Comment on “Retinal pulse wave velocity measurement using spectral‐domain optical coherence tomography”

This paper comments on the article “Retinal pulse wave velocity measurement using spectral‐domain optical coherence tomography” by Qian Li et al. The authors propose a method to determine the pulse wave velocity in retinal arteries and veins. This method should enable a noninvasive determination of biomechanical properties of the vessel network, particularly the elasticity of the vessel walls. Although the observations the authors made might seem reasonable at first glance, they are in fact highly surprising and contradictory to theoretical predictions and previously published results.     

Retinal pulse wave velocity measurement using spectral‐domain optical coherence tomography

The human eyes provide a natural window for noninvasive measurement of the pulse wave velocity (PWV) of small arteries. By measuring the retinal PWV, the stiffness of small arteries can be assessed, which may better detect early vascular diseases. Therefore, retinal PWV measurement has attracted increasing attention. In this study, a jump‐scanning method was proposed for noninvasive measurement of retinal PWV using spectral‐domain optical coherence tomography (SD‐OCT). The jump‐scanning method uses the phase‐resolved Doppler OCT to obtain the pulse shapes. To realize PWV measurement, the jump‐scanning method extracts the transit time of the pulse wave from an original OCT scanning site to another through a transient jump. The measured retinal arterial PWV of a young human subject with normal blood pressure was in the order of 20 to 30 mm/s, which was consistent with previous studies. As a comparison, PWV of 50 mm/s was measured for a young human subject with prehypertension, which was in accordance with the finding of strong association between retinal PWV and blood pressure. In summary, it is believed the proposed jump‐scanning method could benefit the research and diagnosis of vascular diseases through the window of human eyes.      

On the time dependent diffusion of macromolecules through transient open junctions and their subendothelial spread. 2. Long time model for interaction between leakage sites

In Part 1 of this study (Weinbaum et al., 1988) a short time model has been proposed to describe the initial time dependent leakage of macromolecules at short distances (5 microns or less) from the exit of a transient open junction which the authors have hypothesized as a characteristic feature of endothelial cells in the process of turnover (Weinbaum et al., 1985). This open junction pathway has also been proposed (Weinbaum et al., 1988) to be the primary ultrastructural correlate of the 20 nm diameter large pore suggested by Renkin et al. (1977) using the predictions of cylindrical pore theory. The short time model in (Weinbaum et al., 1988), however, has major limitations in that it neglects the interaction between leakage sites, macromolecular entry through other pathways, the finite thickness of the vessel wall and the curvature of the cell perimeter. The longer time model developed herein will attempt to describe each of these features and also present an improved model and analytic solution for the steady state flux and uptake. In the previous steady state model developed by Weinbaum et al. (1985) the effect of the resistance of the transient open junctions and the non-isotropic diffusion in the underlying tissue due to the internal elastic lamina (IEL) were both neglected. New solutions are first presented which describe the effect of these important model refinements on the steady state macromolecular permeability of the major arteries. Time dependent solutions are then presented to predict the transient longer time labeling following the introduction of tracer macromolecules of varying size. These solutions and the corresponding short time solutions in Weinbaum et al. (1988) are the first solutions to our knowledge to describe the difficult time-dependent boundary value problem to determine how the channel exit concentration and flux at a leaky junction vary with time. This is accomplished by casting the boundary value problem in the form of an integral equation for the unknown flux at the cleft exit and then solving this problem using a specially designed numerical technique. The theoretical predictions are used to interpret the behavior of the localized leaks to HRP and albumin that have been reported in Stemerman et al. (1986) and our own recent experiments (Lin et al., 1988).     

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.     

Validity and reproducibility of arterial pulse wave velocity measurement using new device with oscillometric technique: A pilot study

Background  

Availability of a range of techniques and devices allow measurement of many variables related to the stiffness of large or medium sized arteries. There is good evidence that, pulse wave velocity is a relatively simple measurement and is a good indicator of changes in arterial properties. The pulse wave velocity calculated from pulse wave recording by other methods like doppler or tonometry is tedious, time-consuming and above all their reproducibility depends on the operator skills. It requires intensive resource involvement. For epidemiological studies these methods are not suitable. The aim of our study was to clinically evaluate the validity and reproducibility of a new automatic device for measurement of pulse wave velocity that can be used in such studies.     

