scholarly journals A multiphase Cahn–Hilliard–Darcy model for tumour growth with necrosis

2018 ◽  
Vol 28 (03) ◽  
pp. 525-577 ◽  
Author(s):  
Harald Garcke ◽  
Kei Fong Lam ◽  
Robert Nürnberg ◽  
Emanuel Sitka
Keyword(s):  
Tumour Growth ◽  
Chemical Species ◽  
Simultaneous Occurrence ◽  
Darcy Model ◽  
Toxic Agents ◽  
Vessel Growth ◽  
New Feature ◽  
Multiple Chemical ◽  
Matched Asymptotic Analysis ◽  
Modelling Approach

We derive a Cahn–Hilliard–Darcy model to describe multiphase tumour growth taking interactions with multiple chemical species into account as well as the simultaneous occurrence of proliferating, quiescent and necrotic regions. A multitude of phenomena such as nutrient diffusion and consumption, angiogenesis, hypoxia, blood vessel growth, and inhibition by toxic agents, which are released for example by the necrotic cells, are included. A new feature of the modelling approach is that a volume-averaged velocity is used, which dramatically simplifies the resulting equations. With the help of formally matched asymptotic analysis we develop new sharp interface models. Finite element numerical computations are performed and in particular the effects of necrosis on tumour growth are investigated numerically. In particular, for certain modelling choices, we obtain some form of focal and patchy necrotic growth that have been observed in experiments.

scholarly journals The Detailed Emissions Scaling, Isolation, and Diagnostic (DESID) module in the Community Multiscale Air Quality (CMAQ) Modeling System version 5.3

2020 ◽  
Author(s):  
Benjamin N. Murphy ◽  
Christopher G. Nolte ◽  
Fahim Sidi ◽  
Jesse O. Bash ◽  
K. Wyat Appel ◽  
...  
Keyword(s):  
Air Quality ◽  
Atmospheric Chemistry ◽  
Chemical Species ◽  
Energy System ◽  
Reduced Form ◽  
Chemistry Research ◽  
Control Interface ◽  
Source Contributions ◽  
Areas Of Interest ◽  
Multiple Chemical

Abstract. Air quality modeling for research and regulatory applications often involves executing many emissions sensitivity cases to quantify impacts of hypothetical scenarios, estimate source contributions or quantify uncertainties. Despite the prevalence of this task, conventional approaches for perturbing emissions in chemical transport models like the Community Multiscale Air Quality (CMAQ) model require extensive offline creation and finalization of alternative emissions input files. This workflow tends to be time-consuming, error-prone, inconsistent among model users and difficult to document while consuming increased computer storage space. The Detailed Emissions Scaling, Isolation, and Diagnostic (DESID) module, a component of CMAQv5.3 and beyond, addresses these limitations by performing these modifications online during the air quality simulation. Further, the model contains an Emission Control Interface which allows users to prescribe both simple and highly complex emissions scaling operations with control over individual or multiple chemical species, emissions sources, and spatial areas of interest. DESID further enhances the transparency of its operations with extensive error-checking and optional gridded output of processed emission fields. These new features are of high value to many air quality applications including routine perturbation studies, atmospheric chemistry research, and coupling with external models (e.g. energy system models, reduced-form models).

Buffer capacity in multiple chemical reaction systems involving solid phases

2006 ◽  
Vol 84 (8) ◽  
pp. 1036-1044 ◽  
Author(s):  
Ilie Fishtik ◽  
Igor Povar
Keyword(s):  
Chemical Reaction ◽  
Buffer Capacity ◽  
Reaction System ◽  
Chemical Species ◽  
Abundant Species ◽  
Stoichiometric Coefficient ◽  
Reaction Systems ◽  
Chemical Reaction Systems ◽  
Chemical Reaction System ◽  
Multiple Chemical

The buffer capacity of a chemical species in a multiple chemical reaction system is discussed in terms of a special class of stoichiometrically unique reactions referred to as response reactions (RERs). More specifically, it is shown that the buffer capacity may be partitioned into a sum of contributions associated with RERs. This finding provides a deeper understanding of the factors that determine the buffer capacity. In particular, the main contributions to the buffer capacity come from the RERs involving the most abundant species. Concomitantly, the RERs approach provides a simple stoichiometric algorithm for the derivation and analysis of the buffer capacity that may be easily implemented into a computer software.Key words: buffer capacity, response reaction, heterogeneous system, stoichiometric coefficient.

