MRI-based, wireless determination of the transfer function of a linear implant: Introduction of the transfer matrix

An improved method to measure transfer functions using MRI

PURPOSE

A previously published method for MRI-based transfer function assessment makes use of the so-called transceive phase assumption (TPA). This limits its applicability to shorter leads and/or lower field strengths. A new method is presented where the background electric field is determined from bothB 1 + $$ {\mathrm{B}}_1^{+} $$ - andB 1 - $$ {\mathrm{B}}_1^{-} $$ -field distributions, avoiding the TPA and making it more generally applicable.

THEORY AND METHODS

TheseB 1 $$ {\mathrm{B}}_1 $$ -distributions are determined from a spoiled gradient echo multiflip angle acquisition. From the separatedB 1 $$ {\mathrm{B}}_1 $$ -components the background electrical field and the induced current are computed. Further improvement is achieved by recasting theB 1 $$ {\mathrm{B}}_1 $$ -field model as a "magnitude squared least squares" problem. The proposed reconstruction method is used to determine transfer functions of various copper wire lengths up to 40 cm inside an elliptical ASTM phantom. The method is first tested on EM-simulated data and subsequently phantom and bench measurements are used to determine transfer functions experimentally.

RESULTS

In silica reconstructions demonstrate the validity of the proposedB 1 $$ {\mathrm{B}}_1 $$ -field model resulting in highly accurate reconstructedB 1 $$ {\mathrm{B}}_1 $$ -fields, currents, incident electric fields and transfer functions. The experimental results show slight deviations in the field model, however, resulting transfer functions are accurately determined with high similarity to simulations and comparable to bench measurements.

CONCLUSION

A more generally applicable method for MRI-based transfer function assessment is presented. The proposed method circumvents phase assumptions making it applicable for longer objects and/or higher field strengths. Additional improvements are implemented in theB 1 $$ {\mathrm{B}}_1 $$ -mapping method and the solution algorithm.

Towards an integrated radiofrequency safety concept for implant carriers in MRI based on sensor-equipped implants and parallel transmission

To protect implant carriers in MRI from excessive radiofrequency (RF) heating it has previously been suggested to assess that hazard via sensors on the implant. Other work recommended parallel transmission (pTx) to actively mitigate implant-related heating. Here, both ideas are integrated into one comprehensive safety concept where native pTx safety (without implant) is ensured by state-of-the-art field simulations and the implant-specific hazard is quantified in situ using physical sensors. The concept is demonstrated by electromagnetic simulations performed on a human voxel model with a simplified spinal-cord implant in an eight-channel pTx body coil at 3 T . To integrate implant and native safety, the sensor signal must be calibrated in terms of an established safety metric (e.g., specific absorption rate [SAR]). Virtual experiments show that E -field and implant-current sensors are well suited for this purpose, while temperature sensors require some caution, and B 1 probes are inadequate. Based on an implant sensor matrix Q s , constructed in situ from sensor readings, and precomputed native SAR limits, a vector space of safe RF excitations is determined where both global (native) and local (implant-related) safety requirements are satisfied. Within this safe-excitation subspace, the solution with the best image quality in terms of B 1 + magnitude and homogeneity is then found by a straightforward optimization algorithm. In the investigated example, the optimized pTx shim provides a 3-fold higher mean B 1 + magnitude compared with circularly polarized excitation for a maximum implant-related temperature increase ∆ T imp ≤ 1 K . To date, sensor-equipped implants interfaced to a pTx scanner exist as demonstrator items in research labs, but commercial devices are not yet within sight. This paper aims to demonstrate the significant benefits of such an approach and how this could impact implant-related RF safety in MRI. Today, the responsibility for safe implant scanning lies with the implant manufacturer and the MRI operator; within the sensor concept, the MRI manufacturer would assume much of the operator's current responsibility.

A workflow for predicting temperature increase at the electrical contacts of deep brain stimulation electrodes undergoing MRI

Purpose

The purpose of this study is to present a workflow for predicting the radiofrequency (RF) heating around the contacts of a deep brain stimulation (DBS) lead during an MRI scan.

