Determination of the parameters in the designed hemodynamic response function using Nelder-Mead algorithm

In this paper, we have investigated the use of the Nelder-Mead algorithm in determining the parameters of a designed hemodynamic response function (dHRF) instead of using fixed parameters for functional near-infrared spectroscopy (fNIRS). The hemodynamic response (HR) is supposed to be a linear combination of the baseline, the dHRF, and physiological noises (Mayer, cardiac, and respiration). The linear combination of three gamma functions is used to model the dHRF including the initial dip, the conventional HR, and the undershoot afterward. In this formulation, fifteen parameters (9 for dHRF and 6 for physiological noises) are unknown. An objective function is designed and solved using the iterative optimization Nelder-Mead algorithm to determine the unknown parameters of dHRF and physiological noises. The performance of the algorithm is tested using simulated and experimental datasets. The fNIRS experimental data were acquired from five healthy subjects during right-hand thumb finger flexion/extension tasks from the left motor cortex. The results demonstrate that inter-subject differences existed in the dHRF parameters. Therefore, it will be worthwhile to use subject-dependent dHRF parameters for a better estimation of the cortical activation using fNIRS.