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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 INJURY A MATHEMATICAL MODEL OF FLUID RESUSCITATION by REGINA TWUMWAA AMPRATWLJM B.Eng. (Chemical Engineering) University College London, United Kingdom  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES CHEMICAL ENGINEERING  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA December 1993 © Regina Twumwaa Ampratwum, 1993  In presenting this thesis in partial flulfiliment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Department of Chemical Engineering The University of British Columbia Vancouver, Canada  Date: 7  kccbG  19  AB S TRACT  A dynamic model is developed to describe the redistribution of fluid and albumin between the human circulation, interstitium and lymphatics following burn injury. The model is based on the assumption that the human microvascular exchange system (MVES) consists of 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’s Hypothesis and albumin is transported passively by diffusion and convection through the same fluid-carrying channels.  The parameters necessary to frilly describe the model are determined by statistical fitting of model predictions with clinical data from bum patients. The parameters include the perturbation to the filtration coefficient in uninjured and injured tissue, GkFTI and  GkFBT  respectively; the relaxation coefficient, r, which describes the time it takes for the transport coefficients to return to near-normal values following injury, and the exudation factor, EXFAC, which determines the fraction of the interstitial protein concentration which leaves with exudate from the burn wound. Perturbations to other parameters including the permeability coefficient and the albumin reflection coefficient, in the injured and uninjured tissues are obtained from G,TJ and GkFBT, utilizing relationships between all three types of 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  =  optimum parameters are:  0.025 h 4 and EXFAC =  2.0, GkFBT 11  =  =  1.0. For burns greater than 25%, the  9.0, r = 0.025 h-’ and EXFAC  =  0.75. The  sensitivity of the model predictions to changes in  and GkFBT for the two burn  groups are investigated. For burns less than 25%, GkFTI and  GkFBT  values beyond the  ranges 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±0.8 and 9.0±3.0 respectively for burns larger than 25% surface area.  The model and its associated parameters are validated by comparing the predictions of patient 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 observed trends and the absolute values of fluid volume and albumin concentration. The model is also used to simulate the response of a hypothetical individual to three common resuscitation formulae, namely the Evans, Brooke and Parkiand formulae, following two burn sizes, 10% and 50%. The simulated responses are explained in terms of the transport mechanisms, driving forces and perturbations to the transport coefficients following burn injury. The predictions of the model compare satisfactorily with known clinical behaviour of the human MVES with and without fluid resuscitation. This establishes the potential of the patient simulator developed in the current study to be used as a tool for fluid management of burn patients. The effects of different resuscitation formulae can be compared to suggest possible improvements.  As more reliable clinical data become available, all of the essential model parameters can be more definitely determined. In addition, one significant improvement that may be made to the model is the inclusion of cellular compartments. It is expected that, with more accurate parameters and an improved physiological basis, the usefulness of the mathematical burn patient simulator will be enhanced considerably.  111  Table of Contents  Abstract  Table of Contents  iv  List of Tables  ix  List of Figures  xiii  Acknowledgment  xvi  1  Introduction  1  2  Physiological Overview  6  2.1 Introduction  6  2.2 The Circulatory System  6  2.2.1 Description of the Circulatory System  6  2.2.2 Composition and Properties of Blood  10 11  2.3 The Microvascular Exchange System 2.3.1 Description of the Microvascular Exchange System  11 15  2.4 The Interstitium 2.4.1 Structure and Composition of the Interstitium  15  2.4.2 Physicochemical Properties of the Interstitium  16  2.4.2.1 Turnover of Interstitial Plasma Proteins  16  2.4.2.2 Interstitial Volume Exclusion  17  iv  2.4.2.3 Interstitial Compliance 2.5TheSkin  18  2.5.1 Anatomy and Function of Skin 2.6 Transcapillary Exchange 2.6.1 Capillary Filtration  22  2.6.2 Combined Convective and Diffusive Solute Transport  23 23  2.7.1 Damage to Skin  24  2.7.2 Changes to the Microvascular Exchange System  24  2.7.2.1 Transcapillary Exchange in Injured Tissue  27  2.7.2.2 Transcapillary Exchange in Uninjured Tissue  28  2.7.2.3 Systemic Hemodynamic Changes  31  2.8 Fluid Resuscitation  4  18 22  2.7 Physiological Changes Following Injury  3  17  31  2.8.1 Isotonic Crystalloid Fluid Resuscitation  32  2.8.2 Hypertonic Crystalloid Fluid Resuscitation  33  2.8.3 Colloid Fluid Resuscitation  33  2.9 Summary  34  Computer Modelling of the Microvascular Exchange System  36  3.1 Introduction  36  3.2 Modelling of Normal MVES  38  3.3 Modelling of MVES Following Burn Injury  40  Model Formulation  45  4.1 Introduction  45  4.2 Basic Assumptions  46  4.3 Fluid and Protein Input  50 V  4.4 Fluid and Protein Output  5  50  4.4.1 Water Loss by Evaporation  51  4.4.2 Fluid Loss by Exudation  51  4.4.3 Protein Loss via Exudate  52  4.4.4 Blood Loss  53  4.5 Model Equations  53  4.6 Properties of the Microvascular Exchange System  54  4.6.1 Normal Steady-State Conditions  55  4.6.2 Initial Conditions  56  4.6.3 Compliance Relationships  57  4.6.3.1 Circulatory Compliance  57  4.6.3.2 Interstitial Compliance  57  4.6.4 Colloid Osmotic Pressure (COP) Relationship  59  4.6.5 Transport Coefficients  60  4.7 Numerical Solution of Model Equations  64  Parameter Estimation  65  5.1 Introduction  65  5.2 Parameters to be Determined  65  5.3 Clinical Data  67  5.3.1 National Burn Centre (NBC) Data  67  5.3.2 Birkeland Data  68  5.3.3 Arturson Data  69  5.3.4RoaData  69  5.3.5 Normalization of Data  69  5.4 Parameter Estimation Procedure  70 71  5.4.1 Preliminary Tests vi  6  5.4.2 Constraints  78  5.4.3 Modified Optimization Strategy  80  5.4.3.1 Re-assessment of Parameters to be Determined  80  5.4.3.2 Optimization Scheme: “Gridding Approach”  81  5.5 Summary  82  Results and Discussion  83  6.1 Introduction  83  6.2 Estimated Parameters  83  6.2.1 Parameters Determined Using NBC Data  83  6.2.2 Parameters Determined Using Birkeland Data  85  6.2.3 Parameters Determined Using Combination of NBC and Birkeland Data  86  6.2.4 Summary of Parameters  88 91  6.3 Sensitivity Analyses 6.3.1 Sensitivity Analysis of GkFTI  91  6.3.2 Sensitivity Analysis of GkFBT  94  6.3.3 Sensitivity Analyses of EXFAC and r  95 96  6.4 Validation of Model Predictions  96  6.4.1 Partial Validation 6.4.1.1NBCData  96  6.4.1.2 Birkeland’s Data  102 104  6.4.2 Independent Validation 6.4.2.1 Arturson’s Patient Data  104  6.4.2.2 Roa’s Patient Data  106  6.5 Simulation of Fluid Resuscitation According to Different Formulae  108 109  6.5.1 Simulations of 10% Burn vi’  7  6.5.2 Simulations of 50% Burn  117  6.5.3 Simulations by Other Authors  123  6.6 Summary  125  Conclusions and Recommendations  126  7.1 Conclusions  126  7.2 Recommendations  129  Nomenclature  131  References  135  Appendices  143  A Interstitial Fluid Distribution  144  B Transport Parameters  145  B. 1 Normal Transport Parameters for “Reference Man”  145  B.2Transport Coefficients Following Burn Injury  146  C NBC Patient Data  150  D Estimation of Plasma Volume from Hematocrit Data  166  E Estimation of Exudation Rate Based on NBC Patient Data  170  F Birkeland’s Patient Data  174  G Determination of Exudation Rate for Birkeland’s Patients  177  H Clinical Data from Arturson’s Patient  179  I  Clinical Data from Roa’s Patients  181  3  Minimum Objective Function Value Results  188 198  K Computer Program Listing  viii  List of Tables  2.1 Classification of Blood Vessels  14  2.2 Mathematical Description of Human Interstitial Compliance Relationship  20  2.3 Burn Depth Classifications  27  2.4 Changes to Injured Tissue MVES Properties Following Burn Injury  29  4.1 Normal Steady-State Conditions in “Reference Man”  55  5.1 Factorial Experiment Study  81  6.1 Optimum Parameters Determined Using NBC Data  84  6.2 Optimum Parameters for Two Burn Groups Using NBC Data  85  6.3 Optimum Parameters Determined Using Birkeland Data  85  6.4 Optimum Parameters for Two Burn Groups Using Birkeland Data  86  6.5 Optimum Parameter Values for Burns Less Than 25%  87  6.6 Optimum Parameter Values for Burns Greater Than 25%  87  6.7 Coupled Starling Model Parameters  89  6.8 Common Fluid Resuscitation Formulae  109  A. I Interstitial Fluid Distribution in the “Reference Man”  144  C. 1 Admission and Laboratory Data for NBC Patient 1  156  C.2Fluid Inputs and Outputs for NBC Patient 1  157  C.3 Admission and Laboratory Data for NBC Patient 2  158  C.4FIuid Inputs and Outputs for NBC Patient 2  159  ix  C.5Admission and Laboratory Data for NBC Patient 3  160  C.6FJuid Inputs and Outputs for NBC Patient 3  161  C.7Admission and Laboratory Data for NBC Patient 4  162  C.8Fluid Inputs and Outputs for NBC Patient 4  163  C.9Admission and Laboratory Data for NBC Patient 5  164  C. 10 Fluid Inputs and Outputs for NBC Patient 5  165  D. 1 Normal Values for 70-kg, 170-cm Individual  166  F. I Grouping of Birkeland’s Patients  174  F.2 Plasma Volume Data (mL) for Groups of Birkeland’s Patients  176  G. 1 Area of Burn and Exudation Rate Postburn  177  H. 1 Erythrocyte Volume Fraction Data from Birkeland’s Patient  179  H.2 Fluid Inputs and Outputs to Birkeland’s Patient  180  1.1 Personal Data from Roa’s Patients  181  1.2 Fluid Input and Output for Roa Patient 1  182  1.3 Fluid Input and Output for Roa Patient 2  184  1.4 Monitored Clinical Data for Roa Patient 1  186  1.5 Monitored Clinical Data for Roa Patient 2  187  J. 1 Minimum OBJFUN Values for NBC Patient I Based on 12 Data Points  188  J.2 Minimum OBJFUN Values for NBC Patient 2 Based on 20 Data Points  188  J.3 Minimum OBJFUN Values for NBC Patient 3 Based on 22 Data Points  189  J.4 Minimum OBJFUN Values for NBC Patient 4 Based on 21 Data Points  189  x  J.5 Minimum OBJFUN Values for NBC Patient 5 Based on 30 Data Points  190  J.6 Minimum OBJFUN Values for Combination of NBC Patients 2, 3, 4 and 5 190  (Degree of Burn Greater Than 25%) J.7 Minimum OBJFUN Values for Birkeland Burn Group I Based on 6 Data  191  Points J.8 Minimum OBJFUN Values for Birkeland Burn Group II Based on 6 Data  191  Points J.9 Minimum OBJFUN Values for Birkeland Burn Group III Based on 5  192  Data Points J. 10 Minimum OBJFUN Values for Birkeland Burn Group IV Based on 4  192  Data Points J. 11 Minimum OBJFUN Values for Birkeland Burn Group V Based on 4  193  Data Points J. 12 Minimum OBJFUN Values for Combination of Birkeland Burn Groups I and II (Degree of Burn Less Than 25%)  193  J. 13 Minimum OBJFUN Values for Combination of Birkeland Burn Groups III, IV and V (Degree of Burn Greater Than 25%)  194  J. 14 Minimum OBJFUN Values for Combination of NBC and Birkeland Data for Burns Less Than 25% for Factor of 30  194  J.15 Minimum OBJFUN Values for Combination of NBC and Birkeland Data for Burns Greater Than 25% for Factor of 30  195  J. 16 Minimum OBJFUN Values for Combination ofNBC and Birkeland Data for Burns Less Than 25% for Factor of 100  195  J. 17 Minimum ()BJFIJN Values for Combination of NBC and Birkeland Data for Burns Greater Than 25% for Factor of 100  196  J. 18 Minimum OBJFUN Values for Combination of NBC and Birkeland Data for Burns Less Than 25% for Factor of 200 xi  196  J. 19 Minimum OBJFUN Values for Combination of NBC and Birkeland Data for Burns Greater Than 25% for Factor of 200  xli  197  List of Figures  2.1 Human Circulatory System  8  2.2 Lymphatic and Blood Vessels in Area of Bat Wing  9  2.3 Human Microcirculation  12  2.4 Tissue Hydrostatic Pressure as a Function of Interstitial Fluid Volume for Skeletal Muscle and Skin in Rat  19  2.5 Structure of Normal Skin Showing the Categorization of Burn Injury  21  2.6 Rule ofNines for Burn Estimate  25  2.7 Lund-Browder Chart for Burn Estimate: Percentage of Body Area  26  4.1 Schematic of Compartmental Burn Model  47  5.1 Simulation of MVES for NBC Patient 1: Gk  r= 0.025 Ir’; EXFAC  =  =  0.5; GkFBT  10.0;  1.0  72  5.2 Steady-State Simulation of MVES for NBC Patient 1: GkFTI =  =  10.0; r = 0.025 h’; EXFAC  =  =  0.5;  1.0  74  5.3 Model Predicted Response of MVES and “Error-free” Data for NBC  76  Patient 1 5.4 Model Predicted Response of MVES and “Noisy” Data for NBC Patient 1 5.5 Objective Function Surface for NBC Patient 1: GkFTJ r  =  77  0.5; GkFBT = 10.0; 79  ;EXFAC= 1.0 1 0.025 fr  6.1 Sensitivity Plots for Burns Less Than 25%  92  6.2 Sensitivity Plots for Burns Greater Than 25%  93  6.3 Simulation of MVES for NBC Patient 1 Using Global Model Parameters  97  Xlii  6.4 Simulation of MVES for NBC Patient 2 Using Global Model Parameters  98  6.5 Simulation of MVES for NBC Patient 3 Using Global Model Parameters  99  6.6 Simulation of MVES for NBC Patient 4 Using Global Model Parameters  100  6.7 Simulation of MVES for NBC Patient 5 Using Global Model Parameters  101  6.8 Simulation of MVES for Birkeland Patient Groups Using Global Model Parameters  103  6.9 Simulation of MVES for Arturson’s Patient Using Global Model Parameters  105  6.10 Simulation of MVES for Roa’s Patients Using Global Model Parameters  107  6.11 Simulation of MVES with no Fluid Resuscitation Following a 10% Burn  110  6.12 Simulation of MVES According to Evans’ Formula Following a 10% Burn  111  6.13 Simulation of MVES According to Brooke’s Formula Following a 10%Burn  112  6.14 Simulation of MVES According to Parkland’s Formula Following a 10% Burn  113  6.15 Simulation of MVES with no Fluid Resuscitation Following a 50% Burn  118  6.16 Simulation of MVES According to Evans’ Formula Following a 50% 119  Burn 6.17 Simulation of MVES According to Brooke’s Formula Following a 50%  120  Burn 6.18 Simulation of MVES According to Parkland’s Formula Following a 50%  121  Burn  C.1NBC Patient 1 Data Sheet  151  C.2NBC Patient 2 Data Sheet  152  C.3NBC Patient 3 Data Sheet  153 xiv  C.4NBC Patient 4 Data Sheet  154  C.5NBC Patient 5 Data Sheet  155  E. 1 Exudation Relationship Based on NBC Patient Data  173  F. 1 Patient Blood and Plasma Volume Observations on Admission and Prior to Start of Fluid Therapy by Birkeland  175  G. 1 Exudation Relationship Based on Davies’ Patient Data  xv  178  Acknowledgment  The financial support of the Natural Sciences and Engineering Research Council of Canada 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 this study 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 clinical data and the benefit of their professional expertise;  •  Dr. J. Boyle, Ms. T. Staley and all the members of the burn-care team at the Vancouver General Hospital, for the opportunity to visit the unit and to join the patient 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 special  part of me. This one is for you.  xvi  Chapter 1: Introduction  1  CHAPTER 1  INTRODUCTION  Burns are a major cause of traumatic injury in all ages of the population. There are many causes of burns and they occur in a variety of settings including the home and the workplace. 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. Burns are caused by such activities as cooking, bathing or smoking. Younger children usually suffer scald or grease burns when they pull the handles of pots on the stove, knock over hot foods on the table or play with hot water in the bathtub. An unfortunate reality is that some 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 caused by ignited clothing or a flash from an explosion. Electrical burns are not as common as flame 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 usually related to industrial accidents. Extreme exposure to nuclear or solar radiation causes burns of 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 homeostasis maintained in the body is also greatly affected following burn injury. There is a rapid shift of fluid from the circulating plasma into the interstitium, resulting in the accumulation of fluid in the interstitial space. This leads to drastic swelling of the tissue or edema, of such magnitude as to distort body features. The loss of plasma results in an abnormally low circulating blood volume, a condition known as hypovolemia. Fluid replacement is  Chapter 1: Introduction  2  therefore essential in replenishing the lost plasma volume, to avoid the possibility of hypovolemic shock. Approximately thirty years ago, the majority of patients with extensive burns died from hypovolemic shock within the first week following their injuries due to failure of the whole circulatory system [Rylah, 1992]. Today, adoption of the practice of prompt and aggressive fluid resuscitation of the burn victim has resulted in the survival of more patients with severe injury. Consequently, early death can usually be prevented in previously healthy individuals and is only common in patients with near total body 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 volumes and organ blood flows [Evans et al., 1952; Gillespie et al., 1987; Reiss et al., 1953]. These formulae differ in terms of the amount of colloid or electrolyte solution given and the rate and duration of their administration to stabilize the burned and hypovolemic individual, considering the size of the injury and the time postburn. The fluid resuscitation programmes are intended merely as guidelines and are continually adjusted according to the response of individual patients. The empirical formulae for fluid resuscitation may be considered as simplistic models using a “black box” approach, where all the circulatory and interstitial changes are contained within the “black box”, leaving only the fluid inputs and outputs as the manipulated variables. As such, they do not describe the pathophysiological mechanisms which occur following burn injury.  Burn injuries result in complex perturbations to the normal transcapillary transport of fluid and proteins in the human microvascular exchange system (MVES). In the human MVES, fluid and proteins are exchanged between the circulatory system, interstitium and the lymphatics. Consequently, a complete quantitative description of edema formation following a burn injury requires detailed knowledge of a large number of variables describing the normal transcapillary exchange of fluid and proteins as well as the changes  Chapter 1: Introduction  3  in these variables following injury. Mathematical modelling has been used to facilitate understanding of the dynamic behaviour and pathophysiology of a burn injury. Elaborate models have been developed based on detailed mathematical descriptions of fluid and protein transport across the capillary membrane [Arturson et al., 1984, 1988, 1989; Bert et al., 1988, 1989, 1991; Hedlund et al., 1988; Roa et al., 1986, 1988, 1990, 1993]. The potential advantages of these models are manifold. They provide a description of the time course of changes in fluid volumes and protein concentrations in the blood and various tissues in the human MVES. These models can be used to validate and hence predict the reaction of the MVES to different empirical resuscitation protocols following a burn injury. Ultimately, mathematical models may be used to suggest a possible optimum form of fluid replacement therapy.  The development of mathematical models to describe the human MV.ES following thermal injury was pioneered by Arturson et al. [1984] in their description of a computer based burn patient simulator. They have since developed complex multi-compartmental models made up of modules to describe microvascular exchange, hormonal function, renal dynamics 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 and the effect of burn and inhalation injuries on pulmonary capillary dynamics. These groups of workers 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 burn injury, in addition to the MVES. A major fault with their models, however, is that they assume various model parameters and transport mechanisms from the literature, some of which 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 MVES in the burn injured rat. In contrast to the models developed by Arturson Ct al. and Roa et al., the MVES was emphasized due to the critical role it plays in transcapillary exchange  Chapter 1: Introduction  4  following burn injury. In addition, the parameters used in their models were determined by statistical fitting of model predictions to experimental data.  The present research involves computer modelling of the human MVES following burn injury and fluid resuscitation. This work is a continuation of the research effort at UBC by Bert, 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 fluid and plasma proteins in the human MVES following a burn injury;  2.  estimate the model parameters by fitting its predictions to clinical data using suitable optimization techniques;  3.  validate the model by comparing its predictions with other data obtained from burn patients; and  4.  investigate the model-predicted behaviour of the MVES with regard to burn patient fluid therapy using common empirical resuscitation formulae.  In order to provide a basis for understanding the physiological changes that occur in the MVES following burn injury, Chapter 2 provides a brief physiological review of the system being considered. An overview of mathematical models which have been developed 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 the system of interest is described. The patient data used in estimating the unknown model parameters and for validation purposes are discussed in Chapter 5. The statistical procedure adopted to determine the parameters is also described. The best-fit parameter estimates are reported in Chapter 6. The validity of the model is investigated by comparing its predictions with all of the available clinical data, including additional information  Chapter 1: Introduction  5  withheld from the fitting process for this purpose. In addition, simulations using the statistically determined parameters along with fluid inputs based on common resuscitation formulae are presented and discussed. Finally, the major conclusions drawn from the current study and suggestions for fl.irther work are presented in Chapter 7.  6  Chapter 2: Physiological Overview  CHAPTER 2  PHYSIOLOGICAL OVERVIEW  2.1  INTRODUCTION  The extreme complexity of the human body and its regulation continues to provide great challenges to the medical and engineering professions. The current study seeks to assist in the understanding of the role and response of part of this complex system, the microvascular exchange system (MVES), to burn injuries. A brief overview of the general circulatory system and the MVES will provide a basis for understanding the physiological changes that occur in the MVES following thermal injury.  2.2 THE CIRCULATORY SYSTEM  2.2.1  Description of the Circulatory System  The circulatory system serves to transport and distribute essential substances to the tissues and to remove by-products of metabolism. Oxygen from the lungs and nutritional substances absorbed from the gastrointestinal tract are supplied to the tissues of the body via the circulation. Carbon dioxide is transported from the tissues and exchanged in the lungs while other products of metabolism are removed by the kidneys. The circulatory system also shares in such homeostatic mechanisms as body temperature regulation, humoral communication throughout the body and adjustments of oxygen and nutrient supply in different physiological states.  Chapter 2: Physiological Overview  7  The system that accomplishes all these tasks is made up of a pump, the heart, a series of distributing and collecting tubes and an extensive system of small vessels that permit rapid exchange between the tissues and the vascular network. Blood is the transport medium which is pumped through the closed system of vessels by the heart. In mammals, the heart may be considered as two pumps in series (see Figure 2.1). Blood rich in oxygen and nutrients leaves the left ventricle of the heart and is pumped through arteries and arterioles to a bed of capillaries. In this capillary bed, the oxygen and nutrients are transported across 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 the interstitium to the circulating blood. The capillaries drain through venules into veins and back to the right atrium of the heart. Upon leaving the right atrium, this carbon-dioxiderich blood flows to the right ventricle, which pumps the blood through the vessels of the lungs and the left atrium, to the left ventricle. In the lungs, there is counter-exchange of oxygen and carbon dioxide, so that oxygen-rich blood leaves the lung circulatory system to resume its cyclic journey.  In addition, some tissue fluids enter another parallel circulatory system of vessels, the lymphatics, which drain tissue derived fluid via the thoracic duct and the right lymphatic duct into the venous system. This is the lymphatic circulation which is shown in Figure 2.2. The lymphatics are not part of the blood circulatory system per Se, but constitute a one-way route for the movement of interstitial fluid to blood. These thin-walled capillaries have large pores and are permeable to all interstitial fluid constituents, including protein. Thus, the lymphatics carry fluid and proteins from the interstitium to the circulatory system.  Chapter 2: PhysiologicaJ Overview  8  CapilLaries  P4rJç. Arteries to head and upper eztremties  Veins (torn head and uppor extremities  I  Rightataum1/\ and  Hepaticvei  Sptecn  .  1  liVer  Stomach  VTn from abdomen and lower eztemities  -  Pancreas .  Portal vein Intestine  .  :  /  1 7—  b?1  tct7  Figure 2.1: Human Circulatory System  Chapter 2: Physiological Overview  Figure 2.2: Lymphatic and Blood Vessels in Area of Bat Wing: lymphatics (black), blood vessels (shaded) and blood capillaries (lines)  9  Chapter 2: Physiological Overview  2.2.2  10  Composition and Properties of Blood  Blood is the transport medium for oxygen, nutrients, carbon dioxide and metabolic waste products 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 complex aqueous medium known as plasma. The elements of blood serve multiple functions essential 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 a total volume of about 3 L [Berne and Levy, 1988; Ganong, 1991; Reference Man ICRP 23, 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 gaseous oxygen, carbon dioxide and nitrogen. Normally, the composition of blood is maintained at biologically regulated levels by a variety of homeostatic mechanisms. The balance may be upset by impaired function following injuries and in a multitude of disorders, particularly those involving the lungs, cardiovascular system, kidneys, liver and endocrine organs.  There are several different proteins that are dissolved in plasma. In all, plasma normally contains 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 various immunoglobulins, albumin being the most abundant. Albumin, synthesized by the parenchymal cells of the liver, is normally present at an average concentration of about 4 g/dL [Berne and Levy, 1988; Reference Man ICRP 23, 1975]. The exchange of albumin across intact vascular endothelium is restricted and this provides the critical colloid osmotic or oncotic pressure that participates in the regulation of the passage of water and diffusible solutes across the capillaries. A reduction of the albumin concentration in plasma  Chapter 2: Physiological Overview  11  causes shift of fluid to the surrounding tissue space. Excess fluid accumulation in extravascular 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 cells well dispersed throughout the plasma. Centrifugation of a sample of blood to which an anticoagulant is added results in separation of cells from the fluid. This permits determination of the hematocrit or the percentage of the total blood volume which is erythrocytes. The normal hematocrit is approximately between 37 and 49% in men and between 36 and 45% in women [Berne and Levy, 1988; Ganong, 1991; Reference Man ICRP 23, 1975].  The principal protein constituent of the cytoplasm of the mature erythrocyte is hemoglobin, an iron-containing protein which binds oxygen and constitutes approximately one-third of the total weight of the erythrocyte. Normal blood has about 15 g/dL of hemoglobin in adult men and about 13.5 g/dL in adult women [Berne and Levy, 1988).  2.3  THE MICROVASCULAR EXCHANGE SYSTEM  2.3.1  Description of the Microvascular Exchange System  The microvascular exchange system pertains to the portion of the circulatory system that is composed of the capillary network as shown in Figure 2.3. It also comprises the interstitium and the lymphatics. This system is the site of exchange of substances such as fluids and plasma proteins across the capillary membrane.  Chapter 2: Physiological Overview  12  Arteriole AV shunt  Ventjle  Capillaries  Figure 2.3: Human Microcirculation  Chapter 2: Physiological Overview  13  The microcirculation is the part of the circulatory system comprising smaller vessels of diameter up to 100 p.m. A description of these blood vessels is presented in Table 2.1. At any given moment, approximately 5% of the total circulating blood is flowing through the capillaries [Berne and Levy, 1988; Reference Man ICRP 23, 1975; Vander et al., 1985]. It is 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 permeate almost every tissue of the body. There are an estimated 25 000 miles of capillaries in an adult 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 the kidneys, exceeds that reabsorbed by approximately 3 L [Vander et al., 1985]. This excess is returned to the blood via the lymphatics. Partly for this reason, obstruction of the lymphatics leads to increased interstitial fluid or edema. Most capillaries in the body have a slight permeability to protein and accordingly, there is a small, steady movement of protein from the blood to the interstitial fluid. This protein is returned to the circulatory system via the lymphatics. Some protein is normally leaked into the interstitial fluid and failure of the lymphatics to remove it by carrying away the interstitial fluid containing it allows the interstitial protein concentration to increase. This reduces or eliminates the protein concentration difference and thus water-concentration difference across the capillary wall and permits net movement of increased quantities of fluid out of the capillary into the interstitial space.  14  Chapter 2: Physiological Overview  Table 2.1: Classification of Blood Vessels  Description/Function  Blood Vessel Artery  Contains a large amount of elastic tissue which is stretched  Diameter: 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 the  Diameter: 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 from metarteriole. Continually opens and closes to allow intermittent flow through any given capillary. Thin-walled tube of endothelial cells, one-layer thick without any  Capillary Diameter: 5  -  10 tm  surrounding smooth muscle or elastic tissue. Primary site of exchange of water and solutes with interstitial fluid.  Venule  Has some smooth muscle, the contractions of which influence  Diameter: 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 back  Diameter: 0.5 cm  to the heart. Also serves as collecting channel and storage or capacitance vessel.  Chapter 2: Physiological Overview  2.4  THE INTERSTITIUM  2.4.1  Structure and Composition of the Interstitium  15  The interstitium may be defined as the space located between the capillary wall and the cells. The basic structure of the interstitium is similar in all tissues: collagen forms a fibre framework that contains a gel phase made up of glycosaminoglycans and other large macromolecules, a salt solution and proteins derived from plasma. Although the components are principally the same in all tissues, their relative amounts vary greatly. The amount of interstitium varies from about 50% of the wet weight in skin to 10% in skeletal muscle, to even less in the brain [Aukland and Reed, 1993]. The composition and structure 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 and fascia. 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-handed super helix. These three chains constitute the collagen molecule. A collagen fibre consists of an organized array of collagen molecules, arranged in parallel with many stable cross linkages 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 of variable length made from repeating disaccharide units of hexosamine and uronic acid or galactose. The glycosaminoglycans are widely distributed in the organism, but their  Chapter 2: Physiological Overview  16  concentration varies between different organs. About two-thirds of the glycosaminoglycan content in skin is hyaluronan, one of the seven subfamilies of glycosaminoglycans.  