Improved solution for solitary waves in arteries

 Nonlinear waves are investigated numerically by a direct analysis of the field equations, thereby establishing the magnitude of the errors inherent in the commonly used reductive perturbation technique. The method is also applied beyond the long-wave approximation and a comparative assessment of the results obtained is presented. Received: 11 March 1998 / Revised version: 19 May 1998     

Effects of luminal shear stress on cerebral arteries and arterioles

The effect of luminal shear stress was studied in cerebral arteries and arterioles. Middle cerebral arteries (MCA) and penetrating arterioles (PA) were isolated from male Long-Evans rats, mounted in a tissue bath, and pressurized. After the development of spontaneous tone, inside diameters were 186 +/- 5 microm (n = 28) for MCA and 65 +/- 3 microm (n = 37) for PA. MCA and PA constricted approximately 20% with increasing flow. Flow-induced constriction persisted in MCA and PA after removal of the endothelium. After removal of the endothelium, the luminal application of a polypeptide containing the Arg-Gly-Asp amino acid sequence (inhibitor of integrin attachment) abolished the flow-induced constriction. Similarly, an antibody specific for the beta(3)-chain of the integrin complex significantly inhibited the flow-induced constriction. The shear stress-induced constriction was accompanied by an increase in vascular smooth muscle Ca(2+). For example, a shear stress of 20 dyn/cm(2) constricted MCA 8% (n = 5) and increased Ca(2+) from 209 +/- 17 to 262 +/- 29 nM (n = 5). We conclude that isolated cerebral arteries and arterioles from the rat constrict to increased shear stress. Because the endothelium is not necessary for the response, the shear forces must be transmitted across the endothelium, presumably by the cytoskeletal matrix, to elicit constriction. Integrins containing the beta(3)-chain are involved with the shear stress-induced constrictions.     

Mechanical simulation of shear stress on the walls of peripheral arteries

In the last few years many attempts were made to line artificial vascular grafts with in vitro grown endothelial cell layers and thereby to minimize the risk of thromboembolism. However, adherence and resistance against shear stress forces were not tested under physiological pulsatile shear stress forces. In this paper, a mock-circulation apparatus is described, which simulates various forms of pulsatile shear stress, and which at the same time meets the requirements of cell cultivation. It can be sterilized and needs less than 700 ml of culture medium for priming. The generated flow profile can be adapted to a wide range of shear stress and also to different viscosities of used media. To take account of the different viscosities of culture medium and blood, a computerized calculation of the shear stress pattern was performed. Using the results of this computer model, the flow pattern was modified to obtain normal physiological shear stress when using culture medium. Results of pulse generation and simulation for the superficial femoral artery are presented.     

Strain distribution over plaques in human coronary arteries relates to shear stress

Once plaques intrude into the lumen, the shear stress they are exposed to alters with hitherto unknown consequences for plaque composition. We investigated the relationship between shear stress and strain, a marker for plaque composition, in human coronary arteries. We imaged 31 plaques in coronary arteries with angiography and intravascular ultrasound. Computational fluid dynamics was used to obtain shear stress. Palpography was applied to measure strain. Each plaque was divided into four regions: upstream, throat, shoulder, and downstream. Average shear stress and strain were determined in each region. Shear stress in the upstream, shoulder, throat, and downstream region was 2.55+/-0.89, 2.07+/-0.98, 2.32+/-1.11, and 0.67+/-0.35 Pa, respectively. Shear stress in the downstream region was significantly lower. Strain in the downstream region was also significantly lower than the values in the other regions (0.23+/-0.08% vs. 0.48+/-0.15%, 0.43+/-0.17%, and 0.47+/-0.12%, for the upstream, shoulder, and throat regions, respectively). Pooling all regions, dividing shear stress per plaque into tertiles, and computing average strain showed a positive correlation; for low, medium, and high shear stress, strain was 0.23+/-0.10%, 0.40+/-0.15%, and 0.60+/-0.18%, respectively. Low strain colocalizes with low shear stress downstream of plaques. Higher strain can be found in all other plaque regions, with the highest strain found in regions exposed to the highest shear stresses. This indicates that high shear stress might destabilize plaques, which could lead to plaque rupture.     

