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Human microvascular exchange following thermal injury a mathematical model of fluid resuscitation Ampratwum, Regina Twumwaa 1993

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HUMAN MICROVASCULAR EXCHANGE FOLLOWING THERMAL INJURYA MATHEMATICAL MODEL OF FLUID RESUSCITATIONbyREGINA TWUMWAA AMPRATWLJMB.Eng. (Chemical Engineering) University College London, United KingdomA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESCHEMICAL ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIADecember 1993© Regina Twumwaa Ampratwum, 1993In presenting this thesis in partial flulfiliment of the requirements for an advanced degree atthe University of British Columbia, I agree that the Library shall make it freely availablefor reference and study. I further agree that permission for extensive copying of this thesisfor scholarly purposes may be granted by the head of my department or by his or herrepresentatives. It is understood that copying or publication of this thesis for financial gainshall not be allowed without my written permission.Department of Chemical EngineeringThe University of British ColumbiaVancouver, CanadaDate:7 kccbG 19AB STRACTA dynamic model is developed to describe the redistribution of fluid and albumin betweenthe human circulation, interstitium and lymphatics following burn injury. The model isbased on the assumption that the human microvascular exchange system (MVES) consistsof three compartments, the circulation, injured tissue and uninjured tissue compartments,in which the spatial distribution of fluid and albumin properties are homogeneous.Transcapillary exchange in the MVES is described by the Coupled Starling Model (CSM)where fluid is filtered from the capillary to the interstitium according to Starling’sHypothesis and albumin is transported passively by diffusion and convection through thesame fluid-carrying channels.The parameters necessary to frilly describe the model are determined by statistical fittingof model predictions with clinical data from bum patients. The parameters include theperturbation to the filtration coefficient in uninjured and injured tissue, GkFTI and GkFBTrespectively; the relaxation coefficient, r, which describes the time it takes for the transportcoefficients to return to near-normal values following injury, and the exudation factor,EXFAC, which determines the fraction of the interstitial protein concentration whichleaves with exudate from the burn wound. Perturbations to other parameters including thepermeability coefficient and the albumin reflection coefficient, in the injured and uninjuredtissues are obtained from G,TJ and GkFBT, utilizing relationships between all three typesof parameters and capillary pore size.Parameters are determined for two groups of burns: burns less than and greater than 25%surface area. The optimum parameters for burns less than 25% surface area are: GTJ =0.5, GkFBT = 12.0, r = 0.025 h4 and EXFAC = 1.0. For burns greater than 25%, theoptimum parameters are: = 2.0, GkFBT 9.0, r = 0.025 h-’ and EXFAC = 0.75. The11sensitivity of the model predictions to changes in and GkFBT for the two burngroups are investigated. For burns less than 25%, GkFTI and GkFBT values beyond theranges 0.5±0.1 and 12.0±3.0 respectively will significantly affect the model’s predictions.The model predictions will be insensitive to GiTI and GkFBT values in the ranges 2.0±0.8and 9.0±3.0 respectively for burns larger than 25% surface area.The model and its associated parameters are validated by comparing the predictions ofpatient responses to fluid resuscitation, to the clinical data obtained from these patients.The predicted response of the MVES is in generally good agreement with the observedtrends and the absolute values of fluid volume and albumin concentration. The model isalso used to simulate the response of a hypothetical individual to three commonresuscitation formulae, namely the Evans, Brooke and Parkiand formulae, following twoburn sizes, 10% and 50%. The simulated responses are explained in terms of the transportmechanisms, driving forces and perturbations to the transport coefficients following burninjury. The predictions of the model compare satisfactorily with known clinical behaviourof the human MVES with and without fluid resuscitation. This establishes the potential ofthe patient simulator developed in the current study to be used as a tool for fluidmanagement of burn patients. The effects of different resuscitation formulae can becompared to suggest possible improvements.As more reliable clinical data become available, all of the essential model parameters canbe more definitely determined. In addition, one significant improvement that may be madeto the model is the inclusion of cellular compartments. It is expected that, with moreaccurate parameters and an improved physiological basis, the usefulness of themathematical burn patient simulator will be enhanced considerably.111Table of ContentsAbstractTable of Contents ivList of Tables ixList of Figures xiiiAcknowledgment xvi1 Introduction 12 Physiological Overview 62.1 Introduction 62.2 The Circulatory System 62.2.1 Description of the Circulatory System 62.2.2 Composition and Properties of Blood 102.3 The Microvascular Exchange System 112.3.1 Description of the Microvascular Exchange System 112.4 The Interstitium 152.4.1 Structure and Composition of the Interstitium 152.4.2 Physicochemical Properties of the Interstitium Turnover of Interstitial Plasma Proteins Interstitial Volume Exclusion 17iv2.4.2.3 Interstitial Compliance 172.5TheSkin 182.5.1 Anatomy and Function of Skin 182.6 Transcapillary Exchange 222.6.1 Capillary Filtration 222.6.2 Combined Convective and Diffusive Solute Transport 232.7 Physiological Changes Following Injury 232.7.1 Damage to Skin 242.7.2 Changes to the Microvascular Exchange System Transcapillary Exchange in Injured Tissue Transcapillary Exchange in Uninjured Tissue Systemic Hemodynamic Changes 312.8 Fluid Resuscitation 312.8.1 Isotonic Crystalloid Fluid Resuscitation 322.8.2 Hypertonic Crystalloid Fluid Resuscitation 332.8.3 Colloid Fluid Resuscitation 332.9 Summary 343 Computer Modelling of the Microvascular Exchange System 363.1 Introduction 363.2 Modelling ofNormal MVES 383.3 Modelling of MVES Following Burn Injury 404 Model Formulation 454.1 Introduction 454.2 Basic Assumptions 464.3 Fluid and Protein Input 50V4.4 Fluid and Protein Output 504.4.1 Water Loss by Evaporation 514.4.2 Fluid Loss by Exudation 514.4.3 Protein Loss via Exudate 524.4.4 Blood Loss 534.5 Model Equations 534.6 Properties of the Microvascular Exchange System 544.6.1 Normal Steady-State Conditions 554.6.2 Initial Conditions 564.6.3 Compliance Relationships 574.6.3.1 Circulatory Compliance 574.6.3.2 Interstitial Compliance 574.6.4 Colloid Osmotic Pressure (COP) Relationship 594.6.5 Transport Coefficients 604.7 Numerical Solution of Model Equations 645 Parameter Estimation 655.1 Introduction 655.2 Parameters to be Determined 655.3 Clinical Data 675.3.1 National Burn Centre (NBC) Data 675.3.2 Birkeland Data 685.3.3 Arturson Data 695.3.4RoaData 695.3.5 Normalization of Data 695.4 Parameter Estimation Procedure 705.4.1 Preliminary Tests 71vi5.4.2 Constraints 785.4.3 Modified Optimization Strategy 805.4.3.1 Re-assessment of Parameters to be Determined 805.4.3.2 Optimization Scheme: “Gridding Approach” 815.5 Summary 826 Results and Discussion 836.1 Introduction 836.2 Estimated Parameters 836.2.1 Parameters Determined Using NBC Data 836.2.2 Parameters Determined Using Birkeland Data 856.2.3 Parameters Determined Using Combination ofNBC andBirkeland Data 866.2.4 Summary of Parameters 886.3 Sensitivity Analyses 916.3.1 Sensitivity Analysis of GkFTI 916.3.2 Sensitivity Analysis of GkFBT 946.3.3 Sensitivity Analyses of EXFAC and r 956.4 Validation ofModel Predictions 966.4.1 Partial Validation 966.4.1.1NBCData 966.4.1.2 Birkeland’s Data 1026.4.2 Independent Validation 1046.4.2.1 Arturson’s Patient Data 1046.4.2.2 Roa’s Patient Data 1066.5 Simulation of Fluid Resuscitation According to Different Formulae 1086.5.1 Simulations of 10% Burn 109vi’6.5.2 Simulations of 50% Burn 1176.5.3 Simulations by Other Authors 1236.6 Summary 1257 Conclusions and Recommendations 1267.1 Conclusions 1267.2 Recommendations 129Nomenclature 131References 135Appendices 143A Interstitial Fluid Distribution 144B Transport Parameters 145B. 1 Normal Transport Parameters for “Reference Man” 145B.2Transport Coefficients Following Burn Injury 146C NBC Patient Data 150D Estimation ofPlasma Volume from Hematocrit Data 166E Estimation of Exudation Rate Based on NBC Patient Data 170F Birkeland’s Patient Data 174G Determination ofExudation Rate for Birkeland’s Patients 177H Clinical Data from Arturson’s Patient 179I Clinical Data from Roa’s Patients 1813 Minimum Objective Function Value Results 188K Computer Program Listing 198viiiList of Tables2.1 Classification of Blood Vessels 142.2 Mathematical Description of Human Interstitial Compliance Relationship 202.3 Burn Depth Classifications 272.4 Changes to Injured Tissue MVES Properties Following Burn Injury 294.1 Normal Steady-State Conditions in “Reference Man” 555.1 Factorial Experiment Study 816.1 Optimum Parameters Determined Using NBC Data 846.2 Optimum Parameters for Two Burn Groups Using NBC Data 856.3 Optimum Parameters Determined Using Birkeland Data 856.4 Optimum Parameters for Two Burn Groups Using Birkeland Data 866.5 Optimum Parameter Values for Burns Less Than 25% 876.6 Optimum Parameter Values for Burns Greater Than 25% 876.7 Coupled Starling Model Parameters 896.8 Common Fluid Resuscitation Formulae 109A. I Interstitial Fluid Distribution in the “Reference Man” 144C. 1 Admission and Laboratory Data for NBC Patient 1 156C.2Fluid Inputs and Outputs for NBC Patient 1 157C.3 Admission and Laboratory Data for NBC Patient 2 158C.4FIuid Inputs and Outputs for NBC Patient 2 159ixC.5Admission and Laboratory Data for NBC Patient 3 160C.6FJuid Inputs and Outputs for NBC Patient 3 161C.7Admission and Laboratory Data for NBC Patient 4 162C.8Fluid Inputs and Outputs for NBC Patient 4 163C.9Admission and Laboratory Data for NBC Patient 5 164C. 10 Fluid Inputs and Outputs for NBC Patient 5 165D. 1 Normal Values for 70-kg, 170-cm Individual 166F. I Grouping ofBirkeland’s Patients 174F.2 Plasma Volume Data (mL) for Groups ofBirkeland’s Patients 176G. 1 Area of Burn and Exudation Rate Postburn 177H. 1 Erythrocyte Volume Fraction Data from Birkeland’s Patient 179H.2 Fluid Inputs and Outputs to Birkeland’s Patient 1801.1 Personal Data from Roa’s Patients 1811.2 Fluid Input and Output for Roa Patient 1 1821.3 Fluid Input and Output for Roa Patient 2 1841.4 Monitored Clinical Data for Roa Patient 1 1861.5 Monitored Clinical Data for Roa Patient 2 187J. 1 Minimum OBJFUN Values for NBC Patient I Based on 12 Data Points 188J.2 Minimum OBJFUN Values for NBC Patient 2 Based on 20 Data Points 188J.3 Minimum OBJFUN Values for NBC Patient 3 Based on 22 Data Points 189J.4 Minimum OBJFUN Values for NBC Patient 4 Based on 21 Data Points 189xJ.5 Minimum OBJFUN Values for NBC Patient 5 Based on 30 Data Points 190J.6 Minimum OBJFUN Values for Combination ofNBC Patients 2, 3, 4 and 5(Degree of Burn Greater Than 25%) 190J.7 Minimum OBJFUN Values for Birkeland Burn Group I Based on 6 DataPoints 191J.8 Minimum OBJFUN Values for Birkeland Burn Group II Based on 6 DataPoints 191J.9 Minimum OBJFUN Values for Birkeland Burn Group III Based on 5Data Points 192J. 10 Minimum OBJFUN Values for Birkeland Burn Group IV Based on 4Data Points 192J. 11 Minimum OBJFUN Values for Birkeland Burn Group V Based on 4Data Points 193J. 12 Minimum OBJFUN Values for Combination ofBirkeland Burn GroupsI and II (Degree of Burn Less Than 25%) 193J. 13 Minimum OBJFUN Values for Combination of Birkeland Burn GroupsIII, IV and V (Degree of Burn Greater Than 25%) 194J. 14 Minimum OBJFUN Values for Combination ofNBC and BirkelandData for Burns Less Than 25% for Factor of 30 194J.15 Minimum OBJFUN Values for Combination of NBC and BirkelandData for Burns Greater Than 25% for Factor of 30 195J. 16 Minimum OBJFUN Values for Combination ofNBC and BirkelandData for Burns Less Than 25% for Factor of 100 195J. 17 Minimum ()BJFIJN Values for Combination ofNBC and BirkelandData for Burns Greater Than 25% for Factor of 100 196J. 18 Minimum OBJFUN Values for Combination ofNBC and BirkelandData for Burns Less Than 25% for Factor of 200 196xiJ. 19 Minimum OBJFUN Values for Combination ofNBC and BirkelandData for Burns Greater Than 25% for Factor of 200 197xliList ofFigures2.1 Human Circulatory System 82.2 Lymphatic and Blood Vessels in Area of Bat Wing 92.3 Human Microcirculation 122.4 Tissue Hydrostatic Pressure as a Function of Interstitial Fluid Volumefor Skeletal Muscle and Skin in Rat 192.5 Structure ofNormal Skin Showing the Categorization of Burn Injury 212.6 Rule ofNines for Burn Estimate 252.7 Lund-Browder Chart for Burn Estimate: Percentage ofBody Area 264.1 Schematic of Compartmental Burn Model 475.1 Simulation ofMVES for NBC Patient 1: Gk = 0.5; GkFBT = 10.0;r= 0.025 Ir’; EXFAC = 1.0 725.2 Steady-State Simulation of MVES for NBC Patient 1: GkFTI = 0.5;= 10.0; r = 0.025 h’; EXFAC = 1.0 745.3 Model Predicted Response of MVES and “Error-free” Data for NBCPatient 1 765.4 Model Predicted Response of MVES and “Noisy” Data for NBC Patient 1 775.5 Objective Function Surface for NBC Patient 1: GkFTJ = 0.5; GkFBT = 10.0;r 0.025 fr1;EXFAC= 1.0 796.1 Sensitivity Plots for Burns Less Than 25% 926.2 Sensitivity Plots for Burns Greater Than 25% 936.3 Simulation ofMVES for NBC Patient 1 Using Global Model Parameters 97Xlii6.4 Simulation ofMVES for NBC Patient 2 Using Global Model Parameters 986.5 Simulation ofMVES for NBC Patient 3 Using Global Model Parameters 996.6 Simulation of MVES for NBC Patient 4 Using Global Model Parameters 1006.7 Simulation of MVES for NBC Patient 5 Using Global Model Parameters 1016.8 Simulation of MVES for Birkeland Patient Groups Using Global ModelParameters 1036.9 Simulation of MVES for Arturson’s Patient Using Global Model Parameters 1056.10 Simulation ofMVES for Roa’s Patients Using Global Model Parameters 1076.11 Simulation ofMVES with no Fluid Resuscitation Following a 10% Burn 1106.12 Simulation ofMVES According to Evans’ Formula Following a 10%Burn 1116.13 Simulation of MVES According to Brooke’s Formula Following a10%Burn 1126.14 Simulation of MVES According to Parkland’s Formula Following a10% Burn 1136.15 Simulation of MVES with no Fluid Resuscitation Following a 50%Burn 1186.16 Simulation of MVES According to Evans’ Formula Following a 50%Burn 1196.17 Simulation of MVES According to Brooke’s Formula Following a 50%Burn 1206.18 Simulation of MVES According to Parkland’s Formula Following a 50%Burn 121C.1NBC Patient 1 Data Sheet 151C.2NBC Patient 2 Data Sheet 152C.3NBC Patient 3 Data Sheet 153xivC.4NBC Patient 4 Data Sheet 154C.5NBC Patient 5 Data Sheet 155E. 1 Exudation Relationship Based on NBC Patient Data 173F. 1 Patient Blood and Plasma Volume Observations on Admission and Priorto Start of Fluid Therapy by Birkeland 175G. 1 Exudation Relationship Based on Davies’ Patient Data 178xvAcknowledgmentThe financial support of the Natural Sciences and Engineering Research Council ofCanada and the British Columbia Health Research Foundation is gratefhlly acknowledged.My sincere thanks also go to:• my supervisors, Drs. J.L. Bert and B.D. Bowen, for the opportunity to conduct thisstudy and for their guidance during the past 2 years;• Drs. T. Lund and R.K. Reed of the University of Bergen in Norway, for the clinicaldata and the benefit of their professional expertise;• Dr. J. Boyle, Ms. T. Staley and all the members of the burn-care team at theVancouver General Hospital, for the opportunity to visit the unit and to join thepatient rounds;• Mr. T. Nicol, for his assistance with computing difficulties;• friends and colleagues;• my family, for their love and continued support over the years; and• Paa Bissue (Sam), thank you for your love and patience and for being that very specialpart of me. This one is for you.xviChapter 1: Introduction 1CHAPTER 1INTRODUCTIONBurns are a major cause of traumatic injury in all ages of the population. There are manycauses of burns and they occur in a variety of settings including the home and theworkplace. It has been reported that the majority of burn accidents occur in the home,predominantly in the kitchen and the bathroom [Martyn, 1990; McLaughlin, 19901. Burnsare caused by such activities as cooking, bathing or smoking. Younger children usuallysuffer scald or grease burns when they pull the handles of pots on the stove, knock overhot foods on the table or play with hot water in the bathtub. An unfortunate reality is thatsome children are burned due to child abuse. Sources of burn injuries include flame,electrical, chemical and radiation [Harvey et al., 19841. Flame burns are commonly causedby ignited clothing or a flash from an explosion. Electrical burns are not as common asflame burns but may be more serious due to injury to deeper structures of the body.Chemical burns are uncommon and can be caused by an acid or an alkali. They are usuallyrelated to industrial accidents. Extreme exposure to nuclear or solar radiation causes burnsof varying severity.The most immediate and clear evidence of burn injury is damage or destruction to the skin.However, burns affect more than just the skin and can be fatal. The state of homeostasismaintained in the body is also greatly affected following burn injury. There is a rapid shiftof fluid from the circulating plasma into the interstitium, resulting in the accumulation offluid in the interstitial space. This leads to drastic swelling of the tissue or edema, of suchmagnitude as to distort body features. The loss of plasma results in an abnormally lowcirculating blood volume, a condition known as hypovolemia. Fluid replacement isChapter 1: Introduction 2therefore essential in replenishing the lost plasma volume, to avoid the possibility ofhypovolemic shock. Approximately thirty years ago, the majority of patients withextensive burns died from hypovolemic shock within the first week following their injuriesdue to failure of the whole circulatory system [Rylah, 1992]. Today, adoption of thepractice of prompt and aggressive fluid resuscitation of the burn victim has resulted in thesurvival of more patients with severe injury. Consequently, early death can usually beprevented in previously healthy individuals and is only common in patients with near totalbody surface burns, or in those of advanced age or with major concurrent chronic disease.Numerous resuscitation formulae have been developed to restore lost body fluid volumesand organ blood flows [Evans et al., 1952; Gillespie et al., 1987; Reiss et al., 1953]. Theseformulae differ in terms of the amount of colloid or electrolyte solution given and the rateand duration of their administration to stabilize the burned and hypovolemic individual,considering the size of the injury and the time postburn. The fluid resuscitationprogrammes are intended merely as guidelines and are continually adjusted according tothe response of individual patients. The empirical formulae for fluid resuscitation may beconsidered as simplistic models using a “black box” approach, where all the circulatoryand interstitial changes are contained within the “black box”, leaving only the fluid inputsand outputs as the manipulated variables. As such, they do not describe thepathophysiological mechanisms which occur following burn injury.Burn injuries result in complex perturbations to the normal transcapillary transport of fluidand proteins in the human microvascular exchange system (MVES). In the human MVES,fluid and proteins are exchanged between the circulatory system, interstitium and thelymphatics. Consequently, a complete quantitative description of edema formationfollowing a burn injury requires detailed knowledge of a large number of variablesdescribing the normal transcapillary exchange of fluid and proteins as well as the changesChapter 1: Introduction 3in these variables following injury. Mathematical modelling has been used to facilitateunderstanding of the dynamic behaviour and pathophysiology of a burn injury. Elaboratemodels have been developed based on detailed mathematical descriptions of fluid andprotein transport across the capillary membrane [Arturson et al., 1984, 1988, 1989; Bertet al., 1988, 1989, 1991; Hedlund et al., 1988; Roa et al., 1986, 1988, 1990, 1993]. Thepotential advantages of these models are manifold. They provide a description of the timecourse of changes in fluid volumes and protein concentrations in the blood and varioustissues in the human MVES. These models can be used to validate and hence predict thereaction of the MVES to different empirical resuscitation protocols following a burninjury. Ultimately, mathematical models may be used to suggest a possible optimum formof fluid replacement therapy.The development of mathematical models to describe the human MV.ES following thermalinjury was pioneered by Arturson et al. [1984] in their description of a computer basedburn patient simulator. They have since developed complex multi-compartmental modelsmade up of modules to describe microvascular exchange, hormonal function, renaldynamics and cell volume regulation [Arturson et al., 1988, 1989; Hedlund et al., 1988].Roa et al. [1986, 1988, 1990. 1993] also modelled the MVES following burn injury andthe effect ofburn and inhalation injuries on pulmonary capillary dynamics. These groups ofworkers have made valuable contributions in the area of burn injury computer modelling.Their models are complex in that they attempt to model other systems affected by burninjury, in addition to the MVES. A major fault with their models, however, is that theyassume various model parameters and transport mechanisms from the literature, some ofwhich are based on out-dated knowledge regarding the human MVES. Bert et al. [1989,1991; Bowen et al., 1989] have developed compartmental models to describe the MVESin the burn injured rat. In contrast to the models developed by Arturson Ct al. and Roa etal., the MVES was emphasized due to the critical role it plays in transcapillary exchangeChapter 1: Introduction 4following burn injury. In addition, the parameters used in their models were determined bystatistical fitting of model predictions to experimental data.The present research involves computer modelling of the human MVES following burninjury and fluid resuscitation. This work is a continuation of the research effort at UBC byBert, Bowen and colleagues, with vital input from medical professionals in Norway.The specific objectives of the current study are to:1. formulate a model to mathematically describe the distribution and transport of fluidand plasma proteins in the human MVES following a burn injury;2. estimate the model parameters by fitting its predictions to clinical data using suitableoptimization techniques;3. validate the model by comparing its predictions with other data obtained from burnpatients; and4. investigate the model-predicted behaviour of the MVES with regard to burn patientfluid therapy using common empirical resuscitation formulae.In order to provide a basis for understanding the physiological changes that occur in theMVES following burn injury, Chapter 2 provides a brief physiological review of thesystem being considered. An overview of mathematical models which have beendeveloped to describe the normal and thermally injured MVES is presented in Chapter 3.In Chapter 4, the formulation of the current model which will be used to represent thesystem of interest is described. The patient data used in estimating the unknown modelparameters and for validation purposes are discussed in Chapter 5. The statisticalprocedure adopted to determine the parameters is also described. The best-fit parameterestimates are reported in Chapter 6. The validity of the model is investigated by comparingits predictions with all of the available clinical data, including additional informationChapter 1: Introduction 5withheld from the fitting process for this purpose. In addition, simulations using thestatistically determined parameters along with fluid inputs based on common resuscitationformulae are presented and discussed. Finally, the major conclusions drawn from thecurrent study and suggestions for fl.irther work are presented in Chapter 7.Chapter 2: Physiological Overview 6CHAPTER 2PHYSIOLOGICAL OVERVIEW2.1 INTRODUCTIONThe extreme complexity of the human body and its regulation continues to provide greatchallenges to the medical and engineering professions. The current study seeks to assist inthe understanding of the role and response of part of this complex system, themicrovascular exchange system (MVES), to burn injuries. A brief overview of the generalcirculatory system and the MVES will provide a basis for understanding the physiologicalchanges that occur in the MVES following thermal injury.2.2 THE CIRCULATORY SYSTEM2.2.1 Description of the Circulatory SystemThe circulatory system serves to transport and distribute essential substances to the tissuesand to remove by-products of metabolism. Oxygen from the lungs and nutritionalsubstances absorbed from the gastrointestinal tract are supplied to the tissues of the bodyvia the circulation. Carbon dioxide is transported from the tissues and exchanged in thelungs while other products of metabolism are removed by the kidneys. The circulatorysystem also shares in such homeostatic mechanisms as body temperature regulation,humoral communication throughout the body and adjustments of oxygen and nutrientsupply in different physiological states.Chapter 2: Physiological Overview 7The system that accomplishes all these tasks is made up of a pump, the heart, a series ofdistributing and collecting tubes and an extensive system of small vessels that permit rapidexchange between the tissues and the vascular network. Blood is the transport mediumwhich is pumped through the closed system of vessels by the heart. In mammals, the heartmay be considered as two pumps in series (see Figure 2.1). Blood rich in oxygen andnutrients leaves the left ventricle of the heart and is pumped through arteries and arteriolesto a bed of capillaries. In this capillary bed, the oxygen and nutrients are transportedacross the capillary wall or membrane, to the surrounding tissue space, or interstitium.There is also exchange of carbon dioxide and other metabolic waste products from theinterstitium to the circulating blood. The capillaries drain through venules into veins andback to the right atrium of the heart. Upon leaving the right atrium, this carbon-dioxide-rich blood flows to the right ventricle, which pumps the blood through the vessels of thelungs and the left atrium, to the left ventricle. In the lungs, there is counter-exchange ofoxygen and carbon dioxide, so that oxygen-rich blood leaves the lung circulatory systemto resume its cyclic journey.In addition, some tissue fluids enter another parallel circulatory system of vessels, thelymphatics, which drain tissue derived fluid via the thoracic duct and the right lymphaticduct into the venous system. This is the lymphatic circulation which is shown in Figure2.2. The lymphatics are not part of the blood circulatory system per Se, but constitute aone-way route for the movement of interstitial fluid to blood. These thin-walled capillarieshave large pores and are permeable to all interstitial fluid constituents, including protein.Thus, the lymphatics carry fluid and proteins from the interstitium to the circulatorysystem.Chapter 2: PhysiologicaJ Overview 8CapilLariesP4rJç.Veins (torn head and Arteries to head anduppor extremities upper eztremtiesIRightataum1/\andHepaticvei.SptecnliVer 1 StomachVTn from abdomen -and lower eztemities.PancreasPortal vein.Intestine: / 17—b?1tct7Figure 2.1: Human Circulatory SystemChapter 2: Physiological Overview 9Figure 2.2: Lymphatic and Blood Vessels in Area of Bat Wing: lymphatics (black), bloodvessels (shaded) and blood capillaries (lines)Chapter 2: Physiological Overview 102.2.2 Composition and Properties ofBloodBlood is the transport medium for oxygen, nutrients, carbon dioxide and metabolic wasteproducts in all mammals. It makes up between 6 and 8% [Berne and Levy, 1988; Ganong,19911 of the total body weight and is a suspension of various types of cells in a complexaqueous medium known as plasma. The elements of blood serve multiple functionsessential for metabolism and the defense of the body against injury.Plasma: The normal adult has an average of 50 mL of plasma per kg of body weight or atotal volume of about 3 L [Berne and Levy, 1988; Ganong, 1991; Reference Man ICRP23, 1975; Vander et al., 1985]. Plasma contains many substances including erythrocytes,proteins, lipids, carbohydrates (particularly glucose), amino acids, vitamins, hormones,nitrogenous breakdown products of metabolism (such as urea and uric acid) and gaseousoxygen, carbon dioxide and nitrogen. Normally, the composition of blood is maintained atbiologically regulated levels by a variety of homeostatic mechanisms. The balance may beupset by impaired function following injuries and in a multitude of disorders, particularlythose involving the lungs, cardiovascular system, kidneys, liver and endocrine organs.There are several different proteins that are dissolved in plasma. In all, plasma normallycontains about 7 gIdL of protein [Berne and Levy, 1988; Reference Man ICRP 23, 1975;Vander et a!., 1985]. The bulk of protein belongs to two groups, albumin and variousimmunoglobulins, albumin being the most abundant. Albumin, synthesized by theparenchymal cells of the liver, is normally present at an average concentration of about4 g/dL [Berne and Levy, 1988; Reference Man ICRP 23, 1975]. The exchange of albuminacross intact vascular endothelium is restricted and this provides the critical colloidosmotic or oncotic pressure that participates in the regulation of the passage of water anddiffusible solutes across the capillaries. A reduction of the albumin concentration in plasmaChapter 2: Physiological Overview 11causes shift of fluid to the surrounding tissue space. Excess fluid accumulation inextravascular tissues is termed edema.Blood Cells: The cellular constituents of blood include red blood cells (erythrocytes),which make up the vast majority of blood cells, a variety of white blood cells (leukocytes)and platelets or cell fragments. Ordinarily, the constant motion of the blood keeps the cellswell dispersed throughout the plasma. Centrifugation of a sample of blood to which ananticoagulant is added results in separation of cells from the fluid. This permitsdetermination of the hematocrit or the percentage of the total blood volume which iserythrocytes. The normal hematocrit is approximately between 37 and 49% in men andbetween 36 and 45% in women [Berne and Levy, 1988; Ganong, 1991; Reference ManICRP 23, 1975].The principal protein constituent of the cytoplasm of the mature erythrocyte ishemoglobin, an iron-containing protein which binds oxygen and constitutes approximatelyone-third of the total weight of the erythrocyte. Normal blood has about 15 g/dL ofhemoglobin in adult men and about 13.5 g/dL in adult women [Berne and Levy, 1988).2.3 THE MICROVASCULAR EXCHANGE SYSTEM2.3.1 Description of the Microvascular Exchange SystemThe microvascular exchange system pertains to the portion of the circulatory system thatis composed of the capillary network as shown in Figure 2.3. It also comprises theinterstitium and the lymphatics. This system is the site of exchange of substances such asfluids and plasma proteins across the capillary membrane.Chapter 2: Physiological Overview 12CapillariesVentjleArterioleAV shuntFigure 2.3: Human MicrocirculationChapter 2: Physiological Overview 13The microcirculation is the part of the circulatory system comprising smaller vessels ofdiameter up to 100 p.m. A description of these blood vessels is presented in Table 2.1. Atany given moment, approximately 5% of the total circulating blood is flowing through thecapillaries [Berne and Levy, 1988; Reference Man ICRP 23, 1975; Vander et al., 1985]. Itis this 5% which is performing one of the most important ffinctions of the entire system,namely, the exchange of nutrients and metabolic end products. The capillaries permeatealmost every tissue of the body. There are an estimated 25 000 miles of capillaries in anadult person, each individual capillary being only about 1 mm long [Berne and Levy, 1988;Vander et al., 1985].In a normal person, the fluid filtered out of the capillaries each day, excluding those in thekidneys, exceeds that reabsorbed by approximately 3 L [Vander et al., 1985]. This excessis returned to the blood via the lymphatics. Partly for this reason, obstruction of thelymphatics leads to increased interstitial fluid or edema. Most capillaries in the body have aslight permeability to protein and accordingly, there is a small, steady movement of proteinfrom the blood to the interstitial fluid. This protein is returned to the circulatory system viathe lymphatics. Some protein is normally leaked into the interstitial fluid and failure of thelymphatics to remove it by carrying away the interstitial fluid containing it allows theinterstitial protein concentration to increase. This reduces or eliminates the proteinconcentration difference and thus water-concentration difference across the capillary walland permits net movement of increased quantities of fluid out of the capillary into theinterstitial space.Chapter 2: Physiological Overview 14Table 2.1: Classification of Blood VesselsBlood Vessel Description/FunctionArtery Contains a large amount of elastic tissue which is stretchedDiameter: 0.4 cm during systole and recoils on the blood during diastole.Arteriole Muscular vessel which provides major resistance to blood flow.Diameter: 30 .tm Also regulates regional blood flow to the capillary bed.Metarteriole Serves as thoroughfare channels to venules, bypassing theDiameter: 10 - 20 im capillary bed.Alternatively, serves as conduits to supply the capillary bed.Precapillary sphincter Ring of smooth muscle protecting site where capillary exists frommetarteriole.Continually opens and closes to allow intermittent flow throughany given capillary.Capillary Thin-walled tube of endothelial cells, one-layer thick without anyDiameter: 5 - 10 tm surrounding smooth muscle or elastic tissue.Primary site of exchange of water and solutes with interstitialfluid.Venule Has some smooth muscle, the contractions of which influenceDiameter: 20 I.Im capillary pressure.Permits exchange of materials with interstitial fluid.Serves as collecting channel and storage or capacitance vessel.Vein Last set of tubes through which blood flows on its journey backDiameter: 0.5 cm to the heart.Also serves as collecting channel and storage or capacitancevessel.Chapter 2: Physiological Overview 152.4 THE INTERSTITIUM2.4.1 Structure and Composition of the InterstitiumThe interstitium may be defined as the space located between the capillary wall and thecells. The basic structure of the interstitium is similar in all tissues: collagen forms a fibreframework that contains a gel phase made up of glycosaminoglycans and other largemacromolecules, a salt solution and proteins derived from plasma. Although thecomponents are principally the same in all tissues, their relative amounts vary greatly. Theamount of interstitium varies from about 50% of the wet weight in skin to 10% in skeletalmuscle, to even less in the brain [Aukland and Reed, 1993]. The composition andstructure of the interstitium has been the subject of several reviews [Aukland and Reed,1993; Bert and Pearce, 1984; Chapple, 1990; Comper and Laurent, 1978; Gu, 1987; Xie,1992].Collagens: The collagens are a group of proteins consisting of bundles of tiny fibrils,which combine to form the white glistening inelastic fibres of tendons, ligaments andfascia. Their molecules consist of three separate left-handed coiled polypeptide chains,each containing about 1 000 amino acids. Three molecules are coiled into a right-handedsuper helix. These three chains constitute the collagen molecule. A collagen fibre consistsof an organized array of collagen molecules, arranged in parallel with many stable crosslinkages between the molecules. As a result, the collagens have a high tensile strength,resist stretching and maintain the integrity of many different organs.Glycosaminoglycans: The glycosaminoglycans are polyionic polysaccharide chains ofvariable length made from repeating disaccharide units of hexosamine and uronic acid orgalactose. The glycosaminoglycans are widely distributed in the organism, but theirChapter 2: Physiological Overview 16concentration varies between different organs. About two-thirds of the glycosaminoglycancontent in skin is hyaluronan, one of the seven subfamilies of glycosaminoglycans.Elastic Fibres: The elastic fibres provide tissues with elasticity, giving some tissues arubber-like texture. The major part of the elastic recoil of skin after applying tensionwithin physiological limits is attributed to elastin, a three-dimensional network of cross-linked hydrophobic amino acid molecules.Interstitial Plasma Proteins: The plasma proteins contained in the interstitial fluid are thesame as those in plasma. The proteins move from the plasma to the interstitium across thecapillary wall. The interstitial concentration is a function of the selectivity at the capillarybarrier, the transcapillary fluid flux and lymph flow. The physical properties of the plasmaproteins in the interstitial space affect the physiology of this space. Due to its relativeabundance, relatively low molecular weight and high charge density, albumin is a majorcontributor to the interstitial colloid osmotic pressure (COP). The interstitial proteinsreturn to the circulation via the lymph and thus, the interstitium acts as a reservoir forcolloidally active molecules.2.4.2 Physicochemical Properties of InterstitiumCertain properties of the interstitium influence its response to burn injury and will bediscussed in the following section. Turnover of Interstitial Plasma ProteinsThe rate of disappearance of plasma proteins from the interstitium is described as theturnover rate. The turnover of proteins in the interstitium has been quantified in severalways, most commonly by injecting radiolabelled protein into the tissue and measuring itsremoval by external gamma-detecting equipment or by estimating the appearance of tracerChapter 2: Physiological Overview 17in plasma [Hollander et al., 1961; Langgàrd, 1963; Reed et al., 19901. In humans, thenormal removal rate of radioactive albumin injected subcutaneously has been found to bebetween 2 and 2.5% per hour [Hollander et al., 1961; Langgârd, 1963; Xie, 1992]. Interstitial Volume ExclusionMutual exclusion between macromolecules occurs because at any particular time, no twoof these molecules may occupy the same space, and their centres may not come closerthan the sum of their radii. The characteristic components of the interstitium such ascollagenous fibres, have diverse geometric shapes. Their presence thus limits theinterstitial space accessible to plasma proteins and other macromolecules. In vivoexclusion studies predict fractional albumin excluded volumes ranging from about 25% to60% [Granger et al., 1980; Parker Ct al., 1979, 1980; Reed et al., 1990]. Based on thesestudies and the work of Wiederhielm [1979], Bert and Pinder [1982] determined aconstant albumin exclusion fraction of 25% of the normal interstitial volume. Interstitial ComplianceIn order to perform any type of quantitative analysis of interstitial fluid dynamics, it isessential to know the relationship between interstitial fluid pressure and volume in theinterstitial spaces. The interstitial compliance is defined as the ratio of the change ininterstitial fluid volume (V1) to the corresponding change in interstitial hydrostatic pressure(P1), i.e.,Compliance —-. 