Towards accurate transcutaneous CO₂ sensing: A behavioral model using time-correlated single photon counting

We present a behavioral model for estimating the lifetime of rapid fluorescence signals, intended for use in a lifetime-based transcutaneous CO₂ sensing system, an important tool for assessing ventilation effectiveness, implemented with time-correlated single photon counting (TCSPC) and silicon photomultipliers (SiPMs). The model reproduces the complete optical and electronic signal chain using measured and specified component parameters, while incorporating nonidealities such as dark counts, afterpulsing, crosstalk, and excitation leakage. Using an optimized post-processing pipeline, the system successfully recovers fluorescence lifetimes with 86%-93% accuracy at ambient air (∼0.3 mmHg CO₂, approximated as 0 mmHg in the model), and resolves lifetimes as short as 3.5 ns. Performance decreases below this lifetime threshold corresponding to higher CO₂ levels due to increased noise and reduced usable decay slope; however, a range-optimized algorithm is expected to mitigate these limitations. Overall, the findings highlight the model's potential to guide the development of enhanced CO₂ monitoring devices for both clinical and ambulatory applications.