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1.
Lymphatic capillary drainage of interstitial fluid under both steady-state and inflammatory conditions is important for tissue fluid balance, cancer metastasis, and immunity. Lymphatic drainage function is critically coupled to the fluid mechanical properties of the interstitium, yet this coupling is poorly understood. Here we sought to effectively model the lymphatic-interstitial fluid coupling and ask why the lymphatic capillary network often appears with roughly a hexagonal architecture. We use homogenization method, which allows tissue-scale lymph flow to be integrated with the microstructural details of the lymphatic capillaries, thus gaining insight into the functionality of lymphatic anatomy. We first describe flow in lymphatic capillaries using the Navier-Stokes equations and flow through the interstitium using Darcy's law. We then use multiscale homogenization to derive macroscale equations describing lymphatic drainage, with the mouse tail skin as a basis. We find that the limiting resistance for fluid drainage is that from the interstitium into the capillaries rather than within the capillaries. We also find that between hexagonal, square, and parallel tube configurations of lymphatic capillary networks, the hexagonal structure is the most efficient architecture for coupled interstitial and capillary fluid transport; that is, it clears the most interstitial fluid for a given network density and baseline interstitial fluid pressure. Thus, using homogenization theory, one can assess how vessel microstructure influences the macroscale fluid drainage by the lymphatics and demonstrate why the hexagonal network of dermal lymphatic capillaries is optimal for interstitial tissue fluid clearance. 相似文献
2.
To elucidate the clearance of dissolved inert gas from tissues, we have developed numerical models of gas transport in a cylindrical block of tissue supplied by one or two capillaries. With two capillaries, attention is given to the effects of co-current and counter-current flow on tissue gas clearance. Clearance by counter-current flow is compared with clearance by a single capillary or by two co-currently arranged capillaries. Effects of the blood velocity, solubility, and diffusivity of the gas in the tissue are investigated using parameters with physiological values. It is found that under the conditions investigated, almost identical clearances are achieved by a single capillary as by a co-current pair when the total flow per tissue volume in each unit is the same (i.e., flow velocity in the single capillary is twice that in each co-current vessel). For both co-current and counter-current arrangements, approximate linear relations exist between the tissue gas clearance rate and tissue blood perfusion rate. However, the counter-current arrangement of capillaries results in less-efficient clearance of the inert gas from tissues. Furthermore, this difference in efficiency increases at higher blood flow rates. At a given blood flow, the simple conduction-capacitance model, which has been used to estimate tissue blood perfusion rate from inert gas clearance, underestimates gas clearance rates predicted by the numerical models for single vessel or for two vessels with co-current flow. This difference is accounted for in discussion, which also considers the choice of parameters and possible effects of microvascular architecture on the interpretation of tissue inert gas clearance. 相似文献
3.
In order to better understand the mechanisms governing transport of drugs, nanoparticle-based treatments, and therapeutic biomolecules, and the role of the various physiological parameters, a number of mathematical models have previously been proposed. The limitations of the existing transport models indicate the need for a comprehensive model that includes transport in the vessel lumen, the vessel wall, and the interstitial space and considers the effects of the solute concentration on fluid flow. In this study, a general model to describe the transient distribution of fluid and multiple solutes at the microvascular level was developed using mixture theory. The model captures the experimentally observed dependence of the hydraulic permeability coefficient of the capillary wall on the concentration of solutes present in the capillary wall and the surrounding tissue. Additionally, the model demonstrates that transport phenomena across the capillary wall and in the interstitium are related to the solute concentration as well as the hydrostatic pressure. The model is used in a companion paper to examine fluid and solute transport for the simplified case of an axisymmetric geometry with no solid deformation or interconversion of mass. 相似文献
4.
Matched asymptotic expansions are used to study a model of the coupled fluid flow in the capillaries and tissue of the microcirculation. These capillaries are long, narrow cylindrical tubes embedded in a uniform tissue space. The capillary, or intraluminal, flow is assumed to be that of an incompressible Navier-Stokes fluid wherein colloids are represented as dilute solute; the extraluminal flow in the tissue is according to Darcy's law. Central to this fluid exchange is the boundary condition on the fluid radial velocity at the semipermeable wall of the capillary. This boundary condition, involving the local hydrostatic and colloidal osmotic pressures in both the capillary and the tissue, together with the radial gradient of the tissue hydrostatic pressure, couples the intra- and extraluminal flow fields. With this model we investigate the relationship between transport properties, hydrostatic pressures, and flow exchange for a single capillary, and describe the fluid transport in the tissue space produced by an array of such capillaries. 相似文献
5.
