A three-layer continuous model of porous media to describe the first phase of skin irritation

Mechanical skin irritation induces vasodilation on the line of scratch and in the neighboring zone. In order to model the effect of an irritation on the microcirculation, the vascular network has been described using a three-layer model. The first and last layer, considered as horizontal two-dimensional porous media, describe irrigation and drainage of the system, respectively. The intermediate layer, described by means of a lumped parameter method, does not permit horizontal fluxes. Hierarchical fluxes are directed from the first to the second layer and then towards the drainage layer in order to take into account physiological flow direction. Irritation is modeled by changing compliance of vessels situated at the entrance of the micro-circulation. The model permits to investigate the influence of change in compliance on flow and pressure behavior at microscopic and macroscopic level.     

First phase microcirculatory reaction to mechanical skin irritation: a three layer model of a compliant vascular tree

Mechanical skin irritation creates vasodilatation in the line of a stroke and in the surrounding tissue. To obtain further insight on underlying physiological mechanisms we developed a model of the vascular network comprised of three layers, where the first and the last one have a tree structure. They represent the arterial and the venous system, respectively. Both are connected via an intermediate zone representing the core of the microcirculation, which is described by means of a compliant compartment model. Irritation induces change in compliance of vessels situated at the entrance of the intermediate zone. Thus the model describes flow and pressure behavior due to mechanical skin irritation.     

Incorporating an immersed boundary method to study thermal effects of vascular systems during tissue cryo-freezing

In this paper, the three-dimensional thermal effects of a clinically-extracted vascular tissue undergoing cryo-freezing are numerically investigated. Based on the measured experimental temperature field, the numerical results of the Pennes bioheat model combined with the boundary condition-enforced immersed boundary method (IBM) agreed well with experimental data with a maximum temperature discrepancy of 2.9 °C. For simulating the temperature profile of a tumor sited in a dominantly vascularized tissue, our model is able to capture with ease the thermal effects at specified junctions of the blood vessels. The vascular complexity and the ice-ball shape irregularity which cannot be easily quantified via clinical experiments are also analyzed and compared for both two-dimensional and three-dimensional settings with different vessel configurations and developments. For the three-dimensional numerical simulations, a n-furcated liver vessels model from a three-dimensional segmented volume using hole-making and subdivision methods is applied. A specific study revealed that the structure and complexity of the vascular network can markedly affect the tissue's freezing configuration with increasing ice-ball irregularity for greater blood vessel complexity.     

VEGF and imaging of vessels in rheumatoid arthritis

Angiogenesis is a prominent feature of rheumatoid synovitis. Formation of new blood vessels permits a supply of nutrients and oxygen to the augmented inflammatory cell mass and so contributes to perpetuation of joint disease. Vascular endothelial growth factor (VEGF) is a potent endothelial cell-specific growth factor that is upregulated by proinflammatory cytokines and by hypoxia. Serum VEGF concentrations are elevated in rheumatoid arthritis (RA) and correlate with disease activity. Furthermore, serum VEGF measured at first presentation in RA is highly significantly correlated with radiographic progression of disease over the subsequent year. Power Doppler ultrasonography is a sensitive method for demonstrating the presence of blood flow in small vessels and there is a very close relation between the presence or absence of vascular flow signal on power Doppler imaging and the rate of early synovial enhancement on dynamic gadolinium-enhanced magnetic resonance imaging (MRI) of joints with RA. Images obtained by both dynamic enhanced MRI and power Doppler ultrasonography correlate with vascularity of synovial tissue as assessed histologically. In early RA, there is a striking association between joint erosions assessed on high-resolution ultrasonography and vascular signal in power Doppler mode. Collectively, these findings implicate vascular pannus in the erosive phase of disease and strongly suggest that proangiogenic molecules such as VEGF are targets for novel therapies in RA. Animal model data supports this concept. It seems likely that serological and imaging measures of vascularity in RA will become useful tools in the assessment of disease activity and response to therapy.     

A new method to model change in cutaneous blood flow due to mechanical skin irritation part II: parameter identification procedure

Mechanical skin irritation, for example a light scratch with a needle, induces histamine and neuropeptide release on the line of stroke and in the surrounding tissue. Both histamine and neuropeptides are vasodilators. They cause vasodilation by changing the contraction state of the vascular smooth muscles and hence vessel compliance. Smooth muscle contraction state is very difficult to measure in vivo. For that reason we propose in this article an identification procedure to establish an irritation law. The law gives change in vessel compliance as a function of space, time and the intensity of the stroke. We have showed that vessel compliance increases immediately after the stroke not only on the line of stroke, but also in the surrounding tissue. Then, after a short delay, vessel compliance starts decreasing in the surrounding tissue, whereas vessel compliance on the line of stroke keeps increasing. Hence, blood is transported from the surrounding tissue to the line of stroke. In this way, higher blood volume on the line of stroke can be obtained than by only changing vessel compliance locally.     