2.1Information about the compliance of human tissues is lacking. Chapple [1990] developed acompliance relationship for humans based on the work of Stranden and Myhre [19821 andReed and Wiig [1981]. Stranden and Myhre [1982], in the only known study of humancompliance, measured the compliance of lower limb subcutaneous tissue in 46 patients.Chapter 2: Physiological Overview 18However, the data was too scattered to derive a meaningful relationship for humancompliance. Reed and Wiig [19811, after studying the compliance characteristics of skinand skeletal muscle in rat, cat and dog tissues, found that the compliances of both tissuesfollow a similar trend. During severe tissue dehydration, compliance is low while duringsevere tissue overhydration, compliance is high. In between the two extremes, moderatecompliance characteristics prevail. The general shape of the volume-pressure curve isshown in Figure 2.4 [Reed and Wiig, 1981]. Chapple scaled interstitial hydrostaticpressure and interstitial fluid volume data from the rat based on changes observed in theedematous state by Stranden and Myhre. The flat segment of his compliance relationship,representing overhydration, was considered the region most prone to the influence ofexperimental error. As such, two other relationships were investigated by arbitrarilyincreasing the slope of the overhydration segment from 1.8x105 to 5.0x10 and 1.05x 10mmHg/mL. A summary of the three compliance relationships investigated is presented inTable 2.2. The three tissue compliance relationships were used by Xie [1992] in a study todetermine normal transport parameters for the human MVES. The best-fit parameterswere obtained using compliance relationship #3.2.5 THE SKINIn the present study, the properties of the interstitium are assumed to be those of skin andmuscle. A brief discussion of the anatomy and function of the skin provides a basis inunderstanding the microscopic changes that occur in the skin following burn injury.2.5.1 Anatomy and Function of SkinThe skin is the largest organ of the body and has a surface area that ranges from about0.025 m2 in the newborn to 2.0 m2 in the adult [Martyn, 1990; McLaughlin, 1990]. It2—4—6—80 40Figure 2.4: Tissue Hydrostatic Pressure as a Function of Interstitial Fluid Volume forSkeletal Muscle and Skin in Rat [Reed and Wiig, 1981]19Chapter 2: Physiological OverviewnEE‘— 01J(f)C,)0::: —2cLC)I—I(I)00::0>-.LiD(F)(F)I—L-•—. SKIS10 20 30INTERSTITIAL FLUID VOLUME (ml)Chapter 2: Physiological Overview 20Table 2.2: Mathematical Description of Human Interstitial Compliance Relationship[Chapple, 1990]Region of Curve RelationshipDehydration = —0.7+1.96154 x io-(V1 —8.4 X iO)Moderate Hydration Mathematical interpolation of experimental P1 andV1 dataOverhydration:Compliance #1 = 1.88 + 1.8 X iO-(V —1.26 x 1O)Compliance #2 = 1.88 +5.0>< iO-(V —1.26>< 101Compliance #3 = 1.88+1.05 x io(r’ — 1.26x iO)consists primarily of two layers, the epidermis and dermis or corium as shown in Figure2.5. The outermost cells of the epidermis are dead comified cells that act as a toughprotective barrier against the environment. It has high capacity for regeneration. Thestratum corneum in the epidermis has a high electrical impedance which restricts thepassage of electric current. The second, thicker layer, the dermis, is composed chiefly offibrous connective tissue. It contains the blood vessels and nerves to the skin and epithelialappendages of specialized function. The dermis is the barrier that prevents loss of bodyfluids by evaporation and loss of excess body heat. Sweat glands help maintain bodytemperature by controlling the amount of heat loss by evaporation. Beneath the dermis issubcutaneous or adipose tissue which consists mostly of fat. It serves as a means of heatinsulation and as a nutritional source in extreme conditions.Chapter 2: Physiological Overview 21Figure 2.5: Structure ofNormal Skin Showing the Categorization ofBurn InjuryChapter 2: Physiological Overview 222.6 TRANSCAPILLARY EXCHANGEFluid and proteins move across the capillary endothelial wall by filtration, diffbsion andconvection. The transcapillary exchange of fluid and protein is determined by theproperties of the capillary membrane, the transcapillary pressures and the proteinconcentrations.2.6.1 Capillary FiltrationThe magnitude and direction of the movement of fluid across the capillary wall isdetermined by the algebraic differences between the hydrostatic and osmotic pressuresexisting across the membrane. An increase in intracapillary hydrostatic pressure favoursmovement of fluid from the blood vessel to the interstitial space, whereas an increase inthe concentration of osmotically active agents within the vessels favours movement intothe vessels from the interstitial space.The role of the hydrostatic and colloid osmotic pressures in regulating the passage of fluidacross the capillary endothelium was first expounded by Starling in 1896 and constitutesthe Starling Hypothesis. It can be expressed by the equation:F =kA.[(PCIJ)cr(HpLHJ)], 2.2where F is the transmembrane filtration flow, k the hydraulic conductivity of the capillarymembrane per unit area, A the surface area available for exchange, a the capillaryreflection coefficient for the plasma proteins, P and fl are the hydrostatic and colloidosmotic pressures respectively, while the subscripts C, PL and I represent capillary,plasma and interstitial respectively. The product (kA) is referred to as the capillaryfiltration coefficient for the capillary membrane. Filtration occurs when the pressuredriving force, (AP-a.tffl), is positive and re-absorption occurs when it is negative.Chapter 2: Physiological Overview 232.6.2 Combined Convective and Diffusive Solute TransportBresler and Groome [19811 developed an equation for the combined convective anddiffusive protein flux across membranes of finite thickness. The transport equation whichdescribes the solute flux generated when a combined hydrostatic and osmotic pressuredifference and a concentration difference act conjointly across the membrane is— ( ‘ Fr. —c1 .exp(—Pe)]Q F’PI I, .3[ l—exp—Pe; ]where is the rate of solute transport across the membrane, c the concentration ofplasma protein and Pc is a modified Péclet number defined by2.4PSPS is the product of the permeability of the capillary membrane to albumin and themembrane surface area.2.7 PHYSIOLOGICAL CHANGES FOLLOWING INJURYThe physiological changes that result from a burn injury have been reviewed extensively[Gu, 1987; Lund et a!., 1989, 19921. The typical clinical features of thermal injury includevisible swelling of the skin, blister formation and loss of surface-protecting epitheliumwhich leaves wet and weeping surfaces. The swelling is caused by changes in themicrovascular exchange system (MVES), in particular, fluid shifis and losses from thecirculation. Other macroscopic changes occur with respect to areas not directly affectedby the burn. A brief review of these changes will serve as a basis for the formulation of thecurrent model describing the human MVES following burn injury.Chapter 2: Physiological Overview 242.7.1 Damageto SkinThe continued losses of water and heat through burned skin play major roles in thepathophysiological changes seen postburn. Significant swelling may also occur in thesubcutaneous layer of skin. The degree of impairment in the protective characteristics ofnormal skin is dependent on the depth of the burn injury and the extent of injury or thesize of the burn relative to that of the total skin surface area. Traditionally, burn depth hasbeen classified in degrees of injury: first, second and third degree burns. Currently, themore popular classifications are partial-thickness (first and second degree) and full-thickness (third degree) burns. Both classifications use the same criteria based on thedepth of tissue destruction as is shown in Figure 2.5 and described in Table 2.3.The extent of injury indicates the total percentage of the body surface area (TBSA)involved. The “rule of nines” has been used in evaluating the extent of burns, where eacharm is considered to be 9%, each leg 18%, anterior trunk 18%, posterior trunk 18% andhead 9% of TBSA as shown in Figure 2.6. A more accurate method is the use of the Lundand Browder chart shown in Figure 2.7 which divides the body surface by regions, whileaccounting for age group variation [McLaughlin, 19901.2.7.2 Changes to the Microvascular Exchange System (MVES)The abnormal accumulation of fluid in the interstitial spaces of tissues, or edema, is amajor clinical problem after thermal injury. Edema is most prominent in burn tissues or inthe region directly surrounding the burn tissues, but is not uncommon in nonburnedtissues, including the lungs. It is well known that this swelling of tissue is caused by theshift of fluid from the circulating plasma to the interstitial spaces. This internal loss ofplasma volume may result in hypovolemia and eventually in hypovolemic shock. Thepathogenesis of this fluid shift has been the subject of many research efforts [Arturson,1979; Davies, 1982; Leape, 1968], however, it is still not very well understood.Chapter 2: Physiological Overview 25Figure 2.6: Rule of Nines for Burn EstimateC” 0 ‘1 YRY CaC) CD “1r zC,C C,C” C”.iI C4CaCa Ca CaCa CaC” C”C,C,C,C” C,C, C0Ca CaCa CaCC C, tO-a-3CaCD CD -t C.) CD IChapter 2: Physiological Overview 27Table 2.3 : Burn Depth ClassificationsClassification of Burn CharacteristicsFirst degree or Involves only epidermis layer with minimal tissue damage.Superficial partial-thickness Protective functions of skin in dermis remain intact.Causes: overexposure to sunlight or hot liquid scalding.Superficial second degree Involves heat destruction of upper third of dermis.(Deep partial-thickness) Microvessels are injured and permeability increasesresulting in plasma leakage into the interstitium.Blisters form due to loss of epidermis.Mid- to deep dermal second degree Extends well into dermal layer.(Deep partial thickness) Plasma leakage in remaining intact blood vessels isevident.Blood supply is marginal and the potential for the burn toprogress to deeper injury is high.Third degree or Destruction of entire epidermis and dermis.Full thickness Formation of avascular tissue due to heat-coagulation ofdermal blood vessels.Causes: Short exposure to very high temperature orprolonged contact with moderate temperature. Transcapillary Exchange in Injured TissueEdema develops when the rate of fluid filtered from the microvessels exceeds the rate atwhich fluid is drained by the lymphatics or by some other route. Fluid is filtered across thecapillary membrane according to Starling’s hypothesis, which according to the previoussection yieldsChapter 2: Physiological Overview 282.5where .P is the net filtration pressure given by2.6Lymphatic drainage from the tissue is assumed to be linearly dependent on interstitial fluidpressure, i.e.,JL=JL,+LS{F-fJ. 2.7L is the rate of lymphatic drainage from tissue, LS the lymph flow sensitivity coefficientand the subscript NL represents normal steady-state conditions. The influence of burninjury on each of the parameters in Equations 2.5, 2.6 and 2.7, which affect transcapillaryfluid and protein exchange in the injured tissue, is discussed in Table 2.4.Due to the marked increase in capillary permeability to macromolecules and decrease inthe capillary reflection coefficient, there is a high plasma protein content in exudate andblister fluid following burn injury [Arturson, 1979]. This apparent leakiness of thecapillaries results in an increase in the pooi of plasma proteins outside the circulation.Return of this pool to the circulation depends on lymphatic function. The concentration ofplasma proteins in plasma may also be increased through the administration ofresuscitation fluids. Transcapillary Exchange in Uninjured TissueSwelling or edema of uninjured skin, muscle and internal organs distant from the injuredskin areas is also seen following fluid resuscitation of patients with extensive burns.Increases in protein extravasation, tissue protein and fluid content have been reported inuninjured tissue [Carvajal et al., 1979; Lund and Reed, 1986]. These remote effects occurChapter2:Physiological Overview29Table2.4:ChangestoInjuredTissueMVESPropertiesFollowingBurnInjuryPropertyPhysiological ChangesCapillaryFiltrationCoefficient, kAConductivityperunitarea,k,increases.Areamightbereducedduetofallinnumber ofperfusedcapillaries.OveralleffectonkAisthereforeunpredictable.Increasesof upto300%havebeenreportedforkA[ArtursonandMellander,1964;Pittetal.,1987].Netfiltrationpressure,APNormalvalueof APisbetween0.5and1mmHg.Largeincreasesfrom10-25mmHg[Pittetal.,1987] upto250-300mmHg[ArtursonandMellander,1964]reportedimmediatelypostburnexplainearlyedemadevelopment.Capillaryhydrostaticpressure,PPcisnormallydeterminedbyarterialandvenoushydrostaticpressuresaswellasprecapillaryandpostcapillaryresistances.Localandcentralhemodynamicchangeshavestrongeffectsonthesepressuresandmaycauseeitheranincreaseordecreaseinthevalueof P.InterstitialfluidhydrostaticP1isnormallyslightlysubatmospheric(-1to-2mmHg).pressure,P1Increasesinvaluefrom2mmHg[WiigandReed,1981] to7mmHgat6to8hourspostinjury[Watchtel etal.,1983]havebeenreportedfor P1.Anacutemarkeddecreaseof P1toastronglynegativevalueof about-150mmHghasbeenobservedinthefirsthourpostburn[Lund etal.,1988].Chapter 2:Physiological Overview30Table2.4(Continued):Changes toInjuredTissueMVESPropertiesFollowingBurnInjuryPropertyPhysiological ChangesPlasmacolloidosmoticpressureAreductioninthevalueof PLhasbeenobserved[Lundetal.,1986,1988; Onarheimetal.,(COP),1PL1989;Pitkanenetal.,1987; Watchteletal.,1983;ZetterströmandArturson,1980]withorwithoutfluidresuscitation.PLisaffectedbythelossoffluidandproteinsoutofthecirculation,aswellasthelymphaticreturnoffluidpoorinprotein.Theeffectontranscapillaryfluidexchangeistoenhancethenetcapillaryfiltrationof fluid.Interstitial fluidCOP,Fl 1Increasedextravasationoffluidandproteincaneffectatheoreticalincreaseordecreaseinthevalueof T1dependingontheproteinconcentrationof thefiltratecomparedtothatininterstitialfluid.Increasesinthevalueof11[LundandReed,1986] andareversedCOPgradient(pL-Fl1)[Pitkänenetal.,1987]havebeenobserved.ThereversedCOPgradientcouldenhancefluidfiltration,henceplasmavolumeloss.Capillaryreflectioncoefficient, aNormalainskinisreportedtobebetween0.85and0.97[TaylorandGranger,1984].Areductioninthevalueof afrom0.87to0.45hasbeenreported[Pittetal.,1987],associatedwithincreasedproteinpermeability.ThenormallyreabsorptiveCOPgradientacrossthecapillarymembraneisthusreduced.Lymphaticdrainage, LIncreasesinthevalueof Lof upto20timeshasbeenobserved[ArtursonandMellander,1964;Pittetal.,1987;TaylorandGranger,1984].Chapter 2: Physiological Overview 31when the burns cover more than 25% to 30% of the total body surface area (TBSA).Reduced blood flow has also been reported following minor burns [Jelenko et al., 1973].The lungs are of special interest due to the well recognized complication of pulmonaryedema in major body burns. Inhalation injury has direct damaging effects on therespiratory tract and lungs. In the absence of this injury, the lungs are protected againstedema by their ability to increase lymphatic removal of fluid. An additional edema-preventing mechanism results from the removal and dilution of interstitial proteins due to anormally high interstitial COP in the lungs. Systemic Hemodynamic ChangesHypovolemia, resulting from the loss of fluid from the circulation, induces a number ofhemodynamic changes following thermal injury. Cardiac output is reported to fallmarkedly soon after extensive burns. In addition, arterial blood pressure and centralvenous pressure have both been found to decrease. The ratio of the systemic bloodpressure to the cardiac output is a measure of the peripheral resistance. It depends mainlyon the degree of vasoconstriction and on the viscosity of blood, to a lesser extent.Vasoconstriction causes an overall increase in the peripheral resistance, which maymaintain arterial blood pressure for a time, but at the expense of a reduced blood flowthrough the skin and other vital organs.2.8 FLUID RESUSCITATIONHypovolemia resultant from burn injury can rapidly lead to conversion of a viable butischemic deep dermal burn to a nonviable full-thickness burn, further increasing thepossibility of mortality. Death due to the development of hypovolemic shock in the acutephase is also of particular concern. Adequate initial fluid volume resuscitation is thereforeChapter 2: Physiological Overview 32critical to the survival of a major body burn. However, the aggressive correction of theproblem of hypovolemia can result in generalized burn edema formation which is lesslethal than shock, but can result in serious morbidity nonetheless. The subnormal cardiacoutput following burn injury also needs to be promptly restored as near as possible to thenormal value.The greatly increased capillary leakage resulting in progressive edema formation isgreatest during the first eight hours post-burn. Consequently, the two important goals ofearly burn care are the prompt initiation of resuscitation and an adequate volumereplacement regime. Several empirical formulae exist for resuscitation of the burn patientbased on the timing of fluid replacement, as well as on the composition and amount offluid provided. Crystalloids, hypertonic crystalloids and colloidal solutions have been usedfor early fluid therapy.2.8.1 Isotonic Crystalloid Fluid ResuscitationCrystalloids, in particular isotonic solutions such as lactated Ringe?s solution, with asodium concentration of 130 mEqfL, are the most popular resuscitation fluids [Gillespie etal., 1987]. The loss of large quantities of sodium and water from the vascular space intothe burn wound is well recognized. The need for sodium and water replacement to effectsuccessful resuscitation justifies the use of this solution, which closely approximates thecomposition of the extracellular fluid. The amount of fluid to be given over the first 24hours is initially estimated by various formulae such as the Parkland formula (4 mL oflactated Ringer’s /kg/% TBSA burned). The use of lactated Ringer’s solution has beenfound highly effective in preventing early death due to hypovolemia. However, concernsexist due to complications from the administration of large volumes of fluid.Chapter 2: Physiological Overview 332.8.2 Hypertonic Crystalloid Fluid ResuscitationHypertonic solutions with sodium concentrations between 240 and 260 mEqfL, havebecome a popular option in minimizing the total fluid volume administered to burn patientsin the early phase postburn. These hypertonic saline solutions are used to control cellswelling by increasing extracellular osmotic pressure. Water influx into the cells is thusprevented and fluid extravasation into injured tissue is decreased. Extracellular and hence,intravascular volume is maintained with less fluid. However, as these solutions are stillcrystalloids, hypoproteinemia and blood volume are not as well maintained as with colloidsolutions. The safe use of these fluids as a standard solution has been the subject of manyrecent research efforts [Griswold et al., 1991; Gunn et al., 1989].2.8.3 Colloid Fluid ResuscitationThe realization that the fluid lost from the circulation into the burned tissues has thecharacteristics of plasma is justification for using colloidal solutions for the early fluidtherapy. A variety of colloids have been used including human plasma, serum and/oralbumin, modified gelatin and the non-protein colloids such as dextrans and starches(hetastarch and pentastarch).The use of protein solutions has been reported to decrease total fluid requirements[Wilkinson, 19711. The timing of albumin therapy remains controversial as capillarypermeability changes vary considerably in different tissues for different degrees of burninjury. As the fluid requirements and the area of the burn are related, various formulaehave been proposed as guidelines to the requirements of a particular burn patient (Evans;Brooke) [Evans et al., 1952; Reiss et al., 1953j. Due to the very high cost of albumininfhsions, less expensive colloids, not derived from human plasma provide a significantcost benefit. The potential efficacy of nonprotein colloid plasma expanders in burnresuscitation was suggested by experimental studies with dextran [Demling et al., 1984].Chapter 2: Physiological Overview 34Clinically, dextrans have not been widely used primarily due to their potential to induceallergic reactions and increased bleeding. The safety and efficacy of other plasmasubstitutes, including gelatins, for burn resuscitation, remain unresolved. The mostpromising alternative colloid volume expanders are the starches [Waxman et al., 19891.Hetastarch, which closely mimics 5% albumin in normal saline, has been found to increaseclotting and reduce bleeding times in animals. Pentastarch has been found to be a verypromising plasma substitute, with hemodynamic effects equal or superior to albumin.However, ftirther study is required to assess the efficacy of pentastarch within the first 24hours of resuscitation.Formal resuscitation is generally carried out in all adults with burns over 15 to 20%, withsuperficial or first degree burns being excluded. The most reliable clinical parameterreported for evaluating the response of the patient to all these resuscitation formulae isurine output, even though this has been disputed [Dries and Waxman, 19911. In adults, 0.5to 1.0 mL/kglh of urine is the optimum goal.2.9 SUMMARYIn summary, the most important changes that occur following thermal injury which needto be considered when modelling the human microvascular exchange system, are thefollowing:i) the rapid development of edema in the injured tissue resulting from increasedpressure driving forces and the capillary filtration coefficient in this tissue;ii) a dramatic increase in transcapillary transport of plasma proteins in the injuredtissue;iii) a dramatic loss of fluid and protein from the burn wound; andChapter 2: Physiological Overview 35iv) a dramatic reduction by about -150 mmHg in interstitial fluid hydrostatic pressure,creating a strong “suction” in the burned tissue. This very negative tissue pressurehas been observed in rats.Burns covering more than about 25% of the total body surface area initiate local andsystemic effects different from those initiated by smaller burns. Consequently, two burngroups, less than and greater than 25% burn surface area, need to be considered in theanalysis of fluid exchange and resuscitation of burn patients.Chapter 3: Computer Modelling of the MVES 36CHAPTER 3’COMPUTER MODELLING OF THE MICROVASCULAR EXCHANGE SYSTEM3.1 INTRODUCTIONIn order to replace the loss of plasma volume which results in the microvascular exchangesystem (MVES) following a burn injury, and hence to improve the survival of burnvictims, various empirical formulae for fluid therapy have been developed andimplemented with varying degrees of success [Evans et al., 1952; Gillespie et al., 1987;Reiss et al., 1953]. These empirical approaches to treatment are based on clinicalobservations and medical experience from treating burn patients, with limitedunderstanding of the underlying fluid and protein transport phenomena in the MVES.These treatment formulae give the amount of fluid required to stabilize a burned,hypovolemic individual, based on the size of the injury and the time postburn. Fluidresuscitation has been found to correct hypovolemia or low blood volume, but worsensthe edema or swelling process.Mathematical models have been developed to complement this empirical approach topatient care. These models are based on detailed fluid and protein transport mechanismsacross the capillary membrane. The models describe the time course of changes in fluidvolumes and the amount and concentration of protein in the blood and tissues followinginjury. Mathematical models can be used to predict the response of the MVES to differentempirical resuscitation protocols to give an indication of a possible optimum form oftherapy. In describing the human MVES, two different kinds of models have beenconsidered; the distributed and compartmental models.Chapter 3: Computer Modelling of the MVES 37In the distributed model, the fluid and tissue properties are considered to be position-dependent. These spatial properties are difficult to determine experimentally and hence arenot readily available. In addition, a more complex description of fluid and protein transportis required, resulting in a model that consists of a set of partial differential equations,which are difficult to solve mathematically. Distributed models [Gates, 1992; Taylor et al.,1990; Werner, 19811 approximate the real system under investigation more closely thanthe compartmental models. However, due to the mathematical complexity of these modelsand the lack of experimental data required to determine model parameters, it is prematureto consider their inclusion in a burn patient simulator.The compartmental model, as the name suggests, comprises a system of separate, well-mixed compartments in which fluid and proteins are homogeneously distributed. As such,the properties in each compartment represent average values for that compartment. Due tothis spatial averaging, the behaviour of fluid and proteins in the MVES can be describedby a much simpler set of ordinary differential equations. Several compartmentalmathematical models have been developed to describe the distribution and transport offluid and protein between the circulation, interstitium and lymphatics [Arturson et al.,1984; Bert et al., 1982, 1988; Roa and Gomez-Cia, 1986; Wiederhielm, 1979]. Theproposed models generally differ in two aspects: the complexity in the division of theMVES into compartments and the description of fluid and protein exchanges between thecompartments. In most models, the MVES is assumed to comprise the plasmacompartment and interstitial compartments. Additional compartments to describeintracellular and extracellular distribution or renal fhnction for example, are alsoconsidered based on the particular interests of the researchers. Fluid and protein exchangebetween the compartments is based on Starlings concepts on capillary filtration andexchange [Starling, 1896]. The mathematical equations that describe the model areobtained by carrying out fluid and protein balances around the compartments. This resultsChapter 3: Computer Modelling of the MVES 38in a set of ordinary differential equations where the independent variable is time. Theremainder of this chapter will review compartmental models which have been developed todescribe the normal or thermally injured MVES in experimental animals and humans.3.2 MODELLING OF NORMAL MVESA non-linear computer simulation program was developed by Wiederhielm [1979] toanalyze the dynamics of capillary fluid exchange. The simulation program took account ofthe fact that, in addition to plasma proteins, the interstitium also contains other osmoticallyactive substances such as mucopolysaccharides. These substances exert an osmoticpressure and also exhibit unusual physical characteristics in terms of volume exclusion.The interstitium was therefore partitioned into a mucopolysaccharide-containing gel phasein equilibrium with a free fluid-phase, to which the proteins are restricted. Also included inthe simulation was a nonlinear interstitial compliance. Two different modes of transport ofplasma proteins and macromolecules from the circulation into the interstitium wereconsidered: bulk flow at the venous end of the capillary and via diffusion. With this model,steady-state and transient responses to a variety of perturbations, including changes inarterial and venous pressures, plasma oncotic pressure, interstitial mucopolysaccharidecontent and lymphatic obstruction were studied.Bert and Pinder [1982] modified the model of Wiederhielm to incorporate a differentconcept of volume exclusion. The excluded volume in Wiederhielm’s model which was avariable calculated from the concentration of proteoglycans, including hyaluronate in thegel phase, was replaced by a constant value. This constant value for the excluded volumewas based on observations that the volume from which albumin is excluded remainsconstant, even with swelling of the tissue [Meyer et al., 1977] and was due to the presenceof collagenous fibres. The use of this constant value avoided the unprovable assumptionsChapter 3: Computer Modelling of the MVES 39Wiederhielm was forced to make regarding content, composition and interaction ofcomponents of the interstitial space and also simplified the overall model. Bert and Pinderused their model to program perturbations characteristic of different forms of edema, andto record both the transient and steady-state responses, which were found to be in goodagreement with Wiederhielm’s predictions.Bert et al. [1988] developed a dynamic mathematical model to describe the distributionand transport of fluid and plasma proteins between the circulation, interstitial space of skinand muscle, and the lymphatics in the rat. They investigated two descriptions oftranscapillary exchange: a homoporous ‘Starling Model’ (SM) and a heteroporous ‘PlasmaLeak Model’ (PLM). In the SM, water and protein exchanges were assigned to a singlesite in the capillary and were characterized by one pair of transport parameters for eachplasma protein investigated and by one value of capillary hydrostatic pressure. The PLMwas based on fluid filtration in the arterial end of the capillary, reabsorption in the venousend and convective protein transport through nonsieving channels also in the venouscapillaries. Parameters used in these two hypothetical transport mechanisms weredetermined based on statistical fitting of simulation predictions to selected experimentaldata. This aspect of the work by Bert et al. differed from previous computer modellingefforts [Bert and Pinder, 1982; Wiederhielm, 1979]. The fully determined model was usedto simulate steady-state conditions of hypoproteinemia, overhydration and dehydration, aswell as the dynamic response to changes in venous pressure and intravascularlyadministered protein tracers. It was concluded from these studies that the PLM provided abetter description of microvascular exchange in comparison to the SM because it yielded abetter statistical fit of the available experimental data.In order to describe the distribution and transport of fluid and albumin in the humancirculation, the interstitium and the lymphatics, Chapple [1990] formulated a mathematicalChapter 3: Computer Modelling of the MVES 40model to describe the human MVES, continuing the trend set previously by Bert et al.Two transcapillary mass exchange mechanisms, the ‘Coupled Starling Model’ (CSM), inwhich transcapillary albumin diffusion and convection are coupled, and the heteroporousPLM, were investigated, as previously studied in the rat [Bert et al., 1988; Reed et al.,19891. Some of the parameters used in the transport equations were again determinedbased on statistical fitting between simulation predictions and experimental data fromnormal humans and nephrotic patients. Due to the facts that the PLM required moreestimated parameters than the CSM, and that fewer of the transport parameters had beenmeasured experimentally, the model employing a Starling-type exchange mechanism wasfavoured for future studies by the group.In a continuing study, Xie [1992] used the Coupled Starling Model (CSM) to determine aset of transport parameters to describe the transport mechanisms of the normal humanMVES. The transport parameters were determined by fitting model predictions toexperimental data from normal humans, nephrotic patients and patients who had sustainedheart failure. Data from nephrotic and heart-failure patients were selected due to the factthat the MVES is believed to remain in its normal state, altered only by changes in theStarling forces. The fully described model was successfully used to simulate the transientbehaviour of normal humans and patients subjected to saline and albumin solutioninfusions.3.3 MODELLING OF MVES FOLLOWING BURN INJURYCompartmental models have also been developed to study changes in the MVES followingburn injury. Arturson et al. [1984] pioneered the description and development of thesecomputer-based patient simulators. Based on the analog model by Wiederhielm [1979],modifications were made which described the changes that occur postburn. The interstitialChapter 3: Computer Modelling of the MVES 41tissue was divided into two compartments. The injured tissue compartment representedonly injured skin and the second tissue compartment comprised intact tissue (i.e. bothintact skin and muscle). Exchange of fluids and protein between injured and intact tissuewas assumed not to take place. In addition, osmotic effects of electrolytes in plasma, theinterstitial space and cells were not taken into account. Wound fluid loss consisting ofevaporation and exudation were also considered in the model. Data from three patientswith thermal injuries were used to evaluate the model. The validity of the model wasassessed by running simulation tests using constants and parameters determined fromWiederhielm’s study. Subsequent research efforts [Arturson, 1988; Arturson et al., 1989;Hedlund et al., 1988] involved the development of complex multi-compartmental modelsmade up of modules to describe such systems as hormonal function, renal dynamics andcell volume regulation, all in addition to the MVES. Many unmeasured parameters wererequired to fully describe these models.A preliminary mathematical model of plasma water dynamics was developed by Bush et al.