Structural response of microcirculatory networks to changes in demand: information transfer by shear stress

Matching blood flow to metabolic demand in terminal vascular beds involves coordinated changes in diameters of vessels along flow pathways, requiring upstream and downstream transfer of information on local conditions. Here, the role of information transfer mechanisms in structural adaptation of microvascular networks after a small change in capillary oxygen demand was studied using a theoretical model. The model includes diameter adaptation and information transfer via vascular reactions to wall shear stress, transmural pressure, and oxygen levels. Information transfer is additionally effected by conduction along vessel walls and by convection of metabolites. The model permits selective blocking of information transfer mechanisms. Six networks, based on in vivo data, were considered. With information transfer, increases in network conductance and capillary oxygen supply were amplified by factors of 4.9 +/- 0.2 and 9.4 +/- 1.1 (means +/- SE), relative to increases when information transfer was blocked. Information transfer by flow coupling alone, in which increased shear stress triggers vascular enlargement, gave amplifications of 4.0 +/- 0.3 and 4.9 +/- 0.5. Other information transfer mechanisms acting alone gave amplifications below 1.6. Thus shear-stress-mediated flow coupling is the main mechanism for the structural adjustment of feeding and draining vessel diameters to small changes in capillary oxygen demand.     

Experimental determination of wall shear rate in canine carotid arteries perfused in vitro

The mathematical model of Hung (Tsai and Hung, 1984) is employed to determine the wall shear rate acting on canine carotid arteries perfused in vitro. Model equations for pulsatile flow in a deformable vessel are coupled with experimental data of dynamic pressure drop, flow rate, vessel radius and radial wall motion. Derived quantities, e.g. velocity profiles and wall shear, are obtained for vessels exposed to 'normotensive' hemodynamics, 'hypertension' simulations and perfusions in which the compliance of the vessel wall is deliberately altered. Our results indicate that wall shear varies markedly as a function of the hemodynamic environment. The effects of vessel radius vs flow rate on the development of wall shear are also demonstrated. It is found that convective processes correlate with the magnitude of wall shear in the 'hypertension' simulations. The present findings and complementary published data may explain, at least in part, the variations in vessel wall transport and endothelial cell biology we observe as a function of the hemodynamic environment. For example we have documented that the exposure of canine carotids to 'hypertensive' (vs 'normotensive') hemodynamics is associated with an increased flux of lipoproteins (LDL) into the intima and luminal media. Alternations in wall compliance, on the other hand, profoundly influence endothelial shape, orientation and cytoskeletal array.     

Theoretical comparison of wall-derived and erythrocyte-derived mechanisms for metabolic flow regulation in heterogeneous microvascular networks

The objective of this study is to compare the effectiveness of metabolic signals derived from erythrocytes and derived from the vessel wall for regulating blood flow in heterogeneous microvascular networks. A theoretical model is used to simulate blood flow, mass transport, and vascular responses. The model accounts for myogenic, shear-dependent, and metabolic flow regulation. Metabolic signals are assumed to be propagated upstream along vessel walls via a conducted response. Arteriolar tone is assumed to depend on the conducted metabolic signal as well as local wall shear stress and wall tension, and arteriolar diameters are calculated based on vascular smooth muscle mechanics. The model shows that under certain conditions metabolic regulation based on wall-derived signals can be more effective in matching perfusion to local oxygen demand relative to regulation based on erythrocyte-derived signals, resulting in higher extraction and lower oxygen deficit. The lower effectiveness of the erythrocyte-derived signal is shown to result in part from the unequal partition of hematocrit at diverging bifurcations, such that low-flow vessels tend to receive a reduced hematocrit and thereby experience a reduced erythrocyte-derived metabolic signal. The model simulations predict that metabolic signals independent of erythrocytes may play an important role in local metabolic regulation of vascular tone and flow distribution in heterogeneous microvessel networks.     

