A Computationally Efficient and Causal Frequency Domain Formalism for Hemodynamics Allowing for Nonlinearities and Generalized Coupling Conditions

Reduced order hemodynamic models are an increasingly important complementary tool to in vivo measurements. They enable effective creation of large datasets with well-defined parameter variations, which can be used, for example, for training machine learning models, conducting virtual studies of intervention strategies, or for the development of pulse wave analysis algorithms. Here, a 1D frequency domain formalism for pulse wave propagation in the cardiovascular system is presented. Using the scattering matrix formulation, a computationally efficient and causal solution is obtained, including possible source terms and nonideal coupling conditions. Local nonlinear effects, as those seen in stenoses or aneurysms, are introduced via an iterative procedure, achieving as good accuracy as state-of-the-art time-domain solvers while being significantly more computationally efficient. The new formalism has been successfully validated against well-documented reference cases from the literature.