74 research outputs found
Metabifurcation analysis of a mean field model of the cortex
Mean field models (MFMs) of cortical tissue incorporate salient features of
neural masses to model activity at the population level. One of the common
aspects of MFM descriptions is the presence of a high dimensional parameter
space capturing neurobiological attributes relevant to brain dynamics. We study
the physiological parameter space of a MFM of electrocortical activity and
discover robust correlations between physiological attributes of the model
cortex and its dynamical features. These correlations are revealed by the study
of bifurcation plots, which show that the model responses to changes in
inhibition belong to two families. After investigating and characterizing
these, we discuss their essential differences in terms of four important
aspects: power responses with respect to the modeled action of anesthetics,
reaction to exogenous stimuli, distribution of model parameters and oscillatory
repertoires when inhibition is enhanced. Furthermore, while the complexity of
sustained periodic orbits differs significantly between families, we are able
to show how metamorphoses between the families can be brought about by
exogenous stimuli. We unveil links between measurable physiological attributes
of the brain and dynamical patterns that are not accessible by linear methods.
They emerge when the parameter space is partitioned according to bifurcation
responses. This partitioning cannot be achieved by the investigation of only a
small number of parameter sets, but is the result of an automated bifurcation
analysis of a representative sample of 73,454 physiologically admissible sets.
Our approach generalizes straightforwardly and is well suited to probing the
dynamics of other models with large and complex parameter spaces
Agent-based and continuum models for spatial dynamics of infection by oncolytic viruses
The use of oncolytic viruses as cancer treatment has received considerable
attention in recent years, however the spatial dynamics of this viral infection
is still poorly understood. We present here a stochastic agent-based model
describing infected and uninfected cells for solid tumours, which interact with
viruses in the absence of an immune response. Two kinds of movement, namely
undirected random and pressure-driven movements, are considered: the continuum
limit of the models is derived and a systematic comparison between the systems
of partial differential equations and the individual-based model, in one and
two dimensions, is carried out.
In the case of undirected movement, a good agreement between agent-based
simulations and the numerical and well-known analytical results for the
continuum model is possible. For pressure-driven motion, instead, we observe a
wide parameter range in which the infection of the agents remains confined to
the center of the tumour, even though the continuum model shows traveling waves
of infection; outcomes appear to be more sensitive to stochasticity and
uninfected regions appear harder to invade, giving rise to irregular,
unpredictable growth patterns.
Our results show that the presence of spatial constraints in tumours'
microenvironments limiting free expansion has a very significant impact on
virotherapy. Outcomes for these tumours suggest a notable increase in
variability. All these aspects can have important effects when designing
individually tailored therapies where virotherapy is included.Comment: 29 pages, 10 figures. Supplementary material available at
https://tinyurl.com/5c5nxss
Chaotic properties of planar elongational flow and planar shear flow: lyapunov exponents, conjugate-pairing rule, and phase space contraction
The simulation of planar elongational flow in a nonequilibrium steady state for arbitrarily long times has recently been made possible, combining the SLLOD algorithm with periodic boundary conditions for the simulation box. We address the fundamental questions regarding the chaotic behavior of this type of flow, comparing its chaotic properties with those of the well-established SLLOD algorithm for planar shear flow. The spectra of Lyapunov exponents are analyzed for a number of state points where the energy dissipation is the same for both flows, simulating a nonequilibrium steady state for isoenergetic and isokinetic constrained dynamics. We test the conjugate-pairing rule and confirm its validity for planar elongation flow, as is expected from the Hamiltonian nature of the adiabatic equations of motion. Remarks about the chaoticity of the convective part of the flows, the link between Lyapunov exponents and viscosity, and phase space contraction for both flows complete the study
Boundary condition independence of molecular dynamics simulations of planar elongational flow
The simulation of liquid systems in a nonequilibrium steady state under planar elongational flow (PEF) for indefinite time is possible only with the use of the so-called Kraynik-Reinelt (KR) periodic boundary conditions (PBCs) on the simulation cell. These conditions admit a vast range of implementation parameters, which regulate how the unit lattice is deformed under elongation and periodically remapped onto itself. Clearly, nonequilibrium properties of homogeneous systems in a steady state have to be independent of the boundary conditions imposed on the unit cell. In order to confirm the independence of measurable properties of a system under PEF from the particular set of periodic boundary conditions, we compute the Lyapunov spectra, apply the conjugate pairing rule, and carefully analyze the so-called unpaired exponents for an atomic fluid of various sizes and state points. We further compute the elongational viscosity for various implementations of boundary conditions. All our results confirm the independence from KR PBCs for the dynamics of phase-space trajectories and for the transport coefficients
- ā¦