R V Zubanski? 《Arkhiv anatomii, gistologii i émbriologii》1988,95(9):89-97
Time-dependent changes in diameters of various parts of the capillaries, distances between loops of the skin papillary capillaries in the nail wall and number of functioning capillaries per 1 mm2 of the skin surface have been studied biomicroscopically in foreign students, arrived from hot countries, during the process of their adaptation. Reorganization of these skin capillary parameters, actively participating in processes of heat exchange, demonstrate a time-dependent character. Therefore, by means of regressive analysis it is possible to approximate dynamics of the initial data using suitable theoretical models. The dynamics of average meanings of the capillary diameters in the arterial part subordinates to the hyperbolic dependence, changes of other parameters approach the rectilinear regression. 相似文献
6.
A critical parameter for transcapillary exchange of small solutes in countercurrent systems 总被引:1,自引:0,他引:1
Wang W 《Journal of biomechanics》2000,33(5):543-548
Small solute transport by a countercurrent capillary loop was studied using a theoretical model. In the model, the afferent and the efferent limbs of the loop share a common interstitial space, with which exchange of solute occurs. Sources of solute, epithelial cells, exist near capillaries and secret solute into the interstitial fluid. Parameters based on experimental measurements on young Sprague-Dawley rats were used in the model, and asymptotic solutions were derived. Comparison of the solute distribution in the interstitium between a capillary loop and a single capillary reveals that the ratio of the product of permeability (P(1)) and surface area (A(1)) to flow (F(1)) of the afferent limb, gamma(1)=P(1)A(1)/F(1) is a critical parameter for the countercurrent exchange system. It alone determines whether the countercurrent arrangement of capillaries facilitates clearance of solute from the interstitial fluid, a greater axial gradient of solute in the interstitium from the base to the tip of the capillary loop and a greater effect of flow, F, upon this gradient. The properties of the efferent limb affect the results, but it is gamma(1) that determines the characteristic difference between a capillary loop and a single capillary. 相似文献
7.
8.
A model of oxygen exchange between an arteriole or venule and the surrounding tissue 总被引:1,自引:0,他引:1
A mathematical model is developed to study the effect of capillary convection on oxygen transport around segments of arterioles and venules that are surrounded by capillaries. These capillaries carry unidirectional flow perpendicular to the vessel. The discrete capillary structure is distributed in a manner determined by the capillary blood flow and capillary density. A nonlinear oxyhemoglobin dissociation curve described by the Hill equation is used in the analysis. Oxygen flux from the vessel is expressed as a relationship between Sherwood and Peclet numbers, as well as other dimensionless combinations involving parameters of the capillary bed. A numerical solution is obtained with a finite difference method. The numerical results obtained within the physiological range of parameters allow the prediction of longitudinal gradients of hemoglobin-oxygen saturation along the arterioles and venules. 相似文献
9.
A theoretical model is used to analyze oxygen transport in a three-dimensional tissue region containing an arteriole surrounded by an array of capillaries in planes perpendicular to the arteriole. Convective removal of oxygen from the vicinity of the arteriole by nearby capillaries is shown to increase diffusive oxygen loss from the arteriole. This effect depends on the locations of the capillaries, particularly those nearest to the arteriole. The arteriolar oxygen efflux is comparable to that predicted by a previous model which used a continuum approach, but the efflux does not increase with increasing perfusion as rapidly as predicted by the continuum model. Even a small capillary flow rate strongly influences the oxygen field surrounding the arteriole. 相似文献
10.
Morphometric studies have confirmed that the corpus luteum (CL) of the pregnant rat contains luteal cells with numerous microvilli which directly face an extensive network of sinusoidal capillaries. From this it has been suggested that extensive development of transport structures is necessary to support progesterone synthesis and secretion. The present study was carried out to determine whether these transport structures could be related quantitatively to different rates of total progestin (progesterone plus 20 alpha-hydroxypregn-4-en-3-one) secretion reported to be 32, 10, and 23 micrograms/hr per ovary on day 16 and the morning (AM) and afternoon (PM) of day 22, respectively. Histological analysis was carried out on two CL, fixed by immersion, from each of five rats, at each stage of gestation. The important findings to emerge were that when the progestin secretion rate was greater, there was a significant increase in surface specializations on the luteal cell and a thickening of the capillary walls. There was also a greater volume of interstitial space between luteal cells and capillaries. However, due to the development of microvilli and unevenness in the capillary wall, the physiological diffusion distance (harmonic distance) between luteal cell cytoplasm and blood was not increased. Collectively, these results show that changes in the rate of progestin secretion are accompanied by significant, although disproportionate, changes in transport structures and suggest that the latter are important in supporting luteal function. 相似文献
11.
