An Improved Method of Determining Peak Blood ...

10.1109/ULTSYM.2014.0559

An Improved Method of Determining Peak Blood Velocity S. Ricci1, D. Vilkomerson2, R. Matera1, P. Tortoli1 1

Department of Information Engineering, University of Florence, Italy 2 DVX, llc, Princeton, NJ [email protected]

Abstract— The peak blood velocity is used in important diagnostic applications, e.g. for determining the stenosis degree. The peak velocity is typically assessed by detecting the highest frequency in the Doppler spectrum. The selected frequency is then converted to velocity by the Doppler equation. This procedure contains multiple potential sources of error: the peak frequency selection is sensitive to noise and affected by spectral broadening, and the frequency to velocity conversion is altered by the Doppler angle uncertainty. The result is an inaccurate estimate. In this work we propose a new method that removes the aforementioned errors. By exploiting a mathematical model of the Doppler spectrum the exact frequency to be converted to velocity, with no need of broadening compensation, is determined. The angle ambiguity is solved by calculating the Doppler spectra backscattered from two different receive apertures. The proposed methods uses, in transmission and receive, defocused steered waves that produce a wide sample volume. This includes the whole vessel section making the probe positioning quick and easy. The method, validated through Field II simulations and phantom experiments, featured a mean error lower than 1%. Keywords— Blood flow, Doppler spectrum, Maximum velocity detection, Vector Doppler.

I. INTRODUCTION The peak velocity of blood flowing in arteries has significant clinical importance in the current clinical practice. For example, it is used to decide about the need of surgery in case of stenosed vessel [1], and it is the basis for calculation of important indices like wall shear stress [2] or blood volume flow [3]. Echo Doppler ultrasound represents the main investigation method for the measurement of blood peak velocity. A blood particle moving at velocity , and insonated at frequency , produces echoes affected by a phase shift that is quantified by the Doppler equation: =

2cos

(1)

where c is the sound velocity, and θ is the beam-to-flow angle. Currently, the frequency , corresponding to the peak velocity, , through (1), is individuated by setting a threshold that intersects the Doppler power spectrum. Such threshold is typically set just above noise, making this approach strongly noise-dependent. The detected frequency is then translated to velocity through (1) using the Doppler angle θ. Inaccuracies in determining the Doppler angle represent a well-known source of error in velocity measurement, particularly when the angle

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approaches 90°. Furthermore, the frequency should be compensated for spectral broadening. Such compensation depends upon the transducer geometry and the Doppler angle, producing further inaccuracies [4]. In this work, a method for peak velocity measurements that is removes these inaccuracies is presented. The frequency detected from the Doppler spectrum by using the novel technique proposed by Vilkomerson et al. [5] for parabolic flow and uniform insonation, and later extended to more general pressure fields and flow profiles shapes [6]. This method, using a model of the Doppler power spectrum, determines a frequency that can be converted to velocity by (1) without the need of compensation for spectral broadening. The remaining source of error, related to a correct Doppler angle measurement, is solved by a vector Doppler technique [7]. The vessel is insonated by a plane wave transmitted from the central aperture of a linear probe, while two lateral, symmetrical apertures receive the backscattered echoes along different directions. This geometry generates a large sample volume (SV) that includes the whole vessel section for a relative wide axial extension. The proposed method has been validated through simulations and phantom experiments using flows with different velocities, vessels diameters, and probe-to-flow inclinations.

II. MATERIALS AND METHODS A. Maximum Frequency Detection Let us consider a SV covering a cylindrical vessel of radius l over an extension A, insonated by an ultrasound wave at frequency (see Fig.1). The pressure field is supposed to be uniform along the depth (z-axis) and the extension A (x-axis), while features a Gaussian shape along the y-direction, i.e. perpendicular to the plane represented in Fig.1. The vessel can be arbitrarily oriented (angle α between vessel axis and xdirection). The ratio between the -3dB lateral extension of the Gaussian insonation field and the vessel diameter is Wf, which is supposed to be higher than 40% [6]. The vessel is crossed by a parabolic flow of peak velocity . By dividing the flow in M discrete shells of velocity , and summing the contribution of each shell, it has been demonstrated [5][6] that the Doppler power spectrum obtained by an N-point FFT is:

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Power Spectrum

1

f P=2305 Hz

0.8 Th = 0.55

0.6 0.4 0.2 0

0

500

1000

1500 2000 Doppler shift (Hz)

2500

3000

Fig. 2. Spectrum generated by the model by using the parameters of Tab.1. The frequency corresponding to the velocity is reported by the vertical line, which crosses the spectrum at Th = 0.55 level. TABLE I. PARAMETERS USED FOR THE SPECTRA OF FIG. 2

Fig. 1. A flow moving at angle α with peak velocity VP crosses a SV placed at depth d. The SV is insonated for a length A by a plane wave transmitted along the z-axis of a linear probe. The backscattered echoes are received by 2 symmetric apertures along the steering angle ±δ, with no focalization.

,

=

1

,

,

,

2

2

,

,

(2) ,

Parameter Observation Time Insonation length Transmission Frequency Doppler angle Peak Velocity Sound velocity Velocity shells FFT points Insonation ratio

Symbol

Value 64 ms 8 mm 7 MHz 65° 60 cm/s 1540 m/s 500 256 70%

A

c M N Wf

,

while the reduced lateral dimension of the array produces a Gaussian-like field along the y-direction. where is the observation time, is the transit time of the is the frequency pulse , , , particles at velocity generated by the shell at velocity , observed for samples and centered at the Doppler frequency . The coefficient accounts for the Gaussian-shaped insonation [6]. The model (2) can be used to show that the frequency , corresponding through (1) to the peak velocity , can be located in the downslope region of the Doppler power spectrum by using the threshold Th = 0.55 with respect to the maximum amplitude. Fig. 2 reports an example of spectrum generated by (2) employing the parameters listed in Tab. I. As expected, the frequency = 2035 Hz, corresponding to = 60 cm/s, is located where the threshold Th = 0.55 (horizontal dashed line) crosses the downward region of the spectrum.

B. Angle-corrected Velocity Assessment A linear array is longitudinally placed above the vessel (see Fig.1). A central aperture transmits a long defocused wave. Two receiving apertures, symmetrically placed on the array at angles ± δ receive the backscattered echoes. No focusing is applied in transmission nor in receive. This geometry, jointly to the long transmission, produces a large SV that covers the whole vessel section for the axial extension A. The pressure field can be considered roughly uniform in x- and z- directions,

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The data acquired from the left and right apertures are processed to calculate the corresponding Doppler spectra. The frequencies and are found in the left and right Doppler spectrum, respectively, as described in previous section. Such frequencies are combined through a trigonometric triangulation [7] to produce the velocity components along the x- and zdirections (see Fig.1): =

2

∙

;

=

2

∙

1

;

(3)

Finally, the angle corrected maximum velocity is: |

|=

(4)

C. Simulation set-up The method has been tested on Field II [8][9] with steady flows at peak velocities of 0.4, 0.8, 1.2 m/s, pipe diameters of 4, 6, 8 mm, angles between the probe surface and the flow direction of 0°, 10°, 20°, 30°. Thirty-two experiments were performed with different combinations of the aforementioned parameters in the simulation set-up specified in Tab. II. For each experiment the data produced by Field II were saved for about 1200 transmissions, and further processed in MATLAB (The Mathworks, Natick, MA, USA) to calculate the left and and , apply right Doppler spectra, extract the frequencies the triangulation (3) and obtain the final angle-corrected

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% =

∙ 100

(5)

