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Gyenge, C. C., B. D. Bowen, R. K. Reed, and J. L. Bert. Transport of fluid and solutes in the body. I. Formulation of a mathematical model. Am. J. Physiol. 277 (Heart Circ. Physiol. 46): H1215-H1227, 1999.--A compartmental model of short-term whole body fluid, protein, and ion distribution and transport is formulated. The model comprises four compartments: a vascular and an interstitial compartment, each with an embedded cellular compartment. The present paper discusses the assumptions on which the model is based and describes the equations that make up the model. Fluid and protein transport parameters from a previously validated model as well as ionic exchange parameters from the literature or from statistical estimation [see companion paper: C. C. Gyenge, B. D. Bowen, R. K. Reed, and J. L. Bert. Am. J. Physiol. 277 (Heart Circ. Physiol. 46): H1228-H1240, 1999] are used in formulating the model. The dynamic model has the ability to simulate 1) transport across the capillary membrane of fluid, proteins, and small ions and their distribution between the vascular and interstitial compartments; 2) the changes in extracellular osmolarity; 3) the distribution and transport of water and ions associated with each of the cellular compartments; 4) the cellular transmembrane potential; and 5) the changes of volume in the four fluid compartments. The validation and testing of the proposed model against available experimental data are presented in the companion paper. hyperosmolarity; cell volume; interstitial volume; plasma volume expansion; plasma osmolarity

Gyenge, C. C., B. D. Bowen, R. K. Reed, and J. L. Bert. Transport of fluid and solutes in the body. II. Model validation and implications. Am. J. Physiol. 277 (Heart Circ. Physiol. 46): H1228-H1240, 1999.--A mathematical model of short-term whole body fluid, protein, and ion distribution and transport developed earlier [see companion paper: C. C. Gyenge, B. D. Bowen, R. K. Reed, and J. L. Bert. Am. J. Physiol. 277 (Heart Circ. Physiol. 46): H1215-H1227, 1999] is validated using experimental data available in the literature. The model was tested against data measured for the following three types of experimental infusions: 1) hyperosmolar saline solutions with an osmolarity in the range of 2,000-2,400 mosmol/l, 2) saline solutions with an osmolarity of ~270 mosmol/l and composition comparable with Ringer solution, and 3) an isosmotic NaCl solution with an osmolarity of ~300 mosmol/l. Good agreement between the model predictions and the experimental data was obtained with respect to the trends and magnitudes of fluid shifts between the intra- and extracellular compartments, extracellular ion and protein contents, and hematocrit values. The model is also able to yield information about inaccessible or difficult-to-measure system variables such as intracellular ion contents, cellular volumes, and fluid fluxes across the vascular capillary membrane, data that can be used to help interpret the behavior of the system. hyperosmolarity; cell volume; interstitial volume; plasma volume expansion; plasma osmolarity

A heat transfer model was developed for thermal balloon endometrial ablation treatment for menorrhagia. The model includes heat conduction through the uterus wall, cooling due to blood perfusion through the uterine tissue and the contribution of metabolic heat generation. A parameter sensitivity study indicated that metabolic heat generation had a minimal effect, but model predictions were sensitive to blood perfusion rate. However, within the range of expected perfusion rates, the model calculates damage depths (3-6 mm) close to the range for effective treatment. Using a blood perfusion rate of 0.0028 m(3)t m(-3)b s(-1), the predicted burn depth (4 mm) correlated well with experimental measurements (4.2 +/- 0.6 mm) reported elsewhere for a treatment temperature of 92 degrees C and time of 6 mins (Neuwirth, R. S. et al. The endometrial ablator: A new instrument. Obstet. Gynecol. 83:792-796, 1994). If no vaporization of water in the tissue occurs, the model predicts that the same burn depth of 4 mm can be obtained with increased treatment temperature (130 degrees C) and shorter treatment time (1.4 min). Steeper temperature profiles through the uterine wall suggest that, in the absence of other changes due to higher temperatures, the deeper layers of the myometrium and the serosa would be protected from thermal damage when using higher treatment temperatures for a shorter duration. However, if vaporization occurs at 105 degrees C, the model predicts little benefit in using treatment temperatures above 120 degrees C up to 160 degrees C. For further validation of the model, in vivo studies using the high temperature treatments are needed to measure temperature profiles through the uterine wall, blood perfusion rates, and the other effects of temperature on uterine tissue.

