Multiscale modeling of lymphatic drainage from tissues using homogenization theory

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.     

Localization and hormonal regulation of ovarian production of histamine in the sheep

Concentrations of histamine were measured within the follicular wall, follicular fluid and ovarian interstitium throughout the periovulatory period in sheep. Histamine within follicular tissue declined after the onset of the preovulatory surge of luteinizing hormone (LH) and remained low until after ovulation, when levels then increased markedly. Alterations in histamine within the follicular wall were not reflected by corresponding changes within follicular fluid or ovarian interstitium. Release of histamine from tissue during short-term incubation was greatest for follicles obtained after ovulation, which was not influenced by presence of LH in the incubation medium. Luteinizing hormone caused depletion of stores of histamine from the wall of follicles collected before the preovulatory surge of LH. Histamine could act as a paracrine mediator in the follicular mechanisms of ovulation and(or) luteinization.     

Perialveolar interstitial resistance and compliance in isolated rat lung

We have developed a method to characterize fluid transport through the perialveolar interstitium using micropuncture techniques. In 10 experiments we established isolated perfused rat lung preparations. The lungs were initially isogravimetric at 10 cmH2O arterial pressure, 2 cmH2O venous pressure, and 5 cmH2O alveolar pressure. Perialveolar interstitial pressure was determined by micropuncture at alveolar junctions by use of the servo-null technique. Simultaneously a second micropipette was placed in an alveolar junction 20-40 microns away, and a bolus of albumin solution (3.5 g/100 ml) was injected. The resulting pressure transient was recorded for injection durations of 1 and 4 s in nonedematous lungs. The measurements were repeated after gross edema formation induced by elevated perfusion pressure. We model the interstitium as a homogeneous linearly poroelastic material and assume the initial pressure distribution due to the injection to be Gaussian. The pressure decay is inversely proportional to time, with time constant T, where T is a measure of the ratio of interstitial tissue stiffness to interstitial resistance to fluid flow. A linear regression was performed on the reciprocal of the pressure for the decaying portion of the transients to determine T. Comparing pressure transients in nonedematous and edematous lungs, we found that T was 4.0 +/- 1.4 and 1.4 +/- 0.6 s, respectively. We have shown that fluid transport through the pulmonary interstitium on a local level is sensitive to changes in interstitial stiffness and resistance. These results are consistent with the decreased stiffness and resistance in the perialveolar interstitium that accompany increased hydration.     

Multiscale Modelling of Fluid and Drug Transport in Vascular Tumours

A model for fluid and drug transport through the leaky neovasculature and porous interstitium of a solid tumour is developed. The transport problems are posed on a micro-scale characterized by the inter-capillary distance, and the method of multiple scales is used to derive the continuum equations describing fluid and drug transport on the length scale of the tumour (under the assumption of a spatially periodic microstructure). The fluid equations comprise a double porous medium, with coupled Darcy flow through the interstitium and vasculature, whereas the drug equations comprise advection–reaction equations; in each case the dependence of the transport coefficients on the vascular geometry is determined by solving micro-scale cell problems.     

人体纤维结缔组织网络中的主动界面液体流动新现象及其机制研究进展

认识和理解组织液在凝胶样组织间隙中的流动规律和力学机制是近百年来的重大医学科学问题之一。本文回顾了生理学中关于组织液流动的若干代表性研究、颅内血管周围间隙中的液体流动研究及经络示踪成像研究等,并介绍了已有的系列研究结果,即通过追踪人体和动物体内不同部位组织间隙中的示踪剂流动,发现组织液沿动脉和静脉血管外膜、神经和皮肤等至少四种解剖结构进行长程而有序的流动;其中的皮肤组织液长程流动通路与人体四肢远端穴位区相连接;组织液长程流动通路的内部结构是由有序纤维集合而成的纵向纤维束,组织液以纤维等固相结构为轨道而流动,形成贯穿全身的"组织液界面流动网络",具有重要的医学科学和中西医结合研究价值。     

