Endothelial nitric oxide synthase and calcium production in arterial geometries: an integrated fluid mechanics/cell model

Heterogeneous ATP patterns in microvascular networks

ATP is not only an energy carrier but also serves as an important signalling molecule in many physiological processes. Abnormal ATP level in blood vessel is known to be related to several pathologies, such as inflammation, hypoxia and atherosclerosis. Using advanced numerical methods, we analysed ATP released by red blood cells (RBCs) and its degradation by endothelial cells (ECs) in a cat mesentery-inspired vascular network, accounting for RBC mutual interaction and interactions with vascular walls. Our analysis revealed a heterogeneous ATP distribution in the network, with higher concentrations in the cell-free layer, concentration peaks around bifurcations and heterogeneity among vessels of the same level. These patterns arise from the spatio-temporal organization of RBCs induced by the network geometry. It is further shown that an alteration of hematocrit and flow strength significantly affects ATP level as well as heterogeneity in the network. These findings constitute a first building block to elucidate the intricate nature of ATP patterns in vascular networks and the far reaching consequences for other biochemical signalling, such as calcium, by ECs.

A mathematical model for intracellular NO and ROS dynamics in vascular endothelial cells activated by exercise-induced wall shear stress

Vascular endothelial cells (ECs) residing in the innermost layer of blood vessels are exposed to dynamic wall shear stress (WSS) induced by blood flow. The intracellular nitric oxide (NO) and reactive oxygen species (ROS) in ECs modulated by the dynamic WSS play important roles in endothelial functions. Mathematical modeling is a popular methodology for biophysical studies. It can not only explain existing cell experiments, but also reveal the underlying mechanism. However, the previous mathematical models of NO dynamics in ECs are limited to the static WSS induced by constant flow, while arterial blood flow is a periodic pulsatile flow with varying amplitude and frequency at different exercise intensities. In this study, a mathematical model of intracellular NO and ROS dynamics activated by dynamic WSS based on the in vitro cell experiments is developed. With the hypothesis of the viscoelastic body, the Kelvin model is adopted to simulate the mechanosensors on EC. Thus, the NO dynamics activated by dynamic shear stresses induced by constant flow, pulsatile flow, and oscillatory flow are analyzed and compared. Moreover, the roles of ROS have been considered for the first time in the modeling of NO dynamics in ECs based on the analysis of cell experiments. The predictions of the proposed model coincide fairly well with the experimental data when ECs are subjected to exercise-induced WSS. The mechanism is elucidated that WSS induced by moderate-intensity exercise is most favorable to NO production in ECs. This study can provide valuable insights for further study of NO and ROS dynamics in ECs and help develop appropriate exercise regimens for improving endothelial functions.

Mathematical modeling of intracellular calcium in presence of receptor: a homeostatic model for endothelial cell

Calcium is a ubiquitous molecule and second messenger that regulates many cellular functions ranging from exocytosis to cell proliferation at different time scales. In the vasculature, a constant adenosine triphosphate (ATP) concentration is maintained because of ATP released by red blood cells (RBCs). These ATP molecules continuously react with purinergic receptors on the surface of endothelial cells (ECs). Consequently, a cascade of chemical reactions are triggered that result in a transient cytoplasmic calcium (Ca[Formula: see text]), followed by return to its basal concentration. The mathematical models proposed in the literature are able to reproduce the transient peak. However, the trailing concentration is always higher than the basal cytoplasmic Ca[Formula: see text] concentrations, and the Ca[Formula: see text] concentration in endoplasmic reticulum (ER) remains lower than its initial concentration. This means that the intracellular homeostasis is not recovered. We propose, herein, a minimal model of calcium kinetics. We find that the desensitization of EC surface receptors due to phosphorylation and recycling plays a vital role in maintaining calcium homeostasis in the presence of a constant stimulus (ATP). The model is able to capture several experimental observations such as refilling of Ca[Formula: see text] in the ER, variation of cytoplasmic Ca[Formula: see text] transient peak in ECs, the resting cytoplasmic Ca[Formula: see text] concentration, the effect of removing ATP from the plasma on Ca[Formula: see text] homeostasis, and the saturation of cytoplasmic Ca[Formula: see text] transient peak with increase in ATP concentration. Direct confrontation with several experimental results is conducted. This work paves the way for systematic studies on coupling between blood flow and chemical signaling, and should contribute to a better understanding of the relation between (patho)physiological conditions and Ca[Formula: see text] kinetics.

