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Updated: Aug 12, 2026

Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction
Published on: February 13, 2021
Solving the heart mechanics equations with Newton and quasi Newton methods--a comparison
Svein Linge1, Glenn Lines, Joakim Sundnes
1The Norwegian University of Sport and Physical Education, Ullevaal Stadion, NO-0806 Oslo, Norway. sveinlin@simula.no
Abstract:
The non-linear elasticity equations of heart mechanics are solved while emulating the effects of a propagating activation wave. The dynamics of a 1 cm(3) slab of active cardiac tissue was simulated as the electrical wave traversed the muscular heart wall transmurally. The regular Newton (Newton-Raphson) method was compared to two modified Newton approaches, and also to a third approach that delayed update only of some selected Jacobian elements. In addition, the impact of changing the time step (0.01, 0.1 and 1 ms) and the relative non-linear convergence tolerance (10(-4), 10(-3) and 10(-2)) was investigated. Updating the Jacobian only when slow convergence occurred was by far the most efficient approach, giving time savings of 83-96%. For each of the four methods, CPU times were reduced by 48-90% when the time step was increased by a factor 10. Increasing the convergence tolerance by the same factor gave time savings of 3-71%. Different combinations of activation wave speed, stress rate and bulk modulus revealed that the fastest method became relatively even faster as stress rate and bulk modulus was decreased, while the activation speed had negligible influence in this respect.
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