Doppler echocardiography

Doppler echocardiography
Doppler echocardiography
	Mitral valve
MeSH	D015150
OPS-301 code	3-052
	[ edit on Wikidata]

Last updated December 09, 2023

Doppler echocardiography is a procedure that uses Doppler ultrasonography to examine the heart.^[1] An echocardiogram uses high frequency sound waves to create an image of the heart while the use of Doppler technology allows determination of the speed and direction of blood flow by utilizing the Doppler effect.

An echocardiogram can, within certain limits, produce accurate assessment of the direction of blood flow and the velocity of blood and cardiac tissue at any arbitrary point using the Doppler effect. One of the limitations is that the ultrasound beam should be as parallel to the blood flow as possible. Velocity measurements allow assessment of cardiac valve areas and function, any abnormal communications between the left and right side of the heart, any leaking of blood through the valves (valvular regurgitation), calculation of the cardiac output and calculation of E/A ratio ^[2] (a measure of diastolic dysfunction). Contrast-enhanced ultrasound-using gas-filled microbubble contrast media can be used to improve velocity or other flow-related medical measurements.

An advantage of Doppler echocardiography is that it can be used to measure blood flow within the heart without invasive procedures such as cardiac catheterization.

In addition, with slightly different filter/gain settings, the method can measure tissue velocities by tissue Doppler echocardiography. The combination of flow and tissue velocities can be used for estimating left ventricular filling pressure, although only under certain conditions.^[3]

Although "Doppler" has become synonymous with "velocity measurement" in medical imaging, in many cases it is not the frequency shift (Doppler shift) of the received signal that is measured, but the phase shift (when the received signal arrives). However, the calculation result will end up identical.

This procedure is frequently used to examine children's hearts for heart disease because there is no age or size requirement.

2D Doppler imaging

Unlike 1D Doppler imaging, which can only provide one-dimensional velocity and has dependency on the beam to flow angle,^[4] 2D velocity estimation using Doppler ultrasound is able to generate velocity vectors with axial and lateral velocity components. 2D velocity is useful even if complex flow conditions such as stenosis and bifurcation exist. There are two major methods of 2D velocity estimation using ultrasound: Speckle tracking and crossed beam Vector Doppler, which are based on measuring the time shifts and phase shifts respectively.^[5]

Vector Doppler

Vector Doppler is a natural extension of the traditional 1D Doppler imaging based on phase shift. The phase shift is found by taking the autocorrelation between echoes from two consecutive firings.^[6] The main idea of Vector Doppler is to divide the transducer into three apertures: one at the center as the transmit aperture and two on each side as the receive apertures. The phase shifts measured from left and right apertures are combined to give the axial and lateral velocity components. The positions and the relative angles between apertures need to be tuned according to the depth of the vessel and the lateral position of the region of interest.^[5]

Speckle tracking

Speckle tracking, which is a well-established method in video compression and other applications, can be used to estimate blood flow in ultrasound systems. The basic idea of speckle tracking is to find the best match of a certain speckle from one frame within a search region in subsequent frames.^[5] The decorrelation between frames is one of the major factors degrading its performance. The decorrelation is mainly caused by the different velocity of pixels within a speckle, as they do not move as a block. This is less severe when measuring the flow at the center, where the changing rate of the velocity is the lowest. The flow at the center usually has the largest velocity magnitude, called "peak velocity". It is the most needed information in some cases, such as diagnosing stenosis.^[7] There are mainly three methods of finding the best match: SAD (Sum of absolute difference), SSD (Sum of squared difference) and Cross correlation. Assume $X_{0}(i,j)$ is a pixel in the kernel and $X_{1}(i+\alpha ,j+\beta )$ is the mapped pixel shifted by $(\alpha ,\beta )$ in the search region.^[8]

SAD is calculated as: $D(\alpha ,\beta )=\sum _{i=1}\sum _{j=1}|X_{0}(i,j)-X_{1}(i+\alpha ,j+\beta )|$

SSD is calculated as: $D(\alpha ,\beta )=\sum _{i=1}\sum _{j=1}(X_{0}(i,j)-X_{1}(i+\alpha ,j+\beta ))^{2}$

