MS01 - NEUR-1
Suzanne M. Scharer Room (#3146) in The Ohio Union

Mathematical Ophthalmology

Monday, July 17 at 10:30am

SMB2023 SMB2023 Follow Monday during the "MS01" time block.
Room assignment: Suzanne M. Scharer Room (#3146) in The Ohio Union.
Note: this minisymposia has multiple sessions. The other session is MS02-NEUR-1 (click here).

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Paul A. Roberts, Jessica Crawshaw


Mathematical Ophthalmology concerns the use of mechanistic mathematical models to derive insight into the mechanisms underpinning the structure and function of the eye in health, development and disease and to predict the effects of existing and putative treatments. It is an exciting time in Mathematical Ophthalmology. Though a relatively small field, we are reaching a tipping point as the importance of quantitative tools in ophthalmology becomes more widely recognised and the number of those working in the field reaches a critical mass. Thus, we are now at a point where a significant body of substantive research has been built up and where we are gaining increasing recognition as a community. In this minisymposium, we will showcase research in the field to the broader Mathematical Biology community, and aim to build and strengthen connections and collaborations within the Mathematical Ophthalmology community. It is hoped that this session will also encourage other applied mathematicians to conduct research in this exciting area.

Paul A. Roberts

University of Birmingham (Centre for Systems Modelling and Quantitative Biomedicine)
"Mathematical and Computational Ophthalmology: Coming of Age"
This talk will set the scene for those which follow in the Mathematical Ophthalmology minisymposium. I will begin by defining what we mean by the terms Mathematical Ophthalmology (a new term which I have coined) and Computational Ophthalmology (an existing term) and how these fields relate both to each other and to more established experimental and clinical disciplines. I shall give a brief history of these emerging fields, highlighting key case studies, and discuss their future prospects. I will also be announcing and inviting participation in a number of exciting opportunities and initiatives aimed at promoting these fields and supporting those working within them.

Brendan C. Fry

Metropolitan State University of Denver (Department of Mathematics and Statistics)
"Modeling metabolic blood flow regulation and oxygenation in the human retinal microcirculation"
The retinal microcirculation perfuses the retinal cells responsible for vision, and impairments in retinal blood flow and oxygenation are involved in the progression of eye diseases such as glaucoma. Here, an established theoretical hybrid model of a retinal microvascular network will be presented and extended to include effects of local blood flow regulation on oxygenation. A heterogeneous description of the arterioles based on confocal microscopy images is combined with a compartmental representation of the downstream capillaries and venules. To simulate oxygen transport in the arterioles, a Green’s function method is used; in the capillary and venular compartments, a Krogh cylinder model is applied. Acute regulation of blood flow is simulated in response to changes in pressure, shear stress, and metabolism. The model results predict that both an increase in intraocular pressure and an impairment in blood flow regulation can lead to decreased tissue oxygenation, indicating that both mechanisms represent factors that can lead to the impaired oxygenation observed in eye disease. Results from the model further imply that the metabolic response mechanism reduces the fraction of poorly-oxygenated tissue, but that the pressure- and shear-stress-dependent response mechanisms may actually hinder the vascular response to changes in oxygenation. Importantly, the heterogeneity of the microvascular network structure demonstrates that traditionally-reported average values of tissue oxygen levels hide significant localized defects in tissue oxygenation that may be involved in eye disease processes. Going forward, the model framework will help provide comparisons to sectorial-specific clinical data, in order to better assess the role of impaired blood flow regulation in glaucoma.

Julia Arciero

Indiana University - Purdue University Indianapolis (Mathematical Sciences)
"Predicting the impact of capillary density on retinal vessel and tissue oxygenation using a theoretical model"
Impairments in retinal blood flow and oxygenation have been shown to contribute to the progression of glaucoma. In this study, a theoretical model of the human retina is used to predict blood flow and tissue oxygenation in retinal vessels and tissue for varied levels of capillary density. The model includes a heterogeneous representation of retinal arterioles and a compartmental representation of capillaries and venules. A Green’s function method is used to model oxygen transport in the arterioles, and a Krogh cylinder model is used in the capillaries and venules. In our clinical observations, early glaucoma patients are shown to exhibit a 10-12% reduction in capillary density compared to healthy individuals. The model is simulated for capillary density values ranging from 250 to 750 capillaries/mm^2. Oxygen extraction fraction, defined as the ratio of oxygen consumption to oxygen delivery, is calculated for each model simulation. The model predicts a 6% and 53% decrease in mean PO_2 in retinal vessels immediately downstream of the capillaries when capillary density is decreased from its reference value of 500 capillaries/mm^2 by 10% and 50%, respectively. Ultimately, the mathematical model demonstrates the significant detrimental impact of such decreases in capillary density on the oxygenation of retinal tissues.
Additional authors: Brendan Fry, Department of Mathematics and Statistics, Metropolitan State University of Denver; Amanda Albright, Department of Mathematical Sciences, IUPUI; Alice Verticchio, Department of Ophthalmology, Icahn School of Medicine at Mount Sinai Hospital; Brent Siesky, Department of Ophthalmology, Icahn School of Medicine at Mount Sinai Hospital; Alon Harris, Department of Ophthalmology, Icahn School of Medicine at Mount Sinai Hospital;

Remi Hernandez

University of Liverpool (Department of Cardiovascular and Metabolic Medicine)
"Virtual populations of the retina to characterize hypoxia in wet AMD"
Retinal angiograms with high resolution are taken routinely in eye clinics. Several studies have highlighted the association between angiographic parameters and several retinal diseases, including wet age-related macular degeneration (wAMD). These parameters indicate a decline in retinal perfusion which may lead to hypoxia. Because hypoxia may be a trigger of the pathological angiogenesis seen in eyes with wAMD, quantifying it in diseased eyes is important to understand and model the disease and find optimal treatment strategies. We have created synthetic vasculatures using an algorithm mimicking angiogenesis along with convection and reaction-diffusion models of oxygen perfusion. We propose to develop a framework to computationally study hypoxia in 3-dimensional virtual populations of the retina, in health and disease.
Additional authors: W.K. El-Bouri; Y. Zheng; S. Madhusudhan

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