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Fueling Innovation and Discovery The Mathematical Sciences in the 21st Century (2012) / Chapter Skim
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Diffusion Tensor Imaging / A New View of the Brain
Pages 24-28

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From page 24...
... Patients with schizophrenia, Alzheimer's disease, or deterioration due to a stroke, autism, and attention deficit disorder all have detectable changes in diffusion tensor imaging images of their white matter. Even during normal development and learning, the diffusion tensor imaging changes in intriguing ways.
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From page 25...
... allows them to measure the displacement of water molecules over a short period of time -- displacements that are due not to blood flow but to random jitters of the molecules, called Brownian motion. Because Brownian motion underlies the process of diffusion, this technique measures what is called the "apparent diffusion coefficient" in a tiny cubic region of the brain.
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From page 26...
... Thompson, 2011, Diffusion imaging, white matter, and psychopathology, Annual Review of Clinical Psychology 7:63-85, with permission from Annual Reviews, Inc. / Beginning in the early 1990s, researchers noticed a puzzling fact: In the white matter, the apparent diffusion coefficient of a sample seemed to depend on its orientation with respect to the magnetic field.
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From page 27...
... This would require MRI scanners with stronger magnetic fields -- a trend that has continued throughout the past decade. But a less expensive alternative is to develop mathematical methods that would replace ellipsoids with more complicated diffusion surfaces.
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From page 28...
... Thomp son, 2011, Diffusion imaging, white matter, and psychopathology, Annual Review of Clini cal Psychology 7:63-85, with permission from Annual Reviews, Inc. / spectacular detailed images of crossing fibers that would confuse an ordinary diffusion tensor imaging scan.
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Key Terms

  • tensor imaging
  • white matter
  • water molecules
  • fiber integrity
  • apparent diffusion

  • diffusion coefficient
  • fractional anisotropy
  • diffusion imaging
  • brownian motion
  • attention deficit

  • imaging capability
  • standard diffusion
  • diffusion ellipsoids
  • ordinary diffusion
  • skinnier diffusion

  • complicated diffusion
  • diffusion surfaces
  • resolution diffusion
  • called diffusion
  • visualizing white

  • deficit hyperactivity
  • tiny cubic
  • mri called
  • fiber passing
  • mathematical information

  • method called
  • stronger magnetic
  • combines magnetic
  • gray matter
  • imaging changes


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