In general, assessment of mechanical properties relies on the measurement of the strain induced by stressing a sample. Common non-tomographic rheological methods [22, 23] applied to soft biological tissues are coarse and integrative but the stress-strain relationship is almost directly obtained from the applied stress to the sample and its resulting strain which is derived from the displacement (linear or angular) of the actuator. Assuming that the sample is homogeneous and viscoelastic, and that the mechanical stimulation stays in the linear regime, the measurement sensitivity and accuracy relies only on the hardware and its calibration. On the other side, imaging methods require to measure the stress-strain relationship locally. For MRE this is done in two steps. First, an external actuator is used to generate waves within tissues that will locally probe the mechanical response of the tissue. Then imaging of local displacement is done by synchronizing the mechanical excitation with the MRI in order to encode the wave displacement into the phase of the complex MR signal. This allows derivation of both local strain from the displacement and local stress from the second temporal derivative of the displacement. The mechanical properties can then be identified by solving the equation of motion [1]. Therefore, the accuracy of the MRE measurements depends on the quality of the mechanical excitation source, the acquisition method of the displacement map and the reconstruction algorithm used to obtain the shear modulus.

The ability to generate low frequency shear waves of sufficiently high amplitude (about tens of micrometers in the tissue) is mainly constrained by potential loss effects occurring within biological tissues, due to attenuation (i.e., conversion into heat) or scattering (i.e., energy getting dispersed in different directions). This attenuation increases with frequency and with tissue stiffness which may result in a rapid decrease of wave amplitude with tissue depth. In practice, this attenuation can be partially compensated by increasing the excitation amplitude but can induce, close to the mechanical actuator, heavy phase wraps, difficult to eliminate. Therefore, generating high amplitude waves is especially difficult for large and deep organs. Finally, the presence of tissue interfaces might lead to wave absorption and mode conversion. Nonlinear effects induced by varying preloading conditions (a beating heart, respiration etc) can influence the efficiency of high-amplitude mechanical wave transmission within biological tissues. These limitations can be overcome by a recent technique called reverberant shear wave elastography which uses multiple actuators to reinforce multi-directional waves. Unfortunately, this method is not yet available using MRI acquisition and may be limited to frequencies below 200 Hz [24].

From an acquisition point of view, the quality of MRE data can be estimated from phase to noise ratio which in a first approximation is tied to the signal to noise ratio (SNR) and the encoded phase shift [25]. Obviously the SNR will critically rely on the acquisition parameters but also on the spin transverse relaxation time (T₂*) of the tissue that can be really low for example in liver with iron overload [26] or in lungs [27] and lead to very low SNR. Be that as it may, the encoding efficiency can be optimized by the acquisition sequence and the wave amplitude will mainly depend on physical properties and mechanical actuator settings as detailed in the following section.

As can be seen in Figure 1, a mechanical actuator for MRE is composed of a vibration generator which is associated with a coupling part that transmits as much as possible the mechanical excitation up to a piston which is positioned in contact with the surface of the sample. The coupling between the piston and the sample is the most difficult part of the MRE setup and has to be characterized in term of efficiency. When the vibration generator does not induce imaging artifacts, the size of the coupling device can be reduced which minimizes the associated losses. This can facilitate the integration of the mechanical actuator within the magnet bore which leads to additional free space for instruments and a greater ease of use.

Piezoceramic actuators are usually made from Lead Zirconate Titanate (PZT), Barium Titanate (BaTiO₃) or Zinc Oxide (ZnO). Due to its high electromechanical coupling factor (meaning the square root of the ratio of the electrical energy output to the mechanical energy), PZT is often chosen by the industry as the main material for the commercial actuators [69, 70]. The use of piezoelectric actuators is well documented in numerous fields of engineering [70, 71]. One important drawback of piezoelectric actuators is that displacement amplitude is decreasing with the working frequencies. In order to compensate for this, currently, two types of piezoelectric actuators arrangement have emerged:

- Piezoceramic stacks: with longitudinal piezoelectric actuators, an electric field is applied along the polarization vector that generates a material strain. This strain is too small for MRE applications but can be increased by stacking individual actuators. Actuators would be mechanically put in series with each other while being electrically connected in parallel. With such piezoelectric assemblies, nominal displacement generally reaches around 0.10–0.15% of the initial actuator length.

To date, developing a piezoelectric actuator for MRE has not been straight forward and has required combining a piezoelectric material with a mechanical amplifier or with a bending element.

