has been shown to converge near diastolic pressure with increasing cuff width. Occlusion of blood flow near diastolic pressure is an improvement over previous research work that used an occlusion pressure near a systolic level. Tests performed using several cuff widths greater than the limb circumference showed that blood flow was occluded as low as diastolic pressure. This implies that cuff inflation pressure can be further reduced in order to avoid tourniquet related injuries. • An analytical model has been developed which is useful in the understanding and prediction of blood flow occlusion under a pneumatic cuff. The model considered blood flow occlusion in two phases: the compression of the muscles and the constriction of the main blood vessel. In the first phase, the limb was modelled by a thick walled cylinder made of orthotropic material. The internal softtissuepressure was calculated for plane stress and plane strain conditions. The results of these two calculations were considered the outer bounds of the experimental internal pressure measurements. The orthotropic model allows one to predict the pressure at any location in the softtissuesof the limb.  77 In the second phase, the main blood vessel of the limb was modelled by a thin walled pressure vessel with an applied external load. One strip o f the pressure vessel was represented by a flexible beam to obtain an expression predicting occlusion pressure with a specific pressure profile applied on the limb. The equation derived indicates that the occlusion pressure is not significantly affected by variation i n vessel material properties related to bending stiffness i n comparison to the stiffness provided by the internal pressure on the strip of artery. The model supports the hypothesis that full constriction occurs for hemostasis. Occlusion pressure is closely related to the cuff  pressure  distribution applied on the limb and the patient's blood pressure. This makes the selected cuff design an important factor i n the occlusion pressure level. The beam strip model allows prediction o f the occlusion level and thus selection o f the cuff inflation pressure necessary to achieve hemostasis i n normotensive patients.  • The reduction of cuff inflation pressure to achieve blood flow occlusion decreases the risk of neuromuscular injuries. A lower cuff inflation pressure decreases the pressure gradient at the edges of the cuff, that has been previously related to postoperative injuries. H i g h pressure gradients at the edges of the cuff are suspected to cause displacement o f soft tissues away from the center of the cuff which result i n nerve damage. Therefore such a reduction i n cuff inflation pressure and the proportional reduction i n pressure gradients are likely to decrease the possibility o f cutaneous, vascular, and neuromuscular injuries.  6.1.2 Specific Conclusions on Clinical Use of Pneumatic Tourniquet Cuffs In the following section, the main points concerning safe and efficacious clinical use and application o f a pneumatic tourniquet are presented. The conclusions are listed i n order o f priority for proper application of a cuff.  78  • Occlusion pressures are related to cuff design, limb geometry, and patient's blood pressure. Occlusion pressures may be predicted using a simple empirically derived relationship when the blood pressure, the cuff width, and the limb circumference of the patient are known. Curve fitting of the experimental occlusion pressure data generated the relationship: (1) Pocc - Pdia = 16 (Limb Circ) / (Cuff Width) where P cc is the occlusion pressure and Pdi is the diastolic pressure. This equation may G  a  be used to estimate the cuff inflation pressure necessary to arrest blood flow in normotensive patients. • Exsanguination of a limb significantly decreases the occlusion pressure and thus should be performed to allow inflation of the cuff at lower pressure. Clinical measurements of occlusion pressure showed that a much lower cuff inflation pressure is necessary to maintain a bloodless surgical field when exsanguination is performed initially. Curve fitting of the experimental data generated the relationship: (2)  Pocc - Pdia = 8 (Limb Circ) / (Cuff Width) Such a relationship provides an improved estimate of the occlusion pressure over the previous relationship when exsanguination procedures are employed in surgery. Occlusion pressure was also found to be related to the employed method of exsanguination.  Occlusion pressure gradually decreased  with the quality of  exsanguination. • The widest possible tourniquet cuff should be used for surgery. A cuff of maximum width should be selected as long as it does not obstruct the surgical site. The wide cuff should also allow the bladder to conform to the limb geometry in order to deliver a symmetrical pressure distribution about the center of the cuff. The use of a wide  79  cuff lowers the occlusion pressure and therefore decreases the chance of neuromuscular injuries. • The snugness of cuff application directly influences the occlusion pressure. A loosely applied cuff may cause up to a 50% pressure loss in the transmission of cuff pressure. A consistent high degree of cuff snugness is necessary during initial application as it determines the efficacy with which the pressure is transmitted to the soft tissues of the limb. A snug cuff is therefore essential in accurately predicting occlusion pressure and achieving the lowest occlusion pressure. In some cases, overly high inflation pressures necessary to occlude blood flow can be attributed to loose cuff application.  6.2 Recommendations for Clinical Use The experimental, analytical and clinical phases of this research resulted in the identification of cuff parameters and application procedures which could be optimized for currently available and future cuff designs. Although the existing cuffs cannot be easily modified, a more appropriate application of the cuff on the limb can facilitate the occlusion of blood flow while reducing the possibility of cutaneous and structural injuries. Recommendations are made to improve the efficacy of currently available cuff designs, to reduce the risk associated with the use of tourniquet cuffs, and to reduce the inflation pressure. Recommendations for the use of currently available cuff designs are presented in four sections. These sections are related to 1) the proper selection of a cuff for a particular case, 2) the snugness of application, 3) the use of an interfacing layer to protect the limb, and 4) the cuff inflation pressure selection.  80  6.2.1 Proper Selection and Use of Cuffs Adequate selection of a cuff for a specific patient is the first step in safely arresting blood flow. Establishing a perfect fit on every limb using a single cuff design is difficult to achieve due to the large variation in limb geometry and tissue composition. In order to reduce this problem, suggestions are presented to improve the application techniques of currently available cuffs until better designs become available. The design of two existing tourniquet cuffs, the Aspen and Freeman types, were evaluated during the course of this research. The conclusions and recommendations associated with these designs are discussed below and may not apply to other pneumatic cuff designs. • The width of the cuff and the match in cuff design and limb shape are control parameters which affect the soft tissue pressure distribution on the limb and ultimately the occlusion pressure. Applied on a cylindrical limb, the Freeman tourniquet cuff transmits pressure with a symmetrical distribution about the midpoint of the cuff width dimensions. The Aspen tourniquet cuff fits limbs that have a difference in circumference of 1.8 cm to 2.2 cm from the proximal to the distal edges of the cuff. The efficiency of the Aspen is diminished outside this range. When the limb is more tapered than the cuff, it is suggested that a second cuff be inserted under the distal end of the cuff to compensate for the loose fit due to very conical shape of the limb.  • The cuff to limb surface contact discontinuity resulting from the overlap of a thick cuff causes the surface delivered pressure to be unevenly distribute around the limb. A significant local variation in the circumferential surface pressure profile was measured in the Freeman and Aspen tourniquet cuffs at the contact discontinuity point. Such compression patterns may lead to blood flow infiltration into the surgical site, anaesthetic  81  leakage, or venous congestion. The reduction of the overlap discontinuity should be a main consideration in the design of future tourniquet cuffs. • A bladder length that does not cover the entire circumference of the limb causes a surface pressure discontinuity and can cause vascular and anesthetic problems. The selection of a cuff implies choosing an appropriate length in relation to the limb circumference. In the case of the Aspen cuff, the bladder covers only a portion of the length of the cuff due to the presence of a seam around the contour of the cuff. It is important that there be a large cuff overlap around the limb to ensure coverage of the entire circumference of the limb by the bladder. Surface pressure measurements showed that a cuff too short for a limb causes a sharp discontinuity in the compression patterns on the surface of the limb that could cause leakage underneath the pneumatic cuff. A cuff length equivalent to twice the limb circumference may cause difficulties in application of the cuff and a subsequent pressure loss due to a loose fit. No maximum length has yet been determined as the thickness, the material, and the shape of the cuff also affect the ability to properly apply the cuff.  6.2.2 Snugness of Cuff Application • A snugly applied cuff is desirable to ensure maximum cuff pressure transmission to the limb. The use of the pneumatic pressure sensor or the snugness bladder inserted between the cuff and the limb provides a good indication of the level of snugness of the cuff. During compression of the limb, the soft tissues beneath the cuff are pushed laterally away from the center of the cuff causing the cuff to loosen after a period of time. It is thus recommended that monitoring and readjustment of the cuff snugness be performed during surgery as required to keep a constant compression on the limb. It should be remembered that exsanguination of the limb prior to cuff inflation causes the limb to slightly reduce in diameter; therefore the cuff, although applied snugly  82  at the beginning of the operation, may become loose after exsanguination of the limb. It is thus important to tighten the cuff before taking the Esmarch bandage off the limb.  6.2.3 Use of a Protective Interfacing Layer • It was shown that the pressure transmitted to the limb was independent of interface layers between the cuff and the limb. A tight pneumatic cuff applied over several hours causes reddening, burning, and other irritations to the skin. In order to protect cutaneous layers from pinching, it is recommended that one or two layers of Webril bandage, or equivalent soft roll, be wrapped on the limb before the cuff is positioned. A layer of thin foam can also be used in place of the Webril bandage. Some foams have the advantage of not absorbing the preparation solution applied on the limb prior to surgery, which may help prevent chemical burns.  6.2.4 Cuff Inflation Pressure Setting A properly selected cuff that is snugly applied transmits almost the entire inflation pressure distribution to the underlyingtissuesregardless of the condition of the soft tissues. This suggests that, in such circumstances, the occlusion pressure can be predicted predominantly as a function of the cuff width, limb geometry, and the patient's blood pressure, using the graph of occlusion pressure versus cuff width to limb circumference ratio (Figure 3.63). Such a prediction is possible provided the patient has a normotensive pre-operative blood pressure and does not show signs of abnormality or disease. A cuff pressure slightiy higher than the calculated occlusion pressure should be selected since the pressure required for occlusion can fluctuate substantially. The maximum blood pressure drop during surgery observed was evaluated at 35.5 mmHg and the average difference between the experimental and clinical occlusion pressure was evaluated at  83  27.1 mmHg. The setting of cuff pressure should therefore be adequate to safely occlude arterial flow when based on experimental data. Confidence limits were calculated from the theoretical curve of occlusion pressure described by the Taylor series. Figure 6.1 shows the plot of the occlusion to diastolic pressure ratio against the cuff width. The experimental and clinical data appear on the figure with the 95% and 99% confidence limits superimposed on the graph. The current inflation pressures are seen to be representative of the 99% confidence limit. The recommended inflation pressures derived from these limits could be marked directly on the cuff in order to facilitate the pressure setting as a function of the limb circumference.  6.3 Recommendations for the Design of Future Pneumatic Cuffs Improvement in the techniques for selection and application of currently available pneumatic tourniquets was defined as the first step toward obtaining safer blood flow occlusion. The next step is to optimize the design of future occlusive cuffs to apply a uniform pressure distribution around the limb. In this section, recommendations are made to improve the design of the pneumatic cuff in order to provide safer and more efficacious cuffs and thus avoid unnecessary injuries. Suggestions for a new cuff design are presented which involve the shape of the cuff, the incorporation of a snugness bladder, and the selection of cuff material.  6.3.1 Shape of Cuffs The shape of a pneumatic cuff determines the pattern of soft tissue compression and consequently the occlusion of the blood vessels necessary to arrest arterial flow. The width, curvature, and thickness of the cuff have been found to directly affect the pressure distribution.  