The velocity of the arterial pulse wave: a viscous-fluid shock wave in an elastic tube

Background

The arterial pulse is a viscous-fluid shock wave that is initiated by blood ejected from the heart. This wave travels away from the heart at a speed termed the pulse wave velocity (PWV). The PWV increases during the course of a number of diseases, and this increase is often attributed to arterial stiffness. As the pulse wave approaches a point in an artery, the pressure rises as does the pressure gradient. This pressure gradient increases the rate of blood flow ahead of the wave. The rate of blood flow ahead of the wave decreases with distance because the pressure gradient also decreases with distance ahead of the wave. Consequently, the amount of blood per unit length in a segment of an artery increases ahead of the wave, and this increase stretches the wall of the artery. As a result, the tension in the wall increases, and this results in an increase in the pressure of blood in the artery.

Methods

An expression for the PWV is derived from an equation describing the flow-pressure coupling (FPC) for a pulse wave in an incompressible, viscous fluid in an elastic tube. The initial increase in force of the fluid in the tube is described by an increasing exponential function of time. The relationship between force gradient and fluid flow is approximated by an expression known to hold for a rigid tube.

Results

For large arteries, the PWV derived by this method agrees with the Korteweg-Moens equation for the PWV in a non-viscous fluid. For small arteries, the PWV is approximately proportional to the Korteweg-Moens velocity divided by the radius of the artery. The PWV in small arteries is also predicted to increase when the specific rate of increase in pressure as a function of time decreases. This rate decreases with increasing myocardial ischemia, suggesting an explanation for the observation that an increase in the PWV is a predictor of future myocardial infarction. The derivation of the equation for the PWV that has been used for more than fifty years is analyzed and shown to yield predictions that do not appear to be correct.

Conclusion

Contrary to the theory used for more than fifty years to predict the PWV, it speeds up as arteries become smaller and smaller. Furthermore, an increase in the PWV in some cases may be due to decreasing force of myocardial contraction rather than arterial stiffness.     

Angiotensin II injures the arterial wall causing increased aortic stiffening in apolipoprotein E-deficient mice

Cardiovascular diseases, such as atherosclerosis and hypertension, are associated with arterial stiffening. Previous studies showed that ANG II exacerbated atherosclerosis and induced hypertension and aneurysm formation in apolipoprotein E-deficient (apoE-KO) mice. The aim of the present study was to examine the effects of chronic treatment of ANG II on the arterial elastic properties in apoE-KO mice. We hypothesized that ANG II will injure the arterial wall resulting in increased arterial stiffening. Male apoE-KO mice were infused with either ANG II (1.44 mg. kg(-1). day(-1)) or vehicle (PBS) for 30 days. ANG II treatment accelerated atherosclerosis in the carotid artery by sixfold (P < 0.001) and increased blood pressure by 30% (P < 0.05). Additionally, our data demonstrated that ANG II increased arterial stiffening using both in vivo and in vitro methods. ANG II significantly increased pulse wave velocity by 36% (P < 0.01) and decreased arterial elasticity as demonstrated by a more than 900% increase in maximal stiffening (high strain Young's modulus) compared with vehicle (P < 0.05). These functional changes were correlated with morphological and biochemical changes as demonstrated by an increase in collagen content (60%), a decrease in elastin content (74%), and breaks in the internal elastic lamina in the aortic wall. In addition, endothelium-independent vasorelaxation to sodium nitroprusside was impaired in the aortic rings of ANG II-treated mice compared with vehicle. Thus, the present data indicate that ANG II injures the artery wall in multiple ways and arterial stiffening may be a common outcome of ANG II-induced arterial damage.     

