Numerical modeling of fluid flow in solid tumors

A mathematical model of interstitial fluid flow is developed, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for a predefined tumor geometry. The interstitial fluid pressure and velocity are calculated using a numerical method, element based finite volume. Simulations of interstitial fluid transport in a homogeneous solid tumor demonstrate that, in a uniformly perfused tumor, i.e., one with no necrotic region, because of the interstitial pressure distribution, the distribution of drug particles is non-uniform. Pressure distribution for different values of necrotic radii is examined and two new parameters, the critical tumor radius and critical necrotic radius, are defined. Simulation results show that: 1) tumor radii have a critical size. Below this size, the maximum interstitial fluid pressure is less than what is generally considered to be effective pressure (a parameter determined by vascular pressure, plasma osmotic pressure, and interstitial osmotic pressure). Above this size, the maximum interstitial fluid pressure is equal to effective pressure. As a consequence, drugs transport to the center of smaller tumors is much easier than transport to the center of a tumor whose radius is greater than the critical tumor radius; 2) there is a critical necrotic radius, below which the interstitial fluid pressure at the tumor center is at its maximum value. If the tumor radius is greater than the critical tumor radius, this maximum pressure is equal to effective pressure. Above this critical necrotic radius, the interstitial fluid pressure at the tumor center is below effective pressure. In specific ranges of these critical sizes, drug amount and therefore therapeutic effects are higher because the opposing force, interstitial fluid pressure, is low in these ranges.     

Effect of tumor shape and size on drug delivery to solid tumors

ABSTRACT: Tumor shape and size effect on drug delivery to solid tumors are studied, based on the application of the governing equations for fluid flow, i.e., the conservation laws for mass and momentum, to physiological systems containing solid tumors. The discretized form of the governing equations, with appropriate boundary conditions, is developed for predefined tumor geometries. The governing equations are solved using a numerical method, the element-based finite volume method. Interstitial fluid pressure and velocity are used to show the details of drug delivery in a solid tumor, under an assumption that drug particles flow with the interstitial fluid. Drug delivery problems have been most extensively researched in spherical tumors, which have been the simplest to examine with the analytical methods. With our numerical method, however, more complex shapes of the tumor can be studied. The numerical model of fluid flow in solid tumors previously introduced by our group is further developed to incorporate and investigate non-spherical tumors such as prolate and oblate ones. Also the effects of the surface area per unit volume of the tissue, vascular and interstitial hydraulic conductivity on drug delivery are investigated.     

A new method for isolation of interstitial fluid from human solid tumors applied to proteomic analysis of ovarian carcinoma tissue

Major efforts have been invested in the identification of cancer biomarkers in plasma, but the extraordinary dynamic range in protein composition, and the dilution of disease specific proteins make discovery in plasma challenging. Focus is shifting towards using proximal fluids for biomarker discovery, but methods to verify the isolated sample's origin are missing. We therefore aimed to develop a technique to search for potential candidate proteins in the proximal proteome, i.e. in the tumor interstitial fluid, since the biomarkers are likely to be excreted or derive from the tumor microenvironment. Since tumor interstitial fluid is not readily accessible, we applied a centrifugation method developed in experimental animals and asked whether interstitial fluid from human tissue could be isolated, using ovarian carcinoma as a model. Exposure of extirpated tissue to 106 g enabled tumor fluid isolation. The fluid was verified as interstitial by an isolated fluid:plasma ratio not significantly different from 1.0 for both creatinine and Na(+), two substances predominantly present in interstitial fluid. The isolated fluid had a colloid osmotic pressure 79% of that in plasma, suggesting that there was some sieving of proteins at the capillary wall. Using a proteomic approach we detected 769 proteins in the isolated interstitial fluid, sixfold higher than in patient plasma. We conclude that the isolated fluid represents undiluted interstitial fluid and thus a subproteome with high concentration of locally secreted proteins that may be detected in plasma for diagnostic, therapeutic and prognostic monitoring by targeted methods.     

