A minimum assumption approach to MEG sensor array design.


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 meaningfull, 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 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 towards designing better MEG sensor arrays by isolating 
the engineering problem of measuring the neuromagnetic fields out of the bigger
problem of studying the brain function through neuromagnetic measurements.