Abstract: An electrode device for electrophysiological measurement may include an electrode substrate having a surface area. The electrode device may include a central electrode disposed on the electrode substrate around a central portion of the surface area. The electrode device may include a plurality of electrodes disposed on the electrode substrate concentric with the central electrode. The plurality of electrodes may include a first electrode covering a first portion of the surface area of the electrode substrate and a second electrode covering a second portion of the surface area of the electrode substrate. The second portion may be greater than a combined surface area of the first portion and the central portion.

Abstract: A concentric ring electrode (CRE) is provided that can sense characteristics of an electrostatic potential, such as its Laplacian, more accurately than previous systems. The disclosed techniques can include receiving information specifying a geometrical configuration of the CRE. The CRE can include an inner ring and an outer ring. The disclosed techniques can also include estimating a dependence of a functional of the electrostatic potential on a set of potential differences comprising at least a first potential difference corresponding to the inner ring and a second potential difference corresponding to the outer ring. Estimating the dependence can include determining a null space of a matrix associated with a series expansion of the electrostatic potential for the geometrical configuration and determining, based on the null space, a set of coefficients for the dependence.

Abstract: A concentric ring electrode (CRE) is provided that can sense characteristics of an electric potential, such as its Laplacian, more accurately than previous systems. The disclosed system and methods can optimize estimates of the Laplacian based on potentials measured by the CRE's electrodes, and can optimize the geometry of the CRE, in particular the ring electrodes' radii. Given the CRE's geometrical configuration, the system estimates the Laplacian's dependence on the measured potentials by computing a null space of a matrix associated with a series expansion of the potential. The system determines coefficients for the dependence, wherein a first coefficient is between ?10 and 10 times, or between ?6.5 and ?7.5 times, a second coefficient. The system can optimize ranges for the radii by canceling at least one truncation term of the series expansion, estimating a higher-order truncation term as a function of the radii, and minimizing this estimated function.

Abstract: An electrode device for electrophysiological measurement may include an electrode substrate having a surface area. The electrode device may include a central electrode disposed on the electrode substrate around a central portion of the surface area. The electrode device may include a plurality of electrodes disposed on the electrode substrate concentric with the central electrode. The plurality of electrodes may include a first electrode covering a first portion of the surface area of the electrode substrate and a second electrode covering a second portion of the surface area of the electrode substrate. The second portion may be greater than a combined surface area of the first portion and the central portion.