Tissue Strain Mapping Via Magnetic Resonance Elastography Can be Used to Detect Active Lesion Expansion

Abstract

Purpose:

Active lesion expansion is clinically important because it can indicate disease progression and influence management and treatment planning. However, sequential imaging is often unavailable, and rapid growth can only be inferred from indirect findings such as active perilesional tissue injury. This study aimed to implement and test the feasibility of an MR elastography (MRE)-based technique for assessing the expansile nature of mass lesions by detecting stiffness changes caused by mechanical strain manifestations in adjacent tissues.

Methods:

A tissue strain mapping (TSM) algorithm was developed using spatial-temporal directional filtering to reveal the presence of perilesional latent strain that is not apparent in conventional MRE inversions. The technical feasibility was tested in tissue-simulating phantoms containing a mass that was progressively expanded. Preliminary feasibility for clinical application was also demonstrated in representative in vivo examples. Resulting TSM maps were compared with conventional MRE stiffness maps.

Results:

In the phantom experiments, TSM revealed the presence of local strain at the periphery of the expanding mass, with the effect increasing proportionally to the degree of expansion. Conventional MRE did not demonstrate comparable localized stiffening patterns. In vivo examples showed similar perilesional strain features that were not apparent on conventional MRE maps.

Conclusion:

The feasibility of the proposed MRE-based tissue strain mapping technique was demonstrated in phantom and preliminary in vivo studies. These findings suggest that the technique is a promising tool for assessing the expansile nature of mass lesions and motivate further development of the TSM processing and exploration of potential clinical applications.

Introduction

When an imaging examination reveals an abnormal mass, one of the important and challenging tasks for radiologists is determining whether the lesion is aggressively expanding in size. Lesion growth dynamics are highly variable, with reported growth rates spanning orders of magnitude: some tumors expand rapidly and behave as mass-forming lesions, whereas others grow slowly or spread predominantly by infiltration along existing tissue planes (1–3). In the absence of sequential imaging over time, evidence of active expansion might include signs of invasiveness at the lesion boundaries and evidence of injury caused by pressure and deformation in surrounding tissues (4). Recognizing signs of active lesion expansion is an important consideration when diagnosing unknown masses and when managing known neoplastic lesions. Rapid tumor growth is often associated with a more aggressive form of the disease, characterized by increased neoangiogenesis and alterations in the immune microenvironment (5). Previous studies have found correlations between tumor growth rate and treatment response or clinical outcomes in patients with hepatocellular carcinoma, neuroendocrine carcinoma, or renal cell carcinoma (6–8). Furthermore, monitoring tumor growth is vital in assessing cancer therapeutics, as clinical trial endpoints typically involve measuring tumor shrinkage using systems such as RECIST (Response Evaluation Criteria In Solid Tumors), which tracks changes in the sum of the longest diameters of target lesions over time (9). These considerations provide motivation for developing technology to probe the expansile nature of mass lesions from a single examination, as a complement to sequential imaging when follow-up is unavailable.

From a mechanical standpoint, when a lesion behaves as an expanding mass, it can exert pressure on the adjacent tissues. If the adjacent tissues are constrained by surrounding structures and cannot be displaced freely, this will lead to localized deformation, known in engineering terms as strain. Figure 1 illustrates that compression of a material in one direction results in stretching of the tissue perpendicular to the direction of compression. Biological soft tissues are inherently nonlinear materials whose mechanical response depends not only on the magnitude but also on the direction of applied stress (10,11). Because of this nonlinearity, when tissue is stretched, its effective stiffness increases along the direction of stretch, rather than remaining constant as in a linear elastic material. Under continued deformation, however, tissues can partially compensate for this increased tension by lengthening or remodeling to restore mechanical equilibrium (12). Consequently, the apparent stiffness near an expanding lesion reflects a dynamic balance between the rate of imposed strain due to expansion and the tissue’s intrinsic ability to adapt and relax. Rapid volumetric expansion is therefore more likely to generate sustained deformation, whereas slow-growing or predominantly infiltrative lesions may allow tissue remodeling and relaxation that reduce sustained perilesional strain. Regions that stiffen disproportionately may represent areas where mechanical strain exceeds the rate of tissue accommodation, providing a potential mechanical signature of active expansion.

Figure 1.

Diagram illustrating when a force is applied to compress a material along one axis (vertical arrow), it causes a perpendicular expansion along the horizontal axis (horizontal arrows).

Conventional MRI and other cross-sectional imaging techniques lack the capability to depict the mechanical state of strain or the tissue’s dynamic response to deformation. This limitation motivates the development of alternative approaches that can probe tissue mechanics in vivo. Magnetic resonance elastography (MRE) is suited for this purpose, as it quantifies tissue mechanical properties, such as shear stiffness, a parameter sensitive to changes in tissue tension and structure (13,14). Localized stiffening adjacent to an expanding mass may therefore serve as a measurable manifestation of the underlying strain field. Indeed, previous studies have revealed that when isotropic tissue is compressed, its mechanical properties change to become anisotropic, with increased shear stiffness in the direction perpendicular to the compression and little change or slightly decreased stiffness along the compression axis (15–18).

These principles have been applied in attempts to estimate internal tumor pressure. It has been proposed that a nearly spherical, well-separated tumor under high pressure compresses adjacent tissue radially while stretching it circumferentially. Due to mechanical nonlinearity, this results in increased peri-tumoral shear stiffness circumferentially and decreased stiffness radially. Consistent with this theory, several MRE studies have sought to characterize tumor pressure by identifying this specific pattern of heterogeneous shear modulus distribution around tumors (19,20). These studies often use an idealized model that assumes a single dominant wave propagation direction. Results from simulations and phantom experiments show how shear waves used in MRE detect apparent changes in shear modulus along their propagation direction when deformed, suggesting the method’s potential to estimate total tumor pressure. Furthermore, another line of research integrates MRE data with in silico modeling to estimate both displacement and pressure fields in poroelastic biological tissues (21). However, in most practical applications of MRE, the presence of multiple interfaces causes diffraction, reflection, and mode conversion, leading to complex wavefields that do not have a single prominent direction of wave propagation. This complexity presents challenges in applying these techniques in vivo using existing models.

