1,884 research outputs found
Multiscale modelling of intestinal crypt organization and carcinogenesis
Colorectal cancers are the third most common type of cancer. They originate from intestinal crypts, glands that descend from the intestinal lumen into the underlying connective tissue. Normal crypts are thought to exist in a dynamic equilibrium where the rate of cell production at the base of a crypt is matched by that of loss at the top. Understanding how genetic alterations accumulate and proceed to disrupt this dynamic equilibrium is fundamental to understanding the origins of colorectal cancer. Colorectal cancer emerges from the interaction of biological processes that span several spatial scales, from mutations that cause inappropriate intracellular responses to changes at the cell/tissue level, such as uncontrolled proliferation and altered motility and adhesion. Multiscale mathematical modelling can provide insight into the spatiotemporal organisation of such a complex, highly regulated and dynamic system. Moreover, the aforementioned challenges are inherent to the multiscale modelling of biological tissue more generally. In this review we describe the mathematical approaches that have been applied to investigate multiscale aspects of crypt behavior, highlighting a number of model predictions that have since been validated experimentally. We also discuss some of the key mathematical and computational challenges associated with the multiscale modelling approach. We conclude by discussing recent efforts to derive coarse-grained descriptions of such models, which may offer one way of reducing the computational cost of simulation by leveraging well-established tools of mathematical analysis to address key problems in multiscale modelling
A model of spatially evolving herpesvirus epidemics causing mass mortality in Australian pilchard Sardinops sagax
In 1995 mass mortality of pilchards Sardinops sagax occurred along >5000 km of Australian coast; similar events occurred in 1998/99. This mortality was closely associated with a herpesvirus. The pilchard is an important food source for larger animals and supports commercial fisheries. Both epidemics originated in South Australian waters and spread as waves with velocities of 10 to 40 km d-1. Velocity was constant for a single wave, but varied between the epidemics and between the east- and west-bound waves in each epidemic. The pattern of mortality evolved from recurrent episodes to a single peak with distance from the origin. A 1-dimensional model of these epidemics has been developed. The host population is divided into susceptible, infected and latent, infected and infectious, and removed (recovered and dead) phases; the latent and infectious periods are of fixed duration. This model produces the mortality patterns observed locally and during the spread and evolution of the epidemic. It is consistent with evidence from pathology. The wave velocity is sensitive to diffusion coefficients, viral transmission rates and latent period. These parameters are constrained using the local and large-scale patterns of epidemic spread. The relative roles of these parameters in explaining differences between epidemics and between east- and west-bound waves within epidemics are discussed. The model predicts very high levels of infection, indicating that many surviving pilchards recovered following infection. Control appears impracticable once epidemics are initiated, but impact can be minimised by protecting juvenile stocks
Enhanced group analysis and conservation laws of variable coefficient reaction-diffusion equations with power nonlinearities
A class of variable coefficient (1+1)-dimensional nonlinear
reaction-diffusion equations of the general form
is investigated. Different kinds of
equivalence groups are constructed including ones with transformations which
are nonlocal with respect to arbitrary elements. For the class under
consideration the complete group classification is performed with respect to
convenient equivalence groups (generalized extended and conditional ones) and
with respect to the set of all point transformations. Usage of different
equivalences and coefficient gauges plays the major role for simple and clear
formulation of the final results. The corresponding set of admissible
transformations is described exhaustively. Then, using the most direct method,
we classify local conservation laws. Some exact solutions are constructed by
the classical Lie method.Comment: 23 pages, minor misprints are correcte
The Principal Element of a Frobenius Lie Algebra
We introduce the notion of the \textit{principal element} of a Frobenius Lie
algebra \f. The principal element corresponds to a choice of F\in \f^* such
that non-degenerate. In many natural instances, the principal element
is shown to be semisimple, and when associated to \sl_n, its eigenvalues are
integers and are independent of . For certain ``small'' functionals , a
simple construction is given which readily yields the principal element. When
applied to the first maximal parabolic subalgebra of \sl_n, the principal
element coincides with semisimple element of the principal three-dimensional
subalgebra. We also show that Frobenius algebras are stable under deformation.Comment: 10 page
Information Metric on Instanton Moduli Spaces in Nonlinear Sigma Models
We study the information metric on instanton moduli spaces in two-dimensional
nonlinear sigma models. In the CP^1 model, the information metric on the moduli
space of one instanton with the topological charge Q=k which is any positive
integer is a three-dimensional hyperbolic metric, which corresponds to
Euclidean anti--de Sitter space-time metric in three dimensions, and the
overall scale factor of the information metric is (4k^2)/3; this means that the
sectional curvature is -3/(4k^2). We also calculate the information metric in
the CP^2 model.Comment: 9 pages, LaTeX; added references for section 1; typos adde
Projective and Coarse Projective Integration for Problems with Continuous Symmetries
Temporal integration of equations possessing continuous symmetries (e.g.
