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- Herausgeber: Wiley-VCH Verlag GmbH & Co. KGaA
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Magnetic resonance elastography (MRE) is a medical imaging technique that combines magnetic resonance imaging (MRI) with mechanical vibrations to generate maps of viscoelastic properties of biological tissue. It serves as a non-invasive tool to detect and quantify mechanical changes in tissue structure, which can be symptoms or causes of various diseases. Clinical and research applications of MRE include staging of liver fibrosis, assessment of tumor stiffness and investigation of neurodegenerative diseases.
The first part of this book is dedicated to the physical and technological principles underlying MRE, with an introduction to MRI physics, viscoelasticity theory and classical waves, as well as vibration generation, image acquisition and viscoelastic parameter reconstruction.
The second part of the book focuses on clinical applications of MRE to various organs. Each section starts with a discussion of the specific properties of the organ, followed by an extensive overview of clinical and preclinical studies that have been performed, tabulating reference values from published literature. The book is completed by a chapter discussing technical aspects of elastography methods based on ultrasound.
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Veröffentlichungsjahr: 2016
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Table of Contents
Cover
Title Page
Copyright
About the Authors
Foreword
Preface
Acknowledgments
Notation
List of Symbols
Introduction
Part I: Magnetic Resonance Imaging
Chapter 1: Nuclear Magnetic Resonance
1.1 Protons in a Magnetic Field
1.2 Precession of Magnetization
1.3 Relaxation
1.4 Bloch Equations
1.5 Echoes
1.6 Magnetic Resonance Imaging
Chapter 2: Imaging Concepts
2.1 -Space
2.2 -Space Sampling Strategies
2.3 Fast Imaging
Chapter 3: Motion Encoding and MRE Sequences
3.1 Motion Encoding
3.2 Intra-Voxel Phase Dispersion
3.3 Diffusion-Weighted MRE
3.4 MRE Sequences
Part II: Elasticity
Chapter 4: Viscoelastic Theory
4.1 Strain
4.2 Stress
4.3 Invariants
4.4 Hooke's Law
4.5 Strain-Energy Function
4.6 Symmetries
4.7 Engineering Constants
4.8 Viscoelastic Models
4.9 Dynamic Deformation
4.10 Waves in Anisotropic Media
4.11 Energy Density and Flux
4.12 Shear Wave Scattering from Interfaces and Inclusions
Chapter 5: Poroelasticity
5.1 Navier's Equation for Biphasic Media
5.2 Poroelastic Signal Equation
Part III: Technical Aspects and Data Processing
Chapter 6: MRE Hardware
6.1 MRI Systems
6.2 Actuators
Chapter 7: MRE Protocols
Chapter 8: Numerical Methods and Postprocessing
8.1 Noise and Denoising in MRE
8.2 Directional Filters
8.3 Numerical Derivatives
8.4 Finite Differences
Chapter 9: Phase Unwrapping
9.1 Flynn's Minimum Discontinuity Algorithm
9.2 Gradient Unwrapping
9.3 Laplacian Unwrapping
Chapter 10: Viscoelastic Parameter Reconstruction Methods
10.1 Discretization and Noise
10.2 Phase Gradient
10.3 Algebraic Helmholtz Inversion
10.4 Local Frequency Estimation
10.5 Multifrequency Inversion
10.6
10.7 Finite Element Method
10.8 Direct Inversion for a Transverse Isotropic Medium
10.9 Waveguide Elastography
Chapter 11: Multicomponent Acquisition
Chapter 12: Ultrasound Elastography
12.1 Strain Imaging (SI)
12.2 Strain Rate Imaging (SRI)
12.3 Acoustic Radiation Force Impulse (ARFI) Imaging
12.4 Vibro-Acoustography (VA)
12.5 Vibration-Amplitude Sonoelastography (VA Sono)
12.6 Cardiac Time-Harmonic Elastography (Cardiac THE)
12.7 Vibration Phase Gradient (PG) Sonoelastography
12.8 Time-Harmonic Elastography (1D/2D THE)
12.9 Crawling Waves (CW) Sonoelastography
12.10 Electromechanical Wave Imaging (EWI)
12.11 Pulse Wave Imaging (PWI)
12.12 Transient Elastography (
TE
)
12.13 Point Shear Wave Elastography (pSWE)
12.14 Shear Wave Elasticity Imaging (SWEI)
12.15 Comb-Push Ultrasound Shear Elastography (CUSE)
12.16 Supersonic Shear Imaging (SSI)
12.17 Spatially Modulated Ultrasound Radiation Force (SMURF)
12.18 Shear Wave Dispersion Ultrasound Vibrometry (SDUV)
12.19 Harmonic Motion Imaging (HMI)
Part IV: Clinical Applications
Chapter 13: MRE of the Heart
13.1 Normal Heart Physiology
13.2 Clinical Motivation for Cardiac MRE
13.3 Cardiac Elastography
Chapter 14: MRE of the Brain
14.1 General Aspects of Brain MRE
14.2 Technical Aspects of Brain MRE
14.3 Findings
Chapter 15: MRE of Abdomen, Pelvis, and Intervertebral Disc
15.1 Liver
15.2 Spleen
15.3 Pancreas
15.4 Kidneys
15.5 Uterus
15.6 Prostate
15.7 Intervertebral Disc
Chapter 16: MRE of Skeletal Muscle
16.1
In vivo
MRE of Healthy Muscles
16.2 MRE in Muscle Diseases
Chapter 17: Elastography of Tumors
17.1 Micromechanical Properties of Tumors
17.2 Ultrasound Elastography of Tumors
17.3 MRE of Tumors
Part V: Outlook
Appendix A: Simulating the Bloch Equations
Appendix B: Proof that Eq. (3.8) Is Sinusoidal
Appendix C: Proof for Eq. (4.1)
Appendix D: Wave Intensity Distributions
D.1 Calculation of Intensity Probabilities
D.2 Point Source in 3D
D.3 Classical Diffusion
D.4 Damped Plane Wave
References
Index
End User License Agreement
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Guide
Cover
Table of Contents
Foreword
Preface
Introduction
Part I: Magnetic Resonance Imaging
Begin Reading
List of Illustrations
Introduction
Figure 1 Papyrus Ebers, Columns 107 (right) and 108 (left). Demarcated sections highlight descriptions of palpation examinations.
Ebers 872
: If a swelling presents spherical and stiff and recedes pressure of the fingers, then it originates from the vessel and should be treated with a heated knife.
Ebers 873
: If a swelling at internal layers of the skin appears nodular and feels compliant, like air-filled cavities, then it is a tumor of the vessels and you should not treat it (with a knife), but rather use remedies or incantations to improve the condition of the vessel in all affected areas of the human body.
Ebers 867
: If a swelling in any part of the body feels elastic under the fingers and comes apart under constant pressure, it is of fat and should be treated with the knife.
Ebers 868
: If a swelling has the property of a son (or daughter, metastasis?) and it can be found isolated or spread and feels moderately solid, then it should be treated with the knife. (Nonliteral translation by the authors, based on the German text of Wolfhart Westendorf, Handbuch der ägyptischen Medizin, 1999, volume 2, pg. 547, kindly provided by Marko Stuhr, Mayen, Germany.
