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Computational analysis of blood flow in the retinal arteries and veins using fundus image. (English) Zbl 1362.92016

Summary: The retina is the only tissue in which blood vessels can be visualized non-invasively in vivo. Thus, the study of the retinal hemodynamic has special interest for both physiological and pathological conditions. The aim of this study has been to develop a detailed computational model for a quantitative analysis of the blood flow in physiologically realistic retinal arterial and venous networks. The geometrical outlines of both retinal artery and vein have been extracted from the retinal image acquired from a healthy young adult by a retinal camera Topcon TRC-50EX. The microvascular diameter effect (i.e., Fåhraeus-Lindqvist effect) and the hematocrit have been considered in determining the viscosity of the blood in the retinal vessel segments. The blood moves at a velocity that is 2 times less in the veins (maximum 5.4 cm/s) than the velocity at which it moves in the arteries (maximum 11 cm/s) which are in good agreement with in vivo measurements reported in the literature. The pressure drop has been in the range of 11–14 mmHg between the inlet and outlets for the arterial network, and 13–14 mmHg for the vein network. The developed method can be used as a tool for continuous monitoring of the retinal circulation for clinical assessments as well as experimental studies.

MSC:

92C35 Physiological flow
76Z05 Physiological flows
92C55 Biomedical imaging and signal processing

Software:

Matlab; FLUENT
Full Text: DOI

References:

[1] Burgansky-Eliash, Z.; Nelson, D. A.; Bar-Tal, O. P.; Lowenstein, A.; Grinvald, A.; Barak, A., Reduced retinal blood flow velocity in diabetic retinopathy, Retina, 30, 765-773 (2010)
[2] Wong, T. Y.; McIntosh, R., Systemic associations of retinal microvascular signs: a review of recent population-based studies, Ophthalmic. Physiol. Opt., 25, 3, 195-204 (2005)
[3] Kramer, C. K.; Rodrigues, T. C.; Canani, L. H., Diabetic retinopathy predicts all-cause mortality and cardiovascular events in both type 1 and 2 diabetes: meta-analysis of observational studies, Diabetes Care, 34, 1238-1244 (2011)
[4] Guidoboni, G.; Harris, A.; Carichino, L.; Arieli, Y.; Siesky, B. A., Effect of intraocular pressure on the hemodynamics of the central retinal artery: a mathematical model, Math. Biosci. Eng., 11, 3, 523-546 (2014) · Zbl 1298.76245
[5] Liu, D.; Wood, N. B., Computational analysis of oxygen transport in the retinal arterial network, Curr. Eye. Res., 34, 945-956 (2009)
[6] Pries, A. R.; Secomb, T. W.; Gaehtgens, P.; Gross, J. F., Blood flow in microvascular networks. experiments and simulation, Circ. Res., 67, 826-834 (1990)
[7] Nagel, E.; Vilser, D.; Fuhrmann, G.; Vilser, W.; Lang, G., Dilatation of large retinal vessels after increased intraocular pressure, Ophthalmologe, 97, 742-747 (2000)
[8] Nagel, E.; Vilser, W.; Lanzl, I. M., Retinal vessel reaction to short-term IOP elevation in ocular hypertensive and glaucoma patients, Eur. J. Ophthalmol., 11, 338-344 (2001)
[9] Wang, Y. M.; Bower, B. A.; Izatt, J. A.; Tan, O.; Huang, D., In vivo total retinal blood flow measurement by Fourier domain Doppler optical coherence tomography, J. Biomed. Opt., 12, 041215 (2007)
[10] Zhong, Z., Noninvasive measurements and analysis of blood velocity profiles in human retinal vessels, Invest. Ophthalmol. Vis. Sci., 52, 4151-4157 (2011)
[11] Lee, J.; Nellis, S., Modelling study on the distribution of flow and volume in the microcirculation of cat mesentery, Ann. Biomed. Eng., 2, 206-216 (1974)
[12] Lipowsky, H. H.; Zweifach, B. W., Network analysis of microcirculation of cat mesentery, Microvasc. Res., 7, 73-83 (1974)
[13] Lipowsky, H. H.; Kovalcheck, S.; Zweifach, B. W., The distribution of blood rheological parameters in the microvasculature of cat mesentery, Circ. Res., 43, 738-749 (1978)
[14] Kassab, G. S.; Berkley, J.; Fung, Y. C., Analysis of pigs coronary arterial blood flow with detailed anatomical data, Ann. Biomed. Eng., 25, 204-217 (1997)
[15] Olufsen, M. S., Numerical simulation and experimental validation of blood flow in arteries with structured tree outflow conditions, Ann. Biomed. Eng., 28, 1281-1299 (2000)
[16] Mittal, N., Analysis of blood flow in the entire coronary arterial tree, Am. J. Physiol. Heart Circ. Physiol., 289, 1, H439-H446 (2005)
[17] Yang, J.; Yu, L. X.; Rennie, M. Y.; Sled, J. G.; Henkelman, R. M., Comparative structural and hemodynamic analysis of vascular trees, Am. J. Physiol. Heart Circ. Physiol., 298, H1249-H1259 (2010)
[18] Takahashi, T.; Nagaoka, T.; Yanagida, H.; Saitoh, T.; Kamiya, A.; Hein, T., A mathematical model for the distribution of hemodynamic parameters in the human retinal microvascular network, J. Biorheol., 23, 2, 77-86 (2009)
[19] Ganesan, P., Development of an image-based network model of retinal vasculature, Ann. Biomed. Eng., 38, 1566-1585 (2010)
[20] Ganesan, P.; He, S.; Xu, H., Development of an image-based model for capillary vasculature of retina, Comput. Methods Programs Biomed., 102, 35-46 (2011)
[21] Harris, A.; Guidoboni, G.; Arciero, J. C.; Amireskandari, A.; Tobe, L. A.; Siesky, B. A., Ocular hemodynamics and glaucoma: the role of mathematical modeling, Eur. J. Ophthalmol., 23, 139-146 (2013)
[22] Jintao, Y.; Yi, l.; Simon, T.; Grant, C.; Lin, W., Parametric transfer function analysis and modeling of blood flow autoregulation in the optic nerve head, Int. J. Physiol. Pathophysiol. Pharmacol., 6, 13-22 (2014)
[24] Ganesan, P.; He, S.; Xu, H., Analysis of retinal circulation using an image-based network model of retinal vasculature, Microvasc. Res., 80, 99-109 (2010)
[25] Chaudhuri, S.; Chatterjee, S.; Katz, N.; Nelson, M.; Goldbaum, M., Detection of retinal blood vessels in retinal images using two-dimensional matched filters, IEEE Trans. Med. Imaging, 8, 263-269 (1989)
[27] Olufsen, M. S., Structured tree outflow condition for blood flow in larger systemic arteries, Am. J. Physiol., 276, H257-H268 (1999)
[28] Papenfuss, H. D.; Gross, J. F., Microhemodynamics of capillary networks, Biorheology, 18, 673-692 (1981)
[29] Steele, B. N.; Olufsen, M. S.; Taylor, C. A., Fractal network model for simulating abdominal and lower extremity blood flow during resting and exercise conditions, Comput. Methods Biomech. Biomed. Engrg., 10, 1, 39-51 (2007)
[30] Brown, D. L.; Cortez, R.; Minion, M. L., Accurate projection methods for the incompressible Navier-Stokes equation J, Comput. Phys., 168, 2, 464-499 (2001) · Zbl 1153.76339
[31] Rannacher, R., Finite element methods for the incompressible Navier-Stokes equations, (Fundamental Directions in Mathematical Fluid Mechanics (2000)), 191-293 · Zbl 1107.76353
[32] Gabrys, E.; Rybaczuk, M.; Kedzia, A., Blood flow simulation through fractal models of circulatory system, Chaos Solitons Fractals, 27, 1-7 (2006) · Zbl 1140.76506
