IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 58, no. 4, April 2011853

Correspondence
Initial Phantom Validation of Minute Roughness
Measurement Using Phase Tracking for Arterial
Wall Diagnosis Non-Invasively In Vivo
Magnus Cinthio, Hideyuki Hasegawa, and Hiroshi Kanai
Abstract—To detect minute roughness, we utilized the phasechange that occurs in a radio frequency echo from the roughsurface of an object during its lateral motion. The new method
was optimized and validated using saw-tooth-shaped silicone
phantoms sized from 13 to 33 µm; results were compared tothose obtained using a confocal laser scanning microscope.

I. Introduction

A

therosclerosis is an inflammatory disease affecting the arteries, which accumulate sub-endothelial
lipid-laden foam cells and associated T lymphocytes andform non-stenotic fatty streaks [1]. When the fatty streaks
progress, it is highly likely that the inner surface of arterial wall becomes uneven before it becomes thick. However, as far as we know, this has never been investigated.
We believe that by measuring the unevenness of the inner
structures of the arterial wall, i.e., the defect of the endothelium, it may be possible to detect signs of atherosclerosis earlier than using current methods.
To obtain an indirect measure of the unevenness, Pedersen et al. have developed an angular spectrum-based
formulation method [2]–[4]. Zhang et al. have developeda 3-D ultrasound system with the ability to extract surfaces using radial basis functions. This method produces
realistic surfaces with a high level of detail [5], however,
the measurement error was in the millimeter range. Gunarathne et al. have developed an ultrasonic spectroscopic
technique to measure the gross surface texture of nonmedical materials. They introduced a roughness coefficientthat specified the texture on a quantitative basis [6].
Non-invasive in vivo examination of the common carotid artery and other superficial arteries requires ultrasound frequencies of 5 to 15 MHz. At these frequencies,
the magnitude of early roughness is smaller than the
wavelength of the RF signal. To further complicate theManuscript received November 22, 2010; accepted January 24, 2011.
This study was supported by the Japanese Society for the Promotion of
Science and the Swedish Research Council.
M. Cinthio is with Electrical Measurements, Faculty of Engineering, LTH, Lund University, Lund, Sweden (e-mail: magnus.cinthio@
elmat.lth.se).
H. Hasegawa and H. Kanai are with the Department of Biomedical
Engineering, Graduate School of Biomedical Engineering, Tohoku University, Sendai, Japan.
H. Hasegawa and H. Kanai are also with the Department of Electronic
Engineering, Graduate School of Engineering, Tohoku University, Sendai, Japan.
Digital Object Identifier 10.1109/TUFFC.2011.1879

measurement, the arterial wall moves both radially andlongitudinally during the cardiac cycle [7]–[10]. One way
to obtain information regarding roughness which is lessthan the wavelength is to utilize the phase of the RF echo.
The most obvious way is to compare the phase information between several beams along the surface in one frame.
This approach would probably work well in a water tankwhere there are no differences in attenuation or in soundvelocity between the ultrasonic beams. However, whenusing this approach in arterial characterization, a major
problem arises; the small variation in the speed of soundbetween different beams, which is highly likely, introducesaberration error. For example, if the object of interest is
30 mm below the transducer and the speed of sound varies only 0.1% between two beams, this causes a differenceof 0.1% between the distances to the surface. However,this difference corresponds to 30 µm, and in this context
30 µm is much greater than the micro-scale roughness weare interested in determining. Fig. 1 shows the setup andthe resulting ultrasonic B-mode images of a flat glass surface (usually used for optical microscopes) with and without porcine cutlet placed between the transducer and theglass surface. As can be seen in the figure, the aberration
errors make it impossible to estimate the surface profile(highly flat in this case) by comparing the depth positionsof the surface using adjacent ultrasonic beams.
Therefore, Arihara et al. suggested a one-beam approach, which utilizes the fact that the phase of an RF
echo changes because of the change in distance (Fig. 2)
when a rough object is moved laterally. They validated
the approach using a silicone phantom moving laterally
in a water tank [11]. The measurement error was in the
micrometer range.
To further extend this approach for arterial characterization, we recently proposed a method [12] by which theroughness of the inner layer of the arterial wall can bemeasured by combining precise measurement of the axial
motion using phase tracking [11], [13] with measurementof the natural longitudinal movement [9] of the arterial
wall. The aim of the present study was to further examine
this new method’s ability and to validate it using silicone
phantoms, comparing our results with those obtained witha confocal laser scanning microscope.
II. Material and Methods
A. The Algorithm
Let f(mΔx, kΔy, n) (n = 1, 2, …, N) denote a cineloop
consisting of N image frames, where Δx and Δy are thelateral and axial spacing of sampled points, respectively,
and m and k are ultrasonic beam number and sampled
point number, respectively, corresponding to a position