Dynamic capacitance of epicardial coronary arteries in vivo

The dynamic capacitance of epicardial coronary arteries (i.d. greater than or equal to 0.4 mm) in vivo was assessed from the volume stiffness and volume of these arteries. The volume stiffness was derived from the pressure wave front velocity as determined in dogs by measuring the delay time between the pressure pulses recorded proximal and distal to a segment of the anterior descending branch of the left coronary artery. The pressure pulse was generated elsewhere in the arterial system during diastole. The volume of the epicardial coronary arteries was calculated from the lengths and diameters as measured in araldite casts, making corrections for in-vitro/in-vivo differences in dimensions. The dynamic capacitance of the right coronary artery, and the anterior descending and circumflex branches of the left coronary artery at an arterial pressure of 13.3 kPa and a frequency between 7 and 30 Hz was found to be 0.0024 +/- 0.0013, 0.0062 +/- 0.0028 and 0.0079 +/- 0.0035 mL/kPa (mean +/- SD), respectively. The total capacitance of the epicardial coronary arteries was calculated to be (0.007 mL/kPa)/100 g, which is small as compared to the total capacitance of the coronary vasculature, including the intramyocardial compartment, which is in the order of (0.5 mL/kPa)/100 g [1].     

Alternative algebraic rate‐integration approach for progress‐curve analysis of enzyme kinetics

A recent article of Zavrel et al. in this journal (Eng. Life Sci. 2010, 10, 191–200) described a comparison of several computer programs for progress‐curve analysis with respect to different computational approaches for parameter estimation. The authors applied both algebraic and dynamic parameter estimations, although they omitted time‐course analysis through the integrated rate equation. Recently, it was demonstrated that progress‐curve analysis through the integrated rate equation can be considered a simple and useful alternative for enzymes that obey the generalized Michaelis–Menten reaction mechanism. To complete this gap, the time‐dependent solution of the generalized Michaelis–Menten equation is here fitted to the progress curves from the Zavrel et al. reference article. This alternative rate‐integration approach for determining the kinetics parameters of Michaelis–Menten‐type enzymes yields the values with the greatest accuracy, as compared with the results obtained by other (algebraic or dynamic) parameter estimations.     

Baroreceptor reflex and arterial rigidity in schoolchildren

In this work there is shown a variability of heart rate and time delay of pulse wave of main arteries in schoolchildren.There is used the function of ordinary coherence of HR and DPW (time delay of pulse wave). This function reflects the rate of statistical linear relation of two processes in heart and blood vessels. A high tone of sympathetic part of vegetative nervous activity in schoolchildren increases CO (cardeiac out), shortens the hard connection phase of HR and DPW and results in a new system characteristic--arterial rigidity. There are presented results of passive orthostatic test and pharmacological tests on activation of sympathetic part of vegetative nervous activity in schoolchildren with heart rate problems.     

One-dimensional model for propagation of a pressure wave in a model of the human arterial network: comparison of theoretical and experimental results