Figure 2 Example of the importance of mechanical tissue properties in disease: Stiffness (storage modulus ) measured by shear oscillatory rheometry in fibrosis-induced rat livers. Fibrosis is characterized by the accumulation of excess and abnormal extracellular matrix material. Samples were stained for the presence of collagen by sirius red, which detects primarily type I collagen. The time axis indicates time since initiation of fibrosis. Significant changes relative to day 0 are demarcated by asterisks (, ). The data suggest that an increase in liver stiffness precedes fibrosis and that increased liver stiffness may play an important role in initiating early fibrosis.
Figure 3 The “square of viscoelasticity:” viscoelastic properties can be characterized in a two-dimensional plot in terms of viscosity and elasticity. The arrows indicate how viscoelasticity of human organs is affected when the liver becomes fibrotic, when a muscle contracts or when the brain undergoes degradation.
Chapter 1: Nuclear Magnetic Resonance
Figure 1.1 Time evolution of magnetization as seen from the laboratory frame. The black line traces the tip of over time. (a) During a -pulse, the longitudinal equilibrium magnetization is tipped toward the transverse plane. The combination of precession at Larmor frequency and the tipping induced by the pulse causes the magnetization to spiral on a spherical shell from the -axis toward the -plane. (b) After the pulse, the magnetization precesses at Larmor frequency. The transverse component of decays with time constant , whereas the longitudinal component relaxes back toward the equilibrium value with time constant
T
1
(see Section 1.3).
Figure 1.2 Illustration of the quadrature detection step of the MR signal acquisition. Details are explained in the text.
Figure 1.3 Illustration of the spin-echo principle, from the rotating-frame perspective. The arrows correspond to six isochromats at different positions within the imaging plane with different precession frequencies. The direction of the static magnetic field is upward. (a) Equilibrium. (b) Excitation ( pulse). (c) Free precession. (d) pulse. (e) Echo formation. (f) Timing diagram.
Figure 1.4 Illustration of the gradient echo principle, from the rotating-frame perspective. The arrows correspond to six isochromats with different precession frequencies at different positions within the imaging plane. The direction of the static magnetic field is upward. The cone indicates direction and polarity of the gradient. Further explanations are given in the text. (a) Equilibrium. (b) Excitation ( pulse). (c) Dephasing gradient. (d) Dephasing gradient. (e) Rephasing gradient. (f) Echo formation. (g) Timing diagram.
Chapter 2: Imaging Concepts
Figure 2.1 Example of MRI image of an agarose gel phantom with two soft and two hard inclusions, in -space and image space representation. The conversion between the two representations can be achieved by a two-dimensional Fourier transform. The white arrows in the lower left image indicate signal cancellation due to intra-voxel phase dispersion (see Section 3.2), caused by excessive vibration amplitudes. The inclusions are visible in the magnitude image as bright and dark disks. The phase image is affected by phase wraps, which would have to be removed by unwrapping before further processing.
Figure 2.2 An image (a) and its associated -space (b) with the relevant parameters. The RO and PE axes are horizontal and vertical, respectively, as commonly found in MRI literature. represents the pixel spacing (resolution), the spatial extent of the image, the distance between adjacent points in -space, and identifies the corners of -space.
Figure 2.3 Illustration of -space artefacts occurring when the Nyquist–Shannon theorem is violated. (a,d) -Space (magnitude) and image space representation of a fully sampled () -weighted MRI scan. In (b), every second line in -space was set to zero (simulating exclusion of these lines from data acquisition). According to Eq. (2.3), this halves the field of view (FOV) in the direction of the skipped lines. Since the object is larger than the reduced FOV, ghosting occurs, as shown in (e). In (c), only the central -space points were used for image reconstruction. The resulting image (f) has reduced resolution, as predicted by Eqs. (2.1) and (2.2).
Figure 2.4 Timing diagram of a FLASH pulse sequence, according to [14]. Two iterations of the acquisition loop are shown; in practice, one repetition is required for each PE line. Spoiler gradients are shaded in gray. The superimposed PE gradients indicate that a different gradient is used in each iteration; the same holds true for the slice-select spoiler gradient. Abbreviations: SS—slice-selection gradient, PE—phase-encoding gradient, RO—readout gradient, RF—radiofrequency pulses,
TE
—echo time.
Figure 2.5 Two repetitions of the acquisition loop of a balanced steady-state free precession (bSSFP) sequence, according to [14]. Gradients along all three axes are balanced for each
TR
interval. The vertical arrows along the PE axis indicate that the PE gradient and its rewinder are of equal magnitude but opposite polarity. For a list of abbreviations, see Figure 2.4.
Figure 2.6 Diagram of the EPI sequence and its -space trajectory. An explanation is given in the text. RF denotes radiofrequency pulses. RO, PE, and SS refer to readout, phase-encode, and slice-select axes, the three orthogonal gradient directions used for spatial encoding. ADC (analog-to-digital converter) indicates recording of an RF signal. Repetition time (
TR
) is the duration of the acquisition of one slice.
Figure 2.7 Spiral -space sampling, as described in [23] and used in [22]. The RO gradient waveforms for one spiral arm are shown on (a). Note that for spiral imaging there is no in-plane PE gradient; both gradients act as RO gradients. (b) Three spirals are superimposed by modifying the phase of the gradient waveforms. Note that the sampling density is higher in the center of -space than in the periphery, which can be exploited for correcting subject motion [22].
Figure 2.8 Principle of GRAPPA reconstruction for a setup with two coils. Solid lines are acquired while dashed lines are skipped, but are required for artifact-free image reconstruction. The top and bottom rows demonstrate two options for reconstructing the line marked by the arrow on the left-hand side from different blocks of three acquired lines, indicated in gray.
Figure 2.9 Effect of shortening echo time on signal magnitude. The black dots indicate signal strength for two arbitrarily chosen echo times and . The gray diamonds represent the signal amplitudes resulting when two echo times are reduced by the same amount . Obviously, the gain in signal amplitude is much larger for shorter echo times.
Chapter 3: Motion Encoding and MRE Sequences
Figure 3.1 Illustration of wave image processing. In (a), two raw, wrapped phase images and with opposite vibration phase are shown. After unwrapping, each image is a superposition of the propagating wave and the static background. Taking the phase difference image, as prescribed by Eq. (3.3), removes most of the background while preserving the wave information. In (b), a stack of images, capturing the wave at different phases of the vibration cycle, is first subjected to unwrapping and then temporally Fourier-transformed. In the resulting frequency-resolved representation, the static offset caused by the susceptibility and inhomogeneity background is contained in the zero-frequency component, whereas the wave information falls into the first harmonic frequency image. The higher harmonic frequencies contain no information, since only the first harmonic frequency was mechanically stimulated.
Figure 3.2 Diagram of a spin echo EPI-MRE sequence. At the start of the sequence, the MRI scanner sends a trigger (indicated by the black arrow) to the vibration generator to initiate mechanical vibration. The following delay is calculated in such a way that the offset between the trigger and the MEG is exactly 100 ms. In the next repetition, is decreased by (first gray arrow), so that the MEG encodes a slightly shifted wave propagation phase. One iteration of this diagram captures a single slice. EPI-MRE and other MRE sequences will be discussed more thoroughly in Section 3.4.
