Magnetic resonance elastography in a nutshell: Tomographic imaging of soft tissue viscoelasticity for detecting and staging disease with a focus on inflammation

Magnetic resonance elastography (MRE) is an emerging clinical imaging modality for characterizing the visco-elastic properties of soft biological tissues. MRE shows great promise in the noninvasive diagnosis of various diseases, especially those associated with soft tissue changes involving the extracellular matrix, cell density, or fluid turnover including altered blood perfusion – all hallmarks of inflammation from early events to cancer development. This review covers the fundamental principles of measuring tissue viscoelasticity by MRE, which are based on the stimulation and encoding of shear waves and their conversion into parameter maps of mechanical properties by inverse problem solutions of the wave equation. Technical challenges posed by real-world biological tissue properties such as viscosity, heterogeneity, anisotropy, and nonlinear elastic behavior of tissues are discussed. Applications of MRE measurement in both humans and animal models are presented, with emphasis on the detection, characterization, and staging of diseases related to the cascade of biomechanical property changes from early to chronic inflammation in the liver and brain. Overall, MRE provides valuable insights into the biophysics of soft tissues for imaging-based detection and staging of inflammation-associated tissue changes.


Introduction
The mechanical properties of soft tissues play a critical role in the development and progression of disease [1,2].For example, inflammation, a tissue response to injury, can be triggered by chronic mechanical friction, increased vascular pressure, or traumatic mechanical insults [3][4][5][6].Inflammatory tissue itself exhibits altered mechanical properties resulting from a cascade of mechanically relevant processes.For instance, vascular leakage or immune cell infiltration − two hallmarks of inflammation − significantly alter coarse-grained mechanical tissue properties [7,8].Beyond early inflammation, further downstream pathological processes such as matrix protein accumulation and crosslinking typically lead to tissue stiffening while tissue degeneration, atrophy, and necrosis cause softening.Therefore, many disease processes are associated with physical state transitions of the affected tissues over property ranges from soft to stiff and from elastic to viscous [9].
Although they originate at the microscopic level, the physical traits of tissues affect long-range interactions up to and including percolation, i.e., global or whole-organ properties [10].The exceptional sensitivity of manual palpation to detecting lesions and tumors (derived from the Latin for swelling) stems from the fact that such abnormal formations are characterized by a hierarchy of crosslinks and adhesion points that Abbreviations: EAE, experimental autoimmune encephalomyelitis; FE, finite elements; FoV, field of view; LFE, local frequency estimation; MASLD, Metabolic Dysfunction-associated Steatotic Liver Disease; MEG, motion encoding gradient; MRE, magnetic resonance elastography; MRI, magnetic resonance imaging; MS, multiple sclerosis; PNN, perineuronal nets; SWS, shear wave speed; t-FT, temporal Fourier transform; TR, repetition time; USE, ultrasound elastography.add up to a macroscopic scaffold [11].Even the physicians of Pharaoh Ahmose I used their fingers to detect disease, as described in the Ebers Papyrus of 1550 BCE [12].Elastography was developed to give modern medical imaging modalities such as MRI and sonography the tactile senses to access the viscoelastic tissue properties that indicate disease [13].
Whereas ultrasound-based elastography (USE) is widely available, cost-effective, and can provide images in real-time [14], magnetic resonance elastography (MRE) maps soft tissue in three dimensions [15] and is considered the most accurate method for quantifying tissue viscoelasticity, particularly for the detection of liver fibrosis [16].Therefore, MRE has significantly advanced our understanding of the in vivo biomechanical properties of tissues and their changes during disease progression.MRE and USE have been cross validated by simultaneous acquisitions in phantoms [17,18], liver [19,20] and brain [21] showing similar results whenever the same frequency range, inversion method and tissue region is considered.
MRE involves three key technical steps: (i) the stimulation of harmonic shear waves within the body, (ii) their encoding into the phase of the complex MRI signal, and (iii) the conversion of the resulting wave images into viscoelastic parameter maps [10].The viscoelastic parameters that can be obtained include complex shear modulus, shear wave speed, wave attenuation, loss and storage properties, and model-based viscoelasticity [22].
Over the years, different techniques with complementary strengths and challenges have been developed.Upfront: there is no perfect single MRE technique that delivers what is theoretically possible given ideal imaging characteristics and tissue properties captured by our continuum mechanical models.In fact, biological tissue does not yield a single tone upon mechanical excitation but rather generates a full symphony of viscoelastic responses that overlap on a continuum of spatiotemporal scales.This is attributed to the hierarchical, heterogeneous, anisotropic, and nonlinear viscoelastic properties inherent to soft biological tissues.In addition, MRE is fundamentally slow, often taking minutes to acquire a complete data set, during which endogenous and stochastic motion occurs with amplitudes that exceed the induced harmonic deflections, while the intrinsic tissue properties can change.
Thus, MRE must be tailored to different clinical needs to make MRI Fig. 1.Basic viscoelastic models that have been used to explain the dispersion of MRE-derived storage modulus G' and loss modulus G'' (similar functions can be drawn for shear wave speed and penetration rate).Dispersion in the context of MRE often refers to the changes in G' and G'' over frequency, which is a result of the tissue's intrinsic viscosity.While a spring models pure elastic behavior, a dashpot stands for a fluid that does not support shear waves and, consequently, cannot be assessed by MRE.Nevertheless, in combination with a spring, such as in the KV-or Maxwell model, the dashpot mimics the viscous loss encountered in soft biological tissues.The springpot is an interpolation between spring and dashpot with interpolation exponent α.While not supporting static stress, the springpot is the only twoparameter viscoelastic model that predicts a continuous increase in both G' and G'', as observed in most biological soft tissues.
T. Meyer et al. more quantitative, system-independent, and predictive.This article explains, in a nutshell, the basic concepts of MRE, introduces current approaches and validated techniques, and reviews clinical applications including their preclinical references with a focus on inflammatory processes.

