A Minimum Assumption Approach to MEG Sensor Array Design

TL;DR

This paper formulates MEG sensor array design as an engineering problem focused on accurately measuring neuronal magnetic fields, introducing a noise-based figure-of-merit and optimization approach for improved array configurations.

Contribution

It introduces a mathematically rigorous, noise-based figure-of-merit for MEG sensor array design and demonstrates its use in optimizing array configurations with desirable properties.

Findings

Derived a new figure-of-merit for sensor array quality

Optimized array configurations show high information capacity

Proposed a practical optimization method for array design

Abstract

Objective: Our objective is to formulate the problem of the Magnetoencephalographic (MEG) sensor array design as a well-posed engineering problem of accurately measuring the neuronal magnetic fields. This is in contrast to the traditional approach that formulates the sensor array design problem in terms of neurobiological interpretability the sensor array measurements. Approach: We use the Vector Spherical Harmonics (VSH) formalism to define a figure-of-merit for an MEG sensor array. We start with an observation that, under certain reasonable assumptions, any array of $m$ perfectly noiseless sensors will attain exactly the same performance, regardless of the sensors' locations and orientations (with the exception of a negligible set of singularly bad sensor configurations). We proceed to the conclusion that under the aforementioned assumptions, the only difference between different array configurations is the effect of (sensor) noise on their performance. We then propose a figure-of-merit that quantifies, with a single number, how much the sensor array in question amplifies the sensor noise. Main results: We derive a formula for intuitively meaningful, yet mathematically rigorous figure-of-merit that summarizes how desirable a particular sensor array design is. We demonstrate that this figure-of-merit is well-behaved enough to be used as a cost function for a general-purpose nonlinear optimization methods such as simulated annealing. We also show that sensor array configurations obtained by such optimizations exhibit properties that are typically expected of high-quality MEG sensor arrays, e.g. high channel information capacity. Significance: Our work paves the way toward designing better MEG sensor arrays by isolating the engineering problem of measuring the neuromagnetic fields out of the bigger problem of studying brain function through neuromagnetic measurements.