experimental validation of a power doppler performance model.pdf

8/14/2019 Experimental validation of a power Doppler performance model.pdf

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so that (in 1D) zb( x,t ) = zb( x-vt ). We also consider thatthe blood can decorrelate over time, so that the

autocorrelation has some temporal decay profile.

Decorrelation over time may be due to a number of

effects such as intra-pulse type motions of blood

scatterers [4].

III. IDEAL OBSERVER

In [2], a model for the performance of the optimal

Bayesian detection system was described.

Large Ensemble Size: When a large ensemble size is

used, a block-circulant approximation can be made,

which means that Fourier-approximations are

reasonable. In this case the ideal observer signal-to-

noise ratio expressed in the frequency domain is:

∑∫ = +

= L

k k nk c

k b

GNEQ

f S f S H

f S H d SNR

1

2

2

2

),(),()(

),()(

uuu

uuu (2)

where S c and S b are the clutter and blood object powerspectra, S n is the noise power spectrum, H (u) is the

(fast time) Fourier transform of the pulse. In words,

Eq. 2 tells us that the PD detectability is determined

by the ratio of blood power spectral energy (speckle

energy) over spectral energy due to electronic noiseand the clutter speckle. Coherent velocity and

decorrelation shift energy away from the clutter

region, giving improved detectability.

Limited Ensemble Size: Often, ultrasound systems use

only 4-20 pulses and the large ensembleapproximation is inadequate. Here we consider the

case where the clutter is motionless (noise-limited

detection) and does not decorrelate. In this case

+Γ

+= ∫ L H

S

S

S S H L

S H d SNR

n

c

nc

Z

I b )()(

)(

)()(

)()( 2

2

2

2uu

u

uu

uuu (3)

where all temporal information has been integrated

into the factor Γ , which describes everything about

the blood motion and decorrelation. Consider that

blood has coherent velocity v b, and decorrelates with

a decaying exponential trend over slow timet

e ∆−α

.

Then

−−−=Γ ∑=

L

m

mam L L L

1

)(Re2)1()(u , (4)

where bt it eea

vu⋅∆−∆−= π α 2. The dot product between

u and v b acts to select how the system angular

spectrum H (u) will weight different flow velocities. Γ

vanishes when there is no motion or decorrelation – aproblem discussed in [5] for B-mode lesion detection.

IV. MODEL PREDICTIONS AND VALIDATION

Fig. 1 shows model predictions considering a 1D

imaging system. As coherent velocity is increased,the blood spectral energy shifts away from the clutter

region at which point detection performance plateaus.

At twice the aliasing frequency (250 mm/s), blood

power is aliased over the wall filter and detectability

drops, as predicted in Fig. 1(a) and demonstrated

experimentally in Fig. 2.

Decorrelation actually helps rather than hinders

detection, which is in contrast to color flow

techniques for which coherence is important. When

attempting to detect a slowly decorrelating process

such as organ perfusion, detection sensitivity

increases with increasing PRF [Fig. 1(b)]. Also,longer PRI’s are less sensitive to variations in flow

rates, since statistically independent measurements

are obtained at each pulse transmission.

0 100 200 300 400 5000

5

10

15

velocity mm/s

S N R

(a)

0 0.002 0.004 0.006 0.008 0.010

5

10

15

PRI

S N R

(b)

Fig. 1. Ideal observer SNR as a function of (a)

velocity and (b) PRI. In (a) detectability drops at

twice the aliasing velocity. Plot (b) had no coherent

velocity component – only decorrelation.

Fig. 2. Experimental image of flow channel with

maximum velocity at twice the aliasing velocity.

2003 IEEE ULTRASONICS SYMPOSIUM-862



This suggests that different types of information canbe obtained with PD, as illustrated in Fig. 3. The

curves represent the average power across a flow

channel. A recently developed research interface on a

Siemens ANTARES ultrasound scanner allowed us to

access raw RF data and process it with an offline

MATLAB library [6]. The flow is the same for bothcurves but the bottom curve uses a slower PRF. The

top curve is peaked in the center of the vessel where

the flow is fastest – and we dub this a flow-weighted

image. The bottom, slow PRF curve will be termed a

scatterer-density weighted image. For detection tasks

it is desirable to use as much information about the

flow as possible – hence flow-weighted images are

preferred. Other times one is concerned with

estimating microvascular density, and would prefer

that the flow-rate did not bias the observed power. In

this case a scatterer-density weighted image is

preferred. Contrast agents may be necessary.

0 1 2 3 4 5

2000

3000

4000

5000

6000

7000

8000

9000

10000

dis tance in chann el (mm)

P o w e r

Fig. 3. Experimental PD measurements across a flowphantom. The dashed line used a 488 Hz PRF. The

solid line used B-mode frames giving an effective

PRF of 48 Hz.

We used Monte Carlo studies to validate that the idealobserver performance is monotonic with the observed

average Signal to Background Power Ratio (SBPR).

We simulated blood using an exponentially decaying

random process. This was superimposed on a

stationary clutter background, then blurred by aGaussian kernel simulating the system, followed by

addition of electronic noise. Fig. 4 shows the ideal

observer and SBPR performance with increasing

decorrelation rates. The observer monotonicity

validates the utility of the ideal observer model. Therelative inefficiency (~10%) means there is room for

improvement in our processing techniques.