Figure 3.3 Illustration of phase accumulation for a moving spin in the presence of a motion-encoding gradient in the -direction. For the static spin, the effects of the positive and negative lobes of the MEG compensate each other, so that the net phase after the MEG is zero. The moving spin experiences the two lobes at different locations, and hence with different strength, so that a net phase remains. The spin phase after the MEG depends on the actual spin trajectory, and can be calculated using (3.4) (with ).
Figure 3.4 Effect of an unbalanced gradient and zeroth, first, and second gradient moment nulling on a stationary spin outside the scanner isocenter (solid line) and on spins with constant velocity (dotted line) or constant acceleration (dashed line). The plots were obtained by calculating the integral in Eq. (3.4) for different gradient shapes and spin trajectories. The gradient waveform is represented by the thick gray line. The three curves in each diagram represent the phase encoded by the respective gradient for the three types of motion. The scaling of the -axis is arbitrary, but consistent across all plots. It is clearly visible that for the unbalanced gradient, all motion types (including stationary) lead to a nonzero phase for all spins. As the order of gradient moment nulling increases, higher orders of the Taylor expansion of the spin trajectory (Eq. (3.5)) are suppressed at the end of the gradient, thus rendering the spin phase insensitive to these types of motion.
Figure 3.5 Illustration of an MEG waveform with second-order gradient moment nulling and a sinusoidal vibration with angular frequency and phase offset (dashed). The gradient can be composed from a train of plateaus with height and duration , as discussed in the text. Since the gradient is antisymmetric with respect to the origin, accumulated phase (integral over ) is greatest when , according to Eq. (3.17). Because of the symmetry between the MEG and the oscillation, the part for
t
< 0 contributes the same as the part for
t
> 0, so that we only calculate the latter and double the result.
Figure 3.6 Different orders of gradient moment nulling. (a) Waveforms with zeroth (solid), first (dashed), and second (dotted) order moment nulling (mn), composed of individual trapezoidal shapes. For zeroth and first mn, one cycle with period is shown. Second mn can only be implemented with an even number of cycles, each with period . (b) Encoding sensitivity for one cycle with zeroth and first mn with and gradient amplitude in the mechanical vibration frequency range . (c) Encoding sensitivity for two cycles with . All constellations where are referred to as
fractional encoding
.
Figure 3.7 Illustration of the contributions that determine the motion sensitivity in a sequence with fractional encoding as a function of . The final fractional encoding efficiency (bold solid line) is a product of three contributions: , , and , where represents the encoding efficiency, as explained in Figure 3.6. Contribution quantifies the phase-to-noise ratio (PNR), which decreases exponentially with either or , depending on the type of sequence. The third contribution, , relates to the damping of the wave according to the Voigt model (Section 4.8.3), which is larger for higher vibration frequencies. The curves were plotted for the following parameters: ms (, ), Hz (), ms, Voigt model for : kPa, , kg/m
3
, evaluated at a depth of 1 cm.
Figure 3.8 Schematic timing diagram of a FLASH-MRE sequence. In order to acquire the full displacement field, the MEG is applied on all three gradient axes in successive acquisitions, as indicated by the dashed lines. The gray gradients represent spoilers, as explained in Section 2.2.1.1. The scaling of gradient amplitudes and the time axis is not accurate.
Figure 3.9 Illustration of the nonlinear phase response of bSSFP. The solid and dashed lines correspond to the MR signal phase () as a function of the phase increment per
TR
() for two acquisitions with opposite oscillation phase. For a fixed value of , the motion-related phase is half the vertical distance of the two curves. The gray rectangles indicate ranges of with optimal motion sensitivity. In (a), one
TR
matches one vibration cycle, so that the wave has to be inverted (dashed sinusoidal) in order to acquire the second phase image. In (b), one
TR
matches half an oscillation cycle, so that two images with opposite oscillation phase are sampled automatically without the need to invert the oscillation. The two images on the right-hand side illustrate the position dependence of motion sensitivity of a sequence of type (b). The magnitude image (top) suffers from banding, as explained in Section 2.2.1.2. The phase image (bottom) exhibits vertical stripes of high () and low () motion sensitivity, as explained in the text. This modulates the physically correct displacement field and causes problems for the reconstruction of elastic moduli.
Figure 3.10 Different ways of placing MEGs within a spin-echo sequence. (a) A spin-echo sequence with one MEG cycle is shown. If the resulting motion sensitivity is insufficient, a second MEG cycle can be added. (b) The second MEG is appended to the first one. Because of the inherent symmetry of spin-echo sequences, a fill time has to be inserted before the readout so that the refocusing pulse is in the center of the
TE
interval. (c) the MEG is instead inserted between the refocusing pulse and the readout. The timing between the MEGs has to be such that the gap is an integer multiple of the MEG period (shown in dashed gray). Since the refocusing pulse inverts the spin phase, the second MEG has to be of opposite polarity relative to the first one. A fill time has to be inserted in the first half of
TE
to maintain spin-echo symmetry. This constellation leads to a significantly shorter
TE
than in (b). The fill time in (b) could be used for a third MEG cycle; however, in media with short , the increase in
TE
would cause significant signal loss, so that (c) would be the better compromise for that scenario.
Figure 3.11 Simplified timing diagram of a GE-EPI sequence, as used in [39]. Only the image acquisition part is shown, vibration and synchronization are analogous to Figure 3.8. In the original publication, a segmented image acquisition strategy was used, so the process illustrated here has to be repeated several times to obtain a complete -space. The MEG can be applied to all three gradient axes in successive scans.
Chapter 4: Viscoelastic Theory
Figure 4.1 Nomenclature used for positions and displacements in a solid body. The two points and are subject to a displacement . Dashed lines represent connections between points before and after a deformation. Solid lines correspond to displacements. Points and their position vectors before and after deformation are shown in gray.
Figure 4.2 Geometrical representation of shear strain. The dashed rectangle represents the undeformed state and the solid trapezoid the deformed body.
Figure 4.3 Definition of the nomenclature to denote stress tensor elements . The same convention is also used for the strain tensor elements .
Figure 4.5 (a) Shear moduli in a fiber-reinforced transversely isotropic material with planes of symmetry () and a plane of isotropy (). Different types of deformation probe different mechanical moduli: shear deformation perpendicular (b) and parallel (c) to the fibers probes the two shear moduli, and , respectively. Axial deformation along a single axis probes Young's moduli and (d–f).
Figure 4.4 Diagram of applying uniaxial loading to a body to quantify its Young's modulus. The force acting on the plate on top of the body generates a stress according to , where is the contact area between the body and the pressure plate. The resulting strain is . Since the body is not constrained laterally, it can expand perpendicular to the direction of the acting stress. The in-plane strains are then determined by Poisson's ratio, as explained in the text.
Figure 4.6 The real part of an oscillating stress (red) with frequency
, and the resulting strain in a purely elastic (solid) and a purely viscous (dashed) medium. The elastic strain is in phase with the acting stress, whereas the viscous strain lags behind the stress by one quarter of the oscillation period.
Figure 4.7 Summary of important viscoelastic models in elastography assembled from basic spring and dashpot elements. Compliance and modulus are analytically given in the Laplace domain (bars over the symbols, denoting the Laplace domain, have been omitted to improve readability). is plotted over the angular frequency . “log” refers to double logarithmic plots to better illustrate powerlaw behavior. The rightmost column, on a time axis spanning 0.2 s, shows strain in response to a boxcar stress spanning the first half of the time axis, that is, . Further simulation parameters correspond to typical values encountered in elastography of biological tissues (e.g., , , , , , ).
