scholarly journals A Two-Dimensional Model of Hypertension-Induced Arterial Remodeling With Account for Stress Interaction Between Elastin and Collagen

2019 ◽  
Vol 142 (4) ◽  
Author(s):  
Alexander Rachev ◽  
Tarek Shazly
Keyword(s):  
Mixture Theory ◽  
Natural State ◽  
Arterial Remodeling ◽  
Two Dimensional ◽  
Structural Reorganization ◽  
Constrained Mixture Theory ◽  
Novel Structure ◽  
Constrained Mixture ◽  
Arterial Tissue ◽  
The Individual

Abstract We propose a novel structure-based two-dimensional (2D) mathematical model of hypertension-induced arterial remodeling. The model is built in the framework of the constrained mixture theory and global growth approach, utilizing a recently proposed structure-based constitutive model of arterial tissue that accounts for the individual natural configurations of and stress interaction between elastin and collagen. The basic novel predictive result is that provided remodeling causes a change in the elastin/collagen mass fraction ratio, it leads to a structural reorganization of collagen that manifests as an altered fiber undulation and a change in direction of the helically oriented fibers in the tissue natural state. Results obtained from the illustrative simulations for a porcine renal artery show that when remodeling is complete the collagen reorganization might have significant effects on the initial arterial geometry and mechanical properties of the arterial tissue. The proposed model has potential to describe and advance mechanistic understanding of adaptive arterial remodeling, promote the continual refinement of mathematical models of arterial remodeling, and provide motivation for new avenues of experimental investigation.

scholarly journals A constituent-based model of age-related changes in conduit arteries

2011 ◽  
Vol 301 (4) ◽  
pp. H1286-H1301 ◽  
Author(s):  
Alkiviadis Tsamis ◽  
Alexander Rachev ◽  
Nikos Stergiopulos
Keyword(s):  
Mechanical Properties ◽  
Time Course ◽  
Present Report ◽  
Finite Elasticity ◽  
Mixture Theory ◽  
Constrained Mixture Theory ◽  
Age Related ◽  
Constrained Mixture ◽  
Arterial Tissue ◽  
Age Related Changes

In the present report, a constituent-based theoretical model of age-related changes in geometry and mechanical properties of conduit arteries is proposed. The model was based on the premise that given the time course of the load on an artery and the accumulation of advanced glycation end-products in the arterial tissue, the initial geometric dimensions and properties of the arterial tissue can be predicted by a solution of a boundary value problem for the governing equations that follow from finite elasticity, structure-based constitutive modeling within the constrained mixture theory, continuum damage theory, and global growth approach for stress-induced structure-based remodeling. An illustrative example of the age-related changes in geometry, structure, composition, and mechanical properties of a human thoracic aorta is considered. Model predictions were in good qualitative agreement with available experimental data in the literature. Limitations and perspectives for refining the model are discussed.

scholarly journals A Constrained Mixture Theory Model to Study Autoregulation in the Coronary Circulation

2020 ◽  
Author(s):  
Hamidreza Gharahi ◽  
Daniel A. Beard ◽  
C. Alberto Figueroa ◽  
Seungik Baek
Keyword(s):  
Coronary Circulation ◽  
Mixture Theory ◽  
Extensive Literature ◽  
Optimization Approach ◽  
List Type ◽  
Growth And Remodeling ◽  
Constrained Mixture Theory ◽  
Constrained Mixture ◽  
Wide Range

