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Human microvascular exchange following thermal injury a mathematical model of fluid resuscitation

University of British Columbia

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 fully 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, G[sub kf,ti] and G[sub kf,bt] 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[sub kf,ti] and G[sub kf,bt], 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: G[sub kf,ti] = 0.5, G[sub kf,bt] = 12.0, r = 0.025 h⁻¹ and EXFAC = 1.0. For burns greater than 25%, the optimum parameters are: G[sub kf,ti] = 2.0, G[sub kf,bt] 9.0, r = 0.025 h⁻¹ and EXFAC = 0.75. The sensitivity of the model predictions to changes in G[sub kf,ti] and G[sub kf,bt] for the two burn groups are investigated. For burns less than 25%, G[sub kf,ti] and G[sub kf,bt] 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 G[sub kf,ti] and G[sub kf,bt] 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.

Thesis/Dissertation

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2009-02-23

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http://hdl.handle.net/2429/4918

Chemical and Biological Engineering

University of British Columbia

UBCV

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