The goal of this study was to develop, validate through phantom testing, and demonstrate preliminary in vivo feasibility of an MRE-based method for identifying abnormal local tissue strain that is suitable for use with complex, multidirectional shear wave fields. We hypothesized that the proposed MRE-based tissue strain mapping (TSM) technique could depict strain-induced perilesional stiffness changes in expanding lesions that may be undetectable using conventional MRE inversion methods. The methodology applies spatial-temporal directional filters (DFs) to decompose MRE displacement data, separating complex wave fields into components propagating in multiple directions in three-dimensional space. Inversion processing of wave fields propagating parallel to the lesion-host interface is expected to demonstrate locally elevated stiffness in host tissue if the tissue is actively being stretched by an expanding mass lesion, whereas inversions of wave fields in other directions would not depict this anisotropic effect. The multiple inversion results are then combined in a way that preserves local strain-related effects.

The TSM technique was tested in a series of phantom experiments using both linear and nonlinear tissue-simulating materials containing an embedded expandable mass. Preliminary in vivo feasibility was demonstrated in a small number of patient studies, including a case of acute intracranial hemorrhage and two cases of hepatocellular carcinomas (HCC).

Methods

Tissue Strain Mapping (TSM) Hypothesis

When a lesion behaves as an expanding mass, it is expected to exert pressure on adjacent tissues (Figure 2). Initially, these tissues would attempt to adapt to the expansion, but if they are confined by surrounding structures, their compensatory response may be hindered, resulting in significant stretching and high strain in the perilesional region. Biological tissues, which exhibit nonlinear mechanical properties, tend to stiffen when stretched, suggesting that the shear stiffness of the stretched perilesional tissue would increase. Transmitting a planar shear wave through the lesion-host tissue along a single propagation vector k allows the shear waves to register the shear modulus in the direction of propagation. As a result, regions stretched parallel to this direction are likely to exhibit greater shear stiffness than other areas (Figure 2B). Theoretically, if the propagation vector k is adjusted to follow the contour of the lesion-host boundary, spatial variations in apparent stiffness will emerge depending on the direction of wave travel (Figure 2C). Combining stiffness data from all propagation directions using maximum intensity projection (MIP) could therefore reveal a stiffening pattern indicative of abnormal strain effects near the expanding mass. In practice, however, the shear wave field generated by MRE often displays complex directionality and polarization, complicating this process. TSM addresses this by using spatial-temporal directional filters to decompose the complex wave field into directional components, enabling direction-specific inversions and a combination strategy that preserves localized strain-related stiffening.

Figure 2.

Concept of tissue strain mapping (TSM) for detecting strain-induced stiffness changes in tissues adjacent to a rapidly expanding lesion. (A) Rapid lesion growth stretches the surrounding perilesional tissue. (B) Transmission of a planar shear wave through the lesion-host tissue allows for the detection of increased circumferential shear stiffness in regions stretched parallel to the wave propagation direction. (C) Rotation of the wave propagation vector along the lesion-host boundary alters the apparent local shear stiffness. Combining shear stiffness estimates across all propagation directions could reveal local strain effects around the expanding lesion.

Expanding Lesion Phantoms

Three sets of gel phantoms, each containing an embedded balloon, were built to validate the TSM hypothesis (Figure 3). These phantoms simulated an expanding lesion by embedding an inflatable balloon catheter within different gel matrices. To establish a consistent baseline size, each balloon was first evacuated of air and then filled with 50 mL of water.

Figure 3.

Balloon gel-phantoms. (Left panel, Top row) T2W images of Phantom 1, where the balloon was incrementally inflated by 50 mL of water and then decrementally deflated by 100 mL, resulting in a total of 7 measurement states: baseline (50 mL), 100 mL, 150 mL, 200 mL, 250 mL, 150 mL, 50 mL (returning to the baseline size). (Left panel, Bottom row) T2W images of Phantom 2 with the same 7 measurement states. (Right panel) T2W image of Phantom 3 as the negative control, with 250 mL of water injected prior to embedding in the background gel.

Phantom 1: Expanding balloon in bovine gel.

Phantom 1 consisted of the baseline-size inflated balloon embedded in 10% bovine gelatin (Sigma-Aldrich, USA) in a rounded rectangular plastic container (15 cm × 15 cm × 18 cm). The gel concentration was chosen to closely resemble the stiffness of soft biological tissue (~ 2–3 kPa).

Phantom 2: Expanding balloon in bovine/cellulose gel.

To introduce fiber reinforcement intended to increase strain-stiffening/nonlinear response relative to gelatin alone (22–24), Phantom 2 was prepared by embedding a baseline-size inflated balloon in a gel mixture composed of 8% bovine gelatin and 7% insoluble cellulose fiber (NutriCology, Utah, USA). The concentrations were specifically chosen to closely match the baseline stiffness of Phantom 1 while introducing enhanced nonlinear behavior through the inclusion of cellulose fibers. The cellulose was gradually added to molten bovine gelatin under continuous stirring to prevent sedimentation. In subsequent MRE scans, the balloons in Phantom 1 and Phantom 2 were inflated and deflated stepwise by up to 200 mL of additional water and then returned to baseline to simulate varying degrees of mass expansion. A lockable syringe was used for controlled inflation.

Phantom 3: Negative control.

Phantom 3 was designed as a negative control to test whether a static, large mass (i.e., no active expansion during imaging) fails to produce the circumferential stiffening ring observed during active inflation in Phantoms 1 and 2. This design also controls for potential geometric/processing effects associated with a larger balloon boundary during directional filtering. For this purpose, an additional 200 mL of water was injected into the baseline-sized balloon (50 mL) prior to embedding in the 8% gelatin and 7% cellulose mixture. During the scan, no further inflation was performed for Phantom 3. All gels were allowed to solidify at room temperature for 5 days to ensure complete solidification.

