Computational analysis of coupled blood-wall arterial LDL transport

The transport of macromolecules, such as low density lipoproteins (LDLs), across the artery wall and their accumulation in the wall is a key step in atherogenesis. Our objective was to model fluid flow within both the lumen and wall of a constricted, axisymmetric tube simulating a stenosed artery, and to then use this flow pattern to study LDL mass transport from the blood to the artery wall. Coupled analysis of lumenal blood flow and transmural fluid flow was achieved through the solution of Brinkman's model, which is an extension of the Navier-Stokes equations for porous media. This coupled approach offers advantages over traditional analyses of this problem, which have used possibly unrealistic boundary conditions at the blood-wall interface; instead, we prescribe a more natural pressure boundary condition at the adventitial vasa vasorum, and allow variations in wall permeability due to the occurrence of plaque. Numerical complications due to the convection dominated mass transport process (low LDL diffusivity) are handled by the streamline upwind/Petrov-Galerkin (SUPG) finite element method. This new fluid-plus-porous-wall method was implemented for conditions typical of LDL transport in a stenosed artery with a 75 percent area reduction (Peclet number=2 x 10(8)). The results show an elevated LDL concentration at the downstream side of the stenosis. For the higher Darcian wall permeability thought to occur in regions containing atheromatous lesions, this leads to an increased transendothelial LDL flux downstream of the stenosis. Increased transmural filtration in such regions, when coupled with a concentration-dependent endothelial permeability to LDL, could be an important contributor to LDL infiltration into the arterial wall. Experimental work is needed to confirm these results.     

Coupled computational analysis of arterial LDL transport -- effects of hypertension

Hypertension, a risk factor for atherosclerosis, increases the uptake of low density lipoproteins (LDL) by the arterial wall. Our objective in this work was to use computational modeling to identify physical factors that could be partially responsible for this effect. Fluid flow and mass transfer patterns in the lumen and wall of an arterial model were computed in a coupled manner, replicating as closely as possible previous experimental studies in which LDL uptake into the artery wall was measured in straight, excised arterial segments. Under conditions of both flow and no-flow, simulations predicted an increase in concentration polarization of LDL at the artery wall when arterial pressure was increased from 120 to 160 mmHg. However, this led to only a slight increase in mean LDL concentration within the arterial wall. However, if the permeability of the endothelium to LDL was allowed to vary with intra-arterial pressure, then the simulations predicted that the uptake of LDL would be enhanced 1.9-2.6 fold at higher pressure. The magnitude of this increase was consistent with experimental data. We conclude that the concentration polarization effects, enhanced by elevated intra-arterial pressure, cannot explain the increase in LDL uptake seen under hypertensive conditions. Instead, the data are most consistent with a pressure-linked increase in endothelial permeability to LDL.     

Effects of transmural pressure and wall shear stress on LDL accumulation in the arterial wall: a numerical study using a multilayered model

The accumulation of low-density lipoprotein (LDL) is recognized as one of the main contributors in atherogenesis. Mathematical models have been constructed to simulate mass transport in large arteries and the consequent lipid accumulation in the arterial wall. The objective of this study was to investigate the influences of wall shear stress and transmural pressure on LDL accumulation in the arterial wall by a multilayered, coupled lumen-wall model. The model employs the Navier-Stokes equations and Darcy's Law for fluid dynamics, convection-diffusion-reaction equations for mass balance, and Kedem-Katchalsky equations for interfacial coupling. To determine physiologically realistic model parameters, an optimization approach that searches optimal parameters based on experimental data was developed. Two sets of model parameters corresponding to different transmural pressures were found by the optimization approach using experimental data in the literature. Furthermore, a shear-dependent hydraulic conductivity relation reported previously was adopted. The integrated multilayered model was applied to an axisymmetric stenosis simulating an idealized, mildly stenosed coronary artery. The results show that low wall shear stress leads to focal LDL accumulation by weakening the convective clearance effect of transmural flow, whereas high transmural pressure, associated with hypertension, leads to global elevation of LDL concentration in the arterial wall by facilitating the passage of LDL through wall layers.     