84  Occlusive cuffs of various widths should be available to allow selection of the widest cuff which does not interfere with the surgical site for a particular patient. A cuff with an adjustable width would be very convenient although it would entail some design problems. More practically, a few cuffs could be manufactured with widths varying from 10 cm to 30 cm. The curvature of the cuff should fit the shape of the limb and should thus be determined in conjunction with the actual limb geometry. Five basic shapes of cuffs could be designed to fit the entire population studied. Figure 6.2 shows the normal distribution curve of the limb curvature angle divided into five sections. One cuff is recommended per section. The five cuff taper angles recommended are as follows: 0.36°, 1.06o, 1.78o, 2.49o, and 3.20o, where the angle is taken from the surface of the limb to a line parallel to the bone. Methods of applying the cuff on all limb geometries by continuous adjustment of the cuff could replace the various types. The thickness of the cuff should be as thin as possible to minimize the discontinuity in the soft tissue pressure distribution around the limb at the overlap location. A sharp discontinuity in the circumferential surface pressure profile was measured in both the Freeman and Aspen tourniquet cuff designs. Such a non-uniform compression pattern may lead to problems such as blood flow infiltration in the surgical site, anaesthetic leakage or venous congestion. In the case of a thick cuff, the edges of the cuff should be gradually reduced in thickness to smooth the pressure profile on the limb (Figure 3.26b). Obtaining a uniform circumferential distribution through reduction of this discontinuity should be a main consideration in the design of future tourniquet cuffs. Future tourniquet cuffs should also be evaluated in terms of the pressure distribution transmitted onto the surface of the limb. The pressure profile should be of low amplitude and low pressure gradient at the edges of the cuff (Figure 6.3). A wide cuff has been shown to lower occlusion pressure and consequently reduce the peak pressure necessary  85 to produce hemostasis. Pressure gradients can be adjusted by the incorporation o f a stiffener in the cuff design.  6.3.2 Incorporation of a Snugness Bladder The  snugness o f the cuff should be assessed at the time o f application, and i f  possible, monitored during surgery by means o f the previously developed  technique  referenced in section 5.2.3.2. Control of the snugness against cuff relaxation throughout the surgical procedure should be performed to ensure full transmission of cuff pressure to the soft tissues and safe blood flow occlusion.  6.3.3 Material of Fabrication A  durable tourniquet cuff showing repeatability, accuracy and reliability in the  delivery of pressure is desirable. T o achieve this objective, the tourniquet cuff should be fabricated from a durable non-stretching and non-absorbing material. A tourniquet cuff is usually applied for a period of time varying from a few minutes to several hours and must properly retain the pressure inside the cuff during the entire surgical procedure. In comparison, a blood pressure cuff is only used for a few minutes at a time to measure the arterial pressure and therefore the rigidity of the tourniquet cuff is not required. The use of a stiffener in the cuff is an appreciable aid in supporting the bladder, in creating a particular pressure profile, and to prevent wear and tear. The design of the cuff should offer the possibility of removing the stiffener before cleaning and sterilizing the cuff to avoid warping of the stiffener. Due to the need to clean and sterilize the cuff, the material of fabrication should be heat resistant. A n y change in the design of current tourniquet cuff should be made to improve the delivery of pressure on the limb and facilitate the use and maintenance of the cuff.  86  6.4 Recommendation for Further Investigations The prediction of occlusion pressure is possible with knowledge of the compression patterns beneath the cuff and with an understanding of the blood flow in the limb vessels. Recommendations for future work pertaining to pressure profile experiments and blood flow occlusion experiments are presented below.  6.4,1 Pressure Profile Experiments • Surface and internal pressure distributions were measured in limbs encircled by the 8.5 cm Aspen cuff. Although the occlusion pressure test determined that a wide cuff lowers the cuff inflation pressure necessary to arrest the arterial flow, the compression patterns were not evaluated for limbs encircled by wide pneumatic cuffs. The long biomedical pressure transducer, or a new longer version of the sensor, should be used to map the pressure profiles of the softtissuesbeneath the cuff. The measured compression patterns should then be compared with those predicted by the derived model to assess their validity. X-rays should be taken during the internal soft tissue pressure measurements in cadaver limbs in order to ensure proper positioning of the electrical cells of the pressure sensors. Surface and internal soft tissue pressure measurements should also be measured in limbs encircled by dual cuffs inflated simultaneously and alternatively. • Pressure profiles should be measured for limbs encircled by a pneumatic cuff with a warped stiffener in order to evaluate the degree to which the compression patterns are affected. The design of the cuff stiffener could then be optimized. These pressure profiles could be easily evaluated using the pneumatic pressure sensor. • It is standard practice to apply the tourniquet cuffs around the thigh or the upper limb. Blood flow occlusion should be investigated for cases where the cuff is applied around the forearm and the calf. Surface and internal softtissuepressure profiles should be measured in limbs encircled by various cuffs when applied on the distal part of the limbs.  87  The application of a tourniquet cuff around the forearm and the calf should be considered and studied as such an application could be useful in the administration of intravenous anaesthesia. The application of the cuff distal to the present location of application on the limb would reduce the volume of anaesthetics necessary to perform hand or foot surgery. The dual bone architecture of the distal part of the limb should be considered as a main factor affecting the compression patterns and the mechanism of blood flow occlusion. Application of the occlusive cuff to the distal part of the limb should also be evaluated in terms of the potential for nerve injuries, as the muscular system is not as developed in that part of the limb. • A comparison of the turgor of living and dead soft tissues should be carried out to evaluate differences in the internal pressure profiles measurements. This will allow pressure measurements from cadaver limbs to be related to those of living tissues. Internal soft tissue pressures should be measured in vivo by initiating tests in limbs of anesthetized animals. These tests should be refined to obtain a safe experiment that would follow the standard of human experimentation, in order to measure internal pressure in patients undergoing limb surgery. 6.4.2 Blood Flow Occlusion Experiments • Extensive tests should be performed to evaluate occlusion pressures to predict more accurately the minimum cuff inflation pressure required to arrest arterialflow.Obtaining more experimental occlusion pressure data will allow determination of a more precise formulation for predicting occlusion pressure as a function of the cuff width, limb circumference, and patient's blood pressure. • A visualization of the blood vessel during inflation of the tourniquet cuff is desired to determine whether a cessation of bloodflowoccurs with partial or complete constriction of the vessel. To achieve such visualization, a radiopaque dye could be injected  88  intravenously into the distal part of a limb encircled by an inflated pneumatic cuff. The blood flow could then be monitored by following the dye underneath the cuff to determine the point where there is arrest of flow. Such information would help confirm the hypothesis of blood vessel closure as opposed to the accumulation of frictional resistance to flow along the compressed arterial segment as the mechanism of arrest of arterial flow. • To clarify the mechanisms of nerve injuries associated with the application of a pneumatic occlusive cuff around a limb, eletromyography could be performed to monitor the activity of the main nerves during application and inflation of the cuff. The level of neural activity could then be correlated with the compression of the soft tissues. • The time of cuff inflation was not considered in this research and should be investigated as a possible factor in the severity of nerve damage [121-123]. 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Tourniquet-Induced Nerve Ischemia Complicating Knee Ligament Surgery. The American Journal of Sports Medicine, Vol.8, No.2, 98-102, 1980.  113]  S. Sunderland. Nerves and Nerve Injuries. 2d Edition, Churchill Livingstone, Edinburgh, 1978.  114]  G. E. Omer, M. Spinner. Management of Peripheral Nerve Problems.. W. B. Saunders Co., Philadelphia, 487-592, 1980.  115]  H. H. Schaumburg et al. Disorders of Peripheral Nerves. F.AJDavis Co., Philadelphia, 1983.  96  [116]  G. Lundborg et al. Median Nerve Compression in the Carpal Tunnel Functional Response to Experimentally Induced Controlled Pressure. The Journal of Hand Surgery, Vol.7, No.3, 252-259,1981.  [117]  R. M. Rosenblatt, A. Hetherington. Failure of Trans-Cutaneous Electrical Stimulation of Alleviate Experimental Tourniquet Pain. Anesthesia and Analgesia, Vol.60, No.10, 720-722,1981.  [118]  N. Diffrient et al. Humanscale 7/8/9. Henry Dreyfuse Association, 1986.  [119]  J. A. McEwen. Personal Communication, July 11, 1988.  [120]  Zimmer, Aspen Labs. Single and Dual Tourniquet Cuffs. Instruction Manual, Englewood, Colorado.  [121]  L. Klenerman. Tourniquet Time - How Long? The Hand, Vol.12, No.3, 231234,1980.  [122]  J. M. Bruner. Time, Pressure and Temperature Factors in the Safe Use of the Tourniquet. The Hand, Vol.2, 39-42, 1970.  [123]  A. E. Flatt. Tourniquet Time in Hand Surgery. Arch. Surgery, Vol. 104, 190-192, 1972.  97 Table 1 List of Instrumentation and Specifications Transcutaneous Doppler Dynamic Stereo Headphones Ultrasound Transmission Gel Automatic noninvasive arterial blood pressure monitor Arteriosonde Perimed Laser Doppler Pressure Transducer Power Supply Automatic Tourniquet System Computer Analog-digital board Equipment Personnal Computer Double disk drive Printer EPSON  Pneumatic Cuffs  LabTender TECMAR I.B.M. Model 5151 I.B.M. 5150 RX-80 Model P80RA  Length (cm)  Child Aspen Adult Aspen for arm Adult Aspen for leg Large adult Aspen for leg Child dual Aspen Adult dual Aspen Child Freeman Adult Freeman Child dual Freeman Adult dual Freeman Child blood pressure cuff Adult blood pressure cuff Leg blood pressure cuff Narrow plastic bladder Wide plastic bladder Arm splinter Leg splinter  Pnematic Pressure Sensors  Model 801-A Parks Sony Model DR-S3 Aquasonic 100 Parker 07050 Dinamap 845 Critikon no.33607 Roche 1010 no.2461 Periflux Pf2 COBE 5-10 volts. Wilbac 12 volts. Zimmer 500 and 1000  Cell spacing (cm)  Width (cm)  18 24 34 42 18 24 18 24 18 24 23 33 36 50 50&70 75 98  4.5 8.5 8.5 10.0 4.5 4.5 4.5 7.5 4.5 4.5 12.5 15.0 18.0 16.5 19.0 21.0 29.0  Length (cm)  Width (cm)  Short 1.8 17 Long 3.8 25 Material: Mylar, DuPont trademark, 3 and 5 mil thick. Conductive Silver: Electrodag 415SS Acheson Colloids  1.4 1.5  Table 2 Model Parameter Values  Limbs  Upper limb diameter Lower limb diameter  Muscle  Young's modulus  8.6 cm 15.7 cm  Longitudinal direction Radial direction Transverse direction  100 kPa 180 kPa 180 kPa  xy and yz planes xz plane  0.3 - 0.5 0.45 - 0.5  Bone  humerus diameter femur diameter Young's modulus Poisson's ratio Density  2.3 cm 2.8 cm 17.2- 18.6 GPa 0.45 - 0.5 1.6-1.9g/cm3  Arteries  Diameter Cross-section area Length Thickness  0.2 - 0.6 cm 3.0 cm2 .20 cm 0.05 cm  Longitudinal direction Radial direction Transverse direction  200 kPa 550 kPa 550 kPa  xy and yz planes xz plane  0-0.5 0.45 - 0.5  Velocity Reynolds Number Viscosity (37°) Specific gravity (25/4°C) Density (37 °C) Volume/kg body weight Cardiac output Diameter of red cells  20 - 50 cm/sec 110-850 3.0 - 4.0 cP 1.056 1.0499 g/cm3 78 ml 5 l/min 8.4 E-6m  Poisson's ratio  Young's modulus  Poisson's ratio  Blood  Conversion factors  1 P = 0.1 kg/ms 1 mmHg = 133.35 Pa = 1320 dynes/cm2 1 mmHg = 1.93 E-2 p.s.i. 1 p.s.i. = 6895 Pa = 51.71 mmHg  99 Table 3 Occlusion Pressure Data for Similar Systolic Blood Pressures  Systolic Pressure (mmHg)  Circumference (cm)  Diastolic Pressure (mmHg)  Occlusion Pressure (mmHg)  110.3 110.5  51.0 27.2  68.0 45.8  131.5 110.5  111.2 111.5  24.8 26.4  57.5 61.5  118.0 124.5  113.0 113.2  22.8 30.7  69.8 53.4  126.0 120.2  123.5 123.8  27.3 51.3  75.8 70.7  125.0 171.0  125.0 125.2  62.0 58.0  63.2 70.3  189.5 164.2  130.4 130.5 130.8  28.2 51.6 29.7  73.2 77.8 59.2  129.5 161.2 132.5  135.4 135.5 135.8  29.8 51.0 55.2  63.4 86.3 72.0  114.8 160.8 160.5  143.0 143.4  59.1 56.5  83.8 79.8  205.0 155.5  100  Table 4 Occlusion Pressure Data for Similar Systolic and Diastolic B l o o d Pressures Diastolic Pressure (mmHg)  Circumference (cm)  Systolic Pressure (mmHg)  Occlusion Pressure (mmHg)  60.0 60.0  28.3 26.5  118.5 121.0  131.0 115.5  61.5 61.6  26.4 56.0  111.5 137.4  124.5 125.5  63.2 63.4  62.0 29.8  125.0 135.4  189.5 114.8  68.0 68.8 68.0 68.8  51.4 48.9 51.0 48.9  137.2 115.0 110.3 115.0  180.5 170.5 131.5 143.5  70.2 70.3 70.5 70.7  43.8 58.0 54.2 51.3  124.8 125.2 140.8 123.8  136.7 164.2 173.0 171.0  72.5 72.6  53.0 31.3  133.8 129.8  136.8 133.0  74.2 74.4 74.5  53.2 49.5 25.2  120.8 132.8 119.0  125.0 156.2 126.5  75.7 75.8  48.5 27.3  147.0 123.5  158.5 125.0  101  Table 5  Systolic Pressure (mmHg)  Systolic Pressure (mmHg)  Occlusion Pressure Data for Similar Diastolic Blood Pressures  Circumference (cm)  Occlusion Pressure (mmHg)  111.2 111.5  57.5 61.5  24.8 26.4  118.0 124.5  123.5 123.8  75.8 70.7  27.3 51.3  125.0 171.0  125.0 125.2  63.25 70.3  62.0 58.0  189.5 164.2  130.4 130.5  73.2 77.8  28.2 51.6  129.5 161.2  143.0 143.4  83.8 79.8  59.1 56.5  205.0 155.5  102  lucoff ul  • 3 mm from Skin  Halfway between--^. Catheters 1 and 3 ' 1  ^Center of the Limb distal  Figure 2.1  |tt cuff tt|  proximal  Longitudinal View of Dahlin's Limb Model Showing the Slit Catheter Positions (from L. B. Dahlin et al. Distribution of Tissue Fluid Pressure beneath a Pneumatic Tourniquet, 30th Annual ORS, Feb.5, 362, 1984)  Fluid  Tissue Elastic  Model  Tissue  (a)  Solid Model  lb)  Figure 2.2  Griffiths'and Hey wood's Limb Models (a) Core Surrounded by Fluid Tissue (b) Core Surrounded by Elastic Solid Tissue  (from J. C. Griffiths, O. B. Heywood. Bio-Mechanical Aspects of the Tourniquet, The Hand, Vol.5, 115, 1973)  103  Figure 2.4  Element Subjected to Principal Stresses (from J. C. Griffiths, O. B. Heywood. Bio-Mechanical Aspects of the Tourniquet, The Hand, Vol.5, 116, 1973)  104  Figure 2.5  Canine Thigh with the Tourniquet in Place Showing the Withdrawal of the Slit Catheter (from A. C McLaren, C. H. Rorabeck. The Pressure Distribution under Tourniquets, 1 he Journal of Bone and Joint Surgery, Vol.67-A, 434, 1985)  Figure 2.6 (a) Longitudinal View of the Thigh Showing the Five Positions of the Catheter (b) Cross Section of the Thigh Showing the Three Planes of Pressure Measurement (from A. C. McLaren, C. H. Rorabeck. The Pressure Distribution under Tourniquets, The Journal of Bone and Joint Surgery, Vol.67-A, 434, 1985)  105  (a) Tissue Pressure Distribution under the Pneumatic Tourniquet Inflated to 200 mmHg (b) Tissue Pressure Distribution under the Esmarch Bandage Tourniquet Wrapped Six Times around the Limb (from A. C. McLaren, C. H. Rorabcck. The Pressure Distribution under Tourniquets, The Journal of Bone and Joint Surgery, Vol.67-A, 436, 1985)  0 I  I  0  i  I  1  2  i 3  I 4  i 5  WIDTH Figure 2.8  i 6  i 7  i 8  (cm)  Subcutaneous Tissue Pressure versus Position under the Pneumatic Tourniquet and the Esmarch Bandage Tourniquet (from A. C. McLaren, C. H. Rorabeck. The Pressure Distribution under Tourniquets, The Journal of Bone and Joint Surgery, Vol.67-A, 436, 1985)  1  End cap  Grooved sleeve  (.635 cm)  Sloinless steel tubing — (.3175 cm)  /firx" 58 cm  r—-  o o  45 cm  Thin walled  rubber tubing  „,....... '.