a parallel architecture for the color doppler flow technique in ultrasound imaging

Microprocessing and Microprogramming 38 (1993) 545-551 545 North-Holland

A Parallel Architecture for the Color Doppler Flow Technique in Ultrasound Imaging Alessandra Costa, Alessandro De Gloria, Paolo Faraboschi and Mauro Olivieri ~

Dept. of Biophys. and Elect. Eng. (DIBE), University of Genoa V. Opera Pia l l a , 16145 Genova, I taly

In this paper we present an algorithm and an architecture for tile computation of the mean frequency and the variance of a Doppler signal for the implementation of the Color Doppler Flow tech,uque. The Color Doppler Flow is used to simplify the analysis of an echocardiographic image coding the blood velocity with a pseudo-color level, derived from the mean frequency of the Doppler echos. Hence, we have to perform an accurate spectral analysis of the signal to obtain careful results, but we also have to respect strict real-time constraints.

We propose to use all AR algorithm for the spectral estimation, exploiting an a priori knowledge about the shape of the spectrum of the Doppler signal. We also apply the same knowledge to simplify the mean frequency estimation, avoiding the time-consuming operation of integral computations, that is replaced with the evaluation of a maximum. In this case, we show that the resulting architecture is much less expensive, with a comparable accuracy.

A first result of the research has been the design of a parallel architecture for the Color Doppler Flow, composed of 64 DSPs organized on four boards of 16 DSPs each

1. I n t r o d u c t i o n

A Doppler device [2] analyzes a circular sector of tissue, at mos t 90 degrees wide. The device sends a pulse burst on each view line and processes the returning echoes. The device nmst operate in real- t ime mode, and all computa t ion have t.o be completed in a finite amoun t of t ime which depends on the number of bursts for every view-line of the image. As the number of bursts per line increases, the fi 'ame rate of the image is slower if the Pulse Repet i t ion Frequency (PRF) remains the same.

We can say that :

P R F = F~ . N~ • N , (1)

where N~ is the number of view-lines, F~ is the f rame rate of the image and N, is the number of samples (number of burst per line).

Then, on one side we need to have a large number of samples to obtain a precise est imation, while on the other side the f rame rate of the resulting image must be high enough to guarantee a satisfying visual evaluation.

A typical f rame rate can be approximate ly 10 Hz and the P R F between 8 MHz and 20 Mhz. This leads to a number of bursts, i. e. of samples,

f rom 8 to 16 but some of them are el iminated by an MTI (Moving Target. Indicat ion) filter'. The total number of points considered on a view line is 256 and hence we have to perform 256 spectral es t imations in a t ime slot. of ~\'~ • 1

• P R F "

1.1. E c h o c a r d i o g r a p h i e i m a g e s Star t ing from an a p r i o r i knowledge about the

shape of the Power Spectral Density (PSD) of the Doppler Signal, we can say that:

If the axial blood velocity in a. vessel is uniform, the corresponding PSD of the Doppler echoes has only one peak ill the positive (or negative) range of the frequency. If the peak is in the positive range we can conclude that the blood axial velocity is positive; if the peak is in the negative range, we carl conclude for a blood flow with negative axial velocity.

If there is some turbulence in tile vessel, tile PSD of the Doppler signal will present more than a relevant peak.

In the first case the significant information is tied to the mean frequency, in the second case the information is tied to the variance.

546 A. Costa et aL

An echocardiographic device with the Color Doppler Flow technique, overlaps pseudo colors to the t radi t ional echographic image. Pseudo colors are used to give informat ion about the blood velocity and direction in a vessel:

• If we have a uniform velocity, the pseudo color associated with the pixel is red or blue depending on the sign of mean frequency (direction of blood).

• If there is some turbulence, the pseudo color is green or yellow depending on the sign of the p redominan t velocity.

Typically, we can have a number of color levels tha t ranges from 16 to 128. This codification of the blood velocity with a pseudo color level allows both a better visualization and an easier interpretat ion of the echographic linage, leading to a faster and safer diagnosis.

Two are the main problems for the Color Doppler Flow implementa t ion:

• the Spectral Es t imat ion on the basis of a small number of signal samples;

• the Mean Frequency computa t ion in a small t ime slot.

The constraints on the error are not very strict for the Color Doppler Flow technique, as the outcome of the sys tem is a color level. If we decide to code the color informat ion with N bits, the min- i m u m necessary confidence interval is 2 N and it is useless to have an approximat ion with a higher precision. In our application, we decided to code the color level with five bits, hence our precision is 1/32 (approximate ly 3%).