Tumor interstitial fluid — A treasure trove of cancer biomarkers

Tumor interstitial fluid (TIF) is a proximal fluid that, in addition to the set of blood soluble phase-borne proteins, holds a subset of aberrantly externalized components, mainly proteins, released by tumor cells and tumor microenvironment through various mechanisms, which include classical secretion, non-classical secretion, secretion via exosomes and membrane protein shedding. Consequently, the interstitial aqueous phase of solid tumors is a highly promising resource for the discovery of molecules associated with pathological changes in tissues. Firstly, it allows one to delve deeper into the regulatory mechanisms and functions of secretion-related processes in tumor development. Secondly, the anomalous secretion of molecules that is innate to tumors and the tumor microenvironment, being associated with cancer progression, offers a valuable source for biomarker discovery and possible targets for therapeutic intervention. Here we provide an overview of the features of tumor-associated interstitial fluids, based on recent and updated information obtained mainly from our studies of breast cancer. Data from the study of interstitial fluids recovered from several other types of cancer are also discussed. This article is a part of a Special Issue entitled: The Updated Secretome.     

A Mathematical Model of the Enhanced Permeability and Retention Effect for Liposome Transport in Solid Tumors

The discovery of the enhanced permeability and retention (EPR) effect has resulted in the development of nanomedicines, including liposome-based formulations of drugs, as cancer therapies. The use of liposomes has resulted in substantial increases in accumulation of drugs in solid tumors; yet, significant improvements in therapeutic efficacy have yet to be achieved. Imaging of the tumor accumulation of liposomes has revealed that this poor or variable performance is in part due to heterogeneous inter-subject and intra-tumoral liposome accumulation, which occurs as a result of an abnormal transport microenvironment. A mathematical model that relates liposome accumulation to the underlying transport properties in solid tumors could provide insight into inter and intra-tumoral variations in the EPR effect. In this paper, we present a theoretical framework to describe liposome transport in solid tumors. The mathematical model is based on biophysical transport equations that describe pressure driven fluid flow across blood vessels and through the tumor interstitium. The model was validated by direct comparison with computed tomography measurements of tumor accumulation of liposomes in three preclinical tumor models. The mathematical model was fit to liposome accumulation curves producing predictions of transport parameters that reflect the tumor microenvironment. Notably, all fits had a high coefficient of determination and predictions of interstitial fluid pressure agreed with previously published independent measurements made in the same tumor type. Furthermore, it was demonstrated that the model attributed inter-subject heterogeneity in liposome accumulation to variations in peak interstitial fluid pressure. These findings highlight the relationship between transvascular and interstitial flow dynamics and variations in the EPR effect. In conclusion, we have presented a theoretical framework that predicts inter-subject and intra-tumoral variations in the EPR effect based on fundamental properties of the tumor microenvironment and forms the basis for transport modeling of liposome drug delivery.     

Effect of tumor shape,size, and tissue transport properties on drug delivery to solid tumors

Background

The computational methods provide condition for investigation related to the process of drug delivery, such as convection and diffusion of drug in extracellular matrices, drug extravasation from microvessels or to lymphatic vessels. The information of this process clarifies the mechanisms of drug delivery from the injection site to absorption by a solid tumor. In this study, an advanced numerical method is used to solve fluid flow and solute transport equations simultaneously to investigate the effect of tumor shape and size on drug delivery to solid tumor.

Methods

The advanced mathematical model used in our previous work is further developed by adding solute transport equation to the governing equations. After applying appropriate boundary and initial conditions on tumor and surrounding tissue geometry, the element-based finite volume method is used for solving governing equations of drug delivery in solid tumor. Also, the effects of size and shape of tumor and some of tissue transport parameters such as effective pressure and hydraulic conductivity on interstitial fluid flow and drug delivery are investigated.

Results

Sensitivity analysis shows that drug delivery in prolate shape is significantly better than other tumor shapes. Considering size effect, increasing tumor size decreases drug concentration in interstitial fluid. This study shows that dependency of drug concentration in interstitial fluid to osmotic and intravascular pressure is negligible.

Conclusions

This study shows that among diffusion and convection mechanisms of drug transport, diffusion is dominant in most different tumor shapes and sizes. In tumors in which the convection has considerable effect, the drug concentration is larger than that of other tumors at the same time post injection.