Piezoelectric composites have been known for a long time [77, 78]. These materials are made of a piezoelectric inorganic phase combined with a polymer matrix (in most cases not piezoelectric) [79, 80]. The goal is to combine the strong piezoelectric performances of the inorganic ceramics with the mechanical properties of polymers.

Flexible piezoelectric composites have been used as sensors for biomedical applications like the monitoring of biological low frequency signals like cardiac pulses [81–83]. Most of the studies deal with piezo sensors, but some flexible actuators have also been conceived. Dagdeviren et al [84] created a conformal array of actuators and sensors using a PZT composite for soft tissue characterization through mechanical actuation. Each actuator was made with a gold electrode and a platinum electrode deposited around a layer of nanoribbons of PZT before the whole stack was encapsulated in Polyimide. The array was designed to act simultaneously as an actuator inducing a mechanical excitation from 100 to 1,000 Hz in a tissue and a sensor able to detect small deformation at the tissue surface induced by the actuator part. In their work, the elasticity of various tissues was successfully determined. For ex vivo samples, both lung and heart were characterized. In vivo, the conformal modulus sensor was able to detect a difference in elastic modulus between a normal skin and a lesion. Arrays made of piezoelectric composite materials have also been used extensively for ultrasonic transducers [85] and flexible transducers were designed using bulk PZT, polyimide and PDMS [86].

Ferroelectric polymers exhibit an intrinsic piezoelectric effect. There are various polymers exhibiting piezoelectricity, but the best known are mainly polymers based on PVDF and its copolymer of trifluoroethylene (PVDF-TrFE) [87], odd polyamides [88], and polymers of the polyurea [89]. However, the polymers of the PVDF (homopolymer or copolymer) have the highest piezoelectric properties and are therefore the most commonly used in applications. Using a cantilever structure based on a PVDF film, a displacement amplitude of 160 µm was reached [90] but without attempting to create vibrations. Furthermore, a bimorph actuator using two PVDF layers validated the use of such materials with a frequency range of 10 Hz-3 kHz reaching displacement amplitude of a few micrometers [91].

During the last decade, much interest has been devoted to electrostrictive organic materials due to their large strain induced under electric fields, low weight, good mechanical properties, and easy processability. Electrostriction is a common phenomenon encountered in dielectric materials placed under the influence of an external electrical field that generates Maxwell stress which leads to material strain [92, 93]. Any dielectric material is electrostrictive by nature, but strain/stress effects are more pronounced in some of them. Such materials show promising potential in various applications where electromechanical conversion is required, such as low frequency energy harvesting or actuation in micropumps and artificial muscles. Despite lower generated stress than piezoelectric materials, electrostrictive polymers present high levels of electric field induced strain, more than 10-fold higher than piezoelectric fluorinated polymers at constant electric field. Among electrostrictive materials, we choose to underline two types of polymers that show, to our opinion, promising perspectives for the field of MRE actuation: Electrostrictive Polymers (EP) and Dielectric Elastomers (DE).

In addition to piezoelectricity, PVDF and its copolymers also exhibit electrostriction. However, plasticizers are needed to improve the electrostriction behavior and increase the strain that those materials can achieve [94, 95]. As an example of such EP, doped PVDF-TrFE films offer important relative strain (1–5%) under low electrical field. One example of a mechanical actuator based on EP was reported in [96] where a micropump diaphragm was developed. Quasi-constant displacement amplitude of 10–15 μm over a frequency range of 0.1–1000 Hz under high electrical field of 80V/µm was achieved. The frequency range investigated here matches the MRE one but the required electrical field could lead to image artefacts.

Interest in DE increased since Pelrine et al. reported on a commercially available acrylic elastomer able to reach a relative strain of 100% under applied voltage [97]. More theoretical details about those materials can be found in [98]. While their strain can reach higher relative values than other electroactive materials, they usually have low stresses below 10 MPa compared to a hundred of MPa for classical bulk piezoceramic. The mechanical characterizations conducted in [97] of the acrylic elastomer VHB 4910 showed a rapid decrease of strain with frequency which limits its use to low frequency actuation (tens of hertz). However, further studies showed that other material like CF19-2186 silicones can be used at higher frequencies, but with lower achievable strains. In the context of MRI, Vogan et al. [99] used an acrylic DE to reconfigure imaging coils within the bore of a scanner which illustrates both the relatively high blocking stress of those materials (up to half the maximum stress of bulk piezoceramics [100]) and the MRI compatibility of the experimental setup with a DC voltage applied to the polymer [101].

