Efficient cardiac diffusion tenser MRI by three-dimensional reconstructionof solenoidal tensor fields

Tenser tomography is being investigated as a technique for reconstruction o f in vivo diffusion tenser fields that can potentially be used to reduce th e number of magnetic resonance imaging (MRI) measurements. Specifically, as sessments are being made of the reconstruction of cardiac diffusion tenser fields from 3D Radon planar projections using a filtered backprojection alg orithm in order to specify the helical fiber structure of myocardial tissue . Helmholtz type decomposition is proposed for 3D second order tenser field s. Using this decomposition a Fourier projection theorem is formulated in t erms of the solenoidal acid irrotational components of the tenser field. Fr om the Fourier projection theorem, two sets of Radon directional measuremen ts, one that reconstructs the solenoidal component and one that reconstruct s the irrotational component of the tenser field, are prescribed. Based on these observations filtered backprojection reconstruction formulae are give n for the reconstruction of a 3D second order tenser field and its solenoid al and irrotational components from Radon projection measurements. Computer simulations demonstrate the validity of the mathematical formulations and demonstrate that a realistic model of the helical fiber structure of the my ocardial tissue specifies a diffusion tenser field for which the first prin cipal vector (the vector associated with the maximum eigenvalue) of the sol enoidal component accurately approximates the first principal vector of the diffusion tenser. A priori knowledge of this allows the orientation of the myocardial fiber structure to be specified utilizing one half of the numbe r of MRI measurements of a normal diffusion tenser field study. (C) 2001 El sevier Science Inc. All rights reserved.