MR Elastography (MRE) allows estimation of the mechanical properties of tissue in response to compression or vibration. Available as a commercial product from at least three MR vendors, its current principal application is for staging hepatic fibrosis. MRE also shows promise for characterizing lesions of the brain, breast, and heart.
A typical liver MRE exam begins by positioning a plastic diaphragm ("passive driver") over the liver held in place by an elastic band. This is connected by a long hose to a pneumatic pump ("active driver") outside the MRI room that inflates and deflates the diaphragm about 60 times per second. These mechanical impulses induce "seismic" shear waves in the liver that can be detected with phase-sensitive MR sequences. Image acquisition is very fast, a single 2D slice obtained within a 20-25 sec breath hold.
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As tissues become stiffer, waves propagate more rapidly and have longer wavelengths. This can be appreciated by observing the spacing between peak displacements in MRE wave images as shown in the figure. Note the wider wave spacing in the fibrotic liver (lower left) compared to normal liver (upper left). MRE also allows estimation of tissue shear stiffness, typically reported in kiloPascals (kPa). The kPa is an SI unit for pressure and equals 1000 newtons per square meter. Shear stiffness calculations are displayed as color overlays on anatomic images known as an elastogram.
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The pulse sequence used for liver MRE is typically a 2D GRE with short TR, short TE, and low flip angle. Bipolar motion-sensitizing gradients are applied similar to those used for phase-contrast MR angiography. As described in a prior Q&A, moving tissues accumulate a phase-shift when bipolar gradients are applied, but stationary tissues do not. MR image acquisition is synchronized with the mechanical compressions, with both magnitude and phase data reconstructed using 4−8 different time offsets.
Advanced Discussion (show/hide)»
Basic Concepts of Elasticity
Elasticity refers to the ability of a material to return to its normal size and shape after being deformed by an external force. The degree of deformation is measured by strain (ε), defined as the fractional change in an object's length in a given direction (ε = ΔL/L). Being the ratio of two lengths, strain is a dimensionless quantity, often expressed as a percentage or in parts per million (ppm).
The external force (F) deforming a material is applied over a small area (A) on the object's surface. This creates stress (τ), a pressure effect defined as τ = F/A. The SI derived unit for stress is the pascal (Pa), which equals 1 newton per square meter.
The forces creating stress and strain are commonly resolved into components parallel and perpendicular to the object's surface. Perpendicular forces are referred to as compressive, longitudinal, or normal; transverse forces are called shear. Because molecules (and cells) are bonded (connected) to one another, even a pure external compressive force (Fc) can create internal shear forces (Fs), and vice-versa.
If a compressive force is applied in an oscillatory fashion both longitudinal compression waves perpendicular to the surface and transverse (shear) waves are created in the material. The velocities of these waves can be measured using ultrasound or MR elastography and used to predict the elastic properties of tissue.
If a compressive force is applied in an oscillatory fashion both longitudinal compression waves perpendicular to the surface and transverse (shear) waves are created in the material. The velocities of these waves can be measured using ultrasound or MR elastography and used to predict the elastic properties of tissue.
Moduli of Elasticity
The elastic properties of simple materials are typically quantified using three constants or moduli:
- Young's modulus (E), also known as longitudinal elasticity, is the ratio of longitudinal stress/strain such as seen with axial loading of a column of tissue by a compressive force. This relationship is often linear for small deformations.
- Shear modulus (G or μ), also called rigidity, is the ratio of shear stress to shear strain, and measures proportional deformation in response to a transversely directed stress.
- Bulk modulus (K), also known as volume elasticity, reflects a material’s fractional change in volume in response to uniform hydrostatic pressure (such as at the bottom of the ocean). Liquids resist changes in volume but not shape, hence possessing only bulk elasticity. Solid materials resist changes in both shape and volume, possessing all three moduli of elasticity.
An additional elastic index frequently referenced is Poisson's Ratio (ν), defined as the ratio of latitudinal to longitudinal strain. Poisson's ratio thus reflects the compressibility of material perpendicular to applied stress.
For materials with Poisson's ratios close to 0.5, external deformations produce changes in an object's shape but not its volume. Most biological tissues fit into this category, having measured Poisson's ratios in the 0.49−0.50 range. Biological materials are thus considered to be essentially incompressible, possessing extremely large (theoretically infinite) bulk elasticities (K). As such, typically only G, E, and ν values are used when describing the elastic properties of tissues.
An alternative parameterization (popular in geology but also finding its way into the tissue elastography literature) derives from the work of French mathematician Gabriel Lamé (1795−1870). Lamé defined two moduli, λ and μ, known as the Lamé constants. Lamé's second constant (μ) is identical to the shear modulus (G) defined above. Lamé's first constant (λ) has no direct physical interpretation, but is related to other classic elasticity parameters by the equation: λ = K − ⅔G. For incompressible tissues, λ, like K, is very large.
Compression and Shear Waves
When an external force is applied to the surface of an object in a sudden or oscillatory fashion, deformations are transmitted through the material resulting in perpendicular compressive or P-waves and transverse or shear (S)-waves. The velocities of these waves (Vp and Vs) depend on the tissue elasticity properties and can be estimated by the following equations:
where ρ = tissue density, generally assumed to be the same as water (~1.0 g/cm³), G = the shear modulus, and λ = Lamé's first constant. Since tissues are generally considered incompressible, λ is very large. Hence compression wave velocities are several orders of magnitude greater than shear wave velocities and do not differ much between various tissues. MRE analysis thus concentrates nearly exclusively on shear wave velocities (Vs) which are directly related to the shear modulus of elasticity (G).
