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.     

Constructive and destructive addition of forward and reflected arterial pulse waves

Although the physics of arterial pulse wave propagation and reflection is well understood, there is considerable debate as to the effect of reflection on vascular input impedance (Z(in)), pulsatile pressure, and stroke work (SW). This may be related to how reflection is studied. Conventionally, reflection is experimentally abolished (thus radically changing unrelated parameters), or a specific model is assumed from which reflection can be removed (yielding model-dependent results). The present work proposes a simple, model-independent method to evaluate the effect of reflection directly from measured pulsatile pressure (P) and flow (Q). Because characteristic impedance (Z(0)) is Z(in) in the absence of reflection, the P with reflection theoretically removed can be calculated from Q x Z(0). Applying this insight to an illustrative case indicates that reflection has the least effect on P and SW at normal pressure but a greater effect with vasodilation and vasoconstriction. Z(in), P, and SW are increased or decreased depending on the relative amount of constructive and destructive addition of forward and reflected arterial pulse waves.     

Effects of twist on pulse waves in arteries

The artery is treated as a thick-walled cylindrical shell. Using the large deformation theory, an analytical expression for the pulse wave speed is obtained and the effect of twist on the wave speed is discussed. Numerical results indicate that although phase velocity increases with pressure, it decreases with increasing twist angle.     

Is the arterial pulse a soliton?

The recent discovery of arterial smooth muscle contractions which are synchronized with the activity of the right atrial pacemaker in the rabbit heart gives support to the hypothesis that the arterial pulse wave is a soliton. The hypothesis is amenable to experimental tests.     

Frequency analysis of arterial pulse transmission in the cranial cavity]

The changes of intracranial and arterial pulse shape under functional loads (hypervolemia and intracranial hypertension) were compared. The logarithmic amplitude-frequency characteristics were found and used for the synthesis of equivalent electrical circuit of arterial pressure pulses transmission on cerebrospinal fluid (CSF) in the cranial cavity. The model obtained points to the necessity of taking into account the induction which was not performed in the earlier models of the CSF-system. It is found that the attenuation factor permitted to estimate the stability of the intracranial circulation system to input influences under different functional conditions.     

Semiquantitative detection of cytokine messages in X-irradiated and regenerating rat thymus

We investigated the expression of cytokine mRNA derived from thymocytes or thymic epithelial cells in X-irradiated (8 Gy) and recovering rat thymuses, according to our previous observation (Mizutani et al., Radiat. Res. 157, 281-289, 2002). The changes in mRNA expression level of interleukin 2 (Il2), Il4, tumor necrosis factor alpha (Tnf), interferon gamma (Ifng), and transforming growth factor beta (Tgfb) were examined. The mRNA expression of Il2 and Il4 decreased from day 5 to day 14 after irradiation. Thereafter, the expression level of Il2 mRNA recovered to normal control levels; however, the expression of Il4 mRNA tended toward significantly low levels. Tnf mRNA expression decreased on day 5 after irradiation and then showed a gradual increase back to normal control levels. Tgfb mRNA expression did not change significantly. Ifng mRNA expression was transiently enhanced from day 11 to day 14. The mRNA expression levels of Il10 increased significantly from day 3 to day 7 after irradiation. In addition, the mRNA expression of thymic epithelial cell-derived Il7 showed a transient decrease on day 3; however, then it showed a continuous increase from day 5 to day 21, finally reaching twice the normal control levels after X irradiation. These observations suggest that the expression of cytokine messages in the irradiated thymus changed significantly and did not return to normal for a long time after 8 Gy irradiation.     

What Nei Jing and Mai Jing say about arterial pulse waves and our attempt to illustrate some of their statements

A rich group of fluid mechanical problems are suggested in the classical Chinese books Nei Jing and Mai Jing. In this article the methods of pulse wave palpation described in these books are briefly explained, and an attempt to understand some of their statements is presented.     

Angiotensin processing is partially carried out by carboxypeptidases in the rat mesenteric arterial bed perfusate

Here we investigated the possible association between the carboxypeptidase A (CPA)-like activity of the rat mesenteric arterial bed (MAB) perfusate and the ability of this fluid of forming angiotensin (Ang) 1-9 and Ang 1-7 upon incubation with Ang I and Ang II, respectively. Initially, we observed that anion exchange chromatography of the perfusate would consistently split the characteristic Z-Val-Phe-hydrolyzing activity of CPA-like enzymes into five distinct peaks, whose proteolytic activities were then determined using also Ang I and Ang II as substrates. The resulting proteolytic profile for each peak indicated that rat MAB perfusate contains a complex mixture of carboxypeptidases; tentatively, five carboxypeptidases were distinguished based on their substrate preferences toward Z-Val-Phe, Ang I and Ang II. The respective reactions, namely, Z-Val-Phe cleavage, Ang I to Ang 1-9 conversion and Ang II to Ang 1-7 conversion, were inhibited by 1,10-phenanthroline and nearly fully blocked by potato carboxypeptidase inhibitor. Also, all the CPA-like activity peaks prepared by anion exchange chromatography were tested negative for contaminating Ang I-converting enzyme-2, cathepsin A and prolylcarboxypeptidase. Overall, our results indicate that rat MAB perfusate contains a multiplicity of Ang I and Ang II-processing CPA-like enzymes whose proteolytic specificities suggest they might perform peculiar regulatory roles in the local renin-angiotensin system.     

Emission of terahertz waves in the interaction of a laser pulse with clusters

A theory of generation of terahertz radiation in the interaction of a femtosecond laser pulse with a spherical cluster is developed for the case in which the density of free electrons in the cluster plasma exceeds the critical value. The spectral, angular, and energy characteristics of the emitted terahertz radiation are investigated, as well as its spatiotemporal structure. It is shown that the directional pattern of radiation has a quadrupole structure and that the emission spectrum has a broad maximum at a frequency nearly equal to the reciprocal of the laser pulse duration. It is found that the total radiated energy depends strongly on the cluster size. Analysis of the spatiotemporal profile of the terahertz signal shows that it has a femtosecond duration and contains only two oscillation cycles.     

