MEASUREMENT OF TISSUE ELASTICITY USING MAGNETIC RESONANCE ELASTOGRAPHY

MEASUREMENT OF TISSUE ELASTICITY USING MAGNETIC RESONANCE ELASTOGRAPHY J. F. Greenleaf, R. Muthupillai, P. J. Rossman, D. J. Lomas, S. J. Riederer, and R. L. Ehman Mayo Clinic and Mayo Foundation Rochester, MN 55905 INTRODUCTION Palpation is routinely used for the evaluation of mechanical properties of tissue in regions that are accessible to touch. This means of detecting pathology using the "stiffness" of the tissue is more that 2000 years old. Even today it is common for surgeons to find lesions during surgery that have been missed by advanced imaging methods. Palpation is subjective and limited to individual experience and to the accessibility of the tissue region to touch. It appears that a means of noninvasively imaging elastic modulus (the ratio of applied stress to strain) may be useful to distinguish tissues and pathologic processes based on mechanical properties such as elastic modulus [1]. To this end many approaches have been developed over the years [2-9]. The approaches have been to use conventional imaging methods to measure the mechanical response of tissue to mechanical stress. Static, quasi-static or cyclic stresses have been applied. The resulting strains have been measured using ultrasound [1-9] or MRI [10-15] and the related elastic modulus has been computed from visco-elastic models of tissue mechanics. Recently a new MRI phase cantrast technique has been reported in which transverse strain waves propagating in tissue are imaged [13, 14, 16]. Because the wavelengths of propagating waves are related to density and the shear modulus and because the wavelengths of transverse waves for low frequency is on the order of millimeters this method promises to have good resolution and to be sensitive to the shear modulus. This paper reviews the theory of the method, presents some applications and discusses the implications of the method. THEORY We will term the microscopic region of tissue that responds the MRI signal an isochromat. The transverse magnetization phase <l>(t), of an isochromat moving in the Review of Progress m Quantztattve Nondestructlve Evaluatton, Vol. 16 Edtted by D.O. Thompson and D.E. Chtmentt, Plenum Press, New York, 1997 19

presence of a varying magnetic field gradient G(t), is given by: T <I>(r) =I J G(t). r(t)dt, 0 (1) where r(t) is the position vector of the moving isochromat, and 1 is the gyromagnetic ratio which is characteristic of the isochromat under investigation. In the case of a propagating transverse wave in the acoustic frequency range, the position vector can be considered to be a sinusoid and is given by: r(t) = To + [oexp(j(k. r- wt + cp) ), (2) where ro is the mean position of the isochromat, w is the angular frequency of the mechanical excitation causing the strain wave, a is the initial phase offset, k is the wave number of the strain wave, and [o is the peak displacement of the isochromat from its mean position. lf the gradient G(t) is a square wave with magnitude alternating between +IGI and -I GI for N cycles with a period T equal to the strain wave period 2 ;, then the resulting phase shift in the received signal is given by: r=nt <I>(r,t)=l j G(t) [ro+foexp(j(k r-wt+ifj))]dt, 0 (3) Equation 3 illustrates that the phase shift is related to the scalar product of the displacernent vector and the gradient vector, thus projections of the motion can be obtained for all three coordinate axes if three sets of data are obtained with mutually orthogonal gradients. The phase shift is also proportional to the product NT which is the total on-time of the gradient. By varying c/j, the phase offset between the gradients and the mechanical excitation, one can obtain images for different points in time and produce eine loops of images that depict the wave propagation. METHODS To provide examples of applications of the theory, tests were performed in a series of experiments using a 1.5-T Signa imager 1. Phantoms were produced which simulated tissues with varying stiffness, by mixing varying amounts of agarose2 in distilled water at around 70 C. A schematic of the experimental setup for generating strain waves is shown in Figure 1. An electromagnetic electromechanical actuator similar to a speaker mechanism GE Medtcal Systems. Milwaukee, WI Bacto Agar, Dtfco Laboratones, Detrott, MI, 1.0-3.0% w/w. 20

Trigger pulscs from (mager Pulse Wa c Pulse Scquencc ctuator 'oil... Direction of Motion Scnsitizin~ Gradient Figure I. Schematic for producing low frequency transverse waves in phantoms or tissues. The actuator coil is on a shaft that is hinged. When current is passed through the coil, the current causes the coil to align with the B field of the main magnet forcing a plate on the phantom shift back and forth. This produces transverse waves in the phantom. The wave generator is triggered from the MR imager insuring that the gradients within the imager are switched in synchrony with the excitation wave frequency. Reproduced with permission from [16], Williams and Wilkins. was constructed to produce transverse waves in the acoustic frequency range. A waveform generator produced the sinusoidal signal fed to the actuator coil through a stereo amplifier. The sinusoid was triggered from pulses synchronous with the gradient cycles provided by the MR imager. A phase contrast gradient echo sequence was developed with cyclic gradient waveforms as shown in Figure 2. The number of trigger pulses was adjustable and could be started prior to the imaging cycle, producing images of waves already propagating into the phantom or producing a mechanical steady state. Each repetition of imaging pulses was done twice with altemating polarity of the motion-sensitizing gradients (Figure 2). This acquisition scheme reduced phase noise and doubled the sensitivity of the phase measurements to small displacements. In the examples shown the gradients G(t) were colinear with the displacement ~: to measure transverse 21

