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A mathematical model for the distribution of hemodynamic parameters in the human retinal microvascular network

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Journal of Biorheology

Abstract

To quantitatively assess the arteriovenous distribution of hemodynamic parameters throughout the microvascular network of the human retina, we constructed a retinal microcirculatory model consisting of a dichotomous symmetric branching system. This system is characterized by a diameter exponent of 2.85, instead of 3 as dictated by Murray’s law, except for the capillary networks. The value of 2.85 was the sum of a fractal dimension (1.70) and a branch exponent (1.15) of the retinal vasculature. Following the feeding artery (central retinal artery), each bifurcation was recursively developed at a distance of an individual branch length [L(r) = 7.4r 1.15] by a centrifugal scheme. The venular tree was formed in the same way. Using this model, we evaluated hemodynamic parameters, including blood pressure, blood flow, blood velocity, shear rate, and shear stress, within the retinal microcirculatory network as a function of vessel diameter. The arteriovenous distributions of blood pressure and velocity in the simulation were consistent with in vivo measurements in the human retina and other vascular beds of small animals. We therefore conclude that the current theoretical model was useful for quantifying hemodynamics as a function of vessel diameter within the retinal microvascular network.

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Authors and Affiliations

  1. Department of Mathematical Information Science, Asahikawa Medical College, Asahikawa, Hokkaido, 078-8510, Japan

    Tatsuhisa Takahashi

  2. Department of Ophthalmology, Asahikawa Medical College, Asahikawa, Hokkaido, 078-8510, Japan

    Taiji Nagaoka & Akitoshi Yoshida

  3. Department of Informatics, Faculty of Engineering, Yamagata University, Yonezawa, 992-8510, Japan

    Hirotaka Yanagida & Tadashi Saitoh

  4. Research Institute for Interdisciplinary Sciences, Tokyo, 162-0053, Japan

    Akira Kamiya

  5. Departments of System Biology and Translational Medicine, and Ophthalmology, College of Medicine, Texas A&M Health Science Center, Temple, TX, 76504, USA

    Travis Hein & Lih Kuo

Authors
  1. Tatsuhisa Takahashi
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  2. Taiji Nagaoka
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  3. Hirotaka Yanagida
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  4. Tadashi Saitoh
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  5. Akira Kamiya
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  6. Travis Hein
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  7. Lih Kuo
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  8. Akitoshi Yoshida
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Correspondence to Tatsuhisa Takahashi.

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Takahashi, T., Nagaoka, T., Yanagida, H. et al. A mathematical model for the distribution of hemodynamic parameters in the human retinal microvascular network. J Biorheol 23, 77–86 (2009). https://doi.org/10.1007/s12573-009-0012-1

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  • DOI: https://doi.org/10.1007/s12573-009-0012-1

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