Abstract
For obtaining a complete model the diffusion tensor imaging (DTI) method is derived in a new linear algebraic framework in order to include the effect of all of the magnetic field gradients on the MRI signal. In the framework, the coefficient matrix of the estimation equations consists of the sum of three matrices corresponding to diffusion gradients, imaging gradients and the cross-terms between them. The derivations demonstrate that there exists modeling incongruities originating from the choice of phase-encoding gradient magnitude and the read-out gradient affecting the entirety of the signal sample points. These reflect on the cross-terms and the imaging gradient coefficient matrix, revealing the DTI's inadequacy for the inclusion of imaging gradients. The linear algebraic framework mitigates the inadequacy by the utilization of center-symmetric gradient schemes. The observations are verified by the experimental results obtained from an isotropic phantom using several existing diffusion gradient schemes.