Numerical Investigation of a Skin-Interfaced Thermal Sensor for Joint Estimation of Tissue Thermal Conductivity and Blood Velocity

Skin-interfaced thermal sensors offer a promising, portable, and cost-effective alternative for continuous and noninvasive measurements of skin condition and blood flow. Skin condition, especially skin hydration, is reflected by the tissue thermal conductivity. Blood flow is characterized by the average flow velocity through blood vessels in skin. However, the measurement accuracy of tissue thermal conductivity and blood velocity is hindered by the coupled heat conduction and convection in the tissue containing blood vessels. To overcome this bottleneck for precise measurements of tissue thermal conductivity and blood velocity simultaneously, we design a skin-interfaced thermal sensor consisting of a resistive heater and three thermistors. The resistive heater with a diameter of 4 mm consumes a low power of 0.05 W. The three miniature thermistors measure the steady-state temperatures on skin at the middle location of the heater center, upstream flow location, and downstream flow location. Using finite element analysis (FEA) of heat transfer in vascular skin, we optimize the three-thermistor layout, placing the upstream and downstream thermistors 6.0 mm and 2.7 mm from the heater center, respectively. FEA results reveal that the middle-thermistor temperature is predominantly sensitive to tissue thermal conductivity with relatively low flow interference, whereas the temperature difference between upstream and downstream thermistors maintains high sensitivity to blood velocity, and is less affected by tissue thermal conductivity. With the FEA results, we implement a polynomial machine learning model and a physics-informed thermal-resistance reduced-order model to analyze the thermal sensor temperature measurements and jointly predict both quantities. The relative prediction errors are typically below 4% for thermal conductivity and 10% for blood velocity using the machine learning model, and below 1% and 8% using the reduced-order model. This work provides a framework for the development of skin-interfaced thermal sensors capable of intelligent and noninvasive skin and vascular assessment.