scholarly journals Mathematical Modeling and Numerical Simulation of Atherosclerosis Based on a Novel Surgeon’s View

2021 ◽  
Author(s):  
Meisam Soleimani ◽  
Axel Haverich ◽  
Peter Wriggers
Keyword(s):  
Mathematical Modeling ◽  
Inflammatory Response ◽  
Phase Field ◽  
Mechanical Response ◽  
Type Equation ◽  
The Body ◽  
Vasa Vasorum ◽  
Diffusion Reaction ◽  
Dust Particles ◽  
Driving Mechanism

AbstractThis paper deals with the mathematical modeling of atherosclerosis based on a novel hypothesis proposed by a surgeon, Prof. Dr. Axel Haverich (Circulation 135(3):205–207, 2017). Atherosclerosis is referred as the thickening of the artery walls. Currently, there are two schools of thoughts for explaining the root of such phenomenon: thickening due to substance deposition and thickening as a result of inflammatory overgrowth. The hypothesis favored here is the second paradigm stating that the atherosclerosis is nothing else than the inflammatory response of of the wall tissues as a result of disruption in wall nourishment. It is known that a network of capillaries called vasa vasorum (VV) accounts for the nourishment of the wall in addition to the natural diffusion of nutrient from the blood passing through the lumen. Disruption of nutrient flow to the wall tissues may take place due to the occlusion of vasa vasorums with viruses, bacteria and very fine dust particles such as air pollutants referred to as PM 2.5. They can enter the body through the respiratory system at the first place and then reach the circulatory system. Hence in the new hypothesis, the root of atherosclerotic vessel is perceived as the malfunction of microvessels that nourish the vessel. A large number of clinical observation support this hypothesis. Recently and highly related to this work, and after the COVID-19 pandemic, one of the most prevalent disease in the lungs are attributed to the atherosclerotic pulmonary arteries, see Boyle and Haverich (Eur J Cardio Thorac Surg 58(6):1109–1110, 2020). In this work, a general framework is developed based on a multiphysics mathematical model to capture the wall deformation, nutrient availability and the inflammatory response. For the mechanical response an anisotropic constitutive relation is invoked in order to account for the presence of collagen fibers in the artery wall. A diffusion–reaction equation governs the transport of the nutrient within the wall. The inflammation (overgrowth) is described using a phase-field type equation with a double well potential which captures a sharp interface between two regions of the tissues, namely the healthy and the overgrowing part. The kinematics of the growth is treated by classical multiplicative decomposition of the gradient deformation. The inflammation is represented by means of a phase-field variable. A novel driving mechanism for the phase field is proposed for modeling the progression of the pathology. The model is 3D and fully based on the continuum description of the problem. The numerical implementation is carried out using FEM. Predictions of the model are compared with the clinical observations. The versatility and applicability of the model and the numerical tool allow.

scholarly journals Phase-field gradient theory

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Luis Espath ◽  
Victor Calo
Keyword(s):  
Free Energy ◽  
Field Equation ◽  
Field Gradient ◽  
Phase Field ◽  
Constitutive Relations ◽  
The Body ◽  
Second Grade ◽  
Gradient Theory ◽  
Boundary Edge ◽  
Field Equations

AbstractWe propose a phase-field theory for enriched continua. To generalize classical phase-field models, we derive the phase-field gradient theory based on balances of microforces, microtorques, and mass. We focus on materials where second gradients of the phase field describe long-range interactions. By considering a nontrivial interaction inside the body, described by a boundary-edge microtraction, we characterize the existence of a hypermicrotraction field, a central aspect of this theory. On surfaces, we define the surface microtraction and the surface-couple microtraction emerging from internal surface interactions. We explicitly account for the lack of smoothness along a curve on surfaces enclosing arbitrary parts of the domain. In these rough areas, internal-edge microtractions appear. We begin our theory by characterizing these tractions. Next, in balancing microforces and microtorques, we arrive at the field equations. Subject to thermodynamic constraints, we develop a general set of constitutive relations for a phase-field model where its free-energy density depends on second gradients of the phase field. A priori, the balance equations are general and independent of constitutive equations, where the thermodynamics constrain the constitutive relations through the free-energy imbalance. To exemplify the usefulness of our theory, we generalize two commonly used phase-field equations. We propose a ‘generalized Swift–Hohenberg equation’—a second-grade phase-field equation—and its conserved version, the ‘generalized phase-field crystal equation’—a conserved second-grade phase-field equation. Furthermore, we derive the configurational fields arising in this theory. We conclude with the presentation of a comprehensive, thermodynamically consistent set of boundary conditions.

