Dog Heart

Human Heart

Atrial fibrillationAtrial flutterAtrial tachycardiaAV nodal reentrant tachycardiaAV reentrant tachycardiaBigeminPremature ventricular contractionVentricular tachycardiaVentricular fibrillationBundle branch blackHeart block

Heart Problems

Mesh with millions of nodes for good spacial resolution

Bidomain

GPU

CNC

CUBLAS

Reaction

Diffusion

Serial Implementation

Reaction PhaseMesh Nodes GPU Threads

• 33 state + 1 voltage + 1 current variables / node update per time step

• Transmembrane voltage (Vm) and current (Itot) output for diffusion phase

Interfacing With Thirdparty Tools

OpenNL Sparse Matrix interface with CNC ELL support

Exposed Sparse Matrix Vector Multiply in CNC

Conjugate Gradient (CG) handled by CNC

CUBLAS for vector operations

ResultsTime Step 0 ms Time Step 40 ms

8000 iterations

Timing

Limitations: Large number of registers needed per thread per calculation

Frequent use of slow math functions

Limited data storage per thread

Solutions: Tesla architecture with more registers

MPI to better distribute data load

Hardware math functions at a cost of precision

Size of the Laplacian matrices, 32K nodes equals about a 4GB matrix

Using libraries for sparse matrix support, compress 32K x 32K matrix to 16 MB storage

Loss of precision and numerical stability by using single precision floating point numbers

Related WorkRabbit model:• 50 ms activity, timestep 20 μs, 425,000 nodes • run time: 3316 seconds

Carp (MPI, PETSc)

Rabbit model:• 30 ms of activity, 3 million nodes • run time: 13 hours

Human model:• 600 ms activity, time step 10 μs, 55 million nodes• run time: 2 days

Mouse, rabbit model, GPU and GPU/MPI hybrid version:• membrane current computation , time step 25 μs, 10e4 - 10e6 nodes• run time: 104 - 105 seconds

CHASTE(MPI,PETSc)

Potse, Dubé, Vinet, Cardinal (OpenMP)