     

Isolation of interstitial fluid from rat mammary tumors by a centrifugation method

Access to interstitial fluid is of fundamental importance to understand tumor transcapillary fluid balance, including the distribution of probes and therapeutic agents. Tumors were induced by gavage of 9,10-dimethyl-1,2-benzanthracene to rats, and fluid was isolated after anesthesia by exposing tissue to consecutive centrifugations from 27 to 6,800 g. The observed (51)Cr-EDTA (extracellular tracer) tissue fluid-to-plasma ratio obtained from whole tumor or from superficial tumor tissue by centrifugation at 27-424 g was not significantly different from 1.0 (0.92-0.99), suggesting an extracellular origin only. However, fluid collected from excised central tumor parts had a significantly lower ratio (0.66-0.77) for all imposed G forces, suggesting dilution by fluid deriving from a space unavailable for (51)Cr-EDTA. The colloid osmotic pressure in tumor fluid was generally higher than in fluid isolated from the subcutis, attributable to less selective capillaries and impaired lymphatic drainage in tumors. HPLC analysis of tumor fluid showed that low-molecular-weight macromolecules not present in arterial plasma were present in tumor fluid obtained by centrifugation and in venous blood draining the tumor, most likely representing proteins derived from tumor cells. We conclude that low-speed centrifugation may be a simple and reliable method to isolate interstitial fluid from tumors.     

Computational Modeling of 3D Tumor Growth and Angiogenesis for Chemotherapy Evaluation

Solid tumors develop abnormally at spatial and temporal scales, giving rise to biophysical barriers that impact anti-tumor chemotherapy. This may increase the expenditure and time for conventional drug pharmacokinetic and pharmacodynamic studies. In order to facilitate drug discovery, we propose a mathematical model that couples three-dimensional tumor growth and angiogenesis to simulate tumor progression for chemotherapy evaluation. This application-oriented model incorporates complex dynamical processes including cell- and vascular-mediated interstitial pressure, mass transport, angiogenesis, cell proliferation, and vessel maturation to model tumor progression through multiple stages including tumor initiation, avascular growth, and transition from avascular to vascular growth. Compared to pure mechanistic models, the proposed empirical methods are not only easy to conduct but can provide realistic predictions and calculations. A series of computational simulations were conducted to demonstrate the advantages of the proposed comprehensive model. The computational simulation results suggest that solid tumor geometry is related to the interstitial pressure, such that tumors with high interstitial pressure are more likely to develop dendritic structures than those with low interstitial pressure.     

Transcapillary fluid shifts in tissues of the head and neck during and after simulated microgravity.

To understand the mechanism, magnitude, and time course of facial puffiness that occurs in microgravity, seven male subjects were tilted 6 degrees head-down for 8 h, and all four Starling transcapillary pressures were directly measured before, during, and after tilt. Head-down tilt (HDT) caused facial edema and a significant elevation of microvascular pressures measured in the lower lip: capillary pressures increased from 27.7 +/- 1.5 mmHg (mean +/- SE) pre-HDT to 33.9 +/- 1.7 mmHg by the end of tilt. Subcutaneous and intramuscular interstitial fluid pressures in the neck also increased as a result of HDT, whereas interstitial fluid colloid osmotic pressures remained unchanged. Plasma colloid osmotic pressure dropped significantly by 4 h of HDT (21.5 +/- 1.5 mmHg pre-HDT to 18.2 +/- 1.9 mmHg), suggesting a transition from fluid filtration to absorption in capillary beds between the heart and feet during HDT. After 4 h of seated recovery from HDT, microvascular pressures in the lip (capillary and venule pressures) remained significantly elevated by 5-8 mmHg above baseline values. During HDT, urine output was 126.5 ml/h compared with 46.7 ml/h during the control baseline period. These results suggest that facial edema resulting from HDT is caused primarily by elevated capillary pressures and decreased plasma colloid osmotic pressures. The negativity of interstitial fluid pressures above heart level also has implications for maintenance of tissue fluid balance in upright posture.     

Numerical Modeling of Interstitial Fluid Flow Coupled with Blood Flow through a Remodeled Solid Tumor Microvascular Network

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.     