Low Reynolds number steady state flow through a branching network of rigid vessels II. A finite element mixture model

This research aims at formulating and verifying a finite element mixture formulation for blood perfusion. The equations derived in a companion paper [3] are discretized according to the Galerkin method. A flow experiment in a rigid model of a vascular tree of about 500 vessels is performed in order to verify the finite element mixture formulation. Although the comparison of numerical results and experimental measurements is not conclusive as far as the validity of the theory is concerned, the results do suggest that the finite element model has predictive power in the case of low Reynolds number steady-state flow of a Newtonian fluid in a rigid vascular tree.     

Preliminary study of the vascular dynamics of port-wine hemangioma with therapeutic implications for argon laser treatment

The vascular dynamics of port-wine hemangioma have been studied in several ways in order to better understand blood flow factors. Utilizing a laser Doppler velocimeter, differential perfusion/blood flow was studied and contrasted to normal skin, compared to heat and cold challenges, and finally measured in relationship to argon laser treatment. Results indicate that port-wine hemangiomas do not necessarily have different perfusion than normal skin but respond less vigorously to heat challenges. Cooling showed no uniform response by port-wine hemangioma vessels, while injection with Xylocaine plus epinephrine resulted in a markedly decreased perfusion and vasoconstriction contrary to previously held theories. Argon laser treatment did not uniformly alter laser Doppler perfusion to a predictable degree. Laser Doppler velocimeter flow studies were not able to predict future good versus bad results of laser treatment.     

The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model.

Laser Doppler anemometry experiments and finite element simulations of steady flow in a three dimensional model of the carotid bifurcation were performed to investigate the influence of non-Newtonian properties of blood on the velocity distribution. The axial velocity distribution was measured for two fluids: a non-Newtonian blood analog fluid and a Newtonian reference fluid. Striking differences between the measured flow fields were found. The axial velocity field of the non-Newtonian fluid was flattened, had lower velocity gradients at the divider wall, and higher velocity gradients at the non-divider wall. The flow separation, as found with the Newtonian fluid, was absent. In the computations, the shear thinning behavior of the analog blood fluid was incorporated through the Carreau-Yasuda model. The viscoelastic properties of the fluid were not included. A comparison between the experimental and numerical results showed good agreement, both for the Newtonian and the non-Newtonian fluid. Since only shear thinning was included, this seems to be the dominant non-Newtonian property of the blood analog fluid under steady flow conditions.     

Inertial deposition effects: a study of aerosol mechanics in the trachea using laser Doppler velocimetry and fluorescent dye

This study characterizes the axial velocity and axial turbulence intensity patterns noted in the tracheal portion of a cadaver-based throat model at two different steady flow rates (18.1 and 41.1 LPM.) This characterization was performed using Phase Doppler Interferometry (Laser Doppler Velocimetry). Deposition, as assessed qualitatively using fluorescent dye, is related to the position of the laryngeal jet within the trachea. The position of the jet is dependent on the downstream conditions of the model. It is proposed therefore that lung/airway conditions may have important effects on aerosol deposition within the throat. There is no correspondence noted between regions of high axial turbulence intensity and deposition.     

Incorporating measured valve properties into a numerical model of a lymphatic vessel

An existing lumped-parameter model of multiple lymphangions (lymphatic vascular segments) in series is adapted for the incorporation of recent physiological measurements of lymphatic vascular properties. The new data show very marked nonlinearity of the passive pressure–diameter relation during distension, relative to comparable blood vessels, and complex valve behaviour. Since lymph is transported as a result of either the active contraction or the passive squeezing of vascular segments situated between two one-way valves, the performance of these valves is of primary importance. The valves display hysteresis (the opening and closing pressure drop thresholds differ), a bias to staying open (both state changes occur when the trans-valve pressure drop is adverse) and pressure-drop threshold dependence on transmural pressure. These properties, in combination with the strong nonlinearity that valve operation represents, have in turn caused intriguing numerical problems in the model, and we describe numerical stratagems by which we have overcome the problems. The principal problem is also generalised into a relatively simple mathematical example, for which solution detail is provided using two different solvers.     

