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

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Abstract

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.

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Abbreviations

ACV:

Artero-capillary-venous

CRA:

Central retinal artery

CRV:

Central retinal vein

DLA:

Diffusion-limited aggregation

FEM:

Finite element method

FCM:

Fully coupled model

IOP:

Intraocular pressure

\(\hbox {O}_2\) :

Oxygen

PDE:

Partial differential equation

RBC:

Red blood cell

VTN:

Vascular tree network

1/2/3D:

One/two/three-dimensional

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Acknowledgments

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.

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Authors and Affiliations

  1. Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, via Saldini, 50, 20133, Milan, Italy

    Paola Causin

  2. Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis, 402 N. Blackford St., Indianapolis, IN, LD270, USA

    Giovanna Guidoboni

  3. Institut de Recherche en Mathématique, Interactions et Applications (IRMIA), University of Strasbourg, 7 rue René Descartes, 67084, Strasbourg Cedex, France

    Giovanna Guidoboni

  4. Eugene and Marilyn Glick Eye Institute, Indiana University School of Medicine, 1160 W. Michigan St., Indianapolis, IN, LD270, USA

    Francesca Malgaroli & Riccardo Sacco

  5. Dipartimento di Matematica, Politecnico di Milano, Piazza L. da Vinci, 32, 20133, Milan, Italy

    Alon Harris

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  1. Paola Causin
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Correspondence to Paola Causin.

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Causin, P., Guidoboni, G., Malgaroli, F. et al. Blood flow mechanics and oxygen transport and delivery in the retinal microcirculation: multiscale mathematical modeling and numerical simulation. Biomech Model Mechanobiol 15, 525–542 (2016). https://doi.org/10.1007/s10237-015-0708-7

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