Experimental determination of wall shear rate in canine carotid arteries perfused in vitro

The mathematical model of Hung (Tsai and Hung, 1984) is empolyed to determine the wall shear rate acting on canine carotid arteries perfused in vitro. Model equations for pulsatile flow in a deformable vessel are coupled with experimental data of dynamic pressure drop, flow rate, vessel radius and radial wall motion. Derived quantities, e.g. velocity profiles and wall shear, are obtained for vessels exposed to ‘normotensive’ hemodynamics, ‘hypertension’ simulations and perfusions in which the compliance of the vessel wall is deliberately altered. Our results indicate that wall shear varies markedly as a function of the hemodynamic environment. The effects of vessel radius vs flow rate on the development of wall shear are also demonstrated. It is found that convective processes correlate with the magnitude of wall shear in the ‘hypertension’ simulations.The present findings and complementary published data may explain, at least in part, the variations in vessel wall transport and endothelial cell biology we observe as a function of the hemodynamic environment. For example we have documented that the exposure of canine carotids to ‘hypertensive’ (vs ‘normotensive’) hemodynamics is associated with an increased flux of lipoproteins (LDL) into the intima and luminal media. Alternations in wall compliance, on the other hand, profoundly influence endothelial shape, orientation and cytoskeletal array.     

Arterial adaptations to altered blood flow

Arterial remodeling in response to altered blood flow is believed to be critical to vascular adaptations to developmental, physiological, pathological, and therapeutically induced changes in blood flow. To assess this remodeling, we used left-to-right carotid anastomosis to increase blood flow in the right common carotid arteries of adult rabbits by 60%. After 2 months, these vessels exhibited no compensatory enlargement. In contrast, the same procedure performed in 5- to 6-week-old weanling rabbits resulted in accelerated growth of the vessels: diameters exceeded those of control arteries by 19% after 2 months. Common carotid arteries in adult rabbits remodeled to produce a diameter reduced by 23% when blood flow was reduced by 63% by external carotid ligation. This adaptation restored shear stress exerted on the vessel wall to control levels. The reduced diameter was not reversed when the vessels were maximally dilated with nitroprusside, adenosine, and forskolin; however, normal diameters were restored within 1 week when normal blood flows were reestablished. Thus, the adult arteries did not respond to increased blood flow produced by the anastomosis, but this procedure did reverse adaptations to decreased flow. In contrast, immature arteries were responsive to this increase in blood flow, even in the absence of prior flow modulation.     

Structural adaptation of microvascular networks: functional roles of adaptive responses

Terminal vascular beds continually adapt to changing demands. A theoretical model is used to simulate structural diameter changes in response to hemodynamic and metabolic stimuli in microvascular networks. Increased wall shear stress and decreased intravascular pressure are assumed to stimulate diameter increase. Intravascular partial pressure of oxygen (PO(2)) is estimated for each segment. Decreasing PO(2) is assumed to generate a metabolic stimulus for diameter increase, which acts locally, upstream via conduction along vessel walls, and downstream via metabolite convection. By adjusting the sensitivities to these stimuli, good agreement is achieved between predicted network characteristics and experimental data from microvascular networks in rat mesentery. Reduced pressure sensitivity leads to increased capillary pressure with reduced viscous energy dissipation and little change in tissue oxygenation. Dissipation decreases strongly with decreased metabolic response. Below a threshold level of metabolic response flow shifts to shorter pathways through the network, and oxygen supply efficiency decreases sharply. In summary, the distribution of vessel diameters generated by the simulated adaptive process allows the network to meet the functional demands of tissue while avoiding excessive viscous energy dissipation.     

Concentration polarization of atherogenic lipids in the arterial system

Nomenclature c, Normalized LDL concentration (C*/C0); C0, incoming (bulk) LDL concentration (gr/cm3); Cw, LDL concentration on the luminal surface (gr/cm3); ,wC time average value of LDL concentration on the luminal surface (gr/cm3); D, diffusion coef-ficient of LDL (cm2/s); Q, blood flow rate (mL/s); 0R, average internal radius of the artery (cm); Re, Reynolds number (002/Run); Sc, Schmidt number (/Dn); t, normalized time (00*/tuR); u, normalized axial velocity (0*/uu); 0u, time a…     

Branching exponent heterogeneity and wall shear stress distribution in vascular trees

