On Using the Upper Triangular (QR) Decomposition Theorem for Deriving a New Strain Energy Function for the Incompressible and Orthotropic Passive Myocardium
Abstract
Developing models describing myocardial deformation have been central to understanding cardiac function, both normal and abnormal. However, the widely used Fung model is known to have high degeneracy and thus less unique solutions. Therefore, the goal of this work was to derive a strain energy function for the incompressible myocardium with less degeneracy and more uniqueness than the Fung model. The upper triangular (QR) decomposition theorem was leveraged to develop a model that achieved the stated goal. Furthermore, published biaxial data was utilized from studies that measure the stresses of slabs of myocardium to find the respective functional form for the strain energy function using the QR model as well as estimate the resulting material stiffness constants. The respective model was then compared with the strain energy function obtained from the Fung model. The outcome of this work was a model that improves on the Fung model in having fewer constraints and degeneracy that results in a reduction of the uncertainty and enhances the predictability for the mechanical behavior of the heart.
Citation
Hussein, Tawfik Mohammed (2020). On Using the Upper Triangular (QR) Decomposition Theorem for Deriving a New Strain Energy Function for the Incompressible and Orthotropic Passive Myocardium. Master's thesis, Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /192323.