Using Systolic Local Mechanical Load to Predict Fiber Orientation in Ventricles.

A simple rule adopted for myofiber reorientation in the ventricles is pursued by taking the microscopic branching network of myocytes into account. The macroscopic active tension generated on the microscopic branching structure is modeled by a multidirectional active stress tensor, which is defined as a function of the strains in the branching directions. In our reorientation algorithm, the principal direction of the branching network is updated so that it turns in the direction of greater active tension in the isovolumetric systole. Updates are performed step-by-step after the mechanical equilibrium has been attained with the current fiber structure. Starting from a nearly flat distribution of the principal fiber orientation along the circumferential direction, the reoriented fiber helix angles range from 70 to 40° at epicardium and from 60 to 80° at endocardium, in agreement with experimental observations. The helical ventricular myocardial band of Torrent-Guasp's model and the apical spiral structure of Rushmer's model are also reconstructed by our algorithm. Applying our algorithm to the infarcted ventricle model, the fiber structure near the infarcted site is remodeled so that the helix angle becomes steeper with respect to the circumferential direction near the epicardial surface. Based on our numerical analysis, we draw the following conclusions. (i) The multidirectional active tension based on the microscopic branching network is potentially used to seek tighter connection with neighboring aggregates. (ii) The thickening and thinning transitions in response to active tension in each myocyte allow the macroscopic principal fiber orientation of the microscopic branching network to move toward the direction of greater active tension. (iii) The force-velocity relationship is the key factor in transferring the fiber shortening strain to the magnitude of active tensions used in the myofiber reorientation. (iv) The algorithm naturally leads to homogeneity in the macroscopic active tension and the fiber shortening strain, and results in near-optimal pumping performance. (v) However, the reorientation mechanism may degrade the pumping performance if there is severely inhomogeneous contractility resulting from infarction. Our goal is to provide a tool to predict the fiber architecture of various heart disease patients for numerical simulations of their treatment plans.