[1986] to investigate the relative efficacy of alternative modes of fluid therapy. Fluid input,urine output, burn water loss and insensible water losses via the unburned skin, lung andgastrointestinal tract were incorporated in the model. The model was reported to givereasonable responses to a wide range of burns, body sizes, fluid loss factors and rates ofintravenous fluid administration. Due to its comparative simplicity, the model was notrealistic enough to provide answers to unsettled questions concerning conflictingtreatment methods. Useful additions to improve the predictive capabilities of the modelwere suggested, such as the inclusion of burn and nonburn interstitial and intracellularspaces along with their electrolyte and albumin contents.Roa et al. [1986] have also been involved in the development of compartmental burnmodels. They presented an algorithm for the qualitative and quantitative study of theChapter 3: Computer Modelling of the MVES 42variations in the distribution of extracellular fluids and proteins between the vascular andinterstitial spaces in burn patients. Measurements of hematocrit, plasma proteinconcentration, fluid replacement and diuresis were used in the algorithm. Values forplasma, cellular and blood volumes, plasma proteins, evaporative water losses and netfluid and protein shifts were determined using the algorithm. In order to assess thereliability of the algorithm, their results were compared with the clinical progress ofpatients. In addition, agreement was obtained with the experimental and clinical resultsobtained by other authors [Arturson Ct al., 1984]. Roa et al. continued their modellingefforts by developing a non-linear, five-compartment mathematical model [1988]. Controlmechanisms were incorporated to describe the interactions between the extra- andintracellular compartments. The different mechanisms that regulate pulmonary capillarydynamics in burn patients were also studied by including the relevant compartments [Roaet al., 1990]. More recently, Roa et al. [1993] have developed a fluid therapy method(BET) designed by computer simulation, using their previous digital simulationtechniques. The effectiveness of the BET fluid therapy during the shock phase afterburning was investigated and found to show promise.Extension of the mathematical model developed by Bert et al. [1988] to describe normalmicrovascular exchange in the rat, enabled them to study microvascular exchange in therat following a burn injury [Bert et al., 1989; Bowen et al., 19891. The skin compartmentin the previous model was subdivided into two compartments: the burned and thenonburned skin. Perturbations characteristic of relatively small (10% burn surface area)and large (40% burn surface area) burn injuries without fluid resuscitation wereincorporated into the model. They estimated the changes that occur to transportcoefficients and other system parameters subsequent to burns of these sizes by fitting themodel predictions to specific experimental data [Lund and Reed, 1986]. A study by Bertet al. [1991] extended this model fhrther to include the effects of different types of fluidChapter 3: Computer Modelling of the MVES 43resuscitation protocols on the circulatory and microvascular exchange systems. Theyidentified the ranges of model parameters that best described the changes in interstitialfluid volume and protein mass in addition to transcapillary protein extravasation for threesets of experiments: no resuscitation, resuscitation with Ringer’s or resuscitation withplasma.The importance of cellular exchange in the MVES following thermal injury wasinvestigated in a preliminary study [Drysdale, 19881 where the model of fluid resuscitationdeveloped by Bert et al. [1991] was extended to include hypertonic resuscitation in the rat.Adequate compartments to account for intra- and extracellular exchange were added tothe existing model. Trends predicted by the model indicated that hypertonic fluidresuscitation in thermally injured rats mobilized cellular water in an attempt to maintainplasma volume.The above mentioned groups have all made valuable contributions in the area of burninjury computer modelling. The models of Arturson et al. and Roa et al. are relativelycomplex in that they attempt to model other systems also affected by thermal injury, inaddition to the MVES. Their description of the MVES is based primarily on the work ofWiederhielm [1979]. However, current knowledge regarding the MVES has supersededthat proposed by Wiederhielm. In addition, various parameters necessary to fully describetheir models were taken directly from available literature, with no attempt made toestimate them using patient data. Bert et al., on the other hand, have developedcompartmental models, with particular emphasis on the MVES, which plays a critical rolein transcapillary exchange following burn injury. Their models, unlike those mentionedpreviously, use model parameters based on statistical fitting of model predictions toexperimental data. In addition, the physiological concepts employed in formulating thesemodels are based on up-to-date knowledge regarding the MVES.Chapter 3: Computer Modelling of the MVES 44In this study, a mathematical model to investigate fluid resuscitation in humans followingburn injury is developed, based on the simulation work of Xie [1992] who studied thenormal human MVES. In contrast to most previous modelling efforts and continuing thetrend set by Bert et al, the transport parameters necessary to fI.illy describe the model aredetermined based on statistical fitting of model predictions to two specific sets ofexperimental data [Birkeland, 1969; unpublished data from T. Lund]. Current issues andknowledge regarding the human MVES are also incorporated into the model, in anattempt to give a better and more accurate description of fluid and protein distribution inthe human MVES following thermal injury.Chapter 4: Model Formulation 45CHAPTER 4MODEL FORMULATION4.1 INTRODUCTIONSeveral mechanisms of transcapillary fluid and albumin exchange have been investigated asdiscussed in Chapter 3. The Coupled Starling Model (CSM) was found to best describethe normal human microvascular exchange system (MVES) [Xie, 19921. The modeldeveloped in the current study to describe the human MVES following burn injury is anextension of the compartmental model developed by Xie [1992]. The main assumptions,transport mechanisms as well as systemic fluid and protein inputs and outputs for thisextended model are discussed in the first part of this chapter. Normal steady-stateconditions existing in the average human provide a basis for describing conditions in thepatient at the instant the burn takes place. Following burn injury, fluid and proteins in thesystem are redistributed in the different compartments. This results in changes tophysiological properties dependent on the fluid and protein content in the compartments.Additional relationships to describe the postburn physiological properties and transportcoefficients necessary for the model formulation are discussed and developed. Fluid andprotein losses from the burn wound by exudation as well as evaporative fluid losses areimportant issues related to burn injury. These are also discussed and incorporated in themodel. Finally, a description of the simulation algorithm is presented.Chapter 4: Model Formulation 464.2 BASIC ASSUMPTIONS1. It is assumed that the MVES is divided into three well-mixed compartments in whichfluid and proteins are homogeneously distributed. Consequently, the properties in eachcompartment represent average values for that compartment. In contact with thecirculating plasma compartment are two tissue compartments: the uninjured and theinjured tissue compartments, as shown schematically in Figure 4.1. In previousmodelling studies in the rat [Bert et al, 1988; Reed et al., 19891, the uninjuredinterstitium was divided into two separate compartments, muscle and skin. Thisseparation was justified in that many of the characteristics of these two tissues,including the colloid osmotic pressure (COP) dependence on protein concentration,the compliance characteristics and the normal steady-state conditions are known. Theseparation was also possible because separate experimental response data for muscleand skin was available from rat studies by Reed and Wiig [19811. Due to lack ofexperimental information on human tissues, it is assumed in this model that theuninjured tissue compartment consists of unburned skin, muscle and other tissueswhile the injured tissue compartment consists of burned skin. In common with earliermodels, it is also assumed that there is no direct exchange of fluid or plasma proteinsbetween the two tissue compartments. Direct exchanges only occur between thecirculation and each tissue separately.2. In order to appreciate the influence of plasma proteins on the regulation of fluidvolume, knowledge of the effect of protein concentration on COP in eachcompartment is necessary. Due to its relative abundance, relatively low molecularweight and high osmotic activity, albumin is the major contributor to the interstitialCOP. For these reasons, and because albumin was the only protein whoseChapter 4: Model Formulation 47RESUSC RESUSCBloodUninjured Tissue Injured TissueLii • EBT0STI Qs‘EXUcBTQ EXUDBTJ —EVAPTIJ EVARBTLii QL,T ‘‘ LET QL,BT*1*+JURINE BLOOD QBL000Figure 4.1: Schematic of Compartmental Burn ModelChapter 4: Model Formulation 48concentration was monitored in many experiments on rats, albumin was selected as therepresentative protein in previous modelling efforts in the rat [Bert et al, 1988; Reed etal., 19891. In the current study, as in previous modelling studies in humans [Chapple,1990; Xie, 19921, albumin is again chosen to represent all the plasma proteins.3. The importance of cellular exchange in the MVES following thermal injury is wellrecognized, especially with regard to hypertonic fluid resuscitation [Griswold et al.,1991; Gunn et al., 1989]. In the current model, the effect of isotonic fluid resuscitationon the MVES is studied and as such, the transcellular transport of small ions isassumed to be at steady-state conditions. It is also assumed that the concentration ofsmall ions in the blood, interstitium and lymphatics is constant. The effect of cellulardamage resulting from burn injury is not considered in this model.4. Transcapillary exchange in the human MVES is described by the Coupled StarlingModel (CSM) or Patlak Model [Patlak et al., 1963], It is a homoporous model, inwhich the pores in the capillary membrane are assumed to be of a single size,characterized by the value of the albumin reflection coefficient (s). A reflectioncoefficient of unity implies that the membrane is perfectly impermeable to albumin,while a value of zero implies free passage of albumin across the capillary membrane. Inaddition, the pressure within the capillary is assumed to be uniform and represented bya single hydrostatic pressure term. The fluid and protein transport mechanisms whichcharacterize the CSM are described below.a) Fluid is transported from capillary to interstitium by filtration, according to Starling’sHypothesis [Starling, 1896] askF [P — — cY.(HPL —n1)], 4.1Chapter 4: Model Formulation 49where kF is the capillary filtration coefficient, determined as the product of thehydraulic conductivity of the capillary membrane per unit area and the surface areaavailable for fluid exchange, kA, as discussed in Chapter 2.b) Albumin is transported passively by diffusion and convection from capillary tointerstitium through the fluid-carrying channels in the capillary membrane according to—I CIAv .exp(—Pe)]Qs—JFl—orI / \ I’L 1—exp—Pe; jwhere ClAy is the effective interstitial albumin concentration defined byQIClAy= (v—)Q is the albumin content and VIEX the albumin excluded volume, assumed to represent25% of the normal interstitial fluid volume [Bert and Pinder, 1982].c) Under normal conditions, fluid is assumed to flow from the interstitium into thelymphatic system. The fluid is then drained from the lymphatics into the circulation. Itis assumed that the lymph flow rate is always positive. Lymph flow relationships havebeen developed for rats [Bert et al., 1988] and humans [Chapple, 1990] based on theassumption that lymph flow is a linear function of interstitial fluid pressure. Arelationship similar to that adopted by Bert et al. [1988] is employed in the currentmodel. The relationship ensures that lymph flow remains at its normal value undernormal conditions, varies linearly with interstitial pressure near normal conditions butceases when the interstitial fluid volume falls to the excluded volume value.For overhydrated tissue when F 13L.JL=JLNL+LS[P2r—F], 4.4Chapter 4: Model Formulation 50during tissue dehydration when P F >-____LL,NL1 D D I’L1i,w. 1,ExJwhile under conditions where P4.6‘L represents the lymph flow, LS the lymph flow sensitivity coefficient which expressesthe slope of the relationship, I,EX the tissue pressure at the excluded volume, andsubscript NL refers to normal steady-state conditions.d) Albumin is also exchanged across the lymphatic wall according toQL—JLj. 4.74.3 FLUID AND PROTEIN INPUTFollowing burn injury, intravenous infusions of clear fluids such as acetated Ringers,normal saline and dextrose are administered in order to replace volume lost from thecirculating plasma into the tissue compartments. Colloid-containing fluids are alsoadministered to replace protein loss from the circulating plasma. Based on individualpatient responses, the composition, volumes and infusion rate of fluids administered areadjusted accordingly. These inputs to the system are accounted for in the formulation ofthe model equations.4.4 FLUID AND PROTEIN OUTPUTFluid and proteins are also lost from the system following burn injury. These losses mustalso be taken into account in developing the mass balances.Chapter 4: Model Formulation 514.4.1 Water Loss by EvaporationIn a normal adult, the water loss through the skin excluding that lost as sweat is about 750mL/day, as reported by Davies [19821. The destruction of the stratum corneum and lipidsin the skin following burn injury allows increased evaporation of water through the burneschar. Water lost through burned skin via evaporation adds considerably to that normallylost through the lungs [Martyn, 19901. The evaporative water loss from skin followingburn injury may be estimated from the following formula reported by Sundell [1971],‘EVAP =[25+DEGj.TBsA, 4.8where EV is the rate of evaporative fluid loss from injured and uninjured tissue, DEGthe percentage of body surface burned and TBSA the total body surface area in m2,defined byTBSA = W°425 •H°75 •71.84 x 10. 4.9In Equation 4.8, W and H represent the patient’s preburn weight in kg and height in cm,respectively.4.4.2 Fluid Loss by ExudationSignificant volumes of fluid are lost as exudate from the burned surfaces of the body ofinjured patients [Arturson et al., 1984; Davies, 1982]. Knowledge of the loss of sodiuminto dressings and soiled bed linen gives an indication of the volume of exudate. Exudationrates of between 400 and 1000 mL/day have been reported [Davies, 1982] for burns of upto 50% of the total body surface area.In this study, estimates of fluid loss by exudation are made based on fluid balances onindividual patients. The fluid balance is performed between successive times whenmeasurements were available, i.e.,Change in patient weight = Volume of fluids given - Volume of fluids lostChapter 4: Model Formulation 52The fluids given include clear fluids (acetated Ringers, normal saline, dextrose) andprotein-containing fluids (iso-oncotic and hyperoncotic fluids as well as plasma). Thefluids lost include urine, blood loss and evaporative and exudative fluid losses. The fluidloss due to exudation can be estimated from the balance knowing the changes in the otherquantities between two successive times. The exudative fluid loss from patients for whichweight changes were not monitored is estimated from a linear relationship betweenaverage exudate output and the area of burn injury. This relationship is obtained by linearregression of clinical data reported by Davies [19821. The detailed calculations for eachpatient are presented in Appendices E and G.4.4.3 Protein Loss via ExudateLosses of labelled proteins in exudate have been measured by application of absorbentdressings to all burned areas and assay of radioactivity in the dressings after their removal[Davies, 1982]. The exudate losses are directly related to the extent of the burn. Between5 and 10 g of albumin/day have been reported to be lost via exudate with burns coveringbetween 25 and 35% of the body surface [Davies, 1962]. In patients with more severeburns, the equivalent of the albumin content of the normal adult plasma volume has beenreported to be lost over the first week. Protein losses of at least 2 to 3 g of proteinll% ofbody surface burned/day up to 7 to 8 gIl% burn/day have also been reported [Davies,1962]. The rate of albumin loss via exudate is assumed to be described by the followingmodified relationship proposed by Arturson et al. [1984],QEXUD = FXUD X CBT x EXFAC, 4.10where QD is the rate of albumin loss via exudate, EXFAC a factor ranging from 0 to 1and subscript BT represents the injured tissue.Chapter 4: Model Formulation 534.4.4 Blood LossEarly excision and grafting of the burn wound as soon as the patient is hemodynamicallystable, remain the keys to survival for patients with major thermal injuries. Surgicalincisions in the form of escaratomies and fasciotomies are necessary to prevent edemafrom building up sufficient interstitial pressure to impair capillary blood flow, thus causingischemia. Blood loss occurs as burn tissue is removed. The volume and rate of blood lossdepend on the depth of the burn, the area excised and the clotting profile of the patient.Although rates vary between patients, blood losses of as high as 250 mL/min have beenencountered [Martyn, 1990].Data regarding initial volumes of blood lost due to surgical procedures were provided forsome of the patients considered in the current study. The blood losses were clinicalestimates based on the extent of escaratomies. In addition, 10 mL blood samples wereassumed to be taken every 6 hours for laboratory analyses. In order to incorporate theseblood losses in the model equations, the losses were assumed to occur over a period oftime and expressed as blood loss per hour, BLoOD4.5 MODEL EQUATIONSThe equations that describe the model are obtained by carrying out fluid and protein(albumin) balances around each compartment in Figure 4.1, i.e.,Rate of Accumulation = Input Rate - Output Rate.Uninjured Tissue Balances:dVTJJ j j—F,T1 L,TJ EVAP,TIChapter 4: Model Formulation 54dQTI’9‘9 41di — S,T1 L,TIInjured Tissue Balances:dVBTJ_1-J -J 413di — F,BT “L.BT EVAP,BT XUD,BTdQBT 414di — S,BT L.BT EXUD,BTCirculatory Balances:dVPL= RESUSC— F,TI + LTJ — F,BT + LBT — UNE — BLOOD 4.15dQPL= QRESUSC — + QLTJ — QSBT + QL8T — QBLOOD 4.16The subscripts TI, BT and PL refer to the uninjured tissue, injured tissue and plasmacompartments respectively. In Equations 4.15 and 4.16, J and Q are the rates of fluid andalbumin flow respectively, while the subscripts RESUSC, URINE and BLOOD representthe resuscitation fluids, urine and blood respectively.4.6 PROPERTIES OF THE MICROVASCULAR EXCHANGE SYSTEMA set of six ordinary differential equations result from these balances on fluid and albumin.In order to solve these equations the following properties are required:i) hydrostatic pressure relationships for circulatory and tissue compartments(compliance or pressure versus volume relationships);ii) colloid osmotic pressure relationships for circulatory and tissue compartments(H = fii(c)); andiii) transport coefficients.Chapter 4: Model Formulation 55Some of these properties experience changes from their normal values immediatelyfollowing burn injury. In order to facilitate the quantitative analysis of these changes, thenormal steady-state conditions and the initial conditions that prevail in the patientimmediately postburn will first be presented.4.6.1 Normal Steady-State ConditionsIn order to establish reasonable values to describe the physiological conditions that exist inthe average human, a “reference man” has been defined [Reference Man ICRP 23, 19751.This “reference man” is described as a healthy male, 170 cm in height, 70 kg in weight andsupine in position. These normal steady-state conditions in a combined tissue compartmentand the general circulation are those employed by Xie [1992] and are summarized in Table4.1.Table 4.1: Normal Steady-State Conditions in “Reference Man”Tissue CirculationFluid volume, V, L 8.4 3.2Excluded volume, V, L 2.1 -Albumin content, Q, g 141.1 126.1Albumin concentration, c, g/L 16.8 39.4Available albumin concentration, CAV, g/L 22.4 -Hydrostatic pressure, P. mmHg -0.7 1 1.0Colloid osmotic pressure, H, mmHg 14.7 25.9Chapter 4: Model Formulation 56In order to account for the fact that the patients considered in this study differ from the“reference man” in terms of weight, fluid volume and albumin content amongst many otherproperties, the extensive physiological properties are scaled by a weight ratio, WR, where14’R = Weight of Patient 4 17Weight “Reference Man”Albumin concentration, hydrostatic and colloid osmotic pressures in the interstitial fluidand plasma are intensive properties and therefore are unaffected by changes in patientweight.4.6.2 Initial ConditionsThe initial conditions are the conditions that prevail in the patient immediately prior toinjury. Immediately postburn, the tissue compartment is divided into two separatecompartments: the injured tissue and the uninjured tissue compartments as shown inFigure 4.1. The uninjured tissue compartment comprises unburned skin, muscle and allother tissues, while the injured tissue compartment is made up of only burned skin.Partition of body tissue in the two tissue compartments following injury is based on theinterstitial fluid distribution in the “reference man” [Chapple, 19901 described in AppendixA.Let RELSM be the fraction of the total body made up of skin and DEG be the degree ofburn. The fraction of tissue burned isVAFBT = RELSM x DEG. 4.18The fraction of tissue that remains uninjured isVAFTI =[RELSM x(—DEG)]+[1--RELSM]=1-VAFBT. 4.19The extensive properties of the tissue must therefore be modified by the fraction of tissuein each compartment following the injury as follows:Initial value = Weight corrected normal value x VAFTI (or VAFBT). 4.20Chapter 4: Model Formulation 574.6.3 Compliance RelationshipsCompliance relationships are essential for the determination of the hydrostatic pressurefrom the fluid volume in the compartments. The hydrostatic pressures in the compartmentshave important roles in redistributing fluid and albumin following a burn injury. Circulatory ComplianceDue to lack of data from humans, the exact circulatory compliance relationship is not asyet established. As a consequence, a linear relationship is assumed between the capillaryhydrostatic pressure and plasma volume, where the rate of the change in plasma volume tothe change in capillary hydrostatic pressure is constant, i.e.,] =PCO+PCCO.[VpL—VpLO], 4.21where C,COMP is the reciprocal of circulatory compliance and subscript 0 refers to initialconditions. C,COMp has not been measured in humans. An estimate based on scaling upvalues reported for the rat [Bert et al., 1989] yields CCOMp = 0.009659 mmHg/mL. Interstitial ComplianceInformation concerning the compliance of human tissues is scarce. Based on the studies ofReed and Wiig on rat tissues [1981] and Stranden and Myhre on human lower limbsubcutaneous tissue [1982], Chapple [1990] developed the following “most-likely’compliance relationships for humans.Under conditions of dehydration where fr 8.4 x io mL,f =—0.7+1.96154x10.[V—8.4x10], 4.22while during conditions of tissue overhydration where V 12.6 x io mL,F =1.88+1.05x10.[V—1.26x ]. 4.23In the intermediate range, the compliance relationship is obtained by interpolatingexperimental P1 and V1 data by means of cubic splines.Chapter 4: Model Fonnulation 58Following burn injury, the interstitial compliance in uninjured and injured tissue ismodified to account for the partition of tissue in each of the compartments.Uninjured Tissue:During tissue dehydration where V (8.4 x x WI? x VAFTI) mL,P —0.7 + 1.96154 x .[v —(8.4 x x WI? x VAFTI )]. 4.24TI VAFTI x WR TIDuring tissue overhydration where v (12.6 x 1 o x WI? x VAFTI) mL,P =1.88+ 1.05x10 .[V—(126x1Ox’I? xVAFTI)]. 4.25TI VAFTIxWRFor intermediate values of VTI, the compliance relationship is obtained by cubic splineinterpolation of pressure and volume data for normal humans, with the volume datamodified by (WR x VAFTI) to account for tissue partition, i.e.,P1=fii[VxWRxVAFTI]. 4.26Additional relationships are required for the injured tissue compartment to account for thevery negative tissue pressure which has been observed in the burned skin of ratsimmediately postburn [Lund et al., 1988]. Due to lack of data from humans, pressure datafrom these experiments on rats are used to describe the change in interstitial pressure withtime in the first 2.5 hours postburn. Data from unresuscitated rats is used in the initialperiod postburn when no form of fluid treatment is given to the patient. Following thisinitial period up to 2.5 hours postburn when data is available, data from resuscitated rats isused. After 2.5 hours, modified forms of the normal interstitial compliance relationshipsgiven above are employed.Chapter 4: Model Formulation 59Injured Tissue:During the first 2.5 hours postburn, interstitial fluid pressure in injured skin versustime data from experiments on both unresuscitated and resuscitated rats by Lund et a!.[1988] are interpolated by cubic splines according to the general relationPBT=fn(t). 4.27Following this initial 2.5 hour period, the compliance relationships are based on therelationships developed for normal humans, with modifications to account for theinjury, i.e.,during tissue dehydration where VBT (8.4 x i03 x WR x VAFBT) mL,P = _O.7+1.96154x i03.{VBT —(8.4x io x WR xVAFBT)] 4.28BT VAFBT xWRand during tissue overhydration where VBT (12.6 x i03 x WR x VAFBT) mL,P =L88+ 1.05x10 .{v —(12.6x1O xWR xVAFBT)1. 4.29ST VAFBTxWR STFor intermediate values of VBT, the compliance relationship is again determined bypassing cubic splines through the interstitial pressure and volume data for normalhumans, with the volume data modified by (WR x VAFBT), i.e.,F17. =fn[VxWR xVAFBT]. 4.304.6.4 Colloid Osmotic Pressure (COP) RelationshipsColloid osmotic pressure results because the protein molecules cannot transfer freelythrough the semi-permeable capillary membrane. The following relationship betweenplasma albumin concentration and COP was determined by least squares fitting of datafrom the circulatory compartment of patients with nephrotic syndrome by Chapple [1990J:cPL=1.522x10FlPL. 4.31This relationship is assumed applicable to the plasma compartment following burn injury.The proteins contained in interstitial fluid are the same as those in plasma. Assuming thatChapter 4: Model Formulation 60the osmotic pressure exerted by the plasma proteins in plasma is the same as that exertedby proteins in interstitial fluid, similar relationships are applied to the interstitialcompartments following burn injury.Thus, for uninjured tissue,CTIAV =1.522x103.HTJ, 4.32and for injured tissue,CBTAV =1.522x103.HBT. 4.33The effective albumin concentration is used in Equations 4.32 and 4.33, since albumin isexcluded from some of the tissue space.4.6.5 Transport CoefficientsThe transcapillary fluid and protein fluxes depend on the following five transportcoefficients:i) fluid filtration coefficient, kF, reflects the hydraulic conductivity of the capillarymembrane;ii) permeability coefficient, PS, expresses the permeability of the capillarymembrane to albumin;iii) albumin reflection coefficient, a, reflects the relative impediment of thismembrane to the passage of albumin;iv) lymph flowrate under normal steady-state conditions, L,NL; andv) lymph flow sensitivity, LS, characterizes the efficiency of the lymphatic systemin removing accumulated interstitial fluid.Following burn injury, the transient response of these transport coefficients is generallyexpressed as an exponential function of time postburn. Based on the work of Arturson etal. [19841, Bert et al. [19891 proposed the form:Chapter 4: Model Formulation 61IA 1 A Ii r’ —,‘tl,where kA represents the overall transport coefficient, kNL the normal or preburn value ofthe time-dependent coefficient per unit area, A the surface area available for exchange, Gthe perturbation to the transport coefficient immediately postburn and r the relaxationcoefficient, indicating the time required for the transport coefficient to return to normal.The form of Equation 4.34 allows the transport coefficient values to return to normal aftera long period of time, i.e., as the patients wounds heal.The transport coefficient is the product of an area available for exchange term and aconductivity per unit area term, as in previous studies in the injured rat [Bert et al., 1989].It is assumed that, as the plasma volume changes, there is a proportional change in thearea available for mass exchange in the tissues. In addition, it is assumed that burn causesa fractional destruction of the capillary beds in the injured tissue, fbrther reducing the areaavailable for mass transport in this tissue. Consequently, in the uninjured tissue which ismade up of unburned skin, muscle and other tissues in the body, the overall transportcoefficient,‘T becomeskATJ=k.[FATJxVAFTIxWRj.[1+GTI.ej 4.35and the overall transport coefficient in the injured tissue, kAnT becomeskABT kNL[F’ABT xVAFBTxWR].[l+GBT.ej 4.36where FAT! is the fractional area available for exchange in the uninjured tissue, whichchanges with changing plasma volume, and is given byVPL/-VFRA CF4= /VPLQ 4.37I 1-VFRACand FABT is the fractional area available for exchange in the injured tissue, given byChapter 4: Model Formulation 62FABT= •AFRAC. 4.38VFRAC is the fractional plasma volume at which perftision in tissues is zero and AFRACis the fractional perfusion in injured tissue immediately following a burn injury. Bert et al.[19911, determined values for VFRAC and AFRAC by statistical fitting of modelpredictions to experimental data from rats. They found values that produced good fitswere VFRAC = 0.50 and AFRAC = 0.50. These values were also used in the currentstudy.The Fluid Filtration Coefficient, kF, depends on the area available for exchange and hencein uninjured tissue becomeskFTJ ‘F,NL .[FAfl xVAFTI xwi?j.{1+GkFTJ .e], 4.39while in injured tissue,kFBT = kF .[FABT xVAFBT xWR].[1+GkF .eJ. 4.40The Permeability Coefficien4 PS, also depends on the area available for exchange andthus in uninjured tissue isPSTJ = PSNL .[FA1 xVAFTI xWR].{1+Gpj .en1], 4.41and in injured tissue,PSBT = PS .[FABT xVAFBT xWR].[1+GPSBT .e]. 4.42The Albumin Reflection Coefficien4 o, does not depend on the available area forexchange as it indicates the relative impediment to the passage of albumin through thecapillary membrane. In addition, the perturbation to a is negative as this coefficient hasChapter 4: Model Formulation 63been found to decrease rather than increase following burn injury [Pitt et al., 1987]. Thus,in uninjured tissue, it is assumed thatTJ =ONL.[1—GUTreI, 4.43while in injured tissue,0BT NL[1GU,BTj 4.44The Lymph Flowrate under normal steady-state conditions, L’ does not depend on thefractional area available for exchange which changes with plasma volume. It doeshowever, depend on the fractional destruction of the capillary beds in the injured tissue.Thus, in uninjured tissue, L.,NL,TI is given byJL.NL,TJ L,NL .[vAFTI xWRj.[1+GJLTI .e], 4.45while for injured tissue,= L,NL .{AFRAC xVAFBT xWR].[1+GJLBT .e]. 4.46The Lymph Flow Sensitivity Coefficient LS, also depends only on the fractionaldestruction of the capillary beds in the injured tissue. Consequently, in uninjured tissue,LSJisgivenbyLSTJ = LS .