jensen, nikolov, fast simulation of ultrasound images

8/8/2019 Jensen, Nikolov, Fast simulation of ultrasound images

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Fast Simulation of Ultrasound ImagesJgrgen Arendt Jensen and Svetoslav Ivanov Nikolov

Center for Fast Ultrasound Imaging, Department of Information Tech nology, Build. 344,Technical University of Denmark, DK-2800 Lyngby, Denmark

AbstractRealistic B-m ode and flow images can be simulated with scat-tering maps based on optical, CT, or MR images or paramet-ric flow models. The image simulation often includes using200,000 to 1 million point scatterers. On e image line typi-cally takes 1800 seconds to compute on a state-of-the-art PC,and a whole imag e can take a full day. Simulating 3D im-ages and 3D flow takes even more time. A 3D image of 64by 64 ines can take 2 1 days, which is not practical for itera-tive work. This paper presents a new fast simulation methodbased on the Field I1 program. In imaging the same spatialimpu lse respo nse is calculated fo r each of the imag e lines, andmaking 100lines, thus, gives 100 calculations of the sa me im-pulse respo nse delaye d differently for the different lines. Do-ing the focu sing after this point in the simulation can ma ke thecalculation faster. This corres pond s to full synthetic apertureimaging. The received response from each element is calcu-lated, when emittin g with each of the elem ents i n the aperture,and then the responses are subsequently focused. This is theapproach taken in this paper using a modified version of theField I1 prog ram. A 64 element array, thus, gives 4096 re-sponses. For a 7 MHz 64 element linear array the simulationtime for one im age line is 47 1 seconds for 200,000 scattererson a 800 M Hz AMD Athlon PC, corresponding to 17 hoursfor one image with 128 lines. Using the new approach, thecomputation tim e is 10,96 3 secon ds, and the beamformingtime is 9 secon ds, which makes the approach 5.5 times faster.For 3D im ages with 6 4 by 64 lines, the total conventional sim -ulation tim e for one volume is 517hours, whereas the new ap-proach makes the simulation in 6,810 seconds. The time forbeamform ing is 288 seconds, and the new approach is, thus,262 times faster. Th e simulation can also be split among anumber of P Cs for speeding up the simulatio n. A full 3D on esecond volume simulation then takes 7,500 seconds on a 32CPU 6 0 0 MHz Pe ntiu m 111 PC cluster.

1 IntroductionThe simulation of ultrasound imaging using linear acousticshas been extensively used for studying focusing, image for-

0-7803-6365-5/00/$10.00 0 2000 IEEE

objectFigure 1: Set-u p for simulation of ultrasound im aging .

mation, and flow estimation, and it has become a standardtool in ultrasound research. Simula tion, howe ver, still takesa conside rable amo unt of time, when realistic imaging, flow,or 3D imaging are studied. New techniques for reducing thesimulation time a re, thus, desirable.

Th e main part of an ultrasound image con sists of a specklepattern, which emanates from the signal generated by tissuecells, connective tissue, and in general all small perturbationsin speed of sound , density, and attenuation. Th e generationof this can be modeled a s the signal from a large collection ofrandomly placed point scatterers with a Gaussian amplitude.Larger structures as vessel or organ boundaries can be mod-eled as a deterministicly placed set of point scatterer s with adeterministic amplitude. The relative amplitude between thedifferent scatterers is then determined by a scatterer map ofthe structures to be scanned. Such maps can be based on ei-ther optical, C T or MR images, or o n parametric models ofthe organs. Currently the most realistic images are based onoptical images of the anatomy [ 11. Blood flow can also bemodeled by this method. T he red blood cells, mainly respon-sible for the scattering, can be modeled as point scatterers andthe flow of the blood ca n be simulated using either a paramet-ric flow model [2] or through finite elem ent mode ling [3]. T hereceived signal is then calc ulated, and the sca tterers are prop-agated between flow emissions. The simulation of all linearultrasound system s can, thus, be done by finding the sum medsignal from a collection of point scatterers as shown in Fig. 1.Th e random selection of point scatterers should con sist of atleast 10 scatterers per resolution cell to g enera te fully devel-oped speckle, and for a normal ultrasound imag e this results

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in 200,000 to I million scatterers. Th e simulation of the re-sponses from these scatterers must then be don e for each linein the resulting image, and th e simulation for the whole col-lection is typically done 100 times with different delay focus-ing and apod ization. This mak es the simulation take severaldays even on a fast workstation.

