Reusable bi-directional 3ω sensor to measure thermal conductivity of 100-μm thick biological tissues

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.

A micro-thermal sensor for focal therapy applications

“…idealized theoretical calculation 17,23 with the experiment shows that the experimental measurements are consistent with the model trends, and suggest that with proper calibration can be used to measure thickness.…”

“…1(b,d). The exact analytical solution to this conduction problem is well known 12,17,35 . Thermal waves propagate and decay radially away from the heater and PD can be calculated using Eqn (1) …”

“…Figure 1 shows the basic concept of the supported 3ω method 17 . A periodic electrical current (~40 mA rms) of angular frequency 'ω ' is passed through the heater, I = I 0 sin ω t, between the leads I + and I-.…”

“…To avoid dehydration and/or evaporation of water content in the tissue, the sample was encapsulated on the sides and at the top by agar gel (0.5% by weight agarose powder dissolved in water at 65 °C and solidified overnight in a 4 °C refrigerator). The sample-agar gel complex is then covered by a plastic wrap to isolate the sample from evaporative cooling and sublimation which interfere with a consistent and correct measurement 17 . Importantly, in this system, water evaporation or ice sublimation from the tissue was negligible (weight change < 5%) during the measurement in Fig.…”

“…This technique has been commonly used to measure thermal conductivity of inorganic materials [13][14][15][16] . Recently, it has been modified to measure 'k' of biological tissues 17 and even cells 18 . The current article presents proof of principle data to show the ability of the sensor to give thermal conductivity for treatment planning and then extends the sensor use for other measurements relevant for monitoring.…”