Modelling lymph flow in the lymphatic system: from 0D to 1D spatial resolution

2018 ◽  
Vol 13 (5) ◽  
pp. 45 ◽  
Author(s):  
Rufina M. Tretyakova ◽  
Gennady I. Lobov ◽  
Gennady A. Bocharov
Keyword(s):  
Lymphatic Vessels ◽  
Lymph Flow ◽  
Published Data ◽  
Modeling Tools ◽  
Math Model ◽  
Flow Models ◽  
Modelling Studies ◽  
1D Model ◽  
Numer Anal ◽  
The One

In this study, we formulated a core mathematical model for describing the one-dimensional lymph flow in lymphatic vessels and branching network of lymphatic vessels. The 1D model was numerically implemented using the 1D haemodynamic modeling tools developed in T.M. Gamilov et al. and S. Simakov et al. [T.M. Gamilov et al., Transl. Med. 6 (2013) 5–13 and S. Simakov et al., Russian J. Numer. Anal. Math. Model. 28 (2013) 485–504]. The formulated model was calibrated using published data on lymph flow dynamics and other modelling studies of lymph flows. The comparison of 0D and 1D formulations of the lymph flow models is presented.

scholarly journals Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations

2021 ◽  
Author(s):  
Václav Kučera ◽  
Mária Lukáčová-Medvid’ová ◽  
Sebastian Noelle ◽  
Jochen Schütz
Keyword(s):  
Asymptotic Properties ◽  
Reference State ◽  
Math Model ◽  
Implicit Schemes ◽  
Comput Phys ◽  
Weakly Compressible ◽  
Hilbert Expansion ◽  
Imex Schemes ◽  
Numer Anal ◽  
The One

AbstractIn this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Kučera (J Comput Phys 224:208–221, 2007) as well as the class of RS-IMEX schemes (Schütz and Noelle in J Sci Comp 64:522–540, 2015; Kaiser et al. in J Sci Comput 70:1390–1407, 2017; Bispen et al. in Commun Comput Phys 16:307–347, 2014; Zakerzadeh in ESAIM Math Model Numer Anal 53:893–924, 2019). The implicit part is based on a Jacobian matrix which is evaluated at a reference state. This state can be either the solution at the old time level as in Feistauer and Kučera (2007), or a numerical approximation of the incompressible limit equations as in Zeifang et al. (Commun Comput Phys 27:292–320, 2020), or possibly another state. Subsequently, it is shown that this class of methods is asymptotically preserving under the assumption of a discrete Hilbert expansion. For a one-dimensional setting with some limitations on the reference state, the existence of a discrete Hilbert expansion is shown.

scholarly journals Forward: There Are Still Plenty of Opportunities On the Boundaries

2007 ◽  
Vol 1 (2) ◽  
Author(s):  
Yijun Liu
Keyword(s):  
Large Scale ◽  
Anisotropic Elasticity ◽  
Boundary Integral ◽  
Stress Concentrations ◽  
Modeling Tools ◽  
Hypersingular Integrals ◽  
Solid Foundation ◽  
The 1960S ◽  
The One ◽  
Local Integral Equations

<table width="530" border="0" cellspacing="0" cellpadding="0"> <tr> <td align="left" valign="top"> <a name="abstract"></a> <span class="subtitle" style="font-weight:bold">Abstract</span><br /> <p><img src="http://ejbe.libraries.rutgers.edu/files/rizzo.gif" align=left HSPACE=20>This is the second of the two special issues of Electronic Journal of Boundary Elements in honor of Professor Frank Rizzo. There are thirteen technical papers in this issue, contributed by Professor Rizzo’s colleagues, friends and former students. These papers cover a broad range of topics in the boundary integral equation and boundary element method (BIE/BEM), including Galerkin BEM for anisotropic elasticity (Gray, Griffith, et al.), evaluations of hypersingular integrals in Galerkin BEM (Bonnet and Guiggiani), Green’s function BEM for bimaterials (Denda), new 3-D Green’s functions for piezoelectric bimaterials (Pan), new formulations using local integral equations (Sladek and Sladek), BEM in sensitivity analysis with stress concentrations (Burczynski and Habarta), fracture of thermopiezoelectric materials (Qin), BEM for 3-D gradient elastodynamics (Polyzos, Tsepoura and Beskos), time-domain large-scale elastodynamic analysis (Yoshikawa and Nishimura), acoustic BEM for analyzing mufflers and silencers (Wu and Cheng), analysis of solids with randomly distributed inclusions (Yao, Kong and Zheng), thermal and stress analyses of thermal barrier coatings (Lu and Dong), and finally, modeling of carbon nanotube-based composites (Liu and Chen). These authors are gratefully acknowledged for their excellent contributions, and for their patience and cooperation in the process of preparing this special issue. It is interesting to note that the wide applications of the elasticity BIE/BEM in engineering all started with a simple idea. That is, boundary-value problems can be solved by boundary-only methods. The first result in this direction is also amazingly concise. During a recent trip to Urbana, Illinois, I checked out Professor Rizzo’s Ph.D. dissertation from the UIUC library. The thirty-page dissertation is without doubt a masterpiece that many current and future Ph.D. candidates may like to follow, for its originality and succinct writing. The dissertation laid a solid foundation for what is now called the BEM for elasticity and many other problems, and eventually led to the seminal paper of 1967. Behind this masterpiece are Professor Rizzo’s affection and conviction in the BIE/BEM and his willingness to explore a different route in research. This spirit of exploration and his serious attitude in research have inspired and influenced many of his former students and colleagues in the last forty years. Researchers in the pursuit of boundary-only methods can be described as explorers in a Flatland (see Professor Rizzo’s article in Issue No. 1). They can have different perspectives, but can also discover treasures that others could not uncover. As younger researchers come into this playground, new breakthroughs, just like the one made by Professor Rizzo in the 1960s, may not be far away. There will certainly be more innovative boundary-only methods emerging in the near future. More special numerical tools will be developed and more emerging problems will be solved by these new modeling tools. The fields of computational mechanics will be further diversified and thus prosperous. There are still plenty of opportunities on the boundaries! <br /><br /><br /> </td> </tr> </table>

