Wall shear stress and arterial performance: two approaches based on engineering

This is the Abstract of the Article. Copyright @ 2009 Oxford University.This crucially important subject generates a very wide literature and the recent authoritative ‘in vivo’ review of Reneman et al [1] (& [2]), with Vennemann et al [3], are taken as seminal. In this paper we use approaches based on conventional engineering to address two key issues raised in [1]. The first is that of basic theory. To what extent can underlying fluid flow theory complement the in vivo understanding of wall shear stress (WSS)? In [1], which is sub-titled Discrepancies with Theory’, Poiseuille’s Law is used, extended to Murray’s Law in [2]. But they do ’not hold in vivo’ [2] because ‘we are dealing with non-Newtonian fluid, distensible vessels, unsteady flows, and too short entrance lengths’ [1].This comment coincides with the four factors Xu and Collins identified in their early Review of numerical analysis for bifurcations [4]. Subsequently they addressed these factors, with an engineering-based rationale of comparing predictions of Computational Fluid Dynamics (CFD) with Womersley theory, in vitro and in vivo data. This rationale has yet to be widely adopted, possibly due to computing complexities and the wide boundary condition data needed. This is despite uncertainties in current in vivo WSS [2]. Secondly, [1] and [2] focus on endothelial function. WSS is an ‘important determinant of arterial diameter’ and ‘mean (M)WSS is regulated locally’. One pointer is the possible importance of the glycocalyx, so that ‘endothelial cells are not seeing WSS’ and which ‘may be involved in the regulation of the total blood flow’ [3]. A typical glycocalyx is shown in [3]. Such a model should focus on adaptation of arterial diameter by ‘nitric oxide and prostaglandins’ [1]. So, using an engineering approach, can we construct a model for local regulation of MWSS? Again, remarks from [1]-[3] resonate with the conclusions of a review of nanoscale physiological flows [5] undertaken as part of an early Nanotechnology Initiative of the UK’s EPSRC. In [5] is illustrated the fractal nature of the intestinal villi-glycocalyx geometry, together with an engineering-style control loop for nitric oxide release and arterial diameter-flow rate control. Within our discussion we report two studies to obtain CFD predictive data very close to the endothelial surface. In both cases we compared two independent codes, respectively two CFD codes, and CFD and Lattice Boltzmann solvers. We also give an updated version of the endothelium control loop

Optimal and Bounded-Suboptimal Multi-Goal Task Assignment and Path Finding

We formalize and study the multi-goal task assignment and path finding (MG-TAPF) problem from theoretical and algorithmic perspectives. The MG-TAPF problem is to compute an assignment of tasks to agents, where each task consists of a sequence of goal locations, and collision-free paths for the agents that visit all goal locations of their assigned tasks in sequence. Theoretically, we prove that the MG-TAPF problem is NP-hard to solve optimally. We present algorithms that build upon algorithmic techniques for the multi-agent path finding problem and solve the MG-TAPF problem optimally and bounded-suboptimally. We experimentally compare these algorithms on a variety of different benchmark domains.Comment: ICRA 202

Multi-Goal Multi-Agent Pickup and Delivery

In this work, we consider the Multi-Agent Pickup-and-Delivery (MAPD) problem, where agents constantly engage with new tasks and need to plan collision-free paths to execute them. To execute a task, an agent needs to visit a pair of goal locations, consisting of a pickup location and a delivery location. We propose two variants of an algorithm that assigns a sequence of tasks to each agent using the anytime algorithm Large Neighborhood Search (LNS) and plans paths using the Multi-Agent Path Finding (MAPF) algorithm Priority-Based Search (PBS). LNS-PBS is complete for well-formed MAPD instances, a realistic subclass of MAPD instances, and empirically more effective than the existing complete MAPD algorithm CENTRAL. LNS-wPBS provides no completeness guarantee but is empirically more efficient and stable than LNS-PBS. It scales to thousands of agents and thousands of tasks in a large warehouse and is empirically more effective than the existing scalable MAPD algorithm HBH+MLA*. LNS-PBS and LNS-wPBS also apply to a more general variant of MAPD, namely the Multi-Goal MAPD (MG-MAPD) problem, where tasks can have different numbers of goal locations.Comment: IROS 202

Searching with Consistent Prioritization for Multi-Agent Path Finding

We study prioritized planning for Multi-Agent Path Finding (MAPF). Existing prioritized MAPF algorithms depend on rule-of-thumb heuristics and random assignment to determine a fixed total priority ordering of all agents a priori. We instead explore the space of all possible partial priority orderings as part of a novel systematic and conflict-driven combinatorial search framework. In a variety of empirical comparisons, we demonstrate state-of-the-art solution qualities and success rates, often with similar runtimes to existing algorithms. We also develop new theoretical results that explore the limitations of prioritized planning, in terms of completeness and optimality, for the first time.Comment: AAAI 201

Lifelong Path Planning with Kinematic Constraints for Multi-Agent Pickup and Delivery

The Multi-Agent Pickup and Delivery (MAPD) problem models applications where a large number of agents attend to a stream of incoming pickup-and-delivery tasks. Token Passing (TP) is a recent MAPD algorithm that is efficient and effective. We make TP even more efficient and effective by using a novel combinatorial search algorithm, called Safe Interval Path Planning with Reservation Table (SIPPwRT), for single-agent path planning. SIPPwRT uses an advanced data structure that allows for fast updates and lookups of the current paths of all agents in an online setting. The resulting MAPD algorithm TP-SIPPwRT takes kinematic constraints of real robots into account directly during planning, computes continuous agent movements with given velocities that work on non-holonomic robots rather than discrete agent movements with uniform velocity, and is complete for well-formed MAPD instances. We demonstrate its benefits for automated warehouses using both an agent simulator and a standard robot simulator. For example, we demonstrate that it can compute paths for hundreds of agents and thousands of tasks in seconds and is more efficient and effective than existing MAPD algorithms that use a post-processing step to adapt their paths to continuous agent movements with given velocities.Comment: AAAI 201