Physiological blood flow always involves some degree

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1 ieee transations on ultrasonis, ferroeletris, and frequeny ontrol, vol 48, no 3, may A Thin Film Phantom for Blood Flow Simulation and Doppler Test Stephen MAleavey, Zaegyoo Hah, and Kevin Parker, Fellow, IEEE Abstrat The thin film phantom is a new type of ultrasound resolution test objet It onsists of a thin planar substrate that is aoustially mathed to the surrounding media Preisely loated satterers on the surfae of the substrate generate eho signals The patterning of satterers on the substrate allows ehogeniity to be ontrolled as a funtion of position, whih enables the prodution of a test objet with highly reproduible and ontrollable sattering harateristis We show that by vibrating the substrate in a suitable manner, an eho signal may be generated that simulates bi-diretional flow We demonstrate that a vibration of low amplitude at frequeny f produes a Doppler spetral signal at f and ;f, within the limits of aliasing Furthermore, by driving the film with a bandlimited noise signal, we illustrate how a veloity distribution may be simulated A time-varying flow veloity may be simulated by varying the noise bandwidth with time Finally, using this tehnique, we demonstrate a system that simulates an arterial flow pattern, inluding its harateristi veloity distribution in forward and reverse diretions simultaneously I Introdution Physiologial blood flow always involves some degree of veloity gradient beause of the visosity of blood [1] Furthermore, the flow profile an vary signifiantly, even within the same vessel, over time To test the performane of Doppler systems in the presene of flow gradients, it is useful to have a phantom that an produe eho signals that mimi those produed by flowing blood Simulation of these flow gradients with a onventional flow phantom is not a simple task Flow phantoms using blood-mimiking fluids and pumps have been onstruted that apture many of the features of flow in tissue, inluding veloity gradients and, in some ases, time-varying flow [2] [5] Hoskins et al [2] demonstrated a system wherein a omputer-ontrolled pump generates a time-varying flow through a tissuemimiking phantom The flow generated is similar to atual arterial flow, inluding a reverse flow omponent A phantom demonstrated by Boote and Zagzebski [5] also produes a pulsatile flow Suh phantoms represent the gold-standard for flow simulation but are omplex in their design, operation, and maintenane Manusript reeived April 13, 2; aepted November 14, 2 The authors are grateful for support from the NIH SBIR grant program (1 R43 HL6241-1A1) The authors are with the Department of Eletrial and Computer Engineering, University of Rohester, Rohester, NY ( maleave@eerohesteredu) Moving string and belt phantoms are simpler from a mehanial standpoint than flow phantoms [6] [8] Timevarying flow is simulated with some of these devies by hanging the veloity of the string or belt in time, as in the work of Russell et al [6] Rikey and Fenster [7] have presented a moving belt phantom, where a stationary lutter signal is superimposed on the moving belt eho String and belt phantoms are simpler to operate than flow phantoms but have a limited ability to simulate veloity gradients Here we present a phantom apable of simulating timevarying and veloity-dispersed flow The peak flow veloity, the flow profile, and the flow rate versus time are all ontrollable This is ahieved with a solid, thin film as a test target, using a simple piezoeletri element to indue small-sale motion of the film A onsequene of this approah, however, is that the simulated flow appears to be bi-diretional That is, simulation of flow toward the transduer at veloity ν also results in simulated flow away from the transduer at the same veloity At least one ommerial phantom (DSP-1; JJA Instruments) uses a vibrating target to generate a Doppler signal The phantom desribed here, however, allows a greater degree of ontrol over the Doppler signal than any other vibrating target phantoms of whih the authors are aware II Theory Holen et al [9] demonstrated that a vibrating target results