Both stretching and C48/80 have been hypothesized to cause disruption of cell-matrix adhesions and thereby affect the dynamics of fluid balance in tissues. We investigated the effect of sinusoidal stretching and/or C48/80 on the morphology of fibroblasts in skin excised from the backs of Wistar-Möller rats in order to assess how these stimuli affect cellular interactions in tissues. Tissue samples were either soaked in Krebs' buffer with and without C48/80, or sinusoidally stretched (20% strain) in buffer with and without C48/80. Control skin was fixed immediately after excision. All tissues were processed for transmission electron microscopy. Morphometric analyses demonstrated that sinusoidal stretching of the skin results in the retraction or disruption of fibroblast cytoplasmic extensions, rounding up of the cell bodies and subsequently in increased tissue water content. C48/80 had no apparent effect on fibroblast morphology and adherence in tissues.

In order to understand better the complex, dynamic behaviour of the redistribution and exchange of fluid and solutes administered to normal individuals or to those with acute hypovolemia, mathematical models are used in addition to direct experimental investigation. Initial validation of a model developed by our group involved data from animal experiments (Gyenge, C.C., Bowen, B.D., Reed, R.K. & Bert, J.L. 1999b. Am J Physiol 277 (Heart Circ Physiol 46), H1228-H1240). For a first validation involving humans, we compare the results of simulations with a wide range of different types of data from two experimental studies. These studies involved administration of normal saline or hypertonic saline with Dextran to both normal and 10% haemorrhaged subjects. We compared simulations with data including the dynamic changes in plasma and interstitial fluid volumes VPL and VIT respectively, plasma and interstitial colloid osmotic pressures PiPL and PiIT respectively, haematocrit (Hct), plasma solute concentrations and transcapillary flow rates. The model predictions were overall in very good agreement with the wide range of experimental results considered. Based on the conditions investigated, the model was also validated for humans. We used the model both to investigate mechanisms associated with the redistribution and transport of fluid and solutes administered following a mild haemorrhage and to speculate on the relationship between the timing and amount of fluid infusions and subsequent blood volume expansion.

Airway responsiveness is exaggerated in infancy and declines with maturation. These age-related differences (R.S. Tepper, T. Du, A. Styhler, M. Ludwig, and J.G. Martin. Am. J. Respir. Crit. Care Med. 151: 836-840, 1995; R.S. Tepper, S.J. Gunst, C.M. Doerschuk, Y. Shen, and W. Bray. J. Appl. Physiol. 78: 505-512, 1995; R.S. Tepper, J. Stevens, and H. Eigen. Am. J. Respir. Crit. Care Med. 149: 678-681, 1994) could be due to changes in the smooth muscle, the lung, and/or the airway wall. Folding of the mucosal membrane can provide an elastic load (R.K. Lambert, J. Appl. Physiol. 71: 666-673, 1991), which impedes smooth muscle shortening. We hypothesized that increased stiffness of the mucosal membrane occurs during aging, causing an increased mechanical load on airway smooth muscle and a decrease in airway responsiveness. Forty female New Zealand White rabbits between 0.75 and 35 mo of age were studied. Rectangular mucosal membrane strips oriented both longitudinally and circumferentially to the long axis of the trachea were dissected, and the stress-strain relationships of each strip were tested. The results showed that the membrane was stiffer in the longitudinal than in the circumferential direction of the airway. However, there was no significant change with age in either orientation. We conclude that the mechanical properties of the airway mucosal membrane did not change during maturation and were not likely to influence age-related changes in airway responsiveness.

Folding of the airway mucosal membrane provides a mechanical load that impedes airway smooth muscle contraction. Mechanical testing of rabbit tracheal mucosal membrane showed that the membrane is stiffer in the longitudinal than in the circumferential direction of the airway. To explain this difference in the mechanical properties, we studied the morphological structure of the rabbit tracheal mucosal membrane in both longitudinal and circumferential directions. The collagen fibers were found to form a random meshwork, which would not account for differences in stiffness in the longitudinal and circumferential directions. The volume fraction of the elastic fibers was measured using a point-counting technique. The orientation of the elastic fibers in the tissue samples was measured using a new method based on simple geometry and probability. The results showed that the volume fraction of the elastic fibers in the rabbit tracheal mucosal membrane was approximately 5% and that the elastic fibers were mainly oriented in the longitudinal direction. Age had no statistically significant effect on either the volume fraction or the orientation of the elastic fibers. Linear correlations were found between the steady-state stiffness and the quantity of the elastic fibers oriented in the direction of testing.