A bifurcating arterial system with Poiseuille flow can function at minimum cost and with uniform wall shear stress if the branching exponent (z) = 3 [where z is defined by (D(1))(z) = (D(2))(z) + (D(3))(z); D(1) is the parent vessel diameter and D(2) and D(3) are the two daughter vessel diameters at a bifurcation]. Because wall shear stress is a physiologically transducible force, shear stress-dependent control over vessel diameter would appear to provide a means for preserving this optimal structure through maintenance of uniform shear stress. A mean z of 3 has been considered confirmation of such a control mechanism. The objective of the present study was to evaluate the consequences of a heterogeneous distribution of z values about the mean with regard to this uniform shear stress hypothesis. Simulations were carried out on model structures otherwise conforming to the criteria consistent with uniform shear stress when z = 3 but with varying distributions of z. The result was that when there was significant heterogeneity in z approaching that found in a real arterial tree, the coefficient of variation in shear stress was comparable to the coefficient of variation in z and nearly independent of the mean value of z. A systematic increase in mean shear stress with decreasing vessel diameter was one component of the variation in shear stress even when the mean z = 3. The conclusion is that the influence of shear stress in determining vessel diameters is not, per se, manifested in a mean value of z. In a vascular tree having a heterogeneous distribution in z values, a particular mean value of z (e.g., z = 3) apparently has little bearing on the uniform shear stress hypothesis.     

Development of a general method for designing microvascular networks using distribution of wall shear stress

In the present study, theoretical formulations for calculation of optimal bifurcation angle and relationship between the diameters of mother and daughter vessels using the power law model for non-Newtonian fluids are developed. The method is based on the distribution of wall shear stress in the mother and daughter vessels. Also, the effect of distribution of wall shear stress on the minimization of energy loss and flow resistance is considered. It is shown that constant wall shear stress in the mother and daughter vessels provides the minimum flow resistance and energy loss of biological flows. Moreover, the effects of different wall shear stresses in the mother and daughter branches, different lengths of daughter branches in the asymmetric bifurcations and non-Newtonian effect of biological fluid flows on the bifurcation angle and the relationship between the diameters of mother and daughter branches are considered. Using numerical simulations for non-Newtonian models such as power law and Carreau models, the effects of optimal bifurcation angle on the pressure drop and flow resistance of blood flow in the symmetric bifurcation are investigated. Numerical simulations show that optimal bifurcation angle decreases the pressure drop and flow resistance especially for bifurcations at large Reynolds number.     

Comparative study of Newtonian and non-Newtonian simulations of drug transport in a model drug-eluting stent

To elucidate the difference between Newtonian and shear thinning non-Newtonian assumptions of blood in the analysis of DES drug delivery, we numerically simulated the local flow pattern and the concentration distribution of the drug at the lumen-tissue interface for a structurally simplified DES deployed in a curved segment of an artery under pulsatile blood flow conditions. The numerical results showed that when compared with the Newtonian model, the Carreau (shear thinning) model could lead to some differences in the luminal surface drug concentration in certain areas along the outer wall of the curved vessel. In most areas of the vessel, however, there were no significant differences between the 2 models. Particularly, no significant difference between the two models was found in terms of the area-averaged luminal surface drug concentration. Therefore, we believe that the shear thinning property of blood may play little roles in DES drug delivery. Nevertheless, before we draw the conclusion that Newtonian assumption of blood can be used to replace its non-Newtonian one for the numerical simulation of drug transport in the DES implanted coronary artery, other more complex mechanical properties of blood such as its thixotropic behavior should be tested.     

Concentration polarization of atherogenic lipids in the arterial system

The transport of atherogenic lipids (LDL) in a straight segment of an artery with a semi-permeable wall was simulated numerically. The numerical analysis predicted that a mass transport phenomenon called ’concentration polarization’ of LDL might occur in the arterial system. Under normal physiological flow conditions, the luminal surface LDL concentration was 5%–14% greater than the bulk concentration in a straight segment of an artery. The luminal surface LDL concentration at the arterial wall was flow-dependent, varying linearly with the filtration rate across the arterial wall and inversely with wall shear rate. At low wall shear rate, the luminal surface LDL concentration was very sensitive to changes in flow conditions, decreasing sharply as wall shear rate increased. In order to verify the numerical analysis, the luminal surface concentration of bovine serum albumin (as a tracer macromolecule) in the canine carotid artery was measured in vitro by directly taking liquid samples from the luminal surface of the artery. The experimental result was in very good agreement with the numerical analysis. The authors believe that the mass transport phenomenon of ‘concentration polarization’ may indeed exist in the human circulation and play an important role in the localization of atherosclerosis.     