MRE Setup and Phantom Scanning

Mechanical vibrations at 80 Hz were introduced into the phantoms using a commercially available pneumatic active driver (Resoundant Inc., Minnesota, USA) connected to a custom-designed MRE passive driver. Each phantom was placed on top of the passive driver, which was designed to induce uniform axial motion of the entire phantom within the container, resulting in the side walls of the container serving as sources of shear wave generation (25). All MR experiments were performed on a 3.0T scanner (SIGNA Premier, GE HealthCare, Wisconsin, USA) using a 20-channel body coil (AIR^™, GE HealthCare, Wisconsin, USA). The imaging was conducted in the coronal plane relative to the scanner bore and produced axial cross-sections of the phantom. A dual-motion encoding, spin-echo echo planar imaging (SE-EPI) MRE sequence (26) was used with the following imaging parameters: repetition time (TR) = 4000 ms, echo time (TE) = 72 ms, field of view (FOV) = 24 cm, acquisition matrix: 80×80, 80 contiguous coronal slices (3-mm thickness). The motion encoding gradients were applied in the positive and negative x-, y-, and z-axis directions with 4 equally spaced phase offsets sampled over one period of the 80-Hz motion.

As shown in Figure 3, during each MRE acquisition for Phantom 1 and Phantom 2, the balloon was inflated in 50 mL increments using a lockable syringe and then deflated stepwise by extracting 100 mL of water. This process resulted in seven measurement states: baseline (50 mL), 100 mL, 150 mL, 200 mL, 250 mL, 150 mL, and 50 mL (returning to the baseline size). Each state was maintained for ~10 min (including the inflation/deflation processes, stabilization of the setup, and MRE acquisition) before proceeding to the next state. To estimate the balloon size and position, high-resolution (0.9 mm in-plane resolution) coronal T2-weighted (T2W) images were collected at each state.

Data Processing for Phantom Study

The MRE phase was unwrapped using the dual-motion encoding approach (26). The first temporal harmonic of the curl of the displacement fields was calculated to remove contributions from the longitudinal wave.

TSM workflow.

TSM consists of directional decomposition of the MRE wave field followed by direction-specific inversion and a max-type directional combination designed to preserve localized directional stiffening. A schematic of the inversion pipeline is shown in Figure 4. More specifically, after phase unwrapping and curl processing, the curl wave field was separated into N directionally filtered components (here N = 20, dodecahedral direction set) using a 3D spatial-temporal DF with a spatial frequency cutoff of 4.17–166.67 m⁻¹ (corresponding to 1–40 cycles/FOV) (27). A six-direction DF set (±x, ±y, ±z) was evaluated only as a sensitivity comparison (Supplementary materials). For each direction n, a direction-specific elastogram was calculated using a 3D direct inversion (DI) algorithm with 3 × 3 × 3 Laplacian 6 nearest neighbor kernel (28).

Figure 4.

Flowchart illustrating the tissue strain mapping (TSM) inversion process.

Two different combinations of the direction-specific elastograms were then formed. For the conventional elastogram, ${\mu }_{\mathit{\text{conv}}}$, the direction-specific elastograms were combined using an amplitude-weighted average, where the weight for each direction was proportional to the squared amplitude in the corresponding filtered curl wave field. The resulting elastogram (${\mu }_{\mathit{\text{conv}}}$) was smoothed using a 3 × 3 × 3 cubic spatial median filter to improve regional homogeneity of stiffness estimates. In contrast, the TSM elastogram, ${\mu }_{\mathit{\text{TSM}}}$, was computed using a maximum-intensity projection (MIP) across directions on a voxelwise basis to preserve the strongest directional response, subject to amplitude-based masking described below.

Because directional filtering can yield low-amplitude regions that produce unstable inversion artifacts, an amplitude cutoff was applied prior to MIP to exclude these unreliable regions. To implement this, the phantom was semi-automatically segmented from the magnitude images, and a phantom mask was created by excluding the background and balloon interior. Within this mask, the amplitude of each directionally filtered curl field was calculated as $A_n=\sqrt{A_{xn}^2+A_{yn}^2+A_{zn}^2}$, where A represents the amplitude of each curl component, and n = 1, 2, …, N and N is the number of directional filters applied. The threshold was set to 10% of the global maximum amplitude across all directions. The number of eligible DF directions per voxel was quantified by counting how many directionally filtered curl amplitudes exceeded the cutoff (i.e., the number of directions that contribute to the MIP at that voxel). Direction-specific elastograms were smoothed using the spatial median filter and combined via MIP using only eligible directions, resulting in ${\mu }_{\mathit{\text{TSM}}}$. Supplementary Figure S1 displays example directionally filtered wave amplitudes and stiffness maps, with low-amplitude regions indicated. Unless otherwise noted, both ${\mu }_{\mathit{\text{TSM}}}$ and ${\mu }_{\mathit{\text{conv}}}$ were reported as the magnitude of the complex shear modulus.

TSM assumes that strain-/prestress-dependent nonlinear mechanics near an actively expanding interface can produce elevated apparent stiffness for wave components propagating approximately parallel to the lesion-host boundary. To evaluate whether the MIP preferentially selects surface-parallel (tangential) propagation directions as hypothesized, the DF direction index (out of 20 directions) that produces the maximum stiffness contributing to the MIP was recorded for each voxel, subject to the same amplitude-threshold masking used above. Using the segmented balloon mask, the local surface-normal field along the balloon-gel interface was calculated and the angle θ between the MIP-selected DF direction vector and the balloon’s local surface normal was computed. Under the surface-parallel (tangential) hypothesis, tangential propagation corresponds to θ near 90° (i.e., the selected direction is approximately orthogonal to the surface normal). Angle maps were generated for the phantom states, and a 3×3×3 averaging filter was applied to reduce isolated undefined pixels.

Mean stiffness values were measured and reported from annular regions of interest (ROIs) on the central slice at the equatorial section of the balloon, where the expansion effect was greatest. The annular ROI had a width of seven pixels, with the inner boundary positioned three pixels away from the balloon edge to minimize edge effects.

In vivo examples

This retrospective analysis was conducted under an institutional review board (IRB) waiver of informed consent. These in vivo cases are presented as feasibility demonstrations of the processing pipeline and contrast mechanism.

