Rosemary S. Thompson

Doppler ultrasound waveform indices: A/B ratio, pulsatility index and Pourcelot ratio

Summary. Three different indices, the A/B ratio, the pulsatility index (PI) and the Pourcelot ratio (PR), are in common use for quantitative analysis of umbilical artery Doppler ultrasound waveforms. A detailed examination of the similarities and differences between these indices, together with the expected errors for each, was undertaken to enable informed comparisons and choices to be made. The indices were calculated from 133 last trimester recordings using an objective and very reliable computer analysis technique. The PI is more difficult to calculate than the other two quantities and the extra computation does not provide any extra information. The A/B ratio appears the simplest index to use but the values are not normally distributed. With the PR a normal distribution of values can be assumed. A theoretical consideration of errors showed that none of the indices is intrinsically less error prone for last trimester waveforms overall. The errors in the A/B ratio increase as the value of the index increase, whereas the converse holds for the PI and PR.

Low-dose aspirin therapy improves fetal weight in umbilical placental insufficiency

A randomized, placebo-controlled, double-blind trial was carried out to evaluate the fetal benefits of low-dose aspirin (150 mg/day) as a treatment of placental insufficiency during the last trimester of pregnancy. Forty-six women referred for study because there was concern about fetal welfare were found to have an elevated umbilical artery wave form systolic/diastolic ratio. Mothers with severe hypertension were excluded because fetal condition would not necessarily be the dominant determinant of obstetric decision making. A distinction was made between a high systolic/diastolic ratio (greater than 95th but less than 99.95th percentile) and an extreme systolic/diastolic ratio (greater than 99.95th percentile). There were 34 patients in the high ratio group and 12 in the extreme group. Aspirin therapy was associated with an increase in birth weight (mean difference 526 gm [p less than 0.02]), head circumference (1.7 cm [p less than 0.025]), and placental weight (136 gm [p less than 0.02]) in those patients with a high initial umbilical artery systolic/diastolic ratio. For the 12 women with an extreme initial systolic/diastolic ratio, aspirin therapy did not result in a significantly different pregnancy outcome.

Doppler waveform pulsatility index and resistance, pressure and flow in the umbilical placental circulation: An investigation using a mathematical model

A mathematical model of the umbilical placental circulation was used to examine the effect of different physiological variables on the pulsatility index (PI) of the umbilical artery Doppler waveform. The variables include the umbilical and placental resistances, the volume flow rate and the pressure. In the model the branching structure of the placental villous tree is considered in detail, while each arterial branch is itself represented simply using a resistor and a capacitor. Placental vascular disease is modelled as obliteration of a fraction of the terminal branches of the tree. The model umbilical artery PI depends on the ratio of the placental resistance to the umbilical artery resistance. The PI increases with vascular disease, but the rate of increase is not uniform. Initially, the placental resistance and the PI increase very slowly with vessel obliteration. Once the level of vessel obliteration has reached a large enough value--typically between 60% and 90% obliteration--the PI begins to rise sharply. A larger placental vascular bed can accommodate a greater level of vessel obliteration before this rapid PI rise begins. The umbilical artery PI also depends on the pulsatility of the input (aortic bifurcation) pressure waveform, but blood pressure variations in the physically attainable range cannot account for the very high PI values associated with fetal compromise. Physically attainable pressure waveform changes would, however, enable the fetus with substantial placental vascular disease to maintain umbilical volume flow rate, and at the same time exhibit a raised umbilical artery PI value.

Umbilical artery velocity waveforms: normal reference values for A/B ratio and Pourcelot ratio

Summary. Normal reference values for the umbilical artery Pourcelot ratio and A/B ratio are reported. Thirty‐five normal patients were studied serially from 20 weeks to term. The A/B ratio centilcs were corrected for non‐normality of the underlying distribution by transforming from the Pourcelot ratio values. The correction needed was small during the last trimester, but larger for second trimester data. Of the 35 patients 24 were nulliparous and there was a slight tendency for the waveform indices to be higher in the nulliparae, but the numbers in this study were too small to be conclusive about the effect of parity.

An ODE Model of Early Stages of Atherosclerosis: Mechanisms of the Inflammatory Response

Atherosclerosis is a chronic disease of the large arteries, characterized by fatty cholesterol-filled streaks and plaque build-up within the artery wall. Within the past decade, inflammation has been determined as a crucial factor in all stages of lesion formation, however, many of the mechanisms involved are not yet fully understood. We present a simplified ODE model that explores the role of inflammation in atherosclerosis. The model incorporates two of the main lesion constituents, cholesterol-carrying modified Low Density Lipoproteins (LDLs) and macrophage foam cells. Their complex interactions are combined into general functions, and the long-term model behaviour is investigated through phase plane analysis and simulations. Our results indicate that the underlying mechanisms of macrophage uptake of modified LDL can have a deep impact on the cellular dynamics in the lesion. Our model demonstrates that it is macrophage proliferation and constant signalling to the endothelial cells, rather than an increasing influx of modified LDL, that drives lesion instability.

