Translation of two aggregated low-density lipoproteins within blood plasma: a mathematical model.

Arteriosclerosis is a disease in which the artery walls get thicker and harder. Atherosclerosis is a specific form of arteriosclerosis which allows less blood to travel through the artery and increases blood pressure. Low-density lipoproteins (LDLs) and their ability to aggregate are important in atherosclerosis. In the present study we develop a mathematical model that describes the translation of two aggregated LDSs through blood plasma. We model the two aggregated LDLs as an inverted oblate spheroid and the flow as a creeping steady incompressible axisymmetric one. The mathematical tools that we used are the Kelvin inversion and the semi-separation of variables in the spheroidal coordinate systems. The stream function is given as a series expansion of even order terms of combinations of Gegenbauer functions of angular and radial dependence. The analytical solution is expected to give insight into the study of the various chemical precipitation methods used for the precipitation of lipoproteins, as this is the first step for the measurement of their concentration within blood plasma.