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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.

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 approximately 270 mosmol/l and composition comparable with Ringer solution, and 3) an isosmotic NaCl solution with an osmolarity of approximately 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.

A dynamic mathematical model is formulated and used 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. Two descriptions of transcapillary exchange are investigated: a homoporous "Starling model" and a heteroporous "plasma leak model." Parameters used in the two hypothetical transport mechanisms are determined based on statistical fitting procedures between simulation predictions and selected experimental data. These data consist of interstitial fluid volume and colloid osmotic pressure measurements as a function of venous pressure for muscle and interstitial colloid osmotic pressure vs. venous pressure for skin. The values determined for the transport parameters compare well with data in the literature. The fully determined model is 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. Comparisons between the simulation predictions and experimental data for these various perturbations are made. The plasma leak model appears to provide a better description of microvascular exchange.

The present work uses and extends a dynamic mathematical model [J. L. Bert, B. D. Bowen, and R. K. Reed. Am. J. Physiol. 254 (Heart Circ. Physiol. 23): H384-H399, 1988] to investigate microvascular exchange and interstitial fluid volume regulation in the rat. Alternative concepts of transcapillary exchange as well as other parametric changes were incorporated into the model. In all cases, predictions resulting from these changes did not describe the available experimental information as well as the original model. A sensitivity analysis of the model showed the microvascular exchange system to be well regulated near its normal steady-state conditions through passive readjustment of the forces participating in the volume regulation. The transient rates of fluid and protein exchange were studied in order to determine the mechanisms inherent in the model that lead to fluid volume regulation during episodes of increased venous pressure and hypoproteinemia. In addition to interstitial compliance, lymph flow characteristics, and washdown of interstitial proteins, it was found that the magnitude and direction of reabsorption played an important role in the regulation process. Edema was always associated with a permanent reversal of the reabsorptive flow.