Pulse wave evaluation is an effective method for arteriosclerosis screening. In a previous study, we verified that pulse waveforms change markedly due to arterial stiffness. However, a pulse wave consists of two components, the incident wave and multireflected waves. Clarification of the complicated propagation of these waves is necessary to gain an understanding of the nature of pulse waves in vivo. In this study, we built a one-dimensional theoretical model of a pressure wave propagating in a flexible tube. To evaluate the applicability of the model, we compared theoretical estimations with measured data obtained from basic tube models and a simple arterial model. We constructed different viscoelastic tube set-ups: two straight tubes; one tube connected to two tubes of different elasticity; a single bifurcation tube; and a simple arterial network with four bifurcations. Soft polyurethane tubes were used and the configuration was based on a realistic human arterial network. The tensile modulus of the material was similar to the elasticity of arteries. A pulsatile flow with ejection time 0.3 s was applied using a controlled pump. Inner pressure waves and flow velocity were then measured using a pressure sensor and an ultrasonic diagnostic system. We formulated a 1D model derived from the Navier-Stokes equations and a continuity equation to characterize pressure propagation in flexible tubes. The theoretical model includes nonlinearity and attenuation terms due to the tube wall, and flow viscosity derived from a steady Hagen-Poiseuille profile. Under the same configuration as for experiments, the governing equations were computed using the MacCormack scheme. The theoretical pressure waves for each case showed a good fit to the experimental waves. The square sum of residuals (difference between theoretical and experimental wave-forms) for each case was <10.0%. A possible explanation for the increase in the square sum of residuals is the approximation error for flow viscosity. However, the comparatively small values prove the validity of the approach and indicate the usefulness of the model for understanding pressure propagation in the human arterial network.     

Wave Propagation through a Viscous Fluid Contained in a Tethered, Initially Stressed, Orthotropic Elastic Tube

To give a realistic representation of the pulse propagation in arteries a theoretical analysis of the wave propagation through a viscous incompressible fluid contained in an initially stressed elastic tube is considered. The tube is assumed to be orthotropic and its longitudinal motion is constrained by a uniformly distributed additional mass, a dashpot and a spring. The fluid is assumed to be Newtonian. The analysis is restricted to propagation of small amplitude harmonic waves whose wavelength is large compared to the radius of the vessel. Elimination of arbitrary constants from the general solutions of the equations of motion of the fluid and the wall gives a frequency equation to determine the velocity of propagation. Two roots of this equation give the velocity of propagation of two distinct outgoing waves. One of the waves propagates slower than the other. The propagation properties of s lower waves are very slightly affected by the degree of anisotropy of the wall. The velocity of propagation of faster waves decreases as the ratio of the longitudinal modulus of elasticity to the circumferential modulus decreases; transmission of these waves is very little affected. The influence of the tethering on the propagation velocity of slower waves is negligibly small; transmission of these waves is seriously affected. In tethered tubes faster waves are completely attenuated.     

Attractor models of working memory and their modulation by reward

This work reports an empirical examination of two key issues in theoretical neuroscience: distractibility in the context of working memory (WM) and its reward dependence. While these issues have been examined fruitfully in isolation (e.g. Macoveanu et al. in Biol Cybern 96(4): 407–19, 2007), we address them here in tandem, with a focus on how distractibility and reward interact. In particular, we parameterise an observation model that embodies the nonlinear form of such interactions, as described in a recent neuronal network model (Gruber et al. in J Comput Neurosci 20:153–166, 2006). We observe that memory for a target stimulus can be corrupted by distracters in the delay period. Interestingly, in contrast to our theoretical predictions, this corruption was only partial. Distracters do not simply overwrite target; rather, a compromise is reached between target and distracter. Finally, we observed a trend towards a reduced distractibility under conditions of high reward. We discuss the implications of these findings for theoretical formulations of basal and dopamine (DA)-modulated neural bump- attractor networks of working memory.     

Studies on the relations between pressure and flow in the circulation

Simple theoretical models are proposed for the study of the interdependence between cardiac contraction, arterial pressure, and capillary drainage. The relation between pressure and flow is derived for a model of branching distensible tubes taking into account the finite pulse wave velocity. Equations are derived both for the case where the pulse wave is non-distorted and for the case where the wave is damped and distorted to a limited extent. Following the model of J. W. Remington and W. F. Hamilton (1947), the former case is applied to the larger arteries. Expressions are developed for the stroke volume, cardiac ejection, and systolic arterial storage in both the steady and non-steady states. Expressions for the percentage discrepancy involved in the computation of these quantities from a single tube model as contrasted with a multi-branched model are derived. For typical cases these discrepancies are small and thus credence is lent to the further use of the simpler single tube model which requires fewer independent parameters. It is also shown that the formulae for stroke volume and arterial storage are only slightly sensitive to changes in pulse wave velocities, and that for some purposes it would seem permissible to assume an infinite velocity. The problem of capillary drainage is discussed, and the consequences of equations developed for the case of a distorted wave are shown to compare favorably with published experimental data. An approximate boundary condition for capillary drainage is derived. Finally, A. V. Hill's velocity load equation for muscle is used to obtain a first approximation for the velocity of cardiac contraction in terms of the initial arterial pressure, the heart radius, and the parameters of the heart musculature. It is shown how methods developed for stroke volume determination from the pressure contour may be used to estimate the heart and “air chamber” parameters. Use of these parameters and those obtained by other independent measurements permits the principle variables to be determined numerically.     

