Measurement of Local Wavelength Using MR Elastography with Multiple Phase Offsets

Mikio Suga', Osamu Oshiro', Kotaro Minato', Tetsuya Matsuda2, Masaru Komori2, Takashi Takahashi 2, Jun Okamoto3, Osamu Takizawa3

' Nara Institute of Science and Technology, 8916-5 Takayama, Ikoma Nara, 630-0101, Japan * Kyoto University Hospital, 54 Syogoin-Kawahara, Sakyou, Kyoto, 606-8507, Japan

Siemens-Asahi Medical Technologies Ltd., 20-14, Higashi-Gotanda 3, Shinagawa, Tokyo, 141-8644, Japan

Abstract Magnetic resonance elastography (MRE) is a phase-

contrast-based MR method that can visualize propagating strain waves in materials. The quantitative values of shear modulus can be calculated by estimating the local wavelength (LW) of the wave pattern. Low frequency mechanical motion must be used for soft tissue-like materials, because strain waves rapidly attenuate as higher frequency. Therefore, it is difficult to estimate LW with high spatial resolution especially from noisy MRE image. In the MRE sequence, motion- sensitizing gradient (MSG) is synchronized with the mechanical cyclic motion. MRE images with multiple phase offsets can be generated with increasing delays between MSG and the mechanical excitation. In this report, we describe the new algorithm in order to measure LW in higher spatial resolution using MRE images with multiple phase offsets. This method was evaluated by the computer simulation and the phantom study. The result shows LW was successively estimated.

I. INTRODUCTION Tissue elasticity is fundamental and important information

for the physician's diagnoses and surgeon's procedures. Elasticity is an indispensable parameter of the virtual reality (VR) system, for instance tele-palpation and surgical simulators [1,2]. There are no currently available datasets on the elastic parameter map of whole human body like the Visible Human Project at the U S . National Library of Medicine [3]. In the existing surgical simulators, the fidelity of haptic feedback is limited because data are based on the subjective evaluation of an expert-user and not on objective model-based or empirical data-based methods. This paper deals with establishing the measurement of elastic modulus using the MRE image with multiple initial phase offsets.

II. TOOLS & METHODS

A. Acquisition of MR elastography image We use MRE measurement method based on the paper by

Muthupillai [4]. MRE experiments were performed with 1.5T whole-body MR scanner (MAGNETOM Vision Plus, Siemens AG, Erlangen, Germany). Acoustic strain waves were generated by an electro-mechanical actuator. TWO types of actuators were developed for the transverse wave and longitudinal wave. These actuators were driven by a wave

form generator. And the wave form generator was synchronized with an MR scanner by trigger pulse. Gradient echo sequence and spin echo sequence were developed for MR elastography. To encode the acoustic strain wave, motion-sensitizing gradient (MSG) was used like a phase contrast MR angiography sequence [5]. The wave form of the MSG was a sinusoidal wave. Typically, 125 or 250 Hz MSG was used. Other typical parameters are the followings; repetition times 100 to 500 msec, echo time 34 to 47 msec, slice thickness 1Omm.

B. Post-processing of the acquired MRE data to convert into absolute elasticity values

I ) Local wavelength estimation algorithm using MRE images with multiple initial phases offsets

The quantitative values of shear modulus can be calculated by estimating the local wavelength (LW) of the wave pattern. In principle, the spatial resolution is equal to the LV. Low frequency mechanical motion must be used for soft tissue-like materials, because strain waves rapidly attenuate at higher frequencies (Figure 1). Therefore, it is difficult to estimate LW with a high spatial resolution especially from a noisy MRE image. In the MRE sequence, MSG is synchronized with the mechanical cyclic motion. MRE images with multiple initial phase offsets can be generated with increasing delays between MSG and externally applied mechanical excitation [4]. Therefore, we developed a new algorithm to measure LW at a higher spatial resolution using MRE images with multiple initial phase offsets. The algorithm is described below.

Shear modulus, y, is given by

(a) (b) (c) Figure 1: Propagating shear waves. (a) T2-weighted MR image of a heterogeneous poly vinyl alcohol (PVA) hydrogel phantom. The phantom comprised an oblique slab of soft PVA hydrogel (7.5%) bounded on either side by stiff PVA hydrogel (10%). (b,c) MRE images depicting strain waves. The frequency of mechanical excitation was 250 Hz (b) and 400 Hz (c). As higher frequency, strain waves rapidly attenuate and could not observe waves in the depth.

