Computer Vision News - September 2022

50 AI Research paper The incomplete physical model is the Mitchell and Schaeffer (2003) two-variable (v, h) model for cardiac electrophysiology simulation. The variable v represents normalized, dimensionless transmembrane potential while the "gating" variable h controls the repolarization (return to the initial state). This physical model for membrane potential dynamics has been successfully used in patient- specific modelling. It covers general electrophysiology dynamics and is flexible in terms of spatial and temporal steps. Assuming that we can obtain the coordinates of an applied electrical stimulation from the data and using v(t= 0) ≡ 0 and h(t= 0) ≡ 1, we can calculate an approximation of h for any time point t with the help of a simple integration scheme. For the data/deep learning component a ResNet architecture is used because it can accurately reproduce transmembrane potential dynamics. The stability of the ResNet was examined and proved to be best for this specific case. Now, instead of solving the ODE in the previous equation, an integral trajectory-based approach is used calculating an (integral) approximate solution of the problem. To avoid difficulties with high timescale required in this numerical scheme, they use two different integration schemes for the physical component and the final forecast given by the framework using automatic differentiation, as shown in the figure below. The figure specifically shows the predicted dynamics for the diffusion of the transmembrane potential for different timings. Training and data To study how stable the forecast is, the model is trained using a horizon of 6 frames and training 10 epochs until full model convergence. They use ADAM, with initial learning rate at 10 −3 . They also set lambda0 and τ to 1 and 10^3 respectively. All the code is open sourced in the GitHub repository of the project, which is great!