Modeling ATP-mediated endothelial cell elongation on line patterns

Endothelial cell (EC) migration is crucial for a wide range of processes including vascular wound healing, tumor angiogenesis, and the development of viable endovascular implants. We have previously demonstrated that ECs cultured on 15-μm wide adhesive line patterns exhibit three distinct migration phenotypes: (a) “running” cells that are polarized and migrate continuously and persistently on the adhesive lines with possible spontaneous directional changes, (b) “undecided” cells that are highly elongated and exhibit periodic changes in the direction of their polarization while maintaining minimal net migration, and (c) “tumbling-like” cells that migrate persistently for a certain amount of time but then stop and round up for a few hours before spreading again and resuming migration. Importantly, the three migration patterns are associated with distinct profiles of cell length. Because of the impact of adenosine triphosphate (ATP) on cytoskeletal organization and cell polarization, we hypothesize that the observed differences in EC length among the three different migration phenotypes are driven by differences in intracellular ATP levels. In the present work, we develop a mathematical model that incorporates the interactions between cell length, cytoskeletal (F-actin) organization, and intracellular ATP concentration. An optimization procedure is used to obtain the model parameter values that best fit the experimental data on EC lengths. The results indicate that a minimalist model based on differences in intracellular ATP levels is capable of capturing the different cell length profiles observed experimentally.

Coronary Smooth Muscle Cell Calcium Dynamics: Effects of Bifurcation Angle on Atheroprone Conditions

This work investigates the effect of arterial bifurcation angulation on atherosclerosis development through in-silico simulations of coupled cell dynamics. The computational model presented here combines cellular pathways, fluid dynamics, and physiologically-realistic vessel geometries as observed in the human vasculature. The coupled cells model includes endothelial cells (ECs) and smooth muscle cells (SMCs) with ion dynamics, hetero and homotypic coupling, as well as electro-diffusive coupling. Three arterial bifurcation surface models were used in the coupled cells simulations. All three simulations showed propagating waves of Ca²⁺ in both the SMC and EC layers, following the introduction of a luminal agonist, in this case ATP. Immediately following the introduction of ATP concentration Ca²⁺ waves propagate from the area of high ATP toward the areas of low ATP concentration, forming complex patterns where waves interact with eachother, collide and fade. These dynamic phenomena are repeated with a series of waves of slower velocity. The underlying motivation of this research was to examine the macro-scale phenomena, given that the characteristic length scales of atherosclerotic plaques are much larger than a single cell. The micro-scale dynamics were modeled on macro-scale arterial bifurcation surfaces containing over one million cells. The results of the simulations presented here suggest that susceptibility to atherosclerosis development depends on the bifurcation angulation. In conjunction with findings reported in the literature, the simulation results demonstrate that arterial bifurcations containing wider angles have a more prominent influence on the coupled cells pathways associated with the development of atherosclerosis, by means of disturbed flow and lower SMC Ca²⁺ concentrations. The discussion of the results considers the findings of this research within the context of the potential link between information transport through frequency encoding of Ca²⁺ wave dynamics and development of atheroprone conditions.

Effect of spatial heterogeneity and colocalization of eNOS and capacitative calcium entry channels on shear stress-induced NO production by endothelial cells: A modeling approach

Introduction

Colocalization of endothelial nitric oxide synthase (eNOS) and capacitative Ca²⁺ entry (CCE) channels in microdomains such as cavaeolae in endothelial cells (ECs) has been shown to significantly affect intracellular Ca²⁺ dynamics and NO production, but the effect has not been well quantified.

