A new active contraction model for the myocardium using a modified hill model

This study develops a new hybrid active contraction model for myocardial dynamics abstracted from sarcomere by combining the phenomenologically active-stress based Hill model and the micro-structurally motivated active strain approach. This new model consists of a passive branch and a parallel active branch that consists of a serial passive element for active tension transmission and a contractile unit for active tension development. This rheology represents an additive decomposition of the total stress into a passive and active response. The active stress is formulated following the active strain approach based on the sliding filament theory by multiplicatively decomposing the stretch of the contractile element into a fictitious and an active part. The length-dependence and force-velocity are further incorporated in the active strain. We estimate the passive stiffness of the serial passive element using literature data, which is 250 kPa, then the active stress is computed from the serial passive element in the active branch because of its force transmission structure. This one-dimensional contraction model is further generalized to three dimensions for modelling myocardial dynamics. Our results demonstrate that the proposed active contraction model has a high descriptive capability for various experiments, including both isometric and isotonic contraction compared to existing active strain approaches. We also show that it can simulate physiologically accurate cardiac dynamics in humans. The excellent agreement with experimental data and a local sensitivity study highlight the importance of length-dependence and force-velocity in the active strain approach. Our results further show that there exists a tight interaction between the length-dependence and force-velocity relationships. This new hybrid model serves as a step forward in personalized cardiac modelling using an active-strain based contraction model and has the potential to understand the multi-scale coupling in active contraction according to the sliding filament theory.