Finite Element Study of Oxygen Diffusion in the Intervertebral Disc

2000 ◽  
Author(s):  
E. Sélard ◽  
A. Shirazi-Adl ◽  
J. P. G. Urban
Keyword(s):  
Intervertebral Disc ◽  
Blood Supply ◽  
Oxygen Diffusion ◽  
Consumption Rate ◽  
The Body ◽  
Cellular Viability ◽  
Two Dimensional ◽  
Concentration Gradients ◽  
Exchange Area ◽  
The Matrix

Abstract The intervertebral disc consists of a water-rich extra-cellular matrix which is synthesized and maintained by its cells. The disc is the largest avascular tissue in the body with its cells lying as much as 8mm away from the blood supply. Nutrients, essential for maintaining cellular viability, diffuse through the matrix from blood supply under a concentration gradient arising from cellular demand. The oxygen concentration gradients in the intervertebral disc are investigated to examine the effects of exchange area and disc thickness on oxygen flux in the disc. The concentration gradients are computed using the two-dimensional Poisson’s equation and measured values for oxygen consumption rate and oxygen diffusion.

Numerical Simulation of a Soil Filtration Treatment Based on Balance

1986 ◽  
Vol 18 (7-8) ◽  
pp. 391-396
Author(s):  
M. Suzuki ◽  
H. Kawashima ◽  
T. Kawanishi
Keyword(s):  
Oxygen Diffusion ◽  
Infiltration Rate ◽  
Distribution Patterns ◽  
Operating Conditions ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Matrix Potential ◽  
Two Dimensional Model ◽  
The Matrix ◽  
Soil Filtration

A sophisticated two-dimensional model to simulate the concentration distributions of BOD, oxygen and biomass in a soil filtration treatment system is presented. The model incorporates, in addition to infiltration of wastewater, oxygen diffusion in a soil and bacterial growth and respiration. The matrix potential concept was used to describe two-dimensional infiltration from the source. The model showed that the distribution patterns of biomass in a soil are governed both by the rate of oxygen diffusion and by the wastewater infiltration rate. Applying the model to a trench type plant under ordinary operating conditions, it became apparent that only the soil adjacent to the trench is utilized for the treatment.

scholarly journals Tunable characteristics of low-frequency bandgaps in two-dimensional multivibrator phononic crystal plates under prestrain

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hai-Fei Zhu ◽  
Xiao-Wei Sun ◽  
Ting Song ◽  
Xiao-Dong Wen ◽  
Xi-Xuan Liu ◽  
...  
Keyword(s):  
Phononic Crystal ◽  
Real Life ◽  
Low Frequency ◽  
Acoustic Vibration ◽  
Crystal Plate ◽  
Frequency Noise ◽  
Two Dimensional ◽  
The Matrix ◽  
Noise Frequency ◽  
Realtime Control

AbstractIn view of the influence of variability of low-frequency noise frequency on noise prevention in real life, we present a novel two-dimensional tunable phononic crystal plate which is consisted of lead columns deposited in a silicone rubber plate with periodic holes and calculate its bandgap characteristics by finite element method. The low-frequency bandgap mechanism of the designed model is discussed simultaneously. Accordingly, the influence of geometric parameters of the phononic crystal plate on the bandgap characteristics is analyzed and the bandgap adjustability under prestretch strain is further studied. Results show that the new designed phononic crystal plate has lower bandgap starting frequency and wider bandwidth than the traditional single-sided structure, which is due to the coupling between the resonance mode of the scatterer and the long traveling wave in the matrix with the introduction of periodic holes. Applying prestretch strain to the matrix can realize active realtime control of low-frequency bandgap under slight deformation and broaden the low-frequency bandgap, which can be explained as the multiple bands tend to be flattened due to the localization degree of unit cell vibration increases with the rise of prestrain. The presented structure improves the realtime adjustability of sound isolation and vibration reduction frequency for phononic crystal in complex acoustic vibration environments.

scholarly journals The Dimension of the Body in Higher Education: Matrix of Meanings in Students’ Diaries

