Monte Carlo study of noise-induced phase angle errors in low-frequency tetrapolar bioimpedance measurements
- 1Department of Physics, University of Oslo, Oslo, Norway
- 2Department of Clinical and Biomedical Engineering, Oslo University Hospital, Oslo, Norway
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 (SNRout) of about 3 or higher, the standard deviation of the phase error was close to 57° divided by SNRout, and 95% of the errors were within about twice this value. At SNRout = 10 the error standard deviation was 6°; at SNRout = 1 it was 64° and 16% of the measurements were wrong by more than 90°. As SNRout 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.
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BibTeX
@article{hou2026monte,
title = {{Monte Carlo study of noise-induced phase angle errors in low-frequency tetrapolar bioimpedance measurements}},
author = {Jie Hou and Sisay Mebre Abie and Ørjan G. Martinsen},
journal = {Journal of Electrical Bioimpedance},
year = {2026},
month = oct,
doi = {10.2478/joeb-2026-0017},
url = {https://doi.org/10.2478/joeb-2026-0017},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Monte Carlo study of noise-induced phase angle errors in low-frequency tetrapolar bioimpedance measurements
AU - Jie Hou
AU - Sisay Mebre Abie
AU - Ørjan G. Martinsen
PY - 2026
DA - 2026/10/01
JO - Journal of Electrical Bioimpedance
DO - 10.2478/joeb-2026-0017
UR - https://doi.org/10.2478/joeb-2026-0017
AB - 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 (SNRout) of about 3 or higher, the standard deviation of the phase error was close to 57° divided by SNRout, and 95% of the errors were within about twice this value. At SNRout = 10 the error standard deviation was 6°; at SNRout = 1 it was 64° and 16% of the measurements were wrong by more than 90°. As SNRout 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.
SN - 1891-5469
ER -