Measurements of wave speed and reflected waves in elastic tubes and bifurcations

Wave intensity analysis is a time domain method for studying waves in elastic tubes. Testing the ability of the method to extract information from complex pressure and velocity waveforms such as those generated by a wave passing through a mismatched elastic bifurcation is the primary aim of this research. The analysis provides a means for separating forward and backward waves, but the separation requires knowledge of the wave speed. The PU-loop method is a technique for determining the wave speed from measurements of pressure and velocity, and investigating the relative accuracy of this method is another aim of this research.We generated a single semi-sinusoidal wave in long elastic tubes and measured pressure and velocity at the inlet, and pressure at the exit of the tubes. In our experiments, the results of the PU-loop and the traditional foot-to-foot methods for determining the wave speed are comparable and the difference is on the order of 2.9+/-0.8%. A single semi-sinusoidal wave running through a mismatched elastic bifurcation generated complicated pressure and velocity waveforms. By using wave intensity analysis we have decomposed the complex waveforms into simple information of the times and magnitudes of waves passing by the observation site.We conclude that wave intensity analysis and the PU-loop method combined, provide a convenient, time-based technique for analysing waves in elastic tubes.     

Wave dissipation in flexible tubes in the time domain: in vitro model of arterial waves

Earlier work of wave dissipation in flexible tubes and arteries has been carried out predominantly in the frequency domain and most of the studies used the measured pressure waveform for presenting the results. In this work we investigate the pattern of wave dissipation in the time domain using the separated forward and backward travelling waves in flexible tubes. We tested four sizes of latex tubes of 2m in length each, where a single semi-sinusoidal in shape, pressure wave, was produced at the inlet of each tube. Simultaneous measurements of pressure and flow waveforms were recorded every 5cm along the tubes and wave speed was determined using the pressure-velocity loop method (PU-loop). The measured data and wave speed were used to separate the pressure waveform and wave intensity, into their forward and backward directions, using wave intensity analysis (WIA). Also, the energy carried by the wave was calculated by integrating the relevant area under the wave intensity curve. The peak of the measured pressure waveform increased downstream, however, the peak of the separated forward pressure waveform decreased exponentially along the tube. Wave intensity and energy also dissipated exponentially along the travelling distance. The peaks of the separated pressure and wave intensity decreased in the forward in a similar exponential way to that in the backward direction in all four tube sizes. Also, the smaller the size of the tube the greater wave dissipation it caused. We conclude that wave separation is useful in studying wave dissipation in elastic tubes, and WIA provides a convenient method for determining the dissipation of the energy carried by the wave along the travelled distance. The separated pressure waveform, wave intensity and wave energy dissipate exponentially with the travelling distance, and wave dissipation varies conversely with the diameter of elastic tubes.     

Blind identification of the aortic pressure waveform from multiple peripheral artery pressure waveforms

We have developed a new technique to estimate the clinically relevant aortic pressure waveform from multiple, less invasively measured peripheral artery pressure waveforms. The technique is based on multichannel blind system identification in which two or more measured outputs (peripheral artery pressure waveforms) of a single-input, multi-output system (arterial tree) are mathematically analyzed so as to reconstruct the common unobserved input (aortic pressure waveform) to within an arbitrary scale factor. The technique then invokes Poiseuille's law to calibrate the reconstructed waveform to absolute pressure. Consequently, in contrast to previous related efforts, the technique does not utilize a generalized transfer function or any training data and is therefore entirely patient and time specific. To demonstrate proof of concept, we have evaluated the technique with respect to four swine in which peripheral artery pressure waveforms from the femoral and radial arteries and a reference aortic pressure waveform from the descending thoracic aorta were simultaneously measured during diverse hemodynamic interventions. We report that the technique reliably estimated the entire aortic pressure waveform with an overall root mean squared error (RMSE) of 4.6 mmHg. For comparison, the average overall RMSE between the peripheral artery pressure and reference aortic pressure waveforms was 8.6 mmHg. Thus the technique reduced the RMSE by 47%. As a result, the technique also provided similar improvements in the estimation of systolic pressure, pulse pressure, and the ejection interval. With further successful testing, the technique may ultimately be employed for more precise monitoring and titration of therapy in, for example, critically ill and hypertension patients.     