Methods

We developed a two-dimensional continuum model of an EC integrating shear stress-mediated ATP production, intracellular Ca²⁺ mobilization, and eNOS activation to investigate the effects of spatial colocalization of plasma membrane eNOS and CCE channels on Ca²⁺ dynamics and NO production in response to flow-induced shear stress. Our model examines the hypothesis that subcellular colocalization of cellular components can be critical for optimal coupling of NO production to blood flow.

Results

Our simulations predict that heterogeneity of CCE can result in formation of microdomains with significantly higher Ca²⁺ compared to the average cytosolic Ca²⁺. Ca²⁺ buffers with lower or no mobility further enhanced Ca²⁺ gradients relative to mobile buffers. Colocalization of eNOS to CCE channels significantly increased NO production.

Conclusions

Our results provide quantitative understanding for the role of spatial heterogeneity and the compartmentalization of signals in regulation of shear stress-induced NO production.

Shear-Induced Nitric Oxide Production by Endothelial Cells

We present a biochemical model of the wall shear stress-induced activation of endothelial nitric oxide synthase (eNOS) in an endothelial cell. The model includes three key mechanotransducers: mechanosensing ion channels, integrins, and G protein-coupled receptors. The reaction cascade consists of two interconnected parts. The first is rapid activation of calcium, which results in formation of calcium-calmodulin complexes, followed by recruitment of eNOS from caveolae. The second is phosphorylation of eNOS by protein kinases PKC and AKT. The model also includes a negative feedback loop due to inhibition of calcium influx into the cell by cyclic guanosine monophosphate (cGMP). In this feedback, increased nitric oxide (NO) levels cause an increase in cGMP levels, so that cGMP inhibition of calcium influx can limit NO production. The model was used to predict the dynamics of NO production by an endothelial cell subjected to a step increase of wall shear stress from zero to a finite physiologically relevant value. Among several experimentally observed features, the model predicts a highly nonlinear, biphasic transient behavior of eNOS activation and NO production: a rapid initial activation due to the very rapid influx of calcium into the cytosol (occurring within 1-5 min) is followed by a sustained period of activation due to protein kinases.

Mathematical model for shear stress dependent NO and adenine nucleotide production from endothelial cells

We developed a mass transport model for a parallel-plate flow chamber apparatus to predict the concentrations of nitric oxide (NO) and adenine nucleotides (ATP, ADP) produced by cultured endothelial cells (ECs) and investigated how the net rates of production, degradation, and mass transport for these three chemical species vary with changes in wall shear stress (τw). These simulations provide an improved understanding of experimental results obtained with parallel-plate flow chambers and allows quantitative analysis of the relationship between τw, adenine nucleotide concentrations, and NO produced by ECs. Experimental data obtained after altering ATP and ADP concentrations with apyrase were analyzed to quantify changes in the rate of NO production (RNO). The effects of different isoforms of apyrase on ATP and ADP concentrations and nucleotide-dependent changes in RNO could be predicted with the model. A decrease in ATP was predicted with apyrase, but an increase in ADP was simulated due to degradation of ATP. We found that a simple proportional relationship relating a component of RNO to the sum of ATP and ADP provided a close match to the fitted curve for experimentally measured changes in RNO with apyrase. Estimates for the proportionality constant ranged from 0.0067 to 0.0321 μM/s increase in RNO per nM nucleotide concentration, depending on which isoform of apyrase was modeled, with the largest effect of nucleotides on RNO at low τw (<6 dyn/cm(2)).

The role of nitric oxide in neurovascular coupling

Nitric oxide (NO) is a neurotransmitter known to act as a potent cerebral vasodilator. Its role in neurovascular coupling (NVC) is discussed controversially and one of the main unanswered questions is which cell type provides the governing source of NO for the regulation of vasodynamics. Mathematical modelling can be an appropriate tool to investigate the contribution of NO towards the key components of NVC and analyse underlying mechanisms. The lumped parameter model of a neurovascular unit, including neurons (NE), astrocytes (AC), smooth muscle cells (SMC) and endothelial cells (EC), was extended to model the NO signalling pathway. Results show that NO leads to a general shift of the resting regional blood flow by dilating the arteriolar radius. Furthermore, dilation during neuronal activation is enhanced. Simulations show that potassium release is responsible for the fast onset of vascular response, whereas NO-modulated mechanisms maintain dilation. Wall shear stress-activated NO release from the EC leads to a delayed return to the basal state of the arteriolar radius. The governing source of vasodilating NO that diffuses into the SMC, which determine the arteriolar radius, depends on neuronal activation. In the resting state the EC provides the major contribution towards vasorelaxation, whereas during neuronal stimulation NO produced by the NE dominates.

