## Further references

@article{ozarslan2003gen, title={Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging.}, author={Ozarslan, E. and Mareci, T.H.}, journal={Magn Reson Med}, volume={50}, number={5}, pages={955-65}, year={2003}, abstract={A new method for mapping diffusivity profiles in tissue is presented. The Bloch-Torrey equation is modified to include a diffusion term with an arbitrary rank Cartesian tensor. This equation is solved to give the expression for the generalized Stejskal-Tanner formula quantifying diffusive attenuation in complicated geometries. This makes it possible to calculate the components of higher-rank tensors without using the computationally-difficult spherical harmonic transform. General theoretical relations between the diffusion tensor (DT) components measured by traditional (rank-2) DT imaging (DTI) and 3D distribution of diffusivities, as measured by high angular resolution diffusion imaging (HARDI) methods, are derived. Also, the spherical tensor components from HARDI are related to the rank-2 DT. The relationships between higher- and lower-rank Cartesian DTs are also presented. The inadequacy of the traditional rank-2 tensor model is demonstrated with simulations, and the method is applied to excised rat brain data collected in a spin-echo HARDI experiment.} }

TY - JOUR AU - Ozarslan, E AU - Shepherd, TM AU - Vemuri, BC AU - Blackband, SJ AU - Mareci, TH TI - Fast orientation mapping from HARDI. AB - This paper introduces a new, accurate and fast method for fiber orientation mapping using high angular resolution diffusion imaging (HARDI) data. The approach utilizes the Fourier relationship between the water displacement probabilities and diffusion attenuated magnetic resonance (MR) signal expressed in spherical coordinates. The Laplace series coefficients of the water displacement probabilities are evaluated at a fixed distance away from the origin. The computations take under one minute for most three-dimensional datasets. We present orientation maps computed from excised rat optic chiasm, brain and spinal cord images. The developed method will improve the reliability of tractography schemes and make it possible to correctly identify the neural connections between functionally connected regions of the nervous system. JO - Med Image Comput Comput Assist Interv Int Conf Med Image Comput Comput Assist Interv PY - 2005 VL - 8 IS - Pt 1 SP - 156-63 SN - -------- TY - JOUR AU - Jian, B AU - Vemuri, BC AU - Ozarslan, E AU - Carney, PR AU - Mareci, TH TI - A novel tensor distribution model for the diffusion-weighted MR signal. AB - Diffusion MRI is a non-invasive imaging technique that allows the measurement of water molecule diffusion through tissue in vivo. The directional features of water diffusion allow one to infer the connectivity patterns prevalent in tissue and possibly track changes in this connectivity over time for various clinical applications. In this paper, we present a novel statistical model for diffusion-weighted MR signal attenuation which postulates that the water molecule diffusion can be characterized by a continuous mixture of diffusion tensors. An interesting observation is that this continuous mixture and the MR signal attenuation are related through the Laplace transform of a probability distribution over symmetric positive definite matrices. We then show that when the mixing distribution is a Wishart distribution, the resulting closed form of the Laplace transform leads to a Rigaut-type asymptotic fractal expression, which has been phenomenologically used in the past to explain the MR signal decay but never with a rigorous mathematical justification until now. Our model not only includes the traditional diffusion tensor model as a special instance in the limiting case, but also can be adjusted to describe complex tissue structure involving multiple fiber populations. Using this new model in conjunction with a spherical deconvolution approach, we present an efficient scheme for estimating the water molecule displacement probability functions on a voxel-by-voxel basis. Experimental results on both simulations and real data are presented to demonstrate the robustness and accuracy of the proposed algorithms. JO - Neuroimage PY - 2007 SN - 10538119 TY - JOUR AU - Ozarslan, E AU - Shepherd, TM AU - Vemuri, BC AU - Blackband, SJ AU - Mareci, TH TI - Resolution of complex tissue microarchitecture using the diffusion orientation transform (DOT). AB - This article describes an accurate and fast method for fiber orientation mapping using multidirectional diffusion-weighted magnetic resonance (MR) data. This novel approach utilizes the Fourier transform relationship between the water displacement probabilities and diffusion-attenuated MR signal expressed in spherical coordinates. The radial part of the Fourier integral is evaluated analytically under the assumption that MR signal attenuates exponentially. The values of the resulting functions are evaluated at a fixed distance away from the origin. The spherical harmonic transform of these functions yields the Laplace series coefficients of the probabilities on a sphere of fixed radius. Alternatively, probability values can be computed nonparametrically using Legendre polynomials. Orientation maps calculated from excised rat nervous tissue data demonstrate this technique's ability to accurately resolve crossing fibers in anatomical regions such as the optic chiasm. This proposed methodology has a trivial extension to multiexponential diffusion-weighted signal decay. The developed methods will improve the reliability of tractography schemes and may make it possible to correctly identify the neural connections between functionally connected regions of the nervous system. JO - Neuroimage PY - 2006 SN - 10538119 TY - JOUR AU - Freidlin, RZ AU - Ozarslan, E AU - Komlosh, ME AU - Chang, L AU - Koay, CG AU - Jones, DK AU - Basser, PJ TI - Parsimonious model selection for tissue segmentation and classification applications: a study using simulated and experimental DTI data. AB - One aim of this work is to investigate the feasibility of using a hierarchy of models to describe diffusion tensor magnetic resonance (MR) data in fixed tissue. Parsimonious model selection criteria are used to choose among different models