Multi-Channel-Based Differential Pathlength Factor Estimation for Continuous-Wave fNIRS

Functional near-infrared spectroscopy (fNIRS) in brain imaging needs to be robust to subject-wise variability. The use of a fixed differential pathlength factor (DPF) per wavelength for the entire brain will degrade the accuracy of hemodynamic responses. Since the tissue composition varies within the brain, correct DPF values should be used for various emitter-detector distances and brain regions. In this article, a DPF estimation method combining a state-space model of the modified Beer-Lambert law (mBLL), a parameter model for estimating the reduced scattering coefficients, and dual square-root cubature Kalman filters (SCKFs) is proposed. To validate the proposed method, known light intensities (six channels, two wavelengths) and reference DPFs are generated using NIRFAST (a Matlab toolbox) using a presumed paradigm, known tissue properties, a Balloon model, and a finite element head model consisting of 58,818 mesh elements. Then, the DPF values are estimated using a Jacobian matrix from the head model and the mBLL. The results show that the estimated concentration changes correlate well with the reference data. Also, the estimated DPFs showed relative errors less than 1.33% maximum and 0.75% on average. A one-tailed $t$ -test revealed that the estimated DPFs matched the reference DPFs with more than 99.9% confidence. The developed method can efficiently access the actual DPFs even if emitter-detector distances vary significantly and the tissue properties are not uniform. With the developed state-space models for dual SCKFs, real-time estimation of the DPFs from one experiment to another has become plausible.