Simulation of Angiogenesis in Three Dimensions: Development of the Retinal Circulation

Jonathan P. Alberding, Timothy W. Secomb

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


A theoretical model is used to describe the three-dimensional development of the retinal circulation in the human eye, which occurs after the initial spread of vasculature across the inner surface of the retina. In the model, random sprouting angiogenesis is driven by a growth factor that is produced in tissue at a rate dependent on oxygen level and diffuses to existing vessels. Vessel sprouts connect to form pathways for blood flow and undergo remodeling and pruning. These processes are controlled by known or hypothesized vascular responses to hemodynamic and biochemical stimuli, including conducted responses along vessel walls. The model shows regression of arterio-venous connections on the surface of the retina, allowing perfusion of the underlying tissue. A striking feature of the retinal circulation is the formation of two vascular plexuses located at the inner and outer surfaces of the inner nuclear layer within the retina. The model is used to test hypotheses regarding the formation of these structures. A mechanism based on local production and diffusion of growth factor is shown to be ineffective. However, sprout guidance by localized structures on the boundaries of the inner nuclear layer can account for plexus formation. The resulting networks have vascular density, perfusion and oxygen transport characteristics consistent with observed properties. The model shows how stochastic generation of vascular sprouts combined with a set of biologically based response mechanisms can lead to the generation of a specialized three-dimensional vascular structure with a high degree of organization.

Original languageEnglish (US)
Article number27
JournalBulletin of Mathematical Biology
Issue number4
StatePublished - Apr 2023


  • Angiogenesis
  • Blood flow
  • Microcirculation
  • Oxygen transport
  • Retina
  • Structural remodeling

ASJC Scopus subject areas

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


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