Nonlinear Inverse Problems in Imaging

Chapter 10

Magnetic Resonance Elastography

Magnetic resonance elastography (MRE) is an imaging modality capable of visualizing the stiffness of biological tissues by measuring the propagating strain waves in an object of interest (Low et al. 2010; Muthupillai et al. 1995; Papazoglou et al. 2005; Sack et al. 2002; Sinkus et al. 2000). Since MRE provides non-invasive assessment of variations in tissue elasticity, it has been used for non-invasive diagnosis of liver disease or for detecting prostate cancer. Tissue elasticity can change with disease, and the shear modulus (or modulus of rigidity) varies over a wide range, differentiating various pathological states of tissues (Venkatesh et al. 2008; Yin et al. 2007). It also has potential applications in studying skeletal muscle biomechanics (Papazoglou et al. 2005; Uffmann et al. 2004).

Tissue elasticity refers to the ability of a tissue to deform its shape when a mechanical force is applied and to regain its original shape after the force is removed; tumor tissue is less compressible than normal tissue. For centuries, palpation using the surface of the finger or palm has been used to measure tissue stiffness; it can be viewed as an elasticity measurement technique to feel the degree of tissue distortion (strain) due to pressure (stress) on the tissue. As a visual palpation, elastography using ultrasound was developed in the late 1980s (Lerner and Parker 1987; Ophir et al. 1991). This ultrasound elastography influenced the early development ...