Biomechanics and Modeling in Mechanobiology

, Volume 15, Issue 3, pp 525–542 | Cite as

Blood flow mechanics and oxygen transport and delivery in the retinal microcirculation: multiscale mathematical modeling and numerical simulation

  • Paola Causin
  • Giovanna Guidoboni
  • Francesca Malgaroli
  • Riccardo Sacco
  • Alon Harris
Original Paper


The scientific community continues to accrue evidence that blood flow alterations and ischemic conditions in the retina play an important role in the pathogenesis of ocular diseases. Many factors influence retinal hemodynamics and tissue oxygenation, including blood pressure, blood rheology, oxygen arterial permeability and tissue metabolic demand. Since the influence of these factors on the retinal circulation is difficult to isolate in vivo, we propose here a novel mathematical and computational model describing the coupling between blood flow mechanics and oxygen (\(\hbox {O}_2\)) transport in the retina. Albeit in a simplified manner, the model accounts for the three-dimensional anatomical structure of the retina, consisting in a layered tissue nourished by an arteriolar/venular network laying on the surface proximal to the vitreous. Capillary plexi, originating from terminal arterioles and converging into smaller venules, are embedded in two distinct tissue layers. Arteriolar and venular networks are represented by fractal trees, whereas capillary plexi are represented using a simplified lumped description. In the model, \(\hbox {O}_2\) is transported along the vasculature and delivered to the tissue at a rate that depends on the metabolic demand of the various tissue layers. First, the model is validated against available experimental results to identify baseline conditions. Then, a sensitivity analysis is performed to quantify the influence of blood pressure, blood rheology, oxygen arterial permeability and tissue oxygen demand on the \(\hbox {O}_2\) distribution within the blood vessels and in the tissue. This analysis shows that: (1) systemic arterial blood pressure has a strong influence on the \(\hbox {O}_2\) profiles in both blood and tissue; (2) plasma viscosity and metabolic consumption rates have a strong influence on the \(\hbox {O}_2\) tension at the level of the retinal ganglion cells; and (3) arterial \(\hbox {O}_2\) permeability has a strong influence on the \(\hbox {O}_2\) saturation in the retinal arterioles.


Retinal microcirculation Ocular blood flow mechanics  Oxygen in blood Oxygen in tissue Capillary plexi model Mass transport Multiscale model 





Central retinal artery


Central retinal vein


Diffusion-limited aggregation


Finite element method


Fully coupled model


Intraocular pressure

\(\hbox {O}_2\)



Partial differential equation


Red blood cell


Vascular tree network





This work has been partially supported by the NSF DMS-1224195, NIH1R21EY022101-01A1, the Indiana University Collaborative Research Grant of the Office of the Vice President for Research and the Chair Gutenberg funds and has been partially supported by an Unrestricted Grant from “Research to Prevent Blindness.” We thank the anonymous Reviewers for their thorough revision work and for their suggestions which helped to improve this paper.

Supplementary material

10237_2015_708_MOESM1_ESM.pdf (3.7 mb)
Supplementary material 1 (pdf 3829 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Paola Causin
    • 1
  • Giovanna Guidoboni
    • 2
    • 3
  • Francesca Malgaroli
    • 4
  • Riccardo Sacco
    • 4
  • Alon Harris
    • 5
  1. 1.Dipartimento di Matematica “F. Enriques”Università degli Studi di MilanoMilanItaly
  2. 2.Department of Mathematical SciencesIndiana University - Purdue University IndianapolisIndianapolisUSA
  3. 3.Institut de Recherche en Mathématique, Interactions et Applications (IRMIA)University of StrasbourgStrasbourg CedexFrance
  4. 4.Eugene and Marilyn Glick Eye InstituteIndiana University School of MedicineIndianapolisUSA
  5. 5.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly

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