Acute hematoma:

TSM was retrospectively applied to a patient with an acute intraparenchymal hematoma to demonstrate the feasibility of TSM in a case with recently documented hematoma expansion and mass effect on surrounding brain parenchyma. Brain MRE/MRI scans were performed using previously described acquisition methods (29), and detailed MRE acquisition parameters are provided in the Supplementary Materials. For the conventional comparison, the curl wave field was decomposed using the same 3D 20-direction DF as in the phantom experiments, elastograms were computed for each DF direction using 3D direct inversion, and the resulting stiffness maps were combined using a weighted average across directions. For TSM, the same 3D 20-direction DF configuration was applied to the reconstructed coronal slices, combined using MIP following the same post-processing procedures as in the phantom study.

Peri-lesional behavior was then assessed by constructing a radial (distance-from-hematoma) profile of the TSM-conventional difference using concentric shells derived from a 3D hematoma mask. The hematoma was segmented as a 3D binary mask on the T1-weighted image after registration to the MRE space. From this mask, a peri-hematoma shell stack consisting of five concentric layers was generated, each ~6 mm thick, using iterative morphological dilation followed by shell subtraction. For each shell, the mean and 95% confidence interval of the percent-difference between ${\mu }_{\mathit{\text{TSM}}}$ and ${\mu }_{\mathit{\text{conv}}}$ were calculated, and this value was plotted versus distance from the hematoma boundary. To assess robustness to hematoma delineation, two independent readers repeated the hematoma segmentation and shell generation workflow. The resulting distance-dependent profiles were compared qualitatively to evaluate inter-reader consistency.

Hepatocellular carcinoma (HCC):

TSM was also retrospectively applied to two patients with pathologically confirmed HCCs to demonstrate the feasibility of TSM in two patients with large HCCs exhibiting varying degrees of mass effect on surrounding liver parenchyma. Liver MRE/MRI scans were performed as previously described (30). Conventional liver MRE processing used a 3D DF with 20 propagation directions, followed by weighted averaging of the resulting stiffness maps, as implemented in this study (31). Correspondingly, TSM reconstruction for the liver used the same 20-direction DF configuration and the same post-processing procedures as in the phantom study.

Similar to the brain example, a shell-based (radial) analysis was performed for the two HCC cases. For each case, the tumor was segmented to generate a 3D tumor mask. Concentric peri-tumoral shells were then generated by iterative outward dilation of the tumor mask, forming multiple non-overlapping layers of fixed thickness (~ 5.25 mm per layer), with the tumor interior excluded. Shells were restricted to voxels within the liver parenchyma mask to avoid including background. For each shell, the mean and 95% confidence interval of the percent-difference between ${\mu }_{\mathit{\text{TSM}}}$ and ${\mu }_{\mathit{\text{conv}}}$ were calculated, and this value was plotted versus distance from the tumor boundary.

Results

Phantom results

Figure 5 illustrates the stiffness maps obtained using both conventional inversion and TSM (with 20-direction 3D DF) for Phantoms 1 and 2 at three states: baseline, peak inflation, and deflation to baseline. Figure 6 displays the corresponding changes in mean stiffness values measured from the peri-balloon regions during the inflation and deflation phases. As hypothesized, TSM showed an increase in stiffness surrounding the inflating balloon in both phantoms, with Phantom 2 exhibiting a more pronounced stiffening response due to the inclusion of cellulose fibers. This is evidenced by the steeper rise in mean stiffness values for Phantom 2 in Figure 6. Although both phantoms started with similar baseline stiffness, Phantom 2 demonstrated a stronger nonlinear stiffening effect at the same rate of balloon inflation. Upon water extraction to release the pressure, the stiffness values in both phantoms returned to baseline levels. In contrast, the conventional inversion failed to capture this trend distinctly. Only a modest increase in stiffness was observed for Phantom 2, which was far less pronounced than that detected by TSM. In comparison, the control Phantom 3, despite its large size, did not exhibit a circumferential stiffening ring, supporting the interpretation that the stiffening ring in Phantoms 1–2 is linked to active inflation rather than inclusion size or geometric/processing effects (Figure 7). Supplementary Table S1 provides an additional quantitative assessment of the TSM-conventional difference. Voxelwise percentage differences between ${\mu }_{\mathit{\text{TSM}}}$ and ${\mu }_{\mathit{\text{conv}}}$, summarized within the ring ROIs and stratified by the number of eligible DF directions, were consistently higher during inflation than at baseline and in the negative-control phantom across all direction-count bins (e.g., mean difference of 40.6–80.0% at peak inflation vs 10.4–23.8% at baseline in Phantom 2 or 12.8–34.0% in passive control Phantom 3).

Figure 5.

Stiffness maps obtained using conventional inversion (top two rows) and TSM (bottom two rows) for Phantoms 1 and 2 at baseline (50 mL), peak inflation (250 mL), and deflation to baseline states, respectively. A 20-direction 3D directional filter (DF) was used for analysis. Black annular ROIs indicate the regions used to calculate mean stiffness values for each state. TSM revealed a circumferential stiffening ring around the expanding balloon in both phantoms (middle column). Although baseline stiffness was similar, Phantom 2 with cellulose fibers exhibited a more pronounced stiffening effect than Phantom 1 at the same level of balloon inflation. Stiffness returned to baseline levels upon water extraction. In contrast, conventional inversion did not demonstrate these trends.

Figure 6.

Changes in mean stiffness values measured from peri-balloon regions (black annular ROIs shown in Figure 5) during balloon inflation and deflation for all three phantoms. The analysis was performed using a 20-direction 3D directional filter (DF). TSM results demonstrate a clear increase in stiffness during balloon inflation, particularly in Phantom 2, followed by a return to baseline upon deflation, whereas conventional inversion results show minimal stiffness variation. The dotted line represents stiffness measured from Phantom 3, which served as a non-pressurizing control.

Figure 7.