Effect of the endothelial surface layer on transmission of fluid shear stress to endothelial cells

Responses of vascular endothelial cells to mechanical shear stresses resulting from blood flow are involved in regulation of blood flow, in structural adaptation of vessels, and in vascular disease. Interior surfaces of blood vessels are lined with a layer of bound or adsorbed macromolecules, known as the endothelial surface layer (ESL). In vivo investigations have shown that this layer has a width of order 1 microm, that it substantially impedes plasma flow, and that it excludes flowing red blood cells. Here, the effect of the ESL on transmission of shear stress to endothelial cells is examined using a theoretical model. The layer is assumed to consist of a matrix of molecular chains extending from the surface, held in tension by a slight increase in colloid osmotic pressure relative to that in free-flowing plasma. It is shown that, under physiological conditions, shear stress is transmitted to the endothelial surface almost entirely by the matrix, and fluid shear stresses on endothelial cell membranes are very small. Rapid fluctuations in shear stress are strongly attenuated by the layer. The ESL may therefore play an important role in sensing of shear stress by endothelial cells.     

Mechanical properties of the coronary vasculature: indirect evaluation.

Information on the mechanical properties of the coronary vascular bed can be obtained indirectly by modelling the vascular system. This indirect approach, unlike 'in vitro' measurements, allows to take into account the vasomotor conditions of the circulatory district as well as the effect of the surrounding embedding tissue on the vascular performance. An experimental manoeuvre of sudden occlusion and subsequent release of the thoracic descendent aorta on 5 anaesthetized dogs with open pericardium induces a step-like variation in the coronary perfusion pressure and the occurrence of oscillations in the mean coronary flow. Such a behaviour can be described using a second-order model ('windkessel'+inductance, which takes into account blood inertia in the large vessels). The value of the coefficients entering the equations have been obtained with a 'best-fit' procedure (minimum of the chi-squared variable) on the haemodynamical data. Coefficient variations are in agreement with the direct estimation of the myocardial compliance and volume, measured by Ultrasound Echocardiographic imaging (4-chamber projection mode).     

Pulsatile blood flow in the entire coronary arterial tree: theory and experiment

The pulsatility of coronary circulation can be accurately simulated on the basis of the measured branching pattern, vascular geometry, and material properties of the coronary vasculature. A Womersley-type mathematical model is developed to analyze pulsatile blood flow in diastole in the absence of vessel tone in the entire coronary arterial tree on the basis of previously measured morphometric data. The model incorporates a constitutive equation of pressure and cross-section area relation based on our previous experimental data. The formulation enables the prediction of the impedance, the pressure distribution, and the pulsatile flow distribution throughout the entire coronary arterial tree. The model is validated by experimental measurements in six diastolic arrested, vasodilated porcine hearts. The agreement between theory and experiment is excellent. Furthermore, the present pulse wave results at low frequency agree very well with previously published steady-state model. Finally, the phase angle of flow is seen to decrease along the trunk of the major coronary artery and primary branches toward the capillary vessels. This study represents the first, most extensive validated analysis of Womersley-type pulse wave transmission in the entire coronary arterial tree down to the first segment of capillaries. The present model will serve to quantitatively test various hypotheses in the coronary circulation under pulsatile flow conditions.     

Predicted permeability parameters of human ovarian tissue cells to various cryoprotectants and water