Shear and compression modulus
Like any other mechanical test, MRE exploits Hooke's law, which describes the linear elastic deformation a material undergoes upon exposure to mechanical stresses [23].In the simplest case, this deformation (strain) response is determined by a shear and compression modulus, both in units of kPa.While the shear modulus denotes the inherent resistance of a material to lateral deformation, meaning that the tissue volume does not change, the compression modulus is related to compression or dilation, i.e., changes in volume.Although it may seem academic to distinguish between shear and volumetric strain, their respective moduli are worlds apart.The compression modulus, in the range of gigapascals, is relatively uniform throughout the body, while the shear modulus varies by more than eight orders of magnitude and is in the range of tens to thousands of pascals in soft tissues [24].Palpating fingers test the shear modulus by shifting tissue layers without volume changes for sensing the microarchitectural characteristics that are associated with disease.By contrast, the compression modulus is mainly determined by the tissue's high water content of 70 to 80 % evoking rather incompressible material properties.The situation is different at slower time scales when tissue fluid is allowed to be displaced or shifted during deformation [25].At such scales, poroelastic effects provide sensitivity to blood perfusion and vascular pressure [26][27][28], illustrating the importance of excitation frequency in MRE.In a nutshell, higher stimulation frequencies probe solid-elastic properties, while shear waves at lower frequencies are influenced by elements that can permanently change position, such as fluids, motile cells, or vesicles [11].

Viscoelasticity
While strain energy is stored and re-stored in elastic materials, it is completely converted to kinetic energy and heat in fluids [29].Thus, elastic solids and viscous fluids represent the two extremes of the spectrum of viscoelastic properties; between them, the recovery of shape after stress relaxation is delayed [12].For harmonically oscillating stress, as in MRE, this delay causes a phase shift in the strain response that is proportional to the phase angle φ of the complex shear modulus G * = |G * |expiφ.G* can also be represented by its real part, storage modulus G', and its imaginary part, loss modulus G'', i.e., G * = G ʹ + iGʹʹ.The phase angle of the complex shear modulus, also called loss angle, is then obtained as φ = atanG ʹʹ /Gʹ [22].An elastic solid has no loss modulus (G''=0) or loss angle (φ = 0) and does not exhibit frequency dispersion of G*=G', i.e., elasticity is constant over oscillation frequency.The opposite is true for pure fluids, which have no storage modulus (G'=0) and maximum loss angle (φ = π/2), giving rise to marked frequency dispersion of G*=G''.However, this hypothetical limit of maximum frequency dispersion with a loss angle of π/2 does not satisfy the wave equation because shear waves are not supported by fluids, rendering MRE unfeasible.Nevertheless, from solid G*=G' to fluid properties of G*=G'', G* becomes more and more dispersive, indicating increasing fluid material properties.Such a continuous transition from solid to fluid is nicely represented by an increase in loss angle φ from 0 to π/2 with π/4, indicating balanced solid-fluid properties [30].Notably, φ as a measure of tissue fluidity increases with loss modulus G'' regardless of water content, while the fluidity of pure liquids is highest at zero viscosity.In essence, MRE is sensitive to elasticity through G' and viscosity either through G'' or φ.Because G* is a solid property, all MRE-derived parameters are related to the motility of particles and structures that transmit shear forces.Viscoelastic models are required to infer frequency-independent, intrinsic material parameters such as elasticity and viscosity from G', G'' or φ.The basic rheological models that relate two independent viscoelastic parameters to G* are the Kelvin-Voigt, the Maxwell, and the spring-pot model.Their representations assembled from basic spring and dashpot elements as well as dispersion functions are shown in Fig. 1.In biological soft tissues, most experiments have shown that G' and G'' increase with stimulation frequency [31,32].These observations suggest that there is no independent material response of elasticity and viscosity, but rather an inherent mixture of the two, measured by MRE as viscoelasticity.