The effects of variation in the arterial pulse waveform on perivascular flow

Cerebrospinal fluid (CSF) enters nervous tissues through perivascular spaces. Flow through these pathways is important for solute transport and to prevent fluid accumulation. Syringomyelia is commonly associated with subarachnoid space obstructions such as Chiari I malformation. However, the mechanism of development of these fluid-filled cavities is unclear. Studies have suggested that changes in the arterial and CSF pressures could alter normal perivascular flow. This study uses an idealised model of the perivascular space to investigate how variation in the arterial pulse influences fluid flow. The model used simulated subarachnoid pressures from healthy controls (N = 9), Chiari patients with (N = 7) and without (N = 8) syringomyelia. A parametric analysis was conducted to determine how features of the arterial pulse altered flow. The features of interest included: the timing and magnitude of the peak displacement, and the area under the curve in the phases of uptake and decline. A secondary aim was to determine if the previously observed differences between subject groups were sensitive to variation in the arterial pulse wave. The study demonstrated that the Chiari patients without a syrinx maintained a significantly higher level of perivascular inflow over a physiologically likely range of pulse wave shapes. The analysis also suggested that age-related changes in the arterial pulse (i.e. increased late systolic pulse amplitude and faster diastolic decay), could increase resistance to perivascular inflow affecting solute transport.     

Theoretical analysis of pressure pulse propagation in arterial vessels.

An original mathematical model of viscous fluid motion in a tapered and distensible tube is presented. The model equations are deduced by assuming a two-dimensional flow and taking into account the nonlinear terms in the fluid motion equations, as well as the nonlinear deformation of the tube wall. One distinctive feature of the model is the formal integration with respect to the radial coordinate of the Navier-Stokes equations by power series expansion. The consequent computational frame allows an easy, accurate evaluation of the effects produced by changing the values of all physical and geometrical tube parameters. The model is employed to study the propagation along an arterial vessel of a pressure pulse produced by a single flow pulse applied at the proximal vessel extremity. In particular, the effects of the natural taper angle of the arterial wall on pulse propagation are investigated. The simulation results show that tapering considerably influences wave attenuation but not wave velocity. The substantially different behavior of pulse propagation, depending upon whether it travels towards the distal extremity or in the opposite direction, is observed: natural tapering causes a continuous increase in the pulse amplitude as it moves towards the distal extremity; on the contrary, the reflected pulse, running in the opposite direction, is greatly damped. For a vessel with physical and geometrical properties similar to those of a canine femoral artery and 0.1 degree taper angle, the forward amplification is about 0.9 m-1 and the backward attenuation is 1.4 m-1, so that the overall tapering effect gives a remarkably damped pressure response. For a natural taper angle of 0.14 degrees the perturbation is almost extinct when the pulse wave returns to the proximal extremity.     

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.     

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.     

Pulse Decomposition Analysis of the digital arterial pulse during hemorrhage simulation

Background

Markers of temporal changes in central blood volume are required to non-invasively detect hemorrhage and the onset of hemorrhagic shock. Recent work suggests that pulse pressure may be such a marker. A new approach to tracking blood pressure, and pulse pressure specifically is presented that is based on a new form of pulse pressure wave analysis called Pulse Decomposition Analysis (PDA). The premise of the PDA model is that the peripheral arterial pressure pulse is a superposition of five individual component pressure pulses, the first of which is due to the left ventricular ejection from the heart while the remaining component pressure pulses are reflections and re-reflections that originate from only two reflection sites within the central arteries. The hypothesis examined here is that the PDA parameter T13, the timing delay between the first and third component pulses, correlates with pulse pressure. T13 was monitored along with blood pressure, as determined by an automatic cuff and another continuous blood pressure monitor, during the course of lower body negative pressure (LBNP) sessions involving four stages, -15 mmHg, -30 mmHg, -45 mmHg, and -60 mmHg, in fifteen subjects (average age: 24.4 years, SD: 3.0 years; average height: 168.6 cm, SD: 8.0 cm; average weight: 64.0 kg, SD: 9.1 kg).

Results

Statistically significant correlations between T13 and pulse pressure as well as the ability of T13 to resolve the effects of different LBNP stages were established. Experimental T13 values were compared with predictions of the PDA model. These interventions resulted in pulse pressure changes of up to 7.8 mmHg (SE = 3.49 mmHg) as determined by the automatic cuff. Corresponding changes in T13 were a shortening by -72 milliseconds (SE = 4.17 milliseconds). In contrast to the other two methodologies, T13 was able to resolve the effects of the two least negative pressure stages with significance set at p < 0.01.

Conclusions

The agreement of observations and measurements provides a preliminary validation of the PDA model regarding the origin of the arterial pressure pulse reflections. The proposed physical picture of the PDA model is attractive because it identifies the contributions of distinct reflecting arterial tree components to the peripheral pressure pulse envelope. Since the importance of arterial pressure reflections to cardiovascular health is well known, the PDA pulse analysis could provide, beyond the tracking of blood pressure, an assessment tool of those reflections as well as the health of the sites that give rise to them.     

Automatic detection of the upstroke on peripheral pulse waveforms

A number of analogue systems have been described which can be used to provide automatic detection of the upstroke on a peripheral pulse wave. Functional characteristics have been established which lead to the selection of the most effective system. This system has been shown to give a high performance in satisfying the original specification; dynamic range of signal 6 dB, detection repeatability ± 3ms, high noise immunity.