Origin of orientation-dependent R1 (=1/T1 ) relaxation in white matter.

PURPOSE: In a recent MRI study, it was shown that the longitudinal relaxation rate, R1 , in white matter (WM) is influenced by the relative orientation of nerve fibers with respect to the main magnetic field (B0 ). Even though the exact nature of this R1 orientation dependency is still unclear, it can be assumed that the origin of the phenomenon can be attributed to the anisotropic and unique molecular environment within the myelin sheath surrounding the axons. The current work investigates the contribution of dipolar induced R1 relaxation of the myelin associated hydrogen nuclei theoretically and compares the results with the experimentally observed R1 orientation dependency. METHODS: Atomistic molecular dynamics simulations were employed and the R1 relaxation rate of hydrogen nuclei of a myelin-alike molecular environment was calculated for various orientations of the trajectory sets relative to the B0 -field. Based on the calculated relaxation rates, the observable R1 relaxation was simulated for various fiber orientations and fitted to the experimental data using a suitable signal weighting-scheme. RESULTS: The results obtained show that the R1 relaxation rate of both solid myelin (SM) and myelin water (MW) depends on the fiber orientation relative to the main B0 -field. Moreover, employing a realistic signal weighing scheme and tissue characteristics, the theoretically investigated R1 orientation dependency matches the experimental data well. CONCLUSION: The good agreement between theoretical and experimental findings indicates that the R1 orientation dependency in WM mainly originates from anisotropic dipole-dipole interactions between hydrogen nuclei located within the myelin sheath.

Dipolar induced spin-lattice relaxation in the myelin sheath: A molecular dynamics study.

Interactions between hydrogen protons of water molecules and macromolecules within the myelin sheath surrounding the axons are a major factor influencing the magnetic resonance (MR) contrast in white matter (WM) regions. In past decades, several studies have investigated the underlying effects and reported a wide range of R1 rates for the myelin associated compartments at different field strengths. However, it was also shown that the experimental quantification of the compartment-specific R1 rates is associated with large uncertainties. The current study therefore investigates the longitudinal relaxation rates within the myelin sheath using a molecular dynamic (MD) simulation. For this purpose, a realistic molecular model of the myelin sheath was employed to determine the dipole-dipole induced R1 relaxation rate of the hydrogen protons at clinically relevant field strengths. The results obtained clearly reflect the spatial heterogeneity of R1 with a increased relaxivity of myelin water due to a reduced molecular mobility near the membrane surface. Moreover, the calculated R1 rates for both myelin water and macromolecules are in excellent agreement with experimental findings from the literature at different field strengths.

Fibre-orientation dependent R1(=1/T1) relaxation in the brain: The role of susceptibility induced spin-lattice relaxation in the myelin water compartment.

We have recently observed a dependence of the longitudinal relaxation rate, R1, on the orientation of nerve fibres with respect to the main magnetic field. A similar dependence of R2∗ is long established and can be well explained by spin-dephasing in an inhomogeneous magnetic field induced by the susceptibility shift between myelin and water protons. The current study investigates if the same effect can also explain the R1 dependence, neglecting a possible directional dependence of magnetisation transfer between solid myelin and myelin water. A molecular model of the myelin lipid bilayer was employed to simulate the susceptibility induced fields on a microscopic scale for the different nerve fibre orientations. The resulting simulated magnetic fields were used to calculate an orientation dependent relaxation offset, ΔR1, based on both first-order perturbation theory and a simulation of the spin transition probabilities. Even though both methods yielded consistent orientation dependent relaxation offsets with a distribution that resembles the experimental data, the determined ΔR1 values are too low to explain the reported R1 angular dependency. Therefore, unlike R2∗, susceptibility induced spin flips can be excluded as a dominant source for the observed R1 angular dependence.

Statistical learning of mobility patterns from long-term monitoring of locomotor behaviour with body-worn sensors.

