Condition number as a measure of noise performance of diffusion tensor data acquisition schemes with MRI

Diffusion tensor mapping with MRI can noninvasively track neural connectivi ty and has great potential for neural scientific research and clinical appl ications. For each diffusion tensor imaging (DTI) data acquisition scheme, the diffusion tensor is related to the measured apparent diffusion coeffici ents (ADC) by a transformation matrix. With theoretical analysis we demonst rate that the noise performance of a DTI scheme is dependent on the conditi on number of the transformation matrix. To test the theoretical framework, we compared the noise performances of different DTI schemes using Monte-Car lo computer simulations and experimental DTI measurements. Both the simulat ion and the experimental results confirmed that the noise performances of d ifferent DTI schemes are significantly correlated with the condition number of the associated transformation matrices. We therefore applied numerical algorithms to optimize a DTI scheme by minimizing the condition number, hen ce improving the robustness to experimental noise. In the determination of anisotropic diffusion tensors with different orientations, MRI data acquisi tions using a single optimum b value based on the mean diffusivity can prod uce ADC maps with regional differences in noise level. This will give rise to rotational variances of eigenvalues and anisotropy when diffusion tensor mapping is performed using a DTI scheme with a limited number of diffusion -weighting gradient directions. To reduce this type of artifact, a DTI sche me with not only a small condition number but also a large number of evenly distributed diffusion-weighting gradients in 3D is preferable. (C) 2000 Ac ademic Press.