Pulse wave propagation in a model human arterial network: assessment of 1-D numerical simulations against in vitro measurements

A numerical model based on the nonlinear, one-dimensional (1-D) equations of pressure and flow wave propagation in conduit arteries is tested against a well-defined experimental 1:1 replica of the human arterial tree. The tree consists of 37 silicone branches representing the largest central systemic arteries in the human, including the aorta, carotid arteries and arteries that perfuse the upper and lower limbs and the main abdominal organs. The set-up is mounted horizontally and connected to a pulsatile pump delivering a periodic output similar to the aortic flow. Terminal branches end in simple resistance models, consisting of stiff capillary tubes leading to an overflow reservoir that reflects a constant venous pressure. The parameters required by the numerical algorithm are directly measured in the in vitro set-up and no data fitting is involved. Comparison of experimental and numerical pressure and flow waveforms shows the ability of the 1-D time-domain formulation to capture the main features of pulse wave propagation measured throughout the system test. As a consequence of the simple resistive boundary conditions used to reduce the uncertainty of the parameters involved in the simulation, the experimental set-up generates waveforms at terminal branches with additional non-physiological oscillations. The frequencies of these oscillations are well captured by the 1-D model, even though amplitudes are overestimated. Adding energy losses in bifurcations and including fluid inertia and compliance to the purely resistive terminal models does not reduce the underdamped effect, suggesting that wall visco-elasticity might play an important role in the experimental results. Nevertheless, average relative root-mean-square errors between simulations and experimental waveforms are smaller than 4% for pressure and 19% for the flow at all 70 locations studied.     

Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements

The accuracy of the nonlinear one-dimensional (1-D) equations of pressure and flow wave propagation in Voigt-type visco-elastic arteries was tested against measurements in a well-defined experimental 1:1 replica of the 37 largest conduit arteries in the human systemic circulation. The parameters required by the numerical algorithm were directly measured in the in vitro setup and no data fitting was involved. The inclusion of wall visco-elasticity in the numerical model reduced the underdamped high-frequency oscillations obtained using a purely elastic tube law, especially in peripheral vessels, which was previously reported in this paper [Matthys et al., 2007. Pulse wave propagation in a model human arterial network: Assessment of 1-D numerical simulations against in vitro measurements. J. Biomech. 40, 3476-3486]. In comparison to the purely elastic model, visco-elasticity significantly reduced the average relative root-mean-square errors between numerical and experimental waveforms over the 70 locations measured in the in vitro model: from 3.0% to 2.5% (p<0.012) for pressure and from 15.7% to 10.8% (p<0.002) for the flow rate. In the frequency domain, average relative errors between numerical and experimental amplitudes from the 5th to the 20th harmonic decreased from 0.7% to 0.5% (p<0.107) for pressure and from 7.0% to 3.3% (p<10(-6)) for the flow rate. These results provide additional support for the use of 1-D reduced modelling to accurately simulate clinically relevant problems at a reasonable computational cost.     

Assessing non-uniform stiffening of the achilles tendon noninvasively using surface wave

Currently, noninvasive cost-effective techniques capable of quantifying non-uniform degradation of tendon’s mechanical and structural properties associated with localized tendon injuries are not readily available. This study demonstrates the applicability of a simple surface-wave elastography (SURF-E) method for assessing the stiffness of the Achilles Tendon by measuring the propagation velocity of surface waves along the tendon in a much broader range of values than currently available Ultrasound-based or MRI-based elastography methods do. Results from this study confirm the non-uniform stiffening of the AT during passive ankle dorsiflexions.     

Arias-Stella atypia in a paratubal cyst: a rare phenomenon with potential diagnostic pitfalls

