Richard S. C. Cobbold

Improved phase-resolved optical Doppler tomography using the Kasai velocity estimator and histogram segmentation

Significant improvements are reported in the measurable velocity range and tissue motion artefact rejection of a phase-resolved optical coherence tomography and optical Doppler tomography system. Phase information derived from an in-phase and quadrature demodulator is used to estimate the mean blood flow velocity by the Kasai autocorrelation algorithm. A histogram-based velocity segmentation algorithm is used to determine block tissue movement and remove tissue motion artefacts that can be faster or slower in velocity than that of the microcirculation. The minimum detectable Doppler frequency is about 100 Hz, corresponding to a flow velocity resolution of 30 μm/s with an axial-line scanning frequency of 8.05 kHz and a mean phase change measured over eight sequential scans; the maximum detectable Doppler frequency is ±4 kHz (for bi-directional flow) before phase wrap-around.

Pulsatile flow through constricted tubes: an experimental investigation using photochromic tracer methods

A photochromic tracer method has been used to record pulsatile flow velocity profiles simultaneously at three axial locations along a flow channel. Two major advantages of this multiple-trace method are that it enables velocity data to be acquired in an efficient non-invasive manner and that it provides a detailed description of the spatial relationship of the flow field. The latter is found to be particularly useful in the investigation of transitional type flows; for example, in describing coherent flow structures. Studies of the flow patterns in tubes with mild to moderate degrees of vessel constriction were performed using a 2.9 Hz sinusoidal flow superimposed on a steady flow (frequency parameter of 7.5; mean and modulation Reynolds numbers of 575 and 360, respectively). With mild constrictions (

A comparative study and assessment of doppler ultrasound spectral estimation techniques part II: Methods and results

Various alternative spectral estimation methods are examined and compared in order to assess their possible application for real-time analysis of Doppler ultrasound arterial signals. Specifically, five general frequency domain models are examined, including the periodogram, the general autoregressive moving average (ARMA) model which has the autoregressive (AR) and moving average (MA) models as special cases, and Capons maximum likelihood spectral model. A stimulated stationary Doppler signal with a known theoretical spectrum was used as the reference test sequence, and white noise was added to enable various signal/noise conditions to be created. The performance of each method representative of each spectral model was assessed using both qualitative and quantitative schemes that convey information related to the bias and variance of the spectral estimates. Three integrated performance indices were implemented for quantitative analysis. The relative computational complexity for each algorithm was also investigated. Our results indicate that both the AR(Yule-Walker) and ARMA(singular value decomposition) models of orders (8) and (4,4), respectively, show good agreement with the theoretical spectrum, and yield estimates with variances considerably less than the Fast Fourier Transform (FFT). Preliminary results obtained with these methods using a clinical, non-stationary Doppler signal supports these observations.

A unified approach to modeling the backscattered Doppler ultrasound from blood

A unified approach to modeling the backscattered Doppler ultrasound signal from blood is presented. The approach consists of summing the contributions from elemental acoustic voxels, each containing many red blood cells (RBCs). For an insonified region that is large compared to a wavelength, it is shown that the Doppler signal is a Gaussian random process that arises from fluctuation scattering, which implies that the backscattered power is proportional to the variance of local RBC concentrations. As a result, some common misconceptions about the relationship between the backscattering coefficient and hematocrit can be readily resolved. The unified approach was also used to derive a Doppler signal simulation model which shows that, regardless of flow condition, the power in the Doppler frequency spectrum is governed by the exponential distribution. For finite beamwidth and paraxial flow, it is further shown that the digitized Doppler signal can be modeled by a moving average random process whose order is determined by the signal sampling rate as well as the flow velocity profile.<<ETX>>

Modeling of nonlinear ultrasound propagation in tissue from array transducers

A computationally efficient model capable of simulating finite-amplitude ultrasound beam propagation in water and in tissue from phased linear arrays and other transducers of arbitrary quasiplanar geometry is described. It is based on a second-order operator splitting approach [Tavakkoli et al., J. Acoust. Soc. Am. 104, 2061-2072 (1998)], with a fractional step-marching scheme, whereby the effects of diffraction, attenuation, and nonlinearity can be computed independently over incremental steps. This approach is an extension to that of Christopher and Parker [J. Acoust. Soc. Am. 90, 507-521; 90, 488-499 (1991)], wherein linear and nonlinear effects are propagated separately over incremental steps, and the computation of the diffractive substeps are based on an angular spectrum technique with a modified sampling scheme for accurate and efficient implementation of diffractive propagation from nonradially symmetric sources. Results of the model are compared with published data. Predicted field profiles for nonlinear propagation in tissue from realistic array transducers using the pulse inversion method are presented.

