Effect of initial stresses on the wave propagation in arteries

A theoretical analysis for the problem of wave propagation in arteries is presented. Blood is treated as a Newtonian, viscous incompressible fluid. On the basis of information derived from experimental investigations on the mechanical properties of wall tissues, the arterial wall is considered to be nonlinearly viscoelastic and orthotropic. The analysis is carried out for a cylindrical artery, under the purview of membrane theory, by taking account the effect of initial stresses. The motion of the wall and that of the fluid are assumed to be axisymmetric. Particular emphasis has been paid to the propagation of small amplitude harmonic waves whose wavelength is large compared to the radius of the vessel. By employing the equations of motion of the fluid and those for the wall, together with the equations of continuity, a frequency equation is derived by exploiting the conditions of continuity of the velocity of the arterial wall and that of blood on the endosteal surface of the wall. In order to illustrate the validity of the derived analytical expressions a quantitative analysis is made for the variations of the phase velocities as well as the transmission coefficient with frequency corresponding to different transmural pressures which relate to different initial stresses. Computational results indicate that phase velocities increase with the increase of transmural pressures.     

Unsteady and three-dimensional simulation of blood flow in the human aortic arch

A three-dimensional and pulsatile blood flow in a human aortic arch and its three major branches has been studied numerically for a peak Reynolds number of 2500 and a frequency (or Womersley) parameter of 10. The simulation geometry was derived from the three-dimensional reconstruction of a series of two-dimensional slices obtained in vivo using CAT scan imaging on a human aorta. The numerical simulations were obtained using a projection method, and a finite-volume formulation of the Navier-Stokes equations was used on a system of overset grids. Our results demonstrate that the primary flow velocity is skewed towards the inner aortic wall in the ascending aorta, but this skewness shifts to the outer wall in the descending thoracic aorta. Within the arch branches, the flow velocities were skewed to the distal walls with flow reversal along the proximal walls. Extensive secondary flow motion was observed in the aorta, and the structure of these secondary flows was influenced considerably by the presence of the branches. Within the aorta, wall shear stresses were highly dynamic, but were generally high along the outer wall in the vicinity of the branches and low along the inner wall, particularly in the descending thoracic aorta. Within the branches, the shear stresses were considerably higher along the distal walls than along the proximal walls. Wall pressure was low along the inner aortic wall and high around the branches and along the outer wall in the ascending thoracic aorta. Comparison of our numerical results with the localization of early atherosclerotic lesions broadly suggests preferential development of these lesions in regions of extrema (either maxima or minima) in wall shear stress and pressure.     

Studies on the neurosecretory system of Ranatra elongata fabricius (Hemiptera: Nepidae) with reference to the distal fate of NCC I and II

With the help of PF and PAVB bulk-stained preparations and sections the neurosecretory system of Ranatra elongata has been described. Two medial, each of 9-10 cells, and two lateral, each of 3-4 cells, groups of neurosecretory cells have been observed in the protocerebrum. Only the A-cells have been found to be positive to PAVB histo- and cyto-chemical technique. Axons of the A-cells after traversing the proto- and deuto-cerebrum emerge from the tritocerebrum as the NCC I. The NCC I after bypassing the corpora cardiaca penetrate the aorta wall. There is no physical continuity between the corpora cardiaca and the NCC I and the two are separable. The NSM from the A-cells, transported by their nerve fibers, has been observed in the aorta wall. On the basis of large accumulation on NSM in the aorta wall the latter has been considered as the storage-and-release organ for the A-material. Corpora cardiaca are found to be devoid of A-material. Axons from the B-cells, after emergence from the tritocerebrum as the NCC II, have been observed to penetrate the corpora cardiaca. On the basis of ample amounts of B-material the glands have been considered as the storage-and-release organ for the B-material only. Observations are compared with results on related species and it is concluded that two independent organ complexes constitute the neurosecretory systemt of R. elongata. The A-cells, their pathways, the NCC I, and the aorta wall comprise the first; and the B-cells, their pathways, the NCC II, and the corpora cardiaca the second. The former is concerned with the elaboration, transportion, storage-and-release of the A-material and the latter with the B-material. Finally arguments are presented to include the aorta wall in the neurosecretory system.     