Relative contribution of articular cartilage’s constitutive components to load support depending on strain rate

Cartilage is considered a biphasic material in which the solid is composed of proteoglycans and collagen. In biphasic tissue, the hydraulic pressure is believed to bear most of the load under higher strain rates and its dissipation due to fluid flow determines creep and relaxation behavior. In equilibrium, hydraulic pressure is zero and load bearing is transferred to the solid matrix. The viscoelasticity of the collagen network also contributes to its time-dependent behavior, and the osmotic pressure to load bearing in equilibrium. The aim of the present study was to determine the relative contributions of hydraulic pressure, viscoelastic collagen stress, solid matrix stiffness and osmotic pressure to load carriage in cartilage under transient and equilibrium conditions. Unconfined compression experiments were simulated using a fibril-reinforced poroviscoelastic model of articular cartilage, including water, fibrillar viscoelastic collagen and non-fibrillar charged glycosaminoglycans. The relative contributions of hydraulic and osmotic pressures and stresses in the fibrillar and non-fibrillar network were evaluated in the superficial, middle and deep zone of cartilage under five different strain rates and after relaxation. Initially upon loading, the hydraulic pressure carried most of the load in all three zones. The osmotic swelling pressure carried most of the equilibrium load. In the surface zone, where the fibers were loaded in tension, the collagen network carried 20 % of the load for all strain rates. The importance of these fibers was illustrated by artificially modifying the fiber architecture, which reduced the overall stiffness of cartilage in all conditions. In conclusion, although hydraulic pressure dominates the transient behavior during cartilage loading, due to its viscoelastic nature the superficial zone collagen fibers carry a substantial part of the load under transient conditions. This becomes increasingly important with higher strain rates. The interesting and striking new insight from this study suggests that under equilibrium conditions, the swelling pressure generated by the combination of proteoglycans and collagen reinforcement accounts cartilage stiffness for more than 90 % of the loads carried by articular cartilage. This finding is different from the common thought that load is transferred from fluid to solid and is carried by the aggregate modulus of the solid. Rather, it is transformed from hydraulic to osmotic swelling pressure. These results show the importance of considering both (viscoelastic) collagen fibers as well as swelling pressure in studies of the (transient) mechanical behavior of cartilage.     

A microstructurally based continuum model of cartilage viscoelasticity and permeability incorporating measured statistical fiber orientations

The remarkable mechanical properties of cartilage derive from an interplay of isotropically distributed, densely packed and negatively charged proteoglycans; a highly anisotropic and inhomogeneously oriented fiber network of collagens; and an interstitial electrolytic fluid. We propose a new 3D finite strain constitutive model capable of simultaneously addressing both solid (reinforcement) and fluid (permeability) dependence of the tissue’s mechanical response on the patient-specific collagen fiber network. To represent fiber reinforcement, we integrate the strain energies of single collagen fibers—weighted by an orientation distribution function (ODF) defined over a unit sphere—over the distributed fiber orientations in 3D. We define the anisotropic intrinsic permeability of the tissue with a structure tensor based again on the integration of the local ODF over all spatial fiber orientations. By design, our modeling formulation accepts structural data on patient-specific collagen fiber networks as determined via diffusion tensor MRI. We implement our new model in 3D large strain finite elements and study the distributions of interstitial fluid pressure, fluid pressure load support and shear stress within a cartilage sample under indentation. Results show that the fiber network dramatically increases interstitial fluid pressure and focuses it near the surface. Inhomogeneity in the tissue’s composition also increases fluid pressure and reduces shear stress in the solid. Finally, a biphasic neo-Hookean material model, as is available in commercial finite element codes, does not capture important features of the intra-tissue response, e.g., distributions of interstitial fluid pressure and principal shear stress.     

Evaluation of a Voxelized Model Based on DCE-MRI for Tracer Transport in Tumor

Recent advances in the treatment of cancer involving therapeutic agents have shown promising results. However, treatment efficacy can be limited due to inadequate and uneven uptake in solid tumors, thereby making the prediction of drug transport important for developing effective therapeutic strategies. In this study, a patient-specific computational porous media model (voxelized model) was developed for predicting the interstitial flow field and distribution of a systemically delivered magnetic resonance (MR) visible tracer in a tumor. The benefits of a voxel approach include less labor and less computational time (approximately an order of magnitude reduction compared to the traditional computational fluid dynamics (CFD) approach developed earlier by our group). The model results were compared with that obtained from a previous approach based on unstructured meshes along with MR-measured tracer concentration data within tumors, using statistical analysis and qualitative representations. The statistical analysis indicated the similarity between the structured and unstructured models' results with a low root mean square error (RMS) and a high correlation coefficient. The voxelized model captured features of the flow field and tracer distribution such as high interstitial fluid pressure inside the tumor and the heterogeneous distribution of the tracer. Predictions of tracer distribution by the voxelized approach also resulted in low RMS error when compared with MR-measured data over a 1?h time course. The similarity in the voxelized model results with experiment and the nonvoxelized model predictions were maintained across three different tumors. Overall, the voxelized model serves as a reliable and swift alternative to approaches using unstructured meshes in predicting extracellular transport within tumors.     

