Ashraf W. Khir

Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements

The accuracy of the nonlinear one-dimensional (1-D) equations of pressure and flow wave propagation in Voigt-type visco-elastic arteries was tested against measurements in a well-defined experimental 1:1 replica of the 37 largest conduit arteries in the human systemic circulation. The parameters required by the numerical algorithm were directly measured in the in vitro setup and no data fitting was involved. The inclusion of wall visco-elasticity in the numerical model reduced the underdamped high-frequency oscillations obtained using a purely elastic tube law, especially in peripheral vessels, which was previously reported in this paper [Matthys et al., 2007. Pulse wave propagation in a model human arterial network: Assessment of 1-D numerical simulations against in vitro measurements. J. Biomech. 40, 3476–3486]. In comparison to the purely elastic model, visco-elasticity significantly reduced the average relative root-mean-square errors between numerical and experimental waveforms over the 70 locations measured in the in vitro model: from 3.0% to 2.5% (p<0.012) for pressure and from 15.7% to 10.8% (p<0.002) for the flow rate. In the frequency domain, average relative errors between numerical and experimental amplitudes from the 5th to the 20th harmonic decreased from 0.7% to 0.5% (p<0.107) for pressure and from 7.0% to 3.3% (p<10−6) for the flow rate. These results provide additional support for the use of 1-D reduced modelling to accurately simulate clinically relevant problems at a reasonable computational cost.

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

Abstract 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.

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(+/-)/dlnD(+/-)). When only unidirectional waves are present, this relationship describes a linear relationship between lnD and U. Therefore, constructing a lnDU-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.

Noninvasive determination of local pulse wave velocity and wave intensity: changes with age and gender in the carotid and femoral arteries of healthy human

We recently introduced noninvasive methods to assess local pulse wave velocity (PWV) and wave intensity ((n)dI) in arteries based on measurements of flow velocity (U) and diameter (D). Although the methods were validated in an experimental setting, clinical application remains lacking. The aim of this study was therefore to investigate the effect of age and gender on PWV and (n)dI in the carotid and femoral arteries of an existing population. We measured D and U in the carotid and femoral arteries of 1,774 healthy subjects aged 35-55 yr, a subgroup of the Asklepios population. With the use of the lnDU-loop method, we calculated local PWV, which was used to determine arterial distensibility ((n)Ds). We then used the new algorithm to determine maximum forward and backward wave intensities ((n)dI(+max) and (n)dI(-min), respectively) and the reflection index ((n)RI). On average, PWV was higher, and (n)Ds was lower in the femoral than at the carotid arteries. At the carotid artery, PWV increased with age, but (n)Ds, (n)dI(+max), and (n)dI(-min) decreased; (n)RI did not change with age. At the femoral artery, PWV was higher, and (n)Ds was lower in male, but all parameters did not change significantly with age in both women and men. We conclude that the carotid artery is more affected by the aging process than the femoral artery, even in healthy subjects. The new techniques provide mechanical and hemodynamic parameters, requiring only D and U measurements, both of which can be acquired using ultrasound equipment widely available today, hence their advantage for potential use in the clinical setting.

How much of the intraaortic balloon volume is displaced toward the coronary circulation

Objective During intraaortic balloon inflation, blood volume is displaced toward the heart (Vtip), traveling retrograde in the descending aorta, passing by the arch vessels, reaching the aortic root (Vroot), and eventually perfusing the coronary circulation (Vcor). Vcor leads to coronary flow augmentation, one of the main benefits of the intraaortic balloon pump. The aim of this study was to assess Vroot and Vcor in vivo and in vitro, respectively. Methods During intraaortic balloon inflation, Vroot was obtained by integrating over time the aortic root flow signals measured in 10 patients with intraaortic balloon assistance frequencies of 1:1 and 1:2. In a mock circulation system, flow measurements were recorded simultaneously upstream of the intraaortic balloon tip and at each of the arch and coronary branches of a silicone aorta during 1:1 and 1:2 intraaortic balloon support. Integration over time of the flow signals during inflation yielded Vcor and the distribution of Vtip. Results In patients, Vroot was 6.4% ± 4.8% of the intraaortic balloon volume during 1:1 assistance and 10.0% ± 5.0% during 1:2 assistance. In vitro and with an artificial heart simulating the native heart, Vcor was smaller, 3.7% and 3.8%, respectively. The distribution of Vtip in vitro varied, with less volume displaced toward the arch and coronary branches and more volume stored in the compliant aortic wall when the artificial heart was not operating. Conclusion The blood volume displaced toward the coronary circulation as the result of intraaortic balloon inflation is a small percentage of the nominal intraaortic balloon volume. Although small, this percentage is still a significant fraction of baseline coronary flow.

