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Duan et al. Soft Sci. 2025, 5, 4 https://dx.doi.org/10.20517/ss.2024.46 Page 7 of 15

difference in impedance between the two gradually converging to 0 with increasing frequency, further
validating the usability of the chitosan-acetate gel. As illustrated in Figure 2G, the impedance difference
between the commercial gel and the chitosan-acetate gel is considerable at low frequencies of 10 and
100 Hz. The impedance of the chitosan-acetate gel and commercial conductive gel under dry skin is
2.0886e7 and 1.8449e7 Ω, respectively, with an error rate of 13.21%. At 10 , 10 , and 10 Hz, the error rate
4
3
5
decreased gradually to 0.561%. At higher frequencies, the effect of frequency on the impedance is weakened.
This is due to the fact that as the frequency increases, the signal tends to be distributed on the surface of the
conductor, resulting in a decrease in current density and inductance. At a certain frequency, the decrease in
inductance can be ignored and remains unchanged, resulting in a stabilized change of impedance [45,46] . In
this study, 50-60 kHz was selected as the measurement frequency for the human bladder impedance. At this
frequency range, the chitosan-acetate gel exhibited lower impedance and superior conductivity.
Furthermore, the chitosan-acetate electrode patch demonstrated enhanced conductivity across a range of
frequencies in comparison to the commercial conductive gel electrode patch [Supplementary Figure 4B].

RESULTS AND DISCUSSION
Analysis of measurement and design principles for wireless electronics
The state change of the human bladder tissue exhibits nonlinear behavior, which is dependent on the
dielectric constant and frequency. BIA is a technique that measures the electrical properties of biological
tissues to assess their physiological status. In the context of bladder monitoring, BIA works by applying a
small alternating current through the bladder tissue and measuring the resultant impedance. We employed
multi-frequency BIA as a technique to measure tissue resistance across various biological structures.
Different tissues, such as fat, muscle, and skin, exhibit unique conductive properties; thus, using multi-
frequency signals enables us to quantify each tissue’s contribution to total impedance. Low-frequency
currents primarily traverse the extracellular fluid, allowing us to measure fat thickness and other
characteristics, while high-frequency currents penetrate cell membranes and access intracellular regions. By
analyzing data across multiple frequencies, we can distinguish impedance characteristics among fat,
subcutaneous tissue, and surrounding bladder tissues, allowing for an accurate calculation of bladder
impedance. Changes in impedance are sensitive to variations in bladder volume, as these affect the
[47]
distribution and properties of intracellular and extracellular fluids . This phenomenon is characterized by
non-uniform phenomena such as charge migration during the change .
[48]

As illustrated in Figure 3A, the inner membrane of the bladder is observed to be full of folds when the
bladder is initially empty. With the accumulation of urine, the increased bladder volume gradually unfolds
the bladder membrane, resulting in a smoother inner membrane surface. This unfolding process affects the
dielectric properties of the bladder tissue, which in turn influences the impedance values measured by BIA.
Specifically, as the bladder fills, the capacitance of the intracellular membrane decreases, reflecting changes
in tissue structure. Simultaneously, the intracellular fluid resistance of the bladder cells increases due to
urine accumulation, while the extracellular fluid resistance of the bladder cells remains relatively stable [49,50] .

In light of the aforementioned considerations, the Cole-Cole model was selected to elucidate the intricate
electrical dynamics observed in the bladder . This model has a multitude of applications, including the
[51]
investigation of conductivity, dielectric constant, and resonant frequency in dielectric materials. By applying
the Cole-Cole model to bladder tissue, it is possible to create an equivalent electrical model that accurately
reflects the impedance characteristics of a single bladder cell under different volume conditions. In this
instance, the equivalent model of bioelectrical impedance of a single cell in bladder tissue is depicted in
Figure 3B.