Increasing pulse wave velocity in a realistic cardiovascular model does not increase pulse pressure with age

The mechanism of the well-documented increase in aortic pulse pressure (PP) with age is disputed. Investigators assuming a classical windkessel model believe that increases in PP arise from decreases in total arterial compliance (C(tot)) and increases in total peripheral resistance (R(tot)) with age. Investigators assuming a more sophisticated pulse transmission model believe PP rises because increases in pulse wave velocity (c(ph)) make the reflected pressure wave arrive earlier, augmenting systolic pressure. It has recently been shown, however, that increases in c(ph) do not have a commensurate effect on the timing of the reflected wave. We therefore used a validated, large-scale, human arterial system model that includes realistic pulse wave transmission to determine whether increases in c(ph) cause increased PP with age. First, we made the realistic arterial system model age dependent by altering cardiac output (CO), R(tot), C(tot), and c(ph) to mimic the reported changes in these parameters from age 30 to 70. Then, c(ph) was theoretically maintained constant, while C(tot), R(tot), and CO were altered. The predicted increase in PP with age was similar to the observed increase in PP. In a complementary approach, C(tot), R(tot), and CO were theoretically maintained constant, and c(ph) was increased. The predicted increase in PP was negligible. We found that increases in c(ph) have a limited effect on the timing of the reflected wave but cause the system to degenerate into a windkessel. Changes in PP can therefore be attributed to a decrease in C(tot).     

Input-dependent wave attenuation in a critically-balanced model of cortex

A number of studies have suggested that many properties of brain activity can be understood in terms of critical systems. However it is still not known how the long-range susceptibilities characteristic of criticality arise in the living brain from its local connectivity structures. Here we prove that a dynamically critically-poised model of cortex acquires an infinitely-long ranged susceptibility in the absence of input. When an input is presented, the susceptibility attenuates exponentially as a function of distance, with an increasing spatial attenuation constant (i.e., decreasing range) the larger the input. This is in direct agreement with recent results that show that waves of local field potential activity evoked by single spikes in primary visual cortex of cat and macaque attenuate with a characteristic length that also increases with decreasing contrast of the visual stimulus. A susceptibility that changes spatial range with input strength can be thought to implement an input-dependent spatial integration: when the input is large, no additional evidence is needed in addition to the local input; when the input is weak, evidence needs to be integrated over a larger spatial domain to achieve a decision. Such input-strength-dependent strategies have been demonstrated in visual processing. Our results suggest that input-strength dependent spatial integration may be a natural feature of a critically-balanced cortical network.     

Energy dissipation and pulse wave attenuation in the canine carotid artery

This paper presents methods for calculating, for a segment of artery in vivo, (1) viscous and viscoelastic energy dissipation as a function of time, and (2) the viscous and viscoelastic components of the frequency-dependent attenuation coefficient. The calculations require measurement of arterial diameter and of intra-arterial pressure and flow-rate at two sites along the vessel. Viscous energy dissipation is calculated from the radius-dependent velocity shear in the lumen given by linear theory from the pressure measurements. The attenuation coefficient for a given harmonic of heart rate is calculated as half the sum of the viscous and viscoelastic components at that frequency of the energy dissipated per unit length by forwardtravelling waves, divided by the forward-wave flow work input to the segment at that frequency. Measurements in canine carotid arteries indicate that wall viscoelasticity contributes relatively little to energy dissipation per cardiac cycle and pulse wave attenuation.     

The prediction of stress-relaxation of ligaments and tendons using the quasi-linear viscoelastic model

Recent studies have questioned the ability of the quasi-linear viscoelastic (QLV) model to predict stresses and strains in response to loading conditions other than those used to fit the model. The objective of this study was to evaluate the ability of several models in the literature to predict the elastic stress response of ligament and tendon at strain levels higher than the levels used to fit the model. The constitutive models were then used to evaluate the ability of the QLV model to predict the overall stress response during stress relaxation. The models expressing stress as an exponential function of strain significantly overestimated stress when used at higher strain levels. The polynomial formulation of the Mooney–Rivlin model more accurately predicted the stress–strain behavior of ligament and tendon. The results demonstrate that the ability of the QLV model to accurately predict the stress-relaxation response is dependent in part on the accuracy of the function used to model the elastic response of the soft tissue.     