Figure 4.8 2D simulation of the field generated by a point source according to Eqs. (4.170)–(4.172). The source is located in the center of the image and oscillates in the -direction, as indicated by the red arrows. The (horizontal) and (vertical) components of the resulting displacement fields are shown, as indicated by the white arrows. The simulation was performed assuming shear wave and pressure wave velocity to be identical, which is unphysical but helps to appreciate the patterns created by each mode. As a consequence, the components of the shear and compression fields are identical, which would not be the case if the velocities were different. Note that the near field decreases much faster with the distance from the source than the far fields.
Figure 4.9 Illustration of the nomenclature for shear waves in a transversely isotropic medium. Wave modes polarized parallel to the fiber direction are referred to as “fast transverse” (FT), whereas those polarized perpendicular to the fibers are called “slow transverse” (ST).
Figure 4.10 Shear wave modes in a transversely isotropic medium with fibers along the -axis. The first row represents wave propagation in the plane of isotropy (-plane) and the second row depicts one plane of symmetry (-plane). The three columns represent three orthogonal modes of excitation along the three principal axes. The curved lines indicate wave fronts emanating from the center of the image. Since only shear waves are considered here, propagation cannot be parallel to the polarization direction.
Figure 4.11 -Space representation of iso surfaces representing constant wave velocity for fast transverse and slow transverse shear modes, that is, the solutions of the Christoffel equation (4.184) for fixed values of and , plotted in 2D and 3D. The oblate ellipsoid represents the slow transverse mode (Eq. (4.193), basically describing an ellipsoid with half axes and ). The more irregular surface corresponds to the fast transverse wave mode, reflecting the more complex structure of Eq. (4.192). Note that this representation is given in un-normalized -space; therefore, the coordinates are actual -values rather than their normalized equivalents .
Figure 4.12 Illustration of reflection and transmission of an incident wave with wave vector at an interface between two different media. Medium (2) is softer than medium (1), therefore the wavelength of the transmitted wave is shorter than the wavelength of the incident and reflected waves. The amplitudes of the incident, transmitted, and reflected waves are such that the conservation of energy is fulfilled and that continuity of the displacement at the interface according to Eq. (4.229) is maintained.
Figure 4.13 Plot of transmission and reflection coefficients for a welded (a) and slip interface (b). The points correspond to measurements performed using MRE on two blocks made of the same agarose gel, either with a direct contact interface, or with a layer of a more liquid gel as a lubricant to allow slip. The dashed lines represent least-squares fits of Eqs. (4.236) and (4.237), respectively, while the solid lines indicate the margins of error.
Figure 4.14 Example of a spatial interface between two media with wave speeds (white) and (gray). The wave propagates along the -direction and is refracted at . The slope corresponds to the wave speed.
Figure 4.15 Example of a temporal interface. The wave propagates in the -direction. At , the properties of the medium change instantaneously, and the wave speed increases from to , causing a shortening of the cycle period, (thus increasing the frequency), of both the reflected and the transmitted waves. The slope represents wave speed.
Figure 4.16 Illustration of discrete waves (a) and random walk (b). If the wave is at , then the probabilities and are all equal to 1. For the random walk, we show all possibilities that lead to the particle (indicated by the diamond) being found at .
Figure 4.17 Three out of infinitely many possible paths from to . Since the path lengths differ, waves emitted at at the same time will arrive at with different delays. Therefore, phase coherence between waves is lost, and the resulting intensity at cannot be predicted.
Figure 4.18 Intensity profiles and radial profiles for different real and hypothetical types of wave phenomena. (a) Intensity probabilities for different types of waves. See Table 4.1 for the corresponding formulas. (b) Radial intensity profiles. The diffusive wave scenario does not account for speckle patterns and is therefore unphysical. (c) Hypothetical case of wave diffusion with a single excitation and multiple repeated excitations. The curves are normalized to unity amplitude at the origin to illustrate how repeated excitation makes the curve broader and flatter. This plot results from the application of the diffusion equation to intensity (see Appendix D.3), which is unphysical.
Chapter 5: Poroelasticity
Figure 5.1 Illustration of three scenarios for mechanical testing of a poroelastic material. On top, a tissue volume consisting of fluid space (dark gray) and solid (light gray) is shown. The fluid is assumed incompressible. Applying a pressure can yield different results, depending on the properties of the solid and the interaction between the compartments. In scenario 1, the solid is compressed whereas the fluid volume is preserved, resulting in a compressible effective medium. In scenario 2, one phase can locally expand if the other phase can be pushed out of the way. The total volume is preserved (the effective medium is thus incompressible), and the local distribution of the two phases is temporarily altered. In scenario 3, fluid is allowed to leave the system, thus resulting in a compressible effective material even when both phases are incompressible. The term “jacketed” refers to testing conditions that surround the material with an impermeable jacket that prevents fluid from being squeezed out.
Figure 5.2 Illustration of the definition of tortuosity of a line that is used in the text. is the length of the curve and is the Euclidean distance of its endpoints.
Figure 5.3 Plot of the pressure wave speed for the two modes in a poroelastic medium for the following parameters: (assuming the compressibility of water), , . (a) variable, kg/m
3
. (b) variable, .
Figure 5.4 The detected MRE signal in a biphasic poroelastic model. The contributions and from the two compartments add to form the combined signal .
Chapter 7: MRE Protocols
Figure 7.1 Sequence diagram of the FLASH-based sequence used for cardiac MRE [177]. The symbol F indicates the readout of a single -space line with a motion-sensitized FLASH kernel, as shown in Figure 3.8, but without the trigger and the delays preceding the RF pulse. Each line in -space is sampled at 360 time points, over approximately two cardiac cycles. The process is repeated for each of the 48 -space lines. Using GRAPPA with an acceleration factor of 2 allows for the reconstruction of 96 -space lines. The measurement is performed thrice, for three different directions of the motion-encoding gradient to sample all three Cartesian components of the displacement field.
Figure 7.2 MRE protocol of an EPI-based multifrequency exam of human liver. Each row represents a concatenation of several instances of the process illustrated in the row above. Within one breath-hold period of 15 s (“respiration”), the whole volume, consisting of 10 slices, is sampled eight times to obtain eight different points of the oscillation cycle (“wave dynamics”). A total of 12 breath-hold intervals is required to acquire three Cartesian components of the displacement field (“MEG axis”) and four frequencies. Total acquisition time is 6–8 min, depending on the duration of the recovery phases between breath-holds.
Figure 7.3 MRE protocol of an EPI-based exam of human lung at a single-vibration frequency of 50 Hz. Within one breath-hold period of 24 s (“respiration”), the imaging volume, consisting of six slices, is scanned 24 times to acquire six points of the oscillation cycle (“wave dynamics”) and four repetitions for online signal averaging. This process is repeated thrice for offline averaging (thus yielding 12 signal averages). The measurement is then repeated to acquire three Cartesian components of the displacement field (“MEG axis”), and finally two different respiratory states are probed. The total measurement time is 9–12 min (depending on the duration of the recovery phases between breath-holds), split across 18 breath-hold intervals. The high number of signal averages is necessary since the lung, due to its low density, yields a very weak MR signal with intrinsically low SNR.