{& 't :  \ .'••.1:-:-x-,'v< -:• :•*  Non-expansible cloth cuff  •>f.:i :W:>.:::>.:.;..«  "CT  Pressure P r o b e used b y S h a w a n d M u r r a y to M e a s u r e Soft T i s s u e Pressures beneath a P n e u m a t i c T o u r n i q u e t (from J. A. Shaw, D. G. Murray. The Relationship Between Tourniquet Pressure and Underlying Soft-Tissue Pressure in the Thigh. The Journal of Bone and Joint Surgery. Vol.64-A, 1148, 1982)  107  Kidde pressure  H.P 4 channel recorder  Figure 2.10  Schematic Representation of Shaw and Murray's Experimental Configuration (from J. A. Shaw, D. G. Murray. The Relationship Between Tourniquet Pressure and Underlying Soft-Tissue Pressure in the Thigh. The Journal of Bone and Joint Surgery. Vol.64-A, 1149, 1982)  108  1.Subcutaneous 2.Subfascial 3 . Mid-muscle 4. Bone  THIGH  Figure 2 . 1 1  Positions of Slit Catheter Used by Hargens et al. in Disarticulated Upper and Lower Limbs (from A. R. Hargen et al. Local Compression Patterns beneath Pneumatic Tourniquet Applied to Arms and Thighs of Human Cadavera. Journal of Orthopaedic Research Vol.5, No.2, 249, 1987)  109  300  200 X  E E -  100  CO CO LU 0C  0_  Q  300  Z3  LU  200 -  co CO  I—  100  DISTANCE FROM PROXIMAL EDGE OF CUFF ( c m )  Figure 2.12  Pressure Profiles for the Arm and the Thigh under the Pneumatic Tourniquet Inflated to 300 mmHg (from A. R. Hargen et al. Local Compression Patterns beneath Pneumatic Tourniquet Applied to Arms and Thighs of Human Cadavera. Journal of Orthopaedic Research, Vol.5, No.2, 250, 1987)  y  • 230  50\  1100  '.150  150  • IB  100  ;30  •  CUFF HUMERUS  so  75  MOO  ?5:  •  50'  CUFF  BFEMUR  -±_J 150 mmHg  Figure 2.13  300 mmHg  Correlation between Longitudinal and Radial Pressure Profiles (from A. R. Hargen et al. Local Compression Patterns beneath Pneumatic Tourniquet Applied to Arms and Thighs of Human Cadavera. Journal of Orthopaedic Research, Vol.5, No.2, 250, 1987)  70  t Cross-Section  I  .1  of  the  Limb  1 1  1  \  *  \  1  Pneumatic  Bags  Frame Wooden B l o c k s  Figure 2.14  Special Clamp Used by Parkes to Apply Selective Pneumatic Pressure to the Limb (from A. Parkes. Ischaemic Effects of External and Internal Pressure on the Unner Limb. Hand, Vol.5, 106, 1973) 1 1  Ill 500 r -  TOURNIQUET PRESSURE (mm Hq)  500 400  300 200 100 30  40  50  60  L E G C I R C U M F E R E N C E (cm)  Figure 2.15  Nomogram Relating Tourniquet Pressure to Underlying Soft Tissue Pressure and Leg Circumference (from J. A. Shaw, D. G. Murray. The Relationship Between Tourniquet Pressure and Underlying Soft-Tissue Pressure in the Thigh. The Journal of Bone and Joint Surgery. Vol.64-A, 1150, 1982)  200  180  e  a  _-  160  LU CC  r> U~>  UJ  CC Q. =3  OC o  8.0  10.0  15.5  20.0  CUFF WIDTH (cm )  Figure 2.16 Graph of the Doppler Occlusion Pressure as a Function of Cuff Width (from M. R. Moore et al. Wide Tourniquets Eliminate Blood Flow at Low Inflation Pressures. The Journal of Hand Surgery, Vol.l2-A, No.6, 1007, 1987)  Electrical Switches "ON". External pressure < Internal pressure  Deflated  Sensor  Electrical Switches "OFF"  Figure 3.1  Pneumatic Pressure Sensor Operation  113  / .2.0.  TTT  21.5  1.8  JL  7.2 8.0  i A l l measurements i n cm Scale 1:1  Figure 3.2  Sketch o f the Electrical Circuit Printed onto Mylar with Conductive Ink  114  Electrical  Connector  Figure 3.4  Sketch of the Pneumatic Pressure Sensor  115 Reinforcing  Plastic  Pieces  L ? )  Jl  L o —  i  Pneumatic  o o  Fitting  Ll  Electrical  Connector  Figure 3.5 Sketch of the Pneumatic Pressure Sensor Plastic Reinforcements  BI  Figure 3.6  • ft  Position of the Pneumatic Pressure Sensor Relative to the Tourniquet Cuff Applied on the Limb  116  Electrical C o n t r o l Box  Jk \ Manometer  Figure 3.7 Pneumatic System Used to Individually Calibrate the Pressure Sensors  117  TOURNIQUET  T ASPEN .PRESSURE CONTROLLER  Z7Z7  Z7/  L200  |  <H£EWX> DAMPER BLADDER  INTERFACE  BOARD  7?^  m  Figure 3.8 Data Acquisition System Used to Measure Surface and Internal Soft Tissue Pressure  •4  COBE Pressure. < Transducer I  Air  source  Tourniquet  Clippard  Pressure  A/D Board Labtender Teciiiar  va ves  I  if  Applied Physical Pressure Drain  Desired Tissue Pressure  Drain Cl i p p a r d valve  High Impedence Op-amplifier COBE Pressure. Transducer  I I  I I  _4_ Tourniquet Sensor  Air  source <  co  Figure 3.9  Block Diagram of the Double Feedback Loop Control Software  MAIN CONTROL  -e  Convert c u f f and sensor p r e s s u r e d a t a i n p r e s s u r e u n i t (mmHg)  P l o t the r e s u l t i n g pressure d i s t r i b u t i o n and d i s p l a y a l l d i g i t a l pressure values  Figure 3.10 Algorithm of the Program "DATA" (a) Inflation and Deflation Control of the Pressure Sensor and the Cuff  120  MAIN CONTROL Inflate tourniquet cuff quickly Measure cuff pressure T Inflate pressure sensor slowly  Check status of cell Check status of cell  n n  Check status of cell #3 Check status of cell #4 Check status of cell #5  :C3sJUcells) == 5  1  ~T7es Deflate pressure sensor slowly  •' Check status of cell #1 Check status of cell  n  Check status of cell #3 Check status of cell #4 Check status of cell #5  Yes  Calculate each pressure cell average and hysterisis  *Note: Contact ON = 1 Contact OFF = 0  Deflate tourniquet cuff  Figure 3.10 Algorithm of the Program "DATA" (b) Status Check Control of the Pneumatic Pressure Sensor Electrical Contacts  121  Figure 3.11  Plexiglass Models Representing the Upper and Lower Limbs  Figure 3.12  Sketch of the Foam Addition on Opposite Sides of the Cylinder to Simulate the Oval Shape of the Upper Limb  123  2 Turns  1 3/4 Turns  1 Turn  Proximal  Figure 3.13  Distal  Preparation of Limb Models (a) Bare Plexiglass Cylinder Wrapped twice with the Aspen Cuff (b) Cylinder Coated with one Layer of Foam (c) Cylinder Coated with One Half Width Layer of Foam and Full Width Layer of Foam  124  Pressure  Distribution  300 P (mm  Inf1 a t e  /  Hg)  200  100 *  o  values  *  *  * *  * *  * *  *  *  *  *  *  *  *  Deflate  *  *  * **  * * * *  * * * *  * *  * *  * *  1  2  3  4  5  * *  * *  PROXIMAL  sensor  #1 #2 #3 #4 #5  #  * * * * * * . * *  DISTAL  (mm  Hg)  31.30 178.41 200.32 203.45 150.24  (mm  Hg)  81.38 131.46 162.76 122.07 65.73 t_slope s_slope  = =  file  Figure 3.14  values  3.20 3.13 =  b:test9.dat  Typical Pressure Distribution underneath the Pneumatic Tourniquet C u f f  .125  Figure 3.15  Pressure Sensor Locations around the Limb  126 P  (mm Hg)  inflating deflating (mm Hg) (mm Hg)  300  98 .41 180.95 180.95 142.86 44 . 44  200  100 # # # # #  # # # #  # # # # # # # # # #  1  PROXIMAL  # # # # # # # # # #  # # # # # # # # # #  2  # # # # # # # #  # # # # # # # #  3  # # # # #  4  79.37 187.30 155.56 •85.71 9.52  ptissue pline diff Aspen # # # #  5  DISTAL  hysteresis (mm Hg) 19. 05 -6. 35 25. 40 57. 14 34 .92  = 1 8 4 . 13 = 165. 08 = - 1 9 . 05 = 200. 00  spO = 1 3 1 . 00 tpO = 1 2 6 . 00 t_slope 3. 17 s slope 3. 17  sensors Figure 3.16  Anterior Surface Pressure Profile  P  (mm Hg)  inflating deflating (mm Hg) (mm Hg)  300  126.98 168.25 193.65 174.60 34.92  200  100  0  # # # # # # #  # # # # # #  # # # # # # # # #  1 •  # # # # # # # # # #  2  PROXIMAL  # # # # # # # # # #  # # # # # # # # # #  3  # # # # # # # # #  # # # # # # #  4  # # # 5  hysteresis (mm Hg)  104.76 180.95 180.95 123.81 9.52  ptissue pline diff Aspen  = 1 8 7 30 . = 1 6 1 . 90 = - 2 5 . 40 = 2 0 0 00 .  spO tpO t slope s slope  = 1 3 1 .00 = 1 2 600 . = 3. 17 = 3.17  DISTAL  sensors Figure 3.17 Medial Surface Pressure Profile  22 .22 -12 .70 12 .70 50 .79 25 .40  127  P (mm Hg) 3  2  0  0  inflating (mm Hg)  0  0  # # # # # # # # # # # # #  100  .. # # # # # # # # # # # #  # # # # # # # # # # # #  # # # # # # # #  1 2 PROXIMAL  # # # # # # # # # # # #  # # # # # # # # # # 3  deflating (mm Hg)  149.21 193.65 196.83 200.00 38.10  # # # # # 4  53.97 123.81 142.86 92.06 3.17  p t i s s u e == pline = diff = Aspen = # # #  5 DISTAL  hysteresis (mm Hg) 95.24 69.84 53.97 107.94 34.92  169..84 152,.38 -17..46 200,. 00  spO = 131..00 tpO = 126., 00 t__slope = 3., 17 s_slope = 3.. 17  sensors Figure 3.18  Posterior Surface Pressure Profile  P (mm Hg) inflating (mm Hg)  300  200  100  0  # # # # #  # # # # #  # # # # # # # # #  # # # # # # # # # #  # # # # # # #  # # # # # # # # #  # # # # # # # # # # # # #  95 .24 177 .78 193 . 65 180 . 95 69 . 84  # # # # #  5 DISTAL  PROXIMAL  deflating (mm Hg) 95.24 126.98 168.25 50.79 0.00  0. 00 50 .79 25. 40 130 .16 69. 84  ptissue pline diff Aspen  = 180. 95 = 177. 78 = - 3 . 17 = 200. 00  spO tpO t_slope s slope  = 131. 00 = 126. 00 = 3.17 = 3.17  sensors Figure 3.19  hysteresis (mm Hg)  Lateral Surface Pressure Profile  128 inflating (mm Hg)  P (mm  deflating (mm Hg)  hysteresis (mm Hg)  Hg) 49.76 163.35 175.63 175.63 123.44  300  200  *  * * * * * * *  * * * * * * * * *  100  * * * *  * * * * * * * * * * * * * * *  * * * * * * * * *  PROXIMAL  * * * * * * * * *  101.95 148.00 169.49 169.49 77.39  -52.19 15 . 35 6.14 6.14 46.05  Aspen P pdesired pline ptissue diff error  = = = = = =  250.00 170.00 163.96 172.56 -8.61 10.00  spO tpO s slope t slope  = =  130.79 126.94 3.07 3.09  DISTAL sensors  Figure 3.20 Example of Surface Pressure Measurement  P (mm  inflating (mm Hg)  Hg)  300  65 21 70 77 51  200  100  * * * * * *  * * * *  * * * * * * * *  * * * *  * * * * * * * * * * * * * *  * * * * * * * * * * * * * * *  * * * * * * k  * * *  5 DISTAL  PROXIMAL  deflating hysteresis (mm Hg) (mm Hg) 95 151 172 169 83  . 81 .07 .56 .49 . 53  3 6 . 84 6. 14 6. 14 •12. 28 42 . 98  Aspen P pdesired pline ptissue diff error  = = = = =  2 5 0 .00 170 .00 167 . 05 1 7 5 . 63 -8 .59 10 .00  spO tpO s_slope t__slope  = =  130 . 7 9 1 2 6 . 94 3 .07 3 .09  sensors  Figure 3.21 Repetition of the Previous Pressure Measurement Following a Recovery Period  129 P (mm  Hg) inflating (mm Hg)  300  200  100  #  #• # 0  # #  # # # # # # # # #  # # # # # # # # #  # # # # # # # # # #  1 2 PROXIMAL  # # # # # # # # # #  # # # # # # # # #  3  # # # # # # # # # 4  deflating (mm Hg)  71.25 163.35 181.77 163.35 58.97  # # # #  5 DISTAL  hysteresis (mm Hg)  15.99 163.35 187.91 163.35 15.99  ptissue pline diff Aspen  = = = =  spO tpO t_slope s_slope  = 130.79 = 126.94 = 3.0 9 = 3.07  55.26 0.00 -6.14  184.84 188.68 3.83 200.00  sensors  Figure 3.22 Second Example of Surface Pressure Measurement  P (mm 3  0  Hg) inflating (mm Hg)  0  200  100  # # # # #  # # # # # #  # # # # # # # # #  1 2 PROXIMAL  # # # # # # # # #  # # # # # # # # # #  # # # # # # # # # 3  # # # # # # # # # #  # # # # # # # # # 4  deflating (mm Hg)  129.58 160.28 172.56 169.49 101.95  # # # # # # # # # 5 DISTAL  hysteresis (mm Hg)  65.11 163.35 181.77 181.77 40.55  ptissue pline diff Aspen  = 1 7 7 . 17 = 1 8 5 . 59 = 8. 42 = 2 0 0 . 00  spO tpO t slope s slope  = 1 3 0 . 79 = 1 2 6 . 94 = 3. 09 = 3. 07  64 -3 -9 12 61  .47 . 07 .21 .28 .40  sensors  Figure 3.23 Repetion of the Previous Pressure Measurement without a Recovery Period  130  120 110 100 -  •  Breaull  +  McLaren  90 80 -  •  70 -  +  60 50 40 30 TD  a  20 10 20  Jo  1  Jo  r  80  100  Cuff Length (%)  Figure 3.24  Pressure Profile Comparison to McLaren's Results  120  131  Overlap  Figure 3.25 Three-Dimensional View of the Pressure Distribution on the Upper Limb Produced by the 24" Freeman Tourniquet Cuff  Actual Design  Figure 3.26 Sketch of the Gap Created by the Overlapping of a Thick Cuff  133  Figure 3.28  Surface Pressure Distribution Discontinuity at Location #3  134  Figure 3.30  Surface Pressure Distribution Discontinuity at Location #5  Figure 3.31 Sketch Showing the Location of the Median Nerve in the Upper Limb of a Cadaver  Figure 3.32 Sketch Showing the Location of the Radial Nerve in the Upper Limb of a Cadaver  (from G. E. Omer, M . Spinner, Management of Peripheral Nerve Problems. W. B. Saunders Co., Philadelphia,324, 1980)  (from G. E. Omer, M . Spinner, Management of Peripheral Nerve Problems W B Saunders Co., Philadelphia,323, 1980)  cn  136  Figure 3.33 Sketch Showing the Location of the Sciatic Nerve in the Lower Limb of a Cadaver (f Q. E . Omer, M . Spinner, Management of Peripheral Nerve Problems. W. B. rom  Saunders Co., Philadelphia.340, 1980)  137  Obliquus Abdominis Internus Illacus Femoral nerve artery vein  Ilio-hypogastrie nerve Ilio-inguinal nerve  Adductor Longus -Gracilis fProfunda femoris art. \Adductor Brevis Cutaneous br. of obtux&tor nerve  Obturator  Femoral  Adductor Magnus  Saphenous  Sartorius  Anterior femoral cutaneous  (  nerve vein artery  Figure 3.34 Sketch Showing the Location of the Saphenous Nerve and the Femoral Artery in the Lower Limb of a Cadaver (from J. A. Anderson, Grant's Atlas of Anatomy. 8th Edition, Williams & Wilkins, baltimore, 4.25, 1983)  138 300 280  WeAve  260  -  240  -  (Limb)  Aadiat {Kijght) median [night] iuAface [night] nadUl [lef>t) median Ue.lt) Aun.&ace lle.it)  220 200 180 -  5 ~  5  160 140 120 100 80 60 40 -I 20 -| 0  Vn.ox.imat  Edge  1  Cu(,i Centen.  1  Vii tat Edge  J  # Sensor Contact Figure 3.35  Internal Pressure Distribution in the Right and Left Upper Limbs of Cadaver #1  300 280  Henve lUmb)  260 -  a +• O A X v  240 220 200 &3  iclaXlc [le{t] iaphenoui [le^t] iuA^act Ue&t) iCMVtic [night] iaphenoui [night] iuA&-.ce [night]  180 160 -| 140  2! a S3  120 -| 100 80 -A 60  -I  40 20 0  Pioxlmat Edge J  Cu&d Centex  Viitat Edge  T # Sensor Contact  Figure 3.36  Internal Pressure Distribution in the Right and Left Lower Limb of Cadaver #1  139 300 280 260  Median n.  240 220 200  s s a  to to  180 160 140  A  120 100  80  A  60  \  40 20 0  ,  j  ,  .  j  ,  # Sensor Contact Figure 3.37  Distribution of the Averaged Internal Pressures in the Upper Limb of Cadaver #3  300 280  Surface  o  260 4.  240 -  Saphenous nerve  220 -  .5?  