AbstractCoronary autoregulation is a short-term response manifested by a relatively constant flow over a wide range of perfusion pressures for a given metabolic state. This phenomenon is thought to be facilitated through a combination of mechanisms, including myogenic, shear dependent, and metabolic controls. The study of coronary autoregulation is challenging due to the coupled nature of the mechanisms and their differential effects through the coronary tree. In this paper, we developed a novel framework to study coronary autoregulation based on the constrained mixture theory. This structurally-motivated autoregulation model required calibration of anatomical and structural parameters of coronary trees via a homeostatic optimization approach using extensive literature data. Autoregulation was then simulated for two different coronary trees: subepicardial and subendocardial. The structurally calibrated model reproduced available baseline hemodynamics and autoregulation data for each coronary tree. The autoregulation analysis showed that the diameter of the intermediate and small arterioles varies the most in response to changes in perfusion pressure. Finally, we demonstrated the utility of the model in two application examples: 1) response to drops in epicardial pressure, and 2) response to drug infusion in the coronary arteries. The proposed structurally-motivated model could be extended to study long-term growth and remodeling in the coronary circulation in response to hypertension, atherosclerosis, etc.Key pointsCoronary autoregulation is defined as the capability of the coronary circulation to maintain the blood supply to the heart over a range of perfusion pressures. This phenomenon is facilitated through intrinsic mechanisms that control the vascular resistance by regulating the mechanical function of smooth muscle cells. Understanding the mechanisms involved in coronary autoregulation is one of the most fundamental questions in coronary physiology.This paper presents a structurally-motivated coronary autoregulation model that uses a nonlinear continuum mechanics approach to account for the morphometry and vessel wall composition in two coronary trees in the subepicardial and subendocardial layers.The model is calibrated against diverse experimental data from literature and is used to study heterogeneous autoregulatory response in the coronary trees. This model drastically differs from previous models, which relied on lumped parameter model formulations, and is suited to the study of long-term pathophysiological growth and remodeling phenomena in coronary vessels.

scholarly journals VASCULAR MECHANICS, MECHANOBIOLOGY, AND REMODELING

2009 ◽  
Vol 09 (02) ◽  
pp. 243-257 ◽  
Author(s):  
J. D. HUMPHREY
Keyword(s):  
Constitutive Relations ◽  
Mixture Theory ◽  
Clinical Treatment ◽  
Vascular Mechanics ◽  
Growth And Remodeling ◽  
Theoretical Frameworks ◽  
Future Directions ◽  
Constrained Mixture Theory ◽  
Constrained Mixture ◽  
Recent Developments

Arteries exhibit a remarkable ability to adapt in response to sustained alterations in hemodynamic loading as well as to disease, injury, and clinical treatment. A better understanding of such adaptations will be aided greatly by formulating, testing, and refining appropriate theoretical frameworks for modeling the biomechanics and associated mechanobiology. The goal of this brief review is to highlight some recent developments in the use of a constrained mixture theory of arterial growth and remodeling, with particular attention to the requisite constitutive relations, and to highlight future directions of needed research.

scholarly journals EXPRESS: Sources of Variation In Search and Foraging A Theoretical Perspective

2021 ◽  
pp. 174702182110503
Author(s):  
Alastair David Smith ◽  
Carlo De Lillo
Keyword(s):  
Spatial Scales ◽  
Theoretical Perspective ◽  
Search Space ◽  
Visual Exploration ◽  
Two Dimensional ◽  
Search Behaviour ◽  
Wide Range ◽  
Search Processes ◽  
Sources Of Variation ◽  
The Individual

Search – the problem of exploring a space of alternatives in order to identify target goals – is a fundamental behaviour for many species. Although its foundation lies in foraging, most studies of human search behaviour have been directed towards understanding the attentional mechanisms that underlie the efficient visual exploration of two-dimensional scenes. With this review, we aim to characterise how search behaviour can be explained across a wide range of contexts, environments, spatial scales, and populations, both typical and atypical. We first consider the generality of search processes across psychological domains. We then review studies of interspecies differences in search. Finally, we explore in detail the individual and contextual variables that affect visual search and related behaviours in established experimental psychology paradigms. Despite the heterogeneity of the findings discussed, we identify that variations in control processes, along with the ability to regulate behaviour as a function of the structure of search space and the sampling processes adopted, to be central to explanations of variations in search behaviour. We propose a tentative theoretical model aimed at integrating these notions and close by exploring questions that remain unaddressed.

