Optimizing Retinal Prosthetic Stimuli with Conditional Invertible Neural Networks

TL;DR

This work addresses the challenge of limited information transfer in retinal prostheses by optimizing electrical stimuli to evoke percepts more faithfully. It introduces conditional invertible neural networks (cINN) and an INN-MMD variant to learn an inverse mapping from percepts to stimuli, guided by a physiologically validated Axon Map Model as the forward simulator, and leverages exact likelihoods through normalizing flows with p(x) = π(\mathbf{z}) |det J_h(\mathbf{x})|. The approach uses the NLL loss on invertible architectures and a maximum mean discrepancy (MMD) regularization to handle non-bijective mappings, with conditioning to steer stimulus generation toward target percepts. Empirical results on a 9×9 electrode array with MNIST-based targets show that cINN-based stimulation yields superior reconstruction quality across multiple metrics (MAE, MSE, SSIM, PSNR, ACC), especially at higher percept resolutions, indicating strong potential for improving patient-specific retinal prostheses.

Abstract

Implantable retinal prostheses offer a promising solution to restore partial vision by circumventing damaged photoreceptor cells in the retina and directly stimulating the remaining functional retinal cells. However, the information transmission between the camera and retinal cells is often limited by the low resolution of the electrode array and the lack of specificity for different ganglion cell types, resulting in suboptimal stimulations. In this work, we propose to utilize normalizing flow-based conditional invertible neural networks to optimize retinal implant stimulation in an unsupervised manner. The invertibility of these networks allows us to use them as a surrogate for the computational model of the visual system, while also encoding input camera signals into optimized electrical stimuli on the electrode array. Compared to other methods, such as trivial downsampling, linear models, and feed-forward convolutional neural networks, the flow-based invertible neural network and its conditional extension yield better visual reconstruction qualities w.r.t. various metrics using a physiologically validated simulation tool.

Figures (7)

• Figure 1: (a) Anatomy of the retina with an electrical epiretinal implant. Modified based on Retinal Implant by Mbuerki under CC BY-SA 3.0 wiki:retinal. (b) Electrode activation with the axon map model (top, by Beyeler et al.beyeler2019model under CC BY 4.0) and a retinal implant with a $9\times9$ electrode grid on the axon map (bottom, generated with pulse2perceptmichael_beyeler-proc-scipy-2017 ).
• Figure 2: A schematic overview of the stimulation optimization for retinal prostheses. The visual signals are converted directly into electrical signals on the electrodes through an optimization process, constrained by a simulation model of the visual pathway.
• Figure 3: Training and evaluation pipelines for the stimulation optimization with (a) invertible neural networks with maximum mean discrepancy loss (INN-MMD) ardizzone2018analyzingardizzone2019guided and (b) conditional invertible neural networks (cINN) ardizzone2021conditional.
• Figure 4: We follow ardizzone2019guidedardizzone2021conditional to design the INN and cINN architectures with Glow coupling layers kingma2018glow. The conditional input $\mathbf{c}$ in both forward and inverse Glow coupling blocks is the only difference between the INN and the cINN approach.
• Figure 5: MSE loss values of the INN-MMD training ardizzone2018analyzing (a) for percept-to-stimulus being the forward process and (b) for stimulus-to-percept being the forward process. We observe that the MSE loss values of inverse processes are always larger than the supervised forward processes, which implies that the invertibility using a supervised INN is not guaranteed. We report the results of the setup (a) in \ref{['tab:1']}, as the optimized stimulus is desired.