Effects of twist on pulse waves in arteries

The artery is treated as a thick-walled cylindrical shell. Using the large deformation theory, an analytical expression for the pulse wave speed is obtained and the effect of twist on the wave speed is discussed. Numerical results indicate that although phase velocity increases with pressure, it decreases with increasing twist angle.     

Influence of non-Newtonian properties of blood on the wall shear stress in human atherosclerotic right coronary arteries

The objective of this work is to investigate the effect of non-Newtonian properties of blood on the wall shear stress (WSS) in atherosclerotic coronary arteries using both Newtonian and non-Newtonian models. Numerical simulations were performed to examine how the spatial and temporal WSS distributions are influenced by the stenosis size, blood viscosity, and flow rate. The computational results demonstrated that blood viscosity properties had considerable effect on the magnitude of the WSS, especially where disturbed flow was observed. The WSS distribution is highly non-uniform both temporally and spatially, especially in the stenotic region. The maximum WSS occurred at the proximal side of the stenosis, near the outer wall in the curved artery with no stenosis. The lumen area near the inner wall distal to the stenosis region experienced a lower WSS during the entire cardiac cycle. Among the factors of stenosis size, blood viscosity, and flow rate, the size of the stenosis has the most significant effect on the spatial and temporal WSS distributions qualitatively and quantitatively.     

The role of shear stress in atherosclerosis

Atherosclerotic lesions preferentially localize near side branches or curved vessels. During the last few decades, research has been shown that low or low and oscillating shear stress is associated with plaque location. Despite ample evidence, the precise mechanism is unknown. This is mainly because of a lack of appropriate animal models. We describe two novel methods to study the hypothesis that shear stress acts through endothelial gene expression or shear stress acts through localizing of inflammation. Both literature evidence and own findings support a role for both mechanisms in atherosclerosis.     

Maximal wall shear stress in arterial stenoses: application to the internal carotid arteries

Maximal wall shear stress (MWSS) in the convergent part of a stenosis is calculated by the interactive boundary-layer theory. A dimensional analysis of the problem shows that MWSS depends only on a few measurable parameters. A simple relationship between MWSS and these parameters is obtained, validated, and used to calculate the magnitude of MWSS in a carotid stenosis, as a function of the patency of the circle of Willis and the stenotic pattern. This demonstrates the huge effect of collateral pathways. Elevated MWSS are observed even in moderate stenoses, provided they are associated with a contralateral occlusion, a large anterior, and narrow posterior communicating arteries, suggesting a potential risk of embolus release in this configuration.     

The nature of phonons and solitary waves in alpha-helical proteins.

A parametric study of the Davydov model of energy transduction in alpha-helical proteins is described. Previous investigations have shown that the Davydov model predicts that nonlinear interactions between phonons and amide-I excitations can stabilize the latter and produce a long-lived combined excitation (the so-called Davydov soliton), which propagates along the helix. The dynamics of this solitary wave are approximately those of solitons described using the nonlinear Schr?dinger equation. The present study extends these previous investigations by analyzing the effect of helix length and nonlinear coupling efficiency on the phonon spectrum in short and medium length alpha-helical segments. The phonon energy accompanying amide-I excitation shows periodic variation in time with fluctuations that follow three different time scales. The phonon spectrum is highly dependent upon chain length but a majority of the energy remains localized in normal mode vibrations even in the long chain alpha-helices. Variation of the phonon-exciton coupling coefficient changes the amplitudes but not the frequencies of the phonon spectrum. The computed spectra contain frequencies ranging from 200 GHz to 6 THz, and as the chain length is increased, the long period oscillations increase in amplitude. The most important prediction of this study, however, is that the dynamics predicted by the numerical calculations have more in common with dynamics described by using the Frohlich polaron model than by using the Davydov soliton. Accordingly, the relevance of the Davydov soliton model was applied to energy transduction in alpha-helical proteins is questionable.(ABSTRACT TRUNCATED AT 250 WORDS)     

The effect of fluid shear stress on fibroblasts and stem cells on plane and groove topographies

ABSTRACT

In this study, we aimed to study the effect of fluid shear stress on fibroblasts and BMSCs on plane and groove topographies. The results showed that 0.6-Hz stress had the greatest influence on the alignment, polarity, migration and adhesion of fibroblasts on plane by increasing the expression of reoriented actin and vinculin; whereas 1.0-Hz stress promoted differentiation of fibroblasts into myofibroblasts by increasing Col-I and α-SMA expression. Interestingly, under the given frequency stress, the groove structure strengthened the above characteristics of fibroblasts beyond adhesion, and promoted differentiation of BMSCs into myofibroblasts. The above results indicate that 0.6 Hz may improve the implant-tissue sealing, while 1.0-Hz stress probably causes the disordered fiber deposition around implants.     

