# Apparent Diffusion

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### Robert V. Mulkern – One of the best experts on this subject based on the ideXlab platform.

• ##### normal brain and brain tumor multicomponent ApparentDiffusion coefficient line scan imaging
Co-Authors: Stephan E. Maier, Péter Bogner, Gábor Bajzik, Hatsuho Mamata, Yoshiaki Mamata, Imre Repa, Ferenc A. Jolesz, Robert V. Mulkern

Abstract:

Magnetic resonance line scan Diffusion imaging of the brain, with Diffusion weighting between 5 and 5,000 sec/mm2, was performed in healthy subjects and patients with a 1.5-T machine. For each voxel, biexponential signal decay fits produced two Apparent Diffusion constants and respective signal amplitudes. Images based on these parameters show potential for use in the differentiation of gray and white matter, edema, and tumor.

• ##### Normal Brain and Brain Tumor: Multicomponent ApparentDiffusion
, 2001
Co-Authors: Stephan E. Maier, Péter Bogner, Gábor Bajzik, Hatsuho Mamata, Yoshiaki Mamata, Imre Repa, Ferenc A. Jolesz, Robert V. Mulkern

Abstract:

Magnetic resonance line scan Diffusion imaging of the brain, with Diffusion weighting between 5 and 5,000 sec/mm 2 , was performed in healthy subjects and patients with a 1.5-T machine. For each voxel, biexponential signal decay fits produced two Apparent Diffusion constants and respective signal amplitudes. Images based on these parameters show potential for use in the differentiation of gray and white matter, edema, and tumor.

• ##### Multi-component ApparentDiffusion coefficients in human brain.
NMR in biomedicine, 1999
Co-Authors: Robert V. Mulkern, Hakon Gudbjartsson, Carl-fredrik Westin, Hale Pinar Zengingonul, Werner Gartner, Charles R.g. Guttmann, Richard L. Robertson, Walid E. Kyriakos, Richard B. Schwartz, David Holtzman

Abstract:

The signal decay with increasing b-factor at fixed echo time from brain tissue in vivo has been measured using a line scan Stejskal–Tanner spin echo Diffusion approach in eight healthy adult volunteers. The use of a 175 ms echo time and maximum gradient strengths of 10 mT/m allowed 64 b-factors to be sampled, ranging from 5 to 6000 s/mm2, a maximum some three times larger than that typically used for Diffusion imaging. The signal decay with b-factor over this extended range showed a decidedly non-exponential behavior well-suited to biexponential modeling. Statistical analyses of the fitted biexponential parameters from over 125 brain voxels (15 × 15 × 1 mm3 volume) per volunteer yielded a mean volume fraction of 0.74 which decayed with a typical Apparent Diffusion coefficient around 1.4 µm2/ms. The remaining fraction had an Apparent Diffusion coefficient of approximately 0.25 µm2/ms. Simple models which might explain the non-exponential behavior, such as intra- and extracellular water compartmentation with slow exchange, appear inadequate for a complete description. For typical Diffusion imaging with b-factors below 2000 s/mm2, the standard model of monoexponential signal decay with b-factor, Apparent Diffusion coefficient values around 0.7 µm2/ms, and a sensitivity to Diffusion gradient direction may appear appropriate. Over a more extended but readily accessible b-factor range, however, the complexity of brain signal decay with b-factor increases, offering a greater parametrization of the water Diffusion process for tissue characterization. Copyright © 1999 John Wiley & Sons, Ltd.

### Rachid Deriche – One of the best experts on this subject based on the ideXlab platform.

• ##### ApparentDiffusion coefficients from high angular resolution Diffusion imaging estimation and applications
Magnetic Resonance in Medicine, 2006
Co-Authors: Maxime Descoteaux, Elaine Angelino, Shaun Fitzgibbons, Rachid Deriche

Abstract:

High angular resolution Diffusion imaging (HARDI) has recently been of great interest in characterizing non-Gaussian Diffusion processes. In the white matter of the brain, non-Gaussian Diffusion occurs when fiber bundles cross, kiss or diverge within the same voxel. One important goal in current research is to obtain more accurate fits of the Apparent Diffusion processes in these multiple fiber regions, thus overcoming the limitations of classical Diffusion tensor imaging (DTI). This paper presents an extensive study of high order models for Apparent Diffusion coefficient estimation and illustrates some of their applications. In particular, we first develop the appropriate mathematical tools to work on noisy HARDI data. Using a meaningful modified spherical harmonics basis to capture the physical constraints of the problem, we propose a new regularization algorithm to estimate a diffusivity profile smoother and closer to the true diffusivities without noise. We define a smoothing term based on the Laplace-Beltrami operator for functions defined on the unit sphere. The properties of the spherical harmonics are then exploited to derive a closed form implementation of this term into the fitting procedure. We next derive the general linear transformation between the coefficients of a spherical harmonics series of order $\ell$ and the independent elements of the rank-$\ell$ high order Diffusion tensor. An additional contribution of the paper is the careful study of the state of the art anisotropy measures for high order formulation models computed from spherical harmonics or tensor coefficients. Their ability to characterize the underlying Diffusion process is analyzed. We are able to reproduce published results and also able to recover voxels with isotropic, single fiber anisotropic and multiple fiber anisotropic Diffusion. We test and validate the different approaches on Apparent Diffusion coefficients from synthetic data, from a biological phantom and from a human brain dataset.

• ##### ApparentDiffusion Coefficients from High Angular Resolution Diffusion Images: Estimation and Applications
, 2006
Co-Authors: Maxime Descoteaux, Elaine Angelino, Shaun Fitzgibbons, Rachid Deriche

Abstract:

High angular resolution Diffusion imaging (HARDI) has recently been of great interest in characterizing non-Gaussian Diffusion processes. In the white matter of the brain, non-Gaussian Diffusion occurs when fiber bundles cross, kiss or diverge within the same voxel. One important goal in current research is to obtain more accurate fits of the Apparent Diffusion processes in these multiple fiber regions, thus overcoming the limitations of classical Diffusion tensor imaging (DTI). This paper presents an extensive study of high order models for Apparent Diffusion coefficient estimation and illustrates some of their applications. In particular, we first develop the appropriate mathematical tools to work on noisy HARDI data. Using a meaningful modified spherical harmonics basis to capture the physical constraints of the problem, we propose a new regularization algorithm to estimate a diffusivity profile smoother and closer to the true diffusivities without noise. We define a smoothing term based on the Laplace-Beltrami operator for functions defined on the unit sphere. The properties of the spherical harmonics are then exploited to derive a closed form implementation of this term into the fitting procedure. We next derive the general linear transformation between the coefficients of a spherical harmonics series of order $\ell$ and the independent elements of the rank-$\ell$ high order Diffusion tensor. An additional contribution of the paper is the careful study of the state of the art anisotropy measures for high order formulation models computed from spherical harmonics or tensor coefficients. Their ability to characterize the underlying Diffusion process is analyzed. We are able to reproduce published results and also able to recover voxels with isotropic, single fiber anisotropic and multiple fiber anisotropic Diffusion. We test and validate the different approaches on Apparent Diffusion coefficients from synthetic data, from a biological phantom and from a human brain dataset.