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[pixel]

Sin (2d30)

Si n(2d30+7c) - Sin (2d30+d2) - Si n(2d30+n3/2)

0 2 4 6 8 1 0 1 2 1 4 0 2 4 6 8 1 0 1 2 1 4 ... 0 2 4 6 8 1 0 1 2 1 4 ... (e) (f) (g)

Figure 2: The local wavelength estimation algorithm. (a) Sinusoidal waves of multiple phase offsets (for example 0, n /2, n, 3 d 2 ) and some examples of the patches. The width of a patch was decided by the assumed local wavelength over the number of phase offsets. Synthesized waves (b-d) are combined with these patches, and these power spectrums are shown in (e-g) respectively. When the synthesized wavelength close to the original wavelength, relative power of fist harmonics becomes maximized.

where y is the depth, f is the externally applied mechanical excitation frequency and p(y) and h(y) are the density of the

wavelength, power spectrum of J is localized at a fundamental frequency (Figure 20. If the assumed wavelength W is far from the local wavelength, the power spectrum of J is distributed widely and not localized at the fundamental object and the Lv at depth Y ? respectively. Shear wave at

time t is described by

S(t,y) = A sin(2.n f t-cp(y))

frequency (Figure 2e, g). Using these properties, we can assume the likely estimate of the local wavelength at yo by

(2) retrieving J which maximizes (fundamental frequency spectrum power) / (all frequency spectrum power). Using this

(3) algorithm, the spatial resolution is improved N times compared to N=l.

where A is the peak amplitude of MRE image and q(y) is the phase delay from the object surface.

A series of snapshots of the mechanical wave propagating within the material were obtained with increasing delays between the mechanical excitation and the MSG waveform. If the delay was set to 1/Nf, observed shear waves are described by equation 4 (Figure 2a).

S(n/Nf,y) = A sin(2.n (n/N- q(y)) {n=1,2, ..., N-I)

Synthesized wave J (Figure 2b, c, d) is described by

J(y, yo, W, N) =

(4)

( 5 ) N-I

S(n/Nf,y).h(y, yo . W I N ) "=a

W is the assumed local wavelength around the depth yo and h is the window function and Ay is the window size. If assumed wavelength W is approximate to the local

2) Evaluation of proposed algorithm by computer simulation To evaluate frequency characteristics of the proposed

algorithm, computer simulation was performed. In the

- change of local wavelength -simulated shear wave (initial phase offset=O)

20 1500

1000

-1 000

10 -1500

0 5 10 15 20 25 30 35 depth [pixel]

Figure 3: Assumed wavelength and simulated wave (initial phase offset 0)

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+estimated wavelength with 1 phase offsets -+-estimated wavelength with 2 phase offsets

estimated wavelength with 4 phase offsets estimated wavelength with 8 phase offsets

+estimated wavelength with 16 phase offsets

U y;;; ;;i 2 2000

0

I

- f

" ' I ' ' , ' ' . ' I

1 4 7 10 13 16 19 spatial frequencychange on elastic

modulus per 40 pixel

~ ( t without noize -c- normal distribution noise (M=O, SD=20)

normal distribution noise (M=O, SD=40) -+-normal distribution noise (M=O, SD=80)

L m $ 2

E l

c m

c 0 2 0

1 4 7 10 13 16 19 spatial frequencychange on elastic

modulus per 40 pixel

(b)

Figure 4: Noise characteristic of proposed method. (a) Estimated wavelength with I , 2, 4, 8, 16 phase offsets (without noise), (b) Estimated wavelength with 16 phase offsets (with and without noise)

simulation, we use the parameters as an actual condition. Shear modulus of the human body was reported within 5 to 77kPa [6,7]. The heights of the object is 40 pixel (40mm) and the wavelength is around 10 to 20 pixel when the mechanical cyclic motion is 125 or 250 Hz. Therefore, assumed wavelength, h, was defined as,

h(y) = 5 s i n ( 2 . n ~ ~ /40)+15 (7) K is a wave number (K=I to 19). The example wave ( ~ = l )

is shown in (Figure 3). Noise characteristics of the proposed method are shown in Figure 4a and 4b. It was shown that the spatial resolution is improved using multiple initial phase offsets, while averaging the repetitive measurements improves the signal to noise ratio for additive white noise.

