Medical Image Analysis 5 (2001) 237–254
www.elsevier.com/ locate /media
Magnetic resonance elastography: Non-invasive mapping of tissue
elasticity
*
A. Manduca , T.E. Oliphant, M.A. Dresner, J.L. Mahowald, S.A. Kruse, E. Amromin,
J.P. Felmlee, J.F. Greenleaf, R.L. Ehman
st
Mayo Clinic and Foundation, 200 1 St. SW, Rochester, MN 55901, USA
Received 20 February 2000; received in revised form 22 September 2000; accepted 6 October 2000
Abstract
Magnetic resonance elastography (MRE) is a phase-contrast-based MRI imaging technique that can directly visualize and quantitatively
measure propagating acoustic strain waves in tissue-like materials subjected to harmonic mechanical excitation. The data acquired allows
the calculation of local quantitative values of shear modulus and the generation of images that depict tissue elasticity or stiffness. This is
significant because palpation, a physical examination that assesses the stiffness of tissue, can be an effective method of detecting tumors,
but is restricted to parts of the body that are accessible to the physician’s hand. MRE shows promise as a potential technique for
‘palpation by imaging’, with possible applications in tumor detection (particularly in breast, liver, kidney and prostate), characterization of
disease, and assessment of rehabilitation (particularly in muscle). We describe MRE in the context of other recent techniques for imaging
elasticity, discuss the processing algorithms for elasticity reconstruction and the issues and assumptions they involve, and present recent
ex vivo and in vivo results.  2001 Elsevier Science B.V. All rights reserved.
Keywords: Elasticity; Elastography; Strain imaging; Non-invasive palpation; Tumor detection
1. Introduction properties depicted by conventional medical imaging mo-
dalities are distributed over a much smaller numerical
There is strong precedent in clinical medicine for the range.
concept that tissue viscoelastic properties, assessed by Over the last decade, the recognition of the potential
palpation, are markedly affected by a variety of disease diagnostic value of characterizing mechanical properties
processes. Student physicians learn that the presence of a has led a number of investigators to seek methods for
hard mass in the thyroid, breast or prostate is suspicious imaging tissue elasticity. In materials science, the classic
for malignancy. Indeed, many tumors of these structures approach for measuring the elastic modulus of a sample is
are still first detected by touch. It is not uncommon for to apply a known stress and to measure the resulting strain.
surgeons at the time of laparotomy to palpate tumors that Refinements of this method involve the use of multiple
were undetected in preoperative imaging by CT, MRI or measurements with varying stress, and/or the application
ultrasound. None of these modalities provide the infor- of dynamic rather than static stress. Most of the proposed
mation about the elastic properties of tissue elicited by methods for elasticity imaging follow a similar approach.
palpation. The elastic moduli of various human soft tissues A stress is applied to tissue and the resulting strain
are known to vary over a wide range (more than four distribution is observed or measured using a conventional
orders of magnitude). In contrast, most of the physical imaging technique such as ultrasonography. The mode of
stress application can be static, quasi-static, or dynamic. A
recent review of such work is given by Gao et al. (1996).
*Corresponding author. Tel.: 11-507-284-8163; fax: 11-507-284-
Magnetic resonance elastography (MRE) is a recently
9420.
E-mail address: manduca@mayo.edu (A. Manduca). developed technique that can directly visualize and quan-
1361-8415/01/$ – see front matter  2001 Elsevier Science B.V. All rights reserved.
PII: S1361-8415(00)00039-6

238 A. Manduca et al. / Medical Image Analysis 5 (2001) 237 –254
titatively measure propagating acoustic strain waves in transverse contraction per unit breadth divided by longi-
tissue-like materials subjected to harmonic mechanical tudinal extension per unit length. These parameters are
excitation (Muthupillai et al., 1995, 1996a). Shear waves at interrelated, so that knowledge of any two allows calcula-
frequencies in the 10–1000 Hz range are used as a probe tion of the other two.
because they are much less attenuated than at higher Most soft tissues have mechanical properties that are
frequencies, their wavelength in tissue-like materials is in intermediate between those of fluids and solids. The value
the useful range of millimeters to tens of millimeters, and of Poisson’s ratio for soft tissues is in the range of
because shear modulus varies widely in bodily tissues. A v5 0.490–0.499, which is very close to the value for
phase-contrast MRI technique is used to spatially map and liquids (v5 0.500). In this case the Young’s modulus and
measure the shear wave displacement patterns. From this shear modulus differ only by a scaling factor (E5 3m).
