Ultrasonic diagnostic imaging with harmonic contrast agents

Abstract

Apparatus and methods are disclosed for the detection and imaging of ultrasonic harmonic contrast agents. The harmonic echo effect is detected through alternate polarity acquisition of harmonic contrast agent effects, which provides the benefits of suppressing the harmonic components of the transmitted signal while eliminating clutter.

Description

where k₁ and k₂ are parametrically related to the acoustic properties of the microbubble such as size, viscosity, surface tension, ambient pressure, etc.

Now assume that the microbubble is excited by two narrow band signals at different times but with the same magnitude p and at the same frequency ω, but with opposite polarity: p_i1=p cos ωt and p_i2=−p cos ωt. Then the back-scattered pressure wave from p_i1=p cos ωt is
p_B1(ω,t)=k₁(ω,t)p+k₂(ω,t)p²  (2)
and from p_i1=−p cos ωt is
p_B2(ω,t+δt)=k₁(ω,t+δt)p+k₂(ω,t+δt)p²  (3)
Then the total backscattered pressure magnitude may be obtained by summing Equations (2) and (3),
S=p_B1+p_B2=(k₁(ω,t)−k₁(ω,t+δt))p+(k₂(ω,t)+k₂(ω,t+δt))p²  (4)
≈2k₂(ω)p²
Equation (4) shows that the primary component is eliminated if k₁(ω) and k₂(ω) do not change substantially in the time duration δt, where δt is small.

Assume the backscattering from microbubbles is quasi-stationary over T, where T is the pulse repetition interval. Therefore, the average nonlinear acoustic properties are not changed over time T, or
E{k₁(ω,t)}≅E{k₁(ω,t+T)}
and
E{k₂(ωt)}≅E{k₂(ω,t+T)}.
The relationship of Equation (4) will hold by summing the pulse echoes from two pulses which are time-diverse in T. The quasi-stationary assumption is valid for slow perfused flow, such as myocardial perfusion.

When the bandwidth of the incident pressure wave is wide, the wideband excitation wave P(t) may be represented by a Fourier series

$P\left(t\right)=\sum _{i}A\left({\omega }_i\right)\cos {\omega }_{i}t$
Thus the backscattered pressure magnitude of the microbubbles from P(t) may be written as

$\begin{array}{cc}{P}_{B1}=\sum _i{k}_1\left({\omega }_i\right)A\left({\omega }_i\right)+\sum _i{k}_2\left({\omega }_i\right)A^2\left({\omega }_i\right)& \left(5\right)\end{array}$
and the backscattered pressure magnitude of the microbubbles from −P(t) may be written as

$\begin{array}{cc}{P}_{B2}=\underset{i}{-\sum }{k}_1\left({\omega }_i\right)A\left({\omega }_i\right)+\sum _i{k}_2\left({\omega }_i\right)A^2\left({\omega }_i\right)& \left(6\right)\end{array}$
Summing Equations (5) and (6), one may obtain

$\begin{array}{cc}S=p_{B1}+p_{B2}=2\sum _i{k}_2\left({\omega }_i\right)A^2\left({\omega }_i\right)& \text{(7)}\end{array}$
Again, the harmonic component is extracted and the primary component is eliminated.

Let us assume the nonlinearity in tissue is negligible. Since the backscattered pressure in a linear medium is linearly proportional to the incident pressure wave, the polarity of the backscattered wave will be changed as the polarity of the incident pressure wave is changed. Assuming the tissue is relatively stationary during the period of two consecutive pulses, summing the pulse echoes from consecutive pulses with opposite polarity will cancel the echo response from tissue. Thus, tissue clutter will be suppressed.

The concept of summing the pulse echoes from two pulses of opposite polarity may be generalized into processing echoes from multiple pulses with alternate polarity to maximize the sensitivity and minimize the variance, assuming the tissue is stationary during the pulsing interval. Let the pulse sequence be
P={p −p p− p p− p * *−p p}
and the pulse echoes be
E={E₁ E₂ E₃ E₄ E₅ E₆ · · · E_n}
Accumulating the partial sum of consecutive pairs of echoes results in

$S=\sum _{j=1}^{n-1}{E}_j+E_{j+1}=2\left(n-1\right)\sum _i{k}_2\left({\omega }_i\right)A^2\left({\omega }_i\right)$

Claims

1. A method of ultrasonically detecting the ultrasonic response of an ultrasonic contrast agent comprising the steps of:

transmitting a first ultrasonic pulse to said ultrasonic contrast agent to cause a first harmonic response;

transmitting a second ultrasonic pulse of a different polarity than said first ultrasonic pulse to said harmonic contrast agent to cause a second harmonic response;

detecting said first and second harmonic responses; and

combining said first and second harmonic responses.