Shear waves
Remote palpation needs waves to transfer elastic energy deep into the tissue.While compression waves are polarized longitudinally with respect to their propagation direction, shear waves are transversely polarized.The first implies changes in density, which are associated with compression, the latter type of waves relates to shear modulus.Therefore, compression waves travel approximately 1000 times faster in soft biological tissue than shear waves (1500 m/s versus 1.5 m/s) [33].As a result, at relatively low drive frequencies as used in MRE, compression waves have lengths on the order of 30 m and appear in MRE wave images without significant curvature while shorter shear waves of approximately 3 cm length are superimposed.The shear wave is the desired probe for remote palpation: the longer the shear wave, the higher the shear wave speed and corresponding shear modulus.Without viscoelastic dispersion, the shear wavenumber grows linearly with excitation frequency, making higher frequencies more favorable for wave analysis algorithms.However, it is a fundamental principle in acoustics that amplitude attenuation through viscous damping increases with wavenumber or excitation frequency.Therefore, the optimal range of excitation frequencies in MRE needs to be carefully balanced: on the one hand, wave analysis algorithms measure strain, i.e., the curvature of the waves, which should be sufficiently high relative to the achieved spatial resolution.On the other hand, the signal-to-noise ratio (SNR) of strain depends on total deflection amplitude [34], which decreases with frequency [35].Therefore, MRE performed in clinical scanners balances the range of vibration frequencies between wave damping and shear strain, typically between 20 and 50 Hz for the brain [36], while most clinical studies investigating liver fibrosis are performed at 50 to 60 Hz [37].Smaller and more heterogeneous organs such as the heart and prostate are typically investigated at higher frequencies of 60 to 150 Hz [38][39][40].Notably, in the same way that viscoelastic damping impedes the use of higher frequencies, it supports low frequencies: according to the spring-pot viscoelastic model as shown in Fig. 1, tissue often behaves very soft at low excitation frequencies, giving rise to surprisingly short wavelengths even at extremely low excitation frequencies on the order of 10 Hz [41,42].Adjusting wavelengths and strain SNR by increasing or decreasing excitation frequency makes MRE a multiscale method [43][44][45].In small animals or tissue samples, higher vibration frequencies are required in order to squeeze several wave numbers into the smaller field of view [46][47][48].Therefore, in the mouse brain, MRE operates in the kilohertz range, which provides higher shear modulus values than typically obtained in the range of clinical MRE, again due to the dispersion of the shear modulus [49].Even when dispersion of shear modulus is ignored, relative conclusions in terms of stiffer or softer can be consistently drawn across the hierarchy of scales from the cell scale to coarse-grained in vivo properties measured by MRE [50,51].

Mechanical excitation of shear waves
MRE relies on continuous, time-harmonic vibrations, i.e., sinusoidal T. Meyer et al. motion, in the frequency ranges mentioned above.This does not mean that MRE actuators have to perform strictly harmonic motion.MRE can also use transient impulses that are converted into harmonic motion within the tissue.As a natural protective mechanism, soft biological tissue attenuates high-strain shear waves and favors harmonic motion at the lowest (fundamental) frequency.Consequently, as the waves propagate through the tissue, the fundamental frequency of 1/TR increasingly dominates any periodic stimulation with repetition time TR.Typical TRs between consecutive RF excitations in MRI sequences are in the range of tens of milliseconds, resulting in frequencies <100 Hz when a mechanical pulse is applied at each TR [10].
Although there is flexibility in the way motion is induced, including various strategies such as scanner-intrinsic vibrations [52], piezoelectric actuators [53,54], Lorentz coils [55][56][57], loudspeakers [58,59], rotating masses [60], or compressed air pulses [61], MRE actuators should meet some important requirements: first, they should avoid magnetic field Fig. 2. Types of MRE vibration hardware used in clinical MRI scanners, including clinical and preclinical applications with resulting stiffness-related parameter maps.Three clinical driver systems are shown.They are based on an acoustic voice coil system [181], compressed air drivers [61], and a rotational eccentric mass driver [60].The use of several drivers allows multidirectional wave excitation, supporting the generation of tomographic stiffness maps, as illustrated by the grayscale shear wave speed image of human abdominal organs.Therefore, no organ-specific region is delineated.The experimental setup for preclinical applications is based on a piezoelectrical actuator, which can be driven at higher frequencies (300 to 800 Hz) than used in patients (20 to 80 Hz).
interactions [62,63].Nonmetallic actuators are preferred, while nonmagnetic actuators are mandatory for MRI safety.In addition, the timing of driver motion should be precisely controllable by the MRI sequence, either by resynchronizing each TR with trigger pulses or by locking the clock of the wave generator to the MRI [64].While the first principle introduces slight phase distortions that interrupt the continuous flow of shear wave energy, the second principle requires a level of precision that is on the order of a µs per second of run time (e.g., 1 µs accumulates to 0.24 ms after 4 min of MRE scan time, which adds up to nearly 9 • of phase shift for a 100 Hz vibration).Fig. 2 illustrates the current principles of MRE motion generation used in clinical MRI scanners for patient studies and preclinical research.Homogeneous delivery of vibration amplitudes to the region of interest is desirable to achieve sufficient strain SNR over the entire field of view (FoV).Full illumination of organs and tissues by shear waves is necessary for MRE to generate tomographic maps of mechanical properties across the full FoV.Therefore, use of several drivers placed around the region of interest, ideally combined with repeated acquisition at multiple frequencies, provides a wealth of mechanical information, regionally and dynamically, that stabilizes the inverse problem solutions as explained below [65].

