**3.3. Case study: amagnetic rotary actuator for ankle dorsiflexion during MEG and fMRI acquisitions**

#### *3.3.1. Concept*

110 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

but design solutions are possible for SMA actuators.

**3.2. Compatible design guidelines** 

intervene and perturb the movement.

SQUID (Superconducting Quantum Interference Device) gradiometers, which convert the magnetic flux threading a pick-up coil into voltage. Since the magnetic fields to be measured are extremely small as compared to the Earth's magnetic field (10-5-10-4T), MEG measures are carried out in a shielded room that minimises interference. Of course, any electromagnetic noise should be avoided inside the acquisition room: there is no safety issue for the patient connected with this constraint, but if not respected the measure would be impossible because SQUID channels would saturate rapidly and would remain unusable as long as the pick-up coils are in the superconductive state. Unlike the case of MRI, theoretically any material could enter an MEG acquisition room. In practice, objects made of conductive materials should remain still inside the shielded room, as any movement would generate an artefact. These constraints are very demanding for most actuation technologies,

Some design indications could be useful for devices intended for either fMRI or MEG studies. In particular, the SMA element should have a shape or should be arranged in a way that limits to a great extent the magnetic fields induced by eddy-currents and by the current used for Joule's heating. For example, the coil of a spring is not particularly indicated, as the intensity of the magnetic field is proportional to the number of turns. Moreover, the SMA actuator should be supplied with a dc-current rather than other types of time-varying currents (pulse-width modulation, sinusoidal current…). In fact, this could help reduce the magnetic field induced by currents flowing into the SMA elements. Power generators and control systems should be positioned outside the acquisition room and wires passed through. As these cables could act as antennas that radiate electromagnetic noise, some countermeasures should be adopted: shielded or twisted cables can limit pick-up of stray frequencies, while using proper filters when connecting the wires inside and outside the acquisition room can help rejecting the time-varying components of the power signal. Coming to the control strategy, an open-loop may be preferred (for its simplicity), as both fMRI and MEG data analysis generally need a precise windowing of signals that matches different phases of movement, in order to extract features of interest with statistical significance. So, closed-loop architectures could be used e.g. to control precise abidance to set movement speed evolution, but might not be strictly necessary if the experimental protocol only requires repeatable ranges of motion in a given time. In fact, within the very protected environments of the shielded rooms, often no major disturbances are expected to

Additional recommendations apply only to devices for use in the MRI acquisition room: in particular, ferromagnetic materials should be avoided for safety reasons, even if small parts could be tolerated in some cases. On the other hand, as we said before, during MEG acquisition conductive materials should not move inside the shielded room. Translating this information into design specifications, a first recommendation would be that the moving parts should not mount conductive materials, including the SMA actuators. However, the principle of SMA actuation is that metal moves! The geometry of the SMA element should A possible device for ankle dorsiflexion could be devised as a leg part and a foot part connected by planar hinges parallel to the ankle joint, in a similar way to the device presented in section 2.4.2. Two SMA rotary actuators mounted externally with respect to the hinges promote the dorsiflexion of the foot part with respect to the leg part, while plantarflexion and position reset is left to viscoelastic resistance and foot weight (Figure 7). It should be noticed that the requirements for the ranges of movement are different in this application, as the purpose is to produce a clearly detectable movement without muscular stretching. This can be done maintaining joint angle negative or slightly positive (i.e. extended). The objective of the study was to test healthy subject, so it can be estimated that maximum resisting torque will be in the range 200-250Ncm (see Figure 2).

A rotary SMA actuator can be generally described as a structure in which the SMA wire connects parts that can rotate relative to one another about a central axis: when the elongated SMA wire is heated above *Af* and recovers its deformation, the linear stroke *ΔL* is converted into a rotation *Δθ* of the moving parts. However, it is likely that a conspicuous length of wire is needed to produce a suitable amount of rotary stroke *Δθ* for ankle dorsiflexion. As we already said, in such cases coiling the wire could improve conveniently overall compactness of the actuator. Unfortunately, this design decision contrasts with the aim of fabricating an amagnetic actuator, as the electric current flowing in coils of wire produces, according to Ampère's Law, an overall magnetic field along the central axis of the solenoid, which is proportional to the number of turns. A very simple solution can be found exploiting the same physical laws of electromagnetic fields. In fact, the magnetic field vector is directed according to the right hand rule with respect to the direction in which the current flows that induced it. Thus, theoretically, given two identical and concentric solenoids traversed by the same electric current in opposite directions, the magnetic fields generated by the coils will mutually annihilate. Moreover, no ferromagnetic materials should be employed in the implementation of all other components of such actuator, as well as the assembled device.