Extracellular superoxide dismutase attenuates release of pulmonary hyaluronan from the extracellular matrix following bleomycin exposure

The major pulmonary antioxidant enzyme involved in the protection of the lung interstitium from oxidative stress is extracellular superoxide dismutase (EC-SOD). It has been previously shown that EC-SOD knock-out mice are more susceptible to bleomycin-induced lung injury, however, the molecular mechanism(s) remains unclear. We report here that bleomycin-induced lung damage, in EC-SOD KO mice, is associated with increased hyaluronan release into alveolar fluid. Analysis of hyaluronan synthase gene expression and hyaluronan molecular weight distribution suggested that elevated levels of hyaluronan in the alveolar fluid are mostly due to its release from the interstitium. Our results indicate that EC-SOD attenuates bleomycin-induced pulmonary injury, at least in part, by preventing superoxide-mediated release of hyaluronan into alveolar space.     

A model of unsteady-state transvascular fluid and protein transport in the lung

Models of steady-state fluid and solute transport in the microcirculation are used primarily to characterize filtration and permeability properties of the transport barrier. Important transient relationships, such as the rate of fluid accumulation in the tissue, cannot be predicted with steady-state models. In this paper we present three simple models of unsteady-state fluid and protein exchange between blood plasma and interstitial fluid. The first treats the interstitium as a homogeneous well-mixed compliant compartment, the second includes an interstitial gel, and the third allows for both gel and free fluid in the interstitium. Because we are primarily interested in lung transvascular exchange we used the multiple-pore model and pore sizes described by Harris and Roselli (J. Appl. Physiol.: Respirat . Environ. Exercise Physiol. 50: 1-14, 1981) to characterize the microvascular barrier. However, the unsteady-state transport theory presented here should apply to other organ systems and can be used with different conceptual models of the blood-lymph barrier. For a step increase in microvascular pressure we found good agreement between theoretical and experimental lymph flow and lymph concentrations in the sheep lung when the following parameter ranges were used: base-line interstitial volume, 150-190 ml; interstitial compliance, 7-10 ml/Torr; initial interstitial fluid pressure, -1 Torr; pressure in initial lymphatics, -5 to -6 Torr; and conductivity of the interstitium and lymphatic barrier, 4.25 X 10(-4) ml X s-1 X Torr-1. Based on these values the model predicts 50% of the total change in interstitial water volume occurs in the first 45 min after a step change in microvascular pressure.(ABSTRACT TRUNCATED AT 250 WORDS)     

Ovulation and the mechanism of follicle rupture

Summary The rabbit Graafian follicles are encircled by a capillary network between the theca interna and the avascular membrana granulosa. After injection of an ovulatory dose of human chorionic gonadotrophin (HCG) the theca interna cells showed an increase in the amount of smooth endoplasmic reticulum, lipid droplets and mitochondria with tubular cristae. In addition, considerably more junctions, similar to the abutment nexuses of granulosa cells were found; annular nexuses also appeared. At 4 hours after injection of HCG a prominent oedema was evident in the theca interna layer, particularly in the apical region.Small fenestrations in the endothelium of the blood capillaries increased in amount after HCG injection, and close to the time of ovulation, large gaps or perforations, 1–3 in diameter, were found in the thin, distended part of the endothelial cells. The surrounding basement membrane became fragmented and partly lost, so that a seemingly free passage from the capillary lumen to the interstitium was eventually established. Leakage of fluid, causing interstitial oedema, presumably proceeds until the pressure in the pericapillary interstitium has risen to the pressure in the capillaries. Some hours before and up to ovulation the pericapillary interstitium has also broad communications with the cavity of the follicles. Therefore, both pressure and fluid can be passed from the capillaries-via the interstitium-to the follicle antrum. However, influx of fluid with subsequent follicle expansion and ovulation-at constant pressure-does not occur until the tensile strength of the follicle wall has decreased.This investigation was supported by grants from the Swedish Medical Besearch Council (Projects No. B72-12X-78-07A, B73-12X-78-08B and B74-12X-78-09C). The technical assistance of Miss Ingalis Fransson, Miss Kerstin Nilsson, and Mrs. Ulla-Britt Westman is greatly appreciated.     