A viscoelastic model for use in predicting arterial pulse waves

In nonlinear mathematical models of the arterial circulation, the viscoelasticity of the vessel walls has generally been neglected or only taken into account in a highly approximate manner. A new method is proposed to simulate the nonlinear viscoelastic properties of the wall material with the aid of a convolution integral of the creep function and the pressure history. With this simulation it is possible to properly describe the measured characteristics of arterial viscoelasticity. Moreover, it is utilized in a mathematical model of arterial pulse propagation to study the influence of the internal wall friction on the shape, amplitude and mean value of pressure and flow pulses. The corresponding predictions are in much better agreement with in-vivo measurements, especially for the distal part of the circulation, than those obtained without viscoelasticity.     

Experimental validation of a time-domain-based wave propagation model of blood flow in viscoelastic vessels

Time-domain-based one-dimensional wave propagation models of the arterial system are preferable over one-dimensional wave propagation models in the frequency domain since the latter neglect the non-linear convection forces present in the physiological situation, especially when the vessel is tapered. Moreover, one-dimensional wave propagation models of the arterial system can be used to provide boundary conditions for fully three-dimensional fluid-structure interaction computations that are usually defined in the time domain. In this study, a time-domain-based one-dimensional wave propagation model in a cross-sectional area, flow and pressure (A,q,p)-formulation is developed. Using this formulation, a constitutive law that includes viscoelasticity based on the mechanical behaviour of a Kelvin body, is introduced. The resulting pressure and flow waves travelling through a straight and tapered vessel are compared to experimental data obtained from measurements in an in vitro setup. The model presented shows to be well suited to predict wave propagation through these straight and tapered vessels with viscoelastic wall properties and hereto can serve as a time-domain-based method to model wave propagation in the human arterial system.     

Interrelation between arterial pressure and speed of the pulse wave spreading

To describe the dependence of arterial pressure on the speed of spreading of pulse wave, an curvilinear regression equation with two constants was proposed. The causes of the discrepancy in the dependences reported in literature are discussed.     

Arterial pulse pressure and vasopressin release during graded water immersion in humans

Previous results indicate that arterial pulse pressure modulates release of arginine vasopressin (AVP) in humans. The hypothesis was therefore tested that an increase in arterial pulse pressure is the stimulus for suppression of AVP release during central blood volume expansion by water immersion. A two-step immersion model (n = 8) to the xiphoid process and neck, respectively, was used to attain two different levels of augmented cardiac distension. Left atrial diameter (echocardiography) increased from 28 +/- 1 to 34 +/- 1 mm (P < 0.05) during immersion to the xiphoid process and more so (P < 0.05), to 36 +/- 1 mm, during immersion to the neck. During immersion to the xiphoid process, arterial pulse pressure (invasively measured in a brachial artery) increased (P < 0.05) from 44 +/- 1 to 51 +/- 2 mmHg and to the same extent from 42 +/- 1 to 52 +/- 2 mmHg during immersion to the neck. Mean arterial pressure was unchanged during immersion to the xiphoid process and increased during immersion to the neck by 7 +/- 1 mmHg (P < 0.05). Arterial plasma AVP decreased from 2.5 +/- 0.7 to 1.8 +/- 0.5 pg/ml (P < 0. 05) during immersion to the xiphoid process and significantly more so (P < 0.05), to 1.4 +/- 0.5 pg/ml, during immersion to the neck. In conclusion, other factors besides the increase in arterial pulse pressure must have participated in the graded suppression of AVP release, comparing immersion to the xiphoid process with immersion to the neck. We suggest that when arterial pulse pressure is increased, graded distension of cardiopulmonary receptors modulate AVP release.     

On the propagation of a wave front in viscoelastic arteries

In formulating a mathematical model of the arterial system, the one-dimensional flow approximation yields realistic pressure and flow pulses in the proximal as well as in the distal regions of a simulated arterial conduit, provided that the viscoelastic damping induced by the vessel wall is properly taken into account. Models which are based on a purely elastic formulation of the arterial wall properties are known to produce shocklike transitions in the propagating pulses which are not observed in man under physiological conditions. The viscoelastic damping characteristics are such that they are expected to reduce the tendency of shock formation in the model. In order to analyze this phenomenon, the propagation of first and second-order pressure waves is calculated with the aid of a wave front expansion, and criteria for the formation of shocks are derived. The application of the results to the human arterial system show that shock waves are not to be expected under normal conditions, while in case of a pathologically increased pressure rise at the root of the aorta, shocklike transitions may develop in the periphery. In particular, it is shown that second-order waves never lead to shock formation in finite time for the class of initial conditions and mechanical wave guides which are of interest in the mammalian circulation.     