Synchronous trigger pul e I I I I I I I I I 01HJUUU Motion- ensitizing gradient RF ~~--------------~~~o*aw~---------------- ---// Ov C\ t,_l v II C\ v Repetition I Repclilion 2 Figure 2. Pulses to trigger the waveform generator, shown in Figure 1, are produced in synchrony with the motion sensitizing gradients. The phase relationship between the gradients and the mechanical drive </J, can be altered. The motion-sensitizing gradients can be applied along arbitrary axes allowing measurement of displacement along any axis. Two repetitions are used with opposite motion-sensitizing gradients to subtract out systematic phase errors and to double sensitivity (NT in Equation 3) to synchronaus motion. Reproduced with permission from [16], Williams and Wilkins. waves. Ranges of data acquisition parameters were: Repetition time: 50-300 msec; echo time: 15-60 msec; acquisition matrix: 128-256: acquisition time: 20-120 seconds; ftip angle: 10-60 deg. The frequency of mechanical excitation ranged from 100-1100 Hz and the nurober of gradient pulses (N) ranged from 2-30 cycles. The images are of phase displacement computed from Equation 3, after correction for the balanced acquisition. APPLICATIONS Measurement of transverse strain waves in an agarose gel phantom is shown in Figure 3. The motion of the actuator was orthogonal to the plane of the figure and colinear with the sensitizing gradients. In one case, contact on the phantom was a point and in the other a plane. The results were spherical transverse waves and plane transverse waves respectively. The images represent measurements produced from motion-sensitizing gradients that were initiated after a near steady state condition was achieved by the actuator. 22

Point Sourcc Mechanical E'l(citation (Lhrough plane) at400hz Planar Source Mechanical Excitation at 400Hz - 5.() - 2.S f) Uisplaccmcnl (microns) 2.H 5.6 Figure 3. Images of transverse waves produced at 400 Hz in agar phantom material using the actuator of Figure l. A point contact produced spherical transverse waves (left) and a planar contact produced plane waves (right). The nurober of gradient cycles used for the measurement was 15. Equation 3 was used for the calibration scale. Reproduced with permission from [16], Williams and Wilkins. The point source image illustrates the inverse radius relationship of amplitude and shows some faint reflections from the walls of the phantom. The plane source image illustrates edge waves produced by the "aperture" and some reflections from the walls. Wave propagation can similarly be investigated in a heterogeneaus phantom. Figure 4 illustrates the propagation of a transverse pulse through a phantom consisting of two hardnesses. The barder gel (2% agar) is at the top and the softer gel (1.25%) is poured in the container at an angle. Refraction of wave propagation is clearly evident in the area marked by the arrow. Application of this method to quantitative assessment of shear modulus for inhomogeneaus material is shown in Figure 5. Two agarose gel cylinders of high and low stiffness were embedded in an agarose phantom of medium stiffness. The resulting displacement image was obtained at 250 Hz using plane wave excitation. Panel (A) depicts the displacement of transverse waves propagating through the phantom and the two cylinders. The stiffer cylinder on the left displays larger wavelengths and the softer 23

Mcchanical Excitation at 250Hz Figure 4. Refraction of a propagating transverse wave is exhibited in this displacement image for mechanical excitation of 250 Hz. Six gradient-sensitizing cycles were used. White arrow depicts wave propagation direction for the agarase gel poured into the phantom container at an angle. Reproduced with permission from [16], Williams and Wilkins. cylinder on the right shorter wavelengths than the background material. This image was processed with a local wavelength estimation filter [17] to compute the local shear modulus assuming the density of the material to be constant at 1.0 g/cm3. The resulting quantitative image of shear modulus is shown in panel (B). DISCUSSION Using synchronaus motion-sensitizing gradients, Magnetic Resonance Elastography (MRE) is capable of producing either snapshots or eine loops of cyclic displacement caused by extemally applied transverse waves in the acoustic range. The displacement can be measured in the three orthogonal directions providing a vector valued function ({(r, t) in Equation 3). The method can be used to study propagation effects such as refraction and diffraction and can provide quantitative measures of shear modulus. The advantages of the method are that it can provide images virtually anywhere in the body and in any orientation. For qualitative sturlies of wave propagation, such as refraction and diffraction (Figures 3 and 4), MRE has the same resolution as a standard MR imaging 24