Determination of wave speed and wave separation in the arteries using diameter and velocity

The determination of arterial wave speed and the separation of the forward and backward waves have been established using simultaneous measurements of pressure (P) and velocity (U). In this work, we present a novel algorithm for the determination of local wave speed and the separation of waves using the simultaneous measurements of diameter (D) and U. The theoretical basis of this work is the solution of the 1D equations of flow in elastic tubes. A relationship between D and U is derived, from which, local wave speed can be determined; C=±0.5(dU_±/d ln D_±). When only unidirectional waves are present, this relationship describes a linear relationship between ln D and U. Therefore, constructing a ln DU-loop should result in a straight line in the early part of the cycle when it is most probable that waves are running in the forward direction. Using this knowledge of wave speed, it is also possible to derive a set of equations to separate the forward and backward waves from the measured D and U waveforms. Once the forward and backward waveforms of D and U are established, we can calculate the energy carried by the forward and backward waves, in a similar way to that of wave intensity analysis. In this paper, we test the new algorithm in vitro and present results from data measured in the carotid artery of human and the ascending aorta of canine. We conclude that the new technique can be reproduced in vitro, and in different vessels of different species, in vivo. The new algorithm is easy to use to determine wave speed and separate D and U waveforms into their forward and backward directions. Using this technique has the merits of utilising noninvasive measurements, which would be useful in the clinical setting.     

Experimental validation of non-invasive and fluid density independent methods for the determination of local wave speed and arrival time of reflected wave

The relationship between the vessel diameter (D) and fluid velocity (U) in arteries and flexible tubes has been recently characterized as linear in the absence of wave reflections. This relationship allowed for determining local wave speed (C(DU)) using the lnDU-loop method. Using C(DU), it was possible to separate U and D waveforms into their forward and backward components. It was also possible to calculate wave intensity (dI(DU)), using D and U, from which the arrival time of reflected wave (Trw(DU)) could be determined. These techniques are fluid density independent and require only non-invasive measurements of D and U. In this work we experimentally validate the relative accuracy of these new techniques in vitro, by comparing their results of C(DU) and Trw(DU) to those determined by the established techniques, PU-loop and wave intensity analysis, C and Trw, respectively. We generated a single semi-sinusoidal wave in long flexible tubes, and simultaneously measured pressure (P), D, and U at the same site. Sequentially in time, we repeated this experiment at three sites along each of the flexible tubes, which were made of different materials and sizes, and three fluids of different densities. C(DU) compared well with that C and likewise Trw(DU) was very similar to Trw. Varying fluid density did not appreciably change the difference between the results of the two techniques. We conclude that the new techniques for determining C(DU) and Trw(DU), although independent of density, provide relatively accurate estimates of wave speed and arrival times of reflected waves in vitro. The new techniques require only non-invasive measurements of D and U, and further in vivo validation is required to establish its advantage in the clinical setting.     

Differences in cardiac microcirculatory wave patterns between the proximal left mainstem and proximal right coronary artery

Despite having almost identical origins and similar perfusion pressures, the flow-velocity waveforms in the left and right coronary arteries are strikingly different. We hypothesized that pressure differences originating from the distal (microcirculatory) bed would account for the differences in the flow-velocity waveform. We used wave intensity analysis to separate and quantify proximal- and distal-originating pressures to study the differences in velocity waveforms. In 20 subjects with unobstructed coronary arteries, sensor-tipped intra-arterial wires were used to measure simultaneous pressure and Doppler velocity in the proximal left main stem (LMS) and proximal right coronary artery (RCA). Proximal- and distal-originating waves were separated using wave intensity analysis, and differences in waves were examined in relation to structural and anatomic differences between the two arteries. Diastolic flow velocity was lower in the RCA than in the LMS (35.1 +/- 21.4 vs. 56.4 +/- 32.5 cm/s, P < 0.002), and, consequently, the diastolic-to-systolic ratio of peak flow velocity in the RCA was significantly less than in the LMS (1.00 +/- 0.32 vs. 1.79 +/- 0.48, P < 0.001). This was due to a lower distal-originating suction wave (8.2 +/- 6.6 x 10(3) vs. 16.0 +/- 12.2 x 10(3) W.m(-2).s(-1), P < 0.01). The suction wave in the LMS correlated positively with left ventricular pressure (r = 0.6, P < 0.01) and in the RCA with estimated right ventricular systolic pressure (r = 0.7, P = 0.05) but not with the respective diameter in these arteries. In contrast to the LMS, where coronary flow velocity was predominantly diastolic, in the proximal RCA coronary flow velocity was similar in systole and diastole. This difference was due to a smaller distal-originating suction wave in the RCA, which can be explained by differences in elastance and pressure generated between right and left ventricles.     

