Exploring the fractional haemodynamics in fMRI data

Functional Magnetic Resonance Imaging (fMRI) is one of the more popular non-invasive methods to map the brain. A patient is asked to perform a simple task and based on this simple task the brain is scanned for activation. The brain is partitioned in volume elements or voxels. The current induced in the MRI coils by each voxel due to the changes of the blood flow is measured. These signals per voxel are modeled by a Haemodynamic Response Function (HRF). In practice the HRF is either parametrized in such a way that the individual parameters receive physical interpretation, or one desires to keep the model of the HRF as flexible as possible to avoid biased models. The latter implies that the physical interpretation of the parameters is lost. In this paper, we propose to use fractional models or fractional haemodynamics. We show that these models allow physical interpretation of the parameters in the classical way with the additional advantage of retaining maximal flexibility of the model. This allows better fitting the data to the model without the need to increase the model complexity.