A Poroelastic-Viscoelastic Limit for Modeling Brain Biomechanics

2015 ◽  
Vol 1753 ◽  
Author(s):  
Md. Mehedi Hasan ◽  
Corina S. Drapaca
Keyword(s):  
Brain Tissue ◽  
Solid Phase ◽  
Soil Mechanics ◽  
Equations Of Motion ◽  
Elastic Solid ◽  
Two Phase ◽  
Fluid Mixture ◽  
Brain Responses ◽  
Brain Biomechanics ◽  
The Central Nervous System

ABSTRACTThe brain, a mixture of neural and glia cells, vasculature, and cerebrospinal fluid (CSF), is one of the most complex organs in the human body. To understand brain responses to traumatic injuries and diseases of the central nervous system it is necessary to develop accurate mathematical models and corresponding computer simulations which can predict brain biomechanics and help design better diagnostic and therapeutic protocols. So far brain tissue has been modeled as either a poroelastic mixture saturated by CSF or as a (visco)-elastic solid. However, it is not obvious which model is more appropriate when investigating brain mechanics under certain physiological and pathological conditions. In this paper we study brain’s mechanics by using a Kelvin-Voight (KV) model for a one-phase viscoelastic solid and a Kelvin-Voight-Maxwell-Biot (KVMB) model for a two-phase (solid and fluid) mixture, and explore the limit between these two models. To account for brain’s evolving microstructure, we replace in the equations of motion the classic integer order time derivatives by Caputo fractional order derivatives and thus introduce corresponding fractional KV and KVMB models. As in soil mechanics we use the displacements of the solid phase in the classic (fractional) KVMB model and respectively of the classic (fractional) KV model to define a poroelastic-viscoelastic limit. Our results show that when the CSF and brain tissue in the classic (fractional) KVMB model have similar speeds, then the model is indistinguishable from its equivalent classic (fractional) KV model.

On the Natural Lubrication of Synovial Joints: Normal and Degenerate

1977 ◽  
Vol 99 (2) ◽  
pp. 163-172 ◽  
Author(s):  
Joseph M. Mansour ◽  
Van C. Mow
Keyword(s):  
Articular Cartilage ◽  
Solid Phase ◽  
Articular Surface ◽  
Moving Load ◽  
Frictional Resistance ◽  
Elastic Solid ◽  
Surface Load ◽  
Two Phase ◽  
Tissue Properties ◽  
Synovial Joints

Fluid flow and mass transport mechanisms associated with articular cartilage function are important biomechanical processes of normal and pathological synovial joints. A three-layer permeable, two-phase medium of an incompressible fluid and a linear elastic solid are used to model the flow and deformational behavior of articular cartilage. The frictional resistance of the relative motion of the fluid phase with respect to the solid phase is given by a linear diffusive dissipation term. The subchondral bony substrate is represented by an elastic solid. The three-layer model of articular cartilage is chosen because of the known histological, ultrastructural, and biomechanical variations of the tissue properties. The calculated flow field shows that for material properties of normal healthy articular cartilage the tissue creates a naturally lubricated surface. The movement of the interstitial fluid at the surface is circulatory in manner, being exuded in front and near the leading half of the moving surface load and imbibed behind and near the trailing half of the moving load. The flow fields of healthy tissues are capable of sustaining a film of fluid at the articular surface whereas pathological tissues cannot.

A regularized isothermal phase-field model of two-phase solid–fluid mixture and its spatial dissipative discretization equations

2021 ◽  
Vol 36 (4) ◽  
pp. 197-217
Author(s):  
Vladislav Balashov
Keyword(s):  
Phase Field ◽  
Solid Phase ◽  
Numerical Study ◽  
Strain Tensor ◽  
Phase Field Model ◽  
Evolutionary Equation ◽  
Two Phase ◽  
Fluid Mixture ◽  
Component Mixture ◽  
Eulerian Description

Abstract The present paper is devoted to a model describing a two-phase isothermal mixture, in which one of the phases obeys solid-like (namely, elastic) rheology. A fully Eulerian description is considered. To describe the stress–strain behaviour of the solid phase the elastic energy term is added to the Helmholtz free energy. The term depends on Almansi strain tensor. In its turn, the strain tensor is defined as the solution of the corresponding evolutionary equation. Considered model belongs to the phase field family. Formally it describes two-component mixture and uses mass densities of the components as order parameters. A distinctive feature of the considered model is its preliminary regularization according to the quasi-hydrodynamic framework. The dissipativity in total energy is proved when periodic boundary conditions are imposed. A spatial dissipative semi-discrete (continuous in time and discrete in space) scheme based on staggered grids is suggested. The theoretical results remain valid in the absence of the regularization. The results of a numerical study in a 2D setting are presented.