s  200 180 160  A  140  «o to  120  fc  100  A  80 60 40 20 0 0  1 # Sensor Contact  Figure 3.38  Distribution of the Averaged Internal Pressures in the Lower Limb of Cadaver #3  140  # Sensor Contact Figure 3.39 Internal Pressure Profiles for Three Different Cuff Inflation Pressures in the Upper Limb  Figure 3.40 Averaged Pressure Profiles in the Upper Limb Three Different Cuff Inflation Pressures  350  50 H  Sensor Cell # Figure 3.41 Variation of Internal Soft Tissue Pressure in Cadaver #4 Caused by Oedema  Figure 3.42 Averaged Pressure Distribution for the Upper Limbs of Three Cadavers  144  1 2 3 4  Limb (upper or lower) Bone (humerus or femur) Cuff A r t e r y ( b r a c h i a l or femoral)  Figure 3.44 Longitudinal Cross-Section of die L i m b Showing the Pressure on the M a i n Artery and Nerves  P (mmHg) with Ultrasonic Doppler Figure 3.45  Comparison of the Pressure Outputs between the Laser and Ultrasonic Dopplers  300 280  •  260  + 0 A X V  240  £  160  Freeman (7.5 cm) Aspen (8.5 cm) Baum (12.5 cm) Wide Baum (15.5 cm) P l a s t i c (19.5 cm) S p l i n t (42-55 cm)  -  st  •+  [2%  O  A  w  V  80  v  X  V  v  vv  W  60  0 0  0.2  0.4  0.6  0.8  1.2  1.4  1.6  1.8  ratio = width/circumference  Figure 3.46 Plot of Occlusion Pressure versus the Ratio of Cuff Width to Limb Circumference for the Upper Limb  500  • B  • 400  -  O • A X V  •  5  I  300  Dual Aspen (4.5 cm) Aspen 18" (5.5 cm) Freeman (7.5 cm) Aspen 34" (8.5 cm) Aspen 42" (10.0 cm) Wide Baum (15.5 cm) Leg Baum (18.0 cm) S p l i n t (65.0-80.0 cm)  -  200  100  V V  i  1 0.2  1  1 0.4  1  1 0.6  1  1 0.8  Ratio =  1  r 1  1.2  1.4  \  1.6  I  i  1.8  Width/Circumference  Figure 3.47 Plot of Occlusion Pressure versus the Ratio of Cuff Width to Limb Circumference for the Lower Limb  500  • 400  9 300 i i  200 -  L9• • c t ,  d  •  100  •  C P  • • r j ]  • • —i 0  1  1  0.2  Figure 3.48  1  0.4  1  1  1  1  1  1  1  1  •  n •  1  0.6 0.8 1 1.2 Ratio = Width/Circumference  i 1.4  •  D  i  r 1.6  •  i  n  r~ 1.8  Plot of Occlusion Pressure as a Function of the Ratio of Cuff Width to Limb Circumference for Upper and Lower Limbs  QD  148  s 3 to  to  Cuff Width (cm) Figure 3.49 Graph of the Averaged Occlusion Pressure as a Function of Cuff Width for the Upper Limbs of Normotensive Subjects  120  To  1  Jo  Upper Cuff Pressure (mmHg)  100  Figure 3.50 Graph of Occlusion Pressure as a Function of the Pre-Occlusive Proximal Cuff Pressure when Utilizing Two Cuffs  +  +  i  i  i  0.2  Figure 3.51  -H-  +  +  +  + ^ +V +  +  +  i 0.4  i—~i  i  1  1  1  1  1  1  r  0.6 0.8 1 1.2 1.4 Ratio = Cuff Width I Limb Circumference  1  1  i ~r~ r  1.6  1.8  Plot of Occlusion Pressure versus Cuff Width to Limb Circumference Ratio Obtained from Clinical Data  200 190  a No Exia.ngijiA.yiatA.on + EizvaXJjon (5 nuln) o Slzzvz (75 mmHg) A S£eeve (7 25 mmHg)  180 170 -|  X  E&maAch bandage  160 £5 5  1 V. 3  >>  150  -  • 140  -  130  m  g  120 ft, © 110 -  •  + X  3 •»»  100  •  •  • + O  A  $  -  90 80 70 60 - I 50 0.1  0.14  0.18  0.22  0.26  0.3  0.34  0.38  Ratio = 8.5cmlCircumf  Figure 3.52 Plot of Occlusion Pressure versus Cuff Width to Limb Circumference Ratio for Exsanguinated Limbs  C71  O  Ratio = Width/Circumference Figure 3.53 Plots of the Difference in Occlusion and Blood Pressures versus Cuff Width to Limb Circumference Ratio  300 • + O A X V  Freeman (7.5 cm) Aspen (8.5 cm) Baum (12.5 cm) Wide Baum (15.5 cm) P l a s t i c (19.5 cm) S p l i n t (42-55 cm)  ratio = width/circumference r—•  Figure 3.54 Plot of the Difference in Occlusion and Diastolic Pressures versus Cuff Width to Limb Circumference Ratio for the Upper Limb  cn  ^  500  400  • • + 0 • A X V  -  300  •  Dual Aspen (4.5 cm) Aspen 13" (5.5 cm) Freeman (7.5 cm) Aspen 34" (8.5 cm) Aspen 42" (10.0 cm) Wide Baum (15.5 cm) Leg Baum (18.0 cm) S p l i n t (65.0-80.0 cm)  9 _©  |  200  3  ft.  100  -  -100  Ratio = Width/Circumference  Figure 3.55 Plot of the Difference between Occlusion and Diastolic Pressures versus Cuff Width to Limb Circumference Ratio for the Lower Limb  154 500  400 -  Ratio = Width/Circumference Figure 3.56 Plot of the Difference between Occlusion and Diastolic Pressures versus Cuff Width to Limb Circumference Ratio for Upper and Lower Limbs 500  400 -  S  5  .<S 3  5  300  200 -  100 CO  +  •100  ~\  i 02  i  +  +  +  i 0.4  i  +  i 0.6  +  +  i  i 0.8  i  i 1  i  i 1.2  i  i 1.4  i  Cuff Width I Limb Circumference  i 1.6  i  i  r  1.8  Figure 3.57 Plot of the Difference between Occlusion and Diastolic Pressures versus Cuff Width to Limb Circumference Ratio Obtained from the Clinical Data  500  400  to  |  300  200  u u o  ft*.  ai 100  0  -100 0.6  0.8  1  Ratio=Cuff Width/Circumference  Figure 3.58 Superposition of the Clinical and Experimental Data Plots of the Difference between Occlusion and Diastolic Pressures versus Cuff Width to Limb Circumference Ratio  cn  500  400 -  5  O + O A X  No Exsanguination Elevation Sleeve (low pressure) Sleeve (high pressure] Esmarch bandage  300  .«3  =5 200 »3  100 -  ft.  -100 Ratio = 8.5cm/Circumf  Figure 3.59 Plot of the Difference between Occlusion and Diastolic Pressures versus Cuff Width to Limb Circumference Ratio  a-.  157 •  • +  rJP <<  2  fi  4 -  Experimental Data Clinical Data  D  • in  <o  t ft.  [Dh  +  D  + n  n  n  u n  D  D  0.2  0.4  0.6  0.8  1.2  1  1.4  1.6  1.8  Ratio-CuffWidth/Circumference Figure 3.60 Plot of Nondimensional Pressure versus Cuff Width to Limb Circumference Ratio for Experimental and Clinical Data  •  5 —-  No Exsanguination Elevation Sleeve (low pressure) Sleeve (high pressure) Esmarch bandage  + o A X  to  I  to  ft.  -  .5  •  i  fl ^  V) tj ©  ft,  _]  —  J  r—  ,  1  1  1  1  1  1  1  1  1  1  1  .1  1  1  1  Ratio = 8.5cm/Circumf Figure 3.61  Plot of Nondimensional Pressure versus Cuff Width to Limb Circumference Ratio for Exsanguinated Limbs  500  400  A  300  A  200  A  100 A Y=16/X  0 LTD  -i00  -200  i  ~i  0.2  i  i  0.4  i  i  0.6  1  1  0.8  1  r  1  —1  1  1.2  1  1.4  1  1  1.6  1  1  1.8  Ratio = Width/Circumference  Figure 3.62 Mathematical Correlation of Experimental Occlusion Pressure Data  1—  2  500  •  Experimental Data  +  Clinical Data  400  I  300  Vl  o  V)  o ft.  100  II  •Y = 16/x •  -Q-LT0  V= •100 1  o\l  '  *!<  '  0\6  '  ^  '  w  8lx  i  zflP  '  i  '  1^  '  i ! *'  '  2  X = Cuff Width I Limb Circumference cn  Figure 3.63 Mathematical Correlations of Experimental and Clinical Occlusion Pressure Data  5 -  •  8  Experimental Data  + ¥  4  A  3  -  Clinical Data  to  Vl  1  2 -  ©  ft, II  1 -  y=  —i 0  1  0.2  1  1  0.4  1  1  1  1  1  H6x  1  1  1  1  1  0.6 0.8 1 1.2 1.4 X = Cuff Width I Limb Circumference  i  r 1.6  i  T~  r  1.8  Figure 3.64 Mathematical Correlations of Nondimensionalized Experimental and Clinical Occlusion Pressure Data  CTl O  Transverse cervical a. [Transversa colli a.]  161  v  SUBCLAVIAN  ARTERY  Suprascapular a Acromion Thoraco-acromial a Lateral thoracic a. Posterior humeral circumflex a. Anterior humeral circumflex a  ascending branch  Profunda brachii a.  Cuff Compression Area  Interosseous recurrent a. Radial recurrent a Common interosseous a Posterior interosseous a. RADIAL ARTERY  Dorsal carpal br. • Palmar carpal arch Pisiform bone • Deep palmar arch ' Palmar metacarpal aa. • Superf, palmar arch •Common palmar digital aa. - Palmar digital aa.  Figure 4.1  Arterial Tree of the Upper Limb Showing the Region of Compression (from J. A. Anderson, Grant's Atlas of Anatomy, 8lh Edition, Williams & Wilkins, baltimore, 6.3,1983)  162  Figure 4.2  Longitudinal and Cross-Secion Views of the Thick Walled Cylinder Showing an Infinitesimal Element  Radial Pressure Change (%) from Surface to Nerve Location  Radial Pressure Change (%) from Surface to Nerve Location  165  SYSTEMIC BLOOD PRESSURE  DISTAL BLOOD PRESSURE  PRESSURE DIFFERENTIAL  PERIPHERAL  Velocity of Flow  RESISTANCE  STENOSIS RADIUS  Viscosity of Blood  Length of Stenosis  Figure 4 . 4  S c h e m a t i c o f a S t e n o s i s i n a n A r t e r y C a u s i n g a D i f f e r e n t i a l i n P r e s s u r e f r o m the I n l e t to the O u t l e t o f the V e s s e l (from J. A. Mannick, J. D. Coffman. Ischemic Limbs Surgical Approach and Physiological Principles. Grurie & Stratton, New York, 2, 1973)  75  •0 Coritrocifon 8  Viscous  SO Poientiol Energy  E«pons'ion  (Pressure)  25  0  J  0.5 c m  0  Figure 4.5  i • 1 L E N G T H (cm)  j  2  S k e t c h S h o w i n g the P r e s s u r e L o s s a l o n g the T u b e C a u s e d b y a S t e n o s i s (from R. E. Zierler, D. E. Strandness, Hemodynamics for the Vascular Surgeons, Vascular Surgery, 2d Edition, Grunc & Stratton Inc., 177, 1986)  .166  %  STENOSIS  O K) 20 30 40 50 60  70  KX3  KX)  CP X  E E  <  )5  0.4  0.3  0.2  Ql  OO  INSIDE RADIUS OF STENOSIS - cm  Figure 4.6  Effect of the Stenosis Radius on the Pressure Loss  (from R. E. Zierler, D. E. Strandncss, Hemodynamics for the Vascular Surgeons, Vascular Surgery, 2d Edition, Grune & Stratton Inc., 178, 1986)  FLOW cm\%ec  PERCENT STENOSIS O  0 2 0 M  40 50  SO  TO  BO  90  95  100 5.0  AP mm Hg 26.6  25.0 -4.0  O  200  2 3  2 x <  15.0  • 2.0  z  10.0  UJ  a a.  • 5.0  0.0 0.5  Ot«  0.3  0.2  Ql  - 0.0  OO  INSIDE RADIUS OF STENOSIS - cm  Figure 4.7  Effect the Stenosis Radius on the Flow and the Pressure Loss (from R. E. Zierler, D. E. Strandness, Hemodynamics for the Vascular Surgeons, Vascular Surgery, 2d Edition, Grune & Stratton Inc., 179, 1986)  167  Figure 4 . 8  OPEN Vessel  CONSTRICTED  Section of an Artery  - Blood Flow  Vessel  - No Blood Flow  Figure 4 . 9 Combined Effect of Fluid Friction and Vessel Constriction on Hemostasis  168  (a)  Open Vessel Pext< Pcrit  (b)  Partially Pext ^  Pcrit  Collapsed Pext >  Figure 4.10  Collapsed  Vessel  Pcrit  Collapsible Tube Structural Model of a Artery (a) Open Vessel (b) Partially Collapsed Vessel (c) Collapsed Vessel  Vessel  1-69  Beam Element  Artery  Figure 4.11  Structural Model of the Artery Showing a Beam Element Removed from the Cylinder  Figure 4.12 Initial and Final States of the Cylinder Divided into Beam Elements Showing One Deflected Element in the Final State  Pext  t  Figure 4.13  T  T  T  T  +  I  T  T  Pi  Lateral View of the Beam with Loads Applied it and the Resulting Deflection  20  -X-  19 18 17  • + 0 A  16  2 a 15  to to  14  X V  13 to  12  Experimental Data Uniform Cosine Linear Taylor wlo Taylor wl  11 10  a  9  I  8  t«3  a  •»»» o  7 6 5 4 3 2  oo  x><>U*  0<  \ !  1  i  m  j  0 12  H! i i 16  20  24  Cuff Width (cm) Figure 4.14  Plot of the Occlusion to Diastolic Pressure Ratio versus Cuff Width for Various Loads Applied on the Beam  o  20 19 18  • + O A  17 16  o A  fc 15 a to  Experimental (Diastolic) Experimental (Systolic) Taylor's series(McLaren) Taylor's series(Breault)  14 13  O  12  5  11  fc  10  a  to to  9  ft*  8  to  7  »•»» u  6  fc  a  o A  5 4 3  +  2 1 0  0  4  i  8  12  16  20  24  Cuff Width (cm)  Figure 4.15 Plot of the Occlusion to Blood Pressure Ratio versus Cuff Width for Various Loads Applied on the Beam  172  4.3 cm  Figure 5.1  Displacement of Tissue Layers through Interlayer Slippage ana* Compression  300 280 260  -  240  5  D  •  180  • •  a to  140  CP  I  tg,o  ° Jb  c  % r  to  a  20 0  ~  I  T.  20  1  ~1  40  1  r—  60  1  r-  80  100  Circumference (cm)  Figure 5.2  Graph of Occlusion Pressure as a Function of Limb Circumference  173  t r u e node  S c h w a n n cell  "pseudo-node"  basement membrane axon myelin  nodal  Figure 5.3  end  loops  of  myelin  Schwann  cell p r o c e s s e s  Details of the Peripheral Nerve Showing the Invagination of a Paranode by an Adjacent One from Right to Left (from G. E. Omer, M . Spinner. Management of Peripheral Nerve Problems, W. B. Saunders Co., Philadelphia, 491, 1980)  Figure 5.4  Low Power Electron Micrograph of Abnormal Myelinated Fiber Showing the Indentation at Schwann Cell Junction (from G. E. Omcr, M . Spinner. Management of Peripheral Nerve Problems, W. B. Saunders Co., Philadelphia, 491,1980)  174  proximal  distal  Figure 5.5 Schematic of the Displacement of the Nodes of Ranvier beneath the Edges of the Tourniquet Cuff (from J. Ochoa et al., Anatomical Changes in Peripheral Nerves Compressed by a Pneumatic Tourniquet. Journal of Anatomy, Vol.113, 441, 1972)  1  2  5  Figure 5.6  &  ) °r  AH.  Progressive Stages of Nerve Delamination and Conduction Blockage (from S. Sunderland. Nerves and Nerve Injuries, 2d Edition, Curchill Livingstone, Edinburgh, 1978)  175  Figure 5.7  Cross-Section Area of a Limb Encircled by an Inflated Cuff  0.16  Limb Circumference (cm) Figure 5.8  Normalized Limb Circumference Distributions for the Upper and Lower Limbs  .177 OS  arm leg  0.4  S  03 A  Mean=1.246 cm Std= l . i l cm  s a 02  Mean=1.252 cm Std= 1.01 cm  A  OJ A  0.2  1.8  i  2.2  Limb Circumference Difference (cm)  Figure 5.9a  Normal Distributions of the Difference between Limb Circumference at the Proximal and Distal Ends of the Cuffs for the Upper and Lower Limbs  s;  ••a s 3 •»»  5 -0.01  0.01  0.03  0.05  0.07  Curvature Angle (radians)  Figure 5.9b  Normal Distribution Curve of the Curvature Angle Combining Upper and Lower Limb Data  178  Blood Pressure cuff  300  (mm Hg> 200  tt tt tt tt tt tt tt  100  tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt  tt tt tt tt tt tt tt  1  - -*r tt  L 1  **~  tt tt tt tt tt. tt tt tt tt tt # tt tt tt  tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt  2  tt tt tt s tt tt tt tt tt tt tt tt tt tt tt tt #  4  PROXIMAL  F l a t curve  >  >  5 DISTAL  sensors  300  Surgical  P  (mm Hg)  Tourniquet fc'tt s'K tt / # # tt tt tt tt  200  100  'tttttt  /'tt  tt  tt  tt tt tt tt  tt  0  tt  tt tt tt tt tt tt tt tt  tt  » #  1  tt tt  tt tt ttNt-  tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt \  tt tt tt tt tt tt ' tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt  parabolic shape  « tt tt tt tt tt  2  4  PROXIMAL  5 DISTAL  sensors  Figure 5.10  Comparison between the Pressure Profiles of the Tourniquet and the Blood Pressure Cuffs  179  P  (mm Hg) i n f l a t i n g deflating hysteresis (mm Hg) (mm Hg) (mm Hg)  300  106.25 159.38 159.38 # # 150.00 # # 193.75  200  100  0  # # # # # #  # # # # # #  1  # # # # # # # #  PROXIMAL  Figure 5.11  # # # # # # # #  2  # # # # #• # # #  # # # # # # # #  3 sensors  # # # # # # # #  # # # # # # # #  4  # # # # # # # #  # # # # # # # #  5  DISTAL  ptissue pline diff Aspen  112.50 159.38 159.38 153.13 184.38  -6. 25 0. 00 0. 00 -3. 13 9. 38  = 159. 38 = 203. 17 = 43. 80 = 200. 00  spO = 131. 00 tpO = 126. 00 t slope 3. 17 s slope 3. 13  Pressure Profile on a Tappered Limb Produced by a Blood Pressure Cuff  180  Freeman Tourniquet (Straight  Cuff  Cuff)  on a C y l i n d r i c a l  Limb  P (mm  Hg) inflating (mm Hg)  3 (JO  200  100  0  tt # # # tt tt # # tt tt tt  tt tt tt # tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt  1 PROXIMAL  tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt  3>  tt tt tt tt tt tt # tt # tt tt tt tt tt tt tt tt # tt tt tt tt tt tt 4  deflating (mm Hg)  95. BI 101.95 12. 47 200.19 37.03 •' 224.75 237.03 224.75 151. 