Basic Cardiovascular Computer Model Shows System Degeneracy When Used in Reverse on Standard Measured Parameters

Abstract

Physiology-based computer models are used to simulate the cardiovascular system. When used in reverse the state of a cardiovascular system is determined from measured values and results are used in patient-specific medicine. However, reverse approach is limited by system degeneracy—a situation where the measured values are same but the system states are different. By using uniqueness analysis we explored the origin of system degeneracy by studying it in the most basic two parameter cardiovascular physiological models: Wind-Kessel model of aortic flow. From the model a parameter space of compliance, resistance and a measurement space of peak, mean pressure were generated. Pairs in the parameter space were obtained by gradually increasing each parameter throughout its physiological range. Pairs in the measurement space were equidistant and within the physiological range. Then in parameter space, a family of values was found such that yield peak, the mean pressure within measurement error distance from measurement space pair. The family members when present in the parameter space formed connected components. Number and shape of these components served us to determine the degree of degeneracy. We found that the component in parameter space remains non-divided for all values in measurement space. However, the shape of the component is asymmetrical and depends on the measured value. Compliance showed large uncertainty up to ±31% of its physiological range while uncertainty in peripheral resistance was well ±5%. The large uncertainty in one parameter is a form of degeneracy and we found that it exists already when using the simplest physiological two-parameter model. Models and measured parameters used in reverse engineering need to be carefully evaluated for degeneracy.