Digital heart rate monitor derived from the arterial pressure pulse

This monitor displays heart rate without the need for electrical contact with the experimental animal. The device uses a quartz pressure transducer connected to an arterial catheter and has a full scale accuracy of ± 3 beats min⁻¹; its range is 0–400 beats min⁻¹. There is an output voltage proportional to heart rate and internal calibration facilities are provided at 60 and 360 beats min⁻¹.     

An approach to determine pressure profile generated by compression bandage using quasi-linear viscoelastic model

Understanding the stress relaxation behavior of the compression bandage could be very useful in determining the behavior of the interface pressure exerted by the bandage on a limb during the course of the compression treatment. There has been no comprehensive study in the literature to investigate the pressure profile (interface pressure with time) generated by a compression bandage when applied at different levels of strain. The present study attempts to describe the pressure profile, with the use of a quasi-linear viscoelastic model, generated by a compression bandage during compression therapy. The quasi-linear viscoelastic (QLV) theory proposed by Fung (Fung, 1972, "Stress Strain History Relations of Soft Tissues in Simple Elongation," Biomechanics: Its Foundations and Objectives, Y. C. Fung, N. Perrone, and M. Anliker, eds., Prentice-Hall, Englewood Cliffs, NJ, pp. 181-207). was used to model the nonlinear time- and history-dependent relaxation behavior of the bandage using the ramp strain approach. The regression analysis was done to find the correlation between the pressure profile and the relaxation behavior of the bandage. The parameters of the QLV model, describing the relaxation behavior of the bandage, were used to determine the pressure profile generated by the bandage at different levels of strain. The relaxation behaviors of the bandage at different levels of strain were well described by the QLV model parameters. A high correlation coefficient (nearly 0.98) shows a good correlation of the pressure profile with the stress relaxation behavior of the bandage.The prediction of the pressure profile using the QLV model parameters were in agreement with the experimental data. The pressure profile generated by a compression bandage could be predicted using the QLV model describing the nonlinear relaxation behavior of the bandage. This new application of the QLV theory helps in evaluating the bandage performance during compression therapy as scientific wound care management.     

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).     

Equivalence between "feeling the pulse" on the human wrist and the pulse pressure wave at fingertip

Feeling the pulse on the wrist is the regular diagnostic method in traditional Chinese medicine. However it is natural to ask whether there is any difference between feeling the pulse on the wrist or at any other part of the body: such as the fingertips at which it is easily measured by electronic devices. We employ a series of neural networks to model blood pressure propagation from the wrist to the fingertip. In order to avoid the problem of over-fitting we apply information theoretic criterion to determine the optimal model in these networks and then apply surrogate data method to the residuals in this model. We demonstrate the application of this method to recordings of human pulse in six subjects. Our result indicates that there is no significant difference between pulse waveform measure on the lateral arterial artery (wrist) and at the fingertip.     

Characterizing viscoelastic properties of breast cancer tissue in a mouse model using indentation

Breast cancer is one of the leading cancer forms affecting females worldwide. Characterizing the mechanical properties of breast cancer tissue is important for diagnosis and uncovering the mechanobiology mechanism. Although most of the studies were based on human cancer tissue, an animal model is still describable for preclinical analysis. Using a custom-build indentation device, we measured the viscoelastic properties of breast cancer tissue from 4T1 and SKBR3 cell lines. A total of 7 samples were tested for each cancer tissue using a mouse model. We observed that a viscoelastic model with 2-term Prony series could best describe the ramp and stress relaxation of the tissue. For long-term responses, the SKBR3 tissues were stiffer in the strain levels of 4–10%, while no significant differences were found for the instantaneous elastic modulus. We also found tissues from both cell lines appeared to be strain-independent for the instantaneous elastic modulus and for the long-term elastic modulus in the strain level of 4–10%. In addition, by inspecting the cellular morphological structure of the two tissues, we found that SKBR3 tissues had a larger volume ratio of nuclei and a smaller volume ratio of extracellular matrix (ECM). Compared with prior cellular mechanics studies, our results indicated that ECM could contribute to the stiffening the tissue-level behavior. The viscoelastic characterization of the breast cancer tissue contributed to the scarce animal model data and provided support for the linear viscoelastic model used for in vivo elastography studies. Results also supplied helpful information for modeling of the breast cancer tissue in the tissue and cellular levels.     

Minimal model for representing the central and peripheral pulse based on the pulse wave theory]

The present paper discusses an optimized model for describing central and peripheral pulse waves. On the basis of these computer-aided calculations, further haemodynamic data may be evaluated with the aim of improving the possibilities of clinically invasive diagnostic evaluation of cardiovascular diseases.