07 101.95 tt tt tt tt tt tt tt tt tt tt tt tt tt tt  5 DISTAL  hysteresis (mm Hg)  —6. 14 12. 28 12. 28 12. 28 49. 12  p t i s s u e = 230. B9 pline 03 diff 4. 13 Aspen = 250. 00 spO = 130. 79 tpO = 126. 94 t__sl ope ~ 3. 09 s__sl ope 07  sensors  Figure 5.12  Pressure Profile on a Cylindrical Limb Produced by the Freeman Cuff  181  Freeman T o u r n i q u e t (Straight on a C o n i c a l  Cuff  Cuff) Limb  P  inflating deflating (mm Hg) (mm Hg)  (ram Hg)  hysteresis (mm Hg)  300 160.28 190.98 194.05 151.07 65.11  200  100  # # # # # # # # #  # # # # # # #  1  # # # # # # # # # #  PROXIMAL  # # # # # # # # #  # # # # # # # # # #  # # # # # # # # #  2  # # # # # # # #  # # # # # # #  ptissue pline diff Aspen  # # # #  5  135.72 175.63 172.56 120.37 0.00 = = = =  24 .56 15. 35 21.49 30.70 65.11  183. 31 163. 96 -19. 35 200 . 00  spO = 130. 79 tpO = 126. 94 t slope = 3. 09 s_slope 3. 07  DISTAL  sensors  Figure 5.13 Pressure Profile on a Tapered Limb Produced by the Freeman Cuff  182  Aspen T o u r n i q u e t  Cuff  (Tapered Cuff), on a C y l i n d r i c a l  Limb  P (mm  Hg)  inflating (mm Hg)  deflating (mm Hg)  hysteresis (mm Hg)  300 37.48 123 .44 190.98 187 .91 151 .07  200  100 # # # # # #  # # # # # # #  1  # # # # 2  PROXIMAL  # # # # # # # # # #  # # # # # # # # # # 3  # # # # # # # # # #  # # # # # # # # # # 4  # # # # # # # #  # # # #  5 DISTAL  ptissue pline diff Aspen  65.11 65.11 181.77 181.77 65 .11 = = = =  •27 . 63 58 . 33 9.21 6.14 85.96  1 8 6 . 38 1 6 3 . 96 - 2 2 . 42 2 0 0 . 00  = 1 3 0 . 79 spO = 1 2 6 . 94 tpO t slope 3. 09 3. 07 s slope  sensors  Figure 5.14  Pressure Profile on a Cylindrical Limb Produced by the Aspen Cuff  183  Aspen Tourniquet pered on a C o n i c a l  Cuff  Cuff) Limb  P (mm Hg) inflating (mm Hg)  300  200  100 # # # #  # # # # # # # # # #  # # # # # # # # #  # # # # # # # # # #  # # # # # # # # #  # # # # # # # # # #  # # # # # # # # #  0.64 187.91 187.91 181.77 89.67  # # # # # # # #  5 DISTAL  PROXIMAL  deflating (mm Hg)  65.11 169.49 163.35 160.28 58.97  hysteresis (mm Hg)  -64.47 18.42 24.56 21.49 30.70  ptissue pline diff Aspen  = 178 .70  spO tpO t_slope s slope  = 130 .79 = 1 2 6 . 94 3 .09 = 3 .07 =  173 .23  = -5 .48 = 2 0 0 .00  sensors  Figure 5.15  Pressure Profile on a Tapered Limb Encircled by the Aspen Cuff  184  Aspen T o u r n i q u e t (Tappered  Cuff  Cuff)  on a C y l i n d r i c a l  Limb Model  made C o n i c a l  P (mm  Hg) inflating (mm Hg)  3(JO  200  100  O  tt tt  tt  tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt  1 2 PROXIMAL  tt tt tt tt tt tt tt tt tt tt tt tt tt # tt # tt tt tt tt 3  # tt tt tt tt tt tt # tt tt tt tt tt tt tt  deflating hysteresis (mm Hg) (mm Hg)  3.71 , 177.12 200.19 190.98 9. B5  20. 27 187. 9.1 178.70 95. 81 15. 99  pt i ssue p 1 i ne diff Aspen  = 192. 52 = 188. 68 — —3. B4 = 200. 00  spO tt tt tpO t_slope 4 5 s slope DISTAL  = 130. 79 = 126. 94 = 3.09 = 3.07  -24. 56 9. 21 21 .49 95. 17 -6. 14  sensors  Figure 5.16  Pressure Profile on a Stepped Cylindrical Limb Model Produced by the Aspen Cuff  185  Figure 5.17  Schematic Showing a Proper and an Improper Cuff Fit on the Limb (from C. H. Rorabeck, J. C. Kennedy. Tourniquet-Induced Nerve Ischemia Complicating Knee Ligament Surgery. The American Journal of Sports Medicine, Vol.8, No.2, 101, 1980)  186  P (mm  Hg) inflating (mm Hg)  300  200 tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt  tt tt tt tt tt tt tt tt tt tt tt tt tt  100  0  tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt  tt tt tt tt tt tt tt tt tt tt tt tt tt tt  138.79 166.42 175.63 175.63 108.09 tt tt tt tt tt tt #  5 DISTAL  PROXIMAL  deflating (mm Hg)  hysteresis (mm Hg)  111.16 141.86 123.44 98.88 3.71  27.63 24.56 52.19 76.75 104.38  ptissue pline diff Aspen  = 154.14 = 173.23 = 19.08 «= 200. 00  spO tpO t_slope s_slope  = 130.79 = 126.94 3.09 = 3.07  sensors  P (mm  Hg)  inflating  TiCifi  100  (mm  tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt  tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt  1 2 PROXIMAL  tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt  tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt tt  3  4  Hg)  deflating (mm  169.49 184.84 151.07 163 . 35 126 .51 tt tt tt tt tt tt tt tt tt tt  5' DISTAL  hysteresis  Hg)  163.35 148.00 138.79 151 . 07 58. 97  (mm  Hg)  6.14 36.84 12.28 12. 28 67. 54  p t i s s u e = 166. 42 p i i ne = 176. diff 9. 89 Aspen = 200. 00 spO tpO t_slope 5_slope  = 130. 79 - 126. 94 = 3.09 == 3.07  sensors  Figure 5.18  Variation in Pressure Profiles Due to a Small Displacement of the Cuff  Sensor position along the Limb Figure 5.19 Pressure Distribution on a Limb Produced by the Freeman Cuff Showing the Degree of Snugness for Loose, Medium-Loose, Medium, and Tight Cuff Fits  Figure 5.20 Pressure Distribution on a Limb Produced by the Aspen Cuff Showing the Degree of Snugness for Loose, Medium-Loose, Medium, and Tight Cuff Fits  188  Syringe (cc)  Figure 5.21 Experimental Configuration for the Cuff Snugness Test  190 500 A  a +  400  o A  fc  300  A  200  A  s  Loose Medium-Loose Medium Tight  + + o  9 • •  A A  •  A  o A  ioo A  D • •  •  20  Volume (cc) Figure 5.23 Plot of Cuff Pressure versus Volume Generated from the Snugness Test on the Upper Limb  500  400  ffj  A  • +  O A  Loose M cdium-Loose Medium Tight  300  S  A A  fc 200  A  ft  +  ioo A  20  40  Volume (cc) Figure 5.24 Plot of Cuff Pressure versus Volume Generated from the Snugness Test on the Lower Limb  Loose Medium  o  Tight  0  Too Snug  o  + +  Normal  Too  • +  Loose  1  I  1  20  1  1  40 Volume (cc)  Figure  5.26  P l o t o f C u f f Pressure versus V o l u m e for the U p p e r and L o w e r L i m b s  ,  60  260 240 220  5 noAmot&niive.  A  3 maJLu,  2  iubjzct6  boji<L cu^  Izmalu  200 180 _ 160  A  j  A  140  wzbnil  (/]  uJzbA.il  (2)  loam  (7)  loam  (2)  thick  loam  % 120  3 £ 100 80 60 40 20 4 Sensor Contact #  Figure 5.27 Pressure Distributions underneath the 24" Aspen Cuff with Different Interfacial Materials  260 240 -I 5 noAmotzm-Lvz  220  3 mcLc&i,  4ufa/e.cX4  baAt c a ^  Z j$ema£ea  200 -  web^c£  (r)  web-^U  (2)  ioam (J)  180 -  _  160 -  J  140 A  1  120  A  100  - I  tfoam (2) thick ^oam  s £  80 60 40 20  0  2  3  4  Sensor Contact # Figure  5.28  Pressure Distributions underneath the 34" Aspen Cuff with Different Interfacial Materials  Occlusion Pressure I Diastolic Pressure  561  Cuff §3 0.0310 r a d  Cuff 0.0062 .0558 r a d  -0.01  0.03  Curvature Angle (radians)  Figure 6.2  Normal Distribution Curve of the Limb Curvature Angle Showing Five Recommended Cuff Designs  0.07  -197  Pressure D i s t r i b u t i o n C u f f Width Actual  P  versus  Designs  t  L narrow  Desired Pressure  Distribution  P  L wide  Figure 6.3  Sketch of the Most Desirable Pressure Distribution for Future Cuff Designs  198  APPENDIX A - PERIODIC TRANSDUCER CALIBRATION The calibration of the Cobe transducers is done periodically prior to each set of soft tissue pressure measurements by calling the subroutine "calibrate" (Appendix B). This subroutine first calibrates the transducer attached to the pressure sensor and then the transducer attached to the cuff. The reference pressure is set by the Aspen tourniquet system (A.T.S. 500) which itself is compared to a mercury manometer for accuracy. The output voltages of the transducers are converted to unit of pressure (mmHg) via an analog-digital converting board. The voltage output of the pressure transducer is recorded when the sensor is deflated. This first value is stored in the variable SpO. The sensor is then inflated to a preset pressure value by the source pressure controller. The voltage output of the transducer during full inflation is store in the variable SpAspen. A linear curve is plotted through the two voltage points, spO and spAspen (Figure A.1). The following equation is obtained: Pressure Value = (Voltage Output - Reference Value) * Slope [mmHg] = [mV - mV] * [(mmHg)/(mV)] The slope of the curve and the reference value on the abscissa are used to convert further voltage readouts to values of pressure. The transducer attached to the cuff is then calibrated after the deflation of the pressure sensor. The same calibration subroutine is used with variables called TpO and TpAspen. The accuracy of the calibrated transducers was ensured by evaluating the preset inflation pressure to the transferred pressure. A test was performed to validate the calibration. Two tourniquet cuff models were used to compare the inflation pressure of the cuff to the pressure delivered to the surface of the limb. The black Freeman 24" tourniquet cuff was tested on a limb model made of a plexiglass cylinder covered with layers of foam. A pressure sensor was inserted between the cylinder and the cuff to measured the delivered pressure. Only the third cell reading was recorded. The same test was performed with the blue Aspen tourniquet cuff on a tapered upper limb of normal size. The delivered pressure was measured for cuff inflation pressures varying from 0 mmHg to 350 mmHg by increment of 50 mmHg. The two curves of cuff pressure as a function of delivered pressure are shown on Figure A.2. Both curves are linear with an average delivered pressure loss of 3.5% with respect to the inflation pressure. The difference in cuff inflation pressure and delivered pressure is considered negligible and independent of the calibration. This observed loss of pressure is due to small leakage through the various connections of the hardware, time delay between the measurements, and material tension in the cuff.  199  300 280  -  260 (spAspen,  Aspen)  140  Aspen  120  (spAspen-spO)  100  /  80 60 40 20 0  / 100  i  i  p  (spO.O) i r i 140 160  i— i 180  T  i 200  Voltage Output Figure A . l  i — i — \ — i — i — i — i — i — i — 220 240 260 300  (mV)  Graph of Pressure versus Transducer Voltage Output  400  •  350 -  +  Freeman  on  Cylinder  Aspen on Arm  300 250 -  B V.  200  I  ISO -  3  to to  100 50 -  l o o  1  2T0  1  Pressure Transferred to the Surface Figure A.2  3~h~o  400  (mmHg)  Graph of Cuff Pressure versus Pressure Transferred to the Surface  200  APPENDIX B - CONTROL SOFTWARE b:data.obj+ /*DATA.ARF */ b:dattot.obj b:data.exe b:data.map/map a:ibmpcs.1ib+ a:c86s2s.lib  /* DEFINES.H  */ /'factory  • d e f i n e BASE /* PRESSURE  Ide f i ne m i d l  /* main program to o b t a i n the p r e s s u r e beneath a t o u r n i q u e t c u f f /•data.c*/  ltdef ine prox_sens sens 1 d e f i n e tnid2_nens ( d e f i n e mid3 sens Ide f ine d i s t sens  MEASUREMENT SYSTEM */  /Mth  distribution  version */  linclude "stdio.h" ((include " d e f i n e s . h " linclude "totvars.h" main  ()  /'values  0 2 4  /•D/A /•D/A /•D/A  channels channels  Idefine Idefine Idefine Idefine  11 13 1 0  /•A/D /*A/D  channels channels  l i n e press sens p r e s s open close  channels  :  /* OUTVAR.H */ extern by manual  calibration*/  extern  histogram ( a s p e n , d i f f ) ; i f ( r e s u l t == 1) hardcopy () ; scanf ("%d", Sreponse); crt_mode(2); p r l n t f ( " D o you want t o take more measurements? \n") ; scanf ("%d",(answer); i f (answer == 1) goto loop; p r i n t f ( " D a t a System o f f " ) ; finishO ;  pline, idata(6),  double  tpO  spress_data() ,  t p r e s s data () , sensor (); e x t e r n double max(), maxsensorO, p c o n t r o l (), c o n v e r s i o n () , c a l i b r a t e ! ) , '  )  f i n i s h () ; p r i n t f ("dif f=%6.2f\n", d i f f ) ;  datamax,  , ddata(6);  e x t e r n char drive[20),name(20) ; extern double s_slope, t _ s l o p e , spU,  loop:  / ' p r l n t f ( " Aspen p r e s s u r e = ?\n"); */ / • s c a n f ( " % f " , s a s p e n ) ; */ there: p r l n t f ( " D o you want to get the r e s u l t s i n a f i l e ? \ n " ) scanf ( " % d " , s r e s u i t ) ; i f ( r e s u l t == 1) ( p r i n t f ("name?\n"); scanf ("%s",drive); s p r i n t f (name,"%1.2s%1.0s%1.4s","b:",drive, ".dat") ; ) /•main c o n t r o l o f the program*/ d i f f = p c o n t r o l () ;  double  avdataf6]  s s l o p e = 3.07; spO = 130.79; t _ s l o p e = 3.09; tpO - 12 6.94; goto t h e r e ;  )  •define t i n f valve Idefine tdef valve (define s_valve  double maxsensorO, calibrate)), - p c o n t r o l () , h y s t e r e s i s (6); c o n v e r s i o n ()  1 )  obtained  channels 7 ./ c h n n n e 1 s 0 ./ channels 9 ./ channels 10 . / channels 11./  char drive(20),name[201; double s p r e 3 s _ d a t a (), tpress_data(), sensor () , max () ;  ( c a l i b r a t e (aspen); goto t h e r e ;  else I  /•A/D /*A/0 /•A/D /•A/D / * A/D  double datamax, pline, idata[6], ddata(6), s_slope; double c_siope, spO, tpO , h y s t e r e s i s ( 6 ] , avdata[6J;  start: crt_mode(2); p r i n t f ( " D a t a system ON.\n"); p r i n t f ( " P n e u m a t i c t o u r n i q u e t used to o b t a i n p r e s s u r e distribution.\n\n"); p r i n t f ( " D o you want t o c a l i b r a t e the t r a n s d u c e r s ? (yes=l)\n") ; scanf("%d",& r e p l y ) ; p r i n t f C Aspen p r e s s u r e = ?\n"); s c a n f ( " % f",&aspen); (reply  15 17 19 21 23  TOTVARS.H  I int reply,answer,reponse,result; f l o a t aspen; double d i f f ;  if  address=D1G*/  0x330  /•dattot.c*/ /•including ;  datl,dat2,dat3,dat1,dat5,dat6,  dat8,dat9, dat10,dat11,dat12, d a t l 3 /•datl.c*/ linclude linclude linclude  "stdio.h" "defines.h" "outvar.h"  double c a l i b r a t e f l o a t aspen;  (aspen)  i n t ready, i , j , k, r e f , rep; double tp200, sp200; / • c a l i b r a t i o n done manually •/ /•sensor p=3.07(reading-130.79)*/ /•tourniquet P=3.09(reading-126.94)*/  201  1  *******'calibrate  sensor*/  p r i n t ! ( " s e n s o r open t o atmosphere \ n " ) ; p r i n t f ("Sensor measured at 0 mmHg \n"), f o r ( i = 0; K 5 0 0 ; i + + ) close_valve (s_valve); sp0=spress_data () ; p r i n t f ("sp()=%6. 2 f \ n " , spO) ;  double p t i s s u e , d i f f ; i n t r e p , i , r e a d y , n , j , y; p r i n t f ("Connect the t o u r n i q u e t t o pressure source\n"); p r i n t f ("Enter (1) when ready\n"); scanf ("%d",Sready);  p r i n t f ( " S e n s o r i s pressurized \n"); f o r ( j = 0;. j<5000; f o r (k = 0; k<10; k + + ) open_valve ( s_valve ); sp200 = s p r e s s _ d a t a ( ) ; c l c s e _ v a l v e (s v a l v e ) ; . p r i n t f ("sp200=$G.2f\n",sp200);  /'tourniquet  p r i n t f ("pline ON\n"); f o r (1=0; i<500;i++) f o r (j=0; j<100; j + + ) open_valve ( t i n f _ v a l v e ) ; close valve  /' s slope p r i n t f ("  (aspen)/(sp200-sp0); s_slope=%6.2f\n\n",  /....