Tensor tomography

Tensors of diffusion, deformation (stress and strain), and conductivity are physical quantities of biological tissue, which can be used to, characteri ze particular disease states. Tensor tomography may be a useful imaging tec hnique for eliciting these tensor quantities when applied in conjunction wi th an imaging modality such as magnetic resonance imaging (MRI). This paper presents a method for reconstructing a 2x2 second-order tensor field from scalar projection measurements of the tensor field. The reconstruction of t he four components of a 2x2 tensor may require as many as four distinct sca lar measurements for each projection ray through the tensor field. Fourier projection theorems have been developed for the reconstruction of a tensor field which is decomposed into solenoidal and irrotational components. Resu lts of a computer simulation that demonstrate the validity of the mathemati cal formulations are presented. A method is also proposed to obtain a diffu sion tensor field tomographically from MRI projection measurements of the d iffusion tensor field. The method is evaluated experimentally and results o f an MRI phantom study are presented.