D. Phantom experiments The experiments were performed in a flow phantom based on a peristaltic pump (Watson-Marlow Pumps Group, Falmouth, UK) that moved a blood-mimicking fluid in circuit from a reservoir at air pressure, where the fluid was continuously stirred, to the measuring cell and then back to the reservoir. A flowmeter was inserted in the circuit. A straight plastic tube of 4 mm internal diameter crossed the measuring cell. A micromechanical position system held the linear array probe LA533 (Esaote s.p.a., Firenze, Italy) over the tube, and allowed to tilt the probe at specific angles. The probe was connected to the ULA-OP [10] research system. ULA-OP is based on 5 Field Programmable Gate Arrays (FPGAs) that perform the most calculation-intensive tasks, and a Digital Signal Processor (DSP) in which different software modules, which implement standard and/or custom modes, can simultaneously run. 1 GB of memory is available for saving data from all segments of the processing chain. ULA-OP is connected to a PC where a specific software manages the acquisition parameters, displays in real-time the results and holds the acquired raw data. The scanner was programmed to excite the central 54-element aperture of the probe with the same pulses as used for the simulations (see Tab. I). In receive, two 64-element apertures were positioned and steered as reported in Tab. II and Fig.1. A large SV was generated and positioned across the pipe by observing on the real-time display of the echograph the PW signals elaborated from the 2 apertures.

This set-up was used for 60 experiments with steady flow of 0.5-0.8 m/s peak velocities, and flow-to-probe angles of 0°30°. The raw data saved from ULA-OP were processed according to the same procedure used for simulations. The , was compared to the reference, : measured velocity, =

A. Simulations Fig. 3 reports the error distributions calculated from the 32 Field II simulations. The errors are grouped for reference velocity (top) and tube-to-probe angle (bottom). In particular, the bottom and top of the boxes visible in Fig. 3 indicate the 25th and 75th percentiles; the internal horizontal segment shows the median value; the outer whiskers are the maximum and minimum errors. The horizontal dashed line represents the average error calculated on the whole population, which corresponds to a mean underestimation of - 0.13 %. B. Phantom experiments Fig. 4 reports the measurements together with the identity line (dotted-black) and the regression line (dashed- red), which was calculated according to the model y=a·x + b. The results of

2

Aperture elements Transmission cycles Apodization window Pulse Repetition Frequency Apertures elements Apertures center position Steering angles Apodization window

Reception Xca -

0 -2 0.4 m/s

Value 1540 m/s 50 MHz 0.245 mm 192

0.8 m/s Peak Velocity VR

1.2 m/s

2 Error (%)

Speed of sound Sampling Frequency Element pitch Probe elements

Symbol General c fc Transmission -

(6)

III. RESULTS

TABLE II. PARAMETERS USED IN SIMULATIONS Parameter



where Q is the flow measured by the flowmeter and S is the tube section.

Error (%)

velocity through (4). The detected velocity, , was set in the simulation to compared to the reference velocity produce the relative error:

54 80 Tukey 2 kHz

0 -2 0°

64 ±9.97 mm ±14° Tukey

10°

Angle α

20°

30°

Fig. 3. Errors measured in simulations for different peak velocities (top) and tube orientations (bottom). The box represents the 25th to 75th percentile range, the internal segment reports the median value, the whiskers account for the minimum and maximum error.

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the method suitable for use in the clinic to provide more accurate and useful information about blood flow.

0.9

Measurements (m/s)

0.8

ACKNOWLEDGMENT

0.7

This work was supported in part by the Italian Ministry of Education, University and Research (PRIN 2010-2011), by the European Fund for Regional Development for the 2007–2013 programming period (POR FESR 2007-2013 CReO, ASSO project) and by NHLBI/NIH HL071359.

0.6 0.5 0.4 0.3 0.2 0.1 0.1

0.2

0.3

0.4 0.5 0.6 Reference (m/s)

0.7

0.8

REFERENCES

0.9

[1]

Fig. 4. Each circle represents a phantom measurement. The regression and identity lines are reported in red-dashed and black-dotted stroke, respectively. TABLE III. Parameter Gain error Offset Coefficient of determination Root mean square error

LINEAR REGRESSION ANALYSIS Symbol a b R2 Rmse

Value 0.967 0.08469 0.9921 0.184 cm/s

the regression analysis are listed in Tab. III. Gain and offset of about a = 0.96 and b = 0.085 cm/s, respectively, were obtained. The coefficient of determination, R2, was very close to 1. The root mean square error (Rmse), calculated between the measurements and the regression line, was quite low.

