Math Model Tracks Macular Degeneration Progression

Math (geometrical and algebraic calculations) has been in existence since about 1750 BC approximately 2,590 years ago. It began shortly after the development of language when humans started counting on their fingers. Since this inception, math has been the cornerstone of small and huge leaps in human technological advancement. As math catapulted so many inventions to bring us to the rapid digital pace we are now immersed in, it is also responsible for a variety of predictive algorithms, particularly in the medical field. 

When it comes to disease, math has shown to be an excellent tool in finding out the complex paths pathology can take when disease eludes researchers. Recent research into the unknown origins of macular degeneration, the number one eye disease that causes blindness, shows how a math model tracks macular degeneration progression and may help in essential treatment.

Mathematical Simulation

Researchers from the Universidad Carlos III de Madrid (UC3M) have developed a specialized ‘mathematical mannequin’ to be able to display the unknown origin of macular degeneration. Although this is still considered a prototype model, it is the closest researchers have come to a solid application of how macular degeneration may develop. 

Recreating the progression of macular degeneration offers several scenarios that, eventually, can be broken down into predictive patterns. One scenario includes angiogenesis (the spread of blood capillaries) that is shown, through acquired accumulated medical data, as a computational model capable of mathematically enhancing progression before it occurs. 

According to co-author of the mathematical research, Luis L. Bonilla, from the “Gregorio Millán Barbany” University Institute on Modeling and Simulation in Fluid Dynamics, Nanoscience and Industrial Mathematics at UC3M, 

“In this case, what happens is that, with age, a barrier (called Bruch’s membrane) that separates the capillaries from the inner part of the retina becomes less permeable and, therefore, oxygen does not reach nor sufficient nutrients to the photoreceptors. Then they emit a signal (called growth factor) that spreads, passes where the blood vessels are and causes this angiogenesis to appear, which is what causes the disease [macular degeneration].”

Following the Markers 

Numerical simulations of when photoreceptors may begin to become compromised suggest when to apply specific treatments. These treatments can target how to decrease the growth factors mentioned above along with ways to minimize the production of proteins that contribute to the development of angiogenesis. When the predictive mathematical model identifies a particular beginning angiogenesis marker, such treatments can immediately be implemented to slow the disease. In addition, other therapies can also be applied to improve such factors as cell adhesion which, over time, could be a significant player in avoiding future damage caused by macular degeneration.

The study from the Universidad Carlos III de Madrid, ‘Anomalous Angiogenesis in Retina’ published in Biomedicines, describes the importance of using a math model to track macular degeneration, stating that,

“Numerical simulations of the model show that choroid neovascularization mainly results from three causes: (i) impairment of the adhesion between retinal pigmentation epithelium cells, between these cells and Bruch’s membrane and among endothelial cells; (ii) excess VEGF producing strong gradients thereof; (iii) excess Jagged production. Anti-VEGF and anti-Jagged treatments address (ii) and (iii) and could halt angiogenesis on a temporary basis,…Modeling and numerical simulation could thus be key to identifying the critical experiments that are most likely to improve our understanding of AMD and possible treatments.” 

Professor Bonilla comments on the model which is in the form of a mannequin as a simulated human replica,

“The mannequin has a number of parameters that characterize the development of the illness. One can change them and predict how the illness will progress in response to values, so it may be used to regulate how the method occurs,” 

By following these predictive markers, ophthalmologists can recognize anomalies that were undetectable in past routine eye checkups. Once there is a ‘red flag,’ treatment can immediately start, slowing the disease.

More Model Predictions

As the use of mathematical models advances so too does the predictive research. This has been significantly applied to AI (artificial intelligence) learning algorithms particularly for wet age-related macular degeneration (AMD). Wet AMD is a major cause of rapid visual deterioration due to leaking blood vessels within the retina.

Nature Medicine published a study titled, ‘Predicting conversion to wet age-related macular degeneration using deep learning’ which found that,

“In patients diagnosed with exAMD [exudative, meaning discharge or wet] in one eye, we introduce an artificial intelligence (AI) system to predict progression to exAMD in the second eye. By combining models based on three-dimensional (3D) optical coherence tomography images and corresponding automatic tissue maps, our system predicts conversion to exAMD within a clinically actionable 6-month time window,…Moreover, we show that automatic tissue segmentation can identify anatomical changes before conversion and high-risk subgroups. This AI system overcomes substantial inter-observer variability in expert predictions, performing better than five out of six experts, and demonstrates the potential of using AI to predict disease progression.”

These models are just small examples of the path research is taking to predict future AMD progression. In addition to immediately administering treatments to slow the disease, these models may continue to be developed into deeper applications that could, eventually, lead to the root cause. There is also the ability to follow, notate, and predict the mathematical path of anti-vascular endothelial growth factor (anti-VEGF) injection treatments. These injections are often followed through weekly checkups but once a mathematical model can be applied to each individual patient, the exact elapsed timing can corroborate with future injections to overlap and increase treatment for the most beneficial results. 

As each math model tracks macular degeneration progression, other disease research may also follow the same algorithms, turning medical science into mathematical science as well. Possibly, in the not so distant future, these models could help avoid invasive testing, missed diagnosis, and ineffective dosages to create precision medicine rather than blanket applications which often work more on hope than mathematical certainties.  

Sources:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7927046/

Mathematics to enhance macular degeneration remedy

Mathematics to improve the treatment of macular degeneration

https://www.nature.com/articles/s41591-020-0867-7