MS02 - NEUR-1
Suzanne M. Scharer Room (#3146) in The Ohio Union

Mathematical Ophthalmology

Monday, July 17 at 04:00pm

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

Jessica Crawshaw

University of Oxford (Mathematical Institute)
"The role of hierarchical Bayesian inference in understanding macular degeneration treatment strategies"
Wet age-related macular degeneration (AMD) is a disease which slowly destroys ones’ central vision, with a huge impact on quality of life. It is the leading cause of central blindness worldwide. Wet AMD is characterised by neovascularisation, triggered by an unhealthy abundance of vascular endothelial growth factor (VEGF). These newly formed capillaries allow fluids to seep into the retina, damaging the local photoreceptors (critical light-sensing cells). Currently, there is no definitive cure for wet AMD. As such, intraocular injections of anti-angiogenic drugs to reduce the abundance of retinal VEGF is the clinical gold standard for disease management, slowing the progression of vision loss. However, injections into the eye are unpleasant, and the fluid dynamics within the eye leads to relatively rapid drug elimination, resulting in the need for regular intraocular injections. In this talk, we will present and analyse a pharmacokinetic/pharmacodynamic (PK/PD) model of a standard-of-care antibody, ranibizumab, targeting VEGF. This model has been developed to improve our understanding of the ocular pharmacology of ranibizumab and to provide a robust understanding of ranibizumab retention in the eye. Results from this PK/PD model are compared to published animal (cynomolgus monkey) and human data. We present a hierarchical Bayesian inference strategy to determine relevant parameter distributions. Using this strategy, we provide insight into the clinically observed inter-patient variability in VEGF suppression and drug retention. Finally, this model establishes the initial basis for a computational framework we are developing to mathematically compare the ocular PK/PD of ranibizumab with novel therapeutic strategies and other clinical anti-VEGF drugs in the treatment of AMD.
Additional authors: Jessica Crawshaw, Antonello Caruso, Michael Gertz, David Augustin, Philip Maini, Eamonn Gaffney

Moussa A. Zouache

University of Utah (John A. Moran Eye Center, Department of Ophthalmology & Visual Sciences)
"Predicting Physiology from Structure in the Human Choriocapillaris"
The choroidal vasculature and its microvascular bed, the choriocapillaris, support the metabolic requirements of the outer half of the retina, which includes the photoreceptors, cells that have one of the highest metabolic rates of any cell of the human body. The choriocapillaris has evolved a vascular geometry that differs markedly from branched vasculatures. It consists of a layer of densely organized capillaries contained between two continuous and approximately parallel sheets. Blood enters and leaves the choriocapillaris through a set of arterioles and venules connected to capillaries perpendicularly to its plane. Because of this unusual geometry, theoretical and experimental approaches traditionally applied to characterize blood flow and mass exchange in branched microvasculatures are not adapted to the choriocapillaris. As a result, it has been difficult to assess the role that this vascular bed plays in the onset and progression of inflammatory and degenerative diseases of the back of the eye. We developed a framework to predict aspects of the physiology of the choriocapillaris from experimentally accessible vascular parameters. This framework relies on three-dimensional mathematical models of the choriocapillaris informed by the angioarchitecture of the choroid as observed through immunohistochemistry of human tissue. Blood was modelled as a Newtonian fluid, and analytical and numerical solutions for the blood flow were obtained by solving the Navier-Stokes equation. The salient features of mass exchange with the retina were determined by solving the advection-diffusion equation for a scalar while imposing either a Dirichlet or a Neumann boundary condition on the surface of the choriocapillaris. Topological analysis of the flow field revealed that the blood flow in the choriocapillaris is decomposed into contiguous subsets separated by separation surfaces across which there is no flow. This segmentation is at the origin of the previously unexplained lobular appearance of the choriocapillaris observed during fluorescent dye angiography. The segmentation of the blood flow is associated with spatially heterogeneous dominant transport mechanisms. The boundaries between subsets of the flow field form regions, where the transport of material is dominantly diffusive. These regions represent areas of reduced exchange with the outer retina and are ubiquitous across the choriocapillaris. The width of diffusion-limited regions is determined by the relative distribution of arteriolar and venular insertions into the choriocapillaris, arterial flow rate and molecular diffusivity. Salient characteristics of the blood flow and passive transport in the choriocapillaris differ markedly from branched vasculatures. The geometry of the choriocapillaris is associated with segmented blood flow and spatially heterogeneous exchange with the outer retina. This heterogeneity may explain the spatial selectivity in pathologies associated with retinal diseases.

Richard Braun

University of Delaware (Department of Mathematical Sciences)
"Semi-automated Tear Breakup Detection and Modeling on the Ocular Surface"
The tear film is a thin fluid multilayer left on the eye surface after a blink. A good tear film is essential for health and proper function of the eye. Millions of people have a condition called dry eye disease (DED) that is thought to be closely linked to the tear film. DED inhibits vision and may lead to inflammation and ocular surface damage. However, there is little quantitative data about tear film failure, often called tear break up (TBU). Currently, it is not possible to directly measure important variables such as tear osmolarity (saltiness) within areas of TBU. We present a mostly automatic method that we have developed to extract data from video of the tear film dyed with fluorescein (for visualization). We have extracted data for 15 healthy subjects resulting in 467 instances of TBU. Using parameter identification from fits to appropriate math models, we estimate which mechanisms are most important in each instance and determine critical variables such as osmolarity within regions of TBU. Not only is new data obtained, but far more data, enabling statistical methods to be applied. So far, the methods provide baseline data for TBU in healthy subjects; future work will produce data from DED subjects.
Additional authors: TA Driscoll, U of Delaware; RA Luke, Johns Hopkins U and NIST; CG Begley, Indiana U; D Awis-Gyau, Alcon Research LLC.

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Annual Meeting for the Society for Mathematical Biology, 2023.