in a frequeny modulation of the toneburst used in Doppler ultrasound They showed that sinusoidally osillating strutures an produe Doppler signals in whih energy is foused at integer multiples of the vibration frequeny, when the vibration yle is shorter than the FFT (fast Fourier transform) window size The energy weighting of eah frequeny multiple is determined by a Bessel funtion of the first kind [1] A Eho Signal An expression for the eho reeived from an osillating point target may be developed with the aid of a range-time graph (Fig 1), as in [1] and [11] The graph depits the relationship of the target, the transduer, and the sound pulse; the range dimension along the absissa; and the temporal dimension along the ordinate The target, loated a mean distane d from the transduer, is immersed in a propagating medium with speed of sound The position of the satterer is given by x(t) =d + A os(ω t), where /$1 21 IEEE

2 738 ieee transations on ultrasonis, ferroeletris, and frequeny ontrol, vol 48, no 3, may 21 Solving for t e, t e t r 2d 2A ( {ω os t r d )} Fig 1 Range-time graph depiting the relationship between target and pulse position in time A is the vibration amplitude and ω is the vibration frequeny The transduer, loated at x =, launhes a pulse at time t e toward the target If we let t i bethetimewhen the pulse and target interat, then (t i t e ) = d + A os(ω t i ) (1) To aid in alulating t i, we break it into three parts, letting t i = t e +d /+ε, wherethed / term represents the average path delay between the soure and target and ε is the omponent of the delay aused by the target osillation Eq (1) may then be rewritten as t i t e = d + A os ( ( ) ) d ω + ε + t e (2) Eq (2) may be expanded in a Taylor series on ε t i t e d + A { ( [ ]) d os ω + t e ω ε sin ( [ ]) d ω + t e } The maximum value of ε is A/ For typial values of the parameters (A 1 4 m, 15 m/s, ω 1 3 ), ω ε is on the order of 1 4 Thus,wemayalulatet i by evaluating x(t)/ at t = d / + t e without inurring signifiant error, and t i = d + A { ( )} os d ω + t e + t e Let us define a propagation time t p as t p = t i t e The return path for the pulse is idential to the transmit path; thus, the time of reeption of the pulse t r is t e +2t p and t r = 2d + 2A { ( )} os d ω + t e t e where the approximation is due to neglet of a 2ω ε term in the argument of the osine For typial values of ω ( 1 3 ) and ε( 1 6 ), this yields a negligible error Let us all the transmitted signal s(t) Assuming a linear propagation model, the reeived signal from a point target will be a delayed and saled version of the transmitted signal Using the relationship t r t e = 2t p and replaing t r with t, weobtain ( r(t) =αs t 2d 2A ( {ω os t d )} ) (3) Given this expression for the reeived signal in terms of the transmitted signal, we are now in a position to estimate the response of ontinuous wave (CW) and pulsed wave (PW) Doppler systems to a vibrating target B CW Doppler Signal For CW systems, the transmitted ultrasound signal is s(t) =os(ω t), where ω is the radian frequeny of the signal Substituting this expression for s(t) into(3) yields r(t) =α os { (ω t 2d 2A { (ω os t d })} ) Typial Doppler systems perform quadrature demodulation, where the reeived signal is multiplied with in-phase and quadrature sinusoids at the transmit frequeny and low-pass filtered, as desribed in [1] Beause the amplitude of target osillation is small, the demodulated signal may be approximated as r d (t) 1 ( 2d ) { ω 2 ej 1+j 2Aω { os (ω t d }) } (4) From (4), we see that the demodulated signal is idential to the target vibration signal to within a phase shift and saling Thus, the output frequeny of the CW Doppler instrument will be equal to the target osillation frequeny as long as the small angle approximation is satisfied C PW Doppler Signal For PW Doppler systems, the transmitted signal is a train of windowed sinusoid bursts, s(t) = ( { 1 π t 2πnk }) { os (ω t 2πnk }), T ω n ω where k is an integer, and ω /k is the pulse repetition frequeny (PRF) is a retangular window funtion, equal