A fast computational model for circulatory dynamics: effects of left ventricle–aorta coupling

The course of diseases such as hypertension, systolic heart failure and heart failure with a preserved ejection fraction is affected by interactions between the left ventricle (LV) and the vasculature. To study these interactions, a computationally efficient, biophysically based mathematical model for the circulatory system is presented. In a four-chamber model of the heart, the LV is represented by a previously described low-order, wall volume-preserving model that includes torsion and base-to-apex and circumferential wall shortening and lengthening, and the other chambers are represented using spherical geometries. Active and passive myocardial mechanics of all four chambers are included. The cardiac model is coupled with a wave propagation model for the aorta and a closed lumped-parameter circulation model. Parameters for the normal heart and aorta are determined by fitting to experimental data. Changes in the timing and magnitude of pulse wave reflections by the aorta are demonstrated with changes in compliance and taper of the aorta as seen in aging (decreased compliance, increased diameter and length), and resulting effects on LV pressure–volume loops and LV fiber stress and sarcomere shortening are predicted. Effects of aging of the aorta combined with reduced LV contractile force (failing heart) are examined. In the failing heart, changes in aortic properties with aging affect stroke volume and sarcomere shortening without appreciable augmentation of aortic pressure, and the reflected pressure wave contributes an increased proportion of aortic pressure.

     

Velocity distribution along an elastic model of human arterial tree

An experimental investigation of an elastic model of the human arterial tree, has been performed for physiological type flow by pulsed Doppler ultrasonic velocimetry. The arterial tree model, fabricated in clear polyurethane, includes the aortic arch, with a Starr-Edwards ball valve mounted in the root of the aorta, the descending aorta and the iliac bifurcation. Our study showed that the velocity profile, a few centimeters beyond the valve, is skewed, with higher velocities towards the top and the inner wall (anatomically the posterior and left lateral wall). An inward shift of the maximum velocity and reverse flow are denoted along the inner wall of the aortic arch. The velocity profiles in the descending aorta are blunted. Downstream from the vertex of the iliac bifurcation, there is vorticity creation, but the branching effect is quickly damped by the pulsatility of the flow and the elasticity of the wall.     

Effects of wall motion and compliance on flow patterns in the ascending aorta

Helical flows have been observed in the ascending aorta in vivo, and geometric curvature has been suggested to be a major contributing factor. We employed magnetic resonance imaging (MRI) and velocity mapping to develop a computational model to examine the effects of curvature and also wall compliance and movement upon flow patterns. In the computational model, MRI-derived geometry and velocities were imposed as boundary conditions, which included both radial expansion-contraction and translational motion of the wall. The computed results were in agreement with the MR data only when full wall motion was included in the model, suggesting that the flow patterns observed in the ascending aorta arise not only from geometric curvature of the arch but also from the motion of the aorta resulting from its attachment to the beating heart.     

Mathematical model analysis of pressure pulse propagation of the aortic wall

A mathematical blood vessel mode is established of a semi-infinite, fluid filled, cylindrical, elastic tube where a pressure wave is propagated in the fluid. This model has assigned to it physical values of the aorta and is subject to a pressure pulse at the origin of the same configuration and magnitude as that observed in the human. The resulting mathematical solution demonstrates wall displacement in agreement with observed phenomena of (a) a high frequency component analogous to cardiovascular sounds; (b) a low frequency component resembling the pressure pulse analogous to the pulsatile movement of the vessel wall.     

Variability in the Presence of Elastic Fibre-like Structures in the Ventral Aorta of Agnathans (Hagfishes and Lampreys)

This paper investigates whether elastic fibre-like structures are present in the ventral aorta of hagfishes and lampreys. Fibres, which are morphologically similar to the elastic fibres of gnathostomatous (jawed) vertebrates, are shown to be present in the ventral aorta of the hagfish Paramyxine atami, and also, but to a lesser extent, the dorsal aorta of this species and the ventral aorta of another hagfish, Eptatretus stouti.The ‘elastic’ tissue formed irregular sheet-like aggregates, comprising well-defined amorphous material surrounded by tubular microfibrils, whose diameters ranged from 10 to 15 nm. While this tissue was most abundant in the same region of the aortae as that occupied by the elastica interna in the blood vessels of gnathostomes, it was also found deeper in the wall of these blood vessels. Although tubular microfibrils were found in the ventral aorta of the hagfish Myxine glutinosaand the lamprey Geotria australis, these were never associated with well–defined, amorphous material. This parallels the results of previous studies on Myxine glutinosaand another species of lamprey, Petromyzon marinus.Thus, the elastic fibre–like tissues found in the ventral aortae of P. atamiand E. stoutiprovide the first examples of such structures in this region in agnathan vertebrates.     

