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SPM-Haemodynamic Response Function

Generally speaking, cognitive processing is associated with increases in neuronal firing rates. The increased neural activity lead to increased metabolic requirements for the neurons. The onset of neural activity leads to a systematic series of physiological changes in the local network of blood vessels that include changes in the cerebral blood volume per unit of brain tissue (CBV), changes in the rate of cerebral blood flow (CBF), and changes in the concentration of oxyhaemoglobin and deoxyhaemoglobin.

There are different fMRI techniques that can pick up a functional signal corresponding to changes in each of the previously mentioned components of the haemodynamic response. The most common functional imaging signal is the Blood Oxygenation Level Dependent signal (BOLD), which primarily corresponds to the concentration of deoxyhaemoglobin. In simple terms, the magnetic resonance signal comes from exciting hydrogen nuclei with a radiofrequency pulse, and detecting the radio waves emitted as the nuclei return to a lower-energy configuration. Deoxyhaemoglobin has different magnetic properties than oxyhaemoglobin– it is paramagnetic, which means that it will make the local magnetic field over a microscopic domain inhomogenous. This has the effect of dephasing the signal emitted by the nuclei in this domain, causing destructive interference in the observed MR signal. Over a macroscopic domain (i.e., one functional voxel) greater amounts of deoxyhaemoglobin lead to less signal. The functional BOLD signal is seen as an increase in the MR signal that corresponding to a decrease in the concentration of deoxyhaemoglobin. The decrease of deoxy-Hb is seen because the increase in CBF following neural activity more than accounts for the effect of increased uptake of oxygen.


For the purposes of estimating the BOLD signal in an experimental paradigm, SPM makes use of a canonical haemodynamic response function (HRF). This function is assumed to be the response of the system (as reflected by the MR signal) to a brief, intense period of neural stimulation. The SPM HRF is shown above, and exhibits a rise peaking around 6 sec, followed by an undershoot that persists for a considerable period. The code for this graph is below.

>> RT = 1; hrf = spm_hrf(RT); plot(0:RT:32, hrf);

In this graph, the y-axis is in arbitrary units. A common way to plot the impulse response is in units of percent signal change from a baseline condition. A very robust stimulus (such as a contrast taken between a flickering visual stimulus and no visual stimulus) may produce changes on the order of 2%-4% in the BOLD signal. The change observed in contrasts involving higher-level cognitive processes is typically much smaller.


SPM version 8b statistical parametric mapping MATLAB

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The SPM approach in brief

The Statistical Parametric Mapping approach is voxel based:

  • Images are realigned, spatially normalised into a standard space, and smoothed.
  • Parametric statistical models are assumed at each voxel, using the General Linear Model GLM to describe the data in terms of experimental and confounding effects, and residual variability.
  • For fMRI the GLM is used in combination with a temporal convolution model.
  • Classical statistical inference is used to test hypotheses that are expressed in terms of GLM parameters. This uses an image whose voxel values are statistics, a Statistic Image, or Statistical Parametric Map (SPM{t}, SPM{Z}, SPM{F})
  • For such classical inferences, the multiple comparisons problem is addressed using continuous random field theory RFT, assuming the statistic image to be a good lattice representation of an underlying continuous stationary random field. This results in inference based on corrected p-values.
  • Bayesian inference can be used in place of classical inference resulting in Posterior Probability Maps PPMs .
  • For fMRI, analyses of effective connectivity can be implemented using Dynamic Causal Modelling DCM.


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janvier 2021