3 maleavey et al: blood flow simulation and doppler test 739 to1from 5 to 5 and elsewhere T is the window length Substitution into (3) yields r(t) = n ( ) 1 ( ) π T ϕ n(t) os ω ϕ n (t) where ϕ n (t) =t 2πnk 2d ω 2A { (ω os t 2d } ) A baseband signal is obtained by multipliation with a synhronized omplex sinusoid, low-pass filtering, and sampling [1] The demodulated signal is given by r d,n =1+j 2Aω { ( 2πnk os ω + d ) } (5) ω under the small angle approximations Here, as in the CW ase, the demodulated signal is a saled, phase-shifted version of the vibration signal In the PW ase, the signal is sampled at the PRF ω /k D General Vibration Signals From (4) and (5), it is seen that both CW and PW Doppler presented with a vibrating target generate output signals whose frequeny is idential to that of the target vibration signal Furthermore, as long as the restritions on the amplitude of vibration are observed, that is, that 2Aω / << 1, the proess is approximately linear Thus, not only simple sinusoids but any low amplitude signal may be applied to the target to generate a partiular Doppler signal For a vibration signal ν(t), the output of the PW Doppler system would be r d,n =1+j 2Aω ( 2πnk ν + d ) (6) ω The 1s in (4), (5), and (6) represent the arrier omponent of the reeived signal and are removed by the wall filter in a Doppler instrument The remaining signal desribes the target s osillation This result is onsistent with the results of Holen et al [9] when small amplitudes were applied to their equation When the FFT of r d (t) isdisplayed as a Doppler spetrum, the result will be horizontal bands in the Doppler spetral display at ±ω Hz This derivation did not onsider the angle of inidene of the ultrasound beam to the target The beam angle may be aounted for by saling the vibration amplitude A by a fator of os θ Varying the angle between the ultrasound beam and the plane of target vibration does not alter the frequeny of the target vibration and, therefore, does not alter the frequeny ontent of the demodulated Doppler signal The only effet of varying θ is to diminish the amplitude of the Doppler signal E Simulation offlow Signals The flow profile of a fluid in a tube depends on the visosity of the fluid and the rate of flow, as well as the presene of any disturbanes to flow within the tube For low flow rates (ie, those with a Reynolds number below 2), a suffiient distane from any disturbane to flow, a paraboli flow profile develops The veloity profile flattens from a true parabola with inreasing flow rate, beoming uniform in the limit of high veloity A paraboli flow profile produes a uniform Doppler spetral display; flatter profiles result in a greater emphasis of high frequenies when the vessel is uniformly insonified [1] In the limit of a uniform flow profile, the Doppler signal is a delta funtion in the frequeny domain, negleting beam modulation effets To produe a display similar to that observed with a paraboli flow profile with a vibrating target, a signal with a uniform spetrum up to some ut-off frequeny is required A bandlimited noise soure an be onstruted to satisfy this requirement Here, a summation of randomphase osines was used to generate the bandlimited noise The signal is given by s(t) = N os (ω nt + φ n ) n= where eah φ n represents a random variable uniformly distributed on ( π, π) The Fourier transform of this signal is a olletion of delta funtions of equal strength ω radians apart from Nω to Nω The value of ω is hosen to be suffiiently small so that the individual deltas are not resolved by the FFT used to generate the Doppler spetral displays For the signals used in the experiments, ω was hosen to be 2π/496, rendering the individual deltas quite invisible to the 128- or 256-point FFTs used to examine the Doppler signals When s(t) is used to drive the target, the resulting Doppler spetral display is uniform from Nω /2π to Nω /2π Hz as long as the restritions on vibration amplitude are observed Although the signal here was hosen to have a flat spetrum, by appropriate weighting of the osines, any desired spetral distribution may be developed to simulate non-paraboli flow profiles The veloity of flow in the arteries varies with time and is assoiated with the yli pulsation harateristi of the human irulatory system It would be desirable to model this with the vibrating thin film target This may be ahieved by varying the bandwidth of the vibration signal desribed previously with time To simulate periods of slow flow, the bandwidth is redued; inreasing the noise bandwidth simulates higher veloities To onstrut this signal, the following tehnique may be used Let ν p (t) be a signal that desribes the peak simulated Doppler frequeny shift versus time For normal arterial flow, ν p (t) is expeted to be quasi-periodi on the sale of a seond or so Fig 2 shows the ν p (t) used in these

