It is known that most cardiovascular emergencies are caused by coronary artery disease. Nevertheless, in the last decade’s related literature, data about mathematical models of heart and heart vessels along with NMR/MRI features is not accordingly abundant. In fact there are inherent difficulties in developing this type of mathematical models to completely describe the real or ideal geometries of heart arterial system.

In this study, a mathematical formulation for the NMR diffusion partial differential equation derived from the Bloch NMR flow equations to describe in detail the activities in lower heart coronary artery is presented. Based on the Bloch NMR flow equations, we deduce analytical expressions to describe in detail the NMR transverse magnetizations and signals as a function of some NMR flow and geometrical parameters which are invaluable for the analysis of blood flow in heart vessels. The boundary conditions are inherently introduced based on the properties of the Boubaker polynomials expansion scheme BPES.

Phase contrast technique employs the phase shift in the MR signal that is induced by the flowing blood in heart vessels. The merit of investigations on MR signals in heart disease treatments, heart tomographic imaging and discrimination between infracted, ischemic or normal myocardium has been early highlighted during the last decades through the works i.e. of Berman et al.

More recently, confirmation of accuracy and efficiently have been reported by several studies. In this technique setup, blood spins moving along an applied gradient acquire a phase shift which is proportional to the strength and the duration of the gradient and the motion of the spins. This phase shift is proportional to the velocity of the moving spins, as long as the velocity of the spins is constant.

Thus the phase signal of stationary spins will be zero and this means that small heart arteries can be visualized, even with slowly moving blood. The phase shift of moving spins will be proportional to their constant velocity. The phase shift due to higher order motions, for example, acceleration, pulsation, etc, can be neglected under normal physiological condition. The errors of ignoring the higher order motions can be minimized by using short echo times (TE) especially in distributed flow.

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ISSN: 2155-9880

Current Issue: Volume 11, Issue 9

Journal of Clinical and Experimental Cardiology welcomes submissions with cutting-edge research in the field of Cardiology. Manuscripts including research articles, commentaries, and other reports will also be considered for publication and should be submitted either online or through mail.

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Calvin Parker,
Editorial Manager,
Journal of Clinical and Experimental Cardiology