Neurovascular coupling and the influence of luminal agonists via the endothelium

A numerical model of neurovascular coupling (NVC) is presented based on neuronal activity coupled to vasodilation/contraction models via the astrocytic mediated perivascular K(+) and the smooth muscle cell Ca(2+) pathway. Luminal agonists acting on P2Y receptors on the endothelial cell surface provide a flux of IP3 into the endothelial cytosol. This concentration of IP3 is transported via gap junctions between endothelial and smooth muscle cells providing a source of sacroplasmic derived Ca(2+) in the smooth muscle cell. The model is able to relate a neuronal input signal to the corresponding vessel reaction. Results indicate that blood flow mediated IP3 production via the agonist ATP has a substantial effect on the contraction/dilation dynamics of the SMC. The resulting variation in cytosolic Ca(2+) can enhance and inhibit the flow of blood to the cortical tissue. IP3 coupling between endothelial and smooth muscle cells seems to be important in the dynamics of the smooth muscle cell. The VOCC channels are, due to the hyperpolarisation from K(+) SMC efflux, almost entirely closed and do not seem to play a significant role during neuronal activity. The current model shows that astrocytic Ca(2+) is not necessary for neurovascular coupling to occur in contrast to a number of experiments outlining the importance of astrocytic Ca(2+) in NVC, however this Ca(2+) pathway is not the only one mediating NVC. Importantly agonists in flowing blood have a significant influence on the endothelial and smooth muscle cell dynamics.

Shear stress-induced NO production is dependent on ATP autocrine signaling and capacitative calcium entry

Flow-induced production of nitric oxide (NO) by endothelial cells plays a fundamental role in vascular homeostasis. However, the mechanisms by which shear stress activates NO production remain unclear due in part to limitations in measuring NO, especially under flow conditions. Shear stress elicits the release of ATP, but the relative contribution of autocrine stimulation by ATP to flow-induced NO production has not been established. Furthermore, the importance of calcium in shear stress-induced NO production remains controversial, and in particular the role of capacitive calcium entry (CCE) has yet to be determined. We have utilized our unique NO measurement device to investigate the role of ATP autocrine signaling and CCE in shear stress-induced NO production. We found that endogenously released ATP and downstream activation of purinergic receptors and CCE plays a significant role in shear stress-induced NO production. ATP-induced eNOS phophorylation under static conditions is also dependent on CCE. Inhibition of protein kinase C significantly inhibited eNOS phosphorylation and the calcium response. To our knowledge, we are the first to report on the role of CCE in the mechanism of acute shear stress-induced NO response. In addition, our work highlights the importance of ATP autocrine signaling in shear stress-induced NO production.

Flow-induced ATP release in patient-specific arterial geometries--a comparative study of computational models

The importance of the endothelium in the local regulation of blood flow is reflected by its influence on vascular tone by means of vasodilatory responses to many physiological stimuli. Regulatory pathways are affected by mass transport and wall shear stress (WSS), via mechanotransduction mechanisms. In the present work, we review the most relevant computational models that have been proposed to date, and introduce a general framework for modelling the responses of the endothelium to alteration in the flow, with a view to understanding the biomechanical processes involved in the pathways to endothelial dysfunction. Simulations are performed on two different patient-specific stenosed carotid artery geometries to investigate the influence of WSS and mass transport phenomena upon the agonist coupling response at the endothelium. In particular, results presented for two different models of WSS-dependent adenosine-5'-triphosphate (ATP) release reveal that existing paradigms may not account for the conditions encountered in vivo and may therefore not be adequate to model the kinetics of ATP at the endothelium.

