Direct strain estimator for measuring elastic properties of tissue
Ultrasound data of a biological tissue is acquired in a relaxed state and a tensed state. A strain is estimated directly from the relaxed state ultrasound data and the tensed state ultrasound data by way of an imaginary part of a complex correlation function. In estimating the strain, the tensed state ultrasound data is re-stretched, and the imaginary part of the complex correlation function is calculated from this re-stretched ultrasound data and the relaxed state ultrasound data. A slope factor is also calculated, and the strain is estimated from this slope factor and the imaginary part of the complex correlation function.
1. An ultrasound system comprising:
an ultrasound device configured to acquire a pair of ultrasound data sets from a biological tissue, the pair of ultrasound data sets comprising acquired ultrasound data of the biological tissue in a relaxed state and in a tensed state, respectively;
a computer programmed to:
(a) stretch the tensed state ultrasound data set;
(b) calculate an imaginary part of a complex correlation function between the relaxed state ultrasound data set and the stretched tensed state ultrasound data set;
(c) calculate a slope factor (SF) using one of a single set data method, a direct method, and an adaptive method, wherein:
the single set data method is
SF
=
ω
0
R
0
=
ω
0
∫
window
r
~
(
t
)
2
t
ⅆ
t
;
the direct method is SF=ω 0 ·∫ 0 T t·|{tilde over (r)}(t)|·|{tilde over (s)}*(t)|dt; and
the adaptive method is
SF
=
𝔍
{
∫
0
T
r
~
(
t
)
·
r
~
*
(
t
(
1
-
ɛ
0
)
)
ⅆ
t
}
ɛ
0
,
wherein:
ω 0 corresponds to the center frequency of the relaxed state ultrasound data,
R
0
=
∫
window
r
~
(
t
)
2
t
ⅆ
t
,
T corresponds to a length of a correlation window used for strain estimation,
{tilde over (r)}(t) corresponds to an analytic signal version of the relaxed state ultrasound data,
{tilde over (s)}(t) corresponds to an analytic signal version of the tensed state ultrasound data,
{tilde over (r)}* corresponds to a complex conjugate of the relaxed state ultrasound data,
{tilde over (s)}* corresponds to a complex conjugate of the tensed state ultrasound data,
ε 0 corresponds to a defined amount of stretching applied to the relaxed state ultrasound data; and
(d) estimate a strain of the biological tissue from a relationship between the calculated imaginary part and the slope factor.
2. The ultrasound system of claim 1 wherein the computer is further programmed to perform functions (a)-(d) for a pre-determined number of iterations to minimize the imaginary part of the complex correlation function.
3. The ultrasound system of claim 1 wherein the computer is further programmed to calculate a pre-delay for a subsequent correlation window based on the estimated strain.
4. The ultrasound system of claim 3 wherein the computer is further programmed to:
apply the pre-delay to the subsequent correlation window; and
perform functions (a)-(d) for the subsequent correlation window.
5. The ultrasound system of claim 3 wherein the computer is further programmed to perform an initialization, and wherein performing the initialization further comprises:
setting the pre-delay to a value of zero;
setting an initial estimated strain to a value of zero; and
performing functions (a)-(d) in a first iteration for the pre-delay having the value of zero and the initial estimated strain having the value of zero.
6. The ultrasound system of claim 1 wherein the computer is further programmed to adjust a pre-delay based on a correlation coefficient.
7. The ultrasound system of claim 4 wherein the computer is further programmed to calculate the stretched tensed state ultrasound data set by applying the pre-delay and the estimated strain to the tensed state ultrasound data set.
8. The ultrasound system of claim 1 wherein the computer is further programmed to:
set a minimum strain threshold and a maximum strain threshold for the estimated strain; and
perform one of a clipping function, a zeroing function, and an interpolating function on the estimated strain for estimated strains above the maximum strain threshold and below the minimum strain threshold.
9. The ultrasound system of claim 1 wherein the computer is further programmed to:
set a correlation window threshold for a change in the estimated strain from a current correlation window to a subsequent correlation window; and
perform one of a clipping function, a zeroing function, and an interpolating function on the estimated strain if the change in the estimated strain exceeds the correlation window threshold.
