A solution to Bloch NMR flow equations for the analysis of hemodynamic functions of blood flow system using m-Boubaker polynomials

This paper proposes a solution to Bloch NMR flow equations in biomedical fluid dynamics using a new set of real polynomials. In fact, the authors conjugated their efforts in order to take benefit from similarities between independent Bloch NMR flow equations yielded by a recent study and the newly proposed characteristic differential equation of the m-Boubaker polynomials. The main goal of this study is to establish a methodology of using mathematical techniques so that the accurate measurement of blood flow in human physiological and pathological conditions can be carried out non-invasively and becomes simple to implement in medical clinics. Specifically, the polynomial solutions of the derived Bloch NMR equation are obtained for use in biomedical fluid dynamics. The polynomials represent the T2-weighted NMR transverse magnetization and signals obtained in terms of Boubaker polynomials, which can be an attractive mathematical tool for simple and accurate analysis of hemodynamic functions of blood flow system. The solutions provide an analytic way to interpret observables made when the rF magnetic fields are designed based on the Chebichev polynomials. The representative function of each component is plotted to describe the complete evolution of the NMR transverse magnetization component for medical and biomedical applications. This mathematical technique may allow us to manipulate microscopic blood (cells) at nano-scale. We may be able to theoretically simulate nano-devices that may travel through tiny capillaries and deliver oxygen to anemic tissues, remove obstructions from blood vessels and plaque from brain cells, and even hunt down and destroy viruses, bacteria, and other infectious agents.