Modeling of the wave transmission properties of large arteries using nonlinear elastic tubes

A thin-walled carotid vessel phantom for Doppler ultrasound flow studies

A technique is discussed for producing a robust ultrasound (US)-compatible flow phantom that consists of a thin-walled silicone-elastomer vessel with a lumen of arbitrary geometry, embedded in an agar-based tissue-mimicking material (TMM). The TMM has an acoustic attenuation of 0.56 dB cm(-1) MHz(-1) at 5 MHz, with nearly linear frequency-dependence and acoustic velocity of 1539 +/- 4 m s(-1). The vessel-mimicking material (VMM) has an acoustic attenuation of 3.5 dB cm(-1) MHz(-1) with linear frequency-dependence and an acoustic velocity of 1020 +/- 20 m s(-1). Scattering particles, which are added to the VMM to increase echogenicity and add speckle texture, lead to higher attenuation, depending on particle concentration and frequency. The VMM is stable over time, with a Young's elastic modulus of 1.3 to 1.7 MPa for strains of up to 10%, which mimics human arteries under typical physiological conditions. The phantom is sealed to prevent TMM exposure to air or water, to avoid changes to the acoustic velocity.

Electrical lumped model for arterial vessel beds

Numerous electrical analog models of the circulatory system have been proposed. However, conventional models are either too simple, focusing exclusively on heart function, or overly complex, characterizing arteries in excessive detail. The vessel beds, which comprise arteries, capillaries and veins, are well known to be responsible for most of the pressure drop in blood pressure and to dominate the draining of blood flow. Consequently, electrical analog models of the circulatory system should pay more attention to the vessel beds. This investigation divided the arterial system into several aortic segments with vessel beds, and proposed a model that used electrical lumped elements to represent the vessel beds. The model was adopted to simulate blood pressure propagation by considering each vessel bed as an isolated subsystem. The transfer function between the terminals of isolated subsystems was used to identify the electrical components of the lumped elements that characterized the vessel beds. Simulation results reveal that the compliance and impedance of the vessel beds are larger than in previous models that focused on the aorta or arteries. The proposed electrical lumped model could deal with much more information than the simple models due to the lumped element structure. Furthermore, its isolated subsystem approach also makes the proposed model significantly easier to use than the complex models.

Use of intravascular ultrasound to measure local compliance of the pediatric pulmonary artery: in vitro studies

BACKGROUND

The accurate measurement of local pulmonary artery compliance in pediatric pulmonary hypertension is an important step toward further understanding the biomechanical and hemodynamic aspects of the disease. The emergence of intravascular ultrasound (IVUS) imaging techniques promises the ability to make such measurements clinically. However, the use of IVUS for compliance measurements has not been validated. Furthermore, confusion exists regarding the most appropriate method to measure compliance.

METHODS

This study validated IVUS measurements against a laser micrometer standard for 4 elastic tubes of varying compliance. Two methods of quantifying local compliance were explored: The pressure-strain modulus (E(p)), (E(p)(g/cm(2)) = DeltaP x R(d)/DeltaR (Where DeltaP is pulse pressure, R(d) is diastolic radius, and DeltaR is systolic minus diastolic radii) and the dynamic compliance (C(dyn)), (C(dyn)(%/100 mm Hg) = [DeltaD/(DeltaP x D(d))] x 10(4) Where DeltaD is systolic minus diastolic diameters and D(d) is diastolic diameter.

RESULTS

IVUS diameter measurements agreed well with laser micrometer data although slight overestimation (mean = 3.67% +/- 2.78%) was present. Mean values of E(p) ranged from 353.3 g/cm(2) to 2676.0 g/cm(2); mean C(dyn) values ranged from 5.7% diametric change/100 mm Hg to 39.5% diametric change/100 mm Hg for all tube models. Although mean values of E(p) and C(dyn) could be distinguished among the various tubes, the extremely large measurement uncertainty for E(p) precluded statistical differentiation. The uncertainty in E(p) increased inversely with the diametric change, indicating a potential limitation of E(p) associated with stiffening arteries.

