B-splines are commonly utilized to construct the transformation model in free-form deformation (FFD) based registration. B-splines become smoother with increasing spline order. However, a higher-order B-spline requires a larger support region involving more control points, which means higher computational cost. In general, the third-order B-spline is considered as a good compromise between spline smoothness and computational cost. A lower-order function is seldom used to construct the transformation model for registration since it is less smooth. In this research, we investigated whether lower-order B-spline functions can be utilized for more efficient registration, while preserving smoothness of the deformation by using a novel random perturbation technique. With the proposed perturbation technique, the expected value of the cost function given probability density function (PDF) of the perturbation is minimized by a stochastic gradient descent optimization. Extensive experiments on 2D synthetically deformed brain images, and real 3D lung and brain scans demonstrated that the novel randomly perturbed free-form deformation (RPFFD) approach improves the registration accuracy and transformation smoothness. Meanwhile, lower-order RPFFD methods reduce the computational cost substantially.

Both normal aging and neurodegenerative diseases such as Alzheimer's disease cause morphological changes of the brain. To better distinguish between normal and abnormal cases, it is necessary to model changes in brain morphology owing to normal aging. To this end, we developed a method for analyzing and visualizing these changes for the entire brain morphology distribution in the general aging population. The method is applied to 1000 subjects from a large population imaging study in the elderly, from which 900 were used to train the model and 100 were used for testing. The results of the 100 test subjects show that the model generalizes to subjects outside the model population. Smooth percentile curves showing the brain morphology changes as a function of age and spatiotemporal atlases derived from the model population are publicly available via an interactive web application at agingbrain.bigr.nl.

Purpose
A novel three-dimensional (3D) T1 and T2 mapping protocol for the carotid artery is presented.

Methods
A 3D black-blood imaging sequence was adapted allowing carotid T1 and T2 mapping using multiple flip angles and echo time (TE) preparation times. B1 mapping was performed to correct for spatially varying deviations from the nominal flip angle. The protocol was optimized using simulations and phantom experiments. In vivo scans were performed on six healthy volunteers in two sessions, and in a patient with advanced atherosclerosis. Compensation for patient motion was achieved by 3D registration of the inter/intrasession scans. Subsequently, T1 and T2 maps were obtained by maximum likelihood estimation.

Results
Simulations and phantom experiments showed that the bias in T1 and T2 estimation was < 10% within the range of physiological values. In vivo T1 and T2 values for carotid vessel wall were 844 ± 96 and 39 ± 5 ms, with good repeatability across scans. Patient data revealed altered T1 and T2 values in regions of atherosclerotic plaque.

Conclusion
The 3D T1 and T2 mapping of the carotid artery is feasible using variable flip angle and variable TE preparation acquisitions. We foresee application of this technique for plaque characterization and monitoring plaque progression in atherosclerotic patients. Magn Reson Med 75:1008–1017, 2016.