A fully coupled porous media and channels flow approach for simulation of blood and bile flow through the liver lobules

Two dimensional, steady state, and incompressible blood and bile flows through the liver lobules are numerically simulated. Two different geometric models A and B are proposed to study the effects of lobule structure on the fluid flow behaviour. In Model A, the lobule tissue is represented as a hexagonal shape porous medium with a set of flow channels at its vertices accounting for the hepatic artery, portal and central veins along with bile ductules. Model B is a channelized porous medium constructed by adding a set of flow channels, representing the bile canaliculies and lobule sinusoids, to Model A. The bile and blood flow through the lobule is simulated by the finite element approach, based on the Darcy/Brinkman equations in the lobule tissue and the Navier-Stokes (or Stokes) equations in the flow channels. In Model B, a transmission factor on the boundaries of the bile canaliculies is introduced to connect the bile and blood flows. First, a single regular lobule is utilized to exhibit the fluid flow pattern through the liver lobule represented by proposed geometric models. Then, the model is extended to a group of liver lobules to demonstrate the flow through a liver slice represented by irregular lobules. Numerical results indicate that the Darcy and Brinkman equations provide nearly the same solutions for Model A and similar solutions with a little difference for Model B. It is shown that the existence of sinusoids and bile canaliculies inside the liver lobules has noticeable effects on its fluid flow pattern, in terms of pressure and velocity fields.     

Mathematical modeling of the circulation in the liver lobule

In this paper, we develop a mathematical model of blood circulation in the liver lobule. We aim to find the pressure and flux distributions within a liver lobule. We also investigate the effects of changes in pressure that occur following a resection of part of the liver, which often leads to high pressure in the portal vein. The liver can be divided into functional units called lobules. Each lobule has a hexagonal cross-section, and we assume that its longitudinal extent is large compared with its width. We consider an infinite lattice of identical lobules and study the two-dimensional flow in the hexagonal cross-sections. We model the sinusoidal space as a porous medium, with blood entering from the portal tracts (located at each of the vertices of the cross-section of the lobule) and exiting via the centrilobular vein (located in the center of the cross-section). We first develop and solve an idealized mathematical model, treating the porous medium as rigid and isotropic and blood as a Newtonian fluid. The pressure drop across the lobule and the flux of blood through the lobule are proportional to one another. In spite of its simplicity, the model gives insight into the real pressure and velocity distribution in the lobule. We then consider three modifications of the model that are designed to make it more realistic. In the first modification, we account for the fact that the sinusoids tend to be preferentially aligned in the direction of the centrilobular vein by considering an anisotropic porous medium. In the second, we account more accurately for the true behavior of the blood by using a shear-thinning model. We show that both these modifications have a small quantitative effect on the behavior but no qualitative effect. The motivation for the final modification is to understand what happens either after a partial resection of the liver or after an implantation of a liver of small size. In these cases, the pressure is observed to rise significantly, which could cause deformation of the tissue. We show that including the effects of tissue compliance in the model means that the total blood flow increases more than linearly as the pressure rises.     

Functional recovery of fluid drainage precedes lymphangiogenesis in acute murine foreleg lymphedema

Secondary lymphedema in humans is a common consequence of axillary lymph node dissection (ALND) to treat breast cancer. It is commonly hypothesized that lymphatic growth is required to increase fluid drainage and ameliorate lymphedema. Although there is a pronounced alteration in the balance of interstitial forces regulating fluid transport that sustains the chronic form of lymphedema, it is presently unknown whether changes occur to the balance of interstitial forces during acute lymphedema that may play a role in the recovery of fluid drainage. Here, we compared the relative importance of lymphangiogenesis of lymphatic vessels and interstitial flows for restoring fluid drainage and resolving acute lymphedema in the mouse foreleg after ALND. We found that removal of the axillary lymph nodes reduced lymph drainage in the foreleg at days 0 and 5 postsurgery, with fluid tracer spreading interstitially through subcutaneous tissues. Interstitial fluid drainage returned to normal by day 10, whereas functional regrowth of lymphatic vessels was first detected by indocyanine green fluorescence lymphography at day 15, demonstrating that the recovery of interstitial fluid drainage preceded the regrowth of lymphatic vessels. This was confirmed by the administration of VEGF receptor-3-neutralizing antibodies, which completely blocks lymphatic regrowth. It was found that the recovery of interstitial fluid drainage and the natural resolution of acute lymphedema produced by ALND were not hindered by VEGF receptor-3 neutralization, demonstrating that interstitial fluid drainage recovery and the resolution of acute lymphedema are lymphangiogenesis independent. The data highlight the central role of the interstitial environment in adapting to lymphatic injury to increase fluid drainage.     

