The mathematical aspects of diffusion tensor magnetic resonance imaging (DTMRI, or DTI), the measurement of the diffusion tensor by magnetic resonance imaging (MRI), are discussed in this three-part series. In part I, some general features of diffusion imaging are presented briefly, including the relationship between the diffusion ellipsoid and the diffusion tensor. Rotations of vectors and ten...

Gliomas are the most common intra-axial primary brain tumour; therefore, predicting glioma grade would influence therapeutic strategies. Although several methods based on single or multiple parameters from diagnostic images exist, a definitive method for pre-operatively determining glioma grade remains unknown. We aimed to develop an unsupervised method using multiple parameters from pre-operat...

In the Biomedical Medical Research laboratory in St. Louis Missouri there is an ongoing project to characterize water diffusion in fixed baboon brain using diffusion weighted magnetic resonance imaging as a means of monitoring development throughout gestation. Magnetic resonance images can be made sensitive to diffusion by applying magnetic field gradients during the pulse sequence. Results fro...

Magnetic resonance electrical impedance tomography (MREIT) is an emerging method to visualize electrical conductivity and/or current density images at low frequencies (below 1 KHz). Injecting currents into an imaging object, one component of the induced magnetic flux density is acquired using an MRI scanner for isotropic conductivity image reconstructions. Diffusion tensor MRI (DT-MRI) measures...

INTRODUCTION Diffusion tensor MRI (DT-MRI) provides a discrete representation of the diffusion tensor field ofwater in living tissues. A graphical means to display the diffusion tensor field, '[\]is to construct diffusion ellipsoid maps or images (1). Moreover, from the diffusion tensor field, one can infer the fiber-tract direction field in some anisotropic tissues (1). 1n white matter and ske...

Diffusion tensor imaging (DTI) provides a powerful tool for identifying white matter (WM) alterations in clinical populations. The prevalent method for group-level analysis of DTI is statistical comparison of the diffusion tensor fractional anisotropy (FA) metric. The FA metric, however, does not capture the full orientational information contained in the diffusion tensor. For example, the FA t...

Diffusion-weighted magnetic resonance imaging (DW-MRI) is a recognized tool for early detection of infarction of the human brain. DW-MRI uses the signal loss associated with the random thermal motion of water molecules in the presence of magnetic field gradients to derive parameters that reflect the translational mobility of the water molecules in tissues. If diffusion-weighted images with diff...

We propose a novel method for deformable tensor-to-tensor registration of Diffusion Tensor Imaging (DTI) data. Our registration method considers estimated diffusion tensors as normally distributed random variables whose covariance matrices describe uncertainties in the mean estimated tensor due to factors such as noise in diffusion weighted images (DWIs), tissue diffusion properties, and experi...