Coupled modeling of blood perfusion in intravascular, interstitial spaces in tumor microvasculature

The coupling of intravascular and interstitial flow is a distinct feature of tumor microcirculation, due to the high vessel permeability, the low osmotic pressure gradient as well as the absence of functional lymphatic system inside tumors. In this paper, a coupled mathematical model of tumor microcirculation is developed, which provides the link between microvasculature and interstitial space perfusion through the matrices determining a neighbor point belonging to either connected vessel (matrix B) or interstitial space (matrix A), and combines the intravascular and interstitial flow by vascular leaky terms. In addition, the compliance of tumor vessels, blood rheology with hematocritic distribution at branches is also considered. The microvascular network, on which the microcirculation calculation is carried out, is generated from our two-dimensional 9-point (2D9P) model of tumor angiogenesis, improved from the previous 2D5P one. A specific coupling procedure is developed in the study to couple the intravascular and interstitial flow. It is based on the iteratively numerical simulation techniques, including local iterations at individual parameter level and one global loop to provide coupling and simulation convergence. The simulation results not only present the basic features and characteristics of tumor microcirculation, which agree with the corresponding experimental observations reported, but also predict an intimate relationship between the tumor intravascular and interstitial flow quantitatively. Among the parameters, the vascular leakiness is a key to govern the systemic flowing pattern, influence the tumor internal environment and contribute to the metastasis of tumor cells, which could not be presented by the previous uncoupled models.     

Regulation of tumor invasion by interstitial fluid flow

The importance of the tumor microenvironment in cancer progression is undisputed, yet the significance of biophysical forces in the microenvironment remains poorly understood. Interstitial fluid flow is a nearly ubiquitous and physiologically relevant biophysical force that is elevated in tumors because of tumor-associated angiogenesis and lymphangiogenesis, as well as changes in the tumor stroma. Not only does it apply physical forces to cells directly, but interstitial flow also creates gradients of soluble signals in the tumor microenvironment, thus influencing cell behavior and modulating cell-cell interactions. In this paper, we highlight our current understanding of interstitial fluid flow in the context of the tumor, focusing on the physical changes that lead to elevated interstitial flow, how cells sense flow and how they respond to changes in interstitial flow. In particular, we emphasize that interstitial flow can directly promote tumor cell invasion through a mechanism known as autologous chemotaxis, and indirectly support tumor invasion via both biophysical and biochemical cues generated by stromal cells. Thus, interstitial fluid flow demonstrates how important biophysical factors are in cancer, both by modulating cell behavior and coupling biophysical and biochemical signals.     

Pulmonary edema: ischemia reperfusion endothelial injury and its reversal by c-AMP.

A review of the factors that oppose pulmonary edema formation (alveolar flooding) when capillary pressure is elevated are presented for a normal capillary endothelial barrier and for damaged endothelium associated with ischemia/reperfusion in rabbit, rat, and dog lungs. Normally, tissue pressure, the plasma protein osmotic pressure gradient acting across the capillary wall and lymph flow (Edema Safety Factors) increase to prevent the build-up of fluid in the lung's interstitium when capillary pressure increases. No measureable alveolar edema fluid accumulates until capillary pressure exceeds 30 mmHg. When the capillary wall has been damaged, interstitial edema develops at lower capillary pressures because the plasma protein osmotic pressure will not change greatly to oppose capillary filtration, but lymph flow increases to very high levels to remove the increased filtrate and the result is that capillary pressures can increase to 20-25 mmHg before alveolar flooding results. In addition, the mechanisms responsible for producing pulmonary endothelial damage with ischemia/reperfusion are reviewed and the effects of O2 radical scavengers, neutrophil depletion or altering their adherence to the endothelium, and increasing cAMP on reversing the damage to the pulmonary endothelium is presented.     

