Abstract
In the human cardiovascular system, there are more than 1010 capillary blood vessels the diameter of which is about the same size as that of blood cells. When blood flows through the capillaries, the blood cells have to be squeezed, deformed and move in single files. This makes it very difficult to analyse blood flow in these microscopic blood vessels in terms of classical mechanical quantities. The focus of this chapter is the application of known quantum mechanical formulations and models to the Bloch NMR flow equations; it provides a theoretical foundation that may enhance accurate understanding of the transport of nanodevices in microscopic blood vessels used in nanomedicine.
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Allen, T. M., & Cullis, P. R. (2004). Drug delivery systems: Entering the mainstream. Science, 303(5665), 1818–1822.
Aruldhas, G. (2009). Quantum mechanics. PHI learning private limited.
Awojoyogbe, O. B. (2002). A mathematical model of the Bloch NMR equations for quantitative analysis of blood flow in blood vessels with changing cross-section—I. Physica A: Statistical Mechanics and its Applications, 303(1–2), 163–175.
Awojoyogbe, O. B. (2003). A mathematical model of Bloch NMR equations for quantitative analysis of blood flow in blood vessels of changing cross-section—PART II. Physica A: Statistical Mechanics and its Applications, 323, 534–550.
Awojoyogbe, O. B. (2004). Analytical solution of the time-dependent Bloch NMR flow equations: A translational mechanical analysis. Physica A: Statistical Mechanics and its Applications, 339(3–4), 437–460.
Awojoyogbe, O. B. (2007). A quantum mechanical model of the Bloch NMR flow equations for electron dynamics in fluids at the molecular level. Physica Scripta, 75(6), 788–794.
Awojoyogbe, O. B., & Boubaker, K. (2009). A solution to Bloch NMR flow equations for the analysis of hemodynamic functions of blood flow system using m-Boubaker polynomials. Current Applied Physics, 9(1), 278–283.
Awojoyogbe, O. B., Dada, M., Faromika, O. P., Moses, O. F., & Fuwape, I. A. (2009). Polynomial solutions of Bloch NMR flow equations for classical and quantum mechanical analysis of fluid flow in porous media. Open Magnetic Resonance Journal, 2, 46–56.
Boisseau, P., & Loubaton, B. (2011). Nanomedicine, nanotechnology in medicine. Comptes Rendus Physique, 12(7), 620–636.
Bolger, A. F., Heiberg, E., Karlsson, M., Wigstrom, L., Engvall, J., Sigfridsson, A., Ebbers, T., Kvitting, J. E., Carlhall, C. J., & Wranne, B. (2007). Transit of blood flow through the human left ventricle mapped by cardiovascular magnetic resonance. Journal of Cardiovascular Magnetic Resonance, 9, 741–747.
Cowan, B. P. (1997). Nuclear magnetic resonance and relaxation (1st ed.). Cambridge University Press.
Dada, M., Awojoyogbe, O. B., Moses, O. F., Ojambati, O. S., & De, D. K. (2009). A mathematical analysis of stenosis geometry, NMR magnetizations and signals based on the Bloch NMR flow equations, Bessel and Boubaker polynomial expansions. Journal of Biological Physics and Chemistry, 9(3), 101–106.
Glaser, R. (2012). Biophysics: An introduction (p. 233). Springer Science & Business Media.
Haacke, E. M., Lin, W., & Li, D. (2000). Whole body magnetic resonance angiography. In I. R. Young (Ed.), Methods in biomedical magnetic resonance imaging and spectroscopy (pp. 488–500). John Wiley & Sons.
Jiang, S., Gnanasammandhan, M. K., & Zhang, Y. (2010). Optical imaging-guided cancer therapy with fluorescent nanoparticles. Journal of the Royal Society Interface, 7(42), 3–18.
Jorgensen, W. L. (2004). The many roles of computation in drug discovery. Science, 303(5665), 1813–1818.
Kundu, P. K., & Cohen, I. M. (2004). Fluid mechanics. Elsevier Academic Press.
Libby, P. (1995). Molecular bases of the acute coronary syndromes. Circulation, 91(11), 2844–2850.
Marieb, E. N., & Hoehn, K. (2013). The cardiovascular system: Blood vessels. Human anatomy & physiology (p. 712). Pearson.
Moghimi, S. M., Hunter, A. C., & Murray, J. C. (2005). Nanomedicine: Current status and future prospects. The FASEB Journal, 19(3), 311–330.
Moratal, D., Brummer, M. E., MartÃ-BonmatÃ, L., & Vallés-Lluch, A. (2006). NMR imaging. In Wiley encyclopedia of biomedical engineering.
Morrisett, J., Vick, W., Sharma, R., Lawrie, G., Reardon, M., Ezell, E., Schwartz, J., & Gorenstein, D. (2003). Discrimination of components in atherosclerotic plaques from human carotid endarterectomy specimens by magnetic resonance imaging ex vivo. Magnetic Resonance Imaging, 21(5), 465–474.
Shankar, R. (2012). Principles of quantum mechanics. Springer Science & Business Media.
Tang, C. L. (2005). Fundamentals of quantum mechanics for solid state electronics and optics. Cambridge University Press.
Thirring, W. (2013). Quantum mathematical physics: Atoms, molecules and large systems. Springer Science & Business Media.
Tortora, G. J., & Derrickson, B. (2012). The cardiovascular system: Blood vessels and hemodynamics. Principles of anatomy and physiology (p. 817). John Wiley & Sons.
Watson, G. N. (1966). A treatise on the theory of Bessel functions (2nd ed.). Cambridge University Press.
Jain, K. K. (2008). Nanomedicine: Application of nanobiotechnology in medical practice. Medical Principles and Practice, 17(2), 89–101.
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Dada, M.O., Awojoyogbe, B.O. (2021). Quantum Mechanical Model of the Bloch NMR Flow Equations for Transport Analysis of Quantum-Drugs in Microscopic Blood Vessels Applicable in Nanomedicine. In: Computational Molecular Magnetic Resonance Imaging for Neuro-oncology. Biological and Medical Physics, Biomedical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-76728-0_7
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