The influence of vessel wall elasticity and peripheral resistance on the carotid artery flow wave form: a CFD model compared to in vivo ultrasound measurements

The Doppler flow wave form and its derived measures such as the pulsatility index provide clinically important tools for the investigation of arterial disease. The typical shape of Doppler flow wave forms is physiologically known to be largely determined by both peripheral resistance and elastic properties of the arterial wall. In the present study we systematically investigate the influence of both vessel wall elasticity and peripheral resistance on the flow wave form obtained from a CFD-simulation of blood flow in the carotid bifurcation. Numerical results are compared to in vivo ultrasound measurements. The in vivo measurement provides a realistic geometry, local elasticities and an input flow wave form for the numerical experiment. Numerical and experimental results are compared at three different sites in the carotid branches. Peripheral resistance has a profoundly decreasing effect on velocities in the external carotid artery. If elasticity is taken into account, the computed peak systolic velocities are considerably lower and a more realistic smoothing of the flow wave form is found. Together, the results indicate that only if both vessel wall elasticity and positive peripheral resistance are taken into account, experimentally obtained Doppler flow wave forms can be reproduced numerically.     

Analysis and Modeling of Lithium Flows in Porous Materials

One of the primary conditions necessary for the success of magnetic fusion reactors is the ability to mitigate damage to the first wall during ELMs and plasma disruptions. A potential solution involves the use of flowing liquid metals such as lithium as a first wall, but ensuring its stability under the extreme environments in the reactor would be imperative. The conditions leading to instabilities on the free surface of flowing liquid lithium (LL) layers on a substrate and in a porous material are investigated using both analytical methods and computational modeling, with consideration for the effects of LL velocity, LL layer thickness, substrate porosity, LL permeability, and hydrogen (H) plasma velocity. Linear stability analysis is used to predict the critical velocity and wavelength-dependence of wave growth, as well as the onset of instability. The modeling of LL flows is performed on a flat substrate and in a porous material for various LL thicknesses, LL and H plasma velocities to analyze the conditions leading to droplet formation and ejection.     

A study of protoplasmic streaming inPhysarum by laser Doppler spectroscopy

Summary Protoplasmic streaming in the slime moldPhysarum polycephalum has been characterized using laser Doppler spectroscopy. Measurement of the spectrum of scattered laser light permits simultaneous determination of the velocities of all particles in the laser beam, with the relative intensity from each particle proportional to its light scattering cross-section. Simple experimental modifications allow the tracking of the oscillations of the streaming velocities. Rhythmic wall contractions can be monitored simultaneously with the flow velocities. Interpretation of the Doppler spectra shows that a small fraction of the particles in the flowing protoplasm are moving with velocities two to four times greater than the characteristic velocities reported by optical microscopy. Transverse velocities in the tubes are nearly as great as the longitudinal velocities. The shape of the Doppler spectrum at the maximum of the oscillation cycle is consistent with a spatial velocity profile which is sharper than parabolic, presumably because of a viscosity gradient from the center to the walls of the plasmodial tubes. The shape of the Doppler spectrum of depolarized scattered light is of approximately the same form. The response of the plasmodium to increased temperature is an increase in the frequency of the velocity oscillations with little change in the magnitude of the velocities. The response of the plasmodium to very high intensities of laser light is to gel at the point of incidence.     

Multiphoton imaging of the effect of monosaccharide diffusion and formation of fluorescent advanced end products in porcine aorta

Prolonged exposure of tissues to elevated blood sugar levels lead to the formation of advanced glycation end products (AGEs), thus contributing to diabetic complications. Since the vascular system is in immediate contact with blood, diabetic effects on aorta is a major health concern. However, the relative effect of the diffusion of sugar molecular through the vascular wall and the rate of AGE formation is not known. In this study, we aim to address this issue by incubating excised porcine aorta in D-glucose, D-galactose, and D-fructose solutions for different periods. The tissue specimens were then excised for multiphoton imaging of autofluorescence intensity profiles across the aorta wall. We found that for Days 4 to 48 incubation, autofluorescence is constant along the radial direction of the aorta sections, suggesting that monosaccharide diffusion is rapid in comparison to the rate of formation of fluorescent AGEs (fAGEs). Moreover, we found that in porcine aorta, the rate of fAGE formation of D-fructose and D-glucose are factors 2.08 and 1.14 that of D-galactose. Our results suggest that for prolonged exposure of the cardiovascular system to elevated monosaccharides 4 days or longer, damage to the aorta is uniform throughout the tissues.     