scholarly journals Simulation of Diffusion Processes in Chemical and Thermal Processing of Machine Parts

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 698
Author(s):  
Kateryna Kostyk ◽  
Michal Hatala ◽  
Viktoriia Kostyk ◽  
Vitalii Ivanov ◽  
Ivan Pavlenko ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Temperature Distribution ◽  
Thermal Treatment ◽  
Diffusion Processes ◽  
Nitrogen Concentration ◽  
The Body ◽  
Functional Dependencies ◽  
Technological Parameters ◽  
Gas Nitriding ◽  
Temperature State

To solve a number of technological issues, it is advisable to use mathematical modeling, which will allow us to obtain the dependences of the influence of the technological parameters of chemical and thermal treatment processes on forming the depth of the diffusion layers of steels and alloys. The paper presents mathematical modeling of diffusion processes based on the existing chemical and thermal treatment of steel parts. Mathematical modeling is considered on the example of 38Cr2MoAl steel after gas nitriding. The gas nitriding technology was carried out at different temperatures for a duration of 20, 50, and 80 h in the SSHAM-12.12/7 electric furnace. When modeling the diffusion processes of surface hardening of parts in general, providing a specifically given distribution of nitrogen concentration over the diffusion layer’s depth from the product’s surface was solved. The model of the diffusion stage is used under the following assumptions: The diffusion coefficient of the saturating element primarily depends on temperature changes; the metal surface is instantly saturated to equilibrium concentrations with the saturating atmosphere; the surface layer and the entire product are heated unevenly, that is, the product temperature is a function of time and coordinates. Having satisfied the limit, initial, and boundary conditions, the temperature distribution equations over the diffusion layer’s depth were obtained. The final determination of the temperature was solved by an iterative method. Mathematical modeling allowed us to get functional dependencies for calculating the temperature distribution over the depth of the layer and studying the influence of various factors on the body’s temperature state of the body.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

scholarly journals Carbohydrate response element binding protein (ChREBP) modulates the inflammatory response of mesangial cells in response to glucose

2018 ◽  
Vol 38 (6) ◽  
Author(s):  
Yan Chen ◽  
Yan-Jun Wang ◽  
Ying Zhao ◽  
Jin-Cheng Wang
Keyword(s):  
Diabetes Mellitus ◽  
Inflammatory Response ◽  
Mesangial Cells ◽  
Binding Protein ◽  
The Body ◽  
Mrna Levels ◽  
Diabetic Mice ◽  
Response Element ◽  
Tnf Α ◽  
Element Binding Protein

Diabetic nephropathy (DN) is one of the most devastating complications of diabetes mellitus. Carbohydrate response element binding protein (ChREBP) is a basic helix–loop–helix leucine zipper transcription factor that primarily mediates glucose homeostasis in the body. The present study investigated the role of ChREBP in the pathogenesis of DN. The expression of ChREBP was detected in patients with type 2 diabetes mellitus (T2DM), diabetic mice, and mesangial cells. ELISA was used to measure cytokine production in mesangial cells. Flow cytometry analysis was performed to detect the apoptosis of mesangial cells in the presence of high glucose. The expression levels of ChREBP and several cytokines (TNF-α, IL-1β, and IL-6) were up-regulated in T2DM patients. The mRNA and protein levels of ChREBP were also significantly elevated in the kidneys of diabetic mice. Moreover, glucose treatment promoted mRNA levels of TNF-α, IL-1β, and IL-6 in mesangial cells. Glucose stimulation induced significant apoptosis of SV40 MES 13 cells. In addition, transfection with ChREBP siRNA significantly inhibited ChREBP expression. Consequently, the inflammatory responses and apoptosis were inhibited in SV40 MES 13 cells. These results demonstrated that ChREBP could mediate the inflammatory response and apoptosis of mesangial cells, suggesting that ChREBP may be involved in the pathogenesis of DN.