Encoding shear waves by phase-contrast MRI sequences
Once shear waves have been induced in the tissue, the next step in MRE is to encode the resulting tissue deflections using phase-contrast MRI.In the presence of magnetic field gradients, the complex MRI signal is sensitive to motion.When the spins − the signal-emitting particles − move in a spatially varying magnetic field, their frequency changes slightly with their position within the field.This results in spins experiencing a net phase shift proportional to their displacement [66].In this way, motion is imprinted on the phase of the complex MRI signal.In MRE, motion-encoding gradients (MEGs) are bipolar, mimicking a sine or cosine function over time to suppress the phase accrual of static and continuously moving spins, respectively [41].Fig. 3 illustrates how the accumulated MRI phase increases over the time of the MEG with a spin motion that is zero, has constant velocity, is accelerated, or sinusoidal.It can be seen that the MEG acts as a finite difference operator in time and suppresses static phase shifts (zero moment nulling), flow (first moment nulling), or accelerating spins (second moment nulling).Consequently, the resulting phase images do not reflect true tissue deflections u(t), but rather their first-or second-time derivative depending on the shape of the MEG, e.g., displacement velocity u(t) in flow MRI or phase-shifted oscillatory motion in MRE (first moment nulling: dsin(t) dt = cos(t), second moment nulling: d 2 sin(t) dt 2 = − sin(t)).Since the MEG can be Fig. 3. Motion encoding in phase-contrast MRI, which requires encoding gradients, which in turn result in phase accumulation of the complex-valued MRI signal.As the encoding gradient is applied, static particles (blue lines) accumulate spin phase only with unbalanced gradients.In motion-sensitive PC-MRI, these spins are suppressed by using balanced gradients with 0th, 1st, or 2nd moment nulls, which suppress the spins of static, flowing (red lines), and accelerated (yellow lines) particles, respectively (2nd moment zero not shown).MRE is based on harmonic motion (green lines), whose maximum accumulated phase is indicated by green arrows.deployed along any Cartesian axis i = {x, y, z}, MRE has the unique ability to encode full 3D vector fields u i (t) [67].Fig. 4 shows a set of raw MRE phase data representing the encoded motion at different time steps over one vibration period, in three orthogonal encoding directions, and at different frequencies.

Postprocessing of raw phase images in MRE
An MRE experiment typically consists of repeated encodings with shifted wave phase in order to capture motion u i (t) at N different time points over a vibration period.This allows extraction of fundamental frequency f from the phase images by performing a temporal Fourier transformation (t-FT) over N time points for each pixel.The generation of complex wave images ũi (f) is a key step in MRE postprocessing as it suppresses signals from other Fourier components such as induced by breathing [68].Furthermore, t-FT collapses the relevant time information into a harmonic wave field that satisfies the complex wave equation [29].In addition, complex wave images ũi (f) have a factor ̅̅̅̅̅̅̅̅̅ N/2 √ higher SNR than raw data u i (t).However, t-FT is not the first step in MRE postprocessing as it must be applied to unwrapped phase images.Thus, elimination of aliased phases as shown in Fig. 4 requires unwrapping algorithms to be applied to noisy raw data, which still contain stochastic, nonharmonic, motion.Therefore, robust unwrapping algorithms have been developed, which deliver smooth phases but do not necessarily reflect the ground truth of wave phases in 3D and time.Physically correct unwrapped phases are often not easy to attain due to motion inconsistencies or rapid patient movements of only a few microns occurring between time points, field components, or adjacent image slices [69].Stable unwrapping methods widely used in MRE include techniques based on 2D pathfinding, which, however, are sometimes disturbed at discontinuities [70] and Laplacian-operator-based methods, which generate smooth but sometimes biased wave fields [12].To improve unwrapping, dual encoding strategies have been proposed, which basically combine raw phase images encoded with different gradient sensitivities to generate images that are widely wrapfree, however, at the expense of longer acquisition time [71,72].In essence, MRE wave images should be high-dimensional to mitigate phase inconsistencies due to stochastic motion, phase jitter, inefficient encoding, or wave attenuation [69,73].In fact, the overdetermination of MRE information by repeated acquisitions of wave phases, components and frequencies provides stability for efficient solutions to multidimensional unwrapping and wave inversion [74].