ON THE SEMILOCAL CONVERGENCE OF NEWTON'S METHOD FOR SECTIONS ON RIEMANNIAN MANIFOLDS

2014 ◽  
Vol 07 (01) ◽  
pp. 1450007
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Convergence Analysis ◽  
Lipschitz Condition ◽  
Riemannian Manifolds ◽  
Newton’S Method ◽  
Newton's Method ◽  
Geometric Model ◽  
Semilocal Convergence ◽  
Convergence Result ◽  
Numer Anal ◽  
The One

We present a semilocal convergence analysis of Newton's method for sections on Riemannian manifolds. Using the notion of a 2-piece L-average Lipschitz condition introduced in [C. Li and J. H. Wang, Newton's method for sections on Riemannian manifolds: Generalized covariant α-theory, J. Complexity24 (2008) 423–451] in combination with the weaker center 2-piece L1-average Lipschitz condition given by us in this paper, we provide a tighter convergence analysis than the one given in [C. Li and J. H. Wang, Newton's method for sections on Riemannian manifolds: Generalized covariant α-theory, J. Complexity24 (2008) 423–451] which in turn has improved the works in earlier studies such as [R. L. Adler, J. P. Dedieu, J. Y. Margulies, M. Martens and M. Shub, Newton's method on Riemannian manifolds and a geometric model for the human spine, IMA J. Numer. Anal.22 (2002) 359–390; F. Alvarez, J. Bolte and J. Munier, A unifying local convergence result for Newton's method in Riemannian manifolds, Found. Comput. Math.8 (2008) 197–226; J. P. Dedieu, P. Priouret and G. Malajovich, Newton's method on Riemannian manifolds: Covariant α-theory, IMA J. Numer. Anal.23 (2003) 395–419].

Lymph flow in sheep with rapid cardiac ventricular pacing

1997 ◽  
Vol 272 (5) ◽  
pp. R1595-R1598 ◽  
Author(s):  
R. E. Drake ◽  
S. Dhother ◽  
R. A. Teague ◽  
J. C. Gabel
Keyword(s):  
Heart Failure ◽  
Flow Rate ◽  
Mediastinal Lymph Node ◽  
Venous Pressure ◽  
Lymphatic Vessels ◽  
Lymph Flow ◽  
Ventricular Pacing ◽  
Fluid Filtration ◽  
Flow Rates ◽  
Lymphatic Flow

Increases in systemic venous pressure (Pv) associated with heart failure cause an increase in microvascular fluid filtration into the tissue spaces. By removing this excess filtrate from the tissues, lymphatic vessels help to prevent edema. However, the lymphatics drain into systemic veins and an increase in Pv may interfere with lymphatic flow. To test this, we cannulated caudal mediastinal node efferent lymphatics in sheep. We used rapid cardiac ventricular pacing (240-275 beats/min) to cause heart failure for 4-7 days. Each day we determined the lymph flow rate two ways. First, we adjusted the lymph cannula height so that the pressure at the outflow end of the lymphatic was zero. After we determined the lymph flow with zero outflow pressure, we raised the cannula so that outflow pressure was equal to the actual venous pressure. We quantitated the effect of venous pressure on lymph flow rate by comparing the flow rate with outflow pressure = Pv to the flow rate with zero out low pressure. At baseline, Pv = 5.0 +/- 2.5 (SD) cmH2O and we found no difference in the two lymph flow rates. Pacing caused Pv and both lymph flow rates to increase significantly. However for Pv < 15 cmH2O, we found little difference in the two lymph flow rates. Thus increases in Pv to 15 cmH2O at the outflow to the lymphatics had little effect on lymph flow. By comparison, Pv > 15 cmH2O slowed lymph flow by 55 +/- 29% relative to the lymph flow rate with zero outflow pressure. Thus Pv values > 15 cmH2O interfere with lymph flow from the sheep caudal mediastinal lymph node.

