A simple cardiovascular model for the study of haemorrhagic shock

Abstract

Mathematical models and numerical simulations have been used to better understand the physiology of the cardiovascular system and certain pathological processes. Specifically, they have been relied on to estimate the parameters that allow us to represent the most relevant underlying mechanisms in identifiable mathematical terms. After a comprehensive literature search of mathematical modeling techniques, we arrived at our approach to simulating the complex responses of the system to hemorrhage with the aim of first determining the hemodynamic effects of various bleeding rates in the absence of fluid infusion and, in prospective, also taking into account eventual pre- and post- hemorrhagic emergency therapies. Indeed, severe hemorrhage and/or hemorrhagic shock are major causes of permanent organ dysfunction and death in traumatic injuries. Prompt and sustained treatments have been shown to improve survival in trauma patients. Ours is a simplified, ordinary differential equation model of the cardiovascular system geared to analyzing and simulating the quantitative and qualitative responses to acute alterations in blood volume and intravascular fluids. The rationale and design of the model was based on pursuing an acceptable trade-off between complexity-physiological fidelity and alignment with the empirical data. The parameters of the model were identified based on hemodynamic measurements in experimental animal studies. In the more preliminary phases, the model had to undergo progressive fine-tuning. In particular our model was subjected to validation of model predictions through comparisons to empirical in vivo data derived from laboratory animals (i.e. swine). As of yet, albeit on a still limited but ongoing dataset, the model fit has proven valid: simulations conducted thus far have proven the model to perform correctly, also in qualitative terms, with regard to the targeted, clinically relevant, physiological responses. From the perspective of the practice of medicine, the most desirable applications of mathematical modeling would likely address the potential for both "predicting" system behavior and controlling physiologic processes (optimization of therapy). Acknowledging the oft cited words of George Box, "All models are wrong, but some are useful" we propose to define the circumstances under which our model is demonstrably useful.