A novel approach to in vivo mitral valve stress analysis

Abstract

Three-dimensional (3-D) echocardiography allows the generation of anatomically correct and time-resolved geometric mitral valve (MV) models. However, as imaged in vivo, the MV assumes its systolic geometric configuration only when loaded. Customarily, finite element analysis (FEA) is used to predict material stress and strain fields rendered by applying a load on an initially unloaded model. Therefore, this study endeavors to provide a framework for the application of in vivo MV geometry and FEA to MV physiology, pathophysiology, and surgical repair. We hypothesize that in vivo MV geometry can be reasonably used as a surrogate for the unloaded valve in computational (FEA) simulations, yielding reasonable and meaningful stress and strain magnitudes and distributions. Three experiments were undertaken to demonstrate that the MV leaflets are relatively nondeformed during systolic loading: 1) leaflet strain in vivo was measured using sonomicrometry in an ovine model, 2) hybrid models of normal human MVs as constructed using transesophageal real-time 3-D echocardiography (rt-3DE) were repeatedly loaded using FEA, and 3) serial rt-3DE images of normal human MVs were used to construct models at end diastole and end isovolumic contraction to detect any deformation during isovolumic contraction. The average linear strain associated with isovolumic contraction was 0.02 ± 0.01, measured in vivo with sonomicrometry. Repeated loading of the hybrid normal human MV demonstrated little change in stress or geometry: peak von Mises stress changed by <4% at all locations on the anterior and posterior leaflets. Finally, the in vivo human MV deformed minimally during isovolumic contraction, as measured by the mean absolute difference calculated over the surfaces of both leaflets between serial MV models: 0.53 ± 0.19 mm. FEA modeling of MV models derived from in vivo high-resolution truly 3-D imaging is reasonable and useful for stress prediction in MV pathologies and repairs.

Fig. 1.

Linear strain according to anterior leaflet sonomicrometry array. Linear strain of a quadrangular array of sonomicrometry transducers on the anterior mitral leaflet of a normal ovine mitral valve (MV). Electrocardiogram and aortic blood pressure (ABP) traces are also displayed to allow identification of relevant time points in the cardiac cycle.

Fig. 2.

Von Mises stress (A and B) and principal strain (C and D) on the MV predicted by finite element analysis during repeated loading. A and C: initial loading of the normal human hybrid MV model. B and D: subsequent reloading of the deformed valve, demonstrating little difference in the magnitude or distribution of pressure-derived mechanical stress or principal strain. Stress magnitude predicted in the second loading step was withing 4% of stress magnitude predicted in the initial loading step at all MV leaflet elements. Max, maximum; Min, minimum.

Fig. 3.

Three-dimensional model of MV at end diastole and end isovolumic contraction. Normal human MV model in 2 views generated from real-time 3-dimensional echocardiography by transesophageal echocardiography at end diastole (white spheres) and end isovolumic contraction (shaded dark gray) demonstrated minimal deformation during the loading of isovolumic contraction.