Equations of Motion of Two-Phase Variable Mass Systems With Solid Base

1994 ◽  
Vol 61 (4) ◽  
pp. 855-860 ◽  
Author(s):  
F. O. Eke ◽  
Song-Min Wang
Keyword(s):  
Solid Phase ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Fluid Phase ◽  
Solid Base ◽  
Phase Variable ◽  
Dynamical Equations ◽  
Two Phase ◽  
Attitude Stability ◽  
Variable Mass Systems

This paper develops dynamical equations for variable mass systems that can be viewed, at any given instant, as comprising a solid phase and a fluid phase. The equations of translational and rotational motion are presented, and several versions of each are given. It is shown that some versions have major advantages over others because they involve parameters that are relatively easy to estimate in practical problems, and make close-form solutions possible without the usual penalty of drastic simplifying assumptions. A simple rocket example is presented, and shows that instability cannot be ruled out for such systems. It is shown that system and combustion chamber geometry play a crucial role in the attitude stability of such systems.

Modeling Welding by Surface Heating

1992 ◽  
Vol 114 (4) ◽  
pp. 439-449 ◽  
Author(s):  
I. C. Sheng ◽  
Y. Chen
Keyword(s):  
Energy Equation ◽  
Solid Phase ◽  
Equations Of Motion ◽  
Fluid Phase ◽  
Equation Of Motion ◽  
Avrami Equation ◽  
Moving Heat Source ◽  
Stress Evolution ◽  
Fluid Mixture ◽  
Traction Boundary Conditions

A mathematical model has been developed in describing the temperature distribution, the flow of the molten fluid and the stress field in the solid during welding. In modeling the properties of the material during welding, the solid phase is assumed to behave as a thermoviscoplastic solid obeying Bodner-Partom/Walker type constitutive equation, whereas the fluid phase as a thermoviscous incompressible fluid. Three regions exist: pure solid, pure fluid, and the transition (solid-fluid mixture). In the formulation of the boundary value problem, the energy equation is coupled to the equation of motion through the terms of mechanical work and the latent heat of the phases, whereas the equations of motion of the solid and the fluid are decoupled. Appropriate thermal and traction boundary conditions are detailed in the text. Phase transformation activities during cooling are monitored by CCT diagram and Avrami equation. An arbitrary Lagrangian and Eulerian method is used to accommodate the kinematic description of both the solid and the fluid phases. A representative plane perpendicular to the moving heat source is analyzed. Results of sample calculations are presented to show the temperature and the stress evolution in time. Residual stress and microstructure patterns are presented.

SYNTHESIS OF HYDROGEN IN ACOUSTOPLASMA DISCHARGE IN A LIQUID-PHASE STREAM

2019 ◽  
pp. 42-48 ◽  
Author(s):  
N. A. Bulychev
Keyword(s):  
Liquid Phase ◽  
Organic Compounds ◽  
Electrode Materials ◽  
Solid Phase ◽  
Plasma Discharge ◽  
Raw Material ◽  
Two Phase ◽  
Reduced Pressure ◽  
External Power Source ◽  
Phase Medium

In this paper, the plasma discharge in a high-pressure fluid stream in order to produce gaseous hydrogen was studied. Methods and equipment have been developed for the excitation of a plasma discharge in a stream of liquid medium. The fluid flow under excessive pressure is directed to a hydrodynamic emitter located at the reactor inlet where a supersonic two-phase vapor-liquid flow under reduced pressure is formed in the liquid due to the pressure drop and decrease in the flow enthalpy. Electrodes are located in the reactor where an electric field is created using an external power source (the strength of the field exceeds the breakdown threshold of this two-phase medium) leading to theinitiation of a low-temperature glow quasi-stationary plasma discharge.A theoretical estimation of the parameters of this type of discharge has been carried out. It is shown that the lowtemperature plasma initiated under the flow conditions of a liquid-phase medium in the discharge gap between the electrodes can effectively decompose the hydrogen-containing molecules of organic compounds in a liquid with the formation of gaseous products where the content of hydrogen is more than 90%. In the process simulation, theoretical calculations of the voltage and discharge current were also made which are in good agreement with the experimental data. The reaction unit used in the experiments was of a volume of 50 ml and reaction capacity appeared to be about 1.5 liters of hydrogen per minute when using a mixture of oxygen-containing organic compounds as a raw material. During their decomposition in plasma, solid-phase products are also formed in insignificant amounts: carbon nanoparticles and oxide nanoparticles of discharge electrode materials.

