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. 2013 Aug 26:6:83-93.
doi: 10.4137/MRI.S12195. eCollection 2013.

Magnetic Resonance Imaging-derived Flow Parameters for the Analysis of Cardiovascular Diseases and Drug Development

Dada O Michael  1 , Awojoyogbe O Bamidele  1 , Adesola O Adewale  1 , Boubaker Karem  2
Affiliations

Magnetic Resonance Imaging-derived Flow Parameters for the Analysis of Cardiovascular Diseases and Drug Development

Dada O Michael et al. Magn Reson Insights. .

Abstract

Nuclear magnetic resonance (NMR) allows for fast, accurate and noninvasive measurement of fluid flow in restricted and non-restricted media. The results of such measurements may be possible for a very small B 0 field and can be enhanced through detailed examination of generating functions that may arise from polynomial solutions of NMR flow equations in terms of Legendre polynomials and Boubaker polynomials. The generating functions of these polynomials can present an array of interesting possibilities that may be useful for understanding the basic physics of extracting relevant NMR flow information from which various hemodynamic problems can be carefully studied. Specifically, these results may be used to develop effective drugs for cardiovascular-related diseases.

Keywords: Bloch NMR flow equations; Boubaker polynomials; Legendre polynomials; NMR transverse magnetization; cardiovascular diseases; drug discovery; rotational diffusion coefficient.

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Figures

Figure 1
Figure 1
Illustration of the changes occurring in an ischemic cardiovascular accident and geometrical consideration in coronary artery with atherosclerosis diseases.
Figure 2
Figure 2
Effect of constriction on the velocity profile in a blood vessel: (ab) Laminar flow velocity V, (bc) High velocity V1, (de) Turbulent, and (eg) Laminar flow. The diameter of the blood vessel is h. Reprinted with permission of the Collegium Basilea.
Figure 3
Figure 3
The n-indexed solutions.
Figure 4
Figure 4
Plots of transverse magnetization as a function of xl at l = 2.5 μm for x between 0 and (a) 1.0 m (b) 1.0 × 10−3 m (c) 1.0 × 10−6 m (d) 1.0 × 10−9 m (e) 1.0 × 10−12 m (f) 1.0 × 10−12 m.
Figure 5
Figure 5
The plots of the fluid velocity for molecules of (a) cerebrospinal fluid around a “micro-sized” plague (b) cerebrospinal fluid around a “nano-sized” plague (c) oxygenated blood around a “micro-sized” plague (d) oxygenated blood around a “nano-sized” plague.
Figure 6
Figure 6
The velocity distribution across l and x, according to equation (7) and the corresponding density image for l ranging from 0 to (a) 9.0 × 10−3 m (b) 9.0 × 10−6 m (c) 9.0 × 10−9 m (d) 9.0 × 10−12 m. The relaxations times used are T1 = 1.03s and T2 = 0.06s.
See this image and copyright information in PMC

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References

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