Multi-layer self-calibrated algorithm for transabdominal fetal pulse oximetry: simulation and <i>in vivo</i> validation

Transabdominal fetal pulse oximetry offers a promising approach to non-invasively monitor fetal arterial oxygen saturation (SaO₂), potentially enhancing clinical decision-making and reducing unnecessary interventions during delivery. However, accurate estimation of fetal SaO₂ (denoted as SpO₂ when measured non-invasively) is complicated by the multi-layer maternal-fetal tissue structure, distinct maternal and fetal physiological signals, and inherently low fetal oxygen saturation levels. A multi-layer self-calibrated algorithm was developed by combining the multi-layer modified Beer-Lambert law with an analytical photon partial pathlength model. This approach distinguishes maternal and fetal tissue contributions, enabling more accurate fetal SpO₂ estimation. Validation was performed using Monte Carlo photon simulations of multi-layer tissue geometries, where synthetic optical signals representing fetal cardiac pulsations were generated under two fetal depths and randomly varied maternal and fetal oxygen saturations and optical properties. Further validation was performed using <i>in vivo</i> sheep data, where fetal SpO₂ values derived from transabdominal continuous-wave near-infrared spectroscopy measurements were compared against reference fetal SaO₂ from CO-oximetry. In simulations, the algorithm achieved a mean absolute error (MAE) below 5% and a Pearson correlation coefficient (<i>R</i>) of 0.98 between estimated fetal SpO₂ and ground truth fetal SaO₂ when using optimal input parameters. In the sheep experiment, agreement with reference measurements was maintained (MAE = 10.3%, <i>R</i> = 0.91). However, algorithm performance was highly sensitive to accurate optical properties and tissue layer thicknesses inputs, which may be challenging to obtain in clinical settings. These results demonstrate proof-of-concept feasibility for the multi-layer self-calibrated algorithm in both simulated and <i>in vivo</i> conditions. While further refinement, particularly in optical property estimation and fetal depths in human pregnancies, is necessary, this work provides a foundational framework for the future clinical translation of non-invasive fetal SpO₂ monitoring.