Transport of ions across the blood-brain barrier 总被引:2,自引:0,他引:2
A L Betz 《Federation proceedings》1986,45(7):2050-2054
Capillaries in the brain are formed by a uniquely specialized endothelial cell that regulates the movement of substances between blood and brain. Although they provide an impermeable barrier to some solutes, brain capillary endothelial cells facilitate the transcapillary exchange of others. In addition, they contain specific enzymes that contribute to a metabolic blood-brain barrier by limiting the movement of compounds such as neurotransmitters across the capillary wall. Studies of sodium and potassium transport by brain capillaries indicate that the endothelial cell contains distinct types of ion transport systems on the two sides of the capillary wall, i.e., the luminal and antiluminal membranes of the endothelial cell. As a result, specific solutes can be pumped across the capillary against an electrochemical gradient. These transport systems are likely to play a role in the active secretion of fluid from blood to brain and in maintaining a constant concentration of ions in the brain's interstitial fluid. In this way, the brain capillary endothelium is structurally and functionally related to an epithelium. 相似文献
12.
Uzarski J Drelles MB Gibbs SE Ongstad EL Goral JC McKeown KK Raehl AM Roberts MA Pytowski B Smith MR Goldman J 《American journal of physiology. Heart and circulatory physiology》2008,294(3):H1326-H1334
Lymphangiogenesis is considered a promising approach for increasing fluid drainage during secondary lymphedema. However, organization of lymphatics into functional capillaries may be dependent upon interstitial flow (IF). The present study was undertaken to determine the importance of lymphangiogenesis for lymphedema resolution. We created a lymphatic obstruction that produces lymphedema in mouse tail skin. The relatively scar-free skin regeneration that occurred across the obstruction allowed the progression of lymphangiogenesis to be observed and compared with the evolution of lymphedema. The role of vascular endothelial growth factor-C (VEGF-C)/VEGF receptor (VEGFR)-3 signaling in lymphedema resolution was investigated by exogenous administration of VEGF-C or neutralizing antibodies against VEGFR-3. VEGF-C protein improved lymphedema at 15 days [reducing dermal thickness from 742 +/- 105 to 559 +/- 141 microm with 95% confidence intervals (CIs), P < 0.05] without increasing lymphatic capillary coverage (11.6 +/- 6.4% following VEGF-C treatment relative to 9.6 +/- 6.2% with 95% CIs, P > 0.50). Blocking VEGFR-3 signaling did not inhibit lymphedema resolution at 25 days (dermal thickness of 462 +/- 127 microm following VEGFR-3 inhibition relative to 502 +/- 87 microm with 95% CIs) or inhibit IF, although VEGFR-3 blocking prevented lymphangiogenesis (reducing lymphatic coverage to 0.2 +/- 0.7% relative to 8.7 +/- 7.3% with 95% CIs, P < 0.005). A second mouse tail lymphedema model was employed to investigate the ability of VEGF-C to increase fluid drainage across a scar. We found that neither neutralization of VEGFR-3 nor administration of VEGF-C affected the course of skin swelling over 25 days. These findings suggest that resolution of lymphedema in the mouse tail skin may be more dependent upon IF and regeneration of the extracellular matrix across the obstruction than lymphatic capillary regeneration. 相似文献
13.
