Comparison of numerical-integration-based methods for blood flow estimation in diffuse correlation spectroscopy

Background and Objective: Diffuse correlation spectroscopy (DCS) is an optical blood flow monitoring technology that has been utilized in various biomedical applications. In signal processing of DCS, nonlinear fitting of the experimental data and the theoretical model can be a hindrance in real-time blood flow monitoring. As one of the approaches to resolve the issue, INISg1, the inverse of numerical integration of squared g₁ (a normalized electric field autocorrelation function), that could surpass the state-of-the-art technique at the time in terms of signal processing speed, has been introduced. While it is possible to implement INISg1 using various numerical integration methods, no relevant studies have been performed. Meanwhile, INISg1 was only tested within limited experimental conditions, which cannot guarantee the robustness of INISg1 in various experimental conditions. Thus, this study aims to introduce variants of INISg1 and perform a thorough comparison of the original INISg1 and its variants. Methods: In this study, based on the right Riemann sum (RR) and trapezoid rule (TR) of numerical integration, INISg1_RR and INISg1_TR are suggested. They are thoroughly compared with the original INISg1 using model-based simulations that offer us control of most of the experimental conditions, including integration time, β, and photon count rate. Results: Except for some extreme cases, INISg1 performed more robustly than INISg1_RR and INISg1_TR. However, in extreme conditions, variants of INISg1 performed better than INISg1. With the same condition, the signal processing speed of INISg1 was 1.63 and 1.98 times faster than INISg1_RR and INISg1_TR, respectively. Conclusion: This study shows that INISg1 is robust in most cases and the study can be a guide for researchers using INISg1 and its variants in different types of DCS applications.