Calculation of Tissue Oxygenation via an Inverse Boundary Problem for Transcutaneous Oxygenation Wearable Applications

In this article, we present a toolset to fully leverage a previously developed transcutaneous oxygenation monitor (TCOM) wearable technology to accurately measure skin oxygenation values. We describe numerical models and experimental characterization techniques that allow for the extraction of precise tissue oxygenation measurements. The numerical model is based on an inverse boundary problem of the parabolic equation with Dirichlet boundary conditions. To validate this model and characterize the diffusion of oxygen through the oxygen sensing materials, we designed a series of control/calibration experiments modeled after the device’s clinical application using oxygenation values in the physiological range expected for healthy tissue. Our results demonstrate that it is possible to obtain accurate tissue pO₂ measurements without the need for long equilibration times with a small wearable device.