Normalized cross correlation coefficient is calculated as: $\rho (\alpha ,\beta )={\frac {\sum _{i=1}\sum _{j=1}(X_{0}(i,j)-{\bar {X_{0}}})(X_{1}(i+\alpha ,j+\beta )-{\bar {X_{1}}})}{\sqrt {(\sum _{i=1}\sum _{j=1}(X_{0}(i,j)-{\bar {X_{0}}})^{2})(\sum _{i=1}\sum _{j=1}(X_{1}(i+\alpha ,j+\beta )-{\bar {X_{1}}})^{2})}}}$

where ${\bar {X_{0}}}$ and ${\bar {X_{1}}}$ are the average values of $X_{0}(i,j)$ and $X_{1}(i,j)$ respectively. The $(\alpha ,\beta )$ pair that gives the lowest D for SAD and SSD, or the largest ρ for the cross correlation, is selected as the estimation of the movement. The velocity is then calculated as the movement divided by the time difference between the frames. Usually, the median or average of multiple estimations is taken to give more accurate result.^[8]

Sub pixel accuracy

In ultrasound systems, lateral resolution is usually much lower than the axial resolution. The poor lateral resolution in the B-mode image also results in poor lateral resolution in flow estimation. Therefore, sub pixel resolution is needed to improve the accuracy of the estimation in the lateral dimension. In the meantime, we could reduce the sampling frequency along the axial dimension to save computations and memories if the sub pixel movement is estimated accurately enough. There are generally two kinds of methods to obtain the sub pixel accuracy: interpolation methods, such as parabolic fit, and phase based methods in which the peak lag is found when the phase of the analytic cross correlation function crosses zero.^[9]

Interpolation method (parabolic fit)

As shown in the right figure, parabolic fit can help find the real peak of the cross correlation function. The equation for parabolic fit in 1D is:^[4] $k_{int}=k_{s}-{\frac {(R_{12}(k_{s}+1)-R_{12}(k_{s}-1))}{2(R_{12}(k_{s}+1)-2R_{12}(k_{s})+R_{12}(k_{s}-1))}}$

where $R_{12}$ is the cross correlation function and $k_{s}$ is the originally found peak. $k_{int}$ is then used to find the displacement of scatterers after interpolation. For the 2D scenario, this is done in both the axial and lateral dimensions. Some other techniques can be used to improve the accuracy and robustness of the interpolation method, including parabolic fit with bias compensation and matched filter interpolation.^[10]

Phase based method

The main idea of this method is to generate synthetic lateral phase and use it to find the phase that crosses zero at the peak lag.^[9]

The right figure illustrates the procedure of creating the synthetic lateral phase, as a first step. Basically, the lateral spectrum is split in two to generate two spectra with nonzero center frequencies. The cross correlation is done for both the up signal and down signal, creating $R_{up}$ and $R_{down}$ respectively.^[9] The lateral correlation function and axial correlation function are then calculated as follows: $R_{lateral}=R_{up}*R_{down}^{*};R_{axial}=R_{up}*R_{down}$

where $R_{down}^{*}$ is the complex conjugate of $R_{down}$ .

They have the same magnitude, and the integer peak is found using traditional cross correlation methods. After the integer peak is located, a 3 by 3 region surrounding the peak is then extracted with its phase information. For both the lateral and axial dimensions, the zero crossings of a one-dimensional correlation function at the other dimension’s lags are found, and a linear least squares fitted line is created accordingly. The intersection of the two lines gives the estimate of the 2D displacement.^[9]

Comparison between vector Doppler and speckle tracking

Both methods could be used for 2D Velocity Vector Imaging, but Speckle Tracking would be easier to extend to 3D. Also, in Vector Doppler, the depth and resolution of the region of interest are limited by the aperture size and the maximum angle between the transmit and receive apertures, while Speckle Tracking has the flexibility of alternating the size of the kernel and search region to adapt to different resolution requirement. However, vector Doppler is less computationally complex than speckle tracking.^{[ citation needed ]}

Volumetric flow estimation

Velocity estimation from conventional Doppler requires knowledge of the beam-to-flow angle (inclination angle) to produce reasonable results for regular flows and does a poor job of estimating complex flow patterns, such as those due to stenosis and/or bifurcation. Volumetric flow estimation requires integrating velocity across the vessel cross-section, with assumptions about the vessel geometry, further complicating flow estimates. 2D Doppler data can be used to calculate the volumetric flow in certain integration planes.^[11] The integration plane is chosen to be perpendicular to the beam, and Doppler power (generated from power Doppler mode of Doppler ultrasound) can be used to differentiate between the components that are inside and outside the vessel. This method does not require prior knowledge of the Doppler angle, flow profile and vessel geometry.^[11]

