Simulating left ventricular fluid–solid mechanics through the cardiac cycle under LVAD support

In this study we have integrated novel modifications of the standard Newton–Raphson/line search algorithm and optimisation of the interpolation scheme at the fluid–solid boundary to enable the simulation of fluid–solid interaction within the cardiac left ventricle under the support of a left ventricular assist device (LVAD). The line search modification combined with Jacobian reuse produced close to an order of magnitude improvement in computational time across both test and whole heart simulations. Optimisation of element interpolation schemes on the fluid–solid boundary highlights the impact this choice can have on problem stability and demonstrates that, in contrast to linear fluid elements, higher order interpolation produces improved error reduction per degree of freedom. Incorporating these modifications enabled a full heart cycle under LVAD support to be modelled. Results from these simulations show that there is slower clearance of blood entering the chamber during early compared to late diastole under conditions of constant LVAD flow.