Effects of arterial pressure on endothelial transport of macromolecules

The effects of variations in transmural pressure over a range of 0 to 200 mmHg on transendothelial transport of macromolecules were studied in the canine common carotid artery. The uptake of 125I-albumin per unit artery weight increased with rising pressure. There was no significant difference in albumin permeability per unit luminal surface area between 0 and 100 mmHg, but permeability nearly doubled when pressure was raised to 200 mmHg. The contribution of an increased rate of transendothelial vesicle diffusion, as evaluated from the experimental determination of the ratio of attached-to-free vesicles and theoretical modeling, was found to be negligible. The reduction in transendothelial vesicle diffusion distance due to pressure-induced thinning of the peripheral zone contributes to a 25% increase in permeability. With the use of colloidal Ag and Au of various sizes, vesicle loading of particles with diameters greater than or equal to 15 nm was found to be severely restricted at transmural pressure less than or equal to 100 mmHg, but it was significantly enhanced at 200 mmHg, when particles as large as 25 nm became detectable in endothelial vesicles and subendothelial space. This hypertension-induced increase in macromolecular transport across the endothelium may cause an overloading of the arterial wall with low-density lipoproteins and play a significant role in atherogenesis.     

Effect of pressure on circumferential order of adventitial collagen in human brain arteries.

A key factor in the contribution of collagen fibres to tissue mechanics is the alignment of the fibres, which we studied in brain arteries, focussing on alignment changes with distending pressure. Arteries from autopsy were cannulated and fixed at different distending pressures from 0 to 200 mmHg (1 mmHg = 133.32 Pa), alcohol dehydrated, paraffin embedded, sectioned, and stained for birefringent enhancement. The polarized light microscope was set for extinction and fibre orientations were precisely determined at the rotational position of extinction for 200 positions around the artery wall. Results from 22 arterial cross sections revealed, with fixation pressure, a significant but incomplete straightening of collagen (even at 200 mmHg). The mean angular deviation of alignment of fibres was +/- 30 degrees for arteries fixed at zero transmural pressure, which in contrast was +/- 7 degrees for the inner and +/- 13 degrees for the mid-adventitia for arteries fixed at 200 mmHg transmural pressure. We verified on vessels fixed at low pressure, by using a full wave plate in conjunction with the specificity of the interference colours, that the measurements were correct and not confused with angles at 90 degrees to the morphological axis. Alternative tissue processing was done with two arteries fixed at 120 mmHg and processed for frozen sections; the results showed diminished variability in alignment but within the range of measurements for wax embedded tissue. We concluded that the collagen fabric could contribute to the mechanics of brain arteries but that it would be with sinusoidal rather than straightened fibres of collagen.     

Characteristics of the myogenic behaviour of arteries of the common European frog (Rana temporaria)

Mammalian small arteries exhibit pressure-dependent myogenic behaviour characterised by an active constriction in response to an increased transmural pressure or an active dilatation in response to a decreased transmural pressure. This study aimed to determine whether pressure-dependent myogenic responses are a functional feature of amphibian arteries. Mesenteric and skeletal muscle arteries from the common European frog (Rana temporaria) were cannulated at either end with two fine glass micropipettes in the chamber of an arteriograph. Arterial pressure-diameter relationships (5-40 mmHg) were determined in the presence and absence of Ca2+. All arteries dilated passively with increasing pressure in the absence of Ca2+. In the presence of Ca2+ proximal mesenteric branches and tibial artery branches dilated with increasing transmural pressure but tone (p < 0.05) was evident in both arteries. A clear myogenic response to a step increase or decrease in pressure was observed in small distal arteries (6 of 13 mesenteric and 7 of 10 sciatic branches) resulting in significantly (p < 0.05) narrower diameters in Ca2+ in the range 10-40 mmHg in mesenteric and 20-40 mmHg in sciatic arteries, respectively. The results demonstrate that arteries of an amphibian can generate spontaneous pressure-dependent tone. This is the first study to demonstrate myogenic contractile behaviour in arteries of nonmammalian origin.     

