Wave reflection: Myth or reality?

Estimation of carotid-femoral pulse wave velocity from finger photoplethysmography signal

Objective. This project compared a new method to estimate the carotid-femoral pulse wave velocity (cf-PWV) to the gold-standard cf-PWV technique.Approach. The cf-PWV was estimated from the pulse transit time (FPS-PTT) calculated by processing the finger photoplethysmographic signal of Finapres (FPS) and subject's height only (brief mode) as well as along with other variables (age, heart rate, arterial pressure, weight; complete mode). Doppler ultrasound cf-PWVs and FPS-PTTs were measured in 90 participants equally divided into 3 groups (18-30; 31-59; 60-79 years). Predictions were performed using multiple linear regressions (MLR) and with the best regression model identified by using MATLAB Regression Learner App. A validation set approach (60 training datasets, 30 testing datasets; VSA) and leave-one-out cross-validation (LOOCV) were used.Main results. With MLR, the discrepancies were: 0.01 ± 1.21 m s^-1(VSA) and 0.001 ± 1.11 m s^-1(LOOCV) in brief mode; -0.02 ± 0.83 m s^-1(VSA) and 0.001 ± 0.84 m s^-1(LOOCV) in complete mode. Using a linear support vector machine model (SVM) in brief mode, the discrepancies were: 0.01 ± 1.19 m s^-1(VSA) and -0.01 ± 1.06 m s^-1(LOOCV). Using an Exponential Gaussian process regression model (GPR) in complete mode, the discrepancies were: -0.03 ± 0.79 m s^-1(VSA) and 0.01 ± 0.75 m s^-1(LOOCV).Significance. The cf-PWV can be estimated by processing the FPS-PTT and subjects' height only, but the inclusion of other variables improves the prediction performance. Predictions through MLR qualify as acceptable in both brief and complete modes. Predictions via linear SVM in brief mode improve but still qualify as acceptable. Interestingly, predictions through Exponential GPR in complete mode improve and qualify as excellent.

Experimental investigation into the effect of compliance of a mock aorta on cardiac performance

Demand for heart transplants far exceeds supply of donated organs. This is attributed to the high percentage of donor hearts that are discarded and to the narrow six-hour time window currently available for transplantation. Ex-vivo heart perfusion (EVHP) provides the opportunity for resuscitation of damaged organs and extended transplantation time window by enabling functional assessment of the hearts in a near-physiologic state. Present work investigates the fluid mechanics of the ex-vivo flow loop and corresponding impact on cardiac performance. A mechanical flow loop is developed that is analogous to the region of the EVHP system that mimics in-vivo systemic circulation, including the body’s largest and most compliant artery, the aorta. This investigation is focused on determining the effect of mock aortic tubing compliance on pump performance. A custom-made silicone mock aorta was developed to simulate a range of in-vivo conditions and a physiological flow was generated using a commercial ventricular assist device (VAD). Monitored parameters, including pressure, tube distension and downstream velocity, acquired using time-resolved particle imaging velocimetry (PIV), were applied to an unsteady Bernoulli analysis of the flow in a novel way to evaluate pump performance as a proxy for cardiac workload. When compared to the rigid case, the compliant mock aorta case demonstrated healthier physiologic pressure waveforms, steadier downstream flow and reduced energetic demands on the pump. These results provide experimental verification of Windkessel theory and support the need for a compliant mock aorta in the EVHP system.

Novel Geometric Representation for One-Dimensional Model of Arterial Blood Pulse Wave Propagation

This paper proposes a novel one-dimensional graphical representation to model the phenomenon of blood pulse wave propagation in major arteries. In particular, a tree data structure, as opposed to the existing purely linear structures, is used to accommodate arterial branching. The model is qualitatively validated and its demonstrated reliability by evaluating the phenomenon of wave reflection and pulse pressure amplification with a sample in-vivo arterial segment length measurements.

The Clinical Significance and Application of Vascular Stiffness Measurements

Increasing evidence points out at vascular stiffness (and in particular aortic stiffness measured by pulse wave velocity) as a reliable biomarker of vascular aging, able to integrate in a single measure the overall burden of cardiovascular (CV) risk factors on the vasculature over time; furthermore, it may be per se a mechanism of disease, by inducing microcirculatory damage and favoring CV events. Increased aortic stiffness has been shown to predict future CV events and improve risk reclassification in those at intermediate risk. However, several questions in this field are still open, limiting the wide use of these tools in the clinical practice. This article will review the basic aspects of physiology of large artery stiffness, as well as current evidence about its possible clinical applications.