Noninvasive pressure pulse waveform analysis of flow-mediated vasodilation evoked by post-occlusive reactive hyperemia maneuver

Post-occlusive reactive hyperemia (PORH) assesses flow-mediated vasodilation at microvascular level due to bioactivity of endothelial-derived factors. Ordinary augmentation index that quantifies endothelial response is based on an ensemble-averaged waveform that limits its short-time application. This study proposes a mathematical model and two corresponding indices to evaluate arterial pressure response after blood flow restoration. Radial pressure pulse waveforms were acquired by a 12 bits acquisition board at a sampling rate of 1.0 kHz using a piezoelectric transducer. Signals were stored during 30 s at baseline condition and 60 s after 5-min occlusion using an arm-cuff placed over the brachial artery. In both conditions, the pressure pulse waveform presents systolic and diastolic phases with progressive and regressive pulse waveforms, respectively. Changes in pulse wave morphology were also observed and comprised attenuation of the pulse pressure amplitude (markedly first and second systolic peaks). This characteristic of the pulse pressure was described by the time-domain summation of two pairs of Gaussian-like waveforms (representing independent progressive and regressive components) with parameters related to amplitude, time lag, and duration for each component. A steepest descent optimization routine was used to fit the model parameters to experimental data of normotensive and subjects with hypertension. The optimized parameters were used to calculate two indices, RIx_1,2 (second-to-first systolic peak ratio) and RIx_1,3 (first diastolic-to-first systolic ratio). The observed responses between groups suggest that RIx_1,2 is related to an endothelial response to the ischemic process and could be used as a clinical tool to assess endothelial function in hypertension.     

Improved pulse transit time estimation by system identification analysis of proximal and distal arterial waveforms

We investigated the system identification approach for potentially improved estimation of pulse transit time (PTT), a popular arterial stiffness marker. In this approach, proximal and distal arterial waveforms are measured and respectively regarded as the input and output of a system. Next, the system impulse response is identified from all samples of the measured input and output. Finally, the time delay of the impulse response is detected as the PTT estimate. Unlike conventional foot-to-foot detection techniques, this approach is designed to provide an artifact robust estimate of the true PTT in the absence of wave reflection. The approach is also applicable to arbitrary types of arterial waveforms. We specifically applied a parametric system identification technique to noninvasive impedance cardiography (ICG) and peripheral arterial blood pressure waveforms from 15 humans subjected to lower-body negative pressure. We assessed the technique through the correlation coefficient (r) between its 1/PTT estimates and measured diastolic pressure (DP) per subject and the root mean squared error (RMSE) of the DP predicted from these estimates and measured DP. The technique achieved average r and RMSE values of 0.81 ± 0.16 and 4.3 ± 1.3 mmHg. For comparison, the corresponding values were 0.59 ± 0.37 (P < 0.05) and 5.9 ± 2.5 (P < 0.01) mmHg for the conventional technique applied to the same waveforms and 0.28 ± 0.40 (P < 0.001) and 7.2 ± 1.8 (P < 0.001) mmHg for the conventional technique with the ECG waveform substituted for the ICG waveform. These results demonstrate, perhaps for the first time, that the system identification approach can indeed improve PTT estimation.     

Prosthetic heart valves: waveform comparisons and average value disposition for pulsatile flow in vitro

With the development of the in vitro testing of heart valves, the standardization of the test methods becomes increasingly important and they should also be improved continuously. This paper discusses the problems of waveform comparison and average value dispositions. In the pulsatile model driven by pneumatics, the pressures before and after the valve, and the flow through it, are measured as three one-dimensional variates. The mean values are calculated according to the FDA and the ISO. A comparison and analysis of experimental waveforms indicate that, for basically the same ranges of pressures and flow rate, the flow curves of different types of valve are clearly different. The mean values and the waveforms in the time domain should be taken into consideration synthetically so that the pusatile characteristics of the valve can be more completely reflected. Using numerical filtering methods to treat the waveforms allows for better comparisons between the measured results taken from the different devices. By means of the constellation graphical method for treating mean values as multivariates, it is feasible to classify the valves and to judge their qualities under conditions of pulsatile flow.     