Human Arenas ◽  
2021 ◽  
Author(s):  
Ramiro Tau ◽  
Laure Kloetzer ◽  
Simon Henein
Keyword(s):  
Higher Education ◽  
Performing Arts ◽  
Teaching And Learning ◽  
Educational Practice ◽  
The Body ◽  
Cultural Perspective ◽  
General Process ◽  
Emotional Dimension ◽  
The Matrix ◽  
The Mind

AbstractIn this paper, we attempt to show some consequences of bringing the body back into higher education, through the use of performing arts in the curricular context of scientific programs. We start by arguing that dominant traditions in higher education reproduced the mind-body dualism that shaped the social matrix of meanings on knowledge transmission. We highlight the limits of the modern disembodied and decontextualized reason and suggest that, considering the students’ and teachers’ bodies as non-relevant aspects, or even obstacles, leads to the invisibilization of fundamental aspects involved in teaching and learning processes. We thus conducted a study, from a socio-cultural perspective, in which we analyse the emerging matrix of meanings given to the body and bodily engagement by students, through a systematic qualitative analysis of 47 personal diaries. We structured the results and the discussion around five interpretative axes: (1) the production of diaries enables historicization, while the richness of bodily experience expands the boundaries of diaries into non-textual modalities; (2) curricular context modulates the emergent meanings of the body; (3) physical and symbolic spaces guide the matrix of bodily meanings; (4) the bodily dimension of the courses facilitates the emergence of an emotional dimension to get in touch with others and to register one's own emotional experiences; and (5) the body functions as a condition for biographical continuity. These axes are discussed under the light of the general process of consciousness-raising and resignification of the situated body in the educational practice.

scholarly journals Involvement of Autophagy in Rat Tail Static Compression-Induced Intervertebral Disc Degeneration and Notochordal Cell Disappearance

2021 ◽  
Vol 22 (11) ◽  
pp. 5648
Author(s):  
Takashi Yurube ◽  
Hiroaki Hirata ◽  
Masaaki Ito ◽  
Yoshiki Terashima ◽  
Yuji Kakiuchi ◽  
...  
Keyword(s):  
Intervertebral Disc ◽  
Disc Degeneration ◽  
Time Course ◽  
The Body ◽  
Terminal Deoxynucleotidyl Transferase ◽  
Autophagic Flux ◽  
Static Compression ◽  
Notochordal Cell ◽  
Notochordal Cells ◽  
Rat Tail

The intervertebral disc is the largest avascular low-nutrient organ in the body. Thus, resident cells may utilize autophagy, a stress-response survival mechanism, by self-digesting and recycling damaged components. Our objective was to elucidate the involvement of autophagy in rat experimental disc degeneration. In vitro, the comparison between human and rat disc nucleus pulposus (NP) and annulus fibrosus (AF) cells found increased autophagic flux under serum deprivation rather in humans than in rats and in NP cells than in AF cells of rats (n = 6). In vivo, time-course Western blotting showed more distinct basal autophagy in rat tail disc NP tissues than in AF tissues; however, both decreased under sustained static compression (n = 24). Then, immunohistochemistry displayed abundant autophagy-related protein expression in large vacuolated disc NP notochordal cells of sham rats. Under temporary static compression (n = 18), multi-color immunofluorescence further identified rapidly decreased brachyury-positive notochordal cells with robust expression of autophagic microtubule-associated protein 1 light chain 3 (LC3) and transiently increased brachyury-negative non-notochordal cells with weaker LC3 expression. Notably, terminal deoxynucleotidyl transferase dUTP nick end labeling-positive apoptotic death was predominant in brachyury-negative non-notochordal cells. Based on the observed notochordal cell autophagy impairment and non-notochordal cell apoptosis induction under unphysiological mechanical loading, further investigation is warranted to clarify possible autophagy-induced protection against notochordal cell disappearance, the earliest sign of disc degeneration, through limiting apoptosis.

scholarly journals Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

scholarly journals A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Asim Khan ◽  
Norhashidah Hj. Mohd Ali ◽  
Nur Nadiah Abd Hamid
Keyword(s):  
Finite Difference ◽  
Stokes Problem ◽  
Stability And Convergence ◽  
Second Grade ◽  
Group Method ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
The Matrix ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