Stiffness maps obtained using conventional inversion and TSM for Phantoms 2 and 3. Phantom 2 is shown at peak inflation (250 mL), while control Phantom 3 represents the baseline state with the same total volume but without active inflation. TSM clearly revealed a circumferential stiffening ring surrounding the expanding balloon in Phantom 2. In contrast, Phantom 3 exhibited no stiffening ring, confirming that it did not exert pressure on the surrounding gel. The analysis was performed using a 20-direction 3D directional filter (DF).

Supplementary Figure S2 provides a more detailed comparison of stiffness maps obtained from the 20 directionally filtered wave fields for Phantom 2 at baseline, peak inflation, and for the control Phantom 3. The results further illustrate that the circumferential stiffening pattern appears only during peak inflation of Phantom 2, whereas both the baseline Phantom 2 and control Phantom 3 lack such features. Supplementary Figure S3 further characterizes how the MIP combination performs across directions. During peak inflation in Phantoms 1 and 2, the DF directions selected by MIP within the peri-interface stiffening ring are predominantly tangential to the balloon-gel interface, with θ values clustered near 90°. This tangential preference is not observed at baseline or in the negative-control Phantom 3. In addition, after amplitude thresholding, the MIP elastogram within the ring ROI remains supported by multiple DF directions per voxel, with the mean number of contributing directions ranging from 13 to 18 across phantom states.

Supplementary Figures S1 and S4–S7 provide detailed views of the curl wave fields, directionally filtered wave fields, wave amplitudes with low-amplitude exclusion regions marked, and the corresponding stiffness maps for each directional filter. These figures include Phantoms 1 and 2 at their baseline and peak inflation states, as well as the baseline control Phantom 3. Supplementary Figure S8 summarizes the stiffness maps across all seven inflation and deflation states for Phantoms 1 and 2, and compares results obtained using two directional filter configurations (6- and 20-direction). In this phantom setting, the key findings were qualitatively similar between the two DF configurations.

In vivo example of acute intracranial hematoma

Figure 8 illustrates a large, acute left cerebral intraparenchymal hemorrhage in a 60-year-old female patient with intraventricular extension and substantial mass effect, status post left temporal craniotomy/clot evacuation with external ventricular drainage. Brain MRE/MRI was performed ~6 days after CT-documented rapid hematoma enlargement, which occurred within hours (from ~4.9 × 2.8 cm to ~8.4 × 3.2 cm) and was accompanied by new intraventricular extension, hydrocephalus, and progression of midline shift (from ~2 mm to ~8–10 mm) with concern for impending herniation. Imaging ~2 days before MRE described a similar-sized hematoma, whereas MRI on the day of MRE again showed persistent edema/sulcal effacement with increased rightward midline shift and findings suggesting ventricular entrapment, consistent with a subacute post-intervention state with ongoing mass effect. The mass effect is evident as pronounced sulcal effacement throughout the left hemisphere (Figure 8A, white arrow) and rightward midline shift (white arrowhead). The corresponding stiffness maps (Figure 8B) show that ${\mu }_{\mathit{\text{TSM}}}$ demonstrates stronger perilesional elevations than ${\mu }_{\mathit{\text{conv}}}$, in regions adjacent to the hematoma and along the direction of mass effect. This difference is summarized by a radial profile of the shell-wise percent difference, which was highest in shells closest to the hematoma boundary and decreased monotonically with increasing distance (Figure 8C). Two independent readers produced consistent distance-dependent decay profiles, supporting that the observed TSM-conventional difference is localized to the peri-hematoma region and is not driven by a single subjective ROI placement. These findings demonstrate the enhanced sensitivity of TSM in detecting localized stiffness changes in the vicinity of a lesion associated with recent rapid expansion and persistent mass effect.

Figure 8.

In vivo demonstration of TSM in an acute intracranial hematoma with recent rapid expansion. (A) Coronal T2-FLAIR shows a large left intraparenchymal hemorrhage with substantial mass effect, including sulcal effacement (white arrow) and rightward midline shift (white arrowhead). (B) Top row shows the T1-weighted image with overlaid concentric peri-hematoma shell ROIs (coronal, sagittal, and axial views) derived from the 3D hematoma mask; middle and bottom rows show the corresponding ${\mu }_{\mathit{\text{TSM}}}$ and ${\mu }_{\mathit{\text{conv}}}$ stiffness maps, respectively. (C) Shell-wise radial profile of the percent difference plotted versus distance from the hematoma boundary, showing the largest differences in shells closest to the hematoma and a monotonic decay with increasing distance. Profiles derived from two independent readers are shown to assess robustness to hematoma delineation.

In vivo examples of hepatocellular carcinomas (HCC)

Figure 9A presents a large, stiff, well-circumscribed, and heterogeneous HCC located centrally in the liver of a patient without underlying liver disease. MRI/MRE was performed ~4 weeks after the earliest available CT. At MRI/MRE, the tumor measured ~13 × 11 cm, involved the caudate and right lobe, and demonstrated heterogeneous arterial enhancement with washout and a pseudocapsule. The patient underwent locoregional therapy (TACE) shortly after MRI/MRE. Over the short interval preceding MRI/MRE, reports described no substantial change in overall size but persistent compressive effects. The mass effect exerted on the liver hilum resulted in obstruction of the biliary ducts, as evidenced by diffuse intrahepatic ductal dilation (white arrows). There were also compression and effacement of the inferior vena cava (IVC, arrowhead) and significant constriction of the central hepatic veins. Conventional MRE showed elevated peri-tumoral stiffness despite the absence of radiologic or laboratory evidence of cirrhosis. This finding suggests that the elevated stiffness in the peri-tumoral region could be due to the large deformation and stretching caused by the mass-forming HCC. The TSM results further supported this interpretation. In the shell-based analysis, this tumor exhibited a large TSM-conventional difference that was maximal near the tumor boundary and decayed with distance (45% in the innermost shell, decreasing to 26% in the outer shells), supporting a prominent localized peri-tumoral effect.

Figure 9.