Flow-dependent concentration polarization of plasma proteins at the luminal surface of a semipermeable membrane

The effect of steady shear flow on concentration polarization of plasma proteins and lipoproteins at the luminal surface of a semipermeable vessel wall was studied experimentally using suspensions of these molecules in a cell culture medium and a semipermeable membrane dialysis tube which served as a model of an implanted vascular graft or an artery. The study was carried out by flowing a cell culture medium containing fetal calf serum or bovine plasma lipoproteins or bovine albumin through a 7.5 mm diameter, 60 mm-long dialysis tube in steady flow under a physiologic mean arterial perfusion pressure of 100 mmHg, and measuring the filtration velocity of water (cell culture medium) at the vessel wall which varied as a consequence of the change in concentration of plasma protein particles at the luminal surface of the semipermeable membrane dialysis tube. It was found that for perfusates containing plasma proteins and/or lipoproteins, filtration velocity of water was the lowest in the absence of flow, and it increased or decreased as the flow rate (hence wall shear rate) increased or decreased from a certain non-zero value, indicating that surface concentration of protein particles varied reversibly as a direct function of flow rate. It was also found that at particle concentrations equivalent to those found in a culture medium containing serum at 5% by volume, plasma lipoproteins which were much smaller in number and lower in concentration but larger in size than albumin, had a much larger effect on the filtration velocity of water than albumin. These findings were very much the same as those previously obtained with a cultured endothelial cell monolayer, strongly suggesting that the flow-dependent variation in filtration velocity of water at a vessel wall results from a physical phenomenon, that is, flow-dependent concentration polarization of low density lipoproteins at the luminal surface of the endothelial cell monolayer.     

Nitric Oxide Resistance Reduces Arteriovenous Fistula Maturation in Chronic Kidney Disease in Rats

Background

Autologous arteriovenous (AV) fistulas are the first choice for vascular access but have a high risk of non-maturation due to insufficient vessel adaptation, a process dependent on nitric oxide (NO)-signaling. Chronic kidney disease (CKD) is associated with oxidative stress that can disturb NO-signaling. Here, we evaluated the influence of CKD on AV fistula maturation and NO-signaling.

Methods

CKD was established in rats by a 5/6^th nephrectomy and after 6 weeks, an AV fistula was created between the carotid artery and jugular vein, which was followed up at 3 weeks with ultrasound and flow assessments. Vessel wall histology was assessed afterwards and vasoreactivity of carotid arteries was studied in a wire myograph. The soluble guanylate cyclase (sGC) activator BAY 60–2770 was administered daily to CKD animals for 3 weeks to enhance fistula maturation.

Results

CKD animals showed lower flow rates, smaller fistula diameters and increased oxidative stress levels in the vessel wall. Endothelium-dependent relaxation was comparable but vasorelaxation after sodium nitroprusside was diminished in CKD vessels, indicating NO resistance of the NO-receptor sGC. This was confirmed by stimulation with BAY 60–2770 resulting in increased vasorelaxation in CKD vessels. Oral administration of BAY 60–2770 to CKD animals induced larger fistula diameters, however; flow was not significantly different from vehicle-treated CKD animals.

Conclusions

CKD induces oxidative stress resulting in NO resistance that can hamper AV fistula maturation. sGC activators like BAY 60–2770 could offer therapeutic potential to increase AV fistula maturation.     

