Trends in cardiac dynamics : towards coupled models of intracavity fluid dynamics and deformable wall mechanics

We report here preliminary results in the development of a computational model in cardiac mechanics which takes into account the coupled effects of ventricular mechanics and intracardiac hemodynamics. In this first work, complex geometrical, architectural and rheological properties of the organ have been strongly simplified in order to propose a “quasi-analytical” model. We assume axisymmetrical geometry of the ventricle and myocardium material to be made of a sheath of a composite, collagenic, fibrous and active muscle medium inside which the blood dynamics is dominated by unsteady inertial effects. Moreover, we have made grossly simplifying assumptions concerning rather stringent and unusual functioning conditions about the mechanical behavior of the input and output valvular and vascular impedances as well as the biochemical action of the fiber. By imposing the time variation of the input and output flow rate and activation function, it is possible, assuming uniformity of the pressure stresses applied to the internal wall surface at every instant of the cardiac cycle, to calculate the overall distribution of fluid pressure and velocity inside the cavity as well as the distributions of stresses and strains inside the wall. It was shown that under the action of a given biochemical activation function, both kinematics of the wall and induced motion of the fluid are such that the boundary conditions concerning normal pressure stresses conservation was constantly satisfied. Moreover, the results concerning the dynamics of the blood flow, as viewed through the human clinical investigations using velocimetric technology based upon color doppler ultrasound, are in accordance with those obtained from such a model, at least during the ejection phase. In particular, contrarily to the filling phase processes, the ejection dynamics is such that the time evolution of the blood velocity measured along the cavity axis does not display any phase shift characterizing an effect similar to a velocity propagation phenomenon. This model reveals to be interesting by its dual point of view permitting to characterize the cardiac performance from both the fluid and envelope kinematics data, given a few number of parameters related to the geometrical and rheological properties of the heart