Wave inversion
The final step in MRE is the conversion of complex wave fields ũi (f) into parameter maps.Reconstruction of maps of shear modulus from harmonic wave fields requires solution of the inverse problem of timeharmonic waves [75,76].In other words, wave inversion infers material properties from the curvature and attenuation of local displacements.Both the curvature and attenuation of a wave are determined by relative changes in local deflections on a spatial scale.Therefore, classical MRE reconstruction relies on the determination of spatial gradients, not absolute deflections.Mathematically, this is prescribed in the wave equation, a second-order partial differential equation that incorporates Laplacian field Δũ i (f).In its simplest form, the wave equation is a scalar equation with only one unknown, the shear modulus: G * = − ρ2πfũ i /Δũ i (with ρ denoting mass density).However, to arrive at this simplification, known as direct Helmholtz inversion, one must make several assumptions which are hard to justify from a rigorous biomechanics perspective.These assumptions with their consequences in brackets are: • Small strain (the MRE-induced deflection amplitudes satisfy the limit of linear elasticity of Hooke's law) [  The MRE maps shown here were generated using phase-gradient-based multifrequency inversion (for shear wave speed, SWS, and penetration rate, PR), as explained in [182], or phase-angle-based direct inversion (for loss angle or fluidity φ), as explained in [74].
• Incompressibility, no compression wave, no pressure offset in ũi (all terms in the motion equation related to volumetric changes can be omitted) [83,84] • Local homogeneity, viscoelastic properties change only shallowly, no distinct interfaces between tissues of different mechanical properties (constant G*, spatial derivatives of G* equal zero) [85][86][87] Small strain seems to be a valid assumption given that strain amplitudes in MRE are on the order of 10 -3 for shear waves and 10 -4 for compression waves [88,89] as long as we ignore the fact that some tissue types, e.g., tumors or dilated lung and myocardium, are pre-strained [90][91][92][93][94][95].Arguably, the other three assumptions listed above are likely to be invalid.Worse, the assumption of homogeneity, for example, calls into question the whole approach of generating parameter maps by MRE, since the very purpose of these maps is to represent exactly what is ignored here: the heterogeneity of viscoelasticity.Additionally, there are a few numerical challenges in solving the Helmholtz equation on the finite grid that represents the digital support for MRE wave images.First, numerical gradient operators have a finite size within which derivatives across boundaries are biased.Second, the digital support of waves is either too small or too large, causing overestimation of valuesthe discretization biasor noise-related underestimation, respectively [96].Only in a very narrow window of 8 to 12 pixels per wavelengths do discretization bias and noise effects cancel each other in MRE direct inversion [96,97].To illustrate, the estimation of MRE is analogous to the attempt to quantify the slope of the local incline of individual steps on a staircase, where the height of each step may fluctuate to an unknown extent.The elastogram is then obtained by dividing the staircase by the noisy slopes.Obviously, careful denoising is needed here to extract meaningful information.Several robust denoising approaches have been reported in the literature, including bandpass filters of desired wavenumbers (k) in k-space [98], multidimensional derivative kernels of extended sizes in image space [99], wavelets [100], and forward model fitting by expanding MRE wave images into sets of harmonic base functions [85,[101][102][103].Artificial neural networks have also been trained to mitigate the noise curvature problem in MRE by patch-wise comparison of complex wave images with simulated superposition of traveling waves [104,105].Nonetheless, the quest is still open for solutions that avoid a priori assumptions about wanted signal (shear waves in a predefined k-band) versus unwanted signal (low-k compression waves and high-k noise).It seems as if the wave equation takes its toll: second spatial derivatives suffer from noise, while variational approaches involve closed-path integration that again resembles a difference operator [85,86].Forward solutions are computationally expensive and require knowledge of boundary conditions [12].One way to trick the wave equation is based on its solution: Manduca et al. proposed to derive the phase gradient of a single k-wave (plane wave) [106].The basic idea is that the phase of a complex plane wave accrues linearly along the propagation axis x.The slope of this wave phase is equal to the wavenumber k x , which is retrieved as the x-derivative, i.e., the plane wave phase gradient.Since frequency f is known in MRE, wavenumbers are easily converted into shear wave speed SWS, which is a proxy for storage modulus (SWS ). Computing first-order phase gradients is indeed a unique way to avoid second-order noise-sensitive derivatives as required by other solutions of the wave equation [107].However, the challenge here lies in k x , the wavenumber in x-direction.Since the acquired field ũi (f) is a superposition of multidirectional waves, one needs directional filtering to decompose the full field into unidirectional wavenumbers such as k x and k y before computing the phase gradient [108].A similar approach is local frequency estimation (LFE), in which a band of k-space filtered waves is inverted [109].The lognormal filters used in LFE can be tuned to resemble either first or second derivatives in k-space.Irrespective of whether first or second derivatives are employed, it has been shown that solutions to the inverse problem can be stabilized by multifrequency, multi-component averaging prior to inversion [61,107].This multi-inversion approach has been termed tomoelastography as it produces viscoelastic parameter maps with a detail resolution similar to that of standard MRI (tomographic) images (see Fig. 4) [65].In a nutshell, first-order MRE inversion techniques (phase gradient and LFE) fundamentally differ from second-order inversions (direct Helmholtz inversion, variational methods) in that they operate on solutions of the wave equation (plane waves) instead of solving the wave equation itself.Consequently, first-order methods are robust against noise but need preprocessing such as directional filtering, which can degrade detail resolution in SWS maps.In contrast, secondorder methods, including Helmholtz inversion, satisfy Huygens' principle of superimposed multisource wave fields and, thus, provide G * -maps without prior decomposition of wave fields.The parameters that can be retrieved by MRE inversion techniques are summarized in Table 1.