Two-dimensional gel electrophoresis of human brain proteins. I. Technique and nomenclature of proteins.

1982 ◽  
Vol 28 (4) ◽  
pp. 782-789 ◽  
Author(s):  
D E Comings
Keyword(s):  
Human Brain ◽  
Gel Electrophoresis ◽  
Urea Solution ◽  
Two Dimensional ◽  
Two Dimensional Gel Electrophoresis ◽  
Polypeptide Patterns ◽  
Normal Individuals ◽  
Molecular Masses ◽  
Group B ◽  
The Individual

Abstract To understand at a molecular level the basis of the normal and pathological genetic differences between individuals it is necessary to begin a detailed two-dimensional gel electrophoretic mapping of the proteins of the human brain in normal individuals and those with various genetic neurological disorders. The present study is an examination of the polypeptide patterns of extracts of the human brain made with 9 mol/L urea solution. Details of the technique and the nomenclature of the patterns obtained are presented. the gels are separated into 20 sub-sections, based on standards with known molecular masses and isoelectric points. Groups of polypeptides within these sub-sections are identified by a number and a letter; the individual proteins are identified by a number. Thus, protein 1 in subsection 8, group b, would be designated 8b: 1. Subsequent papers in this series identify many of these proteins; show which proteins belong to the cytosol, synaptosome, myelin, and other brain fractions; show how these patterns vary between normal individuals and those with different neurological and psychiatric conditions; examine the effect of severe gliosis; and present the results of non-equilibrium gel electrophoresis for the more basic proteins.

Preface

1997 ◽  
Vol 11 (07) ◽  
pp. 1023-1024
Author(s):  
Serge Miguet ◽  
Annick Montanvert ◽  
P. S. P. Wang
Keyword(s):  
Finite State Machine ◽  
Finite Automata ◽  
Upper Bounds ◽  
Two Dimensional ◽  
Turing Machines ◽  
Closure Properties ◽  
Working Space ◽  
Finite State ◽  
The Individual ◽  
Alternating Turing Machines

Several nonclosure properties of each class of sets accepted by two-dimensional alternating one-marker automata, alternating one-marker automata with only universal states, nondeterministic one-marker automata, deterministic one-marker automata, alternating finite automata, and alternating finite automata with only universal states are shown. To do this, we first establish the upper bounds of the working space used by "three-way" alternating Turing machines with only universal states to simulate those "four-way" non-storage machines. These bounds provide us a simplified and unified proof method for the whole variants of one-marker and/or alternating finite state machine, without directly analyzing the complex behavior of the individual four-way machine on two-dimensional rectangular input tapes. We also summarize the known closure properties including Boolean closures for all the variants of two-dimensional alternating one-marker automata.

scholarly journals Dynamics in Braess Paradox with Nonimpulsive Commuters

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Arianna Dal Forno ◽  
Ugo Merlone ◽  
Viktor Avrutin
Keyword(s):  
Fixed Point ◽  
Global Attractivity ◽  
Unique Fixed Point ◽  
Social Dilemma ◽  
Rigorous Proof ◽  
Two Dimensional ◽  
Cost Difference ◽  
Braess Paradox ◽  
The Individual ◽  
The Cost

In Braess paradox the addiction of an extra resource creates a social dilemma in which the individual rationality leads to collective irrationality. In the literature, the dynamics has been analyzed when considering impulsive commuters, i.e., those who switch choice regardless of the actual difference between costs. We analyze a dynamical version of the paradox with nonimpulsive commuters, who change road proportionally to the cost difference. When only two roads are available, we provide a rigorous proof of the existence of a unique fixed point showing that it is globally attracting even if locally unstable. When a new road is added the system becomes discontinuous and two-dimensional. We prove that still a unique fixed point exists, and its global attractivity is numerically evidenced, also when the fixed point is locally unstable. Our analysis adds a new insight in the understanding of dynamics in social dilemma.

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