title: The Generalized Hill Model: A Kinematic Approach Towards Active Muscle Contraction.
abstract: Excitation-contraction coupling is the physiological process of converting an electrical stimulus into a mechanical response. In muscle, the electrical stimulus is an action potential and the mechanical response is active contraction. The classical Hill model characterizes muscle contraction though one contractile element, activated by electrical excitation, and two non-linear springs, one in series and one in parallel. This rheology translates into an additive decomposition of the total stress into a passive and an active part. Here we supplement this additive decomposition of the stress by a multiplicative decomposition of the deformation gradient into a passive and an active part. We generalize the one-dimensional Hill model to the three-dimensional setting and constitutively define the passive stress as a function of the total deformation gradient and the active stress as a function of both the total deformation gradient and its active part. We show that this novel approach combines the features of both the classical stress-based Hill model and the recent active-strain models. While the notion of active stress is rather phenomenological in nature, active strain is micro-structurally motivated, physically measurable, and straightforward to calibrate. We demonstrate that our model is capable of simulating excitation-contraction coupling in cardiac muscle with its characteristic features of wall thickening, apical lift, and ventricular torsion.
authors.affiliation: Department of Civil Engineering, Middle East Technical University, TR-06800 Ankara, Turkey.
authors.forename: Serdar
authors.initials: S
authors.lastname: Göktepe
authors.affiliation: Institute of Mechanics, TU Dortmund, Leonhard-Euler-Str. 5, D-44227 Dortmund, Germany ; Division of Solid Mechanics, Lund University, P.O. Box 118, SE-22100 Lund, Sweden.
authors.forename: Andreas
authors.initials: A
authors.lastname: Menzel
authors.affiliation: Departments of Mechanical Engineering, Bioengineering, and Cardiothoracic Surgery, Stanford University, Stanford, CA 94305, USA.
authors.forename: Ellen
authors.initials: E
authors.lastname: Kuhl
keywords: Active-Strain; Coupled Cardiac Electromechanics; Excitation-Contraction; Finite Elements