[33] Vignon-Clementel, I. E.; Figueroa, C. A.; Jansen, K. E.; Taylor, C. A., Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries, Comput. Methods Appl. Mech. Engrg., 195, 3776-3796 (2006) · Zbl 1175.76098
[34] Quarteroni, A.; Veneziani, A.; Zunino, P., Mathematical and numerical modeling of solute dynamics in blood flow and arterial walls, SIAM J. Numer. Anal., 39, 1488-1511 (2002) · Zbl 1022.76059
[35] Fåhraeus, R.; Lindqvist, T., The viscosity of blood in narrow capillary tubes, Am. J. Physiol., 96, 562-568 (1931)
[36] Pries, A. R.; Secomb, T. W.; Gaehtgens, P., Biophysical aspects of blood flow in the microvasculature, Cardiovasc. Res., 32, 654-667 (1996)
[38] Myron, Y., Ophthalmology, 518-521 (2009), Mosby/Elsevier
[39] Duker, J.; Weiter, J. J., Ocular circulation, (Tasman, W.; Jaeger, E. A., Duanes Foundations of Clinical Ophthalmology (1991), J.B. Lippincott: J.B. Lippincott New York), 1-34
[40] Fung, Y. C., Biomechanics, Mechanical Properties of Living Tissues (1993), Springer Verlag: Springer Verlag New York
[41] Iftimia, N. V.; Hammer, D. X.; Bigelow, C. E., Toward noninvasive measurement of blood hematocrit using spectral domain low coherence interferometry and retinal tracking, Opt. Exp., 14, 3377-3388 (2006)
[42] Murray, C. D., The physiological principle of minimum work. I. the vascular system and the cost of blood volume, Proc. Natl. Acad. Sci. USA, 12, 207-214 (1926)
[43] Zamir, M., Nonsymmetrical bifurcations in arterial branching, J. Gen. Physiol., 72, 837-845 (1978)
[44] Iberall, A. S., Anatomy and steady flow characteristics of the arterial system with an introduction to its pulsatile characteristics, Math. Biosci., 1, 375-395 (1967)
[45] Zamir, M., On fractal properties of arterial trees, J. Theoret. Biol., 197, 517-526 (1999)
[46] Karch, R.; Neumann, F.; Neumann, M.; Schreiner, W., Staged growth of optimized arterial model trees, Ann. Biomed. Eng., 28, 1-17 (2000)
[47] Martinez-Perez, M. E., Computer Analysis of the Geometry of the Retinal Vasculature (2000), Imperial College: Imperial College London, (Ph.D. thesis)
[48] Mendfvil, A.; Cuartero, V.; Mendfvil, M. P., Ocular blood flow velocities in patients with proliferative diabetic retinopathy and healthy volunteers: a prospective study, Br. J. Ophthalmol., 79, 413-416 (1995)
[49] Pournaras, C. J.; Riva, C. E., Retinal blood flow evaluation, Ophthalmologica, 229, 61-74 (2013)
[50] Werkmeister, R. M.; Dragostinoff, N.; Palkovits, S.; Told, R.; Boltz, A.; Leitgeb, R. A.; Gröschl, M.; Garhöfer, G.; Schmetterer, L., Measurement of absolute blood flow velocity and blood flow in the human retina by dual-beam bidirectional Doppler-Fourier-domain optical coherence tomography, Invest. Ophthalmol. Vis. Sci., 53, 6062-6071 (2012)
[51] Riva, C. E.; Grunwald, J. E.; Sinclair, S. H.; Petrig, B. L., Blood velocity and volumetric flow rate in human retinal vessels, Invest. Ophthalmol. Vis. Sci., 26, 1124-1132 (1985)
[52] Grunwald, J. E.; Riva, C. E.; Baine, J.; Brucker, A. J., Total retinal volumetric blood flow rate in diabetic patients with poor glycemic control, Invest. Ophthalmol. Vis. Sci., 33, 356-363 (1992)
[53] Guran, T.; Zeimer, R. C.; Shahidi, M.; Mori, M. T., Quantitative analysis of retinal hemodynamics using targeted dye delivery, Invest. Ophthalmol. Vis. Sci., 31, 2300-2306 (1990)
[54] Stodtmeister, R., Enhanced pressure in the central retinal vein decreases the perfusion pressure in the prelaminar region of the optic nerve head, Invest. Ophthalmol. Vis. Sci., 54, 4698-4704 (2013)
[55] Hubbard, L. D.; Brothers, R. J.; King, W. N., Methods for evaluation of retinal microvascular abnormalities associated with hypertension/sclerosis in the Atherosclerosis Risk in Communities (ARIC), Study Ophthalmol., 106, 2269-2280 (1999)
[59] Fronek, K.; Zweifach, B. W., Microvascular pressure distribution in skeletal muscle and the effect of vasodilation, Am. J. Physiol., 228, 791-796 (1975)
[60] The Eugene M. Landis Award Lecture 2001, Microcirculation, 8, 365-375 (2001)
[61] Jensen, P. S.; Glucksberg, M. R., Regional variation in capillary hemodynamics in the cat retina, Invest. Ophthalmol. Vis. Sci., 39, 407-415 (1998)
[62] Williamson-Noble, F. A., Venous pulsation, Trans. Ophthalmol. Soc. U.K., 72, 317-326 (1952)
[63] Fåhraeus, R., The suspension stability of the blood, Physiol. Rev., 9, 241-274 (1929)
[64] Zamir, M., Shear forces and blood vessel radii in the cardiovascular system, J. Gen. Physiol., 69, 449-461 (1977)
[65] Zamir, M., The Physics of Coronary Blood Flow (2005), Springer Science and Business Media: Springer Science and Business Media USA · Zbl 1121.92024
[66] Glucksberg, M. R.; Dunn, R., Direct measurement of retinal microvascular pressures in the live, anesthetized cat, Microvasc. Res., 2, 158-165 (1993)
[67] Gore, R. W., Pressures in cat mesenteric arterioles and capillaries during changes in systemic arterial blood pressure, Circ. Res., 34, 581-591 (1974)
[68] Caca, I.; Nazaroglu, H.; Unlu, K.; Cakmak, S. S.; Ari, S.; Sakalar, Y. B., Color Doppler imaging of ocular hemodynamic changes in Behetś cisease, Jpn. J. Ophthalmol., 48, 2, 101-105 (2004)
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