scholarly journals Effects of tidal volume and respiratory frequency on lung lymph flow

2005 ◽  
Vol 99 (2) ◽  
pp. 556-563 ◽  
Author(s):  
David B. Pearse ◽  
Robert M. Searcy ◽  
Wayne Mitzner ◽  
Solbert Permutt ◽  
J. T. Sylvester
Keyword(s):  
Tidal Volume ◽  
Lymphatic Vessels ◽  
Lymph Flow ◽  
Edema Formation ◽  
Fluid Filtration ◽  
Induced Changes ◽  
Lung Lymph ◽  
Lung Lymph Flow

Ventilation (V̇) increases lung lymph flow (Q̇l), but the separate effects of tidal volume (Vt) and frequency (f) and the role of V̇-induced changes in edema formation are poorly understood. An isolated, in situ sheep lung preparation was used to examine these effects. In eight sheep with f = 10 min−1, results obtained during 30-min periods with Vt = 5 or 20 ml/kg were compared with values obtained during bracketed 30-min control periods (Vt = 12.5 ml/kg). Eight other sheep with constant Vt (12.5 ml/kg) were studied at f = 5 or 20 min−1 and compared with f = 10 min−1. Three additional groups of six sheep were perfused for 100 min with control V̇ (10 ml/kg, 10 min−1). Vt was then kept constant or changed to 20 or 3 ml/kg during a second 100-min period. Increases in Vt or f increased Q̇l and vice versa, without corresponding effects on the rate of edema formation. For the same change in V̇, changing Vt had a greater effect on Q̇l than changing f. The change in Q̇l caused by an increase in Vt was significantly greater after the accumulation of interstitial edema. The change in Q̇l caused by a sustained increase in Vt was transient and did not correlate with the rate of edema formation, suggesting that V̇ altered Q̇l through direct mechanical effects on edema-filled compartments and lymphatic vessels rather than through V̇-induced changes in fluid filtration.

Relationship between intracranial pressure and cervical lymphatic pressure and flow rates in sheep

1999 ◽  
Vol 277 (6) ◽  
pp. R1712-R1717 ◽  
Author(s):  
I. Silver ◽  
B. Li ◽  
J. Szalai ◽  
M. Johnston
Keyword(s):  
Cerebrospinal Fluid ◽  
Intracranial Pressure ◽  
Jugular Vein ◽  
Lymphatic Vessels ◽  
Lymph Flow ◽  
Cranial Vault ◽  
Perfusion System ◽  
Flow Rates ◽  
Cisterna Magna ◽  
Mesenteric Lymph

Previous reports from our group demonstrated that about one-half of the total volume of cerebrospinal fluid (CSF) removed from the cranial vault in sheep is transported into extracranial lymphatics, especially cervical lymphatic vessels in the neck. In this study, we tested the hypothesis that an elevation of intracranial pressure (ICP) would increase cervical lymphatic pressure and lymph flow rates in anesthetized sheep. Catheters were inserted into both lateral ventricles, the cisterna magna, cervical lymphatics, and the jugular vein. A ventriculo-cisternal perfusion system was employed to regulate ICP. Mean ( P = 0.008), peak ( P = 0.007), and baseline ( P = 0.013) cervical lymphatic pressures increased as ICP was elevated from 10 to 70 cmH2O in 20-cmH2O increments. Similarly, cervical lymph flow rates increased ( P < 0.001), with flows at 70 cmH2O ICP observed to be approximately fourfold higher than those at 10 cmH2O ICP. No changes were observed in mesenteric lymph flow rates (vessels not expected to drain CSF). We conclude that cervical lymphatic vessels play an important role in the transport of CSF from the cranial vault when ICP is elevated.

