Optimal control theory has recently been introduced to nuclear magnetic resonance (NMR) spectroscopy as a means to systematically design and optimize pulse sequences for liquid- and solid-state applications. This has so far primarily involved numerical optimization using gradient-based methods, which allow for the optimization of a large number of pulse sequence parameters in a concerted way to maximize the efficiency of transfer between given spin states or shape the nuclear spin Hamiltonian to a particular form, both within a given period of time. Using such tools, a variety of new pulse sequences with improved performance have been developed, and the NMR spin engineers have been challenged to consider alternative routes for analytical experiment design to meet similar performance. In addition, it has lead to increasing demands to the numerical procedures used in the optimization process in terms of computational speed and fast convergence. With the latter aspect in mind, here we introduce an alternative approach to numerical experiment design based on the Krotov formulation of optimal control theory. For practical reasons, the overall radio frequency power delivered to the sample should be minimized to facilitate experimental implementation and avoid excessive sample heating. The presented algorithm makes explicit use of this requirement and iteratively solves the stationary conditions making sure that the maximum of the objective is reached. It is shown that this method is faster per iteration and takes different paths within a control space than gradient-based methods. In the present work, the Krotov approach is demonstrated by the optimization of NMR and dynamic nuclear polarization experiments for various spin systems and using different constraints with respect to radio frequency and microwave power consumption.

Increasing interest in the structural and functional organisation of the human brain encourages the acquisition of big data sets comprising multiple neuroimaging modalities, often accompanied by additional information obtained from health records, cognitive tests, biomarkers and genotypes. Diffusion weighted magnetic resonance imaging data enables a range of promising imaging phenotypes probing structural connections as well as macroanatomical and microstructural properties of the brain. The reliability and biological sensitivity and specificity of diffusion data depend on processing pipeline. A state‐of‐the‐art framework for data processing facilitates cross‐study harmonisation and reduces pipeline‐related variability. Using diffusion magnetic resonance imaging (MRI) data from 218 individuals in the UK Biobank, we evaluate the effects of different processing steps that have been suggested to reduce imaging artefacts and improve reliability of diffusion metrics. In lack of a ground truth, we compared diffusion metric sensitivity to age between pipelines. By comparing distributions and age sensitivity of the resulting diffusion metrics based on different approaches (diffusion tensor imaging, diffusion kurtosis imaging and white matter tract integrity), we evaluate a general pipeline comprising seven postprocessing blocks: noise correction; Gibbs ringing correction; evaluation of field distortions; susceptibility, eddy‐current and motion‐induced distortion corrections; bias field correction; spatial smoothing and final diffusion metric estimations. Based on this evaluation, we suggest an optimised processing pipeline for diffusion weighted MRI data.

Sex hormones such as estrogen fluctuate across the female lifespan, with high levels during reproductive years and natural decline during the transition to menopause. Women's exposure to estrogen may influence their heightened risk of Alzheimer's disease (AD) relative to men, but little is known about how it affects normal brain aging. Recent findings from the UK Biobank demonstrate less apparent brain aging in women with a history of multiple childbirths, highlighting a potential link between sex‐hormone exposure and brain aging. We investigated endogenous and exogenous sex‐hormone exposure, genetic risk for AD, and neuroimaging‐derived biomarkers for brain aging in 16,854 middle to older‐aged women. The results showed that as opposed to parity, higher cumulative sex‐hormone exposure was associated with more evident brain aging, indicating that i) high levels of cumulative exposure to sex‐hormones may have adverse effects on the brain, and ii) beneficial effects of pregnancies on the female brain are not solely attributable to modulations in sex‐hormone exposure. In addition, for women using hormonal replacement therapy (HRT), starting treatment earlier was associated with less evident brain aging, but only in women with a genetic risk for AD. Genetic factors may thus contribute to how timing of HRT initiation influences women's brain aging trajectories.

The use of increasingly strong magnetic fields in magnetic resonance imaging (MRI) improves sensitivity, susceptibility contrast, and spatial or spectral resolution for functional and localized spectroscopic imaging applications. However, along with these benefits come the challenges of increasing static field (B0) and rf field (B1) inhomogeneities induced by radial field susceptibility differences and poorer dielectric properties of objects in the scanner. Increasing fields also impose the need for rf irradiation at higher frequencies which may lead to elevated patient energy absorption, eventually posing a safety risk. These reasons have motivated the use of multidimensional rf pulses and parallel rf transmission, and their combination with tailoring of rf pulses for fast and low-power rf performance. For the latter application, analytical and approximate solutions are well-established in linear regimes, however, with increasing nonlinearities and constraints on the rf pulses, numerical iterative methods become attractive. Among such procedures, optimal control methods have recently demonstrated great potential. Here, we present a Krotov-based optimal control approach which as compared to earlier approaches provides very fast, monotonic convergence even without educated initial guesses. This is essential for in vivo MRI applications. The method is compared to a second-order gradient ascent method relying on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method, and a hybrid scheme Krotov-BFGS is also introduced in this study. These optimal control approaches are demonstrated by the design of a 2D spatial selective rf pulse exciting the letters “JCP” in a water phantom.

Schizophrenia (SZ) and bipolar disorder (BD) share substantial neurodevelopmental components affecting brain maturation and architecture. This necessitates a dynamic lifespan perspective in which brain aberrations are inferred from deviations from expected lifespan trajectories. We applied machine learning to diffusion tensor imaging (DTI) indices of white matter structure and organization to estimate and compare brain age between patients with SZ, patients with BD, and healthy control (HC) subjects across 10 cohorts. We trained 6 cross-validated models using different combinations of DTI data from 927 HC subjects (18-94 years of age) and applied the models to the test sets including 648 patients with SZ (18-66 years of age), 185 patients with BD (18-64 years of age), and 990 HC subjects (17-68 years of age), estimating the brain age for each participant. Group differences were assessed using linear models, accounting for age, sex, and scanner. A meta-analytic framework was applied to assess the heterogeneity and generalizability of the results. Tenfold cross-validation revealed high accuracy for all models. Compared with HC subjects, the model including all feature sets significantly overestimated the age of patients with SZ (Cohen's d = -0.29) and patients with BD (Cohen's d = 0.18), with similar effects for the other models. The meta-analysis converged on the same findings. Fractional anisotropy-based models showed larger group differences than the models based on other DTI-derived metrics. Brain age prediction based on DTI provides informative and robust proxies for brain white matter integrity. Our results further suggest that white matter aberrations in SZ and BD primarily consist of anatomically distributed deviations from expected lifespan trajectories that generalize across cohorts and scanners.