Simulating physiological interactions in a hybrid system of mathematical models

Abstract

Mathematical models can be deployed to simulate physiological processes of the human organism. Exploiting these simulations, reactions of a patient to changes in the therapy regime can be predicted. Based on these predictions, medical decision support systems (MDSS) can help in optimizing medical therapy. An MDSS designed to support mechanical ventilation in critically ill patients should not only consider respiratory mechanics but should also consider other systems of the human organism such as gas exchange or blood circulation. A specially designed framework allows combining three model families (respiratory mechanics, cardiovascular dynamics and gas exchange) to predict the outcome of a therapy setting. Elements of the three model families are dynamically combined to form a complex model system with interacting submodels. Tests revealed that complex model combinations are not computationally feasible. In most patients, cardiovascular physiology could be simulated by simplified models decreasing computational costs. Thus, a simplified cardiovascular model that is able to reproduce basic physiological behavior is introduced. This model purely consists of difference equations and does not require special algorithms to be solved numerically. The model is based on a beat-to-beat model which has been extended to react to intrathoracic pressure levels that are present during mechanical ventilation. The introduced reaction to intrathoracic pressure levels as found during mechanical ventilation has been tuned to mimic the behavior of a complex 19-compartment model. Tests revealed that the model is able to represent general system behavior comparable to the 19-compartment model closely. Blood pressures were calculated with a maximum deviation of 1.8% in systolic pressure and 3.5% in diastolic pressure, leading to a simulation error of 0.3% in cardiac output. The gas exchange submodel being reactive to changes in cardiac output showed a resulting deviation of less than 0.1%. Therefore, the proposed model is usable in combinations where cardiovascular simulation does not have to be detailed. Computing costs have been decreased dramatically by a factor 186 compared to a model combination employing the 19-compartment model.