4 74 ieee transations on ultrasonis, ferroeletris, and frequeny ontrol, vol 48, no 3, may 21 Fig 2 Peak veloity funtion used in the generation of the syntheti arterial drive signal experiments We onstruted the drive signal s(t) aording to the equation s(t) = m n (t)os(ω nt + φ n ) n= where { 1 if ν p (t) nω m n (t) = if ν p (t) <nω ; m n (t) is a windowing funtion used in ombination with ν p (t) to determine whih random-phase sinusoids to inlude in the summation at a given instant m n (t) passes all the sinusoids of frequeny up to and inluding the value of ν p (t) to the summation Thus, at time t, s is the summation of random phase sinusoids of frequenies up to and inluding those less than the value of ν at time t The bandwidth of s(t) does not stritly follow ν(t), beause the swithing of osines in and out of the summation introdues high frequeny omponents In effet, the osines are multiplied with square-wave funtions The result in the frequeny domain is the onvolution of the transform of the square wave with the desired spetrum III Experiment The mehanial details of the experimental setup are illustrated in Fig 3 The film is made of Vesiular (Xidex Corporation) mirofihe film The satterers in the film exist as olletions of small ( 1 µm) nitrogen gas bubbles within the film, generated through a photographi exposure and development proess The bubbles are patterned in halftone fashion to generate the desired target shape [12] The film is held flat and in tension by a set of four springs attahed at the ends of the support rails and the walls of the tank The tank is filled with degassed, Fig 3 Shemati drawing of the mehanial setup used in the experiments The thin film target is loated within the san plane of the transduer The target motion is in the plane of the page, toward and away from the transduer de-ionized water in these experiments, to eliminate effets aused by attenuation The phantom is normally designed for use with an aoustially non-sattering, attenuating medium A piezoeletri disk transduer, whih drives the thin film target, is attahed to the upper end of one rail When a voltage exitation is applied to the transduer, the rail and film are driven into motion in a vertial plane, relative to the illustrated setup A small iruit was onstruted to onvert digital waveforms, synthesized in MATLAB aording to the equations given in Setion II, into an analog drive signal for the piezoeletri element of suffiient amplitude to ahieve the desired effet Four drive signals were generated: the arterial signal, linear and logarithmi frequeny sweeps, and a melodious sequene of pure tones The synthesized waveform vetors were stored in an EPROM The iruit onverts the waveform samples to an analog voltage at a 1-kHz sampling rate The overall signal gain is adjustable to provide a maximum output of 8 V peak-peak The signal soure was onstruted as a matter of onveniene; any soure with suffiient drive apaity would do The film was sanned in these experiments with a Quantum QAD-1 sanner (Siemens Medial Systems, In, Ultrasound Group, Issaquah, WA) operated in PW Doppler mode A 75-MHz transduer was used, fixed in a lamp over the film in a manner suh that the thin film target wasinsanplane IV Results Figs 4 and 5 are Doppler spetral displays aptured from the QAD-1 sanner The Doppler spetral display in Fig 4(a) was generated with a low amplitude frequeny sweep The drive signal varies linearly from to 3 khz in 64 s Beause this amounts to a frequeny shift of only 6 Hz within a Doppler FFT window, the drive frequeny