Chapter 8: Numerical Methods and Postprocessing
Figure 8.1 Process of denoising. Prior knowledge is used to construct a dictionary of predictors, known as an estimator. The noisy observables are then projected onto the estimator space to sparsify the data. A filtering or thresholding operation suppresses noise while retaining signal, and the noise-reduced signal is recovered through an inverse transform.
Figure 8.5 Denoising in -space. The dictionary used is the Fourier basis vectors in 2D; real components of a small sample are shown. The filtering operation is a Butterworth filter. This results in smoothed data with very small and very large frequencies removed.
Figure 8.2 Schematic of denoising applied to Savitsky–Golay filtering. Prior knowledge models the data as a low-rank polynomial across a window. In this case, the data are modeled as third-order over a window. This yields a dictionary of ten basis vectors (DC not shown). Each sliding window is projected onto the polynomial basis. The data are then smoothed by retaining the zeroth-order coefficient at the center.
Figure 8.3 Stencil and surface plot for Gaussian kernel with .
Figure 8.4 Frequency response plots of three common filters: (a) Five-tap moving average filter; (b) Gaussian smoothing kernel, width 5, = 1.3; (c) Fourth-order Butterworth filter, with normalized frequency cutoff of 0.6.
Figure 8.7 Comparison of Fourier and complex dual-tree wavelet transforms of a (a) single-frequency wave with a discontinuity and 5% noise. The discontinuity does not have a sparse (b) Fourier representation, causing ringing throughout the image. However, the MRA handles both smooth and discontinuous elements sparsely. The Fourier domain denoise, with a fourth-order Butterworth filter, rounds and shifts the feature (g), while the wavelet domain hard thresholding maintains feature sharpness and location while removing noise (h). The lines (c) through (f) represent the wavelet decomposition from finest (c) to coarsest. It is obvious that the wavelet scaling function captures the global shape of the signal, whereas the finer resolutions are necessary to deal with the localized discontinuity.
Figure 8.6 Examples of three commonly used wavelet functions. As the name suggests, they have the appearance of isolated waves. Wavelets are a sparser basis than the frequency domain for piecewise smooth images with discontinuities.
Figure 8.8 Denoising in wavelet space. The dictionary used is one of 2D wavelets. They are applied recursively using the fast wavelet transform (FWT) to generate a multi-resolution analysis (MRA). The wavelet coefficients are then thresholded, and the image is recovered using an inverse FWT (IFWT).
Figure 8.9 Comparative denoising results on central slice of muscle and brain acquisitions. Images (a) and (e) are phase-unwrapped, but not denoised (blue lines in plot); (b) and (f) show denoising results for a low-pass filter cutoff of 10 mm (green lines in plot); (c) and (g) show the impact of the divergence-free wavelet denoising, which removes some of the low-frequency spectrum (yellow lines); (d) and (h) show the additional impact of the CDT wavelet denoising (red line). In order to study the denoising results, a vertical plot line was drawn across heterogeneous tissue features in each image. Comparison of the dark red and dark green lines shows the increase in detail from wavelet-basis multiscale filtering (red) as opposed to low-pass filtering (green), even as both produce data sufficiently smoothed for wave inversion.
Figure 8.10 Illustration of the effect of directional filters. Real and imaginary parts of a superposition of waves propagating in different directions are shown in the first column. The block in the center depicts 12 directional filters corresponding to Eq. (8.15) with .The block on the right-hand side represents the real part of the corresponding directionally filtered waves (shown in the same order as the filter kernels).
Figure 8.11 Directional filtering. As spatial frequencies are targeted, prior knowledge is used to project the complex wave field onto the Fourier basis. Here, the filtering process is redundant, using a bank of filters to generate a bank of directionally decomposed waves. The waves can then be inverted using inversion assumptions that do not account for superposition.
Figure 8.13 Simulation results demonstrating the noise sensitivity of different numerical derivative schemes. For the comparison, a wave with a wave speed of 1.5 m/s at a frequency of 30 Hz was simulated. Different amounts of Gaussian noise were added to the real and imaginary parts. The noise level was defined as , with and denoting the energy contained in the wave and the noise spectrum, respectively. One cycle of such a wave at three different noise levels is shown in (a). First- and second-order spatial derivatives were calculated for these waves using three different schemes: forward differences (Eq. (8.23b)), symmetric differences (Eq. (8.23c)), and the Anderssen gradient scheme (Eq. (8.35)) with . (b) Shows the relative error for the calculation of the first and second (by repeated application of the operators) derivatives relative to the noiseless case. (c) The -space representations of the three schemes are shown for the first and second derivatives.
Figure 8.12 Illustration of the relationship between the step width and the frequency–space characteristics of difference schemes approximating first- and second-order derivatives. In the -space representation, the ideal characteristic is shown as the dashed straight line (first derivative) and the dashed parabola (second derivative) for a very small step size . Apparently, the approximation becomes better as decreases. Both schemes ultimately fail when (indicated by the black arrows), which represents the Nyquist criterion. However, even when the Nyquist criterion is satisfied, the difference between the actual and ideal characteristics can be substantial, especially for larger values of . Therefore, the stricter criterion should be applied to obtain reliable numerical differences.
Figure 8.14 Frequency response plots for: ideal gradient, forward difference, centered difference, Anderssen gradient, and compact Laplacian operator.
Figure 8.15 1D (a) and 2D (b) simulations of 2D wave fields from a point source in the center of the object (indicated by arrows in the 1D case) with different types of boundary conditions. The 2D simulations were performed with the code shown in Algorithm 8.1.
Chapter 9: Phase Unwrapping
Figure 9.1 Wrapping and unwrapping of a smooth one-dimensional function. The solid and dashed lines on (a) represent the function before and after wrapping according to Eq. (9.1). The circles and boxes indicate samplings of the wrapped data at two sampling rates (differing by a factor of 2). In (b), the sampled data are shown after applying a one-dimensional unwrapping operator as described in Algorithm 9.1. The data series with the higher sampling density, denoted by squares, is reconstructed correctly, since all jumps between adjacent data points are less than . For the series with the lower sampling rate, there are jumps larger than (indicated by the arrow in (a)), and the unwrapping hence fails.
Figure 9.2 Comparison of different 2D phase unwrapping methods in the liver (upper row) and brain (bottom row). While Flynn's method performs well in the brain, it is disturbed in regions of multiple wraps in the liver (arrow). Furthermore, Flynn's algorithm adds an arbitrary global phase offset , . Gradient unwrapping, which is stable but direction-dependent and noisy, can be used as a high-pass filter or for subsequent curl calculations. Laplacian-based unwrapping is stable, noise-robust, and suppresses zeroth- and first-order components of the field, which are often undesirable. However, the Laplacian averages information from adjacent pixels, and unwrapping based on the Laplacian does not reconstruct the real wave field.