Applications
In vivo MRE opens the door to a world of biomechanical interactions that are not yet fully understood.According to what we currently know, the convergence of mechanobiology and continuum mechanics is primarily driven by observational studies that address monocausal correlations.Nevertheless, these studies contribute important pieces to the puzzle of which MRE parameters can be used to detect and stage diseases and ultimately predict disease courses.Much insight has been gained from experiments in well-defined phantoms that mimic basic structural features of biological tissues [7,110,111] or modified ex vivo specimens that simulate mechanically relevant processes in vivo [28,[112][113][114][115][116][117].To provide a hands-on understanding of the basic interactions to which MRE is potentially sensitive, we will not list here the large body of literature on MRE applications but briefly discuss a few studies that highlight the biomechanical effects to be harnessed as diagnostic MRE markers.Moreover, in doing so, we will only discuss pathophysiological hallmarks related to inflammation, from early events in the inflammatory cascade to tissue remodeling at the stage of chronic inflammation.Finally, we attempt to disentangle the mechanical signature of inflammation-affected tissues with a focus on the liver and the brain.

Vascular leakage, blood perfusion, and pressure
Vascular leakage is a critical initial response of biological tissues to injury and can be seen as a precursor to several subsequent inflammatory and healing processes.The immediate response to tissue injury involves disruption of endothelial glycocalyx and cell junctions at the microvascular level.The resulting increase in vascular permeability fosters the exudation of plasma proteins and fluids into the interstitial space, contributing to the formation of edema.Such edematous accumulation of fluid within soft tissues not only dilutes local toxins and facilitates the entry of immune cells including neutrophils and macrophages but also results in the characteristic swelling of the affected tissue.
While fluid accumulation clearly has a mechanical effect, immune cell migration is unlikely to alter the macroscopic mechanical tissue properties to any degree [118].Fig. 5 illustrates the different effects of fluid accumulation on the mechanical properties of soft tissues: encapsulated tissues, such as those surrounded by connective tissue and ligaments, cannot expand freely upon fluid infiltration.Therefore, edema is often felt as a firm bump resulting from nonlinear stretching of connective tissue.Similarly, overstretched cell membranes or pressurized blood vessels have been seen as macroscopic stiffening in several MRE studies investigating different scenarios and entities [26].Fundamental research was performed by Parker et al. who developed a microfluidflow model and validated it in liver tissue [27,28] and placenta [119].While a study in sheep livers demonstrated an increase in whole-organ stiffness and elucidated the way in which this was brought about by vascular expansion at higher portal pressure [88], the opposite was observed in smaller specimens such as rat livers [114].Without the constriction imposed by bulky tissues and promoted by vascular leakage, liver tissue was observed to become softer with increased portal pressure [114].These two studies nicely illustrate the bidirectional effect of fluids on soft tissue stiffness: confinement promotes stiffening, which is likely related to the generation of tissue pressure, whereas an increase in the fluid content of distensible tissue leads to its expansion and softening [65].Because the liver capsule prevents expansion, studies in both patients and animal models show correlations between portal pressure and tissue stiffness [120,121].In healthy volunteers, the amount of blood perfusing the liver, which can be modulated by breathing [64], abdominal pressure [122,123], eating [124,125], or water intake [65,126], has been found to be an influencing factor affecting liver stiffness.These observations suggest that any change in blood perfusion, including edematous water accumulation, congestion, or increased perfusion pressure, as often associated with inflammation, leads to higher liver stiffness.Since stiffening is also a hallmark of fibrosis, viscosity-related markers such as loss modulus or damping ratio (see Table 1) raise the exciting prospect of distinguishing fluid-driven inflammatory processes from matrix accumulation in fibrosis [120].Indeed, recent studies in patients have corroborated these findings by demonstrating liver tissue fluidity and damping ratio to be sensitive to inflammation independent of fibrosis [127,128].
In the brain, tissue stiffening generated by vascular effects or driven by fluid accumulation has been observed after formation of cytotoxic edema [129], hypercapnia [130,131], Valsalva maneuver [130], venous drainage [132], functional activation [133,134], elevated intracranial pressure [135,136], and arterial pulsation [137].All of these stiffening effects may be explained by hyperelastic dilatation of cell membranes or blood vessels, resulting in an overall increase in brain stiffness on a coarse-grained scale.The opposite was reported in scenarios of impaired vascular integrity as a symptom of a disrupted blood-brain barrier [8] or reduced cerebral blood flow due to dehydration [138] or hypothermia [139].Unlike higher blood perfusion, increased tissue water, as in peritumoral edema, was not associated with marked changes in viscoelasticity, suggesting a fine balance between confinement and expansion of brain tissue [140].However, in cortical areas, where brain tissue can better expand than in the bulk, the amount of tissue water was negatively associated with stiffness [141].This observation supports the hypothesis that water content or fluid fraction in the absence of pressure correlates with tissue softening.
Notably, MRE in other organs than the liver and brain revealed similar mechanical patterns upon inflammation, with a tendency toward either liver-like stiffening or brain-like softening.For example, pancreatitis [142,143] and inflammatory bowel disease [144] were associated with markedly elevated tissue stiffness, which, against the soft background of normal pancreatic or colon tissue, provided excellent MRE contrast for detecting local inflammatory activity [145].Otherwise, nephritis was shown to be associated with significant softening even at asymptomatic filtration rates based on blood markers [146,147].This soft signature of renal inflammation was likely associated with decreased capillary perfusion pressure and increased free water pools, as discussed above for the brain [148,149].