In vivo demonstration of TSM in two hepatocellular carcinomas with differing degrees of mass effect. (A) Tumor 1: dynamic contrast-enhanced MRI shows a large, well-circumscribed HCC. The mass effect caused biliary ductal obstruction with diffuse intrahepatic ductal dilatation (white arrows), compression and effacement of the inferior vena cave (IVC, arrowhead), and severe compression of the central hepatic veins. Concentric peri-tumoral shell ROIs overlaid on MRI are shown, together with the corresponding ${\mu }_{\mathit{\text{TSM}}}$ and ${\mu }_{\mathit{\text{conv}}}$ stiffness maps. (B) Tumor 2: a second large HCC with comparatively minimal mass effect; corresponding shell ROIs and stiffness maps are shown. (C) Shell-wise radial profile of the percent difference plotted versus distance from the tumor surface, demonstrating a larger near-boundary TSM-conventional difference for Tumor 1 and a smaller, more uniform difference for Tumor 2. Error bars indicate the 95% confidence interval within each shell.

In contrast, Figure 9B displays another large, stiff, and heterogeneous HCC located in the posterior segment of the right hepatic lobe in a different patient. MRI/MRE was performed approximately one week after an outside contrast-enhanced MRI used for diagnostic evaluation. The tumor was again described as very large (approximately 10 × 14 × 20 cm), and the report did not describe a definitive interval size change over the short comparison interval. The patient proceeded to definitive management shortly after MRI/MRE as part of surgical planning. In this case, only minimal mass effect was observed. Peri-tumoral stiffness measurements were within the normal range for both TSM and conventional inversion. Consistent with this qualitative impression, the shell-based analysis showed a much smaller TSM-conventional difference (12% near the boundary, decreasing to 5% distally), indicating a potentially stable lesion with limited expansile loading at the time of imaging.

Discussion

In this study, we introduced tissue strain mapping (TSM), a new MRE-based method developed to evaluate strain-induced perilesional stiffness changes associated with expanding lesions. The technique is grounded in the hypothesis that actively expanding lesions result in significant stretching and high strain in the perilesional area. This leads to a dependency of the probed shear stiffness variations in the perilesional tissue on the direction of shear wave propagation, considering the nonlinear elastic behavior of biological tissues. By applying spatial-temporal DF to decompose complex wave fields following the contour of the lesion-host boundary, TSM enables selective inversion and reconstruction of stiffness maps that reveal localized stiffening patterns indicative of abnormal strain near an expanding mass.

MRE has been well established as a noninvasive technique for quantifying tissue biomechanical properties across multiple organs, including the characterization of tumor stiffness. Many studies have demonstrated the clinical potential of MRE in assessing cancer severity, evaluating treatment response, and predicting patient outcomes (14,32–34). In addition to conventional stiffness characterization, recent research has sought to quantify tissue deformation responses to external or internal mechanical forces, thereby accounting for the nonlinear behavior of soft tissues (17,19,20,35–37). A recent MRE study developed an analytical framework to model heterogeneous shear modulus distributions around pressurized tumors and validated the approach using phantom experiments (19,20). This framework directly motivated and underpinned our current work. In their study, MRE was performed on gelatin phantoms containing spherical balloon inclusions subjected to varying levels of compression, with results compared to finite element simulations. The findings demonstrated that, under the assumption of a single dominant shear wave propagation direction, the axisymmetric deformation of the peri-balloon gel can directly impact the apparent shear modulus measured by MRE due to nonlinear effects.

In the proposed TSM technique, a directional filter was integrated to capture nonlinear effects arising from abnormal local strain caused by expanding lesions within complex, multidirectional shear wave fields. In the balloon phantoms, 3D displacement was introduced, and directional filtering was applied to isolate wave components propagating parallel to the balloon-gel interface. The resulting inversions revealed heterogeneous shear modulus distributions that varied with wave propagation direction. Areas of gel adjacent to the balloon exhibited a pronounced stiffness increase for interface-parallel components (including those aligned with the through-plane propagation direction) in inflated states relative to baseline. This directional dependence contributed to the circumferential stiffening ring observed when the direction-specific inversions were combined using MIP. To rule out the possibility that such an effect was merely due to the geometric changes in the balloon, a control phantom with a balloon fixed at the same size as the fully inflated condition was examined. This control did not exhibit increased stiffness, supporting the interpretation that the observed stiffening in Phantoms 1 and 2 is attributable to the increased deformation and stretching from the expanding balloon, due to nonlinear mechanical effects.

Consistent with this observation, the directions contributing to the MIP within the peri-interface stiffening ring preferentially aligned tangentially to the balloon-gel interface during peak inflation, whereas this tangential preference was not observed at baseline or in the negative-control phantom 3 (Supplementary Fig. S3). Although MIP selects the maximum across directions at each voxel, the peri-interface ring typically retains a broad set of eligible directions after amplitude thresholding (~13–18 directions per voxel on average), indicating that MIP is generally informed by multiple DF directions per voxel. Furthermore, it should be noted that TSM can appear globally higher than the weighted-average elastogram because a max-type operator introduces an upward bias relative to averaging. To evaluate whether the observed TSM-conventional differences simply reflect this bias, we quantified voxelwise percentage differences between ${\mu }_{\mathit{\text{TSM}}}$ and ${\mu }_{\mathit{\text{conv}}}$. Differences were consistently larger at peak inflation than at baseline and in the negative-control phantom (Supplementary Table S1), suggesting that the observed contrast cannot be attributed to a global MIP bias alone. Together, these findings support the pragmatic use of MIP processing in the TSM pipeline.

Directional filtering serves as a key processing step in TSM by decomposing complex wave fields into directional components defined by propagation vectors. In principle, the DF set can be selected to emphasize directions expected to be most sensitive to strain-induced stiffening near the lesion-host interface (e.g., tangential directions along the local boundary). However, in vivo, defining a “true” lesion boundary can be uncertain due to segmentation variability, partial volume, edema/hemorrhage boundaries, and irregular lesion geometry. An approach less dependent on accurate segmentation (e.g., MIP) therefore improves robustness and practicality for clinical translation, while surface-referenced analyses can be incorporated when a reliable interface definition is available. Directional filtering can also reduce SNR in the filtered wave images, as certain components of the original signal may be attenuated or removed. This can make the subsequent analysis and inversion more challenging due to compromised input data quality. To mitigate this, we calculated the amplitude of each directionally filtered wave and applied an empirical threshold to exclude low-amplitude regions from the MIP combination. Moreover, the performance of the directional filter depends on the selection of appropriate filter parameters, such as bandwidth and orientation. In this proof-of-concept study, we adopted commonly used filter parameters from previous MRE work, although they are not yet optimized.