Chapter 10: Viscoelastic Parameter Reconstruction Methods
Figure 10.1 Illustration of the effect of noise on the magnitude of a measured signal in the complex plane. The true quantity is an arbitrary vector in the complex plane. We simulate the effect of noise by attaching a vector , representing the noise contribution of the measurement, to the tip of , yielding the measured magnitude . The dashed circle around the origin indicates all possible signals with a magnitude equal to . The solid circle around the tip of represents all possible values if and are fixed and only the noise phase is variable. Since we assumed to be uniformly distributed over , the measured signal is uniformly distributed over the black solid circle; and the probability of finding in a given segment of that circle is proportional to the arc length of the segment. The dashed circle divides the solid circle into two segments, the “inside” (light gray) and “outside” (dark gray). The arc length of the outside segment (where ) is larger than the arc length of the inside segment, where . Hence, the probability for is larger than that for . This means that, on average, noise tends to increase the magnitude of a complex quantity. The effect becomes more significant as the magnitude of the noise increases. This argument holds true if we consider the fact that usually the noise amplitude is not fixed, but distributed according to some probability density function.
Figure 10.2 Illustration of the effect of discretization and noise on the reconstructed shear wave velocity. Displacement fields acquired at drive frequencies (and hence different wavelengths) from 10 to 100 Hz were subjected to algebraic Helmholtz inversion (AHI, Section 10.3) and the shear wave speed at each frequency was retrieved. It is obvious that for low resolution, discretization artifacts dominate and the wave speed (and hence the elastic modulus) is overestimated. For higher resolutions, discretization effects are suppressed and noise-induced underestimation of the wave speed and elastic modulus occurs.
Figure 10.3 Comparison of different inversion methods in the literature. (a) Simulated data and the LFE, direct inversion (DI, here: AIDE), and phase gradient (PG) reconstructions for the noiseless data (from left to right). LFE is smoother than DI and PG. Since no directional filters were used, PG is badly disturbed by phase discontinuities. (b) Phantom data reconstructed by LFE, DI, and PG, here including directional filters prior to the inversions. With directional filters, PG performs better; however, artifacts below the inclusions presumably due to diffraction are still more apparent than in other methods. Of note, phantom data comprise only a single wave field component at a single frequency. Multicomponent, multifrequency data can further reduce those artifacts toward the method described as inversion (see Section 10.6).
Figure 10.4 Comparison of the two formulas for the reconstruction of , Eq. (10.52) (“method A”) and Eq. (10.53) (“method B”). Noisy one-dimensional waves were subjected to inversion at different SNR levels. Ideally, the true phase angle (which was used as the simulation parameter, plotted on the horizontal axis) should equal the calculated phase angle (obtained from the inversion, shown on the vertical axis). For method A, the agreement between the two values is indistinguishable from the ideal line even at a very low SNR = 1. For method B, we see a systematic overestimation of the calculated -value due to the bias of the arccos function toward positive values, especially when is close to zero. Method B only yields accurate results in the noise-free case. Every inversion step was repeated 10
5
times, and the averaged results are shown to minimize stochastic fluctuation.
Figure 10.5 Illustration of the principle behind in the abdomen. (a) 12 direction-filtered images at 45 Hz vibration. Each image is the superposition of the three displacement components, and the white arrows indicate the direction of the directional filter. (b) Wave speed images for individual frequencies, and the final imaging combining all frequencies (bottom right). Each single-frequency image is the superposition of 12 direction-filtered images, as shown in (a). The compound image thus incorporates all three Cartesian components of the displacement field, captured at seven vibration frequencies.
Figure 10.6 Simulated sensitivity of and direct inversion to noise. Simulations were based on one-dimensional waves with m/s and two frequencies (30 and 60 Hz). Gaussian noise was added to a complex harmonic function with 2 mm pixel spacing. The resulting noisy waves were subsequently analyzed by () and direct inversion based on AHI (). performs well even at low SNR whereas AHI severely underestimates values due to second-order derivatives in the Laplacian.
Figure 10.7 Discretization of the problem domain in 3D. A block of material is indented locally, and the resulting deformation is reflected in the deformation of the mesh.
Figure 10.8 Illustration of the shape functions on a one-dimensional mesh with equidistantly spaced nodes.
Figure 10.9 Illustration of the local coordinate system used in waveguide elastography.
Chapter 11: Multicomponent Acquisition
Figure 11.1 Illustration of the encoding principle behind SLIM-MRE. A sinusoidal signal is sampled with eight points across one (), two (), and three () periods. The spectra resulting from these sampling strategies are shown in the three boxes. The original information is encoded in three different frequency bins of the frequency spectrum.
Chapter 12: Ultrasound Elastography
Figure 12.1 Categorization of the most common USE methods in terms of tissue excitation method and measurement quantity.
Chapter 13: MRE of the Heart
Figure 13.1 Normal heart physiology. The upper row schematically depicts electrical stimulation phases of the heart beginning with depolarization of the sinus in the right atrium ➀, disseminated depolarization of right and left atria, which triggers atrial systole ➁, depolarization of the right and left ventricles at early systole (➂, ➃) and the repolarization phase at the beginning of diastole ➄. ➊ and ➋ demarcate the heart sounds produced by closure of the AV and semilunar valves, respectively. Note that stroke volumes are identical for LV and RV. Abbreviations: IVC—isovolumetric contraction time, IVR—isovolumetric relaxation time, LV—left ventricle, RV—right ventricle.
Figure 13.2 Myocardial fibers of the left ventricle around the apex of the heart. (a) Tissue specimen. (b) Simplified model of the helical ventricular myocardial band illustrating the crossing of fibers due to descendant and ascendant segments.
Figure 13.3 LV pressure–volume relationship in normal hearts and hearts with abnormal systolic and diastolic function. (a) Schematic – cycles, normal and altered by systolic dysfunction (SD) and diastolic dysfunction (DD). While left ventricular (LV) pressure is normal in SD, DD is characterized by a significantly elevated LV pressure. Conversely, as LV volumes are increased in SD (with reduced EF), DD does not change LV volumes, rendering an image-based diagnosis more challenging than the diagnosis of SD. (b) LV diastolic pressure–volume data from normal controls (solid line), patients with diastolic heart failure (DHF) (dotted line), and patients with systolic heart failure (SHF) (dashed line). In DHF, the – cycle displays normal volumes but elevated pressure, indicating increased passive stiffness of myocardium.
Figure 13.4 Myocardial stiffness measured by SWI in a perfused Langendorff rat heart, and LV pressure evolution on the same time axis (a). (b) Linear relationship between systolic shear modulus of the LV wall and LV pressure. LV pressure was modified by isoproterenol infusion.
Figure 13.5 Shear wave dispersion ultrasound vibrometry (SDUV) of exposed pig hearts
in vivo
. Shear modulus (a) and viscosity (b) (corresponding to and of the Voigt model in Section 4.8) were measured in normal LV wall and after reperfused acute myocardial infarction. Notably, the highest increase in stiffness following infarction and reperfusion was observed in diastole.
Figure 13.6 Cardiac MRE in pigs to test the correlation between MRE and invasively measured LV pressure. ((a) Kolipaka 2010 [298]. Reproduced with permission of Wiley and (b) [308] used under CC BY 2.0 licence.)
Figure 13.7 Illustration of cardiac steady-state FLASH MRE (Elgeti 2010 [177]). (a) Collecting morphological information such as LV diameter from magnitude MRE images. (b) Analysis of phase MRE images comprising (i) unwrapping using gradient unwrapping corresponding to Eq. (9.10) but along the time axis, yielding phase velocity and (ii) calculation of the wave deflection amplitude from by accounting for all three vector field components of the displacement. Figure (c) illustrates the relative timing of the sequence.