Morphological analysis of the hagfish heart. II. The venous pole and the pericardium

The morphological characteristics of the venous pole and pericardium of the heart were examined in three hagfish species, Myxine glutinosa, Eptatretus stoutii, and Eptatretus cirrhatus. In these species, the atrioventricular (AV) canal is long, funnel‐shaped and contains small amounts of myocardium. The AV valve is formed by two pocket‐like leaflets that lack a papillary system. The atrial wall is formed by interconnected muscle trabeculae and a well‐defined collagenous system. The sinus venosus (SV) shows a collagenous wall and is connected to the left side of the atrium. An abrupt collagen‐muscle boundary marks the SV‐atrium transition. It is hypothesized that the SV is not homologous to that of other vertebrates which could have important implications for understanding heart evolution. In M. glutinosa and E. stoutii, the pericardium is a closed bag that hangs from the tissues dorsal to the heart and encloses both the heart and the ventral aorta. In contrast, the pericardium is continuous with the loose periaortic tissue in E. cirrhatus. In all three species, the pericardium ends at the level of the SV excluding most of the atrium from the pericardial cavity. In M. glutinosa and E. stoutii, connective bridges extend between the base of the aorta and the ventricular wall. In E. cirrhatus, the connections between the periaortic tissue and the ventricle may carry blood vessels that reach the ventricular base. A further difference specific to E. cirrhatus is that the adipose tissue associated with the pericardium contains thyroid follicles. J. Morphol. 277:853–865, 2016. © 2016 Wiley Periodicals, Inc.     

Spectrum analysis of turbulence in the canine ascending aorta measured with a hot-film anemometer

We measured turbulence velocity in the canine ascending aorta using a hot-film anemometer. Blood flow velocity was measured at various points across the ascending aorta approximately 1.5-2 times the diameter downstream from the aortic valve. The turbulence spectrum was calculated and its characteristics were examined in connection with the mean Reynolds number and/or measuring positions. In the higher wave number range the values of the turbulence spectra were higher at larger mean Reynolds number. In the higher wave number range, the values of the turbulence spectra were higher at points closer to the centerline of the aorta, when the mean Reynolds number was relatively large. The patterns of the turbulence spectra at various points outside the boundary layer on the aortic wall were similar.     

Kelp versus coralline: cellular basis for mechanical strength in the wave‐swept seaweed Calliarthron (Corallinaceae,Rhodophyta)1

Previous biomechanical studies of wave‐swept macroalgae have revealed a trade‐off in growth strategies to resist breakage in the intertidal zone: growing in girth versus growing strong tissues. Brown macroalgae, such as kelps, grow thick stipes but have weak tissues, while red macroalgae grow slender thalli but have much stronger tissues. For example, genicular tissue in the articulated coralline Calliarthron cheilosporioides Manza is more than an order of magnitude stronger than some kelp tissues, but genicula rarely exceed 1 mm in diameter. The great tissue strength of Calliarthron genicula results, at least in part, from a lifelong strengthening process. Here, a histological analysis is presented to explore the cellular basis for mechanical strengthening in Calliarthron genicula. Genicula are composed of thousands of fiber‐like cells, whose cell walls thicken over time. Thickening of constitutive cell walls likely explains why older genicula have stronger tissues: a mature geniculum may be >50% cell wall. However, the material strength of genicular cell wall is similar to the strength of cell wall from a freshwater green alga, suggesting that it may be the quantity—not the quality—of cell wall material that gives genicular tissue its strength. Apparent differences in tissue strength across algal taxa may be a consequence of tissue construction rather than material composition.     

Immunofluorescent and calcofluor white staining of developing tracheary elements inZinnia elegans L. Suspension cultures

Summary Xylogenesis has been studied in primary suspension cultures ofZinnia elegans L.: The wall patterns produced in culture closely resemble those described for intact tissues (annular, spiral, reticulate, scalariform, pitted). Using fluorescence microscopy and immuno-cytochemical techniques we have followed both the changes in wall deposition and microtubule organization during xylogenesis. Calcofluor white has been used to detect secondary wall deposition before it can be observed using either phase contrast or polarization optics. The development of tracheary elements can be divided into three stages: 1. microtubules grouped into bands without secondary wall deposition evident; 2. groups of microtubules subtending wall material only visible using Calcofluor white; 3. a complex microtubule pattern reflected by well developed wall thickenings detected using Calcofluor, phase contrast and polarization optics.     