3) Evaluation elastic modulus by proposed algorithm We applied this proposed method to MRE images which

obtained by the PVA phantoms and to an excised porcine liver study, and generate the elastic maps. The first object to be imaged was a homogeneous 5 % cylindrical PVA hydrogel phantom. The second object was a simple heterogenous phantom, comprised of a horizontal slab of stiff 10% PVA hydrogel resting on a horizontal slab of soft 5% PVA hydrogel. Heights and diameters of these two objects were O.llm. The third object is an excised porcine liver. It is put into the container, height is 0.10m and diameter is 0.15m.

III. RESULTS In the first set of experiments, with 5% PVA hydrogel,

shear modulus map was analyzed by the proposed method using MRE with 4 phase offsets (Figure 5) . The average of the shear modulus was 10.1 (SD=1.3) [ e a ] . In the second set of experiments, with two-decker PVA hydrogel (Figure 6a) with 16 phase offsets (Figure 6b, c), between 10% and 5% PVA hydrogel is well represented by the proposed method using MRE with 16 phase offsets (Figure 6d). Spatial resolution of the map was sufficiently high despite the long local wavelength. The wave front undergoes refraction at the interface between the stiff and soft medium. Acoustic phenomena such as reflection, refraction. attenuation, and dispersion make it difficult to measure the local wavelength. In the third set of experiments, with excised porcine liver, the shear modulus is analyzed by the proposed method using MRE with 16 phase offsets. The average of the shear modulus is 10.6 (SE2.8) [ P a ] . The modulus is in the previously known range [7,8].

(b) Figure 5 : MRE image and analyzed shear modulus map. (a) 5% PVA hydrogel MRE image. (b) analyzed shear modulus map using MRE with 4 phase offsets

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(a) (b) (C)

+shear modulus ---tntensityof T2 wated MRI

120000 r _ " - " 1 1050 - a" 100000 U

80000

60000 E 40000

- 3

m a, f 20000

0

1000

950

900 850

800

750 0 10 20 30 40 50 60 70

depth [mm]

(4 Figure 6 10% and 5% PVA hydrogel using MRE with 16 phase offsets. (a) 10% and 5% PVA MRI (T2) image. (b) 10% and 5% PVA hydrogel MRE image with 125Hz mechanical cyclic motion. (c) A small strip, shown in (b) dotted line, extracted from MRE image with 16 phase offsets. (d) shear modulus map of 10% and 5% PVA hydrogel using MRE with 16 phase offsets

IV. CONCLUSIONS In this report, we describe the new algorithm to measure

local wavelength in a higher spatial resolution using magnetic resonance elastography images with multiple initial phase offsets . This method was evaluated by the computer simulation and the phantom study. The result shows local wavelength was successively estimated. These results suggest

MR elastography makes it possible to measure the elastic modulus in vivo.

V. ACKNOWLEDGMENTS This work was supported by the Special Coordination

Funds of the Science and Technology Agency of the Japanese Government and Research for the Future program of the Japan Society for the Promotion of Science.

x. REFERENCES

[ l ] N. Suzuki, et al., Simulator for virtual surgery using deformable organ models and force feedback system. Mediacine Meets Vertual Reality 50, Amsterdam: 1 0 s Press, 1998, pp. 227-233.

[2] L. Hiemenz, et al., Development of the force-feedback model for an epidural needle insertion simulator. Mediacine Meets Vertual Reality 50, Amsterdam: 10s Press, 1998, pp. 272-277

[3] http://www.nlm.nih.gov/researc~visible/visible-human.h tml

[4] R. Muthupillai, et al., Magnetic Resonance Elastography by Direct Visualization of Propagating Acoustic Strain Waves. SCIENCE, pp. 1854-1857, 1995.

[5] C.L. Dumoulin, et al., Three-Dimensional Phase Contrast Angiography. Magn. Reson. Med. 9, p.139, 1989.

[6] R. Muthupillai, et al., Magnetic Resonance Imaging of Transverse Acoustic Strain Waves. M a p . Reson. Med.,

[7] J.A. Smith, et al., Tissue characterization using magnetic resonance elastography. Proceedings of the ISMRM, p.1903, 1997.

[8] D.J. Lomas, et al., D.G.D Wight, MR elastography of human liver: preliminary results. Proceedings of the ISMRM, p.2177, 1998.

pp. 266-274, 1996.

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