Intra-aortic balloon pumping: effects on left ventricular diastolic function.

OBJECTIVE The intra-aortic balloon pump is the most widely used form of temporary cardiac assist and often utilised in patients before and after cardiac surgery. Several effects of balloon counter-pulsation have been reported previously, but its effect on left ventricular diastolic function has not been thoroughly investigated. The aim of this study is to examine the effect of the intra-aortic balloon pump on left ventricular wall motion and transmitral flow. METHODS We studied 20 patients in the intensive care unit, less than 36 h following cardiac surgery. We recorded left anterior descending coronary artery and transmitral E-wave flow velocities using transesophageal echocardiography pulsed Doppler. We also recorded left ventricular long axis free-wall movement using M-mode. The intra-aortic balloon pump was set to full augmentation and recordings were made at pumping cycles 1:1, 1:2, 1:3, and when the pump was on stand-by, leaving a minimum of 5 min between the pumping modes to allow the return to control conditions. In order to eliminate time effects, the sequence of recording was varied between patients using a 4 by 4 Latin-square. RESULTS The peak diastolic left anterior descending coronary artery and transmitral E-wave flow velocities, and left ventricular free-wall early diastolic lengthening velocity increased significantly with intra-aortic balloon pumping cycles 1:1, 1:2 and 1:3 compared to their value with the pump on stand-by, all P < 0.001. The increase in peak transmitral E-wave flow velocity correlated with the increase in peak left anterior descending coronary artery diastolic flow velocity (r = 0.74, P = 0.02), and with the increase in left ventricular free-wall early diastolic lengthening velocity (r = 0.80, P < 0.001). CONCLUSION Using the intra-aortic balloon pump post-cardiac surgery significantly increases peak diastolic left anterior descending coronary artery flow velocities and left ventricular free-wall early diastolic lengthening velocity, whose increase explains the increase in peak transmitral E-wave velocity. Although coronary flow is epicardial and mitral flow is intracardial, their close relationship suggests an improvement in left ventricular diastolic function with intra-aortic balloon pump.

Discerning aortic waves during intra-aortic balloon pumping and their relation to benefits of counterpulsation in humans

An explanation of the mechanisms leading to the beneficial hemodynamic effects of the intra-aortic balloon pump (IABP) is lacking. We hypothesized that inflation and deflation of the balloon would generate a compression (BCW) and an expansion (BEW) wave, respectively, which, when analyzed with wave intensity analysis, could be used to explain the hemodynamic benefits of IABP support. Simultaneous ascending aortic pressure (Pao) and flow rate (Qao) were recorded in 25 patients during control conditions and with IABP support of 1:1 and 1:2. Diastolic aortic pressure augmentation (Paug) and end-diastolic aortic pressure (ED Pao) reduction were calculated from Pao. Energies of the BCW and BEW were obtained by integrating the wave intensity contour over time. Paug was 19.1 mmHg (SD 13.6) during 1:2 support. During 1:1 support significantly higher Paug of 21.1 mmHg (SD 13.4) was achieved (P < 0.001). ED Pao decreased from 50.9 mmHg (SD 15.1) to 43.9 mmHg (SD 15.7) (P < 0.0001) during 1:1 assistance and the decrease was not statistically different with 1:2. During 1:1 support the energy of BCW was correlated positively to Paug (r = 0.83, P < 0.0001) and energy of the BEW correlated negatively to ED Pao (r = 0.78, P < 0.005); these relationships were not statistically different during 1:2. In conclusion, the energies of the BCW and BEW are directly related to Paug and ED Pao, which are the conventional hemodynamic parameters indicating IABP benefits. These findings imply a cause and effect mechanism between the energies of BCW and BEW, and IABP hemodynamic effects.