2. P r o b l e m R e s o l u t i o n

2.1. S p e c t r a l E s t i m a t i o n As we have said, the problem in the Spectral

Es t imat ion is the very small number of samples. We have two alternatives for the spectral estimation: the use of FFT-based techniques, or the use of A R M A methods .

The use of an FFT-based techniqu is not a good choice in this case, because it leads to approximated spectra with poor resolution [4, 5].

Wi th the use of FFT-based techniques we assume necessarily tha t the observation interval is time bounded. Wi th this assumpt ion we consider the samples out of tile observat ion interval as zeros, and this is a non realistic assumption. The win- dowing in the t ime domain causes a convolution of the true Power Spect rum Density with a sync function in the frequency domain. If the original signal is narrow-lmnd, like in our case, the convolution causes a widening of the band of the signal and a. poor resolution too. This effect is much more evident if the observation interval is short, i. e. the number of the samples is small, and this is our case.

Hence we decided to use "non classical" esti- lnat ion techniques that are based on parametr ic descriptions. Therefore we assume to have an a priori knowledge about the signal, i. e. we choose a model tha t contains a set of unknown l)aram- eters. Then, fl'om the observation and the processing of the samples we determine the values of the parameters and the model itself.

The most general l)arametric polynomial model is the A R M A method, tha t can models both nar row-band and wide-band processes [3]. As we know tha t in case of a Doppler signal the spec- truln is narrow-banded, we can use a subclass of the A R M A model, the AR model, tha t improves the a lgor i thm simplicity. The choice of an Al l me thod needs the solution of a set. of linear equations (Yule-Walker syst.em [3]) which simplifies the computa t ion .

Once we have decided to use an AH. model, we must select, tile order of the nlode], i. e. the nun> ber of its paralneters. The choice of the order is critical for the application: if we choose a too high order, the corresponding spect rum can have spurious peaks [6], but if the selected order is too low, the resulting spect, ral definition will be poor. Some algebraic criteria to select, the model order have been proposed in the past [6], but none of them seems to be unfailing. A practical rule for the model order selection states tha t it. must be lower than half the number of samples. In our case we can use 8 samples for the spectral esti- mat ion and the model order can be 3 or 2. We chose to use an order 2 tha t leads to a simplified computa t ion , btll. at, l.he same t.ime keeps a. good

Color Doppler flow technique in ultrasound imaging 547

accuracy. To solve the Yule-Walker set of equations we

have considered three methods: Burg, Autocor- relation and Covariance. To evaluate their perfor- mances first we have generated a set of test sam- pies from the theoretical spectrum, then we have tested the three methods on these samples computing the AR parameters, adding white gaussian noise with different Signal-Noise ratio to the test samples. Finally we have calculated the commit- ted error in the approximation of the real spectrum in terms of the percentage difference between the computed and real mean frequency.

If,~r - / , , , s I (2) Eerr - fma,: -- f,~i,~

where f r e t is the real mean frequency of the model, f , ,~ is the approximated mean frequency with the considered method and f,,,i,~, f,,~,:, are the bounds of the considered frequency range. In our case the frequency domain is normalized, hence f,n~. = 0.5 and fmi,,. = -0.5 .

The obtained results are shown in Table 1. Our theoretical spectrum has only one predominant peak and we use eight samples to approximate it.

From the analysis of table 1, we can see that the best results are obtained using Burg and Modi- fied Covariance methods. The Autocorrelation method leads to the poorest estilnation, above all in presence of noise, i. e. in the real work situation. We can then conclude that, from an accuracy point of view, the best. method is the Modified Covariance. However, as we are interested in real-time ap- plications of the methods, we have also to take into account the computational load, in order to find which technique represents the best tradeoff between quality of the result and computational cost. Figure 1 shows the behavior of the computational load of the three methods. From a comparison of figure 1 and table 1, we can conclude that the Burg method is the best choice for the resolution of our problem.

2.2. Mean F r e q u e n c y C o m p u t a t i o n The second problem in the realization of a sys-

tem for the Color Doppler Flow techniques, is the

computation of the mean frequency of the signal.

f" ' = f+-~o~ P~:x(f)df (3)

As we can see from equation 3, this operation in- volves the computation of two integrals. It" we use numerical methods the consequ('ut load is very high, especially if the signal spectrum is narrow- band like in our case. If wc decide to use a no/ ellough small integration step, tlmr(, is the possi- bility to ignore the sharp peak of the spe(trmlJ with a consequent leakage of precision; on the other hand if the integration step is too sluall, t.h(" number of required operations will be too high for the time constraints and for iml)lementation cost considerations.