Hemodynamics

A review is presented of the physical principles governing the distribution of blood flow and blood pressure in the vascular system. The main factors involved are the pulsatile driving pressure generated by the heart, the flow characteristics of blood, and the geometric structure and mechanical properties of the vessels. The relationship between driving pressure and flow in a given vessel can be understood by considering the viscous and inertial forces acting on the blood. Depending on the vessel diameter and other physical parameters, a wide variety of flow phenomena can occur. In large arteries, the propagation of the pressure pulse depends on the elastic properties of the artery walls. In the microcirculation, the fact that blood is a suspension of cells strongly influences its flow properties and leads to a nonuniform distribution of hematocrit among microvessels. The forces acting on vessel walls include shear stress resulting from blood flow and circumferential stress resulting from blood pressure. Biological responses to these forces are important in the control of blood flow and the structural remodeling of vessels, and also play a role in major disease processes including hypertension and atherosclerosis. Consideration of hemodynamics is essential for a comprehensive understanding of the functioning of the circulatory system.

Stochastic sensitivity analysis for timing and amplitude of pressure waves in the arterial system

In the field of computational hemodynamics, sensitivity quantification of pressure and flow wave dynamics has received little attention. This work presents a novel study of the sensitivity of pressure-wave timing and amplitude in the arterial system with respect to arterial stiffness. Arterial pressure and flow waves were simulated with a one-dimensional distributed wave propagation model for compliant arterial networks. Sensitivity analysis of this model was based on a generalized polynomial chaos expansion evaluated by a stochastic collocation method. First-order statistical sensitivity indices were formulated to assess the effect of arterial stiffening on timing and amplitude of the pressure wave and backward-propagating pressure wave in the ascending aorta, at the maximum pressure and inflection point in the systolic phase. Only the stiffness of aortic arteries was found to significantly influence timing and amplitude of the backward-propagating pressure wave, whereas other large arteries in the systemic tree showed marginal impact. Furthermore, the ascending aorta, aortic arch, thoracic aorta, and infrarenal abdominal aorta had the largest influence on amplitude, whereas only the thoracic aorta influenced timing. Our results showed that the non-intrusive polynomial chaos expansion is an efficient method to compute statistical sensitivity measures for wave propagation models. These sensitivities provide new knowledge in the relative importance of arterial stiffness at various locations in the arterial network. Moreover, they will significantly influence clinical data collection and effective composition of the arterial tree for in-silico clinical studies.

A computational study of pressure wave reflections in the pulmonary arteries

Experiments using wave intensity analysis suggest that the pulmonary circulation in sheep and dogs is characterized by negative or open-end type wave reflections, that reduce the systolic pressure. Since the pulmonary physiology is similar in most mammals, including humans, we test and verify this hypothesis by using a subject specific one-dimensional model of the human pulmonary circulation and a conventional wave intensity analysis. Using the simulated pressure and velocity, we also analyse the performance of the P-U loop and sum of squares techniques for estimating the local pulse wave velocity in the pulmonary arteries, and then analyse the effects of these methods on linear wave separation in the main pulmonary artery. P-U loops are found to provide much better estimates than the sum of squares technique at proximal locations, but both techniques accumulate progressive error at distal locations away from heart, particularly near junctions. The pulse wave velocity estimated using the sum of squares method also gives rise to an artificial early systolic backward compression wave. Finally, we study the influence of three types of pulmonary hypertension viz. pulmonary arterial hypertension, chronic thromboembolic pulmonary hypertension and pulmonary hypertension associated with hypoxic lung disease. Simulating these conditions by changing the relevant parameters in the model and then applying the wave intensity analysis, we observe that for each group the early systolic backward decompression wave reflected from proximal junctions is maintained, whilst the initial forward compression and the late systolic backward compression waves amplify with increasing pathology and contribute significantly to increases in systolic pressure.

