Brain functional BOLD perturbation modelling for forward fMRI and inverse mapping

PLoS One. 2018 Jan 19;13(1):e0191266. doi: 10.1371/journal.pone.0191266. eCollection 2018.


Purpose: To computationally separate dynamic brain functional BOLD responses from static background in a brain functional activity for forward fMRI signal analysis and inverse mapping.

Methods: A brain functional activity is represented in terms of magnetic source by a perturbation model: χ = χ0 +δχ, with δχ for BOLD magnetic perturbations and χ0 for background. A brain fMRI experiment produces a timeseries of complex-valued images (T2* images), whereby we extract the BOLD phase signals (denoted by δP) by a complex division. By solving an inverse problem, we reconstruct the BOLD δχ dataset from the δP dataset, and the brain χ distribution from a (unwrapped) T2* phase image. Given a 4D dataset of task BOLD fMRI, we implement brain functional mapping by temporal correlation analysis.

Results: Through a high-field (7T) and high-resolution (0.5mm in plane) task fMRI experiment, we demonstrated in detail the BOLD perturbation model for fMRI phase signal separation (P + δP) and reconstructing intrinsic brain magnetic source (χ and δχ). We also provided to a low-field (3T) and low-resolution (2mm) task fMRI experiment in support of single-subject fMRI study. Our experiments show that the δχ-depicted functional map reveals bidirectional BOLD χ perturbations during the task performance.

Conclusions: The BOLD perturbation model allows us to separate fMRI phase signal (by complex division) and to perform inverse mapping for pure BOLD δχ reconstruction for intrinsic functional χ mapping. The full brain χ reconstruction (from unwrapped fMRI phase) provides a new brain tissue image that allows to scrutinize the brain tissue idiosyncrasy for the pure BOLD δχ response through an automatic function/structure co-localization.

Publication types

  • Research Support, N.I.H., Extramural

MeSH terms

  • Adult
  • Brain / anatomy & histology
  • Brain / diagnostic imaging
  • Brain / physiology
  • Brain Mapping / statistics & numerical data*
  • Computer Simulation
  • Humans
  • Image Interpretation, Computer-Assisted
  • Image Processing, Computer-Assisted
  • Imaging, Three-Dimensional
  • Magnetic Resonance Imaging / statistics & numerical data*
  • Models, Neurological*
  • Oxygen / blood
  • Signal-To-Noise Ratio
  • Task Performance and Analysis


  • Oxygen