Figure 13.8
In vivo
WAV-based MRE and ultrasound-based cardiac elastography (USE) in healthy volunteers. The principal finding is that cardiac wall motion (geometry) lags behind wave amplitudes (elastography). The delay between the curves of geometry and elastography represents the isovolumetric contraction and relaxation times, IVC and IVR, respectively. Gray arrows in the USE plot point to modulations that are related to temporal scattering as explained in Section 4.12.2. ((a) Sack 2009 [208]. Reproduced with permission of Wiley. (b) Tzschätzsch 2012 [257]. Reproduced with permission of Elsevier.)
Figure 13.9
In vivo
– cycles determined in two volunteers. The dashed line indicates mild mitral valve insufficiency, which results in a lower pressure increase than seen during normal IVC. relates to Eq. (5). (Based on data published in [309].)
Figure 13.10 Shear wave amplitude maps generated using WAV-MRE (steady-state cardiac FLASH-MRE). Short-axis views of the heart and corresponding amplitude maps of a normal volunteer (young), a normal volunteer (old), and patients with mild, moderate, and severe diastolic dysfunction. The white solid line outlines the outer contour of the left ventricle during systole. The region of interest for normalizing the induced shear waves anterior to the heart is outlined by a white dashed line.
Chapter 14: MRE of the Brain
Figure 14.1 Multifrequency MRE of the brain for recovery of shear modulus dispersion. (a) 2D MRE from 25 to 62.5 Hz vibration frequency and 3D MRE from 10 to 50 Hz vibration frequency reconstructed for magnitude shear modulus by sliding window three-frequency MDEV inversion (Left-hand side: Sack 2009 [331]. Reproduced with permission of Wiley. Right-hand side: Based on data published in [69]. Reproduced with permission of Wiley.) Fit lines of storage and loss modulus data, and , represent springpot model dispersion. (b) Elastograms of obtained by three-frequency MDEV inversion in three different frequency ranges.
Figure 14.2 Elastograms obtained by intrinsically activated MRE displaying the shear modulus corresponding to 1 Hz harmonic motion [336].
Figure 14.3 Two types of actuators for mouse brain MRE based on a piezo driver ((a), Clayton 2011 [341]. Reproduced with permission of Institute of Physics.) and a Lorentz coil in the fringe field of the MRI scanner (b) as it was used in multiple studies [121–124].
Figure 14.4 Brain shear modulus and brain volume in adults versus age.
Figure 14.5 High-resolution MRE based on multifrequency MRE from 30 to 60 Hz and MDEV inversion. (a) Group-averaged maps of magnitude shear modulus () and shear modulus phase angle () Guo [329]. (b) An MDEV-based elastogram () together with a standard -weighted image acquired at 7 T magnetic field strength. High signal intensities in correspond to high stiffness. Scaling from 0 to 2 kPa. Image voxel size was 1 mm
3
, allowing distinction of cortical gray matter from white matter based on their mechanical properties. (Braun 2014 [38]. Reproduced with permission of Elsevier.)
Figure 14.6 Preliminary functional MRE at four mechanical excitation frequencies. The global response of to visual stimulation (averaged over five transverse slices) is shown for 60 experiments in which a checkerboard pattern was repeatedly (six times) shown during five consecutive MRE scans followed by five baseline scans without visual stimulation. In the 25 Hz response, the inverse BOLD effect (quantifying neuronal activity based on the oxygen level of the blood) is also included which was derived from the 3D fMRI data in the same subjects (). In all cases, a decrease in due to visual stimulation was observed.
Figure 14.7 MRE in multiple sclerosis (MS). (a) The plot summarizes the MS-induced decrease in shear modulus, , and power law exponent, , according to the springpot model. Three stages of MS are compared: the
clinically isolated syndrome
(CIS) is considered one of the earliest manifestations of MS, although the disease may remain silent in some cases;
remitting-relapsing
(RR) is a solid manifestation of MS, but still considered an early phase;
primary
and
secondary chronic progressive
disease (PP and SP) represent chronic phases of MS. Notably, reduction in occurs at a very early time point of disease progression. (Fehlner 2015 [68]. Reproduced with permission of Wiley.) (b) Springpot constants and for the detection of MS (PP&SP). The area under the receiver operator characteristics curve (AUROC) values for separating healthy volunteers from MS patients was 0.896 and 0.936 for and , respectively.
Figure 14.8 Correlation between storage modulus and number of neurons in the murine brain. (a) Time courses of the storage modulus in the hippocampus region in a Parkinson mouse model. MPTP (1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine) was administered on day 20, causing a transient increase in neuronal proliferation. The significant increase in storage modulus on day 6 after injection followed by a decay to baseline values is correlated with the number of new neurons. (Based on data published in [122].) (b) Inversely to (a), a decrease in the number of neurons by middle cerebral artery occlusion (MCAO) correlates with a decline of the storage modulus in the mouse brain.
Chapter 15: MRE of Abdomen, Pelvis, and Intervertebral Disc
Figure 15.1 Overview of abdominal organs, most of which have been studied using MRE. Organ-specific discussion will be presented in the following sections.
Figure 15.2 Morphology of the liver and architecture of liver tissue with liver lobules as basic anatomical units and hepatocytes as the main constituents of liver parenchyma.
Figure 15.3 Schematic cross-sectional view of a liver lobule illustrating blood and bile flow. The hepatic artery, portal vein, and bile duct are arranged in a distinctive pattern known as the portal triad or portal field at the center of liver lobules.
Figure 15.4 Progression of liver fibrosis with characteristic changes in structure and function. Starting from initial insults and progression over many years, liver cirrhosis marks the end stage of liver diseases with an increased risk of hepatocellular carcinoma.
Figure 15.5 (a) Schematic view of healthy liver parenchyma. (b) Schematic view of fibrotic liver parenchyma showing characteristic alterations such as an increase in activated myofibroblasts and fibril-forming collagens, enlarged portal fields, loss of endothelial fenestration, distortion of veins, as well as changes in the basal membrane.
Figure 15.6 Simplified process chart of the pathogenesis of liver diseases with liver injury caused by hepatotoxic agents. Bold font indicates liver diseases and dashed arrows indicate potential self-perpetuating processes. For further details, see text.
Figure 15.7 Histological micrographs of human fibrotic liver showing fibrosis stages F1–F4 according to the METAVIR classification system.
Figure 15.8 Summary of microstructural changes associated with the pathogenesis of liver fibrosis as revealed by basic experiments in animal models and cell cultures. In the pre-inflammation stage of early liver injury, HSCs can express both collagen and collagen cross-linking enzymes, leading to ECM stiffening already at an initial stage of disease.
Figure 15.9 Principle and early results of MRE of the liver. (a) Wave images of two patients with mild (F1) and severe (F4) fibrosis. The apparent increase in shear wavelength reflects stiffening of liver tissue with progressing fibrosis. (b,c) Box plots showing elasticity in kPa based on the Voigt model (b) and viscosity in Pa s (c) in patients with hepatic fibrosis. Both, elasticity and viscosity increase with the stage of fibrosis.
Figure 15.10 AUROC analysis of the diagnostic accuracy of MRE for liver fibrosis staging. The inserted table shows the values for AUROC, cutoff values for liver elasticity, and the corresponding sensitivity and specificity for each test.
