|Ph.D Student||Rambod Edmond|
|Subject||Flow Dynamics of Mechanical Heart Valve Closure:|
Formation of Gas Microbubbles
|Department||Department of Medicine||Supervisor||Clinical Professor Simcha Milo|
Background: Various clinical reports have described echocardiographic observations of High Intensity Transient Signals (“HITS”) in the left atrium of patients with mechanical heart valves (MHV). According to their Doppler signal intensities, they have been classified as gaseous emboli. However, the mechanism of their formation has remained unclear. The preliminary in-vitro observations in this research study have confirmed formation of gaseous microbubbles associated with all mitral MHV and occurs at the peak of closure backflow. Under flow conditions, some of these tiny bubbles (< 5 mm) grow explosively and form larger and more persistent bubbles. In this respect, this study has aimed at developing a mathematical-physical model that describes formation of microbubbles at mitral MHV closure and the threshold conditions for their growth.
Method: The mathematical-physical model is based on the physiological flow, pressure and gas concentration conditions at the peak of mitral MHV closure backflow, with liquid velocity at valve closure set to 15 m/s, and vapor pressure of the liquid at about 47.07 mmHg. The model has considered the growth of microbubbles to be attributed to the effects of mass diffusion and, primarily, due to sudden pressure reduction caused by valve closure and vortex formation. Spherical diffusion equation and Prosperetti’s differential equation were solved numerically for diffusion and pressure drop effects, respectively.
Results: The numerical results have confirmed that mass diffusion (being a relatively slow process) contributes only to the growth of nuclei of known radii to a critical radius, CNR. On the other hand, pressure reduction following valve closure appears to be the major contributor to the rapid growth of microbubbles, given a threshold size of the nuclei, to another critical radius, CMR. The results have shown that there is a threshold diameter of about 1.2 mm from which the microbubbles grow explosively. Combination of the unsteady Bernoulli’s equation and the well-known Rayleigh-Plesset yielded a new expression for the growth rate of microbubbles, which also considers the impact of closing gap size (a valve design parameter) and surface tension. Reduction of the closing gap between the leaflets and the housing ring also plays a major role in the microbubble growth, due to squared velocity term. To the lesser extent, reduction of the liquid’s surface tension contributes to the microbubble growth. The physical model and its numerical results were validated by a 2-dimensional experimental study of valvular closure.
Conclusions: Growth of microbubbles at mitral MHV closure is a function of the size of nuclei. While diffusion has little contribution to the growth process, pressure reduction appears to be the major factor with the gap size being the possible additional parameters.