Modelling the effect of a functional endothelium on the development of in-stent restenosis

Treatment of stenosed coronary arteries by balloon angioplasty and stenting results in arterial injury including severe damage to the endothelium at the site of treatment and initiates a complex cascade of inflammatory processes that may lead to the development of in-stent restenosis (ISR). Many clinical and biological factors involved in the progression of restenotic lesions have been studied in detail over the past few years but the mystery behind the pathophysiological mechanisms of this disease is still unresolved. In the present work, the effects of re-endothelialization and nitric oxide release on neointimal growth are investigated in-silico using a two dimensional multi-scale model of ISR. The effect of stent deployment depths on the development of ISR is studied as a function of time after stenting. Two dimensional domains were prepared by deploying bare metal stent struts at three different deployment depths into the tissue. Shear stress distribution on endothelial cells, obtained by blood flow simulations, was translated into nitric oxide production that keeps the smooth muscle cells in quiescent state. The cellular growth trends were plotted as a function of time and the data indicate a positive correlation between the neointimal growths and strut deployment depths in the presence of a functional endothelium, in qualitative agreement with in-vivo data. Additionally, no ISR is observed if a functional endothelium appears much earlier.

Simulation of intrathrombus fluid and solute transport using in vivo clot structures with single platelet resolution

The mouse laser injury thrombosis model provides up to 0.22 μm-resolved voxel information about the pore architecture of the dense inner core and loose outer shell regions of an in vivo arterial thrombus. Computational studies were conducted on this 3D structure to quantify transport within and around the clot: Lattice Boltzmann method defined vessel hemodynamics, while passive Lagrangian Scalar Tracking with Brownian motion contribution simulated diffusive-convective transport of various inert solutes (released from lumen or the injured wall). For an input average lumen blood velocity of 0.478 cm/s (measured by Doppler velocimetry), a 0.2 mm/s mean flow rate was obtained within the thrombus structure, most of which occurred in the 100-fold more permeable outer shell region (calculated permeability of the inner core was 10(-11) cm(2)). Average wall shear stresses were 80-100 dyne/cm(2) (peak values >200 dyne/cm(2)) on the outer rough surface of the thrombus. Within the thrombus, small molecule tracers (0.1 kDa) experienced ~70,000 collisions/s and penetrated/exited it in about 1 s, whereas proteins (~50 kDa) had ~9000 collisions/s and required about 10 s (tortuosity ~2-2.5). These simulations help define physical processes during thrombosis and constraints for drug delivery to the thrombus.

Numerical simulation of nucleotide transport in the human thoracic aorta

Extracellular adenine nucleotides ATP and ADP on vascular endothelial cells may play a role in the localization of atherogenesis by regulating the release of nitric oxide from endothelial cells and modulating intracellular calcium levels. To quantitatively investigate the concentration distribution of nucleotides on the luminal surface of the human thoracic aorta, we numerically simulated the transport of nucleotides using an aorta model constructed based on MRI images and analyzed the effects of different factors on nucleotide transport, such as ATP release rate (S(ATP)), pulsatile flow and the absence of ATP in the main blood stream. The numerical results revealed that the combined concentration of ATP and ADP (c(w-ATP+ADP)) on the aortic surface varied from place to place, being relatively low in disturbed flow regions. In addition, c(w-ATP+ADP) was significantly affected by S(ATP). For relatively slow S(ATP), such as the moderate sigmoidal release model, c(w-ATP+ADP) was very low in certain flow regions with low wall shear stress. However, for very rapid S(ATP), such as the rapid linear release model, c(w-ATP+ADP) was relatively high in these same regions. The results also demonstrated that for relatively slow S(ATP), pulsatile blood flow enhanced c(w-ATP+ADP). However, for very rapid S(ATP), pulsatile blood flow would reduce c(w-ATP+ADP). Moreover, the absence of ATP within the main blood stream would not influence the distribution of c(w-ATP+ADP). In conclusion, the concentration distribution of nucleotides along the aortic wall was quite uneven and determined by both the ATP release rate and the blood flow pattern in the aorta.