[VAFTI x WR}.[1+GLSTJ .e], 4.47while for injured tissue,LSBT = LSNL .[AFRAC x VAFBT x WRJ.[1 + GLSBT .e} 4.48The normal values for these transport coefficients have been determined for the ‘referenceman’ by Xie [1992] (see Appendix B.1). The capillary membrane parameters thatdetermine the exchange of albumin are kF, c and PS. These individual transportcoefficients are not independent, but are linked to each other via changes in the capillarypore radius. Thus, once the perturbation to kF is known for the injured and uninjuredChapter 4: Model Formulation 64tissue, the perturbations to a and PS for both tissues may be estimated based on theseinterrelationships (see Appendix B.2). Current knowledge regarding changes in thelymphatic system following thermal injury is very limited. Consequently, the perturbationsto LNL and LS in the injured and uninjured tissue postburn are assumed to be zero.4.7 NUMERICAL SOLUTION OF MODEL EQUATIONSFor given patient data (degree of burn, weight and height of patient) and resuscitationprotocol (fluid and protein input), simulation of the MVES following injury involvessolving the six first-order ordinary differential equations (Equations 4.11 - 4.16), arisingfrom the fluid and albumin balances. These differential equations must be solvedsimultaneously with the relationships defining interstitial and plasma hydrostatic andcolloid osmotic pressures as well as the other auxiliary equations. Due to the nonlinearityof some of these relationships, the differential equations cannot be solved analytically.Consequently, the classic fourth-order Runge-Kutta numerical integration method is usedto solve the equations, with a global accuracy of 0.00 1 mL and 0.00 1 mg for fluid andalbumin contents respectively. The computer program is documented in Appendix KChapter 5: Parameter Estimation 65CHAPTER 5PARAMETER ESTIMATION5A iNTRODUCTIONThe model equations developed in Chapter 4 contain unknown parameters which need tobe determined in order to simulate the behaviour of the microvascular exchange systemfollowing a burn injury. In the first part of this chapter, the parameters to be determinedare presented. This is followed by a description of the clinical data used for theidentification of the parameters and the validation of the model. Finally, the optimizationprocedure is discussed.5.2 PARAMETERS TO BE DETERMINEDThe transcapillary fluid and protein fluxes depend on five transport coefficients: the fluidfiltration coefficient, kF, permeability coefficient, PS, albumin reflection coefficient, a,lymph flowrate under normal steady-state conditions, 3LNL and lymph flow sensitivitycoefficient, LS. The transient response of these transport coefficients to burn injury isexpressed as an exponential function of time postburn as described in Chapter 4. Ingeneral, the time-dependent transport coefficients have the form:kA=k.A.[1+G.ej. 4.34The unknown parameters identified from the above relationship include the perturbationsto the transport coefficients in both the injured and uninjured tissues and the relaxationcoefficient as follows:Chapter 5: Parameter Estimation 66i) perturbation to the fluid filtration coefficient: GTI, GBT (in Equations 4.39and 4.40);ii) perturbation to the permeability coefficient: GPSTI, GPSBT (in Equations 4.41and 4.42);iii) perturbation to the albumin reflection coefficient: Ga,Tj, Ga,BT (in Equations4.43 and 4.44);iv) perturbation to the lymph flowrate: GNLTf, GNLBT (in Equations 4.45 and4.46);v) perturbation to the lymph flow sensitivity: GTI, GBT (in Equations 4.47 and4.48); and thevi) relaxation coefficient: r.The factor, EXFAC, in Equation 4.10 describing the protein loss via exudate wasestimated by Arturson et al. [19841 to be one fourth of the proteins originally associatedwith the exuded fluid. Fluid loss due to exudation has been reported by Davies [1982] toaccount for 5 to 10 g of albumin per day when the burn covers between 25 and 35% of thebody surface. Protein losses in exudate from the burn wound are therefore significant andcontribute to a decrease in albumin concentration observed during the early phasepostburn. The basis for the estimation of EXFAC by Arturson et al. is unclear and as such,EXFAC was also considered as an unknown parameter to be determined.The capillary membrane parameters which determine the exchange of albumin are kF,and PS. As discussed in Appendix B.2, these transport parameters are not independent,but are linked to each other via changes in the capillary pore radius. Based on relationshipsreported by Reed et al. [1991], the perturbations to the albumin reflection coefficient andpermeability coefficient in injured and uninjured tissues can be determined from the valuesof the perturbations to the filtration coefficient in both tissues, GkFTJ and 0kF,BT• TheChapter 5: Parameter Estimation 67mathematical manipulations are presented in Appendix B.2. GLNLTJ, GNLBT, GTI andare assumed to be equal to zero due to the lack of information concerning changesto the lymphatics following injury. In the final analysis, only four parameters remained tobe determined, namely GTJ, GB r and EXFAC.5.3 CLINICAL DATAThe most common measurements made to monitor burn patient conditions include venoushematocrit and plasma protein or albumin concentration. The response of the patient tofluid replacement is also monitored through the hourly production of urine, vital signs,plasma electrolyte concentrations such as sodium, potassium or chloride ions, and thevalue of hematocrit. Other measurements including central venous and arterial pressuresare also made when the state of the patient requires it. Four different sets of clinical datawere used in this study for parameter estimation or model validation. These are presentedbelow.5.3.1 National Burn Centre (NBC) DataDr. T. Lund and his colleagues working at the National Burn Centre in Norway, kindlyprovided specific information for five patients admitted to the Burn Centre, who hadsuffered deep cutaneous burns. This patient information was unique in that, in addition tothe most commonly made measurements mentioned in the previous section, they alsomeasured the transcapillary colloid osmotic pressures (COPs) in injured and non-injuredskin of these seriously burned patients. The raw data were manipulated to convert theminto a form that could be used in this study. The manipulations included the determinationof plasma volume from hematocrit and the estimation of exudative fluid loss from the burnwound by fluid balances. These are detailed in Appendices D and E respectively. The finalform of the patient data and the individual resuscitation protocols are also presented inChapter 5: Parameter Estimation 68Appendix C. This patient information was used directly in the parameter estimationprocedure.5.3.2. Birkeland DataDr. Birkeland, in a collection of articles published in the Journal of the Oslo City Hospitals[1969], reported results from a study of over 100 patients. The burn patients weregrouped according to the percentage burn surface area sustained and were observed priorto start of replacement therapy. Data of direct interest in the current study were theplasma volume changes in five groups of burn patients as presented in Appendix F. Thesedata were especially useful for investigating the response of the microvascular exchangesystem during the initial period postburn, when no form of fluid therapy was administered.As such, it was also used directly in the parameter estimation procedure.Due to lack of information concerning urine production, it was assumed that the kidneysshut down in the initial period postinjury. In addition, due to the unavailability of specificadmission information concerning the weight and height of the patients studied, standardweights and heights of 70-kg and 170-cm respectively were assumed. The normal steady-state conditions in each of the patients were also assumed to be those in the reference manwhich are presented in Table 4.1. Exudative fluid losses were estimated based on dataavailable from a study by Davies [1982]. The rate of exudative fluid loss from patientswith different burn areas was monitored during the initial period postburn before fluidtherapy was initiated. To the best of the author’s knowledge, these were the only suitabledata that could be used to estimate the initial exudative fluid loss from the patients studiedby Birkeland. The details of this estimation are presented in Appendix G.Chapter 5: Parameter Estimation 695.3.3. Arturson DataPublished information by Dr. Arturson and his colleagues in Sweden [1989] concerningthe treatment of a patient with thermal injury was used to validate the predictions of themodel developed in this study. The monitored physiological variable of direct applicationto the current study was the erythrocyte volume fraction or hematocrit. The patient dataand the fluid resuscitation protocol are presented in Appendix H. Based on the fluidtherapy, cumulative urine production and change in body mass information, it was possibleto estimate exudative fluid loss by fluid balances as described in Appendix E.5.3.4. Roa DataDr. Roa and her colleagues in Spain have also been actively involved in the developmentof mathematical models to investigate microvascular exchange in burn patients. Thetreatment of two burn patients and clinical data collected from these patients werepresented in a publication by this group [1990]. This information, together withinformation provided by Dr. Roa through personal communications were also used toindependently validate the predictions of the model developed in this study. The relevantinformation including the resuscitation protocol, urine volume, hematocrit and plasmaprotein concentration is presented in Appendix I.5.3.5. Normalization of DataThe four different data sets described previously consist of one or more of the followingquantities: plasma volume, VPL, albumin concentration in plasma, CPL and colloid osmoticpressures (COPs) in plasma, injured and uninjured tissues, 11PL’ 11BT and T1 respectively.In order to make these quantities comparable so that they could be used collectively in theparameter estimation procedure, it was first necessary to normalize them. The plasmavolumes and albumin concentrations were normalized with respect to their preburn valuesChapter 5: Parameter Estimation 70based on normal steady-state values for the reference man, scaled to account for differingpreburn weights where appropriate, i.e.,X=-- 5.1xo,where X refers to the measured physiological quantity and subscripts 0 and t refer to thepreburn and postburn times, respectively.The availability of COP data made it possible to investigate the distribution of protein inplasma and the injured and uninjured tissue compartments. However, there appears tohave been a systematic error in the COP measurements made by Lund et al. The measuredvalues were lower than what were generally expected. In order to use these data, theinjured and uninjured tissue COPs were normalized with respect to the plasma COP tonullify the effect of the systematic errors in the measurements, i.e.,=/flp 52fl//PL,o5.4 PARAMETER ESTIMATION PROCEDUREThe proposed method to determine the identified model parameters was based on thefitting of predicted results from the model to clinical data. The adopted procedure entailedfinding the parameters which gave the best statistical fit between the model predictionsand the clinical data based on the weighted least-squares criterion. The optimumparameters were those which would minimize an objective function, OBJFUN, which isthe sum of the squares of the deviations of the normalized clinical data from the predictedvalues, i.e.,Chapter 5: Parameter Estimation 71OBJFUN = w(x.- XpDi=I j=1where N represents the number of data points for the ith variable, M the number ofvariables monitored, X, the experimental or clinical value, X1,,, the predicted valuefrom the simulation and WF is the weight for each data point.In order to indicate the significance or relative importance attached to each data pointwithin a data set, each point was assigned a weighting factor, WF. Normally, WF is setequal to the inverse of the error in measurement (or the standard deviation squared) ofeach data point. Due to the unavailability of information concerning the experimentalerrors involved in the clinical measurements, it was not possible to assign weightingfactors to the data in this manner. As a result, each data point was weighted equally byassigning a weight of unity to each point.A standard constrained optimization technique was selected to estimate the unknownparameters by finding the minimum of the nonlinear objective function, subject toconstraints, if any. This technique is a slightly modified version of K. Schittkowski’simplementation of the recursive quadratic approximation method of Wilson, Han andPowell [1981].5.4.1 Preliminary TestsThe model was tested by performing a simulation with assumed, but physiologicallyreasonable values of the four parameters, GTI, GBT, r and EXFAC. Predictions of theresponse of one of the NBC patients to fluid therapy are presented in Figure 5.1. Patient 1,a 30-year old male who sustained a 21% burn surface area injury, was treated according tothe fluid resuscitation protocol presented in Table C.2. The trends predicted by the model-JC)C0ICwC)C0C)CE.0Chapter 5: Parameter Estimation 721.1•1’I•I’I’16000 —VTIVGT14000 VPL4:::::8000>600040002000015 PBTPPL1*—100)IE5EU)U)-50C)-10U)0>I-20-250)IEEU)IU)C’,U)I—C-)0EC’,000()0 10 20 30 40 50 60 70Time, hours postburn0 10 20 30 40 50 60 70Time, hours postburnFigure 5.1: Simulation of MVES for NBC Patient IGKFTI=0.5; GKFBTI 0.0; r0.025 Ih; EXFAC= 1.00Chapter 5: Parameter Estimation 73were in agreement with trends observed clinically. Following burn injury, fluid is lost fromthe burn wound due to exudation and evaporation and protein is also lost via exudate.However, immediately postburn and prior to the start of fluid therapy, large amounts offluid and protein are transferred to the injured tissue from the circulating plasma. Thisresults in edema formation as well as a considerable increase in the albumin content in theinjured tissue compartment. The circulating plasma experiences a loss in fluid volume andprotein content due to the increased rate of transfer into the injured tissue. The uninjuredtissue compartment experiences a loss in fluid volume, resulting in an increase in albuminconcentration. Fluid resuscitation is started one hour after injury and soon afterwards, thedecrease in plasma volume is reversed, increasing towards its normal volume of about4023 mL. The injured tissue however, continues to increase in its fluid volume but startsto resolve after about 1.5 days. The uninjured tissue responds to the fluid therapy almostimmediately and becomes swollen, but to a lesser extent than the injured tissue. After 1.5days, the uninjured tissue volume starts decreasing towards its normal volume of about630 mL. The albumin concentration in plasma continues to decrease during the first dayfollowing fluid resuscitation but then starts to increase in the second day. A detaileddiscussion of these trends will be presented in Chapter 6. These initial results confirmedthe adequacy of the model to describe the phenomena which occur in the MVES followingburn injury. A steady-state simulation was also performed by solving the model equationsover a long period of 480 hours (20 days). The results are shown in Figure 5.2. The mostimportant observation was the ability of the model to predict the return of the systemvariables to their normal values after a long period. The model was also able to predict theequalization of the opposing fluid and protein fluxes in the injured and non-injured tissuesin the steady state. This further confirmed the ability of the model to correctly predict theresponse of the microvascular exchange system to burn injury. As such, the model couldbe confidently used in the parameter estimation algorithm.Chapter 5: Parameter EstimationFigure 5.2: Steady-State Simulation of MVES for NBC Patient IGKFTI=O.5; GKFBTIO.O, rO.O25 /h; EXFAC=1.OO745550-JEE0>U--J)45co 40353000 2520< 15‘ICTJCBTCPLPTIPBTPPL—PITIP1STPIPL’I2520C)EE 10U)U) Qci_-5C)• -10(0o -15I—> -20-2512001000800.c 600E 400200-200-400-60034)32E 30E 2822C.) 201816C 141200 10350003000025000920000U-.9 1500021000050000—QSTIQSBTQLTI -——QLBT0 50 100 150 200 250 300 350 400 450Time, hours postburn0 50 100 150 200 250 300 350 400 450Time, hours postburnChapter 5: Parameter Estimation 75The optimization technique was also tested in two ways. Plasma volume and albuminconcentration as well as plasma, injured and uninjured tissue COP data were generated bysimulating the response of NBC Patient 1 to fluid therapy with assumed values of GTI,GBT, r and EXFAC. In the first test, these “error-free” data were used in estimating themodel parameters which were assumed unknown. The optimization technique requiredthat initial values for the parameters be provided from which the search for the optimumvalues could begin. The optimizer successfiully identified the parameter values used togenerate the “error-free” data set, irrespective of the initial values provided to initiate thesearch. For example, the “error-free” data set was generated using the following parametervalues: GTI = 0.50; GkFBT = 10.0; r 0.025 h’ and EXFAC = 1.00. These data werethen used in the optimization program to obtain “best-fit” values for GTI and GBTstarting with initial estimates of 1.0 and 15.0 respectively. Optimum values and confidenceintervals estimated for G,TI and GkFBT were 0.37±0.30 and 11.2±2.3 respectively. Theexpected good fits between the clinical data and the model predicted responses areillustrated in Figure 5.3. The optimization procedure was then repeated using perturbeddata values obtained by generating random errors on the “error-free” data. The optimizeridentified the following optimum parameter values and confidence intervals: 0TI =0.70±0.31 and GkFBT = 11.5±3.2. The clinical data and the model predicted responses areshown in Figure 5.4. It was observed however, that using the “noisy” data, as the numberof parameters to be determined increased to include r and EXFAC, the optimizer wasunable to identifS’ the expected optimum values.Following on from these tests, the optimization technique was next used to determineparameter values based on the clinical data obtained from the NBC patients. Differentinitial estimates were provided to the program from which the search for the optimumvalues could begin. The optimizer was unsuccessful in determining global optimum valuesfor all the parameters. Different “optimum” values were obtained from the routineChapter 5: Parameter Estimation 7642004000-J380036003400LL 32003000-JD) 4004-4-cU)C.)0(-). 25E2003.5U) 3.0:3U)U)a)0... 2.0C)1.5o 1.0•0o 0.50o 0.00 10 20 30 40 50 60 70Time, hours postburnFigure 5.3: Model Predicted Response of MVES and “Error-free”Data for NBC Patient 1‘ I ‘ I • I•• • I • I ‘ I ‘ I—PITIR—— PIBTR —• PITIRexp• PIBTRex—a• I • I • I • I • I • IChapter 5: Parameter Estimation 778000 i ‘ i ‘ i ‘ i ‘ i ‘ i ‘ i—J 6000E4000____________________2000U••0 •• I i I I i II Ii ‘ i ‘ i i i6050 -•:. 100 I I II I I035•—PITIR-——PIBTR -PITIRexpu 2.5 — • PIBTRex0 2.0 • \•0. ••I -0.50.0 I I • I •I I i I0 10 20 30 40 50 60 70Time, hours postburnFigure 5.4: Model Predicted Response of MVES and “Noisy Datafor NBC Patient IChapter 5: Parameter Estimation 78depending on the initial values specified. Ideally, the initial values should be as close to theglobal optimum values as possible to reduce the chances of encountering local optima andof false convergence. The results therefore suggested that the “multi-dimensional surface”of the objective function had several saddle-points or shallow depressions. The nature ofthis objective function surface for Patient 1 is shown in Figure 5.5.The results from this preliminary study suggested the need to:i) introduce constraints to ensure physiologically feasible predictions by the model;ii) develop a more appropriate optimization scheme;iii) further scrutinize the patient data; andiv) re-assess the parameters to be determined by the statistical procedure.5.4.2 ConstraintsSimulation predictions based on parameters determined from the preliminary studies usingthe real patient data indicated that certain trends predicted were either not physiologicallyfeasible or were not consistent with clinical observations. Consequently, constraints wereimposed such that:i) GBT is always greater than GTT due to the fact that following injury, it isobserved that the injured tissue undergoes relatively larger changes than theuninjured tissue; andii) the injured tissue volume at any time postburn, VBT, is always greater than itsinitial volume, VBTO. This ensures that the injured tissue compartment is notdehydrated at any time postburn, in accordance with clinical observations.Chapter 5: Parameter Estimation 79Figure 5.5: Objective Function Surface for NBC Patient 1GKFTIO. 5; GKFB T= 10.0; r=O. 025 /7?; EXFAC= 1.0(The shallow depressions represent local minima)100a):3Cu>0C:3LI>G)-D01ooChapter 5: Parameter Estimation 805.4.3 Modified Optimization Strategy5.4.3.1 Re-assessment of Parameters to be DeterminedAnalysis of the clinical data used in the optimization procedure revealed that the qualityand in particular, the quantity of the data did not justif,’ estimating all four parameters,GTJ, GkFBT, r and EXFAC by statistical fitting. Consequently, it was proposed that GTIand GBT be determined by the fitting procedure, while r and EXFAC were investigatedonly at discrete values.Relaxation Coefficient r. Information concerning the time it takes for the transportcoefficients to return to normal is sparse. Bert et al. in their studies concerned with rats[1989] assumed that the transport coefficients approximately return to their normal valuesafter about 12 hours. Due to the larger body size of humans as compared to rats, a longerresponse time would be anticipated. Arturson et al. [1984] assumed that normal plasmaleakage occurs after about 70 hours postburn in the case of local edema. Roa et al. [1988]reported that the capillary permeability coefficient in burned tissue returns to its normalvalue in between 48 and 72 hours postinjury. In the current study, two values of r wereconsidered, 0.025 h’ and 0.008 h’, suggesting that the transport coefficients return to95% of their normal values in 5 and 15 days respectively.Exudation Factor, EXFAC. The exudation factor, which is the fraction of protein in theinjured tissue interstitial fluid which is lost with the exudate, must range from 0 to 1. Indetermining the optimum value, four values of EXFAC were considered: 0.25, 0.50, 0.75and 1.00.With these redefined search levels for r and EXFAC, the strategy of the parameterestimation procedure was to determine the pair of values of GkFTI and GkFBT which gaveChapter 5: Parameter Estimation 81the minimum objective function for each of the eight possible combinations of r andEXFAC in the experimental design shown in Table 5.1. The optimum GkFTI and GBT fora given patient were then determined as the pair which yielded the minimum objectivefunction amongst the eight combinations of r and EXFAC. Optimization Scheme: “Gridding Approach”It was also evident from the initial tests that the quality and quantity of clinical dataavailable did not warrant a formal optimization technique. As such, an approach wasdevised to ensure that global optima as opposed to local optima, were obtained. Thisapproach was based on a “surface gridding” technique described below.Table 5.1: Factorial Experiment Study___________EXFACr 0.25 0.50 0.75 1.000.008 * * * *0.025 * * * *The major steps in the search method were as follows:i) Select wide ranges for GkF,TJ and GkFBT which are physiologically acceptableand within which the optimum values can be located. Ranges of 0 - 10 and 0 -100 were selected for GkF,TI and GkFBT respectively.ii) Divide the ranges of GkFTI and GBT with variable step sizes to form a coarsegrid: step sizes of 1.0 and 10.0 for GkFTt and GBT respectively.Chapter 5: Parameter Estimation 82iii) Determine the objective function for all the nodes (GTI, GBT) in the grid,which satisfy the conditions that GkFTI < GkFBT and VBT> VBTO. This resultedin a surface with several depressions or minima.iv) Select a narrower range of values for GTI and GBT which contains theshallowest depression.v) Construct a finer grid by subdividing the narrow ranges with smaller step For all the grid nodes which satisfy the constraints GTJ < 0kF,BT and VBT>VBTO, calculate the objective function values. This resulted in a surface with asingle depression.vii) The pair of values of and G,BT corresponding to the shallowest point isconsidered the optimum.Using this successive gridding process, a well defined single depression was obtained in allthe cases considered in the current study. For each burn patient or group, the searchscheme was applied to each of the eight combinations of r and EXFAC in the factorialdesign shown in Table 5.1. The optimum values for a given patient or group wereconsidered to be those corresponding to the minimum objective function for valuesamongst the eight cases.5.5 SUMMARYIn summary, a simple but reliable method was developed to determine the modelparameters, The method ensured that the selection of the optimum parameters was basedon the global minima as opposed to local minima. The model parameters determined usingthis method and the model validation are discussed in Chapter 6.Chapter 6: Results and Discussion 83CHAPTER 6RESULTS AND DISCUSSION6.1 INTRODUCTIONSimulation of the response of the human microvascular exchange system (MVES) to fluidresuscitation following thermal injury is only feasible if all the model parameters areknown. Based on the procedure discussed in Chapter 5, it was possible to determine themodel parameters required to fhlly describe the model. The parameters obtained using theNational Burn Centre (NBC) and Birkeland data sets independently are first presentedfollowed by a discussion of the global parameters obtained using a combination of the twodata sets. A description of sensitivity tests conducted to investigate the influence of theseglobal parameters on the model predictions is then presented. Using the global parameters,the ability of the model to satisfactorily predict the response of patients monitored in otherindependent studies is examined. As this latter patient information was not used in theparameter estimation procedure, this constitutes independent validation of the model.Finally, the model is used to predict patient response to three commonly used resuscitationformulae.6.2 ESTIMATED PARAMETERS6.2.1 Parameters Determined Using NBC DataThe objective fi.inction value (OBJFUN) described in Chapter 5 was estimated usingplasma volume, albumin concentration and colloid osmotic pressure data from fivepatients receiving various forms of fluid therapy. For each patient, the values of GTJ andChapter 6: Results and Discussion 84GBT which gave the minimum objective function value for all eight combinations of rand EXFAC were determined. The results are presented in Appendix J. The fourparameters, GkFTI, GBT, r and EXFAC, which gave the minimum objective functionvalue were considered the optimum for each patient. These patient results are presented inTable 6.1.Table 6.1: Optimum Parameters Determined Using NBC DataPatient Degree, % GkF,1 GkPRT r, h1 EXFAC OBIFUN NEXP1 21 0.0 8.0 0.025 1.0 0.48 122 51 0.5 4.0 0.025 1.0 1.63 203 80 0.0 6.0 0.025 1.0 3.65 224 59 1.0 5.0 0.025 1.0 2.83 215 72 0.5 5.0 0.025 0.75 3.75 30Clinical observations [Arturson, 1961; Lund et al., 19921 indicate that burns which exceed25% of the total body surface area initiate both systemic and localized changes whichdiffer from burns Less than 25%. Burns less than 25% of the total body surface areagenerally cause smaller changes in the uninjured tissue as compared to burns exceeding25%. Generalized edema has been observed [Arturson, 19611 when the extent of theburned tissue is greater than 25% of the total body surface area. Consequently, the fiveNBC patients were separated into two groups: less than 25% and greater than 25% of thetotal body surface area. Patient 1 was the only patient with a less than 25% burn. Theremaining four patients sustained burns greater than 25%. The combination of the fourparameters which gave the minimum objective function was then determined for each ofthe two groups. This was based on the sum of the objective function values for theChapter 6: Results and Discussion 85individual patients in a particular group for the same values of the four parameters. Theresults are shown in Table 6.2.Table 6.2: Optimum Parameters for Two Burn Groups Using NBC DataBurn Group, % GkFTI GkERT r, h-’ EXFAC OBJFUN NEXP0- 25 0.0 8.0 0.025 1.0 0.48 1225 - 100 0.5 5.0 0.025 1.0 12.47 936.2.2 Parameters Determined Using Birkeland DataThe burn patients studied by Birkeland were grouped according to the percentage burnsurface area and monitored prior to the start of fluid replacement therapy. The objectivefbnction values for each burn group were based on plasma volume data only. The valuesof GTJ and GBT which yielded the minimum objective fhnction value for all eightcombinations of r and EXFAC for each burn group are detailed in Appendix J. The fourparameters which gave the minimum objective function value for each of the five groupsof patients are presented in Table 6.3.Table 6.3: Optimum Parameters Determined Using Birkeland DataBurn Group Degree, % GkFTT GkF nr r, fr1 EXFAC OBJFUN NEXPI 2-9 0.6 3.0 0.008 0.25 2.01x10 6II 10- 19 1.1 8.0 0.025 1.00 0.86x10-3 6III 20 - 30 3.4 8.0 0.008 0.25 7.73x10-3 5IV 39-49 5.8 6.0 0.008 0.25 5.68x10-3 4V 54-90 5.8 6.0 0.008 0.25 4.09x10-2 4Chapter 6: Results and Discussion 86The five groups were then separated into two large groups of burns less than 25% andburns greater than 25%, as for the NBC data set. Patients in burn groups I and II sustainedburns less than 25% while patients in groups II, IV and V suffered burns greater than25%. The parameters giving the minimum objective function for each of these two groupsare presented in Table 6.4.Table 6.4: Optimum Parameters for Two Burn Groups Using Birkeland DataBurn Group, % GkF,1 GkFRT r, h’ EXFAC OBJFUN NEXP0 - 25 0.5 12.0 0.008 0.25 9.02x10-3 1225 - 100 3.8 8.0 0.008 0.25 6.56x 10-2 136.2.3 Parameters Determined Using Combination of NBC and Birkeland DataThe NBC and Birkeland data sets were combined to determine global parameters whichwould be representative for any patient in the two burn groups, less than and greater than25%. The procedure was based on the sum of the objective function values of the samecombinations ofG TI’ G,BT, r and EXFAC for each patient in a given group.The magnitudes of the objective function values based on Birkeland’s data differed fromthose based on the NBC data because of differences in the quantity and type of data usedin their estimation. The objective function values determined using the NBC patient datawere about two orders of magnitude higher than those obtained using Birkeland’s databecause a greater amount and different types of patient data were available. Thus,optimization based on the direct summation of objective function values from the twoindividual data sets would be erroneous. The higher values from the NBC data woulddominate the overall objective function value and thus mask any meaningful contributionChapter 6: Results and Discussion 87from Birkeland’s data. As such, a scaling factor was applied to the objective fUnctionvalues from Birkeland’s burn groups before combining the two independent data sets. Itwas necessary to find a suitable factor that would give equal weighting to the two datasets. The results obtained using three different scaling factors, 30, 100 and 200, arepresented in Tables 6.5 and 6.6.Table 6.5: Optimum Parameter Values for Burns Less Than 25%Factor GkFTJ GkF RT r, h’ EXFAC OBJFUN30 0.5 10.0 0.025 1.0 1.19100 0.5 12.0 0.025 1.0 2.00200 0.5 13.0 0.025 1.0 3.08Table 6.6: Optimum Parameter Values for Burns Greater Than 25%Factor GkFTT GkFRT r, h’ EXFAC OBJFUN30 1.0 8.0 0.025 0.75 26.26100 2.0 9.0 0.025 0.75 37.01200 2.5 9.0 0.025 0.75 46.64Using a scaling factor of 100, the magnitude of the objective function values determinedusing Birkeland’s patient data were comparable with the values determined using the NBCpatient data. In other words, direct summation of the objective function values from bothdata sets resulted in an approximately equal contribution to the overall objective functionvalue for burns less than and greater than 25% of the total body surface area. The NBCpatient data had a larger influence on the overall objective function value with a factor ofChapter 6: Results and Discussion 8830, while Birkeland’s patient data were more influential with a factor of 200. The resultsobtained with a factor of 100 were therefore chosen as the optimum global parameters.Clinical data from Birkeland’s patients were available for up to 12 hours postburn in thecase of patients from burn groups I, II and III and 4 hours postburn from burn groups IVand V. On the other hand, data from the NBC patients were available for up to 72 hourspostburn during which fluid therapy was administered. Using the two data setsindependently gave different results with regards to the relaxation coefficient, r and theexudation factor, EXFAC. The relaxation coefficient represents the time it takes for thetransport coefficients to return to their normal values. Two discrete values wereinvestigated in the current study, 0.025 h’ and 0.008 h’, suggesting that the transportcoefficients return to 95% of their normal values in 5 and 15 days respectively. With theNBC patient data, a value of 0.025 fr1 for r was obtained while Birkeland’s patient dataresulted in a value of 0.008 h-’. EXFAC values of 1.00 and 0.25 were obtained for the twodata sets respectively. The NBC patient data, which spanned 3 days, had a larger influenceon the final results for r and EXFAC when the two independent data sets were combined.During this longer time period, more information concerning the response of the transportcoefficients to burn injury and protein loss from the burn wound via exudate could beinferred. In addition, Birkeland’s data contained no information about protein behaviour.Thus, EXFAC values estimated using the NBC patient data would be more meaningful.6.2.4 Summary of ParametersAs discussed in Chapter 5, the other model parameters GPSTI, GPSBT, G1 and GaBT canbe determined from the values of GkF,TI and GBT. A summary of optimum modelparameters found in this study is presented in Table 6.7.Chapter 6: Results and Discussion 89Table 6.7: Coupled Starling Model ParametersBurns less than 25% Burns greater than 25%Uninjured Injured Tissue Uninjured Injured TissueTissue TissueGfrF 0.5 12.0 2.0 9.0G5 6.3 45.9 18.5 41.7Ga 0.1 0.8 0.3 0.7G11 NI 0.0 0.0 0.0 0.0G1 0.0 0.0 0.0 0.0r, h-’ 0.025 0.025 0.025 0.025EXFAC - 1.00 - 0.75The results obtained indicate that following burn injury, the injured tissue generallyundergoes a much greater change than the uninjured tissue. Immediately following burnsless than 25%, the filtration coefficient in uninjured tissue increases to 1.5 times its normalvalue while the injured tissue experiences a greater change by a factor of 13. Burns inexcess of 25% cause more pronounced changes in the uninjured tissue as compared tothose experienced following smaller burns where the uninjured tissue filtration coefficientincreases to 3 times its normal value. The injured tissue coefficients on the other hand,experience changes similar to those experienced following smaller burns. The filtrationcoefficient increases to 10 times its normal value immediately postburn. Perturbations tothe normal lymph fiowrate and lymph flow sensitivity coefficient were set to zero in bothtissues and for both degrees of burn due to lack of pertinent information.Chapter 6: Results and Discussion 90As discussed previously, due to the fact that data from the NBC patients were availablefor a longer period postburn as compared to data from Birkeland’s patients, thecontribution of the latter data set to the global value of r was minimal. Using the NBCpatient data independently, a value 0.025 h’ was obtained for r while Birkeland’s patientdata resulted in a value of 0.008 h1. A global value of 0.025 h’ was obtained when thetwo sets were combined for both burn groups, less than and greater than 25%. Thissuggests that irrespective of the size of the burn injury, the tissue transport propertiesreturn to 95% of their normal values in about 5 days. As was the case with the relaxationcoefficient, the global value of the exudation factor, EXFAC, was more stronglyinfluenced by the NBC data set. The rate of exudative protein loss from the injured tissuefollowing smaller burns was found to be similar to that lost following large burns.To the best of the author’s knowledge, no clinical data are available with which to directlycompare these estimated parameters. However, best fit perturbed parameter values havebeen reported in burn injured rats with and without fluid resuscitation [Bert et al., 1989,1991]. In studies of nonresuscitated injury in rats, the filtration coefficient in injured tissuewas found to decrease to 50% of the normal value at time zero, decaying with a timeconstant of 0.231 h’ following a 10% surface area injury. Following burns of 40% surfacearea, the filtration coefficient in the injured skin was found to be reduced to 5% of thenormal value and return to normal after about 12 hours as for the smaller burn. Studies offluid resuscitated rats resulted in a perturbation in the fluid filtration coefficient in theinjured tissue of the order of a factor of 10 in the best-fit region. No changes in filtration inintact tissue were required to obtain a good fit of the data, therefore the perturbation wasconsidered to be zero.Based on the results obtained from the rat studies, the parameters obtained in the currentstudy are encouraging. However, the only way of validating these model parameters is toChapter 6: Results and Discussion 91investigate how well the model predicts the response of burn patients to fluid resuscitationusing the parameters determined. The influence of the individual parameters on thepredictability of the model is discussed in the next section.6.3 SENSITIVITY ANALYSESThe method employed in determining the model parameters made it impossible to give anaccurate estimate of the confidence intervals for the parameters. Therefore, sensitivityanalyses were performed to investigate the influence of the model parameters on theobjective function values. In order to assess the effect of one of the four parameters on theobjective function value, the other three were maintained at their optimum values, whilethe parameter being investigated was varied on either side of its optimum and thecorresponding objective function value determined.6.3.1 Sensitivity Analysis of GTIFor burns less than 25%, varying GTI from 0 to 1.4 reveals a deep and almostsymmetrical distribution of the objective function values about the minimum as shown inFigure 6.1. A 25% change in GkFTJ from its optimum value of 0.5 yields a 27% change inthe objective function value. Consequently, the model predictions would be very sensitiveto changes in the value ofG TI•For values of GTJ in the range selected, which satisfy the constraint that VBT> VBTO, thesensitivity curve for burns greater than 25%, given in Figure 6.2, shows an asymmetricdistribution about the optimum value of 2.0. For values of GTI less than 1.0, theobjective function value changes by about 14 per unit change in GTI. For values between1.0 and 1.5, the objective function value changes by about 7 per unit change in GTI. Thissuggests that values of GkF,TI less than 1.5 will greatly influence the model predictions. OnChapter 6: Results and DiscussionFigure 6.1: Sensitivity Plots for Burns Less Than 25%921210I’.)