A finite difference model of O2 transport in aortic valve cusps: importance of intrinsic microcirculation

Abstract

Recent studies have reported the presence of a microcirculation within the tissue of aortic valves. To test the hypothesis that this vascular bed is needed to satisfy the oxygen demands of the cusp tissue, a two-dimensional (2D) finite difference model of oxygen diffusion was developed. The in vivo environment was modeled for vascular and avascular cusps using thickness data from precise radiographic measurements of fresh porcine valves, and O2 diffusivity (Do2) and O2 consumption (Vo2) values from experimental data. The location and density of the cusp vasculature were determined by the model to prevent oxygen levels from falling to zero. Validation of the model was performed by simulation of the experimental measurements of cusp Do2 and Vo2. For a test cusp with uniform thickness, the model returned simulated Do2 and Vo2 measurements within 1.43% and 0.18% difference of the true parameter values, respectively. For native cusps, the simulated Do2 measurements were sensitive to thickness variations (–38 to +21% difference), whereas the Vo2 measurements were minimally affected (8% difference). An improved Do2 measurement technique was found to reduce these errors to <5% and is recommended for analysis of experimental data. In the avascular case, the model predicted large regions of hypoxic tissue, whereas in the vascular case, the model predicted vessel locations and densities similar to what was experimentally observed in porcine cusps. Overall, the in vivo model developed in this study confirmed the need for an intrinsic microcirculation in the thicker basal regions of aortic cusps.