MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA, cilt.34, ss.433-467, 2017 (SCI İndekslerine Giren Dergi)
In this work, we constructed a novel collagen fibre remodelling algorithm that incorporates the complex nature of random evolution acting on single fibres causing macroscopic fibre dispersion. The proposed framework is different from the existing remodelling algorithms, in that the microscopic random force on cellular scales causing a rotational-type Brownian motion alone is considered as an aspect of vascular tissue remodelling. A continuum mechanical framework for the evolution of local dispersion and how it could be used for modeling the evolution of internal radius of biaxially strained artery structures under constant internal blood pressure are presented. A linear evolution form for the statistical fibre dispersion is employed in the model. The random force component of the evolution, which depends on the mechanical stress stimuli, is described by a single parameter. Although the mathematical form of the proposed model is simple, there is a strong link between the microscopic evolution of collagen dispersion on the cellular level and its effects on the macroscopic visible world through mechanical variables. We believe that the proposed algorithm utilizes a better understanding of the relationship between the evolution rates of mean fibre direction and fibre dispersion. The predictive capability of the algorithm is presented using experimental data. The model has been simulated by solving a single-layered axisymmetric artery (adventitia) deformation problem. The algorithm performed well for estimating the quantitative features of experimental anisotropy, the mean fibre direction vector and the dispersion (kappa) measurements under strain-dependent evolution assumptions.