P.A.J. Bascom

Influence of spectral broadening on continuous wave doppler ultrasound spectra: A geometric approach

A model is presented that enables the detailed effects of spectral broadening to be calculated for a continuous wave (CW) Doppler system by using geometric boundary arguments. The model assumes a uniform distribution of isotropic scatterers and treats the transmitter and receiver crystals as incremental sources and receivers. Detailed results for rectangular and circular geometries are presented in order to provide a physical understanding of the manner in which spectral broadening arises. Results are given for the circular geometry, to illustrate the manner in which the received spectrum is affected by the transducer size and distance from the vessel.

Effect of placental resistance, arterial diameter, and blood pressure on the uterine arterial velocity waveform: A computer modeling approach

A computer model was used to simulate velocity waveforms that can be visualized in the human uterine artery using Doppler ultrasound. It was found that increasing uteroplacental vascular resistance from normal caused an increase in the systolic/diastolic velocity ratio (S/D) and pulsatility index (PI) of the waveform. Increasing uteroplacental resistance also caused the appearance of a dicrotic notch. Reducing the uterine artery radius increased the S/D and PI and this effect was accentuated at high placental resistance. In contrast, increasing mean arterial pressure in the uterine artery had little effect on S/D and PI. Results suggest that waveform shape abnormalities observed in obstetric patients with pregnancy-induced hypertension are primarily caused by high uteroplacental vascular resistance and a reduced uterine arterial diameter.

Uterine artery flow velocity waveforms in normal and growth-retarded pregnancies☆

Uterine artery flow velocity waveforms were measured by continuous-wave Doppler ultrasound in 15 normal pregnant women studied from midgestation until term. Results were analyzed by calculation of the pulsatility index and the systolic/diastolic blood velocity [corrected] ratio. Both indices decreased from 16 to 20 weeks (indicating a lowering of resistance) and thereafter remained stable until term. Resistance was lower when waveforms were recorded directly over the placenta or from the uterine artery close to the placenta. A group of women with severe intrauterine growth retardation were also studied. In preeclampsia, uterine artery resistance was increased in almost all patients. In pregnancies complicated by intrauterine growth retardation of non preeclamptic origin, a wide range of results was obtained.

On a fractal packing approach for understanding ultrasonic backscattering from blood

A new theoretical model is proposed to explain the change in the backscattered Doppler power with flow conditions. It defines a fractional packing dimension to represent the manner in which red blood cells are packed and this in turn is related to the variance of the scatterer number density. An explicit expression for the packing factor in terms of the integral of the pair correlation function is presented. Comparison of published experimental results for the backscattered power versus hematocrit with the theoretical model suggests that turbulence reduces the packing dimension. This reduction reflects a modification of the pair correlation function caused by changes in the flow field.

RELATION OF THE FLOW FIELD DISTAL TO A MODERATE STENOSIS TO THE DOPPLER POWER

An experimental investigation was undertaken to establish how different flow regimes affect the Doppler signal. A rigid tube model consisting of a 70% asymmetric area stenosis was used with steady and pulsatile flow conditions. The characteristics of the flow field at various sites was determined using a photochromic flow visualization method. Continuous-wave Doppler measurements were made using a 41% suspension of human red blood cells (RBCs) in saline as well as a dilute suspension of 4% fixed RBCs. For steady flow, the photochromic results indicated that for Reynolds numbers (Re) of 545 and 1410, turbulence was generated and the length of the turbulent region was found to increase with increasing Re. Under pulsatile flow conditions, turbulence was triggered around peak systole and began to dissipate in late deceleration, and by the end of diastole the flow field almost relaminarized. During the turbulent phase of the flow cycle, the poststenotic flow field was seen to consist of four distinct flow regimes similar to those observed for steady flow. For higher Womersley parameters and Reynolds numbers the turbulent zone was found to be larger and to occupy a greater fraction of the flow cycle. These flow visualization results were compared with the Doppler power measurements made at the same locations and under similar flow conditions. At physiological hematocrits (41%) the onset of turbulence for both steady and pulsatile flow increased the backscattered Doppler power. The location of the peak Doppler power coincided with the region of maximum turbulence observed using the photochromic technique.