Background: Although prostate cancer is the most common life-threatening cancer among males in North America, relatively little is known about its etiology. We have conducted a proportional mortality study to generate hypotheses concerning occupational risk factors for the disease., Methods: Age standardized proportional mortality ratios (PMR) for prostate cancer were calculated for a total of 216 occupations and 88 industries. Separate calculations were done for all male deaths age 20 and up and for deaths that occurred during men's working lifetime (age 20-65)., Results: Elevated mortality from prostate cancer was seen among business owners and managers (PMR = 110; 95% CI = 101-118), brokers (PMR = 184; 95% CI = 122-266), farmers and farm managers (PMR = 112; 95% CI = 105-120), and school teachers (PMR = 133; 95% CI = 101-174). Evaluation by industry shows elevated prostate cancer mortality in agriculture (PMR = 110; 95% CI = 103-118), financial institutions (PMR = 138, 95% CI = 112-170), and transportation equipment manufacture (PMR = 136; 95% CI = 109-168)., Conclusions: The findings suggest that workers in a number of occupations have elevated risks of prostate cancer including farmers and teachers. More detailed cohort and case-control studies, evaluating specific exposures are required before primary prevention programs in the workplace are feasible.

We propose an improvement to the dynamic oscillation method using as an example the measurement of the tensile stiffness of the rabbit tracheal mucosal membrane. A sine wave oscillation technique was used to study the tissue mechanical properties. A mathematical model was developed using fast Fourier analysis. After mathematically eliminating the machine response, this analysis reveals the tissue frequency response over a wide range of frequencies. This study addresses the advantages of using Fourier analysis to interpret dynamic properties of biological tissue and provides a complete description of how to obtain the pure tissue response.

A dynamic compartmental model is developed to describe the redistribution of fluid and albumin between the circulation and the intact and injured interstitia following burn injury in humans. Transcapillary fluid and albumin exchange is described by a coupled Starling mechanism, while the effect of the burn is represented by time-dependent perturbations to all three compartments. The unknown model parameters are determined for two groups of patients, having less than and greater than 25% total body surface area burns, by statistical fitting of model predictions to patient data from two sources. The parameters include the perturbations to the fluid filtration coefficients in uninjured and injured tissue, GkF,Tl and GkF,BT, respectively, the relaxation coefficient, r, which describes the exponential decay of the perturbations, and the exudation factor, EXFAC, which relates the protein concentration in the exudate to that in the injured tissue. Perturbations to other parameters, including the membrane permeability-surface area product and the albumin reflection coefficient in the injured and uninjured tissues, are determined based on interrelationships with GkF,Tl and GkF,BT. The values of GkF,BT, when corrected for tissue destruction and decreased post-injury perfusion, are in reasonable agreement with the limited experimental data available from the literature. The model and its parameters are further validated by comparing the simulated patient responses to the clinical data used in the parameter estimation as well as to data available from two additional sources.

The flow rate of phosphate buffered saline through dermis was measured as a function of applied pressure. Hyaluronan and collagen, the two principal materials which confirm resistance to flow in dermis, were not lost from the tissue during the experiments which lasted up to two days. From Darcy's Law, the average flow conductivities were 2 to 6 x 10(-12) cm4/dyn x s and decreased with increasing applied pressure. We conclude that the tissue is compacted in proportion to the applied pressure during the flow experiments. The hydraulic flow conductivity is described mathematically as a function of compaction induced by the applied pressure.

A mathematical model is formulated and used to describe the distribution and transport of fluid and albumin in the human circulation, interstitium and lymphatics. Two transcapillary mass exchange mechanisms are investigated: a homoporous 'coupled Starling model', in which transcapillary albumin diffusion and convection occur within the same pathway, and a heteroporous 'plasma leak model', in which variations in structure and pressure are permitted along the length of the capillary. Parameters used in the transport models are determined based on statistical fitting of simulation predictions to experimental data from normal humans and nephrotic patients. The data consists of interstitial fluid volumes and interstitial colloid osmotic pressures as functions of plasma colloid osmotic pressure. Model validation is carried out based on comparison of (i) simulation predictions with experimental data used in parameter estimation, (ii) estimated transport parameters with experimentally determined values, and (iii) simulation predictions with a set of dynamic data from an albumin infusion study. While both models with their best-fit parameter estimates provide a good representation of experimental data, the drawbacks of the plasma leak model are three-fold: it requires more estimated parameters than the coupled Starling model, little experimental information exists with which to compare these parameters and, with the best fit values obtained, the plasma leak mechanism becomes insignificant. The model that employs a Starling-type exchange mechanism will therefore be favoured in future applications.

