Abstract
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.
Highlights
The differential pathlength factor (DPF) in optics is defined as a ratio between the total traveling distance of light and the geometric distance between light source and detector on the tissue surface
This paper presented an estimation method of the differential pathlength factor in functional near-infrared spectroscopy system (fNIRS) systems using dual square-root cubature Kalman filters (DSCKF) and a multidistance optical model
The SCKF was often used in the industry [57, 58], this is the first application in the fNIRS field
Summary
The differential pathlength factor (DPF) in optics is defined as a ratio between the total traveling distance of light and the geometric distance between light source and detector on the tissue surface. Once a wavelength is given, the DPF value is assumed constant regardless of tissue properties when the optode spacing is larger than 25 mm [1]. The DPF depends on the tissue’s composition and micro/macroscopic structures, and underneath blood flow. It varies upon a subject’s head locations and across subjects. The misuse of a wrong DPF value may lead to incorrect oxy- and deoxy-hemoglobin (HbO, HbR) concentrations when using the modified Beer-Lambert law (mBLL). The correct use of DPF values is essential for an accurate disease diagnosis [2]. This paper develops a DPF estimation algorithm for a continuous-wave functional near-infrared spectroscopy system (fNIRS)
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