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IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 58, no. 4, April 2011

Fig. 1. The setup and the resulting ultrasonic B-mode image of a flat glass surface (a) without and (b) with a 1-cm-thick porcine cutlet placed between the transducer and the glass surface. Note the severe aberration errors in (b) that make it impossible to compare adjacent ultrasonic beams
to estimate the roughness of the surface.

Fig. 2. Schematic of roughness measurement utilizing the phase of an ultrasonic beam. (a) The phase is measured at one position during lateral
movement of the object. The lateral movement is measured using 2-D high-resolution echo-tracking. (b) The object and the resulting echoes at two
successive frames are shown enlarged. (c) One enlarged saw tooth at two successive frames and the resulting echoes are shown. ∆x = the lateraldisplacement between two frames. ∆d(m,n) = the resulting phase change between two frames.

in the lateral x and axial y directions in the image plane.
When a rough surface is moved laterally, as in the caseof an arterial wall [10], the corresponding time delay ofan echo becomes different (Fig. 2). This change in timedelay can be detected as an axial displacement d(mΔx,n) at beam position mΔx in frame n using a phase-sensitive axial displacement estimator [13]. When the artery isscanned in the longitudinal direction, the axial and lateral
movements correspond to the arterial radial and longitudinal directions, respectively.
By defining the axial displacements induced by surface
roughness as ds(mΔx, n) and the global motion that arises
from transducer motion, leaning surfaces, and the change
in lumen diameter as dg(mΔx, n), the axial displacementd(mΔx, n) estimated by the phase-sensitive axial displacement estimator is expressed as follows:d(m Dx, n) = d s(m Dx, n) + d g(m Dx, n).

(1)

The axial displacements induced by surface roughness
have a high spatial frequency, whereas axial transducer
motion, as well as a leaning surface moving longitudinally,
introduces axial motion that is equal at different positions
laterally, i.e., a spatial frequency close to zero. Regarding
the lumen diameter change, the pulse-wave velocity in theartery is typically 5 m/s and the main frequency components of the pulsation of the artery are less than 10 Hz.
This corresponds to a wavelength of the pulse-wave that iscinthio et al.: initial phantom validation of minute roughness measurement

longer than 50 cm. Because the longitudinal movement of
the arterial wall is less than 2 mm and the maximum scanning area is 20 mm, the region of interest can be considered short. Furthermore, the viscoelastic properties of thearteries in very early-stage atherosclerosis are considered
to be homogeneous. Thus, we can assume that the axial
movement induced by pulsation of the heart does not depend on the lateral position, i.e., spatial frequency is also
close to zero in the case of the change in diameter.
Measured displacement d(mΔx, n) can be differentiatedwith respect to lateral position x as follows:¶d(m Dx, n)»d((m + 1)Dx, n) - d(m Dx, n)

¶x
Dx
		

= Dd(m Dx, n).
(2)

By applying the Fourier transform to (2), the following
relationship is obtained:1
FTx[d((m + 1)Dx, n) - d(m Dx, n)]Dx1={exp(j2p f x Dx ) - 1} × FTx[d(m Dx, n)]Dx= H (f x ) × FTx[d(m Dx, n)],(3)

m + Dmå Dx × Dd(iDx, n)i =m -Dmcorrelation [10], the roughness profile r(xn) of the surface
is obtained as follows:r(x n ) = r(l(m, n)) = d s,Dm(m, n).

(5)

B. Measurement System
All of the measurements were performed using a modified commercial ultrasound system (Prosound II, Aloka,
Tokyo, Japan). The system was equipped with a 10-MHz
linear array transducer 40 mm in width. It was desirable
to achieve the best possible spatial and temporal quantification and, thus, the number and interval of scan lines
were set as small as possible, resulting in a frame rate of
70 Hz and scan line intervals of 100 µm. These settings
allowed a lateral image width of 20 mm. The sampling
frequency of RF echoes was 40 MHz.
C. Algorithm Evaluation

where FTx[·] is the Fourier transform with respect to x
and H(fx) = {exp(j 2π fx Δx − 1) − 1}/Δx is the transfer
function of the differential operation. Obviously, |H(fx)| iszero at fx = 0, i.e., spatial high-pass filtering. Therefore,
after the differentiation of d(mΔx, n) with respect x, global motion dg(mΔx, n) in (1) can be removed, and only thedisplacement ds(mΔx, n) induced by surface roughness remains. However, the differentiated displacement Δd(mΔx,n) is dimensionless. To obtain the surface profile (roughness) in meters, differentiated displacement Δd(mΔx, n)
is integrated with respect to lateral position x as follows:d Dm(m Dx, n) =