On the Doppler signal from a steady flow asymmetrical stenosis model : effects of turbulence

A steady flow model with a 70% (by area) asymmetrical stenosis was used to examine how changing flow regimes (laminar to turbulent) affect the Doppler signal. Human red blood cells (RBCs) (Hct = 42%) in saline were employed at a flow rate corresponding to a Reynolds number of approximately 545. A dilute suspension of 4% fixed RBCs was also used for the purpose of backscattered power comparison. Measurements of the Doppler signal enabled the backscattered power, time domain statistics, frequency spectra, frequency domain statistics, various spectral indices, autocorrelation function and decorrelation time to be calculated as a function of distance from the stenosis. It is shown that the characteristics of the Doppler signal measured at each site provide information on the nature of the insonated flow field and these correlate well with those expected. The results demonstrate that the onset of turbulence not only affects the Doppler spectrum but also has a profound effect on the signal power, the decorrelation time and the signal statistics.

Origin of the Doppler ultrasound spectrum from blood

Backscattering of an incident ultrasound beam by blood gives rise to a Doppler spectrum whose characteristics are affected not only by the velocity distribution, but also by certain basic aspects of the red blood cells (RBCs) behavior. Starting from fundamental assumptions, an explicit expression is derived for the Doppler spectrum in terms of the variance in the scatterer number density and the backscattering cross section. This shows that the Doppler power at a given frequency is weighted by the backscattering cross section and the manner in which the RBCs are packed (packing factor). Since spatial variations in the flow field can result in changes in the variance and backscattering cross section, the mean Doppler frequency will not necessarily be proportional to the mean flow through the sample volume. Experimental results for two different flow fields are used to illustrate these effects. The implications of these findings are discussed in relation to volumetric flow estimation and the power mode display used in some color Doppler flow imaging systems.

Interpretation of power changes in Doppler signals from human blood-in vitro studies

Extensive in vitro measurements of the received Doppler power have been made in order to understand the origin of the large power changes that have been previously reported for carotid and umbilical Doppler signals over a cardiac cycle. Variations in the backscattered Doppler power with flow have been investigated using both fixed human red cells at a hematocrit of 4% and heparinized human blood at hematocrits of up to 42%. Measurements were made under both steady and pulsatile flow conditions using a waveform similar to that seen in the carotid artery. A pulsed Doppler system was used to study the power variations at various radial positions in the vessel, while a continuous-wave system provided a measure of the power across the vessel. These studies show that the backscattered power is independent of the flow rate provided that the flow is laminar. However, as the flow rate is increased, it was found that at the onset of turbulence the Doppler power increases and the statistical properties of the signal change. It is also shown that, under normal clinical pulsatile flow conditions, any power change that is observed to occur over the cardiac cycle is unlikely to be caused by changes in flow rate.<<ETX>>

Simulation of red blood cell aggregation in shear flow.

A simulation model has been developed for red blood cell (RBC) aggregation in shear flow. It is based on a description of the collision rates of RBC, the probability of particles sticking together, and the breakage of aggregates by shear forces. The influence of shear rate, hematocrit, aggregate fractal dimension, and binding strength on aggregation kinetics were investigated and compared to other theoretical and experimental results. The model was used to simulate blood flow in a long large diameter tube under steady flow conditions at low Reynolds numbers. The time and spatial distribution of the state of aggregation are shown to be in qualitative agreement with previous B-mode ultrasound studies in which a central region of low echogenicity was noted. It is suggested that the model can provide a basis for interpreting prior measurements of ultrasound echogenicity and may help relate them to the local state of aggregation.

Effects of transducer beam geometry and flow velocity profile on the Doppler power spectrum: A theoretical study

A theoretical model is used to show how the Doppler spectrum for various axisymmetric velocity profiles is affected by beam misalignment and incomplete insonation. Results are presented for both circular and square beam geometries. Moreover, a closed-form expression is derived for the power spectral density received by an on-axis transducer with a Gaussian beam profile. It is shown that the error incurred in measuring the mean Doppler frequency with such a profile will generally be bounded by the results for the circular and square beam geometries. The effects of an ideal high-pass filter on the mean Doppler frequency and the backscattered Doppler power are examined. It is shown that such a filter can introduce large differences in the measured systolic to diastolic power ratios. Finally, theoretical expressions and results are presented for the spectral broadening index (SBI), normalized spectral variance (NSV), coefficient of kurtosis (CK), the coefficient of skewness (CS) as functions of the axisymmetric velocity profile shape assuming complete uniform insonation.