Lorentzian Parameterization of MEG Power Spectra in Alzheimer’s Disease

Overview

This repository implements and motivates a Lorentzian parameterization of MEG power spectra designed to study neurophysiological alterations in Alzheimer’s disease (AD). It's ambition is not to give a full framework, but more as a proposition to study. It is partially derived from FOOOF/Specparam, it is focused on the Lorentzian parameterization of the power spectrum, it has been developed for the following data: https://osf.io/t753c/.

Why a Lorentzian model?

A Lorentzian spectrum emerges naturally from first order filters.

$$ \text{logPSD}(f) = A - \text{log}(1+(\frac{f}{f_c})^{-B}) $$

where:

• $A$ reflects the gain
• $f_c$ is a cutoff frequency linked to the synaptic time constant
• $B$ controls the approximate power-law decay at high frequencies ($f >> f_c$)

Implementation details

1. Fit a first Lorentzian to 4–45 Hz, then correct for chosen standard deviation of the residuals and fit a second Lorentzian
2. Fit peaks by taking the highest point in the residuals and iteratively fitting a Gaussian model until a stopping threshold (as in FOOOF/Specparam)
3. Fit a power-law below 4 Hz in log–log space