MR Elastography Using the Gravitational Transducer

Abstract

MR elastography is a non-invasive imaging technique that provides quantitative maps of tissue biomechanical properties, i.e., elasticity and viscosity. Currently, hepatic MR elastography is deployed in the clinic to assess liver fibrosis in MAFLD patients. In addition, research has demonstrated MR elastography's ability to non-invasively assess chronic liver disease and to characterize breast cancer lesions and brain tumors. MR elastography requires efficient mechanical wave generation and penetration, motion-sensitized MRI sequences, and MR elastography inversion algorithms to retrieve the biomechanical properties of the tissue. MR elastography promises to enable non-invasive and versatile assessment of tissue, leading to better diagnosis and staging of several clinical conditions.

Keywords: MALFD; MR elastography; biomechanics; elastography; engineering; liver.

Figure 1

Dependence of shear wavelength on local stiffness. (A) Finite element simulation of a wavefield with a homogeneous background and a hard inclusion. (B) The corresponding line profile shows that the local wavelength (green arrows) changes depending on the underlying stiffness. Additionally, the amplitude of the wave drops due to an intrinsic loss mechanism (viscosity). “Imaging” the shear wave allows the local biomechanical properties to be recovered in return.

Figure 2

Gravitational transducer concept. (A) The gravitational transducer consists of a casing that hosts a spinning eccentric mass (a) which is connected via a gearbox (b,c) to an external flexible driveshaft (d). (B) The closed transducer is very compact, and for abdominal applications, it is strapped to the patient’s body via an elastic belt. (C) Its generic design allows seamless integration into concepts that enable, for instance, cranial MRE. (D) The frequency response spectrum when operated at 30 Hz shows no upper harmonics. (E) The research demonstrator version of the gravitational MRE concept had the driving unit outside the MRI room with the flexible driveshaft going through the waveguide towards the patient table. The picture shows the installation at the University Hospital Frankfurt am Main, Hesse, Germany. (F) To improve patient comfort for abdominal applications, the transducer has a curved contact plate with a gel pad. Curvature and size of the contact plate are easily adaptable to different applications.

Figure 3

MRE sequence concepts. (A) Sinusoidal mechanical vibration generated by the MRE transducer is for clinical applications typically in the 40–60 Hz range. Thus, one period corresponds to roughly Tvib~20 ms. (B) SE-based sequences typically use MEGs (green) that operate at the vibration frequency. This leads to a long shot duration, i.e., the time interval encompassing excitation and readout. Temporal delays (red rectangle) are used to shift to the next wave phase $\mathsf{\Phi }$ once all slices Si have been acquired (i ∈ [1, 2, 3 … N], N = # of slices). (C) Fractional motion encoding concepts enable significant scan time reduction at the cost of a loss to motion sensitivity. Initial approaches still had the temporal delays separate from each shot, thereby perturbing eddy current steady state [12]. (D) More sophisticated concepts overcame this by incorporating the delays into each shot, thereby further reducing scan time. (E) SMS finally opened a straightforward way to acquire 3D MRE datasets within a single breath hold.

Figure 4

From MRE raw data to wavefield displacement vector. The MRE data acquisition provides snapshots of the propagating wave. When looked at pixel-wise, a sinusoidal modulation of the MRI phase is observed for each of the three encoding directions (readout [M], phase encoding [P], slice direction [S]). A temporal Fourier transform yields the corresponding amplitudes $A_i$ and phases ${\phi }_j$ of the complex-valued displacement vector of the wavefield in direction i ∈ (M, P, S). This approach assumes a temporal steady state, i.e., there are no transient effects, and the time component is purely described by sinusoidal temporal modulation at the driving frequency.

Figure 5

Mathematical foundations of MRE reconstruction. (A) In general, any wavefield is the sum of three fields that exhibit very different mathematical properties: a source field, a rotational field, and a transport field. In our case, the total displacement vector is the sum of the compressional (source) and the transverse (rotational, shear) wave, because there are no transport effects in our experiments. (B) Both waves exhibit very different mathematical properties and different wavelengths since they are coupled to different mechanical properties of tissue; here, as shown for in vivo data in breast tissue: the compressional wave in our frequency domain has a very long wavelength (~m) as it is linked to the bulk modulus. Remember that tissue is incompressible, leading to a bulk modulus of the order of GPa. Conversely, the shear wave is relatively short (~m) as it is linked to the shear modulus (~kPa). Bear in mind that both moduli differ by 6 orders of magnitude! The final solution of the complex-valued shear modulus can now be interpreted in many ways: one possibility is to view tissue as if shear stiffness (elasticity, spring) and shear loss (viscosity, dashpot) were organized as spring and dashpot connected in a parallel fashion (Voigt model). In reality, tissue exhibits a more complex mechanical response function leading to fractal-like mathematical representations due to its hierarchical organization.