Elastic Fibres: The elastic fibres provide tissues with elasticity, giving some tissues a rubber-like texture. The major part of the elastic recoil of skin after applying tension within physiological limits is attributed to elastin, a three-dimensional network of crosslinked hydrophobic amino acid molecules.  Interstitial Plasma Proteins: The plasma proteins contained in the interstitial fluid are the same as those in plasma. The proteins move from the plasma to the interstitium across the capillary wall. The interstitial concentration is a function of the selectivity at the capillary barrier, the transcapillary fluid flux and lymph flow. The physical properties of the plasma proteins in the interstitial space affect the physiology of this space. Due to its relative abundance, relatively low molecular weight and high charge density, albumin is a major contributor to the interstitial colloid osmotic pressure (COP). The interstitial proteins return to the circulation via the lymph and thus, the interstitium acts as a reservoir for colloidally active molecules.  2.4.2  Physicochemical Properties of Interstitium  Certain properties of the interstitium influence its response to burn injury and will be discussed in the following section.  2.4.2.1 Turnover of Interstitial Plasma Proteins The rate of disappearance of plasma proteins from the interstitium is described as the turnover rate. The turnover of proteins in the interstitium has been quantified in several ways, most commonly by injecting radiolabelled protein into the tissue and measuring its removal by external gamma-detecting equipment or by estimating the appearance of tracer  Chapter 2: Physiological Overview  17  in plasma [Hollander et al., 1961; Langgàrd, 1963; Reed et al., 19901. In humans, the normal removal rate of radioactive albumin injected subcutaneously has been found to be between 2 and 2.5% per hour [Hollander et al., 1961; Langgârd, 1963; Xie, 1992].  2.4.2.2 Interstitial Volume Exclusion Mutual exclusion between macromolecules occurs because at any particular time, no two of these molecules may occupy the same space, and their centres may not come closer than the sum of their radii. The characteristic components of the interstitium such as collagenous fibres, have diverse geometric shapes. Their presence thus limits the interstitial space accessible to plasma proteins and other macromolecules. In vivo exclusion studies predict fractional albumin excluded volumes ranging from about 25% to 60% [Granger et al., 1980; Parker  Ct  al., 1979, 1980; Reed et al., 1990]. Based on these  studies and the work of Wiederhielm [1979], Bert and Pinder [1982] determined a constant albumin exclusion fraction of 25% of the normal interstitial volume.  2.4.2.3 Interstitial Compliance In order to perform any type of quantitative analysis of interstitial fluid dynamics, it is essential to know the relationship between interstitial fluid pressure and volume in the interstitial spaces. The interstitial compliance is defined as the ratio of the change in ) to the corresponding change in interstitial hydrostatic pressure 1 interstitial fluid volume (V ), i.e., 1 (P Compliance  —-.  2.1  Information about the compliance of human tissues is lacking. Chapple [1990] developed a compliance relationship for humans based on the work of Stranden and Myhre [19821 and Reed and Wiig [1981]. Stranden and Myhre [1982], in the only known study of human compliance, measured the compliance of lower limb subcutaneous tissue in 46 patients.  Chapter 2: Physiological Overview  18  However, the data was too scattered to derive a meaningful relationship for human compliance. Reed and Wiig [19811, after studying the compliance characteristics of skin and skeletal muscle in rat, cat and dog tissues, found that the compliances of both tissues follow a similar trend. During severe tissue dehydration, compliance is low while during severe tissue overhydration, compliance is high. In between the two extremes, moderate compliance characteristics prevail. The general shape of the volume-pressure curve is shown in Figure 2.4 [Reed and Wiig, 1981]. Chapple scaled interstitial hydrostatic pressure and interstitial fluid volume data from the rat based on changes observed in the edematous state by Stranden and Myhre. The flat segment of his compliance relationship, representing overhydration, was considered the region most prone to the influence of experimental error. As such, two other relationships were investigated by arbitrarily 1.8x10 to 5.0x10 5 and 1.05x 10 increasing the slope of the overhydration segment from 5 mmHg/mL. A summary of the three compliance relationships investigated is presented in Table 2.2. The three tissue compliance relationships were used by Xie [1992] in a study to determine normal transport parameters for the human MVES. The best-fit parameters were obtained using compliance relationship #3.  2.5  THE SKIN  In the present study, the properties of the interstitium are assumed to be those of skin and muscle. A brief discussion of the anatomy and function of the skin provides a basis in understanding the microscopic changes that occur in the skin following burn injury.  2.5.1  Anatomy and Function of Skin  The skin is the largest organ of the body and has a surface area that ranges from about 2 in the adult [Martyn, 1990; McLaughlin, 1990]. It 0.025 m 2 in the newborn to 2.0 m  Chapter 2: Physiological Overview  19  2  n  E E  ‘—  0  1J  (f) C,)  0::: —2  cL  C) I— I —4 (I)  0  0:: 0 >-.  L-  —6  •—. SKIS  Li  D  (F)  (F) I—  —8  0  10  20  30  40  INTERSTITIAL FLUID VOLUME (ml)  Figure 2.4: Tissue Hydrostatic Pressure as a Function of Interstitial Fluid Volume for Skeletal Muscle and Skin in Rat [Reed and Wiig, 1981]  Chapter 2: Physiological Overview  20  Table 2.2: Mathematical Description of Human Interstitial Compliance Relationship [Chapple, 1990]  Relationship  Region of Curve Dehydration Moderate Hydration  =  —0.7+1.96154 x  1 —8.4 X iO) io-(V  1 and Mathematical interpolation of experimental P 1 data V  Overhydration: Compliance #1  =  1.88 + 1.8 X iO-(V —1.26 x 1O)  Compliance #2  =  1.88 +5.0>< iO-(V —1.26>< 101  Compliance #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 Figure 2.5. The outermost cells of the epidermis are dead comified cells that act as a tough protective barrier against the environment. It has high capacity for regeneration. The stratum corneum in the epidermis has a high electrical impedance which restricts the passage of electric current. The second, thicker layer, the dermis, is composed chiefly of fibrous connective tissue. It contains the blood vessels and nerves to the skin and epithelial appendages of specialized function. The dermis is the barrier that prevents loss of body fluids by evaporation and loss of excess body heat. Sweat glands help maintain body temperature by controlling the amount of heat loss by evaporation. Beneath the dermis is subcutaneous or adipose tissue which consists mostly of fat. It serves as a means of heat insulation and as a nutritional source in extreme conditions.  Chapter 2: Physiological Overview  Figure 2.5: Structure of Normal Skin Showing the Categorization of Burn Injury  21  22  Chapter 2: Physiological Overview  2.6  TRANSCAPILLARY EXCHANGE  Fluid and proteins move across the capillary endothelial wall by filtration, diffbsion and convection. The transcapillary exchange of fluid and protein is determined by the properties of the capillary membrane, the transcapillary pressures and the protein concentrations.  2.6.1  Capillary Filtration  The magnitude and direction of the movement of fluid across the capillary wall is determined by the algebraic differences between the hydrostatic and osmotic pressures existing across the membrane. An increase in intracapillary hydrostatic pressure favours movement of fluid from the blood vessel to the interstitial space, whereas an increase in the concentration of osmotically active agents within the vessels favours movement into the vessels from the interstitial space.  The role of the hydrostatic and colloid osmotic pressures in regulating the passage of fluid across the capillary endothelium was first expounded by Starling in 1896 and constitutes the Starling Hypothesis. It can be expressed by the equation: F  where  F  =kA.[(PCIJ)cr(HpLHJ)],  2.2  is the transmembrane filtration flow, k the hydraulic conductivity of the capillary  membrane per unit area, A the surface area available for exchange, a the capillary reflection coefficient for the plasma proteins, P and fl are the hydrostatic and colloid osmotic pressures respectively, while the subscripts C, PL and I represent capillary, plasma and interstitial respectively. The product (kA) is referred to as the capillary filtration coefficient for the capillary membrane. Filtration occurs when the pressure driving force, (AP-a.tffl), is positive and re-absorption occurs when it is negative.  23  Chapter 2: Physiological Overview  2.6.2  Combined Convective and Diffusive Solute Transport  Bresler and Groome [19811 developed an equation for the combined convective and diffusive protein flux across membranes of finite thickness. The transport equation which describes the solute flux generated when a combined hydrostatic and osmotic pressure difference and a concentration difference act conjointly across the membrane is  Q where  —  (  ‘  Fr.  F’PI  [  .exp(—Pe)] I, l—exp—Pe; ] 1 —c  .3  is the rate of solute transport across the membrane, c the concentration of  plasma protein and Pc is a modified Péclet number defined by  PS  2.4  PS is the product of the permeability of the capillary membrane to albumin and the membrane surface area.  2.7  PHYSIOLOGICAL CHANGES FOLLOWING INJURY  The 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 include visible swelling of the skin, blister formation and loss of surface-protecting epithelium which leaves wet and weeping surfaces. The swelling is caused by changes in the microvascular exchange system (MVES), in particular, fluid shifis and losses from the circulation. Other macroscopic changes occur with respect to areas not directly affected by the burn. A brief review of these changes will serve as a basis for the formulation of the current model describing the human MVES following burn injury.  Chapter 2: Physiological Overview  2.7.1  24  Damageto Skin  The continued losses of water and heat through burned skin play major roles in the pathophysiological changes seen postburn. Significant swelling may also occur in the subcutaneous layer of skin. The degree of impairment in the protective characteristics of normal skin is dependent on the depth of the burn injury and the extent of injury or the size of the burn relative to that of the total skin surface area. Traditionally, burn depth has been classified in degrees of injury: first, second and third degree burns. Currently, the more popular classifications are partial-thickness (first and second degree) and fullthickness (third degree) burns. Both classifications use the same criteria based on the depth 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 each arm is considered to be 9%, each leg 18%, anterior trunk 18%, posterior trunk 18% and head 9% of TBSA as shown in Figure 2.6. A more accurate method is the use of the Lund and Browder chart shown in Figure 2.7 which divides the body surface by regions, while accounting 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 a major clinical problem after thermal injury. Edema is most prominent in burn tissues or in the region directly surrounding the burn tissues, but is not uncommon in nonburned tissues, including the lungs. It is well known that this swelling of tissue is caused by the shift of fluid from the circulating plasma to the interstitial spaces. This internal loss of plasma volume may result in hypovolemia and eventually in hypovolemic shock. The pathogenesis 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  Figure 2.6: Rule of Nines for Burn Estimate  25  I  CD -t C.) CD  CD  -3  Ca C”  C”  C”  C”  tO  C,  CC  C0  C,  C,  C”  C,  C,  C,  Ca  Ca  Ca  Ca  Ca  Ca  Ca  C,  C,  C  z  r  Ca  Ca  Ca  .  C4  iI  -a  Ca  Y  YR  ‘1  0  C”  “1  CD  C)  27  Chapter 2: Physiological Overview  Table 2.3 : Burn Depth Classifications  Characteristics  Classification of Burn First 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 increases resulting 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 is evident. Blood supply is marginal and the potential for the burn to progress to deeper injury is high.  Third degree or  Destruction of entire epidermis and dermis.  Full thickness  Formation of avascular tissue due to heat-coagulation of dermal blood vessels. Causes: Short exposure to very high temperature or prolonged contact with moderate temperature.  2.7.2.1 Transcapillary Exchange in Injured Tissue Edema develops when the rate of fluid filtered from the microvessels exceeds the rate at which fluid is drained by the lymphatics or by some other route. Fluid is filtered across the capillary membrane according to Starling’s hypothesis, which according to the previous section yields  28  Chapter 2: Physiological Overview  2.5  where .P is the net filtration pressure given by 2.6 Lymphatic drainage from the tissue is assumed to be linearly dependent on interstitial fluid pressure, i.e., JL=JL,+LS{F-fJ. L  2.7  is the rate of lymphatic drainage from tissue, LS the lymph flow sensitivity coefficient  and the subscript NL represents normal steady-state conditions. The influence of burn injury on each of the parameters in Equations 2.5, 2.6 and 2.7, which affect transcapillary fluid 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 in the capillary reflection coefficient, there is a high plasma protein content in exudate and blister fluid following burn injury [Arturson, 1979]. This apparent leakiness of the capillaries 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 of plasma proteins in plasma may also be increased through the administration of resuscitation fluids.  2.7.2.2 Transcapillary Exchange in Uninjured Tissue Swelling or edema of uninjured skin, muscle and internal organs distant from the injured skin areas is also seen following fluid resuscitation of patients with extensive burns. Increases in protein extravasation, tissue protein and fluid content have been reported in uninjured tissue [Carvajal et al., 1979; Lund and Reed, 1986]. These remote effects occur  1 pressure, P  Interstitial  fluid  -  -  and postcapillary resistances. Local and central hemodynamic changes have strong effects on these pressures and may cause either an increase or decrease in the value of P.  Normal value of AP is between 0.5 and 1 mmHg. Large increases from 10 25 mmHg [Pitt et al., 1987] up to 250 300mmHg [Arturson and Mellander, 1964] reported immediately postburn explain early edema development. Pc is normally determined by arterial and venous hydrostatic pressures as well as precapillary  observed in the first hour postburn [Lund et al., 1988].  1 is normally slightly subatmo spheric (-1 to -2 mmHg). hydrostatic P Increases in value from 2 mmHg [Wiig and Reed, 1981] to 7 mmHg at 6 to 8 hours postinjury . 1 [Watchtel et al., 1983] have been reported for P 1 to a strongly negative value of about -150 mmHg has been An acute marked decrease of P  Capillary hydrostatic pressure, P  Net filtration pressure, AP  Conductivity per unit area, k, increases. Area might be reduced due to fall in number of perfused capillaries. Overall effect on kA is therefore unpredictable. Increases of up to 300% have been reported for kA [Arturson and Mellander, 1964; Pitt et al.,  Capillary Filtration Coefficient, kA  1987].  Physiological Changes  29  Property  Table 2.4: Changes to Injured Tissue MVES Properties Following Burn Injury  Chapter 2: Physiological Overview  30  Physiological Changes  Lymphatic drainage,  L  Capillary reflection coefficient, a  1 Interstitial fluid COP, Fl  Pitt et al., 1987; Taylor and Granger, 1984].  with increased protein permeability. The normally reabsorptive COP gradient across the capillary membrane is thus reduced. Increases in the value of L of up to 20 times has been observed [Arturson and Mellander, 1964;  -  fluid. ) 1 Increases in the value of 11 [Lund and Reed, 1986] and a reversed COP gradient (pL Fl [Pitkänen et al., 1987] have been observed. The reversed COP gradient could enhance fluid filtration, hence plasma volume loss. Normal a in skin is reported to be between 0.85 and 0.97 [Taylor and Granger, 1984]. A reduction in the value of a from 0.87 to 0.45 has been reported [Pitt et al., 1987], associated  return of fluid poor in protein. The effect on transcapillary fluid exchange is to enhance the net capillary filtration of fluid. Increased extravasation of fluid and protein can effect a theoretical increase or decrease in the value of T1 depending on the protein concentration of the filtrate compared to that in interstitial  Plasma colloid osmotic pressure A reduction in the value of PL has been observed [Lund et al., 1986, 1988; Onarheim et al., 1989; Pitkanen et al., 1987; Watchtel et al., 1983; Zetterström and Arturson, 1980] with or (COP), 1 PL without fluid resuscitation. loss of fluid and proteins out of the circulation, as well as the lymphatic PL is affected by the  Property  Table 2.4 (Continued): Changes to Injured Tissue MVES Properties Following Burn Injury  Chapter 2: Physiological Overview  Chapter 2: Physiological Overview  31  when 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 pulmonary edema in major body burns. Inhalation injury has direct damaging effects on the respiratory tract and lungs. In the absence of this injury, the lungs are protected against edema by their ability to increase lymphatic removal of fluid. An additional edemapreventing mechanism results from the removal and dilution of interstitial proteins due to a normally high interstitial COP in the lungs.  2.7.2.3 Systemic Hemodynamic Changes Hypovolemia, resulting from the loss of fluid from the circulation, induces a number of hemodynamic changes following thermal injury. Cardiac output is reported to fall markedly soon after extensive burns. In addition, arterial blood pressure and central venous pressure have both been found to decrease. The ratio of the systemic blood pressure to the cardiac output is a measure of the peripheral resistance. It depends mainly on the degree of vasoconstriction and on the viscosity of blood, to a lesser extent. Vasoconstriction causes an overall increase in the peripheral resistance, which may maintain arterial blood pressure for a time, but at the expense of a reduced blood flow through the skin and other vital organs.  2.8  FLUID RESUSCITATION  Hypovolemia resultant from burn injury can rapidly lead to conversion of a viable but ischemic deep dermal burn to a nonviable full-thickness burn, further increasing the possibility of mortality. Death due to the development of hypovolemic shock in the acute phase is also of particular concern. Adequate initial fluid volume resuscitation is therefore  Chapter 2: Physiological Overview  32  critical to the survival of a major body burn. However, the aggressive correction of the problem of hypovolemia can result in generalized burn edema formation which is less lethal than shock, but can result in serious morbidity nonetheless. The subnormal cardiac output following burn injury also needs to be promptly restored as near as possible to the normal value.  The greatly increased capillary leakage resulting in progressive edema formation is greatest during the first eight hours post-burn. Consequently, the two important goals of early burn care are the prompt initiation of resuscitation and an adequate volume replacement regime. Several empirical formulae exist for resuscitation of the burn patient based on the timing of fluid replacement, as well as on the composition and amount of fluid provided. Crystalloids, hypertonic crystalloids and colloidal solutions have been used for early fluid therapy.  2.8.1  Isotonic Crystalloid Fluid Resuscitation  Crystalloids, in particular isotonic solutions such as lactated Ringe?s solution, with a sodium concentration of 130 mEqfL, are the most popular resuscitation fluids [Gillespie et al., 1987]. The loss of large quantities of sodium and water from the vascular space into the burn wound is well recognized. The need for sodium and water replacement to effect successful resuscitation justifies the use of this solution, which closely approximates the composition of the extracellular fluid. The amount of fluid to be given over the first 24  hours is initially estimated by various formulae such as the Parkland formula (4 mL of lactated Ringer’s /kg/% TBSA burned). The use of lactated Ringer’s solution has been found highly effective in preventing early death due to hypovolemia. However, concerns exist due to complications from the administration of large volumes of fluid.  Chapter 2: Physiological Overview  2.8.2  33  Hypertonic Crystalloid Fluid Resuscitation  Hypertonic solutions with sodium concentrations between 240 and 260 mEqfL, have become a popular option in minimizing the total fluid volume administered to burn patients in the early phase postburn. These hypertonic saline solutions are used to control cell swelling by increasing extracellular osmotic pressure. Water influx into the cells is thus prevented and fluid extravasation into injured tissue is decreased. Extracellular and hence, intravascular volume is maintained with less fluid. However, as these solutions are still crystalloids, hypoproteinemia and blood volume are not as well maintained as with colloid solutions. The safe use of these fluids as a standard solution has been the subject of many recent research efforts [Griswold et al., 1991; Gunn et al., 1989].  2.8.3  Colloid Fluid Resuscitation  The realization that the fluid lost from the circulation into the burned tissues has the characteristics of plasma is justification for using colloidal solutions for the early fluid therapy. A variety of colloids have been used including human plasma, serum and/or albumin, 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 capillary permeability changes vary considerably in different tissues for different degrees of burn injury. As the fluid requirements and the area of the burn are related, various formulae have 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 albumin infhsions, less expensive colloids, not derived from human plasma provide a significant cost benefit. The potential efficacy of nonprotein colloid plasma expanders in burn resuscitation was suggested by experimental studies with dextran [Demling et al., 1984].  Chapter 2: Physiological Overview  34  Clinically, dextrans have not been widely used primarily due to their potential to induce allergic reactions and increased bleeding. The safety and efficacy of other plasma substitutes, including gelatins, for burn resuscitation, remain unresolved. The most promising alternative colloid volume expanders are the starches [Waxman et al., 19891. Hetastarch, which closely mimics 5% albumin in normal saline, has been found to increase clotting and reduce bleeding times in animals. Pentastarch has been found to be a very promising plasma substitute, with hemodynamic effects equal or superior to albumin. However, ftirther study is required to assess the efficacy of pentastarch within the first 24 hours of resuscitation.  Formal resuscitation is generally carried out in all adults with burns over 15 to 20%, with superficial or first degree burns being excluded. The most reliable clinical parameter reported for evaluating the response of the patient to all these resuscitation formulae is urine output, even though this has been disputed [Dries and Waxman, 19911. In adults, 0.5 to 1.0 mL/kglh of urine is the optimum goal.  2.9  SUMMARY  In summary, the most important changes that occur following thermal injury which need to be considered when modelling the human microvascular exchange system, are the following: i) the rapid development of edema in the injured tissue resulting from increased  pressure driving forces and the capillary filtration coefficient in this tissue; ii) a dramatic increase in transcapillary transport of plasma proteins in the injured tissue; iii) a dramatic loss of fluid and protein from the burn wound; and  Chapter 2: Physiological Overview  35  iv) a dramatic reduction by about -150 mmHg in interstitial fluid hydrostatic pressure, creating a strong “suction” in the burned tissue. This very negative tissue pressure has been observed in rats. Burns covering more than about 25% of the total body surface area initiate local and systemic effects different from those initiated by smaller burns. Consequently, two burn groups, less than and greater than 25% burn surface area, need to be considered in the analysis of fluid exchange and resuscitation of burn patients.  Chapter 3: Computer Modelling of the MVES  36  CHAPTER 3’  COMPUTER MODELLING OF THE MICROVASCULAR EXCHANGE SYSTEM  3.1  INTRODUCTION  In order to replace the loss of plasma volume which results in the microvascular exchange system (MVES) following a burn injury, and hence to improve the survival of burn victims, various empirical formulae for fluid therapy have been developed and implemented 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 clinical observations and medical experience from treating burn patients, with limited understanding 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. Fluid resuscitation has been found to correct hypovolemia or low blood volume, but worsens the edema or swelling process.  Mathematical models have been developed to complement this empirical approach to patient care. These models are based on detailed fluid and protein transport mechanisms across the capillary membrane. The models describe the time course of changes in fluid volumes and the amount and concentration of protein in the blood and tissues following injury. Mathematical models can be used to predict the response of the MVES to different empirical resuscitation protocols to give an indication of a possible optimum form of therapy. In describing the human MVES, two different kinds of models have been considered; the distributed and compartmental models.  Chapter 3: Computer Modelling of the MVES  37  In the distributed model, the fluid and tissue properties are considered to be positiondependent. These spatial properties are difficult to determine experimentally and hence are not readily available. In addition, a more complex description of fluid and protein transport is 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 than the compartmental models. However, due to the mathematical complexity of these models and the lack of experimental data required to determine model parameters, it is premature to consider their inclusion in a burn patient simulator.  The compartmental model, as the name suggests, comprises a system of separate, wellmixed compartments in which fluid and proteins are homogeneously distributed. As such, the properties in each compartment represent average values for that compartment. Due to this spatial averaging, the behaviour of fluid and proteins in the MVES can be described by a much simpler set of ordinary differential equations. Several compartmental mathematical models have been developed to describe the distribution and transport of fluid and protein between the circulation, interstitium and lymphatics [Arturson et al., 1984; Bert et al., 1982, 1988; Roa and Gomez-Cia, 1986; Wiederhielm, 1979]. The proposed models generally differ in two aspects: the complexity in the division of the MVES into compartments and the description of fluid and protein exchanges between the compartments. In most models, the MVES is assumed to comprise the plasma compartment and interstitial compartments. Additional compartments to describe intracellular and extracellular distribution or renal fhnction for example, are also considered based on the particular interests of the researchers. Fluid and protein exchange between the compartments is based on Starlings concepts on capillary filtration and exchange [Starling, 1896]. The mathematical equations that describe the model are obtained by carrying out fluid and protein balances around the compartments. This results  Chapter 3: Computer Modelling of the MVES  38  in a set of ordinary differential equations where the independent variable is time. The remainder of this chapter will review compartmental models which have been developed to describe the normal or thermally injured MVES in experimental animals and humans.  3.2  MODELLING OF NORMAL MVES  A non-linear computer simulation program was developed by Wiederhielm [1979] to analyze the dynamics of capillary fluid exchange. The simulation program took account of the fact that, in addition to plasma proteins, the interstitium also contains other osmotically active substances such as mucopolysaccharides. These substances exert an osmotic pressure and also exhibit unusual physical characteristics in terms of volume exclusion. The interstitium was therefore partitioned into a mucopolysaccharide-containing gel phase in equilibrium with a free fluid-phase, to which the proteins are restricted. Also included in the simulation was a nonlinear interstitial compliance. Two different modes of transport of plasma proteins and macromolecules from the circulation into the interstitium were considered: 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 in arterial and venous pressures, plasma oncotic pressure, interstitial mucopolysaccharide content and lymphatic obstruction were studied.  Bert and Pinder [1982] modified the model of Wiederhielm to incorporate a different concept of volume exclusion. The excluded volume in Wiederhielm’s model which was a variable calculated from the concentration of proteoglycans, including hyaluronate in the gel phase, was replaced by a constant value. This constant value for the excluded volume was based on observations that the volume from which albumin is excluded remains constant, even with swelling of the tissue [Meyer et al., 1977] and was due to the presence of collagenous fibres. The use of this constant value avoided the unprovable assumptions  Chapter 3: Computer Modelling of the MVES  39  Wiederhielm was forced to make regarding content, composition and interaction of components of the interstitial space and also simplified the overall model. Bert and Pinder used their model to program perturbations characteristic of different forms of edema, and to record both the transient and steady-state responses, which were found to be in good agreement with Wiederhielm’s predictions.  Bert et al. [1988] developed a dynamic mathematical model to describe the distribution and transport of fluid and plasma proteins between the circulation, interstitial space of skin and muscle, and the lymphatics in the rat. They investigated two descriptions of transcapillary exchange: a homoporous ‘Starling Model’ (SM) and a heteroporous ‘Plasma Leak Model’ (PLM). In the SM, water and protein exchanges were assigned to a single site in the capillary and were characterized by one pair of transport parameters for each plasma protein investigated and by one value of capillary hydrostatic pressure. The PLM was based on fluid filtration in the arterial end of the capillary, reabsorption in the venous end and convective protein transport through nonsieving channels also in the venous capillaries. Parameters used in these two hypothetical transport mechanisms were determined based on statistical fitting of simulation predictions to selected experimental data. This aspect of the work by Bert et al. differed from previous computer modelling efforts [Bert and Pinder, 1982; Wiederhielm, 1979]. The fully determined model was used to simulate steady-state conditions of hypoproteinemia, overhydration and dehydration, as well as the dynamic response to changes in venous pressure and intravascularly administered protein tracers. It was concluded from these studies that the PLM provided a better description of microvascular exchange in comparison to the SM because it yielded a better statistical fit of the available experimental data.  In order to describe the distribution and transport of fluid and albumin in the human circulation, the interstitium and the lymphatics, Chapple [1990] formulated a mathematical  Chapter 3: Computer Modelling of the MVES  40  model to describe the human MVES, continuing the trend set previously by Bert et al. Two transcapillary mass exchange mechanisms, the ‘Coupled Starling Model’ (CSM), in which transcapillary albumin diffusion and convection are coupled, and the heteroporous PLM, 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 determined based on statistical fitting between simulation predictions and experimental data from normal humans and nephrotic patients. Due to the facts that the PLM required more estimated parameters than the CSM, and that fewer of the transport parameters had been measured experimentally, the model employing a Starling-type exchange mechanism was favoured for future studies by the group.  