Windkessel Model for Hemodynamics in Arterial Systems

Windkessel models describe the dynamics of the heart pumping blood through the arterial system. This Demonstration considers a three-element Windkessel model to describe the hemodynamics of blood transport. Synthetic (Gaussian) and real inflow data are considered. All units are in CGS (except pressure, which is expressed in mmHg).

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Given an inlet blood inflow , the pressure over the venous circulatory system can be modeled through a Windkessel RCR model [1, 2]. The model is based on an electrical analog and describes the hemodynamics of the arterial system in terms of resistance and compliance. More precisely, we consider the following electrical circuit:
where is the peripheral resistance, is the total arterial compliance, is the characteristic impedance and is the venous pressure. The peripheral resistance represents the sum of all resistances in the microcirculation, and the total arterial compliance represents the elastance of large vessels. The equations for this system are
.
In this Demonstration, we solve these equations numerically using an explicit Euler method. It allows a choice between synthetic and real inflow data. In the latter case, this Demonstration allows tuning the parameters to fit the actual pressure data, which was obtained from [3].
References
[1] N. Westerhof, J.-W. Lankhaar and B. E. Westerhof, "The Arterial Windkessel," Medical & Biological Engineering & Computing, 47(2), 2009 pp. 131–141. doi:10.1007/s11517-008-0359-2.
[2] S. Pant, B. Fabrèges, J.-F. Gerbeau and I. E. Vignon-Clementel, "A Methodological Paradigm for Patient-Specific Multi-scale CFD Simulations: From Clinical Measurements to Parameter Estimates for Individual Analysis," International Journal for Numerical Methods in Biomedical Engineering, 30(12), 2014 pp. 1614–1648. doi:10.1002/cnm.2692.
[3] MICCAI 2013. "2nd CFD Challenge Predicting Patient-Specific Hemodynamics at Rest and Stress through an Aortic Coarctation." (Feb 13, 2018) www.vascularmodel.org/miccai2013.
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