of diffusion within tissue. Using this information, we assess whether we can perform simultaneous tissue segmentation and classification. Both numerical phantoms and diffusion weighted imaging (DWI) data obtained from excised pig spinal cord are used to test and validate this model selection framework. Three hierarchical approaches are used for parsimonious model selection: the Schwarz criterion (SC), the F-test t-test (F- t), proposed by Hext, and the F-test F-test (F-F), adapted from Snedecor. The F - t approach is more robust than the others for selecting between isotropic and general anisotropic (full tensor) models. However, due to its high sensitivity to the variance estimate and bias in sorting eigenvalues, the F-F and SC are preferred for segmenting models with transverse isotropy (cylindrical symmetry). Additionally, the SC method is easier to implement than the F - t and F - F methods and has better performance. As such, this approach can be efficiently used for evaluating large MRI data sets. In addition, the proposed voxel-by-voxel segmentation framework is not susceptible to artifacts caused by the inhomogeneity of the variance in neighboring voxels with different degrees of anisotropy, which might contaminate segmentation results obtained with the techniques based on voxel averaging. JO - IEEE Trans Med Imaging PY - 2007 VL - 26 IS - 11 SP - 1576-84 SN - 02780062 TY - JOUR AU - Bar-Shir, A AU - Avram, L AU - Ozarslan, E AU - Basser, PJ AU - Cohen, Y TI - The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: Experiments and simulations. AB - q-Space diffusion MRI (QSI) provides a means of obtaining microstructural information about porous materials and neuronal tissues from diffusion data. However, the accuracy of this structural information depends on experimental parameters used to collect the MR data. q-Space diffusion MR performed on clinical scanners is generally collected with relatively long diffusion gradient pulses, in which the gradient pulse duration, delta, is comparable to the diffusion time, Delta. In this study, we used phantoms, consisting of ensembles of microtubes, and mathematical models to assess the effect of the ratio of the diffusion time and the duration of the diffusion pulse gradient, i.e., Delta/delta, on the MR signal attenuation vs. q, and on the measured structural information extracted therefrom. We found that for Delta/delta approximately 1, the diffraction pattern obtained from q-space MR data are shallower than when the short gradient pulse (SGP) approximation is satisfied. For long delta the estimated compartment size is, as expected, smaller than the real size. Interestingly, for Delta/delta approximately 1 the diffraction peaks are shifted to even higher q-values, even when delta is kept constant, giving the impression that the restricted compartments are even smaller than they are. When phantoms composed of microtubes of different diameters are used, it is more difficult to estimate the diameter distribution in this regime. Excellent agreement is found between the experimental results and simulations that explicitly account for the use of long duration gradient pulses. Using such experimental data and this mathematical framework, one can estimate the true compartment dimensions when long and finite gradient pulses are used even when Delta/delta approximately 1. JO - J Magn Reson PY - 2008 SN - 15578968 Amnon Bar-Shir, Liat Avram, Evren Ozarslan, Peter J. Basser, Yoram Cohen, The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: Experiments and simulations, Journal of Magnetic ResonanceIn Press, Corrected Proof, , Available online 15 July 2008. (http://www.sciencedirect.com/science/article/B6WJX-4T0FFBG-2/2/02689bd9ad22d75f15717f8a045d0457) Abstract: q-Space diffusion MRI (QSI) provides a means of obtaining microstructural information about porous materials and neuronal tissues from diffusion data. However, the accuracy of this structural information depends on experimental parameters used to collect the MR data. q-Space diffusion MR performed on clinical scanners is generally collected with relatively long diffusion gradient pulses, in which the gradient pulse duration, [delta], is comparable to the diffusion time, [Delta]. In this study, we used phantoms, consisting of ensembles of microtubes, and mathematical models to assess the effect of the ratio of the diffusion time and the duration of the diffusion pulse gradient, i.e., [Delta]/[delta], on the MR signal attenuation vs. q, and on the measured structural information extracted therefrom. We found that for [Delta]/[delta] ~ 1, the diffraction pattern obtained from q-space MR data are shallower than when the short gradient pulse (SGP) approximation is satisfied. For long [delta] the estimated compartment size is, as expected, smaller than the real size. Interestingly, for [Delta]/[delta] ~ 1 the diffraction peaks are shifted to even higher q-values, even when [delta] is kept constant, giving the impression that the restricted compartments are even smaller than they are. When phantoms composed of microtubes of different diameters are used, it is more difficult to estimate the diameter distribution in this regime. Excellent agreement is found between the experimental results and simulations that explicitly account for the use of long duration gradient pulses. Using such experimental data and this mathematical framework, one can estimate the true compartment dimensions when long and finite gradient pulses are used even when [Delta]/[delta] ~ 1. Keywords: Diffusion; NMR; q-Space; QSI; Diffraction; Diffusion time; Pulse duration @article{barshir2008edt, title={{The effect of the diffusion time and pulse gradient duration ratio on the diffraction pattern and the structural information estimated from q-space diffusion MR: Experiments and simulations}}, author={Bar-Shir, A. and Avram, L. and {\"O}zarslan, E. and Basser, P.J. and Cohen, Y.}, journal={Journal of Magnetic Resonance}, year={2008}, publisher={Elsevier} } @article{avram2008tdw, title={{Three-dimensional water diffusion in impermeable cylindrical tubes: theory versus experiments.}}, author={Avram, L. and Ozarslan, E. and Assaf, Y. and Bar-Shir, A. and Cohen, Y. and Basser, P.J.}, journal={NMR Biomed}, volume={21}, pages={1--11}, year={2008} }