Probing the effect of morphology on lymphatic valve dynamic function

The lymphatic system is vital to the circulatory and immune systems, performing a range of important functions such as transport of interstitial fluid, fatty acid, and immune cells. Lymphatic vessels are composed of contractile walls and lymphatic valves, allowing them to pump lymph against adverse pressure gradients and to prevent backflow. Despite the importance of the lymphatic system, the contribution of mechanical and geometric changes of lymphatic valves and vessels in pathologies of lymphatic dysfunction, such as lymphedema, is not well understood. We develop a fully coupled fluid–solid, three-dimensional computational model to interrogate the various parameters thought to influence valve behavior and the consequences of these changes to overall lymphatic function. A lattice Boltzmann model is used to simulate the lymph, while a lattice spring model is used to model the mechanics of lymphatic valves. Lymphatic valve functions such as enabling lymph flow and preventing backflow under varied lymphatic valve geometries and mechanical properties are investigated to provide an understanding of the function of lymphatic vessels and valves. The simulations indicate that lymphatic valve function is optimized when valves are of low aspect ratio and bending stiffness, so long as these parameters are maintained at high enough values to allow for proper valve closing. This suggests that valve stiffening could have a profound effect on overall lymphatic pumping performance. Furthermore, dynamic valve simulations showed that this model captures the delayed response of lymphatic valves to dynamic flow conditions, which is an essential feature of valve operation. Thus, our model enhances our understanding of how lymphatic pathologies, specifically those exhibiting abnormal valve morphologies such as has been suggested to occur in cases of primary lymphedema, can lead to lymphatic dysfunctions.     

Liver units in three dimensions: I. Organization of argyrophilic connective tissue skeleton in porcine liver with particular reference to the "compound hepatic lobule"

Liver units were investigated in pig livers by means of histologic serial tracing, physical model building, and computer-aided three-dimensional imaging. Observations of the argyrophilic connective tissue skeleton were based mainly on the celloidin-embedded serial sections treated with silver impregnation. The parenchymal mass that clothed the initial segments of hepatic venous radicles was demarcated by fibrous septa which formed isolable units with two basic patterns: the simple hepatic lobule (SHL) and the compound hepatic lobule (CHL). Both lobule types presented regular limiting structures circumscribing each unit. Three-dimensional studies revealed that 25% of the lobules in a section belonged to the SHL type and 75% to the CHL type, the latter being predominant among the surface lobules. When considered in only two dimensions, however, the SHL-like lobules constituted the majority. Polygonal analysis disclosed that the pentagonal lobule was the most typical, instead of the "hexagonal" or "classic" lobule. The CHLs represented a multiaxial unit containing a system of venous tributaries in accordance with intralobular septation, whereas the SHLs were found with one axial vessel having a dendritic tendency at the incipient end; some SHLs were drained eccentrically by separate vessels into a sublobular vein. It was observed that, in dividing CHLs, whereas particular sinosoids were transformed into portal twigs, other sinusoids were changed into central venous tributaries. Fibrous deposition occurred along the septal-line sinusoids, bringing into view the septum-initiating plane. Fibroconnective tissue was supplied from the portal area and central (sublobular) adventitia, where portal triad structures and adventitial arterioles, respectively, were included. The findings of the present study facilitate the understanding of several characters of the lobules that have been reported previously, or occasionally postulated, such as the portal-central bridging tendency, the intralobular arterioles or ductules, the translobular artery or portal vein, the "portal-portal" or "portal-central" anastomoses, and the apposition of pericentral zone close to periportal zone. Based on differences in argyrophilia of sinusoidal reticulum, in proportion of lobule types, and in vasculature, the anatomic heterogeneity of liver unit was demonstrable in zonality, regionality, and locality.     