Abstract In this article, a new explicit group iterative scheme is developed for the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid. The proposed scheme is based on the high-order compact Crank–Nicolson finite difference method. The resulting scheme consists of three-level finite difference approximations. The stability and convergence of the proposed method are studied using the matrix energy method. Finally, some numerical examples are provided to show the accuracy of the proposed method.

scholarly journals Lymphocyte locomotion and attachment on two-dimensional surfaces and in three-dimensional matrices

1982 ◽  
Vol 92 (3) ◽  
pp. 747-752 ◽  
Author(s):  
WS Haston ◽  
JM Shields ◽  
PC Wilkinson
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Collagen Gels ◽  
Peripheral Lymph Node ◽  
Cellulose Esters ◽  
Peripheral Lymph ◽  
The Matrix ◽  
Identical Material ◽  
Variable Morphology ◽  
Collagen Lattices

The adhesion and locomotion of mouse peripheral lymph node lymphocytes on 2-D protein- coated substrata and in 3-D matrices were compared. Lymphocytes did not adhere to, or migrate on, 2-D substrata suck as serum- or fibronectin-coated glass. They did attach to and migrate in hydrated 3-D collagen lattices. When the collagen was dehydrated to form a 2-D surface, lymphocyte attachment to it was reduced. We propose that lymphocytes, which are poorly adhesive, are able to attach to and migrate in 3-D matrices by a nonadhesive mechanism such as the extension and expansion of pseudopodia through gaps in the matrix, which could provide purchase for movement in the absence of discrete intermolecular adhesions. This was supported by studies using serum-coated micropore filters, since lymphocytes attached to and migrated into filters with pore sizes large enough (3 or 8 mum) to allow pseudopod penetration but did not attach to filters made of an identical material (cellulose esters) but of narrow pore size (0.22 or 0.45 mum). Cinematographic studies of lymphocyte locomotion in collagen gels were also consistent with the above hypothesis, since lymphocytes showed a more variable morphology than is typically seen on plane surfaces, with formation of many small pseudopodia expanded to give a marked constriction between the cell and the pseudopod. These extensions often remained fixed with respect to the environment as the lymphocyte moved away from or past them. This suggests that the pseudopodia were inserted into gaps in the gel matrix and acted as anchorage points for locomotion.

scholarly journals Spinning rough disc moving in a rarefied medium

2010 ◽  
Vol 466 (2119) ◽  
pp. 2033-2055 ◽  
Author(s):  
Alexander Plakhov ◽  
Tatiana Tchemisova ◽  
Paulo Gouveia
Keyword(s):  
The Body ◽  
Two Dimensional ◽  
Zero Temperature ◽  
Optimal Mass Transport ◽  
Dense Gases ◽  
Magnus Effect ◽  
Inverse Effect ◽  
Transversal Force ◽  
The Moment ◽  
Complementary Mechanism

We study the Magnus effect: deflection of the trajectory of a spinning body moving in a gas. It is well known that in rarefied gases, the inverse Magnus effect takes place, which means that the transversal component of the force acting on the body has opposite signs in sparse and relatively dense gases. The existing works derive the inverse effect from non-elastic interaction of gas particles with the body. We propose another (complementary) mechanism of creating the transversal force owing to multiple collisions of particles in cavities of the body surface. We limit ourselves to the two-dimensional case of a rough disc moving through a zero-temperature medium on the plane, where reflections of the particles from the body are elastic and mutual interaction of the particles is neglected. We represent the force acting on the disc and the moment of this force as functionals depending on ‘shape of the roughness’, and determine the set of all admissible forces. The disc trajectory is determined for several simple cases. The study is made by means of billiard theory, Monge–Kantorovich optimal mass transport and by numerical methods.