Promise of 3D

Until recently, ultrasound images have been 2D views and have relied on highly-trained specialists to properly orient the probe and select the position within the body to image with only few and complex visual cues. The complete measurement of 3D velocity vectors makes many post-processing techniques possible. Not only is the volumetric flow across any plane measurable, but also, other physical information such as stress and pressure can be calculated based on the 3D velocity field. However, it is quite challenging to measure the complex blood flow to give velocity vectors, due to the fast acquisition rate and the massive computations needed for it. Plane wave technique is thus promising as it can generate very high frame rate.^[12]

Related Research Articles

Rayleigh fading is a statistical model for the effect of a propagation environment on a radio signal, such as that used by wireless devices.

The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems by minimizing the sum of the squares of the residuals made in the results of each individual equation.

In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the gamma distribution. There are two equivalent parameterizations in common use:

With a shape parameter $and a scale parameter .$
With a shape parameter $and an inverse scale parameter, called a rate parameter.$

Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices.

The Gauss–Newton algorithm is used to solve non-linear least squares problems, which is equivalent to minimizing a sum of squared function values. It is an extension of Newton's method for finding a minimum of a non-linear function. Since a sum of squares must be nonnegative, the algorithm can be viewed as using Newton's method to iteratively approximate zeroes of the components of the sum, and thus minimizing the sum. In this sense, the algorithm is also an effective method for solving overdetermined systems of equations. It has the advantage that second derivatives, which can be challenging to compute, are not required.

In statistics, the coefficient of determination, denoted R² or r² and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s).

In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable in the input dataset and the output of the (linear) function of the independent variable.

The principle of detailed balance can be used in kinetic systems which are decomposed into elementary processes. It states that at equilibrium, each elementary process is in equilibrium with its reverse process.

In statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared estimate of errors (SSE), is the sum of the squares of residuals. It is a measure of the discrepancy between the data and an estimation model, such as a linear regression. A small RSS indicates a tight fit of the model to the data. It is used as an optimality criterion in parameter selection and model selection.

In statistics, simple linear regression (SLR) is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable and finds a linear function that, as accurately as possible, predicts the dependent variable values as a function of the independent variable. The adjective simple refers to the fact that the outcome variable is related to a single predictor.

Cochrane–Orcutt estimation is a procedure in econometrics, which adjusts a linear model for serial correlation in the error term. Developed in the 1940s, it is named after statisticians Donald Cochrane and Guy Orcutt.

In statistics, semiparametric regression includes regression models that combine parametric and nonparametric models. They are often used in situations where the fully nonparametric model may not perform well or when the researcher wants to use a parametric model but the functional form with respect to a subset of the regressors or the density of the errors is not known. Semiparametric regression models are a particular type of semiparametric modelling and, since semiparametric models contain a parametric component, they rely on parametric assumptions and may be misspecified and inconsistent, just like a fully parametric model.

Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations. There are many similarities to linear least squares, but also some significant differences. In economic theory, the non-linear least squares method is applied in (i) the probit regression, (ii) threshold regression, (iii) smooth regression, (iv) logistic link regression, (v) Box–Cox transformed regressors ( $).$

The Vortex lattice method, (VLM), is a numerical method used in computational fluid dynamics, mainly in the early stages of aircraft design and in aerodynamic education at university level. The VLM models the lifting surfaces, such as a wing, of an aircraft as an infinitely thin sheet of discrete vortices to compute lift and induced drag. The influence of the thickness and viscosity is neglected.

The purpose of this page is to provide supplementary materials for the ordinary least squares article, reducing the load of the main article with mathematics and improving its accessibility, while at the same time retaining the completeness of exposition.

<span class="mw-page-title-main">Speckle tracking echocardiography</span>

In the fields of cardiology and medical imaging, speckle tracking echocardiography (STE) is an echocardiographic imaging technique. It analyzes the motion of tissues in the heart by using the naturally occurring speckle pattern in the myocardium.

The multivariate stable distribution is a multivariate probability distribution that is a multivariate generalisation of the univariate stable distribution. The multivariate stable distribution defines linear relations between stable distribution marginals. In the same way as for the univariate case, the distribution is defined in terms of its characteristic function.