In a continuing study, Xie [1992] used the Coupled Starling Model (CSM) to determine a set of transport parameters to describe the transport mechanisms of the normal human MVES. The transport parameters were determined by fitting model predictions to experimental data from normal humans, nephrotic patients and patients who had sustained heart failure. Data from nephrotic and heart-failure patients were selected due to the fact that the MVES is believed to remain in its normal state, altered only by changes in the Starling forces. The fully described model was successfully used to simulate the transient behaviour of normal humans and patients subjected to saline and albumin solution infusions.  3.3  MODELLING OF MVES FOLLOWING BURN INJURY  Compartmental models have also been developed to study changes in the MVES following burn injury. Arturson et al. [1984] pioneered the description and development of these computer-based patient simulators. Based on the analog model by Wiederhielm [1979], modifications were made which described the changes that occur postburn. The interstitial  Chapter 3: Computer Modelling of the MVES  41  tissue was divided into two compartments. The injured tissue compartment represented only injured skin and the second tissue compartment comprised intact tissue (i.e. both intact skin and muscle). Exchange of fluids and protein between injured and intact tissue was assumed not to take place. In addition, osmotic effects of electrolytes in plasma, the interstitial space and cells were not taken into account. Wound fluid loss consisting of evaporation and exudation were also considered in the model. Data from three patients with thermal injuries were used to evaluate the model. The validity of the model was assessed by running simulation tests using constants and parameters determined from Wiederhielm’s study. Subsequent research efforts [Arturson, 1988; Arturson et al., 1989; Hedlund et al., 1988] involved the development of complex multi-compartmental models made up of modules to describe such systems as hormonal function, renal dynamics and cell volume regulation, all in addition to the MVES. Many unmeasured parameters were required 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 and gastrointestinal tract were incorporated in the model. The model was reported to give reasonable responses to a wide range of burns, body sizes, fluid loss factors and rates of intravenous fluid administration. Due to its comparative simplicity, the model was not realistic enough to provide answers to unsettled questions concerning conflicting treatment methods. Useful additions to improve the predictive capabilities of the model were suggested, such as the inclusion of burn and nonburn interstitial and intracellular spaces along with their electrolyte and albumin contents.  Roa et al. [1986] have also been involved in the development of compartmental burn models. They presented an algorithm for the qualitative and quantitative study of the  Chapter 3: Computer Modelling of the MVES  42  variations in the distribution of extracellular fluids and proteins between the vascular and interstitial spaces in burn patients. Measurements of hematocrit, plasma protein concentration, fluid replacement and diuresis were used in the algorithm. Values for plasma, cellular and blood volumes, plasma proteins, evaporative water losses and net fluid and protein shifts were determined using the algorithm. In order to assess the reliability of the algorithm, their results were compared with the clinical progress of patients. In addition, agreement was obtained with the experimental and clinical results obtained by other authors [Arturson Ct al., 1984]. Roa et al. continued their modelling efforts by developing a non-linear, five-compartment mathematical model [1988]. Control mechanisms were incorporated to describe the interactions between the extra- and intracellular compartments. The different mechanisms that regulate pulmonary capillary dynamics in burn patients were also studied by including the relevant compartments [Roa et al., 1990]. More recently, Roa et al. [1993] have developed a fluid therapy method (BET) designed by computer simulation, using their previous digital simulation techniques. The effectiveness of the BET fluid therapy during the shock phase after burning was investigated and found to show promise.  Extension of the mathematical model developed by Bert et al. [1988] to describe normal microvascular exchange in the rat, enabled them to study microvascular exchange in the rat following a burn injury [Bert et al., 1989; Bowen et al., 19891. The skin compartment in the previous model was subdivided into two compartments: the burned and the nonburned skin. Perturbations characteristic of relatively small (10% burn surface area) and large (40% burn surface area) burn injuries without fluid resuscitation were incorporated into the model. They estimated the changes that occur to transport coefficients and other system parameters subsequent to burns of these sizes by fitting the model predictions to specific experimental data [Lund and Reed, 1986]. A study by Bert et al. [1991] extended this model fhrther to include the effects of different types of fluid  Chapter 3: Computer Modelling of the MVES  43  resuscitation protocols on the circulatory and microvascular exchange systems. They identified the ranges of model parameters that best described the changes in interstitial fluid volume and protein mass in addition to transcapillary protein extravasation for three sets of experiments: no resuscitation, resuscitation with Ringer’s or resuscitation with plasma.  The importance of cellular exchange in the MVES following thermal injury was investigated in a preliminary study [Drysdale, 19881 where the model of fluid resuscitation developed 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 to the existing model. Trends predicted by the model indicated that hypertonic fluid resuscitation in thermally injured rats mobilized cellular water in an attempt to maintain plasma volume.  The above mentioned groups have all made valuable contributions in the area of burn injury computer modelling. The models of Arturson et al. and Roa et al. are relatively complex in that they attempt to model other systems also affected by thermal injury, in addition to the MVES. Their description of the MVES is based primarily on the work of Wiederhielm [1979]. However, current knowledge regarding the MVES has superseded that proposed by Wiederhielm. In addition, various parameters necessary to fully describe their models were taken directly from available literature, with no attempt made to estimate them using patient data. Bert et al., on the other hand, have developed compartmental models, with particular emphasis on the MVES, which plays a critical role in transcapillary exchange following burn injury. Their models, unlike those mentioned previously, use model parameters based on statistical fitting of model predictions to experimental data. In addition, the physiological concepts employed in formulating these models are based on up-to-date knowledge regarding the MVES.  Chapter 3: Computer Modelling of the MVES  44  In this study, a mathematical model to investigate fluid resuscitation in humans following burn injury is developed, based on the simulation work of Xie [1992] who studied the normal human MVES. In contrast to most previous modelling efforts and continuing the trend set by Bert et al, the transport parameters necessary to fI.illy describe the model are determined based on statistical fitting of model predictions to two specific sets of experimental data [Birkeland, 1969; unpublished data from T. Lund]. Current issues and knowledge regarding the human MVES are also incorporated into the model, in an attempt to give a better and more accurate description of fluid and protein distribution in the human MVES following thermal injury.  Chapter 4: Model Formulation  45  CHAPTER 4  MODEL FORMULATION  4.1  INTRODUCTION  Several mechanisms of transcapillary fluid and albumin exchange have been investigated as discussed in Chapter 3. The Coupled Starling Model (CSM) was found to best describe the normal human microvascular exchange system (MVES) [Xie, 19921. The model developed in the current study to describe the human MVES following burn injury is an extension of the compartmental model developed by Xie [1992]. The main assumptions, transport mechanisms as well as systemic fluid and protein inputs and outputs for this extended model are discussed in the first part of this chapter. Normal steady-state conditions existing in the average human provide a basis for describing conditions in the patient at the instant the burn takes place. Following burn injury, fluid and proteins in the system are redistributed in the different compartments. This results in changes to physiological properties dependent on the fluid and protein content in the compartments. Additional relationships to describe the postburn physiological properties and transport coefficients necessary for the model formulation are discussed and developed. Fluid and protein losses from the burn wound by exudation as well as evaporative fluid losses are important issues related to burn injury. These are also discussed and incorporated in the model. Finally, a description of the simulation algorithm is presented.  Chapter 4: Model Formulation  4.2  46  BASIC ASSUMPTIONS  1. It is assumed that the MVES is divided into three well-mixed compartments in which fluid and proteins are homogeneously distributed. Consequently, the properties in each compartment represent average values for that compartment. In contact with the circulating plasma compartment are two tissue compartments: the uninjured and the injured tissue compartments, as shown schematically in Figure 4.1. In previous modelling studies in the rat [Bert et al, 1988; Reed et al., 19891, the uninjured interstitium was divided into two separate compartments, muscle and skin. This separation 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. The separation was also possible because separate experimental response data for muscle and skin was available from rat studies by Reed and Wiig [19811. Due to lack of experimental information on human tissues, it is assumed in this model that the uninjured tissue compartment consists of unburned skin, muscle and other tissues while the injured tissue compartment consists of burned skin. In common with earlier models, it is also assumed that there is no direct exchange of fluid or plasma proteins between the two tissue compartments. Direct exchanges only occur between the circulation and each tissue separately.  2. In order to appreciate the influence of plasma proteins on the regulation of fluid volume, knowledge of the effect of protein concentration on COP in each compartment is necessary. Due to its relative abundance, relatively low molecular weight and high osmotic activity, albumin is the major contributor to the interstitial COP. For these reasons, and because albumin was the only protein whose  47  Chapter 4: Model Formulation  RESUSC  RESUSC  Blood Uninjured Tissue  Lii  Injured Tissue  •  STI 0  EBT Qs ‘EXUcBT  J  Q EXUDBT —  EVAPTI  J Lii  EVARBT QL,T  ‘‘  LET QL,BT  *1*+ JURINE  BLOOD  QBL000  Figure 4.1: Schematic of Compartmental Burn Model  48  Chapter 4: Model Formulation  concentration was monitored in many experiments on rats, albumin was selected as the representative protein in previous modelling efforts in the rat [Bert et al, 1988; Reed et al., 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 well recognized, especially with regard to hypertonic fluid resuscitation [Griswold et al., 1991; Gunn et al., 1989]. In the current model, the effect of isotonic fluid resuscitation on the MVES is studied and as such, the transcellular transport of small ions is assumed to be at steady-state conditions. It is also assumed that the concentration of small ions in the blood, interstitium and lymphatics is constant. The effect of cellular damage resulting from burn injury is not considered in this model.  4. Transcapillary exchange in the human MVES is described by the Coupled Starling Model (CSM) or Patlak Model [Patlak et al., 1963], It is a homoporous model, in which 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 reflection coefficient 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. In addition, the pressure within the capillary is assumed to be uniform and represented by a single hydrostatic pressure term. The fluid and protein transport mechanisms which characterize the CSM are described below.  a) Fluid is transported from capillary to interstitium by filtration, according to Starling’s Hypothesis [Starling, 1896] as kF [P  — —  cY.(HPL  ], —n ) 1  4.1  49  Chapter 4: Model Formulation  where kF is the capillary filtration coefficient, determined as the product of the hydraulic conductivity of the capillary membrane per unit area and the surface area available for fluid exchange, kA, as discussed in Chapter 2.  b) Albumin is transported passively by diffusion and convection from capillary to interstitium through the fluid-carrying channels in the capillary membrane according to CIAv  I  Qs—JFl—orI —  L  where  ClAy  .exp(—Pe)] /  \  1—exp—Pe;  I’  j  is the effective interstitial albumin concentration defined by QI  ClAy =  (v  —)  Q is the albumin content and VIEX the albumin excluded volume,  assumed to represent  25% of the normal interstitial fluid volume [Bert and Pinder, 1982].  c) Under normal conditions, fluid is assumed to flow from the interstitium into the lymphatic system. The fluid is then drained from the lymphatics into the circulation. It is assumed that the lymph flow rate is always positive. Lymph flow relationships have been developed for rats [Bert et al., 1988] and humans [Chapple, 1990] based on the assumption that lymph flow is a linear function of interstitial fluid pressure. A relationship similar to that adopted by Bert et al. [1988] is employed in the current model. The relationship ensures that lymph flow remains at its normal value under normal conditions, varies linearly with interstitial pressure near normal conditions but ceases when the interstitial fluid volume falls to the excluded volume value.  For overhydrated tissue when F , S[P —F] 2 JL=JLNL+L r  L. 13  4.4  50  Chapter 4: Model Formulation  F  during tissue dehydration when P  >  -  1 LL,NL  D  ,w. iL 1  I’  D ,ExJ 1 1  while under conditions where P 4.6 ‘L  represents the lymph flow, LS the lymph flow sensitivity coefficient which expresses  the slope of the relationship,  I,EX  the tissue pressure at the excluded volume, and  subscript NL refers to normal steady-state conditions.  d) Albumin is also exchanged across the lymphatic wall according to QL—JLj.  4.3  4.7  FLUID AND PROTEIN INPUT  Following burn injury, intravenous infusions of clear fluids such as acetated Ringers, normal saline and dextrose are administered in order to replace volume lost from the circulating plasma into the tissue compartments. Colloid-containing fluids are also administered to replace protein loss from the circulating plasma. Based on individual patient responses, the composition, volumes and infusion rate of fluids administered are adjusted accordingly. These inputs to the system are accounted for in the formulation of the model equations.  4.4  FLUID AND PROTEIN OUTPUT  Fluid and proteins are also lost from the system following burn injury. These losses must also be taken into account in developing the mass balances.  51  Chapter 4: Model Formulation  4.4.1  Water Loss by Evaporation  In a normal adult, the water loss through the skin excluding that lost as sweat is about 750 mL/day, as reported by Davies [19821. The destruction of the stratum corneum and lipids in the skin following burn injury allows increased evaporation of water through the burn eschar. Water lost through burned skin via evaporation adds considerably to that normally lost through the lungs [Martyn, 19901. The evaporative water loss from skin following burn injury may be estimated from the following formula reported by Sundell [1971],  where  EV  4.8  =[25+DEGj.TBsA,  ‘EVAP  is the rate of evaporative fluid loss from injured and uninjured tissue, DEG  , 2 the percentage of body surface burned and TBSA the total body surface area in m defined by TBSA  =  4.9  75 •71.84 x 10. 425 •H° W°  In 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 Exudation  Significant volumes of fluid are lost as exudate from the burned surfaces of the body of injured patients [Arturson et al., 1984; Davies, 1982]. Knowledge of the loss of sodium into dressings and soiled bed linen gives an indication of the volume of exudate. Exudation rates of between 400 and 1000 mL/day have been reported [Davies, 1982] for burns of up to 50% of the total body surface area.  In this study, estimates of fluid loss by exudation are made based on fluid balances on individual patients. The fluid balance is performed between successive times when measurements were available, i.e., Change in patient weight  =  Volume of fluids given  -  Volume of fluids lost  Chapter 4: Model Formulation  52  The fluids given include clear fluids (acetated Ringers, normal saline, dextrose) and protein-containing fluids (iso-oncotic and hyperoncotic fluids as well as plasma). The fluids lost include urine, blood loss and evaporative and exudative fluid losses. The fluid loss due to exudation can be estimated from the balance knowing the changes in the other quantities between two successive times. The exudative fluid loss from patients for which weight changes were not monitored is estimated from a linear relationship between average exudate output and the area of burn injury. This relationship is obtained by linear regression of clinical data reported by Davies [19821. The detailed calculations for each patient are presented in Appendices E and G.  4.4.3  Protein Loss via Exudate  Losses of labelled proteins in exudate have been measured by application of absorbent dressings 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. Between 5 and 10 g of albumin/day have been reported to be lost via exudate with burns covering between 25 and 35% of the body surface [Davies, 1962]. In patients with more severe burns, the equivalent of the albumin content of the normal adult plasma volume has been reported to be lost over the first week. Protein losses of at least 2 to 3 g of proteinll% of body 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 following modified relationship proposed by Arturson et al. [1984], QEXUD = FXUD X CBT  where  QD  x EXFAC,  4.10  is the rate of albumin loss via exudate, EXFAC a factor ranging from 0 to 1  and subscript BT represents the injured tissue.  53  Chapter 4: Model Formulation  4.4.4  Blood Loss  Early excision and grafting of the burn wound as soon as the patient is hemodynamically stable, remain the keys to survival for patients with major thermal injuries. Surgical incisions in the form of escaratomies and fasciotomies are necessary to prevent edema from building up sufficient interstitial pressure to impair capillary blood flow, thus causing ischemia. Blood loss occurs as burn tissue is removed. The volume and rate of blood loss depend 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 been encountered [Martyn, 1990].  Data regarding initial volumes of blood lost due to surgical procedures were provided for some of the patients considered in the current study. The blood losses were clinical estimates based on the extent of escaratomies. In addition, 10 mL blood samples were assumed to be taken every 6 hours for laboratory analyses. In order to incorporate these blood losses in the model equations, the losses were assumed to occur over a period of time and expressed as blood loss per hour,  4.5  BLoOD  MODEL EQUATIONS  The 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 —  F,T1  jL,TJ  jEVAP,TI  -  54  Chapter 4: Model Formulation  dQTI’9 S,T1 di  ‘9  41  L,TI  —  Injured Tissue Balances: dVBTJ F,BT di  _1  —  dQBT di  —  “L.BT  -JEVAP,BT -JXUD,BT  414  EXUD,BT  L.BT  S,BT  413  Circulatory Balances: dVPL = RESUSC  —  F,TI  dQPL = QRESUSC  —  +  LTJ  + QLTJ  —  F,BT  —  QSBT  + LBT  —  + QL8T  UNE  —  —  BLOOD  4.15 4.16  QBLOOD  The subscripts TI, BT and PL refer to the uninjured tissue, injured tissue and plasma compartments respectively. In Equations 4.15 and 4.16, J and  Q  are the rates of fluid and  albumin flow respectively, while the subscripts RESUSC, URINE and BLOOD represent the resuscitation fluids, urine and blood respectively.  4.6  PROPERTIES OF THE MICROVASCULAR EXCHANGE SYSTEM  A 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)); and iii) transport coefficients.  Chapter 4: Model Formulation  55  Some of these properties experience changes from their normal values immediately following burn injury. In order to facilitate the quantitative analysis of these changes, the normal steady-state conditions and the initial conditions that prevail in the patient immediately postburn will first be presented.  4.6.1  Normal Steady-State Conditions  In order to establish reasonable values to describe the physiological conditions that exist in the 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 and supine in position. These normal steady-state conditions in a combined tissue compartment and the general circulation are those employed by Xie [1992] and are summarized in Table 4.1.  Table 4.1: Normal Steady-State Conditions in “Reference Man”  Tissue  Circulation  Fluid volume, V, L  8.4  3.2  Excluded volume, V, L  2.1  -  141.1  126.1  16.8  39.4  22.4  -  Hydrostatic pressure, P. mmHg  -0.7  1 1.0  Colloid osmotic pressure, H, mmHg  14.7  25.9  Albumin content,  Q, g  Albumin concentration, c, g/L Available albumin concentration,  CAV,  g/L  Chapter 4: Model Formulation  56  In 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 other properties, the extensive physiological properties are scaled by a weight ratio, WR, where 14’R  =  Weight of Patient Weight “Reference Man”  4 17  Albumin concentration, hydrostatic and colloid osmotic pressures in the interstitial fluid and plasma are intensive properties and therefore are unaffected by changes in patient weight.  4.6.2  Initial Conditions  The initial conditions are the conditions that prevail in the patient immediately prior to injury. Immediately postburn, the tissue compartment is divided into two separate compartments: the injured tissue and the uninjured tissue compartments as shown in Figure 4.1. The uninjured tissue compartment comprises unburned skin, muscle and all other 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 the interstitial fluid distribution in the “reference man” [Chapple, 19901 described in Appendix A.  Let RELSM be the fraction of the total body made up of skin and DEG be the degree of burn. The fraction of tissue burned is VAFBT  =  RELSM x DEG.  4.18  The fraction of tissue that remains uninjured is VAFTI =[RELSM x(—DEG)]+[1--RELSM]=1-VAFBT.  4.19  The extensive properties of the tissue must therefore be modified by the fraction of tissue in each compartment following the injury as follows: Initial value  =  Weight corrected normal value x VAFTI (or VAFBT).  4.20  Chapter 4: Model Formulation  4.6.3  57  Compliance Relationships  Compliance relationships are essential for the determination of the hydrostatic pressure from the fluid volume in the compartments. The hydrostatic pressures in the compartments have important roles in redistributing fluid and albumin following a burn injury.  4.6.3.1 Circulatory Compliance Due to lack of data from humans, the exact circulatory compliance relationship is not as yet established. As a consequence, a linear relationship is assumed between the capillary hydro static pressure and plasma volume, where the rate of the change in plasma volume to the change in capillary hydrostatic pressure is constant, i.e., ] =PCO+PCCO.[VpL—VpLO], where  C,COMP  conditions.  4.21  is the reciprocal of circulatory compliance and subscript 0 refers to initial  C,COMp  has not been measured in humans. An estimate based on scaling up  values reported for the rat [Bert et al., 1989] yields CCOMp  =  0.009659 mmHg/mL.  4.6.3.2 Interstitial Compliance Information concerning the compliance of human tissues is scarce. Based on the studies of Reed and Wiig on rat tissues [1981] and Stranden and Myhre on human lower limb subcutaneous 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], while during conditions of tissue overhydration where V —1.26x10]. 1 F =1.88+1.05x10.[V  4.22 12.6 x io mL, 4.23  In the intermediate range, the compliance relationship is obtained by interpolating experimental P 1 and V 1 data by means of cubic splines.  Chapter 4: Model Fonnulation  58  Following burn injury, the interstitial compliance in uninjured and injured tissue is modified to account for the partition of tissue in each of the compartments.  Uninjured Tissue: During tissue dehydration where V PTI  —0.7  +  1.96154 x VAFTI x WR  .[vTI —(8.4 x  During tissue overhydration where PTI =1.88+  (8.4 x  v  x WI? x VAFTI) mL, x WI? x VAFTI  )].  4.24  (12.6 x 1 o x WI? x VAFTI) mL,  1.05x10 .[V—(126x1Ox’I? xVAFTI)]. VAFTIxWR  4.25  For intermediate values of VTI, the compliance relationship is obtained by cubic spline interpolation of pressure and volume data for normal humans, with the volume data modified by (WR x VAFTI) to account for tissue partition, i.e., =fii[VxWRxVAFTI]. 1 P  4.26  Additional relationships are required for the injured tissue compartment to account for the very negative tissue pressure which has been observed in the burned skin of rats immediately postburn [Lund et al., 1988]. Due to lack of data from humans, pressure data from these experiments on rats are used to describe the change in interstitial pressure with time in the first 2.5 hours postburn. Data from unresuscitated rats is used in the initial period postburn when no form of fluid treatment is given to the patient. Following this initial period up to 2.5 hours postburn when data is available, data from resuscitated rats is used. After 2.5 hours, modified forms of the normal interstitial compliance relationships given above are employed.  Chapter 4: Model Formulation  59  Injured Tissue: During the first 2.5 hours postburn, interstitial fluid pressure in injured skin versus time data from experiments on both unresuscitated and resuscitated rats by Lund et a!. [1988] are interpolated by cubic splines according to the general relation 4.27  PBT=fn(t).  Following this initial 2.5 hour period, the compliance relationships are based on the relationships developed for normal humans, with modifications to account for the injury, i.e., during tissue dehydration where PBT  =  VBT  3 x WR x VAFBT) mL, (8.4 x i0  3 _O.7+1.96154 x i0 .{VBT —(8.4x io x WR xVAFBT)] VAFBT xWR  and during tissue overhydration where VBT PST =L88+  1.05x10 VAFBTxWR  4.28  3 x WR x VAFBT) mL, (12.6 x i0  .{vST —(12.6x1O xWR xVAFBT)1.  4.29  For intermediate values of VBT, the compliance relationship is again determined by passing cubic splines through the interstitial pressure and volume data for normal humans, with the volume data modified by (WR x VAFBT), i.e., 17 =fn[VxWR xVAFBT]. F .  4.6.4  4.30  Colloid Osmotic Pressure (COP) Relationships  Colloid osmotic pressure results because the protein molecules cannot transfer freely through the semi-permeable capillary membrane. The following relationship between plasma albumin concentration and COP was determined by least squares fitting of data from the circulatory compartment of patients with nephrotic syndrome by Chapple [1990J: cPL=1.522x10FlPL.  4.31  This 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 that  60  Chapter 4: Model Formulation  the osmotic pressure exerted by the plasma proteins in plasma is the same as that exerted by proteins in interstitial fluid, similar relationships are applied to the interstitial compartments following burn injury.  Thus, for uninjured tissue, CTIAV  4.32  .HTJ, 3 =1.522x10  and for injured tissue, CBTAV  4.33  .HBT. 3 =1.522x10  The effective albumin concentration is used in Equations 4.32 and 4.33, since albumin is excluded from some of the tissue space.  4.6.5  Transport Coefficients  The transcapillary fluid and protein fluxes depend on the following five transport coefficients: i)  fluid filtration coefficient, kF, reflects the hydraulic conductivity of the capillary membrane;  ii) permeability coefficient, PS, expresses the permeability of the capillary membrane to albumin; iii) albumin reflection coefficient, a, reflects the relative impediment of this membrane to the passage of albumin; iv) lymph flowrate under normal steady-state conditions,  L,NL;  and  v) lymph flow sensitivity, LS, characterizes the efficiency of the lymphatic system in removing accumulated interstitial fluid. Following burn injury, the transient response of these transport coefficients is generally expressed as an exponential function of time postburn. Based on the work of Arturson et al. [19841, Bert et al. [19891 proposed the form:  61  Chapter 4: Model Formulation  IA  A  1  Ii  r’  —,‘tl ,  where kA represents the overall transport coefficient, kNL the normal or preburn value of the time-dependent coefficient per unit area, A the surface area available for exchange, G the perturbation to the transport coefficient immediately postburn and r the relaxation coefficient, 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 after a 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 a conductivity 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 the area available for mass exchange in the tissues. In addition, it is assumed that burn causes a fractional destruction of the capillary beds in the injured tissue, fbrther reducing the area available for mass transport in this tissue. Consequently, in the uninjured tissue which is made up of unburned skin, muscle and other tissues in the body, the overall transport coefficient,  ‘T  becomes  kATJ=k.[FATJxVAFTIxWRj.[1+GTI.ej  4.35  and the overall transport coefficient in the injured tissue, kAnT becomes kABT  kNL[F’ABT  xVAFBTxWR].[l+GBT.ej  4.36  where FAT! is the fractional area available for exchange in the uninjured tissue, which changes with changing plasma volume, and is given by  =  F4 I  VPL/ /VPLQ  -  VFRA C  1-VFRAC  and FABT is the fractional area available for exchange in the injured tissue, given by  4.37  62  Chapter 4: Model Formulation  4.38  •AFRAC.  FABT=  VFRAC is the fractional plasma volume at which perftision in tissues is zero and AFRAC is 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 model predictions to experimental data from rats. They found values that produced good fits were VFRAC  =  0.50 and AFRAC  =  0.50.  These values were also used in the current  study.  The Fluid Filtration Coefficient, kF, depends on the area available for exchange and hence in uninjured tissue becomes kFTJ  ‘F,NL  .[FAfl xVAFTI xwi?j.{1+GkFTJ .e],  4.39  while in injured tissue, kFBT  =  kF  .[FABT xVAFBT xWR].[1+GkF .eJ.  4.40  The Permeability Coefficien4 PS, also depends on the area available for exchange and thus in uninjured tissue is PSTJ  =  1 xVAFTI xWR].{1+Gpj PSNL .[FA  .en1],  4.41  and in injured tissue, PSBT  =  PS .[FABT xVAFBT xWR].[1+GPSBT .e].  4.42  The Albumin Reflection Coefficien4 o, does not depend on the available area for exchange as it indicates the relative impediment to the passage of albumin through the capillary membrane. In addition, the perturbation to a is negative as this coefficient has  63  Chapter 4: Model Formulation  been found to decrease rather than increase following burn injury [Pitt et al., 1987]. Thus, in uninjured tissue, it is assumed that TJ  4.43  =ONL.[1—GUTreI,  while in injured tissue, 4.44  NL[1GU,BTj  T 0 B  The Lymph Flowrate under normal steady-state conditions,  L’  does not depend on the  fractional area available for exchange which changes with plasma volume. It does however, depend on the fractional destruction of the capillary beds in the injured tissue. Thus, in uninjured tissue, L,NL  JL.NL,TJ  L.,NL,TI  .[vAFTI  is given by  xWRj.[1+GJLTI .e],  4.45  while for injured tissue, = L,NL  The Lymph Flow  .{AFRAC xVAFBT xWR].[1+GJLBT .e].  Sensitivity Coefficient  4.46  LS, also depends only on the fractional  destruction of the capillary beds in the injured tissue. Consequently, in uninjured tissue, LSJisgivenby LSTJ  =  LS .[VAFTI x WR}.[1+GLSTJ .e],  4.47  while for injured tissue, LSBT  =  LSNL  .[AFRAC  x  VAFBT x WRJ.[1 + GLSBT .e}  4.48  The normal values for these transport coefficients have been determined for the ‘reference man’ by Xie [1992] (see Appendix B.1). The capillary membrane parameters that determine the exchange of albumin are kF, c and PS. These individual transport coefficients are not independent, but are linked to each other via changes in the capillary pore radius. Thus, once the perturbation to kF is known for the injured and uninjured  64  Chapter 4: Model Formulation  tissue, the perturbations to a and PS for both tissues may be estimated based on these interrelationships (see Appendix B.2). Current knowledge regarding changes in the lymphatic system following thermal injury is very limited. Consequently, the perturbations to  LNL  4.7  and LS in the injured and uninjured tissue postburn are assumed to be zero.  