Methods

The induced RF current on the DBS lead accumulates electric charge on the metallic contacts, which may cause a high local specific absorption rate (SAR), and therefore, heating. The accumulated charge was modeled by imposing a voltage boundary condition on the contacts in a quasi‐static electromagnetic (EM) simulation allowing thermal simulations to be performed with the resulting SAR distributions. Estimating SAR and temperature increases from a lead in vivo through EM simulation is not practical given anatomic differences and variations in lead geometry. To overcome this limitation, a new parameter, transimpedance, was defined to characterize a given lead. By combining the transimpedance, which can be measured in a single calibration scan, along with MR‐based current measurements of the lead in a unique orientation and anatomy, local heating can be estimated. Heating determined with this approach was compared with results from heating studies of a commercial DBS electrode in a gel phantom with different lead configurations to validate the proposed method.

Results

Using data from a single calibration experiment, the transimpedance of a commercial DBS electrode (directional lead, Infinity DBS system, Abbott Laboratories, Chicago, IL) was determined to be 88 Ω. Heating predictions using the DBS transimpedance and rapidly acquired MR‐based current measurements in 26 different lead configurations resulted in a <23% (on average 11.3%) normalized root‐mean‐square error compared to experimental heating measurements during RF scans.

Conclusion

In this study, a workflow consisting of an MR‐based current measurement on the DBS lead and simple quasi‐static EM/thermal simulations to predict the temperature increase around a DBS electrode undergoing an MRI scan is proposed and validated using a commercial DBS electrode.

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A single setup approach for the MRI-based measurement and validation of the transfer function of elongated medical implants

PURPOSE

To propose a single setup using the MRI to both measure and validate the transfer function (TF) of linear implants. Conventionally, the TF of an implant is measured in one bench setup and validated using another.

METHODS

It has been shown that the TF can be measured using MRI. To validate this measurement, the implant is exposed to different incident electric fields, while the temperature increase at the tip is monitored. For a good validation, the incident electric fields that the implant is exposed to should be orthogonal. We perform a simulation study on six different methods that change the incident electric field. Afterward, a TF measurement and validation study using the best method from the simulations is performed. This is done with fiberoptic temperature probes at 1.5 T for four linear implant structures using the proposed single setup.

RESULTS

The simulation study showed that positioning local transmit coils at different locations along the lead trajectory has a similar validation quality compared with changing the implant trajectory (ie, the conventional validation method). For the validation study that was performed, an R2 ≥ 0.91 was found for the four investigated leads.

CONCLUSION

A single setup to both measure and validate the transfer function using local transmit coils has been shown to work. The benefits of using the proposed validation method are that there is only one setup required instead of two and the implant trajectory is not varied; therefore, the relative distance between the leap tip and the temperature probe is constant.

Rapid safety assessment and mitigation of radiofrequency induced implant heating using small root mean square sensors and the sensor matrix Qs

PURPOSE

Rapid detection and mitigation of radiofrequency (RF)-induced implant heating during MRI based on small and low-cost embedded sensors.

THEORY AND METHODS

A diode and a thermistor are embedded at the tip of an elongated mock implant. RF-induced voltages or temperature change measured by these root mean square (RMS) sensors are used to construct the sensor Q-Matrix (Q_S ). Hazard prediction, monitoring and parallel transmit (pTx)-based mitigation using these sensors is demonstrated in benchtop measurements at 300 MHz and within a 3T MRI.

RESULTS

Q_S acquisition and mitigation can be performed in <20 ms demonstrating real-time capability. The acquisitions can be performed using safe low powers (<3 W) due to the high reading precision of the diode (126 µV) and thermistor (26 µK). The orthogonal projection method used for pTx mitigation was able to reduce the induced signals and temperatures in all 155 investigated locations. Using the Q_S approach in a pTx capable 3T MRI with either a two-channel body coil or an eight-channel head coil, RF-induced heating was successfully assessed, monitored and mitigated while the image quality outside the implant region was preserved.

CONCLUSION

Small (<1.5 mm³ ) and low-cost (<1 €) RMS sensors embedded in an implant can provide all relevant information to predict, monitor and mitigate RF-induced heating in implants, while preserving image quality. The proposed pTx-based Q_S approach is independent of simulations or in vitro testing and therefore complements these existing safety assessments.