Genesis of the characteristic pulmonary venous pressure waveform as described by the reservoir-wave model

Conventional haemodynamic analysis of pulmonary venous and left atrial (LA) pressure waveforms yields substantial forward and backward waves throughout the cardiac cycle; the reservoir wave model provides an alternative analysis with minimal waves during diastole. Pressure and flow in a single pulmonary vein (PV) and the main pulmonary artery (PA) were measured in anaesthetized dogs and the effects of hypoxia and nitric oxide, volume loading, and positive-end expiratory pressure (PEEP) were observed. The reservoir wave model was used to determine the reservoir contribution to PV pressure and flow. Subtracting reservoir pressure and flow resulted in 'excess' quantities which were treated as wave-related.Wave intensity analysis of excess pressure and flow quantified the contributions of waves originating upstream (from the PA) and downstream (from the LA and/or left ventricle (LV)).Major features of the characteristic PV waveform are caused by sequential LA and LV contraction and relaxation creating backward compression (i.e.pressure-increasing) waves followed by decompression (i.e. pressure-decreasing) waves. Mitral valve opening is linked to a backwards decompression wave (i.e. diastolic suction). During late systole and early diastole, forward waves originating in the PA are significant. These waves were attenuated less with volume loading and delayed with PEEP. The reservoir wave model shows that the forward and backward waves are negligible during LV diastasis and that the changes in pressure and flow can be accounted for by the discharge of upstream reservoirs. In sharp contrast, conventional analysis posits forward and backward waves such that much of the energy of the forward wave is opposed by the backward wave.

Modelling arterial pressure waveforms using Gaussian functions and two-stage particle swarm optimizer

Changes of arterial pressure waveform characteristics have been accepted as risk indicators of cardiovascular diseases. Waveform modelling using Gaussian functions has been used to decompose arterial pressure pulses into different numbers of subwaves and hence quantify waveform characteristics. However, the fitting accuracy and computation efficiency of current modelling approaches need to be improved. This study aimed to develop a novel two-stage particle swarm optimizer (TSPSO) to determine optimal parameters of Gaussian functions. The evaluation was performed on carotid and radial artery pressure waveforms (CAPW and RAPW) which were simultaneously recorded from twenty normal volunteers. The fitting accuracy and calculation efficiency of our TSPSO were compared with three published optimization methods: the Nelder-Mead, the modified PSO (MPSO), and the dynamic multiswarm particle swarm optimizer (DMS-PSO). The results showed that TSPSO achieved the best fitting accuracy with a mean absolute error (MAE) of 1.1% for CAPW and 1.0% for RAPW, in comparison with 4.2% and 4.1% for Nelder-Mead, 2.0% and 1.9% for MPSO, and 1.2% and 1.1% for DMS-PSO. In addition, to achieve target MAE of 2.0%, the computation time of TSPSO was only 1.5 s, which was only 20% and 30% of that for MPSO and DMS-PSO, respectively.

Wave potential and the one-dimensional windkessel as a wave-based paradigm of diastolic arterial hemodynamics

Controversy exists about whether one-dimensional wave theory can explain the "self-canceling" waves that accompany the diastolic pressure decay and discharge of the arterial reservoir. Although it has been proposed that reservoir and wave effects be treated as separate phenomena, thus avoiding the issue of self-canceling waves, we have argued that reservoir effects are a phenomenological and mathematical subset of wave effects. However, a complete wave-based explanation of self-canceling diastolic expansion (pressure-decreasing) waves has not yet been advanced. These waves are present in the forward and backward components of arterial pressure and flow (P ± and Q ±, respectively), which are calculated by integrating incremental pressure and flow changes (dP ± and dQ ±, respectively). While the integration constants for this calculation have previously been considered arbitrary, we showed that physiologically meaningful constants can be obtained by identifying "undisturbed pressure" as mean circulatory pressure. Using a series of numeric experiments, absolute P ± and Q ± values were shown to represent "wave potential," gradients of which produce propagating wavefronts. With the aid of a "one-dimensional windkessel," we showed how wave theory predicts discharge of the arterial reservoir. Simulated data, along with hemodynamic recordings in seven sheep, suggested that self-canceling diastolic waves arise from repeated and diffuse reflection of the late systolic forward expansion wave throughout the arterial system and at the closed aortic valve, along with progressive leakage of wave potential from the conduit arteries. The combination of wave and wave potential concepts leads to a comprehensive one-dimensional (i.e., wave-based) explanation of arterial hemodynamics, including the diastolic pressure decay.

Inverse problems in 1D hemodynamics on systemic networks: a sequential approach

In this work, a sequential approach based on the unscented Kalman filter is applied to solve inverse problems in 1D hemodynamics, on a systemic network. For instance, the arterial stiffness is estimated by exploiting cross-sectional area and mean speed observations in several locations of the arteries. The results are compared with those ones obtained by estimating the pulse wave velocity and the Moens-Korteweg formula. In the last section, a perspective concerning the identification of the terminal models parameters and peripheral circulation (modeled by a Windkessel circuit) is presented.