Optimal hemodynamic response model for functional near-infrared spectroscopy

Functional near-infrared spectroscopy (fNIRS) is an emerging non-invasive brain imaging technique and measures brain activities by means of near-infrared light of 650-950 nm wavelengths. The cortical hemodynamic response (HR) differs in attributes at different brain regions and on repetition of trials, even if the experimental paradigm is kept exactly the same. Therefore, an HR model that can estimate such variations in the response is the objective of this research. The canonical hemodynamic response function (cHRF) is modeled by two Gamma functions with six unknown parameters (four of them to model the shape and other two to scale and baseline respectively). The HRF model is supposed to be a linear combination of HRF, baseline, and physiological noises (amplitudes and frequencies of physiological noises are supposed to be unknown). An objective function is developed as a square of the residuals with constraints on 12 free parameters. The formulated problem is solved by using an iterative optimization algorithm to estimate the unknown parameters in the model. Inter-subject variations in HRF and physiological noises have been estimated for better cortical functional maps. The accuracy of the algorithm has been verified using 10 real and 15 simulated data sets. Ten healthy subjects participated in the experiment and their HRF for finger-tapping tasks have been estimated and analyzed. The statistical significance of the estimated activity strength parameters has been verified by employing statistical analysis (i.e., t-value > t critical and p-value < 0.05).