Bayesian Analysis of Fiber Impedance Measurements

The resistivities of microscale components of excitable tissue include the longitudinal intracellular and interstitial resistivities and the membrane resistivity. Measurements of these tissue micro impedances have rarely been obtained, mainly because of the lack of a satisfactory measurement system. Here we evaluate a possible strategy for obtaining such measurements, and begin with a simulation. In the model, a one-dimensional fiber was stimulated with closely space interstitial electrodes at four frequencies, and the voltage differences that occurred in response were recorded. We then considered the inverse question, asking if tissue micro impedances could be found from the voltage measurements plus additive noise. In so doing, we used a Bayesian interpretation of the measured data to find the probability that each of the longitudinal and transmembrane resistivity sets was their origin. The Bayesian procedure proved better suited for interpreting the measurements than was conventional least-squares analysis. It was better because all known data, including realistic noise specifications and a priori probabilities, were included in the defined procedure. The results show that the micro impedances were found satisfactorily using realistic parameters and noise levels. The overall quantitative evaluation is promising for future experimental measurements.