This study presents a generic numerical model to simulate the coupled solute and solvent transport in human ovarian tissue sections during addition and removal of chemical additives or cryoprotective agents (CPA). The model accounts for the axial and radial diffusion of the solute (CPA) as well as axial convection of the CPA, and a variable vascular surface area (A) during the transport process. In addition, the model also accounts for the radial movement of the solvent (water) into and out of the vascular spaces. Osmotic responses of various cells within an human ovarian tissue section are predicted by the numerical model with three model parameters: permeability of the tissue cell membrane to water (L(p)), permeability of the tissue cell membrane to the solute or CPA (omega) and the diffusion coefficient of the solute or CPA in the vascular space (D). By fitting the model results with published experimental data on solute/water concentrations within an human ovarian tissue section, I was able to determine the permeability parameters of ovarian tissue cells in the presence of 1.5M solutions of each of the following: dimethyl sulphoxide (DMSO), propylene glycol (PROH), ethylene glycol (EG), and glycerol (GLY), at two temperatures (4 degrees C and 27 degrees C). Modeling Approach 1: Assuming a constant value of solute diffusivity (D = 1.0 x 10(-9) m(2)/sec), the best fit values of L(p) ranged from 0.35 x 10(-14) to 1.43 x 10(-14) m(3)/N-sec while omega ranged from 2.57 x 10(-14) to 70.5 x 10(-14) mol/N-sec. Based on these values of L(p) and omega, the solute reflection coefficient, sigma defined as sigma = 1-omega v(CPA)/L(P) ranged from 0.9961 to 0.9996. Modeling Approach 2: The relative values of omega and sigma from our initial modeling suggest that the embedded ovarian tissue cells are relatively impermeable to all the CPAs investigated (or omega approximately 0 and sigma approximately 1.0). Consequently the model was modified and used to predict the values of L(p) and D assuming omega = 0 and sigma = 1.0. The best fit values of L(p) ranged from 0.44 x 10(-14) to 1.2 x 10(-14) m(3)/N-sec while D ranged from 0.85 x 10(-9) to 2.08 x 10(-9) m(2)/sec. Modeling Approach 3: Finally, the best fit values of D from modeling approach 2 were incorporated into model 1 to re-predict the values of L(p) and omega. It is hoped that the ovarian tissue cell parameters reported here will help to optimize chemical loading and unloading procedures for whole ovarian tissue sections and consequently, tissue cryopreservation procedures.     

Irritative effects of some pesticides and a technical component on tissue structure of the chorioallantoic membrane

The chorioallantoic membrane (CAM) is a complete tissue that responds to injury with a complete inflammatory reaction, this process similar to that induced by chemicals in the conjunctival tissue of the rabbit eye. During the study chemicals are placed directly onto the chorioallantoic membrane and the occurrence of vascular injury or coagulation in response to a compound is as an indication of the potential of a chemical to damage mucous membranes. In our study irritant pesticides (Fusilade S, Karathane LC) and a technical pesticide component (Trend) were tested and their effects on the tissue structures of CAM were examined. After treatment with the test materials, first lysis and then haemorrhage were observed macroscopically on CAM. In histological pictures stained with H-E the rupture of the blood vessel wall was seen and blood was observed around the blood vessels in the middle layer. The histological findings correlated well with the macroscopic appearance in this study. In general a good correlation was found between the HET-CAM results and reported data from Draize test. The subjective nature of the evaluation is reduced through the histological examination of treated CAM. The HET-CAM test can be a useful component of a battery of tests needed for replacing the Draize rabbit eye irritation test.     

Two-equation turbulence modeling of pulsatile flow in a stenosed tube

The study of pulsatile flow in stenosed vessels is of particular importance because of its significance in relation to blood flow in human pathophysiology. To date, however, there have been few comprehensive publications detailing systematic numerical simulations of turbulent pulsatile flow through stenotic tubes evaluated against comparable experiments. In this paper, two-equation turbulence modeling has been explored for sinusoidally pulsatile flow in 75% and 90% area reduction stenosed vessels, which undergoes a transition from laminar to turbulent flow as well as relaminarization. Wilcox's standard k-omega model and a transitional variant of the same model are employed for the numerical simulations. Steady flow through the stenosed tubes was considered first to establish the grid resolution and the correct inlet conditions on the basis of comprehensive comparisons of the detailed velocity and turbulence fields to experimental data. Inlet conditions based on Womersley flow were imposed at the inlet for all pulsatile cases and the results were compared to experimental data from the literature. In general, the transitional version of the k-omega model is shown to give a better overall representation of both steady and pulsatile flow. The standard model consistently over predicts turbulence at and downstream of the stenosis, which leads to premature recovery of the flow. While the transitional model often under-predicts the magnitude of the turbulence, the trends are well-described and the velocity field is superior to that predicted using the standard model. On the basis of this study, there appears to be some promise for simulating physiological pulsatile flows using a relatively simple two-equation turbulence model.     

Cat lung hemodynamics: comparison of experimental results and model predictions

Commonly, attempts have been made to learn about the structure and function of the pulmonary vascular bed from measurements of arterial and venous pressures and blood flow rate under steady-state conditions (e.g., from pressure vs. flow data) or dynamic conditions (e.g., from vascular occlusion data). Zhuang et al. (J. Appl. Physiol. 55: 1341-1348, 1983) have presented a detailed model of steady-state cat lung hemodynamics based on direct measurements of anatomical and elasticity data. This model provides an opportunity to better understand the information content of the hemodynamic data. Therefore, in the present study we carried out a series of steady-state and dynamic experiments on isolated cat lungs. We then compared the results with those predicted by the model. We found that the model provided a good fit to the steady-state data. However, to fit the dynamic data, some modifications were necessary to account for the viscous behavior of the vessel walls and to move the first moment of the distribution of vascular resistance toward the arterial end of the vascular bed relative to that of the distribution of vascular compliance. Due to the sensitivity of the vascular resistance to small changes in vessel diameters and branching ratio, the modifications in morphometry represent small changes in morphometric data and are probably within the range of uncertainty in such data. The modifications had little effect on the steady-state model simulations but substantially improved the dynamic model simulations, suggesting that the dynamic data are quite sensitive to small changes in the relative distributions of vessel diameters and elasticity.     

