Multiresolution voxel decomposition of complex-valued BOLD signals reveals phasor turbulence

Zikuan Chen, Zeyuan Chen, Vince Calhoun

Research output: Chapter in Book/Report/Conference proceedingConference contribution


High spatial resolution functional MRI (fMRI) technology continues to enable smaller voxel sizes, providing details about neuronal activity in terms of spatial localization and specificity. The BOLD contrast mechanism can be examined by numerical simulation. By representing a complex timeseries with a dynamic phasor in a polar coordinate system, a complex-valued BOLD signal manifests as an inward spiral: the radial distance represents the signal amplitude and the polar angle the signal phase angle. For normal fMRI settings (millimeter resolution, 3T main field, and 30ms relaxation time), the BOLD phasors usually evolve in a form of inward spiraling. Under some extreme parameter settings (high resolution, high field, or long relaxation time), the phasors may become turbulent (i.e. exhibit disordered spiraling). In this paper, we will report on a BOLD phasor turbulence phenomenon resulting from coarse-to-fine multiresolution voxel decomposition. In our implementation, a vasculature-laden voxel (320×320×320 micron3) is decomposed into a sequence of subvoxels (160×160 ×160, 80×80×80, 40×40×40, 20×20×20 micron 3). Our simulations reveal the following phenomena: 1) Ultrahigh spatial resolution (several tens of microns, e.g. 20micron) BOLD fMRI may cause signal turbulence, primarily occurring at vessel boundaries; 2) The intravascular signal is prone to turbulence but its contribution to the voxel signal is greatly suppressed by the blood volume fraction; 3) There is no signal turbulence under small angle condition; 4) For millimeter-resolution fMRI with small relaxation time (< 30ms), signal turbulence is unlikely to occur. We explain the high-resolution BOLD signal turbulence from the perspective of the emergence of BOLD field irregularity.

Original languageEnglish (US)
Title of host publicationMedical Imaging 2011
Subtitle of host publicationPhysics of Medical Imaging
StatePublished - May 13 2011
Externally publishedYes
EventMedical Imaging 2011: Physics of Medical Imaging - Lake Buena Vista, FL, United States
Duration: Feb 13 2011Feb 17 2011

Publication series

NameProgress in Biomedical Optics and Imaging - Proceedings of SPIE
ISSN (Print)1605-7422


OtherMedical Imaging 2011: Physics of Medical Imaging
Country/TerritoryUnited States
CityLake Buena Vista, FL


  • BOLD simulation
  • Computational fMRI
  • field inhomogeneity
  • histogram
  • multiresolution BOLD signal
  • phasor turbulence
  • small angle approximation

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Biomaterials
  • Atomic and Molecular Physics, and Optics
  • Radiology Nuclear Medicine and imaging


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