‘1)(U>C00CLIa)>C-)0a,(‘3>C0C-)zU-a)>0a)-o0GKFTI108642012108642012 -—108642I • I • I6 8 10 12 14 16GKFBTI • • • I •0.6 0.8 1.0EXFAC0.005 0.010 0.015 0.020 0.025r0.2 0.4Chapter 6: Results and Discussion6 8 10 12 14 16 18 20 2GKFBT50454039 I • I I0.2 0.4 0.6 0.8 1.0EXFACFigure 6.2: Sensitivity Plots for Burns Greater Than 25%935550454035>0(.5:5U-a)>13ci)06055a)Cu> 500C)CI145C-)a)-Q00.5 1.0 1.5 2.0 2.5GKFTII —- I • I • 60554035 —0.005 0.010 0.015 0.020 0.025rChapter 6: Results and Discussion 94the other hand, for values of GTJ between 1.5 and 2.5, the objective function valuechanges by only about 0.8 per unit change in GkFTI. This suggests that for burns exceeding25%, the model predictions would be relatively insensitive to values of GkFTI near theoptimum value in the range of about 2.0±0.8.The range of values of GTI which will produce only a 10% change in the objectivefunction value and therefore not significantly affect the model’s predictions are thereforeestimated to be 0.5±0.1 for burns less than 25% of the total body surface area and 2.0±0.8for larger burn injuries. The differing behaviour of the uninjured tissue in each burn groupis an encouraging outcome of the current study. In practice, the uninjured tissueexperiences greater changes following large burns as compared to smaller burns due to therelease of circulating factors in more extensive bums [Lund et al., 1992].6.3.2 Sensitivity Analysis of GBTA very shallow distribution of the objective function values about the minimum withvarying GBT is depicted in Figure 6.1 for burns less than 25%. A 20% change in GBTfrom its optimum value of 12.0 results in a 6% change in the objective function value. Theextensive plateau of objective function values around the optimum GBT value suggeststhat for burns less than 25%, a wide range of values spanning the optimum GkFBT could beconsidered without an appreciable change in the model predictions.For bums greater than 25%, the sensitivity curve in Figure 6.2 depicts symmetry about theminimum of 9.0 and in the range 9.0±3.0 for GBT. A change of about 20% in GkFBTfrom its optimum value also results in a change in the objective function of 8%. However,for values of GkFBT beyond 12.0, there is a significant increase in the objective functionvalues with GkFBT by about 1.6 per unit change in GkFBT. Hence, for burns greater thanChapter 6: Results and Discussion 9525% the model predictions would be relatively insensitive to GkFBT values within the range9.0±3.0 and very sensitive to values greater than about 12.0.The model predictions would therefore be insensitive to values of GkFBT for burns lessthan 25% and greater than 25% in the ranges 12.0±3.0 and 9.0±3.0 respectively. Theseranges represent the values of GBT that produce a 10% change in the objective functionvalue. It has been generally observed that the changes experienced in the injured tissuefollowing small burns are similar to those experienced following larger burns [Lund et al.,1992]. The results obtained from the current study are therefore consistent with what isexpected.6.3.3 Sensitivity Analysis of EXFAC and rAs mentioned in Chapter 5, EXFAC and r were only investigated using relatively coarsediscrete changes and were not rigorously estimated using the optimization techniqueadopted. Four discrete values of EXFAC ranging from 0.25 to 1.0 and two values of r,0.008 h-’ and 0.025 h-’ were investigated. As such, the sensitivity curves obtained forthese parameters may not necessarily provide sufficient information concerning thesensitivity of the model predictions to r and EXFAC.The curves obtained for burns less than 25% shown in Figure 6.1 depict a slight steadydecrease in the objective function with increasing values of EXFAC and r. For burnsexceeding 25%, the steady decrease in the objective function is more pronounced withincreasing values of EXFAC and r. In the case of EXFAC, there is a reversal in the trendat the optimum value of 0.75, Therefore, irrespective of the size of the burn injury, theinjured and uninjured tissue transport coefficients return to near-normal values after about5 days while the exudation factor lies between 0.75 and 1.0.Chapter 6: Results and Discussion 966.4 VALIDATION OF MODEL PREDICTIONSThe optimum model parameters can be used to predict the response of the MVES tospecific fluid replacement therapy in a burn patient. These model predictions can then becompared to the actual monitored responses of the patient to investigate how well themodel performs.6.4.1 Partial ValidationThe global parameters obtained by combining the data sets from the NBC and Birkelandwere used in simulating the response of the MVES of the individual patients and groups inthese two sets. Since these data were used in the identification of the parameters,comparison of the model predictions with the monitored physiological variables was notconsidered true validation. However, the predictive capabilities of the model, as well asthe validity of the global parameters could be investigated from these simulations. NBC DataSimulation results for the NBC patients and the measured data and are presented inFigures 6.3 to 6.7. Plasma volume, albumin concentration and colloid osmotic pressures(COPs) in plasma and injured and uninjured tissues were monitored over 3 days. The onlypatient with burn injuries of less than 25% of the total body surface area was Patient 1. Allthe other patients sustained injuries greater than 25%.Almost immediately following burn injury, the injured tissue becomes edematous due tofluid shifts from the circulating plasma and to a lesser extent from the uninjured tissue.Subsequent to fluid resuscitation, the injured tissue fluid volume continues to increasewhile the plasma and uninjured tissue volumes start to increase for all degrees of burninjury. After 24 hours, the fluid resuscitation protocol was adjusted so that reducedChapter 6: Results and Discussion 9730000‘ i ‘ i ‘ i ‘ i ‘25000 - — VBT- - -- VPL20000 • VPLexpa)E2 15000 -100005000 -•0 — — — — I I t I • I I i I Ii ‘ i • i • i ‘ i •—CTI-—CBT35 ----CPL —30 — — ——• CPLexpU) 25 “- --.. ——-- .---o20 --c15.10<50 ‘ I • I • I I • I • I •• I ‘ I ‘ I ‘ I ‘ I •4 —PITIRci) —— PIBTR• PITIRexpg 3 • PIBTRexp -C)E 10Time, hours postburnFigure 6.3: Simulation of MVES for NBC Patient I Using GlobalModel ParametersChapter 6: Results and Discussion 9830000 i ‘ i ‘ i ‘ t ‘ i ‘ i ‘ i—VT!25000 - - VBT -- - -- VPLE 20000• VPLexp -I::5000 -0 —— — — I I i I I i — — I — I — Ii ‘ i ‘ ‘ i ‘ i ‘ i—Cli-— CBTg35 ----CPL -• CPLexpo 20 - -4 —PITIR ——— PIBTR*:i)• PITIRexpCl) 3 — • PIBTRexp_- / •I I i I i I i I , I i I i I0 10 20 30 40 50 60 70Time, hours postburnFigure 6.4: Simulation of MVES for NBC Patient 2 Using GlobalModel ParametersChapter 6: Results and Discussion 993000025000-JE 20000115000100005000045-Jg35P0a) 25C-)o 20C-)c 15D<5004-.c4C,)Cl)0C-)ECi)000C-)0Time, hours postburnFigure 6.5: Simulation of MVES for NBC Patient 3 Using Global‘ I ‘ I ‘ I ‘ I ‘ I • I ‘ I.—CTI ——--CBT- -- CPL -• CPLexp —,.‘.- I- • . - - - - .1- -0 10 20 30 40 50 60 70Model Parameters0CU:3Cd)U)a)aC.)2U)0:2100C-)0Figure 6.6: Simulation of MVES for NBC Patient 4 Using GlobalModel Parameters100Chapter 6: Results and Discussion3000025000-J2 2000015000:2 10000:3U-50000—i-- 1 —‘I45-Jg353025o 20C-)c 15:i<50‘ I • I •—CTI——CBT- - -- CPL —CPLexp—S•5—.5—0 10 20 30 40 50 60 70Time, hours postburnChapter 6: Results and Discussion 101‘ I ‘ 1 ‘ I3000025000-JE 2000015000- 100005000045-J—4g35w 25C.)o 20C)15<500Coc4DC/)C’,a)00EU)00(0‘ I ‘ I ‘ 1 ‘—CTI -——CBT-: - - - - CPL -CPLexp/ .___ a — — -I I • I I • — I • ____I__i I •‘ I ‘ I • I • I • I • I • I—PITIR ——— PIBTR• PITIRexp• PIBTRexp\/I • I I • I • I I • I0 10 20 30 40 50 60 70Time, hours postburnFigure 6.7: Simulation of MVES for NBC Patient 5 Using GlobalModel ParametersChapter 6: Results and Discussion 102volumes of fluid were given to the patients. This results in the uninjured and injured tissuevolumes decreasing towards their normal values. Additionally, the increased flux ofalbumin from the circulating plasma into the tissues results in an initial decrease in albuminconcentration in plasma and a corresponding increase in the injured and uninjured tissuealbumin concentration. Introduction of fluid therapy results in a continuing decrease in theplasma albumin concentration and a decrease in the injured and uninjured tissue albuminconcentrations towards their normal values. After 24 hours, the albumin concentration inplasma starts to increase towards its normal value as less protein-poor fluids areadministered. Due to proportionality between the effective albumin concentration and thecolloid osmotic pressure, COP, the trends in albumin concentration are reflected in theCOP predictions. In general, the model predictions of plasma volume changes were ingood agreement with the actual monitored changes. The model also successfully predictedthe monitored trends in plasma protein concentration and hence, colloid osmotic ratios,despite the scarceness of this data. Birkeland’s DataSimulations of Birkeland’s patient groups and the data monitored are presented in Figure6.8. Plasma volume was monitored over the first 12 hours postburn in the smaller burnsand over the first 4 hours postburn in the larger burns. This data made it possible toinvestigate the response of the MVES in the initial period postburn when no form of fluidtherapy was started. Patients in burn groups I and II sustained burn injuries to less than25% of their total body surface area, while patients in groups III, IV and V sustainedlarger burns.Immediately postburn, the circulating plasma and uninjured tissue compartments undergolosses in fluid volume as fluid is shifted to the injured tissue compartment. The injuredtissue experiences an increase in its fluid volume. The rate of fluid loss from the circulatingVBTVPL• VPLexp0 2 4 6 8 10 12Time, hours postburnFigure 6.8: Simulation of MVES for Birkeland Patient GroupsUsing Global Model ParametersChapter 6: Results and Discussion 103• utfl_flJ8000-JE6000E0> 4000•0:5LI2000I,I flflñflGroup I1000080006000400020000Group IV80006000400020000IIGroup IIw-JE45)E:50>-o:5U--J2a)2:50>0:5U-Group V8000600040002000 ./C0 1 2 3 4Time, hours postburn80006000400020000Group IIIChapter 6: Results and Discussion 104plasma increases with increasing severity of the burn injury. Generally, this trend is wellpredicted by the model. In the larger burns however, the model slightly underestimates theloss in plasma volume at later times.6.4.2 Independent ValidationClinical data from two other patient studies were considered to test the model further.These patient data were not used in the identification of the parameters. Hence, the abilityof the model to predict the response of these patients to fluid therapy provides anindependent validation of the model and its parameters. Arturson’s Patient DataIn a study by Arturson et al. [1989], a 62-year old, 77-kg man who had sustained a 58%total area burn was treated during the first 48 hours postburn. Information concerningfluid therapy of the patient, cumulative urine production and the changes in body massover the initial 48-hour period is reported. The patient information is presented inAppendix H. Predictions of the erythrocyte volume fraction (or hematocrit) using themodel developed in this study were compared with the monitored response in the patient,as shown in Figure 6.9. In the first hour postburn, the model predicts an elevated (30%)hematocrit resulting from plasma volume loss. The start of fluid therapy results in therapid fall of hematocrit as indicated by the patient’s response and the model prediction.Between 26.5 and 30 hours postburn, primary excision and grafting with synthetic skinwas performed. The model could not be used to predict the response of the patient bothduring and after the operation since information concerning this operation period wasunavailable. It can be envisaged that inclusion of the volume of blood lost during theoperation would enable the model to correctly predict the lower erythrocyte volumefraction observed clinically. The close agreement between the model predicted andChapter 6: Results and Discussion 1051.00.90.8013U0)E0)02 0.3w0., hours postburnFigure 6.9: Simulation of MVES for Arturson’s Patient Using0 5 10 15 20 25 30 35 40 45Global Model ParametersChapter 6: Results and Discussion 106clinically monitored erythrocyte volume fraction prior to the operation however, issatisfactory validation of the model and its associated parameters. Ro&s Patient DataThe treatment of two burn patients and the clinical data collected from these patients werereported by Roa Ct al. [1990] and are presented in Appendix I. Patients 1 and 2 sustainedburn injuries to 75 and 80% of their total body surface areas respectively. Intravenous andcolloid input, as well as the urine produced by these two patients were used to predict thechanges in hematocrit and plasma protein concentration in the MVES following injury.Predictions using the model and clinically monitored responses of the two patients arepresented in Figure 6.10. The initial elevation in hematocrit and the subsequent gradualreturn to normal observed in both patients is well predicted by the model. Clinically,reduced plasma protein concentrations are usually observed soon after burning as was thecase in the two patients treated. The model successfully predicted this reduction, however,it slightly overestimated the rate of reduction in Patient 2.Hence, using the global parameters determined for large burns exceeding 25%of the totalbody surface area, the model was able to predict the response of the MVES followingfluid therapy in patients treated by Arturson et al. [1989] and Roa et al. [1990]. The modelpredictions agreed favourably with the clinical data available from individual patients. Asthe clinical data were not used in the parameter estimation procedure, the ability of themodel to simulate the response of the patients constituted independent validation of themodel. The successful outcome of this independent validation establishes some confidencein the ability of the model and its associated parameters to predict patient responses tofluid therapy following burn injury.Chapter 6: Results and Discussion 10700CuEa)z00CUI—a)00()CE-Q1.0 •• Patient I0.80.21.0Patient 20.8:-‘0.20.0 10 20 30 40 0 10 20 30 40Time, hours postburn Time, hours postburnFigure 6.10: Simulation of MVES for Roa’s Patients UsingGlobal Model ParametersChapter 6: Results and Discussion 1086.5 SIMULATION OF FLUID RESUSCITATION ACCORDING TO DIFFERENTFORMULAEThe use of resuscitation formulae in the treatment of burn patients was discussed inChapter 2. In order to illustrate the potential use of a model such as that developed in thecurrent study, the response of the MVES, following burn injury, to three commonresuscitation formulae was simulated. The response of the MVES to no fluid resuscitationwas also simulated to clearly show the influence of fluid resuscitation on the behaviour ofthe MVES following burn injury.The amounts of fluid to be given according to the Evans, Brooke and Parkland formulaeduring the first two 24-hour periods are shown in Table 6.8. These general formulae wereapplied to a 70-kg man with two different total body surface area burns: 10% and 50%full-thickness burns. The model was used to simulate the response of the MVES to thethree different resuscitation formulae following the two burns.The Parkland formula for fluid resuscitation differs markedly from the Evans and Brookeformulae. During the first 24-hour period, the Evans formula uses a slightly hypertonicsodium chloride solution and colloid solution in equal volumes. Brooke’s formula includesan isotonic lactated Ringer’s solution and colloid solution in proportions 3:1. Parkland’sformula on the other hand, only uses isotonic lactated Ringer’s solution in very largequantities. In addition, about 2000 mL of 5% glucose in water is given per day accordingto the Evans and Brooke formulae, but not in the Parkland protocol.During the second 24-hour period, half of the amount of electrolytes and colloidscompared with the first 24-hours is given according to the formulae of Evans and Brooke.Colloids only are given according to the Parkiand formula. 2000 mL of 5 % glucose inChapter 6: Results and Discussion 109water is again given during the second day according to Evans’ and Brook&s formulae,while the amount required to maintain adequate urine output is administered according toParkiand’s formula.Table 6.8 : Common Fluid Resuscitation Formulae [Arturson et al., 19891Fluids Evans Formula Brooke Formula Parkiand FormulaFirst 24 hoursElectrolytes 1.0 mL/kg/% 1.5 rnL/kg/% 4.0 mL/kg/%Glucose/water 2000 mL 2000 mL NonePlasma 1.0 mL/kg/% 0.5 mL/kg/% NoneSecond 24 hoursElectrolytes 0.5 mL/kg/% 0.75 mL/kg/% NoneGlucose/water 2000 mL 2000 mL As required forurine outputPlasma 0.5 mL/kg/% 0.25 mL/kg/% 500 - 2000 mL asrequired to maintainurine_output6.5.1 Simulations of 10% BurnSimulations of the response of the MVES to no fluid resuscitation and the Evans, Brookeand Parkland formulae following a 10% burn injury are depicted in Figures 6.11 to 6.14. Itwas assumed that the fluid resuscitated patient lost 1.5 L of urine each day over the 2-dayperiod simulated. Fluid loss due to evaporation was determined using Equation 4.7.Exudative fluid loss from the burn wound was estimated based on the relationship derivedfrom the NBC patient data (Equation E. 1) as described in Appendix E. In addition,Chapter 6: Results and Discussion 110-JEa)E0>Li1000020000PTIPBT. PPL. I’I’I,JFTIJFBTI JLTI—— JLBTczzzzzz. I I I • I —*Figure 6.11: Simulation of MVES with no Fluid ResuscitationFollowing a 10% Burn—-VTIVBTVPL8000 •—-—--—60004000- I • • ICTCBTCPL50-J0) 45a) 35C)0C)CE 25.02015451°35U)U)0) 30IaC-)25EC,,0200o 15C-)1600014000200010000. 8000E6000400020000150) 10E(0-5a 10Cu.(1)t20:2ExLi•0U-—PITIPIBTPIPL-25600500400300200100a-100-200.0I I IQSBTQLTI—— QLBT.Time, hours postburn0 10 20 30 40Time, hours postburnI’’—CTICBTCPL5550-J0)45a) 35C-)C0C-)CE 2520Chapter 6: Results and DiscussionI —VTI10000 VBTVPL8000 _-_--——————---—-——-__.......-JE6000400020000-• I •150) 10EU)U)-510C)-15U)0-20>,-25600500400300E 200ii: 100-D2 0-100-200—PTPPL450)I 40EE35U,U) 30C)25EI.’,020•005 15C.)—PITtPIBTPIPL0 10 20 30Time, hours postbum40 10 20 30Time, hours postburnFigure 6.12: Simulation of MVES According to Evan’s FormulaFollowing a 10% BurnChapter 6: Results and Discussion 112Figure 6.13: Simulation of MVLS According to Brooke’s FormulaFollowing a 10% Burn—VTIVBVPL—CTICPL—PT.--—--PBTPPL100008000-JE6000400020000—15) 102:EEU)U) 5a 10(U(I,2-2O-25600500400-c 300E2001000-100-200I I • I • I—PmPIPL555045040C0C) 35C0o 30CED 25.0201545-35U)Cl)30a025Eo 20081516000—QSTIQSBT14000 QLTI12000 QLBT100008000600000Time, hours postburn• I—JFTIJF8TJLTI——JLBT• I I • I0 10 20 30 40Time, hours postburn-cLD)ExDUCED.0Chapter 6: Results and Discussion 113Figure 6.14: Simulation of MVES According to Parkland’s FormulaFollowing a 10% burn-J6II)6:30>-D:3U-VTt10000VBTVPL8000600040002000I•15•- 1 I-- ICTICBTCPL20PTIPBTPPL4I I I I55_i 50C)c_ 45040C1)350C.)30625C)I66:3(I)0a)0C,0EU)00001600014000120001000080006000400020000C)10665U)U)a -0. -10>. -20-25600500400300200LI- 1000U--100-200JFTIJFBTJLTI—— JLBTI I0 10 20 30 40Time, hours postburn-CC)6x:3LIC6:3—QSTIQSBTQLTIQLBTzz:-zz::zzTime, hours postburn40Chapter 6: Results and Discussion 114200 mL of blood were assumed to be lost in the first hour postburn due to surgicalprocedures. The perturbations which describe the changes to the transport coefficientsfollowing a 10% burn surface area injury were those obtained for burns less than 25% andare presented in Table 6.7.Immediately following burn injury, fluid and albumin are transferred from the circulatingplasma compartment to the injured tissue compartment due to increased conductance andpermeability of the capillary membrane. Edema results in the injured tissue, with itsvolume approximately doubling within 2 hours. The patient plasma volume decreases dueto the low circulating blood volume which results from the fluid shift. The uninjured tissuealso experiences a small decrease in fluid volume as it also acts as a source of fluid for theplasma compartment. The concentration of albumin in the circulating plasma alsodecreases as albumin is shifted into the tissue compartments. The albumin concentrationtherefore increases steadily following injury in both tissue compartments, but to a greaterextent in the injured tissue. Fluid therapy according to all three formulae was started 1hour after injury in order to replace the lost fluid volume and albumin content fromplasma.The transcapillary fluid shifts of fluid and albumin following burn injury can be explainedby analyzing the fluid and albumin fluxes in the three compartments. The hydrostatic andcolloid osmotic pressures in the plasma and tissue compartments are the forces that drivethe fluid and albumin exchange. These pressures and the fluid and albumin fluxes are alsoshown in Figures 6.11 to 6.14.The very strong negative pressure in the injured tissue, BT, in the first few hourspostburn, as well as the initial increase in the filtration coefficient results in an increasedrate of fluid and albumin transport from the circulating plasma into the injured tissue.Chapter 6: Results and Discussion 115Reduction of the capillary reflection coefficient, TBT, associated with increased proteinpermeability, also influences the increased filtration rate. Lymph flow from the injuredtissue which is restricted to non-negative values, is virtually nonexistent also due to thevery negative tissue pressure. However, the injured tissue loses fluid by evaporation andexudation and albumin via exudate from the burn wound. Despite these losses, the greatincrease in the rate of fluid and albumin transfer into the injured tissue results in a rise inboth fluid volume and plasma protein content in this tissue during this initial periodpostburn. Consequently, edema develops in the injured tissue because the rate of fluidfiltration from the capillaries exceeds the rate at which fluid is removed from the tissue viathe lymphatics and other routes. In addition, the injured tissue albumin concentration, CBTand hence the colloid osmotic pressure, 11BT’ increase while the plasma albuminconcentration, CPL and colloid osmotic pressure, PL decrease. Immediately postburn, theuninjured tissue experiences a decrease in its hydrostatic pressure due to loss of fluidvolume from this compartment. In the first few hours postburn, the hydrostatic pressure inthe capillary falls much more markedly than that in the uninjured tissue compartment. Thiscauses a reduction in the filtration rate despite the small increase in the filtrationcoefficient. The uninjured tissue fluid volume therefore decreases while its albuminconcentration increases.Fluid therapy, where applicable, was started 1 hour postinjury. The interstitial fluidpressure in the injured skin of rats has been observed to approach normal values within 2to 3 hours [Lund et al., 1988]. During the first 2.5 hours postburn, interstitial pressureversus time data from experiments on both unresuscitated and resuscitated rats [Lund etal., 1988] were used to describe the injured tissue compliance. After 2.5 hours, the injuredtissue hydrostatic pressure was linked to changes in interstitial fluid volume resulting in anincrease in BT, approaching more positive values between 2,5 and 3 hours postburn. Thisinfluences the rate at which fluid and albumin is shifted from the circulating plasmaChapter 6: Results and Discussion 116compartment. Transcapillary fluid and albumin transport also continually readjustdepending on the fluid and colloid input to the system. Fluid resuscitation according toEvan& and Brook&s formulae results in similar responses by the MVES. The injured tissuefluid volume starts to decrease approaching normal values. However, the albuminconcentration, CBT, continues to increase. The plasma volume on the other hand, remainslow despite the input of fluid to the system and the albumin concentration also continuesto decrease despite colloidal infusions. This results in the injured tissue COP, 11BT’exceeding that of plasma, 11PL’ early in the postburn phase. These trends could be areflection of the resuscitation protocol with regards to protein replacement. In contrast tothe generally accepted view that colloids should be withheld for the first 12 to 24 hourspostburn, the Evans and Brooke formulae require that colloids be administered in the first24 hours. It appears that there is continued protein transfer into the injured tissue resultingin the continued increase in CBT and hence 11BT as predicted by the model. Pitkanen et al.[1987], in their studies in burn injured patients, found a higher injured skin COP thanplasma COP up to 12 hours postburn. Voluminous crystalloid infusions were sited asbeing partially responsible for the postburn incidence of hypoproteinemia [Pitkänen et al.,1987]. Spontaneous decreases in plasma COP have also been reported following burninjuries in man [Davies, 1982] and in anaesthetized and unresuscitated burned rats [Lundand Reed, 1986]. Later in the resuscitation period, the uninjured tissue compartmentexperiences a slight increase in tissue volume, out of phase with the injured tissue edemaas shown in Figures 6.12 to 6.14. During the second 24-hour period, the uninjured tissuevolume starts to decrease, tending towards its normal value. This ensures continuedincrease in albumin concentration, c and hence COP, TI’ but to a lesser degree than thatexperienced in the injured tissue.Fluid resuscitation according to Parkland#s formula resulted in a slightly different responsein the MVES in the second 24-hour period postburn. The large volume of only protein-Chapter 6: Results and Discussion 117poor fluid infusions in the first 24-hour period resulted in a larger decrease in the albuminconcentration in the circulating plasma than with Evans’ and Brooke’s formulae. However,plasma as well as a significantly reduced volume of glucose in water were administered inthe second 24-hour period. This resulted in an increase in the plasma albuminconcentration and hence the plasma COP.6.5.2 Simulations of 50% BumFigures 6.15 to 6.18 show predictions of the response of the MVES to no fluidresuscitation, the Evans, Brooke and Parkiand formulae following a 50% bum. Similarassumptions regarding fluid and albumin losses from the patient following a 10% burnwere applied in this case. In order to describe the changes to the transport coefficientsfollowing a burn of this size, perturbed parameter values determined for bums exceeding25% of the total body surface area were applied.The response of the MVES without fluid therapy is shown in Figure 6.15. The extent ofthe burn injury results in a relatively greater shift of fluid and albumin from the circulatingplasma into the injured tissue as compared to the smaller burn. Edema results in theinjured tissue despite the loss of fluid due to exudation and evaporation. This is due toincreased filtration from the circulating plasma, encouraged by a very strong negativeinjured tissue pressure, an initial increase in kF and a decrease in the capillary reflectioncoefficient associated with increased protein permeability. The uninjured tissuecompartment acts as a source of fluid for the depleting plasma compartment and hence itsfluid volume also decreases. In addition, albumin is transferred to both tissuecompartments from plasma. This results in an increase in the concentration of albumin andhence COP in the tissues, while the plasma albumin concentration and hence COPdecrease as in the smaller burn.Chapter 6: Results and Discussion 118-JEE0>•01I14000VBT12000 VPL100008000600040002000 .:r——=:::• I • • ICTlCBTCPL15 —PTI0) PBTZ10 PPLEE :a) I-5!ci-10Cu-150-20z-25I I • I—PmPBTPIPL__.__5045-JC.2 35•3Qa)I.)g 25C-)C 20E.o 151O400)I 35EE30U)U)a)Ia.200E(I)o 150010C-)40000—QSTI35000 QSBTQLTI30000 —— QLBT25000200001500010000500:•-:;E:::::::-r--6><DU--oU-1500 .JFTlJFBT1000 JLTIJLBT5000 •-‘----— —-500I I I I0 10 20 30 40-C0)6xU-CE.04:Time, hours postburn0 10 20 30 40Time, hours postburnFigure 6.15: Simulation of MVES with no Fluid ResuscitationFollowing a 50% BurnChapter 6: Results and Discussion 119Figure 6.16: Simulation of MVES According to Evans’ FormulaFollowing a 50% Burn-JE0E:30>-D:3U-—CTI--—--CBTCPL14000VBT12000 VPL100008000600040002000‘-.._p • I I I20 III—PTIz 15E--—--PBTE 10 PPLa) 5.3.2-15>‘-20-25• I I45-JC4825E 35230:3Cl)25O 20EU)00001.4000035000- 300000,6 2500020000150001000050000-L—PITI--—--PIBTPIPL-c6><:3IL:3ILJFTIJFBTJLTJLBTx:3IL10005000-500—QSTIQSBTQLTIQLBT0 10 20 30 40Time, hours postburn0 10 20 30 40Time, hours postburn-cxU45-JC.2 35(U• 30a)C.)25C-). 20E-D 15IEEa)I00(1)1UC-)0E00-U00C-)120CBTCPLChapter 6: Results and Discussion14000 • I.VBT12000VPL-JE 100008000:2 6000U-40002000 ..• I • I •2015 —PTIcI 10 PPL.E-10(U 15o- -20>‘-25I • I • IJFTIJFBTJLTIJLBT1040 .