Parasites of round goby, Neogobius melanostomus, currently invading the Elbe River

2019 ◽  
Vol 48 (1) ◽  
pp. 56-65 ◽  
Author(s):  
Yuriy Kvach ◽  
Markéta Ondračková ◽  
Michal Janáč ◽  
Vadym Krasnovyd ◽  
Mária Seifertová ◽  
...  
Keyword(s):  
Round Goby ◽  
Parasite Community ◽  
Neogobius Melanostomus ◽  
Published Data ◽  
Tidal Zone ◽  
New Host ◽  
The North ◽  
Round Gobies ◽  
The Elbe River ◽  
The One

Abstract The round goby, Neogobius melanostomus, is a Ponto-Caspian fish species currently found in many parts of Europe, including the North Sea riverine deltas. The objective of this study was to examine the parasite community of fish caught in the lower Elbe (Süderelbe – tidal zone; Geesthacht – non-tidal) in Germany and compare it with published data from the upper Elbe (Ústí nad Labem) in the Czech Republic. Twelve parasite taxa were recorded in the lower Elbe, six in the Süderelbe and nine near the city of Geesthacht. Süderelbe fish were mainly infected with Angullicola crassus larvae, while gobies from Geesthacht – with glochidia and sporadically occurring Pomporhynchus laevis, and the opposite situation was observed at Ústí nad Labem. It appears that a large tidal weir at Geesthacht significantly contributes to the division of the round goby population, with the Geesthacht parasite community being more similar to that at Ústí nad Labem than the one from the Süderelbe, thus increasing the likelihood that shipping from Hamburg was the introduction vector to Ústí nad Labem. We also recorded Acanthocephalus rhinensis in the Elbe for the first time, and in a new host – the round goby. Thus, round gobies may represent a new vector for the introduction of this parasite along the Elbe.

scholarly journals Lymphatic Vessels and Their Surroundings: How Local Physical Factors Affect Lymph Flow

Biology ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 463
Author(s):  
Eleonora Solari ◽  
Cristiana Marcozzi ◽  
Daniela Negrini ◽  
Andrea Moriondo
Keyword(s):  
Shear Stress ◽  
Lymphatic Vessels ◽  
Lymph Flow ◽  
Cellular Systems ◽  
Physical Factors ◽  
Hydraulic Pressure ◽  
Cellular Mechanisms ◽  
Intrinsic Mechanism ◽  
Physical Stimuli ◽  
External Forces

Lymphatic vessels drain and propel lymph by exploiting external forces that surrounding tissues exert upon vessel walls (extrinsic mechanism) and by using active, rhythmic contractions of lymphatic muscle cells embedded in the vessel wall of collecting lymphatics (intrinsic mechanism). The latter mechanism is the major source of the hydraulic pressure gradient where scant extrinsic forces are generated in the microenvironment surrounding lymphatic vessels. It is mainly involved in generating pressure gradients between the interstitial spaces and the vessel lumen and between adjacent lymphatic vessels segments. Intrinsic pumping can very rapidly adapt to ambient physical stimuli such as hydraulic pressure, lymph flow-derived shear stress, fluid osmolarity, and temperature. This adaptation induces a variable lymph flow, which can precisely follow the local tissue state in terms of fluid and solutes removal. Several cellular systems are known to be sensitive to osmolarity, temperature, stretch, and shear stress, and some of them have been found either in lymphatic endothelial cells or lymphatic muscle. In this review, we will focus on how known physical stimuli affect intrinsic contractility and thus lymph flow and describe the most likely cellular mechanisms that mediate this phenomenon.

Thoracic duct lymph flow and its measurement in chronically catheterized sheep fetus

1989 ◽  
Vol 256 (1) ◽  
pp. H16-H20 ◽  
Author(s):  
R. A. Brace
Keyword(s):  
Flow Rate ◽  
Thoracic Duct ◽  
Lymphatic Vessels ◽  
Lymph Flow ◽  
Thoracic Duct Lymph ◽  
Computer Technique ◽  
Venous Circulation ◽  
Duct Lymph ◽  
Unit Body Weight ◽  
Sheep Fetus

A method was developed for chronic catheterization of the left thoracic lymph duct at the base of the neck in the sheep fetus, which did not disrupt the other major lymphatic vessels that join the venous circulation at the same location. The lymphatic catheter was connected to a catheter in a jugular vein when lymph flow was not being recorded, so that the lymph continuously returned to the fetal circulation. Special consideration of catheter size to minimize flow resistance and treatment to prevent clotting were required. Individual animals were maintained up to 17 days with lymph flow continuing. In 13 fetuses averaging 128 days gestation (term = 147 days) at the time of catheterization, lymph flow rate was measured for 1 h each day for the first 7 postsurgical days with an on-line computer technique that continuously calculated lymph flow rate. Lymph flow averaged 0.64 +/- 0.17 (SD) ml/min in fetuses weighing 2.3-4 kg and tended to undergo a nonsignificant increase with time. Lymph and plasma protein concentrations did not change with time. In individual fetuses, large spontaneous variations in lymph flow rate occurred over periods of several seconds to a few minutes. Analysis showed that these variations in flow rate were not associated with fetal breathing movements. Thus the present study describes a technique for studying the dynamics of lymph flow in the unanesthetized sheep fetus in utero over a time period limited primarily by the length of gestation. In addition, it appears that thoracic duct lymph flow rate in the fetus per unit body weight averages three to four times that in the adult.

Sign in / Sign up

Export Citation Format

Share Document