Effect of accurately calculated b matrix on the evaluation of the diffusion tensor using echoplanar diffusion tensor imaging

Diffusion-weighted magnetic resonance imaging is a recognised tool in early detection of infarction of the human brain. If diffusion weighted-images with different values of b matrix are acquired during one individual investigation, it is possible to calculate diffusion coefficient maps that are elements of the diffusion tensor: they represent the apparent diffusion coefficient of protons of water molecules in each pixel in the corresponding sample. The relationship between signal intensity in the diffusion-weighted images, diffusion tensor and b matrix is derived from the Bloch equations. Our goal is to establish the error made in the calculation of the elements of the diffusion tensor when imaging gradients are ignored in the calculation of the b matrix elements. The numerical calculation of the b matrices show that a systematic error of up to 7% is introduced in the derived diffusion tensor elements when neglecting imaging gradients.