Figure 15.11 Staging of hepatic fibrosis with different biomarkers. (a) MRE; (b) transient ultrasound elastography (
TE
, Section 12.12); and (c) APRI.
Figure 15.12 Multifrequency MRE of the liver and spleen based on
k
-MDEV inversion (see Section 10.6). (a) -weighted images of a healthy volunteer and patients with hepatic fibrosis of grades F2 and F4. (b) Stiffness maps, represented by shear wave speed. An increase in elasticity can be observed for both organs with fibrosis progression; however, this increase is clearly more pronounced in the liver than in the spleen.
Figure 15.13 Changes in elasticity and the springpot parameter for progressing liver fibrosis (F0–F4).
Figure 15.14 Schematic representation of major vessels of the hepatic portal system. The hepatic portal vein is one of the largest veins in the abdomen, connecting the spleen and the gastrointestinal tract with the liver. The hepatic vein, which begins at the junction of the splenic vein and the superior mesenteric vein, drains the blood coming from the large and small intestine as well as from the spleen into the liver.
Figure 15.15 Normal -weighted MRI and maps of volumetric strain in a patient with hepatic hypertension before and after TIPS intervention demonstrating an increase in volumetric strain (reduced compression modulus) following TIPS.
Figure 15.16 Linear regression analysis of the relative change in volumetric strain after TIPS versus HVPG.
Figure 15.17 MRE magnitude images and corresponding elastograms of a patient before and after TIPS demonstrating lower values in liver and spleen in the post-TIPS experiment.
Figure 15.18 Linear correlation between relative changes in spleen stiffness and relative changes in the HVPG (). No such correlation was found for the liver. The relative changes are shown as percentages calculated by dividing the difference of pre-TIPS and post-TIPS values by the pre-TIPS values.
Figure 15.19 Renal MRE. (a) MMRE and MDEV inversion of central slices in a healthy volunteer. The anatomical regions for spatial averaging of are encircled by green (cortex), cyan (medulla), and red (hilus) lines. (Streitberger 2014 [102]. Reproduced with permission of Elsevier.) (b) MMRE and
k
-MDEV inversion showing superior detail resolution in the wavespeed maps.
Figure 15.20 MMRE of the uterus from [105]. Shown are standard -weighted MRI (MRE magnitude), , and in a representative image slice of the uterus of a healthy volunteer. The uterine corpus, endometrium, and cervix are demarcated by red, blue, and green lines, respectively.
Figure 15.21 Variation of over the menstruation cycle in a healthy volunteer: (a) of myometrium (filled circles) and endometrium (open circles) plotted separately over the normalized menstrual cycle days. (b) of endometrium covering two complete menstrual cycles, the beginning of menstruation is indicated by arrows. Mean values and standard deviations of in the endometrium (c) and the myometrium (d) in the proliferative (PP) and the secretory phase (SP).
Figure 15.22 Results of MRE of the IVD obtained in
ex vivo
bovine samples by static indentation (a) or by MRE at two different states of the disc, once in its native state and a second time in a compressed state to simulate tissue degeneration (b). (c) Results from
in vivo
experiments in healthy volunteers of two IVD (L3/4, L4/5) with varying degrees of degeneration according to the Pfirrmann score.
Chapter 16: MRE of Skeletal Muscle
Figure 16.1 Sketch of the hierarchy of tissue architecture in skeletal muscle.
Figure 16.2 Appearance of shear waves in MRE of skeletal muscle. (a): Imaging planes relative to the muscle. Two typical scenarios are shown for measuring the ST wave mode (polarization/propagation directions are perpendicular/parallel to the principal axis of the muscle, respectively) in a plane of symmetry (sym) or the plane of isotropy (iso). Therefore, vibration is induced at the distal or proximal end of the muscle (blue arrow) and free wave propagation is captured within the imaging planes aligned with the coordinate axes of the elasticity system (sym and iso). (b): Example MRE magnitude images (left) and wave images (right) showing the preferred direction of wave propagation along the muscle fibers within the plane of symmetry. Both motion encoding and vibration direction are through-plane (blue cross). This scenario corresponds to the lower left panel in Figure 4.10. (c): Appearance of shear waves (in-plane curl component, ) in the lower extremity muscles (right leg and left leg) at different frequencies. In contrast to (b) and as prescribed by the plane of isotropy in TI media, no preferred directionality of the shear wave patterns is apparent.
Chapter 17: Elastography of Tumors
Figure 17.1 Creep experiments with the optical cell stretcher (each curve is the average of more than 500 cells, G3 and G3+ denote stage 3 cancer without and with nodal metastasis, respectively). Cancer cell compliance increases with the tumor stage. Cancer cells become softer, but show faster relaxation due to increased contractility. This tendency is more pronounced for breast cancer and is in agreement with observations that breast cancer is more invasive than cervical cancer.
Figure 17.2 Stiffness response of breast tumor samples to microindentation. Left-hand side: Biopsy-wide histograms showing stiffness distribution for normal glandular breast tissue, benign lesion, and invasive cancer. Normal tissue appears to be homogenously soft. The benign lesion exhibits a similar unimodal stiffness distribution, however, with a higher stiffness than healthy breast tissue. By contrast, invasive cancer is identified by heterogeneous stiffness distribution with a characteristic soft peak for malignant tumor tissue. Corresponding micrographs of H&E-stained histological sections are shown on the right-hand side (scale bar applies to all images, 50 ).
Figure 17.3 Strain-based elastography and quantitative shear wave elastography for characterization of invasive ductal mammary carcinoma. The tumor presents with irregularly shaped boundaries and perifocal edema in B-mode US. Both strain and shear wave speed maps indicate high tumor stiffness (corresponding to low strain amplitudes), which is typical for invasive ductal carcinoma. The shear wave speed map is confused by artifacts related to the near field of the US probe.
Figure 17.4 Multiparametric image fusion in prostate cancer. (a) hypointense tumor in -weighted MRI (left) and contrast-enhanced ultrasound (CEUS) showing increased perfusion related to high aggressiveness of the tumor (Gleason-socre 4+4, right). (b) -weighted MRI (left) with strain image showing the tumor as a solid-encapsulated mass. (c) Shear wave elastography revealing high stiffness within the tumor boundaries. This elasticity-based contrast could be used for guidance of the biopsy. Notably, this patient received previously two biopsies without result. SWE could increase the detection rate of prostate tumors.
Figure 17.5 MRE-derived viscoelasticity (storage modulus , loss modulus ) versus cell density and microvessel density obtained in mouse models of intracranial tumors.
Figure 17.6 Mechanical properties of seven
in vivo
tumors (three glioblastoma multiforme (GBM), one metastasis (MET), one astrocytoma WHO II (AC2), two meningioma (MEN)) measured by multifrequency MRE (MMRE) and the optical stretcher.
Figure 17.7
In vivo
MRE of liver tumors. (a) A stiffness threshold of 5 kPa separates malignant liver tumors from benign tumors
Figure 17.8
k
-MDEV-based multifrequency MRE in a patient with hepatocellular carcinoma. (a) Standard proton-density (PD) and -weighted (w) MRI. (b) Wave speed map. (c) Cross-sectional view through the excised tumor. (d) Micrographs of histological analysis (H&E stain) corresponding to regions identified by arrows 1–3 in the
