Analytical solution to a simplified circulatory model using piecewise linear elastance function

Circuit-based lumped parameter representations of the hemodynamic system are commonly used in teaching and research to analyze the system-level behavior of the circulation. While efficient numerical methods exist to solve the governing differential equations numerically, we present an analytical solution of a simplified hemodynamic model that is based on a piecewise linear ventricular elastance function. It will be shown that the analytical solution is very close to the simulation output of the circuit analog representation, and that computational time can be reduced significantly. Furthermore, we apply parameter estimation techniques to the analytical solution to construct an estimator for the elastance parameters based on experimental hemodynamic waveforms.