0.5 1 1.5 2

2

4

6

8

10

12

Decorre la tion ra te [x PRF ]

S N R

Idea l Observer SNRMonte Car lo SBPR

Fig. 4. Ideal Observer SNR (solid line) and SBPR

obtained from Monte Carlo simulation of a

decorrelating blood process with a large motionless

clutter component 40 dB below the blood. The clutterto noise ratio was –26 dB.

The ideal observer tells us about the system design.From a simplistic point of view (i.e. 1D A-scan lines),

our model predicts that wide bandwidth, high-energypulses give optimal detection performance. The

theory can also show that aperture broadening can

also contribute to enhanced detection.

V. NONPREWHITENING OBSERVER

We now model an observer that does not prewhiten

the data as does the ideal observer. We take the

average power in a region of interest as a statistic.

The test statistic can be histogrammed over a largenumber of target present and target absent images.

The better the separation of the target present and

target absent distributions the better the detection

performance. A threshold can be set on the

distributions to make a decision. A Receiver

Operating Characteristic curve is a plot of the true

positive probability/fraction (TPF) for a fixed false

positive probability level (FPF), and is the gold

standard for quantifying decision tasks. In some cases

the squared peak separation normalized by the

average variance [SNRλ2] is a useful measure of

performance.We consider 2-D “correlation regions” of the 3-D

RF data. Correlation regions can be defined as the

spatial extent of data correlations. These regions can

be broader than speckle spots because successive A-

scan lines may demonstrate coherent motion – asource of correlation. With the correlation region




0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

FPF

T P F

long pulse

short pulse with same amplitude

short pulse with equal energy

concept in hand, we can write the SNRλ2 of the test

average power as:

[ ]( )

2

22

2

2

2 / o

c

I SNRS

ASNR =

+

−=

−+

−+

σ σ

λ λ , (5)

where A is the target area and S c is the area of the

correlation region. SNRo is the signal-to-noise of a PDpixel, and may be expressed as:

[ ]{ }[ ] [ ]22

2

2

−+

−+

+

−=

KK

KK

tr tr

tr SNRo (6)

where the signal present covariance is the covarianceof post wall-filtered slow-time echo data ro at a single

spatial location. This can also be decomposed into a

spectral representation by a discrete Karhunen-Loeve

transformation (i.e. eigendecomposition)

[ ]Φ+Φ=+= ++ ncb

H t

oorrK . (7)

Thus[ ]{ }

( )[ ] ( )[ ]{ } 2 / 22

2

2

ncncb

b

otr tr

tr SNR

+++∝

+

. (8)

When considering decorrelation processes, the

spectra are approximately independent of the pulse

shape, only pulse energy. Noise limited detection is

when the noise is the dominant factor hindering the

task. Clutter limited detection occurs when the post-wall filtered clutter spectrum is the primary factor

confounding detection, and when the noise spectrum

is relatively insignificant.

Long or at least energy-rich pulses areadvantageous in noise limited situations. Codedexcitation techniques are one way of loading more

energy into a pulse. Matched filtering or

deconvolution [7] can be used to recover spatial

resolution. For clutter limited situations, short pulses

(broadband) are seen to be better (Fig. 5). This isbecause broadband pulses give more independent

correlation regions to make a decision. Thus

shrinking the pulse duration shrinks the variance of

the average power (and thus bigger A/S c), while

having little effect on SNRo.

VI. SUMMARY AND CONCLUSIONS

Changing the PRI can lead to different types of PD

information: flow/perfusion-rate weighted images and

scatterer density-weighted images. PD levels are seen

to drop at twice the aliasing velocity. Short pulses

(wideband) pulses are preferred in clutter-limited

situations, while narrowband or coded excitationpulses are preferred in noise-limited cases.

Fig. 5. ROC curve from Monte Carlo simulations

aimed to detect slow decorrelating flow in thepresence of decorrelating clutter.

VII. ACKNOWLEGEMENTS

Thanks to Jerome Mai and Siemens Medical

Solutions for work on the ANTARES URI and OPT.

We acknowledge funding from NIH R01 CA 82497.

VIII. REFERENCES

[1] J.M. Rubin, R.O. Bude, P.L. Carson, R.L. Bree, R.S.

Alder, “Power Doppler US: A Potentially UsefulAlternative to Mean Frequency-based Color Doppler US”,

Radiology, March 1994.

[2] R.J. Zemp, C.K. Abbey, M.F. Insana, “Ideal Observer

Model for Detection of Blood Perfusion and Flow Using

Ultrasound” Information Processing in Medical Imaging

2003, Ambleside, UK.

[3] R. J. Zemp, C.K. Abbey, M.F. Insana, “Linear System

Models in Ultrasound: Application to Signal Statistics”,

IEEE Trans. Ultrason. Ferroelect, Freq. Contr. Vol. 50, No.

6, 642-654, June 2003.

[4] V.L. Newhouse, D. Censor, T. Voutz, “Ultrasound

Doppler Probing of Flows Transverse with respect to Beam

Axis,” IEEE Trans. Biomed. Eng. Vol. 34, pg779-89, 1987[5] R. J. Zemp, C.K. Abbey, M.F. Insana, “Generalized

NEQ for Assessment of Ultrasound Image Quality”, SPIE,

Physics of Medical Imaging, 2003.

[6] http://www.bme.ucdavis.edu/URI/

[7] Bruno Haider, Peter A. Lewin and Kai E. Thomenius,

"Pulse Elongation and Deconvolution Filtering for Medical

Ultrasonic Imaging", IEEE on UFFC, pp 98-113, vol 45,

No 1, 1998


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