10. The ultrasound system of claim 1 wherein the computer is further programmed to:
set a quality coefficient threshold on a quality coefficient; and
perform one of a clipping function, a zeroing function, and an interpolating function on the estimated strain if the quality coefficient is below the quality coefficient threshold, wherein the quality coefficient is one of a correlation value, strain value, location, and strain derivative.
11. The ultrasound system of claim 1 wherein the computer is further programmed to:
filter the estimated strain by at least one of a spatial filtering and a temporal filtering; and
replace the estimated strain with the filtered estimated strain.
12. The ultrasound system of claim 11 wherein the computer is further programmed to weight the filtered estimated strain by a correlation coefficient.
13. The ultrasound system of claim 11 wherein the computer is further programmed to:
set a filtering threshold for a difference between the estimated strain and the filtered estimated strain; and
replace the estimated strain with the filtered estimated strain if the difference between the estimated strain and the filtered estimated strain exceeds the filtering threshold.
14. The ultrasound system of claim 1 wherein the computer is further programmed to retrospectively process the estimated strain to obtain an updated estimated strain based on an initial strain estimate and a pre-delay from a subsequent correlation window.
15. The ultrasound system of claim 1 wherein the computer is further programmed to:
prospectively identify low signal regions in a B-mode image; and
set the estimated strain to a value of zero for the low signal regions.
16. The ultrasound system of claim 1 wherein the computer is further programmed to normalize the relaxed state ultrasound data set and the tensed state ultrasound data set to reduce effect of an amplitude of an ultrasound signal on the estimated strain.
17. A method of determining strain in an elastic tissue comprising:
a) accessing a first set of ultrasound data acquired from the elastic tissue in an unstressed state;
b) accessing a second set of ultrasound data acquired from the elastic tissue in a stressed state;
c) applying a pre-delay and an initial estimated strain to the stressed ultrasound data signal to obtain a re-stressed ultrasound data signal;
d) calculating an imaginary part of a complex correlation function between the unstressed ultrasound data signal and the re-stressed ultrasound data signal;
e) calculating a slope factor using one of a single set data method, a direct method, and an adaptive method, wherein:
the single set data method is
SF
=
ω
0
R
0
=
ω
0
∫
window
r
~
(
t
)
2
t
ⅆ
t
;
the direct method is
SF
=
ω
0
·
∫
0
T
t
·
r
~
(
t
)
·
s
~
*
(
t
)
ⅆ
t
;
and
the adaptive method is
SF
=
𝔍
{
∫
0
T
r
~
(
t
)
·
r
~
*
(
t
(
1
-
ɛ
0
)
)
ⅆ
t
}
ɛ
0
,
wherein:
ω 0 corresponds to the center frequency of the relaxed state ultrasound data,
R
0
=
∫
window
r
~
(
t
)
2
t
ⅆ
t
,
T corresponds to a length of a correlation window used for strain estimation,
{tilde over (r)}(t) corresponds to an analytic signal version of the relaxed state ultrasound data,
{tilde over (s)}(t) corresponds to an analytic signal version of the tensed state ultrasound data,
{tilde over (r)}* corresponds to a complex conjugate of the relaxed state ultrasound data,
{tilde over (s)}* corresponds to a complex conjugate of the tensed state ultrasound data,
ε 0 corresponds to a defined amount of stretching applied to the relaxed state ultrasound data;
f) estimating a local strain of the elastic tissue based on the imaginary part of the complex correlation function and the slope factor;
g) repeating steps (c)-(f) for a pre-determined number of iterations; and
h) calculating a pre-delay for a subsequent correlation window based on the estimated local strain.
18. The method of claim 17 further comprising performing an initialization for the correlation window, wherein performing the initialization further comprises:
setting the pre-delay to a value of zero;
setting the initial estimated strain to a value of zero; and
performing functions (c)-(f) in a first iteration for the pre-delay having the value of zero and the initial estimated strain having the value of zero.
19. The method of claim 17 wherein the repeating of steps (c)-(f) for a pre-determined number of iterations minimizes the imaginary part of the complex correlation function.