Estimation of changes in instantaneous aortic blood flow by the analysis of arterial blood pressure

The purpose of this study was to introduce and validate a new algorithm to estimate instantaneous aortic blood flow (ABF) by mathematical analysis of arterial blood pressure (ABP) waveforms. The algorithm is based on an autoregressive with exogenous input (ARX) model. We applied this algorithm to diastolic ABP waveforms to estimate the autoregressive model coefficients by requiring the estimated diastolic flow to be zero. The algorithm incorporating the coefficients was then applied to the entire ABP signal to estimate ABF. The algorithm was applied to six Yorkshire swine data sets over a wide range of physiological conditions for validation. Quantitative measures of waveform shape (standard deviation, skewness, and kurtosis), as well as stroke volume and cardiac output from the estimated ABF, were computed. Values of these measures were compared with those obtained from ABF waveforms recorded using a Transonic aortic flow probe placed around the aortic root. The estimation errors were compared with those obtained using a windkessel model. The ARX model algorithm achieved significantly lower errors in the waveform measures, stroke volume, and cardiac output than those obtained using the windkessel model (P < 0.05).     

Numerical assessment of time-domain methods for the estimation of local arterial pulse wave speed

A local estimation of pulse wave speed c, an important predictor of cardiovascular events, can be obtained at arterial locations where simultaneous measurements of blood pressure (P) and velocity (U), arterial diameter (D) and U, flow rate (Q) and cross-sectional area (A), or P and D are available, using the PU-loop, sum-of-squares (∑(2)), lnDU-loop, QA-loop or new D(2)P-loop methods. Here, these methods were applied to estimate c from numerically generated P, U, D, Q and A waveforms using a visco-elastic one-dimensional model of the 55 larger human systemic arteries in normal conditions. Theoretical c were calculated from the parameters of the model. Estimates of c given by the loop methods were closer to theoretical values and more uniform within each arterial segment than those obtained using the ∑(2). The smaller differences between estimates and theoretical values were obtained using the D(2)P-loop method, with root-mean-square errors (RMSE) smaller than 0.18 ms(-1), followed by averaging the two c given by the PU- and lnDU-loops (RMSE <2.99 ms(-1)). In general, the errors of the PU-, lnDU- and QA-loops decreased at locations where visco-elastic effects were small and nearby junctions were well-matched for forward-travelling waves. The ∑(2) performed better at proximal locations.     

Electrical penetration graphs from Cicadulina mbila on maize, the fine structure of its stylet pathways and consequences for virus transmission efficiency

Five distinct electrical penetration graph waveforms characterising the feeding behaviour of the leafhopper Cicadulina mbila Naudé (Homoptera: Cicadellidae) on maize (Zea mays L.) were obtained using a DC based system. The waveforms were distinguished by spectral features and by statistical analysis of their median voltages, durations and time to first waveform recording. By changing the polarity of the system voltage and the level of the input resistor it was shown that the waveforms are mainly determined by the electromotive force (emf) component. Based on the correlation between waveforms and the fine structure of the stylet pathways observed by transmission electron microscopy, insect's activities have been associated with five waveforms: stylet pathway formation (waveform 1), active ingestion (waveform 2), putative stylet work (waveform 3), salivation (waveform 4) and passive ingestion (waveform 5). Like waveform E1 and E2 of aphids, waveforms 4 and 5 of C. mbila correspond to feeding activities in sieve tubes. However, unlike aphids which probe briefly in non-vascular cells, waveform 2 corresponds to active ingestion in cells, where the cell content is partially ingested and hence the organelles' integrity severely affected. These observations suggest that this specific feeding feature, typical of leafhoppers, determines their ability to acquire geminivirus virions located in the plant cell nucleus.     