The sensitivity of the phantom findings to the angular sampling density of the DF set was evaluated by comparing a 6-direction orthogonal DF configuration with the 20-direction dodecahedral configuration. In this phantom setting, the key observations were qualitatively similar across the two DF sets (Supplementary Fig. S8), suggesting that the dominant strain-sensitive propagation components are captured even with sparse directional sampling under relatively clean and reproducible excitation conditions. Nevertheless, the 20-direction DF set provides more uniform orientation coverage for curved interfaces and is preferable, particularly for in vivo applications where wavefields are more complex and the dominant propagation directions may vary spatially.

Despite the use of non-optimized directional filtering parameters and the empirical wave amplitude cutoff, the results from both phantom experiments and in vivo examples are consistent with the underlying hypothesis of TSM. Phantoms 1 and 2 exhibited a nonlinear stiffening ring surrounding the rapidly expanding balloon, an effect that was absent in control Phantom 3. The in vivo applications further demonstrate the clinical relevance and feasibility of TSM. In the case of an acute intracranial hematoma, TSM demonstrated stronger peri-lesional stiffness elevations than the conventional elastogram. Similarly, the HCC cases demonstrated the potential of TSM in characterizing stiffness alterations associated with different pressure states, which may reflect varying tumor growth dynamics. However, longitudinal imaging of these proof-of-concept in vivo examples was not available because patients proceeded to definitive clinical management shortly after diagnosis, precluding research follow-up of tumor growth dynamics. Furthermore, although the observed peri-lesional stiffness elevations were interpreted as consistent with strain-/prestress-related effects from expansile loading, the current data cannot distinguish this mechanism from other contributors such as edema, inflammation, fibrosis, or longer-term tissue remodeling. Therefore, the cases should be interpreted as demonstrating feasibility rather than confirming ongoing growth. Longitudinal studies will be required to relate TSM patterns to lesion growth rate and to validate TSM as an imaging biomarker for assessing the expansile nature of mass lesions.

It is important to emphasize, however, that the implementation of TSM in vivo can be technically complex. In brain MRE, for example, directional filtering can be influenced by waveguide effects, particularly in regions with large white matter tracts such as the corpus callosum. The performance of directional filtering under these conditions depends on the filter orientation relative to the underlying fiber architecture, making the selection of optimal filter orientations challenging. One potential extension is to combine TSM-style directional contrast with advanced inversions that incorporate structural anisotropy and/or initial stress and boundary (waveguide) effects (38), which may improve specificity in selected applications. In addition, directional filters inherently have a large spatial footprint, which can introduce blurring near tissue interfaces and attenuate fine wavefield features. For instance, in the HCC examples, TSM enhanced visualization of stiffness increases in the peritumoral regions compared with conventional inversion. However, some intratumoral details of two heterogeneous HCCs were lost, which could be valuable for assessing tumor heterogeneity and overall characterization. Therefore, while this study establishes TSM as a proof of concept, future work should focus on optimizing filter design and parameterization for specific anatomical contexts and lesion geometries to improve the accuracy and robustness of the technique in clinical applications.

It should also be noted that the conventional DF-based processing uses an amplitude-weighted average across directions to produce a stable stiffness estimate intended for quantitative tissue characterization. In contrast, TSM is not proposed as an alternative stiffness inversion for absolute quantification, but uses a max-type operator (MIP) to preserve direction-specific stiffness “anomalies” that occur near an actively expanding lesion under strain. As a result, TSM is intended as a strain-sensitive contrast mechanism rather than a replacement for conventional stiffness quantification. Furthermore, TSM is expected to be most sensitive to lesions that produce appreciable mass effect through relatively rapid, mass-forming expansion. When the expansion rate exceeds the mechanical equivalent of creep in the surrounding tissue, it results in strain hardening due to active tension.

Some limitations of the study should be acknowledged. First, although the study focused on detecting strain-induced perilesional stiffness changes in expanding lesions, it did not establish a direct quantitative relationship between the observed stiffness pattern and the actual lesion expansion rate. Nevertheless, the method holds promise as a strain-sensitive contrast mechanism that, in future longitudinal studies, could be evaluated for its ability to relate perilesional mechanical signatures to lesion growth behavior. Second, because the phantom protocol was not designed to ensure full mechanical equilibrium at each inflation level, viscoelastic relaxation may influence the magnitude of the observed TSM contrast. In addition, although Phantom 3 serves an important negative control, showing that a large, static inclusion does not reproduce the circumferential stiffening ring seen during active expansion, embedding a pre-inflated balloon may not represent a true static equilibrium. A dedicated equilibrium-hold study (e.g., repeated scans after longer hold times at each inflation level) would be useful as an additional phantom-based characterization of the time dependence of the TSM signal under controlled conditions. Third, although no visible gel damage was observed and the return-to-baseline state remained qualitatively similar to the initial baseline, repeated inflation/deflation cycling could still introduce subtle irreversible changes (e.g., microstructural rearrangement) that may influence the stiffness-volume relationship. Dedicated mechanical testing after repeated cycling would help quantify any cycle-dependent effects. Fourth, the limited number of in vivo cases with extreme growth rates or pre-existing pressure, which was already identified by anatomical MRI, may not be representative of the broader patient population. These initial cases primarily serve as a starting point to demonstrate the potential of TSM in clinical applications. Further research and optimization of the TSM method are necessary to enhance its sensitivity and applicability in vivo.