A multiscale sliding filament model of lymphatic muscle pumping

The lymphatics maintain fluid balance by returning interstitial fluid to veins via contraction/compression of vessel segments with check valves. Disruption of lymphatic pumping can result in a condition called lymphedema with interstitial fluid accumulation. Lymphedema treatments are often ineffective, which is partially attributable to insufficient understanding of specialized lymphatic muscle lining the vessels. This muscle exhibits cardiac-like phasic contractions and smooth muscle-like tonic contractions to generate and regulate flow. To understand the relationship between this sub-cellular contractile machinery and organ-level pumping, we have developed a multiscale computational model of phasic and tonic contractions in lymphatic muscle and coupled it to a lymphangion pumping model. Our model uses the sliding filament model (Huxley in Prog Biophys Biophys Chem 7:255–318, 1957) and its adaptation for smooth muscle (Mijailovich in Biophys J 79(5):2667–2681, 2000). Multiple structural arrangements of contractile components and viscoelastic elements were trialed but only one provided physiologic results. We then coupled this model with our previous lumped parameter model of the lymphangion to relate results to experiments. We show that the model produces similar pressure, diameter, and flow tracings to experiments on rat mesenteric lymphatics. This model provides the first estimates of lymphatic muscle contraction energetics and the ability to assess the potential effects of sub-cellular level phenomena such as calcium oscillations on lymphangion outflow. The maximum efficiency value predicted (40%) is at the upper end of estimates for other muscle types. Spontaneous calcium oscillations during diastole were found to increase outflow up to approximately 50% in the range of frequencies and amplitudes tested.

     

Influence of interstitial fluid dynamics on growth and therapy of angiogenic tumor. Analysis by mathematical model

We have developed a spatially distributed mathematical model of angiogenic tumor growth in tissue with account of interstitial fluid dynamics and bevacizumab monotherapy. In this model the process of neovascularization is initiated by tumor cells in a state of metabolic stress, vascular endothelial growth factor (VEGF) being its main mediator. The model takes into consideration the convection flows arising in dense tissue due to active proliferation and migration of tumor cells as well as interstitial fluid inflow from blood vascular system, its outflow through lymphatic system and redistribution in the area of tumor growth. The work considers the diffusive approximation of interstitial fluid dynamics in tumor and normal tissue. Numerical study of the model showed that in absence of therapy a peritumoral edema is formed due to the increase of interstitial fluid inflow from angiogenic capillaries. In the case of rapid interstitial fluid outflow through lymphatic system and its fast transport from necrotic zone to normal tissue the regimes of full growth stop are observed in case of low-invasive tumor. Under bevacizumab monotherapy the peritumoral edema vanishes and low-invasive tumor may not only decelerate its growth, but also start shrinking for a large range of parameters.     

Perfusion characteristics of the human hepatic microcirculation based on three-dimensional reconstructions and computational fluid dynamic analysis