data, local quantitative values of shear modulus can be Another characteristic that soft tissues share with liquids is
calculated and images (elastograms) that depict tissue that they are nearly incompressible. In contrast to the many
elasticity or stiffness can be generated. In this paper we orders of magnitude over which the Young’s and shear
briefly summarize other techniques for imaging elasticity moduli are distributed, the bulk moduli of most soft tissues
and describe the principles of MRE. We then consider the differ by less than 15% from that of water (Goss et al.,
equations of harmonic motion in soft tissue and describe 1978). The density of soft tissue also differs little from that
various approaches for reconstructing elastograms from of water (Burlew et al., 1980).
MRE data and the assumptions inherent in each. These These concepts represent a simplification of the me-
algorithms are then tested on synthetic and physical chanical behavior of soft tissues, which in general can be
phantom data sets of known stiffness and issues such as anisotropic, non-Hookean and viscoelastic.
noise sensitivity and resolution are discussed. Finally, a
summary of recent ex vivo and in vivo results is presented.
3. Elasticity imaging techniques
2. Elastic properties of soft tissue Much of the pioneering work in elasticity imaging has
been accomplished using ultrasound and either a quasi-
It is ironic that while the elastic properties of structural static stress model (Ophir et al., 1991; O’Donnell et al.,
materials have been extensively characterized by engineers 1994; Cespedes et al., 1993; Garra et al., 1997) or a
and physicists for more than a century, these properties are dynamic stress model (Gao et al., 1995; Huang and Roach,
virtually unknown for biological soft tissues. The scarcity 1991; Lee et al., 1991; Lerner et al., 1990; Parker et al.,
of such data in the literature most likely stems from the 1990; Parker and Lerner, 1992; Rubens et al., 1995).
technical difficulty of measuring the elastic properties of The quasi-static stress method employs an ultrasound
semisolid biologic tissues using conventional laboratory transducer to apply a small axial compression to tissue.
methods such as mechanical load-cell testing devices, Sonograms obtained without and with compression are
which rely on well-defined boundary conditions (Fung, correlated to determine the displacement at each location,
1993). While limited, this data does indicate that quantita- thereby revealing the longitudinal strain distribution. The
tive measurements of mechanical properties may be useful local strain is a relative measure of elasticity since it
in distinguishing between benign and malignant tissues. depends on the magnitude of compression and on the
For example, data from breast tissue specimens have elastic modulus of the material. Images depicting this local
consistently shown that the measured shear moduli of strain estimate have been shown to provide an informative
various types of carcinomas are much higher than the shear qualitative depiction of the elasticity of materials in tissue-
moduli of normal adipose-glandular tissue (Sarvazyan et simulating phantoms and surgical tissue specimens
al., 1994; Burke et al., 1990; Krouskop et al., 1998). It is (O’Donnell et al., 1994). In vivo studies of the method
generally agreed that no other physical parameter of tissue have demonstrated the feasibility of delineating breast
is changed by pathological or physiological processes to as cancer (Cespedes et al., 1993) by elastography. Such
great an extent as its elasticity. images can also be processed to compute a quantitative
In isotropic tissues, the proportionality constant that map of regional elastic modulus (E). The calculation
describes the amount of longitudinal deformation (ex- requires an estimate of local stress distribution, which in
pressed in terms of strain) that occurs in a given material in turn depends on the spatial composition of the object and
response to an applied longitudinal force (expressed in knowledge of the applied stress distribution (Ponnekanti et
terms of stress) is known as Young’s modulus (E) of al., 1992, 1994, 1995).
elasticity. The shear modulus (m) relates transverse strain The sonoelasticity method developed by Parker and
to transverse stress. Similarly, the bulk modulus (K) of coworkers (Parker et al., 1990; Parker and Lerner, 1992)
elasticity describes the change in volume of a material to employs a vibrational mechanical stress, typically in the
external stress. Another physical property of isotropic range of 20–400 Hz. Tissue is imaged with Doppler
Hookean solids is Poisson’s ratio (v), which is the ratio of ultrasonography to observe the regional amplitude of the