The human heart: Application of the golden ratio and angle

The golden ratio, or golden mean, of 1.618 is a proportion known since antiquity to be the most aesthetically pleasing and has been used repeatedly in art and architecture. Both the golden ratio and the allied golden angle of 137.5° have been found within the proportions and angles of the human body and plants. In the human heart we found many applications of the golden ratio and angle, in addition to those previously described. In healthy hearts, vertical and transverse dimensions accord with the golden ratio, irrespective of different absolute dimensions due to ethnicity. In mild heart failure, the ratio of 1.618 was maintained but in end-stage heart failure the ratio significantly reduced. Similarly, in healthy ventricles mitral annulus dimensions accorded with the golden ratio, while in dilated cardiomyopathy and mitral regurgitation patients the ratio had significantly reduced. In healthy patients, both the angles between the mid-luminal axes of the pulmonary trunk and the ascending aorta continuation and between the outflow tract axis and continuation of the inflow tract axis of the right ventricle approximate to the golden angle, although in severe pulmonary hypertension, the angle is significantly increased. Hence the overall cardiac and ventricular dimensions in a normal heart are consistent with the golden ratio and angle, representing optimum pump structure and function efficiency, whereas there is significant deviation in the disease state. These findings could have anatomical, functional and prognostic value as markers of early deviation from normality.

Accuracy of commercial devices and methods for noninvasive estimation of aortic systolic blood pressure a systematic review and meta-analysis of invasive validation studies.

Background: Although compelling evidence has established the physiological and clinical relevance of aortic SBP (a-SBP), no consensus exists regarding the validity of the available methods/techniques that noninvasively measure it. Objectives: The systematic review and meta-analysis aimed to determine the accuracy of commercial devices estimating a-SBP noninvasively, which have been validated by invasive measurement of a-SBP. Moreover their optimal mode of application, in terms of calibration, as well as specific technique and arterial site of pulse wave acquisition were further investigated. Methods: The study was performed according to the PRISMA guidelines; 22 eligible studies were included, which validated invasively 11 different commercial devices in 808 study participants. Results: Overall, the error in a-SBP estimation (estimated minus actual value) was −4.49 mmHg [95% confidence interval (CI): −6.06 to −2.92 mmHg]. The estimated (noninvasive) a-SBP differed from the actual (invasive) value depending on calibration method: by −1.08 mmHg (95% CI: −2.81, 0.65 mmHg) and by −5.81 mmHg (95% CI: −7.79, −3.84 mmHg), when invasively and noninvasively measured brachial BP values were used respectively; by −1.83 mmHg, (95% CI: −3.32, −0.34 mmHg), and by 7.78 mmHg (95% CI: −10.28, −5.28 mmHg), when brachial mean arterial pressure/DBP and SBP/DBP were used, respectively. Conclusion: Automated recording of waveforms, calibrated noninvasively by brachial mean arterial pressure/DBP values seems the most promising approach that can provide relatively more accurate, noninvasive estimation of a-SBP. It is still uncertain whether a specific device can be recommended as ‘gold standard’; however, a consensus is currently demanding.

A Mock Circulatory System With Physiological Distribution of Terminal Resistance and Compliance: Application for Testing the Intra-Aortic Balloon Pump

A mock circulatory system (MCS) was designed to replicate a physiological environment for in vitro testing and was assessed with the intra-aortic balloon pump (IABP). The MCS was comprised of an artificial left ventricle (LV), connected to a 14-branch polyurethane-compound aortic model. Physiological distribution of terminal resistance and compliance according to published data was implemented with capillary tubes of different sizes and syringes of varying air volume, respectively, fitted at the outlets of the branches. The ends of the aortic branches were connected to a common tube representing the venous system and an overhead reservoir provided atrial pressure. An IABP operating a 40-cc balloon was set to counterpulsate with the LV. Total arterial compliance of the system was 0.94 mL/mm Hg and total arterial resistance was 20.3 ± 3.3 mm Hg/L/min. At control, physiological flow distribution was achieved and both mean and phasic aortic pressure and flow were physiological. With the IABP, aortic pressure exhibited the major features of counterpulsation: diastolic augmentation during inflation, inflection point at onset of deflation, and end-diastolic reduction at the end of deflation. The contribution of balloon inflation and deflation was also evident on the aortic flow pattern. This MCS was verified to be suitable for IABP testing and with further adaptations it could be used for studying other hemodynamic problems and ventricular assist devices.