Reusable bi-directional 3<i>ω</i> sensor to measure thermal conductivity of 100-<i>μ</i>m thick biological tissues

TLDR

Accurate knowledge of the thermal conductivity of biological tissues is crucial for cryopreservation, thermal ablation, and cryosurgery. The study adapts the 3ω method into a reusable sensor to measure the thermal conductivity of soft biological samples up to two orders of magnitude thinner than conventional methods. Analytical and numerical analyses quantify errors of the boundary‑mismatch approximation in the bi‑directional 3ω geometry, confirm the generalized slope method is exact at low frequencies, bound its error at finite frequencies, and validate the device experimentally to within ±2 % for liquid water and ±5 % for ice. Measurements of mouse liver from −69 °C to +33 °C show results independent of sample thickness from 3 mm to 100 µm and agree with literature for non‑mouse liver within measurement scatter.

Abstract

Accurate knowledge of the thermal conductivity (k) of biological tissues is important for cryopreservation, thermal ablation, and cryosurgery. Here, we adapt the 3ω method—widely used for rigid, inorganic solids—as a reusable sensor to measure k of soft biological samples two orders of magnitude thinner than conventional tissue characterization methods. Analytical and numerical studies quantify the error of the commonly used “boundary mismatch approximation” of the bi-directional 3ω geometry, confirm that the generalized slope method is exact in the low-frequency limit, and bound its error for finite frequencies. The bi-directional 3ω measurement device is validated using control experiments to within ±2% (liquid water, standard deviation) and ±5% (ice). Measurements of mouse liver cover a temperature ranging from −69 °C to +33 °C. The liver results are independent of sample thicknesses from 3 mm down to 100 μm and agree with available literature for non-mouse liver to within the measurement scatter.