Modeling ventricular repolarization: effects of transmural and apex-to-base heterogeneities in action potential durations

Heterogeneities in the densities of membrane ionic currents of myocytes cause regional variations in action potential duration (APD) at various intramural depths and along the apico-basal and circumferential directions in the left ventricle. This work extends our previous study of cartesian slabs to ventricular walls shaped as an ellipsoidal volume and including both transmural and apex-to-base APD heterogeneities. Our 3D simulation study investigates the combined effect on repolarization sequences and APD distributions of: (a) the intrinsic APD heterogeneity across the wall and along the apex-to-base direction, and (b) the electrotonic currents that modulate the APDs when myocytes are embedded in a ventricular wall with fiber rotation and orthotropic anisotropy. Our findings show that: (i) the transmural and apex-to-base heterogeneities have only a weak influence on the repolarization patterns on myocardial layers parallel to the epicardium; (ii) the patterns of APD distribution on the epicardial surface are mostly affected by the apex-to-base heterogeneities and do not reveal the APD transmural heterogeneity; (iii) the transmural heterogeneity is clearly discernible in both repolarization and APD patterns only on transmural sections; (iv) the apex-to-base heterogeneity is clearly discernible only in APD patterns on layers parallel to the epicardium. Thus, in our orthotropic ellipsoidal wall, the complex 3D electrotonic modulation of APDs does not fully mix the effects of the transmural and apex-to-base heterogeneity. The intrinsic spatial heterogeneity of the APDs is unmasked in the modulated APD patterns only in the appropriate transmural or intramural sections. These findings are independent of the stimulus location (epicardial, endocardial) and of Purkinje involvement.     

The effect of the endothelial glycocalyx layer on concentration polarisation of low density lipoprotein in arteries

It has been postulated that a flow-dependent (and hence spatially varying) low density lipoprotein (LDL) concentration polarisation layer forms on the luminal surface of the vascular endothelium. Such a layer has the potential to cause heterogeneity in the distribution of atherosclerotic lesions by spatially modulating the rate of LDL transport into the arterial wall. Theoretical analysis suggests that a transmural water flux which is spatially heterogeneous at the cellular scale can act to enhance LDL concentration polarisation in a shear dependent fashion. However, such an effect is only observed if a relevant Peclet number (i.e. the ratio of LDL convection to LDL diffusion) is of order unity or greater. Based on the diffusivity of LDL in blood plasma, such a Peclet number is found to be far less than unity, implying that the aforementioned enhancement and shear dependence will not occur. However, this conclusion ignores the existence of the endothelial glycocalyx layer (EGL), which may inhibit the diffusion of LDL near the luminal surface of the endothelium, and hence raise any Peclet number associated with the transport of LDL. The present study numerically investigates the effect of the EGL, as well as a heterogeneous transmural water flux, on arterial LDL concentration polarisation. Particular attention is paid to measures of LDL concentration polarisation thought relevant to the rate of transendothelial LDL transport. It is demonstrated that an EGL is unlikely to cause any additional shear dependence of such measures directly, irrespective of whether or not LDL can penetrate into the EGL. However, it is found that such measures depend significantly on the nature of the interaction between LDL and the EGL (parameterised by the height of the EGL, the depth to which LDL penetrates into the EGL, and the diffusivity of LDL in the EGL). Various processes may regulate the interaction of LDL with the EGL, possibly in a flow dependent and hence spatially non-uniform fashion. It is concluded that any such processes may be as important as vascular scale flow features in terms of spatially modulating transendothelial LDL transport via an LDL concentration polarisation mechanism.     

A theory for water and macromolecular transport in the pulmonary artery wall with a detailed comparison to the aorta

The pulmonary artery (PA) wall, which has much higher hydraulic conductivity and albumin void space and approximately one-sixth the normal transmural pressure of systemic arteries (e.g, aorta, carotid arteries), is rarely atherosclerotic, except under pulmonary hypertension. This study constructs a detailed, two-dimensional, wall-structure-based filtration and macromolecular transport model for the PA to investigate differences in prelesion transport processes between the disease-susceptible aorta and the relatively resistant PA. The PA and aorta models are similar in wall structure, but very different in parameter values, many of which have been measured (and therefore modified) since the original aorta model of Huang et al. (23). Both PA and aortic model simulations fit experimental data on transwall LDL concentration profiles and on the growth of isolated endothelial (horseradish peroxidase) tracer spots with circulation time very well. They reveal that lipid entering the aorta attains a much higher intima than media concentration but distributes better between these regions in the PA than aorta and that tracer in both regions contributes to observed tracer spots. Solutions show why both the overall transmural water flow and spot growth rates are similar in these vessels despite very different material transport parameters. Since early lipid accumulation occurs in the subendothelial intima and since (matrix binding) reaction kinetics depend on reactant concentrations, the lower intima lipid concentrations in the PA vs. aorta likely lead to slower accumulation of bound lipid in the PA. These findings may be relevant to understanding the different atherosusceptibilities of these vessels.     