A second possibility is to do fully synthe tic aperture imag-ing in which the received respo nse by all elements are found,when transm itting with each of the eleme nts in the array. Th eresponse of each element is then only calculated once, andthe simulation time can be significantly reduced . This is theapproach suggested in this paper. A second advan tage of suchan approach is that the image is focu sed after the field simu-lation. Th e sam e data can, thus, be used for testing a num berof focusing strategies without redoing the simulation. Thismakes is easier to find optimized focusing strategies.

2 TheoryThe field simulation must find the received signal from a col-lection of point scatterers. Using linear acoustics the receivedvoltage signal is [4]:

where deno tes spatial convolution , temporal convo-lution, and 71 the position of the point scatterer. v p Y ( t ) sthe pulse-echo wavelet, which inc ludes both the transducerexcitation an d the electro-mech anical impulse response dur-ing emission an d reception of the pulse. fm accounts for theinhomogeneities in the tissue due to density and speed ofsound perturbations that generates the scattering, and h,, isthe pulse-echo sp atial impulse response that relates the trans-ducer g eometry to the spatial extent of the scattered field. Ex-plicitly written out the latter term is:

where hr (71 t ) is the spatial im pulse response for the trans-mitting a perture and h,(31 , t ) s the spatial impulse responsefor the receiving aperture. Both im pulse responses are a su-perposition o f spatial impu lse responses from the individualelements of a multi-element aperture properly delayed andapodized. Each impulse response is:

where a , ( t )denotes the apodization and A,([) focusing delay,which both are a function of position in tissue and therebytime. Ne is the number of transducer elements.

Th e received signal from each scatterer must be calculatedfor each new fo cusing s chem e corresponding to the differentlines in an imag e. Th e resulting @sig nal is then found by

summing the responses from the individual scatterers using( I ) . Th e number of evaluations of spatial impulse respon sesfor individual transducer elements is:

Nh = 2N,N,N,, (4 )where N, s the number of point scatterers and Ni is the num-ber of imaging directions. It is assumed that the number ofelements in both transmitting and receiving apertu re are thesame, and that the apodization and focusing are included inthe calculation. A convolution betw een h,(?l , t ) ,h,(7l , t ) andvPe(t)must be do ne for each scatterer and each imaging di-rection. T his amoun ts to

convolutions for simulating on e image.The same spatial impulse response for the individual el-

ements are, thus, being evaluated Ni t imes for making animage, and an obvious reduction in calculation time can begained by just evaluating the response once. T his can be do neby making a synthetic aperture simulation approach. Herethe response on each of the receiving elem ents from excita-tion of each of the transmitting elements are calculated. Thereceived responses from the individual elements are beam-formed afterwards. Hereb y the number of evaluation s of thespatial imp ulse responses is

Nhs = NeN , . (6)Th e number of convolution s is increased to

N,., = N,N: f N J " , (7)since all emission s must be convolved with the respon se fromall receiving elements and vPe(t)must be con volved with theresponses. T his can be reduced to

if the transmitting and receiving elements are the same,whereby the signal received is the same d ue to acoustic reci-procity [SI, when the transmitting and receiving elemen ts areinterchanged. Th e beamforming is done after th e calculation,but this can be done very efficiently as demonstrated in Sec-tion 3 . The improvement in calculation of responses is givenbv

and for th e convolutions(10)4N,I - 2N,Ni -

C - 0.5Ny(N:+ 3N e ) - (N:+ 3N e )For a 64 element array and an image with 100 directions,the theoretical im provem ents are l h = 200 an d I , = 0.0933 =

