1. 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

2. 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

3. 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

4. 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

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.

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

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

8. 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