Viscoelasticity
Tissues are considered to be viscoelastic, having both solid (elastic) properties as well as liquid-like (viscous) ones. When a sudden force is applied to a viscoelastic material, a time delay is present before its response is complete. In viscoelastic substances stress (τ) is proportional to both to the strain (ε) and the rate the strain changes with time (dε/dt). Viscoelasticity models often consider tissues to be a network of springs and dashpots ("shock absorbers") in series and/or parallel configurations. This produces a set of first order partial differential equations whose parameters can be inversely estimated by numerical methods.
More Advanced Models
The use of the simple constant moduli described above applies only to isotropic perfectly elastic materials, where stress (τ) is linearly proportional to strain (ε). Although biological tissues have an inherently non-linear behavior, they may reasonably be considered linear provided strains are relatively small.
A more advanced step in tissue modeling is to remove the isotropic limitation, allowing for elastic properties to have different values in different directions. Under this analysis stress and strain are considered to be tensors rather than scalar quantities, similar to the concepts underlying diffusion tensor imaging. A complete 3D representation requires use of a complex stiffness tensor having as many as 36 independent elements (depending on the symmetry of the material). Although standard inversion MRE algorithms typically assume a symmetric tensor, look for such models to be used more frequently in the future.
A more advanced step in tissue modeling is to remove the isotropic limitation, allowing for elastic properties to have different values in different directions. Under this analysis stress and strain are considered to be tensors rather than scalar quantities, similar to the concepts underlying diffusion tensor imaging. A complete 3D representation requires use of a complex stiffness tensor having as many as 36 independent elements (depending on the symmetry of the material). Although standard inversion MRE algorithms typically assume a symmetric tensor, look for such models to be used more frequently in the future.
Advanced Reference
Oliphant TE, Manduca A, Ehman arl, Greenleaf JF. Complex-valued stiffness reconstruction for magnetic resonance elastography by algebraic inversion of the differential equation. Magn Reson Med 2001; 45:299-310.
Oliphant TE, Manduca A, Ehman arl, Greenleaf JF. Complex-valued stiffness reconstruction for magnetic resonance elastography by algebraic inversion of the differential equation. Magn Reson Med 2001; 45:299-310.
References
Babu AS, Wells ML, Teytelboym OM, et al. Elastography in chronic liver disease: modalities, techniques, limitations, and future directions. RadioGraphics 2016; 36:1987-2006. [DOI Link] (Good review of MRE and US elastography in the liver).
Dong H, White RD, Kolipaka A. Advances and future direction of magnetic resonance elastography. Top Magn Reson Imaging 2018; 27:363-384. [DOI Link] (excellent recent review with potential new MRE techniques and applications outside the liver)
Glaser KJ, Manduca A, Ehman RL. Review of MR elastography applications and recent developments. J Magn Reson Imaging 2012; 36:757-774. [DOI Link] (Good review by RL Ehman's group at Mayo, who are responsible for many current advances in MRE)
Guglielmo FF, Venkatesh, Mitchell DG. Liver MR elastography technique and image interpretation: pearls and pitfalls. RadioGraphics 2019; 39:1983-2002. [DOI Link] (Good recent review including how to evaluate image quality)
Li Z, Sun J, Yang X. Recent advances in molecular magnetic resonance imaging of liver fibrosis. Biomed Res Internat 2015; ID 5954767:1-12. [DOI Link]
Low G, Kruse SA, Lomas DJ. General review of magnetic resonance elastography. World J Radiol 2016; 8:59-72. [DOI Link] (describes MRE applications outside the liver).
Sarvazyan A, Hall TJ, Urban MW, et al. An overview of elastography — an emerging branch of medical imaging. Curr Med Imaging Rev 2011; 7:255-282. [DOI Link] (Good review of physics of elastography, including both MRE and US applications)
Venkatesh SK, Yin M, Ehman RL. Magnetic resonance elastography of liver: technique, analysis, and clinical applications. J Magn Reson Imaging 2013; 37:544-555. [DOI Link] (Another review by the Ehman group)
Babu AS, Wells ML, Teytelboym OM, et al. Elastography in chronic liver disease: modalities, techniques, limitations, and future directions. RadioGraphics 2016; 36:1987-2006. [DOI Link] (Good review of MRE and US elastography in the liver).
Dong H, White RD, Kolipaka A. Advances and future direction of magnetic resonance elastography. Top Magn Reson Imaging 2018; 27:363-384. [DOI Link] (excellent recent review with potential new MRE techniques and applications outside the liver)
Glaser KJ, Manduca A, Ehman RL. Review of MR elastography applications and recent developments. J Magn Reson Imaging 2012; 36:757-774. [DOI Link] (Good review by RL Ehman's group at Mayo, who are responsible for many current advances in MRE)
Guglielmo FF, Venkatesh, Mitchell DG. Liver MR elastography technique and image interpretation: pearls and pitfalls. RadioGraphics 2019; 39:1983-2002. [DOI Link] (Good recent review including how to evaluate image quality)
Li Z, Sun J, Yang X. Recent advances in molecular magnetic resonance imaging of liver fibrosis. Biomed Res Internat 2015; ID 5954767:1-12. [DOI Link]
Low G, Kruse SA, Lomas DJ. General review of magnetic resonance elastography. World J Radiol 2016; 8:59-72. [DOI Link] (describes MRE applications outside the liver).
Sarvazyan A, Hall TJ, Urban MW, et al. An overview of elastography — an emerging branch of medical imaging. Curr Med Imaging Rev 2011; 7:255-282. [DOI Link] (Good review of physics of elastography, including both MRE and US applications)
Venkatesh SK, Yin M, Ehman RL. Magnetic resonance elastography of liver: technique, analysis, and clinical applications. J Magn Reson Imaging 2013; 37:544-555. [DOI Link] (Another review by the Ehman group)
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