„........».».........H  s_slope),  c a l i b r a t e tourniquet * /  pi-int f ("tourniquet open t o atmosphere \n") ; p r i n t f ( " T o u r n i q u e t measured a t 0 mmHg \n"); close_valve (tinf_valve); for (1 = 0; K30000; i + + ) open_valve ( t d e f _ v a l v e );  sens: / " s t o r e p t i s s u e value i n datamax*/ p t i s s u e = maxsensor ( ) ; /* close valve (tinf_valve); */ pline= conversion (tpress data(),0); p r i n t f ("Do you want t o r e l n f l a t e the sensor? \n " ) ; scanf ("%d",6rep); i f (rep == 1) goto sens;  d i ff=pline-pt issue; return ( d i f f ) ;  ) \n");  /*dat3.c*/ J include ((include  f o r (1 = 0; K 1 0 0 0 0 ; i t + ) ( open_valve ( t d e f _ v a l v e ); close_valve (tinf_valve);  (  )  (aspen)/(tp200-tp0); t_slope=%6.2f\n\n",t  if(channel<8) /'sends out 0V*/ 1 outportb(BASE+4, channel); outportb(BASE+5,128); outportb(BASE+4,channel+8); outportb(BASE+4, channel);  slope);  )  else  p r i n t f ( " D o you want t o keep these c o n v e r s i o n values?\n") p r i n t f ( " y e s ^ l no=2\n"); scanf ("%d",Srep); i f (rep == 2) ( p r i n t f ("What are your c o n v e r s i o n f a c t o r s ? \ n " ) ; p r i n t f ("s_slope= \ n " ) ; scanf ("%f",&s s l o p e ) ; p r i n t f ("spO= \ n " ) ; scanf ("%f ", sspO) ; p r i n t f ("t_slope \n"); scanf ( " % f " , s t s l o p e ) ; p r i n t f ("tp0= Yn"); scanf ("% f." , &tpO) ; ;s  )  pr i n t f ( " c a 1 i b r a t i o n done.Xn"); )  channel-channel-8; outportb(BASE+4,channel); outportb(BASE+5,128); outportb(BASE+4,channel+16); outportb (BASE+4,channel);  ) open_valve(channel) i n t channel; ( If (channel<8) /'sends out 5V*/ < outportb(BASE + 4,channel) ; o u t p o r t b (BASE + 5,255); outportb(BASE+4,channel + 8) ; outportb(BASE + 4,channel) ;  )  /*dat2.c*/ I  tinclude t Include linclude  else (  "stdio.h" "defines.h" "outvar.h"  double p c o n t r o l I  "stdio.h" "defines.h"  close_valve(channel) i n t channel;  close_valve (tdef_valve); printf("tp200=%6.2f\n",tp200); t_slope printf("  (tinf valve);  finish 0 ;  tpO=tpress_data(); close_valve (tdef v a l v e ) ; printf("tpO=%6.2fYn", tpO) ; printf("Tourniquet i s pressurized for (j=0; j<1000; j + + ) f o r (k=0; k<100; k++) open_valve ( t i n f _ v a l v e ); tp200 = t p r e s s _ d a t a ( ) ; c l o s e _ v a l v e ( t i n f _ v a l v e );  inflation*/  0  )  channel=channel-8; outportb(BASE+4,channel); outportb(BASE+5,255); outportb(BASE+4, channel+16), outportb(BASE+4, channel); )  202  /•datl.c*/ t include I include  /*dat8.c*/  "stdio.h" "defines.h"  linclude (include t p r e s s _ d a t a () double ( double d a t a ; /* A/D l i n e p r e s s u r e */ outportb(BASE, i i n e _ p r e s s ) ; w h i l e ( inportb(BASE) < 128) p r i n t f ("t-loop\n"); data= (double) inportb(BASE+1); r e t u r n (data) ; I  double  spress_data()  )  max( p 2 _ p r e s s u r e _ d a t a *p2_pressure_data;  int i ; double  maxdata;  (  return  "stdio.h" "defines.h"  if  double adata; i n t p o i n t [ 6 );  outportb (BASE,point[i)); w h i l e ( i n p o r t b (BASE) <128); adata= (double) i n p o r t b (BASE+1); p r i n t f C'_%4 .Of", adata) ; /* i f the c o n t a c t o f the sensor i s c l o s e d 0<V<2.5*/ /• i f t h e c o n t a c t o f t h e sensor i s open 2.5<V<5 */ return (adata);  for  (value,n)  s(i)=close; i d a t a U ] = d d a t a ( i ) = 0;  while ( s [ l ] + s [ 2 ) + s ( 3 ) + s [ 4 ] + s ( 5 ] < 5 ) ( open_valve ( s _ v a l v e ) ; i f ( s e n s o r ( l ) > 175 &s s ( l ) = = c l o s e )  (  i d a t a | l ) = conversion (spress_data(),1) ; s[l)=open;  i n t ready,answer; double slope,newvalue;  )  if  (newvalue);  (i=0; i<6; ++i)  p r i n t f ( " s e n s o r i s INFLATED (from 0 t o 1 ) \ n " ) ; i = 0; / • p r e s s u r e up*/  i n t n; double v a l u e ; (  return  (  )  "stdio.h" "defines.h" "outvar.h"  (value-128)  (0x0b) & OxOOff)  double maxsensorO ( /•idata[i)....pressure i n c r e a s i n g the sensor*/ /•ddata(i)....pressure d e c r e a s i n g the s e n s o r * / i n t i , s [6], y, j , n;  ) /*dat6.c*/  (n =- 1) slope= s _ s l o p e ; else slope= t _ s l o p e ;  ( (bdos  == OxOOff) return (1); else return (0);  p o i n t 111=prox_sens; point(2]=midl_sens; p o i n t [ 3 j =mid2_sens; p o i n t j 4)=mid3_sens; point[5)=dist_sens;  newvalue=  "stdio.h" "defines.h" "outvar.h"  I -  (  double c o n v e r s i o n  ( maxdata );  unsigned s h o r t key ()  sensor(i)  linclude linclude linclude  )  /•dat9.c*/ linclude linclude linclude  /*dat5.c*/  double int i ;  double double  maxdata = p 2 _ p r e s s u r e _ d a t a [ 1 ]; f o r ( i = l ; i<5; ++i) if( p 2 _ p r e s s u r e _ d a t a [ i ]> maxdata) maxdata = p 2 _ p r e s s u r e d a t a ( i );  double data; /* sensor p r e s s u r e */ outportb(BASE,sens_press); while(inportb(BASE)<128) prlntf("s-loop\n"); data= (double) inportb(BASE+1); r e t u r n (data);  linclude I include  "stdio.h" "defines.h"  /• mmHg/digital * slope-  */  i f ( sensor(2) > 175 && s[2)==close) ( idata[21 = c o n v e r s i o n (spress_data() , 1) , s(2)=open;  ) i f ( sensor(3) > 175 «& s[31==close) ( idata[3] = conversion (spress_data(),1) , s[3]=open; )  203  e l s e i f ( d d a t a ( i ) == 0) avdatatil = idata(i); else avdatalil = (idata[i] + ddata[i]  i f ( s e n s o r i a l > 175 i i s(4]==close) ( i d a t a ( 4 ) = c o n v e r s i o n (spress_data () , 1) ; s[4)=open;  )12;  )  )  /* I f one o f the data vanishes, the other the average one.*/ f o r ( i = l ; i<6; i++) hysteresis[ij = idata[i)-ddata[i1; datamax = max(avdata); ) p r l n t f (''***** **DATAMAX=%6.2f mmHg* * * * * *\n" printfr %2d %2d %2d %2d %2d\n", s [ 1 ] , s (2 ] , s [ 3 ] , ,datamax); s(4],s[5]) ; r e t u r n (datamax); i f (key() == 1) getchar (); goto i n f _ d a t a ; /•datlO.c*/ i f ( sensor(5) > 175 i i s[5]==close) ( i d a t a [ 5 ) = c o n v e r s i o n ( s p r e s s _ d a t a () , 1) ; s[5]=open;  I  inf_data: p r i n t f (" INFLATING DATA\n") ; p r i n t f ("%7.2f %7.2f %7.2f %7.2f %7.2f\n\n", idata[2),idata(3),idata p r i n t f ( " s e n s o r i s now DEFLATED i = 0; /•pressure while  idata[l],  (from 1 t o 0 )\n");  down*/  (  ddata (1] «= c o n v e r s i o n ( s p r e s s _ d a t a (), 1) ; s(11=close; }  close_valve (s_valve); i f ( sensor(2) < 175 i i s[2]==open) ( ddata [2) = c o n v e r s i o n ( s p r e s s _ d a t a ( ) , 1 ) ; s(2)=close; if  ( sensor(3)  "stdio.h" "defines.h" "outvar.h"  histogram  (aspen,diff)  f l o a t aspen; double d i f f ;  (  ( s t l ) + s [ 2 ] + s [ 3 ] + s [ 4 ) + s [ 5 ) > 0) ( open_valve ( s _ v a l v e ) ; i f ( s e n s o r ( l ) < 175 i i s[l)==open)  )  Dinclude linclude linclude  < 175 i i s[31==open)  (  ddata I 3] = c o n v e r s i o n ( s p r e s s _ d a t a ( ) , 1) ; s(3)=close;  ) i f ( sensor(4) < 175 i i s[4]==open) ( ddata(4) = c o n v e r s i o n ( s p r e s s _ d a t a ( ) , 1) ; sI 4)=close; ) i f ( sensor(5) < 175 i i s[5]==open) ( ddata(5) = c o n v e r s i o n ( s p r e s s _ d a t a ( ) , 1 ) ; s(5)=close; 1  printf(" %2d %2d %2d %2d %2d\n", s [ l ) , s [ 2 ] , s p ] ,s[4] , s(5]) ; (keyO == 1)  if ( getcha r () ; goto d e f _ d a t a ; ) I de f d a t a :  print r ( " DEFLATING D A T A W ) ; o r i n t f ( " * 7 . 2 f %7.2f %7.2f %7.2f %7.2f\n\n", ddata[1],ddata(2J ddatat31.ddata(' f o r ( i = l ; 1<6; i++) I i f ( l d a t a ( i ) == 0) avdatall] = ddata[i);  int i ; c r t mode (2); crt_srcp(3,14,0); printf ("Pressure D i s t r i b u t i o n " ) ; c r t s r c p (1,4,0); c r t 2 s r c p ( 2 , 1,0) ;  printf printf  ("P"); ("(mm Hg)"),  c r t _ s r c p (5,43,0) crt_srcp(5,50,0) crt_srcp(5,57,0) c r t _ s r c p ( 5 , 64, 0)  printf print f printf printf  ("mmHg"); ("mmHg"); ("mmHg"); ("mmHg");  crt_srcp(5,37,0) crt_srcp(4,43,0) crt_srcp(4,50,0) crt_srcp(4,57,0) c r t _ s r c p ( 4 , 63,0)  printf printf printf printf printf  ("I"); ("infl"), ("defl"), ("hyst"); ("average"),  c r t _ s r c p (8,37,0) ; crt_srcp(9,37,0); c r t _ s r c p ( 1 0 , 37,0); c r t _ s r c p ( l l , 37, 0) ; crt_srcp(12,37,0);  p r i n t f ("1") p r i n t f ("2") p r i n t f ("3") p r i n t f ("4") p r i n t f ("5")  f o r ( i = l ; i<6; i++) I crt_srcp(7+i,56,0) h y s t e r e s i s ( i J); c r t _ s r c p (7 + i,64,0) • ^avdata[i)); c r t _ s r c p (14,50,0); *6. 2f datamax) ; c r t _ s r c p ( 1 5 , 50, 0) ; %6.2f",pline): crt_srcp(16,50,0); %6.2f",diff) ; crt_srcp(17,50,0); %6.2 f " , a s p e n ) ; c r t _ s r c p (19, 50, 0) ; %6.2f",spO); crt_srcp(20,50,0); %6.2f",tp0) ; crt_srcp(21,50,0); *6.2f",t slope); crt_srcp(22,50,0); %6.2 f " , s s l o p e ) ; crt_srcp(24,55,0);  printf  ("%6.2f",  printf  ("%6.2f",  p r i n t f ( "ptissue = printf(  "pline  printff  "diff  printf  ("Aspen  p r i n t f ("spO p r i n t f ("tpO printf  ("t_slope =  printf  ("s_slope =  printf  ("file=%s",name)  204 values () , bars () crt_srcp(22,12,0); crt_srcp(22,18,0); crt_srcp(22,24,0); c r t _ s r c p (22, 30,0) ; cct_srcp(22,36,0);  printf printf printf printf printf  (  ("1") ("2") ("3") ("4") ("5")  bars ( ) ; c r t _ s r c p ( 2 3 , 9, 0) ; printf c r t _ s r c p ( 2 3 , 33, 0) ; p r i n t f c r t _ s r c p ( 2 4 , 22, 0) ; p r i n t f c r t _ s r c p ( 5,3,0); c r t _ s r c p ( 1 0 , 3,0); crt_srcp(15,3,0); c r t _ s r c p (20,3,0);  ("PROXIMAL"), ("DISTAL"); ("sensors");  printf("300") printf("200") printf("100") , printf("0");  bargraph( bargraph( ba rgraph( bargraph( bargraph(  idata(1), i d a t a [ 2 I, idata[31, idata(4], i d a t a [5],  11 17 23 29 35  bargraph( bargraph( bargraph( bargraph( bargraph( )  ddata(l), ddata(2), ddata[3l, ddata (4 ], ddata [5],  13 19 25 31 37  /*datl3.c*/  )  IInclude tinclude  "stdio.h" "defines.h"  /•datll.c*/ linclude linclude linclude  "stdio.h" "defines.h" "outvar.h"  f i n i s h () int i,k;  bargraph ( p r e s s , y ) double int y;  close_valve (tinf_valve); close_valve (s_valve); f o r ( i = 0 ; i<200; i++) f o r (k=0; k<100; k++)  press;  (  (  int block,i; / " c o n v e r s i o n from v o l t t o g r a p h i c b l o c k * / / " s t a r t i n g a t x=19 t o p r e s s u r e v a l u e */ /* IS b l o c k s / 300 mm Hg = .05 */  )  close_valve (tdef_valve); ) /*datl4.c*/  b l o c k = 20 - ( i n t ) (0.05 * press) i f (block < 5) block-=5; f o r <i=20; i >= b l o c k ; --1) ( c r t _ s r c p (1, y, 0) ; /* p r i n t f <"%c",OxOOdb);*/ p r i n t f ("%c" )•  linclude "stdio.h" linclude "defines.h" • i n c l u d e "outvar.h" hardcopy ()  ' ft' > ,  /*datl2.c*/ I include I include I include  int i,j,value; FILE * f p _ d a t a ,  "stdio.h" "defines.h" "outvar.h"  fp_data=fopen for  va l u e s ( ) ( int i ; /* c o n v e r s i o n f a c t o r from v o l t s t o mmHg */ /* 0 mmHg = 128 d i g i t a l s */  )  printf! printf( prlntfl printf ( printf (  "%7.2f, "%7.2f", "%7.2f", "%7.2f", "%7.2f",  idata( idata] idata[ idatal idatat  1 2 3 4 5  ) ) J ) ]  c r t _ s r c p (8,47,0); c r t _ s r c p (9,47,0); crt_srcp(10,47,0); c r t _ s r c p ( l l , 47, 0) ; crt_srcp(12,47 0); )  printf( printf( printf( printff printf(  "%7.2f", "%7.2f", "%7.2f", • %7.2f", "%7.2f",  ddata[ ddata[ ddata[ ddataf ddatat  1 2 3 4 5  1 ), ) ), )) ))  ,  ); ); ), ), ),  *fopen(); (name,  "w");  (i = 0; K 4 0 0 0 ; i + = 160) ( f o r ( j = 0 ; j<160; j+=2) ( v a l u e = peek ( i + j , OXbOOO) sOXOOff; f p r i n t f (fp data, "%c", v a l u e ) ,  )  c r t _ s r c p (8,40,0); c r t _ s r c p (9,40,0); crt_srcp(10,40,0); crt_srcp(11,40,0); crt_srcp(12,40,0);  r  close_valve (tinf_valve) , open_valve ( t d e f _ v a l v e ) ;  fprintf  fclose  (fp data,  (fp_data);  "\n");  APPENDIX C - PROTOCOLS  C . l Surface Pressure Measurements Preparation 1. The blood pressure of the subject is taken twice on the right arm with a non-invasive pressure monitor (Dinamap 845). Systolic and diastolic pressure values are averaged and recorded. 2. The pneumatic pressure sensor (Chapter 3, section 3.1.1.1) is externally calibrated by inserting it in an constrained bladder inflated to a known pressure by an tourniquet system (A.T.S. 1000). The pressure sensor is inflated with an air bulb and a manometer is used to record the pressure sensor value. 3. The circumference of the limb is measured and four equidistant points around the limb are marked. Starting at a specific landmark, the positions are as follows: anterior, lateral, posterior, and medial. 4. Powder is applied to the limb as a lubricant to facilitate the positioning of the pressure sensor underneath the tourniquet cuff. Configuration 1. The pressure sensor is positioned on the proximal portion of the arm or the leg ensuring that it is straight and the air channel is not crimped. A Velcro band, wrapped around the limb, secures the sensor in place. 2. The cuff is then applied over the sensor in a snug manner, so that one finger can be inserted without difficulty between the cuff and the limb at the proximal edge. Three fingers could be inserted only with difficulty. 3. The sensor is repositioned relative to the cuff to ensure that all five contacts lie in an area underneath the cuff. 4. The tourniquet system is hooked up to the pressure measurement system, set to a predetermined pressure and is switched on. This allows the internal volumes of the system to be filled. Data Collection 1. The program is run by typing "data" (Appendix B). 2. The sensor transducer and the tourniquet transducer are calibrated. The digital values obtained from the analog/digital board (A/D Board: Tecmar LabTender) determine the conversion factors to be used to obtain proper pressure units. The pressure measurements are carried on if these factors are comparable to the one previously calculated.  206  3. The program automatically causes the cuff to be inflated by the tourniquet system. The pressure sensor is inflated until all five contacts are open and then deflated until the contacts are closed. 4. The ten pressure measurements are displayed as a histogram that is saved on a floppy diskette. 5. The sensor is gendy moved to the consecutive position on the limb and the program is initiated again. Data Analysis 1. The blood pressure is taken again two more times at the end of all surface pressure measurements. The values are compared to the initial ones and averaged with them. 2. All histograms are analyzed and compared with the previous results. A full threedimensional view is obtained for a particular limb.  C.2 Internal Pressure Measurements (Cadaver Tests) Preparation 1. The data acquisition system is inspected prior moving it into the morgue to ensure perfect functioning of all components. Extra tubings, electrical and pneumatic connections are attached to the systems. Sensors of various dimensions are assembled together. 2. Some labels are prepared to identify the position of the sensors inserted in the limbs. Tests 1. The cadaver is taken out of the refrigerator and left at room temperature for fifteen minutes. The specimen is uncovered and the four limbs exposed to prepare for dissection. 2. The proximal and distal edges of each limb is measured and recorded. The average circumference is calculated. 3. The limb is carefully dissected by an orthopaedic surgeon, avoiding cutting the main structures. The main nerves are clearly exposed: radial and median nerves in the case of the upper limb and sciatic and saphenous in the case of the lower limb. 4. A pneumatic sensor is delicately inserted in the limb, running along the nerve of concern. The sensor is positioned as flat as possible in the limb. A label is attached to the pneumatic connector for further reference. 