IV. DISCUSSION AND CONCLUSION In this work, an accurate method for peak velocity measurements has been presented. The proposed method, based on a non-heuristic threshold, is robust to noise, unaffected by spectral broadening, and angle-corrected. The method was tested with simulations and experiments. The error obtained in Field II simulations shows a regular trend for different velocities and probe orientations, (see Fig. 3) with very low bias (-0.13%) and error always lower than ± 2%. Phantom measurements confirmed the low bias and featured a low gain error, too. Like other vector Doppler techniques, this method exploits the transmission of plane waves [11]. Differently from the others, which aim at producing high resolution maps by using small SVs, the presented method exploits a very large SV that includes the whole vessel section. Thus positioning the probe is eased and not critical. This makes

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E. Grant, C. Benson, G. Moneta, A. Alexandrov, J. Baker, E. Bluth et al., “Carotid Artery Stenosis: Gray-Scale and Doppler US Diagnosis – Society of Radiologists in Ultrasound Consensus Conference”, Radiology, vol. 229, no. 2, pp. 340-346, 2003, http://dx.doi.org/10.1148/radiol.2292030516. [2] C. Carallo, L.F. Lucca, M. Ciamei, S. Tucci, M.S. de Franceschi, “Wall shear stress is lower in the carotid artery responsible for a unilateral ischemic stroke”, Atherosclerosis, vol. 185, no.1, pp. 108–113, 2006, http://dx.doi.org/10.1016/j.atherosclerosis.2005.05.019 [3] S. Ricci, M. Cinthio, T.R. Ahlgren, P. Tortoli, “Accuracy and Reproducibility of a Novel Dynamic Volume Flow Measurement Method”, Ultrasound Med. Biol., vol. 39. no. 10, pp. 1903-1914, 2013, http://dx.doi.org/10.1016/j.ultrasmedbio.2013.04.017 [4] E.Y.L. Lui, A.H. Steinman, R.S.C. Cobbold, K.W. Johnston, “Human factors as a source of error in peak Doppler velocity measurement”, J Vasc Surg, vol. 42, no. 5, pp. 972–972, 2005, http://dx.doi.org/10.1016/j.jvs.2005.07.014 [5] D.Vilkomerson, S. Ricci, P.Tortoli, “Finding the Peak Velocity in a Flow from its Doppler Spectrum”, IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 60, no. 10, pp. 2079-2088, 2013, http://dx.doi.org/10.1109/TUFFC.2013.2798 [6] S. Ricci, R. Matera, P. Tortoli, “An Improved Doppler Model for Obtaining Accurate Maximum Blood Velocities”, Ultrasonics, 2014, vol. 54, no. 7, pp. 2006-2014, 2014, http://dx.doi.org/10.1016/j.ultras.2014.05.012 [7] M. D. Fox, “Multiple crossed-beam ultrasound Doppler velocimetry,” IEEE Trans. Sonics Ultrason., vol. 25, no. 5, pp. 281–286, 1978, http://dx.doi.org/10.1109/T-SU.1978.31028 [8] J. A. Jensen and N. B. Svendsen, “Calculation of pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 39 no. 2, pp. 262–267, 1992, http://dx.doi.org/10.1109/58.139123 [9] J.A. Jensen: “Field: A Program for Simulating Ultrasound Systems”, Medical & Biological Engineering & Computing, vol. 34, no. 1, pp. 351-3531996. [10] E. Boni, L. Bassi, A. Dallai, F. Guidi, A. Ramalli, S. Ricci, J. Housden, P. Tortoli, “A reconfigurable and programmable FPGA-based system for nonstandard ultrasound methods”, IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 59 no. 7, pp. 1378 – 1385, 2012, http://dx.doi.org/10.1109/TUFFC.2012.2338 [11] S. Ricci, L. Bassi, P. Tortoli, “Real Time Vector Velocity Imaging through Multigate Doppler and Plane Waves”, IEEE Trans. Ultrason. Ferroelectr. Freq. Control., vol. 62, no. 2, pp. 314-324, 2014, http://dx.doi.org/10.1109/TUFFC.2014.2911

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