Computational study of LDL mass transport in the artery wall

A two-dimensional (2D) numerical simulation of convective–diffusive transport of LDL in the artery wall, coupled with the wall shear stress gradient (WSSG)-dependent LDL consumption of smooth muscle cells (SMCs) is presented. SMCs are modeled as an array of solid cylindrical pillars embedded in a continuous porous media which represents the interstitial proteoglycan and collagen fiber matrix. The internal elastic lamina (IEL), which separates the artery media from the intima, is modeled as an impermeable barrier to both water and LDL except for the fenestral pores that are assumed to be uniformly distributed over the IEL. The predictions demonstrate a range of interesting features of LDL transport and uptake in the media. For cells immediately below the fenestral pores, LDL uptake of SMCs is highly dependent on WSSG. Moreover, the rate of LDL consumption by SMCs is also affected by the diameter of the fenestral pore. This will be helpful in understanding the involvement of transmural transport processes in the initiation and development of atherosclerosis.     

Structural deformation of the preterm trachea during acute distention and collapse.

The compliant airways of the premature neonate undergo episodic distention and collapse in response to changes in transmural pressure such as occur during spontaneous breathing, mechanical ventilation, and various therapeutic maneuvers. To identify and quantitate the effects of distending and collapsing transmural pressures on the structure of immature airways, tracheal segments from fetal rabbits, fixed at 0, +30, and -30 cm H2O transmural pressure, were examined using histologic and morphometric techniques. In comparison to control sections fixed at 0 cm H2O transmural pressure, application of distending pressures led to evagination of the posterior tracheal wall and significantly increased (P less than 0.05) cross-sectional area, antero-posterior diameter, circumference and muscle length, and decreased muscle thickness. Collapsed tracheal segments (-30 cm H2O) demonstrated invagination of the posterior wall and significantly (P less than 0.05) lower cross-sectional area, and antero-posterior diameter compared to the control segments; all the other parameters remained relatively unchanged. These data demonstrate extreme changes in tracheal geometry in response to the acute application of transmural pressure. From a methodological perspective, these observations suggest that fixation pressures may present significant artifact in histological analyses. Functionally, the noted deformation may lead to alterations in anatomic dead space and airway resistance, and mechanical function of the airways; all of which may compromise respiratory status in ventilated premature infant.     

Transmural strain distribution in the blood vessel wall

The transmural distributions of stress and strain at the in vivo state have important implications for the physiology and pathology of the vessel wall. The uniform transmural strain hypothesis was proposed by Takamyzawa and Hayashi (Takamizawa K and Hayashi K. J Biomech 20: 7-17, 1987; Biorheology 25: 555-565, 1988) as describing the state of arteries in vivo. From this hypothesis, they derived the residual stress and strain at the no-load condition and the opening angle at the zero-stress state. However, the experimental evidence cited by Takamyzawa and Hayashi (J Biomech 20: 7-17, 1987; and Biorheology 25: 555-565, 1988) to support this hypothesis was limited to arteries whose opening angles (theta) are <180 degrees. It is well known, however, that theta > 180 degrees do exist in the cardiovascular system. Our hypothesis is that the transmural strain distribution cannot be uniform when theta; is >180 degrees. We present both theoretical and experimental evidence for this hypothesis. Theoretically, we show that the circumferential stretch ratio cannot physically be uniform across the vessel wall when theta; exceeds 180 degrees and the deviation from uniformity will increase with an increase in theta; beyond 180 degrees. Experimentally, we present data on the transmural strain distribution in segments of the porcine aorta and coronary arterial tree. Our data validate the theoretical prediction that the outer strain will exceed the inner strain when theta > 180 degrees. This is the converse of the gradient observed when the residual strain is not taken into account. Although the strain distribution may not be uniform when theta exceeds 180 degrees, the uniformity of stress distribution is still possible because of the composite nature of the blood vessel wall, i.e., the intima-medial layer is stiffer than the adventitial layer. Hence, the larger strain at the adventitia can result in a smaller stress because the adventitia is softer at physiological loading.     

