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5.13 Active Contraction Model
A time varying “elastance” active contraction model  was added to the transversely isotropic materials. When active contraction is activated, the total Cauchy stress is defined as the sum of the active stress tensor and the passive stress tensor : where a is the deformed fiber vector (unit length), defined as . The time varying elastance model is a modification of the standard Hill equation that scales the standard equation by an activation curve . The active fiber stress is defined as: where is the isometric tension under maximal activation at the peak intracellular calcium concentration of . The length dependent calcium sensitivity is governed by the following equation: where is the maximum peak intracellular calcium concentration, governs the shape of the peak isometric tension-sarcomere length relation, is the sarcomere length at which no active tension develops, and is the sarcomere length which is the product of the fiber stretch and the sarcomere unloaded length .