Summary In the present study we followed with the electron microscope the changes which the lipids undergo during their transport between the blood and the fat cells in both impletion and depletion of the fat depots. Impletion was studied in tissues from mice on the first or second day after birth, when the storage of fat begins, and from newborn mice and young rats that were refed after periods of starvation. Fat depots in the state of depletion were taken from the starving animals.During impletion the chylomicrons were found to be attached to the endothelium of the capillaries in the fat organs, where they seem to break up into smaller and less electron-dense particles. The absorption of the lipids by the capillary endothelial cells could not be observed, since no osmiophilic material was found within the capillary wall. No such material was present within the interstitial connective tissue between capillaries and fat cell. When the lipids enter the fat cell they again become observable as osmiophilic granules. These lipomicrons seem to represent the absorbed lipid material in transit between the surface of the fat cells and the fat droplets in the cells. Although dispersed throughout the cytoplasm, the lipomicrons were often accumulated at, and attached to, the surface of the growing fat droplets. They lost their identity when they were incorporated into the homogeneous material of the fat droplets.According to these observations, several steps were distinguished during impletion and were localized at the surface of the capillaries, at the plasma membrane of the fat cells, and at the surface of the fat droplet. The findings were discussed in the light of the physiological and biochemical literature concerning the clearance of the chylomicrons from the blood.The static pictures of the fat cells in the depleting state are very similar to those of the impleting cells. Lipomicrons are present, and they seem to emerge from the surface of the diminishing fat droplets. Also in these cells they seem to represent the lipids in transit, but in the reverse direction. At the cell border they disappear, and no osmiophilic material could be discovered within the interstitial tissue or within the capillary wall. Occasionally osmiophilic globules were found within the capillaries of the depleting fat organs, but they did not show the same relationship to the endothelium as the chylomicrons. We concluded from the similarity between the static pictures of depleting and impleting cells that the processes distinguished and localized during impletion are reversed when the cell releases fat. If this is correct, our pictures illustrate the lability of the fat organs, which respond to changing conditions by reversing the processes involved in their twofold activity of absorbing and releasing fat. The lipomicron pool in the fat cell seems to represent the lipids most immediately available either for storage or for release under ordinary nutritional conditions, where such drastic changes as in our experimental material do not occur. During both impletion and depletion the mitochondria were found to be profoundly changed. It is believed that these changes are mainly due to an infiltration of the mitochondria by lipomicrons. However, these observations do not permit us to draw conclusions as to the function of the mitochondria in the storage or release of fat.Work performed under the auspices of the U.S. Atomic Energy Commission. 相似文献
14.
A computational study of the effect of capillary network anastomoses and tortuosity on oxygen transport 总被引:1,自引:0,他引:1
The objective of this study was to investigate the effects of capillary network anastomoses and tortuosity on oxygen transport in skeletal muscle, as well as the importance of muscle fibers in determining the arrangement of parallel capillaries. Countercurrent flow and random capillary blockage (e.g. by white blood cells) were also studied. A general computational model was constructed to simulate oxygen transport from a network of blood vessels within a rectangular volume of tissue. A geometric model of the capillary network structure, based on hexagonally packed muscle fibers, was constructed to produce networks of straight unbranched capillaries, capillaries with anastomoses, and capillaries with tortuosity, in order to examine the effects of these geometric properties. Quantities examined included the tissue oxygen tension and the capillary oxyhemoglobin saturation. The computational model included a two-phase simulation of blood flow. Appropriate parameters were chosen for working hamster cheek-pouch retractor muscle. Our calculations showed that the muscle-fiber geometry was important in reducing oxygen transport heterogeneity, as was countercurrent flow. Tortuosity was found to increase tissue oxygenation, especially when combined with anastomoses. In the absence of tortuosity, anastomoses had little effect on oxygen transport under normal conditions, but significantly improved transport when vessel blockages were present. 相似文献
15.
A simple model is presented for one-dimensional diffusion in an ensemble of semi-infinite and finite pores or capillaries in which the boundary at one end of each capillary is allowed to fluctuate randomly between a perfectly reflecting barrier and a perfectly absorbing barrier. The model is independent of the spatial distribution of the capillaries; it is only assumed that there are a large number of them and that they are noninteracting. Exact solutions are possible and results are obtained, in terms of the fluctuation parameters, for the total amount per unit area of solute passed through the capillary system in the semi-infinite case, and for a permeability coefficient and time lag to steady state in the finite system. Applications of the model to diffusion in biological membranes are discussed. 相似文献
16.
The influence on fluid flow of the fixed charge on the surface of capillaries is calculated using the linearised Poisson-Boltzmann equations. The results depend strongly upon the ratio of the capillary radius to the Debye length. At physiological ionic strength, the Debye length is less than 1 nm and electrostatic effects are negligible. In particular, they can not explain the Copley-Scott Blair phenomenon in artificial capillaries. Electrostatic effects can be significant in smaller channels and it is calculated that in intercellular clefts in the capillary endothelium the apparent viscosity of the fluid may increase more than 50%. These effects can also be important in the flow in the narrow gap between a red cell and the blood capillary wall. Using the Fitzgerald-Lighthill model of this flow and parameters typical of the human microcirculation, the theory predicts that the apparent viscosity in the gap will be increased by about 5%. 相似文献
17.