scholarly journals Systemic inflammatory response syndrome and multiple-organ damage / dysfunction in complicated canine babesiosis

2001 ◽  
Vol 72 (3) ◽  
Author(s):  
C. Welzl ◽  
A.L. Leisewitz ◽  
L.S. Jacobson ◽  
T. Vaughan-Scott ◽  
E. Myburgh
Keyword(s):  
Central Nervous System ◽  
Nervous System ◽  
Systemic Inflammatory Response Syndrome ◽  
Inflammatory Response ◽  
Renal Involvement ◽  
Organ Damage ◽  
Multiple Organ ◽  
Systemic Inflammatory Response ◽  
The Body ◽  
Increased Risk

This study was designed to document the systemic inflammatory response syndrome (SIRS) and multiple-organ dysfunction syndrome (MODS) in dogs with complicated babesiosis, and to assess their impact on outcome. Ninety-one cases were evaluated retro-spectively for SIRS and 56 for MODS. The liver, kidneys, lungs, central nervous system and musculature were assessed. Eighty-seven percent of cases were SIRS-positive. Fifty-two percent of the cases assessed for organ damage had single-organ damage and 48 % had MODS. Outcome was not significantly affected by either SIRS or MODS, but involvement of specific organs had a profound effect. Central nervous system involvement resulted in a 57 times greater chance of death and renal involvement in a 5-fold increased risk compared to all other complications. Lung involvement could not be statistically evaluated owing to co-linearity with other organs, but was associated with high mortality. Liver and muscle damage were common, but did not significantly affect outcome. There are manysimilarities between the observations in this study and previous human and animal studies in related fields, lending additional support to the body of evidence for shared underlying pathophysiological mechanisms in systemic inflammatory states.

scholarly journals The Effects of Combined Therapy With Metformin and Hydroxypropyl-β-Cyclodextrin in a Mouse Model of Niemann-Pick Disease Type C1

2022 ◽  
Vol 12 ◽  
Author(s):  
Jiang Du ◽  
Xinlei Liu ◽  
Yan Zhang ◽  
Xiaojing Han ◽  
Chunya Ma ◽  
...  
Keyword(s):  
Body Weight ◽  
Inflammatory Response ◽  
Mouse Model ◽  
Survival Time ◽  
Free Cholesterol ◽  
Disease Type ◽  
The Body ◽  
Niemann Pick Disease ◽  
Niemann Pick ◽  
Pick Disease

Niemann–Pick disease type C1 (NPC1) is a neurodegenerative disorder characterized by lysosomal storage of free cholesterol. 2-Hydroxypropyl-β-cyclodextrin (HPβCD) is a cyclic oligosaccharide derivative that is being developed to treat NPC1. Recently, metformin was reported to be beneficial in various neurodegenerative diseases, such as Alzheimer’s and Huntington’s diseases. In this study, we examined the effects of combined treatment with HPβCD and metformin on Npc1−/− mice. Unfortunately, body weight and survival rates showed that cotreatment with metformin did not extend survival time and increase the body weight of HPβCD-treated Npc1−/− mice. However, cotreatment with metformin reduced inflammatory response and inhibited the proinflammatory cytokine release in the brain, liver and spleen of HPβCD-treated Npc1−/− mice. Furthermore, metformin did not reduce the free cholesterol levels in Npc1−/− brain tissue or fibroblasts. In conclusion, our results demonstrate that metformin does not show beneficial effects on body weight or survival time but reduced the inflammatory response in a mouse model of NPC1 when combined with HPβCD.

