Causal Multiscale Modeling of Ocular FLASH Electroretinography: Model Development, Experimental Fitting, and Spin-Glass--Percolation Predictions

Abstract

\textbf{Purpose:} To develop a causal multiscale model of retinal electroretinography (ERG) after ocular ultrahigh-dose-rate (FLASH) and conventional-dose-rate (CONV) irradiation, evaluate the framework against published ocular ERG data, and derive prospective dose-response predictions for future validation. \textbf{Methods:} The retina was coarse-grained into $N=200$ functional modules. Local rate equations were formulated as Hodgkin--Huxley-inspired conductance-balance/RC reductions of retinal ion-channel and synaptic pathways. Radiation generated an injury field that altered phototransduction, a-wave and b-wave dynamics and, in the network extension, inter-module coupling and bond survival. A reduced amplitude benchmark and nested M0/M1/M2 causal models were evaluated. \textbf{Results:} The reduced benchmark achieved $R^2=0.9721$ and RMSE $=11.94~\mu$V. M0, M1, and M2 yielded $R^2=0.8546$, 0.8559, and 0.8560, respectively, indicating limited independent identifiability of the network terms from amplitude data alone. Under an exploratory 50\% retained-gain criterion, the reduced benchmark predicted a-wave preservation thresholds of 28.6 Gy for FLASH and 23.7 Gy for CONV, and b-wave thresholds of 29.2 Gy and 24.1 Gy, respectively, corresponding to a model-based functional dose-modifying factor (DMF) of 1.21. \textbf{Conclusion:} The ERG amplitude data support the causal radiation-injury-to-ERG framework, while additional observables will be needed to distinguish the predicted collective-network contributions. The model also provides quantitative dose targets for prospective studies of the FLASH retinal-preservation window and a framework for testing how local retinal injury may propagate into collective dysfunction.