The effect of asymmetry in abdominal aortic aneurysms under physiologically realistic pulsatile flow conditions

In the abdominal segment of the human aorta under a patient's average resting conditions, pulsatile blood flow exhibits complex laminar patterns with secondary flows induced by adjacent branches and irregular vessel geometries. The flow dynamics becomes more complex when there is a pathological condition that causes changes in the normal structural composition of the vessel wall, for example, in the presence of an aneurysm. This work examines the hemodynamics of pulsatile blood flow in hypothetical three-dimensional models of abdominal aortic aneurysms (AAAs). Numerical predictions of blood flow patterns and hemodynamic stresses in AAAs are performed in single-aneurysm, asymmetric, rigid wall models using the finite element method. We characterize pulsatile flow dynamics in AAAs for average resting conditions by means of identifying regions of disturbed flow and quantifying the disturbance by evaluating flow-induced stresses at the aneurysm wall, specifically wall pressure and wall shear stress. Physiologically realistic abdominal aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50 < or = Rem < or = 300, corresponding to a range of peak Reynolds numbers 262.5 < or = Repeak < or = 1575. The vortex dynamics induced by pulsatile flow in AAAs is depicted by a sequence of four different flow phases in one period of the cardiac pulse. Peak wall shear stress and peak wall pressure are reported as a function of the time-average Reynolds number and aneurysm asymmetry. The effect of asymmetry in hypothetically shaped AAAs is to increase the maximum wall shear stress at peak flow and to induce the appearance of secondary flows in late diastole.     

The effect of blood viscoelasticity on pulsatile flow in stationary and axially moving tubes

An analytical solution for pulsatile flow of a generalized Maxwell fluid in straight rigid tubes, with and without axial vessel motion, has been used to calculate the effect of blood viscoelasticity on velocity profiles and shear stress in flows representative of those in the large arteries. Measured bulk flow rate Q waveforms were used as starting points in the calculations for the aorta and femoral arteries, from which axial pressure gradient ▿P waves were derived that would reproduce the starting Q waves for viscoelastic flow. The ▿P waves were then used to calculate velocity profiles for both viscoelastic and purely viscous flow. For the coronary artery, published ▿P and axial vessel acceleration waveforms were used in a similar procedure to determine the separate and combined influences of viscoelasticity and vessel motion.Differences in local velocities, comparing viscous flow to viscoelastic flow, were in all cases less than about 2% of the peak local velocity. Differences in peak wall shear stress were less than about 3%.In the coronary artery, wall shear stress differences between viscous and viscoelastic flow were small, regardless of whether axial vessel motion was included. The shape of the wall shear stress waveform and its difference, however, changed dramatically between the stationary and moving vessel cases. The peaks in wall shear stress difference corresponded with large temporal gradients in the combined driving force for the flow.     

Breaking symmetry in non-planar bifurcations: distribution of flow and wall shear stress

Non-planarity in blood vessels is known to influence arterial flows and wall shear stress. To gain insight, computational fluid dynamics (CFD) has been used to investigate effects of curvature and out-of-plane geometry on the distribution of fluid flows and wall shear stresses in a hypothetical non-planar bifurcation. Three-dimensional Navier-Stokes equations for a steady state Newtonian fluid were solved numerically using a finite element method. Non-planarity in one of the two daughter vessels is found to deflect flow from the inner wall of the vessel to the outer wall and to cause changes in the distribution of wall shear stresses. Results from this study agree to experimental observations and CFD simulations in the literature, and support the view that non-planarity in blood vessels is a factor with important haemodynamic significance and may play a key role in vascular biology and pathophysiology.     

Transendothelial flow inhibits neutrophil transmigration through a nitric oxide-dependent mechanism: potential role for cleft shear stress

Endothelial cells in vivo are well known to respond to parallel shear stress induced by luminal blood flow. In addition, fluid filtration across endothelium (transendothelial flow) may trigger nitric oxide (NO) production, presumably via shear stress within intercellular clefts. Since NO regulates neutrophil-endothelial interactions, we determined whether transendothelial flow regulates neutrophil transmigration. Interleukin-1beta-treated human umbilical vein endothelial cell (HUVEC) monolayers cultured on a polycarbonate filter were placed in a custom chamber with or without a modest hydrostatic pressure gradient (DeltaP, 10 cm H(2)O) to induce transendothelial flow. In other experiments, cells were studied in a parallel plate flow chamber at various transendothelial flows (DeltaP = 0, 5, and 10 cm H(2)O) and luminal flows (shear stress of 0, 1, and 2 dyn/cm(2)). In the absence of luminal flow, transendothelial flow reduced transmigration of freshly isolated human neutrophils from 57% to 14% (P < 0.05) and induced an increase in NO detected with a fluorescent assay (DAF-2DA). The NO synthase inhibitor L-NAME prevented the effects of transendothelial flow on neutrophil transmigration, while a NO donor (DETA/NO, 1 mM) inhibited neutrophil transmigration. Finally, in the presence of luminal flow (1 and 2 dyn/cm(2)), transendothelial flow also inhibited transmigration. On the basis of HUVEC morphometry and measured transendothelial volume flow, we estimated cleft shear stress to range from 49 to 198 dyn/cm(2). These shear stress estimates, while substantial, are of similar magnitude to those reported by others with similar analyses. These data are consistent with the hypothesis that endothelial cleft shear stress inhibits neutrophil transmigration via a NO-dependent mechanism.     

