Mitral Regurgitation PISA Doppler Map 2D

This top-down 2D companion to the 3D mitral-valve-prolapse simulator swaps the rendered leaflet mesh and instanced-particle jet for the actual clinical measurement technique used at the bedside: a PISA (proximal isovelocity surface area) color-flow map. The same posterior-leaflet-prolapse, annular-diameter and heart-rate controls open the same coaptation gap and drive the same orifice geometry, but here that geometry sets a true flow rate that is pushed through the continuity equation to build nested isovelocity shells around the orifice — colored the way a color Doppler ultrasound image actually looks — and a live flow strip-chart shows the systolic regurgitant burst as a genuine time series rather than a spray of particles. A second, independently derived EROA read off the flow-convergence radius is checked live against the geometric orifice area, demonstrating numerically why the clinical PISA formula works.