The perfusion of the liver microcirculation is often analyzed in terms of idealized functional units (hexagonal liver lobules) based on a porous medium approach. More elaborate research is essential to assess the validity of this approach and to provide a more adequate and quantitative characterization of the liver microcirculation. To this end, we modeled the perfusion of the liver microcirculation using an image-based three-dimensional (3D) reconstruction of human liver sinusoids and computational fluid dynamics techniques. After vascular corrosion casting, a microvascular sample (±0.134 mm(3)) representing three liver lobules, was dissected from a human liver vascular replica and scanned using a high resolution (2.6 μm) micro-CT scanner. Following image processing, a cube (0.15?×?0.15?×?0.15 mm(3)) representing a sample of intertwined and interconnected sinusoids, was isolated from the 3D reconstructed dataset to define the fluid domain. Three models were studied to simulate flow along three orthogonal directions (i.e., parallel to the central vein and in the radial and circumferential directions of the lobule). Inflow and outflow guidances were added to facilitate solution convergence, and good quality volume meshes were obtained using approximately 9?×?10(6) tetrahedral cells. Subsequently, three computational fluid dynamics models were generated and solved assuming Newtonian liquid properties (viscosity 3.5 mPa s). Post-processing allowed to visualize and quantify the microvascular flow characteristics, to calculate the permeability tensor and corresponding principal permeability axes, as well as the 3D porosity. The computational fluid dynamics simulations provided data on pressure differences, preferential flow pathways and wall shear stresses. Notably, the pressure difference resulting from the flow simulation parallel to the central vein (0-100 Pa) was clearly smaller than the difference from the radial (0-170 Pa) and circumferential (0-180 Pa) flow directions. This resulted in a higher permeability along the central vein direction (k(d,33)?=?3.64?×?10(-14) m(2)) in comparison with the radial (k(d,11)?=?1.56?×?10(-14) m(2)) and circumferential (k(d,22)?=?1.75?×?10(-14) m(2)) permeabilities which were approximately equal. The mean 3D porosity was 14.3. Our data indicate that the human hepatic microcirculation is characterized by a higher permeability along the central vein direction, and an about two times lower permeability along the radial and circumferential directions of a lobule. Since the permeability coefficients depend on the flow direction, (porous medium) liver microcirculation models should take into account sinusoidal anisotropy.     

Intralobular Pulmonary Lymphatic Distribution in Normal Human Lung Using D2-40 Antipodoplanin Immunostaining

It has been assumed for a long time that except for limited areas close to respiratory bronchioles or their satellite arteries, there is no evidence of lymphatic vessels deep in the pulmonary lobule. An immunohistochemical study using the D2-40 monoclonal antibody was performed on normal pulmonary samples obtained from surgical specimens, with particular attention to the intralobular distribution of lymphatic vessels. This study demonstrated the presence of lymphatics not only in the connective tissue surrounding the respiratory bronchioles but also associated with intralobular arterioles and/or small veins even less than 50 μm in diameter. A few interlobular lymphatic vessels with a diameter ranging from 10 μm to 20 μm were also observed further away, in interalveolar walls. In conclusion, this study, using the D2-40 monoclonal antibody, demonstrated the presence of small lymphatic channels within the normal human pulmonary lobules, emerging from interalveolar interstitium, and around small blood vessels constituting the paraalveolar lymphatics. This thin intralobular lymphatic network may play a key pathophysiological role in a wide variety of alveolar and interstitial lung diseases and requires further investigation. (J Histochem Cytochem 57:643–648, 2009)     

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.     

On the intrinsic innervation of normal rat liver

Summary With the Bodian method stained fibers were observed in the lobules of the rat liver and with the modified Karnovsky and Roots thiocholine method cholinesterase (presumably acetylcholinesterase (AChE))-positive nerve fibers were found in a pattern similar to that of the Bodian-stained fibers. The AChE positive nerve fibers form a network in the liver lobules in close relation to hepatocytes and sinusoids. Fluorescent varicose nerve fibers demonstrated by the glyoxylic acid and Falck-Hillarp fluorescence methods were found only in the interlobular spaces associated with vessels. As no overlapping of distribution patterns of AChE-positive nerve fibers and fluorescent nerve fibers occurs, the AChE activity of the nerves of the liver lobules probably reflects the associated presence of acetylcholine in the nerve fibers. In consequence we suggest that nerves of the liver lobules belong to the autonomic parasympathetic nervous system.SEM of liver tissue revealed light cords apparently situated in smooth surfaced channels between adjacent hepatocytes and in the space of Disse, where fibers also cross sinusoids. We tentatively suggest that the cords of the SEM represent the AChE-positive nerve fibers of our LM observations'.The skilled assistance of Dr. Esther Hage, Department of Pathology, Odense Sygehus, Denmark, in the Falck-Hillarp fluorescence work is gratefully acknowledged     