Theoretical study on flow-dependent concentration polarization of low density lipoproteins at the luminal surface of a straight artery

It is suspected that physical and fluid mechanical factors play important roles in the localization of atherosclerotic lesions and intimal hyperplasia in man by affecting the transport of cholesterol in flowing blood to arterial walls. Hence, we have studied theoretically the effects of various physical and fluid mechanical factors such as wall shear rate, diffusivity of low density lipoproteins (LDL), and filtration velocity of water at the vessel wall on surface concentration of LDL at an arterial wall by means of a computer simulation of convective and diffusive transport of LDL in flowing blood to the wall of a straight artery under conditions of a steady flow. It was found that under normal physiologic conditions prevailing in the human arterial system, due to the presence of a filtration flow of water at the vessel wall, flow-dependent concentration polarization (accumulation or depletion) of LDL occurs at a blood/endothelium boundary. The surface concentration of LDL at an arterial wall takes higher values than that in the bulk flow in that vessel, and it is affected by three major factors, that is, wall shear rate, gamma w, filtration velocity of water at the vessel wall, Vw, and the distance from the entrance of the artery, L. It increases with increasing Vw and L, and decreasing gamma w hence the flow rate. Thus, under certain circumstances, the surface concentration of LDL could rise locally to a value which is several times higher than that in the bulk flow, or drop locally to a value even lower than a critical concentration for the maintenance of normal functions and survival of cells forming the vessel wall. These results suggest the possibility that all the vascular phenomena such as the localization of atherosclerotic lesions and intimal hyperplasia, formation of cerebral aneurysms, and adaptive changes of lumen diameter and wall structure of arteries and veins to certain changes in hemodynamic conditions in the circulation are governed by this flow-dependent concentration polarization of LDL which carry cholesterol.     

The influence of out-of-plane geometry on pulsatile flow within a distal end-to-side anastomosis

We present an experimental and computational investigation of time-varying flow in an idealized fully occluded 45 degrees distal end-to-side anastomosis. Two geometric configurations are assessed, one where the centerlines of host and bypass vessels lie within a plane, and one where the bypass vessel is deformed out of the plane of symmetry, respectively, termed planar and non-planar. Flow experiments were conducted by magnetic resonance imaging in rigid wall models and computations were performed using a high order spectral/hp algorithm. Results indicate a significant change in the spatial distribution of wall shear stress and a reduction of the time-averaged peak wall shear stress magnitude by 10% in the non-planar model as compared to the planar configuration. In the planar geometry the stagnation point follows a straight-line path along the host artery bed with a path length of 0.8 diameters. By contrast in the non-planar case the stagnation point oscillates about a center that is located off the symmetry plane intersection with the host artery bed wall, and follows a parabolic path with a 0.7 diameter longitudinal and 0.5 diameter transverse excursion. A definition of the oscillatory shear index (OSI) is introduced that varies between 0 and 0.5 and that accounts for a continuous range of wall shear stress vector angles. In both models, regions of elevated oscillatory shear were spatially associated with regions of separated or oscillating stagnation point flow. The mean oscillatory shear magnitude (considering sites where OSI>0.1) in the non-planar geometry was reduced by 22% as compared to the planar configuration. These changes in the dynamic behavior of the stagnation point and the oscillatory shear distribution introduced by out-of-plane graft curvature may influence the localization of vessel wall sites exposed to physiologically unfavorable flow conditions.     

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.