Effect of viscosity on the wave propagation: Experimental determination of compression and expansion pulse wave velocity in fluid-fill elastic tube

Wave propagation through a viscous fluid-filled elastic tube under initial pressure: theoretical and biophysical model

The velocity of propagation of pulse waves through the arteries is one of the indicators of the health of the cardiovascular system. By measuring the pulse wave velocity, cardiologists estimate the elasticity of the blood vessel walls and the changes that occur with aging. When the Moens-Korteweg equation is used in analysis, it leads to an erroneous assessment. This paper presents the solution of Navier-Stokes equations for propagation of pulse waves through an elastic tube filled with viscous fluid under initial pressure. The equation for pulse wave velocity depending on viscosity, density and initial fluid pressure, density and elasticity of the wall and geometry of the tube is derived. The results of the equation were compared with experimental results measured using a biophysical model of the cardiovascular system.

Acute Effects of Short-Term Warm Water Immersion on Arterial Stiffness and Central Hemodynamics

Warm water immersion (WWI) has a potentially favorable effect on vascular health. However, the effects of short-term WWI on vascular function and central hemodynamics remain unclear. The present study aimed to determine the acute effects of short-term WWI on arterial stiffness and central hemodynamics in healthy men. Ten healthy men (27–57 years, 44 ± 12 years of mean age) underwent 5-min WWI (40–41°C) at the heart level. Systemic hemodynamics and tympanic temperature were monitored during WWI. Furthermore, pulse wave velocity (PWV) and aortic hemodynamics were measured before and 10 min after WWI. Cardiac output (CO) (via the Modelflow method) increased (P = 0.037), whereas tympanic temperature did not change (P = 0.879) during WWI. After 5-min WWI, heart rate (HR) and brachial diastolic blood pressure (BP) were significantly decreased. Aortic and leg PWV were decreased by 7.5 and 3.1%, respectively (P = 0.006 and P = 0.040). Femoral arterial blood flow was increased by 45.9% (P = 0.002), and leg vascular resistance was decreased by 29.1% (P < 0.001). Regarding central hemodynamic variables (estimated by general transfer function), aortic BP and augmentation index (AIx) did not change significantly, but the subendocardial viability ratio (SEVR), an index of coronary perfusion, was increased (P = 0.049). Our results indicate that a short-term WWI acutely improves aortic and peripheral arterial stiffness and coronary perfusion. Further studies to determine the interaction between the residual effect of a single bout of short-term WWI and chronic change (e.g., adaptation) in arterial stiffness and central hemodynamics are needed.

Biophysical modeling of wave propagation phenomena: experimental determination of pulse wave velocity in viscous fluid-filled elastic tubes in a gravitation field

Biophysical understanding of arterial hemodynamics plays an important role in proper medical diagnosis and investigation of cardiovascular disease pathogens. One of the major cardiovascular parameters is pulse wave velocity (PWV), which depends on the mechanical properties of the arterial wall. The PWV contains information on the condition of the cardiovascular system as well as its physiological age. In humans and most animals, blood flow through the blood vessels is affected by several internal and external forces. The most influencing external force on blood flow is gravity. In the upright position of the body, blood moves from heart to head, opposite to gravity, and from the heart to the legs, in direction of the gravitational force. To investigate how gravity affects PWV, we have developed a biophysical model of cardiovascular system that simulates blood flow in the upright position of the body. The paper presents the results of measurement of PWV in an elastic tube filled with fluids of different viscosities in the gravitational field.

In vivo repeatability of the pulse wave inverse problem in human carotid arteries

Accurate arterial stiffness measurement would improve diagnosis and monitoring for many diseases. Atherosclerotic plaques and aneurysms are expected to involve focal changes in vessel wall properties; therefore, a method to image the stiffness variation would be a valuable clinical tool. The pulse wave inverse problem (PWIP) fits unknown parameters from a computational model of arterial pulse wave propagation to ultrasound-based measurements of vessel wall displacements by minimizing the difference between the model and measured displacements. The PWIP has been validated in phantoms, and this study presents the first in vivo demonstration. The common carotid arteries of five healthy volunteers were imaged five times in a single session with repositioning of the probe and subject between each scan. The 1D finite difference computational model used in the PWIP spanned from the start of the transducer to the carotid bifurcation, where a resistance outlet boundary condition was applied to approximately model the downstream reflection of the pulse wave. Unknown parameters that were estimated by the PWIP included a 10-segment linear piecewise compliance distribution and 16 discrete cosine transformation coefficients for each of the inlet boundary conditions. Input data was selected to include pulse waves resulting from the primary pulse and dicrotic notch. The recovered compliance maps indicate that the compliance increases close to the bifurcation, and the variability of the average pulse wave velocity estimated through the PWIP is on the order of 11%, which is similar to that of the conventional processing technique which tracks the wavefront arrival time (13%).

An inverse approach to determining spatially varying arterial compliance using ultrasound imaging

The mechanical properties of arteries are implicated in a wide variety of cardiovascular diseases, many of which are expected to involve a strong spatial variation in properties that can be depicted by diagnostic imaging. A pulse wave inverse problem (PWIP) is presented, which can produce spatially resolved estimates of vessel compliance from ultrasound measurements of the vessel wall displacements. The 1D equations governing pulse wave propagation in a flexible tube are parameterized by the spatially varying properties, discrete cosine transform components of the inlet pressure boundary conditions, viscous loss constant and a resistance outlet boundary condition. Gradient descent optimization is used to fit displacements from the model to the measured data by updating the model parameters. Inversion of simulated data showed that the PWIP can accurately recover the correct compliance distribution and inlet pressure under realistic conditions, even under high simulated measurement noise conditions. Silicone phantoms with known compliance contrast were imaged with a clinical ultrasound system. The PWIP produced spatially and quantitatively accurate maps of the phantom compliance compared to independent static property estimates, and the known locations of stiff inclusions (which were as small as 7 mm). The PWIP is necessary for these phantom experiments as the spatiotemporal resolution, measurement noise and compliance contrast does not allow accurate tracking of the pulse wave velocity using traditional approaches (e.g. 50% upstroke markers). Results from simulations indicate reflections generated from material interfaces may negatively affect wave velocity estimates, whereas these reflections are accounted for in the PWIP and do not cause problems.