Alternatively, we can try to exploit the narrow- band feature of the signal to reduce the number of computations needed. How we have said, if the blood axial velocity is uniform in a vessel, the corresponding narrow-band spectrum of the signal has only one peak in the positive or in tim nega.tive range of the frequencies. As a conse- quence, the lnean frequency can be approxinaated with t, he maxinluln frequellc.y with a small error. Otherwise, if there is more than o,le peak or if there is a single wide peak around the origin, we can conclude for a non unifonn blood flow (turbulence). The variance can be computed from the estimated width of the detected peaks.

We have developed a heuristic algorithnl for the Color Doppler Flow [1], t.hat takes into a.ccount these considerations, and achieves good results with an acceptable conqmtalional load.

* The selected AR lnetl,od is Burg.

• Once we have estimated t.hc All coelficient, we search the frequency' peaks with a dico- tomic technique applied t.wice, both iu the negative and positive range of the frequencies. To have an acceptable error, we have measured that eighl steps of the proce- dure are sufficient: the obtained error for the peaks detection is approximately 0.4%,. Therefore the total error thai. we comlnit in the meall ['requency evaluation

548 A. Costa et aL

Table 1 Compar ison between errors (%) observed with the different lnethods in computa t ion of mean Dequency for order 2 A R model with different signal/noise ratios

Method S / N = OdB S / N = 5dB S / N = lOdB ,5"/N = ,x, % % % %

Burg 7.8 4.2 2.3 1.5 AutoCorrelation 12.4 6.8 4.9 4.1 Mod. Covariance 7.3 4.0 2.1 t.3

is 2%+0 .4%=2 .4% (Burg and peak detection). Wi th 32 color levels this error is less than the required precision (13%) and we can accept it.

* Once we have calculate the frequency peaks fp and fn in the positive range and in the negative range, we calculate the corresponding values of the spec t rum (h v = P S D ( f v ) and hn = P S D ( f n ) ) and we coin- pare them to establish if blood flow is uniform or turbulent . Three cases can occur:

1.

.

The two peaks are comparable (h v .~ h~): a turbulence is detected. The pixel color is green or yellow, depending on which peak is more relevant, with an intensity propor t ional to the variance of the spectrum. We perform the comparison using a. user-provided threshold e as follows:

Ih,, - hvl

Ih~+hvl > e (4)

In this case the variance 6 can be ap- D.-h~l proximated as: 6 = a , . [ h . + h , I where

cr is a proper fitting paralneter;

A peak is much more relevant than the other (h v > > h , or h,~ > > hv). In this case we check that the greater peak is not too wide. If it is, we conclude for the presence of blood turbulences in the vessel and the outcome of the system is a green or yellow level. The compar ison is made with another user-

.

provided value :~.l;,.a,,::

P S D . ( f . + __kfi ......... ) > 0.001 (5)

In this case we approximate the variance as a = 9 ' & f where ~./' is the imrma.lized widt.h of' the peak and 3 is a fitting constrant,.

A peal< is much more relevant con> pared with the other and it. is sharp (hj, > > b,, or h,, > > by and P , S D . (],, + &f, ........ .)/h,, < 0.001). In this case we conclude that there is a uniform blood flow in the vessel. The outcome of the syst.em is a blue or red level with int.ensity proport ional t.o .f,, or J~,.

The presence of two user-provided thresholds for the color level conlputa t ion is a relevant t~a.- tures of our project. This l)erlnits to increase the versatility of the system in different, diagnosis sit- uations.

2.3. A r c h i t e c t u r a l s u p p o r t To inaplelnent the Color Doppler Flow tech-

nique we decided to design a parallel architecture. For the initial project, because of cost and flexibility considerations, we decided to use DSPs for the architecture realization. The total number of DSPs is 64 arranged on four boards of 16 DSPs each. We decided to use the Analog De- vices ADSP-2105 (40 Mhz). The DSPs oil the single board are connected with a 64 bits bus and between the 16 bits DSP and the 64 bits bus there is a transmission inl.erfaco ( f igure 2).

Each DSP processes the samples coming from four different points for each view-line, each sam-


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4J

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q-i 0

b4 (1)

Z

16

14

12

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8 i

6

4

2

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1 I

2 3 4

- - - - - covariance

burg

......... autocorrelation

Figure 1. Computa t ional load of the different methods expressed in terms of number of operations

pie being a complex number represented with its real and imaginari parts. The computat ion is to- tally independent and for this reason the DSPs do not need to communicate.