Matrix accumulation, crosslinking, and cellular changes
Chronic inflammation of the liver causes matrix accumulation, which is associated with tissue stiffening, making MRE a sensitive biomarker for the noninvasive staging of hepatic fibrosis [59,[150][151][152][153][154][155].However, collagen deposition in the liver is not a uniform process but exhibits spatial variance and heterogeneous mechanical effects.For example, the outgrowth of collagen fibers from the portal triad into the liver parenchyma establishes a basic network of fiber bundles and can occur without crosslinking [156].Therefore, the overall effect of septal infiltration on liver stiffness is not necessarily larger than in pericellular fibrosis, where loose collagen aggregates are mainly deposited in the interstitial spaces between hepatocytes [118].Otherwise, pericellular fibrosis has been associated with increased vascular resistance, which may contribute to the aforementioned cascade of vascular effects on liver stiffness [157].Beyond the sheer amount of matrix proteins that contribute to the expansion of ECM from 0.3 % in healthy livers to 30 % in cirrhosis, crosslinking and fiber bridging are the critical steps that are expected to increase tissue stiffness by orders of magnitude [47,158].Therefore, significant stiffening is seen in bridging fibrosis, which is characterized by uninterrupted collagenous septa that form a continuous mechanical mesh over great distances.Although, in histologic slides, bridging fibrosis can be as delicate as septal infiltration or pericellular fibrosis, it represents mechanical gap closures, which usually have larger effects on the stiffness of scaffolds [118].On the cellular level, inflammation triggers an influx of immune cells into the liver, including macrophages, neutrophils, and lymphocytes, which aim to eliminate pathogens or toxins.In the liver, portal and lobular inflammation are features of Metabolic Dysfunction-associated Steatotic Liver Disease (MASLD), which describes the inflammatory infiltration of the portal triad, primarily by lymphocytes.This cell infiltration is often associated with the formation of edema and, as discussed earlier, may alter the mechanical properties of the tissue, but is unlikely to cause a direct mechanical response related to cell number [118].Also, in the brain, changes in mechanical properties in cortical areas were not correlated with leukocyte infiltration in experimental autoimmune encephalomyelitis, a mouse model of multiple sclerosis, but rather with chondroitin sulfate remodeling [159].Because the number of leukocytes in perivascular spaces increases with vascular permeability [160] a significant correlation was found between leukocyte infiltration and brain tissue softening, which, however, is most likely driven by water content rather than cell number [8].
Direct intrinsic cellular responses such as hepatocytic ballooning in MASLD have been observed to increase liver stiffness, probably due to the hyperelastic prestretch of cell membranes and intracellular fluid retention [118].Moreover, liver stiffness is also affected by metabolic cell function.For example, Shahryari et al. showed that stiff livers in rabbits had a reduced capacity for triacylglycerol storage, but increased gluconeogenesis capacities and increased cholesterol synthesis [161].In particular, triacylglycerides and cholesterol esters have a role in the production of infectious viruses such as hepatitis C [162].Antiviral therapy in hepatitis C improves hepatocyte function [163], prompting liver softening as a promising marker for monitoring antiviral therapy [164,165].It should be noted, though, that aberrant metabolic activity of hepatocytes due to inflammation overlaps with fibrosis, making blood markers such as glutamate-oxaloacetate transaminase for lipotoxicity an important tool for obtaining additional information [166,167].Also, the hormones released during pregnancy affect the function and activity of the gallbladder and of hepatocytes, leading to reversible stiffening of the liver in pregnant women [168].Here, bile accumulation, hepatocyte apoptosis, and hypertrophy have been discussed as possible factors causing the observed stiffening of liver tissue [169,170].Although the specific mechanisms of how cell metabolism relates to tissue mechanics are still vague, we may assume that cellular swelling, prestretched cell membranes, and a shift of water from the extracellular pool into cells partially contribute to the sensitivity of MRE to liver function [169].How drastically the macroscopic biomechanical properties of the liver change upon disruption of cell membranes can be seen after freezing and thawing liver tissue.MRE and histology showed that cell membrane disruption and sinusoidal endothelial cell detachment reduce tissue stiffness by a factor of 10 [116].Similar mechanisms occur in the brain, where neuronal swelling and cytotoxic edema formation in the course of dying were found to lead to a marked increase in tissue stiffness [129].
Conversely, processes involved in neuroinflammation underlying multiple sclerosis (MS) or neuromyelitis optica have been shown to be associated with brain softening [171][172][173][174].In experimental autoimmune encephalomyelitis (EAE), the animal model of MS, MRE detected softening in areas where contrast-enhanced MRI showed typical hallmarks of neuroinflammation, such as gliosis, leukocyte extravasation, and reduced sulfation of glycosaminoglycans [8].Similarly, the extent of tissue remodeling at sites of blood-brain barrier disruption, as indicated by fibronectin overexpression in acute EAE lesions, correlated with the degree of tissue softening in the mouse cerebellum [175,176].In EAE, fibronectin reflects the detachment of astrocytic endfeet from blood vessels with weakening of glial-vascular mechanical cross-links and thus tissue softening.This mechanism partially explains why the brain softens during the acute phase of EAE and stiffens during EAE remission [176,177].In addition, adhesion of neurons to their matrix through perineuronal networks (PNN) plays a critical role in brain stiffness.Therefore, PNN degradation has been shown to be associated with tissue softening following the remitting-relapsing course of EAE [159].This loss of PNN integrity in cortical brain regions is specific to inflammation and is associated with marked tissue softening, which is why MRE has been proposed as an imaging marker of cortical tissue involvement in MS patients [159].Neuroinflammation is a good example of the emergent effects of different substructures on coarsegrained mechanical tissue properties.Mechanical weakening of dendrites through demyelination [178], detachment of astrocytic endfeet from microvessels [176], and PNN degradation [159] − these processes collectively shape the mechanical response of the brain to neuroinflammation and prompt tissue softening as an MRE marker for treatment monitoring in MS.
Fig. 6 summarizes viscoelastic matrix remodeling and cellular changes reported in association with hepatic and neuronal inflammation.
Overall, the reports discussed here illustrate the sensitivity of MRE to tissue remodeling and inflammation-related processes.Soft tissues affected by inflammation develop their own specific signatures of changes in mechanical properties, which are potentially detectable by MRE.Detection and staging of inflammation could provide early warning of many diseases and thus allow initiation of individualized therapies before the development of serious symptoms, end-stage diseases, such as cancer, or whole-organ failure.However, it remains to be seen how MRE can be further sensitized to the discussed mechanical features of inflammation − from vascular leakage to cell swelling, to matrix changes.For example, MRE could be tailored towards higher sensitivities to fluid-solid interactions by the use of low-frequency vibrations [25,179] or shear wave dispersion quantification as a measure of tissue fluidity [180].

