Biomedical subjects

W L Capper

Publications and source records attributed to W L Capper.

7 recordsLinked to original sources

PubMed2004

Exponential taper in arteries: an exact solution of its effect on blood flow velocity waveforms and impedance.

The dimensions and wall elasticity commonly taper along the length of mammalian arteries. The effects of taper on flow velocity waveforms can be included by either of two methods; to theoretically divide the artery into short sections wherein the properties are assumed constant (the approximate solution); or to find an exact solution incorporating the effects of taper. In this paper, an exact solution to the resulting, and previously unsolved nonlinear Ricatti equation for the impedance, is obtained by a process of substitutions. This solution is utilised to develop an exact expression for the flow velocity in the artery. The transmission line equations are then combined into a single integral expression for the entire artery and an exact solution to this is evaluated. This is the first solution to simultaneously account for both geometric and elastic taper, and it has been validated by comparing simulations of flow in the aorta of a dog to those using an infinitesimal approximate solution. The Pulsatility Index of the approximate solution requires at least 10 segments to converge to within 5% of that using the exact solution. The exact solution thus accurately accounts for the effects of exponential taper, and may be used to improve existing arterial models, which use the less accurate and more computationally cumbersome approximate solution.

Anatomy, Cross-Sectional↗

PubMed2002

A transmission line model of the human foetal circulatory system.

A transmission line model of the human foetal circulatory system is presented. The model has been developed in the frequency domain with the cardiac input modeled as a flow rather than as a pressure pulse and is structured upon electrical transmission line analogies. The model is formed by cascading solutions to the two-dimensional Navier-Stokes equations for both oscillatory and steady, laminar viscous fluid flow in isotropic visco-elastic tubes with thick walls, which are constrained by surrounding tissues. Simulations allow for representation of both forward and retrograde travelling flow and pressure waves in all of the main foetal arterial vessels. The solution is verified by a comparison of model generated Doppler indices in the thoracic aorta, abdominal aorta, iliac artery and both ends of the umbilical arteries with previously published indices obtained by clinical measurements in these arteries. For simulations of blood flow in a healthy foetus, the model generated Pulsatility and Resistance indices were on average within 8% of the corresponding clinical measurements. The model results also demonstrates that placental resistance must increase by a factor of three, corresponding to a 60% decrease in flow to the placenta, before umbilical arterial absent end diastolic flow is observed. Differences between indices obtained from simulations at opposite ends of the umbilical arteries increase with increasing placental resistance.

Blood Flow Velocity↗

PubMed2001

Analytical solution for pulsatile axial flow velocity waveforms in curved elastic tubes.

An analytical solution for pulsatile axial flow velocity waveforms in curved elastic tubes is presented. The result is obtained by exact solution of linearized Navier-Stokes and tube motion equations in a torroidal coordinate system. Fourier analysis is used to divide the flow into constant and oscillatory components which are separately considered. The solution is used to investigate the effects of curvature on volumetric axial velocity flow waveforms, as would be measured by Doppler ultrasound techniques. In typical human arteries, the greatest effects of curvature on the volumetric axial flow are exerted on the constant component and at low values of the frequency parameter for the oscillatory components. Here, the magnitude and phase angle of oscillatory flow in the curved tube, relative to that in the straight tube, differ by maximum values of 1.2% and 0.15 rad, respectively. However, constant flow may vary by as much as 60% at high Dean numbers. The solution is presented in a form similar to Womersley's solution for the straight elastic tube and may, thus, be incorporated into a transmission-line analog model. These models are frequently used to investigate axial flow velocity variations in mamillian circulatory systems and this work offers a tool which may extend these models to incorporate the effects of curvature.

Algorithms↗

PubMed1991

The estimation of tube wall compliance using acoustic input impedance.