An assessment of intra-patient variability on observed relationships between wall shear stress and plaque progression in coronary arteries

Background

Wall shear stress (WSS) has been associated with sites of plaque localization and with changes in plaque composition in human coronary arteries. Different values have been suggested for categorizing WSS as low, physiologic or high; however, uncertainties in flow rates, both across subjects and within a given individual, can affect the classification of WSS and thus influence the observed relationships between local hemodynamics and plaque changes over time. This study examines the effects of uncertainties in flow rate boundary conditions upon WSS values and investigates the influence of this variability on the observed associations of WSS with changes in VH-IVUS derived plaque components.

Methods

Three patients with coronary artery disease underwent baseline and 12 month follow-up angiography and virtual histology-intravascular ultrasound (VH-IVUS) measurements. Coronary artery models were reconstructed from the data and models with and without side-branches were created. Patient-specific Doppler ultrasound (DUS) data were employed as inflow boundary conditions and computational fluid dynamics was used to calculate the WSS in each model. Further, the influence of representative coronary artery flow waveforms upon WSS values was investigated and the concept of treating WSS using relative, rather than actual, values was explored.

Results

Models that included side-branch outflows and subject-specific DUS velocities were considered to be the reference cases. Hemodynamic differences were caused by the exclusion of side-branches and by imposing alternative velocity waveforms. One patient with fewer side-branches and a scaled generic waveform had little deviation from the reference case, while another patient with several side-branches excluded showed much larger departures from the reference situation. Differences between models and the respective reference cases were reduced when data were analyzed using relative, rather than actual, WSS.

Conclusions

When considering individual subjects, large variations in patient-specific flow rates and exclusion of multiple side-branches in computational models can cause significant differences in observed associations between plaque evolution and ranges of computed WSS. These differences may contribute to the large variability typically found among subjects in pooled populations. Relative WSS may be more useful than actual WSS as a correlative variable when there is a large degree of uncertainty in flow rate data.

     

Characterization of the in vivo wall shear stress environment of human fetus umbilical arteries and veins

The endothelial cells of the umbilical vessels are frequently used in mechanobiology experiments. They are known to respond to wall shear stress (WSS) of blood flow, which influences vascular growth and remodeling. The in vivo environment of umbilical vascular WSS, however, is not well characterized. In this study, we performed detailed characterization of the umbilical vascular WSS environments using clinical ultrasound scans combined with computational simulations. Doppler ultrasound scans of 28 normal human fetuses from 32nd to 33rd gestational weeks were investigated. Vascular cross-sectional areas were quantified through 3D reconstruction of the vascular geometry from 3D B-mode ultrasound images, and flow velocities were quantified through pulse wave Doppler. WSS in umbilical vein was computed with Poiseuille’s equation, whereas WSS in umbilical artery was obtained via computational fluid dynamics simulations of the helical arterial geometry. Results showed that blood flow velocity for umbilical artery and vein did not correlate with vascular sizes, suggesting that velocity had a very weak trend with or remained constant over vascular sizes. Average WSS for umbilical arteries and vein was 2.81 and 0.52 Pa, respectively. Umbilical vein WSS showed a significant negative correlation with the vessel diameter, but umbilical artery did not show any correlation. We hypothesize that this may be due to differential regulation of vascular sizes based on WSS sensing. Due to the helical geometry of umbilical arteries, bending of the umbilical cord did not significantly alter the vascular resistance or WSS, unlike that in the umbilical veins. We hypothesize that the helical shape of umbilical arteries may be an adaptation feature to render a higher constancy of WSS and flow in the arteries despite umbilical cord bending.     

