A closed-loop cardiovascular model as a teaching framework for physics, mathematical modeling, and scientific computing

Source abstract

Abstract We present a closed-loop lumped-parameter cardiovascular model implemented in Python and organized as a potential teaching framework for computational physics, biophysics, and mathematical modeling in higher education. Rather than proposing a new physiological model, the work reorganizes a classical zero-dimensional (0D) formulation around the electrical analogy between hemodynamic variables and resistor–inductor–capacitor (RLC) circuits. Circuit constitutive relations and Kirchhoff’s laws yield a state-space system of twelve coupled nonlinear ordinary differential equations, integrated with an adaptive Runge–Kutta integration scheme. The modular, object-oriented implementation separates parameters, governing equations, integration, post-processing, and visualization, supporting transparent and reproducible computational investigations. Numerical consistency was evaluated through a 100-cycle baseline simulation, quantitative comparison of cycles 99 and 100, and verification of closed-loop blood-volume conservation. Controlled variations in systemic resistance and aortic-valve properties show how localized parameter changes reorganize pressures, flow rates, ventricular volumes, cardiac output, and pressure–volume loops. The converged responses establish the framework’s physical interpretability, numerical consistency, and reproducibility, providing a coherent setting in which physical assumptions connect directly to observable numerical behavior and guided computational exploration. Because no classroom intervention or formal assessment of learning outcomes was conducted, the educational contribution is presented as a technically developed, testable proposal whose pedagogical effectiveness remains to be evaluated empirically.