Mojtaba F. Fathi, Roshan M. D'souza Seizure Onset and Source Detection Through ECoG Signals Using Dynamic Mode Decomposition Mojtaba F. Fathi, Roshan M. D'souza

Introduction Dynamic Mode Decomposition (DMD) A data-based method for extracting dynamic information from the data No need to having any knowledge about the underlying model A general-purpose tool for studying the dynamics of various types of nonlinear systems Dynamic Mode Decomposition with Control (DMDc) is an extension to DMD DMDc Accounts for complex dynamic systems with input We are applying DMD to ECoG recordings of a patient who is suffering seizures A seizure is a sudden surge of electrical activity in the brain

Method Get ECoG data with seizure as a matrix Apply Short-Term Fourier Transform (STFT) to each channel (each row) Stack the frequency spectrum matrices of all channels as a single matrix Construct the matrices Xk and Xk+1 Find The optimal Singular Value Hard Threshold (SVHT) of the matrix Xk to get the minimum number of dynamic modes Define the fake input U

Method (continued) Apply DMDc to find the two matrices 𝑨 and 𝑩 corresponding to the linear model 𝑿 𝑘+1 = 𝑨𝑿 𝑘 +𝑩𝑼 Define 𝑼 ′ as 𝑼 ′ = 𝑩 † 𝑿 𝑘+1 − 𝑨𝑿 𝑘 Use a moving average to smooth out short-term fluctuations in 𝑼 ′ . Define the smoothed matrix as 𝑼 ∗ . Reconstruct the input matrix 𝑼 as 𝑢 𝑖 = 0 if 𝑢 𝑖 ∗ <0.5 1if 𝑢 𝑖 ∗ ≥0.5

Results The data from two separate ECoG recordings were used for analysis There was a total of 80 electrodes sampled at 1 kHz. The size of the matrices 𝑿 𝑘 and 𝑿 𝑘+1 was 40,080 by 1,886. The optimal number of modes was found to be 644 out of 40,080 (1.6%). The fake input matrix 𝑼 was defined by eyeballing. The length of the moving average window was 4. The reconstructed input matrix 𝑼 had a 98% match with the matrix 𝑼.

Plot of ECoG recording with seizure Results (continued) Plot of ECoG recording with seizure

Plot of the reconstructed input Results (continued) Plot of the reconstructed input

Conclusion and Future Work The preliminary results show DMDc method could detect the seizure with 98% accuracy. Using a fraction of the dynamic modes is enough for detecting seizure onsets Using more datasets for DMDc analysis Evaluating the extracted linear model with a new test dataset Increasing the number of possible values of the fake input Combining DMDc with Granger causality Using a broader range of transfer functions Using kernel-based methods Using compressed sensing to lower the number of channels