Continuity of arterial and venous extra-alveolar interstitium in excised rabbit lungs

We studied the interdependence of arterial and venous extra-alveolar vessel (EAV) leakage on the rate of pulmonary vascular fluid filtration (measured as the change in lung weight over time). Edema was produced in continually weighed, excised rabbit lungs kept in zone 1 (alveolar pressure = 25 cmH2O) by increasing pulmonary arterial (Ppa) and/or venous (Ppv) pressure from 5 to 20 cmH2O (relative to the lung base) and continuing this hydrostatic stress for 3-5 h. Raising Ppa and Ppv simultaneously produced a lower filtration rate than the sum of the filtration rates obtained when Ppa and Ppv were raised separately, while the lung gained from 20 to 95% of its initial weight. When vascular pressure was elevated in either EAV segment, fluid filtration always decreased rapidly as the lung gained up to 30-45% of its initial weight. Filtration then decreased more slowly. The lungs became isogravimetric at 60 and 85% weight gain when the Ppa or Ppv was elevated, respectively; when Ppa and Ppv were raised simultaneously substantial fluid filtration continued even after 140% weight gain. We conclude that the arterial and venous EAV's share a common interstitium in the zone 1 condition, this interstitium cannot be represented as a single compartment with a fixed resistance and compliance, and arterial and venous EAV leakage influences leakage from the other segment.     

A Model for Fluid Drainage by the Lymphatic System

This study investigates the fluid flow through tissues where lymphatic drainage occurs. Lymphatic drainage requires the use of two valve systems, primary and secondary. Primary valves are located in the initial lymphatics. Overlapping endothelial cells around the circumferential lining of lymphatic capillaries are presumed to act as a unidirectional valve system. Secondary valves are located in the lumen of the collecting lymphatics and act as another unidirectional valve system; these are well studied in contrast to primary valves. We propose a model for the drainage of fluid by the lymphatic system that includes the primary valve system. The analysis in this work incorporates the mechanics of the primary lymphatic valves as well as the fluid flow through the interstitium and that through the walls of the blood capillaries. The model predicts a piecewise linear relation between the drainage flux and the pressure difference between the blood and lymphatic capillaries. The model describes a permeable membrane around a blood capillary, an elastic primary lymphatic valve and the interstitium lying between the two.     

Effects of albumin, dextran, and hyaluronidase on pulmonary interstitial conductivity

The fluid conductivity of albumin solutions of various concentrations relative to that of saline was measured in the interstitium surrounding a short segment of a large (1.5- to 3-mm-diam) blood vessel of an isolated rabbit lung of which air spaces and vasculature were filled with silicon rubber. At a constant driving pressure, the flow of the following solutions was measured sequentially: normal saline and albumin solution (3, 5.5, 8, or 15 g/100 ml saline), hyaluronidase solution (0.02 g/100 ml), and albumin solution (same concentration used before hyaluronidase solution). The albumin-to-saline flow ratios averaged 1.00 +/- 0.23 (SD), 1.01 +/- 0.21, 1.32 +/- 0.63, and 1.54 +/- 0.36 for albumin concentrations of 3, 5.5, 8, and 15 g/100 ml, respectively. These ratios were higher than the corresponding values of 0.88, 0.78, 0.72, and 0.5 expected if the flow of albumin solution were to depend only on fluid viscosity. The flow of dextran and hyaluronan solutions was more viscosity dependent than the flow of albumin solutions. The increased flow of albumin solution could be the result of a reduced excluded volume of albumin caused by collagen and glycosaminoglycans with an increased albumin concentration. The flow of hyaluronidase solution was 24 +/- 22 (SD)-fold (n = 36) larger than the flow of albumin solution. Thus hyaluronan was responsible for most of the hydraulic resistance of the interstitium to bulk flow. After its degradation, the flow of albumin solution became more viscosity dependent. The interaction between plasma proteins and glycosaminoglycans in the pulmonary interstitium could serve to enhance clearance of microvascular filtrate, particularly under conditions of large protein leaks.     