• ____PIBT35PIPL3025--._201010005000-500. I • I30 4035000 QSBTQLTI30000 ——QLBT2500020000U1500010000 1500:0 10 20Time, hours postburn10 20 30 40Time, hours postburnFigure 6.17: Simulation of MVES According to Brooke’s FormulaFollowing a 50% BurnChapter 6: Results and Discussion 121Figure 6.18: Simulation of MVES According to Parkland’s FormulaFollowing a 50% burn-JEa)E0>-oIL1400012000100008000600040002000201510VTII • •-J0)C0CuC1)C-)C0C)CE.00)IEECoCoa)IaC)0SCo000C)50-5-10-15-20-25—PTIPBTPPL•, I I • I I0)ISSI—CoCoIaC)CUCO20>—SxILDU-15001000500-5004000035000300002500020000015000QSBTQLTIQLBT::;:-10000500010 20Time, hours postburn00 10 20 30 40Time, hours postburnChapter 6: Results and Discussion 122As was the case for the smaller burn, fluid therapy was started 1 hour postinjury. Theinjured tissue hydrostatic pressure returns to more positive and near-normal values and thetranscapillary fluid and albumin fluxes continually readjust depending on the fluid andalbumin input to the system. As a result, the injured tissue volume starts to decrease whilethe plasma volume starts to increase, tending towards their normal volumes. Fluidresuscitation with the larger volumes of fluid results in more extensive edema formation inthe uninjured tissue as compared to that experienced following a 10% burn injury. Areversal of plasma and injured tissue COP is again predicted as the injured tissue albuminconcentration exceeds that in the circulating plasma following resuscitation according toall three formulae. However, the redistribution of albumin in the three compartmentsdiffers following fluid resuscitation according to the three formulae after about 10 hourspostburn. Discontinuities in the predicted trends 24-hours postburn are reflections of thechange in resuscitation protocol and are more evident following the larger burn.Resuscitation according to the Evans formula results in similar trends in CBT and 11BT asobserved following the 10% burn. The albumin concentration in injured tissue continuedto increase while that in plasma continued to decrease up until 10 hours postburn. Thetrend in plasma was then reversed and continued to increase in the second 24-hour period.The injured tissue on the other hand experienced slight fluctuations in fluid volumeresulting in a continued increase in CBT and HBT but at a greatly reduced rate.Administration of fluid and plasma according to Brook&s formula results in similarbehaviour in the circulating plasma. The injured tissue albumin concentration however,decreases after 10 hours postburn and continues to decrease steadily in the second 24hours. The decrease in cPL and the increase in CBT are more pronounced using Parkland’sformula in the first 24 hour period. It is widely accepted that resuscitation with colloidfree solutions produces a decrease in HPL due to dilution of plasma proteins. In the second24-hour period, CPL starts to increase rapidly as protein-rich fluid is administered accordingChapter 6: Results and Discussion 123to Parkiand’s formula. The injured tissue albumin concentration also starts to increasefollowing fluid therapy but at a reduced rate.6.5.3 Simulations by Other AuthorsArturson et al. [1989] and Roa et al. [1993] used their models to simulate the response ofthe standard 70-kg man with a 40% burn surface area to one or more of the resuscitationformulae discussed previously. The predictions made by the models of these authors arediscussed and compared to those obtained with the model developed in the current study.A mathematical model developed by Arturson et al. [1989] was used to simulate theresponse of a 70-kg man with a 40% fhll thickness burn to fluid therapy according to theEvans, Brooke and Parkland formulae. The model described the distribution of body fluidsin vascular, interstitial and intracellular compartments, influenced by the flows of fluids,electrolytes and colloids, taking place across the capillary beds and cell membranes.Changes in plasma volume and interstitial volume in noninjured and injured tissue weresimulated. Their model predicted the decrease in plasma and uninjured tissue volume andthe increase in injured tissue volume that is experienced postburn with no fluid therapy.Treatment according to Evan& formula resulted in an increase in the plasma volume duringthe first eight hours followed by a slow and steady decrease towards its normal value.Edema in the injured tissue started to resolve 18 hours postburn while the uninjured tissuecontinued to experience a decrease in its fluid volume. Use of the Brooke formula resultedin a continued slow and steady decrease of the plasma and uninjured tissue volumes fromtheir normal values. The increased injured tissue volume however, started to decrease 18hours postburn. Fluid therapy according to Parkiand’s formula caused a reversal in thedecreasing trend, increasing towards the normal plasma volume during the second 24-hourperiod. Edema in the injured tissue was more pronounced with Parkland’s formula butstarted to resolve during the second 24 hour period. The uninjured tissue however,Chapter 6: Results and Discussion 124experienced an increase in fluid volume following fluid resuscitation and continued toincrease over the 2-day period. The shift of fluid into the injured tissue causing edema andthe subsequent decrease towards normal values predicted by the current model is inagreement with Arturson’s predictions. Fluid therapy according to Parkland’s formula isable to restore the lost plasma volume but causes extensive edema in the uninjured tissue.However, the redistribution of fluid in the uninjured tissue and plasma using Evans’ andBrooke’s formulae differ between the two studies. With Arturson’s model, a steadydecrease in uninjured tissue fluid volume is predicted following resuscitation with the twoformulae. This is in contrast to the predicted increase in fluid volume in the first 24 hoursfollowed by a decrease towards the normal value by the current model.A simulator developed by Roa and Gomez-Cia [1993] was recently used to design a fluidtherapy method for burn patients during the acute phase following burn. The interactionsbetween the intracellular and extracellular compartments, normal and burned capillarydynamics, hemodynamic regulation of the systemic circulation, lymphatic systems in thenormal and burned areas and renal fhnction were all considered in the simulation. Theresponse of a 70-kg, 170-cm tall individual with a 40% burn to the Brooke and Parklandformulae were simulated and compared to the fluid therapy method designed. The trendsin plasma and uninjured tissue volumes predicted by their simulator were similar to thoseobtained in the current study. Fluid resuscitation according to the Brooke and Parklandformulae resulted in an increase in the plasma volume following the initial decrease whenno form of fluid therapy was administered. The Parkland formula caused a greater increasein the uninjured tissue fluid volume as compared to Brooke’s formula, as also predicted bythe current model.Chapter 6: Results and Discussion 1256.6 SUMMARYIn the current study, clinical data were used to estimate transport parameters and othersignificant parameters in the model. This aspect of the current study represents asignificant difference in the approach to model formulation as compared to the models ofArturson et al. [1984, 1988, 19891 and Roa et al. [1986, 1988, 1990, 1993J. Additionally,in contrast to the other models discussed, microvascular exchange was emphasized andthe formulation of the current model was based on up-to-date information and concepts.However, despite the relative complexity of the models developed by Arturson et a!. andRoa et a!. as compared to that developed in the current study, the simulations show manysimilar trends in terms of the response of the human MVES to fluid therapy according tothe Evans, Brooke and Parkiand formulae. Inclusion of cellular compartments as in thecase of the other models would be an improvement to the model, to further enhance itspredictive capabilities. As more clinical data become available, a more accurate parameterestimation procedure can be adopted in the development of a model that will better reflectthe dynamic behaviour of fluid and proteins in the MVES following a burn injury.Chapter 7: Conclusions arid Recommendations 126CHAPTER 7CONCLUSIONS AND RECOMMENDATIONS7.1 CONCLUSIONSA compartmental model has been developed to describe the human microvascularexchange system following burn injury. One of the objectives of the current study was todetermine the unknown model parameters by statistical fitting of model predictions toclinical data. An optimization scheme was implemented to determine the °best-fit”parameters. The scheme ensured that the optimum model parameters were those whichyielded the global minimum of the objective function value.Clinical observations indicate that burns less than 25% of the total body surface areainitiate systemic and localized changes which differ from those caused by burns exceeding25%. Therefore global parameters were determined for burns less than and greater than25%. The results obtained indicate that, immediately postburn, the injured tissueundergoes greater change compared to the uninjured tissue for all degrees of burn injury.Immediately following bums less than 25%, the filtration coefficient in uninjured tissueincreases to 1.5 times its normal value while the injured tissue transport coefficientchanges by a factor of 13. Burns in excess of 25% initiate more pronounced changes in theuninjured tissue filtration coefficient, by a factor of 3 while the injured tissue coefficientincreases to 10 times its normal value. Therefore burns exceeding 25% of the total bodysurface area cause greater changes in the uninjured tissue as compared to smaller burns.However, the injured tissue undergoes similar changes for all burns. The transportcoefficients were found to return to near-normal values in about 5 days following bumChapter 7: Conclusions and Recommendations 127injuries of all sizes. The exudation factor, which determines the fraction of the interstitialprotein concentration which leaves with exudate from the burn wound, was found to be inthe range 0.75 to 1.00 for all degrees of burn injury.The sensitivity of the model’s predictions to changes in the model parameters from theiroptimum values was also investigated. The analyses revealed that for burns less than 25%,the model predictions would be more sensitive to smaller changes in GbTI compared toGkFBT. The model predictions would not be significantly affected by values of GTJwithin the range ±0.1 about the optimum value of 0.5 and values of GkFBT within therange ±3.0 about the optimum value of 12.0. Beyond these ranges, appreciable changes inthe model predictions would be observed. Values ofG TI within the range ±0.8 about theoptimum value of 2.0 and values of GkF,BT within the range ±3.0 about the optimum valueof 9.0 would not significantly affect the model’s predictions. As the model parametersEXFAC and r were investigated using relatively coarse discrete changes, limitedinformation could be inferred concerning the sensitivity of the model predictions toEXFAC and r.The model and its associated parameters were validated by comparing model predictionsof patient responses to fluid therapy, to the clinical data obtained from those patients.Simulation of the response of patients whose clinical data was not used in estimating theparameters constituted independent validation of the model and its parameters. The modelpredicted response of the MVES to burn injury was in agreement with the observed trendsand the absolute values of fluid volume and plasma protein concentration. Immediatelypostburn, there was an initial elevation in hematocrit due to fluid loss from the circulatingplasma. Administration of fluid therapy initiated the return of hematocrit to normal values.In addition, the reduction in plasma protein concentration observed clinically soon afterburn injury was successfully predicted by the model.Chapter 7: Conclusions and Recommendations 128The other major objective of the current study was to develop a burn patient simulator.The model could be used to investigate the response of the MVES to fluid resuscitationfollowing a particular burn injury. The patient simulator could also be used to compare theeffects of different recommended resuscitation formulae, to suggest possibilities for thedesign of optimal fluid resuscitation programs in terms of the fluid composition, volumeand infusion rate. Areas of further investigation with respect to fluid management of burnpatients could also be suggested using the model. To this end, the model was used tosimulate the response of the MVES following burn injury to no form of fluid therapy andthen to three common resuscitation protocols, namely the Evans, Brooke and Parklandformulae. The simulated responses of the MVES were explained in terms of the transportmechanisms, driving forces and perturbations to the transport coefficients following twodegrees of burn injury, 10% and 50%. In general, it was found that the very strongnegative injured tissue pressure as well as the initial increase in the filtration coefficientand the reduction of the capillary reflection coefficient resulted in an increased flux of fluidand albumin from the circulating plasma into the injured tissue. This resulted in the injuredtissue becoming edematous, while the circulating plasma continued to lose fluid volume.The concentration of albumin in the injured tissue also increased steadily while that inplasma decreased following injury. This resulted in a reversal of the colloid osmoticpressure difference between the injured tissue and plasma. The response of the MYES tofluid therapy according to the Evans and Brooke formulae was similar. The injured tissuehydrostatic pressure increased approaching normal values and the transcapillary flux offluid and albumin continually readjusted depending on the fluid and colloid input to thesystem. Parklandtsformula initiated slightly different and more pronounced responses dueto the large volume of colloid-free fluid given in the first 24-hours followed by colloidalinfusions in the second 24-hours. The major difference between the two burn degrees wasthe relative greater shift of fluid and albumin from the circulating plasma into the injuredChapter 7: Conclusions and Recommendations 129and uninjured tissues following the 50% burn injury as compared to the 10% injury.Similar predictions from models developed by other workers confirmed the ability of thepresent model to adequately predict the response of the human MVES to fluid therapyfollowing burn injury.The model parameters estimated in the current study may be considered as estimates dueto the extreme complexity of the MVES and the lack of experimental data. As morereliable and useable clinical data becomes available, more accurate parameters may beestimated to better reflect the dynamic behaviour of the MVES. However, the simulatedresults illustrate the utility of the model in predicting non-measureable variables in theMVES.7.2 RECOMMENDATIONSThe various problems encountered as well as the results obtained in the current study formthe basis for the following recommendations for future developments to the current model.1) The use of clinical data to estimate transport coefficients and other significant modelparameters sets the current model apart from those developed by other workers. Thereis therefore absolute need for more reliable clinical data in terms of both quantity andquality, to enable a more detailed identification of all the model parameters includingthe relaxation coefficient and exudation factor. This would undoubtedly improve theability of the model to adequately predict the response of the complex system to fluidresuscitation following thermal injury.2) In order to verify the model predictions, additional clinical data or information isrequired:Chapter 7: Conclusions and Recommendations 130• measurements of the changes to the injured and uninjured tissue transportcoefficients following burn injury;• estimates of burn wound fluid and protein loss due to exudation; and• estimates of fluid loss due to evaporation.3) Improvements to the current model might include:• replacement of the “most-likely” human tissue compliance relationship withclinically determined relationships for the injured and uninjured tissue as the databecomes available;• investigation of the possible change in the vascular compliance during the courseof fluid resuscitation;• determination of the lymph flow changes in the injured and uninjured tissuesfollowing burn injury as this information becomes available;• subdivision of the uninjured tissue compartment comprising uninjured skin, muscleand other tissues into the individual components. This will only be possible whenclinical data regarding the colloid osmotic pressure dependence on proteinconcentration, the compliance characteristics and the normal steady-stateconditions of the individual tissues become available; and• extension of the current model to include intra- and extracellular compartments toallow for fluid, protein and small ion exchange between compartments. This wouldenable the simulation of the response of the MVES to hypertonic fluidresuscitation following thermal injury.Nomenclature 131NOMENCLATURESymbol Description Unitsa Ratio of albumin molecule radius to poreradiusA Surface area available for exchange m2AFRAC Fractional perfusion in injured tissueimmediately following burn injuryMbTo Albumin turnover rate h-’AR Acetated Ringers solutionBV Blood Volume mLc Albumin concentration g/LCOP Colloid osmotic pressure mmHgCSM Coupled Starling ModelCV Cell Volume niLDEG Percentage of body surface burned %Solute free diffusion coefficient cm2/sD5W DextroseEXFAC Exudation factorFA Fractional area available for exchangefn () Function ofG Perturbation to the transport coefficientpostburnH Patient height cmHct Hematocrit %1-IR Hypertonic Ringer’s solutionNomenclature 132Symbol Description UnitsJ Fluid transport rate mL/hk Time-dependent coefficientkA Overall transport coefficientkF Filtration coefficient mL/mmHg-hk1 a. Steric fractional drag coefficientLS Lymph flow sensitivity coefficient mL/mmHg-hM Number of variables monitoredMVES Microvascular Exchange SystemN Number of data pointsNBC National Burn CentreNEXP Number of experimental data pointsNS Normal salineOBJFUN Objective function valueP Hydrostatic pressure mniHgC,COMP Reciprocal of circulatory compliance mmHg/mLPe Modified Péclet numberPS Membrane permeability coefficient mL/hPLM Plasma Leak ModelPV Plasma volume mLQ Albumin content mgQ Albumin transport rate mg/hr Relaxation coefficient h-’rpore Radius of pore mrsolute Radius of solute mRELSM Fraction of total body comprising skinSM Starling ModelNomenclature 133Symbol Description UnitsSM Starling Modelt Time hTBSA Total body surface areaV Fluid volume mLVAFTI Fraction of tissue which remains uninjuredVAFBT Fraction of tissue which is injuredVFRAC Fractional plasma volume at whichperfusion in tissues is zeroW Patient body weight kgWR Weight ratioWF Weighting factor for each data pointX Data pointH Colloid osmotic pressure mmHga Albumin reflection coefficientViscosity of water glcm-s(1- a) Partition coefficientA ChangeAX Thickness of capillary membrane cmNomenclature 134Subscripts and SuperscriptsSymbol DescriptionAV Volume available to albuminBLOOD Blood lossBT Injured tissueC CapillaryCLF Clear fluidend End of time periodEVAP EvaporationEX ExcludedEXP ExperimentalEXUD ExudationF FiltrationI InterstitiumL LymphNL Normal steady-state conditions0 Initial conditionsPB PostburnPCF Protein-containing fluid or colloidal fluidPL PlasmaPRED PredictedRESUSC ResuscitationS Solutestart Start of time periodTI Uninjured tissueURII’4E UrineReferences 135REFERENCESArturson, G., Pathophysiological aspects of the burn syndrome, Acta Chir. Scanci(SuppL), 274:1, 1961.Arturson, G. and S. Mellander, Acute changes in capillary filtration and diffusion inexperimental burn injury, Ada PhysioL Scand., 62:457, 1964.Arturson, G., Microvascular permeability to macromolecules in thermal injury, ActaPhysiol. Scand. (Suppi.), 463:111-122, 1979.Arturson, G., T. Groth, A. Hedlund and B. Zaar, Potential use of computer simulation intreatment of burns with special regard to edema formation, Scand. J. Plast. Reconstr.Surg., 18:39-48, 1984.Arturson, G., Computer simulation of fluid resuscitation in thermal injury. A.B. WallaceMemorial Lecture, 1987, Burns, 14(4):257-268, 1988.Arturson, G., T. Groth, A. Hedlund and B. Zaar, Computer simulation of fluidresuscitation in trauma. First pragmatic validation in thermal injury, .1 Burn CareRehabil., 10:292-299, 1989.Aukland, K. and R.K. Reed, Interstitial-lymphatic mechanisms in the control ofextracellular fluid volume, Physiol. Rev., 73(1):1-74, 1993.Baxter, C. and T. 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Bowen, R.K. Reed and H. Onarheim, Microvascular exchange duringburn injury. IV: Fluid resuscitation model, Circ. Shock, 34:285-297, 1991.Birkeland, S., Methods for blood volume determination. Early replacement therapy,Universitetsforlaget, Oslo-Bergen-Tromso, 1969.Bowen, B.D., J.L. Bert, X. Gu, T. Lund and R.K. Reed, Microvascular exchange duringburn injury. III: Implications of the model, Circ. Shock, 28:221-233, 1989.Bresler, E.H. and L.J. Groome, On equations for combined convective and diffusivetransport of neutral solute across porous membranes, Am. J PhysioL 241 (RenalFluid Electrolyte PhysioL 10): F469-F476, 1981.Bush, J.W., A.M. Schneider, T.L. Wachtel and J.E. Brimm, A simulation analysis ofplasma water dynamics and treatment in acute burn resuscitation, J. Burn CareRehabil., 7(2):86-95, 1986.Carvajal, H.F., H.A. Linares and B.H. Brouhard, Relationship of burn size to vascularpermeability changes in rats, Surg. Gynecol. Obstet. 149:193, 1979.Chapple, C., A compartmental model of microvascular exchange in humans, M.A.Sc.Thesis, Department of Chemical Engineering, University of British Columbia, 1990.References 137Comper, W.D. and T.C. Laurent, Physiological function of connective tissuepolysaccharides, PhysioL Rev., 58:255-315, 1978.Davies, J.W.L., C.R. Ricketts and J.P. Bull, Studies of plasma protein metabolism. I.Albumin in burned and injured patients, Clin. Sci., 23:411-423, 1962.Davies, J.W.L., Physiological responses to burning injury, Academic Press, 1982.Demling, R.H., Burns. In: Edema, Staub, N.C. and A.E. Taylor, (editors.), Raven Press,New York, 1984, pp. 579-599.Demling, R.H., G.C. Kramer, R. Gunther, Effect of non-protein colloid on postburnedema formation in soft tissues and lung, Surgery, 95:593-602, 1984.Dries, D.J. and K. Waxman, Adequate resuscitation of burn patients may not be measuredby urine output and vital signs, Critical Care Medicine, 19(3):327-329, 1991.Drysdale, S.A., Computer simulation of microvascular exchange after thermal injury,Chemical Engineering 492 Thesis, University of British Columbia, 1988.Evans, El., 0.3. Purnell, P.W. Robinett, A. Batchelor and M. Martin, Fluid andelectrolyte requirements in severe burns, Ann. Surg., 135:804-817, 1952.Ganong, W.F., Review of Medical Physiology, 15th ed., Appleton & Lange, 1991.Gates, I., Microvascular exchange in human tissue, M.A.Sc. Thesis, Department ofChemical Engineering, University of British Columbia, 1992.Gillespie, R., A. Dimick and P. Hallberg-Gillespie, Advanced Burn Life SupportInstructo?s Manual, Lincoln, Neb., Nebraska Burn Institute, 1987, pp. 111-123.Gomez-Cia, T. and L. Roa, A burn patient resuscitation therapy designed by computersimulation (BET). Part 2: Initial clinical validation, Burns, 19(4):332-338, 1993.References 138Granger, D.N., N,A. Mortillaro, P.R. Kvietys, G. Rutili, J.C. Parker and A.E. Taylor, Roleof the interstitial matrix during intestinal volume absorption, Am. J PhysioL 238(Gastrointest. Liver Physiol. 1): G183-G189, 1980.Griswold, J.A., B.L. Anglin, R.T. Love and C. Scott-Conner, Hypertonic salineresuscitation: Efficacy in a community-based burn unit, Southern Medical Journal,84(6):692-696, 1991.Gu, X., Computer simulation of microvascular exchange after thermal injury, M.A.Sc.Thesis, Department of Chemical Engineering, University of British Columbia, 1987.Gunn, M.L., J.F. Hansbrough, J.W. Davis, S.R. Furst and T.O. Field, Prospective,randomized trial of hypertonic sodium lactate versus lactated Ringer’s solution forburn shock resuscitation, J Trauma, 29(9): 1261-1267, 1989.Guyton, A.C., Function of the Human Body, W.B. Saunders Company, 3rd ed., 1969.Guyton, A.C., A.E. Taylor and H.J. Granger, Circulatory physiology II: Dynamics andcontrol of the body fluids, W.B. Saunders Company, 1975.Harvey J.S., G.M. Watkins and R.T. Sherman, Emergent care, Southern Medical Journal,77(2):204-214, 1984.Hedlund, A., B. Zaar, T. Groth and G. Arturson, Computer simulation of fluidresuscitation in trauma. I. Description of an extensive pathophysiological model andits first validation, Computer Methods and Programs in Biomedicine, 27:7-2 1, 1988.Hollander, W., P. Reilly and B.A. Burrows, Lymphatic flow in human subjects asindicated by the disappearance of 131j -labelled albumin from the subcutaneous tissue,J Clin. Invest., 40:222-233, 1961.International Commission on Radiological Protection, No. 23, Report of the Task Groupon Reference Man, Pergamon Press, 1975.Jelenko, C., W.D. Jennings, W.R. OKelley and H.C. Byrd, Threshold burning effects ondistant microcirculation, Arch. Surg., 106:3 17, 1973.References 139Langgârd, H., The subcutaneous absorption of albumin in edematous states, Acta. MedScand., 174:645-650, 1963.Leape, L.L., Early burn wound changes, .1 Pediatr. Surg., 3:292, 1968.Lund, T. and R.K. Reed, Microvascular fluid exchange following thermal kin injury in therat: Changes in extravascular colloid osmotic pressure, albumin mass and watercontent, Circ. Shock, 20:91-104, 1986.Lund, T., H. Wiig and R.K. Reed, Acute postburn edema: Role of strongly negativeinterstitial fluid pressure, Am. J Physiol. 255 (Heart Cire. Physiol. 24): H1069-H1074, 1988.Lund, T., J.L. Bert, H. Onarheim, B.D. Bowen and R.K. Reed, Microvascular exchangeduring burn injury. I: A review, Circ. Shock, 28:179-197, 1989.Lund T., H. Onarheim and R.K. Reed, Pathogenesis of edema formation in burn injuries,WorldJ Surg., 16:2-9, 1992.Martyn, J.A.J., Acute management of the burned patient, W.B. Saunders Company, 1990.McLaughlin, E.G. (editor), Critical burn care of the burn patient. A case study approach,Aspen Publishers Inc., Rockville, Maryland, 1990.Meyer, F.A., M. Koblentz and A. Silberberg, Structural investigation of loose connectivetissues using a series of dextran fractions as non-interacting macromolecular probes,Biochem. .1, 161:285-291, 1977.Onarheim, H., T. Lund and R.K. Reed, Thermal skin injury: II. Effects on edemaformation and albumin extravasation of fluid resuscitation with lactated Ringer’s,plasma and hypertonic saline (2 400 mosmolll), Circ. Shock, 27:25, 1989.Pappenheimer, J.R., Passage of molecules through capillary walls, Physiol. Rev., 33:387-423, 1953.References 140Parker, J.C., H.J. Falgout, RE. Parker, D.N. Granger and A.E. Taylor, The effect of fluidvolume loading on exclusion of interstitial albumin and lymph flow in the dog lung,Circ. Res., 45:440-450, 1979.Parker, J.C., H.J. Falgout, F.A. Grimbert and A.E. Taylor, The effect of increasedvascular pressure on albumin-excluded volume and lymph flow in the dog lung, Circ.Res., 47:866-875, 1980.Patlak, C.S., D.A. Goldstein and J.F. Hoffman. The flow of solute and solvent across atwo-membrane system. J. Theoret. Blot., 5:426-442, 1963.Pitkanen, J., T. Lund, L. Aanderud and R.K. Reed, Transcapillary colloid osmoticpressures in injured and non-injured skin of seriously burned patients, Burns, 13:198,1987.Pitt, R.M., J.C. Parker, G.J. Jurkovich, A.E. Taylor and P.W. Curreri, Analysis of alteredcapillary pressure and permeability after thermal injury, J. Surg. Res., 42:693, 1987.Reed, R.K. and H. Wiig, Compliance of the interstitial space in rats. I. Studies on hindlimbskeletal muscle, ActaPhysiol. Scand., 113:297-305, 1981.Reed, R.K., B.D. Bowen and J.L Bert, Microvascular exchange and interstitial volumeregulation in the rat: Implications of the model, Am. J PhysioL 257 (Heart Circ.Physiol. 26): H2081-H2091, 1989.Reed, R.K., T.C. Laurent and A.E. Taylor, Hyaluronan in prenodal lymph from skin:changes with lymph flow, Am. .1 Physiol. 259 (Heart Circ. Physiol. 28): H1097-Hi 100, 1990.Reed, R.K., M.I. Townsley, R.J. Korthuis and A.E. Taylor, Analysis of lymphatic proteinflux data. V. Unique PS products and aS at low lymph flows, Am. J PhysloL 261(Heart Circ. Physiol. 30): H728-H740, 1991.Reiss, E., J.A. Stirman, C.P. Artz, J.H. Davies and W.H. Amspacher, Fluid and electrolytebalance in burns, J Amer. Med. Ass., 152:1309-13 13, 1953.References 141Roa, L. and T. Gomez-Cia, Analysis of the extracellular protein and fluid shifts in burnedpatients, Burns, 12:337-342, 1986.Roa, L.M., T. Gomez-Cia and A. Cantero, Analysis of burn injury by digital simulation,Burns, 14(3):201-209, 1988.Roa, L., T. Gomez-Cia and A. Cantero, Pulmonary capillary dynamics and fluiddistribution after burn and inhalation injury, Burns, 16(1):25-35, 1990.Roa, L. and T. Gomez-Cia, A burn patient resuscitation therapy designed by computersimulation (BET). Part 1: Simulation studies, Burns, 19(4):324-33 1, 1993.Rylah, L.T.A. (editor), Critical care of the burned patient, Cambridge University Press,1992.Schittkowski, K., The nonlinear programming method of Wilson, Han and Powell with anaugmented Lagrangian-type line search function. Part 1: Convergence analysis,Numerische Mathematik, 38(1): 83-114, 1981.Starling, E.H., On the absorption of fluids from connective tissue spaces, J Physiol.,19:312-326,1896.Stranden, E. and HO. Myhre, Pressure-volume recordings of human subcutaneous tissue:A study in patients with edema following arterial reconstruction for lower limbatherosclerosis, Microvasc. Res., 24:241-248,1982.Sundell, B., Evaluation of fluid resuscitation in the burned patient, Ann. Chir. Gyn. Fenn.,60:192-195, 1971.Taylor, A.E. and D.N. Granger, Exchange of macromolecules across the microcirculation,In: Handbook of Physiology, The Cardiovascular System, Vol. IV: MicrocirculationPart 1, Renkin, E.M. and C.C. Michel, (editors.), Bethesda, The AmericanPhysiological Society, 1984, pp. 467-520.Taylor, D.G., J.L. Bert and B.D. Bowen, A mathematical model of interstitial transport.II. Microvascular exchange in mesentery, Microvasc. Res., 39(3):279-306, 1990.References 142Vander, A.J., J.H. Sherman and D.S. Luciano, Human physiology. The mechanisms ofbody function, 4th ed., McGraw Hill Inc., 1985.Wachtel, T.L., H.A. Frank, R. Sanders, A.R. Hargens and R.M. Peters, Definition of theStarling forces with wick catheter in burned patients, I Burn Care RehabiL, 4:331,1983.Waxman, K., R. Holness, G. Tominaga, P. Chela and J. Grimes, Hemodynamic andoxygen transport effects of pentastarch in burn resuscitation, Ann. Surg., 209(3):341-345, 1989.Werner, 3., Control aspects of human temperature regulation in man, Automatica, 17:351,1981.Wiederhielm, C.A., Dynamics of capillary fluid exchange: A nonlinear computersimulation, Microvasc. Res., 18:48-82, 1979.Wiig, H. and R.K. Reed, Compliance of the interstitial space in rats. II. Studies on skin,ActaPhysioL Scand, 113:307, 1981.Wilkinson, A.W., Limited volume therapy with colloid. In: Contemporary burnmanagement, Polk, H. and H. Stone (editors), pp. 5 8-69, Little Brown, Boston, 1971.Xie, S., A compartmental model of human microvascular exchange, M.A.Sc. Thesis,Department of Chemical Engineering, University of British Columbia, 1992.ZetterstrOm, H., and G. Arturson, Plasma oncotic pressure and plasma proteinconcentration in patients following burn injury, Acta AnaesthesioL Scand., 24:288,1980.Appendices 143AppendicesAppendix A: Interstitial Fluid DistributionAppendix B: Transport ParametersAppendix C: NBC Patient DataAppendix D: Estimation of Plasma Volume from Hematocrit DataAppendix E: Estimation of Exudation Rate Based on NBC Patient DataAppendix F: Birkeland’s Patient DataAppendix G: Determination of Exudation Rate for Birkeland’s PatientsAppendix H: Clinical Data from Arturson’s PatientAppendix I: Clinical Data from Roa’s PatientAppendix J: Minimum Objective Function Value ResultsAppendix K: Computer Program ListingAppendix A 144Appendix A: Interstitial Fluid DistributionThe interstitial fluid distribution in the “Reference Man” has been reported [Chapple,1990] as shown in Table A. 1.Table A. 1: Interstitial Fluid Distribution in the “Reference Man”Tissue Interstitial Fluid Volume, LTotal Skin 2.39Skeletal Muscle 4.51Other Tissue 1.50Total Body 8.40Appendix B 145Appendix B: Transport ParametersB, 1 Normal Transport Parameters for “Reference Man”Normal values for five transport coefficients have been determined using the CoupledStarling Model (CSM) for the normal 70-kg man by Xie [19921. Values for the lymphflow sensitivity coefficient, LS and the albumin reflection coefficient, a, were determinedby statistical fitting of the CSM model predictions to experimental human MVES responsedata. The lymph flowrate, 3L’ permeability coefficient, PS and filtration coefficient, kF arecalculated from the following relationships based on the estimated values ofLS and a:— A1bTQ(1—cJ).exp(—PeNL) i[1—exp(—Pe)].[J’NL“J,E’] “- ‘NL L,NL B2NL—1fl[ 1NL —(1—).cJAVWL[ cJ—(1—NL).cpLNLkFNL , B.31C,NL — — 111,NL)where Pe is a modified Péclet number which can also be shown to be_i cINL—(1—J).cIAvNLPeNL—ln . B.4CJNL-NL)PL,NLSubscript NL refers to normal steady-state values and AIbTO is the albumin turnover rate,which expresses the rate of disappearance of albumin from the interstitial compartmentand has been found to be between 2 and 2.5% per hour [Hollander et al., 1961; Langgârd,19631. In the current study, a value of 0.025 fr’ is used.Appendix B 146The normal values of the transport coefficients, as estimated from the above relationshipsfrom the values of LS and a found by Xie are as follows:LSNL = 43.08 mL/mmHg-hPSNL = 72.98 mL/hkFNL = 120.64 mL/mmHg-hL,NL = 75.46 mL/h= 0.9888.As explained in Chapter 4, these transport coefficients, with the exception of the albuminreflection coefficient, are scaled with respect to the weight ratio, WR, to account for the“real patient”.B.2 Transport Coefficients Following Burn InjuryMost proteins in plasma cross capillary walls, diffuse through tissues and return to theplasma via the lymphatic system. It is well known that the concentration of amacromolecule in lymph is a function of its molecular size and that capillaries areheteroporous, i.e., both small and large pores are necessary to describe the movement oflarge molecules across capillary walls [Taylor and Granger, 1984]. The capillarymembrane parameters which determine the exchange of plasma proteins, represented byalbumin in the current study, are kF, a and PS. These transport parameters are notindependent, but are linked to each other via changes in the capillary pore radius. Reed etal. [1991] report the following relationships for the transport coefficients kF, a and PS,based on the radius of the capillary pore and the radius of solute, which is albumin in thiscase:k’ = rpore2 B.5F 8..AX16 2 20 7 B.63 3 3Appendix B 147(1—a)2PS’= B.7k.c1 •AXwhere a is the ratio of the solute radius, rsolute, to the pore radius, rpore, i.e.,B.8rporeii is the viscosity of water (p. = 0.006915 g/cm-s at 37°C), AX the thickness of thecapillary membrane (AX = 5000A = 5x 10 cm), (1- a) the partition coefficient, D5 thesolute free difihision coefficient in cm2/s and k a is the steric fractional drag coefficientwhich is dimensionless. The units of k’F and PS’ are cm/s-mmHg and cm/s respectively,while a is dimensionless.A normal value for a is determined from Equation B.6, based on normal values for theradius of the albumin molecule [Taylor and Granger, 1984] and the albumin reflectioncoefficient:= 0.9888 = ![16.a2—20.aNL3+7.a,4j.Solving this equation yields:a 0.89Recall that following burn injury, the transient response of the transport coefficients isexpressed in the following general form:kA=kWL.ANL.[1+G.e] 4.34Considering kF, by the definition above, at time t 0,k=1+GkF,NLIn the current study, it is assumed that following burn injury, the capillary membrane poresexperience changes in radii. From equation B.5, kF cx r2 pore. Thus:Appendix B 148rpore=l+Gk, B.9r pore,NLwhere rporeNL is the normal capillary pore radius. Setting rpore = r, and rporeNL= 1NL’Equation B.9 can be expressed asr=rNL.[1+Gk]. B.10From Equations B.8 and B. 10, the ratio of albumin and capillary pore radii following burninjury may be defined as follows:clba,,8——rrNI\l+Gk)In addition, under normal conditions,a —From equations B. 11 and B. 12,Taib 1aNL TNL.