Flow-dependent mass transfer may trigger endothelial signaling cascades

It is well known that fluid mechanical forces directly impact endothelial signaling pathways. But while this general observation is clear, less apparent are the underlying mechanisms that initiate these critical signaling processes. This is because fluid mechanical forces can offer a direct mechanical input to possible mechanotransducers as well as alter critical mass transport characteristics (i.e., concentration gradients) of a host of chemical stimuli present in the blood stream. However, it has recently been accepted that mechanotransduction (direct mechanical force input), and not mass transfer, is the fundamental mechanism for many hemodynamic force-modulated endothelial signaling pathways and their downstream gene products. This conclusion has been largely based, indirectly, on accepted criteria that correlate signaling behavior and shear rate and shear stress, relative to changes in viscosity. However, in this work, we investigate the negative control for these criteria. Here we computationally and experimentally subject mass-transfer limited systems, independent of mechanotransduction, to the purported criteria. The results showed that the negative control (mass-transfer limited system) produced the same trends that have been used to identify mechanotransduction-dominant systems. Thus, the widely used viscosity-related shear stress and shear rate criteria are insufficient in determining mechanotransduction-dominant systems. Thus, research should continue to consider the importance of mass transfer in triggering signaling cascades.

Exaggerated vasopressor response to exercise and cerebral blood flow velocity

We studied 10 young adults, normotensive at rest, comprising a control group (n = 5) with normal blood pressure responsiveness to exercise and an experimental group exhibiting greater percentage of body fat and body mass index (BMI) than the controls, with exaggerated blood pressure (vasopressor) responsiveness to exercise (EEBPR) (n = 5). Lower absolute and varying oxygen consumption/body weight normalized units of middle cerebral arterial blood flow velocity (MCAV) were found during exercise in the experimental group (P < .01). These findings support the hypothesis that the combination of EEBPR and high BMI is associated with low MCAV that may put such individuals at risk for cerebral hypoperfusion and cognitive deficits.

Nitric oxide signaling in the microcirculation

Several apparent paradoxes are evident when one compares mathematical predictions from models of nitric oxide (NO) diffusion and convection in vasculature structures with experimental measurements of NO (or related metabolites) in animal and human studies. Values for NO predicted from mathematical models are generally much lower than in vivo NO values reported in the literature for experiments, specifically with NO microelectrodes positioned at perivascular locations next to different sizes of blood vessels in the microcirculation and NO electrodes inserted into a wide range of tissues supplied by the microcirculation of each specific organ system under investigation. There continues to be uncertainty about the roles of NO scavenging by hemoglobin versus a storage function that may conserve NO, and other signaling targets for NO need to be considered. This review describes model predictions and relevant experimental data with respect to several signaling pathways in the microcirculation that involve NO.

Multiscale modeling of intracranial aneurysms: cell signaling, hemodynamics, and remodeling

The genesis, growth, and rupture of intracranial aneurysms (IAs) involve physics at the molecular, cellular, blood vessel, and organ levels that occur over time scales ranging from seconds to years. Comprehensive mathematical modeling of IAs, therefore, requires the description and integration of events across length and time scales that span many orders of magnitude. In this letter, we outline a strategy for mulstiscale modeling of IAs that involves the construction of individual models at each relevant scale and their subsequent combination into an integrative model that captures the overall complexity of IA development. An example of the approach is provided using three models operating at different length and time scales: 1) shear stress induced nitric oxide production; 2) smooth muscle cell apoptosis; and 3) fluid-structure-growth modeling. A computational framework for combining them is presented. We conclude with a discussion of the advantages and challenges of the approach.