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1/10.7. Th e efficiency of the approach is, thus, very dep en-dent o n the actual balance between evaluating the spatial im-pulse responses and performing convolutions. A significantspeed-up is attained for few elements and many imaging di-rections, since few convolutions are performed. T he balanceis affected by th e metho d for calculating the spatial impulseresponses. The simulation prog ram Field I1 [6 ,7] offers threedifferent possibilities, which are all based on dividing the

k ,Ne

I fn I 7 MHz I Transducer centerfreauencv I

O . l h / 2 Kerf between elem ents64 Number of elements

Decimation factor for R F datapitch Distance between elements

transducer into smaller elements. The program uses a far-field rectangle so lution [6], a full solution for triangles [SI, ora boundin g line solution [9]. Th e first solution is very fast,whereas the last two so lutions are highly accurate but signif-icantly slower. Th e choice of method will, thus, affect thebalance.

A seco nd aspect, in the implementation of the appro ach, isthe use of memory . The num ber of bytes, when using doubleprecision data, is

Table 1: Simulation Parameters for Phased m a y imaging.

B, .= SN:Nr (1 I )where Nr is the number of samples in the response. For at64 elements array covering a depth of 15 cm, this gives 625MB ytes at a sampling frequency of 100MH z. Th is is clearlytoo much for current standard PCs and even for som e work-stations. The simulation must be made at a high samplingfrequency to yield precise results, but the data can, however,be reduced by decimating the signals after simulation of in-dividual responses. A factor of 4 can e.g. be used for a 3or 5 M Hz transducer. The memory requirement is then 156MBytes, which is more acceptable. It is, however, still large,and much larger than the cache in the computer. It is there-fore necessary to reduce the number of cache misses. This issought achieved in the program by sorting the scatterers ac-cording to the d istance to the array, which give s results thatare placed close in the memory. The memory interface ofthe computer is, however, very important in obtaining a fastsimulation.

A significant reduction can in general be attained with theapproach as will be show n later, and the method mak es it veryeasy and fast to try o ut new focusing schem es once the basicdata has been sim ulated. This would d eman d a full recalcula-tion in the old approach.

3 ExamplesAll the examples in the following section have been madeby a modified version of the Field I1 simulation system. Theparameters used in the simulation are shown in Table 1.An artificial kid ney phanto m based on data from the Vis-ible Hu man Pro ject' has been used as the simulation object.Th e phantom consists of 200 ,000 point scatterers within a boxof 100 x 100 x 35 mm (lateral, axial, elevation d imension ),

'Optical, CT and M R images from this project can be found at:http://www.nlm.nih gov/research/visible/visibIe-human.htm1

Figure 2 : Optical image from th e visual human project of aright kidney and a liver lobe.

which gives a realistic size for a full com puter simulation of aclinical imag e. The optical image in Fig. 2 is used for scalingthe standard deviation of the Gaussian random amplitudes ofthe scatterers. The relation between the gray level value inthe image and the scatterer am plitude scaling is given by:

a = IO~exp(img(?',,)/IOO) (12)where img is the gray-level image data with v alues from 0 to127, an d 7 k is the discrete position of the scatterer. This scal-ing ensures a proper dynamic range i n the scatterering fromthe various structures. T he resulting imag e using a syntheticaperture simu lation is shown in Fig. 3

The sim ulations have been carried out using a standard PCwith 512 MBytes RAM and an Athlon 800 M H z CPU run-ning Linux RedHat 6.2. The various simulation times areshown in Table 2 . These data also include the beam focus-ing for the synthetic aperture simulation, which took 9 sec-onds in all cases. It can be seen that the simulation timesincrease nearly linearly with the num ber of elements, and lin-early with the number of scatterers. Th e improvem ent fo r aphased array image with 128 lines is roughly a factor 5.5 to6, which lies between the two bou ndaries given earlier. The

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-50 0Laioral distance lmml

20,00020,000

Figure 3: Synthetic ultrasound image of right kidney and liverbased on an optical image from the visual human project.