NUMERICAL SOLUTION OF MODEL EQUATIONS  For given patient data (degree of burn, weight and height of patient) and resuscitation protocol (fluid and protein input), simulation of the MVES following injury involves  solving the six first-order ordinary differential equations (Equations 4.11  -  4.16), arising  from the fluid and albumin balances. These differential equations must be solved simultaneously with the relationships defining interstitial and plasma hydrostatic and colloid osmotic pressures as well as the other auxiliary equations. Due to the nonlinearity of some of these relationships, the differential equations cannot be solved analytically. Consequently, the classic fourth-order Runge-Kutta numerical integration method is used to solve the equations, with a global accuracy of 0.00 1 mL and 0.00 1 mg for fluid and albumin contents respectively. The computer program is documented in Appendix K  65  Chapter 5: Parameter Estimation  CHAPTER 5  PARAMETER ESTIMATION  5A  iNTRODUCTION  The model equations developed in Chapter 4 contain unknown parameters which need to be determined in order to simulate the behaviour of the microvascular exchange system following a burn injury. In the first part of this chapter, the parameters to be determined are presented. This is followed by a description of the clinical data used for the identification of the parameters and the validation of the model. Finally, the optimization procedure is discussed.  5.2  PARAMETERS TO BE DETERMINED  The transcapillary fluid and protein fluxes depend on five transport coefficients: the fluid filtration coefficient, kF, permeability coefficient, PS, albumin reflection coefficient, a, lymph flowrate under normal steady-state conditions,  LNL 3  and lymph flow sensitivity  coefficient, LS. The transient response of these transport coefficients to burn injury is expressed as an exponential function of time postburn as described in Chapter 4. In general, the time-dependent transport coefficients have the form: kA=k.A.[1+G.ej.  4.34  The unknown parameters identified from the above relationship include the perturbations to the transport coefficients in both the injured and uninjured tissues and the relaxation coefficient as follows:  66  Chapter 5: Parameter Estimation  i)  perturbation to the fluid filtration coefficient: GTI, GBT (in Equations 4.39 and 4.40);  ii) perturbation to the permeability coefficient: GPSTI,  GPSBT  (in Equations 4.41  and 4.42); iii) perturbation to the albumin reflection coefficient: Ga,Tj, Ga,BT (in Equations 4.43 and 4.44); iv) perturbation to the lymph flowrate:  GNLTf, GNLBT  (in Equations 4.45 and  4.46); v) perturbation to the lymph flow sensitivity: GTI, GBT (in Equations 4.47 and 4.48); and the vi) relaxation coefficient: r.  The factor, EXFAC, in Equation 4.10 describing the protein loss via exudate was estimated by Arturson et al. [19841 to be one fourth of the proteins originally associated with the exuded fluid. Fluid loss due to exudation has been reported by Davies [1982] to account for 5 to 10 g of albumin per day when the burn covers between 25 and 35% of the body surface. Protein losses in exudate from the burn wound are therefore significant and contribute to a decrease in albumin concentration observed during the early phase postburn. 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 relationships reported by Reed et al. [1991], the perturbations to the albumin reflection coefficient and permeability coefficient in injured and uninjured tissues can be determined from the values of the perturbations to the filtration coefficient in both tissues, GkFTJ and  F,BT• 0 k  The  67  Chapter 5: Parameter Estimation  mathematical manipulations are presented in Appendix B.2.  GLNLTJ, GNLBT, GTI  and  are assumed to be equal to zero due to the lack of information concerning changes to the lymphatics following injury. In the final analysis, only four parameters remained to be determined, namely GTJ, GB r and EXFAC.  5.3  CLINICAL DATA  The most common measurements made to monitor burn patient conditions include venous hematocrit and plasma protein or albumin concentration. The response of the patient to fluid replacement is also monitored through the hourly production of urine, vital signs, plasma electrolyte concentrations such as sodium, potassium or chloride ions, and the value of hematocrit. Other measurements including central venous and arterial pressures are also made when the state of the patient requires it. Four different sets of clinical data were used in this study for parameter estimation or model validation. These are presented below.  5.3.1  National Burn Centre (NBC) Data  Dr. T. Lund and his colleagues working at the National Burn Centre in Norway, kindly provided specific information for five patients admitted to the Burn Centre, who had suffered deep cutaneous burns. This patient information was unique in that, in addition to the most commonly made measurements mentioned in the previous section, they also measured the transcapillary colloid osmotic pressures (COPs) in injured and non-injured skin of these seriously burned patients. The raw data were manipulated to convert them into a form that could be used in this study. The manipulations included the determination of plasma volume from hematocrit and the estimation of exudative fluid loss from the burn wound by fluid balances. These are detailed in Appendices D and E respectively. The final form of the patient data and the individual resuscitation protocols are also presented in  Chapter 5: Parameter Estimation  68  Appendix C. This patient information was used directly in the parameter estimation procedure.  5.3.2. Birkeland Data  Dr. 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 were grouped according to the percentage burn surface area sustained and were observed prior to start of replacement therapy. Data of direct interest in the current study were the plasma volume changes in five groups of burn patients as presented in Appendix F. These data were especially useful for investigating the response of the microvascular exchange system 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 kidneys shut down in the initial period postinjury. In addition, due to the unavailability of specific admission information concerning the weight and height of the patients studied, standard weights and heights of 70-kg and 170-cm respectively were assumed. The normal steadystate conditions in each of the patients were also assumed to be those in the reference man which are presented in Table 4.1. Exudative fluid losses were estimated based on data available from a study by Davies [1982]. The rate of exudative fluid loss from patients with different burn areas was monitored during the initial period postburn before fluid therapy was initiated. To the best of the author’s knowledge, these were the only suitable data that could be used to estimate the initial exudative fluid loss from the patients studied by Birkeland. The details of this estimation are presented in Appendix G.  Chapter 5: Parameter Estimation  69  5.3.3. Arturson Data  Published information by Dr. Arturson and his colleagues in Sweden [1989] concerning the treatment of a patient with thermal injury was used to validate the predictions of the model developed in this study. The monitored physiological variable of direct application to the current study was the erythrocyte volume fraction or hematocrit. The patient data and the fluid resuscitation protocol are presented in Appendix H. Based on the fluid therapy, cumulative urine production and change in body mass information, it was possible to estimate exudative fluid loss by fluid balances as described in Appendix E.  5.3.4. Roa Data Dr. Roa and her colleagues in Spain have also been actively involved in the development of mathematical models to investigate microvascular exchange in burn patients. The treatment of two burn patients and clinical data collected from these patients were presented in a publication by this group [1990]. This information, together with information provided by Dr. Roa through personal communications were also used to independently validate the predictions of the model developed in this study. The relevant information including the resuscitation protocol, urine volume, hematocrit and plasma protein concentration is presented in Appendix I.  5.3.5. Normalization of Data  The four different data sets described previously consist of one or more of the following quantities: plasma volume,  VPL,  albumin concentration in plasma,  pressures (COPs) in plasma, injured and uninjured tissues,  CPL  PL’ 11 11 BT  and colloid osmotic  and  T1  respectively.  In order to make these quantities comparable so that they could be used collectively in the parameter estimation procedure, it was first necessary to normalize them. The plasma volumes and albumin concentrations were normalized with respect to their preburn values  70  Chapter 5: Parameter Estimation  based on normal steady-state values for the reference man, scaled to account for differing preburn weights where appropriate, i.e., X=--  xo,  5.1  where X refers to the measured physiological quantity and subscripts 0 and t refer to the preburn and postburn times, respectively.  The availability of COP data made it possible to investigate the distribution of protein in plasma and the injured and uninjured tissue compartments. However, there appears to have been a systematic error in the COP measurements made by Lund et al. The measured values were lower than what were generally expected. In order to use these data, the injured and uninjured tissue COPs were normalized with respect to the plasma COP to nullify the effect of the systematic errors in the measurements, i.e.,  =  /flp fl/  52  /PL,o  5.4  PARAMETER ESTIMATION PROCEDURE  The proposed method to determine the identified model parameters was based on the fitting of predicted results from the model to clinical data. The adopted procedure entailed finding the parameters which gave the best statistical fit between the model predictions and the clinical data based on the weighted least-squares criterion. The optimum parameters were those which would minimize an objective function, OBJFUN, which is the sum of the squares of the deviations of the normalized clinical data from the predicted values, i.e.,  71  Chapter 5: Parameter Estimation  w (x.  OBJFUN =  -  XpD  i=I j=1  where N represents the number of data points for the ith variable, M the number of ,, the predicted value X , variables monitored, X, the experimental or clinical value, 1 from the simulation and WF is the weight for each data point.  In order to indicate the significance or relative importance attached to each data point within a data set, each point was assigned a weighting factor, WF. Normally, WF is set equal to the inverse of the error in measurement (or the standard deviation squared) of each data point. Due to the unavailability of information concerning the experimental errors involved in the clinical measurements, it was not possible to assign weighting factors to the data in this manner. As a result, each data point was weighted equally by assigning a weight of unity to each point.  A standard constrained optimization technique was selected to estimate the unknown parameters by finding the minimum of the nonlinear objective function, subject to constraints, if any. This technique is a slightly modified version of K. Schittkowski’s implementation of the recursive quadratic approximation method of Wilson, Han and Powell [1981].  5.4.1  Preliminary Tests  The model was tested by performing a simulation with assumed, but physiologically reasonable values of the four parameters, GTI, GBT, r and EXFAC. Predictions of the response 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 to the fluid resuscitation protocol presented in Table C.2. The trends predicted by the model  72  Chapter 5: Parameter Estimation  1.1•1’I•I’I’  —VTI VGT VPL  16000 14000  -J C)  4:::::  C 0 I  C  w  C) C 0  8000  >  C) C  6000  E .0  4000 2000 0  PBT PPL  15  0)  10  I  E E  0)  I  E 5 E U) U)  U)  I  1*—  -5  U) C’,  U)  I—  C-)  0  0  C)  E C’, 0  -10 U)  0 0 >  0  I  () -20 -25 0  10  20  30  40  50  Time, hours postburn  60  70  0  10  20  30  40  50  60  Time, hours postburn  Figure 5.1: Simulation of MVES for NBC Patient I GKFTI=0.5; GKFBTI 0.0; r0.025 Ih; EXFAC= 1.00  70  Chapter 5: Parameter Estimation  73  were in agreement with trends observed clinically. Following burn injury, fluid is lost from the 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 of fluid and protein are transferred to the injured tissue from the circulating plasma. This results in edema formation as well as a considerable increase in the albumin content in the injured tissue compartment. The circulating plasma experiences a loss in fluid volume and protein content due to the increased rate of transfer into the injured tissue. The uninjured tissue compartment experiences a loss in fluid volume, resulting in an increase in albumin concentration. Fluid resuscitation is started one hour after injury and soon afterwards, the decrease in plasma volume is reversed, increasing towards its normal volume of about 4023 mL. The injured tissue however, continues to increase in its fluid volume but starts to resolve after about 1.5 days. The uninjured tissue responds to the fluid therapy almost immediately and becomes swollen, but to a lesser extent than the injured tissue. After 1.5 days, the uninjured tissue volume starts decreasing towards its normal volume of about 630 mL. The albumin concentration in plasma continues to decrease during the first day following fluid resuscitation but then starts to increase in the second day. A detailed discussion of these trends will be presented in Chapter 6. These initial results confirmed the adequacy of the model to describe the phenomena which occur in the MVES following burn injury. A steady-state simulation was also performed by solving the model equations over a long period of 480 hours (20 days). The results are shown in Figure 5.2. The most important observation was the ability of the model to predict the return of the system variables to their normal values after a long period. The model was also able to predict the equalization of the opposing fluid and protein fluxes in the injured and non-injured tissues in the steady state. This further confirmed the ability of the model to correctly predict the response of the microvascular exchange system to burn injury. As such, the model could be confidently used in the parameter estimation algorithm.  Chapter 5: Parameter Estimation  74  55  ‘I  CTJ CBT CPL  50 -J  )45  c o 40  -J  E  35  E 30  0  0  >  0 25  U-  20 < 15  25 20  C)  34  PTI PBT PPL  E 30 E 28  E  E  10  U) U)  Q  ci_  -5  22 C.)  C)  20 18  • -10  16  (0  -15 o I— >  —PITI P1ST PIPL’  )32  C  14  -20  12  -25  0 10  0  I  1200  —QSTI QSBT QLTI QLBT  35000 1000 30000  800  -  ——  .c  25000  600  9  E 400  20000 U-  200  .9 15000  2 10000 -200 5000  -400 -600  0  50  100 150 200 250 300 350 400 450  Time, hours postburn  0 0  50  100 150 200 250 300 350 400 450  Time, hours postburn  Figure 5.2: Steady-State Simulation of MVES for NBC Patient I GKFTI=O.5; GKFBTIO.O, rO.O25 /h; EXFAC=1.OO  Chapter 5: Parameter Estimation  75  The optimization technique was also tested in two ways. Plasma volume and albumin concentration as well as plasma, injured and uninjured tissue COP data were generated by simulating 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 the model parameters which were assumed unknown. The optimization technique required that initial values for the parameters be provided from which the search for the optimum values could begin. The optimizer successfiully identified the parameter values used to generate the “error-free” data set, irrespective of the initial values provided to initiate the search. For example, the “error-free” data set was generated using the following parameter values: GTI  =  0.50; GkFBT  =  10.0; r  0.025 h’ and EXFAC  =  1.00. These data were  then used in the optimization program to obtain “best-fit” values for  GTI  and  GBT  starting with initial estimates of 1.0 and 15.0 respectively. Optimum values and confidence intervals estimated for  G,TI  and GkFBT were 0.37±0.30 and 11.2±2.3 respectively. The  expected good fits between the clinical data and the model predicted responses are illustrated in Figure 5.3. The optimization procedure was then repeated using perturbed data values obtained by generating random errors on the “error-free” data. The optimizer identified the following optimum parameter values and confidence intervals: 0.70±0.31 and GkFBT  =  0 T I  =  11.5±3.2. The clinical data and the model predicted responses are  shown in Figure 5.4. It was observed however, that using the “noisy” data, as the number of parameters to be determined increased to include r and EXFAC, the optimizer was unable to identifS’ the expected optimum values.  Following on from these tests, the optimization technique was next used to determine parameter values based on the clinical data obtained from the NBC patients. Different initial estimates were provided to the program from which the search for the optimum values could begin. The optimizer was unsuccessful in determining global optimum values for all the parameters. Different “optimum” values were obtained from the routine  Chapter 5: Parameter Estimation  76  4200 4000 -J  3800 3600 3400 LL  3200 3000  -J D)  40  0 4-  4-  c  U) C.)  0  (-) . 25 E 20  0  3.5 U) :3  ‘  I  ‘  I  I••  •  •  I  •  I  ‘  3.0  ——  U) U)  a) 0... C)  I ‘ I —PITIR PIBTR — • PITIRexp • PIBTRex  2.0 a  —  1.5  o  1.0  •0  o  0.5  0  o 0.0  •  0  I  10  •  I  20  •  I  30  •  I  40  •  50  I  60  •  I  70  Time, hours postburn  Figure 5.3: Model Predicted Response of MVES and “Error-free” Data for NBC Patient 1  Chapter 5: Parameter Estimation  8000  —J  E  i  77  i  ‘  i  ‘  i  ‘  i  ‘  ‘  i  i  ‘  6000  4000 2000 U ••  I  ••  0  i  I  I  i  ‘  i  I  i  i  i  ‘  I  I  i  60 50  -  •: .  10  0  35  I  I  I  I  0  •  2.5  —  \  • .  -  ——  0 2.0 •0  I  —PITIR PIBTR PITIRexp PIBTRex •  -  u  I  •  •  I  -  0.5 0.0  0  10  I  I  20  30  •  I  •  40  I  I  50  60  i  I  70  Time, hours postburn  Figure 5.4: Model Predicted Response of MVES and “Noisy Data for NBC Patient I  Chapter 5: Parameter Estimation  78  depending on the initial values specified. Ideally, the initial values should be as close to the global optimum values as possible to reduce the chances of encountering local optima and of false convergence. The results therefore suggested that the “multi-dimensional surface” of the objective function had several saddle-points or shallow depressions. The nature of this 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; and iv) re-assess the parameters to be determined by the statistical procedure.  5.4.2  Constraints  Simulation predictions based on parameters determined from the preliminary studies using the real patient data indicated that certain trends predicted were either not physiologically feasible or were not consistent with clinical observations. Consequently, constraints were imposed such that: i)  GBT is always greater than GTT due to the fact that following injury, it is observed that the injured tissue undergoes relatively larger changes than the uninjured tissue; and  ii) the injured tissue volume at any time postburn, VBT, is always greater than its initial volume, VBTO. This ensures that the injured tissue compartment is not dehydrated at any time postburn, in accordance with clinical observations.  Chapter 5: Parameter Estimation  79  a)  :3 Cu  > 0 C :3 LI > G) -D  0  100  1oo  Figure 5.5: Objective Function Surface for NBC Patient 1 GKFTIO. 5; GKFB T= 10.0; r=O. 025 /7?; EXFAC= 1.0 (The shallow depressions represent local minima)  Chapter 5: Parameter Estimation  5.4.3  80  Modified Optimization Strategy  5.4.3.1 Re-assessment of Parameters to be Determined Analysis of the clinical data used in the optimization procedure revealed that the quality and in particular, the quantity of the data did not justif,’ estimating all four parameters, GTJ, GkFBT, r  and  GBT  and EXFAC by statistical fitting. Consequently, it was proposed that  GTI  be determined by the fitting procedure, while r and EXFAC were investigated  only at discrete values.  Relaxation Coefficient r. Information concerning the time it takes for the transport coefficients 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 values after about 12 hours. Due to the larger body size of humans as compared to rats, a longer response time would be anticipated. Arturson et al. [1984] assumed that normal plasma leakage 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 normal value in between 48 and 72 hours postinjury. In the current study, two values of r were considered, 0.025 h’ and 0.008 h’, suggesting that the transport coefficients return to 95% of their normal values in 5 and 15 days respectively.  Exudation Factor, EXFAC. The exudation factor, which is the fraction of protein in the injured tissue interstitial fluid which is lost with the exudate, must range from 0 to 1. In determining the optimum value, four values of EXFAC were considered: 0.25, 0.50, 0.75 and 1.00.  With these redefined search levels for r and EXFAC, the strategy of the parameter estimation procedure was to determine the pair of values of GkFTI and GkFBT which gave  Chapter 5: Parameter Estimation  81  the minimum objective function for each of the eight possible combinations of r and EXFAC in the experimental design shown in Table 5.1. The optimum GkFTI and GBT for a given patient were then determined as the pair which yielded the minimum objective function amongst the eight combinations of r and EXFAC.  5.4.3.2 Optimization Scheme: “Gridding Approach” It was also evident from the initial tests that the quality and quantity of clinical data available did not warrant a formal optimization technique. As such, an approach was devised to ensure that global optima as opposed to local optima, were obtained. This approach was based on a “surface gridding” technique described below.  Table 5.1: Factorial Experiment Study  EXFAC r  0.25  0.50  0.75  1.00  0.008  *  *  *  *  0.025  *  *  *  *  The major steps in the search method were as follows: i)  Select wide ranges for GkF,TJ and GkFBT which are physiologically acceptable and 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 coarse grid: step sizes of 1.0 and 10.0 for GkFTt and GBT respectively.  Chapter 5: Parameter Estimation  82  iii) Determine the objective function for all the nodes (GTI, GBT) in the grid, which satisfy the conditions that GkFTI < GkFBT and VBT> VBTO. This resulted in a surface with several depressions or minima. iv) Select a narrower range of values for GTI and GBT which contains the  shallowest depression. v) Construct a finer grid by subdividing the narrow ranges with smaller step sizes. vi) For all the grid nodes which satisfy the constraints GTJ  <  kF,BT 0  and VBT>  VBTO, calculate the objective function values. This resulted in a surface with a single depression. vii) The pair of values of  and G,BT corresponding to the shallowest point is  considered the optimum.  Using this successive gridding process, a well defined single depression was obtained in all the cases considered in the current study. For each burn patient or group, the search scheme was applied to each of the eight combinations of r and EXFAC in the factorial design shown in Table 5.1. The optimum values for a given patient or group were considered to be those corresponding to the minimum objective function for values amongst the eight cases.  5.5  SUMMARY  In summary, a simple but reliable method was developed to determine the model parameters, The method ensured that the selection of the optimum parameters was based on the global minima as opposed to local minima. The model parameters determined using this method and the model validation are discussed in Chapter 6.  83  Chapter 6: Results and Discussion  CHAPTER 6  RESULTS AND DISCUSSION  6.1  INTRODUCTION  Simulation of the response of the human microvascular exchange system (MVES) to fluid resuscitation following thermal injury is only feasible if all the model parameters are known. Based on the procedure discussed in Chapter 5, it was possible to determine the model parameters required to fhlly describe the model. The parameters obtained using the National Burn Centre (NBC) and Birkeland data sets independently are first presented followed by a discussion of the global parameters obtained using a combination of the two data sets. A description of sensitivity tests conducted to investigate the influence of these global 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 other independent studies is examined. As this latter patient information was not used in the parameter estimation procedure, this constitutes independent validation of the model. Finally, the model is used to predict patient response to three commonly used resuscitation formulae.  6.2  ESTIMATED PARAMETERS  6.2.1  Parameters Determined Using NBC Data  The objective fi.inction value (OBJFUN) described in Chapter 5 was estimated using plasma volume, albumin concentration and colloid osmotic pressure data from five patients receiving various forms of fluid therapy. For each patient, the values of GTJ and  84  Chapter 6: Results and Discussion  GBT which gave the minimum objective function value for all eight combinations of r and EXFAC were determined. The results are presented in Appendix J. The four parameters, GkFTI,  GBT,  r and EXFAC, which gave the minimum objective function  value were considered the optimum for each patient. These patient results are presented in Table 6.1.  Table 6.1: Optimum Parameters Determined Using NBC Data  EXFAC  OBIFUN  NEXP  0.025  1.0  0.48  12  4.0  0.025  1.0  1.63  20  0.0  6.0  0.025  1.0  3.65  22  59  1.0  5.0  0.025  1.0  2.83  21  72  0.5  5.0  0.025  0.75  3.75  30  Patient  Degree, %  GkF,1  GkPRT  1  21  0.0  8.0  2  51  0.5  3  80  4 5  r,  1 h  Clinical observations [Arturson, 1961; Lund et al., 19921 indicate that burns which exceed 25% of the total body surface area initiate both systemic and localized changes which differ from burns Less than 25%. Burns less than 25% of the total body surface area generally cause smaller changes in the uninjured tissue as compared to burns exceeding 25%. Generalized edema has been observed [Arturson, 19611 when the extent of the burned tissue is greater than 25% of the total body surface area. Consequently, the five NBC patients were separated into two groups: less than 25% and greater than 25% of the total body surface area. Patient 1  was  the only patient with a less than 25% burn. The  remaining four patients sustained burns greater than 25%. The combination of the four parameters which gave the minimum objective function was then determined for each of the two groups. This was based on the sum of the objective function values for the  85  Chapter 6: Results and Discussion  individual patients in a particular group for the same values of the four parameters. The results are shown in Table 6.2.  Table 6.2: Optimum Parameters for Two Burn Groups Using NBC Data  Burn Group, %  GkFTI  GkERT  r, h-’  EXFAC  OBJFUN  NEXP  0 25  0.0  8.0  0.025  1.0  0.48  12  0.5  5.0  0.025  1.0  12.47  93  -  25  100  -  Parameters Determined Using Birkeland Data  6.2.2  The burn patients studied by Birkeland were grouped according to the percentage burn surface area and monitored prior to the start of fluid replacement therapy. The objective fbnction values for each burn group were based on plasma volume data only. The values of GTJ and GBT which yielded the minimum objective fhnction value for all eight combinations of r and EXFAC for each burn group are detailed in Appendix J. The four parameters which gave the minimum objective function value for each of the five groups of patients are presented in Table 6.3.  Table 6.3: Optimum Parameters Determined Using Birkeland Data  Burn Group  Degree, %  GkFTT  GkF nr  1 r, fr  EXFAC  OBJFUN  NEXP  I  2-9  0.6  3.0  0.008  0.25  2.01x10  6  II  10- 19  1.1  8.0  0.025  1.00  0.86x10-3  6  III  20 30  3.4  8.0  0.008  0.25  7.73x10-3  5  IV  39-49  5.8  6.0  0.008  0.25  5.68x10-3  4  V  54-90  5.8  6.0  0.008  0.25  4.09x10-2  4  -  86  Chapter 6: Results and Discussion  The five groups were then separated into two large groups of burns less than 25% and burns greater than 25%, as for the NBC data set. Patients in burn groups I and II sustained burns less than 25% while patients in groups II, IV and V suffered burns greater than 25%. The parameters giving the minimum objective function for each of these two groups  are presented in Table 6.4.  Table 6.4: Optimum Parameters for Two Burn Groups Using Birkeland Data  Burn Group, %  GkF,1  GkFRT  0 25  0.5  12.0  3.8  8.0  -  25  6.2.3  -  100  EXFAC  OBJFUN  NEXP  0.008  0.25  9.02x10-3  12  0.008  0.25  6.56x 10-2  13  r,  h’  Parameters Determined Using Combination of NBC and Birkeland Data  The NBC and Birkeland data sets were combined to determine global parameters which would be representative for any patient in the two burn groups, less than and greater than 25%. The procedure was based on the sum of the objective function values of the same combinations of G 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 from those based on the NBC data because of differences in the quantity and type of data used in their estimation. The objective function values determined using the NBC patient data were about two orders of magnitude higher than those obtained using Birkeland’s data because a greater amount and different types of patient data were available. Thus, optimization based on the direct summation of objective function values from the two individual data sets would be erroneous. The higher values from the NBC data would dominate the overall objective function value and thus mask any meaningful contribution  Chapter 6: Results and Discussion  87  from Birkeland’s data. As such, a scaling factor was applied to the objective fUnction values from Birkeland’s burn groups before combining the two independent data sets. It was necessary to find a suitable factor that would give equal weighting to the two data sets. The results obtained using three different scaling factors, 30, 100 and 200, are presented 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  OBJFUN  30  0.5  10.0  0.025  1.0  1.19  100  0.5  12.0  0.025  1.0  2.00  200  0.5  13.0  0.025  1.0  3.08  Table 6.6: Optimum Parameter Values for Burns Greater Than 25%  Factor  GkFTT  GkFRT  r, h’  EXFAC  OBJFUN  30  1.0  8.0  0.025  0.75  26.26  100  2.0  9.0  0.025  0.75  37.01  200  2.5  9.0  0.025  0.75  46.64  Using a scaling factor of 100, the magnitude of the objective function values determined using Birkeland’s patient data were comparable with the values determined using the NBC patient data. In other words, direct summation of the objective function values from both data sets resulted in an approximately equal contribution to the overall objective function value for burns less than and greater than 25% of the total body surface area. The NBC patient data had a larger influence on the overall objective function value with a factor of  88  Chapter 6: Results and Discussion  30, while Birkeland’s patient data were more influential with a factor of 200. The results obtained 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 the case of patients from burn groups I, II and III and 4 hours postburn from burn groups IV and V. On the other hand, data from the NBC patients were available for up to 72 hours postburn during which fluid therapy was administered. Using the two data sets independently gave different results with regards to the relaxation coefficient, r and the exudation factor, EXFAC. The relaxation coefficient represents the time it takes for the transport coefficients to return to their normal values. Two discrete values were investigated in the current study, 0.025 h’ and 0.008 h’, suggesting that the transport coefficients return to 95% of their normal values in 5 and 15 days respectively. With the 1 for r was obtained while Birkeland’s patient data NBC patient data, a value of 0.025 fr resulted in a value of 0.008 h-’. EXFAC values of 1.00 and 0.25 were obtained for the two data sets respectively. The NBC patient data, which spanned 3 days, had a larger influence on 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 transport coefficients to burn injury and protein loss from the burn wound via exudate could be inferred. 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 Parameters  1 and GaBT can As discussed in Chapter 5, the other model parameters GPSTI, GPSBT, G be determined from the values of  GkF,TI  and GBT. A summary of optimum model  parameters found in this study is presented in Table 6.7.  