Computation of aortic pulse wave velocity and aortic pulse wave velocity and aortic extensibility from pressure gradient measurements.

This study is concerned with the computation of aortic pulse wave velocity based on simultaneous recordings of the aortic pressure gradient and first-time derivative of aortic pressure. These variables were recorded by means of a double-lumen catheter introduced in the aorta of four anesthetized closed chest dogs, and connected to critically damped manometer systems. Results of aortic pulse wave velocity were then compared: (i) to the true phase velocity obtained from spectra of apparent phase velocity, and (ii) to the pulse wave velocity computed from the time shift between maximum slopes of the pressure wave. From the aortic valves to 37 cm down the aortic trunk, pulse wave velocity increased from 410-460 cm/s to approximately 600-800 cm/s. Based on the wave propagation equation presented of Bramwell and Hill (Bramwell, J.C., and Hill, A. V. 1922. Proc. R. Soc. 93, 298-306), volumetric extensibility coefficients were computed from pulse wave velocity data. Results indicated that, from the aortic valves to 37 cm down to the aorta, the mean volumetric extensibility decreased from 0.43-0.56% deltaV/cm H2O to 0.16-0.25% deltaV/cm H2O (1 cm H2O = 94.1 N/m2).     

Pulse Wave Velocity Testing in the Baltimore Longitudinal Study of Aging

Carotid-femoral pulse wave velocity is considered the gold standard for measurements of central arterial stiffness obtained through noninvasive methods¹. Subjects are placed in the supine position and allowed to rest quietly for at least 10 min prior to the start of the exam. The proper cuff size is selected and a blood pressure is obtained using an oscillometric device. Once a resting blood pressure has been obtained, pressure waveforms are acquired from the right femoral and right common carotid arteries. The system then automatically calculates the pulse transit time between these two sites (using the carotid artery as a surrogate for the descending aorta). Body surface measurements are used to determine the distance traveled by the pulse wave between the two sampling sites. This distance is then divided by the pulse transit time resulting in the pulse wave velocity. The measurements are performed in triplicate and the average is used for analysis.     

Heart‐beat‐phase‐coherent Doppler optical coherence tomography for measuring pulsatile ocular blood flow

We introduce a Doppler OCT (DOCT) platform that is fully synchronized with the heart‐beat via a pulse oximeter. The system allows reconstructing heart‐beat‐phase‐coherent quantitative DOCT volumes. The method is to acquire a series of DOCT volumes and to record the pulse in parallel. The heartbeat data is used for triggering the start of each DOCT volume acquisition. The recorded volume series is registered to the level of capillaries using a cross‐volume registration. The information of the pulse phase is used to rearrange the tomograms in time, to obtain a series of phase coherent DOCT volumes over a pulse. We present Doppler angle independent quantitative evaluation of the absolute pulsatile blood flow within individual retinal vessels as well as of the total retinal blood flow over a full heartbeat cycle. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optical‐resolution photoacoustic microscopy with ultrafast dual‐wavelength excitation