scholarly journals A Cahn–Hilliard–Darcy model for tumour growth with chemotaxis and active transport

2016 ◽  
Vol 26 (06) ◽  
pp. 1095-1148 ◽  
Author(s):  
Harald Garcke ◽  
Kei Fong Lam ◽  
Emanuel Sitka ◽  
Vanessa Styles
Keyword(s):  
Active Transport ◽  
Tumour Growth ◽  
Specific Growth ◽  
Matched Asymptotic Expansion ◽  
Transport Mechanisms ◽  
Darcy Model ◽  
Nutrient Density ◽  
Nutrient Diffusion ◽  
Transport Term

Using basic thermodynamic principles we derive a Cahn–Hilliard–Darcy model for tumour growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and proliferation. In contrast to earlier works, the model is based on a volume-averaged velocity and in particular includes active transport mechanisms which ensure thermodynamic consistency. We perform a formally matched asymptotic expansion and develop several sharp interface models. Some of them are classical and some are new which for example include a jump in the nutrient density at the interface. A linear stability analysis for a growing nucleus is performed and in particular the role of the new active transport term is analysed. Numerical computations are performed to study the influence of the active transport term for specific growth scenarios.

Angiogenesis

2016 ◽  
pp. 49-60
Author(s):  
Yull E. Arriaga ◽  
Arthur E. Frankel
Keyword(s):  
Extracellular Matrix ◽  
Tumour Growth ◽  
Predictive Biomarkers ◽  
Biochemical Processes ◽  
Vessel Growth ◽  
Molecular Signals ◽  
Near Future ◽  
Multiple Cells ◽  
Tip Cells ◽  
Tumour Proliferation

Angiogenesis, the process of vessel growth from preexistent blood vessels, is a necessary step in tumour growth and metastasis. The tumour angiogenic process is complex and involves multiple cells including tumour cells, endothelial tip and stalk and phalanx cells, mural pericytes–smooth muscle cells–fibroblasts,and recruited macrophages–neutrophils–marrow progenitors. The molecular signals among these cell participants lead sequentially to breakdown of the extracellular matrix, loosening of endothelial adhesions, invasion of tip cells towards the tumour, proliferation of stalk cells, fusion of neighbouring branches, lumen formation, phalanx quiescence, engagement of pericytes, and maturation of a new extracellular matrix. Multiple, redundant, and interactive molecules achieve each milestone. Therapeutics aimed at inhibiting or modifying tumour angiogenesis have reached clinical practice with modest benefit. Application of knowledge of the biologic and biochemical processes should yield predictive biomarkers and improved antitumour angiogenesis regimens in the near future.

Single Photon Laser Ionization as an In-Situ Diagnostic for MBE Growth

1993 ◽  
Vol 324 ◽  
Author(s):  
April L. Alstrin ◽  
Adina K. Kunz ◽  
Paul G. Strupp ◽  
Stephen R. Leone
Keyword(s):  
Film Growth ◽  
Single Photon ◽  
Chemical Species ◽  
Growth Monitoring ◽  
Laser Ionization ◽  
Mbe Growth ◽  
Single Photon Ionization ◽  
Photon Ionization ◽  
Multiple Chemical

AbstractSingle photon laser ionization time-of-flight mass spectroscopy (SPI-TOFMS) is used to monitor the gaseous fluxes of Ga and Asn, during molecular beam epitaxy of GaAs. This noninvasive and real-time probe measures densities, and hence fluxes, of multiple chemical species impinging on or scattered from a substrate during conventional MBE. With single photon ionization at 118 nm (10.5 eV, ninth harmonic of Nd:YAG laser), the photon energy is large enough to ionize the species, but insufficient to both ionize and fragment. The lack of molecular dissociation of As2 and As4 greatly simplifies the interpretation of mass spectra. Additionally, the geometry of the single photon ionization TOFMS permits simultaneous film growth monitoring using RHEED. Results will be presented on the probing of scattering and desorption of III-V MBE species during GaAs growth. This technique promises to be a valuable in-situ diagnostic for III-V and II-VI MBE.

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