89  Chapter 6: Results and Discussion  Table 6.7: Coupled Starling Model Parameters  Burns less than 25% Uninjured  Injured Tissue  Burns greater than 25%  Uninjured  Injured Tissue  Tissue  Tissue GfrF  0.5  12.0  2.0  9.0  5 G  6.3  45.9  18.5  41.7  Ga  0.1  0.8  0.3  0.7  0.0  0.0  0.0  0.0  1 G  0.0  0.0  0.0  0.0  r, h-’  0.025  0.025  0.025  0.025  1.00  -  0.75  1 G 1  NI  EXFAC  -  The results obtained indicate that following burn injury, the injured tissue generally undergoes a much greater change than the uninjured tissue. Immediately following burns less than 25%, the filtration coefficient in uninjured tissue increases to 1.5 times its normal value while the injured tissue experiences a greater change by a factor of 13. Burns in excess of 25% cause more pronounced changes in the uninjured tissue as compared to those experienced following smaller burns where the uninjured tissue filtration coefficient increases to 3 times its normal value. The injured tissue coefficients on the other hand, experience changes similar to those experienced following smaller burns. The filtration coefficient increases to 10 times its normal value immediately postburn. Perturbations to the normal lymph fiowrate and lymph flow sensitivity coefficient were set to zero in both tissues and for both degrees of burn due to lack of pertinent information.  Chapter 6: Results and Discussion  90  As discussed previously, due to the fact that data from the NBC patients were available for a longer period postburn as compared to data from Birkeland’s patients, the contribution of the latter data set to the global value of r was minimal. Using the NBC patient data independently, a value 0.025 h’ was obtained for r while Birkeland’s patient . A global value of 0.025 h’ was obtained when the 1 data resulted in a value of 0.008 h two sets were combined for both burn groups, less than and greater than 25%. This suggests that irrespective of the size of the burn injury, the tissue transport properties return to 95% of their normal values in about 5 days. As was the case with the relaxation coefficient, the global value of the exudation factor, EXFAC, was more strongly influenced by the NBC data set. The rate of exudative protein loss from the injured tissue following 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 directly compare these estimated parameters. However, best fit perturbed parameter values have been 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 tissue was found to decrease to 50% of the normal value at time zero, decaying with a time constant of 0.231 h’ following a 10% surface area injury. Following burns of 40% surface area, the filtration coefficient in the injured skin was found to be reduced to 5% of the normal value and return to normal after about 12 hours as for the smaller burn. Studies of fluid resuscitated rats resulted in a perturbation in the fluid filtration coefficient in the injured tissue of the order of a factor of 10 in the best-fit region. No changes in filtration in intact tissue were required to obtain a good fit of the data, therefore the perturbation was considered to be zero.  Based on the results obtained from the rat studies, the parameters obtained in the current study are encouraging. However, the only way of validating these model parameters is to  Chapter 6: Results and Discussion  91  investigate how well the model predicts the response of burn patients to fluid resuscitation using the parameters determined. The influence of the individual parameters on the predictability of the model is discussed in the next section.  6.3  SENSITIVITY ANALYSES  The method employed in determining the model parameters made it impossible to give an accurate estimate of the confidence intervals for the parameters. Therefore, sensitivity analyses were performed to investigate the influence of the model parameters on the objective function values. In order to assess the effect of one of the four parameters on the objective function value, the other three were maintained at their optimum values, while the parameter being investigated was varied on either side of its optimum and the corresponding objective function value determined.  6.3.1  Sensitivity Analysis of GTI  For burns less than 25%, varying GTI from 0 to 1.4 reveals a deep and almost symmetrical distribution of the objective function values about the minimum as shown in Figure 6.1. A 25% change in GkFTJ from its optimum value of 0.5 yields a 27% change in the objective function value. Consequently, the model predictions would be very sensitive to changes in the value of G TI•  For values of GTJ in the range selected, which satisfy the constraint that VBT> VBTO, the sensitivity curve for burns greater than 25%, given in Figure 6.2, shows an asymmetric distribution about the optimum value of 2.0. For values of GTI less than 1.0, the objective function value changes by about 14 per unit change in GTI. For values between 1.0 and 1.5, the objective function value changes by about 7 per unit change in GTI. This suggests that values of GkF,TI less than 1.5 will greatly influence the model predictions. On  Chapter 6: Results and Discussion  92  12  I’.)  10  10  ‘1)  8  (U  > C 0  0 C  6  LI  a)  >  C-)  4  0 2  0  I  I  •  6  GKFTI 12  I  •  8  10  12  14  16  GKFBT  12  -—  10  10  8  8  6  6  4  4  2  2  a, (‘3  > C 0 C-)  z a)  U>  0  a) -o  0  0.005  0.010  0.015  r  0.020  0.025  0  I  0.2  •  •  0.4  •  0.6  I  •  0.8  EXFAC  Figure 6.1: Sensitivity Plots for Burns Less Than 25%  1.0  Chapter 6: Results and Discussion  93  55  >  50  0 (.5 :5 U-  a) > 13  45  ci)  0 40  1.0  0.5  2.5  2.0  1.5  35  8  6  10  GKFTI  60  I  —-  I  •  12  14  16  18  20  2  GKFBT  I  60  •  55  55  > 50  50  a) Cu  0 C) C I1  45  45  40  40  C-) a) -Q  0  35 0.005  39  —  0.010  0.020  0.015  r  0.025  I  0.2  •  I  0.4  I  0.6  0.8  1.0  EXFAC  Figure 6.2: Sensitivity Plots for Burns Greater Than 25%  Chapter 6: Results and Discussion  94  the other hand, for values of GTJ between 1.5 and 2.5, the objective function value changes by only about 0.8 per unit change in  GkFTI.  This suggests that for burns exceeding  25%, the model predictions would be relatively insensitive to values of GkFTI near the  optimum 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 objective  function value and therefore not significantly affect the model’s predictions are therefore estimated to be 0.5±0.1 for burns less than 25% of the total body surface area and 2.0±0.8 for larger burn injuries. The differing behaviour of the uninjured tissue in each burn group is an encouraging outcome of the current study. In practice, the uninjured tissue experiences greater changes following large burns as compared to smaller burns due to the release of circulating factors in more extensive bums [Lund et al., 1992].  6.3.2  Sensitivity Analysis of GBT  A very shallow distribution of the objective function values about the minimum with varying GBT is depicted in Figure 6.1 for burns less than 25%. A 20% change in GBT from its optimum value of 12.0 results in a 6% change in the objective function value. The extensive plateau of objective function values around the optimum GBT value suggests that for burns less than 25%, a wide range of values spanning the optimum GkFBT could be considered without an appreciable change in the model predictions.  For bums greater than 25%, the sensitivity curve in Figure 6.2 depicts symmetry about the minimum of 9.0 and in the range 9.0±3.0 for GBT. A change of about 20% in GkFBT from 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 function values with GkFBT by about 1.6 per unit change in GkFBT. Hence, for burns greater than  Chapter 6: Results and Discussion  95  25% the model predictions would be relatively insensitive to GkFBT values within the range 9.0±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 less than 25% and greater than 25% in the ranges 12.0±3.0 and 9.0±3.0 respectively. These ranges represent the values of GBT that produce a 10% change in the objective function value. It has been generally observed that the changes experienced in the injured tissue following 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 is expected.  6.3.3  Sensitivity Analysis of EXFAC and r  As mentioned in Chapter 5, EXFAC and r were only investigated using relatively coarse discrete changes and were not rigorously estimated using the optimization technique adopted. 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 for these parameters may not necessarily provide sufficient information concerning the sensitivity of the model predictions to r and EXFAC.  The curves obtained for burns less than 25% shown in Figure 6.1 depict a slight steady decrease in the objective function with increasing values of EXFAC and r. For burns exceeding 25%, the steady decrease in the objective function is more pronounced with increasing values of EXFAC and r. In the case of EXFAC, there is a reversal in the trend at the optimum value of 0.75, Therefore, irrespective of the size of the burn injury, the injured and uninjured tissue transport coefficients return to near-normal values after about 5 days while the exudation factor lies between 0.75 and 1.0.  Chapter 6: Results and Discussion  6.4  96  VALIDATION OF MODEL PREDICTIONS  The optimum model parameters can be used to predict the response of the MVES to specific fluid replacement therapy in a burn patient. These model predictions can then be compared to the actual monitored responses of the patient to investigate how well the model performs.  6.4.1  Partial Validation  The global parameters obtained by combining the data sets from the NBC and Birkeland were used in simulating the response of the MVES of the individual patients and groups in these two sets. Since these data were used in the identification of the parameters, comparison of the model predictions with the monitored physiological variables was not considered true validation. However, the predictive capabilities of the model, as well as the validity of the global parameters could be investigated from these simulations.  6.4.1.1. NBC Data Simulation results for the NBC patients and the measured data and are presented in Figures 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 only patient with burn injuries of less than 25% of the total body surface area was Patient 1. All the other patients sustained injuries greater than 25%.  Almost immediately following burn injury, the injured tissue becomes edematous due to fluid 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 increase while the plasma and uninjured tissue volumes start to increase for all degrees of burn injury. After 24 hours, the fluid resuscitation protocol was adjusted so that reduced  97  Chapter 6: Results and Discussion  30000  i  ‘  i  ‘  i  ‘  ‘  i  ‘  25000  —  -  -  -  -  -  a)  •  20000  E 2 15000  VBT VPL VPLexp  -  10000  5000  -  0  •  — —  —  I  I  t  I  •  i  I  •  I  i  I  i  i  ‘  •  i  ‘  i  • —CTI -—CBT ----CPL • CPLexp  35 30  25  U)  —  I  —  —  —  —  —  “-  --..  .---  ——--  o20  --  c15. 10  <5 0  ‘  •  I  •  I  •  I  I  ‘  I  ‘  I  ‘  I  •  I  ‘  4 ci)  g  I  •  I  •  I • —PITIR PIBTR • PITIRexp • PIBTRexp ——  3  C) 1  E  0 Time, hours postburn  Figure 6.3: Simulation of MVES for NBC Patient I Using Global Model Parameters  -  98  Chapter 6: Results and Discussion  30000  i  i  ‘  i  ‘  t  ‘  i  ‘  i  ‘  ‘  —VT! VBT VPL • VPLexp  25000  i -  -  -  -  -  -  -  E 20000  I:: 5000  0  -  -  — ——  I  I  i  ‘  i  ‘  I  I  i  i  ‘  —  —  I  I  —  —  I  —  i  ‘  i  i  ‘  —Cli CBT ----CPL • CPLexp -  —  g35  o 20  -  -  -  4  —PITIR PIBTR • PITIRexp • PIBTRexp_ —  ——  *:i) Cl)  3  —  -  /  •  I  0  I  10  i  I  20  i  I  30  i  I  ,  40  I  50  i  I  60  i  I 70  Time, hours postburn  Figure 6.4: Simulation of MVES for NBC Patient 2 Using Global Model Parameters  Chapter 6: Results and Discussion  99  30000 25000 -J  E 20000  115000 10000 5000 0 45  I  ‘  -J  ‘  I  ‘  I  ‘  I  I  ‘  I  •  g35  -  C-)  -  -  0 P a)  I.  ‘  —CTI —--CBT CPL • CPLexp  —  -  —  25  ,.‘.-  I  o 20 C-) c 15  •  -  .  -  -  -  -  .1-  -  D  <5 0 0 4-.  c4 C,) Cl)  0 C-)  E  Ci)  0 0 0  C-)  0 0  10  20  30  40  50  60  70  Time, hours postburn  Figure 6.5: Simulation of MVES for NBC Patient 3 Using Global Model Parameters  100  Chapter 6: Results and Discussion  30000 25000 -J  2 20000 15000 :2 10000 :3 U-  5000 0 45  —i--  -J  1  ‘  —‘  I  •  I  •  —CTI ——CBT CPL CPLexp  g35  -  -  -  -  30  —  I  25 —S  —.5—  o 20  •5  C-)  c 15 :i  <5 0 0 CU  :3  Cd)  U)  a)  a C.)  2 U) 0 :21 0  0  C-)  0 0  10  20  30  40  50  60  70  Time, hours postburn  Figure 6.6: Simulation of MVES for NBC Patient 4 Using Global Model Parameters  101  Chapter 6: Results and Discussion  30000 25000 -J  E 20000 15000 -  10000 5000 0 45  I  ‘  -J  1  ‘  I  ‘  I  ‘  I  ‘  ‘  -:  w 25 C.)  /  ‘  —CTI ——CBT CPL CPLexp  —4 g35  1  -  -  —  —  a  .___  -  -  -  -  -  o 20 15  C)  <5 0  I  I  •  I  ‘  I  ‘  I  0 Co  I •  •  I  —  I  • ____I__i  I  •  I  •  •  c4  I  •  I I —PITIR PIBTR • PITIRexp • PIBTRexp •  —  —  —  D C/) C’,  a) 0  \  0  /  E U) 0 0  (0  I  0  10  •  I  I  20  30  •  I  •  40  I  I  50  60  •  I  70  Time, hours postburn  Figure 6.7: Simulation of MVES for NBC Patient 5 Using Global Model Parameters  Chapter 6: Results and Discussion  102  volumes of fluid were given to the patients. This results in the uninjured and injured tissue volumes decreasing towards their normal values. Additionally, the increased flux of albumin from the circulating plasma into the tissues results in an initial decrease in albumin concentration in plasma and a corresponding increase in the injured and uninjured tissue albumin concentration. Introduction of fluid therapy results in a continuing decrease in the plasma albumin concentration and a decrease in the injured and uninjured tissue albumin concentrations towards their normal values. After 24 hours, the albumin concentration in plasma starts to increase towards its normal value as less protein-poor fluids are administered. Due to proportionality between the effective albumin concentration and the colloid osmotic pressure, COP, the trends in albumin concentration are reflected in the COP predictions. In general, the model predictions of plasma volume changes were in good agreement with the actual monitored changes. The model also successfully predicted the monitored trends in plasma protein concentration and hence, colloid osmotic ratios, despite the scarceness of this data.  6.4.1.2 Birkeland’s Data Simulations of Birkeland’s patient groups and the data monitored are presented in Figure 6.8. Plasma volume was monitored over the first 12 hours postburn in the smaller burns and over the first 4 hours postburn in the larger burns. This data made it possible to investigate the response of the MVES in the initial period postburn when no form of fluid therapy was started. Patients in burn groups I and II sustained burn injuries to less than 25% of their total body surface area, while patients in groups III, IV and V sustained  larger burns.  Immediately postburn, the circulating plasma and uninjured tissue compartments undergo losses in fluid volume as fluid is shifted to the injured tissue compartment. The injured tissue experiences an increase in its fluid volume. The rate of fluid loss from the circulating  103  Chapter 6: Results and Discussion  10000  • utfl_flJ  Group IV  Group I 8000  8000 -J  E  6000  6000  E 0  >  4000  4000  •0 :5 LI  2000  2000  0  I, I flflñfl  I  Group V  Group II 8000  8000 -J  E  6000  6000  45)  E  :5 0  4000  4000  > -o :5 U-  w  ./  2000  2000  C  0  0  1  4  3  2  Time, hours postburn  Group III 8000 -J  2 a)  6000  2  :5 0  >  4000  0 :5 U-  2000  •  0 0  2  4  6  8  10  VBT VPL VPLexp  12  Time, hours postburn  Figure 6.8: Simulation of MVES for Birkeland Patient Groups Using Global Model Parameters  Chapter 6: Results and Discussion  104  plasma increases with increasing severity of the burn injury. Generally, this trend is well predicted by the model. In the larger burns however, the model slightly underestimates the loss in plasma volume at later times.  6.4.2  Independent Validation  Clinical 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 ability of the model to predict the response of these patients to fluid therapy provides an independent validation of the model and its parameters.  6.4.2.1 Arturson’s Patient Data In 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 concerning fluid therapy of the patient, cumulative urine production and the changes in body mass over the initial 48-hour period is reported. The patient information is presented in Appendix H. Predictions of the erythrocyte volume fraction (or hematocrit) using the model 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 the rapid 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 skin was performed. The model could not be used to predict the response of the patient both during and after the operation since information concerning this operation period was unavailable. It can be envisaged that inclusion of the volume of blood lost during the operation would enable the model to correctly predict the lower erythrocyte volume fraction observed clinically. The close agreement between the model predicted and  105  Chapter 6: Results and Discussion  1.0 0.9 0.8 0  13 0.7 U 0)  0.6  E 0.5 0)  0.4  0  2 0.3  w 0.1 0.0 0  5  10  15  20  25  30  35  40  45  Time, hours postburn  Figure 6.9: Simulation of MVES for Arturson’s Patient Using Global Model Parameters  Chapter 6: Results and Discussion  106  clinically monitored erythrocyte volume fraction prior to the operation however, is satisfactory validation of the model and its associated parameters.  6.4.2.2 Ro&s Patient Data The treatment of two burn patients and the clinical data collected from these patients were reported by Roa Ct al. [1990] and are presented in Appendix I. Patients 1 and 2 sustained burn injuries to 75 and 80% of their total body surface areas respectively. Intravenous and colloid input, as well as the urine produced by these two patients were used to predict the changes in hematocrit and plasma protein concentration in the MVES following injury. Predictions using the model and clinically monitored responses of the two patients are presented in Figure 6.10. The initial elevation in hematocrit and the subsequent gradual return 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 the case 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 total body surface area, the model was able to predict the response of the MVES following fluid therapy in patients treated by Arturson et al. [1989] and Roa et al. [1990]. The model predictions agreed favourably with the clinical data available from individual patients. As the clinical data were not used in the parameter estimation procedure, the ability of the model to simulate the response of the patients constituted independent validation of the model. The successful outcome of this independent validation establishes some confidence in the ability of the model and its associated parameters to predict patient responses to fluid therapy following burn injury.  107  Chapter 6: Results and Discussion  1.0  1.0  •  Patient 2  Patient I  •  0.8  0.8  0 0 Cu  E a) z  ‘  :-  0.2  0.2  0.0  0.0  1.0  0.8  0  0  0.6  CU  I—  a)  0 0  ()  0.4  C  E -Q  0.2  0.0 0  10  20  30  Time, hours postburn  40  0  10  20  30  Time, hours postburn  Figure 6.10: Simulation of MVES for Roa’s Patients Using Global Model Parameters  40  Chapter 6: Results and Discussion  6.5  108  SIMULATION OF FLUID RESUSCITATION ACCORDING TO DIFFERENT FORMULAE  The use of resuscitation formulae in the treatment of burn patients was discussed in Chapter 2. In order to illustrate the potential use of a model such as that developed in the current study, the response of the MVES, following burn injury, to three common resuscitation formulae was simulated. The response of the MVES to no fluid resuscitation  was also simulated to clearly show the influence of fluid resuscitation on the behaviour of the MVES following burn injury.  The amounts of fluid to be given according to the Evans, Brooke and Parkland formulae during the first two 24-hour periods are shown in Table 6.8. These general formulae were applied 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 the three different resuscitation formulae following the two burns.  The Parkland formula for fluid resuscitation differs markedly from the Evans and Brooke formulae. During the first 24-hour period, the Evans formula uses a slightly hypertonic sodium chloride solution and colloid solution in equal volumes. Brooke’s formula includes an isotonic lactated Ringer’s solution and colloid solution in proportions 3:1. Parkland’s formula on the other hand, only uses isotonic lactated Ringer’s solution in very large quantities. In addition, about 2000 mL of 5% glucose in water is given per day according to the Evans and Brooke formulae, but not in the Parkland protocol.  During the second 24-hour period, half of the amount of electrolytes and colloids compared 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 in  109  Chapter 6: Results and Discussion  water 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 to Parkiand’s formula.  Table 6.8 : Common Fluid Resuscitation Formulae [Arturson et al., 19891  Fluids  Evans Formula  Brooke Formula  Parkiand Formula  1.0 mL/kg/%  1.5 rnL/kg/%  4.0 mL/kg/%  2000 mL  2000 mL  None  1.0 mL/kg/%  0.5 mL/kg/%  None  0.5 mL/kg/%  0.75 mL/kg/%  None  2000 mL  2000 mL  As required for  First 24 hours Electrolytes  Glucose/water Plasma Second 24 hours Electrolytes Glucose/water  urine output Plasma  0.5 mL/kg/%  0.25 mL/kg/%  500 2000 mL as -  required to maintain urine_output  6.5.1  Simulations of 10% Burn  Simulations of the response of the MVES to no fluid resuscitation and the Evans, Brooke and Parkland formulae following a 10% burn injury are depicted in Figures 6.11 to 6.14. It was assumed that the fluid resuscitated patient lost 1.5 L of urine each day over the 2-day period 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 derived from the NBC patient data (Equation E. 1) as described in Appendix E. In addition,  110  Chapter 6: Results and Discussion  —-VTI VBT VPL  10000  8000  CT CBT CPL  50 -J 0)  45  •—-—--—  -J  E a)  E  6000  a) 35 C)  0  >  0  4000  C) C  E 25  Li  2000  .0  20 0  I  -  •  15  I  •  45 15 0)  PTI  1°  PBT PPL  10 .  —PITI PIBT PIPL  35  E U) U)  0)  (0  I  C-)  a 10  25  E C,,  Cu.  020  (1)  0  t20  o 15 C-)  -25 600  I’I’I,  .  I  400 I ——  x  I  14000 2000  ——  QSBT QLTI QLBT.  300 10000 200 .  Li •0  I  16000  JFTI JFBT JLTI JLBT  500  :2 E  30  a  -5  E  100  .0 a  8000 6000  czzzzzz  U-  4000 -100 2000 -200 .  0  I  I  I  10  20  30  •  Time, hours postburn  I  40  —*  0  Time, hours postburn  Figure 6.11: Simulation of MVES with no Fluid Resuscitation Following a 10% Burn  I’’  Chapter 6: Results and Discussion  55 —VTI VBT VPL  I  10000  —CTI CBT CPL  50 -J 0)45  —-__.......  ——---—-—  8000  _-_--————  -J  E 6000  a) 35  C-) C 0  C-)  4000  C  E 25 2000  20 •  -  I  •  0  45 15 0)  —  PT  —PITt PIBT PIPL  0)  I 40  10  PPL  E E  35  E U,  U)  U) U)  30  -5 C)  C) U)  25  10  EI.’,  -15  020  0  -20  •0 0  -25  C.)  >,  5 15  600 500 400 300  E ii:  200 100  -D  2  0 -100 -200 0  10  20  30  Time, hours postbum  40  10  20  30  Time, hours postburn  Figure 6.12: Simulation of MVES According to Evan’s Formula Following a 10% Burn  112  Chapter 6: Results and Discussion  55 —  10000  —CTI  VTI VB VPL  8000  50 CPL  45 0  -J  E  40 C 0 C) C 0  6000  35  o  4000  30  C  E 25  D .0  2000  20 15  0—  45 15 )  2:  I  —PT. --—--PBT PPL  10  I  •  I  I  •  —Pm PIPL  E E  -  35  U) Cl) U) U)  30  a  5  0  a  25  10  E  (U  o  (I,  2  0  -2O  815  -25 600  I  •  —JFTI JF8T JLTI JLBT  500 400  -c  20  ——  300  16000  -c  E 12000 x  D U C  E 200  14000  LD)  —QSTI QSBT QLTI QLBT  10000 8000  E  D .0  100  6000  0 -100 -200 •  0  10  I  I  20  30  •  Time, hours postburn  I  40  00  Time, hours postburn  Figure 6.13: Simulation of MVLS According to Brooke’s Formula Following a 10% Burn  113  Chapter 6: Results and Discussion  55 VTt VBT VPL  10000  _i C)  • -  I  I--  CTI CBT CPL  50  c_ 45  8000  1  0  -J  6 II)  6  40 C 1)  6000  35  :3 0  > -D :3 U-  0  C.) 4000  30  6  25 2000  20 I •  PTI PBT PPL  15 C)  10  6 65  C)  I  6 6 :3 (I)  U) U)  a 0 .  >.  0  4  a) 0  -  C,  0  -10  EU) 0  -20  0  -25  0  0  I  I  I  I  600 JFTI JFBT JLTI JLBT  500 400  ——  16000 14000 -C C)  12000  —QSTI QSBT QLTI QLBT  6  300  x 10000  :3 LI C  200 LI0  100  6 :3  U-  8000 6000 4000  -100 2000 -200 0  10  I  I  20  30  Time, hours postburn  0  zz:-zz::zz 40  40  Time, hours postburn  Figure 6.14: Simulation of MVES According to Parkland’s Formula Following a 10% burn  114  Chapter 6: Results and Discussion  200 mL of blood were assumed to be lost in the first hour postburn due to surgical procedures. The perturbations which describe the changes to the transport coefficients following a 10% burn surface area injury were those obtained for burns less than 25% and are presented in Table 6.7.  Immediately following burn injury, fluid and albumin are transferred from the circulating plasma compartment to the injured tissue compartment due to increased conductance and permeability of the capillary membrane. Edema results in the injured tissue, with its volume approximately doubling within 2 hours. The patient plasma volume decreases due to the low circulating blood volume which results from the fluid shift. The uninjured tissue also experiences a small decrease in fluid volume as it also acts as a source of fluid for the plasma compartment. The concentration of albumin in the circulating plasma also decreases as albumin is shifted into the tissue compartments. The albumin concentration therefore increases steadily following injury in both tissue compartments, but to a greater extent in the injured tissue. Fluid therapy according to all three formulae was started 1 hour after injury in order to replace the lost fluid volume and albumin content from plasma.  The transcapillary fluid shifts of fluid and albumin following burn injury can be explained by analyzing the fluid and albumin fluxes in the three compartments. The hydrostatic and colloid osmotic pressures in the plasma and tissue compartments are the forces that drive the fluid and albumin exchange. These pressures and the fluid and albumin fluxes are also shown in Figures 6.11 to 6.14.  The very strong negative pressure in the injured tissue,  BT,  in the first few hours  postburn, as well as the initial increase in the filtration coefficient results in an increased rate of fluid and albumin transport from the circulating plasma into the injured tissue.  115  Chapter 6: Results and Discussion  Reduction of the capillary reflection coefficient,  BT, T  associated with increased protein  permeability, also influences the increased filtration rate. Lymph flow from the injured tissue which is restricted to non-negative values, is virtually nonexistent also due to the very negative tissue pressure. However, the injured tissue loses fluid by evaporation and exudation and albumin via exudate from the burn wound. Despite these losses, the great increase in the rate of fluid and albumin transfer into the injured tissue results in a rise in both fluid volume and plasma protein content in this tissue during this initial period postburn. Consequently, edema develops in the injured tissue because the rate of fluid filtration from the capillaries exceeds the rate at which fluid is removed from the tissue via the lymphatics and other routes. In addition, the injured tissue albumin concentration, and hence the colloid osmotic pressure, concentration,  CPL  BT’ 11  and colloid osmotic pressure,  CBT  increase while the plasma albumin  PL  decrease. Immediately postburn, the  uninjured tissue experiences a decrease in its hydrostatic pressure due to loss of fluid volume from this compartment. In the first few hours postburn, the hydrostatic pressure in the capillary falls much more markedly than that in the uninjured tissue compartment. This causes a reduction in the filtration rate despite the small increase in the filtration coefficient. The uninjured tissue fluid volume therefore decreases while its albumin concentration increases.  Fluid therapy, where applicable, was started 1 hour postinjury. The interstitial fluid pressure in the injured skin of rats has been observed to approach normal values within 2 to 3 hours [Lund et al., 1988]. During the first 2.5 hours postburn, interstitial pressure versus time data from experiments on both unresuscitated and resuscitated rats [Lund et al., 1988] were used to describe the injured tissue compliance. After 2.5 hours, the injured tissue hydrostatic pressure was linked to changes in interstitial fluid volume resulting in an increase in  BT,  approaching more positive values between 2,5 and 3 hours postburn. This  influences the rate at which fluid and albumin is shifted from the circulating plasma  116  Chapter 6: Results and Discussion  compartment. Transcapillary fluid and albumin transport also continually readjust depending on the fluid and colloid input to the system. Fluid resuscitation according to Evan& and Brook&s formulae results in similar responses by the MVES. The injured tissue fluid volume starts to decrease approaching normal values. However, the albumin concentration,  CBT,  continues to increase. The plasma volume on the other hand, remains  low despite the input of fluid to the system and the albumin concentration also continues to decrease despite colloidal infusions. This results in the injured tissue COP, exceeding that of plasma,  BT’ 11  early in the postburn phase. These trends could be a  PL’ 11  reflection of the resuscitation protocol with regards to protein replacement. In contrast to the generally accepted view that colloids should be withheld for the first 12 to 24 hours postburn, the Evans and Brooke formulae require that colloids be administered in the first 24 hours. It appears that there is continued protein transfer into the injured tissue resulting in the continued increase in  CBT  and hence  BT 11  as predicted by the model. Pitkanen et al.  [1987], in their studies in burn injured patients, found a higher injured skin COP than plasma COP up to 12 hours postburn. Voluminous crystalloid infusions were sited as being partially responsible for the postburn incidence of hypoproteinemia [Pitkänen et al., 1987]. Spontaneous decreases in plasma COP have also been reported following burn injuries in man [Davies, 1982] and in anaesthetized and unresuscitated burned rats [Lund and Reed, 1986]. Later in the resuscitation period, the uninjured tissue compartment experiences a slight increase in tissue volume, out of phase with the injured tissue edema as shown in Figures 6.12 to 6.14. During the second 24-hour period, the uninjured tissue volume starts to decrease, tending towards its normal value. This ensures continued increase in albumin concentration, c and hence COP,  TI’  but to a lesser degree than that  experienced in the injured tissue.  Fluid resuscitation according to Parkland#s formula resulted in a slightly different response in the MVES in the second 24-hour period postburn. The large volume of only protein-  Chapter 6: Results and Discussion  117  poor fluid infusions in the first 24-hour period resulted in a larger decrease in the albumin concentration 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 in the second 24-hour period. This resulted in an increase in the plasma albumin concentration and hence the plasma COP.  6.5.2  Simulations of 50% Bum  Figures 6.15 to 6.18 show predictions of the response of the MVES to no fluid resuscitation, the Evans, Brooke and Parkiand formulae following a 50% bum. Similar assumptions regarding fluid and albumin losses from the patient following a 10% burn were applied in this case. In order to describe the changes to the transport coefficients following a burn of this size, perturbed parameter values determined for bums exceeding 25% of the total body surface area were applied.  The response of the MVES without fluid therapy is shown in Figure 6.15. The extent of the burn injury results in a relatively greater shift of fluid and albumin from the circulating plasma into the injured tissue as compared to the smaller burn. Edema results in the injured tissue despite the loss of fluid due to exudation and evaporation. This is due to increased filtration from the circulating plasma, encouraged by a very strong negative injured tissue pressure, an initial increase in kF and a decrease in the capillary reflection coefficient associated with increased protein permeability.  The uninjured tissue  compartment acts as a source of fluid for the depleting plasma compartment and hence its fluid volume also decreases. In addition, albumin is transferred to both tissue compartments from plasma. This results in an increase in the concentration of albumin and hence COP in the tissues, while the plasma albumin concentration and hence COP decrease as in the smaller burn.  118  Chapter 6: Results and Discussion  50 14000  VBT VPL  12000  CTl CBT CPL  45 -J C  -J  E 10000  .2 35  E 8000  •3Q  a)  I.)  0  > 6000 •0 1I  g  25  C  20  C-)  E  4000  .o 15 2000 .:r——=::: •  I  1O  I  •  •  40  —PTI PBT PPL  15 0)  Z10  —Pm PBT PIPL  0)  I 35  E E  E  30  E : a)  U)  I  U)  a) I a .20  -5! ci -10 Cu  0  E (I)  -15  o  -20  0 0  0  __.__  15  10 C-)  z -25 I  I  1500  •  I  40000  .  