Abstract Perivascular spaces are important highways for fluid and solute transport in the brain enabling efficient waste clearance during sleep. However, underlying mechanisms augmenting perivascular flow sleep unknown. Using two-photon imaging of naturally sleeping male mice we demonstrate cycle-dependent vascular dynamics pial arteries penetrating arterioles: slow, large-amplitude oscillations NREM sleep, a vasodilation REM vasoconstriction upon awakening at end cycle microarousals...

We present the first application of an artificial neural network trained through a deep reinforcement learning agent to perform active flow control. It is shown that, in two-dimensional simulation Kármán vortex street at moderate Reynolds number ( $Re=100$ ), our able learn control strategy from experimenting with mass rates two jets on sides cylinder. By interacting unsteady wake, successfully stabilizes alley and reduces drag by approximately 8 %. This performed while using small for...

In this paper, we study a mathematical model of cardiac tissue based on explicit representation individual cells. EMI model, the extracellular (E) space, cell membrane (M) and intracellular (I) space are represented as separate geometrical domains. This introduces modelling flexibility needed for detailed properties cells including their membrane. particular, will show that allows ion channels to be non-uniformly distributed along cell. Such features difficult include in classical...

We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train while respecting PDEs as strong constraint optimisation apposed making them part loss function. resulting models are discretised space by finite element method (FEM). applies both stationary and transient well linear/nonlinear PDEs. describe implementation an extension existing FEM framework FEniCS its algorithmic...

In recent years, a plethora of methods combining neural networks and partial differential equations have been developed. A widely known example are physics-informed networks, which solve problems involving by training network. We apply the finite element method to estimate diffusion coefficient governing long term spread molecules in human brain from magnetic resonance images. Synthetic testcases created demonstrate that standard formulation network faces challenges with noisy measurements...

.We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity strength of the interface coupling deteriorates performance standard methods. We focus on aggregation-based algebraic multigrid with custom smoothers preserve information each coarse level. prove that, proper choice subspace splitting, we obtain uniform convergence in discretization physical parameters two-level setting. Additionally, show parameter robustness...

We study a thermo-poroelasticity model which describes the interaction between deformation of an elastic porous material and fluid flow under non-isothermal conditions. The involves several parameters that can vary significantly in practical applications, posing challenge for developing discretization techniques solution algorithms handle such variations effectively. propose four-field formulation apply conforming finite element discretization. primary focus is on constructing analyzing...

The mechanisms of intracranial solute transport are fundamental to human brain health, with alterations often linked disease and functional impairment, distinct opportunities for personalized diagnostics treatment. However, our understanding these their interplay remains incomplete, in part due the complexity integrating insights across scales, between species from different modalities. Here, we combine mixed-dimensional modelling, multi-modal magnetic resonance images, high performance...

Analysis and Approximation of Mixed-Dimensional PDEs on 3D-1D Domains Coupled with Lagrange Multipliers

Mesh degeneration is a bottleneck for fluid–structure interaction (FSI) simulations and shape optimization via the method of mappings. In both cases, an appropriate mesh motion technique required. The choice typically based on heuristics, e.g., solution operators partial differential equations (PDE), such as Laplace or biharmonic equation. Especially latter, which shows good numerical performance large displacements, expensive. Moreover, from continuous perspective, choosing to certain...

We study preconditioners for a model problem describing the coupling of two elliptic subproblems posed over domains with different topological dimension by parameter dependent constraint. A pair robust and efficient is proposed analyzed. Robustness efficiency demonstrated numerical experiments.

Objective. Mechanistic modeling of neurons is an essential component computational neuroscience that enables scientists to simulate, explain, and explore neural activity. The conventional approach simulation extracellular recordings first computes transmembrane currents using the cable equation then sums their contribution model potential. This two-step relies on assumption space infinite homogeneous conductive medium, while measurements are performed probes. main purpose this paper assess...

Coupled multiphysics problems often give rise to interface conditions naturally formulated in fractional Sobolev spaces. Here, both positive and negative fractionality are common. When designing efficient solvers for discretizations of such it would therefore be useful have a preconditioner the Laplacian. In this work, we develop an additive multigrid Laplacian with show uniform bound on condition number. For case fractionality, reuse developed left-right multiply regular obtain desired...

Cardiomyocytes are the functional building blocks of heart-yet most models developed to simulate cardiac mechanics do not represent individual cells and their surrounding matrix. Instead, they work on a homogenized tissue level, assuming that cellular subcellular structures processes scale uniformly. Here we present mathematical numerical framework for exploring tissue-level microscale given an explicit three-dimensional geometrical representation embedded in We defined model over such...

Multiscale or multiphysics problems often involve coupling of partial differential equations posed on domains different dimensionality. In this work, we consider a simplified model problem 3 d ‐1 and the main objective is to construct algorithms that may utilize standard multilevel for domain, which has dominating computational complexity. Preconditioning system two elliptic posed, respectively, in three‐dimensional domain an embedded one dimensional curve coupled by trace constraint...

We develop robust solvers for a class of perturbed saddle-point problems arising in the study second-order elliptic equation mixed form (in terms flux and potential), four-field formulation Biot's consolidation problem linear poroelasticity (using displacement, filtration flux, total pressure, fluid pressure). The stability continuous variational problems, which hinges upon using adequately weighted spaces, is addressed detail; efficacy proposed preconditioners, as well their robustness with...

Intrathecal drug and gene vector delivery is a procedure to release solute within the cerebrospinal fluid. This currently used in clinical practice shows promise for treatment of several central nervous system pathologies. However, intrathecal protocols systems are not yet optimized. The aim this study was investigate effects injection parameters on distribution cervical subarachnoid space using numerical platform. We developed model based patient-specific three dimensional geometry with...

We construct mesh-independent and parameter-robust monolithic solvers for the coupled primal Stokes--Darcy problem. Three different formulations their discretizations in terms of conforming nonconforming finite element methods volume are considered. In each case, robust preconditioners derived using a unified theoretical framework. particular, suggested utilize operators fractional Sobolev spaces. Numerical experiments demonstrate parameter-robustness proposed solvers.

ABSTRACT Perivascular spaces (PVS) are important highways for fluid and solute transport in the brain enabling efficient waste clearance during sleep. Using two-photon imaging of naturally sleeping mice we demonstrate sleep cycle-dependent PVS dynamics – slow, large-amplitude oscillations NREM, a reduction REM an enlargement upon awakening at end cycle. By biomechanical modeling that these drive flow transport.

The coupled Darcy–Stokes problem is widely used for modeling fluid transport in physical systems consisting of a porous part and free part. In this work we consider preconditioners monolithic solution algorithms the problem, where Darcy primal form. We employ operator preconditioning framework utilize fractional solver at interface between problems to obtain order optimal schemes that are robust with respect material parameters, i.e. permeability, viscosity Beavers–Joseph–Saffman condition....

The process of a circular free falling jet entering an idle pool was studied with the objective determining relation between naturally occurring disturbances on surface and air entrainment. To this end instabilities were characterized compared bubble count distribution estimated amount entrained in plume. Different lengths considered. aeration captured through image sequences. Individual analysis each disturbance made. Our results show that both have linear steepness disturbances. Moreover,...

Abstract Flow of cerebrospinal fluid through perivascular pathways in and around the brain may play a crucial role metabolite clearance. While driving forces such flows remain enigmatic, experiments have shown that pulsatility is central. In this work, we present novel network model for simulating pulsatile flow networks, taking form system Stokes–Brinkman equations posed over graph. We apply to study physiological questions concerning mechanisms governing branching vascular networks....