Monte Carlo study of noise-induced phase angle errors in low-frequency tetrapolar bioimpedance measurements
Year: 2026
Type: article
Abstract: Phase angles measured at low frequencies with the tetrapolar technique are sometimes scattered or even positive. We used Monte Carlo simulations of lock-in detection to quantify how large phase errors that measurement noise alone can cause. For a signal-to-noise ratio after demodulation (SNR out ) of about 3 or higher, the standard deviation of the phase error was close to 57° divided by SNR out , and 95% of the errors were within about twice this value. At SNR out = 10 the error standard deviation was 6°; at SNR out = 1 it was 64° and 16% of the measurements were wrong by more than 90°. As SNR out decreased towards zero, the phase gradually approached a completely random value. In an illustrative low-frequency tetrapolar measurement, the absolute phase errors were small (standard deviation 0.007° at 1 Hz and 0.04° at 0.1 Hz), but the true tissue phase was even smaller. The error was therefore 1.2 times the true phase at 1 Hz and 37 times at 0.1 Hz, and the measured phase had the wrong sign in 20% and 49% of the measurements, respectively. The sign of a small phase angle is only reliable (wrong in less than 1% of measurements) when the true phase is larger than 2.3 times the error standard deviation.
Authors: Jie Hou, Sisay Mebre Abie, Ørjan G. Martinsen
Institutions: University of Oslo, Oslo University Hospital
Language: English
Subfield: Electrical and Electronic Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $400
OpenAlex ID: W7225230720