Theoretical Model of Blood Flow in the Human Retinal Vasculature - - PowerPoint PPT Presentation

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Theoretical Model of Blood Flow in the Human Retinal Vasculature

Mandy Abernathy

Wisconsin Lutheran College February 2, 2020

• M. Abernathy

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Background Mathematical Model Hemodynamics Heterogeneous Model Results

Background

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Biological Background

Glaucoma is a serious ocular disease that results in irreversible vision loss Increased intraocular pressure damages the optic nerve Almost one third of glaucoma patients do not exhibit elevated pressures There are other factors that cause continuing damage

Source: Murata Eyecare Optometry

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Biological Motivation

Possible correlation between impaired blood flow and glaucoma-related damage Impaired oxygenation could be a cause or an effect of retinal ganglion cell death and loss of retinal function

Source: Concepts of Biology

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Mathematical Model

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Heterogeneous Model

Provides more accurate depiction of

• xygen delivery

A previous heterogeneous model predicts retinal oxygenation in the mouse Differences between mouse and man: vessel size four arterial branches vs. six fovea

Figure: Arteriolar Network in the Mouse Retina

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Research Goals

Objective To develop a theoretical model of the human retinal arterioles based

• n oximetry data to predict retinal blood and tissue oxygenation
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Hemodynamics

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Blood Flow

Poiseuille’s Law

Q = π(∆P)D4 128Lµ

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Oxygen Transport - Green’s Function Model

Source: Secomb et al. 2004

This more realistic model of oxygen transport accounts for the diffusion of oxygen from multiple blood vessels Vessel points are considered oxygen sources and tissue points are considered

• xygen sinks
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Green’s Function Model

By the conservation of mass, oxygen diffusion is equal to oxygen consumption, Dα∇2P = M(P) (1) P - tissue PO2 Dα - rate of oxygen diffusion M(P) - consumption rate The Green’s function G(x, x∗) represents the PO2 at a point x, resulting from a unit point source at x∗, and is the solution to Dα∇2G = −δ3(x − x∗) (2) Oxygen levels at each tissue point are calculated by summing the oxygen fields from these sources, P = ΣG(x, x∗)q(x∗) (3) q(x∗) - strength of oxygen source

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Heterogeneous Model

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Vascular Networks

Mouse Vasculature Human Vasculature

Superior Temporal Nasal Inferior

Source: Ganessan et al. 2010 Source: Stefánsson et al. 2019

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Mouse to Man Scaling Factor

Blood Vessel Diameters (µm) Branch

• Inf. Nasal
• Sup. Nasal
• Sup. Temporal
• Inf. Temporal

Mouse 30.42 26.94 24.02 28.48 Human 94 97 111 117 A scaling factor of 3.8 was determined by comparing diameter values for the four main arterial branches

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Results

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Blood Flow Computed along Single Vessel Pathway

1000 2000 3000 4000 5000 6000 1000 2000 3000 4000 5000 6000 7000 8000 9000 Flow (nL/min) Distance from CRA (µm)

Flow vs. Distance from CRA CRA terminal node

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Network Oxygenation

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Future Work

Continue adapting the model to represent the human retinal blood vessels Develop a hybrid model of the retinal microvasculature that connects the capillaries and veins to the arterial network Relate our understanding of retinal blood flow to visual function and glaucoma-related damage

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Acknowledgments

Mentor Julia Arciero, Department of Mathematical Sciences, IUPUI Collaborators Hannah Scanlon (Mathematics, Wake Forest University) Brendan Fry (Mathematics, Metropolitan State University of Denver) Alon Harris (Ophthalmology, IU School of Medicine) Brent Siesky (Ophthalmology, IU School of Medicine) Alice Verticchio (Ophthalmology, IU School of Medicine) Funding and Support This research has been funded and initiated by the Mathematical Biosciences Institute and the National Science Foundation under grant DMS 1757423.

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Questions

Contact Information mandy.abernathy@mail.wlc.edu

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