5. Once the two pressure sensors have been cautiously placed at proximity of the nerves, the layers of muscles are flapped over the sensors, leaving the electrical and pneumatic connectors outside the limb. The main subcutaneous layers of tissues are sewed back together to reconstitute an intact limb. Few suture stitches cover the proximal part of the  207  sensor leaving a small opening for the pneumatic sensor ensuring a fixed position of the sensor during inflation. 6. A third sensor, used for control, is placed on the skin over a larger muscle mass. 7. The standard Aspen cuff is wrapped around the limb in a snug manner. Care is taken to cover the region of the limb where the sensors are inserted. 8. The sensors are alternatively connected to the pressure acquisition system and the program "data" is run. 9. All pressure measurements are saved on floppy diskettes. 10. Once the measurements are taken, the sensors are taken out of the limb and the incisions are sewed back before covering the specimen. Data Analysis  1. All histograms are printed out for a comparative analysis. 2. The measured pressures are evaluated as a function of the inflation pressure and general conclusions are drawn from the obtained profiles.  C.3 Limb-Cuff Interface Tests Preparation  1. Hospital soft bandage (Webril) and 1/4 inch foam are cut out to fit the width of the tourniquet cuff. 2. The surface pressure data acquisition system is set ready to take the measurements. Tests  1. The pneumatic pressure sensor is taped onto the limb in a flat position. The standard Aspen tourniquet cuff is wrapped over it. 2. The sensor is connected to the tourniquet system and the program "data" is initialized in order to measure the surface pressure along the five contacts of the sensor. 3. One, three, and six layers of soft bandage are subsequentiy wrapped around the limb, over the pressure sensor, and procedures 1 and 2 are repeated. 4. One and two layers of foam are wrapped on the limb and procedures 1 and 2 are repeated.  208 Analysis 1. The pressure profiles obtained with the various conditions of skin-cuff interface are plotted on the same graph for comparison purpose.  C.4 Occlusion Pressure Tests Preparation 1. The blood pressure of the patient, in a supine position, is taken twice with an noninvasive blood pressure monitor. 2. The tourniquet cuff is snugly applied around the limb. 3. A main artery is located by feeling the pulse with the tips of the fingers. Generally the brachial artery at the elbow region is the easiest one to locate. The artery may also be located at the level of the wrist. In the case of measurement on the lower limbs, the femoral artery, at the level of the knee is difficult to locate because of the depth of the blood vessel. It is recommended to locate the heart pulse on the internal face of the ankle. Once a clear heart pulse is located, the sensing element of the ultrasonic doppler flowmeter, covered with conductive gel, is taped on the limb over the region previously located. Measurements 1. The blood pressure monitor is left on during the test, recording the systolic and diastolic blood pressures of the patient every eight minutes. 2. The tourniquet cuff is rapidly inflated to a pressure of 200 mmHg and 250 nimHg in the case of upper and lower limb measurements respectively. 3. The tourniquet is then slowly deflated, by steps of 5 mmHg initially down to unity steps at about 50 mmHg above the systolic blood pressure of the patient. A muffled sound is heard via the headphones at the onset on bloodflow.The tourniquet system is then quickly re-inflated and a second measurement is taken for the occlusion pressure. 4. The cuff is fully deflated for a few minutes to allow blood to flow back in the limb. A second series of tests is run again. 5. The blood pressure of the patient is taken simultaneously with the onset of blood flow. 6. The tourniquet and blood pressure cuffs are removed from the limbs. The ultrasonic doppler flowmeter and the conductive gel are taken off the limb. 7. The circumference of the limb is taken at the proximal and distal edges of the cuff at the imprints left by the seams of the cuff.  209  Analysis 1. The ratio of cuff width over limb circumference is calculated for each occlusion pressure measurement taken. The occlusion pressure is divided by the diastolic blood pressure of the patient. 2. A graph of occlusion pressure over diastolic blood pressure as a function of the ratio of cuff width over limb circumference is generated.  C.5 Clinical Trials for Occlusion Pressure Measurements Preparation 1. The 19 cm wide tourniquet cuff bladder is checked for leaks prior to the tests. As the patient is waiting for the operation, the circumference of the concerned limb is measured. 2. As the patient is put under general anaesthesia, a soft bandage is wrapped two or three times around the upper limb. The bladder is wrapped over the bandage and is fixed in a snug manner with surgical tape. With Velcro attachments, a band of inextensible material covers the bladder to protect it and to limit its inflation. 3. The single inlet of the tourniquet bladder is connected to the tourniquet system (A. T. S. 500), pre-set at 200 mmHg. Operation 1. Pre-operative and operative blood pressure of the patient, taken by the anesthetist, is noted throughout the surgery. 2. The limb is elevated and exsanguinated and the surgery is carried out with the bladder inflated to a pressure of 200 mmHg. At the end of the procedure, while the surgical site is still open, the tourniquet system is slowly deflated by increment of 5 mmHg down to the systolic blood pressure and by increment of 1 mmHg until the orthopaedic surgeon notifies of thefirstappearance of blood in the surgical site. The pressure read off the tourniquet system is recorded as the occlusion pressure. 3. Simultaneously, the systolic and diastolic blood pressures are noted. 4. At the completion of the surgery, the tourniquet is removed from the limb. Analysis 1. The ratio of cuff width over limb circumference is calculated for each patient. 2. The occlusion pressure data are plotted versus the ratio. The ratio of occlusion data over diastolic pressure are also plotted against the ratio.  210  C.6 Exsanguination Tests Preparation 1. The volunteer is asked to lie down in order to carry on with the test. The blood pressure is then taken. 2. The standard 24" and 34" Aspen tourniquet cuffs are wrapped on the upper and lower extremities respectively. 3. The sensing element of the ultrasonic doppler flowmeter is taped on the brachial or femoral artery. Ultrasonic transmission gel is used for better clarity of the sound via the headphones. 4. The tourniquet system is turned on and set at 200 mmHg. Tests 1. The tourniquet cuff is inflated and the limb is lowered down to the horizontal position. 2. The pressure inside the bladder is slowly reduced until the ultrasound signals the onset of blood flow. 3. The limb is elevated for 5 minutes and procedures 1 and 2 are repeated. 4. A pneumatic sleeve is slid on the limb up to the distal edge of the tourniquet cuff. The sleeve is inflated up to 50 mmHg. The tourniquet is then inflated and the sleeve deflated. Procedures 1 and 2 are repeated. 5. The same sleeve is inflated up to 100 mmHg. The tourniquet is then inflated, the sleeve is deflated and procedures 1 and 2 are repeated. 6. With the limb elevated, an Esmarch bandage is wrapped around the limb up to the distal edge of the tourniquet cuff. The cuff is inflated, the limb is lowered, and procedures 1 and 2 are repeated. 7. The blood pressure of the volunteer is taken at the end of the test. 8. The circumference of the limb is measured at the location of the imprints left by the tourniquet. 9. Ratio of cuff width over limb circumference is calculated. 10. All plots of occlusion pressure versus ratio for each degree of exsanguination are superposed on the same graph.  211  C.7 Physical Evaluation of Standard Cuffs 1. The physical dimensions of the main tourniquet cuffs are measured with a Vernier Caliper. The tourniquets used are the single and dual 24" Freeman, the single, dual, and banana 24" Aspen. 2. The tourniquet cuffs are inflated to 200 mmHg with the tourniquet system and the width, length, and thickness of the cuffs are measured. 3. A full view of the tourniquet cuffs, inflated and non-inflated is drawn.  C.8 Snugness Tests Snugness Test (I) 1. The tourniquet is loosely applied on the skin so that three fingers can be inserted between the cuff and the limb. 2. The pneumatic pressure sensor is place underneath the cuff along the limb and is taped in position. 3. The surface pressure program is run for the tourniquet inflated at 100 mmHg, 200 mmHg, and 300 mmHg. 4. The tourniquet cuff is tightened up so that only two fingers can be inserted between the cuff and the limb. The program "data" is run to obtain the pressure distribution data across the width of the cuff for the three inflation cuff pressures. 5. The cuff is further tightened until one finger can barely be inserted between the cuff and the limb. The pressure profile is obtained for the three inflation cuff pressures. 6. All pressure profiles are superposed on the same graph to evaluate the transmission of pressure on the limb regarding the level of snugness of the cuff.  Snugness Test (II) 1. A child blood pressure cuff (Critikon #3) is used as a small controlling bladder to quantify snugness during the application of a tourniquet cuff on the limb. The Aspen tourniquet cuff is cut open in order to insert the Critikon bladder between the bladder and stiffener of the tourniquet cuff. The tourniquet cuff is temporarily closed with duct tape. 2. The child bladder is connected in series to a sphygmomanometer and a 60 cm3 syringe. 3. The cuff assembly is applied on the limb in a loose manner so that three fingers may be inserted between the cuff and the skin. Volumes of 15 cm3, 30 cm3, and 45 cm3 are subsequently injected in the Critikon bladder while the pressure is measured via the manometer. 4. The cuff is tightened up so that two fingers may be inserted between the skin and the cuff. The three tests at various air volumes are repeated.  212  5. The cuff is tightened to the maximum and the three tests are carried out. 6. A graph of air volume versus bladder pressure is generated for further references of cuff application.  APPENDIX D - THICK WALLED CYLINDER DERIVATIONS The radial soft tissue pressure distribution in a limb is analyzed by developing two limb models. The first model assumes that the limb is made of isotropic elastic soft tissues. The second model considers the limb to be made of orthotropic elastic material.  D.l Limb Made of Isotropic Material The internal soft tissue pressure are derived from the theory of elasticity. Generalized Hooke's law equations are applied to the isotropic material model (Figure 4.1). The strain equations in the radial, tangential, and longitudinal directions are the following: (1)  e = 1/E (a - DoO r  r  (2)  e = 1/E (-Or + at) t  (3)  e = 1/E (-ua - -ua ) z  r  t  From these equation of elasticity, the principal stress equations are obtained.: ZF = 0 r  (4)  O = E/( 1-1)2) (e + D£ ) R  r  t  (5)  c = E/(l-<D2)(a)e + e) t  r  t  The principal stress equations are used to solve the static equilibrium expression of the thick-walled cylinder. The sum of radial forces must vanish in order to have static equilibrium. The following equation describes static equilibrium: (6) doydr + [(c - a )/r] = 0 r  t  Equations (4) and (5) are substituted in (6): d/dr [E/(l--u2) (e+i)e)] + l/r[E/(l-a)2) (er+o)e) - E/(l-i)2) (\)e+e)] = 0 r  t  t  r  t  d/dr [(e+-ue)] + 1/r [(er+DeO - Cuer+eO] = 0 r  t  (7)  d/dr [(er+uet)] + 1/r [(l-u)(er-et)] = 0  213  In order to simplify the equation of equilibrium, the geometric compatibility equations are used. These equations describe the strain in the radial and tangential directions. (8) e = du/dr (9) r  Et  = u/r  The radial and tangential strains (8) and (9) are substituted in equation (7). d/dr (du/dr + x> u/r) + (l-\))/r (du/dr - u/r) = 0 (10) d2 /dr2 + 1/r du/dr - u/r2 = 0 u  The differential equation (10) is solved by assuming a solution. The soft tissue displacement solution and the derivative of the displacement are the following: (ID  u = Ai r + A2/r (12) du/dr = Ai - A2/r2 The constants Ai and A 2 are evaluated for plane stress and plane strain conditions. Plane stress condition: Ai = (1-D)/E [(P-Ri2 - PoRo )/(Ro2 - Ri2)] 2  A = (l+\))/E [(Pj - P ) Ri Ro / (Ro - Ri )] 2  2  2  2  2  0  Plane strain condition: Ai = (1+D)(1-2D)/E [(PjRi - PoRo )/(Ro - Ri )] 2  2  2  2  A = (1+U)/E [^ - P ) Ri2 RQ2 / (R 2 . 2 ) ] 2  0  0  Ri  These solutions are used to calculate the pressure drop from the surface to the bone of the limb. A new set of stress equations are obtained by substituting equations (11) and (12) in (4) and (5): (13) o = E/(l-i)2) [Ai - Ai/r2 + <o/r(Ai r + A /r)] r  2  (14) c = E/(l-i)2) [\)(Ai - A2/r) t  + l/r(Ai r + A2/r)]  The thick walled cylinder theory is used to calculate the radial pressure distribution from the surface of the limb to the bone-muscle interface. The displacement of the bone is equal to the displacement of the muscle at the interface radius.The internal pressure Pi  was calculated by the program "TK-Solver". An average limb was used for the solution in cases of plane stress and plane strain conditions. Since the muscle is attached to the bone, the internal pressure Pi may also be calculated by directly equating the displacement of the muscle and the displacement of the bone at the bone radius. The displacement of the muscle is described by the following equation: (15)  u  m  = {(1-D)/E [(P-Ri2 - PoRo2)/(Ro2-Ri2)]}r  + {(1+D)/E [(Pj - P ) Ri2 R 2 / (Ro - Ri2)]}/r 2  D  0  The displacement of the bone is described by the following equation: (16)  u = - RiPi(l-Db)/Eb b  For equilibrium, Ub = Um  (17) -Ri Pi (l--Ob)ZEb = {(1-D)/E [(P R 2-P R 2) / (R^-R^)]} i  i  0  0  + {(l+-o)/E[(P -Po)Ri2R 2/(R 2 - Ri2)]}/ 0  i  0  r  r  When r is set to Ri, the only unknown of this equation is Pi. (18) (l-D)P 2R 2/(Ri2-Ri2) + (1+D) P R 2/(R 2.R 2) 0  0  Q  0  i  0  Pl= E/E (Db-l) + (1-D) Ri2/(Ri2-Ro2) + (1+D) R 2/(R 2.R 2) b  0  i  0  The radial pressure may subsequendy be evaluated by knowing the two boundary pressure values at the surface of the limb and at the bone-muscle interface. The internal pressure was calculated with the "T-K Solver" program for the upper and lower limbs. Plane stress and plane strain conditions were considered.  