Effect of a cylindrical refracting interface on ultrasound intensity and the CW Doppler spectrum

The insonation of axisymmetric flow in a tube by an ultrasound beam which is refracted at the tube surface is considered. A three-dimensional (3-D) model for refraction at a cylindrical interface is developed. The incident beam, which is planar but otherwise arbitrary, is refracted at a single acoustic impedance interface between the medium within the tube and the surrounding medium. A ray approximation is used as the ultrasonic wavelength is small compared to the radius of curvature of the tube. A parametric form for the ray paths is obtained and used to derive an expression for the intensity. The intensity depends on the specific position within the tube, as well as the ratio of sound speeds, N, and the Doppler angle /spl theta//sub D/. A diverging (N=1.2, /spl theta//sub D/=45/spl deg/) and a converging (N=0.8, /spl theta//sub D/=45/spl deg/) case are presented in detail. The converging interface results in more extreme intensity distortion. The regions of maximum and minimum intensity over a tube slice are immediately adjacent in both diverging and converging cases. Once the intensity distribution across a tube slice is known, the previously reported (Aldis and Thompson, 1992) volume integral method for the calculation of continuous wave (CW) Doppler spectral power density (spd) functions may be used. The effect of refraction of the incident beam on the spd function is shown for both an infinite beam and a circular beam with radius equal to the tube radius. A curved acoustic impedance interface, as may be encountered in vitro in flow phantoms or in vivo in vascular disease, leads to nonuniform insonation and spectral distortion which depends on transducer orientation.

Acoustic intensity for a long vessel with noncircular cross section

The acoustic intensity distribution around and within long vessels of noncircular cross section was investigated for parameters typical of biomedical ultrasound and blood vessels. We have developed a collocation method for finding the acoustic field when a uniform plane wave is obliquely incident on a long, not necessarily cylindrical, impedance interface. Results are presented for vessels of noncircular cross section and for vessels with thick walls of nonuniform thickness. The intensity in the vicinity of the vessel, throughout the lumen, and in the wall, is calculated for intermediate length scales, i.e., vessel radius and wall thickness in the range 1 to 10 wavelengths. The intensity distribution is an interference pattern, with complicated regions of increased and decreased intensity. These results are compared with approximate intensity obtained using ray theory. Effects not predicted by ray theory and intensity variations that will be significant in any close ultrasonic investigation of these vessels are revealed.

Flow imaging with pulsed Doppler ultrasound and flow phantoms

The use of a multigate profiling system with steady laminar flow in plastic tubes revealed spectral artifacts not previously described. In particular, a double or split profile was often observed. In this paper, these artifacts are related to the dual mode ultrasound propagation in the plastic tube. The propagation speeds and, therefore, refraction angles and propagation paths are different for the longitudinal and the shear wave. The power transmission can be extraordinarily sensitive to small variations in the angle of incidence, and this may combine with the existence of a range of angles of incidence within any focused ultrasound beam to produce spectral distortions. The plastic tube is thus shown equivalent to a selective filter, which diminishes some frequency components in the Doppler spectrum relative to others. The spectral artifacts are explained in terms of the relative power transmitted by each mode, and the degree of beam defocusing experienced by each. Spectral distortions persist even when the beam-to-flow orientation is well away from the critical angle. The results of this study show that it is feasible to understand the acoustic transmission behavior of a flow phantom, based on a knowledge of the material properties, and to demonstrate the usefulness of doing so.

Athero-protective Effects of High Density Lipoproteins (HDL): An ODE Model of the Early Stages of Atherosclerosis

We present an ODE model which we use to investigate how High Density Lipoproteins (HDL) reduce the inflammatory response in atherosclerosis. HDL causes atherosclerotic plaque stabilisation and regression, and is an important potential marker and prevention target for cardiovascular disease. HDL enables cholesterol efflux from the arterial wall, macrophage and foam cell emigration, and has other athero-protective effects. Our basic inflammatory model is augmented to include several different ways that HDL can act in early atherosclerosis. In each case, the action of HDL is represented via a parameter in the model. The long-term model behaviour is investigated through phase plane analysis and simulations. Our results indicate that only HDL-enabled cholesterol efflux can stabilise the internalised lipid content in the lesion so that it does not continue to grow, but this does not reduce macrophage numbers which is required to stabilise the lesion or prevent rupture. HDL-enabled macrophage emigration guarantees lesion stabilisation by maintaining stable macrophage content.

Neural model with probabilistic firing behavior. II. One- and two-neuron networks

Abstract A detailed analysis is undertaken of one- and two-neuron networks of Littles model neurons. A single model neuron can produce a wide range of average output patterns, including spontaneous bursting and tonic firing. The probability distribution of interspike intervals in the model compares well with the various types of experimental interval histograms. We consider some specific examples from the pyloric system of the lobster stomatogastric ganglion. Model neurons are found which reproduce the main features of the output from various pyloric neurons. These are then used to model four distinct types of two-neuron interaction found in the system. Despite the fact that specifying the synaptic connectivity considerably limits the range of possible outputs, it is found that in every case the model can successfully simulate the physical behavior. Further, we show that two reciprocally inhibitory tonic model neurons can generate a clear-cut alternate bursting pattern. It was found that model units with physically significant output always had order (as defined in Part I), but the converse was not true. Finally, the significance of Littles neuron as a basis for the modeling of more complex systems is discussed.