Genetic and least squares algorithms for estimating spectral EIS parameters of prostatic tissues

Abstract

We employed electrical impedance spectroscopy (EIS) to evaluate the electrical properties of prostatic tissues. We collected freshly excised prostates from 23 men immediately following radical prostatectomy. The prostates were sectioned into 3 mm slices and electrical property measurements of complex resistivity were recorded from each of the slices using an impedance probe over the frequency range of 100 Hz to 100 kHz. The area probed was marked so that following tissue fixation and slide preparation, histological assessment could be correlated directly with the recorded EIS spectra. Prostate cancer (CaP), benign prostatic hyperplasia (BPH), non-hyperplastic glandular tissue and stroma were the primary prostatic tissue types probed. Genetic and least squares parameter estimation algorithms were implemented for fitting a Cole-type resistivity model to the measured data. The four multi-frequency-based spectral parameters defining the recorded spectrum (ρ∞, Δρ, fc and α) were determined using these algorithms and statistically analyzed with respect to the tissue type. Both algorithms fit the measured data well, with the least squares algorithm having a better average goodness of fit (95.2 mΩ m versus 109.8 mΩ m) and a faster execution time (80.9 ms versus 13 637 ms) than the genetic algorithm. The mean parameters, from all tissue samples, estimated using the genetic algorithm ranged from 4.44 to 5.55 Ω m, 2.42 to 7.14 Ω m, 3.26 to 6.07 kHz and 0.565 to 0.654 for ρ∞, Δρ, fc and α, respectively. These same parameters estimated using the least squares algorithm ranged from 4.58 to 5.79 Ω m, 2.18 to 6.98 Ω m, 2.97 to 5.06 kHz and 0.621 to 0.742 for ρ∞, Δρ, fc and α, respectively. The ranges of these parameters were similar to those reported in the literature. Further, significant differences (p < 0.01) were observed between CaP and BPH for the spectral parameters Δρ and fc; this is especially important since current prostate cancer screening methods do not reliably differentiate between these two tissue types.