A conjugate-gradient sparse-matrix method for efficient computation of a cardiovascular model

A conjugate-gradient (CG) sparse-matrix (SIM) method was applied to an integrated cardiovascular model for improving its computational efficiency. The model was previously developed by combining a 3D finite element model (FEM) of the left ventricle with an analog electrical model of the circulatory system. The computation of this integrated model was dominated by the FEM, which consumed 99.9% of the run time. A computational bottleneck (98.6%) was the solution of the simultaneous equations in the global stiffness matrix and the nodal displacement vectors. For a 40% infarct size in the FEM the computational time for a cardiac cycle with a 5-ms time resolution and a heart rate of 71 bpm was reduced from 20 min to 6 min. Depending on the infarct size, the CGSM method reduced the computational time to 30-60% of that obtained by use of a conventional QR decomposition method.