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

      research-article
      1 ,
      Theoretical Biology & Medical Modelling
      BioMed Central

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          Abstract

          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.

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          Most cited references17

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          Speed and size of the Sumatra earthquake

          Our seismological results reveal that Indonesia's devastating Sumatra-Andaman earthquake on 26 December 2004 was 2.5 times larger than initial reports suggested--second only to the 1960 Chilean earthquake in recorded magnitude. They indicate that it slowly released its energy by slip along a 1,200-km fault, generating a long rupture that contributed to the subsequent tsunami. Now that the entire rupture zone has slipped, the strain accumulated from the subduction of the Indian plate beneath the Burma microplate has been released, and there is no immediate danger of a similar tsunami being generated on this part of the plate boundary, although large earthquakes on segments to the south still present a threat.
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            Aortic pulse wave velocity is associated with the presence and quantity of coronary artery calcium: a community-based study.

            We investigated the relationship of aortic pulse wave velocity (aPWV), a measure of central arterial stiffness, with the presence and quantity of coronary artery calcium (CAC) in a community-based sample of adults without prior history of heart attack or stroke (n=401, mean age 59.8 years, 53% men). ECG-gated waveforms of the right carotid and right femoral artery were obtained by applanation tonometry, and aPWV was calculated using established methods. CAC was measured noninvasively by electron beam computed tomography, and CAC score was calculated. aPWV was significantly correlated with log(CAC +1; r=0.41; P<0.0001) and pulse pressure (r=0.47; P<0.0001). Multivariable logistic and linear regression models were used to identify independent predictors of the presence and quantity of CAC, respectively. In multivariable logistic regression analyses, aPWV was associated with the presence of CAC (P=0.011) after adjustment for age, male sex, total cholesterol, high-density lipoprotein cholesterol, diabetes, history of smoking, systolic blood pressure, body mass index, and use of hypertension and statin medications. In multivariable linear regression analyses, aPWV was significantly associated with log(CAC +1) after adjustment for the covariates enumerated above (P<0.0001). aPWV remained significantly associated with both the presence and quantity of CAC even after the additional adjustment for diastolic blood pressure. We conclude that aPWV is related to subclinical coronary atherosclerosis independent of conventional risk factors (including indices of blood pressure) and may be a biomarker of cardiovascular risk in asymptomatic individuals.
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              Arterial stiffness independently predicts cardiovascular events in an elderly community -- Longitudinal Investigation for the Longevity and Aging in Hokkaido County (LILAC) study.

              We investigated the predictive value of arterial stiffness to assess cardiovascular risk in elderly community-dwelling people by means of a multivariate Cox model. In 298 people older than 75 years (120 men and 178 women, average age: 79.6 years), brachial-ankle pulse wave velocity (baPWV) was measured between the right arm and ankle in a supine position. The LILAC study started on July 25, 2000, consultation was repeated yearly, and the last follow-up ended on November 30, 2004. During this follow-up span of 1227 days, there were nine cardiovascular deaths, the cause of death being myocardial infarction for two men and three women or stroke for two men and two women. In Cox proportional hazard models, baPWV as well as age, Mini-Mental State Examination (MMSE), Hasegawa Dementia Scale Revised (HDSR) and the low-frequency/high-frequency (LF/HF) ratio showed a statistically significant association with the occurrence of cardiovascular death. A two-point increase in MMSE and HDSR score significantly protected against cardiovascular death, the relative risk (RR) being 0.776 (P = 0.0369) and 0.753 (P = 0.0029), respectively. The LF/HF ratio also was significant (P = 0.025), but the other indices of HRV were not. After adjustment for age and HDSR, a 200 cm/s increase in baPWV was associated with a 30.2% increase in risk (RR = 1.302, 95% CI: 1.110-1.525), and a 500 cm/s increase in baPWV with a 93.3% increase in risk (RR = 1.933, 95% CI: 1.300-2.874, P = 0.0011), whereas the LF/HF ratio was no longer associated with a statistically significant increase in cardiovascular mortality. In elderly community-dwelling people, arterial stiffness measured by means of baPWV predicted the occurrence of cardiovascular death beyond the prediction provided by age, gender, blood pressure and cognitive functions. baPWV should be added to the cardiovascular assessment in various clinical settings, including field medical surveys and preventive screening. The early detection of risk by chronomics allows the timely institution of prophylactic measures, thereby shifting the focus from rehabilitation to prehabilitation medicine, as a public service to several Japanese towns.
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                Author and article information

                Journal
                Theor Biol Med Model
                Theoretical Biology & Medical Modelling
                BioMed Central
                1742-4682
                2008
                29 July 2008
                : 5
                : 15
                Affiliations
                [1 ]Office of Environmental Health Hazard Assessment, California Environmental Protection Agency, P. O. Box 4010, Sacramento, CA 95812, USA
                Article
                1742-4682-5-15
                10.1186/1742-4682-5-15
                2527553
                18664288
                e5ed67f2-f36f-4112-95ab-2c315ea63260
                Copyright © 2008 Painter; licensee BioMed Central Ltd.

                This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 11 April 2008
                : 29 July 2008
                Categories
                Research

                Quantitative & Systems biology
                Quantitative & Systems biology

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