Image Processing Reference
In-Depth Information
14.2
ELASTIC PROPERTIES OF SOFT TISSUE
In isotropic Hookean materials, the proportionality constant that describes the
amount of longitudinal deformation (expressed in terms of strain) that occurs in
a given material in response to an applied longitudinal force (expressed in terms
of stress) is known as the
Young's modulus
(E) of elasticity. The
shear modulus
(
(K) of elasticity
describes the change in volume of a material due to external stress. Poisson's
ratio (
µ
) relates transverse strain to transverse stress. The
bulk modulus
) is the ratio of transverse contraction per unit breadth divided by longi-
tudinal extension per unit length. These parameters are interrelated so that knowl-
edge of any two allows calculation of the other two.
Most soft tissues have mechanical properties that are intermediate between
those of fluids and solids. The value of Poisson's ratio for soft tissues, which can
be directly calculated from the ratio of longitudinal- to shear-wave speeds, is
typically 0.499999, very close to the value for liquids (
v
0.500). In this case the
Young's modulus and shear modulus differ only by a scaling factor (
v
=
).
Another characteristic that soft tissues share with liquids is that they are nearly
incompressible. In contrast to the many orders of magnitude over which the Young's
and shear moduli are distributed, the bulk moduli of most soft tissues differ by less
than 15% from that of water [10]. Also the density of soft tissues differs little from
that of water [11]. These concepts represent a simplification of the mechanical
behavior of soft tissues, which in general can be anisotropic, non-Hookean, and
viscoelastic.
E
=
3
µ
14.3
MR ELASTICITY IMAGING TECHNIQUES
Much of the pioneering work in elasticity imaging has been accomplished using
ultrasound and either a quasi-static stress model [12-15] or a dynamic stress
model [16-19]. Ultrasound elastography continues to be a very active area of
research [20-22] but will not be further discussed here.
Other investigators have proposed several approaches for delineating tissue
elasticity using MRI. Saturation-tagging methods have been used in applications
as diverse as evaluating the local motion of cardiac muscle [23,24] and observing
connective motion in vibrated granular material [25]. A grid of saturation tags
can be applied to the tissue before it is deformed by an applied static stress [26].
The pattern of deformation of the grid of saturation tags can then be analyzed to
provide a map of local strain. A mathematical model of stress distribution within
the object could also be used, in principle, to convert this map of local strain into
a quantitative depiction of the regional elastic modulus [27].
Another well-known MRI method for measuring local motion is motion-
encoded phase-contrast imaging. This has been used clinically in applications such
as assessing regional myocardial motion, CSF pulsation, and intravascular blood
flow [28-30]. Plewes et al. proposed a method for elastography involving use of a
phase-contrast imaging sequence to estimate the spatial strain distribution resulting
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