Real-time interactive simulations of large-scale systems on personal computers and cell phones: Toward patient-specific heart modeling and other applications

Figures

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  Fig. 1. Spiral waves of electrical activity in heart tissue. As indicated by the color bar, blue is tissue that is polarized at −80 mV and red is excited tissue that is depolarized at +20 mV. (A and B) Examples of spiral wave dynamics in two regimes. Experimental optical mapping (top) and numerical using the OVVR model (bottom) showing three snapshots from a rotating spiral waves that follows a linear core trajectory (left) and circular core trajectory (right) traced in black. (C) Example of parameter sweep using the OVVR model in 2D. A transition from linear to circular with some complex EAD formation in between is shown. (D) Effect of blocking the potassium IKr current and development of EADs that lead to fibrillation only in 2D. See the Supplementary Materials for examples of other tip trajectories, another parameter space study, and animations from the experimental data, and Supplementary Programs to run the WebGL codes.

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  Fig. 2. Progression of an almost straight 3D scroll wave into complex turbulence in a box of 256 × 256 × 256 elements. Four snapshots of the evolution of a 3D scroll wave denoted by a voltage surface plot (top) and its vortex filament (bottom). A negative tension instability elongates the vortex filament that separates into new filaments as it touches the edges of the tissue. See Supplementary Programs to run the WebGL code.

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  Fig. 3. Single and multiple spiral wave activity on realistic 3D heart geometries. (A to D) Comparing experimental data with the interactive simulations. (A) Single spiral wave (VT) and (B) fibrillation in porcine ventricles. (C) VT in rabbit with drug DAM. (D) Fibrillation in rabbit with drug CytoD. (E and F) Simulations of AF from models fitted to patient data. See the Supplementary Materials for animations and details and Supplementary Programs to run the WebGL codes.

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  Fig. 4. High-performance simulations on a cell phone (Galaxy S8). (A and B) 2D spiral wave and (C and D) 3D reentry in rabbit ventricles with TP and OVVR models. Up to 1.7 billion ODEs can be solved per second using this phone. See the Supplementary Materials for details and animations and Supplementary Programs to run the WebGL codes.

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  Fig. 5. High-performance simulations of fluid flow past a stationary cylinder in WebGL. (A) Vortex shedding from the stationary cylinder at Re = 54. (B) Vortex shedding is suppressed at Re = 54 by adding stationary obstacles downstream of the cylinder. (C) The Reynolds number is increased to Re = 64; we can see clear vortex shedding from the added obstacles, but the effects on the upstream cylinder are minimal. (D) Upon further increase of the Reynolds number to 80, the downstream vortex shedding becomes more pronounced, the flow around the upstream cylinder becomes unstable, and the oscillatory force is restored.

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  Fig. 6. High performance simulations of crystal growth under different Damkohler numbers, fluid flow conditions and number of nucleation cites using WebGL. Damkohler numbers are Da = 2 in (A), (C), and (E) and Da = 160 in (B), (D) and (F). Fluid flow conditions are ux = 0 in (A), (B), (E) and (F) and ux = 0.15 in (C) and (D). (A) to (D) have a single nucleation cite at the center of the domain, while (E) and (F) have five distinct nucleation sites. The crystals are colored on the basis of their crystallization time.