Transdermal extraction of clinically relevant analytes offers a potentially noninvasive method of diagnostics. However, development of such a method is limited by the low permeability of skin. In this paper, we present a potential method for noninvasive diagnostics based on ultrasonic skin permeabilization and subsequent extraction of interstitial fluid (ISF) across the skin using vacuum. ISF extracted by this method was collected and analyzed for glucose and other analytes. Glucose concentration in the extracted fluid correlates well with blood glucose concentration over a range of 50-250 mg/dl. A mathematical model describing vacuum-induced transport of ISF through ultrasonically permeabilized skin is presented as well. The model accounts for convective, as well as diffusive, transport processes across blood capillaries, epidermis, and the stratum corneum. The overall predictions of the model compare favorably with the experimental observations. 相似文献
18.
Modeling of interstitial fluid flow involves processes such as fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. To date, majority of microvascular flow modeling has been done at different levels and scales mostly on simple tumor shapes with their capillaries. However, with our proposed numerical model, more complex and realistic tumor shapes and capillary networks can be studied. Both blood flow through a capillary network, which is induced by a solid tumor, and fluid flow in tumor’s surrounding tissue are formulated. First, governing equations of angiogenesis are implemented to specify the different domains for the network and interstitium. Then, governing equations for flow modeling are introduced for different domains. The conservation laws for mass and momentum (including continuity equation, Darcy’s law for tissue, and simplified Navier–Stokes equation for blood flow through capillaries) are used for simulating interstitial and intravascular flows and Starling’s law is used for closing this system of equations and coupling the intravascular and extravascular flows. This is the first study of flow modeling in solid tumors to naturalistically couple intravascular and extravascular flow through a network. This network is generated by sprouting angiogenesis and consisting of one parent vessel connected to the network while taking into account the non-continuous behavior of blood, adaptability of capillary diameter to hemodynamics and metabolic stimuli, non-Newtonian blood flow, and phase separation of blood flow in capillary bifurcation. The incorporation of the outlined components beyond the previous models provides a more realistic prediction of interstitial fluid flow pattern in solid tumors and surrounding tissues. Results predict higher interstitial pressure, almost two times, for realistic model compared to the simplified model. 相似文献
19.
Salathe EP 《Journal of mathematical biology》2003,46(4):287-308
An approach is presented for modeling transport and exchange in skeletal muscle that can be used to analyze vascular beds
consisting of a large number of interacting capillaries. First the oxygen concentration is determined in a functional unit
consisting of a single capillary surrounded by a region of tissue in which a flux is prescribed on the outer boundary of the
region. This flux, which is a result of the interaction among all of the capillaries comprising the vascular bed, is then
found by matching the concentration along the borders between adjacent units. This leads to a system of ordinary differential
equations for the oxygen concentration in the capillaries coupled with a system of algebraic equations for the fluxes. The
method is illustrated by obtaining the oxygen concentration within an array of capillaries for the case when each capillary
has a different initial concentration and for the case when each capillary has a different flow rate.
Received: 12 June 2001 / Revised version: 18 April 2002 / Published online: 17 January 2003
Key words or phrases: Skeletal muscle – Transport – Microcirculation 相似文献
20.
C. Pozrikidis 《Journal of mathematical biology》2010,60(1):75-94
A theoretical framework is presented for describing blood flow through the irregular vasculature of a solid tumor. The tumor
capillary bed is modeled as a capillary tree of bifurcating segments whose geometrical construction involves deterministic
and random parameters. Blood flow along the individual capillaries accounts for plasma leakage through the capillary walls
due to the transmural pressure according to Sterling’s law. The extravasation flow into the interstitium is described by Darcy’s
law for a biological porous medium. The pressure field developing in the interstitium is computed by solving Laplace’s equation
subject to derived boundary conditions at the capillary vessel walls. Given the arterial, venous, and tumor surface pressures,
the problem is formulated as a coupled system of integral and differential equations arising from the interstitium and capillary
flow transport equations. Numerical discretization yields a system of linear algebraic equations for the interstitial and
capillary segment pressures whose solution is found by iterative methods. Results of numerical computations document the effect
of the interstitial hydraulic and vascular permeability on the fractional plasma leakage. Given the material properties, the
fractional leakage reaches a maximum at a particular grade of the bifurcating vascular tree. 相似文献