The influence of the Stokes and Archimedes forces on the stability of a two-phase flow

2003 ◽  
Vol 3 ◽  
pp. 266-270
Author(s):  
B.H. Khudjuyerov ◽  
I.A. Chuliev
Keyword(s):  
Spectral Method ◽  
Stability Region ◽  
Gas Flow ◽  
Two Phase Flow ◽  
Solid Phase ◽  
Stability Characteristic ◽  
Phase Flow ◽  
Two Phase ◽  
The Stability

The problem of the stability of a two-phase flow is considered. The solution of the stability equations is performed by the spectral method using polynomials of Chebyshev. A decrease in the stability region gas flow with the addition of particles of the solid phase. The analysis influence on the stability characteristic of Stokes and Archimedes forces.

scholarly journals Altered urinary tetrahydroisoquinoline derivatives in patients with Tourette syndrome: reflection of dopaminergic hyperactivity?

2020 ◽  
Author(s):  
Philipp Capetian ◽  
Veit Roessner ◽  
Caroline Korte ◽  
Susanne Walitza ◽  
Franz Riederer ◽  
...  
Keyword(s):  
Tourette Syndrome ◽  
Diagnostic Value ◽  
Tic Disorders ◽  
Operating Characteristics ◽  
Roc Curve Analysis ◽  
Two Phase ◽  
Dopaminergic Neurotransmission ◽  
Hyperactivity Disorder ◽  
The Central Nervous System ◽  
Chronic Tic Disorders

AbstractTetrahydroisoquinolines (TIQs) such as salsolinol (SAL), norsalsolinol (NSAL) and their methylated derivatives N-methyl-norsalsolinol (NMNSAL) and N-methyl-salsolinol (NMSAL), modulate dopaminergic neurotransmission and metabolism in the central nervous system. Dopaminergic neurotransmission is thought to play an important role in the pathophysiology of chronic tic disorders, such as Tourette syndrome (TS). Therefore, the urinary concentrations of these TIQ derivatives were measured in patients with TS and patients with comorbid attention-deficit/hyperactivity disorder (TS + ADHD) compared with controls. Seventeen patients with TS, 12 with TS and ADHD, and 19 age-matched healthy controls with no medication took part in this study. Free levels of NSAL, NMNSAL, SAL, and NMSAL in urine were measured by a two-phase chromatographic approach. Furthermore, individual TIQ concentrations in TS patients were used in receiver-operating characteristics (ROC) curve analysis to examine the diagnostic value. NSAL concentrations were elevated significantly in TS [434.67 ± 55.4 nmol/l (standard error of mean = S.E.M.), two-way ANOVA, p < 0.0001] and TS + ADHD patients [605.18 ± 170.21 nmol/l (S.E.M.), two-way ANOVA, p < 0.0001] compared with controls [107.02 ± 33.18 nmol/l (S.E.M.), two-way ANOVA, p < 0.0001] and NSAL levels in TS + ADHD patients were elevated significantly in comparison with TS patients (two-way ANOVA, p = 0.017). NSAL demonstrated an AUC of 0.93 ± 0.046 (S.E.M) the highest diagnostic value of all metabolites for the diagnosis of TS. Our results suggest a dopaminergic hyperactivity underlying the pathophysiology of TS and ADHD. In addition, NSAL concentrations in urine may be a potential diagnostic biomarker of TS.

scholarly journals CFD Simulation of Solid Suspension for a Liquid–Solid Industrial Stirred Reactor

2021 ◽  
Vol 11 (12) ◽  
pp. 5705
Author(s):  
Adrian Stuparu ◽  
Romeo Susan-Resiga ◽  
Alin Bosioc
Keyword(s):  
Chemical Reaction ◽  
Cfd Simulation ◽  
Simulation Analysis ◽  
Solid Phase ◽  
Initial Conditions ◽  
Chemical Reactor ◽  
Liquid Mixtures ◽  
Multiphase Model ◽  
Chemical Product ◽  
Two Phase

The present study examines the possibility of using an industrial stirred chemical reactor, originally employed for liquid–liquid mixtures, for operating with two-phase liquid–solid suspensions. It is critical when obtaining a high-quality chemical product that the solid phase remains suspended in the liquid phase long enough that the chemical reaction takes place. The impeller was designed for the preparation of a chemical product with a prescribed composition. The present study aims at finding, using a numerical simulation analysis, if the performance of the original impeller is suitable for obtaining a new chemical product with a different composition. The Eulerian multiphase model was employed along with the renormalization (RNG) k-ε turbulence model to simulate liquid–solid flow with a free surface in a stirred tank. A sliding-mesh approach was used to model the impeller rotation with the commercial CFD code, FLUENT. The results obtained underline that 25% to 40% of the solid phase is sedimented on the lower part of the reactor, depending on the initial conditions. It results that the impeller does not perform as needed; hence, the suspension time of the solid phase is not long enough for the chemical reaction to be properly completed.