Blood circulation disorders in the post-resuscitation period of myocardial infarction and the role of body fluid measurements in their development

Experiments were performed on 43 dogs with injured (infarction) and intact myocardium typical of the cardiac output changes with initial transitory increasing, following decreasing and tendency for restitution in 24 h after resuscitation were established. Similar transferences of fluid in body volumes with initial entrance of fluid in cells, which bring the development of hypovolemia and following return in extracellular volume were shown. More pronounced depression of contractile function of the heart in combination with retarded of restitution plasma volume and delay of fluid in interstitium of dogs with myocardial infarction accompany change for the worse of restitution and survival.     

A one tube flow problem arising in physiology

A mathematical analysis, including existence and uniqueness, is given for some boundary value problems which model the flow of a fluid-solute mixture in a tube which is placed in an interstitium. The model permits an interchange of fluid and solute across the tube walls.     

Human Serum Albumin Can Regulate Amyloid-β Peptide Fiber Growth in the Brain Interstitium: IMPLICATIONS FOR ALZHEIMER DISEASE

Alzheimer disease is a neurodegenerative disorder characterized by extracellular accumulation of amyloid-β peptide (Aβ) in the brain interstitium. Human serum albumin (HSA) binds 95% of Aβ in blood plasma and is thought to inhibit plaque formation in peripheral tissue. However, the role of albumin in binding Aβ in the cerebrospinal fluid has been largely overlooked. Here we investigate the effect of HSA on both Aβ(1-40) and Aβ(1-42) fibril growth. We show that at micromolar cerebrospinal fluid levels, HSA inhibits the kinetics of Aβ fibrillization, significantly increasing the lag time and decreasing the total amount of fibrils produced. Furthermore, we show that the amount of amyloid fibers generated directly correlates to the proportion of Aβ not competitively bound to albumin. Our observations suggest a significant role for HSA regulating Aβ fibril growth in the brain interstitium.     

The morphological basis of fluid balance in the interstitium of the juxtaglomerular apparatus

Summary The morphological basis of fluid balance in the interstitium of the juxtaglomerular apparatus (JGA) was reevaluated in rats, mice and Tupaia. Three ultrastructural features in the region of the vascular pole of the renal corpuscle are described that may be important for the fluid balance in this region: (1) podocyte foot processes in the parietal layer of Bowman's capsule, (2) endothelial fenestrations in the wall of the incoming afferent arteriole, both facing Goormaghtigh and epithelioid cells, and (3) the mesangial type lining of the glomerular stalk. With respect to the relevant pressure gradients, this morphology may provide the basis of bulk-fluid flow directed to the interstitium of the JGA including the Goormaghtigh cell field. Thus, the fluid balance in the lacis area and, consequently, the tubulo-glomerular feedback mechanism, probably does not solely depend upon the reabsorptive transport of the macula densa. Similar considerations may be valid for the humoral control of renin secretion from juxtaglomerular epithelioid cells.These studies were supported by the German Research Foundation within the SFB 90 Cardiovasculäres System     

