In this paper we show and discuss the use of a versatile interaction potential approach coupled with an immersed boundary method to simulate a variety of flows involving deformable bodies. In particular, we focus on two kinds of problems, namely (i) deformation of liquid-liquid interfaces and (ii) flow in the left ventricle of the heart with either a mechanical or a natural valve. Both examples have in common the two-way interaction of the flow with a deformable interface or a membrane. The interaction potential approach (de Tullio & Pascazio, Jou. Comp. Phys., 2016; Tanaka, Wada and Nakamura, Computational Biomechanics, 2016) with minor modifications can be used to capture the deformation dynamics in both classes of problems. We show that the approach can be used to replicate the deformation dynamics of liquid-liquid interfaces through the use of ad-hoc elastic constants. The results from our simulations agree very well with previous studies on the deformation of drops in standard flow configurations such as deforming drop in a shear flow or a cross flow. We show that the same potential approach can also be used to study the flow in the left ventricle of the heart. The flow imposed into the ventricle interacts dynamically with the mitral valve (mechanical or natural) and the ventricle which are simulated using the same model. Results from these simulations are compared with adhoc in-house experimental measurements. Finally, a parallelisation scheme is presented, as parallelisation is unavoidable when studying large scale problems involving several thousands of simultaneously deforming bodies on hundreds of distributed memory computing processors.

In this paper, the structure and the dynamics of the flow in the left heart ventricle are studied for different pumping efficiencies and mitral valve types (natural, biological and mechanical prosthetic). The problem is investigated by direct numerical simulation of the Navier-Stokes equations, two-way coupled with a structural solver for the ventricle and mitral valve dynamics. The whole solver is preliminarily validated by comparisons with ad hoc experiments. It is found that the system works in a highly synergistic way and the left ventricular flow is heavily affected by the specific type of mitral valve, with effects that are more pronounced for ventricles with reduced pumping efficiency. When the ventricle ejection fraction (ratio of the ejected fluid volume to maximum ventricle volume over the cycle) is within the physiological range (50 %-70 %), regardless of the mitral valve geometry, the mitral jet sweeps the inner ventricle surface up to the apex, thus preventing undesired flow stagnation. In contrast, for pathological ejection fractions ( 40 %), the flow disturbances introduced by the bileaflet mechanical valve reduce the penetration capability of the mitral jet and weaken the recirculation in the ventricular apex. Although in clinical practice the fatality rates in the five-year follow-ups for mechanical and biological mitral valve replacements are essentially the same, a breakdown of the deaths shows that the causes are very different for the two classes of prostheses and the present findings are consistent with the clinical data. This might have important clinical implications for the choice of prosthetic device in patients needing mitral valve replacement.

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Mechanical heart valves implanted in mitral position have a great effect on the ventricular flow. Changes include alteration of the dynamics of the vortical structures generated during the diastole and the onset of turbulence, possibly affecting the efficiency of the heart pump or causing blood cell damage. Modifications to the hemodynamics in the left ventricle, when the inflow through the mitral orifice is altered, were investigated in vitro using a silicone rubber, flexible ventricle model. Velocity fields were measured in space and time by means of an image analysis technique: feature tracking. Three series of experiments were performed: one with a top hat inflow velocity profile (schematically resembling physiological conditions), and two with mechanical prosthetic valves of different design, mounted in mitral position-one monoleaflet and the other bileaflet. In each series of runs, two different cardiac outputs have been examined by changing the stroke volume. The flow was investigated in terms of phase averaged velocity field and second order moments of turbulent fluctuations. Results show that the modifications in the transmitral flow change deeply the interaction between the coherent structures generated during the first phase of the diastole and the incoming jet during the second diastolic phase. Top hat inflow gives the coherent structures which are optimal, among the compared cases, for the systolic function. The flow generated by the bileaflet valve preserves most of the beneficial features of the top hat inflow, whereas the monoleaflet valve generates a strong jet which discourages the permanence of large coherent structures at the end of the diastole. Moreover, the average shear rate magnitudes induced by the smoother flow pattern of the case of top hat inflow are nearly halved in comparison with the values measured with the mechanical valves. Finally, analysis of the turbulence statistics shows that the monoleaflet valves yield higher turbulence intensity in comparison with the bileaflet and, with top hat inflow, there is not a complete transition to turbulence

The understanding of the phenomena involved in ventricular flow is becoming more and more important because of two main reasons: the continuous improvements in the field of diagnostic techniques and the increasing popularity of prosthetic devices. On one hand, more accurate investigation techniques gives the chance to better diagnose diseases before they become dangerous to the health of the patient. On the other hand, the diffusion of prosthetic devices requires very detailed assessment of the modifications that they introduce in the functioning of the heart. The present work is focussed on the experimental investigation of the flow in the left ventricle of the human heart with the presence of a tilting-disk valve in the mitral position, as this kind of valve is known to change deeply the structure of such a flow. A laboratory model has been built up, which consists of a cavity able to change its volume, representing the ventricle, on which two prosthetic valves are mounted. The facility is designed to be able to reproduce any arbitrarily assigned law of variation of the ventricular volume with time. In the present experiment, a physiologically shaped curve has been used. Velocity was measured using a feature-tracking (FT) algorithm; as a consequence, the particle trajectories are known. The flow has been studied by changing both the beat rate and the stroke volume. The flow was studied both kinematically, examining velocity and vorticity fields, and dynamically, evaluating turbulent and viscous shear stresses, and inertial forces exerted on fluid elements. The analysis of the results allows the identification of the main features of the ventricular flow, generated by a mitral, tilting-disk valve, during the whole cardiac cycle and its dependence on the frequency and the stroke volume