Microcirculation in Fractal Branching Networks

1. Front Matter

   Pages i-xiii

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2. Branching Systems of Fractal Vascular Trees

   • Tatsuhisa Takahashi

   Pages 1-24

3. A Theoretical Model for the Microcirculatory Network

   • Tatsuhisa Takahashi

   Pages 25-45

4. Oxygen Consumption by Vascular Walls in the Retinal Vasculature

   • Tatsuhisa Takahashi

   Pages 47-69

5. The Fåhraeus–Lindqvist Effect on the Retinal Microcirculation

   • Tatsuhisa Takahashi

   Pages 71-92

6. Effects of a Reduction in the Bifurcation Exponent from 3.00 to 2.85 on Microcirculation

   • Tatsuhisa Takahashi

   Pages 93-112

7. Asymmetrically Branching Microvascular Networks

   • Tatsuhisa Takahashi

   Pages 113-130

8. Back Matter

   Pages 131-138

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This book presents a new method for analyzing the structure and function of the biological branching systems of fractal trees, with a focus on microcirculation. Branching systems in humans (vascular and bronchial trees) and those in the natural world (plants, trees, and rivers) are characterized by a fractal nature. To date, fractal studies have tended to concentrate on fractal dimensions, which quantify the complexity of objects, but the applications for practical use have remained largely unexplored. This book breaks new ground with topics that include the human retinal microcirculatory network, oxygen consumption by vascular walls, the Fåhraeus-Lindqvist effect, the bifurcation exponent, and the asymmetrical microvascular network. Readers are provided with simple formulas to express functions and a simulation graph with in vivo data. The book also discusses the mechanisms regulating blood flow and pressure and how they are related to pathological changes in the human body. Researchers and clinicians alike will find valuable new insights in these pioneering studies.

• Fractal analysis
• Microcirculation
• Murray's model
• Retinal Vasculature
• Shear Rate

• Dept. Mathematical Information Science, Asahikawa Medical University, Asahikawa, Japan

  Tatsuhisa Takahashi

Dr. Takahashi obtained PhD degree in Faculty of Engineering, Graduate School of Engineering, School of Engineering Hokkaido University, Japan in 1993. He started his carrier as an assistant professor at Department of Electrical and Information Engineering (renamed as Department of Bio-system Engineering in 2000) of Yamagata University in the same year. He received ESM Travel Award by the European Society for Microcirculation in 1992. He moved to Department of Mathematical Information Science of Asahikawa Medical University as an associate professor in 2002.

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