Biomechanics and Modeling in Mechanobiology

, Volume 15, Issue 4, pp 893–907 | Cite as

Effect of ocular shape and vascular geometry on retinal hemodynamics: a computational model

  • Andrea Dziubek
  • Giovanna Guidoboni
  • Alon Harris
  • Anil N. Hirani
  • Edmond Rusjan
  • William Thistleton
Original Paper


A computational model for retinal hemodynamics accounting for ocular curvature is presented. The model combines (i) a hierarchical Darcy model for the flow through small arterioles, capillaries and small venules in the retinal tissue, where blood vessels of different size are comprised in different hierarchical levels of a porous medium; and (ii) a one-dimensional network model for the blood flow through retinal arterioles and venules of larger size. The non-planar ocular shape is included by (i) defining the hierarchical Darcy flow model on a two-dimensional curved surface embedded in the three-dimensional space; and (ii) mapping the simplified one-dimensional network model onto the curved surface. The model is solved numerically using a finite element method in which spatial domain and hierarchical levels are discretized separately. For the finite element method, we use an exterior calculus-based implementation which permits an easier treatment of non-planar domains. Numerical solutions are verified against suitably constructed analytical solutions. Numerical experiments are performed to investigate how retinal hemodynamics is influenced by the ocular shape (sphere, oblate spheroid, prolate spheroid and barrel are compared) and vascular architecture (four vascular arcs and a branching vascular tree are compared). The model predictions show that changes in ocular shape induce non-uniform alterations of blood pressure and velocity in the retina. In particular, we found that (i) the temporal region is affected the least by changes in ocular shape, and (ii) the barrel shape departs the most from the hemispherical reference geometry in terms of associated pressure and velocity distributions in the retinal microvasculature. These results support the clinical hypothesis that alterations in ocular shape, such as those occurring in myopic eyes, might be associated with pathological alterations in retinal hemodynamics.


Mathematical modeling Retinal hemodynamics Hierarchical porous medium Ocular curvature Vascular network Finite element exterior calculus 

Mathematics Subject Classification

76S05 93A30 65N30 76M10 



We thank Alexandra Benavente-Perez and Muhammed Ali Alan for helpful discussions. We thank the students who participated in the SUNY STEM summer program 2014. This work has been partially supported by the NSF DMS-1224195, NSF CCF-1064429, NIH 1R21EY022101-01A1, a grant from Research to Prevent Blindness (RPB, NY, USA), an Indiana University Collaborative Research Grant of the Office of the Vice President for Research and the Chair Gutenberg funds.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Andrea Dziubek
    • 1
  • Giovanna Guidoboni
    • 2
    • 3
    • 4
  • Alon Harris
    • 4
  • Anil N. Hirani
    • 5
  • Edmond Rusjan
    • 1
  • William Thistleton
    • 1
  1. 1.Department of Mathematics and SciencesState University of New York Polytechnic InstituteUticaUSA
  2. 2.Department of Mathematical SciencesIndiana University Purdue University IndianapolisIndianapolisUSA
  3. 3.LABEX IRMIAUniversité de StrasbourgStrasbourgFrance
  4. 4.Eugene and Marilyn Glick Eye InstituteIndiana University School of MedicineIndianapolisUSA
  5. 5.Department of MathematicsUniversity of Illinois at Urbana ChampaignUrbanaUSA

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