scholarly journals A biochemo-mechano coupled, computational model combining membrane transport and pericellular proteolysis in tissue mechanics

2017 ◽  
Vol 473 (2199) ◽  
pp. 20160812 ◽  
Author(s):  
A.-T. Vuong ◽  
A. D. Rauch ◽  
W. A. Wall
Keyword(s):  
Porous Medium ◽  
Computational Model ◽  
Solid Phase ◽  
Chemical Species ◽  
Reaction Rates ◽  
Tissue Mechanics ◽  
Diffusion Reaction ◽  
Advection Diffusion ◽  
Reaction Processes ◽  
Pericellular Proteolysis

We present a computational model for the interaction of surface- and volume-bound scalar transport and reaction processes with a deformable porous medium. The application in mind is pericellular proteolysis, i.e. the dissolution of the solid phase of the extracellular matrix (ECM) as a response to the activation of certain chemical species at the cell membrane and in the vicinity of the cell. A poroelastic medium model represents the extra cellular scaffold and the interstitial fluid flow, while a surface-bound transport model accounts for the diffusion and reaction of membrane-bound chemical species. By further modelling the volume-bound transport, we consider the advection, diffusion and reaction of sequestered chemical species within the extracellular scaffold. The chemo-mechanical coupling is established by introducing a continuum formulation for the interplay of reaction rates and the mechanical state of the ECM. It is based on known experimental insights and theoretical work on the thermodynamics of porous media and degradation kinetics of collagen fibres on the one hand and a damage-like effect of the fibre dissolution on the mechanical integrity of the ECM on the other hand. The resulting system of partial differential equations is solved via the finite-element method. To the best of our knowledge, it is the first computational model including contemporaneously the coupling between (i) advection–diffusion–reaction processes, (ii) interstitial flow and deformation of a porous medium, and (iii) the chemo-mechanical interaction impelled by the dissolution of the ECM. Our numerical examples show good agreement with experimental data. Furthermore, we outline the capability of the methodology to extend existing numerical approaches towards a more comprehensive model for cellular biochemo-mechanics.

Critical time scales for advection-diffusion-reaction processes

2012 ◽  
Vol 85 (4) ◽  
Author(s):  
Adam J. Ellery ◽  
Matthew J. Simpson ◽  
Scott W. McCue ◽  
Ruth E. Baker
Keyword(s):  
Time Scales ◽  
Critical Time ◽  
Diffusion Reaction ◽  
Advection Diffusion ◽  
Reaction Processes

scholarly journals Coupling kinetic models and advection-diffusion equations. 1. Framework development and application to sucrose translocation and metabolism in sugarcane

2021 ◽  
Author(s):  
Lafras Uys ◽  
Jan-Hendrik S Hofmeyr ◽  
Johann M Rohwer
Keyword(s):  
Differential Equations ◽  
Kinetic Models ◽  
Numerical Solutions ◽  
Spatial Information ◽  
Initial Conditions ◽  
Reaction Rates ◽  
Diffusion Reaction ◽  
Sucrose Accumulation ◽  
Fluid Medium ◽  
Advection Diffusion

Abstract The sugarcane stalk, besides being the main structural component of the plant, is also the major storage organ for carbohydrates. Previous studies have modelled the sucrose accumulation pathway in the internodal storage parenchyma of sugarcane using kinetic models cast as systems of ordinary differential equations. To address the shortcomings of these models, which did not include subcellular compartmentation or spatial information, the present study extends the original models within an advection-diffusion-reaction framework, requiring the use of partial differential equations to model sucrose metabolism coupled to phloem translocation.We propose a kinetic model of a coupled reaction network where species can be involved in chemical reactions and/or be transported over long distances in a fluid medium by advection or diffusion. Darcy’s law is used to model fluid flow and allows a simplified, phenomenological approach to be applied to translocation in the phloem. Similarly, generic reversible Hill equations are used to model biochemical reaction rates. Numerical solutions to this formulation are demonstrated with time-course analysis of a simplified model of sucrose accumulation. The model shows sucrose accumulation in the vacuoles of stalk parenchyma cells, and is moreover able to demonstrate the up-regulation of photosynthesis in response to a change in sink demand. The model presented is able to capture the spatio-temporal evolution of the system from a set of initial conditions by combining phloem flow, diffusion, transport of metabolites between compartments and biochemical enzyme-catalysed reactions in a rigorous, quantitative framework that can form the basis for future modelling and experimental design.