3D network model of NO transport in tissue

We developed a mathematical model to simulate shear stress-dependent nitric oxide (NO) production and transport in a 3D microcirculatory network based on published data. The model consists of a 100 μm × 500 μm × 75 μm rectangular volume of tissue containing two arteriole-branching trees, and nine capillaries surrounding the vessels. Computed distributions for NO in blood, vascular walls, and surrounding tissue were affected by hematocrit (Hct) and wall shear stress (WSS) in the network. The model demonstrates that variations in the red blood cell (RBC) distribution and WSS in a branching network can have differential effects on computed NO concentrations due to NO consumption by RBCs and WSS-dependent changes in NO production. The model predicts heterogeneous distributions of WSS in the network. Vessel branches with unequal blood flow rates gave rise to a range of WSS values and therefore NO production rates. Despite increased NO production in a branch with higher blood flow and WSS, vascular wall NO was predicted to be lower due to greater NO consumption in blood, since the microvascular Hct increased with redistribution of RBCs at the vessel bifurcation. Within other regions, low WSS was combined with decreased NO consumption to enhance the NO concentration.

ATP transport in saccular cerebral aneurysms at arterial bends

ATP acts as an extracellular signaling molecule in purinergic signaling that regulates vascular tone. ATP binds purinergic P2 nucleotide receptors on endothelial cells. Understanding the mass transport of ATP to endothelial cells by blood flow is thus important to predict functional changes in aneurysmal walls. While some clinical observations indicate a difference of wall pathology between ruptured and unruptured aneurysms, no study has focused on the mass transport in aneurysms. We investigated the characteristics of ATP concentration at aneurysmal wall using a numerical model of ATP transport in aneurysms formed at arterial bends. The magnitude of ATP concentration at the aneurysmal wall was significantly smaller than that at the arterial wall. In particular, significantly low concentration was predicted at the proximal side of the aneurysmal sac. A strong correlation was revealed between the inflow flux at the aneurysmal neck and the resultant concentration at the aneurysmal wall.

Multiple stressors and the response of vascular endothelial cells: the effect of aging and diabetes

BACKGROUND

The present study examined the effects of local heat, global heat, and the interaction between these two endothelial stressors on the blood flow of the skin of the foot in people who are older and who have diabetes.

METHODS

Subjects who were older (mean age 64.2 +/- 5.9 years) and were younger (mean age 25.7 +/- 2.9 years) and subjects who had diabetes (mean age 62 +/- 5.9 years, mean duration 13.2 +/- 9.1 years) participated. Subjects were exposed to three global temperatures (16 degrees C, 24 degrees C, and 32 degrees C), and the blood flow response was recorded on the foot with a laser Doppler flow meter for 30 s following applications of local heat (30 degrees C, 33.5 degrees C, and 37 degrees C) using a Peltier junction to clamp the skin for 2 min.

RESULTS

All three groups significantly increased blood flow from the 16-24 degrees C environments for the 37 degrees C application of local heat (P(Younger) = 0.02, P(Older) = 0.02, P(Diabetes) = 0.01). Those with diabetes and those who were older only increased blood flow 5% and 6% from the 24-32 degrees C environment, which was not statistically significant (P(Older) = 0.12, P(Diabetes) = 0.14).

CONCLUSIONS

There appears to be considerable blood flow reserve in younger subjects to tolerate heat stress. In contrast, older subjects and those with diabetes reach a critical level after which additional heat does not cause in increase in blood flow.

Computer model of nucleotide transport in a realistic porcine aortic trifurcation

Adenosine triphosphate (ATP) is a ubiquitous blood borne agonist which is responsible for the regulation of vascular tone via purinogenic signalling pathways. The present study models the transport of ATP in a realistic porcine aortic trifurcation, which includes multiple branches and bifurcations. The focus of the present study is understanding how pulsatile flow effects mass transfer, observing both mean and transient variations. Unlike in the many idealized models which model transport of low diffusion coefficient species, the realistic geometry leads to very different mass transfer characteristics. These include spiral patterns in the distribution of low concentration fluid. Furthermore, the mean ATP distribution was found to be elevated compared with the steady state; this is attributed to the effects of convective mixing. The results strongly implicate that under certain conditions mass transport in pulsatile flow exhibits different hydrolysis characteristics at the endothelium compared with steady state. Transient variations throughout the the cardiac cycle were found to be small. This small transient response is primarily due to low ATP diffusivity.