Figure 6

Directional wave filtering for 2D MRE and viscosity. (A) Magnitude image of the liver in transverse orientation. The gravitational liver transducer is located on the RHS of the patient with the gel pad visible (arrow). (B) The pattern of the wavefield in through-slice direction shows mainly a plane wave propagating towards the center of the patient (arrow, [mm]). (C) Amplitude of the Fourier transform of the wave image shown in B segmented in a pie chart fashion with additional low-pass, high-pass, and circumferential filters to generate a virtual plane shear wave in image-space after inverse Fourier transform. Bear in mind that the Z-scale is logarithmic. (D) Corresponding plane shear wave image showing longer wavelengths within the liver when compared to regions of subcutaneous fat (arrow). (E) Result of the 2D approximation depicting an elevated shear stiffness of the liver of a patient with severe liver fibrosis (F4-grade) [kPa]. (F) Corresponding map of the shear viscosity resulting from a full 3D inversion of the wavefield [kPa]. Data from University Hospital Frankfurt am Main, Hesse, Germany.

Figure 7

Ultrasound gel phantom results. (A) Magnitude image of the experimental setup. Additionally, a water bottle is attached to the US phantom to increase its weight. (B) Real part of the displacement field in through-slice direction showing a grid-like pattern which originates from the boundary conditions of the phantom, i.e., its semi-flexible plastic surface. (C) One of the plane waves extracted from the directional filter approach presented here is travelling from left to right in the image. (D) Magnitude of the complex shear modulus recovered from the 2D approach. The mean value agrees very well with the corresponding gauge obtained via the 3D inversion (E). (F) Phase angle Y ∈ [0, 1] of the phantom as obtained from the 3D inversion, indicating that the material is exhibiting mainly spring-like properties.

Figure 8

Three-dimensional MRE results in the liver. The outlines of part of the liver and the spleen are highlighted in red and blue respectively. (A) Magnitude image of a liver patient with low-grade fibrosis related to non-alcoholic steatohepatitis (NASH). (B) Magnitude image of the complex shear modulus |G*| [kPa]. (C) Shear elasticity Gd [kPa]. (D) Shear viscosity Gl [kPa]. (E) Shear speed Cs [m/s]. (F) Shear absorption a [1/mm]. (G) Shear wavelength l [mm]. (H) Shear phase angle Y [0–1]. Data from University Hospital Frankfurt am Main, Hesse, Germany. The institutional ethical review board approved this prospective study. Written informed consent was obtained from the participants.

Figure 9

Three-dimensional MRE results in the kidney and the prostate. The outlines of the kidney and the prostate are highlighted in red and blue respectively. (A,B) T2-weighted anatomical image of the kidney and corresponding image of the shear wave speed [m/s]. Data from University Hospital Vienna, Austria. (C,D) T2-weighted anatomical image of the prostate and corresponding image of the shear speed [m/s]. Data from University Hospital Frankfurt am Main, Hesse, Germany. The institutional ethical review board approved this prospective study. Written informed consent was obtained from the participants.

Figure 10

Three-dimensional MRE results in the breast. (A) T1 weighted anatomical image of the breast depicting a tumor within the green ROI. (B) Corresponding Z-component of the curl field demonstrating that wave propagation is not in a plane wave fashion due to the very complex boundary conditions. (C) Resulting shear wave speed image showing the tumor as stiff object within the otherwise rather soft breast tissue. Data from King’s College London, UK. The institutional ethical review board approved this prospective study. Written informed consent was obtained from the participants.

Figure 11

Three-dimensional MRE results in the brain. (A) Axial reformation of a T1-weighted 3D MPRAGE structural image of the brain. (B) Corresponding image of the Z-component of the curl showing the complex and intricate shear wave pattern within the brain. (C) The resulting image of the shear wave speed shows a very high level of symmetry within the brain parenchyma and low values within the lateral ventricles, as expected [m/s]. Data from University Hospital Heidelberg, Germany. The institutional ethical review board approved this prospective study. Written informed consent was obtained from the participants. The data were acquired in one of the investigators in preparation of a study approved by the Ethics Committee of Heidelberg University.