Development of the zebrafish lymphatic system requires VEGFC signaling

Lymphangiogenesis results in the formation of a vascular network distinct from arteries and veins that serves to drain interstitial fluid from surrounding tissues and plays a pivotal role in the immune defense of vertebrates as well as in the progression of cancer and other diseases . In mammals, lymph vessels are lined by endothelial cells possibly sprouting from embryonic veins, and their development appears to be critically dependent on the function of PROX1 and VEGFC signaling . The existence of a lymphatic system in teleosts has been a matter of debate for decades. Here we show on the morphological, molecular, and functional levels that zebrafish embryos develop a lymphatic vasculature that serves to retrieve components of the interstitium to the lymph system. We demonstrate the existence of vessels that are molecularly and functionally distinct from blood vessels and show that the development of these vessels depends on Vegfc and VEGFR-3/Flt4 signaling. These findings imply that the molecular components controlling lymphangiogenesis in zebrafish and mammals are conserved and that the zebrafish lymphatic system develops early enough to allow in vivo observations, lineage tracing, and genetic as well as pharmacological screens.     

The lymphatic system in body homeostasis: physiological conditions

The lymphatic system is an organized network composed of functionally interrelated lymphoid tissue, and transportation pathways of tissue fluid/lymph and lymphoid cells. Its main components are 1. migrating dendritic cells, macrophages and lymphocytes, organized lymphoid tissue such as lymph nodes, thymus, spleen, bone marrow, and lymphoid tissue in gut and lungs, liver lymphoid cells, and the dendritic cell network of nonlymphoid organs; 2. vessels (intercellular space, lymphatics, and perivascular spaces); 3. fluids (tissue fluid and lymph). The lymphatic system can be divided into the following compartments: peripheral (from the interstitial space to and within the nearest lymph node), and central (efferent lymphatics, cysterna chyli, and thoracic duct, all lymphoid organs). Organs and tissues with the most active afferent arm of the lymphatic system are skin, gut, and lungs. These are the body structures exposed to the external environment. All other nonlymphoid bodily tissues are also percolated by tissue fluid/lymph, and contain a network of dendritic cells and macrophages. Data obtained from normal human subjects on lymph composition and flow are presented. Future trends in lymphatic research are outlined.     

Genesis and pathogenesis of lymphatic vessels

The lymphatic system is generally regarded as supplementary to the blood vascular system, in that it transports interstitial fluid, macromolecules, and immune cells back into the blood. However, in insects, the open hemolymphatic (or lymphohematic) system ensures the circulation of immune cells and interstitial fluid through the body. The Drosophila homolog of the mammalian vascular endothelial growth factor receptor (VEGFR) gene family is expressed in hemocytes, suggesting a close relationship to the endothelium that develops later in phylogeny. Lymph hearts are typical organs for the propulsion of lymph in lower vertebrates and are still transiently present in birds. The lymphatic endothelial marker VEGFR-3 is transiently expressed in embryonic blood vessels and is crucial for their development. We therefore regard the question of whether the blood vascular system or the lymphatic system is primary or secondary as open. Future molecular comparisons should be performed without any bias based on the current prevalence of the blood vascular system over the lymphatic system. Here, we give an overview of the structure, function, and development of the lymphatics, with special emphasis on the recently discovered lymphangiogenic growth factors.     

Topographo-anatomic basis for the reconstruction of lymphatic passages and the reinnervation of transplanted kidneys

Topographic anatomy of the deferent lymphatic vessels and the regional lymph nodes of the kidneys have been studied in 35 dogs. Basing on the topographoanatomical investigations performed the authors suggest a rational technique for restoring the lymph outflow combined with the reinnervation of the renal transplant. They suggest to take the right kidney together with the dorsocaval lymph nodes, and the left--with the left lateroaortal lymph nodes simultaneously cutting out the fascial-fatty graft with the nerves situating over the ventral surface of the renal hilar vessels. The lymph outflow is suggested to be restorted by means of anastomosis between the regional lymph nodes of the renal transplant and the iliac node, or the nearest vein, and to innervate the transplant--by means of stitching the fascial-fatty grafts of the anostomized blood vessels.     