The potential applications of TSM are broad, as it enables the detection of actively expanding masses of any kind. Particularly in tumor assessment and treatment, TSM offers a noninvasive mechanical contrast that may help identify lesions associated with pronounced mass effect and strain-related perilesional stiffening. With longitudinal validation and clinical correlation, future studies can evaluate whether TSM-derived signatures relate to lesion growth behavior (e.g., rapid versus slow mass-forming expansion) and whether they add value for risk stratification and treatment monitoring. This capability could provide clinicians with a deeper understanding of tumor pathophysiology, aid in predicting treatment outcomes, and identify therapeutic targets. For instance, this could be particularly valuable in managing HCCs, where radiologists often encounter lesions with indeterminate features based on size or imaging characteristics on conventional imaging. The ability of TSM to provide additional mechanical information can assist radiologists in assessing the level of concern for these lesions, guiding appropriate follow-up intervals, and aiding in the management of patients, particularly those who may be candidates for transplantation. Such information is crucial for transplant surgeons in determining the appropriate course of action and timing for monitoring these lesions.

Conclusion

This proof-of-concept study introduces MRE-based tissue strain mapping (TSM) as an innovative approach for noninvasively assessing strain-induced changes in perilesional stiffness associated with expanding lesions. The results support the feasibility of TSM and motivate future studies to determine whether TSM provides clinically useful information about expansile mass effect beyond conventional MRE, thus enhancing the capabilities of diagnosis, treatment planning, and monitoring. Further research is warranted to refine the TSM methodology, validate its performance in larger patient cohorts with longitudinal follow-up, and explore its potential applications in various clinical settings.

Supplementary Material

Figure S1. Baseline state of Phantom 1 (10% bovine-gel). The figure displays the original curl wave fields, directionally filtered curl wave fields, wave amplitude maps, and corresponding stiffness maps obtained using a 3D 20-direction directional filter (DF). The yellow line contours indicate regions of low wave amplitude, where stiffness estimation is unreliable. These low-amplitude pixels were excluded during maximum intensity projection (MIP) processing to generate the final elastogram (${\mu }_{\mathit{\text{TSM}}}$).

Figure S2. Stiffness maps obtained from 20 directionally filtered wave fields for Phantom 2 at baseline (50 mL), Phantom 2 at peak inflation (250 mL), and control Phantom 3 at baseline (250 mL). Notably, in the through-plane wave directions (directions 9–12), a circumferential zone of increased stiffness surrounding the balloon was observed in Phantom 2 at peak inflation (middle row). In contrast, both the baseline state of Phantom 2 (top row) and control Phantom 3 (bottom row, containing a similarly sized balloon without active inflation), did not exhibit this pattern.

Figure S3. Direction-level characterization of the MIP combination in TSM. Top row: ${\mu }_{\mathit{\text{TSM}}}$ maps for Phantom 1 (baseline and peak inflation), Phantom 2 (baseline and peak inflation), and the negative-control Phantom 3 (baseline, 250 mL). Middle row: angle map θ between the DF direction selected by the MIP at each voxel and the local surface normal of the balloon-gel interface; θ ≈ 90° indicates tangential (surface-parallel) alignment. Bottom row: number of eligible DF directions contributing to the MIP at each voxel (N_valid), defined as the count of DF directions whose curl amplitude exceeded the threshold used for TSM masking. Black contours indicate the peri-balloon shell ROI. The mean number of DF directions contributing to the MIP was 18, 15, 15, 13, and 13 (for Phantom 1 baseline, Phantom 1 peak inflation, Phantom 2 baseline, Phantom 2 peak inflation, and Phantom 3, respectively).

Figure S4. The peak inflation state of Phantom 1 (10% bovine-gel). The figure displays the original curl wave fields, directionally filtered curl wave fields, wave amplitude maps, and corresponding stiffness maps obtained using a 3D 20-direction directional filter (DF). The yellow line contours indicate regions of low wave amplitude, where stiffness estimation is unreliable. These low-amplitude pixels were excluded during maximum intensity projection (MIP) processing to generate the final elastogram (${\mu }_{\mathit{\text{TSM}}}$).

Figure S5. The baseline state of Phantom 2 (Mixture gel of 8% bovine gel and 7% cellulose). The figure displays the original curl wave fields, directionally filtered curl wave fields, wave amplitude maps, and corresponding stiffness maps obtained using a 3D 20-direction directional filter (DF). The yellow line contours indicate regions of low wave amplitude, where stiffness estimation is unreliable. These low-amplitude pixels were excluded during maximum intensity projection (MIP) processing to generate the final elastogram (${\mu }_{\mathit{\text{TSM}}}$).

Figure S6. The peak inflation state of Phantom 2 (Mixture gel of 8% bovine gel and 7% cellulose). The figure displays the original curl wave fields, directionally filtered curl wave fields, wave amplitude maps, and corresponding stiffness maps obtained using a 3D 20-direction directional filter (DF). The yellow line contours indicate regions of low wave amplitude, where stiffness estimation is unreliable. These low-amplitude pixels were excluded during maximum intensity projection (MIP) processing to generate the final elastogram (${\mu }_{\mathit{\text{TSM}}}$).

Figure S7. The baseline state of control Phantom 3 (Mixture gel of 8% bovine gel and 7% cellulose). The figure displays the original curl wave fields, directionally filtered curl wave fields, wave amplitude maps, and corresponding stiffness maps obtained using a 3D 20-direction directional filter (DF). The yellow line contours indicate regions of low wave amplitude, where stiffness estimation is unreliable. These low-amplitude pixels were excluded during maximum intensity projection (MIP) processing to generate the final elastogram (${\mu }_{\mathit{\text{TSM}}}$).

Figure S8. Summary of stiffness map comparisons across all seven inflation and deflation states for Phantoms 1 and 2. Additionally, results obtained using 3D directional filters (DFs) with 6 and 20 directions are compared. No significant difference was observed between the two DF configurations in this phantom setting.

Supplementary Table S1. Voxelwise percent difference between the TSM elastogram and the conventional elastogram, stratified by eligible direction count within the peri-interface ring ROI. For each voxel, the number of eligible DF directions (N_valid) was defined as the count of directionally filtered curl components with amplitude exceeding the threshold used for TSM masking. Within the ring ROI, the percent difference was computed as Δ% = 100 × (μ_TSM-μ_conv)/μ_conv and summarized as mean ± SD for Phantom 2 at baseline and peak inflation, and for the negative-control Phantom 3. A dash indicates that no voxels in the ring ROI fell into that bin.