### *3.3.2. Actuator implementation and mechanical characterisation*

An implementation of the invented amagnetic actuator is shown in Figure 8. Two discs of approximately 10cm in diameter are connected through a central shaft allowing reciprocal rotation, leaving a clearance of 2cm between the two discs. One of the two discs mounts, along its circumference, 6 pins bearing 3 pulleys each, to create a spiralling sequence, along which the SMA wire can be coiled suitably. These pulleys have a double triangular groove, which makes the double coiling as compact as possible. The two ends of the SMA wire are fixed to one disc, while the mid-point of the wire connects to the other disc. The two halves of the wire are would along the pulleys thus creating two concentric coils very close to one another. By providing sufficient current flowing between the two ends of the SMA wire, shape recovery occurs generating a linear stroke Δ*L* that is converted into a reciprocal rotation Δ*θ* of the two discs. Notice that the torque generated is given by twice the crosssection of the wire, while the induced magnetic field is self-compensated to a large extent, as the two coils are traversed by the same electric current in opposite directions [40].

As already described for the linear actuator in paragraph 2.4.3, wire length depends on the expected angular stroke and the working strain level, while torque output is connected to the wire diameter and mean stress on the cross-section. Moreover, the geometrical parameters of the assembled actuator affect both wire length and torque output. The rotary actuator was designed to provide an angular stroke up to 40° against resisting torques in the range 120Ncm-250Ncm. By limiting the linear strain to 3.8%, the required length of NiTi wire can be calculated in 219cm. The selected NiTi wire is 250μm in diameter, corresponding to stresses of 130-270MPa in the above-mentioned range of torques. Taking into account the localized strain on the wire resting on the pulleys, the total maximal strain reaches 4.42%, which in combination with the chosen stress level should guarantee suitable fatigue life (several thousands of cycles). Commercial stabilised NiTi wire was utilised, displaying large deformability (4.5%) at room temperature for stress levels as low as 150MPa [58]. The power dimensioning procedure was similar to the one described in paragraph 2.4.3 and led to utilizing 0.7A at 30V for each actuator. Control is achieved with an open-loop strategy, by which acquisition windows can be synchronised to the ankle movement. Power supply and control appliances are left outside the acquisition room, and shielded cables are let into the shielded room through suitable access vents.

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**Figure 7.** Implementation of an amagnetic device for ankle dorsiflexion with rotary actuators

the two coils are traversed by the same electric current in opposite directions [40].

As already described for the linear actuator in paragraph 2.4.3, wire length depends on the expected angular stroke and the working strain level, while torque output is connected to the wire diameter and mean stress on the cross-section. Moreover, the geometrical parameters of the assembled actuator affect both wire length and torque output. The rotary actuator was designed to provide an angular stroke up to 40° against resisting torques in the

An implementation of the invented amagnetic actuator is shown in Figure 8. Two discs of approximately 10cm in diameter are connected through a central shaft allowing reciprocal rotation, leaving a clearance of 2cm between the two discs. One of the two discs mounts, along its circumference, 6 pins bearing 3 pulleys each, to create a spiralling sequence, along which the SMA wire can be coiled suitably. These pulleys have a double triangular groove, which makes the double coiling as compact as possible. The two ends of the SMA wire are fixed to one disc, while the mid-point of the wire connects to the other disc. The two halves of the wire are would along the pulleys thus creating two concentric coils very close to one another. By providing sufficient current flowing between the two ends of the SMA wire, shape recovery occurs generating a linear stroke Δ*L* that is converted into a reciprocal rotation Δ*θ* of the two discs. Notice that the torque generated is given by twice the crosssection of the wire, while the induced magnetic field is self-compensated to a large extent, as

*3.3.2. Actuator implementation and mechanical characterisation* 

**Figure 8.** Amagnetic SMA rotary actuator, consisting of two coils of wire traversed by the same current in opposite directions. This arrangement produces self-annihilation of induced magnetic fields.

In the present implementation, ferromagnetic materials were avoided. However, it was not possible to exclude completely metallic components, such as the bearing balls, the shafts and the pins. After careful consideration, it was decided that the rotating discs and the frame of the device could be made of an aluminium alloy, in order to minimise structural sections. This choice did not affect the acquisition of biosignals, as will be discussed in the next paragraphs.