Differential effects of the changes of LDL cholesterol and systolic blood pressure on the risk of carotid artery atherosclerosis

ABSTRACT: BACKGROUND: The effects of baseline and changes in blood pressure and low density lipoprotein (LDL) cholesterol on the carotid intima media thickness (IMT) have not been well documented. METHODS: A total of 2572 adults (mean age 53.8 years, 54.6% women) in a Taiwanese community undertook three blood pressure and LDL cholesterol examinations over 6 years. Latent growth curve modeling was used to investigate the effects of baseline and change in blood pressure and LDL cholesterol on IMT. RESULTS: Greater baseline LDL and blood pressure were associated with an increase in IMT (0.005 +/- 0.002 mm per 1 mg/dL [p = 0.006] and 0.041 +/- 0.004 mm mmHg [p <0.0001], respectively. Change in blood pressure was associated with a significant increase in IMT (0.047+/-0.016, P = 0.004), whilst the association between change in LDL and change in IMT was not statistically significant (0.008+/-0.006, P = 0.20). CONCLUSIONS: Carotid IMT was associated with baseline blood pressure and LDL cholesterol, yet only changes of blood pressure, not LDL cholesterol, were related to carotid IMT during the 6- year observation.     

Effect of residual stress and heterogeneity on circumferential stress in the arterial wall

Quantifying the stress distribution through the arterial wall is essential to studies of arterial growth and disease. Previous studies have shown that both residual stress, as measured by opening angle, and differing material properties for the media-intima and the adventitial layers affect the transmural circumferential stress (sigma theta) distribution. Because a lack of comprehensive data on a single species and artery has led to combinations from multiple sources, this study determined the sensitivity of sigma theta to published variations in both opening angle and layer thickness data. We fit material properties to previously published experimental data for pressure-diameter relations and opening angles of rabbit carotid artery, and predicted sigma theta through the arterial wall at physiologic conditions. Using a one-layer model, the ratio of sigma theta at the internal wall to the mean sigma theta decreased from 2.34 to 0.98 as the opening angle increased from 60 to 130 deg. In a two-layer model using a 95 deg opening angle, mean sigma theta in the adventitia increased (112 percent for 25 percent adventitia) and mean sigma theta in the media decreased (47 percent for 25 percent adventitia). These results suggest that both residual stress and wall layers have important effects on transmural stress distribution. Thus, experimental measurements of loading curves, opening angles, and wall composition from the same species and artery are needed to accurately predict the transmural stress distribution in the arterial wall.     

Comparison of norepinephrine and serotonin vasoconstriction of the rat isolated testicular subcapsular artery at physiological and elevated transmural pressures.

This laboratory has previously described an in vitro preparation showing that the isolated testicular subcapsular artery of the adult rat has a novel triphasic transmural pressure-diameter myogenic response curve consisting of vasodilatation from 20 to 40 mm Hg, vasoconstriction from 40 to 100 mm Hg, and vasodilatation from 100 to 180 mm Hg, suggesting that the myogenic response of this artery between 40 and 100 mm Hg may have an important role in the autoregulation of the testicular blood supply. In the present studies, a 10-mm length of the adult rat isolated testicular subcapsular artery was cannulated and pressurized by an adjustable-height reservoir. External and internal arterial diameters were measured by a digital filar micrometer eyepiece. Dose-response curves for norepinephrine and serotonin were generated in a double-bath artery chamber at transmural pressures of 70 and 140 mm Hg, using half of the same artery for each pressure. Norepinephrine (3 x 10(-8) to 1 x 10(-5) M) produced a dose-dependent vasoconstriction at 70 mm Hg, with the highest dose causing a 31.4% decrease in lumen cross-sectional area (p < 0.05). Serotonin (3 x 10(-8) to 1 x 10(-6) M) produced a stronger dose-dependent vasoconstriction at 70 mm Hg, with the highest dose causing a 72.7% decrease in lumen cross-sectional area (p < 0.05). In marked contrast, the same concentration of norepinephrine and serotonin were found to have no statistically significant effect on the lumen cross-sectional area of the isolated testicular subcapsular artery at a transmural pressure of 140 mm Hg.(ABSTRACT TRUNCATED AT 250 WORDS)     