BACKGROUND: Arias-Stella reaction is commonly encountered in the endometrium during the gestational period and puerperium. Similar changes in the tubal epithelium are exceedingly rare. The cytologic findings of this phenomenon have never been described before. CASE: Cytologic findings of Arias-Stella changes in the lining cells of a left paratubal cyst in a 41-year-old woman were examined. The smears showed occasional small clusters or isolated tubal epithelial cells consisting of a mixture of ciliated and secretory cells. Some of the ciliated cells showed a marked increase in nuclear and cytoplasmic volume and possessed coarse chromatin, prominent, angulated nucleoli, dense, amphophilic cytoplasm; and a discrete cell membrane. The nuclear membrane was still thin and regular, and these cells were mitotically inactive. The preservation of apical cilia in some of them ensured their benign nature. In some areas, clusters of secretory cells with an increase in both nuclear and cytoplasmic volume and ample, clear cytoplasm were also found. There were small, monolayered sheets of regular and benign-looking epithelial cells with a honeycomb arrangement, suggesting that the Arias-Stella atypia was focal. CONCLUSION: In view of the presence of scattered giant cells with coarse chromatin and angulated macronucleoli, a false positive cytologic diagnosis of malignancy can be made if one does not pay attention to the coexistence of apical cilia and other subtle changes, including the usual nuclear/cytoplasmic ratio, thin and regular nuclear membrane and absence of mitotic activity.     

Rare lymphoid malignancies of the breast: a report of two cases illustrating potential diagnostic pitfalls

Breast involvement by lymphoma is uncommon and poses challenges in diagnosis. Lymphomas may clinically, radiologically, and morphologically mimic both benign and neoplastic conditions. We describe two cases of lymphoid malignancies predominantly involving the breast, both presenting diagnostic dilemmas. The first case, ALK-negative anaplastic large-cell lymphoma involving a seroma associated with a breast implant, is an emerging clinicopathologic entity. Anaplastic large-cell lymphoma has been identified in association with breast implants and seroma formation relatively recently. The second case, hairy cell leukemia involving the breast and ipsilateral axillary sentinel lymph node, is, to our knowledge, the first reported case of hairy cell leukemia involving the breast at the time of diagnosis. While a localized bone lesion was present at time of diagnosis, bone marrow involvement was relatively mild in comparison to that seen in the breast and lymph node. In the first case, lymphoma occurred in a clinical setting where malignancy was unsuspected, highlighting the importance of careful morphologic evaluation of paucicellular samples, as well as awareness of rare clinicopathologic entities, in avoiding a misdiagnosis of a benign inflammatory infiltrate. In the second case, the lymphoid neoplasm exhibited classic morphologic and immunophenotypic features, but presented at an unusual site of involvement. Knowledge of the patient''s concurrent diagnosis of hairy cell leukemia involving the bone marrow and bone helped avoid a misdiagnosis of carcinoma rather than lymphoma.     

Use of simultaneous pressure and velocity measurements to estimate arterial wave speed at a single site in humans

It has not been possible to measure wave speed in the human coronary artery, because the vessel is too short for the conventional two-point measurement technique used in the aorta. We present a new method derived from wave intensity analysis, which allows derivation of wave speed at a single point. We apply this method in the aorta and then use it to derive wave speed in the human coronary artery for the first time. We measured simultaneous pressure and Doppler velocity with intracoronary wires at the left main stem, left anterior descending and circumflex arteries, and aorta in 14 subjects after a normal coronary arteriogram. Then, in 10 subjects, serial measurements were made along the aorta before and after intracoronary isosorbide dinitrate. Wave speed was derived by two methods in the aorta: 1) the two-site distance/time method (foot-to-foot delay of pressure waveforms) and 2) a new single-point method using simultaneous pressure and velocity measurements. Coronary wave speed was derived by the single-point method. Wave speed derived by the two methods correlated well (r = 0.72, P < 0.05). Coronary wave speed correlated with aortic wave speed (r = 0.72, P = 0.002). After nitrate administration, coronary wave speed fell by 43%: from 16.4 m/s (95% confidence interval 12.6-20.1) to 9.3 m/s (95% confidence interval 6.5-12.0, P < 0.001). This single-point method allows determination of wave speed in the human coronary artery. Aortic wave speed is correlated to coronary wave speed. Finally, this technique detects the prompt fall in coronary artery wave speed with isosorbide dinitrate.     

Mitochondrial-ER tethering: the inheritance of a functional unit

A new study uncovers a novel role for the endoplasmic reticulum in tethering mitochondria specifically at the tip of the growing bud in Saccharomyces cerevisiae. Mitochondrial anchoring to the bud tip requires the tethering factor Mmr1, and the link to the ER is coupled to the cell cycle through a phosphorylation-dependent mechanism.     