JFTl JFBT JLTI JLBT  1000  —QSTI QSBT QLTI QLBT  35000 -C 0)  30000  —  —  6 25000  6  x  500  >< D U-  UC  E  -o —  •-‘----—  0  U-  .0  20000 15000 10000  4:  500: •-:;E:::::::-r--  -500 0  I  I  I  I  10  20  30  40  Time, hours postburn  0  10  20  30  40  Time, hours postburn  Figure 6.15: Simulation of MVES with no Fluid Resuscitation Following a 50% Burn  Chapter 6: Results and Discussion  119  —CTI --—--CBT CPL  14000 45  VBT VPL  12000  -J C4  -J  E 10000 0  E  8000  :3 0  >  825  6000  -D :3 U-  4000 2000  ‘-.._  p  20  I  •  I  I  III  -L  —PTI --—--PBT PPL  z 15 E E 10 a) 5.  E 35 2 30  :3 Cl)  3  —PITI --—--PIBT PIPL  25  .2 O  >‘  E U) 0  -15  20  0  -20  0  01.  -25 •  I  I  40000 JFTI JFBT JLT JLBT  1000  -  30000  0,  6 25000  -c  x  6 500  :3 IL  >< :3 IL :3 IL  —QSTI QSBT QLTI QLBT  35000  20000 15000  0  10000 5000  -500 0 0  10  20  30  Time, hours postburn  40  0  10  20  30  40  Time, hours postburn  Figure 6.16: Simulation of MVES According to Evans’ Formula Following a 50% Burn  Chapter 6: Results and Discussion  120  .  14000  I  •  45  VBT VPL  12000  CBT CPL  -J C  -J  .2 35  E 10000  (U  • 30 8000  a)  6000  C-)  C.)  25 :2  .  4000  -D  2000  15 10  ..  I  •  I  •  •  20  .  40  —PTI  15  c I  20  E  U-  •  ____  PIBT PIPL  I 35  E E a) 30  PPL.  10  E  I  0 0 (1)  25  -  1  -._  U  C-)  (U  o -  >‘  -10  0  15  E 0 0  -20  -U 0  0  -25 I  •  I  JFTI JFBT JLTI JLBT  1000  10  C-)  I  •  20  35000 30000  —  —  -c  QSBT QLTI QLBT  25000 500  20000  x  U  15000  U  0  10000  1  500:  -500 I  .  0  10  20  •  I  30  Time, hours postburn  40  10  20  30  40  Time, hours postburn  Figure 6.17: Simulation of MVES According to Brooke’s Formula Following a 50% Burn  Chapter 6: Results and Discussion  121  VTI  14000  -J 0)  12000  C 0  -J  E 10000  Cu  a) E  C  8000  1) C-)  C 0  0  >  C)  6000  -o  C  IL  E  4000  .0  2000 I  •  •  20 —PTI PBT PPL•  15 0)  I  10  S S  0)  I  E E  5  I—  Co  0  Co Co I  a  C) CU  Co  a) I  -5  a  -10  0  C)  CO  -15  20  -20  >—  S Co 0 0 0  -25 ,  I  I  •  I  I  C) 40000  1500  35000 1000  QSBT QLTI QLBT  30000 25000  S  500  20000  x IL D U-  15000 0 10000 5000 -500  ::;:-  0 10  20  Time, hours postburn  0  10  20  30  40  Time, hours postburn  Figure 6.18: Simulation of MVES According to Parkland’s Formula Following a 50% burn  Chapter 6: Results and Discussion  122  As was the case for the smaller burn, fluid therapy was started 1 hour postinjury. The injured tissue hydrostatic pressure returns to more positive and near-normal values and the transcapillary fluid and albumin fluxes continually readjust depending on the fluid and albumin input to the system. As a result, the injured tissue volume starts to decrease while the plasma volume starts to increase, tending towards their normal volumes. Fluid resuscitation with the larger volumes of fluid results in more extensive edema formation in the uninjured tissue as compared to that experienced following a 10% burn injury. A reversal of plasma and injured tissue COP is again predicted as the injured tissue albumin concentration exceeds that in the circulating plasma following resuscitation according to all three formulae. However, the redistribution of albumin in the three compartments differs following fluid resuscitation according to the three formulae after about 10 hours postburn. Discontinuities in the predicted trends 24-hours postburn are reflections of the change in resuscitation protocol and are more evident following the larger burn.  Resuscitation according to the Evans formula results in similar trends in  CBT  and  BT 11  as  observed following the 10% burn. The albumin concentration in injured tissue continued to increase while that in plasma continued to decrease up until 10 hours postburn. The trend 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 volume resulting 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 similar behaviour in the circulating plasma. The injured tissue albumin concentration however, decreases after 10 hours postburn and continues to decrease steadily in the second 24 hours. The decrease in cPL and the increase in  CBT  are more pronounced using Parkland’s  formula in the first 24 hour period. It is widely accepted that resuscitation with colloid free solutions produces a decrease in HPL due to dilution of plasma proteins. In the second 24-hour period,  CPL  starts to increase rapidly as protein-rich fluid is administered according  Chapter 6: Results and Discussion  123  to Parkiand’s formula. The injured tissue albumin concentration also starts to increase following fluid therapy but at a reduced rate.  6.5.3  Simulations by Other Authors  Arturson et al. [1989] and Roa et al. [1993] used their models to simulate the response of the standard 70-kg man with a 40% burn surface area to one or more of the resuscitation formulae discussed previously. The predictions made by the models of these authors are discussed 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 the response of a 70-kg man with a 40% fhll thickness burn to fluid therapy according to the Evans, Brooke and Parkland formulae. The model described the distribution of body fluids in 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 were simulated. Their model predicted the decrease in plasma and uninjured tissue volume and the 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 during the 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 tissue continued to experience a decrease in its fluid volume. Use of the Brooke formula resulted in a continued slow and steady decrease of the plasma and uninjured tissue volumes from their normal values. The increased injured tissue volume however, started to decrease 18 hours postburn. Fluid therapy according to Parkiand’s formula caused a reversal in the decreasing trend, increasing towards the normal plasma volume during the second 24-hour period. Edema in the injured tissue was more pronounced with Parkland’s formula but started to resolve during the second 24 hour period. The uninjured tissue however,  Chapter 6: Results and Discussion  124  experienced an increase in fluid volume following fluid resuscitation and continued to increase over the 2-day period. The shift of fluid into the injured tissue causing edema and the subsequent decrease towards normal values predicted by the current model is in agreement with Arturson’s predictions. Fluid therapy according to Parkland’s formula is able 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’ and Brooke’s formulae differ between the two studies. With Arturson’s model, a steady decrease in uninjured tissue fluid volume is predicted following resuscitation with the two formulae. This is in contrast to the predicted increase in fluid volume in the first 24 hours followed 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 fluid therapy method for burn patients during the acute phase following burn. The interactions between the intracellular and extracellular compartments, normal and burned capillary dynamics, hemodynamic regulation of the systemic circulation, lymphatic systems in the normal and burned areas and renal fhnction were all considered in the simulation. The response of a 70-kg, 170-cm tall individual with a 40% burn to the Brooke and Parkland formulae were simulated and compared to the fluid therapy method designed. The trends in plasma and uninjured tissue volumes predicted by their simulator were similar to those obtained in the current study. Fluid resuscitation according to the Brooke and Parkland formulae resulted in an increase in the plasma volume following the initial decrease when no form of fluid therapy was administered. The Parkland formula caused a greater increase in the uninjured tissue fluid volume as compared to Brooke’s formula, as also predicted by the current model.  Chapter 6: Results and Discussion  6.6  125  SUMMARY  In the current study, clinical data were used to estimate transport parameters and other significant parameters in the model. This aspect of the current study represents a significant difference in the approach to model formulation as compared to the models of Arturson 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 and the 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!. and Roa et a!. as compared to that developed in the current study, the simulations show many similar trends in terms of the response of the human MVES to fluid therapy according to the Evans, Brooke and Parkiand formulae. Inclusion of cellular compartments as in the case of the other models would be an improvement to the model, to further enhance its predictive capabilities. As more clinical data become available, a more accurate parameter estimation procedure can be adopted in the development of a model that will better reflect the dynamic behaviour of fluid and proteins in the MVES following a burn injury.  Chapter 7: Conclusions arid Recommendations  126  CHAPTER 7  CONCLUSIONS AND RECOMMENDATIONS  7.1  CONCLUSIONS  A compartmental model has been developed to describe the human microvascular exchange system following burn injury. One of the objectives of the current study was to determine the unknown model parameters by statistical fitting of model predictions to  clinical data. An optimization scheme was implemented to determine the °best-fit” parameters. The scheme ensured that the optimum model parameters were those which yielded the global minimum of the objective function value.  Clinical observations indicate that burns less than 25% of the total body surface area initiate systemic and localized changes which differ from those caused by burns exceeding 25%. Therefore global parameters were determined for burns less than and greater than 25%. The results obtained indicate that, immediately postburn, the injured tissue  undergoes greater change compared to the uninjured tissue for all degrees of burn injury. Immediately following bums less than 25%, the filtration coefficient in uninjured tissue increases to 1.5 times its normal value while the injured tissue transport coefficient changes by a factor of 13. Burns in excess of 25% initiate more pronounced changes in the uninjured tissue filtration coefficient, by a factor of 3 while the injured tissue coefficient increases to 10 times its normal value. Therefore burns exceeding 25% of the total body surface area cause greater changes in the uninjured tissue as compared to smaller burns. However, the injured tissue undergoes similar changes for all burns. The transport coefficients were found to return to near-normal values in about 5 days following bum  127  Chapter 7: Conclusions and Recommendations  injuries of all sizes. The exudation factor, which determines the fraction of the interstitial protein concentration which leaves with exudate from the burn wound, was found to be in the 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 their optimum 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 to  GkFBT. The model predictions would not be significantly affected by values of  GTJ  within the range ±0.1 about the optimum value of 0.5 and values of GkFBT within the  range ±3.0 about the optimum value of 12.0. Beyond these ranges, appreciable changes in the model predictions would be observed. Values of G TI within the range ±0.8 about the optimum value of 2.0 and values of GkF,BT within the range ±3.0 about the optimum value of 9.0 would not significantly affect the model’s predictions. As the model parameters EXFAC and r were investigated using relatively coarse discrete changes, limited information could be inferred concerning the sensitivity of the model predictions to EXFAC and r.  The model and its associated parameters were validated by comparing model predictions of 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 the parameters constituted independent validation of the model and its parameters. The model predicted response of the MVES to burn injury was in agreement with the observed trends and the absolute values of fluid volume and plasma protein concentration. Immediately postburn, there was an initial elevation in hematocrit due to fluid loss from the circulating plasma. Administration of fluid therapy initiated the return of hematocrit to normal values. In addition, the reduction in plasma protein concentration observed clinically soon after burn injury was successfully predicted by the model.  Chapter 7: Conclusions and Recommendations  128  The 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 resuscitation following a particular burn injury. The patient simulator could also be used to compare the effects of different recommended resuscitation formulae, to suggest possibilities for the design of optimal fluid resuscitation programs in terms of the fluid composition, volume and infusion rate. Areas of further investigation with respect to fluid management of burn patients could also be suggested using the model. To this end, the model was used to simulate the response of the MVES following burn injury to no form of fluid therapy and then to three common resuscitation protocols, namely the Evans, Brooke and Parkland formulae. The simulated responses of the MVES were explained in terms of the transport mechanisms, driving forces and perturbations to the transport coefficients following two degrees of burn injury, 10% and 50%. In general, it was found that the very strong negative injured tissue pressure as well as the initial increase in the filtration coefficient and the reduction of the capillary reflection coefficient resulted in an increased flux of fluid and albumin from the circulating plasma into the injured tissue. This resulted in the injured tissue becoming edematous, while the circulating plasma continued to lose fluid volume. The concentration of albumin in the injured tissue also increased steadily while that in plasma decreased following injury. This resulted in a reversal of the colloid osmotic pressure difference between the injured tissue and plasma. The response of the MYES to fluid therapy according to the Evans and Brooke formulae was similar. The injured tissue hydrostatic pressure increased approaching normal values and the transcapillary flux of fluid and albumin continually readjusted depending on the fluid and colloid input to the system. Parkland s formula initiated slightly different and more pronounced responses due t to the large volume of colloid-free fluid given in the first 24-hours followed by colloidal infusions in the second 24-hours. The major difference between the two burn degrees was the relative greater shift of fluid and albumin from the circulating plasma into the injured  Chapter 7: Conclusions and Recommendations  129  and 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 the present model to adequately predict the response of the human MVES to fluid therapy following burn injury.  The model parameters estimated in the current study may be considered as estimates due to the extreme complexity of the MVES and the lack of experimental data. As more reliable and useable clinical data becomes available, more accurate parameters may be estimated to better reflect the dynamic behaviour of the MVES. However, the simulated results illustrate the utility of the model in predicting non-measureable variables in the MVES.  7.2  RECOMMENDATIONS  The various problems encountered as well as the results obtained in the current study form the 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 model parameters sets the current model apart from those developed by other workers. There is therefore absolute need for more reliable clinical data in terms of both quantity and quality, to enable a more detailed identification of all the model parameters including the relaxation coefficient and exudation factor. This would undoubtedly improve the ability of the model to adequately predict the response of the complex system to fluid resuscitation following thermal injury.  2) In order to verify the model predictions, additional clinical data or information is  required:  Chapter 7: Conclusions and Recommendations  •  130  measurements of the changes to the injured and uninjured tissue transport coefficients following burn injury;  •  estimates of burn wound fluid and protein loss due to exudation; and  •  estimates of fluid loss due to evaporation.  Improvements to the current model might include:  3) •  replacement of the “most-likely” human tissue compliance relationship with clinically determined relationships for the injured and uninjured tissue as the data becomes available;  •  investigation of the possible change in the vascular compliance during the course of fluid resuscitation;  •  determination of the lymph flow changes in the injured and uninjured tissues following burn injury as this information becomes available;  •  subdivision of the uninjured tissue compartment comprising uninjured skin, muscle and other tissues into the individual components. This will only be possible when clinical data regarding the colloid osmotic pressure dependence on protein concentration, the compliance characteristics and the normal steady-state conditions of the individual tissues become available; and  •  extension of the current model to include intra- and extracellular compartments to allow for fluid, protein and small ion exchange between compartments. This would enable the simulation of the response of the MVES to hypertonic fluid resuscitation following thermal injury.  131  Nomenclature  NOMENCLATURE  Symbol  Description  a  Ratio of albumin molecule radius to pore  Units  radius A  Surface area available for exchange  AFRAC  Fractional perfusion in injured tissue  2 m  immediately following burn injury h-’  MbTo  Albumin turnover rate  AR  Acetated Ringers solution  BV  Blood Volume  mL  c  Albumin concentration  g/L  COP  Colloid osmotic pressure  CSM  Coupled Starling Model  CV  Cell Volume  niL  DEG  Percentage of body surface burned  %  Solute free diffusion coefficient D5W  Dextrose  EXFAC  Exudation factor  FA  Fractional area available for exchange  fn  ()  G  mmHg  /s 2 cm  Function of Perturbation to the transport coefficient postburn  H  Patient height  cm  Hct  Hematocrit  %  1-IR  Hypertonic Ringer’s solution  132  Nomenclature  Symbol  Description  Units  J  Fluid transport rate  mL/h  k  Time-dependent coefficient  kA  Overall transport coefficient  kF  Filtration coefficient  1 a. k  Steric fractional drag coefficient  LS  Lymph flow sensitivity coefficient  M  Number of variables monitored  MVES  Microvascular Exchange System  N  Number of data points  NBC  National Burn Centre  NEXP  Number of experimental data points  NS  Normal saline  OBJFUN  Objective function value  P  Hydrostatic pressure  C,COMP  Reciprocal of circulatory compliance  Pe  Modified Péclet number  PS  Membrane permeability coefficient  PLM  Plasma Leak Model  PV  Plasma volume  mL  Q  Albumin content  mg  Q  Albumin transport rate  mg/h  r  Relaxation coefficient  h-’  rpore  Radius of pore  m  rsolute  Radius of solute  m  RELSM  Fraction of total body comprising skin  SM  Starling Model  mL/mmHg-h  mL/mmHg-h  mniHg mmHg/mL  mL/h  133  Nomenclature  Units  Symbol  Description  SM  Starling Model  t  Time  TBSA  Total body surface area  V  Fluid volume  VAFTI  Fraction of tissue which remains uninjured  VAFBT  Fraction of tissue which is injured  VFRAC  Fractional  h  plasma  mL  volume  at  which  perfusion in tissues is zero W  Patient body weight  WR  Weight ratio  WF  Weighting factor for each data point  X  Data point  H  Colloid osmotic pressure  a  Albumin reflection coefficient Viscosity of water  (1  -  a)  kg  mmHg  glcm-s  Partition coefficient  A  Change  AX  Thickness of capillary membrane  cm  Nomenclature  134  Subscripts and Superscripts  Symbol  Description  AV  Volume available to albumin  BLOOD  Blood loss  BT  Injured tissue  C  Capillary  CLF  Clear fluid  end  End of time period  EVAP  Evaporation  EX  Excluded  EXP  Experimental  EXUD  Exudation  F  Filtration  I  Interstitium  L  Lymph  NL  Normal steady-state conditions  0  Initial conditions  PB  Postburn  PCF  Protein-containing fluid or colloidal fluid  PL  Plasma  PRED  Predicted  RESUSC  Resuscitation  S  Solute  start  Start of time period  TI  Uninjured tissue  URII’4E  Urine  135  References  REFERENCES  Arturson, G., Pathophysiological aspects of the burn syndrome, Acta Chir. 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The flow of solute and solvent across a two-membrane system. J. Theoret. Blot., 5:426-442, 1963. Pitkanen, J., T. Lund, L. Aanderud and R.K. Reed, Transcapillary colloid osmotic pressures 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 altered capillary 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 hindlimb skeletal muscle, ActaPhysiol. Scand., 113:297-305, 1981. Reed, R.K., B.D. Bowen and J.L Bert, Microvascular exchange and interstitial volume regulation 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): H1097Hi 100, 1990. Reed, R.K., M.I. 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Arturson, Plasma oncotic pressure and plasma protein concentration in patients following burn injury, Acta AnaesthesioL Scand., 24:288, 1980.  143  Appendices  Appendices  Appendix A: Interstitial Fluid Distribution  Appendix B: Transport Parameters  Appendix C: NBC Patient Data  Appendix D: Estimation of Plasma Volume from Hematocrit Data  Appendix E: Estimation of Exudation Rate Based on NBC Patient Data  Appendix F: Birkeland’s Patient Data  Appendix G: Determination of Exudation Rate for Birkeland’s Patients  Appendix H: Clinical Data from Arturson’s Patient  Appendix I: Clinical Data from Roa’s Patient  Appendix J: Minimum Objective Function Value Results  Appendix K: Computer Program Listing  144  Appendix A  Appendix A: Interstitial Fluid Distribution  The 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, L  Total Skin  2.39  Skeletal Muscle  4.51  Other Tissue  1.50  Total Body  8.40  Appendix B  145  Appendix B: Transport Parameters  B, 1  Normal Transport Parameters for “Reference Man”  Normal values for five transport coefficients have been determined using the Coupled Starling Model (CSM) for the normal 70-kg man by Xie [19921. Values for the lymph flow sensitivity coefficient, LS and the albumin reflection coefficient, a, were determined by statistical fitting of the CSM model predictions to experimental human MVES response data. The lymph flowrate,  L’ 3  permeability coefficient, PS and filtration coefficient, kF are  calculated from the following relationships based on the estimated values of LS and a:  A1bTQ  —  (1—cJ).exp(—PeNL) [1—exp(—Pe)].[J’NL  ‘NL  -  NL —  fl[ 1NL 1  [  “J,E’]  i “  L,NL  B2  —(1—).cJAVWL  cJ—(1—NL).cpLNL  kFNL  , C,NL 1  —  B.3  111,NL)  —  where Pe is a modified Péclet number which can also be shown to be  _i  cINL—(1—J).cIAvNL  PeNL—ln  .  CJNL  B.4  -NL)PL,NL  Subscript 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 compartment and 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.  146  Appendix B  The normal values of the transport coefficients, as estimated from the above relationships from the values of LS and a found by Xie are as follows: LSNL  =  43.08 mL/mmHg-h  PSNL  =  72.98 mL/h  kFNL  =  120.64 mL/mmHg-h  L,NL  =  75.46 mL/h  0.9888.  =  As explained in Chapter 4, these transport coefficients, with the exception of the albumin reflection coefficient, are scaled with respect to the weight ratio, WR, to account for the “real patient”.  B.2  Transport Coefficients Following Burn Injury  Most proteins in plasma cross capillary walls, diffuse through tissues and return to the plasma via the lymphatic system. It is well known that the concentration of a macromolecule in lymph is a function of its molecular size and that capillaries are heteroporous, i.e., both small and large pores are necessary to describe the movement of large molecules across capillary walls [Taylor and Granger, 1984]. The capillary membrane parameters which determine the exchange of plasma proteins, represented by albumin in the current study, are kF, a and PS. These transport parameters are not independent, but are linked to each other via changes in the capillary pore radius. Reed et al. [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 this case: k’F  2 rpore  =  B.5  8..AX 16 3  2  20 3  7 3  B.6  Appendix B  147  PS’=  (1—a) 2 1 •AX k.c  B.7  where a is the ratio of the solute radius, rsolute, to the pore radius, rpore, i.e., B.8 rpore  ii  is the viscosity of water (p.  capillary membrane (AX  =  =  5000A  0.006915 g/cm-s at 37°C), AX the thickness of the =  5x 10  cm), (1  -  a) the partition coefficient, D 5 the  solute free difihision coefficient in cm /s and k a is the steric fractional drag coefficient 2 which 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 the radius of the albumin molecule [Taylor and Granger, 1984] and the albumin reflection coefficient: =  0.9888 = ![16.a2 —20.aNL 3  +7.a,4j.  Solving this equation yields: a 0.89  Recall that following burn injury, the transient response of the transport coefficients is expressed in the following general form: 4.34  kA=kWL.ANL.[1+G.e]  Considering kF, by the definition above, at time t  k F,NL  0,  =1+Gk  In the current study, it is assumed that following burn injury, the capillary membrane pores experience changes in radii. From equation B.5, kF  cx  2 pore. r  Thus:  Appendix B  148  rpore  r  where  B.9  =l+Gk, pore,NL  rporeNL  is the normal capillary pore radius. Setting rpore  =  r, and  rporeNL  =  NL’ 1  Equation B.9 can be expressed as B.10  r=rNL.[1+Gk].  From Equations B.8 and B. 10, the ratio of albumin and capillary pore radii following burn injury may be defined as follows: clb  — 8 a,,  r  —  rNI\l+Gk)  In addition, under normal conditions, a  —  From equations B. 11 and B. 12, 1  Taib aNL  raib  TNL.(1+Gk)  Hence, the ratio of the albumin molecule radius to pore radius, postburn is a  —  a PB  B13  (1+GkF)  Consider PS. Again, by definition, at time t PS  =1+ G,, 8  PSNL  From Equation B.7, PS /  ) 8 1a,,  —1 + G —  2 (1—aWL)  (i a) . Therefore 2 —  0,  Appendix B  149  Hence: I  ) 8 1—a,  ,,  UPSI  i1  aNL)  where aNL = 0.89 and  Consider  .  1  \21  aPB  can be expressed in terms of GkF as in Equation B. 13.  Once again, by definition, at time t  0:  =1-G. !‘JL  Hence: Ga=1L. NL  Substituting for a by Equation B.6: 2_20.ap j416.ap 3 4 8 +7.ap ]1 G  1  0.9888  J  B.15  Again, 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 injured tissue may then be determined using Equations B.14 and B.15.  150  Appendix C  Appendix C: NBC Patient Data  The information provided by Dr. T. Lund for each of the 5 patients studied at the National Burn Centre were as follows: i. Patient data on admission: •  Age and sex  •  Total burn surface area or degree of burn  ii. Laboratory data: •  Hematocrit  •  Plasma albumin concentration  •  COPs in plasma and interstitial fluid from injured and uninjured skin  iii. Weight changes with time postburn iv. Resuscitation protocol: •  Clear fluids:  Acetated Ringers, AR Hypertonic Ringers, HR Normal Saline, NS 5% Dextrose, D5W  •  Colloidal fluids: Iso-oncotic Hyperoncotic  •  Blood transfusions  v. Urine produced vi. Initial blood loss due to surgical procedures The original patient data sheets provided for the current study are presented in Figures C. 1 to C.5. Summaries of the patient information for Patients 1, 2, 3, 4 and 5 are shown in Tables C.1 to C.1O. Most of the information was taken from the patient data sheets in Figures C. 1 to C.5 with the exception of the following:  151  Appendix C  jj  .  * IjJ iiioj4 :‘  I  I 1  H  I I .1. I..J  L  ...‘  I  I  ii  /(  b  —  . —  —  Cl.  --  .S1f4,  ..  —fl-  —  .  .  .zs  .  -  . .j : - -  z...z .‘  ..i  :  j,I  .  .  .L1  .  ——I-—.—-————-—-—--— I  z-  ..  li.Z  .  io -1 31  J:  i.  3Lzj/  .:  P8  vs  At-  o .I...J/.. 1 L...I r  iLL Lii  i —  r—--I ‘  IlL:] iI  1J7  -  -  -  Z  -“r  : bbo  f  .  -  :  t  .. -.-.---.--...--  •  ‘3oo  .  1-LEfrifFL  1  . 11!  -  .  TL.cF  LSb.Q.JI(  -  -  .  -.  .  .41  0 k  .  -  r  .-...-  2_-._-..  O4  .  1V UJL- /‘JL-  CcvosO$:  Igçg  7’  M.AJ.’  2c —--  ...  Figure C. 1: NBC Patient 1 Data Sheet  ,  ‘—/?i  -—  -  -  4: -E  152  Appendix C  I  i  II41UNr I I  I  ii 0 L  I  ILl  p:  ‘.2.Otv  :  3;  ‘13  ill-fl  -s  —  -  ..  iii ...  ...,  ..  .  Hht  .  31  .  .  .  zL zzZ  ‘3  LLJi ‘i  .  ..  ...  .Li_L4__L.LL_i.LL.. .  .( .  . -.  ..  .  .  .  .  ...  i—  .  :DSJ CL.EF Ft  co zz.z.  r  .  .  -  —ft  .  Q. Q  ...  .  .1\  9o/  -  -_*.  .7/_  (4(.1  .  _...L/QQ  c1L1AtL4  Tccr LSO-okI(  ...  .  _./z5Z  —----..  Figure C.2: NBC Patient 2 Data Sheet  w”  -  .500 $  A _—so  L  .u  -  /oqq  153  Appendix C  Vd’.i  -rI9  I I  I.i I  Ar.Hss.o’J  ;-j--v7--, T5tY%  <J. 111.1  p.-JJ:[:  1i_  -  cl  :E .:: z. . :z79:: :z:z W. I•1 kL_ :L±E  . ..  1  I 23  .L4_  .  NS :D’.J’  ..  ‘fr  TcF  .  .--  .  .  y  .  .  S5oo O’)  k•  —  /  ‘—-<  1  -7  f—.  r:,  2-  -—CfL3.j/.  -q 0 ----  ..  ._  -  .  //— 7ôo—  ----.\.i ¶.J/. -h---  Lep-TL  ..  ,.J ..  .  3L I1  .ti1..t-:  *W .  r  (  .Ll.  3  TT’  .._T ... . .  .  ‘351.. .  J.ç  j:  :zz.  .  -  — i  t) (Is1744 -I J 1 •Li 1. .1 /. I  g5 .*  p  P3 P  /)f.j/  Figure Ci: NBC Patient 3 Data Sheet  75Q EF  /Si—  -  154  Appendix C  .  .  3 Z’  AeHISSIOI.)  PT 3 &  •1  .  V  4’  (t52  —  zE:  22  L  .3c-  i3.  hE:  ço  -  ttfhri WLLZ_ LL 1  z I  -  .3.  • LO Iqq  .  —•.  9 --.-s-.--—--..--..-..  rr  ..  Z 32  4’  -  C.L  Ii  I  LI  LILt  ,  “I  1 ENII•. 15  11Wz -3  L..  Z  4-  P  ‘Is 1,)  1(1.,  f———i3—-—- --‘/  --  .  L .4L  ,.  LE-  oo—-  ..  22 Sb-  tSOK .  1)0)  CeU.oiGS  L__  / V  —  V •  .  .  V  . _  .  —  —  ,,  _—‘------  .  Figure CA: NBC Patient 4 Data Sheet  -  155  Appendix C  IDP.fE  $1fjg 4 W//  O75  70 hys P8  AMIss’oJ  All,  -  • CI..  P  3 .3c 1WW4 I  I  -  -4---H----—-  I.  coo  Ns.  -  ._LDSJ_.  -  Te.jcF LSc,-QIK  5On  7SO  -  .  ninC  2o  ç  Figure C.5: NBC Patient 5 Data Sheet  I  156  Appendix C  •  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 1 30 year old male Preburn weight  =  88 kg  Total burn surface area = 21%  Time, hrs  Hct, %  VPL, mL  cPL, W1  postburn 0.0  37  4022.86  39.4  13.0  40  3432.95  31.0  -  -  -  35  4228.03  22.0  -  -  -  37  3851.22  25.0  -  -  -  35  4186.80  16.5 31.0 33.5 55.0 57.5 66.0  -  T1’ 11  BT’ 11  mniHg  mmHg  mmHg  14.7  14.7  25.9  -  -  -  10.0  12.5  11.9  -  -  -  5.0  7.0  12.0  -  -  -  -  12.0  6.0 -  -  -  157  Appendix C  Table C.2: Fluid Inputs and Outputs for NBC Patient 1  T, hours  Tend,  hours  CLF,  mL/h  PCF’  mL/h  UR1NE’  mLfh  postburn  postburn  0.0  1.0  0.00  0.00  75.00  1.0  8.0  642.86  0.00  75.00  8.0  17.0  437.50  0.00  122.35  17.0  19.0  437.50  75.00  122.35  19.0  24.0  437.50  0.00  122.35  24.0  28.0  160.00  187.50  106.58  28.0  48.0  160.00  0.00  106.58  48.0  72.0  125.00  0.00  65.46  Tstart  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 URJNE  is the rate of urine production.  i) Between 0 and 1 hour postburn, 200 mL of blood was lost due to surgical procedures.  ii) Exudation Rate  =  45.09 mL/h  158  Appendix C  Table C.3: Admission and Laboratory Data for NBC Patient 2  42 year old female Preburn weight =65 kg 51%  Total burn surface area  Time, hrs  Hct, %  VPL, mL  c, g/L  postburn  TI’  BT’ 11  PL’ 11  mmHg  mniHg  mmHg  0.0  37  2971.43  39.4  14.7  14.7  25.9  13.0  43  2117.19  19.0  -  -  -  18.0  -  -  10.5  11.5  9.5  20.0  33  3233.92  -  -  -  23.0  32  3384.75  -  -  -  29.0  33  3227.42  -  -  -  32.5  -  -  5.0  6.0  12.0  34.5  33  3220.72  -  -  -  -  -  -  -  -  -  3.5  5.0  10.5  -  -  -  -  -  -  48.0  -  -  -  16.0 -  15.0 -  19.0 14.0 22.0  54.5  29  3851.44  56.5  -  -  72.0  27  3776.6  24.0  89.0  33  2825.01  24.0  -  159  Appendix C  Table C.4: Fluid Inputs and Outputs for NBC Patient 2  mL/h  mL/h  mL’h  T, hours  Td, hours  postburn  postburn  0.0  1.0  0.00  0.00  83.75  1.0  8.0  771.43  71.43  83.75  8.0  24.0  843.75  0.00  30.13  24.0  43.0  247.92  52.63  52.17  43.0  47.0  247.92  125.00  52.17  47.0  48.0  247.92  0.00  52.17  48.0  61.0  166.67  20.83  45.79  61.0  63.0  166.67  168.33  45.79  63.0  72.0  166.67  20.83  45.79  CLF,  PCF,  URINE’  i) 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 the albumin content of this fluid, an “equivalent volume” of 750 mL was assumed. iv) Exudation Rate = 80.89 mL/h  160  Appendix C  Table C.5: Admission and Laboratory Data for NBC Patient 3 55 year old male Preburn weight  =  70 kg  Degree = 80%  Time, hrs  Hct, %  VPL, mL  g/L  c,  postburn 0.0  45  3200.00  39.4  7.0  51  2429.04  23.0  -  -  -  56  1986.43  -  -  13.0  56  1982.03  16.0  57  1903.00  20.0  44  3203.30  28.0  51  2413.95  -  -  36.0  47  2827.47  39.0  40  3761.07  44.0  37  4262.52  -  -  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  9.0 10.0 12.0  30.0  48.0  TI’  BT’ 11  PL’ 11  mmHg  mmHg  mmHg  14.7  14.7  25.9  -  -  -  10.5  11.0  9.5  -  -  -  7.0  9.0  7.0  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  6.0  7.0  12.0  -  -  -  -  -  -  -  -  -  -  -  -  7,0  9.5  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  161  Appendix C  Table C.6: Fluid Inputs and Outputs for NBC Patient 3  mL/h  mL/h  mL/h  Tft, hours  Td, hours  postburn  postburn  0.0  0.8  0.00  0.00  77.17  0.8  6.0  2516.13  0.00  77.17  6.0  14.0  777.78  0.00  37.72  14.0  24.0  1097.78  250.00  37.72  24.0  32.0  229.17  0.00  47.58  32.0  48.0  354.17  125.00  47.58  48.0  53.0  132.69  0.00  63.21  53.0  72.0  172.16  39.47  63.21  CLF,  PCF’  U1UNE’  i) Between 0 and 0.8 hours postburn, 200 mL of blood was lost due to surgical procedures. ii) Exudation Rate  =  136.64 mL/h  162  Appendix C  Table C.7: Admission and Laboratory Data for NBC Patient 4  57 year old male Preburn weight  72 kg  Total burn surface area = 59%  Time, hrs  Hct, %  VPL, ‘-  WL  CPL,  postburn 0.0  45  3291.43  39.4  6.0  48  2868.65  29.0  -  -  -  -  -  52.0  2439.87  19.0  -  -  -  48  2852.19  22.0  -  -  31  5849.39  23.0  -  -  -  40.0  37  4469.40  26.0  54.0  35  4854.18  23.0  61.0  38  4258.89  18.0  8.0 11.0 17.5 24.0 26.0  29.0 34.0 36.0  19.0  22.0  “TI’  mmHg  mmHg  mmHg  14.7  14.7  25.9  -  -  -  8.5  12.0  11.0  -  -  -  -  -  -  9.0  -  7.0  -  -  -  -  -  -  -  -  -  6.5  6.0  8.5  -  -  -  -  -  -  -  -  -  163  Appendix C  Table C.8: Fluid Inputs and Outputs for NBC Patient 4  mL/h  mL/h  mL/h  T, hours  Td, hours  postburn  postburn  0.0  0.5  0.00  0.00  74.50  0.5  6.0  1454.55  0.00  74.50  6.0  8.0  772.22  0.00  74.50  8.0  14.0  772.22  166.67  74.50  14.0  19.0  772.22  0.0  74.50  19.0  22.0  772.22  166.67  74.50  22.0  24.0  772.22  0.00  74.50  24.0  28.0  237.50  0.00  42.75  28.0  48.0  250.00  112.50  42.75  48.0  72.0  233.33  3125  68.96  CLF,  PCF’  UR1NE’  i) Between 0 and 0.5 hours postburn, 100 mL of blood was lost due to surgical procedures. ii) Exudation Rate  =  103.65 mL/h  164  Appendix C  Table C.9: Admission and Laboratory Data for NBC Patient 5 31 year old male Preburn weight  78 kg  Total burn surface area  Time, hrs  Hct, %  =  72%  V, mL  g/L  CPL,  postburn  “TI’  ‘ B 1 T’  P1? 