Overcoming physiologic barriers to cancer treatment by molecularly targeting the tumor microenvironment

It is widely recognized that the vasculature of the tumor is inadequate to meet the demands of the growing mass. The malformed vasculature is at least in part responsible for regions of the tumor that are hypoxic, acidotic, and exposed to increased interstitial fluid pressure. These unique aspects of the tumor microenvironment have been shown to act as barriers to conventional chemotherapy or radiation-based therapies. It now seems that while the vasculature initiates these tumor-specific conditions, the cells within the tumor respond to these stresses and add to the unique solid tumor physiology. Gene expression changes have been reported in the tumor for vascular endothelial growth factor, carbonic anhydrase IX, and pyruvate dehydrogenase kinase 1. The activity of these gene products then influences the tumor physiology through alterations in vascular permeability and interstitial fluid pressure, extracellular acidosis, and mitochondrial oxygen consumption and hypoxia, respectively. Novel molecular strategies designed to interfere with the activities of these gene products are being devised as ways to overcome the physiologic barriers in the tumor to standard anticancer therapies.     

Isolation of rat trachea interstitial fluid and demonstration of local cytokine production in lipopolysaccharide-induced systemic inflammation.

Access to interstitial fluid from trachea is important for understanding tracheal microcirculation and pathophysiology. We tested whether a centrifugation method could be applied to isolate this fluid in rats by exposing excised trachea to G forces up to 609 g. The ratio between the concentration of the equilibrated extracellular tracer 51Cr-labeled EDTA in fluid isolated at 239 g and plasma averaged 0.94 +/- 0.03 (n = 14), suggesting that contamination from the intracellular fluid phase was negligible. The protein pattern of the isolated fluid resembled plasma closely and had a protein concentration 83% of that in plasma. The colloid osmotic pressure in the centrifugate in controls (n = 5) was 18.8 +/- 0.6 mmHg with a corresponding pressure in plasma of 22 +/- 1.5 mmHg, whereas after overhydration (n = 5) these pressures fell to 9.8 +/- 0.4 and 11.9 +/- 0.4 mmHg, respectively. We measured inflammatory cytokine concentration in serum, interstitial fluid, and bronchoalveolar lavage fluid in LPS-induced inflammation. In control animals, low levels of IL-1 beta, IL-6, and TNF-alpha in serum, trachea interstitial fluid, and bronchoalveolar lavage fluid were detected. LPS resulted in a significantly higher concentration in IL-1 beta and IL-6 in interstitial fluid than in serum, showing a local production. To conclude, we have shown that interstitial fluid can be isolated from trachea by centrifugation and that trachea interstitial fluid has a high protein concentration and colloid osmotic pressure relative to plasma. Trachea interstitial fluid may also reflect lower airways and thus be of importance for understanding, e.g., inflammatory-induced airway obstruction.     

Effect of wall compliance and permeability on blood-flow rate in counter-current microvessels formed from anastomosis during tumor-induced angiogenesis

Tumor blood-flow is inhomogeneous because of heterogeneity in tumor vasculature, vessel-wall leakiness, and compliance. Experimental studies have shown that normalization of tumor vasculature by antiangiogenic therapy can improve tumor microcirculation and enhance the delivery of therapeutic agents to tumors. To elucidate the quantitative relationship between the vessel-wall compliance and permeability and the blood-flow rate in the microvessels of the tumor tissue, the tumor tissue with the normalized vasculature, and the normal tissue, we developed a transport model to simultaneously predict the interstitial fluid pressure (IFP), interstitial fluid velocity (IFV) and the blood-flow rate in a counter-current microvessel loop, which occurs from anastomosis in tumor-induced angiogenesis during tumor growth. Our model predicts that although the vessel-wall leakiness greatly affects the IFP and IFV, it has a negligible effect on the intravascular driving force (pressure gradient) for both rigid and compliant vessels, and thus a negligible effect on the blood-flow rate if the vessel wall is rigid. In contrast, the wall compliance contributes moderately to the IFP and IFV, but significantly to the vessel radius and to the blood-flow rate. However, the combined effects of vessel leakiness and compliance can increase IFP, which leads to a partial collapse in the blood vessels and an increase in the flow resistance. Furthermore, our model predictions speculate a new approach for enhancing drug delivery to tumor by modulating the vessel-wall compliance in addition to reducing the vessel-wall leakiness and normalizing the vessel density.