In this paper, a mathematical model of interstitial transport and microvascular exchange within a rigid mesenteric tissue segment is employed to simulate the transient exchange of fluid and plasma proteins following two systemic disturbances: hypoproteinemia and venous congestion. In each case, the model system behavior is studied as a function of interstitial plasma protein transport mechanisms and mesothelial transport properties. Plasma protein washout was generally predicted in cases of hypoproteinemia. However, following venous congestion, the transient change in interstitial plasma protein content also depended on the relative sieving properties of the filtering and draining boundaries. When these boundaries display similar sieving characteristics, the interstitial plasma protein content increases following the disturbance. Such behavior may have some bearing on transient exchange in the hepatic microcirculation during venous congestion.

The present work is a continuation of studies concerned with mathematical modelling and simulation of microvascular fluid and protein exchange following burn injuries [Bert et al.: Circulatory Shock 28: 199-219, 1989: Bowen et al.: Circulatory Shock 28: 221-233, 1989]. The model has been extended to include the effects of different types of fluid resuscitation on the circulatory and microvascular exchange systems. The model and a statistical fitting procedure were used to find the ranges of fitting parameter values that best describe the changes in interstitial fluid volume and protein mass as well as transcapillary protein extravasation for three sets of experiments (no resuscitation, resuscitation with Ringer's or resuscitation with plasma). Typical changes in mass exchange related parameters postburn that resulted in simulation predictions which were a good fit to the experimental data include: an increase in the large pore pathway for protein of 100 times in the injured skin and 5 times in non-injured skin and skeletal muscle, an increase in fluid filtration coefficients in injured skin of 10 times and an instantaneous decrease of 50% in the area available for exchange in injured skin at the time of the burn.

A 10-digit hierarchical method for coding occupationally encountered chemicals offering significant advantages over existing chemical coding systems has been developed and tested. With this unique system, substances are categorized and coded according to their composition and physical natures. Consequently, compounds of similar structure may be distinguished, and classes of similar compounds (for example, all halogenated organic compounds, all inorganic sulfates) can be readily retrieved. This novel coding system was developed to assist primarily in the identification of potential carcinogens in occupational studies using job exposure matrices. However, the system has wider applications as it can be employed by industry to facilitate data management and monitoring programs in the workplace.

A simplified version of the model of interstitial transport developed earlier (D. G. Taylor, J. L. Bert, and B. D. Bowen, 1990, Microvasc. Res. 39, 253-278) is used to investigate microvascular exchange of fluid and a single "aggregate" plasma protein species in mesenteric tissue. The interstitium is approximated by a rigid, rectangular, porous slab displaying two fluid pathways, only one of which is available to plasma proteins. The model is used to explore the effects of the interstitial plasma protein diffusivity, the tissue hydraulic conductivity, the restricted convection of plasma proteins, and the mesothelial transport characteristics on the steady-state distribution and transport of plasma proteins and flow of fluid in the tissue. The simulations predict significant convective plasma protein transport and complex fluid flow patterns within the interstitium. These flow patterns can produce local regions of high fluid and plasma protein exchange along the mesothelium which might be erroneously identified as "leaky sites."

A generalized model is developed to describe the transport of fluid and plasma proteins or other macromolecules within the interstitium. To account for the effects of plasma protein exclusion and interstitial swelling, the interstitium is treated as a multiphase deformable porous medium. Fluid flow is assumed proportional to the gradient in fluid chemical potential and therefore depends not only on the local hydrostatic pressure but also on the local plasma protein concentrations through appropriate colloid osmotic pressure relationships. Plasma protein transport is assumed to occur by restricted convection, molecular diffusion, and convective dispersion. In a companion paper (D. G. Taylor, J. L. Bert, and B. D. Bowen, 1990, Microvasc. Res. 39, 279-306) a simplified version of the model is used to analyze steady-state fluid and plasma protein exchange within mesentery.

An analog computer simulation of human pulmonary microvascular exchange was programmed and tested. This model of blood-to-lymph transport is based on a compartmental analysis of the lungs and has the capacity to describe fluid volumes, plasma protein content, flows and pressures for both normal and perturbed conditions. Normal conditions were predicted and shown to be in agreement with the literature. The trends in the response of the lungs to changes in microvascular pressure is shown also to agree with the literature both for steady state and transient predictions. The results of a sensitivity analysis, which demonstrates the response of the lungs to a variety of perturbations, is also reported. The simulation predicts reasonable results for normal, transient, and perturbed conditions in human lungs.

