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

Collateral artery pathways of the femoral and popliteal artery

Contains fulltext : 174232.pdf (publisher's version ) (Closed access)BACKGROUND: The role of collateral artery circulation in the lower limb is under debate but clinically relevant, particularly when using covered stents for occlusive disease. Covered stents seem to outperform nitinol stents in extensive disease, but collaterals could be essential in case of acute thrombosis. In the present study, we describe the collateral pathways of the deep and superficial femoral artery (DFA, SFA) and the popliteal artery (PA), observed in human cadavers. METHODS: Ten fresh frozen cadaver legs were selected. The SFA and DFA were separately cannulated and injected with a different colored latex mixture simultaneously. After curing of the latex, the circulation was dissected thus visualizing the main arteries and their collateral vessels. The process was photographed and recorded, and collateral pathways were analyzed using a standardized vessel segmentation. The upper leg was divided in three regions, that is, the femoral triangle (F), the adductor canal (H), and the popliteal fossa (P) that, in turn, were split in three segments (1, 2, and 3, from proximal to distal). RESULTS: Overall, 113 collateral vessels were found; 69 originated from the DFA, 34 from the SFA, and 10 from the PA. The majority of collaterals originating from the DFA terminated in the SFA (57%). Fifty-six of 113 collaterals (50%) ended in either the distal adductor channel (H3) or the proximal PA (P1). Another 28 collateral arteries (25%) had their origin in this segment (H3, P1) and mostly connected to the P2 and P3 segments. Forty-three collaterals of the DFA and H3 segment had a direct or indirect connection to below the knee muscles. CONCLUSIONS: The majority of collaterals originate from the DFA, and the greater part of all collaterals has a connection with the H3-P1 segment. This observation may have clinical implications in the planning of endovascular procedures