The quality of the MRE data and elasticity estimations are dictated by the strain-to-noise ratio as explained by [102–104]. However, a mechanical actuator that can generate high wave amplitudes within the region of interest of the investigated tissue is mandatory. To our knowledge, it is unclear exactly what minimum amplitude is necessary for reconstructing an elasticity map. However, none of the actuators shown in Figure 3 have amplitude within the tissue below 7.5 µm. In addition, the mechanical actuator should operate at a well-suited operation frequency that offers the best compromise between spatial resolution and attenuation at a given depth. This mechanical actuator should also be able to run multi-frequency experiments in order to characterize the underlying microarchitecture of the tissue from the frequency dependence of the mechanical properties [38, 52, 105, 106].

As presented in this manuscript, electromagnetic compatibility restrictions near an MRI scanner require in most cases to place the vibration generator away from the center of the scanner. Therefore, a more or less flexible and long coupling device attached to a piston is needed to transmit the vibration to the patient/sample. As illustrated in Figure 3, actuators based on rigid coupling devices are the most frequently used in MRE experiments thanks to their high-fidelity at high frequencies (unlike actuators based on pneumatic coupling device). Nevertheless, the supplementary loading of the coupling device limits the choice of vibration generator that can be used. Larger loudspeaker, higher currents in the case of electromechanical actuators or mechanically amplified piezoceramic stacks must be used in order to create enough displacement under such loading conditions. Thus, the vibration generator is often oversized compare to the minimum requirement which is, as mentioned previously, only to generate few microns within biological tissues. This is particularly true in case of small soft samples (i.e. mainly samples involved in preclinical studies) and in case of superficial organs such as skin [107], breast [49] or muscle MRE [108]. In case of adult brain MRE the question is much different as the generation of wave within the brain relies on both piston-skull and skull-brain coupling. Moreover, the use of a coupling device is often associated with complicated positioning and lack of integration which can limit experimental repeatability and reproducibility.

Regarding the piston, Figure 3 shows that most of them are rigid despite the poor sample coupling that results from it. To our knowledge few groups have design rigid form fitting piston which makes sense to access soft tissue like breast [49], but which is more questionable for the head [40, 109]. Having a flexible form-fitting piston could ensure better sample coupling, in particular when the piston is in contact with a soft surface. To our knowledge only one group reported a flexible form-fitting piston dedicated to endorectal MRE, where the piston is in contact with a soft surface [56]. In this case, an inflatable flexible piston was designed in order to fit as much as possible to the colon wall. In this case, one major drawback is that the piston-sample coupling will critically rely on tissue stiffness which make measurements intra and inter patient dependent.

As seen on Figure 3, most of clinical and human in vivo applications of MRE are in the low range of frequencies (up to 100 Hz). Looking at the wave propagation equations it appears that reaching great depth with great amplitude is easier in this range than it would be at higher frequencies. Pneumatic devices have the drawbacks of inducing phase delay and non-harmonic mechanical excitation. However, these effects are minor in the low frequency range. Moreover, pneumatic devices are the easiest to handle among different coupling devices which explains their widespread use in that frequency range. In the preclinical environment (i.e., small samples in a small-bore preclinical system) where higher frequencies are required, piezoceramic and electromechanical are the go-to solutions as shown on Figure 3 even though they require a more complex set up than pneumatic devices. In fact, attention must be paid for instance to the following fine-tuning operations: i/cable shielding for the high voltage supply in the case of a piezoelectric vibration generator; and ii/the orientation of the electromechanical actuator with regards to the static magnetic field.

There is room for improvement in both clinical and preclinical MRE applications. Smaller, easier to use and more adaptable actuators could generalize the use of MRE in the MRI community. In the path towards a more optimal mechanical actuator two objectives prevail:

- Reducing the number of parts that compose the actuator in order to reduce the load on the vibration generator. A lower load would allow for low stress soft actuators to be used. A reduced number of parts would also result in more compact mechanical actuator which may simplify positioning of the MRE setup in the limited space of the MRI system.

Flexible electroactive materials can be a key component of a new generation of mechanical actuators fulfilling the objectives previously exposed. As discussed above, these materials can require an electric field up to tens of V/μm in order to reach significant strain. Studying the MRI compatibility of working at such high electric fields is the first step towards reducing the number of parts for a better integration of the actuator. If the MRI compatibility of the electroactive material is validated, the piston would be the vibration generator itself without needing a coupling device. The mechanical actuator could be more compact and integrated to the MRI coil and positioned, just as a tiny patch for cardiac monitoring, directly in contact with the patient/sample. Their low blocking stress would no longer be a major issue and their compliance combined with a high strain would make them the perfect material candidate to play the role of a form-fitting mechanical actuator in contact with the patient/sample. As mentioned before, this actuation principle could work preferentially on small soft samples and in case of superficial organs. Nevertheless, to amplify the effect of such “elastography patch”, one could combine such actuators in arrays to increase the penetration depth without increasing too much the applied electrical field.