scholarly journals Moments of action provide insight into critical times for advection-diffusion-reaction processes

2012 ◽  
Vol 86 (3) ◽  
Author(s):  
Adam J. Ellery ◽  
Matthew J. Simpson ◽  
Scott W. McCue ◽  
Ruth E. Baker
Keyword(s):  
Diffusion Reaction ◽  
Advection Diffusion ◽  
Reaction Processes ◽  
Insight Into ◽  
Critical Times

scholarly journals A Review on Recent Progress of Glycan-Based Surfactant Micelles as Nanoreactor Systems for Chemical Synthesis Applications

2021 ◽  
Vol 2 (1) ◽  
pp. 168-186
Author(s):  
Bahareh Vafakish ◽  
Lee D. Wilson
Keyword(s):  
Chemical Synthesis ◽  
Chemical Reactions ◽  
Recent Progress ◽  
Chemical Species ◽  
Reaction Rates ◽  
Bulk Solution ◽  
Surfactant Micelles ◽  
Conventional Surfactant ◽  
Recent Developments ◽  
To Receive

The nanoreactor concept and its application as a modality to carry out chemical reactions in confined and compartmentalized structures continues to receive increasing attention. Micelle-based nanoreactors derived from various classes of surfactant demonstrate outstanding potential for chemical synthesis. Polysaccharide (glycan-based) surfactants are an emerging class of biodegradable, non-toxic, and sustainable alternatives over conventional surfactant systems. The unique structure of glycan-based surfactants and their micellar structures provide a nanoenvironment that differs from that of the bulk solution, and supported by chemical reactions with uniquely different reaction rates and mechanisms. In this review, the aggregation of glycan-based surfactants to afford micelles and their utility for the synthesis of selected classes of reactions by the nanoreactor technique is discussed. Glycan-based surfactants are ecofriendly and promising surfactants over conventional synthetic analogues. This contribution aims to highlight recent developments in the field of glycan-based surfactants that are relevant to nanoreactors, along with future opportunities for research. In turn, coverage of research for glycan-based surfactants in nanoreactor assemblies with tailored volume and functionality is anticipated to motivate advanced research for the synthesis of diverse chemical species.

scholarly journals Estimating the extent of glioblastoma invasion

2021 ◽  
Vol 82 (1-2) ◽  
Author(s):  
Christian Engwer ◽  
Michael Wenske
Keyword(s):  
Analytic Solution ◽  
Glioma Cells ◽  
Diffusion Reaction ◽  
Kpp Equation ◽  
Advection Diffusion ◽  
Clinical Interest ◽  
Inhomogeneous Diffusion ◽  
Reaction Equations ◽  
Advection Diffusion Reaction Equations ◽  
Tumor Extent

AbstractGlioblastoma Multiforme is a malignant brain tumor with poor prognosis. There have been numerous attempts to model the invasion of tumorous glioma cells via partial differential equations in the form of advection–diffusion–reaction equations. The patient-wise parametrization of these models, and their validation via experimental data has been found to be difficult, as time sequence measurements are mostly missing. Also the clinical interest lies in the actual (invisible) tumor extent for a particular MRI/DTI scan and not in a predictive estimate. Therefore we propose a stationalized approach to estimate the extent of glioblastoma (GBM) invasion at the time of a given MRI/DTI scan. The underlying dynamics can be derived from an instationary GBM model, falling into the wide class of advection-diffusion-reaction equations. The stationalization is introduced via an analytic solution of the Fisher-KPP equation, the simplest model in the considered model class. We investigate the applicability in 1D and 2D, in the presence of inhomogeneous diffusion coefficients and on a real 3D DTI-dataset.

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