On the choice of outlet boundary conditions for patient-specific analysis of aortic flow using computational fluid dynamics

Boundary conditions (BCs) are an essential part in computational fluid dynamics (CFD) simulations of blood flow in large arteries. Although several studies have investigated the influence of BCs on predicted flow patterns and hemodynamic wall parameters in various arterial models, there is a lack of comprehensive assessment of outlet BCs for patient-specific analysis of aortic flow. In this study, five different sets of outlet BCs were tested and compared using a subject-specific model of a normal aorta. Phase-contrast magnetic resonance imaging (PC-MRI) was performed on the same subject and velocity profiles extracted from the in vivo measurements were used as the inlet boundary condition. Computational results obtained with different outlet BCs were assessed in terms of their agreement with the PC-MRI velocity data and key hemodynamic parameters, such as pressure and flow waveforms and wall shear stress related indices. Our results showed that the best overall performance was achieved by using a well-tuned three-element Windkessel model at all model outlets, which not only gave a good agreement with in vivo flow data, but also produced physiological pressure waveforms and values. On the other hand, opening outlet BCs with zero pressure at multiple outlets failed to reproduce any physiologically relevant flow and pressure features.     

In vitro validation of finite-element model of AAA hemodynamics incorporating realistic outlet boundary conditions

The purpose of this study is to validate numerical simulations of flow and pressure in an abdominal aortic aneurysm (AAA) using phase-contrast magnetic resonance imaging (PCMRI) and an in vitro phantom under physiological flow and pressure conditions. We constructed a two-outlet physical flow phantom based on patient imaging data of an AAA and developed a physical Windkessel model to use as outlet boundary conditions. We then acquired PCMRI data in the phantom while it operated under conditions mimicking a resting and a light exercise physiological state. Next, we performed in silico numerical simulations and compared experimentally measured velocities, flows, and pressures in the in vitro phantom to those computed in the in silico simulations. There was a high degree of agreement in all of the pressure and flow waveform shapes and magnitudes between the experimental measurements and simulated results. The average pressures and flow split difference between experiment and simulation were all within 2%. Velocity patterns showed good agreement between experimental measurements and simulated results, especially in the case of whole-cycle averaged comparisons. We demonstrated methods to perform in vitro phantom experiments with physiological flows and pressures, showing good agreement between numerically simulated and experimentally measured velocity fields and pressure waveforms in a complex patient-specific AAA geometry.     

Umbilical artery flow velocity waveform analysis in normal ovine pregnancy and after carunculectomy

Twenty fetal lambs were studied in utero using continuous wave Doppler ultrasound to analyse the fetal umbilical artery flow velocity waveforms. Satisfactory waveforms were obtained. Prepregnancy surgical removal of uterine caruncles was used to produce intrauterine fetal growth retardation in 14 of these ovine pregnancies of whom 8 delivered a small for gestational age fetus. In only one fetus was the umbilical artery flow velocity waveform abnormal with a high systolic diastolic ratio. We conclude that the growth restriction occurring in the ovine fetus following a reduction of placental implantation sites is not related to a restriction in the fetoplacental circulation and this is different from the most frequently observed human fetal growth retardation.     

The inverse Womersley problem for pulsatile flow in straight rigid tubes

In this study a numerical solution for the problem of pulsating flow in rigid tubes is described. The method applies to the case of known flow rate waveform, as opposed to Womersley solution where the pressure gradient was the known quantity. The solution provides the pressure gradient and wall shear stress waveforms as well as the instantaneous velocity profiles. Results show that the method can be used to study the blood flow characteristics in large arteries.     

EPG monitoring of the probing behaviour of the common brown leafhopper Orosius orientalis on artificial diet and selected host plants

The common brown leafhopper Orosius orientalis (Hemiptera: Cicadellidae) is a polyphagous vector of a range of economically important pathogens, including phytoplasmas and viruses, which infect a diverse range of crops. Studies on the plant penetration behaviour by O. orientalis were conducted using the electrical penetration graph (EPG) technique to assist in the characterisation of pathogen acquisition and transmission. EPG waveforms representing different probing activities were acquired from adult O. orientalis probing in planta, using two host species, tobacco Nicotiana tabacum and bean Phaseolus vulgaris, and in vitro using a simple sucrose-based artificial diet. Five waveforms (O1?CO5) were evident when O. orientalis fed on bean, whereas only four waveforms (O1?CO4) and three waveforms (O1?CO3) were observed when the leafhopper fed on tobacco and on the artificial diet, respectively. Both the mean duration of each waveform and waveform type differed markedly depending on the food substrate. Waveform O4 was not observed on the artificial diet and occurred relatively rarely on tobacco plants when compared with bean plants. Waveform O5 was only observed with leafhoppers probing on beans. The attributes of the waveforms and comparative analyses with previously published Hemipteran data are presented and discussed, but further characterisation studies will be needed to confirm our suggestions.     