Tissue Doppler echocardiography (TDE) is a medical ultrasound technology, specifically a form of echocardiography that measures the velocity of the heart muscle (myocardium) through the phases of one or more heartbeats by the Doppler effect of the reflected ultrasound. The technique is the same as for flow Doppler echocardiography measuring flow velocities. Tissue signals, however, have higher amplitude and lower velocities, and the signals are extracted by using different filter and gain settings. The terms tissue Doppler imaging (TDI) and tissue velocity imaging (TVI) are usually synonymous with TDE because echocardiography is the main use of tissue Doppler.

Conditional logistic regression is an extension of logistic regression that allows one to account for stratification and matching. Its main field of application is observational studies and in particular epidemiology. It was devised in 1978 by Norman Breslow, Nicholas Day, Katherine Halvorsen, Ross L. Prentice and C. Sabai. It is the most flexible and general procedure for matched data.

<span class="mw-page-title-main">Strain rate imaging</span>

Strain rate imaging is a method in echocardiography for measuring regional or global deformation of the myocardium. The term "deformation" refers to the myocardium changing shape and dimensions during the cardiac cycle. If there is myocardial ischemia, or there has been a myocardial infarction, in part of the heart muscle, this part is weakened and shows reduced and altered systolic function. Also in regional asynchrony, as in bundle branch block, there is regional heterogeneity of systolic function. By strain rate imaging, the simultaneous function of different regions can be displayed and measured. The method was first based on colour tissue Doppler. by using the longitudinal myocardial velocity gradient, already in use transmurally. Later, the regional deformation has also been available by speckle tracking echocardiography, both methods having some, but different methodological weaknesses. Both methods, however, will acquire the same data, and also can be displayed by the same type of display.

References

↑ "Echocardiogram". MedlinePlus . Retrieved 2017-12-15.
↑ Abdul Latif Mohamed, Jun Yong, Jamil Masiyati, Lee Lim, Sze Chec Tee. The Prevalence Of Diastolic Dysfunction In Patients With Hypertension Referred For Echocardiographic Assessment of Left Ventricular Function. Malaysian Journal of Medical Sciences, Vol. 11, No. 1, January 2004, pp. 66-74
↑ Ommen, S. R.; Nishimura, R. A.; Appleton, C. P.; Miller, F. A.; Oh, J. K.; Redfield, M. M.; Tajik, A. J. (10 October 2000). "Clinical Utility of Doppler Echocardiography and Tissue Doppler Imaging in the Estimation of Left Ventricular Filling Pressures : A Comparative Simultaneous Doppler-Catheterization Study". Circulation. 102 (15): 1788–1794. doi: 10.1161/01.CIR.102.15.1788 . PMID 11023933 . Retrieved 12 July 2012.
1 2 J. A. Jensen, Estimation of Blood Velocities Using Ultrasound, A Signal Processing Approach, New York: Cambridge University Press, 1996.
1 2 3 P. S. a. L. L. Abigail Swillens, "Two-Dimensional Blood Velocity Estimation With Ultrasound: Speckle Tracking Versus Crossed-Beam Vector Doppler Based on Flow Simulations in a Carotid Bifurcation Model," IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, pp. 327-338, 2010.
↑ R. S. C. Cobbold, Foundations of Biomedical Ultrasound, Oxford University Press, 2007.
↑ G. Reutern, M. Goertler, N. Bornstein, M. Sette, D. Evans, A. Hetzel, M. Kaps, F. Perren, A. Razumovky, T. Shiogai, E. Titianova, P. Traubner, N. Venketasubramanian, L. Wong and M. Yasaka, "Grading Carotid Stenosis Using Ultrasonic Methods," Stroke, Journal of the American Heart Association, vol. 43, pp. 916-921, 2012.
1 2 J. Luo and E. E. Konofagou, "A Fast Motion and Strain Estimation," in Ultrasound Symposium, 2010.
1 2 3 4 X. Chen, M. J. Zohdy, S. Y. Emelianov and M. O'Donnell, "Lateral Speckle Tracking Using Synthetic Lateral Phase," IEEE Transactions on Ultrasonics, Ferroelectrcs and Frequency Control, vol. 51, no. 5, pp. 540-550, 2004.
↑ X. Lai and H. Torp, "Interpolation Methods for Time-Delay Estimation Using Cross-Correlation Method for Blood Velocity Measurement," IEEE Transactions on Ultrasonics, Ferroelectrcs and Frequency Control, vol. 46, no. 2, pp. 277-290, 1999.
1 2 M. Richards, O. Kripfgans, J. Rubin, A. Hall and J. Fowlkes, "Mean Volume Flow Estimation in Pulsatile Flow Conditions," Ultrasound in Med. & Biol., vol. 35, pp. 1880-1891, 2009.
↑ J. Udesen, F. Gran, K. Hansen, J. Jensen, C. Thomsen and M. Nielsen, "High Frame Rate Blood Vector Velocity Imaging Using Plane Waves: Simulations and Preliminary Experiments," IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 55, no. 8, pp. 1729-1743, 2008.

