Nonlinear voxel-based modelling of the haemodynamic response in fMRI

John Kornak*, Bruce Dunham, Deborah A. Hall, Mark P. Haggard

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


A common assumption for data analysis in functional magnetic resonance imaging is that the response signal can be modelled as the convolution of a haemodynamic response (HDR) kernel with a stimulus reference function. Early approaches modelled spatially constant HDR kernels, but more recently spatially varying models have been proposed. However, convolution limits the flexibility of these models and their ability to capture spatial variation. Here, a range of (nonlinear) parametric curves are fitted by least squares minimisation directly to individual voxel HDRs (i.e., without using convolution). A 'constrained gamma curve' is proposed as an efficient form for fitting the HDR at each individual voxel. This curve allows for spatial variation in the delay of the HDR, but places a global constraint on the temporal spread. The approach of directly fitting individual parameters of HDR shape is demonstrated to lead to an improved fit of response estimates.

Original languageEnglish
Pages (from-to)237-253
Number of pages17
JournalJournal of Applied Statistics
Issue number3
Publication statusPublished - Mar 2009


  • Constrained gamma curve
  • Functional magnetic resonance imaging
  • Haemodynamic response function
  • Least squares estimation
  • Nonlinear curve fitting
  • Polynomial curve fitting

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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