5 maleavey et al: blood flow simulation and doppler test 741 is essentially onstant within any given FFT As a result, there are only signal omponents at the base drive frequeny ω(t), as predited by the theory In Fig 4(b), the Bessel band phenomenon disussed in [9] is illustrated, where the same frequeny sweep signal, as in Fig 4(a), is used, but the amplitude has been inreased by a fator of 5 The Doppler signal is learly visible at multiples of the vibration frequeny ω A synthesized arterial signal is shown in Fig 5 The distribution of veloities up to the maximum veloity is visible The peak veloity funtion ν(t) is also shown Beause of the symmetrial nature of the sonographs generated with this tehnique, the reverse flow setion of ν(t) appears as a smaller hump in the sonograph V Disussion Fig 4 PW Doppler spetra aptured with the Quantum QAD-1 ultrasound system for a) low amplitude and b) high amplitude vibration The desribed system provides signifiant potential for evaluating CW and PW Doppler systems The vibrating target produes a well-ontrolled stimulus to a Doppler system The response of the system to the known signal an be used to assess system performane in terms of Doppler sensitivity and uniformity of spetral response Work by Jensen [13] has shown that wall filters used in Doppler systems have a signifiant impat on the SNR of the Doppler signal and the stability of the resulting veloity estimate The vibrating target does produe a signal that an be deteted by Kasai-type Color Flow Doppler (CFD) systems [14] However, the Kasai algorithm estimates the mean flow veloity within a resolution ell Beause the Doppler signal produed is bi-diretional, estimates of the mean veloity will tend toward zero Thus, the vibrating thin film target does not provide a suitable stimulus for the evaluation of the mean veloity estimation auray of the CFD system Signals may be synthesized that allow one-sided spetra to be generated (low frequeny sawtooth waves), but they tend to be diffiult to realize with a simple mehanial system The vibration of the target and the ativation of the CFD do allow an evaluation of CFD spatial resolution as demonstrated in earlier work by Phillips [1] For orrelation-type Doppler proessors [11], [15], it would be neessary to synhronize the motion of the thin film with the Doppler aquisition and proessing in order to satisfy the underlying assumptions of orrelation systems and obtain meaningful Doppler data VI Conlusion Fig 5 PW Doppler spetrum observed with the simulated arterial signal We have presented a means for simulating a Doppler detetable flow veloity distribution using a single vibrating thin film target By vibrating a target with a bandlimited noise signal, an eho signal is produed that is interpreted by CW and PW Doppler as a distribution of veloities, the weighting of any given veloity determined by the harateristis of the noise signal spetrum We have also demonstrated the ability to simulate a time-dependant flow veloity distribution by varying the signal bandwidth with

6 742 ieee transations on ultrasonis, ferroeletris, and frequeny ontrol, vol 48, no 3, may 21 time Thus, it is possible, by ombining the veloity weighting and time-varying veloity tehniques, to reate a signal that resembles a realisti replia of arterial flow normally displayed by a CW or PW Doppler spetral display Aknowledgments The authors are grateful for ollaboration with Robert Naum of Applied Image, In and the onstrutive omments of the annonymous reviewers Stephen MAleavey was born in Danbury, Connetiut in 1974 He reeived the BS and MS degrees in eletrial engineering in 1996 and 1998, respetively, both from the University of Rohester, Rohester, NY He is presently pursuing the PhD in eletrial and omputer engineering at the University of Rohester Sine 1996, he has held positions as Teahing and Researh Assistant at the University of Rohester His teahing responsibilities have inluded letures on medial imaging and Doppler ultrasound His researh interests are in the area of ultrasound imaging, Doppler tehniques, and implementation signal proessing tehniques He is a member of IEEE and Tau Beta Pi Referenes [1] J A Jensen, Estimation of Blood Veloities Using Ultrasound: A Signal Proessing Approah Cambridge, England: Cambridge University Press, 1996 [2] P R Hoskins, T Anderson, and W N MDiken, A omputer ontrolled flow phantom for generation of physiologial Doppler waveforms, PhysMedBiol, vol 14, no 11, pp , Nov 1989 [3] W N MDiken, A versatile test-objet for the alibration of ultrasoni Doppler flow instruments, Ultrason Med Biol, vol 12, no 3, pp , Mar 1986 [4] D W Rikey, P A Piot, D A Christopher, and A Fenster, A wall-less vessel phantom for Doppler ultrasound studies, Ultrason Med Biol, vol 21, no 9, pp , Sep 1995 [5] E J Boote and J A Zagzebski, Performane tests of Doppler ultrasound equipment with a tissue and blood-mimiking phantom, J Ultrason Med, vol 7, no 3, pp , Mar 1988 [6] S V Russell, D MHugh, and B R Moreman, Programmable motion Doppler string test objet, Phys Med Biol, vol 38, no 11, pp , 1993 [7] D W Rikey and A Fenster, A Doppler ultrasound lutter phantom, Ultrason Med Biol, vol 22, no 6, pp , 1996 [8] WNMDiken,DCMorrison,andDSASmith, Amoving tissue-equivalent phantom for ultrasoni real-time sanning and Doppler tehniques, Ultrason Med Biol, vol 9, no 4, pp L455 L459, Jul-Aug 1983 [9] J Holen, R C Waag, and R Gramiak, Representations of rapidly osillating strutures on the Doppler display, Ultrasound Med Biol, vol 11, no 2, pp , Mar-Apr 1985 [1] D Phillips, S MAleavey, and K J Parker, A new thin film phantom for performane evaluation of ultrasoni Doppler imaging systems, in 1996 IEEE Ultrason Symp Pro, vol 2, pp [11] O Bonnefous and P Pesque, Time domain formulation of pulse-doppler ultrasound and blood veloity estimation by ross orrelation, Ultrason Imaging, vol 8, no 2, pp 73 85, Apr 1986 [12] S A MAleavey, R G Naum, and K J Parker, Charaterization of a thin film phantom for ontrast and resolution measurements, in Pro SPIE The Int So Opt Eng, vol 3658, 1999, pp [13] J A Jensen, Stationary eho aneling in veloity estimation by time-domain ross-orrelation, IEEE Trans Med Imaging, vol 12, no 3, pp , Sep 1993 [14] C Kasai, K Namekawa, A Koyano, and R Omoto, Real-time two-dimensional blood flow imaging using an autoorrelation tehnique, IEEE Trans Sonis Ultrason, vol SU-32, no 3, pp , May 1985 [15] I A Hein, J T Chen, W K Jenkins, and W D O Brien, Jr, A real-time ultrasound time-domain orrelation blood flowmeter I Theory and design, IEEE Trans Ultrason, Ferroelet, Freq Contr, vol 4, no 6, pp , Nov 1993 Zaegyoo Hah was born in Taejeon, Korea in 1962 He reeived BS, MS, and PhD degrees in eletroni engineering in 1985, 1988, and 1993, respetively, from Seoul National University, Seoul, Korea He is Assoiate Professor of Eletroni Engineering at KongJu National University, KongJu, Korea His researh interests inlude ultrasoni propagation, underwater beamforming, and medial appliations of ultrasound He is urrently a visiting sientist at the University of Rohester, Rohester, NY, working with Kevin Parker in the area of thin film phantoms and tissue-mimiking materials Kevin J Parker (S 79 M 81 SM 87 F 95) reeived the BS degree in engineering siene, summa um laude, from SUNY at Buffalo in 1976 Graduate work in eletrial engineering was done at MIT, with MS and PhD degrees reeived in 1978 and 1981 for work in eletrial engineering with a onentration in bioengineering Dr Parker is Professor of Eletrial and Computer Engineering, Radiology, and Bioengineering at the University of Rohester, where he has held positions sine 1981 In 1998, Dr Parker was named Dean of the Shool of Engineering and Applied Sienes at the University of Rohester Dr Parker has reeived awards from the National Institute of General Medial Sienes (1979), the Lilly Teahing Endowment (1982), the IBM Superomputing Competition (1989), the World Federation of Ultrasound in Mediine and Biology (1991), and the Joseph P Holmes Pioneer Award from the AIUM (1999) He is a member of the IEEE, the Aoustial Soiety of Ameria, and the Amerian Institute of Ultrasound in Mediine He was named a Fellow in both the IEEE and the AIUM for his work in medial imaging and in the ASA for his work in aoustis In addition, he reently ompleted a three-year term on the Board of Governors of the AIUM Dr Parker s researh interests are medial imaging, linear and nonlinear aoustis, and digital halftoning