Mathematical Modelling of Abnormal Low and High Wall Shear Stresses Depending on the Basic Morphological Parameters of Aneurysms

Authors: Nina Philipova

Acceptance Date: 04/25/2017


One of the basic hypothesis for the aneurysm formation, growth and rupture is the variation of the wall shear stresses ( ). Both low and high WSS can cause  the aneurysm growth and rupture via different biologic mechanisms. An objective of many studies is to examine the critical values of the WSS that can lead to the aneurysm hemorrhage. Following this aim the author performs numerical simulations in ANSYS Workbench14. Ideal aneurysm geometries are constructed in the commercial code ANSYS Model Designer. Four main morphological factors are investigated: the diameter of parent vessel, the aneurysm diameter, the aneurysm height and the size ratio (the SR is equal to the ratio of the aneurysm height to the parent vessel diameter). Numerical simulations are performed  in  the Commercial code ANSYS Fluent and the WSS on the aneurismal wall are calculated. The author considers  the 25th percentile of the WSS as a statistically averaged limit of the abnormal low WSS. Regression equations are derived for the WSS on aneurysm wall depending on the above mentioned geometric parameters by the applying the Commercial code STATISTIKA. The 81th percentile of the  is considered as a low limit of abnormally high WSS which is reported as a relevant for the aneurysm formation. A regression equation of 81th percentile of the  depending on the parent vessel diameter and the aneurysm high is derived by the applying the Commercial code STATISTIKA.​


ISolving Anisotropic Model Equations Valid for Intimal and Adventitial Layers of Biaxial Stretched Cerebral Tissues

Authors: Nina Philipova

Acceptance Date: 04/25/2017


The mechanical behavior of soft arterial tissues has grasped  the attention of many scientists in the field of  biomechanics. The structural constitutive models took a priority in resent studies as the best suitable ones for reporting the biomechanical response of the constituents of arterial  layers. The author considers the Holzapfel anisotropic model for cerebral vessels describing the biomechanical behavior of the non-collagenous ground matrix and the collagen fibers. The model is applicable for the intimal and the adventitial layers. It reports the dispersion of the collagen fibers’ orientation by means of a mean angle of the distribution of collagen fibers in one family. In this paper, the author analytically solves the Holzapfel model for  the number of collagen fibers’ families equal to six and eight and under assumed other material parameters.  The obtained values for the circumferential and the longitudinal stretch ratios are biomechanically appropriate, hence proving the adequacy of the assumed material parameters.


ISSN: 2378-7384

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Investigations on an Anisotropic Model of Cerebral Adventita Layer

Authors: Nina Philipova