(1+Gk) raibHence, the ratio of the albumin molecule radius to pore radius, postburn isa— aB13PB (1+GkF)Consider PS. Again, by definition, at time t 0,PS=1+ G,,8PSNLFrom Equation B.7, PS (i — a)2. Therefore/1a,,8)—1 G(1—aWL)2+Appendix B 149Hence:I,, 1—a,8)1UPSI \21i 1 aNL)where aNL = 0.89 and aPB can be expressed in terms of GkF as in Equation B. 13.Consider . Once again, by definition, at time t 0:=1-G.!‘JLHence:Ga=1L.NLSubstituting for a by Equation B.6:Gj416.ap82_20.3+7.]1B.151 0.9888 JAgain, aPB can be expressed in terms of Gk as in Equation B. 13.Hence postburn, aPB may be determined based on a value of G for uninjured tissue(G1,TT) and injured tissue (G1BT). The perturbations to PS and a in uninjured and injuredtissue may then be determined using Equations B.14 and B.15.Appendix C 150Appendix C: NBC Patient DataThe information provided by Dr. T. Lund for each of the 5 patients studied at the NationalBurn Centre were as follows:i. Patient data on admission:• Age and sex• Total burn surface area or degree of burnii. Laboratory data:• Hematocrit• Plasma albumin concentration• COPs in plasma and interstitial fluid from injured and uninjured skiniii. Weight changes with time postburniv. Resuscitation protocol:• Clear fluids: Acetated Ringers, ARHypertonic Ringers, HRNormal Saline, NS5% Dextrose, D5W• Colloidal fluids: Iso-oncoticHyperoncotic• Blood transfusionsv. Urine producedvi. Initial blood loss due to surgical proceduresThe original patient data sheets provided for the current study are presented in Figures C. 1to C.5. Summaries of the patient information for Patients 1, 2, 3, 4 and 5 are shown inTables C.1 to C.1O. Most of the information was taken from the patient data sheets inFigures C. 1 to C.5 with the exception of the following:Appendix CFigure C. 1: NBC Patient 1 Data Sheet151:‘ r—--I ‘jinjj.j,jj .*IjJiiioj4 i vs P8I I I I .1. I..J ...‘ L ii I I — At- ——I-—.—-————-—-—--—1L...Io1r.I. J/.. i. . IH .: 3Lzj/ .L1 .S1f4, ..iLL .z-Lii /( — 1-io — —fl-b — — 31 . . .zs . - . .j : - -J: .. z...z. li.Z .‘ : ..i IlL:]. .j,I - 1J7 iICl. ----Z: -“r : tf bbo - . ..•-.-.---.--...--.1 ‘3oo1-LEfrifFL . - . 11! - — - -TL.cF - - .LSb.Q.JI( - . -. .41 k0 2_-._-.. .-...- r..O4 4: -ECcvosO$: 1V UJL- /‘JL- 7’ M.AJ.’Igçg 2c —-- ... , ‘—/?iFigure C.2: NBC Patient 2 Data SheetAppendix C 152II41UN i IrI I ii II -L0 — -sILl ‘.2.Otv 3; ..p: : ill-fl ‘13 iii...,........31 . . . HhtzL zzZ ‘3 - LLJi ‘i......Li_L4__L.LL_i.LL...( . ........ .. .. -.... .:DSJ . i— cozz.z. _...L/QQCL.EF Ft c1L1AtL4 - -Tccr.w” .500 $LSO-okI( r Q. . —ft 9o/Q . . ... .1\ A _—so-L --_*..7/_ (4(.1 . _./z5Z —----.. .u /oqqAppendix C<J. 111.1-rI9I.i IFigure Ci: NBC Patient 3 Data Sheet1531Vd’.iI I Ar.Hss.o’J P3 —;-j--v7--, T5tY% - 1i_ p - J.ç P ip.-JJ:[:g5 t) (Is1744.* cl •Li 1. .1 -I J.L4_ 23I 1 . j: I ( /.:E .:: z..:zz.. 3L 1:z:z:z79::. ‘351.. .ti1..t-: IkL_ W. I•1 . 3 .Ll.:L±E TT’ *W. ..r. .. - ._.. -----q0-.._T ... . . . ,.J .-- . . ... yNS .. ‘fr . .:D’.J’ //— 7ôo— S5oo .Lep-TL----.- .. -h--- O’) — / ‘—-< r:,TcF ¶.J/ \.i k• 2--—-1 75Q EF-CfL3.j/. -7 f—. /)f.j/ /Si—Appendix CFigure CA: NBC Patient 4 Data Sheet154& .. .PT 3•1______ ____ ________AeHISSIOI.)Z’3 4-P.,VZLILt 1,ENII•. -15—zE:“IC.LIi .rr(t5211WzI4’ L..LI22 L.3c- i3.4’ Z 32-ço• LO Iqq9 ‘Is-3ttfhri -hE:WLLZ_1 LL.. z--.-s-.--—--..--..-..I .3.1(1.,—•.1,)f———i3—-—---‘/ -- — —. ,.L .4LLE- oo—- ..tSOK 22 Sb- — -./ • . . V VCeU.oiGS 1)0) V . ,,L__. .__—‘------Figure C.5: NBC Patient 5 Data SheetAppendix C 155IDP.fE W//4$1fjg O75 AMIss’oJ 70 hys P8All,-•CI..P-Ns.._LDSJ_.3 .3c 1WW4I.coo -Te.jcFLSc,-QIKninCI I5Onç-4---H----—--I7SO - .2oAppendix C 156• patient preburn weight estimated based on fluid balances, discussed in Appendix E;and• plasma volumes estimated from hematocrit data, discussed in Appendix D.Table C. 1: Admission and Laboratory Data for NBC Patient 130 year old malePreburn weight = 88 kgTotal burn surface area = 21%Time, hrs Hct, % VPL, mL cPL, W1 11T ’ 11BT’postburn mniHg mmHg mmHg0.0 37 4022.86 39.4 14.7 14.7 25.913.0 40 3432.95 31.0 - - -16.5 - - - 10.0 12.5 11.931.0 35 4228.03 22.0 - - -33.5 - - - 5.0 7.0 12.055.0 37 3851.22 25.0 - - -57.5 - - - 6.0 - 12.066.0 35 4186.80 - - - -Appendix C 157Table C.2: Fluid Inputs and Outputs for NBC Patient 1T, hours Tend, hours CLF, mL/h PCF’ mL/h UR1NE’ mLfhpostburn postburn0.0 1.0 0.00 0.00 75.001.0 8.0 642.86 0.00 75.008.0 17.0 437.50 0.00 122.3517.0 19.0 437.50 75.00 122.3519.0 24.0 437.50 0.00 122.3524.0 28.0 160.00 187.50 106.5828.0 48.0 160.00 0.00 106.5848.0 72.0 125.00 0.00 65.46Tstart and Tend represent the time at which fluid resuscitation starts and ends respectively,and pCF the resuscitation rates of clear and colloidal fluids respectively and URJNEis the rate ofurine production.i) Between 0 and 1 hour postburn, 200 mL of blood was lost due to surgical procedures.ii) Exudation Rate = 45.09 mL/hAppendix C 158Table C.3: Admission and Laboratory Data for NBC Patient 242 year old femalePreburn weight =65 kgTotal burn surface area 51%Time, hrs Hct, % VPL, mL c, g/L TI’ 11BT’ 11PL’postburn mmHg mniHg mmHg0.0 37 2971.43 39.4 14.7 14.7 25.913.0 43 2117.19 19.0 - - -18.0--- 10.5 11.5 9.520.0 33 3233.92 16.0 - - -23.0 32 3384.75 - - --29.0 33 3227.42 15.0 - - -32.5--- 5.0 6.0 12.034.5 33 3220.72 19.0 - - -48.0-- 14.0---54.5 29 3851.44 22.0 - - -56.5--- 3.5 5.0 10.572.0 27 3776.6 24.0 - - -89.0 33 2825.01 24.0 - - -Appendix C 159Table C.4: Fluid Inputs and Outputs for NBC Patient 2T, hours Td, hours CLF, mL/h PCF, mL/h URINE’ mL’hpostburn postburn0.0 1.0 0.00 0.00 83.751.0 8.0 771.43 71.43 83.758.0 24.0 843.75 0.00 30.1324.0 43.0 247.92 52.63 52.1743.0 47.0 247.92 125.00 52.1747.0 48.0 247.92 0.00 52.1748.0 61.0 166.67 20.83 45.7961.0 63.0 166.67 168.33 45.7963.0 72.0 166.67 20.83 45.79i) Between 0 and 1 hour postburn, 400 mL of blood was lost due to surgical procedures.ii) Between 61 and 63 hours, 500 mL of blood was given to this patient.iii) Between 1 and 2.5 hours, 500 mL of hyperoncotic fluid was given. To determine thealbumin content of this fluid, an “equivalent volume” of 750 mL was assumed.iv) Exudation Rate = 80.89 mL/hAppendix C 160Table C.5: Admission and Laboratory Data for NBC Patient 355 year old malePreburn weight = 70 kgDegree = 80%Time, hrs Hct, % VPL, mL c, g/L TI’ 11BT’ 11PL’postburn mmHg mmHg mmHg0.0 45 3200.00 39.4 14.7 14.7 25.97.0 51 2429.04 23.0 - - -9.0 - - - 10.5 11.0 9.510.0 56 1986.43 - - - -12.0 - - - 7.0 9.0 7.013.0 56 1982.03 - - - -16.0 57 1903.00 - - - -20.0 44 3203.30 - - - -28.0 51 2413.95 - - - -30.0 - - - 6.0 7.0 12.036.0 47 2827.47 - - - -39.0 40 3761.07 - - - -44.0 37 4262.52 - - - -48.0 - - - 7,0 9.5 -52.5 38 4078.43 18.0 - - -59.0 31 5555.35 18.0 - - -67.0 32 5290.57 18.0 - - -75.0 31 5534.43 24.0 - - -Appendix C 161Table C.6: Fluid Inputs and Outputs for NBC Patient 3Tft, hours Td, hours CLF, mL/h PCF’ mL/h U1UNE’ mL/hpostburn postburn0.0 0.8 0.00 0.00 77.170.8 6.0 2516.13 0.00 77.176.0 14.0 777.78 0.00 37.7214.0 24.0 1097.78 250.00 37.7224.0 32.0 229.17 0.00 47.5832.0 48.0 354.17 125.00 47.5848.0 53.0 132.69 0.00 63.2153.0 72.0 172.16 39.47 63.21i) Between 0 and 0.8 hours postburn, 200 mL of blood was lost due to surgicalprocedures.ii) Exudation Rate = 136.64 mL/hAppendix C 162Table C.7: Admission and Laboratory Data for NBC Patient 457 year old malePreburn weight 72 kgTotal burn surface area = 59%Time, hrs Hct, % VPL, ‘- CPL, WL “TI’postburn mmHg mmHg mmHg0.0 45 3291.43 39.4 14.7 14.7 25.96.0 48 2868.65 29.0 - - -8.0 - - - 8.5 12.0 11.011.0 - - 19.0 - - -17.5 52.0 2439.87 19.0 - - -24.0 - - - 9.0 - 7.026.0 48 2852.19 22.0 - - -29.0 - - 22.0 - - -34.0 31 5849.39 23.0 - - -36.0 - - - 6.5 6.0 8.540.0 37 4469.40 26.0 - - -54.0 35 4854.18 23.0 - - -61.0 38 4258.89 18.0 - - -Appendix C 163Table C.8: Fluid Inputs and Outputs for NBC Patient 4T, hours Td, hours CLF, mL/h PCF’ mL/h UR1NE’ mL/hpostburn postburn0.0 0.5 0.00 0.00 74.500.5 6.0 1454.55 0.00 74.506.0 8.0 772.22 0.00 74.508.0 14.0 772.22 166.67 74.5014.0 19.0 772.22 0.0 74.5019.0 22.0 772.22 166.67 74.5022.0 24.0 772.22 0.00 74.5024.0 28.0 237.50 0.00 42.7528.0 48.0 250.00 112.50 42.7548.0 72.0 233.33 3125 68.96i) Between 0 and 0.5 hours postburn, 100 mL of blood was lost due to surgicalprocedures.ii) Exudation Rate = 103.65 mL/hAppendix C 164Table C.9: Admission and Laboratory Data for NBC Patient 531 year old malePreburn weight 78 kgTotal burn surface area = 72%Time, hrs Hct, % V, mL CPL, g/L “TI’ ‘1BT’ 11P1?postburn mmHg mmHg mmHg0.0 45 3565.71 39.4 14.7 14.7 25.910.0 56 2221.53 23.0 ---12.0--- 7.5 8.5 8.013.0 53 2502.35 ----15.0 47 3182.03 ----17.0 44 3591.39 ----22.0 43 3734.70 18.0 ---24.0--- 4.0 6.0 6.527.0 42 3884.76 21.0 ---31.0 41 4042.08 23.0 ---36.0 30 6544.54 24.0 7.0 11.0 11.541.0 29 6866.93 18.0 ---45.0 28 7204.89 19.0 ---48.0 29 6852.98 24.0 ---54.0 34 5034.84 22.0--59.0--20.0---72.0 32 5489.94 19.0 ---Appendix C 165Table C. 10: Fluid Inputs and Outputs for NBC Patient 5hours Tend, hours 3CLF’ mTJh PCF’ mLfh URINE’ mL/hpostburn postburn0.0 1.25 0.00 0.00 138.541.25 8.0 1037.04 74.07 138.548.0 12.0 1025.00 0.00 138.5412.0 15.0 1025.00 229.17 138.5415.0 24.0 1115.91 229.17 138.5424.0 26.0 486.74 156.25 43.8326.0 38.0 395.83 156.25 43.8338.0 40.0 645.83 156.25 43.8340.0 48.0 395.83 156.25 43.8348.0 50.0 229.17 52.08 92.5050.0 52.0 229.17 175.83 92.5052.0 72.0 229.17 52.08 92.50i) Between 0 and 1.25 hours postburn, 200 mL of blood was lost due to surgicalprocedures.ii) Between 1.25 and 8 hours, 500 mL of macrodex (dextran 70, 6%) was given. Todetermine the albumin content of this fluid, an “equivalent volume” of 750 mL wasassumed.iii) Exudation Rate = 137.03 mL/hAppendixD 166Appendix D: Estimation of Plasma Volume from Hematocrit DataHematocrit, Hct, is a measure of the packed cell volume of red blood cells and isexpressed as a percentage of the total blood volume, By.Thus:Cell Volume CVHct= =—. DlBlood Volume BVThe plasma and cellular elements of the blood together constitute the total blood volume,i.e.,BV=PV-i-CV. D.2Consequently,PV=BV.[l—Hct]=1-[l—Hct . D.3HctBased on the above relationships and assuming a normal hematocrit of 45% and 41% forthe standard male andfemale respectively [Reference Man ICRP 23, 1975], and a normalplasma volume of 3200 mL, normal values of cell and blood volume for the standard 70kg male and female can be estimated and are shown in Table D. 1.Table D. 1: Normal Values for 70-kg, 170-cm IndividualMale FemaleHematocrit, Hct, % 45 41Plasma Volume, PV, mL 3200.00 3200.00Cell Volume, CV, mL 2618.18 2223.73Blood Volume, By, mL 5818.18 5423.73Appendix D 167In order to account for differing preburn weights of the patients, the various volumes aremodified by a weight ratio, WR, whereWR = Preburn weight of patient 4 1770However, the weight of the patients before injury were unknown on admission. In most ofthe patients studied, the first few weights were recorded 12 hours and then 24 hourspostburn. It was possible to estimate the preburn weight for each patient, based on fluidbalances on the patient between two successive times when measurements of weight,fluids given and fluids lost were available, fromChange in patient weight = Volume of fluids given - Volume of fluids lostThe procedure is described in detail in Appendix E.Following from personal communication with Dr. T. Lund, Patients 1 and 2 wereconsidered to be slightly unusual in that their normal hematocrit were below the normalpopulation value. It was concluded that a value of 37% should be used for the normalhematocrit for these two individuals.Initial blood losses due to escaratomies and fasciotomies were clinically estimated for eachpatient and were also provided [personal communication with Dr. T. Lund]. In addition, itwas assumed that for laboratory purposes, 10 mL blood samples were taken from eachpatient, four times each day over the three-day period. Associated with these blood lossesfrom the circulating plasma is cell loss, and as such, the changing cell volume was takenaccount of in estimating the changing plasma volume.Two patients, 2 and 5, received blood transfusions. This addition to the blood volume andthe resulting change in cell volume was considered in estimating the plasma volume. Anexample of how plasma volumes were estimated is presented in Example D. 1.Appendix D 168Example D. 1: Estimation of Plasma Volume for Patient 1a. Time of injury, t 0Normal values for Hct, CV, PV and BVb. Time of admission, t = 13 hours post-injury200 mL of blood estimated to be lost 1-hour postinjuryTherefore:CV = 2362.63—(200 x 0.37) = 2288.63 mLpv= 2288.63 x[1—0.40]= 3432.95 mL0.40BV = PV+CV = 5721.58 mLc. t = 31 hours post-injury30 mL of blood taken for laboratory analysisTherefore:CV = 2288.63 —(30 x 0.40) = 2276.63 mL2276.63x[1—0.35]= 4228.03 mL0.35BV = 6504.66 mLd. t = 55 hours post-injury40 mL of blood taken for laboratory analysisTherefore:Appendix D 169CV = 2276.63—(40x 0.35) = 2262.63 mL2262.63x(1—O.37)= 3852.59 mL0.37BV =61 15.22 mLe. t = 66 hours post-injury20 mL of blood taken for laboratory analysisTherefore:CV = 2262.63 —(20 x 0.37) = 2255.23 mLpv= 2255.23 x(1—0.35)= 4188.28 mL0.35BV = 6443.51 mLAppendix E 170Appendix E: Estimation of Exudation Rate Based on NBC Patient DataThe rate of exudation from the injured tissue was determined by performing a fluid balanceon each of the 5 patients between two successive measurement times, fromVolume” of fluid in patient Volume of fluids given - Volume of fluids lostwhere the “Volume” of the patient is the product of the weight change of the patient andthe density of fluids in the body, which is assumed to be I kgfL.The fluids given include:(i) clear fluids such as acetated Ringers, hypertonic Ringers and dextrose; and(ii) protein-containing fluids such as iso-oncotic fluids, hyper-oncotic fluids andblood transfusions.The fluids lost include:(i) urine produced;(ii) blood losses;(iii) evaporative fluid, discussed in Chapter 4 and defined as:EVAP =[25+DEG]xTBSA;. 4.8(iv) exudative fluid.Therefore, knowing the change in weight of the patient between two times, the fluidsgiven, urine, blood and evaporative fluid lost, the exudative fluid loss may be determinedfrom the above fluid balance.As discussed previously, preburn patient weights were not known on admission. Thisweight is necessary in estimating the total body surface area, TBSA, to determine theevaporative fluid loss. In most of the patients studied, the first few weights were recorded12 hours postburn and then 24 hours postburn. In order to determine the preburn weightfor each patient, it was assumed that the exudation and evaporation rate during the firstAppendixE 171indicated times when the patient’s weight was recorded, was the same as that in the firstfew hours postburn. For example,Rate between 12 and 24 hours postburn = Rate between 0 and 12 hours postburn.The resulting preburn weight could then be used to estimate the fluid loss due toevaporation and hence, that due to exudation. The sample calculation, Example E. 1,illustrates this procedure.Example E. 1: Sample Calculation - Estimation of Exudation RateIn Patient 1, the first weights were measured 24 and 48 hours postburn.At t = 24 hours, weight 92.4 kgAt t = 48 hours, weight = 89.5 kgHence, change in weight = -2.9 kgAssuming the density of the fluids in the body is 1 kg/L;Change in body volume = -2900 mLFluids given in this period = 3840 mL D5W + 750 mL Iso-oncotic fluid = 4590 mLFluid losses measured in this period = 2558 mL urine + 40 mL blood = 2598 mLFluid lost due to evaporation = (25+21) x 47O.425 x 1700725 x 71.84 x 10The preburn weight, W, is unknown.Therefore:Fluid loss due to both evaporation and exudation = -2900 - 4590 + 25984892 mL in 24 hours = 203.83 mL/hTo determine the preburn weight, consider the period between 0 and 24 hours postburn.Assume the rate of evaporative and exudative fluid loss between 24 and 48 hours is thesame as that between 0 and 24 hours postburn.Change in body weight (92.4 - W) kg = (92.4 —w) xio3 mLAppendixE 172Fluids given in this period = (4500 + 7000) mL AR + 150 mL Iso-oncotic fluid= 11650 mLFluids lost in this period = (600 + 1958) mL urine + (200 + 20) mL blood = 2778 mLFluid loss due to evaporation and exudation = 4892 mL92400—W= 11650—2778—4892W=88420 ml88.4 kgTherefore fluid lost due to evaporation:EvAp =(25+21)x88°’ x170°725 x71.84x10 91.75 mL/hHence, fluid lost due to exudation, E)4892—91.75 112.08 mL/hExudation rates during the subsequent time periods were also determined from fluidbalances as previously described. However, discussions with Dr. T. Lund indicated thatthe patient weights were not taken in a consistent manner. As such, there was variability inthe exudation rates determined for each patient. However, considering the five patientscollectively would give more reasonable estimates for the exudation rate. Consequently,the exudation rate for each of the five patients was estimated based on the first set ofrecorded weights, usually between 12 and 24 hours postburn. It was then assumed that therate of exudation was proportional to the percentage burn surface area or degree of burn.The data from the five patients and the fitted relationship are shown in Figure E. 1. Thefitted relationship was forced to pass through the point ED 0 when DEG = 0%. Therelationship obtained wasEX(JD =0.O244xDEGxW, E.1where E) is the fluid loss due to exudation, DEG the degree of burn and W the patient’spreburn weight. Based on this relationship, an exudative rate was determined and assumedconstant for each patient during the first three days postburn.173Appendix EI ‘ I I I—5-0)-cEuS 3—4JCtanSCt•0Dxl-w0-0 20 40 60 80 100Degree of burn injury, %Figure E.1: Exudation Relationship based on NBC Patient DataAppendix F 174Appendix F: Birkeland’s Patient Data [19691This data was used directly in the parameter estimation procedure. The data which couldbe directly applied in the current study were the plasma volumes of five sets of burnpatients, grouped according to percentage burn surface area as presented in Table F. 1.The curved lines shown in Figure F. I represent graphical estimates of the plasma volumesas a function of time for each burn group. The postburn times and corresponding plasmavolumes shown in Table F.2 were manually extracted from the solid lines shown in FigureF. 1.Table F. 1: Grouping of Birkeland’s PatientsBurn Group Percentage Burn, % Number of Burn PatientsI 2-9 11II 10-18 21III 20-30 17IV 39-49 7V 54-90 11Figure F. 1: Patient Blood and Plasma Volume Observations on Admission and Prior toStart of Fluid Therapy by BirkelandAppendix FBurn .group‘120V/o Of80control600•II iii IV Vaa7175..IPV0/0 ofcontrol120I. I1’..1(20104 & 12 24 4 8 12 24 4 8 12Hou is after burnt4 4 812 24 5 12 Z4Appendix F 176Table F.2: Plasma Volume Data (mL) for Groups of Birkelands PatientsTime, hours Group I Group II Group III Group IV Group Vpostburn0.0 3200.00 3200.00 3200.00 3200.00 3200.001.0 - - - 2460.00 2460.002.0 2950.11 2650.00 2460.00 2050.00 1920.003.0 - - - 1825.44 1550.784.0 2805.78 2450.11 2060.22 1751.11 1351.116.0 2684.44 2373.33 1840.44 - -8.0 2595.56 2325.89 1706.67 - -10.0 2540.00 2284.44 1617.78 - -12.0 2506.67 2270.00 - - -Appendix G 177Appendix G: Determination of Exudation Rate for Birkeland’s PatientsExudative fluid losses from Birkelands patients were estimated based on data availablefrom a study by Davies [1982]. In this study, it was assumed that the sodiumconcentration in the fluid leaking from the burned surface is the same as that of serum. Asa result, chemical analysis of sodium extracted with water from the dressings coveringburned tissue gave an indication of the volume of exudate. The rate of exudative fluid lossfrom patients with different burn areas was monitored during the initial period postburnbefore fluid therapy was initiated. These patient data [Davies, 1982] are presented in TableGi. To the best of the author’s knowledge, this is the only available data that could beused to estimate the initial exudative fluid loss from the patients studied by Birkeland.Table G. 1: Area of Burn and Exudation Rate PostburnArea of Burn, cm2 Average Exudate Output,mL/h7400 26.927960 25.675624 36.717164 22.635890 38.505220 38.794400 12.832970 24.58A linear relationship was determined based on the assumption that the rate of exudationwas proportional to the area of the burn. The clinical data and the fitted relationship areAppendix G 178shown in Figure G. 1. The fitted relationship was forced to pass through the point EX =0 when DEG = 0%. The relationship obtained was8.85XUD xA G.18x103where EX is the rate of exudation and A the area of burn in cm2 given byA=DEGxTBSA. G.2The rate of exudative fluid loss for each group was determined as the valuecorresponding to the mid-point value of the percentage burn surface area of that group.The exudation rates estimated from the NBC patient information were about 8 timesgreater than those reported by Davies for the same burn surface area. This difference maybe explained by the fact that the NBC patients received fluid therapy, while fluidresuscitation had not been initiated in the patients studied by Davies in the period underconsideration. Similarly, the patients in the various groups investigated by Birkelandreceived no fluid therapy during the postburn times indicated in Table F.2.400)30ci)Q 20C0-oD><w00 2000 4000 6000 8000Area of Burn, cm**2Figure G.1: Exudation Relationship based on Davies’ Patient DataAppendix H 179Appendix H: Clinical Data from Arturson’s Patient [Arturson et al., 19891Information regarding the treatment and care of a patient included:i) fluid therapy consisting of acetated Ringers, 5% glucose, plasma and albumininfusions;ii) cumulative urine production;iii) erythrocyte volume fraction; andiv) change in body mass.A summary of this information is presented in Tables H. 1 and H.2. These data were usedto validate the model once the best-fit parameters were determined.The patient, a 62-year-old man with a body mass of 77-kg and a 58% total burn area, wastreated during the first 48 hours. Primary excision and grafting with synthetic skin wasperformed between 26.5 and 30 hours after burn injury.Table H. 1: Erythrocyte Volume Fraction Data [Arturson et a!., 19891Time, hours postburn Erythrocyte VolumeFraction,_%5 5013 5520 4922 4631 4738 4045 35Appendix H 180Table H.2: Fluid Inputs and Outputs to Patient [Arturson et al., 1989]hours Tend, hours CLF’ mL/h PCF’ mL/h 3EXUD’ mL/h URINE, mL/hpostburn postburn0.0 0.5 0.00 0.00 109.56 27.780.5 2.5 1200.00 0.00 109.56 27.782.5 4.5 1125.00 0.00 109.56 27.784.5 8.0 1200.00 0.00 109.56 27.788.0 17.0 600.00 0.00 82.97 27.7817.0 18.0 600.00 48.75 82.97 27.7818.0 24.0 600.00 48.75 82.97 55.5624.0 36.0 225.00 31.69 106.70 55.5636.0 44.0 225.00 31.69 106.70 41.6744.0 48.0 225.00 49.41 106.70 41.67Appendix I 181Appendix I: Clinical Data from RoatsPatients [Roa et al., 1990; personal communication]The information pertaining to two patients included:i) intravenous fluid and colloid input;ii) urine volume;iii) hematocrit; andiv) plasma protein concentration.Personal data was collected on admission and is summarized in Table I. 1. These data wereused to validate the model once the best-fit parameters were determined.Table I. 1: Personal Data from Roa’s Patients [Roa et al., 1990]Patient 1 Patient 2Age 18 29Sex Female MaleHeight, cm 160 160Weight, kg 55 64Burn surface area, % 75 80Appendix I 182Table 1.2: Fluid Input and Output for Patient 1 [Roa et al., 19901T, hours Tfld, hours CLF’ mL/h PCF’ mL/h URINE’ mL/hpostburn postburn0.0 1.0 0.0 0.00 0.001.0 2.0 428.57 0.00 18.182.0 3.0 428.57 0.00 1.183.0 4.0 428.57 0.00 0.004.0 5.0 428.57 0.00 9.095.0 6.0 1464.29 0.00 9.096,0 7.0 1500.00 0.00 36.367.0 8.0 1214.29 0.00 90.918.0 9.0 428.00 0.00 27.279.0 10.0 571.43 164.98 27.2710.0 11.0 571.43 164.98 18.1811.0 12.0 571.43 58.90 54.5512.0 13.0 500.00 58.90 36.3613.0 14.0 500.00 58.90 45.4514.0 15.0 500.00 212.16 63.6415.0 16.0 607.14 212.16 36.3616.0 17.0 607.14 212.16 45.4517.0 18.0 607.14 212.16 36.3618.0 19.0 571.43 212.16 45.4519.0 20.0 571.43 212.16 36.3620.0 22.0 642.86 212.16 45.4522.0 23.0 678.57 212.16 36.3623.0 24.0 500.0 212.16 36.3624.0 25.0 292.86 170.91 45.4525.0 26.0 292.86 170.91 36.3626.0 27.0 292.86 170.91 27.2727.0 28.0 285.71 82.49 36.3628.0 29.0 321.43 129.67 36.3629.0 30.0 321.43 129.67 27.27Appendix 1 183Table 1.2 Continued: Fluid Input and Output for Patient I [Roa et al., 1990]hours Tend, hours CLF, mL/h PCF’ mLIh 3IJRINE’ mL/hpostburn postburn30.0 31.0 292.86 47,18 36.3631.0 32.0 214.29 0.00 36.3632.0 33.0 250.00 47.18 36.3633.0 34.0 285.71 47.18 36.3634.0 35.0 250.00 35.30 36.3635.0 36.0 214.29 0.00 27.2736.0 37.0 250.00 47.18 27.2737.0 38.0 214.29 47.18 36.3638.0 39.0 285.71 47.18 27.2739.0 40.0 278.51 47.18 27.2740.0 41.0 285.71 47.18 36.3641.0 42.0 271.43 47.18 36.3642.0 43.0 285.71 47.18 27.2743.0 44.0 271.43 47.18 36.3644.0 45.0 285.71 47.18 27.2745.0 46.0 278.51 47.18 27.2746.0 47.0 278.51 47.18 36.3647.0 48.0 285.71 47.18 38.18Appendix 1 184Table 1.3: Fluid Input and Output for Patient 2 [Roa et al., 1990]T, hours Td, hours CLF, mL/h pCF’ L,’h URINE’ mL/hpostburn postburn0.0 1.0 1000.00 0.00 227.271.0 2.0 1000.00 0.00 145.462.0 3.0 1071.43 164.98 427.273.0 4.0 1285.71 0.00 245.464.0 5.0 1285.71 0.00 109.095.0 6.0 1285.71 0.00 27.276.0 7.0 1285.71 0.00 18.187.0 8.0 1285.71 0.00 118.188.0 9.0 357.14 0.00 27.2710.0 357.14 0.00 18.1810.0 11.0 1214.29 0.00 54.5511.0 12.0 1250.00 0.00 54.5512.0 13.0 1000.00 0.00 100.0013.0 14.0 750.00 0.00 145.4514.0 15.0 714.29 0.00 81.8215.0 16.0 500.00 0.00 90.9116.0 17.0 500,00 0.00 32.7317.0 18.0 642.86 0.00 27.2718.0 19.0 857.14 0.00 45.4519.0 20.0 285.71 0.00 45.4520.0 22.0 285.71 0.00 18.1822.0 23.0 250.00 0.00 18.1823.0 24.0 428.57 82.49 32.7324.0 25.0 428.57 82.49 9.0925.0 26.0 500.00 0.00 50.9126.0 27.0 500.00 0.00 54.5527.0 28.0 571.43 82.49 50.9128.0 29.0 571.43 82.49 45.4629.0 30.0 500.00 0.00 36.36Appendix I 185Table 1.3 Continued: Fluid Input and Output for Patient 2 [Roa et al., 1990]hours Tend, hours cLF, mL1h 3PCF’ nil1 UR1NE, mL/hpostburn postburn30.0 31.0 500.00 0.00 45.4631.0 32.0 321.43 64.82 36.3632.0 33.0 428.57 64.82 27.2733.0 34.0 507.14 47.13 27.2734.0 35.0 500.00 0.00 27.2735.0 36.0 357.14 82.49 36.3636.0 37.0 357.14 82.49 18,1837.0 38.0 392.86 0.00 14.5538.0 39.0 357.14 0.00 27.2739.0 40.0 500.00 82.49 40.0040.0 41.0 821.43 82.49 45.4641.0 42.0 857.14 0.00 54.5542.0 43.0 357.14 0.00 263.6443.0 44.0 107.14 82.49 112.7344.0 45.0 107.14 82.49 54.5545.0 46.0 85.71 0.00 54.5546.0 47.0 107.14 0.00 36.3647.0 48.0 178,57 82.49 36.36CD 0 0 -I CD z 0 -: CD 0 CDCDL,)Wk’.)ts))C9p)p9°9°..c-..oc‘.occiucccC4cMC.-..0aCCcMcM“0t)cMVi\0400C0-------ViViViViViViViViViViOcts)--IViViVit’J‘‘3C-J’IIVi’C’,VicM-4tCC0C00k’.)C0c..‘•‘c...)-—.CCCVit)Vi00CtJVi..-III.IIIIIIII.C0CViVib-.)00C‘.)tVi(-00C0CONON‘JCt’JON00Appendix 1 187Table 1.4 Continued: Monitored Clinical Data for Patient 1 [Roa et al., 1990]Time, hours Hematocrit, % CPL, WLpostburn36.82 - 35.5637.27 44.44 -37.73 - 36.6738.64 44.44 -39.09 - 36.6742.73 42.22 35.5646.36 38.89 -47.27 - 38.89Table 1.5: Monitored Clinical Data for Patient 2 [Roa et al., 1990]Time, hours Hematocrit, % CPL, g/Lpostburn1.82 56.67 54.4411.36 60.00 -11.82 - 35.5618.18 55.56 -26.36 60.00 32.2235.46 - 28.8941.82 51.11 -44.55 53.33 -45.46 - 30.00Appendix J 188Appendix J: Minimum Objective Function Value ResultsTable J. 1: Minimum OBJFUN Values for NBC Patient 1 Based on 12 Data PointsEXFAC r, h’ GkFTT GkFBT OBJFUN0.25 0.008 0.00 4.00 0.710.50 0.008 0.00 5.00 0.650.75 0.008 0.00 6.00 0.601.00 0.008 0.00 6.00 0.550.25 0.025 0.00 6.00 0.680.50 0.025 0.00 6.00 0.600.75 0.025 0.00 7.00 0.531.00 0.025 0.00 8.00 0,48Table J,2: Minimum OBJFUN Values for NBC Patient 2 Based on 20 Data PointsEXFAC r, h’ OBJFUN0.25 0.008 0.00 3.00 2.910.50 0.008 0.00 4.00 2.670.75 0.008 0.00 4.00 2.431.00 0.008 0.00 5.00 2.230.25 0.025 0.00 5.00 2.560.50 0.025 0.50 3.00 2.180.75 0.025 0.50 3.00 1.881.00 0.025 0.50 4.00 1.63Appendix J 189Table J.3: Minimum OBJFUN Values for NBC Patient 3 Based on 22 Data PointsEXFAC r, h’ GkF GkFRT OBJFUN0.25 0.008 0.00 4.00 5.380.50 0.008 0.00 5.00 5.060.75 0.008 0.00 5.00 4.761.00 0.008 0.00 5.00 4.520.25 0.025 0.00 5.00 4.420.50 0.025 0.00 5.00 4.160.75 0.025 0.00 6.00 3.901.00 0.025 0.00 6.00 3.65Table J.4: Minimum OBJFUN Values for NBC Patient 4 Based on 21 Data PointsEXFAC r, h1 GkF11 RT OBJFUN0.25 0.008 0.50 3.00 3.310.50 0.008 1.00 3.00 3.100.75 0.008 1.00 3.00 2.901.00 0.008 1.00 4.00 2.860.25 0.025 1.00 3.00 3.110.50 0.025 1.00 4.00 2.990.75 0.025 1.00 4.00 2.841.00 0.025 1.00 5.00 2.83AppendixJ 190Table J.5: Minimum OBJFUN Values for NBC Patient 5 Based on 30 Data PointsEXFAC r, h’ 0kFTI GkFRT OBJFUN0.25 0.008 0.00 5.00 4.040.50 0.008 0.00 5.00 3.990.75 0.008 0.00 5.00 3.991.00 0.008 0.00 6.00 4.000.25 0.025 0.50 4.00 3.860.50 0.025 0.50 5.00 3.790.75 0.025 0.50 5.00 3.751.00 0.025 0.50 6.00 3.76Table J.6: Minimum OBJFUN Values for Combination ofNBC Patients 2, 3, 4 and 5(Degrees of Burn Greater Than 25%)EXFAC r, Ir’ GkF GkFlT OBJFUN0.25 0.008 0.00 4.00 16.560.50 0.008 0.00 5.00 15.800.75 0.008 0.00 5.00 15.151.00 0.008 0.00 5.00 14.670.25 0.025 0.50 3.00 14.680.50 0.025 0.50 4.00 13.720.75 0.025 0.50 4.00 13.011.00 0.025 0.50 5.00 12.47Appendix J 191Table J.7: Minimum OBJFUN Values for Birkeland Burn Group I Based on 6 Data PointsEXFAC r, h’ GkFTT GkFRT OBJFUN0.25 0.008 0.60 3.00 2.005x1040.50 0.008 0.60 4.00 2.100x1040.75 0.008 0.60 4.00 2.124x1041.00 0.008 0.60 4.00 2.156x1040.25 0.025 0.70 3.00 3.569x1040.50 0.025 0.70 3.00 3.562x1040.75 0.025 0.70 3.00 3.560x1041.00 0.025 0.60 5.00 4.941x10Table J.8: Minimum OBJFUN Values for Birkeland Burn Group II Based on 6 DataPointsEXFAC r, h-’ GkF GkF RT OBJFUN0.25 0.008 0.90 9.00 1.185x1030.50 0.008 0.90 9.00 1.164x1030.75 0.008 0.90 9.00 1.151x1031.00 0.008 0.90 10.00 1.128x1030.25 0.025 1.00 9.00 0.958x1030.50 0.025 1.10 8.00 0.918x1030.75 0.025 1.10 8.00 0.882x1031.00 0.025 1.10 8.00 0.855x103AppendixJ 192Table J.9: Minimum OBJFUN Values for Birkeland Burn Group III Based on 5 DataPointsEXFAC r, h’ GkFTT GkFRT OBJFUN0.25 0.008 3.40 8.00 7.733x100.50 0.008 3.40 8.00 7.886x1030.75 0.008 3.40 8.00 8.039x10-1.00 0.008 3.20 8.00 8.571x1030.25 0.025 3.80 8.00 9.027x10-30.50 0.025 3.60 8.00 9.281x1030.75 0.025 3.40 9.00 9.874x10-31.00 0.025 7.20 12.00 36.42x10-Table J. 10: Minimum OBJFUN Values for Birkeland Burn Group IV Based on 4 DataPointsEXFAC r, h-1 GkFTI GkFRT OBJFUN0.25 0.008 5.80 6.00 5.682x1030.50 0.008 5.80 6.00 5.728x1030.75 0.008 5.80 6.00 5.773x1031.00 0.008 5.80 6.00 5.819x10-30.25 0.025 5.80 6.00 6.242x10-30.50 0.025 5.80 6.00 6.301x100.75 0.025 5.80 6.00 6.359x101,00 0.025 5.80 6.00 6.418x103Appendix J 193Table J. 11: Minimum OBJFUN Values for Birkeland Burn Group V Based on 4 DataPointsEXFAC r, h’ Gkp GkFRT OBJFUN0.25 0.008 5.80 6.00 4.091x1020.50 0.008 5.80 6.00 4.114x1020.75 0.008 5.80 6.00 4.137x1021.00 0.008 5.80 6.00 4.160x1020.25 0.025 5.80 6.00 4.259x100.50 0.025 5.80 6.00 4.284x100.75 0.025 5.80 6.00 4.309x1021.00 0.025 5.80 6.00 4.334x102Table J. 12: Minimum OBIFUN Values for Combination of Birkeland Burn Groups Iand II (Degree of Burn Less Than 25%)EXFAC r, h’ GkFTT GkFRT OBJFUN0.25 0.008 0.50 12.00 9.021x1030.50 0.008 0.50 12.00 9.175x1030.75 0.008 0.50 12.00 9.324x101.00 0.008 0.50 12.00 9.470x1030.25 0.025 0.60 12.00 9.688x1030.50 0.025 0.60 12.00 9.827x1030.75 0.025 0.60 12.00 9.964x10-31.00 0.025 0.60 12.00 10.10x103Appendix 1 194Table J. 13: Minimum OBJFUN Values for Combination of Birkeland Burn GroupsIII, IV and V (Degrees of Burn Greater Than 25%)EXFAC r, h-’ GkFTI GkFRT OBJFUN0.25 0.008 3.80 8.00 6.557x1020.50 0.008 3.60 8.00 6.735x10-20.75 0.008 3.40 8.00 6.994x10-21.00 0.008 3.80 9.00 7.110x1020.25 0.025 3.80 8.00 6.905x1020.50 0.025 3.60 8.00 7.158x1020.75 0.025 4.00 9.00 7.274x101.00 0.025 5.20 10.00 11.88x10-2Table 3.14: Minimum OBJFUN Values for Combination ofNBC and Birkeland Datafor Burns Less Than 25% for Factor of 30EXFAC r, h’ GkFTJ GkFRT OBJFUN0.25 0.008 0.50 7.00 2.530.50 0.008 0.50 7.00 2.180.75 0.008 0.50 8.00 1.891.00 0.008 0.50 8.00 1.650.25 0.025 0.50 8.00 1.920.50 0.025 0.50 9.00 1.630.75 0.025 0.50 9.00 1.391.00 0.025 0.50 10.00 1.19Appendix J 195Table 3.15: Minimum OBJFUN Values for Combination ofNBC and Birkeland Datafor Burns Greater Than 25% for Factor of 30EXFAC r, h’ GkFTI GkFRT OBJFUN0.25 0.008 0.50 7.00 36.360.50 0.008 0.50 7.00 33.910.75 0.008 0.50 8.00 31.751.00 0.008 0.50 9.00 29.860.25 0.025 0.50 8.00 30.800.50 0.025 1.00 7.00 28.440.75 0.025 1.00 8.00 26.261.00 0.025 1.00 9.00 28.05Table 3.16: Minimum OBJFUN Values for Combination ofNBC and Birkeland Datafor Burns Less Than 25% for Factor of 100EXFAC r, h-’ GkFTI GkFBT OBJFUN0.25 0.008 0.50 10.00 3.440.50 0.008 0.50 10.00 3.040.75 0.008 0.50 11.00 2.701.00 0.008 0.50 11.00 2.430.25 0.025 0.50 11.00 2.820.50 0.025 0.50 11.00 2.500.75 0.025 0.50 12.00 2.221.00 0.025 0.50 12.00 2.00AppendixJ 196Table J. 17: Minimum OBJFUN Values for Combination ofNBC and Birkeland Datafor Burns Greater Than 25% for Factor of 100EXFAC r, h’ GkFTT GkFRT OBJFUN0.25 0.008 1.00 10.00 54.620.50 0.008 1.50 9.00 49.600.75 0.008 2.0 8.00 44.831.00 0.008 2.50 8.00 40.490.25 0.025 1.50 9.00 45.560.50 0.025 2.00 9.00 41.100.75 0.025 2.00 9.00 37.011.00 0.025 2.50 10.00 44.20Table J. 18: Minimum OBJFUN Values for Combination ofNBC and Birkeland Datafor Burns Less Than 25% for Factor of 200EXFAC r, h’ GkFTT GkFBT OBIFUN0.25 0.008 0.50 11.00 4.400.50 0.008 0.50 11.00 4.000.75 0.008 0.50 11.00 3.681.00 0.008 0.50 12.00 3.410.25 0.025 0.50 12.00 3.870.50 0.025 0.50 12.00 3.550.75 0.025 0.50 12.00 3.291.00 0.025 0.50 13.00 3.08Appendix J 197Table J. 19: Minimum OBJFUN Values for Combination of NBC and Birkeland Datafor Burns Greater Than 25% for Factor of 200EXFAC r, h’ GkFTI GkFBT OBJFUN0.25 0.008 2.00 9.00 67.210.50 0.008 2.50 8.00 60.680.75 0.008 3.00 8.00 54.531.00 0.008 2.50 9.00 49.590.25 0.025 2.50 9.00 57.300.50 0.025 2.50 9.00 51.430.75 0.025 2.50 9.00 46.641.00 0.025 3.00 11.00 60.03Appendix K 198Appendix K: Computer Program ListingThis program was written in Fortran and run on an IBM 486 Personal Computer using theMicrosoft Compiler.PRINT*,ENTER SURFACE DATA FILE’Program csml.f: The Coupled Starling Model (Patlak Model). A 3- READ*,SURFILEconipartinental buni model comprising the folloving: uninjured tissue, c 11111111 I I I I I I I 111111111 I I I I I I I I 11111111injured tissue, and plasma (the circulation). c CALCULATE / ASSIGN VARIOUS CONSTANTSC ii II iiiPROGRAM CSMI.F CALL CONSTAII,1I)IICIl:’REis,I_,*8 (a—I,C—Z) C I 11111 I 111111 I I 111111111 liii I liii liiiinclude ‘outputcmn’ c FIT COMPLIANCE DATAiiicludeiiij,utcsiiii’ ciiIiIIiIiiiIiiiIIiiiiiIiIIiIIIiiiiIIiiiIiiIiiiiiinclude ‘initvacmn’ CALL COMSPLimscli.zdenoiiiial.cis’ ciiiiiiiiIiiiiIiiiIiIiIIIiiilIIIiIiiIIIiIiiIiiiiIinclude expdatcmn’ c ADJUST/CALCULATE NORMAL VALUES111111 11111 111111 iii ii ii II 111111 ii Ii ciii 11111111111 Iii ii 11111111111 11111c DATA DECLARATIONS CALL NORMALliii III IIIIIIIIIIIIIIII III 11111 cliii liii III IIIIIIIII1IIIIIIIIIIIIIIIIIIIIII 1111c — Number of parameters to be optimized c ASSIGN/CALCULATE INITIAL VALUEScIliiIIiiIiiIIIiIiIIIIIIIIIIiIIIIIIIIIIIIIIIiIIIIc — Airays for initial guesses for parameters to be optimized CALL