20. The method of claim 17 further comprising:
setting at least one of a strain threshold on the estimated strain, a correlation window threshold for a change in the estimated strain from a current correlation window to the subsequent correlation window, and a correlation coefficient threshold on a correlation coefficient; and
performing one of a clipping function, a zeroing function, and an interpolating function on the estimated strain if the at least one of the strain threshold, the correlation window threshold, and the correlation coefficient threshold is crossed.
21. The method of claim 17 further comprising:
filtering the estimated strain based on at least one of a spatial filter and a temporal filter;
setting a filtering threshold for a difference between the estimated strain and the filtered estimated strain;
replacing the estimated strain with the filtered estimated strain if the difference between the estimated strain and the filtered estimated strain exceeds the filtering threshold; and
if the estimated strain is replaced with the filtered estimated strain, weighting the filtered estimated strain by a correlation value.
22. The method of claim 17 further comprising the step of retrospectively processing the estimated strain to obtain an updated estimated strain based on an initial strain estimate and a pre-delay from a subsequent correlation window.
23. The method of claim 17 further comprising the steps of:
prospectively identifying low signal regions in a B-mode image; and
setting the estimated strain to a value of zero for the low signal regions.
24. A non-transient computer readable storage medium having a computer program to adaptively control an ultrasound system for measuring strain in elastic tissue, the computer program representing a set of instructions that when executed by a computer causes the computer to:
a) analyze ultrasound data acquired from the elastic tissue between a stressed state and an unstressed state;
b) apply a pre-delay and an initial estimated strain to the stressed state ultrasound data to obtain re-stressed state ultrasound data;
c) calculate an imaginary part of a complex correlation function between the unstressed state ultrasound data and the re-stressed state ultrasound data;
d) calculate a slope factor using one of a single set data method, a direct method, and an adaptive method, wherein:
the single set data method is
SF
=
ω
0
R
0
=
ω
0
∫
window
r
~
(
t
)
2
t
ⅆ
t
;
the direct method is
SF
=
ω
0
·
∫
0
T
t
·
r
~
(
t
)
·
s
~
*
(
t
)
ⅆ
t
;
and
the adaptive method is
SF
=
𝔍
{
∫
0
T
r
~
(
t
)
·
r
~
*
(
t
(
1
-
ɛ
0
)
)
ⅆ
t
}
ɛ
0
,
wherein:
ω 0 corresponds to the center frequency of the relaxed state ultrasound data,
R
0
=
∫
window
r
~
(
t
)
2
t
ⅆ
t
,
T corresponds to a length of a correlation window used for strain estimation,
{tilde over (r)}(t) corresponds to an analytic signal version of the relaxed state ultrasound data,
{tilde over (s)}(t) corresponds to an analytic signal version of the tensed state ultrasound data,
{tilde over (r)}* corresponds to a complex conjugate of the relaxed state ultrasound data,
{tilde over (s)}* corresponds to a complex conjugate of the tensed state ultrasound data,
ε 0 corresponds to a defined amount of stretching applied to the relaxed state ultrasound data;
e) estimate the local strain based on the imaginary part of a complex correlation function of the acquired ultrasound data between the stressed state and the unstressed state and the slope factor;
f) repeat steps (b)-(e) for a pre-determined number of iterations; and
g) calculate a pre-delay for a subsequent correlation window based on the estimated local strain.
25. The non-transient computer readable storage medium of claim 24 wherein the set of instructions further causes the computer to:
set at least one of a strain threshold, a correlation window threshold, and a correlation coefficient threshold on the estimated strain; and
perform one of a clipping function, a zeroing function, and an interpolating function on the estimated strain if the at least one of the strain threshold, the correlation window threshold, and the correlation coefficient threshold is crossed.
26. The non-transient computer readable storage medium of claim 24 wherein the set of instructions further causes the computer to:
filter the estimated strain by at least one of a spatial filtering and a temporal filtering;
set a filtering threshold for a difference between the estimated strain and the filtered estimated strain; and
replace the estimated strain with the filtered estimated strain if the difference between the estimated strain and the filtered estimated strain exceeds the filtering threshold.
27. The non-transient computer readable storage medium of claim 26 wherein the set of instructions further causes the computer to weight the filtered estimated strain by a correlation coefficient.