Chloride Regulation at Low Salinities by Nereis Diversicolor (Annelida, Polychaeta)

1970 ◽  
Vol 53 (1) ◽  
pp. 75-92
Author(s):  
RALPH I. SMITH
Keyword(s):  
Electrical Potential ◽  
Urine Volume ◽  
Chloride Concentration ◽  
Pond Water ◽  
The Body ◽  
Salinity Range ◽  
Concentration Gradients ◽  
North Eastern ◽  
Net Uptake ◽  
Chloride Regulation

1. N. diversicolor from estuarine conditions in north-eastern England can be adapted to a chloride concentration in a pond water (PW) medium at least as low as 0.9 mM/l, and shows a net uptake of chloride when returned to a medium 3-10 mM/l more concentrated. But in comparable transfers after adaptation at a chloride concentration of 10 mM/l, net uptake is not measurable. 2. Net uptake of chloride is demonstrable in the lowest salinities, where coelomic chloride concentration drops below the regulatory plateau. Net uptake reaches 3.5 µM/g wet weight/h. 3. Chloride loss is well correlated with weight loss after adaptation in 10 mM/l, but poorly so after adaptation in PW, suggesting that the urine is very hypotonic to body fluid in PW, and isotonic (or less hypotonic) at environmental chloride concentrations of 10 mM/l or higher. 4. Uptake of chloride occurs against both electrical and chemical-concentration gradients over the lower third of the environmental salinity range, which is the range in which hyperosmotic and hyperionic regulation are most pronounced. 5. The electrical potential across the body wall is maximal in PW (17 mV, inside-negative), and decreases to zero in 50 % SW. 6. Chloride influx (as measured with 36Cl) is highest in SW, and decreases in proportion to chloride concentration down to 50-25% SW, rises to a secondary maximum in 10% SW or less, and decreases as fresh water is approached. 7. Urinary chloride loss is low, and proportional to external chloride concentration in higher salinities, maximal in the c. 10% SW range of salinities, and apparently decreases to a minimum in FW. This may be in part the consequence of recovery of chloride from an hypotonic urine, in part the consequence of a reduction in urine volume. Evidence for these last two possibilities will be given in the papers which follow.

Small angle reconstruction of plasma luminosity for spherical tokamak

2020 ◽  
Author(s):  
А.Н. Баженов ◽  
П.А. Затылкин
Keyword(s):  
Power Plants ◽  
Essential Feature ◽  
Real Data ◽  
The Body ◽  
Magnetic Sensors ◽  
Test Problems ◽  
General View ◽  
Central Projection ◽  
The Matrix ◽  
Matrix Detector

Публикация посвящена применению методов вычислительной геометрии, интервального анализа и линейного программирования к задачам физики управляемого термоядерного синтеза. Рассмотрены геометрические аспекты проблемы, получены проекции светимостей различных объемов сферического токамака на плоскость матричного детектора, изучены изображения предполагаемых макроскопических структур и микроскопических включений. Для набора модельных распределений светимости объема токамака поставлена задача восстановления сигнала. Решение получено с использованием задач линейного программирования. The problems of reconstruction of plasma luminosity are important for physics and technology of power plants-tokamaks. The Globus-M research tokamak obtained a large amount of data using a matrix detector in pinhole camera geometry. From the mathematical point of view, finding the luminosity for different regions of the plasma volume according to the matrix detector is an inverse problem related to the field of integral geometry. An essential feature of the particular task is the use of a single fixed camera with a small viewing angle. In this regard, application of methods of harmonic analysis of data is not enough. The paper investigates the geometric aspects of the problem. In the general view, a threedimensional object is projected onto a two-dimensional plane through a diaphragm. Under the assumption of azimuthal symmetry, there is a central projection of the luminosity of the body of rotation onto a flat matrix detector. The initial information for the calculation is the plasma boundary obtained from magnetic sensors. There is no reliable information about the internal structure of the plasma, so its division into regions of the equal luminosity is not unambiguous. The paper presents an algorithm for finding the projections of the luminosity of plasma volumes on the plane of the matrix detector. A set of model direct problems for the construction of algorithms for their recognition according to the detector data was investigated. Images of supposed macroscopic structures and microscopic inclusions were obtained. The methodological basis of the work is the use of interval analysis methods for solving geometric and algebraic problems. This approach allows obtaining qualitative and quantitative results that takes into account the uncertainty of the input data with the minimum amount of computational costs. Algebraic solvability is investigated in the interval formulation using response functionality. Solutions for a set of test problems are obtained, which demonstrate the availability of successful reconstruction for real data. An important result of the study is an information about the presence of uncertainties in geometric data and related calculations by obtaining results about the luminosity of the plasma by solving linear programming problems.

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