The ebbing tide of the reservoir-wave model

Measurement, Analysis and Interpretation of Pressure/Flow Waves in Blood Vessels

The optimal performance of the cardiovascular system, as well as the break-down of this performance with disease, both involve complex biomechanical interactions between the heart, conduit vascular networks and microvascular beds. ‘Wave analysis’ refers to a group of techniques that provide valuable insight into these interactions by scrutinizing the shape of blood pressure and flow/velocity waveforms. The aim of this review paper is to provide a comprehensive introduction to wave analysis, with a focus on key concepts and practical application rather than mathematical derivations. We begin with an overview of invasive and non-invasive measurement techniques that can be used to obtain the signals required for wave analysis. We then review the most widely used wave analysis techniques—pulse wave analysis, wave separation and wave intensity analysis—and associated methods for estimating local wave speed or characteristic impedance that are required for decomposing waveforms into forward and backward wave components. This is followed by a discussion of the biomechanical phenomena that generate waves and the processes that modulate wave amplitude, both of which are critical for interpreting measured wave patterns. Finally, we provide a brief update on several emerging techniques/concepts in the wave analysis field, namely wave potential and the reservoir-excess pressure approach.

The modified arterial reservoir: An update with consideration of asymptotic pressure (P∞) and zero-flow pressure (Pzf)

This article describes the modified arterial reservoir in detail. The modified arterial reservoir makes explicit the wave nature of both reservoir (P_res) and excess pressure (P_xs). The mathematical derivation and methods for estimating P_res in the absence of flow velocity data are described. There is also discussion of zero-flow pressure (P_zf), the pressure at which flow through the circulation ceases; its relationship to asymptotic pressure (P_∞) estimated by the reservoir model; and the physiological interpretation of P_zf . A systematic review and meta-analysis provides evidence that P_zf differs from mean circulatory filling pressure.

Towards a consensus on the understanding and analysis of the pulse waveform: Results from the 2016 Workshop on Arterial Hemodynamics: Past, present and future

This paper aims to summarize and map contemporary views on some contentious aspects of arterial hemodynamics that have remained unresolved despite years of research. These were discussed during a workshop entitled Arterial hemodynamics: past, present and future held in London on June 14 and 15, 2016. To do this we formulated a list of potential consensus statements informed by discussion at the meeting in London and quantified the degree of agreement and invited comments from the participants of the workshop. Overall the responses and comments show a high measure of quantitative agreement with the various proposed 'consensus' statements. Taken together, these statements seem a useful basis for proceeding with a more detailed and comprehensive consensus document on the current understanding and approaches to analysis of the pulse waveform. Future efforts should be directed at identifying remaining areas of dispute and future topics for research.

Effects of pacing modality on noninvasive assessment of heart rate dependency of indices of large artery function

Studies investigating the relationship between heart rate (HR) and arterial stiffness or wave reflections have commonly induced HR changes through in situ cardiac pacing. Although pacing produces consistent HR changes, hemodynamics can be different with different pacing modalities. Whether the differences affect the HR relationship with arterial stiffness or wave reflections is unknown. In the present study, 48 subjects [mean age, 78 ± 10 (SD), 9 women] with in situ cardiac pacemakers were paced at 60, 70, 80, 90, and 100 beats per min under atrial, atrioventricular, or ventricular pacing. At each paced HR, brachial cuff-based pulse wave analysis was used to determine central hemodynamic parameters, including ejection duration (ED) and augmentation index (AIx). Wave separation analysis was used to determine wave reflection magnitude (RM) and reflection index (RI). Arterial stiffness was assessed by carotid-femoral pulse wave velocity (cfPWV). Pacing modality was found to have significant effects on the HR relationship with ED (P = 0.01), central aortic pulse pressure (P = 0.01), augmentation pressure (P < 0.0001), and magnitudes of both forward and reflected waves (P = 0.05 and P = 0.003, respectively), but not cfPWV (P = 0.57) or AIx (P = 0.38). However, at a fixed HR, significant differences in pulse pressure amplification (P < 0.001), AIx (P < 0.0001), RM (P = 0.03), and RI (P = 0.03) were observed with different pacing modalities. These results demonstrate that although the HR relationships with arterial stiffness and systolic loading as measured by cfPWV and AIx were unaffected by pacing modality, it should still be taken into account for studies in which mixed pacing modalities are present, in particular, for wave reflection studies.

Novel wave power analysis linking pressure-flow waves, wave potential, and the forward and backward components of hydraulic power

Wave intensity analysis provides detailed insights into factors influencing hemodynamics. However, wave intensity is not a conserved quantity, so it is sensitive to diameter variations and is not distributed among branches of a junction. Moreover, the fundamental relation between waves and hydraulic power is unclear. We, therefore, propose an alternative to wave intensity called “wave power,” calculated via incremental changes in pressure and flow (dPdQ) and a novel time-domain separation of hydraulic pressure power and kinetic power into forward and backward wave-related components (ΠP± and ΠQ±). Wave power has several useful properties: 1) it is obtained directly from flow measurements, without requiring further calculation of velocity; 2) it is a quasi-conserved quantity that may be used to study the relative distribution of waves at junctions; and 3) it has the units of power (Watts). We also uncover a simple relationship between wave power and changes in ΠP± and show that wave reflection reduces transmitted power. Absolute values of ΠP± represent wave potential, a recently introduced concept that unifies steady and pulsatile aspects of hemodynamics. We show that wave potential represents the hydraulic energy potential stored in a compliant pressurized vessel, with spatial gradients producing waves that transfer this energy. These techniques and principles are verified numerically and also experimentally with pressure/flow measurements in all branches of a central bifurcation in sheep, under a wide range of hemodynamic conditions. The proposed “wave power analysis,” encompassing wave power, wave potential, and wave separation of hydraulic power provides a potent time-domain approach for analyzing hemodynamics.

Evaluating the Hemodynamic Basis of Age-Related Central Blood Pressure Change Using Aortic Flow Triangulation

BACKGROUND

Pulsatile blood pressure rises with age, especially in the aorta. The comparative role of forward and reflected pressure waves (FW and RW, respectively), determined by aortic flow triangulation has not previously been explored in a large clinical cohort. This study aimed to identify the role of FW and RW in the rise in aortic pulse pressure with age.

METHODS

For 879 outpatients, aortic pressure waveforms were generated using a validated generalized transfer function applied to radial pressure waves recorded using applanation tonometry. FW and RW were subsequently determined using aortic flow triangulation. Contributions of FW and RW to rise in aortic pulse pressure with age were determined using multivariate linear regression and product of coefficient mediation analysis, with adjustment for height, weight, heart rate, and mean arterial pressure. Comparisons were made by gender and before and after age 60.

RESULTS

In subjects aged 60 and below, RW was an important contributor to pulsatile pressure elevation with age, but FW was non-contributory in either gender after multivariate correction. In subjects aged above 60, both FW and RW were significant and equal contributors in both genders.

CONCLUSIONS

In a clinical setting, both FW and RW are important to pulsatile aortic blood pressure across the lifespan, but RW appears to have a more pronounced effect across all ages, whereas FW has less effect in younger persons.