| Summary: | <p>Abstract</p> <p>Background</p> <p>Various types of vascular injury have been reported in the medical literature; the isthmic part of the aorta is at particularly high risk of traumatic rupture. Early diagnosis results in better survival, justifying the search for potential risk factors and diagnostic tests. The aim of this research was to investigate the complex mechanism of blunt injury to the vascular wall with particular focus on the branching region of the vessels. Geometric peculiarities were investigated.</p> <p>Methods</p> <p>Multi-phase equations have been used. The system of equations with certain boundary conditions was solved numerically by applying the finite-difference method with order of approximation equal to 0.0001.</p> <p>Results</p> <p>The degree of curvature (the Dean number) is highly informative about the shear stress on the external surface of the vessel. An important function of the blood flow on the external wall is to destroy rouleaux. The viscosity of phase 2 (<it>f</it><sub>2</sub>) exceeds, by many times, the viscosity of phase 1 (<it>f</it><sub>1</sub>). The major stress created by blood flow is expressed as the shear stress of <it>f</it><sub>2</sub>. The volume fraction of rouleaux depends to a greater degree on the concentration of erythrocytes (expressed as the viscosity of the mixture) than on the shear stress. The peculiarities of rouleaux formation were assessed and their impact on the local shear stress and, therefore, on the internal wall was determined in relation to the erythrocyte concentration.</p> <p>Conclusion</p> <p>The results of this research take into account certain geometrical peculiarities of the branching part of the vessel. The mathematical model created in this study will improve our understanding of the complex mechanism of blunt injury to the vascular wall and, therefore, conditions such as aortic rupture and traumatic acute myocardial infarction.</p>
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