855

(4)

= d s,Dm(m Dx, n) º d s,Dm(m, n).
From (4), it can be seen that the axial displacement
ds,Δm(m, n) induced by the surface roughness can be obtained from d(mΔx, n) ≡ d(m, n) measured by ultrasoundafter spatial differentiation and integration. In the spatial
high-pass filtering procedure, Δm = 1 was used, i.e., toobtain axial displacement induced by the roughness in one
position, three (2Δm+1) adjacent scan lines were differentiated and integrated.
The ds,Δm(m, n) corresponds to the change in height ofa surface at beam m from the height at frame 0, inducedby the lateral displacement l(m, n). The lateral position
xn on the surface measured by beam m in frame n canbe obtained by the lateral displacement l(m, n). Therefore, by estimating the lateral displacement l(m, n) using
a high-resolution echo-tracking method based on cross-To confirm the need for the spatial filtering, we conducted an experiment on a flat surface with 1-cm-thickporcine cutlet between the transducer and the surface-ofinterest, which introduced distinct aberration error. Six
replicates were conducted on a flat glass surface with porcine cutlet between the transducer and the glass surface.
The method was evaluated using three silicone phantoms. The silicone phantoms were produced using metallic
molds which were manufactured using a milling machine.
To investigate the ability of the method on both steps andslopes, the molds were saw-tooth-shaped. Ten saw teeth,
whose heights were designed to be 13, 23, and 33 μm,
were milled on the top of the molds, with the width of one
tooth being 0.5 mm.
Reference measurement of the phantoms was made bya confocal laser scanning microscope (VK-9700, Keyence,
Tokyo, Japan). The resolution of the measurement using
the laser system was 14 nm.
The repeatability between measurements and the accuracy of the proposed method was analyzed using themethod of Bland and Altman [14].
III. Results
Fig. 1(b) shows an ultrasonic B-mode image of a flatglass surface when a porcine cutlet was placed between
the transducer and the glass surface. The aberration errors make it impossible to compare ultrasonic beams beside each other to estimate the roughness of the surface.
The roughness of the glass surface estimated during its
lateral movement using our novel approach was 0.43 µm[standard deviation (SD) 0.28 µm].
Fig. 3(a) shows a B-mode image of the phantom with
33-μm saw teeth. As can be seen in Fig. 3(a), it is difficult to measure surface roughness quantitatively using
conventional B-mode images. By using the phase-sensitive

856IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control , vol. 58, no. 4, April 2011displacement estimator [13], the axial displacements ofthe surfaces of the 13-, 23-, and 33-μm phantoms during
their lateral motion were measured as shown in Fig. 3(b).
Because of difficulty in obtaining exact 90° alignment between transducer and phantom, a global displacement up
to hundreds of micrometers occurred axially. By applying
spatial filtering, the roughness curves of four saw teeth at
one beam during the lateral motion were obtained for all
three phantoms, as shown in Fig. 3(c).
The optimal size and position of the correlation kernel
used for estimation of the axial displacement was determined by repetitive measurements of the phantom sothat the difference between the surface profile measured
by ultrasound and that measured by the confocal laser
microscope was minimized. The size and position of thekernel was optimized to be seven samples (0.13 mm) andnine samples (0.17 mm) closer to the ultrasonic probe
than the peak position of the envelope of an echo fromthe surface. The results of the roughness estimations
obtained using the optimized kernel size and position
are summarized in Table I. For the repetitive measurements, the systematic and random differences from theresults obtained by the confocal laser microscope were−0.39 µm and 0.86 µm, respectively. The mean difference
between the results obtained by ultrasound and laser was−7.6 µm (SD 2.8) for the 13-µm phantom; −6.8 µm (SD2.3) for the 23-µm phantom and −6.1 µm (SD 3.4) for
the 33-µm phantom.
IV. Discussion

Fig. 3. (a) Ultrasonic image of the 33-µm phantom with no aberrating
layer between the transducer and the phantom. The phantom is shown
between the arrows. (b) The measured axial displacement of the phantom surface against the measured lateral movement of the phantom at
one beam in the forward and backward (dashed) direction, respectively,
during one measurement on the 33-μm-phantom. Note the different
scales on the axes. (c) Resulting roughness curves of four saw teeth after
spatial filtering for the 33-μm phantom, the 23-μm phantom (dashed),
and the 13-μm phantom (dashed-dotted), respectively.