2. The method of claim 1, wherein said step of combining comprises summing said first and second harmonic responses.

3. The method of claim 1, wherein said step of combining comprises integrating said first and second harmonic responses.

4. The method of claim 1, wherein said transmitting step comprises transmitting pulses which exhibit a pulse energy which is within a range which causes microbubbles of said ultrasonic contrast agent to oscillate without substantial microbubble destruction.

5. A method of ultrasonically detecting the nonlinear response of a substance within the body comprising the steps of:

transmitting at least three ultrasonic pulses into the body which exhibit first and second characteristics that cause a reduction in the linear echo response when echoes received in response to such pulses are combined;

receiving echoes in response to said ultrasonic pulses; and

combining said echoes to produce a nonlinear response.

6. The method of claim 5, wherein said step of receiving echoes comprises receiving echoes from a given location in the body.

7. The method of claim 5, wherein said ultrasonic pulses are transmitted in a sequence in which said first and second characteristics are alternated from pulse to pulse.

8. The method of claim 5, wherein said step of combining comprises summing pairs of echoes.

9. The method of claim 5, wherein said ultrasonic pulses are transmitted in a sequence in which said first and second characteristics are alternated from pulse to pulse; and

wherein said step of combining comprises summing pairs of echoes from successive pulses.

10. The method of claim 5, wherein said first and second characteristics comprise first and second polarities.

11. The method of claim 10, wherein said transmitted ultrasonic pulses are of the form {p −p p . . . }.

12. The method of claim 5, wherein said step of combining produces a sum result S which is substantially equal to

13. The method of claim 12, wherein the number of ultrasonic pulses which is transmitted is three.

14. A method of ultrasonically detecting the nonlinear ultrasonic response of a medium inside the body comprising the steps of:

transmitting a first ultrasonic pulse to said medium to cause a first echo response;

transmitting a second ultrasonic pulse to said medium to cause a second echo response;

transmitting a third ultrasonic pulse to said medium to cause a third echo response which is substantially the same as said first echo response; and

combining said first, second and third echo responses to produce a nonlinear response.

15. The method of claim 14, wherein said transmitted ultrasonic pulses are of the form {p −p p}.

16. The method of claim 14, wherein said step of combining produces a sum result S which is substantially equal to

17. A method of ultrasonically detecting the nonlinear response of a substance within the body comprising the steps of:

transmitting at least three ultrasonic pulses into the body in a sequence which is of the form {p −p p −p . . . −p p};

receiving echoes in response to said ultrasonic pulses which comprise a sequence of the form {E₁ E₂ E₃ E₄ . . . E_n-1 E_n}; and

accumulating said echoes to produce a nonlinear response.

18. The method of claim 17, wherein said step of accumulating comprises accumulating pairs of consecutive echoes.

19. The method of claim 17, wherein said step of accumulating produces a sum result S which is substantially equal to

20. A method of ultrasonically detecting the nonlinear response of a substance within the body comprising the steps of:

transmitting a sequence of at least three ultrasonic pulses into the body which exhibit a transmit characteristic which alternates from pulse to pulse;

receiving echoes in response to said ultrasonic pulses; and

combining said echoes to produce a nonlinear response.

21. The method of claim 20, wherein said pulses are transmitted to a given location in the body; and

wherein said step of combining reduces the primary component of said echoes and produces a harmonic response.

22. The method of claim 20, wherein said step of transmitting produces a sequence of echoes relating to a given location in the body in which the phase of the primary component of echoes produced by one transmit characteristic is out of phase with the phase of the primary component of echoes produced by the alternate transmit characteristic.

23. The method of claim 22, wherein said step of combining reduces the primary component of the combined echoes and produces a harmonic response.

24. The method of claim 23, wherein said transmit characteristic is a polarity differential from pulse to pulse.

25. The method of claim 23, wherein said transmit characteristic is a phase differential from pulse to pulse.