A Stochastic Model of the Backscattered Doppler Ultrasound from Blood

A stochastic model of the continuous wave (CW) Doppler ultrasound signal backscattered from blood is developed. The model incorporates the effects due to the flow-dependent packing and aggregation of red blood cells (RBCs) at a given hematocrit. The Doppler signal is shown to be a zero-mean, stationary, Gaussian random process which can be completely specified by its autocorrelation function. From the autocorrelation function, explicit closed-form expressions are derived for the power spectral density and the backscattering coefficient. Both expressions are found to be more general than those derived from previous blood models. Further, the values of the statistical parameters in the model are discussed in relation to recently published data on the backscattering coefficient of bovine RBCs suspended in saline and of bovine whole blood. It is shown that the change in backscatter with flow conditions can be explained by RBC orientation in saline and by RBC aggregation in whole blood.

A comparative study and assessment of doppler ultrasound spectral estimation techniques part I: Estimation methods

When compared to the classical Discrete Fourier Transform (DFT) or Fast Fourier Transform (FFT) approach, modern estimation methods offer the potential for achieving significant improvements in estimating the power density spectrum of Doppler ultrasound signals. Such improvements, for example, might enable minor flow disturbances to be detected, thereby improving the sensitivity in arterial disease assessment. Specifically, reduction in the variance and bias can be achieved, and this may enable disturbed flow to be detected in a more sensitive manner. The approach taken here, is to consider spectral estimation methods as a problem of fitting an assumed model to the Doppler signal. The models described assume that the signal is stationary. Since the Doppler signal is generally nonstationary, it is assumed that a short enough time window interval can be chosen over which the signal can be considered stationary. We shall review the various methods and when appropriate, relate them to the nature of the Doppler signal.

Speckle in Continuous Wave Doppler Ultrasound Spectra: A Simulation Study

The statistical properties of continuous wave (CW) Doppler ultrasound signals are investigated. First, the analysis of some Doppler data obtained from a human carotiadr tery is reported. Based on the chi-square test, it was found that for each of seven recorded cardiac cycles, the amplitude histogram of a stationary signal segment of a duration of 10 ms around peak systole satisfies the Gaussian hypothesis. Second, it is shown that the Doppler signal, wihs i cehv idently a band-limited Gaussian noise, can be synthesized on a computer using a sinusoidal model. The statistical behavior of the synthesized signals in both the time and the frequency domains, are shown to be in close agreement with the Doppler signals observed over a IO-ms interval around peak systole. This work has led to an understanding of the structure of the conventional grey-scale Doppler spectrogram, particularly its granular structure, which has been likened to the speckle seen in ultrasound B-mode images. Finally, some potential applications of the simulation model are discussed.

A numerical simulation of flow in a two-dimensional end-to-side anastomosis model.

In order to understand the possible role that hemodynamic factors may play in the pathogenesis of distal anastomotic intimal hyperplasia, we carried out numerical simulations of the flow field within a two-dimensional 45 degree rigid-walled end-to-side model anastomosis. The numerical code was tested and compared with experimental (photochromic dye tracer) studies using steady and near-sinusoidal waveforms, and agreement was generally very good. Using a normal human superficial femoral artery waveform, numerical simulations indicated elevated instantaneous wall shear stress magnitudes at the toe and heel of the graft-host junction and along the host artery bed. These sites also experienced highly variable wall shear stress behavior over the cardiac cycle, as well as elevated spatial gradients of wall shear stress. These observations provide additional evidence that intimal hyperplasia may be correlated to wall shear stresses over the cardiac cycle, high wall shear stress gradients, or a combination of the three. The limitations of the present work (especially in regard to the two-dimensional nature of the flow simulations) are discussed, and results are compared to previous observations about distal anastomotic intimal hyperplasia.

Sources of error in maximum velocity estimation using linear phased-array Doppler systems with steady flow.

Using linear-array Doppler ultrasound (US) transducers, the measured maximum velocity may be in error and lead to incorrect clinical diagnosis. This study investigates the existence and cause of maximum velocity estimation errors for steady flow of a blood-mimicking fluid in a tissue-mimicking phantom. A specially designed system was used that enabled fine control of flow rate, transducer positioning and transducer angle relative to the flow phantom. Doppler machine settings (transducer aperture size, focal depth, beam-steering, gain) were varied to investigate a wide range of clinical applications. To estimate the maximum velocity, a new signal-to-noise ratio (SNR) independent method was developed to calculate the maximum frequency from an ensemble averaged Doppler power spectrum. This enabled the impact of each factor on the total Doppler error to be determined. When using the new maximum frequency estimator, it was found that the effect of transducer focal depth, intratransducer, intramachine, intermachine (that was tested) and beam-steering did not significantly contribute to maximum velocity estimation errors. Instead, it was the dependence of the maximum velocity on the Doppler angle that made, by far, the greatest contribution to the estimation error. Because our maximum frequency estimator took into account the effect of intrinsic spectral broadening, the degree of overestimation error was not as great as that previously published. Thus, the effects of Doppler angle and intrinsic spectral broadening are the chief sources of Doppler US error and should be the focus of future efforts to improve the accuracy.