Brief summary
MRE is a versatile technique for imaging the biomechanical properties of soft tissues across a wide range of resolutions, mechanical frequencies, and applications in both clinical diagnosis and biomedical research.By encoding time-harmonic mechanical vibrations using phase-contrast MRI techniques, MRE is an imaging modality that works by capturing shear waves propagating through body tissues.MRE relies on the inversion of shear wave images into viscoelastic parameter maps.The setup of an MRE experiment on clinical MRI scanners is now a standardized procedure that adds diagnostic value to the detection and staging of diseases along the entire pathological cascade of inflammation-associated tissue remodeling from early edema to chronic fibrosis, cirrhosis, and cancer.Despite the overwhelming evidence for MRE sensitivity to inflammation, further research is needed to disentangle the biomechanical hallmarks of inflammation discussed in this article: vascular leakage, altered blood flow, elevated tissue pressure, increased fluid fraction, cellular edema, matrix accumulation, and remodeling.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Fig. 6.Biomechanical effects of abnormal events related to inflammatory processes in the liver and the brain.As discussed, MRE has been proven sensitive to all of these changes in tissue structure.

Fig. 4 .
Fig. 4. Information pipeline in multifrequency MRE.Six-dimensional phase data are acquired for three spatial dimensions (a), phase variations over time (b), three field components (c), and multiple frequencies (d).MRE data processing includes phase unwrapping, temporal Fourier transform to separate the fundamental frequency, and multifrequency inversion.The MRE maps shown here were generated using phase-gradient-based multifrequency inversion (for shear wave speed, SWS, and penetration rate, PR), as explained in[182], or phase-angle-based direct inversion (for loss angle or fluidity φ), as explained in[74].

Fig. 5 .
Fig. 5. Fundamental effects of inflammation are associated with stiffness changes in the liver and brain.While hepatic inflammation has been observed to cause tissue stiffening, neuroinflammatory diseases have been associated with softening.Reasons for the different tissue responses are discussed in the text.

Table 1
Basic tissue parameters that can be measured by MRE.FE: finite element.