D.2 Limb Made of Orthotropic Material A limb made of orthotropic material is now analyzed as the muscle run along the main axis of the limb. For such material, the Young's modulus is different in the longitudinal and the radial directions. The Young's modulus in the radial direction is similar to the one in the transverse direction. The generalized Hooke's law equations for an orthotropic material are the following:  215  (19) e = sn a + r  r  S12  a + i3 o" s  z  t  (20) £t = S12 O + S22 CT + S23 CT r  t  Z  (21) e = si3 a +  S23  r  z  where  cy + S33 a t  z  sn = 1/E  r  512 = -1)21^  513 = -Ul3/E 522  = 1/Et  523 = -D23/E S33  z  z  = 1/E  Z  These new equations of elasticity are used in the solution of the static equilibrium of the material in the radial direction. The program "T-K Solver" was used to obtain the solutions for plane stress and plane strain conditions for the upper limb.  APPENDIX E - C O L L A P S I B L E T U B E D E R I V A T I O N The solution of the critical load of a collapsible tube is derived from the principle of conservation of energy. The elastic energy stored in the deformed body is equal to the work done by a pinching force on the body itself. Explicitly, (1) W=U (2) W = PAA E . l Work Done Figure C l is an element of the tube stretched so that its original circular shape becomes an ellipse. The change in area is equal to: (3)  AA = 1/2 J  2 l t  (r +u)2 d9 - 1/2 J G  2 n  r 2 d9 Q  In order to evaluate the integral, the expression for the deformation u must be obtained. The expression of the displacement is assumed. u = -u cos 20 + a 0  (4)  216  The displacement is derived as a function of the angle 0. (5)  du/d0 = u' = 2u sin 20 0  (6) d2 = u'2 d20 u  The constant a is determined by the change in length in the tube. The change of length of the element is equal to the following: (7) A S = QJ  2  R  T  ( C D - A B )  Where  (8) = r d0  A B  G  (9)  CD2 = CE2 + ED2  (10)  CD2 = (r +u)2 d20 + d u 2  0  (11)  CD2 = [(r +u)2 + u'2] d20 D  (12)  CD = V [ r + 2r u + u2 + u'2] d0 2  0  G  CD = r V [1 + 2u/r + (u +u'2)/2r 2] d0 2  Q  Q  (13)  0  The substitution of V 1 + e by 1 + e/2 - £2/8 lead to the following expression: (14) CD = r [1 + u/r + (u2 + u'2)/r 2 - 1/8 (2u/r )2] d0 0  0  0  0  The change of length of the element simplifies to the following expression: (15)  AS = oJ P (u + u'2/2ro) d0 2  When the tube shape remains circular, there is no change in length. In such case, AS = 0. This is the way the constant a of the displacement is evaluated. (16) 0J2p [(_ os 20 + a) + (4u /2r ) sin2 20)] d0 = 0 2  Uo C  where  0  a = -u /r  0  2  0  0  The displacement u is expressed as follows: (17) u = -UQ cos 20 - u /ro 2  0  217  The displacement is substituted in the expression for the change in area to give the following result: (18) AA = -3K U /2 2  q  From the change in area, the expression for the work done is evaluated. (19)  = P AA  W  W = -3TT.U  2 0  oi  (20)  L / 2  P(x)dx  E.2 Stored Elastic Energy The elastic energy stored in an inextensible ring (Figure E.2) is derived from the principle of Rayleigh deformation [60]. The general expression for the stored energy reads as follows: (21) dU = dA/2E [c  2 x  + Oy - 2D a a + 2(1+D)a ] 2  2  x  y  s  For a plane stress problem, the shear stress vanishes (as = 0). The equation for the elastic stored energy becomes  dU =  EdVOL  (22) (ei + £2 + 2D ei £2) 2  2  2(1-1)2)  The strains describe the increase in curvature and thickness of the tube. Explicitly, (23) ei = -3 u /r 0  2 0  cos (20) y (24)  e = A//(R a ) 2  Q  0  (25) e2 = ib <Po/(Ro oto) cos 0 - u /Ro cos30 0  The change in volume is evaluated by the change in radius and the change in length of the ring, noting that L = RQ a . 0  (26) U = 3 Tt E/8 (1-0)2) u  2 G  h3 L/r 3 0  218 E.3 Critical Load The work done on the ring and the stored elastic energy are used to derive the critical load. For static equilibrium: (27) W=U (28) -3K U o I P(x) dx = [3K E / 8(1-t>)] u h3 L/r 3 2  172  2  2  0  0  [3 7tE/8(l-u )] uo h3L/r 3 2  0J  1 7 2  P (x) dx =  - J P(x)dx= L/2  0  (29)  2  0  -3 K u  2 0  (30)  Eh3L  0  8 (l-\> ) r 3 2  0  The critical load is obtained by integration of this expression over half the width of the beam.  Figure E.l Segment of a Ring Distorted to an Ellipse from a Circle (from J. P. Den Hartog, Advanced Strength of Materials, McGraw-Hill Book Co., New York, 279, 1952)  Figure E.2 Inextensible Ring Deformation (from J. P. Den Hartog, Advanced Strength of Materials. McGraw-Hill Book Co.. New York, 235, 1952)  220  APPENDIX F - B E A M DEFLECTION SOLUTIONS The relationship between occlusion pressure and cuff width is derived from the theory of elasticity. The artery is modelled by a thin walled pressure vessel. The compression of the artery by external load cause the hoop stresses in the wall to be negligible. For this reason, one strip of the artery is represented by a flexible beam. The occlusion pressure is defined as the necessary external load applied on the beam to force a deflection equivalent to the internal radius of the artery. The beam element located at the top of the artery is considered. Let the half cuff width be /, and the internal radius of the artery r. The beam element has the following dimensions: b in width, h in thickness, and L in length. Let /' be the difference between the beam length and the half cuff width. The internal pressure Pi in the artery is represented by a continuous load of constant value distributed over the bottom of the entire beam. The external cuff compression on the artery is represented by a continuous load co(x), function of the length, applied on top of the beam over a length equal the half cuff width. From the beam deflection theory, (1) EId4y/dx4 = G)(x) (2) where I = 1/12 bh3 I is the moment of inertia per unit width (b=l) of the artery and E is the Young's modulus. Four boundary conditions are applied to the beam: (3)  @x = 0, y = 0, (4)  @ x = 0, dy/dx = 0, @ x = L, dy/dx = 0,  (5) (6)  @ x = L, d3y/dx3 = V = 0, where V is the shear stress. The first equation (1) is integrated fourtimesin order to obtain the desired beam deflection expression. All integration constants are solved by applying the boundary conditions. By principle of superposition, the deflection caused by the external and internal loads are added to give the resulting deflection. The deflection equations are derived in two parts. The first part considers the loads applied on top of the beam. The second part considers the load applied against the bottom of the beam.  F . l Deflection due to Internal Pressure The internal pressure in the section of the artery lying beneath the tourniquet cuff is assumed to be constant. A constant load Pi applied against the bottom of the beam element.  221 (7)  EI rJ4y/dx4 = co(x) = Pi Equation (7) is integrated once and the constant of integration is determined by applying boundary condition (6). (8)  EI d3y/dx3 = Pi x + C i Ci  = -PiL  Equation (8) is now integrated before applying the boundary conditions (4) and (5). (9)  EI d2y/dx2 = Pj ( 2/2) - Pi L x + C 2 x  (10)  EI dy/dx - Pi (x3/6) - Pi L (x2/2) + C2 x + C 3 C  2  = PiL2/3 C  3  = 0  A last integration of equation (10) with boundary condition (3) gives the final beam deflection equation. (11)  EI y(x) = Pi (x4/24) - Pi L ( 3/6) + Pi L2/3 (x2/2) + C X  C  4  4  = 0  The maximum deflection of the beam caused by internal load is obtained by rearranging equation (11) and evaluating it for x = L. (12)  y(x) = [Pi/(24 EI)] (x4 - 4L x3 + 4L2 2) x  (13)  y(L) = PiL4/ (24 EI)  F.2 Deflection due to External Load An external load is now applied on top of the beam over a length equal to the cuff half width /. For the case of the standard tourniquet cuffs, the external pressure applied on the limb was experimentally determined to be of parabolic profile. Four functions are used to model the parabolic load distribution: (a) (b) (c) (d)  A constant load distribution equivalent to the applied cuff pressure (P ); A linear ramp relationship where the peak load is equal to 98% of the inflation cuff pressure; A cosine function using two terms; and A Taylor's series expansion using six terms. c  222  Case (a) A constant load, P , is applied on the beam. The beam deflection solution is similar to the one derived on part A. The basic equation for beam deflection theory with the constant external load is expressed as follows: (14) c  EId4y/dx = -Pc<x-/'>0 4  The Macauley's brackets are used to set the external load to 0 anywhere along /'. The Macauley's brackets change the value of the right side of the equation as follows: if x < /' then EI d4y/dx4 = 0 if x > /' then EI d4y/dx4 = -P (x - /')0 c  Successive integrations lead to the following expression: (15) EI y(x) = - P <x-/'>4 /24 + Ci x3/6 + C xV2 + C 3 x + C 4 c  where  2  Ci = P (L-/') c  C = P t(L-/')/L] [(L-/')2/6 - L2/2)] 2  c  C =C =0 3  4  (16) y(x) = - P /EI {<x-/'>4 /24 - (L-/')x3/6 - [(L-/')3/6L - (L-/')L/2)]2/2 } C  X  Equation (16) is evaluated at x = L and the bracket (L-f) is replaced by /. (17) y(L) = - [P /(24 EI)] (/4 + 2 / L3 - 2 / 3L) c  Case (b) To model the cuff pressure profile in a better way, the external load applied on the beam is expressed by a linear ramp profile. It is assumed that the peak pressure delivered to the limb is 98% of the cuff inflation pressure. The beam deflection equation is the following: (18) EI d4y/dx4 = - 0.98 P <x-/'>V(L-/') c  Successive integrations of equation (18) leads to the desired beam deflection expression: (19) y(x) = 1/EI{ - 0.98 P <x-/'>5/120 (L-/') + Ci x3/6 + C x2/2 + C 3 x + C 4 } c  2  223  where  C = 0.98 P (L-/')/2 x  c  C = 0.98 P [(L-/')3/(24L) - (L-/')L/4 ] 2  c  C =C = 0 3  4  Equation (19) is evaluated at x = L and the bracket (L-/') is replaced by/. (20) y(L) = - [0.98 P /(24 EI)] (/4/5 + IV> -13L/2) c  Case (c) A more accurate solution is obtained by expressing the parabolic external load by a periodic cosine function. A curve fitting program (DS-CS) was used to obtain mathematical expressions for the experimental pressure data. The program translated the periodic function to a Fourier series. The experimental pressure data from McLaren et al. and the pressure data obtained in this project were curve fitted. Both sets of pressure data were obtained by using a cuff of width 8.5 cm. The following expressions for the external load were obtained: From McLaren et al.:  (21)  P/P = 0.6367 - 0.3582 cos(coz) - 0.0666 cos(2coz) c  From present data:  (22) P/P = 0.7035 - 0.2802 cos(coz) - 0.0706 cos(2coz) c  co = K 11 z = <x - /'>  where  Only two terms of the mathematical expression derived from McLaren's pressure data, equation (21) are used in this case although three terms will be used in the following case (case d). (23) P/P = 0.6367 - 0.3582 cos(coz) c  The problem is solved by separating the pressure profile in an offset and main parts. (24) P/P =[P/P ]i + [P/P ]2 c  The offset part:  c  c  (25) [P/Pch = 0.2785 The main part: [P/P]2 = 0.6367 - 0.3582 cos(coz) - 0.2785 c  (26)  224  (27)  [P/P]2 = - 0.3582 [cos(coz) - 1] c  The basic equation for the beam is therefore solved in two parts. The deflections from these parts are superposed to give the resultant deflection. Part (1):  (28) EId4y/dx4 = - 0.2785 P  c  Part (2):  (29) EI d4y/dx4 = 0.3582 P [1 - cos(coz)] c  The offset equation (28) of the first part of the problem is solved like the problem in case (a). The following result is obtained: (30) y(L) = - [0.2785 P /(24 EI)] (/4 + 2 / L3 - 2 /3 L) c  The equation of the bell curve (29) in the second part of the solution is integrated successively. The four constants of integration were evaluated by the boundary conditions. (31) Ely(x) = 0.3582 [(L-/')4/7x4cos(coz)-x4/24] + Ci x3/6 + C x2/2 + C 3 X + C4 2  where  Ci = 0.3582 P L C  C = - 0.3582 P L2/3 2  c  C= 0 3  C = - 0.3582 P (L-/')4/TU4 4  c  The solution is evaluated for x = L, where L = / + /'. The resulting equation is the following: (32) y(L) = - [0.3582 P /(24EI)] (48 /4/TC4 + L4) C  The final solution for the periodic cosine equation is the sum of the offset solution and the bell curve solution. Combining (30) and (32), we obtain the following expression: (33) y(L) = - [0.2785 P /(24EI)] (/4 + 2 / L3 - 2/3 L) C  - [0.3582 P /(24EI)] (48 IW + LA) C  (34) y(L) = - [P /(24EI)] [0.2785 (/4 + 2 / L3 - 2/3 L) C  225  + 0.3582 (48 / /7t4 + L-4)] 4  Case (d) This solution replaces the cosine function by an expansion series of Taylor. (35) cos x = 1 - x2/2! + x4/4! - 6/6! + x8/8! - xl0/10! X  The use of the Taylor's series eliminates the Macauley's bracket. Six terms are used to closely approximate the actual cosine function. Although the pressure profiles of McLaren and of this research are used to solve the deflection, a basic 98% cosine curve is used in the following derivation for simplicity. (36) EId4y/dx4 = -0.49P <X-/'>0{1 - cos[7l(x-/')/(L-/')]} C  Substituting the Taylor series in equation the previous equation:  (37)  EI d4y/dx4 = - 0.49P {1-[1- co22/2 + co4 4/24 - co66/720 + C  z  z  z  co88/40320 - coiOiO/3628800]} z  where  z  co = nil = <x - /'> Z  (38) EI d4y/dx4 = - 0.49P { Cfl2 2/2 - Co4 4/24 + Co6 6/720 C  Z  Z  Z  co88/40320 + colOlO/3628800]} Z  z  Equation (38) is solved for x = L and L = /+/' . The evaluation of the constants of integration was evaluated by a computer. In this case the beam deflection equation is: (39) y(L) = - [0.49 P /(24 EI)] [a /4 + b /L3 - c /3L] c  where  a = 7i2/30 -7t4/l680 + 7x6/151200 = 0.28 b = 7x2/3 - 7x4/60 + 7x6/2520 = 2.05 c = 7x2/10 + 7x4/420 - 7x6/30240 = -1.19  The beam deflection for McLaren's pressure profile (21) and the one obtained experimentally (22) were solved with the PC program "TK-Solver".  F.3 Superposition of Deflections The resulting deflection of the beam is determined by the superposition of external and internal loads. The internal load was constant for all cases. Equation (13) represents the beam deflection caused by the internal pressure. The main deflection equation for the beam is the sum of equation (13) and successively of equations (17),(20),(34), and (39) for the constant, linear, parabolic, and cosine external loads respectively. The deflections obtained are the following: (40) y(L) = [1/(24 EI] [Pi L4)] - [C P /H] c  where C is a constant and H is a function of / and L for a particular external load distribution. Constant load:  (41) y(L) = [1/(24 EI)] [Pi L4 - P (14 + 2 / L3 - 2 /3 L) c  Linear ramp load:  (42)  y(L) = [1/(24 EI)] [Pi L4 - 0.98 P (14/5 + / L3 - /3 L/2)] c  Parabolic load (cosine function):  (43)  y(L) = [1/(24 EI)] {Pi L4 - P [0.2785 (/4 + 2 / L3 - 2 /3 L) c  + 0.3582 (48 /4/7T.4 + L4)] } Parabolic load (Taylor expansion series):  (44)  y(L) = [1(24 EI)] [Pi L4 - 0.49 P (a /4 + b / L3 - c /3 L)] c  where  a = 7t2/30 - 7t4/1680 + 7T.6/151200 = 0.28 b = 7i2/3 - 7x4/60 + 7t6/2520 = 2.05 c = 7x2/10 + 7x4/420 - 7x6/30240 = -1.19  227  APPENDIX G - CUFF DRAWINGS  Figure G. 1 Sketch of the 24" Freeman Cuff - All Measurements in cm  0.5  5 .67.0.  •L  ±  II"  1.0  —IL—o.  n.o  1.0  0.5  9.2  5 0.5 67.0.  ••3.5 *  Scale 1 : 3.9 Figure G.2 Sketch of the 24" Dual Freeman Cuff  

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