Technical tests were carried out on the assembled device, to assess its characteristics. Increasing loads were attached to the foot part of the orthosis 13cm from the axis of rotation,

while the device was held aloft by a static support. The weights used in this test produced resisting torques in the range 28-250Ncm. A direct current injection at 30V for 7s was applied to the actuators, connected in parallel; then 30s were allowed for position reset through natural cooling and the action of the weights. The resulting angular upward and downward strokes were measured by means of electrogoniometer SIM-HES-EG 042 (Signo Motus, Messina, Italy). Figures 9 shows the results. At lower values of resisting torques (i.e. in the range 28Ncm-120Ncm), angular stroke is not stabilised and steadily increases from 24° to 36°. For torques above 120Ncm, angular stroke is quite stable at 36°. Curves steadily shift towards negative angles (zero being the horizontal position, and negative in the direction of plantarflexion) with increasing torques. This increase in stroke is caused by the incomplete detwinning of martensite at lower torques: it is worth noticing that anyway, even at the lower values of measured angular stroke, suitable angular strokes are obtained.

**Figure 9.** Angular stroke of the SMA-based exerciser for different resisting static torques. The dotted line is just a guide for the eye.

#### *3.3.3. Tests in a MEG shielded room*

In order to assess compatibility with the MEG technology, neural activity from a healthy subject's brain during repeated passive mobilisation of the ankle by the device was carried out with an MEG system composed of 153 SQUID channels covering the whole surface of the scalp. The electric power generator and the programming computer were kept out of the shielded room, and cables were passed through suitable vents in the shims. The NiTi wire was activated by a current pulse (ramp to 0.7A in 1s, then flat for 9s).

These tests revealed no significant noise on SQUID channels. Figure 10 (left) shows the signal recorded by one representative channel during MEG testing of the healthy volunteer. At t=0s, the actuators on board the orthosis were switched on. There is no artefact at that moment, indicating that the level of noise in the acquisition room has not changed. Furthermore, the right graph in the same Figure demonstrates that the frequency components in the actuator-OFF and actuator-ON states are the same. The variation in intensity of the signal power spectral density (PSD) can be totally accounted for by a change in the cortical reactivity of the subject under testing: this variation is an important part of the measured quantities of interest.

Incidentally, the use of conductive materials in the construction of the device did not affect the acquisition. This is probably due to the slow movement provided by the actuators, which generates low-frequency artefacts that can be suitably eliminated during routine filtering and windowing of the MEG data.

**Figure 10.** Left: MEG signal recorded by a representative SQUID channel from a healthy subject during passive mobilisation of the ankle by the amagnetic exerciser. Right: spectral components of the recorded MEG signal, before and after switching on the actuators at t=0s (black and red line, respectively).

**Figure 11.** Left: fMRI image of metabolic activity in a healthy brain during passive mobilisation of the ankle. Right: time-course of the BOLD signal (arbitrary units) in the area of the brain highlighted in the left figure.

#### *3.3.4. Tests in a MRI acquisition room*

114 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

while the device was held aloft by a static support. The weights used in this test produced resisting torques in the range 28-250Ncm. A direct current injection at 30V for 7s was applied to the actuators, connected in parallel; then 30s were allowed for position reset through natural cooling and the action of the weights. The resulting angular upward and downward strokes were measured by means of electrogoniometer SIM-HES-EG 042 (Signo Motus, Messina, Italy). Figures 9 shows the results. At lower values of resisting torques (i.e. in the range 28Ncm-120Ncm), angular stroke is not stabilised and steadily increases from 24° to 36°. For torques above 120Ncm, angular stroke is quite stable at 36°. Curves steadily shift towards negative angles (zero being the horizontal position, and negative in the direction of plantarflexion) with increasing torques. This increase in stroke is caused by the incomplete detwinning of martensite at lower torques: it is worth noticing that anyway, even at the lower values of measured angular stroke, suitable angular strokes are obtained.

**Figure 9.** Angular stroke of the SMA-based exerciser for different resisting static torques. The dotted

In order to assess compatibility with the MEG technology, neural activity from a healthy subject's brain during repeated passive mobilisation of the ankle by the device was carried out with an MEG system composed of 153 SQUID channels covering the whole surface of the scalp. The electric power generator and the programming computer were kept out of the shielded room, and cables were passed through suitable vents in the shims. The NiTi wire

These tests revealed no significant noise on SQUID channels. Figure 10 (left) shows the signal recorded by one representative channel during MEG testing of the healthy volunteer.

was activated by a current pulse (ramp to 0.7A in 1s, then flat for 9s).

line is just a guide for the eye.

*3.3.3. Tests in a MEG shielded room* 

Magnetic resonance images were collected in a Philips 3T Achieva X-Series Magnetic Resonance scanner. fMRI signals were treated to extract the Blood Oxygen Level Dependent (BOLD) image, which depicts changes in neural metabolism related to neural activity. fMRI images (Figure 11) were not affected by any artefact. The BOLD signal was clearly collected

from all parts of the brain and in some areas seemed to be temporally dependent on the movements of the ankle. The use of conductive materials in the implementation of the device did not affect the acquisition. The distance between the gantry (or head coil) and the ankle probably helped limit any influence on image encoding.
