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ACMD Seminar: Mathematically Investigating Retinitis Pigmentosa

Danielle Brager
Applied and Computational Mathematics Division, NIST

Tuesday, May 11, 3:00 EDT (1:00 MDT)

A video of this talk is available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page.

Abstract:  Retinitis Pigmentosa (RP) is a collection of clinically and genetically heterogeneous degenerative retinal diseases.  Patients with RP experience a loss of night vision that progresses to day-light blindness due to the sequential degeneration of rod and cone photoreceptors.  While known genetic mutations associated with RP affect the rods, the degeneration of cones inevitably follows in a manner independent of those genetic mutations.  Investigation of this secondary death of cone photoreceptors led to the discovery of the rod-derived cone viability factor (RdCVF), a protein secreted by the rods that preserves the cones by accelerating the flow of glucose into cone cells stimulating aerobic glycolysis.  In this work, we formulate a predator-prey style system of nonlinear ordinary differential equations to mathematically model photoreceptor interactions in the presence of RP while accounting for the new understanding of RdCVF's role in enhancing cone survival.  We utilize the mathematical model and subsequent analysis to examine the underlying processes and mechanisms (defined by the model parameters) that affect cone photoreceptor vitality as RP progresses.  The physiologically relevant equilibrium points are interpreted as different stages of retinal degeneration.  We determine conditions necessary for the local asymptotic stability of these equilibrium points and use the results as criteria needed to remain in a stage in the progression of retinal degeneration.  Experimental data is used for parameter estimation.  Pathways to blindness are uncovered via bifurcations and narrows our focus to four of the model equilibria.  Using Latin Hypercube Sampling coupled with partial rank correlation coefficients, we perform a sensitivity analysis to determine mechanisms that have a significant effect on the cones at four stages of RP.  We derive a non-dimensional form of the mathematical model and perform a numerical bifurcation analysis using MATCONT to explore the existence of stable limit cycles because a stable limit cycle is a stable mode, other than an equilibrium point, where the rods and cones coexist.  In our analyses, a set of key parameters involved in photoreceptor outer segment shedding, renewal, and nutrient supply were shown to govern the dynamics of the system.  Our findings illustrate the benefit of using mathematical models to uncover mechanisms driving the progression of RP and opens the possibility to use in silico experiments to test treatment options in the absence of rods.

Bio:  Danielle Brager obtained a B.S. in Mathematics at the University of Houston and a M.S. in Mathematics at Texas Southern University.  She completed her Ph.D. in Applied Mathematics at Arizona State University in 2020 where her thesis involved mathematically modeling photoreceptor interactions in the human eye. She is currently a National Research Council postdoctoral fellow working with Anthony Kearsley at NIST. Her current research includes modeling and simulating Retinitis Pigmentosa, a degenerative eye disease. She also participates in a NIST research group that studies increases in measurement sensitivity and the effect it has on compound identification in analytical chemistry.

Note: This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)



Created April 23, 2021, Updated May 12, 2021