A method for calibrating diffusion gradients in diffusion tensor imaging.

Diffusion tensor imaging (DTI) is a noninvasive magnetic resonance imaging method for measuring microstructural information about biological tissues.1,2 The clinical and research applications of DTI are rapidly expanding. The trace of the diffusion tensor (DT) describes the magnitude of diffusion in tissues. Measures of diffusion anisotropy appear to be highly sensitive to changes in tissue microstructure. Further, white matter tractography algorithms may be used to estimate patterns of white matter connectivity using the major eigenvector. In 1965, Stejskal and Tanner proposed methods for diffusion-weighted (DW) nuclear magnetic resonance using gradient pulses.3 Imperfections of diffusion-weighting gradients may cause errors in estimating the mean diffusivity (MD; trace divided by 3), the fractional anisotropy (FA), and the tensor orientation.4-6 The gradient imperfections may be classified into 3 categories: (1) gradient errors with constant directions including background and imaging gradients, (2) gradient errors whose directions are associated with diffusion-weighting gradients including gradient scaling and residual gradients, and (3) spatial nonuniformity and nonlinearity. Background gradients and imaging gradients may be the most significant sources of gradient errors.5 Many research studies have demonstrated that using opposite diffusion-weighting gradient polarities can eliminate the cross-terms of background gradients7-11 and imaging gradients.12-15 Residual gradients arising from long-term Eddy currents can also be corrected by reversing diffusion-weighting gradients to estimate the symmetry of distortions through a cross-correlation approach.16 Finally, Bammer et al17 developed a method to estimate and correct errors relating to gradient spatial uniformity and linearity using an isotropic water phantom. Herein, we propose a calibration method that uses these correction strategies described above and the basic concept of gradient errors to form a more comprehensive correction protocol. Similar to previous research studies, this method takes advantage of opposite diffusion-weighting gradient polarities and an isotropic phantom. However, the difference is that this method acquires images at multiple diffusion-weighting levels along 3 orthogonal directions, instead of single diffusion-weighting used in previous studies.9-11,14-16 The gradient errors may be estimated through linear regression analyses (one on combined images of opposite gradient polarities and one on images of single polarity) on quadratic functions of the diffusion gradients. A 6-element total effective scaling vector is generated for retrospective correction. This approach corrects all possible gradient errors in a single calibration protocol and is potential for prospective gradient correction if gradient waveforms are available. This protocol does not attempt to calibrate the spatial errors of diffusion-weighting gradients, but there should be no difficulties in combining with the method developed by Bammer et al,17 which also uses an isotropic phantom. In this article, a calibration protocol and gradient error estimation framework are described. The calibration protocol may be applied on a regular basis (ie, weekly) to monitor gradient performances over time and compare measurements between scanners. The calibration protocol lasts less than 10 minutes and is independent of DTI experiments. Therefore, for regular DTI experiments, it does not require any additional images for the purpose of gradient calibration. A retrospective correction is demonstrated on both brain DTI experiments and computer simulations. If the gradient errors are not expected to change dramatically from time to time, the same correction vector may be applied between calibration periods.