Lymphangion coordination minimally affects mean flow in lymphatic vessels

The lymphatic system returns interstitial fluid to the central venous circulation, in part, by the cyclical contraction of a series of "lymphangion pumps" in a lymphatic vessel. The dynamics of individual lymphangions have been well characterized in vitro; their frequencies and strengths of contraction are sensitive to both preload and afterload. However, lymphangion interaction within a lymphatic vessel has been poorly characterized because it is difficult to experimentally alter properties of individual lymphangions and because the afterload of one lymphangion is coupled to the preload of another. To determine the effects of lymphangion interaction on lymph flow, we adapted an existing mathematical model of a lymphangion (characterizing lymphangion contractility, lymph viscosity, and inertia) to create a new lymphatic vessel model consisting of several lymphangions in series. The lymphatic vessel model was validated with focused experiments on bovine mesenteric lymphatic vessels in vitro. The model was then used to predict changes in lymph flow with different time delays between onset of contraction of adjacent lymphangions (coordinated case) and with different relative lymphangion contraction frequencies (noncoordinated case). Coordination of contraction had little impact on mean flow. Furthermore, orthograde and retrograde propagations of contractile waves had similar effects on flow. Model results explain why neither retrograde propagation of contractile waves nor the lack of electrical continuity between lymphangions adversely impacts flow. Because lymphangion coordination minimally affects mean flow in lymphatic vessels, lymphangions have flexibility to independently adapt to local conditions.     

Lymph flow from murine footpad tumors before and after sublethal hyperthermia.

The effect of local hyperthermia (43.5 degrees C for 1 h) on lymph flow from B16-F10 tumor-bearing foot pads of C57BL/6 mice was measured by monitoring the clearance of 99mTc-labeled human serum albumin. The foot was represented by a single-compartment model enabling a quantitative computation of lymphatic flow from the tumor to regional lymph nodes. Lymphatic flow from untreated tumors was 0.0059 +/- 0.0011 ml/min cm3 compared to 0.0118 +/- 0.0027 ml/min cm3 lymphatic flow from tumors immediately following heating. Morphological alterations in tumor blood vessels result in their high vascular permeability. The increase in lymphatic clearance from tumors after sublethal hyperthermia is compatible with the increase in interstitial fluid formation in tumors based on Starling's Law.     

Network Scale Modeling of Lymph Transport and Its Effective Pumping Parameters

The lymphatic system is an open-ended network of vessels that run in parallel to the blood circulation system. These vessels are present in almost all of the tissues of the body to remove excess fluid. Similar to blood vessels, lymphatic vessels are found in branched arrangements. Due to the complexity of experiments on lymphatic networks and the difficulty to control the important functional parameters in these setups, computational modeling becomes an effective and essential means of understanding lymphatic network pumping dynamics. Here we aimed to determine the effect of pumping coordination in branched network structures on the regulation of lymph flow. Lymphatic vessel networks were created by building upon our previous lumped-parameter model of lymphangions in series. In our network model, each vessel is itself divided into multiple lymphangions by lymphatic valves that help maintain forward flow. Vessel junctions are modeled by equating the pressures and balancing mass flows. Our results demonstrated that a 1.5 s rest-period between contractions optimizes the flow rate. A time delay between contractions of lymphangions at the junction of branches provided an advantage over synchronous pumping, but additional time delays within individual vessels only increased the flow rate for adverse pressure differences greater than 10.5 cmH₂O. Additionally, we quantified the pumping capability of the system under increasing levels of steady transmural pressure and outflow pressure for different network sizes. We observed that peak flow rates normally occurred under transmural pressures between 2 to 4 cmH₂O (for multiple pressure differences and network sizes). Networks with 10 lymphangions per vessel had the highest pumping capability under a wide range of adverse pressure differences. For favorable pressure differences, pumping was more efficient with fewer lymphangions. These findings are valuable for translating experimental measurements from the single lymphangion level to tissue and organ scales.     

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)