Propagation of shear waves in muscle tissue

A mathematical model of the propagation of acoustic shear waves in muscle tissue is considered. Muscle is modeled as an incompressible transversely isotropic viscoelastic continuum with quasi-one-dimensional active tension. There are two types of shear waves in an infinite medium. Waves of the second type (transverse) propagate without decay even when myofibril viscosity is taken into account. A problem of standing transverse waves in a rectangular layer was investigated numerically. The values of the problem parameters are found for which one can easily estimate the active tension (or muscle tone) from the characteristics of standing waves. This value is informative for diagnostics of the muscle state.     

Alterations in wall shear stress predict sites of neointimal hyperplasia after stent implantation in rabbit iliac arteries

Restenosis resulting from neointimal hyperplasia (NH) limits the effectiveness of intravascular stents. Rates of restenosis vary with stent geometry, but whether stents affect spatial and temporal distributions of wall shear stress (WSS) in vivo is unknown. We tested the hypothesis that alterations in spatial WSS after stent implantation predict sites of NH in rabbit iliac arteries. Antegrade iliac artery stent implantation was performed under angiography, and blood flow was measured before casting 14 or 21 days after implantation. Iliac artery blood flow domains were obtained from three-dimensional microfocal X-ray computed tomography imaging and reconstruction of the arterial casts. Indexes of WSS were determined using three-dimensional computational fluid dynamics. Vascular histology was unchanged proximal and distal to the stent. Time-dependent NH was localized within the stented region and was greatest in regions exposed to low WSS and acute elevations in spatial WSS gradients. The lowest values of WSS spatially localized to the stented area of a theoretical artery progressively increased after 14 and 21 days as NH occurred within these regions. This NH abolished spatial disparity in distributions of WSS. The results suggest that stents may introduce spatial alterations in WSS that modulate NH in vivo.     

Correlation between quantitative analysis of wall shear stress and intima-media thickness in atherosclerosis development in carotid arteries

Background

This paper presents quantitative analysis of blood flow shear stress by measuring the carotid arterial wall shear stress (WSS) and the intima-media thickness (IMT) of experimental rabbits fed with high-fat feedstuff on a weekly basis in order to cause atherosclerosis.

Methods

This study is based on establishing an atherosclerosis model of high-fat rabbits, and measuring the rabbits’ common carotid arterial WSS of the experimental group and control group on a weekly basis. Detailed analysis was performed by using WSS quantification.

Results

We have demonstrated small significant difference of rabbit carotid artery WSS between the experimental group and the control group (P<0.01) from the 1st week onwards, while the IMT of experimental group had larger differences from 5th week compared with the control group (P<0.05). Next, we have shown that with increasing blood lipids, the rabbit carotid artery shear stress decreases and the rabbit carotid artery IMT goes up. The decrease of shear stress appears before the start of IMT growth. Furthermore, our receiver operator characteristic (ROC) curve analysis showed that when the mean value of shear stress is 1.198 dyne/cm², the rabbit common carotid atherosclerosis fatty streaks sensitivity is 89.8%, and the specificity is 81.3%. The area under the ROC curve is 0.9283.

Conclusions

All these data goes to show that WSS decreasing to 1.198 dyne/cm² can be used as an indicator that rabbit common carotid artery comes into the period of fibrous plaques. In conclusion, our study is able to find and confirm that the decrease of the arterial WSS can predict the occurrence of atherosclerosis earlier, and offer help for positive clinical intervention.

     

Geometry guided data averaging enables the interpretation of shear stress related plaque development in human coronary arteries

The average low shear stress (SS) is known to determine predilection sites of atherosclerotic plaques. However, as plaques encroach into the lumen and thereby increase SS, interpretation of patient-specific data obtained at one moment in time regarding the influence of SS in the generation of atherosclerosis is not straightforward. This study aims to compare two methods of data analysis for the aid of data interpretation: (a) point-wise analysis of the raw data, (b) global analysis: to assess the history related natural SS distribution in coronary arteries by averaging the data in the axial vessel direction. Normal to mildly diseased human coronary arteries were investigated applying a combination of 3-D reconstruction technique and computational fluid dynamics (CFD). Point-wise analysis relating local wall thickness to local SS showed in only 4% of the cases an inverse relationship. In contrast, averaging the data in the axial vessel direction, showed in 38% a significant inverse relation between wall thickness and SS, resulting in an average negative slope of -0.70+/-0.46 mm/Pa. These data suggest that using a geometry guided way of data averaging may reveal history related effects of SS, which in part explains localization of atherosclerotic plaques.