INITVcIiiIiiiiIiIIIIIIiIIIIiiiiIIiIIiIIIIIIIIiIIilIIiIciiIIIiIIiIiIiIIIiIIiIiiIIiIIIIiiiIiiIiiiiIIiIi c PER.FORJvIOPTTJ,4JZATIONc cliii ill iii 11111111 iii III III ill Ii iii 11111111ciIIIIiIiIiIIiIIIIIiIiiIIiIIIIIIiIiIIiiiIiiIiII c—Setiiitialvaluesamidlixxitsofpa.ia.iiietetstoledeteriiiiedINTEGER MXFLSE, MAXIT, LOG, IPRINT, IFAIL, MAXFUN IF ( IFLOPT EQ. 1) THENDIMENSION XXL(NUMP),XXIJ(NUMP) XK(l)=GKFTIREAL*8 ACCUR,SCBOU,F XK(2)=GKFBTPARAMETER( M=l,ME=O) XXL(l)=XL(l)PARAMETER( Nl=NUMP+l, Ml=l) XXL(2)=XL(2)PARAMETER (LWA1=MI, LWA2=Nl, LWA3=Ml*Nl, XXU(l)=XIJ(l)LWA4=M+2*Nl, LWAS=Nl*Nl, LWA6=Nl, LWA7 = 3* NI *Nl XXLJ(2)=XU(2)+2* Ml * Nl+l I *Ml +29*Nl+3*Ml+6O+3*(MIINl+I)) ELSE IF ( IFLOPT .EQ. 2) THENPARAMETER LIWA 18 + (Nl+2+Ml) + Ml + Nl+I, XK(I)=GKFTILJWA=MI+20) XK(2)=GKFBTDIMENSION WORKAI(LWAI), WORKA2 (LWA2), XK(3)=RCOEFWORKA3(LWA3) XXL(l)=XL(l)DIMENSION WORKA4(LWA4) XXL(2)=XL(2)DIMENSION WORKASiLWA5), WORKA6 (LWA6), XXL(3)=XL(3)WORXA7(LWA7) XXU(l)=XU(I)INTEGER IWORKA(LIWA), JWORKA(LJWA) XXU(2)=XU(2)DIMENSION DX(NUMP), HESS(NUMP, NUMP), XXU(3)=XU(3)COVAR(NUMP,NUMP) ELSE IF ( IFLOPT EQ. 3) THENDIMENSION VARICE(NUMP), INDX (NUMP) XK(l)=GKFTICHARACTER*lO SURFILE XK(2)=GKFBTCOMMON /CHSUR/SURFILE XK(3)=RCOEFc I 11111111 1111111c READ INPUT DATA FILE AND OUTPUT RESULTS FILE XXL(I )=XL(l)XXL(2)=XL(2)CALL INPUT XXL(3)=)<L(3)Appendix K 199XXL(4)XL(4) PPJNTXXIJ(l )=XU(l) WRITE(6,205)EXTIIvIF(I),EXPIBT(I),APIBTII)XXIJ(2)=XU(2) ENDIFXXU(3)=XU(3) ENDIFXXU(4)=XIJ(4) IF (IPAR(3) EQ. 1) THENENDIF IF (IRATIO EQ. I) THENIF (IFLOPT .GT. 0) THEN PRINT *,I,EXJ)ITI(I),(PJ)ITJ(I)*PIPLO)/(PJ)lpL(I)tIF(IRATIO EQ. 1) CALL RATION PITIO)CALL SURFACE WRITE(6,205) ExTIMEa). EXPITI(I), (APITI(I) *STOP PIPLO) / (APIPL(I)tPIT10)ENDIF ELSESTOP PRINTt,I,EXPITI(I),APITI(I)END WRfl’E(6,205)EXTIME(I),EXPITI(I), APITI(I)ENDIFc ENDIFSubprogram PAROUT: Outputs estimated parameters and results IF (IPAR(4) EQ. 1) THENc*****************fl4I IF(IRATIO.EQ. I) THENSUBROUTINE PAROUT PRINT *,I,EECPL(I),ACPL(I)/CPLOIMPLICIT REAL*8 (A-KO-Z) WRITE(6,205)EXTIME(I),EXCPL(I), ACPL(I)ICPLOinclude ‘outputcmn’ ELSEinclude ‘inputcmn PRINTt,I,EXCPL(I),ACPL(I)include initva.cmn WRITE(6,205)EXTIME(I),EXCPL(I), ACPL(I)include ‘normal.cmn’ ENDIFinclude ‘expdatcmn’ ENDIFc Ii liii III 111111 I liii 111111 11111 liii 111111 II 10 CONTINUEc OUTPUT ESTIMATED PARAMETERS AND RESULTS WRITE(6,l00)c 11111 III III I I Iii I liii 11111 I III 1111111111 X’lJI’E(6,l00)WRITE(6,100) 100 FORMATQ)\/RJ1’E(5,l03) 103 F0R.kIATI I III I I III 111111111 II’)WRITE(6,l02) GKFTI = GKFTI 102 FORMAT(A30,F18.5)WRITE(6,l02)’ GREET = ,GKFBT 107 FORMAT Time Expt Predicted )WRITE(6,l02) RCOEF=’,RCOEF 108 FORMATç—WRITE(6,102)’ EXFAC = ,EXFAC 110 FORMAT(3Fl8.4)WRITE(6,100) 205 FORMAT(3F18.4)WR.ITE(6, 107) RETURNWRITE(6, 108) ENDDO 10 I=l,NUMEXPIF(IPAR(l) EQ. 1) THEN c******************************************************IF (IRATIO EQ. 1) THEN c Subprogram FUNC: Calculates values of objective fUnction andPRINTt,I,EXVPL(I),AVPL(I)/VPLO constraint fUnctions at current value of XWRITE(6,205)EXTIME(I),EXVPL(I),AVPL(I)/VPLO c******************************************************ELSE SUBROUTINE FUNCQ4ME,MMAxN,FF,qx)PRINTt,I,EXVPL(I),AVPL(I) IMPLICIT REALt8(A-H,O-Z)WRITE(6,205)EXTIIv8E(I),EXVPL(I), AVPL(I) include output.cnmENDIF include ‘input.crnnENDIF include expdst.cmnIF (IPAR(2) .EQ. I) THEN include initvacninIF (IRATIO EQ. 1) THEN PARAMETER (VAL=-999.99)PRINT *j, EXPIBT(I), (APIBT(I) * PIPLO) I (APIPL(I) INTEGER M,MEJvEvIAX,N*PINTO) DIMENSION X(N),G(MMAX)REALt8FFWRITE(6,205)EXTIME(I),EXPIBT(I),APIBT(I)*PIPLO)/(APIPL(I)* c Call simulation module SIMOPT with current guesses x (N)PINTO) CALL SUvlOPTcN)ELSE c —- Calculate objective function valueAppendix K 200FF=0.0DO l0I=l,NUMEXPIF (IPAR(l) EQ. l)THENIF (EXVPLQ) CT, VAL ) THENIF(IRATIO.EQ. l)THENERROR= (EXVPL(I) - AVPL(I) I VPLO )**2ELSEERROR= (EXVPL(l)AVPL(I))**2ENDIFERROR= ERRORISDVPL(I)4t2FF=FF+ERRORENDIFENDIFIF (IPAR(2) EQ. 1) THENIF ( EXPIBT(I) CT. VAL ) THENIF (UIATIO EQ. 1) THENRVAL= (APIBT(I) *flLO) / (APIPL(I) * PIBTO)ERROR= (EXPIBT(I)-RVAL)t2ELSEERROR= (EXPIBT(I)-APIBT(I) )**2ENDIFERROR= ERR0RISDPIBTa)tt2FF=FF+ERRORENDIFENDIFIF (IPAR(3).EQ. I) THENIF (EXPITI(I) CT. VAt) THENIF (IRATIO EQ. 1) THENRVAL__(APITI(I)*PIPLO)/(APIPL(I)*PITIO)ERROR = (EXPITI(I) - RVAL)**2ELSEERROR= (EXPITI(I)-APITI(I) )**2ENDIFERROR= ERRORJSDPITI(I)**2FF=FF+ERRORENDIFENDIFIF (IPAR(4).EQ. 1) THENIF (EXCPL(I) CT. VAL ) THENIF (IRATIO EQ. 1) THENERROR= (EXCPL(I)-ACPL(I) I CPLO) **2ELSEERROR= (EXCPL(I)-ACPL(I) )**2ENDIFERROR= ERROR/SDCPL(I)tt2FF=FF±ERRORENDIFENDIF10 CONTINUEREUJRNENDc Subprogram SIMOPT; Simulates the Microvascular Exchange Processc XK(N) Amy of values of parametersNUMP = Number of parametersSUBROUTINE SIMOPT(XK,NUMP)IMPLICIT REAL4S(A-H,O-Z)include ‘outputcmninclude ‘inputcmninclude compli.cmninclude initva.cmninclude normslcmninclude curent.cmninclude expdatcmnINTEGER NUMPDIMENSION XK(NUMP)e — Extemal SubroutineEXTERNAL MODELc Data for the resolution of modelc-—Number of differential equations to be solvedPARAMETER (NEQ=6)c — Input array into subroutines MODEL and DESOLV or RK4CDIMENSION YA(NEQ)c — Output array from subroutine DESOLV or RK4C (holds values offluid volume and protein contents at the end of each time step)DIMENSION YB(NEQ)c --- Output array from submutine MODEL (holds values of derivatives)DIMENSION DYDX(NEQ)c — Data for Runge HuEs Fehlberg algorithmDATA HHflN,HMAX,HSTART,EPS /1 .D-4, I U-I .1 D-I,l .D-2/cliii 1111111111111 iii 1111111111111111111111 liiiCURRENT VALUES OF PARAMETERS TO BE DETERMINEDiiIF ( IFLOPT EQ. I ) THENGKFTI=XK(l)GKFBT=XK(2)ELSEIF(IFLOPT .EQ.2)THENGKFTI=XK(l)GKFBT=XK(2)RCOEF=XK(3)ELSE IF ( IFLOPT EQ. 3) THENGKFTI=XK(l)GKFBT=XK(2)RCOEF=XK(3)EXFAC=XK(4)ENDIFNPNT=0TIMEW—ODOXl=TIME(l)YA(l )=VTIOYA(2)=QTIOYA(3)=VBTOAppendix K 201YA(4)=QBTO IF (EXrIlvtE(IEXPT) .GT. Xl AND.YA(5)=VPLO EXTIME(IEXPT) .LE. XI÷SYBP AND. IEXPT .LE. NUMEXP)YA(6>=QPLO THENISUPER=l DX= EXTIME(IEXPT)-XlIPEROD=l ELSEc----—--------—--- —------—--—--------— —--—---------—-- DX=SThPc-- Solve model equations using RKF algorithm ENDIFX2’Xl+DXIEXPT=l DEPS=(DX/TFINAL)EPSNFUN=0 CALL RK4C (MODEL, NEQ, Xl, X2, YA, DEPS,c— Set excess/deficient makeup rates to zero since no steady state YB, NFUN, IFLAG)period c — If integration failed( IFLAG —0) exit else save resultsVEXREM=0.D0 IF (IFLAG EQ. 0) THENQEXREM=0.D0 WRJTE(6,15) Xl,X2c— Number of periods STOPNPEROD=NPETUB ELSETFINAL=TEND(NPETUB) DOS K=l,NEQc — Loop over the periods YA(K>YB(K)DO 100 IP=l,NPEROD 5 CONTINUEIPEROD=IP c — Save resultsISUPER=ISUP(IP) IF ( DABS(X2-EXTIME(IEXPT)) .LE. I .OD-6 ) THENA=TSTART(IP) CALL MODEL (X2,YB,DYDXNEQ)B=TEND(IP) CALL SAVRES (X2,YB,DYDXNEQ)XJRES(IP)=XJCLF(rP)+XJPCF(IP) IEXPT=IEXPT+lXl=A ENDIFX2=Xl ENDIFc—---- Change AFRAC after some time IF( X2 .LT. TEND(IP) ) GO TO 900IF (Xl GE. 72.ODO) THEN 100 CONTINUEAFRAC=l.0 5000 CONTINUEELSE 15 FORMAT C No solution between ‘,Fl 8.5.’ and ‘,Fl 8.5)AFRAC’=0,5 RETURNENDIF END900 CONTINUE cXl=X2c—-- Blood removal c Subprogram MODEL: Supplies derivatives of differential equations toIF (Xl .LT. BLSTIM OR Xl GE. BLEND) THEN be solvei to REF algorithmVBLOOD0 0 cELSE SUBROUTINE MODEL cYDYDXN)VBLOOD=BLOOD/(flEND-BLSTIM) IMPLICIT REAL 8 (A-ItO-F)ENDIF include ‘input.cmn’c—-—-- Check if a step of DTAU will overshoot the fmal time for this include compli.cmn’period TEND(IP) include ‘initva.cmnc If it overshoots adjust STEP else STEP = DTAU include ‘normalcmn’IF (Xl+DTAU .GT. TEND(IP) ) THEN include ‘cursnt.cmn’STEP= TEND(IP) - Xl INTEGER NELSE REAL*8 X,Y(N),DYDXIN)STEP DTAU c ---— Calculate fractional areasENDIF FATI=((Y(5)/VPLO)-VFRAc)/(l .D0-VFRAC)c —---- Check if there is an experimental point between Xl and FABT=AFRACFATIXl+STEP cc If there is an experimental point between Xl and Xl+STEP c PLASMAadjust DX else DX= step size STEP calculated above. c --—------- —— —________c — Calculation of CplCPL=Y(6)/Y(5)Appendix KC ---— Calculate osmotic pressure in plasmaPIPL=CPLJI .522D0c — Calculate capillaiy pressurePC=PCO-f-PCCOMP4(Y(5)-VPLO)IF (PC .LT. 3.ODO ) PC=3.ODOUNINJURED TISSUEc — Calculation of C and Cay for uninjured tissueCTI=Y(2)/Y(l)CTIAV=Y(2)I(Y(I)-VETI)c —-- Calculate hydrostatic pressure for uninjured tissuel{PTI=FCOMP(Y(l))c Calculate HPTIEXHPTIEX=FCOMP(VETI)C — Calculate osmotic pressure in uninjured tissuePm=CTIAv/l .522DOc — Calculate fluid fluxes for uninjured tissuec —-- Pore radii changes postbumRPTI = RPNL * (1 DO + GKFTI * DEXP(RCOEF*X))**0.5DOATIPB = RALB/EPTIc—- Lymph flow sensitivityXLSTI=XLSNORM*(l .DO+GLSTI*DEXP(RCOEF*X))c— Fluid filtration coefficientXKFrI=XKFNORM*CORRTI*(l .DO+GKFTI*DEXP(RCOEF*X))*FATIc— Lymph fluid flowXIJLTIO XJLNORM + XLSTI * (HPTI - HPTINL)X2JLTIO = XJLNORM * ((HP’fl- HPTIEX)/(HPTINLHFIEX))IF (HPTI GE. HPTINL) THENXJLTI =XIJLTIO * CORRTIELSEIF (HPTI GE. UPTIEX AND. HPTI .LT. HPTTNL) THENXJLTI = X2JLTIO * CORRTIELSEIF (HPTI .LT. 1-IPTIEX) THENXJLTI = ODOENDIFc----SigmaTOPTI = l6.DO*ATIPB**2.DO - 20.DO*ATIPB**3.DO +7.DO*ATIPB**4.DOSIGTI = TOPTII3.DOc --— Fluid filtration flowXJFTI=XKFTI*(PC.HPTI.SIGTI*(PWL.PITI))c— Calculate protein fluxes for uninjured tissuec— Diffusion coefficientPSTI ((I DO - ATIPB)2.D0) * CONST * CORRTI * FATIc—- Peclet numberPECLTI=(l .DO-SIGTI)XJFTIIPSTIRATIOTI=(CPLCTIAV*DEXP(PECLTI) )I(l .DO-DEXP(PECLTI))c — Transmembrane protein flowQSTI=( I .DO.SIGTI)*XJFTI*RATIOTIc--— Lymph protein flowQLTI=XJLTI*CTIINJURED TISSUEIF ( DEG .GT. 0.ODO) THENCBT=Y(4)/Y(3)CBTAV=Y(4)/(Y(3)-VEBT)c — Calculate hydrostatic pressure for injured tissueIF( IStJPER EQ. 1) THENDO 30 1=1,12IF ( X .LT. BTIMERH(I)) THEN(BTIMERH(I)- BTIMERH(lM))BTIMERH(IM))ENDIF11v11-lSLOPE(BPRESRH(I)-BPRESRH(Uvi)/HPBT= BPRESRH(IM) + SLOPE * (XGOTO 10030 CONTINUEELSE IF( ISUPER EQ. 2) THENHPBT=FCOMBT(Y(3))ENDIF100 CONTINUE— Calculate HPBTEXHPBTEX=FCOMBT(VEBT)c — Calculate osmotic pressure in injured tissuePIBT=CBTAV/1 .522D0c— Calculate fluid fluxes for injured tissuec — Pore radii changes postbumRPBT = RPNL * (I DO + GKFBT DEXP(RCOEF*X))**O.5DOAETPB RALB/RPBTc -—Lymph flow sensitivityXLSBT=XLSNORM*(l .DO+GLSBT*DEXP(RCOEF*X))Fluid filtration coefficientXKFBT=XKFNORM*CORRBT*(l.D0+ GKFBT*DEXP(RCOEF*Xt)*FPBTLymph fluid flowXI JLBTO = XJLNORM ÷ XLSBT * (HPBT- HPTINL)X2JLBTO = XJLNORM * (cHPBT - HPBTE)Q/ (HPTINL -HPBTEX))IF (HPBT GE. HPTINL) THENXJLBT = XIJLBTO * CORRBT * AFRACELSETF (HPBT GE. HPBTEX AND. HPBT .LT.HPTINL) THENXJLBT = X2JLBTO * CORRBT * AFRACELSEIF (HPBT .LT. HPBTEX) THENXJLBT = ODOENDIFFluid filtration flowXJFBT=XKFBT*(PCHPBT.SIGBT*(PlPLPIBT))— Calculate protein fluxes for injured tissue202c— SigmaTOPBT I6DO*ABTPB**2D0 - 20.DO*ABTPB**3.DO+ 7DO*ABTPB**4DOSIGHT = TOPBT/3D0Appendix Kc Diffusion coefficientPSBT = ((IDO - ABTPB)**2D0) * CONST * CORRBT * FABTc — Peclet numberPECLBT=(l .DO-SIGBT) * XJFBT I PSETRATIOBT=(CPLCBTAV*DEXP(PECLBT) )/(l DODEXP(.PECLWr))c ---- Transmembrane protein flowQSBT=(1.DO-SIGBT) * XJFBT *RATIOBTc— Lymph protein flowQLBT=XJLBT*CBTENDIFc FLUID AND PROTEIN BALANCESc----— In actual periodsIF (IPEROD LE. NPETUB ) THENc — Fluid out urine + wound fluid loss +evaporative fluid lossXJEVTI25.DOTBSAXJEVBT=DEG4IOO.DO*TBSAXJMAINODOEXUDN=XJEXUD(IPEROD)URJNE=XJURI(IPEROD)XJREM=URINE + XJEVTI + XJEVBT + EXUDN +c — Protein out = protein in urine + protein in wound fluid lossQEXUD=EXUDN*CBT*EXFACQEVAP=O.DOQURINEO.ODOQREMQEXUD + QEVAP + QURINEc—- In extra period : steady stateELSEc--——Fluidc---Prot.einENDIFXJEVTP=O.ODOXJEVBT=O.ODOXJMATN=O.ODOEXUDNO.ODOURINE=O.ODOXJREM=O.ODOQEXUD=O.ODOQEVAP=O.DOQURINE=O.ODOQEVAP=O.DOQUIUNE=O.ODOELSEIF ( IBLANK EQ. 2) THENXJMAIN=O.000URINE=O.ODOVELOOD=O.ODOQEVAP=O.ODOQURINE=O.ODOENDIFc—— Fluid and protein balances in uninjured tissueDYDX(l)=XJFTI-XJLTI-XIEVTIDYDX(2)=QSTI-QLTIc—- Fluid and protein balances in injured tissueIF(DEG.GT. O)THENDYDX(3)=XJFBT-XJLBT-XJEVBT-EXUDNDYDX(4)=QSBT-QLBT.QEXUDELSEENDIFDYDX(3)=O.ODYDX(4)=’O.O203c—- Fluid and protein balances in plasmaDYDX(5)=XJRBS(IPEROD)-(XJFFI-XJLTI)-(XJFBT-XJLBT)-URINE-VEXREM-VBLOODDYDX(6)=CRES(IPEROD)*XEQPLV (IPERODXQSTI-QLTI)(QSBT.QLBT)QURINE.QEXREM.VBLOOD*cpLoRETURNENDCc Subproam VrNTr: Calculates vanous initial valuesSUBROUTINE INITVIMPLICIT REAL*8 (A-HO-Z)include output.cmninclude input.cmninclude compli.cnsninclude initva.cmninclude normal.cmninclude curent.cmn’include expdat.cmnc— Assii and/or calculate various initial valuesc — Set all outputs to zero for a blank runrF ( IBLANK EQ. 1) THEN—-—Fluidc PLASMA ( CIRCULATION)XJEVTIO.ODOXJEVBT=O.ODOXJMAIN=O.ODOEXUDN=O.ODOURINE=O.ODOXJREM’O.ODOc VandQVPLO=VPLNLQPLO=QPLNLc Calculation of Cpl,oCPLO=QPLO/VPLOc ----- Calculation ofBVO AND BVFBVO=VPLO/(l .O-HCTO)BVF=BVO-BLOOD/(l .ODO-HCTO)c---ProteinQEXUDO.ODOAppendix Kc Calculate initial osmotic pressurePIPLO=CPLO/l .522D0c Calculate initial capillary pressurePCO=PCNLC UNINJURED TISSUEc—V and QforuninjuredtissueVTIO=VTINL*RELSM*DEGM + VTINL * RELMVETI=VETINL*RELSM*DEGM + VETINL * RELMQTIO=QTINL*RELSM*DEGM + QTINL *c Calculation of Co and Cav,oCTIO=QTIO/VTIOCTIAVO=QTIO/(VTIO-VETI)c Calculate hydrostatic pressureHPTIOFCOMP(VTIO)c Calculate initial osmotic pressurePITIO=CTIAVO/l .5221)0c INJURED TISSUEVBTO=VTINL*RBLSM*DEGVEBT=VETINL*RELSM*DEGQBTO=QTINL*RELSM*DEGc Calculation of Co and Cav,oCBTO=QBTO/VBTOCBTAVOQBTO/(VBTO-VEBT)c -— Calculate hydrostatic pressureIIFBTO=FCOMBT(VBTO)c — Calculate initial osmotic pressurePIBTO=CBTAVU/I.522D0ELSEVBTO=0.ODOVEBT=0ODOQBTO=0.ODOCBTO=0.ODOCBTAVO=0.ODOHPBTO=0.ODOPIBTO=0.ODOSUBROUTINE RATIONIMPLICIT REAL*8 (A-H,O-Z)include ‘output.cmninclude ‘inputcmn’include expdat.cmninclude initva.cmnPARAMETER(VAL=-999.99)DO 10 I=l,NUMEXPIF(IPAR(l).EQ. l)THENIF (EXVPL(I) cIT. VAL) EXVPL(I) = EXVPL(I) /VPLOc Subprogram SURFACE; Determine OBJFUN values forcombinations of GKPTI and GKFBTcSUBROUTINE SURFACEIMPLICIT REAL*8 (A-H,O-Z)include output.cmn’include inputcmninclude initva.cmninclude ‘normal.cmn’include expdat.cnmPARAMETER (N=2. M=0, ME=0, MIVIAX=l)PARAMETER(JMAX= 100)DIMENSION XTI(JMAX),XBT(JMAX)DIMENSION X(N)CHARACTER*20 CDATA(1 0)CHARACTER*1 0 SURFILECOMMON ICHSUR/SURFILEOPENIUNIT=7,FILE=SURPILE)READ(7,l 0) NUMTIREAD(7, II) (XTI(1),I=l,NUMTI)READ(7,10) NIJMBTREAD(7,l IXXBT(I),I=l,NUMBT)CLOSE(7)OPEN (UNIT=8, FILE’C:\AMVRESV 1/ RUNID if\//RUNID/fSURF.DAT)DO I I=1,NUMTIX(l)=XTI(I)1)02 J=l,NUMBT204ENDIFIF (IPAR(2) EQ. 1) THENIF (EXPIBT(I) cIT. VAL)* EXPIBT(I) = (EXPJBT(I) * PIPLO ) /(EXPIPL(I)*PIBTO)ENDIFIF(IPAR(3).EQ. I) THENIF (E)’ITI(I) cIT. VAL)* EXPITI(T) = (EXPITI(I) * PIPLO)/(EXPIPL(I)*PITIO)ENDIFIF (IPAR(4).EQ. 1) THENIF (EXCPL(I) cIT. VAL) EXCPL(I) = EXCPL(I) /CPLOENDIF10 CONTINUERETURNENDIF (DEG cIT. 0.01)0) THENc-----VandQENDIFRETURNENDc Subprogram RATION: Normalizes quantities with respect to theirinitial valuesAppendix K 205IMADEHIF (XBT(J) CIT. XTI(I) ) THENX(2)=XBT(J)CALL FUNC (M ME, MMAX N ,OBJVAL,G,X)WRITE(8,200) X(l), X(2), OBJVAL, IDEHYD,ENDW2 CONTINUEI CONTINUECLOSE(8)200 FORMAT(2F10.5,F15.4,213)9991 FORMAT(2(A2OL’),A20)10 FORMAT(I2)11 FORMAT(F18.5)RETURNENDc Subprogram INPUT: Reads input data, calculates certain constants andprints outSUBROUTINE INPUTIMPLICIT REAL48(A-aO-z)include ‘output.cmn’include ‘input.cmn’include ‘initvacmn’include ‘compli.cmn’include ‘norrnal.cmn’include ‘grflle.cmn’include ‘expdst.csnn’CHARACTER415 OUTFILE,CPFILECHARACTER 15 PAFJLE, OTFILE, PVF]LE. BTFILE, TIFILE,EXFILECHARACTER 10 SAVDIR,PATIDCHARACTER48OCOMENT,CDESC(l 0)PARAMETER(SAVDIR=t:\AMVRESV)c DATA INPUTWRITE(6,4)Enter RUN ID’READ(5, RUNIDWRITE(6,4)‘Enter patient data file’READ(5, PAFILEWRITE(6,4)Enter file for other data’READ(5, OTFILEWRITE(6,) ‘Select type of nmWRITE(6,4)‘STRAIGHT RUN =0 yWRITE(6,9’ OPTIMISATION OF GKFTI & GREET 1WRITE(6,4)’OPTIMISATION OF GKFTI, GREET & RCOEF=2 yWRITE(6,4)‘ OPTIMISATION OF GKFTI,GICFBT, RCOEF &EXFAC =3PEftJJ(54)IFLOPTIF(IFLOPT.GT.0)TI-IENWRITE(6,4)‘Use VPL data for optimisation (IYES , 0 NOyPEAD(5, IPAR(l)IF(IPAR(l) EQ. 1) THENWRITE(6,4)Enter VPL experimental data file’p,EpIJ(54) PVFILEENDIFWRITE(6,4)Use PIBT data for optimisation (1 YES • 0 NOyp,aJ)(5,4) IPAR(2)IF(IPAR(2) EQ. 1) THENWRITE(6,4)Enter PIBT Experimental data file’READ(5,’) BTFILEENDIFWRITE(6,4)Use PITI data for optimisation (1’TES ,0 NOP-,EAD(5, IPAR(3)tF(IPAR(3) EQ. 1) TI-lENWRrFE(6,4)Enter PITI experimental data file’REPJJ(5, TIFILEENDIFWRITE(6,4)Use CPL data for optimisation (I =YES , 0 NOyREAD(5. IPAR(4)IF(IPAR(4) EQ. 1) THENWRITE(6,4)Enter CPL experimental data file’P-EAD(5, CPFILEENDIFENDIFOPEN(UMT=6,FILE=SAVDIRJ/RUNIDIFV//RUNID/fRES)c PATIENT DATAOPENQJMT=5,FILE=PAFILE)WRITE(6,200)READ (5,9 COMENTREAD (5,4) PATIDWRITE(6,208)COMENT,PATID208 FORMAT(A80,A1 0,1)READ (5,) (CDESC(IiI=1 A)WRITE(6,209) (CDESC(I),I=l,4)209 FORMAT(A80)c — Weiglst of patientREAD (5,) COMENTREAD (5,4) WEIGHTWRITE(6,20l)COMENT,WEIGHTc—-Height of patientREAD (5,4) COMENTREAD (5,4) HEIGHTWRITE(6,201)COMENTJIEIGHTc — Degree of burnREAD (5,) COMENTREAD (5,) DEGWRITE(6,201)COMENT,DEGc— Initial blood lossREAD (5,4) COMENTREAD(5,4)BLOOD,BLSTIM,BLENDWRITE(6,207) COMENT, BLOOD, BLSTII4 BLENDc — Initial hematocritREAD (5,4) COMENTREAD(5,4)HCTOWRITE(6,217)COMENT,HCTORESUSCITATION 4444444c — Number of resuscitationlperturbation stagesREAD (5,4) COMENTREAD (5,9 NPETUBWRITE(6,202)COMENT,NPETUBc —--- Start time, end time, clear fluid flow rate, protein-containing fluidrate, protein concentration, urinasy loss, equivalent plasma volume, fluidexudation rate and period indicator for each stageREAD (5,4) COMENTREAD(5,4) (TSTART(I), TEND(I), XJCLF(I), XWCF(I),CRES(I), XJURI(I), XEQPLV(I), XJEXUD(I), ISUP(I),1=1 ,NPETUB)WRITE(6,201 )COMENTWRITE(6,206)WRITE(6,205) ( TSTART(I), TRND(I). XJCLF(I). XJPCF(I),CRES(I), XJURIa),XEQPLVO),XJEXUD(I), 1=1 ,NPETUB)OPEN1)JNIT=5,FILE=OTFILE)OPTIMIZATION DATAc -— Change in Kf for uninjured tissueREAD (5,4) COMENTREAD (5,) GKFTI ,XL(l),XU(l)WRITE(6,207) COMENT, GKFTI. XL(l), XU(l)Change in Kf for injured tissueREAD (5,4) COMENTREAD (5,4) GKFBT ,XL(2),XU(2)WRITE(6,207ICOMENT,GKFBT ,XL(2),XU(2)c ----- Relaxation coefficientREAD (5,) COMENTREAD (5,4) RCOEF ,XL(3),XU(3)WRITE(6,207)COMENT,RCOEF,XL(3),XtJ(3)Factor for protein loss due to exudationREAD (5,4) COMENTREAD (5,4) EXFAC ,XL(4),XU(4)WIUTE(6,2O7yDOMENT,E)CFAC,XL(4),XU(4)Accuracy and scaling boundREAD (5,) COMENTREAD (5,4) ACCUR,SCBOUWRITE(6,204)COMENT,ACCURSCBOUc44 MODEL RESOLUTION 4444c Time step for integrationREAD (5,4) COMENTSUBROUTINE CONSTAIMPLICIT REAL’S (A-KO-Z)include ‘output.cmninclude ‘input.cmn’include ‘initva.cmninclude ‘compli.cmninclude nomial.cmn’include ‘grfile.cmninclude ‘expdat.cmnC I I I I I I I I I I I I I I I I I I II I I-I—I--H-++c — Assign change in lymph flow sensitivityclIllIllIllIllIll 11111111111c GLSTIOLSTI = 0.D0c —— OLSBTOLSBT = 0.DOCalculate total surface area of bodyc —---- Set or calculate some constantsDEOM=I .DO-DEGRELM=l .D0-RELSMe —- Normal pore radiusRPNL = RALB/ANLc — Constant for diflirsion coefficient206ENDIFENDIFIF (IPAR(4) EQ. 1) THENOPEN(UNIT=5,FILE=CPFILE)c —— Number of experimental data points to be fittedREAD (5’) NJMEXPc — Experimental time (EXTIME). value (EXCPL) and standarddeviation (SDCPL)IF (NUIvIEXP .OT. 0) ThENREAD(5’X EXTIIvIE(t), EXCPL(I), SDCPL(I),I=l,NIJMEXP)ENDIFENDIFe — Calculate total fluid and protein inputsVJN=O.0QIN=O.0DO 100 IP=l,NPETUBA=TSTART(IP)B=TEND(IP)XJRES(IP)=XJCLF(IP)÷XJPCF(IP)VIN=VIN+(B-A)’XJRES(IP)QIN=QIN+(B-A) * XEQPLV(IP) * CRES(IP)100 CONTINUEc — Formats for printing input dataAppendix KREAD(5,’) DTAUWRITE(6,201 )COMENT,DTAUc ---— Time step for savmg data for outputP,E4D (5,’) COMENTREAD(5,’) OUTIMEWRITE(6,20l)COMENT.OUTIMEc” DATA FOR TYPE OF RUN ‘*“c — Flagfor steady state runP,EAD (5,’) COMENTpaJ3(5*) ISTEDYWRJTE(6,202)COMENT,ISTEDYc — Flag for blank run: if blank run, IBLANK=l otherwise,IBLANK=0READ (5,’) COMENTRE4a33(5.*) IBLANKWRITE(6,2o2)COMENT,IBLANKc” DATA FOR STEADY STATE RUNc -—— Final steady state timeREAD (5,’) COMENTREAD(5,’)WRITE(6,20l)COMENT,STDTIMc—-— Time to start addition/removal of fluid/proteinREAD (5,’) COMENTREAD(5.’) REMSTAWRfl’E(6,201 )COMENT,REMSTAC — Time period for removal/addition offluid/proteinREAD (5,’) COMENTREAD(5,’) DTIMEWRITE(6,201 )COMENT,DTIMEc “FLAG FOR ‘COMPLIANCE DATA”c——Flag for compliance dataREAD (5,’) COMENTREAD (5,’) ICOMPLWRITE(6,202)COMENT,ICOMPLc”4ORAPHPLOTEING DATA“c — Flag to indicate if output data must be saved to plot laterREAD (5,’) COMENTREAD(5,’) IPLOTWRITE(6,202)COMENT,IPLOTc — Flag to indicate if ratios are to be used for optimizationREAD (5,’) COMENTREAD(5,’) IRATIOWRITE(6,202)COMENT,IRATIOc — flag to indicate if experimental data should be randomizedREAD (5,’) COMENTREAD(5,’) IRAND,RANFACWRITE(62l 2)COMENT,IItAND,RANFACc”” EXPERIMENTAL DATA”IF (IPAR(l) EQ. 1) THENOPEN(UNIT=5,FILE=PYFILE)c —-Number of experimental data points to be fittedREAD (5,’) NUIvIEXPc Experimental time (EXTIME), value (EXVPL) and standarddeviation (SDVPL)IF (NUMEXP .GT. 0) THENREAD(5,’) (EXTIME(I), EXVPL(I), SDVPLQ), 1=1,NUMEXP)ENDIFENDIFIF (IPAR(2) EQ. 1) THENOPENI3JNIT=5,FILE=BTFILE)c Number of experimental data points to be fittedREAD (5,’) NUk4EXPc ---— Experimental time (EXTIME), value (EXPIBT) and standarddeviation (SDPIBT)IF (NUMEXP .GT. 0) THENREAD(s,’xEXTIME(t),EXPIFT(I)2xPIPL(I),SDPIFT(I),I=l ,NUIvWXP)ENDIFENDIFIF (IFAR(3) .EQ. I) THENOPEN(HNIT=5,FILE=TIFILE)c Number of experimental data points to be fittedREAD (5,’) NUIvIEXPc — Experimental time (EXTIME), value (EXPITI) and standarddeviation (SDPITI)IF (NUMEXP .GT. 0) THENREAD(5,’XEXTIME(I),EXPITI(I),EXPIFL(I),SDPITI(I), I=l,NUMEXP)200 FORMAT (420X,’INPUT DATA’,/20X,’-)201 FORMAT(ASO,4F20.5)202 FORMAT(AS0J,15)203 FORMAT(AS0,4415)204 FORMAT(A80,42F20.5)205 FORMAT(SFIO.2)206 FORMAT(/5X,’ Start End CF Flow PCF Flow Conc UrineEQPLV EXUDN’)207 FORMAT(AS0,/,3F20.5)217 FORMAT(AS0J,F20.5)212 FORMAT(AS0J,IS,F20.5)701 FORMAT (/,5)VHeight (cm) ,FlS.2)702 FORMAT (/,5X,’Weight (kg) ‘,FlS.2)703 FORMAT (45X,Total body surface area (m”2) =‘,F18.2)704 FORMAT (//2wc’ Resuscitation data’, /20K’—CLOSE(S)RETURNENDc Subpmgsam CONSTA: Calculates/assigns certain constantswTRATI=wEIGHT/WrHTRATI=HEIGHT/HTTBSA=(WEIOHT”0.425D0) * (HEIGHT” 0.725D0) * 71.84D0‘l.D-4II’ PL3.CSV’),I= I ,NPNT)Appendix Kc Fluid volume correction factors for compliance dataVAFTI=RELSM*DEGM+RELMVAFBThRELSM*DEGc —--- Correction factors for KFNORM, LSNORM, PSNORM andJLNORMCORRTI= WTRATI*VAFTICORRBT’= WTRATI*VAFBTRETURNEND207707 FORMAT (/,20X,’OTHER DATA’,/20X,’)708 FORMAT (I,5X, ‘GKFrI ‘, Fl0.2,5X, GICFBT =‘, FlO.2)709 FORMAT (/,SX,’GSIGTI =‘, FlO.2, 5X, ‘GSIGBT =‘, FlO.2)710 FORMAT (I,5)c’GPSTI =‘, Fl0.2, 5X, ‘GPSBT =‘, Fl0.2)ill FORMAT (/,5X.’GLSTI =‘, Fl0.2, 5X ‘GLSBT =Fl0.2)712 FORMAT (/,5X,’VETI =‘,Flo.2,5)c’VEBT , F10.2)713 FORMAT (/,5X,HPTffiX ‘, Fl0.2, 5X HPBTEX =‘,Fl0.2)703 FORMAT (/,5XjotaI body surface area (m**2) =‘.Fl 8.2)601 FORMAT(/)602 FORMAT(A40)603 FORMAT(A45,Fl 8.5)c Subprogram OUTPUT: Prints out all results and makes data files forplotsSUBROUTINE OUTPUTIMPLICIT REAL*8 (A-H,O-Z)include ‘output.cmn’include ‘input.cmn’include ‘initva.crnn’include sormal.cmn’include curentcmn’include ‘grfile.cmn’CHARACTER2O CDATA(l 0)CHARACTER*10 SAVDIRPAAMETER(SAVDIR’C:\AMVRES\)c OUTPUT NORMAL VALUESC— —c OUTPUT RESULTSc — Tabulate all results in a fileWRITE(6,800)WRITE(6,803)VINWRITE(6,804)VOUTWRITE(6,805)QINWRITE(6.8o6)QOurWRITE(6,807)VLNTTWRITE(6,808)VFINALWRITE(6,809)QINITWRITE(6,810)QFINALc — Fluid volumesWRITE (6,901)WRITE (6,935) (TIME(I), AVTI(I), AVBT(I),AVPL(I),}IEMA(I),I=l,NPNT)C — Protein contentsWRITE (6,902)WRITE (6,900) (TIME(I), AQTI(I), AQBT(I), AQPL(I),I=l,NPNT)c Protein concentrationsWRITE (6,903)WRITE (6,950) (TIME(I), ACTI(I), ACBT(I), ACPL(I).ACTIAV(I), ACBTAV(I), I=l,NPNT)c — Hydrostatic pressuresWRITE (6,904)WRITE (6,900) (TIME(I), AHPTI(I), AIIPBT(I), APC(I),I=l,NPNT)c — Osmotic pressuresWRITE (6,905)WRITE (6.950) (TIME(I), APITI(I), APIBT(I), AP]PL(I),APITIR(I), APIBTR(I), I=l,NPNT)c — Fluid fluxesWRITE (6,9l1)WRITE (6.910) (TIME(I), AJFTI(I), AJFBT(I), AJLTI(I),AJLBT(I),I=l,NPNT)c —----- Protein fluxesWRITE (6.912)WRITE (6,9 10) (TIME(I), AQSTI(I), AQSBT(I), AQLTI(I),AQLBT(I), I=l,NPNT)WRITE(6,707)WRITE(6,708) GKFTI,GKFBTWRITE(6,7l I) GLSTI,GLSBTWRITE(6,7l 2) VETI,VEBTWRITE(6,7l3) HPTIEX,HPBTEXWRI’I’E(6,703) TBSAWRITE(6,601)WRITE(6,601)WRITE(6,6O2yNORMAL CONDITIONS’WRITE(6,602yWRITE(6,60l)WR1TE(6,603)Peclet number ,PENORMWRITE(6,603)’Lymph flow, mI/h ‘. XJLNORMWRITE(6,603)Vermeability coefficient, nil/h ‘,PSNORMWRITE(6,603)’Filtration coefficient, nil/h =‘, XKFNORMWRITE(6,6o3yLymph flow sensitivity, mI/mmHg-h=‘,XLSNORMWRITE(6,603)Reflection coefficient =‘, SIGNLWRITE(6,601)WRITE(6,602)PressuresWRITE(6,602)-—-------’WRITE(6,603)Tissue hydrostatic pressure, mmHg = ‘,HPTINL‘.VRJTE(6,6o3yTissue colloid osmotic pressure, mmHg ‘,PITINLWRITE(6,603)Vlssma colloid osmotic pressure, mmHg =‘,PIPLNLWRITE(6,603)’Capillaiy pressure, mmHg ‘, PCNLWRITE(6,601)WRITE(6,602)’Fluid Volumes’WRITE(6,602yWRITE(6,603)Tissue fluid volume, ml ‘, VTINLWRITE(6,603)Plasma fluid volume. ml ‘, VPLNLWRI’I’E(6,60l)WRITE(6,602)Protein Contents’WRITE(6,602)’.—----——--’WRITE(6,603)’Tissue protein content, mg = ‘, QTINLWRITE(6,603)Plasma protein content, mg ‘, QPLNLWRITE(6,60l)WRI’l’E(6,602)Protein Concentrations’WRITE(6,602y--—-----------—-----’WRITE(6,603)Tissue protein concentration, gil = ‘.CTINLWRITE(6,603)Plasma protein concentration, g/l = ‘,CPLNLWRITE(6,601)WRITE(6,602)Fluid Fluxes’WRITE(6,602y-——-----—-’WRITE(6,603)’Lymph flow, mllh ‘, XJLTINLWRITE(6,603)’Filtration flow, nil/h ‘, XJFTINLWRITE(6,601)WRJTE(6,602)Protein fluxes’WRITE(6,602yWRITE(6.603)’Lymph flow, mg/h ‘. QLTINLWRITE(6,603)Transcapillaiy membrane flow, mg/h = ‘,QSTINLc — Put results into files for plottingIF(IPLOT.EQ. l)THENOPEN (UNIT=8. FILE=SAVDIR II RUNID II‘i//RUNID//’PLI .CSV’)WRTI’E (8,1900) (TIME(I) ,AVTI(I), AVBT(I),AVPL(I), I=l,NPNT)CLOSE(8)OPEN (UNTT=8, FILE=SAVOlE if RUNID II‘i//RUNIDIfPL2.CSV)WRITE (8,1900) (TJME(I), AQTI(I), AQBT(I),AQPL(I), 1=1 ,NPNT)CLOSE(8)OPEN (UMT=8, FILE=SAVDIRJI RTJMD//’ V/I RUNIDWRITE (8,1900) (TIME(I). ACTI(I), ACBT(I), ACPL(I)CLOSE(8)OPEN (UNIT=8, FLE=SAVDIR II RUNID II‘VI/RUN1D/FPL4CSV’)WRITE (8,1900) (‘IIME(I), AHPTI(J), AHPBT(I),APC(I), I=I,NPNT)CLOSE(8)OPEN (UNIT=8, FILE=SAVOlE II RUNID II‘fI/RUNIDIfPL5.CSV’)Appendix K 208WRITE (8,1900) (TIME(r). APITI(I), APIBT(1), 9992 FORMAT(4(A20,’,),A20)APIPL(I), I=l,NPNT) 9993 FORMAT(2(A20,,).A20)CLOSE(8) 9994 FORMAT(A20,’,’,A20)OPEN (UNIT=8, FILE= SAVDIR II RUNID RETURN/fW/RUNID/i’PL6.CSV’) END‘.VRITE (8.1930) (TIME(I), AJFTI(I), AJFBT(I), cAJLTI(I), AJLBT(I),I=l,NPNT) cCLOSE(8) c Subprogram COMSPL: Determines compliance relationshipsOPEN (UNIT=8, FILE=SAVDIR II RUNID II c‘V//RUNTD/fPL7.CSV’) SUBROUTINE COMSPLWRITE (8.1930) (TIME(I), AQSTI(I), AQSBT(1). IMPLICIT REAL8 (A-HO-Z)AQLTI(I), AQLBT(I) ,I=1,NPNT) include ‘input cmn’CLOSE(S) include ompli.cmn’OPEN (UNIT=8, FILE=SAVDIR II RUNID II COMMONIBLKA/XSP(10l).YSP(l01),NSP,NMSP‘\V/RUNID/fPLS.CSV) COMMON/BLKB/QSP(100),RSP(l01 ).SSP (100)WRITE (8.1900) (TUvIE(I), AVTI(Iy VTIO, IF(ICOMPL.EQ. 1) THENAVBT(I)/VBTO,AVPL(I)/VPLO .1=1, NPNT) OPEN(UNIT=8,FILE=’COMPLP)CLOSE(S) ELSE IF ( ICOMPL EQ. 2) THENOPEN (UNIT=8, FILE=SAVDIR// RUNID II OPEN(uNrr=8,FILE=’COMPL2’)‘W/RUNID/fPL9.CSV’) ELSE IF ( ICOMPL EQ. 3) THENWRiTE (8,1900) (TIME(I), ACTI(I CTIO, OPEN(NIT=8,FILE=’COMPL3)ACBT(I)/CBTO,ACPL(I)/CPLO .1=1. NPNT) ELSE IF (ICOMPL EQ. 4) THENCLOSE(8) OPEN(UNIT=8,FILE’=’COMPL4’)OPEN(UNIT=8,FILE=SAVDIRIIRUNID/fW/ RUNID ELSE IF ( ICOMPL .EQ. 5) THENIfPKI CS’.”) OPEN(UNIT=8,FILECOMPL5’)WRITE (S1900) (TIME(I), AHPTI(I)f HPTIO, ELSE IF ( ICOMPL EQ. 6) THENAHPBT(I)/HPBTO,APC(I)/PCO ,I= I, NPNT) OPEN UNIT=8,FILE=’COMPL6)CLOSE(S) ELSE IF ( ICOMPL EQ. 7) THENOPEN(UNIT8.FILE=SAVDIR//RUN1D/J’\’// OPEN(UNIT=8.FILE=’COMPL7’)RUNTD/fPK2.CSV) ELSE IF (ICOMPL EQ. 8) THENWRITE (8,1910) (TIME(I), A1’ITIR(I), APIBTR(I), 1= OPEN(UNIT=8,FILECOMPL8’)1,NPN’I’) ENDIFCLOSE(S) READ(8.50) NUMOPEN(UNIT=8,FILESAVDIPJIRUNID/fV// DO 401=1 ,NUMRUNID/fPlC3.CSV’) READ(8,60) BTIMERH(I), BPRESRH(I)WRITE (8,1920) (TIME(I), HEMA(I) .1= l,NPNT) 40 CONTINUECLOSE(S) CLOSE(S)ENDIF OPEN(UN1T=S,FlLE=’COMPL0lc — READ(8,S0) NUMc — Formats for printing results READ(8,60) ( VSP(I),PSP(I),I1,NUM)CLOSE(S)IS FORMA’rçnosolutionat’,Fl8.5) M1’NUM800 FORMAT (I/25X,’ SIMULATION RESULTS’./25X—--------’) MPM=MP-1803 FORMAT (/5X’Total fluid input, ml ,Fl8.5) 50 FORMAT(15)804 FORMAT (/,5X,’Total fluid output, ml ‘,Fl 8.5) 60 FORMAT(2F 10.2)805 FORMAT (/,5X,’Total protein input, mg ‘,FI 8.5) c — Uninjured tissue806 FORMAT (/,5X,’Total protein output, mg ,F18.5) DOS I’l,MP807 FORMAT (/,5X,’Total initial fluid content, ml ,Fl 8.5) VCOMTI(I)VSP(I)*WTRATI*VAFTI808 FORMAT (l,5X.Totsl final fluid content, ml =,F1 8.5) 8 CONTINUE809 FORMAT (/,5X,’Total initial protein content , mg =‘,FI 8.5) IBND”2810 FORMAT (/,5X. ‘Total final protein content, mg “,F18.5) CALL SPLINE (VCOMTI, PSP. MP, MPM, lEND)900 FORMAT (F10.2,3Fl5.2) NTI=NSP935 FORMAT (Fl 0.2,3Fl 5.2.Fl 0.2) NMTI=NMSP901 FORMAT (/20X,’ Table I : — Fluid Volumes —, /2X’ TiME DO 9 Il,NSP‘lOX. ‘VT,10X,’VBT,l0X’VPL’) XTI(I)=XSP(I)902 FORMAT (120X,’ Table 2 — Protein Content —‘, YTI(I)YSP(I)+ /2X,’ TIME ‘lOX, TI’.loX,’QBr.1oXPL’) QTI(I)=QSP(I)903 FORMAT (/20x,’ Table 3 : —-— Protein Concencentrations -- RTI(I)RSP(I)‘,/2X,’ TIME ‘lOX, ‘CTr,1oX,’CBr,lo)c’CPL’.5X’CTIAV’,5X, STI(I)=SSP(I)‘CBTAV’) 9 CONTINUE904 FORMAT (/20K’ Table 4 —-- Hydrostatic pressures — ‘J2X,’ c — Injured tissueTIME’lOX,PTr,lOx,PBr,IOX.PPL) DOll I=1.MP905 FORMAT (/20K’ Table 5 : —---- Osmotic pressures—--— ‘,12X,’ VCOMBT(I) VSP(I) * WTRATI * VAFETTIME ‘lOX. pm’,lo)çPIBT,IOX,PIPL’jX.PITIII’,S)c PIBTR’) 11 CONTINUE910 FORMAT (F10.2,4F15.2) IBND2911 FORMAT (/20)c’ Table 6 : —--— Fluid fluxes ‘,12X,’ TIME CALL SPLINE(VCOMBT.PSP,MP,MPMJBND)‘I OX, ‘JFIT,IOX,’JFBV,I OX.’JLTI’,l 0)c’JLBT) NBT=NSP912 FORMAT (/20X,’ Table 7: Protein fluxes’,/2X,’ TIME lOX, NMBT=NMSP‘QSTI’, lOX, ‘QSBT’, lOX, ‘QLTI’, IOX,’QLBT) DO 12 I=I,NSP915 FORMAT (FIO.2,2Fl5.2) XBT(I)=XSP(I)924 FORMAT (7F10.2) YBT(l)=YSP(I)923 FORMAT (/20X,Table 8 : FLUiD AND PROTEIN BALANCES QBT(I)QSP(I)/ TIME’, 5X, DYDX(lY, 5X,’ DYDX(2), 5X, DYDX(3y, RBT(I)=RSP(I)SX,DYDX(4y. 5X, DYDX(5)’,SX,’DYDX(G)’) SBT(I)=SSP(I)1900 FORMAT(4F20.5) 12 CONTINUE1910 FORMAT(3F20.5) RETURN1920 FORMAT(2F20.5) END1930 FORMAT(5F20.5)9991 FORMAT(3(A20.”),A20)209Appendix KCc Subprogram NORMAL: Adjusts/calculates normal valuesSUBROUTINE NORMALIMPLICIT REALt8(A-lI,O-Z)include ‘inputcmninclude ‘compli.cmn’include ‘initva.cmn’include ‘normal.cmn’CTINL = QTINL/VTINLCTIAVNL = QTINL/(VTINL-VEHNL)CPLNL = QPLNLIVPLNLc — Calculate normal modified Peclet number, PENORMTOP = CTtNL - (l.D0-SIONL) * CTIAVNLBOT = CTINL - (l.D0-SIGNL) * CPLNLPENORM = DLOO(TOP/BOT)c — Calculate normal JL, XJLNORMAA = (I JJ0SIONL)*DEXP(PENORM)RB = (1.00- DEXP(-PENORM)) * (VTINL-VETINL)CC = I .D0/VTINLDIV = AA/BB+CCXJLNORM = ALBTO/DIVc-—Calculate normal PS. PSNORMPSNORM = (l.D0SIGNL)* XJLNORM /PENORMc -— Calculate normal KF, XKFNORMDELP = PCNL - IIPTINL - SIGNL*(PIPLNLPITINL)XKFNORM = XJLNORM / DELPc Adjust protein and fluid contents in real patient as opposed tostandard humanc TissueVTINL=VTINLWTRATIVETINL=VETJNLWTRATIQTrNL=QTINL*WTRATIc —- PlasmaVpLNL=VPLNLWTRATIQPLNL=QPLNL*WrRATIc-—-Assign and/or calculate normal valuesc -—-- Calculate normal albumin concentrations in tissue and plasmaCTINL=QTINLJVTENLCPLNL=QPLNL/VPLNLCTIAVNL= QTINL/(VTINL-VETINL)c — Calculate fluid fluxes for normal tissuec — Lymph fluid flowXJLTINL = XJLNORMWTRATI + XLSNORM *1ffpJjJ*(fflIJJc —-- Fluid filtration flowXJF-ralL=xKFNORMWFRATI4(PCN -HPTINL-SIGNL(PIPLNL-PITINL))Calculate protein fluxes for normal tissueC ---- Peclet numberPECLET=(l .D0SIGNL)*XJFTINL/(PSNORM*WTRATI)RATIO=(CPLNL-CTIAVNLDEXP(-PE LET) )/(I .D0-DEXP(-PECLETflc —-- Transmembrane protein flowQSTINL=(I .D0SIGNL)*XJFTINL*RATIOc ---- Lymph protein flowQLT1NL=)CJLTINL*CTINLC Constant for diffusion coefficientCONST = PSNORM/(l DO - ANL)tt2RETURNENDc Subprogram SAVRES: Saves simulation resultsCSUBROUTINE SAVRESç’cY,DYD)cNEQ)IMPLICIT REAL*8 (A-FLO-Z)include ‘output.emninclude input csnsfinclude ‘initva.cmn’include ‘normal.emninclude ‘eurentemn’DIMENSION y(NEQ),DYDx(NEQ)NPNT=NPNT+lmvffiNPwr)=xRETURNENDAVTIINPNT>Y(l)AQTIINPNT)=Y(2)AVBT(NPNT)Y(3)AQBTQ’IPNT)=Y(4)AVPL(NPNT)=Y(5)AQPL(NPNT)=Y(6)IF(X EQ. 0.ODO ) THENHEMA(NPNT) =HCTOELSEIF (x (IT. BLSTIM AND. X .LE. BLEND)RBV=(BVO-BVF)/(BLEND-BLSTIM)BV=BVO-(X-BLSTIM)tVNEMA(NPI’TI)=l.0-AVPL(NPNT)/BVELSEIF( XGT. BLEND) THENBEMA(NPNT)=l .0-AVPL(NPNT)/BVFENDWAwn(NPNT)=xrnAJLI1(NPNT)XJLTIAQSTI(NPNT)=QSTIAQLTI(NPNT)=QLTIAJFBT(NPNT)=XJFBTAJLBT(NPNT)=XJLBTAQSBT(NPNT)=QSBTAQLBT(NPNT)QLBTA}IPTI(NPNT)=HPTIAPITI(NPNT)=PITIAPITIR(NPNT)=PITIJPIPLAPITIR(NPNT) = (PITI*PIPLO) / (PIPL PITIO)AHPBT(NPNT)=HPBTAPIBT(NPN’r)=PIBTAPIBTR(NPNT)=PIBT/Pll’LAPIBTR(NPNT) = (PIBTtPIPLO) / (PIPL * PIBTO)APC(NPNT)=PCAPIPL(NPNT)=PIPLACTI(NPNT) =CTIACTIAV(NPNT)=CTIAVACBT(NPNT) =CBTACBTAV(NPNT)=CBTAVACPL(NPNT) =CPLBLOCK DATA: Common blocks containing data to be passedbetween the main program and submutine MODELBLOCK DATAIMPLICIT REALt8(A-H,O-Z)include ‘outputemn’include ‘inputcmn’include ‘eompli.emninclude initva.cmn’include nomsal.cmn’include eurent.emn’DATA HT /170.000/DATA WT /70.ODO/DATA XLSNORM /43.08D0/DATA PCCOMP /0.00965900/DATA SIGMA /0.988800/DATA SIGNL /o.9888D0/DATA ALBTO /0.0205D0/DATA ANL /0.89D0/DATA RALB /3.7D0/DATA VFRAC,AFRAC /0.5D0,0.5D0/DATA VT1NL /8400.D0/DATA VETJNL /2100.D0/DATA QTINL /141.ID+3/DATA HPTINL /-0.7D0/DATA PITINL /l4.7D0/DATA HPTIEX /l3.0577D0/DATA HPBTEX /0.00/DATA VPLNL /3200.00/DATA QPLNL /l26.ID+3/DATA PCNL /11.00/DATA PIPLNL /25.900/DATA RELSM /0.2857D0/DATA AB,BS/I .96154D-3,l .05D-4/ENDTHENAppendix K 21010 FORMAT(/’Warning in FCRT4,D10.3,’ is outside rnterpolationc FUNCTION FCOMP: Interpolation function for uninjured tissue rangef)compliance relationship ELSEIF (Z.GT.X(N)) THENe **********4*********fl****************************** I=NMDOUBLE PRECISION FUNCTION FCOMP(Z) WRITE(6.l 0) ZIMPLICIT REAL48(A-H,O-Z) ELSEinclude compli.cmn 11include input.cmn J=NIF (Z .LT. CORRTI4840÷3) THEN 20 K=(I+Jy2.D0FCOMP=-0.7DO+AS/CORRTI(Z-CORRTI *840÷3) IF (Z.LT.X(K)) J=KELSEIF (Z .GT. CORRTI412.604-3) THEN IF (Z.OE.X(K)) I=KFCOMP=l.88D0+BS/CORRTI(Z-CORRTII2.6 +3) IF (J.OT.I+I) 00 TO 20ELSEIF (Z .GE.CORRTI 8.40+3 AND. Z .LE.CORRTI4 ENDIF12.60+3) THEN DX=Z-X(I)FCO1vIPFCTI(Z) FCBT = Y(I) + DX4 (Q(I) + DX * (R(I) + DXS(I)))ENDIF RETURNRETURN ENDENDCc FUNCTION FCOMRT: Interpolation function for injured tissuecompliance relationshipcDOUBLE PRECISION FUNCTION FCOMBT(Z)IMPLICIT RBAL48(A-ItO-Z)include compli.cmninclude inputcmn’IF (Z IT. CORRBT48.4D+3) THENFCOMBT=-0.7DG+AS/CORRBT(Z-CORRBT8.4D 3)ELSEIF (Z LIT. CORRBTI2.6D+3) THENFCOMBT=l .88D0+BS/CORRBT(Z-CORRBT*12.6D+3)ELSEIF (Z .OE.CORRBT4 8.40+3 AND. Z .LE.CORRBT412.60+3) THENFCOMBT=FCBT(Z)ENDIFRETURNENDcc FUNCTION FCTI: Uninjured tissuecDOUBLE PRECISION FUNCTION FCTI(Z)IMPLICIT REAL8 (A-H,O-Z)COMMON/BLKTII/X(l 0l),Y(l0l ),N,NMCOMMON/BLKTI2/Q(1 00),R(l 01 ),S(1 00)IF (Z.LT.X(I)) THEN1=1WRITE(6. 10) Z10 FOR1vIATQ’Waming in FCTI44 ,Dl0.3, is outside interpolationrangeY)ELSEIF (Z.GT.X(N1) THENI=NMWR.ITh(6,lO) ZELSE1=13=N20 K=(I+J)/2.D0IF (Z.LT.X(K)) J=KIF (Z.OE.X(K)) I=KIF (J.GT.I+l) GO TO 20ENDIFDX=Z-X(I)FCTI=Y(I)+DX4(Q(I)+DXRS I)))RETURNENDcc FUNCTION FCBTcDOUBLE PRECISION FUNCTION FCBT(Z)IMPLICIT REAL48(A-ItO-Z)COMMON/BLKBTIIX(l 01 ),Y(10l),N,NMCOMMONIBLKBT2/ Q(I00). R(lOl), S(100)IF (Z.LT.X(1)) THEN1=1WRITE(6,lO) Z


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