(252f) Physics-Informed Neural Networks for Efficient Modeling and Estimation in Bi-Layered Ocular Drug Delivery Systems

Wet age-related macular degeneration (wet AMD) is a chronic disease leading to vision loss, treated with anti-vascular endothelial growth factor (anti-VEGF) drugs typically administered through frequent, costly, and painful intravitreal injections [1]. To address this problem, several drug delivery systems (DDS) have been proposed in the literature to extend anti-VEGF release in the eye and reduce the frequency of injections [2, 3]. Particularly for this study, we focused on drug release from chitosan-polycaprolactone (PCL) microparticles, aiming to optimize DDS design for better wet AMD treatments [4]. A mathematical model of this system has been proposed in previous work that uses Fick’s second law for unsteady-state mass transfer of drug from the DDS into a buffer solution under the following assumptions: constant diffusion coefficients in each medium, no convection or reaction within the DDS, and negligible erosion or swelling [5]. Although one can numerically solve these coupled partial differential equations (PDEs) using established solvers (such as the finite element solvers in COMSOL), the stiff dynamic present at the interface typically make the solution process very computationally demanding. This cost is particularly important when one looks to deploy the model for decision-making tasks such as parameter estimation as well as design optimization.

In this work, we look to leverage physics-informed neural networks (PINNs) [6], which are a type of scientific machine learning technique for solving PDEs, to overcome the computational challenges with traditional solution methods for mathematical models of DDS systems. PINNs represent a mesh-free method for solving PDEs by training a neural network to minimize a loss function that incorporates terms that reflect the initial and boundary conditions along the space-time domain boundary and the PDE residual at points within the domain. A major advantage of PINNs is that the same framework extends directly to the inverse problem wherein one wants to learn unknown model parameters (such as the diffusion coefficient) from experimental data. In traditional PDE solvers, one must converge the numerical solution for every tested parameter value and then apply some outer optimization scheme to select a new value. In PINNs, on the other hand, one only must incorporate a new term in the loss function that accounts for the data prediction error such that the same optimization/training process as the forward problem can be utilized (i.e., this can be interpreted as jointly solving for a neural network that matches the physics and data, which can significantly reduce cost over the former sequential approach), e.g., [7, 8, 9]. We further introduce some important modifications to PINNs to address issues introduced by differences in length- and time-scales and non-smooth transitions that occur near the interface that are particularly relevant for the DDS governing dynamics. Through a variety of simulation examples, we show how the proposed PINN method greatly reduces the cost of obtaining accurate predictions of the drug release behavior in wet AMD treatment. We will also discuss how this new paradigm can be extended to predict a variety of key DDS properties at no additional cost (e.g., cumulative drug release profile, therapeutic release time, and DDS depletion time from input conditions of drug loading) as well as seamlessly incorporate newly collected in vitro and in vivo experimental data.

References

[1] Parravano, M., Costanzo, E., Scondotto, G., Trifirò, G., & Virgili, G. (2021). Anti-VEGF and other novel therapies for neovascular age-related macular degeneration: an update. BioDrugs, 35(6), 673-692.

[2] Luaces-Rodriguez, A., Mondelo-Garcia, C., Zarra-Ferro, I., Gonzalez-Barcia, M., Aguiar, P., Fernandez-Ferreiro, A., & Otero-Espinar, F. J. (2020). Intravitreal anti-VEGF drug delivery systems for age-related macular degeneration. International Journal of Pharmaceutics, 573, 118767.

[3] Chacin Ruiz, E. A., Swindle-Reilly, K. E., & Ford Versypt, A. N. (2023). Experimental and mathematical approaches for drug delivery for the treatment of wet age-related macular degeneration. Journal of Controlled Release 363, 464-483.

[4] Jiang, P., Jacobs, K. M., Ohr, M. P., & Swindle-Reilly, K. E. (2020). Chitosan–polycaprolactone core–shell microparticles for sustained delivery of bevacizumab. Molecular Pharmaceutics, 17(7), 2570-2584.

[5] Chacin Ruiz, E. A., Carpenter, S. L., Swindle-Reilly, K. E., & Ford Versypt, A. N. (2024). Mathematical modeling of drug delivery from bi-layered core-shell polymeric microspheres. bioRxiv, 2024.

[6] Raissi, Maziar, Paris Perdikaris, and George E. Karniadakis. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378: 686-707.

[7] Cuomo, S., Di Cola, V. S., Giampaolo, F., Rozza, G., Raissi, M., & Piccialli, F. (2022). Scientific machine learning through physics–informed neural networks: Where we are and what’s next. Journal of Scientific Computing, 92(3), 88.

[8] Mao, Zhiping, Ameya D. Jagtap, and George Em Karniadakis. (2020). Physics-informed neural networks for high-speed flows. Computer Methods in Applied Mechanics and Engineering, 360, 112789.

[9] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., & Mahoney, M. W. (2021). Characterizing possible failure modes in physics-informed neural networks. Advances in Neural Information Processing Systems, 34, 26548-26560.

Acknowledgements

This work was partially supported by the National Institutes of Health grants R01EB032870 and R35GM133763, NSF grant #2029282, and the University at Buffalo.