Long term monitoring of locomotor behaviour in humans using body-worn sensors can provide insight into the dynamical structure of locomotion, which can be used for quantitative, predictive and classification analyses in a biomedical context. A frequently used approach to study daily life locomotor behaviour in different population groups involves categorisation of locomotion into various states as a basis for subsequent analyses of differences in locomotor behaviour. In this work, we use such a categorisation to develop two feature sets, namely state probability and transition rates between states, and use supervised classification techniques to demonstrate differences in locomotor behaviour. We use this to study the influence of various states in differentiating between older adults with and without dementia. We further assess the contribution of each state and transition and identify the states most influential in maximising the classification accuracy between the two groups. The methods developed here are general and can be applied to areas dealing with categorical time series.

The impact of fibre orientation on T1-relaxation and apparent tissue water content in white matter.

OBJECTIVE: Recent MRI studies have shown that the orientation of nerve fibres relative to the main magnetic field affects the R2*(= 1/T2*) relaxation rate in white matter (WM) structures. The underlying physical causes have been discussed in several studies but are still not completely understood. However, understanding these effects in detail is of great importance since this might serve as a basis for the development of new diagnostic tools and/or improve quantitative susceptibility mapping techniques. Therefore, in addition to the known angular dependence of R2*, the current study investigates the relationship between fibre orientation and the longitudinal relaxation rate, R1 (= 1/T1), as well as the apparent water content. MATERIALS AND METHODS: For a group of 16 healthy subjects, a series of gradient echo, echo-planar and diffusion weighted images were acquired at 3T from which the decay rates, the apparent water content and the diffusion direction were reconstructed. The diffusion weighted data were used to determine the angle between the principle fibre direction and the main magnetic field to examine the angular dependence of R1 and apparent water content. RESULTS: The obtained results demonstrate that both parameters depend on the fibre orientation and exhibit a positive correlation with the angle between fibre direction and main magnetic field. CONCLUSION: These observations could be helpful to improve and/or constrain existing biophysical models of brain microstructure by imposing additional constraints resulting from the observed angular dependence R1 and apparent water content in white matter.

Use of a Lucas-Kanade-Based Template Tracking Algorithm to Examine In Vivo Tendon Excursion during Voluntary Contraction Using Ultrasonography.

Ultrasound imaging can be used to study tendon movement during muscle contraction to estimate the tendon force-length relationship in vivo. Traditionally, such tendon displacement measurements are made manually (time consuming and subjective). Here we evaluated a Lucas-Kanade-based tracking algorithm with an optic flow extension that accounts for tendon movement characteristics between consecutive frames of an ultrasound image sequence. Eleven subjects performed 12 voluntary isometric plantar flexion contractions on a dynamometer. Simultaneously, the gastrocnemius medialis tendon was visualized via ultrasonography. Tendon displacement was estimated manually and by using two different automatic tracking algorithms. Maximal tendon elongation (manual: 17.9 ± 0.3 mm, automatic: 17.0 ± 0.3 mm) and tendon stiffness (209 ± 4 N/mm, 218 ± 5 N/mm) generated by the developed algorithm correlated with those obtained with the manual method (0.87 ≤ R ≤ 0.91), with no differences between methods. Our results suggest that optical flow methods can potentially be used for automatic estimation of tendon movement during contraction in ultrasound images, which is further improved by adding a penalty function.

Transport of solutes undergoing a Freundlich type nonlinear and nonequilibrium adsorption process.

We investigate the behavior of solutes undergoing nonequilibrium adsorption processes that lead to a Freundlich isotherm in equilibrium. In contrast to a frequently used model we do not assume that the adsorption rate is proportional to the difference between adsorbed and equilibrium concentrations, but inspect two nonlinear laws governing the path to equilibrium. With some asymptotic considerations and numerical simulations we find that depending on the model parameters, the concentration in solution and the mass adsorbed by the matrix do not necessarily reach quasiequilibrium.