Fast functional and molecular photoacoustic microscopy requires pulsed laser excitations at multiple wavelengths with enough pulse energy and short wavelength‐switching time. Recent development of stimulated Raman scattering in optical fiber offers a low‐cost laser source for multiwavelength photoacoustic imaging. In this approach, long fibers temporally separate different wavelengths via optical delay. The time delay between adjacent wavelengths may eventually limits the highest A‐line rate. In addition, a long‐time delay in fiber may limit the highest pulse energy, leading to poor image quality. In order to achieve high pulse energy and ultrafast dual‐wavelength excitation, we present optical‐resolution photoacoustic microscopy with ultrafast dual‐wavelength excitation and a signal separation method. The signal separation method is validated in numerical simulation and phantom experiments. We show that when two photoacoustic signals are partially overlapped with a 50‐ns delay, they can be recovered with 98% accuracy. We apply this ultrafast dual‐wavelength excitation technique to in vivo OR‐PAM. Results demonstrate that A‐lines at two wavelengths can be successfully separated, and sO₂ values can be reliably computed from the separated data. The ultrafast dual‐wavelength excitation enables fast functional photoacoustic microscopy with negligible misalignment among different wavelengths and high pulse energy, which is important for in vivo imaging of microvascular dynamics.     

Calcium waves induced by large voltage pulses in fish keratocytes.

Intracellular calcium waves in fish keratocytes are induced by the application of electric field pulses with amplitudes between 55 and 120 V/cm and full width at half-maximum of 65-100 ms. Calcium concentrations were imaged using two-photon excited fluorescence microscopy (Denk et al., 1990 Science. 248:73-76; Williams et al. 1994 FASEB J. 8:804-813) and the ratiometric calcium indicator indo-1. The applied electric field pulses induced waves with fast calcium rise times and slow decays, which nucleated in the lamellipodium at the hyperpolarized side of the cells and, less frequently, at the depolarized side. The effectiveness of wave generation was determined by the change induced in the membrane potential, which is about half the field strength times the cell width in the direction of the field. Stimulation of waves began at voltage drops across the cell above 150 mV and saturated at voltage drops above 300 mV, where almost all cells exhibited a wave. Waves were not induced in low-calcium media and were blocked by the nonselective calcium channel blockers cobalt chloride and verapamil, but not by specific organic antagonists of voltage-sensitive calcium channel conductance. Thapsigargin stopped wave propagation in the cell body, indicating that calcium release from intracellular stores is necessary. Thus a voltage pulse stimulates Ca2+ influx through calcium channels in the plasma membrane, and if the intracellular calcium concentration reaches a threshold, release from intracellular stores is induced, creating a propagating wave. These observations and the measured parameters (average velocity approximately 66 micron/s and average rise time approximately 68 ms) are consistent with a wave amplification model in which[equation, see text] determines the effective diffusivity of the propagating molecules, D approximately 300 micron2/s (Meyer, 1991. Cell. 64:675-678).     

On Estimating the Relationship between Longitudinal Measurements and Time‐to‐Event Data Using a Simple Two‐Stage Procedure

Summary Ye, Lin, and Taylor (2008, Biometrics 64 , 1238–1246) proposed a joint model for longitudinal measurements and time‐to‐event data in which the longitudinal measurements are modeled with a semiparametric mixed model to allow for the complex patterns in longitudinal biomarker data. They proposed a two‐stage regression calibration approach that is simpler to implement than a joint modeling approach. In the first stage of their approach, the mixed model is fit without regard to the time‐to‐event data. In the second stage, the posterior expectation of an individual's random effects from the mixed‐model are included as covariates in a Cox model. Although Ye et al. (2008) acknowledged that their regression calibration approach may cause a bias due to the problem of informative dropout and measurement error, they argued that the bias is small relative to alternative methods. In this article, we show that this bias may be substantial. We show how to alleviate much of this bias with an alternative regression calibration approach that can be applied for both discrete and continuous time‐to‐event data. Through simulations, the proposed approach is shown to have substantially less bias than the regression calibration approach proposed by Ye et al. (2008) . In agreement with the methodology proposed by Ye et al. (2008) , an advantage of our proposed approach over joint modeling is that it can be implemented with standard statistical software and does not require complex estimation techniques.