Convective heat transfer coefficients in the circulation

Convective heat transfer in the vessels of the circulatory system is investigated numerically. In the modeling, account is taken of the non-Newtonian rheological properties of blood and the presence of a cell-depleted plasma layer at the vessel wall. The latter is found to produce a remarkable enhancement of the heat transfer rate in the small vessels, while the effects due to the rheological behavior of blood are comparatively low. A comparison with experimental data available in the open literature is finally attempted.     

A Key Role for the Endothelium in NOD1 Mediated Vascular Inflammation: Comparison to TLR4 Responses

Understanding the mechanisms by which pathogens induce vascular inflammation and dysfunction may reveal novel therapeutic targets in sepsis and related conditions. The intracellular receptor NOD1 recognises peptidoglycan which features in the cell wall of Gram negative and some Gram positive bacteria. NOD1 engagement generates an inflammatory response via activation of NFκB and MAPK pathways. We have previously shown that stimulation of NOD1 directly activates blood vessels and causes experimental shock in vivo. In this study we have used an ex vivo vessel-organ culture model to characterise the relative contribution of the endothelium in the response of blood vessels to NOD1 agonists. In addition we present the novel finding that NOD1 directly activates human blood vessels. Using human cultured cells we confirm that endothelial cells respond more avidly to NOD1 agonists than vascular smooth muscle cells. Accordingly we have sought to pharmacologically differentiate NOD1 and TLR4 mediated signalling pathways in human endothelial cells, focussing on TAK1, NFκB and p38 MAPK. In addition we profile novel inhibitors of RIP2 and NOD1 itself, which specifically inhibit NOD1 ligand induced inflammatory signalling in the vasculature. This paper is the first to demonstrate activation of whole human artery by NOD1 stimulation and the relative importance of the endothelium in the sensing of NOD1 ligands by vessels. This data supports the potential utility of NOD1 and RIP2 as therapeutic targets in human disease where vascular inflammation is a clinical feature, such as in sepsis and septic shock.     

Capillary blood perfusion during postischemic reperfusion in striated muscle.

Monitoring of nutritive blood flow in muscle is of particular importance to reconstructive surgeons, since ischemia/reperfusion in striated muscle is known to result in postischemic microvascular perfusion failure. Laser Doppler flowmetry has recently been introduced as an easy-to-use, noninvasive technique for continuous monitoring of microvascular tissue perfusion. Despite its popularity, there exists a great deal of controversy as to what actually generates the laser Doppler signal recorded from a given tissue. Intravital microscopy is a technique for direct visualization of the nutritional circulation in tissue. By using intravital microscopy, direct measurements of blood perfusion in individual segments of the nutritional microcirculation can be made. In 22 Syrian golden hamsters we performed laser Doppler flowmetry and intravital microscopy measurements in muscle tissue prior to and during reperfusion after 4 hours of tourniquet ischemia using the dorsal skinfold chamber model. Intravital microscopy (n = 10) revealed a heterogeneous capillary perfusion during the early reperfusion phase with a decrease (p less than 0.01) in functional capillary density to 49.4 +/- 17.0 percent of control. No recovery was observed after 24 hours of reperfusion. Laser Doppler flowmetry (n = 12) showed a parallel reduction of capillary red blood cell flux during the early perfusion phase to 43.9 +/- 22.6 percent of control values (p less than 0.01), and no recovery was observed after 24 hours of reperfusion. However, the laser Doppler flowmetry technique was not able to detect the capillary perfusion inhomogeneities shown by intravital microscopy. Postischemic reperfusion in striated muscle is characterized by a decrease in functional capillary density and a heterogeneous capillary perfusion. Laser Doppler flowmetry is a useful tool for monitoring microvascular tissue perfusion, although in striated muscle of the hamster it must be considered that accurate nutritional "capillary" flow readings can be grossly overestimated if larger vessels, such as arterioles and collecting venules, are contained in the measuring field of the laser Doppler probe.