To our knowledge, only [110] succeeded in building a Dielectric Elastomer (DE) and tested its MRI-compatibility on a phantom inside a 3-T MRI scanner. In their work, they started by studying the effect of the high magnetic fields produced by the scanner on the mechanical properties of their actuator and saw no difference regarding whether the actuator was inside or outside the bore of the scanner. Moreover, they also analyzed the image artifacts that their actuator would create. No SNR decrease was observed while increasing the electric field through the elastomer. Both studies helped the authors conclude that DE actuators are fully MRI-compatible and could be used in various MRI-specific applications directly in contact with a biological tissue. However, translating this work into the context of MRE would require additional measurements such as frequency response of the material as well as its achievable motion amplitude in loaded and unloaded conditions. The mechanical capabilities of the actuator were evaluated using a classical Stress/E-field curve but wave amplitude/phase and elasticity studies were not run on a phantom. Additionally, the field-induced image artifact has been characterized up to 8 V/μm and it would be interesting to see if their results remain true at higher electrical fields. Nonetheless, this work is paving the way for a broader use of this type of material in MRE.

From piezoelectric composites materials to dielectric elastomers a wide range of flexible materials have been developed and optimized which make them suitable for applications in energy harvesting, sensing and actuation. The frequency range, the strain and the stress achievable with such materials are compatible with the requirements to build MRE mechanical actuators. Moreover, the relative high “technology readiness level” (5–7 [76]) of these mechanical actuators explains the recent development of commercial solutions that could be adapted to MRE experiments.

As a matter of fact, ready to use PVDF-based transducers are commercially available (Precision acoustics, TE Connectivity, PolyK, Durham Instruments etc). However, they tend to be dedicated to ultrasonic transducing. Nonetheless, thin films of PVDF are also available from the same suppliers in order to build one’s own actuators with specific sets of boundary conditions (clamping, thickness of the electrodes, stiffness of the electrodes, loading) to tailor the frequency behavior of the actuator.

Additionally, Sateco developed an actuator based on a multilayer stack of DE (silicone with carbon electrodes) with a wide operating frequency range from 0 to 2 kHz and a blocking force around 10N. The company has a starter kit with an all-in-one solution containing the actuator and all the necessary software and controllers.

After being actively involved in the field of DE [111, 112], Danfoss shut down its production of their DE solution called InLastor which could achieve an elevated blocking force of 16N, a relative strain of 2–3% and with rather low operating frequency (<100 Hz).

Another commercial solution sold by PI under the name of DuraAct is a flexible piezoelectric actuator based on a thin piezoceramic film. Custom versions with the necessary software and controllers can be ordered for specific applications such as structural health monitoring or precise actuation. The blocking force of the Power Patch model can reach 44N for a 10 μm/V relative axial deformation while working from -20 V up to 120 V.

Smart Material commercialized an alternative to the DuraAct transducers with a piezocomposite solution called Macro Fiber Composite (MFC). The M8557P1 version reaches 150 μm of axial displacement with a blocking force of 900N and an operating range of -500 V up to 1500 V with a maximum working frequency of 10 kHz. As for the previous commercial solutions, Smart Materials also provide the drivers for their actuators.

To perform MRE experiment with one of these commercial transducers will probably require a slight adaptation of the setup to be able to work in the constraint MRI environment. Particular attention must be paid to the MRI compatibility of the actuator that is often compromised by the presence of welds, electric cables and packaging parts. Fortunately, these are not always necessary for the proper operation of the actuator and can be removed with caution on a case-by-case basis.

In conclusion, recent progress made in the field of flexible electroactive materials could lead to a breakthrough in the field of actuators for MRE. These materials offer the possibility to design form-fitting actuators that are MR-compatible and can achieve relatively high displacement amplitudes with moderate blocking stresses. With few frequency limitations, they open a new path toward more adaptability, greater ease-of-use and more compactness of dedicated actuators for MRE of small soft samples and superficial organs such as skin, muscles or breast. These technological advances could be the way towards MRE experiment as easy to perform than ultrasound elastography but in 3D and with a better spatial resolution.