Dependence of local left ventricular wall mechanics on myocardial fiber orientation: a model study.

The dependence of local left ventricular (LV) mechanics on myocardial muscle fiber orientation was investigated using a finite element model. In the model we have considered anisotropy of the active and passive components of myocardial tissue, dependence of active stress on time, strain and strain rate, activation sequence of the LV wall and aortic afterload. Muscle fiber orientation in the LV wall is quantified by the helix fiber angle, defined as the angle between the muscle fiber direction and the local circumferential direction. In a first simulation, a transmural variation of the helix fiber angle from +60 degrees at the endocardium through 0 degrees in the midwall layers to -60 degrees at the epicardium was assumed. In this simulation, at the equatorial level maximum active muscle fiber stress was found to vary from about 110 kPa in the subendocardial layers through about 30 kPa in the midwall layers to about 40 kPa in the subepicardial layers. Next, in a series of simulations, muscle fiber orientation was iteratively adapted until the spatial distribution of active muscle fiber stress was fairly homogeneous. Using a transmural course of the helix fiber angle of +60 degrees at the endocardium, +15 degrees in the midwall layers and -60 degrees at the epicardium, at the equatorial level maximum active muscle fiber stress varied from 52 kPa to 55 kPa, indicating a remarkable reduction of the stress range. Moreover, the change of muscle fiber strain with time was more similar in different parts of the LV wall than in the first simulation. It is concluded that (1) the distribution of active muscle fiber stress and muscle fiber strain across the LV wall is very sensitive to the transmural distribution of the helix fiber angle and (2) a physiological transmural distribution of the helix fiber angle can be found, at which active muscle fiber stress and muscle fiber strain are distributed approximately homogeneously across the LV wall.     

Effect of angiotensin inhibition on the coronary artery lower pressure limit in anesthetized dogs

The renin-angiotensin system plays a critical role in regulating vasoconstriction and vasodilatation that can influence myocardial blood flow and its transmural distribution. We tested the hypothesis that angiotensin inhibition can induce a leftward shift of the coronary autoregulatory pressure-flow relation and preserve distribution of myocardial blood flow at lower coronary perfusion pressures. We established circumflex artery pressure-flow relations under baseline conditions and after intracoronary enalaprilat or losartan potassium. Thereafter, transmural myocardial blood flow was measured at baseline and at the lower coronary pressure limit (LPL). With enalaprilat, the LPL was shifted leftward from 48 +/- 6 mmHg at baseline to 43 +/- 3 mmHg (P = 0.026); with losartan, the LPL was shifted leftward from 48 +/- 10 mmHg at baseline to 41 +/- 5 mmHg (P = 0.027). The leftward shift occurred while cardiac hemodynamics and MVO2 were maintained at control levels. These results indicate that angiotensin inhibition extends the range of coronary autoregulation to lower LPL while preserving myocardial blood flow distribution, a physiologic effect that might explain the lower incidence of coronary events in treated patients.     

Myogenic tone,reactivity, and forced dilatation: a three-phase model of in vitro arterial myogenic behavior

