Diffusion tensor imaging (DTI) is known to have a limited capability of resolving multiple fiber orientations within one voxel. This is mainly because the probability density function (PDF) for random spin displacement is non‐Gaussian in the confining environment of biological tissues and, thus, the modeling of self‐diffusion by a second‐order tensor breaks down. The statistical property of a non‐Gaussian diffusion process is characterized via the higher‐order tensor (HOT) coefficients by reconstructing the PDF of the random spin displacement. Those HOT coefficients can be determined by combining a series of complex diffusion‐weighted measurements. The signal equation for an MR diffusion experiment was investigated theoretically by generalizing Fick's law to a higher‐order partial differential equation (PDE) obtained via Kramers‐Moyal expansion. A relationship has been derived between the HOT coefficients of the PDE and the higher‐order cumulants of the random spin displacement. Monte‐Carlo simulations of diffusion in a restricted environment with different geometrical shapes were performed, and the strengths and weaknesses of both HOT and established diffusion analysis techniques were investigated. The generalized diffusion tensor formalism is capable of accurately resolving the underlying spin displacement for complex geometrical structures, of which neither conventional DTI nor diffusion‐weighted imaging at high angular resolution (HARD) is capable. The HOT method helps illuminate some of the restrictions that are characteristic of these other methods. Furthermore, a direct relationship between HOT and q‐space is also established. Magn Reson Med 51:924–937, 2004.

Background —The stratification of post–myocardial infarction (MI) patients at risk of sudden cardiac death remains important. The aim of the present study was to assess the prognostic value of novel T-wave morphology descriptors derived from resting 12-lead ECGs. Methods and Results —In 280 consecutive post-MI patients, a 12-lead ECG was recorded before discharge, optically scanned, and digitized. For the present study, 5 T-wave morphology descriptors were automatically calculated after singular value decomposition of the ECG signal. The total cosine R-to-T (TCRT [describes the global angle between repolarization and depolarization wavefront]) and the T-wave loop dispersion were univariately associated ( P =0.0002 and P <0.002, respectively, U test) with 27 prospectively defined clinical events in 261 patients (mean follow-up 32±10 months). Kaplan-Meier event probability curves for strata above and below the median confirmed the strong risk discrimination by TCRT and T-wave loop dispersion ( P <0.003 and P <0.001, respectively, log-rank test). On Cox regression analysis, with the entering of age, left ventricular ejection fraction, heart rate, QRS width, reperfusion therapy, β-adrenergic–blocker treatment, and standard deviation of R-R intervals on 24-hour Holter monitoring, TCRT ( P <0.03) yielded independent predictive value, whereas T-wave loop dispersion was of borderline independence ( P =0.064). Heart rate ( P <0.02), left ventricular ejection fraction ( P <0.02), and reperfusion therapy ( P <0.02) also remained in the final model. Conclusions —Computerized T-wave morphology analysis of the 12-lead resting ECG permits independent assessment of post-MI risk and an improved risk stratification when combined with other risk markers.

We developed a novel computer-aided detection (CAD) algorithm called the surface normal overlap method that we applied to colonic polyp detection and lung nodule detection in helical computed tomography (CT) images. We demonstrate some of the theoretical aspects of this algorithm using a statistical shape model. The algorithm was then optimized on simulated CT data and evaluated using a per-lesion cross-validation on 8 CT colonography datasets and on 8 chest CT datasets. It is able to achieve 100% sensitivity for colonic polyps 10 mm and larger at 7.0 false positives (FPs)/dataset and 90% sensitivity for solid lung nodules 6 mm and larger at 5.6 FP/dataset.