Statistical models for the neurovascular response

The next step in analysis is to estimate the strength of the experimentally determined signal change in the time series of magnetic resonance signal measurements at each voxel in the image. This requires some sort of statistical model for the response. The simplest model, for a blocked periodic design, is a square wave at the same frequency as the experimental input function. This model assumes that a brain region activated specifically by condition A will show an immediate increase in signal intensity, which is sustained throughout the epoch until the onset of condition B. The problem with this model is that the increase in magnetic resonance signal during condition A is due to changes in blood flow and oxygenation, which are delayed by several seconds relative to the onset of condition A. Furthermore, this haemodynamic delay between stimulus onset and measurable response will be variable from one fMRI time series to another. Therefore it is important that the experimental effect should be modelled as an increase in signal intensity that is arbitrarily delayed relative to the onset of the activating stimulus. Various suitable models have been proposed for periodic designs, including a phase-shifted sine wave at the frequency of AB alternation ( Fig 1). Failure to allow for a variable haemodynamic delay may cause underestimation of the experimental effect, and subsequent loss of statistical power to detect activated voxels.

No model is perfect and, whatever model is chosen for the neurovascular response in fMRI, there will probably be some mismatch with the data. For xample, both square-wave and sine-wave models for the response to a periodically designed experiment assume that the amplitude of response is exactly the same for each epoch of the activation condition. In fact, it is not unusual for the amplitude of response to vary from one epoch to another. Mismatch between the data and the model means that the residuals obtained by fitting the model to the data may not be pure noise. In turn, this can lead to voxels being incorrectly identified as activated. Another source of this problem is high-frequency physiological movements due to the cardiorespiratory cycle.

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