Parenchymal tethering, airway wall stiffness, and the dynamics of bronchoconstriction.

We do not yet have a good quantitative understanding of how the force-velocity properties of airway smooth muscle interact with the opposing loads of parenchymal tethering and airway wall stiffness to produce the dynamics of bronchoconstriction. We therefore developed a two-dimensional computational model of a dynamically narrowing airway embedded in uniformly elastic lung parenchyma and compared the predictions of the model to published measurements of airway resistance made in rats and rabbits during the development of bronchoconstriction following a bolus injection of methacholine. The model accurately reproduced the experimental time-courses of airway resistance as a function of both lung inflation pressure and tidal volume. The model also showed that the stiffness of the airway wall is similar in rats and rabbits, and significantly greater than that of the lung parenchyma. Our results indicate that the main features of the dynamical nature of bronchoconstriction in vivo can be understood in terms of the classic Hill force-velocity relationship operating against elastic loads provided by the surrounding lung parenchyma and an airway wall that is stiffer than the parenchyma.     

The polymer-supported phospholipid bilayer: tethering as a new approach to substrate-membrane stabilization

We present a new molecular engineering approach in which a polymer-supported phospholipid bilayer is vertically stabilized by controlled covalent tethering at both the polymer-substrate and polymer-bilayer interfaces. This approach is based on lipopolymer molecules, which not only form a polymer cushion between the phospholipid bilayer and a solid glass substrate but also act as covalent connections (tethers) between the bilayer and cushion. Our approach involves Langmuir-Blodgett transfer of a phospholipid-lipopolymer monolayer followed by Schaefer transfer of a pure phospholipid monolayer and is capable of varying the tethering density between the polymer layer and the phospholipid bilayer in a very controlled manner. Further stabilization is achieved if the glass substrate is surface-functionalized with a benzophenone silane. In this case, a photocross-linking reaction between the polymer and benzophenone group allows for the covalent attachment of the polymer cushion to the glass substrate. This approach is similar to that recently reported by Wagner and Tamm in which double tethering is achieved via lipopolymer silanes (Wagner, M. L.; Tamm, L. K. Biophys. J. 2000, 79, 1400). To obtain a deeper understanding of how the covalent tethering affects the lateral mobility of the bilayer, we performed fluorescence recovery after photobleaching (FRAP) experiments on polymer-tethered bilayers at different tethering densities (lipopolymer/phospholipid molar ratios). The FRAP data clearly indicate that the hydrophobic lipopolymer moieties act as rather immobile obstacles within the phospholipid bilayer, thereby leading to hindered diffusion of phospholipids. Whereas the high lateral diffusion coefficient of D = 17.7 mum(2)/s measured at low tethering density (5 mol % lipopolymer) indicates rather unrestricted motion within the bilayer, corresponding values at moderate (10 mol % lipopolymer) and high (30 mol % lipopolymer) tethering densities of D = 9.7 mum(2)/s and D = 1.1 mum(2)/s, respectively, show significant hindered diffusion. These results are contrary to the recent findings on similar membrane systems reported by Wagner and Tamm in which no significant change in phospholipid diffusion was found between 0 and 10 mol % lipopolymer. Our experimental report leads to a deeper understanding of the complex problem of interlayer coupling and offers a path toward a compromise between stability of the whole system and lateral mobility within the bilayer. Furthermore, the FRAP measurements show that polymer-tethered membranes are very interesting model systems for studying problems of restricted diffusion within two-dimensional fluids.     

Frequency response of the arterial wall

The high frequency response of human common iliac arterial segments in vitro was investigated. It was found that at those high frequencies the response resembles that of a second order underdamped system. However, to simulate the arterial response throughout the frequency range, a higher order model is required. A fifth order system appears to describe the observed behaviour in a satisfactory way between 0.02 and 200 Hz.