Comparison of diffuse correlation spectroscopy analytical models for cerebral blood flow measurements

Although multi-layer diffuse correlation spectroscopy (DCS) analytical models have been proposed to reduce contamination from superficial signals when probing cerebral blood flow index (CBFi), a comprehensive comparison and clear guidance for model selection remain lacking. This report aims to address this gap.

We aim to systematically compare three DCS analytical models: the semi-infinite, two-layer, and three-layer models, with a focus on their fundamental differences, data processing approaches, and the accuracy and reliability of CBFi estimation. We also provide practical recommendations for selecting the most appropriate model based on specific application scenarios to support researchers in applying DCS effectively.

Experimental data were generated by simulating a four-layer slab head model using the Monte Carlo eXtreme toolkit. We evaluated various fitting strategies for three DCS models: early time lag range (ETLR) fitting with or without treating the coherence factor $\beta$ as a fitting parameter for the semi-infinite model, single-distance (SD) and multi-distance (MD) fitting for the two- and three-layer models. We then compared their performance in terms of CBF sensitivity, recovery of relative CBFi (rCBFi) changes, accuracy of absolute CBFi estimates across different source-to-detector separations ( $\rho =20$ , 25, 30, and 35 mm), ability to separate the crosstalk from extracerebral layers [scalp BFi (SBFi), and skull BFi (BBFi)], sensitivity to parameter assumption errors, and time-to-result, using the respective optimal fitting strategies for each model.

The optimal fitting methods for estimating CBFi are ETLR fitting with a constant $\beta$ for the semi-infinite model, SD fitting with $\beta$ fixed for the two-layer model, and MD fitting for the three-layer model. The two-layer and three-layer models exhibit enhanced CBFi sensitivity, approaching 100%, compared with 36.8% for the semi-infinite model at $\rho =30\mathrm{mm}$ . The semi-infinite model is suitable only for rCBFi recovery at a larger $\rho$ ( $\ge 30\mathrm{mm}$ ). In contrast, the two-layer model is appropriate for both CBFi and rCBFi recovery across all tested $\rho$ values (20, 25, 30, and 35 mm in this work), although its robustness declines as $\rho$ increases. The three-layer model enables simultaneous recovering of CBFi, SBFi, and rCBFi. Among these, the two-layer model is the most effective at mitigating the influence of extracerebral BFi, whereas CBFi estimates from the semi-infinite and three-layer models remain consistently affected by variations in SBFi and BBFi. Errors in assumed model parameters have minimal impact on rCBFi recovery across all models. In terms of computational efficiency, the semi-infinite model requires only 0.38 s of processing 500 data samples, demonstrating potential for real-time rCBFi inference. In comparison, the two-layer and three-layer models require substantially longer processing times of 9502.18 and 35,099.34 s, respectively.

This systematic comparison of three DCS analytical models demonstrates the superior ability of multi-layer models to reduce the influence of superficial tissue layers, thereby enhancing CBFi and rCBFi sensitivity relative to the semi-infinite model. We evaluated various fitting strategies, and beyond recommending the optimal approach for each model, we provide practical guidance for selecting the most appropriate model based on specific objectives, experimental conditions, and data analysis requirements. We believe we offer a valuable reference for researchers in the field, supporting informed model selection and highlighting key considerations for the effective application of DCS analytical models.