We have recently shown the possibility of measuring
a 12-µm-step surface profile with a measurement error
in the micrometer range using the relative phase changeof one ultrasonic beam using a phase-tracking algorithm
when the object is moved laterally. In the present study,
this concept was extended by a simultaneous measurement of lateral movement of the object using an echotracking algorithm on the same cineloop to make it possible to measure the roughness of the arterial wall. As aresult, detection of a small change in height, [Fig. 3(b)]not noticeable in a conventional B-mode image by the naked eye, was shown to be possible. Furthermore, accurate
and repeatable measurement of the height and width ofsaw tooth profiles was achieved, which shows promise forboth medical and non-medical applications.
As described previously, there was a systematic errorof 7 µm (smaller than the true value). One of the reasonsfor this may have been the width of the ultrasonic beam.
The lateral width at half-maximum of the ultrasonic beam
used was about 0.8 mm, slightly larger than the pitch of
the saw teeth. Therefore, an echo signal obtained at abeam position coinciding with the peak of a saw tooth
contains a weak echo from a dip in addition to the echo
from the peak. In this case, the difference in phases of
echo signals obtained at beam positions coinciding with apeak and a dip decreases, resulting in the underestimation

cinthio et al.: initial phantom validation of minute roughness measurement

857

TABLE I. Summary of Ultrasonic and Laser Measurements of 13-, 23-, and 33-µm Phantoms.
UltrasoundRoughness (µm)

Laser
Width (µm)

Roughness (µm)

Phantom

Mean

SDteethMean

SDteeth

Mean

13 µm
23 µm
33 µm

6.3 (SD 0.1)
16.7 (SD 1.2)
24.5 (SD 1.1)

2.7 (SD 0.0)
3.3 (SD 0.1)
3.8 (SD 0.1)

507 (SD 9)
493 (SD 3)
494 (SD 3)

62 (SD 6)
33 (SD 4)
26 (SD 5)

13.9 (SD 1.5)
23.5 (SD 2.1)
30.6 (SD 1.8)

Mean: the mean and the standard deviation of six measurements. SDteeth: the mean and the standard deviationof the standard deviation within one measurement.

of the roughness. This effect would limit the measurable
lateral pitch of the roughness. Further experiments on different phantom widths and lateral velocities, non-periodic
roughness shapes, more realistic phantoms with 2-D patterns and scatterers should be conducted; thereafter the
proposed method should be tested in vivo.
The spatial differentiation and integration operations
remove the global motion of the arterial wall during the
cardiac cycle by assuming that the global motion is constant among the scan lines used for differentiation andintegration. It is advisable to set the length (the numberof scan lines) for spatial filtering to be as narrow as possible to meet this assumption. Therefore, three scan lines
were used in the spatial high-pass filtering procedure. In
this study, we did not correct for the scan velocity, i.e.,
the three beams were not scanned simultaneously. This
small time delay when the different beams are scanned
may have introduced the small measurement error shownin the experiment on the flat glass surface. Further investigation needs to clarify this and its possible importancein roughness measurements.
In our experiments, we have shown that the spatial
high-pass filter can handle leaning surfaces and global
movement of tens of micrometers (which especially occurred when the direction of motion of the phantom
does not perfectly coincide with the lateral direction).
However, for the in vivo investigation, we also need tohandle global movement which has a limited pulse-wave
velocity. This makes the diameter change, i.e., the global
movement starts at different times at different ultrasonic beams. To overcome this potential problem, it might
be necessary to avoid measurement of the roughness atearly systole.
V. Conclusion
This study showed that by combining measurement of
the axial motion using phase tracking and lateral motion
using high-resolution 2-D cross-correlation, a small changeof 100 µm in height, not noticeable to the naked eye, canbe detected. It was also shown that by applying spatial
high-pass filtering to remove the global motion, the height

and width of saw-tooth profiles on silicone phantoms canbe accurately and repeatedly measured.
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