Tubuloglomerular Feedback Signal Transduction in a Short Loop of Henle

In previous studies, we used a mathematical model of the thick ascending limb (TAL) to investigate nonlinearities in the tubuloglomerular feedback (TGF) loop. That model does not represent other segments of the nephron, the water, and NaCl transport along which may impact fluid flow rate and NaCl transport along the TAL. To investigate the extent to which those transport processes affect TGF mediation, we have developed a mathematical model for TGF signal transduction in a short loop nephron. The model combines a simple representation of the renal cortex with a highly-detailed representation of the outer medulla (OM). The OM portion of the model is based on an OM urine concentrating mechanism model previously developed by Layton and Layton (Am. J. Renal 289:F1346–F1366, 2005a). When perturbations are applied to intratubular fluid flow at the proximal straight tubule entrance, the present model predicts oscillations in fluid flow and solute concentrations in the cortical TAL and interstitium, and in all tubules, vessels, and interstitium in the OM. Model results suggest that TGF signal transduction by the TAL is a generator of nonlinearities: if a sinusoidal oscillation is added to constant intratubular fluid flow, the time required for an element of tubular fluid to traverse the TAL is oscillatory, but nonsinusoidal; those results are consistent with our previous studies. As a consequence, oscillations in NaCl concentration in tubular fluid alongside the macula densa (MD) will be nonsinusoidal and contain harmonics of the original sinusoidal frequency. Also, the model predicts that the oscillations in NaCl concentration at the loop-bend fluid are smaller in amplitude than those at the MD, a result that further highlights the crucial role of TAL in the nonlinear transduction of TGF signal from SNGFR to MD NaCl concentration.     

Relationship between interstitial fluid volume and pressure (compliance) in hypothyroid rats

There is clinical and experimental evidence that lack of thyroid hormones may affect the composition and structure of the interstitium. This can influence the relationship between volume and pressure during changes in hydration. Hypothyrosis was induced in rats by thyroidectomy 8 wk before the experiments. Overhydration was induced by infusion of acetated Ringer, 5, 10, and 20% of the body weight, while fluid was withdrawn by peritoneal dialysis with hypertonic glucose. Interstitial fluid pressure (P(i)) in euvolemia (euvolemic control situation) and experimental situation was measured with micropipettes connected to a servocontrolled counterpressure system. The corresponding interstitial fluid volume (V(i)) was found as the difference between extracellular fluid volume measured as the distribution volume of (51)Cr-labeled EDTA and plasma volume measured using (125)I-labeled human serum albumin. In euvolemia, V(i) was similar or lower in the skin and higher in skeletal muscle of hypothyroid than in euthyroid control rats, whereas the corresponding P(i) was higher in all tissues. During overhydration, P(i) rose to the same absolute level in both types of rats, whereas during peritoneal dialysis there was a linear relationship between volume and pressure in all tissues and types of rats. Interstitial compliance (C(i)), calculated as the inverse value of the slope of the curve relating changes in volume and pressure in dehydration, did not differ significantly in the hindlimb skin of hypothyroid and euthyroid rats. However, in skeletal muscle, C(i) was 1.3 and 2.0 ml. 100 g(-1). mmHg(-1) in hypothyroid and euthyroid rats (P < 0.01), with corresponding numbers for the back skin of 2.7 and 5.0 ml. 100 g(-1). mmHg(-1) (P < 0.01). These experiments suggest that lack of thyroid hormones in rats changes the interstitial matrix, again leading to reduced C(i) and reduced ability to mobilize fluid from the interstitium.     

A critical parameter for transcapillary exchange of small solutes in countercurrent systems

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.     

Three-dimensional tissue deformation in subcutaneous tissues overlying bony prominences may help to explain external load transfer to the interstitium

Anesthetized, carefully positioned, female, weanling, white-haired pigs were used to test the hypothesis that (1) interface pressure, the pressure between the skin and an external load, can be used to predict the interstitial fluid pressure over the wings of ilia and the last dorsal spinous process and (2) three-dimensional tissue deformation of the interstitium under the load could partially explain how the external load is transferred at that site. When a 4 or 8 kg load was distributed over the hips of the pigs, the interface pressures over the ilia were approximately 145 and 207 cm H2O, respectively. Approximately 28% of this pressure was transferred to the tissue, resulting in an increase in interstitial fluid pressure of approximately 39 cm H2O for the 4 kg load and 60 cm H2O for the 8 kg load. However, over the spinous process, about 42-43% of the load was transferred to the interstitium. Subcutaneous tissue marker movement occurred along the gamma and theta spherical coordinate but no significant tissue marker movement along the phi coordinate. The latter indicates no significant twisting of the tissue while the former demonstrates three-dimensional shearing. There were also indications of tissue creep since the markers continued to move with constant loading.