scholarly journals In Vivo and In Vitro Toxicodynamic Analyses of New Quinolone-and Nonsteroidal Anti-Inflammatory Drug-Induced Effects on the Central Nervous System

1999 ◽  
Vol 43 (5) ◽  
pp. 1091-1097 ◽  
Author(s):  
Hideki Kita ◽  
Hirotami Matsuo ◽  
Hitomi Takanaga ◽  
Junichi Kawakami ◽  
Koujirou Yamamoto ◽  
...  
Keyword(s):  
Brain Tissue ◽  
Threshold Concentration ◽  
Current Response ◽  
Drug Induced ◽  
Inhibition Ratio ◽  
New Quinolones ◽  
The Central Nervous System ◽  
Anti Inflammatory

ABSTRACT We investigated the correlation between an in vivo isobologram based on the concentrations of new quinolones (NQs) in brain tissue and the administration of nonsteroidal anti-inflammatory drugs (NSAIDs) for the occurrence of convulsions in mice and an in vitro isobologram based on the concentrations of both drugs for changes in the γ-aminobutyric acid (GABA)-induced current response in Xenopus oocytes injected with mRNA from mouse brains in the presence of NQs and/or NSAIDs. After the administration of enoxacin (ENX) in the presence or absence of felbinac (FLB), ketoprofen (KTP), or flurbiprofen (FRP), a synergistic effect was observed in the isobologram based on the threshold concentration in brain tissue between mice with convulsions and those without convulsions. The three NSAIDs did not affect the pharmacokinetic behavior of ENX in the brain. However, the ENX-induced inhibition of the GABA response in the GABAA receptor expressed in Xenopus oocytes was enhanced in the presence of the three NSAIDs. The inhibition ratio profiles of the GABA responses for both drugs were analyzed with a newly developed toxicodynamic model. The inhibitory profiles for ENX in the presence of NSAIDs followed the order KTP (1.2 μM) > FRP (0.3 μM) > FLB (0.2 μM). These were 50- to 280-fold smaller than those observed in the absence of NSAIDs. The inhibition ratio (0.01 to 0.02) of the GABAA receptor in the presence of both drugs was well-fitted to the isobologram based on threshold concentrations of both drugs in brain tissue between mice with convulsions and those without convulsions, despite the presence of NSAIDs. In mice with convulsions, the inhibitory profiles of the threshold concentrations of both drugs in brain tissue of mice with convulsions and those without convulsions can be predicted quantitatively by using in vitro GABA response data and toxicodynamic model.

Kinematic and Dynamic Parameters of a Liquid-Solid Pipe Flow Using DPIV∕Accelerometry

2007 ◽  
Vol 129 (11) ◽  
pp. 1415-1421 ◽  
Author(s):  
Joseph Borowsky ◽  
Timothy Wei
Keyword(s):  
Pipe Flow ◽  
Solid Phase ◽  
Fluid Phase ◽  
Central Moment ◽  
Steady Flows ◽  
Dynamic Parameters ◽  
Two Phase ◽  
Turbulence Structures ◽  
Two Phases ◽  
Flat Profile

An experimental investigation of a two-phase pipe flow was undertaken to study kinematic and dynamic parameters of the fluid and solid phases. To accomplish this, a two-color digital particle image velocimetry and accelerometry (DPIV∕DPIA) methodology was used to measure velocity and acceleration fields of the fluid phase and solid phase simultaneously. The simultaneous, two-color DPIV∕DPIA measurements provided information on the changing characteristics of two-phase flow kinematic and dynamic quantities. Analysis of kinematic terms indicated that turbulence was suppressed due to the presence of the solid phase. Dynamic considerations focused on the second and third central moments of temporal acceleration for both phases. For the condition studied, the distribution across the tube of the second central moment of acceleration indicated a higher value for the solid phase than the fluid phase; both phases had increased values near the wall. The third central moment statistic of acceleration showed a variation between the two phases with the fluid phase having an oscillatory-type profile across the tube and the solid phase having a fairly flat profile. The differences in second and third central moment profiles between the two phases are attributed to the inertia of each particle type and its response to turbulence structures. Analysis of acceleration statistics provides another approach to characterize flow fields and gives some insight into the flow structures, even for steady flows.

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