Comparative study of viscoelastic arterial wall models in nonlinear one-dimensional finite element simulations of blood flow

It is well known that blood vessels exhibit viscoelastic properties, which are modeled in the literature with different mathematical forms and experimental bases. The wide range of existing viscoelastic wall models may produce significantly different blood flow, pressure, and vessel deformation solutions in cardiovascular simulations. In this paper, we present a novel comparative study of two different viscoelastic wall models in nonlinear one-dimensional (1D) simulations of blood flow. The viscoelastic models are from papers by Holenstein et al. in 1980 (model V1) and Valdez-Jasso et al. in 2009 (model V2). The static elastic or zero-frequency responses of both models are chosen to be identical. The nonlinear 1D blood flow equations incorporating wall viscoelasticity are solved using a space-time finite element method and the implementation is verified with the Method of Manufactured Solutions. Simulation results using models V1, V2 and the common static elastic model are compared in three application examples: (i) wave propagation study in an idealized vessel with reflection-free outflow boundary condition; (ii) carotid artery model with nonperiodic boundary conditions; and (iii) subject-specific abdominal aorta model under rest and simulated lower limb exercise conditions. In the wave propagation study the damping and wave speed were largest for model V2 and lowest for the elastic model. In the carotid and abdominal aorta studies the most significant differences between wall models were observed in the hysteresis (pressure-area) loops, which were larger for V2 than V1, indicating that V2 is a more dissipative model. The cross-sectional area oscillations over the cardiac cycle were smaller for the viscoelastic models compared to the elastic model. In the abdominal aorta study, differences between constitutive models were more pronounced under exercise conditions than at rest. Inlet pressure pulse for model V1 was larger than the pulse for V2 and the elastic model in the exercise case. In this paper, we have successfully implemented and verified two viscoelastic wall models in a nonlinear 1D finite element blood flow solver and analyzed differences between these models in various idealized and physiological simulations, including exercise. The computational model of blood flow presented here can be utilized in further studies of the cardiovascular system incorporating viscoelastic wall properties.     

Including surrounding tissue improves ultrasound-based 3D mechanical characterization of abdominal aortic aneurysms

ObjectivesIn this study the influence of surrounding tissues including the presence of the spine on wall stress analysis and mechanical characterization of abdominal aortic aneurysms using ultrasound imaging has been investigated.MethodsGeometries of 7 AAA patients and 11 healthy volunteers were acquired using 3-D ultrasound and converted to finite element based models. Model complexity of externally unsupported (aorta-only) models was complemented with inclusion of both soft tissue around the aorta and a spine support dorsal to the aorta. Computed 3-D motion of the aortic wall was verified by means of ultrasound speckle tracking. Resulting stress, strain, and estimated shear moduli were analyzed to quantify the effect of adding surrounding material supports.ResultsAn improved agreement was shown between the ultrasound measurements and the finite element tissue and spine models compared to the aorta-only models. Peak and 99-percentile Von Mises stress showed an overall decrease of 23–30%, while estimated shear modulus decreased with 12–20% after addition of the soft tissue. Shear strains in the aortic wall were higher in areas close to the spine compared to the anterior region.ConclusionsImproving model complexity with surrounding tissue and spine showed a homogenization of wall stresses, reduction in homogeneity of shear strain at the posterior side of the AAA, and a decrease in estimated aortic wall shear modulus. Future research will focus on the importance of a patient-specific spine geometry and location.     

An innovative numerical approach to resolve the pulse wave velocity in a healthy thoracic aorta model

Aortic dissection and atherosclerosis are highly fatal diseases. The development of both diseases is closely associated with highly complex haemodynamics. Thus, in predicting the onset of cardiac disease, it is desirable to obtain a detailed understanding of the flowfield characteristics in the human cardiovascular circulatory system. Accordingly, in this study, a numerical model of a normal human thoracic aorta is constructed using the geometry information obtained from a phase-contrast magnetic resonance imaging (PC-MRI) technique. The interaction between the blood flow and the vessel wall dynamics is then investigated using a coupled fluid–structure interaction (FSI) analysis. The simulations focus specifically on the flowfield characteristics and pulse wave velocity (PWV) of the blood flow. Instead of using a conventional PC-MRI method to measure PWV, we present an innovative application of using the FSI approach to numerically resolve PWV for the assessment of wall compliance in a thoracic aorta model. The estimated PWV for a normal thoracic aorta agrees well with the results obtained via PC-MRI measurement. In addition, simulations which consider the FSI effect yield a lower predicted value of the wall shear stress at certain locations in the cardiac cycle than models which assume a rigid vessel wall. Consequently, the model provides a suitable basis for the future development of more sophisticated methods capable of performing the computer-aided analysis of aortic blood flows.     

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

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