Myogenic behavior, prevalent in resistance arteries and arterioles, involves arterial constriction in response to intravascular pressure. This process is often studied in vitro by using cannulated, pressurized arterial segments from different regional circulations. We propose a comprehensive model for myogenicity that consists of three interrelated but dissociable phases: 1) the initial development of myogenic tone (MT), 2) myogenic reactivity to subsequent changes in pressure (MR), and 3) forced dilatation at high transmural pressures (FD). The three phases span the physiological range of transmural pressures (e.g., MT, 40-60 mmHg; MR, 60-140 mmHg; FD, >140 mmHg in cerebral arteries) and are characterized by distinct changes in cytosolic calcium ([Ca(2+)](i)), which do not parallel arterial diameter or wall tension, and therefore suggest the existence of additional regulatory mechanisms. Specifically, the development of MT is accompanied by a substantial (200%) elevation in [Ca(2+)](i) and a reduction in lumen diameter and wall tension, whereas MR is associated with relatively small [Ca(2+)](i) increments (<20% over the entire pressure range) despite considerable increases in wall tension and force production but little or no change in diameter. FD is characterized by a significant additional elevation in [Ca(2+)](i) (>50%), complete loss of force production, and a rapid increase in wall tension. The utility of this model is that it provides a framework for comparing myogenic behavior of vessels of different size and anatomic origin and for investigating the underlying cellular mechanisms that govern vascular smooth muscle mechanotransduction and contribute to the regulation of peripheral resistance.     

A theoretical model to study the effect of convection and leaky junctions on macromolecule transport in artery walls

A mathematical model is presented herein to determine the effect of convection on macromolecular transport across an artery wall due to transmural or osmotic pressure differences. The model is based on an extension of the leaky junction-cell turnover model of Weinbaum et al. (1985) to take into account a combined transport mechanism of convection and diffusion and also to provide the leaky junctions in the model with a finite resistance, thus allowing the results to be extended to intercellular clefts with a retarding extracellular matrix or to macromolecules whose dimensions are nearly the same as the junctional width. The results from this improved model show that the effect of pressure on transarterial macromolecular transport is important especially for cell turnover rates greater than 1% and that significant changes in the equilibrium balance of the cholesterol carrying LDL molecules in the arterial wall can occur due to a very small fraction of leaky junctions. At very high turnover rates (large fraction of leaky junctions) the effect of convection on macromolecular transport becomes dramatic and explains the very large increases in uptake observed experimentally after artificially inducing extensive endothelial damage.     

Transport in rat vessel walls. I. Hydraulic conductivities of the aorta, pulmonary artery, and inferior vena cava with intact and denuded endothelia

In this study, filtration flows through the walls of the rat aorta, pulmonary artery (PA), and inferior vena cava (IVC), vessels with very different susceptibilities to atherosclerosis, were measured as a function of transmural pressure (DeltaP), with intact and denuded endothelium on the same vessel. Aortic hydraulic conductivity (L(p)) is high at 60 mmHg, drops approximately 40% by 100 mmHg, and is pressure independent to 140 mmHg. The trends are similar in the PA and IVC, dropping 42% from 10 to 40 mmHg and flat to 100 mmHg (PA) and dropping 33% from 10 to 20 mmHg and essentially flat to 60 mmHg (IVC). Removal of the endothelium renders L(p)(DeltaP) flat: it increases L(p) of the aorta by approximately 75%, doubles L(p) of the PA, and quadruples L(p) of the IVC. Specific resistance (1/L(p)) of the aortic endothelium is approximately 47% of total resistance; i.e., the endothelium accounts for approximately 47% of the DeltaP drop at 100 mmHg. The PA value is 55% at >40 mmHg, and the IVC value is 23% at 10 mmHg. L(p) of the intact aorta, PA, and IVC are order 10(-8), 10(-7), and 5 x 10(-7) cm.s(-1).mmHg(-1), and wall thicknesses are 145.8 microm (SD 9.3), 78.9 microm (SD 3.3), and 66.1 microm (SD 4.1), respectively. These data are consistent with the different wall structures of the three vessels. The rat aortic L(p) data are quantitatively consistent with rabbit L(p)(DeltaP) (Tedgui A and Lever MJ. Am J Physiol Heart Circ Physiol 247: H784-H791, 1984; Baldwin AL and Wilson LM. Am J Physiol Heart Circ Physiol 264: H26-H32, 1993), suggesting that intimal compression under pressure loading may also play a role in L(p)(DeltaP) in these other vessels. Despite very different driving DeltaP, nominal transmural water fluxes of these three vessels are very similar and, therefore, cannot alone account for their differences in disease susceptibility. The different fates of macromolecular tracers convected by these water fluxes into the walls of these vessels may account for this difference.