Since the acquisition t ime is smaller than the processing time, we must temporari ly store the information in a memory. The scanner re- ceives the samples x / i ] [ t ] , i = 0 . . 255, t = O . . 7

for each view lines, in the or- derx[i][t], x[i+lJ[t] ..... x[iJ[t+l] .... ,

that is in spatial order. As we need to store the samples in t ime order (x['±] [ ' t ] , x [ i ] [ t + l ] . . . . ) in each processor, it is necessary to reorganize memory to perform this shuffle operation. Figure 3 shows the global organization of the system.

Memory Subsystem The memory subsystem is composed of two

banks, one for the results of the computation (Mean Frequency and Variance) a.nd the other one for the hlput samples. The sample memory is rather small, as it needs to store 8 samples (32 bits, 16 for the real and 16 for the imaginary part) for each one of the 256 samples. Since we need to store a new viewline while we are computing the estimation for the previous one, we need two memory banks whose function (computat ion/ load) is toggled at the end of every computat ion cycle. The total amount of memory is then 1(5 l{Bytes.

Bus Organization The bus needs not to be arbitrat, ed: the risk of bus conflicts is avoided because the program flow is completely det, erministic (data independent). Then we can arrange the

550 A. Costa ot al.

BUS

DSP 1

I~/nter fac?

DSP 5

DSP 9 ]

l°SPl, l

DSP 2

Interface

DSP 6

DSP 10 ]

) ¢ los,,,l

DSP 3 DSP 4 I

Ilnterface __~_~ ~__--"~__ Interface i

[ psi, ]

[ DSP 11 DSP 12 ]

[ terra -l°;~..e ¢ ¢ ¢ DSP 15 DSP 16

Figure 2. Block diagram of tile proposed paralM architecture

t iming of the memory access of each DSP statically at compilation tilne.

• a, keyboard, t.o modify (ill real tilne) the Doppler investigat, ion parameters

P r o g r a m M e m o r y The program that each DSP must execute is stored in EPROM memories. If we want to increment the system speed we can use four EPROMs, one for each board.

User I n t e r f a c e The user interface is composed of

• a pre-processor, to transform tile rect- angular matrix into a. circular sector,

* a scan converter, to map the values of the Mean Frequency and the Variance (already expressed with a pseudo color level) on the monitor,

3. C o n c l u s i o n s

In this paper we have presented a parallel a.r- chitecture for the Color Doppler Flow technique.

Our research den,onstrates tha.t, when the number of saml)les is very small, the rise of "non classical" spectral est imators based on rational polynolnial functions give a. better resolution than those FFT-based. Particularly, AR model fits very well tile Doppler signal typical spectrum. Among the AR techniques, we have shown that the Burg method gives a good tradeoff between the accuracy of est.imat.ion and the amount of the computat ional load. In addistion, t.o allow a rea.l-time realization we have proposed an heurist.ic a.lgorithm which per-


Doppler

Signal

MONITOR

DATA BUS 64 bits

Figure 3. Block diagram of the proposed system

mits a significant reduction of the computational load in the Mean Frequency and Variance estimation. The error obtained with our technique is approximately 2.4 % ( including the error derived by the Burg method) and this is sufficient for the required precision of 32 color levels.

Finally, we have proposed a parallel architec- tural realization based on commercial DSP processor, that is characterized by high performance and a remarakble simplicity due to the independent and deterministic nature of the computations.

R E F E R E N C E S

A. Costa, A. De Franciscis, A. De Gloria, P. Faraboschi, and M. Olivieri. Spectral estimation for 2-D Doppler ultrasound imaging.

Electronics Letters, 28(23), 19g)2. 2. C. aoffe. Vascular and Doppler ultrasound.

Churchill Livingstone, 1988. 3. S. Kay. Modern Spectral Esl~mation: lheory

and applicatiou. Prentice Hall, 1988. 4. S. Kay and S. Ma.rl)le. Spectruni analysis-

a modern perspective. Proc. 1EEL'. 69(11), 1981.

5. F. Schlindwein and D. Evans. R.eal-~ime autoregressive spectrum analyizer for Doppler ultrasound signals. UIh"asou~d tn ,Med, and Biol., 15(3), 1989.

6. F. Schlindwein and D. Evans, Selection of the order of autoregressive models for spectral analysis od Doppler ultrasound signals. Ultrasound i~ Med. a~d B~ol.. 16(1), 1990.

a parallel architecture for the color doppler flow technique in ultrasound imaging

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