6,781 research outputs found
Variational theory for physiological flow
AbstractUsing He’s semi-inverse method, a variational principle for physiological flow is established
Computing motion in the primate's visual system
Computing motion on the basis of the time-varying image intensity is a difficult problem for both artificial and biological vision systems. We will show how one well-known gradient-based computer algorithm for estimating visual motion can be implemented within the primate's visual system. This relaxation algorithm computes the optical flow field by minimizing a variational functional of a form commonly encountered in early vision, and is performed in two steps. In the first stage, local motion is computed, while in the second stage spatial integration occurs. Neurons in the second stage represent the optical flow field via a population-coding scheme, such that the vector sum of all neurons at each location codes for the direction and magnitude of the velocity at that location. The resulting network maps onto the magnocellular pathway of the primate visual system, in particular onto cells in the primary visual cortex (V1) as well as onto cells in the middle temporal area (MT). Our algorithm mimics a number of psychophysical phenomena and illusions (perception of coherent plaids, motion capture, motion coherence) as well as electrophysiological recordings. Thus, a single unifying principle ‘the final optical flow should be as smooth as possible’ (except at isolated motion discontinuities) explains a large number of phenomena and links single-cell behavior with perception and computational theory
A Model of Electrodiffusion and Osmotic Water Flow and its Energetic Structure
We introduce a model for ionic electrodiffusion and osmotic water flow
through cells and tissues. The model consists of a system of partial
differential equations for ionic concentration and fluid flow with interface
conditions at deforming membrane boundaries. The model satisfies a natural
energy equality, in which the sum of the entropic, elastic and electrostatic
free energies are dissipated through viscous, electrodiffusive and osmotic
flows. We discuss limiting models when certain dimensionless parameters are
small. Finally, we develop a numerical scheme for the one-dimensional case and
present some simple applications of our model to cell volume control
Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling
Identifying a coupled dynamical system out of many plausible candidates, each
of which could serve as the underlying generator of some observed measurements,
is a profoundly ill posed problem that commonly arises when modelling real
world phenomena. In this review, we detail a set of statistical procedures for
inferring the structure of nonlinear coupled dynamical systems (structure
learning), which has proved useful in neuroscience research. A key focus here
is the comparison of competing models of (ie, hypotheses about) network
architectures and implicit coupling functions in terms of their Bayesian model
evidence. These methods are collectively referred to as dynamical casual
modelling (DCM). We focus on a relatively new approach that is proving
remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid
evaluation and comparison of models that differ in their network architecture.
We illustrate the usefulness of these techniques through modelling
neurovascular coupling (cellular pathways linking neuronal and vascular
systems), whose function is an active focus of research in neurobiology and the
imaging of coupled neuronal systems
Swirling fluid flow in flexible, expandable elastic tubes: variational approach, reductions and integrability
Many engineering and physiological applications deal with situations when a
fluid is moving in flexible tubes with elastic walls. In the real-life
applications like blood flow, there is often an additional complexity of
vorticity being present in the fluid. We present a theory for the dynamics of
interaction of fluids and structures. The equations are derived using the
variational principle, with the incompressibility constraint of the fluid
giving rise to a pressure-like term. In order to connect this work with the
previous literature, we consider the case of inextensible and unshearable tube
with a straight centerline. In the absence of vorticity, our model reduces to
previous models considered in the literature, yielding the equations of
conservation of fluid momentum, wall momentum and the fluid volume. We show
that even when the vorticity is present, but is kept at a constant value, the
case of an inextensible, unshearable and straight tube with elastics walls
carrying a fluid allows an alternative formulation, reducing to a single
compact equation for the back-to-labels map instead of three conservation
equations. That single equation shows interesting instability in solutions when
the vorticity exceeds a certain threshold. Furthermore, the equation in stable
regime can be reduced to Boussinesq-type, KdV and Monge-Amp\`ere equations
equations in several appropriate limits, namely, the first two in the limit of
long time and length scales and the third one in the additional limit of the
small cross-sectional area. For the unstable regime, we numerical solutions
demonstrate the spontaneous appearance of large oscillations in the
cross-sectional area.Comment: 57 pages, 11 figures. arXiv admin note: text overlap with
arXiv:1805.1102
A mixed finite element method for nearly incompressible multiple-network poroelasticity
In this paper, we present and analyze a new mixed finite element formulation
of a general family of quasi-static multiple-network poroelasticity (MPET)
equations. The MPET equations describe flow and deformation in an elastic
porous medium that is permeated by multiple fluid networks of differing
characteristics. As such, the MPET equations represent a generalization of
Biot's equations, and numerical discretizations of the MPET equations face
similar challenges. Here, we focus on the nearly incompressible case for which
standard mixed finite element discretizations of the MPET equations perform
poorly. Instead, we propose a new mixed finite element formulation based on
introducing an additional total pressure variable. By presenting energy
estimates for the continuous solutions and a priori error estimates for a
family of compatible semi-discretizations, we show that this formulation is
robust in the limits of incompressibility, vanishing storage coefficients, and
vanishing transfer between networks. These theoretical results are corroborated
by numerical experiments. Our primary interest in the MPET equations stems from
the use of these equations in modelling interactions between biological fluids
and tissues in physiological settings. So, we additionally present
physiologically realistic numerical results for blood and tissue fluid flow
interactions in the human brain
- …