systems with translational invariance associated with traveling solutions and
scale invariance associated with self-similar solutions) in a ``co-evolving''
frame (i.e. a frame which is co-traveling, co-collapsing or co-exploding with
the evolving solution) leads to improved accuracy because of the smaller time
derivative in the new spatial frame. The slower time behavior permits the use
of {\it projective} and {\it coarse projective} integration with longer
projective steps in the computation of the time evolution of partial
differential equations and multiscale systems, respectively. These methods are
also demonstrated to be effective for systems which only approximately or
asymptotically possess continuous symmetries. The ideas of projective
integration in a co-evolving frame are illustrated on the one-dimensional,
translationally invariant Nagumo partial differential equation (PDE). A
corresponding kinetic Monte Carlo model, motivated from the Nagumo kinetics, is
used to illustrate the coarse-grained method. A simple, one-dimensional
diffusion problem is used to illustrate the scale invariant case. The
efficiency of projective integration in the co-evolving frame for both the
macroscopic diffusion PDE and for a random-walker particle based model is again
demonstrated
Immunomodulatory Therapy for MIS-C.
Studies comparing initial therapy for multisystem inflammatory syndrome in children (MIS-C) provided conflicting results.
To compare outcomes in MIS-C patients treated with intravenous immunoglobulin (IVIG), glucocorticoids, or the combination thereof.
Medline, Embase, CENTRAL and WOS, from January 2020 to February 2022.
Randomized or observational comparative studies including MIS-C patients <21 years.
Two reviewers independently selected studies and obtained individual participant data. The main outcome was cardiovascular dysfunction (CD), defined as left ventricular ejection fraction < 55% or vasopressor requirement ≥ day 2 of initial therapy, analyzed with a propensity score-matched analysis.
Of 2635 studies identified, 3 nonrandomized cohorts were included. The meta-analysis included 958 children. IVIG plus glucocorticoids group as compared with IVIG alone had improved CD (odds ratio [OR] 0.62 [0.42-0.91]). Glucocorticoids alone group as compared with IVIG alone did not have improved CD (OR 0.57 [0.31-1.05]). Glucocorticoids alone group as compared with IVIG plus glucocorticoids did not have improved CD (OR 0.67 [0.24-1.86]). Secondary analyses found better outcomes associated with IVIG plus glucocorticoids compared with glucocorticoids alone (fever ≥ day 2, need for secondary therapies) and better outcomes associated with glucocorticoids alone compared with IVIG alone (left ventricular ejection fraction < 55% ≥ day 2).
Nonrandomized nature of included studies.
In a meta-analysis of MIS-C patients, IVIG plus glucocorticoids was associated with improved CD compared with IVIG alone. Glucocorticoids alone was not associated with improved CD compared with IVIG alone or IVIG plus glucocorticoids
Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
A new approach to group classification problems and more general
investigations on transformational properties of classes of differential
equations is proposed. It is based on mappings between classes of differential
equations, generated by families of point transformations. A class of variable
coefficient (1+1)-dimensional semilinear reaction-diffusion equations of the
general form () is studied from the
symmetry point of view in the framework of the approach proposed. The singular
subclass of the equations with is singled out. The group classifications
of the entire class, the singular subclass and their images are performed with
respect to both the corresponding (generalized extended) equivalence groups and
all point transformations. The set of admissible transformations of the imaged
class is exhaustively described in the general case . The procedure of
classification of nonclassical symmetries, which involves mappings between
classes of differential equations, is discussed. Wide families of new exact
solutions are also constructed for equations from the classes under
consideration by the classical method of Lie reductions and by generation of
new solutions from known ones for other equations with point transformations of
different kinds (such as additional equivalence transformations and mappings
between classes of equations).Comment: 40 pages, this is version published in Acta Applicanda Mathematica
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