Frequency-Dependent Uncertainty Analysis of Bioimpedance in Engineered and Native Muscle

Abstract

Bioimpedance-based characterization of engineered muscle systems is inherently affected by frequency-dependent uncertainty, which limits measurement reliability and interpretability in biomedical and bioinspired applications. A systematic understanding of uncertainty propagation across frequency can therefore benefit the robustness of measurements and enable more consistent comparisons between biological tissues, where an unavoidable source of variability arises from the intrinsic biological nature of the specimens. In this work, a frequency-resolved uncertainty framework was applied to impedance measurement of an engineered muscle system (X-MET) and a native muscle reference, both obtained from a murine model. The method integrated instrumental, repeatability, and biological variability contributions to provide a structured decomposition of total uncertainty in the frequency domain, enabling consistent evaluation of reliability metrics such as relative uncertainty. Importantly, uncertainty analysis was extended beyond electrical measurements to include tissue imaging data, since sample dimensional variability was explicitly quantified and incorporated into the normalized impedance evaluation. This allowed the effect of geometric variability to be consistently propagated within the uncertainty model. Results demonstrated that both engineered and native systems exhibit frequency-dependent behavior, with increasing relative uncertainty at higher frequencies and nonuniform contributions across uncertainty sources. Distinct frequency regimes were identified, characterized by different levels of measurement reliability and signal quality. The engineered system showed reproducible and well-defined uncertainty patterns across the spectrum, despite exhibiting higher relative uncertainty than native muscle. Nevertheless, consistent frequency-dependent trends were preserved, supporting the identification of operational frequency regions despite intrinsic biological variability.