11  mmHg  mmHg  mmHg  0.0  45  3565.71  39.4  14.7  14.7  25.9  10.0  56  2221.53  23.0  -  -  -  12.0  -  -  7.5  8.5  8.0  13.0  53  2502.35  -  -  -  -  15.0  47  3182.03  -  -  -  -  17.0  44  3591.39  -  -  -  22.0  43  3734.70  -  -  -  24.0  -  -  4.0  6.0  6.5  27.0  42  3884.76  21.0  -  -  -  31.0  41  4042.08  23.0  -  -  -  36.0  30  6544.54  24.0  7.0  11.0  11.5  41.0  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  -  -  -  -  18.0 -  165  Appendix C  Table C. 10: Fluid Inputs and Outputs for NBC Patient 5  hours  Tend, hours  CLF’ 3  mTJh  PCF’  mLfh  URINE’  mL/h  postburn  postburn  0.0  1.25  0.00  0.00  138.54  1.25  8.0  1037.04  74.07  138.54  8.0  12.0  1025.00  0.00  138.54  12.0  15.0  1025.00  229.17  138.54  15.0  24.0  1115.91  229.17  138.54  24.0  26.0  486.74  156.25  43.83  26.0  38.0  395.83  156.25  43.83  38.0  40.0  645.83  156.25  43.83  40.0  48.0  395.83  156.25  43.83  48.0  50.0  229.17  52.08  92.50  50.0  52.0  229.17  175.83  92.50  52.0  72.0  229.17  52.08  92.50  i) Between 0 and 1.25 hours postburn, 200 mL of blood was lost due to surgical procedures. ii) Between 1.25 and 8 hours, 500 mL of macrodex (dextran 70, 6%) was given. To determine the albumin content of this fluid, an “equivalent volume” of 750 mL was assumed. iii) Exudation Rate  =  137.03  mL/h  AppendixD  166  Appendix D: Estimation of Plasma Volume from Hematocrit Data  Hematocrit, Hct, is a measure of the packed cell volume of red blood cells and is expressed as a percentage of the total blood volume, By. Thus: Hct=  Cell Volume Blood Volume  CV BV  Dl  =—.  The plasma and cellular elements of the blood together constitute the total blood volume, i.e.,  BV=PV-i-CV.  D.2  Consequently, 1 PV=B [l—H V.[l—ct]. Hct]= Hct  D.3  Based on the above relationships and assuming a normal hematocrit of 45% and 41% for the standard male andfemale respectively [Reference Man ICRP 23, 1975], and a normal plasma volume of 3200 mL, normal values of cell and blood volume for the standard 70 kg male and female can be estimated and are shown in Table D. 1.  Table D. 1: Normal Values for 70-kg, 170-cm Individual  Male  Female  45  41  Plasma Volume, PV, mL  3200.00  3200.00  Cell Volume, CV, mL  2618.18  2223.73  Blood Volume, By, mL  5818.18  5423.73  Hematocrit, Hct, %  Appendix D  167  In order to account for differing preburn weights of the patients, the various volumes are modified by a weight ratio, WR, where WR  =  Preburn weight of patient 70  4 17  However, the weight of the patients before injury were unknown on admission. In most of the patients studied, the first few weights were recorded 12 hours and then 24 hours postburn. It was possible to estimate the preburn weight for each patient, based on fluid balances on the patient between two successive times when measurements of weight, fluids given and fluids lost were available, from Change in patient weight = Volume of fluids given Volume of fluids lost -  The procedure is described in detail in Appendix E.  Following from personal communication with Dr. T. Lund, Patients 1 and 2 were considered to be slightly unusual in that their normal hematocrit were below the normal population value. It was concluded that a value of 37% should be used for the normal hematocrit for these two individuals.  Initial blood losses due to escaratomies and fasciotomies were clinically estimated for each patient and were also provided [personal communication with Dr. T. Lund]. In addition, it was assumed that for laboratory purposes, 10 mL blood samples were taken from each patient, four times each day over the three-day period. Associated with these blood losses from the circulating plasma is cell loss, and as such, the changing cell volume was taken account of in estimating the changing plasma volume.  Two patients, 2 and 5, received blood transfusions. This addition to the blood volume and the resulting change in cell volume was considered in estimating the plasma volume. An example of how plasma volumes were estimated is presented in Example D. 1.  Appendix D  168  Example D. 1: Estimation of Plasma Volume for Patient 1  a. Time of injury, t  0  Normal values for Hct, CV, PV and BV  b. Time of admission, t = 13 hours post-injury 200 mL of blood estimated to be lost 1-hour postinjury Therefore:  CV  =  pv= BV  c. t  =  =  2362.63—(200 x 0.37)  =  2288.63 mL  2288.63 x[1—0.40]= 3432.95 mL 0.40 PV+CV = 5721.58 mL  31 hours post-injury 30 mL of blood taken for laboratory analysis Therefore: CV = 2288.63 —(30 x 0.40)  =  2276.63 mL  2276.63 x[1—0.35]= 4228.03 mL 0.35 BV = 6504.66 mL  d. t  =  55 hours post-injury 40 mL of blood taken for laboratory analysis Therefore:  169  Appendix D  CV  =  2276.63—(40x 0.35)  =  2262.63 mL  2262.63  x(1—O.37)= 3852.59 mL 0.37 BV =61 15.22 mL  e. t = 66 hours post-injury 20 mL of blood taken for laboratory analysis Therefore: CV = 2262.63 —(20 x 0.37) = 2255.23 mL x(1—0.35)= 4188.28 mL pv= 2255.23 0.35  BV  =  6443.51 mL  170  Appendix E  Appendix E: Estimation of Exudation Rate Based on NBC Patient Data  The rate of exudation from the injured tissue was determined by performing a fluid balance on each of the 5 patients between two successive measurement times, from Volume” of fluid in patient  Volume of fluids given Volume of fluids lost -  where the “Volume” of the patient is the product of the weight change of the patient and the 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 and blood 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 fluids given, urine, blood and evaporative fluid lost, the exudative fluid loss may be determined from the above fluid balance.  As discussed previously, preburn patient weights were not known on admission. This weight is necessary in estimating the total body surface area, TBSA, to determine the evaporative fluid loss. In most of the patients studied, the first few weights were recorded 12 hours postburn and then 24 hours postburn. In order to determine the preburn weight for each patient, it was assumed that the exudation and evaporation rate during the first  171  AppendixE  indicated times when the patient’s weight was recorded, was the same as that in the first few 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 to evaporation and hence, that due to exudation. The sample calculation, Example E. 1, illustrates this procedure.  Example E. 1: Sample Calculation Estimation of Exudation Rate -  In Patient 1, the first weights were measured 24 and 48 hours postburn. 92.4 kg  At t  =  24 hours, weight  At t  =  48 hours, weight = 89.5 kg  Hence, change in weight  =  -2.9 kg  Assuming the density of the fluids in the body is 1 kg/L; Change in body volume  =  -2900 mL  Fluids given in this period = 3840 mL D5W + 750 mL Iso-oncotic fluid = 4590 mL Fluid losses measured in this period Fluid lost due to evaporation  =  =  2558 mL urine  +  40 mL blood  =  2598 mL  (25+21) x 47O.425 x 1700725 x 71.84 x 10  The preburn weight, W, is unknown. Therefore: Fluid loss due to both evaporation and exudation = -2900 4590 -  +  2598  4892 mL in 24 hours  =  203.83 mL/h  To 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 the same as that between 0 and 24 hours postburn. Change in body weight  (92.4 W) kg -  =  (92.4  3 —w) xio  mL  172  AppendixE  Fluids given in this period  Fluids lost in this period  =  (4500  +  7000) mL AR + 150 mL Iso-oncotic fluid  =  11650 mL  =  (600  +  1958) mL urine  Fluid loss due to evaporation and exudation  =  +  (200  +  20) mL blood  =  2778 mL  4892 mL  92400—W= 11650—2778—4892 W=88420 ml88.4 kg  Therefore fluid lost due to evaporation: 725 x71.84x10 91.75 mL/h =(25+21)x88°’ x170°  EvAp  Hence, fluid lost due to exudation,  4892 E)  —91.75  112.08 mL/h  Exudation rates during the subsequent time periods were also determined from fluid balances as previously described. However, discussions with Dr. T. Lund indicated that the patient weights were not taken in a consistent manner. As such, there was variability in the exudation rates determined for each patient. However, considering the five patients collectively 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 of recorded weights, usually between 12 and 24 hours postburn. It was then assumed that the rate 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. The fitted relationship was forced to pass through the point  ED  0 when DEG  =  0%. The  relationship obtained was EX(JD  where  E)  =0.O244xDEGxW,  E.1  is the fluid loss due to exudation, DEG the degree of burn and W the patient’s  preburn weight. Based on this relationship, an exudative rate was determined and assumed constant for each patient during the first three days postburn.  173  Appendix E  I  ‘  I  I  I  —  50)  -c  E uS 3—  4J  Ct an S  Ct  •0 D  xlw 00  20  40 60 Degree of burn injury, %  80  100  Figure E.1: Exudation Relationship based on NBC Patient Data  174  Appendix F  Appendix F: Birkeland’s Patient Data [19691  This data was used directly in the parameter estimation procedure. The data which could be directly applied in the current study were the plasma volumes of five sets of burn patients, 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 volumes as a function of time for each burn group. The postburn times and corresponding plasma volumes shown in Table F.2 were manually extracted from the solid lines shown in Figure F. 1.  Table F. 1: Grouping of Birkeland’s Patients  Burn Group  Percentage Burn, %  Number of Burn Patients  I  2-9  11  II  10-18  21  III  20-30  17  IV  39-49  7  V  54-90  11  175  Appendix F  Burn  II  .group  V  IV  iii  ‘120 a  V /o  7  Of  a  80 control  ..  60  0•  120 PV 0/0  I.  I  of  I  control  1’.  (20  .1  4  &  12  24  4  8  12  Hou  is  24  4  after  8  12  t4  4  10  812  24  5  burn  Figure F. 1: Patient Blood and Plasma Volume Observations on Admission and Prior to Start of Fluid Therapy by Birkeland  12  Z4  176  Appendix F  Table F.2: Plasma Volume Data (mL) for Groups of Birkelands Patients  Time, hours  Group I  Group II  Group III  Group IV  Group V  3200.00  3200.00  3200.00  3200.00  3200.00  -  -  -  2460.00  2460.00  2950.11  2650.00  2460.00  2050.00  1920.00  -  -  1825.44  1550.78  1751.11  1351.11  -  -  -  -  -  -  -  -  postburn 0.0 1.0 2.0 3.0  -  4.0  2805.78  2450.11  2060.22  6.0  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  -  177  Appendix G  Appendix G: Determination of Exudation Rate for Birkeland’s Patients  Exudative fluid losses from Birkelands patients were estimated based on data available from a study by Davies [1982]. In this study, it was assumed that the sodium concentration in the fluid leaking from the burned surface is the same as that of serum. As a result, chemical analysis of sodium extracted with water from the dressings covering burned tissue gave an indication of the volume of exudate. The rate of exudative fluid loss from patients with different burn areas was monitored during the initial period postburn before fluid therapy was initiated. These patient data [Davies, 1982] are presented in Table Gi. To the best of the author’s knowledge, this is the only available data that could be used to estimate the initial exudative fluid loss from the patients studied by Birkeland.  Table G. 1: Area of Burn and Exudation Rate Postburn  2 Area of Burn, cm  Average Exudate Output, mL/h  7400  26.92  7960  25.67  5624  36.71  7164  22.63  5890  38.50  5220  38.79  4400  12.83  2970  24.58  A linear relationship was determined based on the assumption that the rate of exudation was proportional to the area of the burn. The clinical data and the fitted relationship are  Appendix G  178  shown in Figure G. 1. The fitted relationship was forced to pass through the point  EX  =  0 when DEG = 0%. The relationship obtained was XUD  8.85 xA 3 8x10  G.1  where EX is the rate of exudation and A the area of burn in cm 2 given by A=DEGxTBSA.  G.2  The rate of exudative fluid loss for each group was determined as the  value  corresponding 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 times greater than those reported by Davies for the same burn surface area. This difference may be explained by the fact that the NBC patients received fluid therapy, while fluid resuscitation had not been initiated in the patients studied by Davies in the period under consideration. Similarly, the patients in the various groups investigated by Birkeland received no fluid therapy during the postburn times indicated in Table F.2.  40 0)  30  ci) Q 20 C 0  -o  D ><  w  0 0  2000  4000  6000  8000  Area of Burn, cm**2 Figure G.1: Exudation Relationship based on Davies’ Patient Data  179  Appendix H  Appendix H: Clinical Data from Arturson’s Patient [Arturson et al., 19891  Information regarding the treatment and care of a patient included: i)  fluid therapy consisting of acetated Ringers, 5% glucose, plasma and albumin infusions;  ii) cumulative urine production; iii) erythrocyte volume fraction; and iv) change in body mass. A summary of this information is presented in Tables H. 1 and H.2. These data were used to 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, was treated during the first 48 hours. Primary excision and grafting with synthetic skin was performed between 26.5 and 30 hours after burn injury.  Table H. 1: Erythrocyte Volume Fraction Data [Arturson et a!., 19891  Time, hours postburn  Erythrocyte Volume Fraction,_%  5  50  13  55  20  49  22  46  31  47  38  40  45  35  Appendix H  180  Table H.2: Fluid Inputs and Outputs to Patient [Arturson et al., 1989]  hours  Tend, hours  CLF’  mL/h  PCF’  mL/h  EXUD’ 3  mL/h  URINE,  mL/h  postburn  postburn  0.0  0.5  0.00  0.00  109.56  27.78  0.5  2.5  1200.00  0.00  109.56  27.78  2.5  4.5  1125.00  0.00  109.56  27.78  4.5  8.0  1200.00  0.00  109.56  27.78  8.0  17.0  600.00  0.00  82.97  27.78  17.0  18.0  600.00  48.75  82.97  27.78  18.0  24.0  600.00  48.75  82.97  55.56  24.0  36.0  225.00  31.69  106.70  55.56  36.0  44.0  225.00  31.69  106.70  41.67  44.0  48.0  225.00  49.41  106.70  41.67  181  Appendix I  s Patients [Roa et al., 1990; personal communication] t Appendix I: Clinical Data from Roa  The information pertaining to two patients included: i)  intravenous fluid and colloid input;  ii) urine volume; iii) hematocrit; and iv) plasma protein concentration. Personal data was collected on admission and is summarized in Table I. 1. These data were used 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 2  Age  18  29  Sex  Female  Male  Height, cm  160  160  Weight, kg  55  64  Burn surface area, %  75  80  Appendix I  182  Table 1.2: Fluid Input and Output for Patient 1 [Roa et al., 19901  mL/h  mL/h  mL/h  T, hours  Tfld, hours  postburn  postburn  0.0  1.0  0.0  0.00  0.00  1.0  2.0  428.57  0.00  18.18  2.0  3.0  428.57  0.00  1.18  3.0  4.0  428.57  0.00  0.00  4.0  5.0  428.57  0.00  9.09  5.0  6.0  1464.29  0.00  9.09  6,0  7.0  1500.00  0.00  36.36  7.0  8.0  1214.29  0.00  90.91  8.0  9.0  428.00  0.00  27.27  9.0  10.0  571.43  164.98  27.27  10.0  11.0  571.43  164.98  18.18  11.0  12.0  571.43  58.90  54.55  12.0  13.0  500.00  58.90  36.36  13.0  14.0  500.00  58.90  45.45  14.0  15.0  500.00  212.16  63.64  15.0  16.0  607.14  212.16  36.36  16.0  17.0  607.14  212.16  45.45  17.0  18.0  607.14  212.16  36.36  18.0  19.0  571.43  212.16  45.45  19.0  20.0  571.43  212.16  36.36  20.0  22.0  642.86  212.16  45.45  22.0  23.0  678.57  212.16  36.36  23.0  24.0  500.0  212.16  36.36  24.0  25.0  292.86  170.91  45.45  25.0  26.0  292.86  170.91  36.36  26.0  27.0  292.86  170.91  27.27  27.0  28.0  285.71  82.49  36.36  28.0  29.0  321.43  129.67  36.36  29.0  30.0  321.43  129.67  27.27  CLF’  PCF’  URINE’  Appendix 1  183  Table 1.2 Continued: Fluid Input and Output for Patient I [Roa et al., 1990] hours  Tend, hours  CLF,  mL/h  PCF’  mLIh  IJRINE’ 3  mL/h  postburn  postburn  30.0  31.0  292.86  47,18  36.36  31.0  32.0  214.29  0.00  36.36  32.0  33.0  250.00  47.18  36.36  33.0  34.0  285.71  47.18  36.36  34.0  35.0  250.00  35.30  36.36  35.0  36.0  214.29  0.00  27.27  36.0  37.0  250.00  47.18  27.27  37.0  38.0  214.29  47.18  36.36  38.0  39.0  285.71  47.18  27.27  39.0  40.0  278.51  47.18  27.27  40.0  41.0  285.71  47.18  36.36  41.0  42.0  271.43  47.18  36.36  42.0  43.0  285.71  47.18  27.27  43.0  44.0  271.43  47.18  36.36  44.0  45.0  285.71  47.18  27.27  45.0  46.0  278.51  47.18  27.27  46.0  47.0  278.51  47.18  36.36  47.0  48.0  285.71  47.18  38.18  Appendix 1  184  Table 1.3: Fluid Input and Output for Patient 2 [Roa et al., 1990]  T, hours  Td, hours  postburn  postburn  0.0  1.0  1000.00  0.00  227.27  1.0  2.0  1000.00  0.00  145.46  2.0  3.0  1071.43  164.98  427.27  3.0  4.0  1285.71  0.00  245.46  4.0  5.0  1285.71  0.00  109.09  5.0  6.0  1285.71  0.00  27.27  6.0  7.0  1285.71  0.00  18.18  7.0  8.0  1285.71  0.00  118.18  8.0  9.0  357.14  0.00  27.27  10.0  357.14  0.00  18.18  10.0  11.0  1214.29  0.00  54.55  11.0  12.0  1250.00  0.00  54.55  12.0  13.0  1000.00  0.00  100.00  13.0  14.0  750.00  0.00  145.45  14.0  15.0  714.29  0.00  81.82  15.0  16.0  500.00  0.00  90.91  16.0  17.0  500,00  0.00  32.73  17.0  18.0  642.86  0.00  27.27  18.0  19.0  857.14  0.00  45.45  19.0  20.0  285.71  0.00  45.45  20.0  22.0  285.71  0.00  18.18  22.0  23.0  250.00  0.00  18.18  23.0  24.0  428.57  82.49  32.73  24.0  25.0  428.57  82.49  9.09  25.0  26.0  500.00  0.00  50.91  26.0  27.0  500.00  0.00  54.55  27.0  28.0  571.43  82.49  50.91  28.0  29.0  571.43  82.49  45.46  29.0  30.0  500.00  0.00  36.36  CLF,  mL/h  pCF’  L,’h  URINE’  mL/h  185  Appendix I  Table 1.3 Continued: Fluid Input and Output for Patient 2 [Roa et al., 1990]  mL1h  nil1  mL/h  postburn  Tend, hours postburn  30.0  31.0  500.00  0.00  45.46  31.0  32.0  321.43  64.82  36.36  32.0  33.0  428.57  64.82  27.27  33.0  34.0  507.14  47.13  27.27  34.0  35.0  500.00  0.00  27.27  35.0  36.0  357.14  82.49  36.36  36.0  37.0  357.14  82.49  18,18  37.0  38.0  392.86  0.00  14.55  38.0  39.0  357.14  0.00  27.27  39.0  40.0  500.00  82.49  40.00  40.0  41.0  821.43  82.49  45.46  41.0  42.0  857.14  0.00  54.55  42.0  43.0  357.14  0.00  263.64  43.0  44.0  107.14  82.49  112.73  44.0  45.0  107.14  82.49  54.55  45.0  46.0  85.71  0.00  54.55  46.0  47.0  107.14  0.00  36.36  47.0  48.0  178,57  82.49  36.36  hours  cLF,  PCF’ 3  UR1NE,  I  c  -  a  00  .  —.  C  c  I  ts) J’  -  L,) oc  I  C  C C  I  -  -..  0  C 0  c..  -  -  ‘.o  k’.)  ts)  C  ON  Vi  Vi  C C  .  •‘  I  t  I  -  cM  ci  ‘  4  -  C  c  W  )  t)  I  cM  u  I  -  “0  c  ON  Vi  Vi  Vi  Vi  C  4 cM  I  I  ‘J  b-.)  Vi’ C C  Vi  t)  cc  I  C’,  Vi  cM Vi  00 00  C \0  I  C  C C  I  cM C  Vi 0  Vi  .-..  Vi  c..  00  Vi  Vi  4  t’J  tJ ‘.)  00  Vi  t  Vi  0 C  ON  Vi  Vi  ..  .)  k’.)  t’J  Vi  (  Vi ‘  -  -  Vi ‘3  9p)p9°9°.  I  C  O C  .  C  -  0  -  0  CD  0  CD  -:  0  z  0 -I CD  0  CD  00  CD  187  Appendix 1  Table 1.4 Continued: Monitored Clinical Data for Patient 1 [Roa et al., 1990]  Time, hours  Hematocrit, %  WL  CPL,  postburn 36.82 37.27 37.73 38.64  -  44.44 -  44.44  35.56 -  36.67 -  -  36.67  42.73  42.22  35.56  46.36  38.89  39.09  47.27  -  -  38.89  Table 1.5: Monitored Clinical Data for Patient 2 [Roa et al., 1990]  Time, hours  Hematocrit, %  g/L  CPL,  postburn 1.82  56.67  11.36  60.00  11.82  -  18.18  55.56  26.36  60.00  35.46  -  41.82  51.11  44.55  53.33  45.46  -  54.44 -  35.56 -  32.22 28.89 -  -  30.00  Appendix J  188  Appendix J: Minimum Objective Function Value Results  Table J. 1: Minimum OBJFUN Values for NBC Patient 1 Based on 12 Data Points  EXFAC  r, h’  GkFTT  GkFBT  OBJFUN  0.25  0.008  0.00  4.00  0.71  0.50  0.008  0.00  5.00  0.65  0.75  0.008  0.00  6.00  0.60  1.00  0.008  0.00  6.00  0.55  0.25  0.025  0.00  6.00  0.68  0.50  0.025  0.00  6.00  0.60  0.75  0.025  0.00  7.00  0.53  1.00  0.025  0.00  8.00  0,48  Table J,2: Minimum OBJFUN Values for NBC Patient 2 Based on 20 Data Points  OBJFUN  EXFAC  r, h’  0.25  0.008  0.00  3.00  2.91  0.50  0.008  0.00  4.00  2.67  0.75  0.008  0.00  4.00  2.43  1.00  0.008  0.00  5.00  2.23  0.25  0.025  0.00  5.00  2.56  0.50  0.025  0.50  3.00  2.18  0.75  0.025  0.50  3.00  1.88  1.00  0.025  0.50  4.00  1.63  189  Appendix J  Table J.3: Minimum OBJFUN Values for NBC Patient 3 Based on 22 Data Points  EXFAC  r, h’  GkF  GkFRT  OBJFUN  0.25  0.008  0.00  4.00  5.38  0.50  0.008  0.00  5.00  5.06  0.75  0.008  0.00  5.00  4.76  1.00  0.008  0.00  5.00  4.52  0.25  0.025  0.00  5.00  4.42  0.50  0.025  0.00  5.00  4.16  0.75  0.025  0.00  6.00  3.90  1.00  0.025  0.00  6.00  3.65  Table J.4: Minimum OBJFUN Values for NBC Patient 4 Based on 21 Data Points  OBJFUN  EXFAC  1 r, h  GkF11  0.25  0.008  0.50  3.00  3.31  0.50  0.008  1.00  3.00  3.10  0.75  0.008  1.00  3.00  2.90  1.00  0.008  1.00  4.00  2.86  0.25  0.025  1.00  3.00  3.11  0.50  0.025  1.00  4.00  2.99  0.75  0.025  1.00  4.00  2.84  1.00  0.025  1.00  5.00  2.83  RT  190  AppendixJ  Table J.5: Minimum OBJFUN Values for NBC Patient 5 Based on 30 Data Points  EXFAC  r, h’  FTI 0 k  GkFRT  OBJFUN  0.25  0.008  0.00  5.00  4.04  0.50  0.008  0.00  5.00  3.99  0.75  0.008  0.00  5.00  3.99  1.00  0.008  0.00  6.00  4.00  0.25  0.025  0.50  4.00  3.86  0.50  0.025  0.50  5.00  3.79  0.75  0.025  0.50  5.00  3.75  1.00  0.025  0.50  6.00  3.76  Table J.6: Minimum OBJFUN Values for Combination of NBC Patients 2, 3, 4 and 5 (Degrees of Burn Greater Than 25%)  EXFAC  r, Ir’  GkF  GkFlT  OBJFUN  0.25  0.008  0.00  4.00  16.56  0.50  0.008  0.00  5.00  15.80  0.75  0.008  0.00  5.00  15.15  1.00  0.008  0.00  5.00  14.67  0.25  0.025  0.50  3.00  14.68  0.50  0.025  0.50  4.00  13.72  0.75  0.025  0.50  4.00  13.01  1.00  0.025  0.50  5.00  12.47  191  Appendix J  Table J.7: Minimum OBJFUN Values for Birkeland Burn Group I Based on 6 Data Points  EXFAC  r, h’  GkFTT  GkFRT  OBJFUN  0.25  0.008  0.60  3.00  4 2.005x10  0.50  0.008  0.60  4.00  4 2.100x10  0.75  0.008  0.60  4.00  4 2.124x10  1.00  0.008  0.60  4.00  4 2.156x10  0.25  0.025  0.70  3.00  4 3.569x10  0.50  0.025  0.70  3.00  4 3.562x10  0.75  0.025  0.70  3.00  4 3.560x10  1.00  0.025  0.60  5.00  4 4.941x10  Table J.8: Minimum OBJFUN Values for Birkeland Burn Group II Based on 6 Data Points  GkF RT  OBJFUN  0.90  9.00  3 1.185x10  0.008  0.90  9.00  3 1.164x10  0.75  0.008  0.90  9.00  3 1.151x10  1.00  0.008  0.90  10.00  3 1.128x10  0.25  0.025  1.00  9.00  3 0.958x10  0.50  0.025  1.10  8.00  3 0.918x10  0.75  0.025  1.10  8.00  3 0.882x10  1.00  0.025  1.10  8.00  3 0.855x10  EXFAC  r, h-’  GkF  0.25  0.008  0.50  AppendixJ  192  Table J.9: Minimum OBJFUN Values for Birkeland Burn Group III Based on 5 Data Points  EXFAC  r, h’  GkFTT  GkFRT  OBJFUN  0.25  0.008  3.40  8.00  3 7.733x10  0.50  0.008  3.40  8.00  3 7.886x10  0.75  0.008  3.40  8.00  3 8.039x10-  1.00  0.008  3.20  8.00  3 8.571x10  0.25  0.025  3.80  8.00  3 9.027x10-  0.50  0.025  3.60  8.00  3 9.281x10  0.75  0.025  3.40  9.00  3 9.874x10-  1.00  0.025  7.20  12.00  3 36.42x10-  Table J. 10: Minimum OBJFUN Values for Birkeland Burn Group IV Based on 4 Data Points  EXFAC  1 r, h-  GkFTI  GkFRT  OBJFUN  0.25  0.008  5.80  6.00  3 5.682x10  0.50  0.008  5.80  6.00  3 5.728x10  0.75  0.008  5.80  6.00  3 5.773x10  1.00  0.008  5.80  6.00  3 5.819x10-  0.25  0.025  5.80  6.00  3 6.242x10-  0.50  0.025  5.80  6.00  3 6.301x10  0.75  0.025  5.80  6.00  3 6.359x10  1,00  0.025  5.80  6.00  3 6.418x10  193  Appendix J  Table J. 11: Minimum OBJFUN Values for Birkeland Burn Group V Based on 4 Data Points  EXFAC  r, h’  Gkp  GkFRT  OBJFUN  0.25  0.008  5.80  6.00  2 4.091x10  0.50  0.008  5.80  6.00  2 4.114x10  0.75  0.008  5.80  6.00  2 4.137x10  1.00  0.008  5.80  6.00  2 4.160x10  0.25  0.025  5.80  6.00  2 4.259x10  0.50  0.025  5.80  6.00  2 4.284x10  0.75  0.025  5.80  6.00  2 4.309x10  1.00  0.025  5.80  6.00  2 4.334x10  Table J. 12: Minimum OBIFUN Values for Combination of Birkeland Burn Groups I and II (Degree of Burn Less Than 25%)  EXFAC  r, h’  GkFTT  GkFRT  OBJFUN  0.25  0.008  0.50  12.00  3 9.021x10  0.50  0.008  0.50  12.00  3 9.175x10  0.75  0.008  0.50  12.00  3 9.324x10  1.00  0.008  0.50  12.00  3 9.470x10  0.25  0.025  0.60  12.00  3 9.688x10  0.50  0.025  0.60  12.00  3 9.827x10  0.75  0.025  0.60  12.00  3 9.964x10-  1.00  0.025  0.60  12.00  3 10.10x10  Appendix 1  194  Table J. 13: Minimum OBJFUN Values for Combination of Birkeland Burn Groups III, IV and V (Degrees of Burn Greater Than 25%)  EXFAC  r, h-’  GkFTI  GkFRT  OBJFUN  0.25  0.008  3.80  8.00  2 6.557x10  0.50  0.008  3.60  8.00  2 6.735x10-  0.75  0.008  3.40  8.00  2 6.994x10-  1.00  0.008  3.80  9.00  2 7.110x10  0.25  0.025  3.80  8.00  2 6.905x10  0.50  0.025  3.60  8.00  2 7.158x10  0.75  0.025  4.00  9.00  2 7.274x10  1.00  0.025  5.20  10.00  2 11.88x10-  Table 3.14: Minimum OBJFUN Values for Combination of NBC and Birkeland Data for Burns Less Than 25% for Factor of 30  EXFAC  r, h’  GkFTJ  GkFRT  OBJFUN  0.25  0.008  0.50  7.00  2.53  0.50  0.008  0.50  7.00  2.18  0.75  0.008  0.50  8.00  1.89  1.00  0.008  0.50  8.00  1.65  0.25  0.025  0.50  8.00  1.92  0.50  0.025  0.50  9.00  1.63  0.75  0.025  0.50  9.00  1.39  1.00  0.025  0.50  10.00  1.19  Appendix J  195  Table 3.15: Minimum OBJFUN Values for Combination of NBC and Birkeland Data for Burns Greater Than 25% for Factor of 30  EXFAC  r, h’  GkFTI  GkFRT  OBJFUN  0.25  0.008  0.50  7.00  36.36  0.50  0.008  0.50  7.00  33.91  0.75  0.008  0.50  8.00  31.75  1.00  0.008  0.50  9.00  29.86  0.25  0.025  0.50  8.00  30.80  0.50  0.025  1.00  7.00  28.44  0.75  0.025  1.00  8.00  26.26  1.00  0.025  1.00  9.00  28.05  Table 3.16: Minimum OBJFUN Values for Combination of NBC and Birkeland Data for Burns Less Than 25% for Factor of 100  EXFAC  r, h-’  GkFTI  GkFBT  OBJFUN  0.25  0.008  0.50  10.00  3.44  0.50  0.008  0.50  10.00  3.04  0.75  0.008  0.50  11.00  2.70  1.00  0.008  0.50  11.00  2.43  0.25  0.025  0.50  11.00  2.82  0.50  0.025  0.50  11.00  2.50  0.75  0.025  0.50  12.00  2.22  1.00  0.025  0.50  12.00  2.00  AppendixJ  196  Table J. 17: Minimum OBJFUN Values for Combination of NBC and Birkeland Data for Burns Greater Than 25% for Factor of 100  EXFAC  r, h’  GkFTT  GkFRT  OBJFUN  0.25  0.008  1.00  10.00  54.62  0.50  0.008  1.50  9.00  49.60  0.75  0.008  2.0  8.00  44.83  1.00  0.008  2.50  8.00  40.49  0.25  0.025  1.50  9.00  45.56  0.50  0.025  2.00  9.00  41.10  0.75  0.025  2.00  9.00  37.01  1.00  0.025  2.50  10.00  44.20  Table J. 18: Minimum OBJFUN Values for Combination of NBC and Birkeland Data for Burns Less Than 25% for Factor of 200  EXFAC  r, h’  GkFTT  GkFBT  OBIFUN  0.25  0.008  0.50  11.00  4.40  0.50  0.008  0.50  11.00  4.00  0.75  0.008  0.50  11.00  3.68  1.00  0.008  0.50  12.00  3.41  0.25  0.025  0.50  12.00  3.87  0.50  0.025  0.50  12.00  3.55  0.75  0.025  0.50  12.00  3.29  1.00  0.025  0.50  13.00  3.08  Appendix J  197  Table J. 19: Minimum OBJFUN Values for Combination of NBC and Birkeland Data for Burns Greater Than 25% for Factor of 200  EXFAC  r, h’  GkFTI  GkFBT  OBJFUN  0.25  0.008  2.00  9.00  67.21  0.50  0.008  2.50  8.00  60.68  0.75  0.008  3.00  8.00  54.53  1.00  0.008  2.50  9.00  49.59  0.25  0.025  2.50  9.00  57.30  0.50  0.025  2.50  9.00  51.43  0.75  0.025  2.50  9.00  46.64  1.00  0.025  3.00  11.00  60.03  Appendix K  198  Appendix K: Computer Program Listing  This program was written in Fortran and run on an IBM 486 Personal Computer using the Microsoft Compiler. PRINT*,ENTER SURFACE DATA FILE’ READ*,SURFILE  Program csml.f: The Coupled Starling Model (Patlak Model). A 3conipartinental buni model comprising the folloving: uninjured tissue,  c 11111111 I I  injured tissue, and plasma (the circulation).  c CALCULATE / ASSIGN VARIOUS CONSTANTS  I I  111111111  I I  I I I  I I 11111111  I  ii II  C  PROGRAM CSMI.F  iii  CALL CONSTA  II,1I)IICIl:’REis,I_,*8 (a—I,C—Z)  C  I  11111 I  111111 I I  111111111  liii  I liii liii  include ‘outputcmn’  c  iiicludeiiij,utcsiiii’  ciiIiIIiIiiiIiiiIIiiiiiIiIIiIIIiiiiIIiiiIiiIiiiii  include ‘initvacmn’  ciiiiiiiiIiiiiIiiiIiIiIIIiiilIIIiIiiIIIiIiiIiiiiI  include expdatcmn’ 111111  c  11111  111111  c ADJUST/CALCULATE NORMAL VALUES ii  iii  II  ii  111111  ii  Ii  ciii  DATA DECLARATIONS  11111111111  Iii  ii  11111111111  11111  CALL NORMAL  liii III IIIIIIIIIIIIIIII III 11111 —  FIT COMPLIANCE DATA  CALL COMSPL  imscli.zdenoiiiial.cis’  c  I I I  Number of parameters to be optimized  cliii liii  c  III IIIIIIIII1IIIIIIIIIIIIIIIIIIIIII 1111  ASSIGN/CALCULATE INITIAL VALUES  cIliiIIiiIiiIIIiIiIIIIIIIIIIiIIIIIIIIIIIIIIIiIIII  c  —  Airays for initial guesses for parameters to be optimized  CALL INITV cIiiIiiiiIiIIIIIIiIIIIiiiiIIiIIiIIIIIIIIiIIilIIiI  PER.FORJvIOPTTJ,4JZATION  ciiIIIiIIiIiIiIIIiIIiIiiIIiIIIIiiiIiiIiiiiIIiIi  c  c  cliii  ciIIIIiIiIiIIiIIIIIiIiiIIiIIIIIIiIiIIiiiIiiIiII  c—Setiiitialvaluesamidlixxitsofpa.ia.iiietetstoledeteriiiied  INTEGER MXFLSE, MAXIT, LOG, IPRINT, IFAIL, MAXFUN  XK(l)=GKFTI  REAL*8 ACCUR,SCBOU,F  XK(2)=GKFBT  PARAMETER( M=l,ME=O)  XXL(l)=XL(l)  PARAMETER  (LWA1=MI,  XXL(2)=XL(2)  LWA2=Nl,  LWA3=Ml*Nl,  LWA4=M+2*Nl, LWAS=Nl*Nl, LWA6=Nl, LWA7  =  3* NI *Nl  +2* Ml * Nl+l I *Ml +29*Nl+3*Ml+6O+3*(MIINl+I))  PARAMETER LIWA  18 + (Nl+2+Ml) + Ml + Nl+I,  WORKA2  (LWA2),  XK(I)=GKFTI XK(3)=RCOEF XXL(l)=XL(l)  DIMENSION WORKA4(LWA4) WORKASiLWA5),  XXL(2)=XL(2) WORKA6  (LWA6),  WORXA7(LWA7)  XXL(3)=XL(3) XXU(l)=XU(I)  INTEGER IWORKA(LIWA), JWORKA(LJWA) DIMENSION  XXLJ(2)=XU(2)  XK(2)=GKFBT WORKAI(LWAI),  WORKA3(LWA3)  DIMENSION  XXU(l)=XIJ(l) ELSE IF ( IFLOPT .EQ. 2) THEN  LJWA=MI+20) DIMENSION  DX(NUMP),  HESS(NUMP,  XXU(2)=XU(2) NUMP),  XXU(3)=XU(3) ELSE IF ( IFLOPT EQ. 3) THEN  COVAR(NUMP,NUMP) DIMENSION VARICE(NUMP), INDX (NUMP)  XK(l)=GKFTI  CHARACTER*lO SURFILE  XK(2)=GKFBT  COMMON /CHSUR/SURFILE  XK(3)=RCOEF 11111111 1111111  c I  READ INPUT DATA FILE AND OUTPUT RESULTS FILE  XXL(I )=XL(l) XXL(2)=XL(2)  CALL INPUT  iii III III ill Ii iii  IF ( IFLOPT EQ. 1) THEN  DIMENSION XXL(NUMP),XXIJ(NUMP)  PARAMETER( Nl=NUMP+l, Ml=l)  c  ill iii 11111111  XXL(3)=)<L(3)  11111111  199  Appendix K  XXL(4)XL(4)  PPJNT  XXIJ(l )=XU(l)  WRITE(6,205)EXTIIvIF(I),EXPIBT(I),APIBTII)  ENDIF  XXIJ(2)=XU(2)  XXU(3)=XU(3)  ENDIF  XXU(4)=XIJ(4)  IF (IPAR(3) EQ. 1) THEN  ENDIF  IF (IRATIO EQ. I) THEN  PRINT *,I,EXJ)ITI(I),(PJ)ITJ(I)*PIPLO)/(PJ)lpL(I)t  IF (IFLOPT .GT. 0) THEN IF(IRATIO EQ. 1) CALL RATION  PITIO) WRITE(6,205) ExTIMEa). EXPITI(I), (APITI(I)  CALL SURFACE  *  PIPLO) / (APIPL(I) t PIT 10)  STOP  ENDIF  ELSE  PRINT t ,I,EXPITI(I),APITI(I)  STOP  END  WRfl’E(6,205)EXTIME(I),EXPITI(I), APITI(I)  ENDIF c  ENDIF Subprogram PAROUT: Outputs estimated parameters and results  IF (IPAR(4) EQ. 1) THEN  I**** 4 c*****************fl  IF(IRATIO.EQ. I) THEN PRINT *,I,EECPL(I),ACPL(I)/CPLO  SUBROUTINE PAROUT IMPLICIT REAL*8 (A-KO-Z)  WRITE(6,205)EXTIME(I),EXCPL(I), ACPL(I)ICPLO  include ‘outputcmn’  ELSE  include ‘inputcmn  PRINT t ,I,EXCPL(I),ACPL(I)  include initva.cmn  WRITE(6,205)EXTIME(I),EXCPL(I), ACPL(I)  include ‘normal.cmn’  ENDIF  include ‘expdatcmn’ c  Ii liii III 111111 I  ENDIF liii 111111 11111 liii 111111  II  10  c OUTPUT ESTIMATED PARAMETERS AND RESULTS  c  11111 III  III I I  Iii I liii  11111  WRITE(6,l00) X’lJI’E(6,l00)  I III 1111111111  100 FORMATQ)  WRITE(6,100)  103 F0R.kIATI I  \/RJ1’E(5,l03) WRITE(6,l02)  CONTINUE  GKFTI = GKFTI  =  WRITE(6,l02)’  GREET  WRITE(6,l02)  RCOEF=’,RCOEF  WRITE(6,102)’  EXFAC  =  III I I III 111111111 II’)  102 FORMAT(A30,F18.5) 107 FORMAT  ,GKFBT  Time  Expt  Predicted  )  108 FORMATç— 110 FORMAT(3Fl8.4)  ,EXFAC  205 FORMAT(3F18.4)  WRITE(6,100) WR.ITE(6, 107)  RETURN  WRITE(6, 108)  END  DO 10 I=l,NUMEXP  c******************************************************  IF(IPAR(l) EQ. 1) THEN  c  IF (IRATIO EQ. 1) THEN  Subprogram FUNC: Calculates values of objective fUnction and  ,I,EXVPL(I),AVPL(I)/VPLO PRINT t  constraint fUnctions at current value of X  WRITE(6,205)EXTIME(I),EXVPL(I),AVPL(I)/VPLO  c****************************************************** SUBROUTINE FUNCQ4ME,MMAxN,FF,qx)  ELSE ,I,EXVPL(I),AVPL(I) PRINT t  IMPLICIT REAL 8 (A-H,O-Z) t  WRITE(6,205)EXTIIv8E(I),EXVPL(I), AVPL(I)  include output.cnm include ‘input.crnn  ENDIF  include expdst.cmn  ENDIF  include initvacnin  IF (IPAR(2) .EQ. I) THEN  PARAMETER (VAL=-999.99)  IF (IRATIO EQ. 1) THEN PRINT *j, EXPIBT(I), (APIBT(I)  *  PIPLO) I (APIPL(I)  INTEGER M,MEJvEvIAX,N  *PINTO)  DIMENSION X(N),G(MMAX) 8FF t REAL  WRITE(6,205)EXTIME(I),EXPIBT(I),APIBT(I)*PIPLO)/(APIPL(I)*  CALL SUvlOPTcN)  PINTO) ELSE  Call simulation module SIMOPT with current guesses x (N)  c c  —-  Calculate objective function value  200  Appendix K  FF=0.0  c Subprogram SIMOPT; Simulates the Microvascular Exchange Process  DO l0I=l,NUMEXP  c  IF (IPAR(l) EQ. l)THEN  XK(N)  Amy of values of parameters  NUMP = Number of parameters  IF (EXVPLQ) CT, VAL ) THEN IF(IRATIO.EQ. l)THEN ERROR= (EXVPL(I) AVPL(I) I VPLO )**2  SUBROUTINE SIMOPT(XK,NUMP)  -  IMPLICIT REAL S (A-H,O-Z) 4  ELSE ERROR= (EXVPL(l)AVPL(I))**2  include ‘outputcmn  ENDIF  include ‘inputcmn  2 4t ERROR= ERRORISDVPL(I)  include compli.cmn include initva.cmn  FF=FF+ERROR  include normslcmn  ENDIF  include curent.cmn  ENDIF  include expdatcmn  IF (IPAR(2) EQ. 1) THEN  INTEGER NUMP  IF ( EXPIBT(I) CT. VAL ) THEN IF (UIATIO EQ. 1) THEN RVAL= (APIBT(I) *flLO) / (APIPL(I)  DIMENSION XK(NUMP) *  PIBTO)  e  —  Extemal Subroutine  EXTERNAL MODEL  2 t ERROR= (EXPIBT(I)-RVAL) ELSE ERROR= (EXPIBT(I)-APIBT(I) )**2  c Data for the resolution of model  ENDIF ERROR= ERR0RISDPIBTa) 2 tt  c-—Number of differential equations to be solved PARAMETER (NEQ=6)  FF=FF+ERROR c  ENDIF  Input array into subroutines MODEL and DESOLV or RK4C  —  DIMENSION YA(NEQ)  ENDIF c  IF (IPAR(3).EQ. I) THEN IF (EXPITI(I) CT. VAt) THEN  —  fluid volume and protein contents at the end of each time step) DIMENSION YB(NEQ)  IF (IRATIO EQ. 1) THEN RVAL__(APITI(I)*PIPLO)/(APIPL(I)*PITIO) ERROR  =  c  ---  (EXPITI(I) RVAL)**2  ERROR= (EXPITI(I)-APITI(I) )**2 ENDIF ERROR= ERRORJSDPITI(I)**2  Output array from submutine MODEL (holds values of derivatives) DIMENSION DYDX(NEQ)  -  ELSE  Output array from subroutine DESOLV or RK4C (holds values of  c  —  Data for Runge HuEs Fehlberg algorithm DATA HHflN,HMAX,HSTART,EPS /1 .D-4, I U-I .1 D-I,l .D-2/  cliii 1111111111111 iii  CURRENT VALUES OF PARAMETERS TO BE DETERMINED  FF=FF+ERROR ENDIF ENDIF IF (IPAR(4).EQ. 1) THEN IF (EXCPL(I) CT. VAL ) THEN  ii  IF ( IFLOPT EQ. I ) THEN GKFTI=XK(l) GKFBT=XK(2) ELSEIF(IFLOPT .EQ.2)THEN GKFTI=XK(l)  IF (IRATIO EQ. 1) THEN ERROR= (EXCPL(I)-ACPL(I) I CPLO) **2  GKFBT=XK(2) RCOEF=XK(3)  ELSE ERROR= (EXCPL(I)-ACPL(I) )**2  ELSE IF ( IFLOPT EQ. 3) THEN  GKFTI=XK(l)  ENDIF ERROR= ERROR/SDCPL(I) 2 tt  GKFBT=XK(2)  FF=FF±ERROR  RCOEF=XK(3) EXFAC=XK(4)  ENDIF ENDIF  10 CONTINUE  1111111111111111111111 liii  ENDIF NPNT=0  REUJRN  TIMEW—ODO  END  Xl=TIME(l) YA(l )=VTIO YA(2)=QTIO YA(3)=VBTO  201  Appendix K  IF  YA(4)=QBTO  Xl  AND.  