A mathematical model of microvascular exchange in the rat following a burn injury was developed by extending an existing model of normal microvascular exchange to include perturbations characteristic of burn injuries without fluid resuscitation. The changes anticipated for small (10% body surface area) and large (40% body surface area) burns are incorporated systematically into the model until there is no improvement in the statistical fit of the simulation predictions with the experimental data of Lund and Reed (Circulatory Shock 20:91-104, 1986). The "best fit" perturbations for the small burn include the experimentally measured changes in mean arterial pressure and injured tissue pressure as well as changes to plasma protein and fluid transport coefficients in the injured tissue. The larger burn "best fit" simulation required changes to the plasma protein transport coefficients in the intact tissues as well as all of the changes listed above. The simulation results are compared with the available experimental information on burn injuries as well as with the specific data of Lund and Reed (Circulatory Shock 20:91-104, 1986).

A previously published analog computer simulation of blood to lymph fluid and protein transport in the human lung [Microvascular Research 27, 51-70 (1984)] has been converted to a digital program. Comparisons have been made between the predictions of the two programs for both transient and steady state responses to perturbations. The advantages of each program are discussed. The FORTRAN simulation, including the input and output files are explained. Copies of the program will be made for anyone who wishes to use it.

A compartmental model of a typical 70-kg male for lead intake, distribution, and transport has been developed based on previous pharmacokinetic models and experimental results for lead in the human body. A set of first-order, linear ordinary differential equations with constant coefficients is solved to predict lead levels in blood, bone, and other compartments as a function of time resulting from inputs from air and/or ingestion. The model has been shown to be in excellent agreement with the measurements of blood lead for a controlled study by M. B. Rabinowitz et al. (1976, J. Clin. Invest., 58, 260-270). Favorable agreement was also found with blood and urine results reported by T. B. Griffin et al. (1975, "Lead," pp. 221-240) providing that an allowance was made for an unmeasured input of lead, originating from smoking, snacks, etc. The predictions of the newly formulated model are compared with those of the established Bernard model (S. F. Bernard, 1977, Health Phys., 32, 44-46). Predictions of blood lead concentration for short periods (on the order of months) are fitted better by the new model, while both models predict similar behavior over the longer term (on the order of 5 years and greater).

The present work investigates the implications of the predictions of a dynamic mathematical model of microvascular exchange following a nonresuscitated burn injury in a rat (Bert et al.: Circulatory Shock 28:199-219, 1989). Transport coefficients, transmicrovascular pressures, and the resultant fluid and protein fluxes were examined in order to assess their quantitative importance to the dynamic behavior of small (10% body surface area) and large (40% body surface area) burns. Edema accumulation in the injured tissue is dependent not only on events occurring in that tissue but is influenced strongly by interaction with the plasma and the noninjured tissue compartments.

This study was designed to measure the effective concentration of plasma albumin in the interstitial space of human dermis. Discs of tissue taken postmortem from four donors have been separately analyzed for their content of plasma albumin and equilibrated with 125I-labeled monomeric plasma albumin in a specially designed cell which limited tissue swelling. The equilibrated discs and their surrounding fluid were assayed for radioactivity and the tissue space accessible to albumin was calculated after correction for swelling. The albumin content of serum was also measured. The concentration of albumin in the accessible space of the tissue ranged from 0.45 to 0.93 that in serum, averaging 0.68. The fraction of the total interstitial fluid accessible to albumin averaged, for three normal dermises, 0.35 and for an overhydrated specimen, 0.51. Thus, the effect of volume exclusion should be considered in measurements of the concentrations of plasma proteins in tissue.

Lymphatic flow characteristics, which include both progressive lymphatic blockage and plateau of lymph flow with increasing interstitial fluid volume, were incorporated into an analog computer simulation of microvascular exchange, and their effects on interstitial fluid volume and protein content were investigated. The steady state and transient response of the microcirculation to changes in the properties of the lymph flow system are reported. The interstitial fluid and protein content is investigated as a function of venous pressure and for changes associated with the lymph flow characteristics. The interstitial protein content is generally more sensitive to changes in the lymph flow properties than is interstitial fluid volume. Properties of lymphatic drainage of tissues as they effect microvascular exchange are discussed.