scholarly journals RESEARCH OF VIBRATION MACHINES DYNAMICS FOR PRODUCT SURFACES PROCESSING BY MATHEMATICAL MODELING

2020 ◽  
pp. 35-43
Author(s):  
Volodymyr Topilnytskyy ◽  
Yaroslav Kusyi ◽  
Dariya Rebot
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Surface Treatment ◽  
Lagrange Equation ◽  
The Body ◽  
Technological Problem ◽  
Surface Processing ◽  
Approximate Methods ◽  
Vibration Machine ◽  
Working Chamber

The article describes the methodology for the study of the dynamics of vibrating machines for surface processing of products by mathematical modeling, which is presented in four main stages. The first stage: analysis of classes of vibrating machines for surface treatment of products, choice of basic for solving the technological problem, project of a unified calculation scheme of the machine. The second stage: development of a nonlinear mathematical model for describing the dynamics of the vibration machine working body and its filling, development of elements of automated calculations of the machine. The third stage: the study of the influence of the parameters of the vibrating machine, product sets and tools (with their various combinations) on the factors of the intensity of products surface processing. The fourth stage: recommendations for choosing vibrating machine parameters and machining bodies that will maximize the processing performance of products with the selected intensity criterion. A mathematical model for describing the motion of a vibrating machine for surface treatment of articles by a set of unrelated bodies of small size is created. It has two unbalance units that generate oscillations of its working body and a spring suspension-mounting of the working chamber (container). The model is parametric and nonlinear, incorporating key dynamic, kinematic and geometric parameters of the vibrating machine in symbolic format. It is constructed by: descriptions of the plane-parallel movement of the mechanical system, the rotational motion of the material point and the body; second-order Lagrange equation; asymptotic (approximate) methods of nonlinear mechanics. With the help of the model it is possible: to describe the oscillatory movement of the working chamber (container) of the vibrating machine; to study the influence of the machine parameters on the efficiency of performance of the set technological task, the conditions of occurrence of non-stationary modes of operation of the vibrating machine and the ways of their regulation.

scholarly journals Investigating the Wound Healing Potential of the Polyherbal Gels Prepared with Ficus Extract

2018 ◽  
Vol 8 (2) ◽  
pp. 13-16
Author(s):  
Mahender K ◽  
Ravi D ◽  
Chaitanya Kumar K ◽  
Mothilal K
Keyword(s):  
Wound Healing ◽  
Inflammatory Response ◽  
Human Body ◽  
Healing Process ◽  
The Body ◽  
Wound Healing Process ◽  
Aqueous Extracts ◽  
Standard Drug ◽  
Carbopol Gel ◽  
Ficus Benghalensis

Wounds are nothing but any damage to the tissue or skin that can be healed. The wound healing process is usually built in the human body to self heal many wounds. When there is an injury in the body, there is an inflammatory response that is generated in the body, and the cells begin to raise the collagen levels in the skin which enables to increase the healing process. Ficus species of plants are famous for their potency to treat diseases in various Indian systems of medicine and the tree is commonly called as a banyan. Especially the plant in the species benghalensis is used to treat rheumatism, wounds and other skin related problems like an ulcer. The herbal gels were prepared using the incorporation of the aqueous extracts of the plant Ficus benghalensis into carbopol gel. They were investigated for the wound healing potential compared to the betadine drug standard. The gels at a concentration 200mg/g of the gel showed better activity compared to the gel at 100mg/g and the standard drug, betadine.

scholarly journals Applying Methods of Mathematical Modeling in Cattle Breeding

2019 ◽  
Vol 8 (12) ◽  
pp. 185-187 ◽  
Keyword(s):  
Mathematical Modeling ◽  
Animal Husbandry ◽  
The Body ◽  
Body Parts ◽  
Method Of Least Squares ◽  
Linear Measurements ◽  
Cattle Breeding ◽  
Modern Methods ◽  
Meat Productivity ◽  
The Relationship

In this manuscript has presented the results of applying modern methods of mathematical modeling in animal husbandry. To conduct the research has used the method of least squares, which has reflected in the work by approximation probabilistic non-linear relations, making it possible to establish the relationship between different measurements the body parts of animal and meat productivity, and linear measurements of the udder.

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