-10.0-5.0 0.0 5.0 10.0 0 5 10 15 20 25 Di placemcm ().Im) Shear Modulu /m 2 ) Figure 5. Magnetic resonance elastography images of two cylinders of agarose with high and low stiffness embedded in a background material with average stiffness. Plane transverse waves were applied at the top of the phantom. The phase image taken at 250 Hz shows large wavelength in the hard cylinder and short wavelength in the soft cylinder (left). Computation of the local wavelength and the assumption of density of Ig/cm3 results in a quantitative image of shear modulus (right). The indicated hardness of the cylinder on the left is about 22kN/m 2 compared to stiffness measurements of large samples of the same gel of 23.8 kn/m 2. system of about 0.5 mm. For shear modulus or wavelength measurements (Figure 5), MRE is quantitative with a spatial resolution of the order of the wavelength of the transverse elastic waves and a contrast resolution of a few percent [18] for stiffness or attenuation. The disadvantages of MRE are that each two-dimensional displacement image requires separate repetitions of the mechanical excitation over a time span of about one minute to acquire data for the image. The acquisition time is multiplied by the number of phase offsets, </J, acquired for the eine loop. MRE provides a practical new experimental tool for measuring propagating transverse waves in tissues and tissue-like media. MRE may also provide a new clinical imaging tool, extending the classic palpation methods to full three-dimensional quantitative Ievels. ACKNOWLEDGMENTS The authors thank Elaine Quarve for secretarial assistance and Randy Kinnick, Ultrasound Laboratory, and T. C. Hulshizer, MRI Research Laboratory, for technical assistance. 25

REFERENCES I. A. Sarvazyan, D. Goukassian, E. Maevsky, G. Oranskaja, G. Mironova, V. Sho1okhov, and V. Ermi1ova, Proc. International Workshop on Interaction of Ultrasound with Bio1ogical Media, pp. 69-81 (1994). 2. T. A. Krouskop, D. R. Dougherty, and F. S. Vinson, J. Rehabil. Res. Dev. 24(2), 1-8 (1987). 3. Y. Yamakoshi, J. Sato, and T. Sato, IEEE Trans. U1trason. Ferroe1ec. Freq. Cont. 37(2), 45-53 (1990). 4. K. J. Parker, S. R. Huang, R. A. Musulin, and R. M. Lerner, Ultrasound Med. Biol. 16(3), 241-246 (1990). 5. R. M. Lerner, S. R. Huang, and K. J. Parker, Ultrasound Med. Biol. 16(3), 231-239 (1990). 6. M. Bertrand, J. Meunier, M. Doucet, and G. Ferland, IEEE 1989 Ultrasonics Symposium Proc. 2, 859-863 (1989). 7. J. Ophir, I. Cespedes, H. Ponnekanti, Y. Yazdi, and X. Li, Ultrason. Imaging 13, 111-134 (1991). 8. A. R. Skovoroda, S. Y. Emelianov, M. A. Lubinski, A. P. Sarvazyan, and M. O'Donnell, IEEE Trans. Ultrason. Ferroe1ec. Freq. Cont. 41(3), 302-313 (1994). 9. M. O'Donnell, A. R. Skovoroda, B. M. Shapo, and S. Y. Emelianov, IEEE Trans. Ultrason. Ferroelec. Freq. Cont. 41(3), 314-325 (1994). 10. C. J. Lewa and J. D. de Certaines, J. Magn. Reson. Imaging 5, 242-244 (1995). 11. C. J. Lewa and J. D. de Certaines, Proceedings, SMR and ESMRMB, 3rd Scientific Mtg., Nice, France, p. 690 (1995). 12. D. B. Plewes, I. Betty, and I Soutar. Proceedings, SMR, 2nd Annual Mtg., San Francisco, CA, p. 410 (1994). 13. R. Muthupillai, D. J. Lomas, P. J. Rossman, J. F. Greenleaf, A. Manduca, and R. L. Ehman, Science 269, 1854-1857 (1995). 14. R. Muthupillai, D. J. Lomas, P. J. Rossman, J. F. Greenleaf, A. Manduca, S. J. Riederer, and R. L. Ehman, Proceedings, SMR and ESMRMB, 3rd Scientific Mtg., Nice, France, p. 189 (1995). 15. J. B. Fowlkes, S. Y. Emelianov, J. P. Pipe, S. R. Skovoroda, P. L. Carson, R. S. Adler, and A. P. Sarvazyan, Med. Phys. 22(11), 1771-1778 (1995). 16. R. Muthupillai, P. J. Rossman, D. J. Lomas, J. F. Green1eaf, S. J. Riederer, and R. L. Ehman, Magn. Reson. lmaging 36, 266-274 (1996). 17. A. Manduca, R. Muthupillai, P. J. Rossman, J. F. Greenleaf, and R. L. Ehman, Medical Imaging 1996: Image Processing, SPIE 2710, 616-623 (1996). 18. J. A. Smith, R. Muthupillai, J. F. Greenleaf, P. J. Rossman, T. C. Hulshizer, and R. L. Ehman, Review of Progress in QNDE, Vol. 16 (in press) (1996). 26