CONCLUSIONS

We conclude that C(dyn) is a more robust mean of quantifying pediatric pulmonary artery compliance, especially as arteries stiffen with chronic pulmonary hypertension.

Pulse wave attenuation measurement by linear and nonlinear methods in nonlinearly elastic tubes

Reasons for the continuing difficulty in making definitive measurements of pulse wave attenuation in elastic tubes and arteries in the presence of reflections are sought. The measurement techniques available were re-examined in elastic tubes mimicking the arterial compliance nonlinearity, under conditions of strong reflection. The pulse was of physiological shape, and two different pulse amplitudes in the physiological range were used. Measurements of pressure, flow-rate and diameter pulsation allowed the deployment of four of the classical linear methods of analysis. In addition, a method of separating the forward- and backward-travelling waves that does not require linearising assumptions was used, and the attenuation in the forward and reverse directions was calculated from the resulting waveforms. Overall, the results obtained here suggest that a fully satisfactory way of measuring arterial attenuation has yet to be devised. The classical linear methods all provided comparable attenuation estimates in terms of average value and degree of scatter across frequency. Increased scatter was generally found at the higher pulse amplitude. When the forward waveforms from the separation were similarly compared in terms of frequency components, the average value at energetic harmonics was similar to both the value indicated by the linear methods and the values predicted from linear theory on the basis of estimated viscous and viscoelastic parameter data. The backward waveforms indicated a physically unreasonable result, attributed as the expression for this technique of the same difficulties that normally manifest in scatter. Data in the literature suggesting that one of the classical methods, the three-point, systematically over-estimates attenuation were not supported, but it was confirmed that this method becomes prone to negative attenuation estimates at low harmonics as pulse amplitude increases. Although the goal of definitive attenuation measurement remains elusive, the task provides a sensitive tool for the examination of the effect of nonlinearities in the arterial system.

Effects of friction and nonlinearities on the separation of arterial waves into their forward and backward components

In this paper we examine the importance of fluid friction and nonlinearities due to the area-pressure relationship and to the convective acceleration on the separation of arterial pressure and flow waves into their forward and backward components. Experiments were run in straight uniform nonlinearly elastic tubes. Different degrees of fluid friction and nonlinearities, covering the physiological range, have been tested. We predicted the forward and backward running pressure components using two wave separation methods: the classical linear method (Westerhof et al., Cardiovasc. Res, 6,648-656, 1972) and the first order correction (FOC) method (Pythoud et al., Trans ASME J. Biomech. Engng, in press) which takes nonlinearities and fluid friction into account. We found that the two methods yield somewhat different predictions. The differences tend to increase with the degree of fluid friction and nonlinearities and are typically of the order of 4-8%. We further compared the transmission ratio of forward and backward waves predicted by both methods. The transmission ratio was found to be overestimated by 10% by the classical linear method. The nonlinear method gave more accurate estimates, consistent with theory. We conclude that, for in vivo applications, the classical linear method should be the method of choice because it is simpler to use and the erros involved (4-8%) are comparable to measurement erros.

A method to evaluate the elastic behavior of vascular stents

PURPOSE

To develop a simple method for determining the elastic behavior of vascular stents.

MATERIALS AND METHODS

An experimental apparatus was constructed to determine the elastic behavior of four different vascular stents. Each stent was expanded within an artificial compliant vessel and was subjected to an increasing external pressure. The cross-sectional area of each stent was recorded at incremental changes in pressure. Compliance was estimated from the slope of a linear regression analysis fit to the pressure-area data in the elastic range of deformation.

RESULTS

The self-expandable stents were the most compliant, and balloon-expandable stents exhibited the least compliance. The balloon- expandable stents initially deformed in an elastic manner and then yielded irrecoverably at higher pressures.

CONCLUSION

A simple method has been devised that allows the elastic behavior of stents to be assessed. Quantification of stent compliance with this method is important as a predictor of stent resistance to compression in vivo.