32 Synthetic 494 5.9664 Line 6528

N, I Ne I Method 1 Time [SI I Improvement20,000 1 32 I Line 1 2944 I20,000200,000

64 Synthetic 1108 5.6564 Line 60288I 200.000 I 64 1 Svnthetic I 10972 I 5.49 ITable 2: Simulation times for scanning the human-liver phan-tom.

actual improvement is dependent on the object size, trans-ducer, sampling frequency, CPU, and memory interface, andthe numbers will be different for other scan situations.A three-dimensional scanning has also been implemented.

A two-dimensional sparse array ultrasound transducer wasused, and a volume consisting of 64 x 64 lines with 200,000scatterers was made. Simulating one line takes 455 seconds,which gives a full simulation time of 1,863,680 seconds (21days and 13 hours). Using the new approach the whole vol-ume can be simulated in one pass. This takes 6,810 secondsand the beamforming 288 seconds, which in total gives animprovement in simulation time by a factor of 262. A furtherbenefit is that different focusing strategies also can be testedwithout a new simulation, and a new volume image can thenbe made in 288 seconds.A parallel simulation has also been performed using aLinux cluster consisting of 16 PCs with dual 600 Pentium I11processors and 256 MBytes of RAM for every 2 CPUs. Thescatterers are then divided into 32 files and the simulation isperformed in parallel on all machines. The total simulationtime is 935 seconds for the 2D simulation and beamform-ing takes 9 seconds, when using 200,000 scatterers for thephantom. A full simulation of a clinical image, thus, takes15 minutes and 44 seconds, which is acceptable for iterative

work. This should be compared with 16 hours and 45 minuteson one CPU using the line based simulation. This approachcan also be employed for the three-dimensional scanning andcan reduce th e time for one volume to roughly 212+288 =500 seconds. Simulating I5 volumes of data correspondingto one second of volumes for a 3D scanner can then be donein 7,500 seconds or roughly 2 hours.

AcknowledgmentThis work was supported by grant 9700883 and 9700563from the Danish Science Foundation and by B-K MedicalA B , Gentofte, Denmark.

References[ l ] J. A. Jensen and P. Munk. Computer phantoms fosimulating ultrasound B-mode and CFM images. In

S . Lees and L. A . Ferrari, editors, Acoustical Imagingvolume 23, pages 75-80,1997.

[2] A . T. Kerr and J. W. Hunt. A method for computer sim-ulation of ultrasound Doppler color flow images - 11Simulation results. Ultrasound M ed. Biol., 18:873-879,1992b.[3 ] F. Forsberg, H. Oung, and H. V. Ortega. Doppler simulation for pulsatile flow having nonaxial components. In

Proc. IEEE Ultrason. Symp., pages 1713-1716,1994.[4 ] J. A . Jensen. A model for the propagation and scatteringof ultrasound in tissue. J. Acoust. Soc. Am. , 89: 182-19 11991a.[5] L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. VSanders. Fundamentals ofAcou stics. John Wiley & SonsNew York, third edition, 1982.[6] J. A . Jensen and N. B. Svendsen. Calculation of pressurefields from arbitrarily shaped, apodized, and excited ul -trasound transducers. IEEE Trans. U ltrason., Ferroelec.

Freq. Contr:,391262-267, 1992.[7] J. A. Jensen. Field: A program for simulating ultrasoundsystems. Med. Biol. Eng. Comp., 10th Nordic-BalticConference on Biomedical Imaging, Vol. 4, Supplement1, Part 1:351-353,1996b.[8] J. A. Jensen. Ultrasound fields from triangular apertures

J. Acoust. SOC.A m . , 100(4):2049-2056,1996a.[9] J. A. Jensen. A new calculation procedure for spatial im-pulse responses in ultrasound. J . Acoust. Soc. Am ., pages3266-3274.1999.

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jensen, nikolov, fast simulation of ultrasound images

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