Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Fast low-angle shot diffusion tensor imaging with stimulated echo encoding in the muscle of rabbit shank.

In the past, spin-echo (SE) echo planar imaging(EPI)-based diffusion tensor imaging (DTI) has been widely used to study the fiber structure of skeletal muscles in vivo. However, this sequence has several shortcomings when measuring restricted diffusion in small animals, such as its sensitivity to susceptibility-related distortions and a relatively short applicable diffusion time. To address these limitations, in the current work, a stimulated echo acquisition mode (STEAM) MRI technique, in combination with fast low-angle shot (FLASH) readout (turbo-STEAM MRI), was implemented and adjusted for DTI in skeletal muscles. Signal preparation using stimulated echoes enables longer effective diffusion times, and thus the detection of restricted diffusion within muscular tissue with intracellular distances up to 100 µm. Furthermore, it has a reduced penalty for fast T2 muscle signal decay, but at the expense of 50% signal loss compared with a SE preparation. Turbo-STEAM MRI facilitates high-resolution DTI of skeletal muscle without introducing susceptibility-related distortions. To demonstrate its applicability, we carried out rabbit in vivo measurements on a human whole-body 3 T scanner. DTI parameters of the shank muscles were extracted, including the apparent diffusion coefficient, fractional anisotropy, eigenvalues and eigenvectors. Eigenvectors were used to calculate maps of structural parameters, such as the planar index and the polar coordinates θ and ϕ of the largest eigenvector. These parameters were compared between three muscles. θ and ϕ showed clear differences between the three muscles, reflecting different pennation angles of the underlying fiber structures. Fiber tractography was performed to visualize and analyze the architecture of skeletal pennate muscles. Optimization of tracking parameters and utilization of T2 -weighted images for improved muscle boundary detection enabled the determination of additional parameters, such as the mean fiber length. The presented results support the applicability of turbo-STEAM MRI as a promising method for quantitative DTI analysis and fiber tractography in skeletal muscles