YA(6>=QPLO  THEN DX= EXTIME(IEXPT)-Xl ELSE  IPEROD=l  c----—--------—----  .GT.  YA(5)=VPLO  ISUPER=l  c  (EXrIlvtE(IEXPT)  EXTIME(IEXPT) .LE. XI÷SYBP AND. IEXPT .LE. NUMEXP)  —------—--—--------—  DX=SThP  —--—---------—--  ENDIF  Solve model equations using RKF algorithm  X2’Xl+DX DEPS=(DX/TFINAL)EPS  IEXPT=l  CALL RK4C (MODEL, NEQ, Xl, X2, YA, DEPS,  NFUN=0 c  —  Set excess/deficient makeup rates to zero since no steady state  YB, NFUN, IFLAG) c  period  If integration failed( IFLAG —0) exit else save results  —  IF (IFLAG EQ. 0) THEN  VEXREM=0.D0  WRJTE(6,15) Xl,X2  QEXREM=0.D0 c  —  STOP  Number of periods ELSE  NPEROD=NPETUB  DOS K=l,NEQ  TFINAL=TEND(NPETUB) c  —  YA(K>YB(K)  Loop over the periods  DO 100 IP=l,NPEROD  5  IPEROD=IP  c  CONTINUE Save results  —  IF ( DABS(X2-EXTIME(IEXPT)) .LE. I .OD-6 ) THEN  ISUPER=ISUP(IP)  CALL MODEL (X2,YB,DYDXNEQ)  A=TSTART(IP)  CALL SAVRES (X2,YB,DYDXNEQ)  B=TEND(IP)  IEXPT=IEXPT+l  XJRES(IP)=XJCLF(rP)+XJPCF(IP) Xl=A  ENDIF  X2=Xl  ENDIF IF( X2 .LT. TEND(IP) ) GO TO 900  c—---- Change AFRAC after some time 100  IF (Xl GE. 72.ODO) THEN  5000 CONTINUE  AFRAC=l.0  15  ELSE  FORMAT C No solution between ‘,Fl 8.5.’ and ‘,Fl 8.5) RETURN  AFRAC’=0,5  END  ENDIF c  CONTINUE  900  CONTINUE  Xl=X2 c Subprogram MODEL: Supplies derivatives of differential equations to  c—-- Blood removal IF (Xl .LT. BLSTIM OR Xl GE. BLEND) THEN  be solvei to REF algorithm c  VBLOOD0 0  SUBROUTINE MODEL cYDYDXN)  ELSE  IMPLICIT REAL 8 (A-ItO-F)  VBLOOD=BLOOD/(flEND-BLSTIM)  include ‘input.cmn’  ENDIF c  —-—--  include compli.cmn’  Check if a step of DTAU will overshoot the fmal time for this  include ‘initva.cmn  period TEND(IP) c  include ‘normalcmn’  If it overshoots adjust STEP else STEP = DTAU  include ‘cursnt.cmn’  IF (Xl+DTAU .GT. TEND(IP) ) THEN  INTEGER N  STEP= TEND(IP) Xl -  REAL*8 X,Y(N),DYDXIN)  ELSE STEP DTAU  c  —----  c  FABT=AFRACFATI  Check if there is an experimental point between Xl and  Xl+STEP If there is an experimental point between Xl and Xl+STEP  adjust DX else DX= step size STEP calculated above.  Calculate fractional areas  FATI=((Y(5)/VPLO)-VFRAc)/(l .D0-VFRAC)  ENDIF c  ---—  c c c c  PLASMA --—-------  —  ——  Calculation of Cpl  CPL=Y(6)/Y(5)  —________  Appendix K  C  ---—  202  Calculate osmotic pressure in plasma  PIPL=CPLJI .522D0  c  INJURED TISSUE  Calculate capillaiy pressure  —  IF ( DEG .GT. 0.ODO) THEN  (Y(5)-VPLO) 4 PC=PCO-f-PCCOMP IF (PC .LT. 3.ODO ) PC=3.ODO  CBT=Y(4)/Y(3) CBTAV=Y(4)/(Y(3)-VEBT)  UNINJURED TISSUE  c  —  Calculate hydrostatic pressure for injured tissue IF( IStJPER EQ. 1) THEN  c  —  Calculation of C and Cay for uninjured tissue  DO 30 1=1,12  IF ( X .LT. BTIMERH(I)) THEN  CTI=Y(2)/Y(l)  CTIAV=Y(2)I(Y(I)-VETI) c  —--  11v11-l  Calculate hydrostatic pressure for uninjured tissue  SLOPE(BPRESRH(I)-BPRESRH(Uvi)/  l{PTI=FCOMP(Y(l)) c  (BTIMERH(I) BTIMERH(lM)) -  Calculate HPTIEX  HPBT= BPRESRH(IM)  HPTIEX=FCOMP(VETI) C  —  Calculate osmotic pressure in uninjured tissue  c  —  —--  Calculate fluid fluxes for uninjured tissue  =  ATIPB c  —-  RPNL =  *  —  ELSE IF( ISUPER EQ. 2) THEN  (1 DO + GKFTI * DEXP(RCOEF*X))**0.5DO  HPBT=FCOMBT(Y(3))  RALB/EPTI  ENDIF  Lymph flow sensitivity  100  CONTINUE  Fluid filtration coefficient  HPBTEX=FCOMBT(VEBT)  c  PIBT=CBTAV/1 .522D0  Lymph fluid flow  X2JLTIO  c  XJLNORM + XLSTI  XIJLTIO  =  Calculate osmotic pressure in injured tissue  —  RCOEF*X))*FATI —  Calculate HPBTEX  —  XKFrI=XKFNORM*CORRTI*(l .DO+GKFTI*DEXP(  c  XJLNORM  *  *  (HPTI HPTINL)  c  -  ((HP’fl  -  HPTIEX)/(HPTINL  —  —  Calculate fluid fluxes for injured tissue Pore radii changes postbum  RPBT = RPNL  HFIEX))  AETPB  IF (HPTI GE. HPTINL) THEN XJLTI =XIJLTIO  *  XJLTI = X2JLTIO  *  XKFBT=XKFNORM*CORRBT*(l .D0+  ODO  Lymph fluid flow  XI JLBTO = XJLNORM ÷ XLSBT X2JLBTO  TOPTI  =  l6.DO*ATIPB**2.DO  -  20.DO*ATIPB**3.DO  +  —  —-  -  XJLBT = X2JLBTO  *  CONST  *  CORRTI * FATI  XJLBT  Peclet number  RATIOTI=(CPLCTIAV*DEXP(PECLTI)  PECLTI)) —  --—  c  —  )I(l .DO-DEXP(  =  -  *  AFRAC  *  CORRBT  *  AFRAC  ODO  Sigma I6DO*ABTPB**2D0 20.DO*ABTPB**3.DO  TOPBT +  -  7DO*ABTPB**4DO  Transmembrane protein flow  SIGHT  =  TOPBT/3D0  Fluid filtration flow XJFBT=XKFBT*(PCHPBT.SIGBT*(PlPLPIBT))  Lymph protein flow  QLTI=XJLTI*CTI  HPBTE)Q/ (HPTINL  ENDIF  QSTI=( I .DO.SIGTI)*XJFTI*RATIOTI c  -  -  ELSEIF (HPBT .LT. HPBTEX) THEN  PECLTI=(l .DO-SIGTI)XJFTIIPSTI  c  (HPBT HPTINL)  HPTINL) THEN  Diffusion coefficient ((I DO ATIPB)2.D0)  *  (cHPBT  ELSETF (HPBT GE. HPBTEX AND. HPBT .LT.  Calculate protein fluxes for uninjured tissue  PSTI  c  *  XJLBT = XIJLBTO * CORRBT  Fluid filtration flow  XJFTI=XKFTI*(PC.HPTI.SIGTI*(PWL.PITI))  c  XJLNORM  IF (HPBT GE. HPTINL) THEN  SIGTI = TOPTII3.DO  —  =  HPBTEX))  7.DO*ATIPB**4.DO  c  GKFBT*DEXP(  RCOEF*Xt)*FPBT  c----Sigma  --—  DEXP(RCOEF*X))**O.5DO  Fluid filtration coefficient  CORRTI  ENDIF  c  (I DO + GKFBT  XLSBT=XLSNORM*(l .DO+GLSBT*DEXP(RCOEF*X))  ELSEIF (HPTI .LT. 1-IPTIEX) THEN =  *  RALB/RPBT  c -—Lymph flow sensitivity  CORRTI  ELSEIF (HPTI GE. UPTIEX AND. HPTI .LT. HPTTNL) THEN  XJLTI  (X  CONTINUE  30  XLSTI=XLSNORM*(l .DO+GLSTI*DEXP(RCOEF*X))  c  *  ENDIF  Pore radii changes postbum  RPTI  SLOPE  GOTO 100  Pm=CTIAv/l .522DO  c  +  BTIMERH(IM))  —  Calculate protein fluxes for injured tissue  Appendix K  c  Diffusion coefficient PSBT  c  203  —  =  QEVAP=O.DO  ((IDO ABTPB)**2D0) -  *  CONST  *  CORRBT  *  FABT  QUIUNE=O.ODO  Peclet number  ELSEIF ( IBLANK EQ. 2) THEN  PECLBT=(l .DO-SIGBT)  *  XJFBT I PSET  XJMAIN=O.000  RATIOBT=(CPLCBTAV*DEXP(PECLBT)  )/(l DO  URINE=O.ODO  DEXP(.PECLWr))  VELOOD=O.ODO  c  QEVAP=O.ODO  ----  Transmembrane protein flow QSBT=(1.DO-SIGBT)  c  —  *  XJFBT *RATIOBT  QURINE=O.ODO  Lymph protein flow  ENDIF  QLBT=XJLBT*CBT  c  Fluid and protein balances in uninjured tissue  ——  ENDIF  DYDX(l)=XJFTI-XJLTI-XIEVTI DYDX(2)=QSTI-QLTI  c FLUID AND PROTEIN BALANCES  c  Fluid and protein balances in injured tissue  —-  IF(DEG.GT. O)THEN c  ----—  In actual periods  DYDX(3)=XJFBT-XJLBT-XJEVBT-EXUDN  IF (IPEROD LE. NPETUB ) THEN c  Fluid out  —  DYDX(4)=QSBT-QLBT.QEXUD  urine + wound fluid loss +evaporative fluid loss  ELSE  XJEVTI25.DOTBSA  DYDX(3)=O.O  I OO.DO*TBSA 4 XJEVBT=DEG  DYDX(4)=’O.O  XJMAINODO  ENDIF  EXUDN=XJEXUD(IPEROD)  c  XJREM=URINE  c  +  XJEVTI  DYDX(5)=XJRBS(IPEROD)-(XJFFI-XJLTI)-(XJFBT-XJLBT)+  XJEVBT  +  EXUDN  Protein out = protein in urine + protein in wound fluid loss  —  Fluid and protein balances in plasma  —-  URJNE=XJURI(IPEROD) +  URINE-VEXREM-VBLOOD DYDX(6)=CRES(IPEROD)*XEQPLV (IPERODXQSTI-QLTI) (QSBT.QLBT)QURINE.QEXREM.VBLOOD*cpLo  QEXUD=EXUDN*CBT*EXFAC  RETURN  QEVAP=O.DO  END  QURINEO.ODO QREMQEXUD + QEVAP + QURINE c  —-  In extra period : steady state  C  c  Subproam VrNTr: Calculates vanous initial values  ELSE c  --——  Fluid  SUBROUTINE INITV XJEVTP=O.ODO  IMPLICIT REAL*8 (A-HO-Z)  XJEVBT=O.ODO  include output.cmn  XJMATN=O.ODO  include input.cmn  EXUDNO.ODO  include compli.cnsn  URINE=O.ODO  include initva.cmn  XJREM=O.ODO  include normal.cmn  c---Prot.ein  include curent.cmn’ QEXUD=O.ODO  include expdat.cmn  QEVAP=O.DO QURINE=O.ODO  c  —  Assii and/or calculate various initial values  ENDIF c  —  Set all outputs to zero for a blank run  rF ( IBLANK EQ. 1) THEN  c  PLASMA ( CIRCULATION)  —-—Fluid XJEVTIO.ODO  c  XJEVBT=O.ODO XJMAIN=O.ODO EXUDN=O.ODO  QPLO=QPLNL c  URINE=O.ODO XJREM’O.ODO c---Protein  VandQ  VPLO=VPLNL Calculation of Cpl,o CPLO=QPLO/VPLO c  -----  Calculation ofBVO AND BVF  BVO=VPLO/(l .O-HCTO)  QEXUDO.ODO  BVF=BVO-BLOOD/(l .ODO-HCTO)  204  Appendix K  include initva.cmn  Calculate initial osmotic pressure  c  PARAMETER(VAL=-999.99)  PIPLO=CPLO/l .522D0  DO 10 I=l,NUMEXP  Calculate initial capillary pressure  c  IF(IPAR(l).EQ. l)THEN  PCO=PCNL  IF (EXVPL(I) cIT. VAL) EXVPL(I) C  =  EXVPL(I) /  VPLO  UNINJURED TISSUE  ENDIF IF (IPAR(2) EQ. 1) THEN  c—V and Qforuninjuredtissue VTIO=VTINL*RELSM*DEGM  +  VTINL  *  VETI=VETINL*RELSM*DEGM + VETINL QTIO=QTINL*RELSM*DEGM  +  QTINL  IF (EXPIBT(I) cIT. VAL)  RELM *  *  RELM  *  EXPIBT(I)  Calculate hydrostatic pressure  EXPITI(T)  *  =  (EXPITI(I)  *  PIPLO)  IF (IPAR(4).EQ. 1) THEN IF (EXCPL(I) cIT. VAL) EXCPL(I)  INJURED TISSUE  /  ENDIF  PITIO=CTIAVO/l .5221)0 c  )  /(EXPIPL(I)*PITIO)  Calculate initial osmotic pressure  c  PIPLO  IF (E)’ITI(I) cIT. VAL)  CTIAVO=QTIO/(VTIO-VETI) HPTIOFCOMP(VTIO)  *  IF(IPAR(3).EQ. I) THEN  CTIO=QTIO/VTIO c  (EXPJBT(I)  ENDIF  Calculation of Co and Cav,o  c  =  (EXPIPL(I)*PIBTO)  =  EXCPL(I) /  CPLO ENDIF  IF (DEG cIT. 0.01)0) THEN  10 CONTINUE RETURN  c-----VandQ VBTO=VTINL*RBLSM*DEG  END  VEBT=VETINL*RELSM*DEG QBTO=QTINL*RELSM*DEG Calculation of Co and Cav,o  c  c  -—  —  Subprogram SURFACE; Determine OBJFUN values for  combinations of GKPTI and GKFBT  CBTAVOQBTO/(VBTO-VEBT)  c  Calculate hydrostatic pressure IIFBTO=FCOMBT(VBTO)  c  c  CBTO=QBTO/VBTO  Calculate initial osmotic pressure PIBTO=CBTAVU/I.522D0  SUBROUTINE SURFACE IMPLICIT REAL*8 (A-H,O-Z) include output.cmn’ include inputcmn include initva.cmn  ELSE VBTO=0.ODO  include ‘normal.cmn’  VEBT=0ODO  include expdat.cnm  QBTO=0.ODO  PARAMETER (N=2. M=0, ME=0, MIVIAX=l)  CBTO=0.ODO  PARAMETER(JMAX= 100)  CBTAVO=0.ODO  DIMENSION XTI(JMAX),XBT(JMAX)  HPBTO=0.ODO  DIMENSION X(N)  PIBTO=0.ODO  CHARACTER*20 CDATA(1 0)  ENDIF  CHARACTER*1 0 SURFILE  RETURN  COMMON ICHSUR/SURFILE  END  OPENIUNIT=7,FILE=SURPILE)  READ(7,l 0) NUMTI READ(7, II) (XTI(1),I=l,NUMTI) c  Subprogram RATION: Normalizes quantities with respect to their  initial values  READ(7,10) NIJMBT READ(7,l IXXBT(I),I=l,NUMBT) CLOSE(7)  SUBROUTINE RATION IMPLICIT REAL*8 (A-H,O-Z) include ‘output.cmn  OPEN  (UNIT=8,  FILE’C:\AMVRESV  \//RUNID/fSURF.DAT) DO I I=1,NUMTI  include ‘inputcmn’  X(l)=XTI(I)  include expdat.cmn  1)02 J=l,NUMBT  1/  RUNID  if  Appendix K  205  ) Use CPL data for optimisation (I =YES 0 NOy 4 WRITE(6, ,  IF (XBT(J) CIT. XTI(I) ) THEN  READ(5. IPAR(4) ) 4 IF(IPAR(4) EQ. 1) THEN  X(2)=XBT(J)  ) Enter CPL experimental data file’ 4 WRITE(6,  CALL FUNC (M ME, MMAX N ,OBJVAL,G,X) WRITE(8,200) X(l), X(2), OBJVAL, IDEHYD, IMADEH  ENDW  c  OPENQJMT=5,FILE=PAFILE) WRITE(6,200) READ (5,9 COMENT  CONTINUE  2 I  P-EAD(5, CPFILE ) 4 ENDIF ENDIF OPEN(UMT=6,FILE=SAVDIRJ/RUNIDIFV//RUNID/fRES) PATIENT DATA  CONTINUE  READ (5,4) PATID WRITE(6,208)COMENT,PATID  CLOSE(8) 200 FORMAT(2F10.5,F15.4,213)  208 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 patient READ (5,) COMENT READ (5,4) WEIGHT  9991 FORMAT(2(A2OL’),A20) 10  FORMAT(I2)  11  FORMAT(F18.5)  —  RETURN  WRITE(6,20l)COMENT,WEIGHT  END  c—-Height of patient c Subprogram INPUT: Reads input data, calculates certain constants and prints out SUBROUTINE INPUT IMPLICIT REAL 8 (A-aO-z) 4 include ‘output.cmn’ include ‘input.cmn’ include ‘initvacmn’ include ‘compli.cmn’ include ‘norrnal.cmn’  include ‘grflle.cmn’ include ‘expdst.csnn’ 4 15 OUTFILE,CPFILE CHARACTER 4 15 PAFJLE, OTFILE, PVF]LE. BTFILE, TIFILE, CHARACTER EXFILE  WRITE(6,202)COMENT,NPETUB  READ (5,4) COMENT  OPTIMISATION OF GKFTI,GICFBT, RCOEF &  PEftJJ(5 IFLOPT ) 4 IF(IFLOPT.GT.0)TI-IEN ) ‘Use VPL data for optimisation (IYES 0 NOy 4 WRITE(6, ) IPAR(l) 4 PEAD(5, IF(IPAR(l) EQ. 1) THEN ) Enter VPL experimental data file’ 4 WRITE(6, p,EpIJ(54) PVFILE ENDIF  c  READ(5,’) BTFILE ENDIF  ) Use PITI data for optimisation (1’TES ,0 NO 4 WRITE(6, ) Enter PITI experimental data file’ 4 WRrFE(6, ) TIFILE 4 REPJJ(5, ENDIF  -—  OPTIMIZATION DATA Change in Kf for uninjured tissue  READ (5,4) COMENT READ (5,) GKFTI ,XL(l),XU(l) WRITE(6,207) COMENT, GKFTI. XL(l), XU(l) Change in Kf for injured tissue READ (5,4) COMENT READ (5,4) GKFBT ,XL(2),XU(2) WRITE(6,207ICOMENT,GKFBT ,XL(2),XU(2)  ,  WRITE(6, Use PIBT data for optimisation (1 YES • 0 NOy ) 4 p,aJ)(5,4) IPAR(2) IF(IPAR(2) EQ. 1) THEN ) Enter PIBT Experimental data file’ 4 WRITE(6,  XWCF(I), ISUP(I),  1=1 ,NPETUB) WRITE(6,201 )COMENT WRITE(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)  EXFAC =3  P-,EAD(5, IPAR(3) ) 4 tF(IPAR(3) EQ. 1) TI-lEN  (TSTART(I), TEND(I), XJCLF(I), XJURI(I), XEQPLV(I), XJEXUD(I),  ) 4 READ(5,  CRES(I),  y ‘  —  —---  ) OTFILE 4 READ(5, WRITE(6,) ‘Select type of nm =0 y ) ‘STRAIGHT RUN 4 WRITE(6, 1 WRITE(6,9’ OPTIMISATION OF GKFTI & GREET )’ OPTIMISATION OF GKFTI, GREET & RCOEF 4 WRITE(6, ) 4 WRITE(6,  —  c Start time, end time, clear fluid flow rate, protein-containing fluid rate, protein concentration, urinasy loss, equivalent plasma volume, fluid exudation rate and period indicator for each stage  DATA INPUT WRITE(6, Enter RUN ID’ ) 4 ) RUNID 4 READ(5, ) ‘Enter patient data file’ 4 WRITE(6, ) PAFILE 4 READ(5, ) Enter file for other data’ 4 WRITE(6,  =2  WRITE(6,201)COMENTJIEIGHT Degree of burn READ (5,) COMENT READ (5,) DEG WRITE(6,201)COMENT,DEG c— Initial blood loss READ (5,4) COMENT ) BLOOD,BLSTIM,BLEND 4 READ(5, WRITE(6,207) COMENT, BLOOD, BLSTII4 BLEND c Initial hematocrit READ (5,4) COMENT ) HCTO 4 READ(5, WRITE(6,217)COMENT,HCTO 4444444 RESUSCITATION c Number of resuscitationlperturbation stages READ (5,4) COMENT READ (5,9 NPETUB c  —  CHARACTER 10 SAVDIR,PATID 8O COMENT,CDESC(l 0) 4 CHARACTER PARAMETER(SAVDIR=t:\AMVRESV)  c  READ (5,4) COMENT READ (5,4) HEIGHT  c  Relaxation coefficient READ (5,) COMENT  -----  READ (5,4) RCOEF ,XL(3),XU(3) WRITE(6,207)COMENT,RCOEF,XL(3),XtJ(3)  Factor for protein loss due to exudation READ (5,4) COMENT READ (5,4) EXFAC ,XL(4),XU(4) WIUTE(6,2O7yDOMENT,E)CFAC,XL(4),XU(4) Accuracy and scaling bound READ (5,) COMENT  READ (5,4) ACCUR,SCBOU WRITE(6,204)COMENT,ACCURSCBOU 4444 44 MODEL RESOLUTION c Time step for integration c READ (5,4) COMENT  206  Appendix K  READ(5,’) DTAU WRITE(6,201 )COMENT,DTAU Time step for savmg data for output c D (5,’) COMENT 4 P,E READ(5,’) OUTIME WRITE(6,20l)COMENT.OUTIME c” DATA FOR TYPE OF RUN ‘*“ c Flagfor steady state run P,EAD (5,’) COMENT paJ3(5*) ISTEDY WRJTE(6,202)COMENT,ISTEDY c Flag for blank run: if blank run, IBLANK=l otherwise, IBLANK=0 READ (5,’) COMENT a33(5.*) IBLANK 4 RE WRITE(6,2o2)COMENT,IBLANK c” DATA FOR STEADY STATE RUN c Final steady state time READ (5,’) COMENT READ(5,’) WRITE(6,20l)COMENT,STDTIM c Time to start addition/removal of fluid/protein READ (5,’) COMENT READ(5.’) REMSTA WRfl’E(6,201 )COMENT,REMSTA C Time period for removal/addition offluid/protein READ (5,’) COMENT READ(5,’) DTIME WRITE(6,201 )COMENT,DTIME c “FLAG FOR ‘COMPLIANCE DATA” c——Flag for compliance data READ (5,’) COMENT READ (5,’) ICOMPL WRITE(6,202)COMENT,ICOMPL 4 ORAPHPLOTEING DATA “ c” c Flag to indicate if output data must be saved to plot later READ (5,’) COMENT READ(5,’) IPLOT WRITE(6,202)COMENT,IPLOT Flag to indicate if ratios are to be used for optimization c READ (5,’) COMENT READ(5,’) IRATIO WRITE(6,202)COMENT,IRATIO c flag to indicate if experimental data should be randomized READ (5,’) COMENT READ(5,’) IRAND,RANFAC WRITE(62l 2)COMENT,IItAND,RANFAC c”” EXPERIMENTAL DATA” IF (IPAR(l) EQ. 1) THEN OPEN(UNIT=5,FILE=PYFILE) c —-Number of experimental data points to be fitted READ (5,’) NUIvIEXP c Experimental time (EXTIME), value (EXVPL) and standard deviation (SDVPL) IF (NUMEXP .GT. 0) THEN READ(5,’) (EXTIME(I), EXVPL(I), SDVPLQ), 1=1, NUMEXP) ENDIF ENDIF IF (IPAR(2) EQ. 1) THEN OPENI3JNIT=5,FILE=BTFILE) Number of experimental data points to be fitted c READ (5,’) NUk4EXP Experimental time (EXTIME), value (EXPIBT) and standard c deviation (SDPIBT) IF (NUMEXP .GT. 0) THEN READ(s,’xEXTIME(t),EXPIFT(I)2xPIPL(I),SDPIFT (I),I=l ,NUIvWXP) ENDIF ENDIF IF (IFAR(3) .EQ. I) THEN OPEN(HNIT=5,FILE=TIFILE) Number of experimental data points to be fitted c READ (5,’) NUIvIEXP Experimental time (EXTIME), value (EXPITI) and standard c deviation (SDPITI) IF (NUMEXP .GT. 0) THEN READ(5,’XEXTIME(I),EXPITI(I),EXPIFL(I),SDPITI (I), I=l,NUMEXP) ---—  —  —  -——  —-—  ENDIF ENDIF IF (IPAR(4) EQ. 1) THEN OPEN(UNIT=5,FILE=CPFILE) Number of experimental data points to be fitted c READ (5’) NJMEXP Experimental time (EXTIME). value (EXCPL) and standard c deviation (SDCPL) IF (NUIvIEXP .OT. 0) ThEN SDCPL(I), EXCPL(I), READ(5’X EXTIIvIE(t), I=l,NIJMEXP) ENDIF ENDIF e Calculate total fluid and protein inputs VJN=O.0 QIN=O.0 DO 100 IP=l,NPETUB A=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 CONTINUE ——  —  —  c  —  Formats for printing input data  —  —  —  —  FORMAT (420X,’INPUT DATA’,/20X,’-) FORMAT(ASO,4F20.5) FORMAT(AS0J,15) FORMAT(AS0,4415) FORMAT(A80,42F20.5) FORMAT(SFIO.2) FORMAT(/5X,’ Start End CF Flow PCF Flow Conc Urine EQPLV 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) RETURN END 200 201 202 203 204 205 206  c Subpmgsam CONSTA: Calculates/assigns certain constants SUBROUTINE CONSTA  IMPLICIT REAL’S (A-KO-Z) include ‘output.cmn include ‘input.cmn’  include ‘initva.cmn include ‘compli.cmn include nomial.cmn’ include ‘grfile.cmn include ‘expdat.cmn C I I I I I I  c  I  I  I I I I I  I I I I I II I I-I—I--H-++  Assign change in lymph flow sensitivity  —  clIllIllIllIllIll 11111111111  c c  ---—  GLSTI OLSTI = 0.D0 OLSBT OLSBT = 0.DO  ——  Calculate total surface area of body wTRATI=wEIGHT/Wr HTRATI=HEIGHT/HT TBSA=(WEIOHT”0.425D0) ‘l.D-4 c  —  e c  —----  *  (HEIGHT” 0.725D0)  Set or calculate some constants  DEOM=I .DO-DEG RELM=l .D0-RELSM Normal pore radius RPNL = RALB/ANL Constant for diflirsion coefficient  —-  —  *  71.84D0  207  Appendix K  c  Fluid volume correction factors for compliance data VAFTI=RELSM*DEGM+RELM VAFBThRELSM*DEG Correction factors for KFNORM, LSNORM, PSNORM and  c JLNORM —---  =‘, =‘,  FlO.2) 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) =‘,  =‘,  ,  CORRBT’= WTRATI*VAFBT RETURN END  ‘,  c Subprogram OUTPUT: Prints out all results and makes data files for plots  OUTPUT RESULTS  c  Tabulate all results in a file WRITE(6,800)  c  SUBROUTINE OUTPUT IMPLICIT 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 SAVDIR PAAMETER(SAVDIR’C:\AMVRES\)  C—  ‘,  =‘,  =‘,  CORRTI= WTRATI*VAFTI  c  707 FORMAT (/,20X,’OTHER DATA’,/20X,’) 708 FORMAT (I,5X, ‘GKFrI Fl0.2,5X, GICFBT 709 FORMAT (/,SX,’GSIGTI FlO.2, 5X, ‘GSIGBT  —  WRITE(6,803)VIN  WRITE(6,804)VOUT WRITE(6,805)QIN WRITE(6.8o6)QOur WRITE(6,807)VLNTT WRITE(6,808)VFINAL WRITE(6,809)QINIT WRITE(6,810)QFINAL Fluid volumes c WRITE (6,901) WRITE (6,935) (TIME(I), }IEMA(I),I=l,NPNT) Protein contents C WRITE (6,902) —  OUTPUT NORMAL VALUES —  WRITE(6,707) WRITE(6,708) GKFTI,GKFBT  AVTI(I),  AVBT(I),AVPL(I),  —  WRITE  WRITE(6,7l I) GLSTI,GLSBT  WRITE(6,7l 2) VETI,VEBT WRITE(6,7l3) HPTIEX,HPBTEX WRI’I’E(6,703) TBSA WRITE(6,601) WRITE(6,601) WRITE(6,6O2yNORMAL CONDITIONS’ WRITE(6,602y WRITE(6,60l) WR1TE(6,603)Peclet number ,PENORM XJLNORM WRITE(6,603)’Lymph flow, mI/h ‘,PSNORM WRITE(6,603)Vermeability coefficient, nil/h XKFNORM WRITE(6,603)’Filtration coefficient, nil/h mI/mmHg-h sensitivity, flow WRITE(6,6o3yLymph =‘,XLSNORM SIGNL WRITE(6,603)Reflection coefficient WRITE(6,601) WRITE(6,602)Pressures WRITE(6,602)-—-------’ ‘,HPTINL WRITE(6,603)Tissue hydrostatic pressure, mmHg ‘.VRJTE(6,6o3yTissue colloid osmotic pressure, mmHg ‘,PITINL WRITE(6,603)Vlssma colloid osmotic pressure, mmHg ‘,PIPLNL PCNL WRITE(6,603)’Capillaiy pressure, mmHg WRITE(6,601) ‘.  =‘,  =‘,  =  =  ‘,  WRITE(6,602)’Fluid Volumes’ WRITE(6,602y WRITE(6,603)Tissue fluid volume, ml WRITE(6,603)Plasma fluid volume. ml WRI’I’E(6,60l)  ‘,  VTINL  ‘,  VPLNL  WRITE(6,602)Protein Contents’ WRITE(6,602)’.—----——--’ WRITE(6,603)’Tissue protein content, mg WRITE(6,603)Plasma protein content, mg  (6,900)  (TIME(I),  QPLNL WRITE(6,60l) WRI’l’E(6,602)Protein Concentrations’ WRITE(6,602y--—-----------—-----’ ‘.CTINL WRITE(6,603)Tissue protein concentration, gil ‘,CPLNL WRITE(6,603)Plasma protein concentration, g/l WRITE(6,601) WRITE(6,602)Fluid Fluxes’ WRITE(6,602y-——-----—-’ XJLTINL WRITE(6,603)’Lymph flow, mllh XJFTINL WRITE(6,603)’Filtration flow, nil/h WRITE(6,601) ‘,  =  =  ‘,  ‘,  —  —-----  AQLBT(I), I=l,NPNT) c  —  Put results into files for plotting  WRITE(6,602y QLTINL WRITE(6.603)’Lymph flow, mg/h WRITE(6,603)Transcapillaiy membrane flow, mg/h ‘.  =  ‘,QSTINL  FILE=SAVDIR II (TIME(I)  ,AVTI(I),  RUNID  II  AVBT(I),  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 RUNID II’ PL3.CSV’) WRITE (8,1900) (TIME(I). ACTI(I), ACBT(I), ACPL(I) ,I= I ,NPNT) 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, ‘fI/RUNIDIfPL5.CSV’)  WRJTE(6,602)Protein fluxes’  AQPL(I),  —  IF(IPLOT.EQ. l)THEN OPEN (UNIT=8. ‘i//RUNID//’PLI .CSV’) WRTI’E (8,1900) AVPL(I), I=l,NPNT) CLOSE(8)  QTINL  AQBT(I),  —  OPEN (UNTT=8, = ‘,  AQTI(I),  I=l,NPNT) Protein concentrations c WRITE (6,903) WRITE (6,950) (TIME(I), ACTI(I), ACBT(I), ACPL(I). ACTIAV(I), ACBTAV(I), I=l,NPNT) Hydrostatic pressures c WRITE (6,904) WRITE (6,900) (TIME(I), AHPTI(I), AIIPBT(I), APC(I), I=l,NPNT) c Osmotic pressures WRITE (6,905) WRITE (6.950) (TIME(I), APITI(I), APIBT(I), AP]PL(I), APITIR(I), APIBTR(I), I=l,NPNT) Fluid fluxes c WRITE (6,9l1) WRITE (6.910) (TIME(I), AJFTI(I), AJFBT(I), AJLTI(I), AJLBT(I),I=l,NPNT) Protein fluxes c WRITE (6.912) WRITE (6,9 10) (TIME(I), AQSTI(I), AQSBT(I), AQLTI(I),  FILE=SAVOlE  II RUNID  II  208  Appendix K  WRITE (8,1900) (TIME(r). APITI(I), APIBT(1), APIPL(I), I=l,NPNT) CLOSE(8) OPEN (UNIT=8, FILE= SAVDIR II RUNID /fW/RUNID/i’PL6.CSV’) ‘.VRITE (8.1930) (TIME(I),  AJFTI(I), AJFBT(I), AJLTI(I), AJLBT(I),I=l,NPNT) CLOSE(8) OPEN (UNIT=8, FILE=SAVDIR II RUNID II ‘V//RUNTD/fPL7.CSV’) WRITE (8.1930) (TIME(I), AQSTI(I), AQSBT(1). AQLTI(I), AQLBT(I) ,I=1,NPNT) CLOSE(S) OPEN (UNIT=8, FILE=SAVDIR II RUNID II ‘\V/RUNID/fPLS.CSV) WRITE (8.1900) (TUvIE(I), AVTI(Iy VTIO, AVBT(I)/VBTO,AVPL(I)/VPLO .1=1, NPNT) CLOSE(S) OPEN (UNIT=8, FILE=SAVDIR// RUNID II ‘W/RUNID/fPL9.CSV’) WRiTE (8,1900) (TIME(I), ACTI(I CTIO, ACBT(I)/CBTO,ACPL(I)/CPLO .1=1. NPNT) CLOSE(8) OPEN(UNIT=8,FILE=SAVDIRIIRUNID/fW/ RUNID IfPKI CS’.”) WRITE (S1900) (TIME(I), AHPTI(I)f HPTIO, AHPBT(I)/HPBTO,APC(I)/PCO ,I= I, NPNT) CLOSE(S) OPEN(UNIT8.FILE=SAVDIR//RUN1D/J’\’// RUNTD/fPK2.CSV) WRITE (8,1910) (TIME(I), A1’ITIR(I), APIBTR(I), 1= 1,NPN’I’) CLOSE(S) OPEN(UNIT=8,FILESAVDIPJIRUNID/fV// RUNID/fPlC3.CSV’) WRITE (8,1920) (TIME(I), HEMA(I) .1= l,NPNT) CLOSE(S) ENDIF c c Formats for printing results  FORMAT(4(A20,’,),A20) 9992 FORMAT(2(A20,,).A20) 9993 FORMAT(A20,’,’,A20) 9994 RETURN END c c c Subprogram COMSPL: Determines compliance relationships c SUBROUTINE COMSPL IMPLICIT REAL8 (A-HO-Z) include ‘input cmn’ include ompli.cmn’  40  —  —  IS FORMA’rçnosolutionat’,Fl8.5) 800 FORMAT (I/25X,’ SIMULATION RESULTS’./25X—--------’) 803 FORMAT (/5X’Total fluid input, ml ,Fl8.5) 804 FORMAT (/,5X,’Total fluid output, ml ‘,Fl 8.5) 805 FORMAT (/,5X,’Total protein input, mg ‘,FI 8.5) 806 FORMAT (/,5X,’Total protein output, mg ,F18.5) 807 FORMAT (/,5X,’Total initial fluid content, ml ,Fl 8.5) 808 FORMAT (l,5X.Totsl final fluid content, ml =,F1 8.5) 809 FORMAT (/,5X,’Total initial protein content mg =‘,FI 8.5) 810 FORMAT (/,5X. ‘Total final protein content, mg “,F18.5) 900 FORMAT (F10.2,3Fl5.2) 935 FORMAT (Fl 0.2,3Fl 5.2.Fl 0.2) /2X’ TiME Fluid Volumes 901 FORMAT (/20X,’ Table I : ‘lOX. ‘VT,10X,’VBT,l0X’VPL’) Protein Content 902 FORMAT (120X,’ Table 2 /2X,’ TIME ‘lOX, TI’.loX,’QBr.1oXPL’) + Protein Concencentrations 903 FORMAT (/20x,’ Table 3 : ‘CTr,1oX,’CBr,lo)c’CPL’.5X’CTIAV’,5X, ‘,/2X,’ TIME ‘lOX, ‘CBTAV’) ‘J2X,’ Hydrostatic pressures 904 FORMAT (/20K’ Table 4 TIME’lOX,PTr,lOx,PBr,IOX.PPL) Osmotic pressures—--— ‘,12X,’ 905 FORMAT (/20K’ Table 5 : TIME ‘lOX. pm’,lo)çPIBT,IOX,PIPL’jX.PITIII’,S)c PIBTR’) 910 FORMAT (F10.2,4F15.2) ‘,12X,’ TIME Fluid fluxes 911 FORMAT (/20)c’ Table 6 : ‘I OX, ‘JFIT,IOX,’JFBV,I OX.’JLTI’,l 0)c’JLBT) Protein fluxes’,/2X,’ TIME lOX, 912 FORMAT (/20X,’ Table 7: ‘QSTI’, lOX, ‘QSBT’, lOX, ‘QLTI’, IOX,’QLBT) 915 FORMAT (FIO.2,2Fl5.2) 924 FORMAT (7F10.2) 923 FORMAT (/20X,Table 8 : FLUiD AND PROTEIN BALANCES / TIME’, 5X, DYDX(lY, 5X,’ DYDX(2), 5X, DYDX(3y, SX,DYDX(4y. 5X, DYDX(5)’,SX,’DYDX(G)’) FORMAT(4F20.5) 1900 FORMAT(3F20.5) 1910 FORMAT(2F20.5) 1920 FORMAT(5F20.5) 1930 FORMAT(3(A20.”),A20) 9991  50 60 c  —  8  ,  —  —  —,  —‘,  --  —-—  —--  —  9 c  —  —----  —--—  COMMONIBLKA/XSP(10l).YSP(l01),NSP,NMSP COMMON/BLKB/QSP(100),RSP(l01 ).SSP (100) IF(ICOMPL.EQ. 1) THEN OPEN(UNIT=8,FILE=’COMPLP) ELSE IF ( ICOMPL EQ. 2) THEN OPEN(uNrr=8,FILE=’COMPL2’) ELSE IF ( ICOMPL EQ. 3) THEN OPEN(NIT=8,FILE=’COMPL3) ELSE IF (ICOMPL EQ. 4) THEN OPEN(UNIT=8,FILE’=’COMPL4’) ELSE IF ( ICOMPL .EQ. 5) THEN OPEN(UNIT=8,FILECOMPL5’) ELSE IF ( ICOMPL EQ. 6) THEN OPEN UNIT=8,FILE=’COMPL6) ELSE IF ( ICOMPL EQ. 7) THEN OPEN(UNIT=8.FILE=’COMPL7’) ELSE IF (ICOMPL EQ. 8) THEN OPEN(UNIT=8,FILECOMPL8’) ENDIF READ(8.50) NUM DO 401=1 ,NUM READ(8,60) BTIMERH(I), BPRESRH(I) CONTINUE CLOSE(S) OPEN(UN1T=S,FlLE=’COMPL0l READ(8,S0) NUM READ(8,60) ( VSP(I),PSP(I),I1,NUM) CLOSE(S) M1’NUM MPM=MP-1 FORMAT(15) FORMAT(2F 10.2) Uninjured tissue DOS I’l,MP VCOMTI(I)VSP(I)*WTRATI*VAFTI CONTINUE IBND”2 CALL SPLINE (VCOMTI, PSP. MP, MPM, lEND) NTI=NSP NMTI=NMSP DO 9 Il,NSP XTI(I)=XSP(I) YTI(I)YSP(I) QTI(I)=QSP(I) RTI(I)RSP(I) STI(I)=SSP(I) CONTINUE Injured tissue DOll I=1.MP VCOMBT(I) VSP(I) * WTRATI * VAFET CONTINUE IBND2 CALL SPLINE(VCOMBT.PSP,MP,MPMJBND) NBT=NSP NMBT=NMSP DO 12 I=I,NSP XBT(I)=XSP(I)  11  YBT(l)=YSP(I)  QBT(I)QSP(I) RBT(I)=RSP(I) SBT(I)=SSP(I) 12 CONTINUE RETURN END  209  Appendix K  AVTIINPNT>Y(l) AQTIINPNT)=Y(2) AVBT(NPNT)Y(3) AQBTQ’IPNT)=Y(4) AVPL(NPNT)=Y(5)  C  Subprogram NORMAL: Adjusts/calculates normal values  c  SUBROUTINE NORMAL  8 (A-lI,O-Z) t IMPLICIT REAL include ‘inputcmn include ‘compli.cmn’ include ‘initva.cmn’ include ‘normal.cmn’ CTINL = QTINL/VTINL CTIAVNL = QTINL/(VTINL-VEHNL) CPLNL = QPLNLIVPLNL Calculate normal modified Peclet number, PENORM c TOP = CTtNL (l.D0-SIONL) * CTIAVNL BOT = CTINL (l.D0-SIGNL) * CPLNL PENORM = DLOO(TOP/BOT) Calculate normal JL, XJLNORM c AA = (I JJ0SIONL)*DEXP(PENORM) RB = (1.00- DEXP(-PENORM)) * (VTINL-VETINL) CC = I .D0/VTINL DIV = AA/BB+CC XJLNORM = ALBTO/DIV c-—Calculate normal PS. PSNORM PSNORM = (l.D0SIGNL)* XJLNORM /PENORM Calculate normal KF, XKFNORM c DELP = PCNL IIPTINL SIGNL*(PIPLNLPITINL) XKFNORM = XJLNORM / DELP  AQPL(NPNT)=Y(6)  IF(X EQ. 0.ODO ) THEN HEMA(NPNT) =HCTO ELSEIF (x (IT. BLSTIM AND. X .LE. BLEND) THEN RBV=(BVO-BVF)/(BLEND-BLSTIM) BV BV=BVO-(X-BLSTIM) R t  NEMA(NPI’TI)=l.0-AVPL(NPNT)/BV ELSEIF( XGT. BLEND) THEN BEMA(NPNT)=l .0-AVPL(NPNT)/BVF  —  -  -  —  -—  -  -  c Adjust protein and fluid contents in real patient as opposed to standard human c  c  c  Tissue VTINL=VTINL W t TRATI VETINL=VETJNLWTRATI QTrNL=QTINL*WTRATI Plasma VpLNL=VPLNLWTRATI QPLNL=QPLNL*WrRATI  —-  Assign and/or calculate normal values  -—-  ENDW  Awn(NPNT)=xrn AJLI1(NPNT)XJLTI AQSTI(NPNT)=QSTI AQLTI(NPNT)=QLTI AJFBT(NPNT)=XJFBT AJLBT(NPNT)=XJLBT AQSBT(NPNT)=QSBT AQLBT(NPNT)QLBT A}IPTI(NPNT)=HPTI APITI(NPNT)=PITI APITIR(NPNT)=PITIJPIPL APITIR(NPNT) = (PITI*PIPLO) / (PIPL PITIO) AHPBT(NPNT)=HPBT APIBT(NPN’r)=PIBT APIBTR(NPNT)=PIBT/Pll’L PIPLO) / (PIPL * PIBTO) t APIBTR(NPNT) = (PIBT APC(NPNT)=PC APIPL(NPNT)=PIPL ACTI(NPNT) =CTI ACTIAV(NPNT)=CTIAV ACBT(NPNT) =CBT ACBTAV(NPNT)=CBTAV ACPL(NPNT) =CPL RETURN END  Calculate normal albumin concentrations in tissue and plasma CTINL=QTINLJVTENL CPLNL=QPLNL/VPLNL CTIAVNL= QTINL/(VTINL-VETINL) Calculate fluid fluxes for normal tissue c Lymph fluid flow c * XJLTINL = XJLNORMWTRATI + XLSNORM 1ffpJjJ*(fflIJJ Fluid filtration flow c FRATI W t XJF-ralL=xKFNORM ( 4 PCNL-HPTINLSIGNL(PIPLNL-PITINL)) Calculate protein fluxes for normal tissue C Peclet number PECLET=(l .D0SIGNL)*XJFTINL/(PSNORM*WTRATI) DEXP(-PECLET) )/(I .D0-DEXP(t RATIO=(CPLNL-CTIAVNL PECLETfl Transmembrane protein flow c QSTINL=(I .D0SIGNL)*XJFTINL*RATIO c Lymph protein flow QLT1NL=)CJLTINL*CTINL Constant for diffusion coefficient C 2 tt CONST = PSNORM/(l DO ANL)  c  -—--  BLOCK DATA: Common blocks containing data to be passed between the main program and submutine MODEL  —  —  —--  ----  —--  ----  -  RETURN  END c Subprogram SAVRES: Saves simulation results C  SUBROUTINE SAVRESç’cY,DYD)cNEQ) IMPLICIT REAL*8 (A-FLO-Z) include ‘output.emn include input csnsf include ‘initva.cmn’ include ‘normal.emn include ‘eurentemn’ DIMENSION y(NEQ),DYDx(NEQ) NPNT=NPNT+l mvffiNPwr)=x  BLOCK DATA 8 (A-H,O-Z) t IMPLICIT REAL include ‘outputemn’ include ‘inputcmn’ include ‘eompli.emn include 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/ END  210  Appendix K  10 FUNCTION FCOMP: Interpolation function for uninjured tissue  c  ,D10.3,’ is outside rnterpolation 4 FORMAT(/’Warning in FCRT  rangef) ELSEIF (Z.GT.X(N)) THEN  compliance relationship  I=NM WRITE(6.l 0) Z  **********4*********fl******************************  e  DOUBLE PRECISION FUNCTION FCOMP(Z) 8 (A-H,O-Z) 4 IMPLICIT REAL  include compli.cmn include input.cmn IF (Z .LT. CORRTI 4 840÷3) THEN (Z-CORRTI *840÷3) 4 FCOMP=-0.7DO+AS/CORRTI 4 12.604-3) THEN ELSEIF (Z .GT. CORRTI 2.6D+3) (Z-CORRTI FCOMP=l.88D0+BS/CORRTI I 4 4 ELSEIF (Z .GE.CORRTI 8.40+3 AND. Z .LE.CORRTI 12.60+3) THEN FCO1vIPFCTI(Z)  ENDIF DX=Z-X(I) 4 (Q(I) + DX FCBT = Y(I) + DX  RETURN END  ENDIF RETURN END C  FUNCTION FCOMRT: Interpolation function for injured tissue compliance relationship c c DOUBLE PRECISION FUNCTION FCOMBT(Z) 8 (A-ItO-Z) 4 IMPLICIT RBAL include compli.cmn include inputcmn’ 8.4D+3) THEN 4 IF (Z IT. CORRBT .4D+3) (Z-CORRBT FCOMBT=-0.7DG+AS/CORRBT 8 4 I2.6D+3) THEN 4 ELSEIF (Z LIT. CORRBT (Z4 FCOMBT=l .88D0+BS/CORRBT CORRBT*12.6D+3) 4 4 8.40+3 AND. Z .LE.CORRBT ELSEIF (Z .OE.CORRBT 12.60+3) THEN FCOMBT=FCBT(Z) ENDIF  RETURN END c c FUNCTION FCTI: Uninjured tissue c DOUBLE PRECISION FUNCTION FCTI(Z) IMPLICIT REAL8 (A-H,O-Z) COMMON/BLKTII/X(l 0l),Y(l0l ),N,NM COMMON/BLKTI2/Q(1 00),R(l 01 ),S(1 00) IF (Z.LT.X(I)) THEN 1=1 WRITE(6. 10) Z 44 ,Dl0.3, is outside interpolation 10 FOR1vIATQ’Waming in FCTI  rangeY) ELSEIF (Z.GT.X(N1) THEN  I=NM WR.ITh(6,lO) Z ELSE 1=1  3=N 20  20  ELSE 11 J=N K=(I+Jy2.D0 IF (Z.LT.X(K)) J=K IF (Z.OE.X(K)) I=K IF (J.OT.I+I) 00 TO 20  K=(I+J)/2.D0 IF (Z.LT.X(K)) J=K IF (Z.OE.X(K)) I=K IF (J.GT.I+l) GO TO 20 ENDIF DX=Z-X(I) (I))) Q(I)+DX R(I)+DX FCTI=Y(I)+DX ( S 4  RETURN END c c FUNCTION FCBT  c DOUBLE PRECISION FUNCTION FCBT(Z) 8 (A-ItO-Z) 4 IMPLICIT REAL COMMON/BLKBTIIX(l 01 ),Y(10l),N,NM COMMONIBLKBT2/ Q(I00). R(lOl), S(100) IF (Z.LT.X(1)) THEN 1=1 WRITE(6,lO) Z  *  (R(I) + DXS(I)))  

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