Novel technique for monitoring micturition and sexual function in male rats using telemetry

We developed a novel technique to simultaneously monitor micturitions and erections in rats by using pressure monitoring within the corpus spongiosum of the penis (CSP). We present data validating this technique and report pressure waveform characteristics of micturition and erectile events during four different behavioral contexts in 10 awake, freely-moving male rats. Telemetric pressure transducers were implanted in the bulb of the CSP. CSP pressure was monitored while the animals were simultaneously recorded on video for determination of presence and volume (n = 7) of micturitions and while the animals underwent behavioral tests for determination of erections. Observed micturitions and CSP pressure waveforms characteristic of micturitions occurred simultaneously (r = 0.98) at a frequency of 32 +/- 4 micturitions per 24 h and with a volume of 0.95 +/- 0.12 ml/urination. Micturition duration recorded by CSP pressure and volume determined by urine weight were highly correlated (r = 0.82). We found that 100% of visually confirmed erectile events occurred simultaneously with CSP pressure waveforms characteristic of erections during ex copula reflex erection tests. During noncontact erection and mating tests more erections were identified by telemetry than by observation alone. Erections during mating tests had a different appearance than those seen in other contexts; they were shorter in duration (P < 0.05) and typically were characterized by a single suprasystolic CSP pressure peak, highlighting the context-specificity of erections. Quality of recordings remained stable in three of four rats we followed for 8 wk. We demonstrate that telemetric recording of CSP pressure provides a quantitative and qualitative assessment of penile erections and micturition in freely behaving rats.     

Effects of gas properties and waveform asymmetry on gas transport in a branching tube network

Local gas transport coefficients, quantifying longitudinal dispersion through a symmetrical constant-diameter tube network, have been measured during oscillation with both symmetrical and nonsymmetrical waveforms. Experiments were carried out over a range of conditions that would prevail in the central to lower airways during high-frequency ventilation at moderate frequency (5 Hz) and tidal volume (15-80 ml). Gas transport coefficients resulting from oscillation of three different resident-trace gas pairs were measured using a new analytic technique. This technique allowed rapid determination of the transport coefficient distribution along the entire network. Results demonstrate a small but significant influence attributable to changes in gas properties that is similar to that found in a straight tube and indicate that augmented dispersion is an important mechanism of axial transport. Gas transport coefficients were found to be unaffected by changes in flow waveform symmetry, suggesting that previously reported improvements in gas exchange associated with decreasing inspiratory to expiratory time ratios are not due to a change in local conditions such as asymmetry in the velocity profile.     

Stylet penetration by larvae of the greenhouse whitefly on cucumber

Probing behaviour of Trialeurodes vaporariorum (Westwood) larvae was monitored using the DC electrical penetration graph (EPG) technique on the host plant cucumber. EPGs were recorded for 16 h, simultaneously with honeydew excretion using a honeydew clock. Three waveforms were distinguished: a pathway waveform (C), and two phloem waveforms, one with a high (H), and one with a low frequency (L) signal. The C waveform mainly occurred in the crawler stage of the 1st instar larvae. EPGs recorded from larvae during and after moulting indicated that the process involves stylet withdrawal; hence the stylets of each new instar need to penetrate again from the leaf surface to the phloem.All sessile stages, from L1 to pre-pupa, spent almost their entire time in waveforms H and L. These waveforms alternated more frequently in the early instars than during the later ones, in which the H waveform became predominant. The H waveform was highly correlated with honeydew excretion and thus phloem sap ingestion. The L waveform was not related to honeydew excretion but EPGs indicated that the stylet tips remain in a sieve element during both waveforms. Periods of honeydew production demonstrated a delay of 30–40 min in relation to the onset and end of H and L waveforms. This delay is presumably related to the time needed for food passing through, or emptying of, the insect's gut. From the 1st instar to the pre-pupa, the frequency of excreted honeydew droplets decreased but their size increased, causing a net increase of the excretion rate.