External links

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[1] "Echocardiogram". MedlinePlus . Retrieved 2017-12-15.

[Mohamed-2] Abdul Latif Mohamed, Jun Yong, Jamil Masiyati, Lee Lim, Sze Chec Tee. The Prevalence Of Diastolic Dysfunction In Patients With Hypertension Referred For Echocardiographic Assessment of Left Ventricular Function. Malaysian Journal of Medical Sciences, Vol. 11, No. 1, January 2004, pp. 66-74

[3] Ommen, S. R.; Nishimura, R. A.; Appleton, C. P.; Miller, F. A.; Oh, J. K.; Redfield, M. M.; Tajik, A. J. (10 October 2000). "Clinical Utility of Doppler Echocardiography and Tissue Doppler Imaging in the Estimation of Left Ventricular Filling Pressures : A Comparative Simultaneous Doppler-Catheterization Study". Circulation. 102 (15): 1788–1794. doi: 10.1161/01.CIR.102.15.1788 . PMID 11023933 . Retrieved 12 July 2012.

[JAJ-4] 1 2 J. A. Jensen, Estimation of Blood Velocities Using Ultrasound, A Signal Processing Approach, New York: Cambridge University Press, 1996.

[PSA-5] 1 2 3 P. S. a. L. L. Abigail Swillens, "Two-Dimensional Blood Velocity Estimation With Ultrasound: Speckle Tracking Versus Crossed-Beam Vector Doppler Based on Flow Simulations in a Carotid Bifurcation Model," IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, pp. 327-338, 2010.

[RSC-6] R. S. C. Cobbold, Foundations of Biomedical Ultrasound, Oxford University Press, 2007.

[GRM-7] G. Reutern, M. Goertler, N. Bornstein, M. Sette, D. Evans, A. Hetzel, M. Kaps, F. Perren, A. Razumovky, T. Shiogai, E. Titianova, P. Traubner, N. Venketasubramanian, L. Wong and M. Yasaka, "Grading Carotid Stenosis Using Ultrasonic Methods," Stroke, Journal of the American Heart Association, vol. 43, pp. 916-921, 2012.

[JLE-8] 1 2 J. Luo and E. E. Konofagou, "A Fast Motion and Strain Estimation," in Ultrasound Symposium, 2010.

[XCM-9] 1 2 3 4 X. Chen, M. J. Zohdy, S. Y. Emelianov and M. O'Donnell, "Lateral Speckle Tracking Using Synthetic Lateral Phase," IEEE Transactions on Ultrasonics, Ferroelectrcs and Frequency Control, vol. 51, no. 5, pp. 540-550, 2004.

[XLH-10] X. Lai and H. Torp, "Interpolation Methods for Time-Delay Estimation Using Cross-Correlation Method for Blood Velocity Measurement," IEEE Transactions on Ultrasonics, Ferroelectrcs and Frequency Control, vol. 46, no. 2, pp. 277-290, 1999.

[MRO-11] 1 2 M. Richards, O. Kripfgans, J. Rubin, A. Hall and J. Fowlkes, "Mean Volume Flow Estimation in Pulsatile Flow Conditions," Ultrasound in Med. & Biol., vol. 35, pp. 1880-1891, 2009.

[12] J. Udesen, F. Gran, K. Hansen, J. Jensen, C. Thomsen and M. Nielsen, "High Frame Rate Blood Vector Velocity Imaging Using Plane Waves: Simulations and Preliminary Experiments," IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 55, no. 8, pp. 1729-1743, 2008.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]