An acoustic-electric analog and transmission line theory have been used to examine acoustic wave propagation in a tube with a compliant wall. The input impedance (i.e., input pressure-flow) has been simulated using a distributed element model. A relative minimum and maximum, denoted by fr and f2, respectively, that are independent of tube length have been identified theoretically and confirmed experimentally from input impedance measurements on a compliant tube. A method has been devised which uses measured values of fr and f2 to deduce the tube wall properties from the theoretical model. This method has been validated on a tube with known wall properties determined using standard methods. In practice, the input impedance is measured through a short section of rigid connecting pipe. In this case fr remains constant while f2 is reduced. This reduction can be accounted for by the volume compliance of the gas within the lumen of the rigid pipe. The theory could have useful applications such as estimating the wall properties of the airways from noninvasive measurements made through the mouth.

Acoustics↗

PubMed1987

Non-invasive assessment of lower limb ischaemia by blood velocity wave-form analysis.

Clinical examination combined with angiography is conventionally used to assess lower limb arterial disease. The shape of the blood velocity wave form in the common femoral artery varies with the extent of proximal arterial disease, suggesting that wave-form analysis may provide additional haemodynamic information of potential value in surgical decision-making. This paper studies the use of two methods of wave-form analysis, pulsatility index and Laplace transform analysis, to assess lower limb arterial disease. The blood velocity wave form was measured non-invasively at the common femoral artery using a locally developed mean frequency processor and a commercial 9.5 MHz bidirectional Doppler ultrasound unit. Wave forms from 70 limbs (35 patients) with suspected atherosclerotic arterial disease and from 20 normal limbs with no history or signs of disease were studied. Both methods of wave-form analysis provided a statistically significant separation between patients with severe and moderate disease as assessed angiographically (P less than 0.001). These results suggest that significant aorto-iliac disease can be virtually excluded by a normal common femoral wave form. Furthermore, wave-form analysis may have an important role in the follow-up of patients after bypass grafting or iliac angioplasty and in the detection of presymptomatic aorto-iliac disease.

Adult↗

PubMed1986

A system for rapid analysis of the femoral blood velocity waveform at the bedside.

The shape of the arterial blood velocity waveform varies with atherosclerotic disease and several methods of quantifying the shape in order to predict the severity of the disease have been described. These methods include pulsatility index, the Laplace transform method, and principal component analysis. This paper describes the development of a system which allows the operator to acquire, display, and store waveforms from each limb and then to quantify the waveforms at the bedside within a few minutes. The system includes a 10 MHz bi-directional Doppler unit, an instantaneous mean frequency processor, and an Apple II microcomputer fitted with an accelerator card. Both the Laplace transform parameters and the pulsatility index are computed and each result is printed in tabular form together with the averaged results of five waveforms from each limb. The printout is suitable for inclusion in the patient's folder. In initial clinical studies Laplace transform analysis exhibited a good correlation with aorto-iliac stenosis as assessed angiographically (R = 0.73 P less than 0.001 t test).

Angiography↗

PubMedDate not supplied

A transfer function-based mathematical model of the fetal-placental circulation.

The circulation of a human fetus has been modeled using a transfer function that is based on the arterial dimensions at 28 weeks gestational age (GA). These dimensions have then been adapted for growth between 28 and 40 weeks GA. The input to the model is a series of current pulses at the fetal heart rate, where current in the model is analogous to volume blood flow in the fetus. The arterial system is divided into short segments that are cascaded together. The respective transfer functions are based on the dimensions, wall properties and fluid characteristics at each frequency and GA. Bleed off conductances distribute current to circuits representing the various anatomical regions. In particular, the placenta is simplified to a symmetrically distributed network of branching vessels, each represented by a transfer function. All calculations are performed in the frequency domain, after which the inverse Fourier transform is used to calculate the currents that represent the time-domain blood flow waveforms. Simulated flow waveform resistance index and pulsatility index values are within 8% of those reported for human clinical studies, at all gestational ages.

Embryonic and Fetal Development↗