New electrical impedance methods for the in situ measurement of the complex permittivity of anisotropic skeletal muscle using multipolar needles

This paper provides a rigorous analysis on the measurement of the permittivity of two-dimensional anisotropic biological tissues such as skeletal muscle using the four-electrode impedance technique. The state-of-the-art technique requires individual electrodes placed at the same depth in contact with the anisotropic material, e.g. using monopolar needles. In this case, the minimum of measurements in different directions needed to estimate the complex permittivity and its anisotropy direction is 3, which translates into 12 monopolar needle insertions (i.e. 3 directions × 4 electrodes in each direction). Here, we extend our previous work and equip the reader with 8 new methods for multipolar needles, where 2 or more electrodes are spaced along the needle’s shaft in contact with the tissue at different depths. Using multipolar needles, the new methods presented reduce the number of needle insertions by a factor of 2 with respect to the available methods. We illustrate the methods with numerical simulations and new experiments on ex vivo ovine skeletal muscle (n = 3). Multi-frequency longitudinal and transverse permittivity data from 30 kHz to 1 MHz is made publicly available in the supplementary material. The methods presented here for multipolar needles bring closer the application of needle electrical impedance to patients with neuromuscular diseases.