A simple, versatile valve model for use in lumped parameter and one‐dimensional cardiovascular models

Abstract

Lumped parameter and one-dimensional models of the cardiovascular system generally employ ideal cardiac and/or venous valves that open and close instantaneously. However, under normal or pathological conditions, valves can exhibit complex motions that are mainly determined by the instantaneous difference between upstream and downstream pressures. We present a simple valve model that predicts valve motion on the basis of this pressure difference, and can be used to investigate not only valve pathology, but a wide range of cardiac and vascular factors that are likely to influence valve motion.

Global sensitivity analysis of a model for venous valve dynamics

“…Further development should allow for modeling of pathological valve regurgitation, which Mynard et al [2012] suggested to implement by an increase in minimal cross-sectional area A min resulting in a valve model that remains partially open. Valve prolapse could be included by defining a negative valve state, as suggested by Pant et al [2015].…”

“…Most models used to represent venous valve dynamics are generally only able to represent the open and closed state (diode) (Fullana and Zaleski [2008]; Müller and Toro [2014]; Zervides et al [2008]), whereas reduced order heart valve models provide more detail (Werner et al [2002]; Zacek and Krause [1996]). More sophisticated reduced-order valve models have been developed by Korakianitis and Shi [2006], who included valve leaflet motion based on a force balance and Mynard et al [2012], who related valve opening state to the pressure drop over the valve. The latter model was extended by Pant et al [2015] to include valve regurgitation due to valve prolapse.…”

“…Our previously presented venous model ) is extended with the versatile valve model of Mynard et al [2012]. The influence of venous filling and valve input parameters on the valve dynamics in a healthy subject is assessed via a sensitivity analysis based on generalized polynomial chaos expansion (gPCE).…”

“…the valve element has no length and spatial parameters are only included for dimensionality) as described by Mynard et al [2012]. Additionally, the viscous losses are included in the pressure flow relation…”

Structural model of the mitral valve included in a cardiovascular closed loop model. Static and dynamic validation

“…The normal motion of the mitral valve during a cardiac cycle has been analyzed by Saito et al [17]. From this qualitative analysis and quantitative values from literature [19][20][21][22][23][24], normal mitral aperture evolution as well as transmitral blood flow during the diastole has been reconstructed, regarding the driving pressure. Figure 5 describes the two peaks E-wave and A-wave corresponding respectively to the passive filling of the ventricle and the active one, due to the atrial contraction.…”