A combined computational and experimental approach to assess the transfer function of real pacemaker leads for MR radiofrequency-induced heating

OBJECTIVE

To propose and validate a variation of the classic techniques for the estimation of the transfer function (TF) of a real pacemaker (PM) lead.

METHODS

The TF of three commercially available PM leads was measured by combining data from experimental measurements and numerical simulations generated by three sources: a) the experimental local SAR at the tip of the PM lead (single measurement point) exposed to a 64 MHz birdcage body coil; b) the experimental current distribution along the PM lead, obtained by directly injecting a 64 MHz signal inside the lead; c) the electric field (E-field) simulated with a computational model of the 64 MHz birdcage body coil adopted in the experimental measurement performed in a). The effect of the lead trajectory on the estimation of the TF was also estimated.

RESULTS

The proposed methodology was validated by comparing the SAR obtained from the PM lead TF with experimental measurements: a maximum difference of 2.2 dB was observed. It was also shown that the estimation of the TF cannot be considered independent with the lead trajectory: a variation of the SAR estimation up to 3.4 dB was observed.

CONCLUSION

For the three PM lead tested, the error in the SAR estimation is within the uncertainty level of SAR measurements (± 2 dB). Additionally, the estimation of the TF using the reciprocity principle is influenced by the particular lead trajectory adopted, even if the consequent variability in the SAR estimation is still close to the uncertainty level of SAR measurements.

Explaining RF induced current patterns on implantable medical devices during MRI using the transfer matrix

PURPOSE

In this work a simulation study is performed to gain insights in the patterns of induced radiofrequency (RF) currents for various implant-like structures at 1.5 T. The previously introduced transfer matrix (TM) is used to determine why certain current patterns have a tendency to naturally occur. This can benefit current safety assessment techniques and may enable the identification of critical exposure conditions.

THEORY AND METHODS

The induced current on an elongated implant can be determined by multiplication of the incident electric field along the implant with its TM. The eigenmode spectrum of the TMs for various lengths and various types of implants are determined. The eigenvector with the highest eigenvalue describes the incident electric field pattern that induces the highest current which in turn will lead to highest heating. Subsequently, a statistical probability analysis is performed using a wide range of potential incident electric field distributions in a representative human subject model during a 1.5 T MR exam which are determined by means of electromagnetic FDTD simulations. These incident electric field distributions and the resulting induced current patterns are projected onto eigenvectors of the TM to determine which eigenmodes of the implant dominate the current patterns.

RESULTS

The eigenvectors of the TM of bare and insulated wires resemble sinusoidal harmonics of a string fixed at both ends similar to the natural-current distribution on thin antennas(1). The currents on implants shorter than 20 cm are generally dominated by the first harmonic (similar to half a sine wave). This is firstly because for these implant lengths (relative to the RF wavelength), the first eigenvalue is more than three times bigger than the second showing the ability of an implant to accommodate one eigenmode better than another. Secondly, the incident electric fields have a high likelihood (≳95,7%) to project predominantly on this first eigenmode.

CONCLUSION

The eigenmode spectrum of the TM of an implant provides insight into the expected shape of induced current distributions and worst-case exposure conditions. For short implants, the first eigenvector is dominant. In addition, realistic incident electric field distributions project more heavily on this eigenvector. Both effects together cause significant currents to always resemble the dominant eigenmode of the TM for short implants at 1.5 T.

Modeling radiofrequency responses of realistic multi-electrode leads containing helical and straight wires

Purpose

To present a modeling workflow for the evaluation of a lead electromagnetic model (LEM) consisting of a transfer function (TF) and a calibration factor. The LEM represents an analytical relationship between the RF response of a lead and the incident electromagnetic field. The study also highlights the importance of including key geometric details of the lead and the electrode when modeling multi-electrode leads.

Methods

The electrical and thermal responses of multi-electrode leads with helical and straight wires were investigated using 3D electromagnetic (EM) and thermal co-simulations. The net dissipated power (P) around each lead electrode and the net temperature increase at the electrodes (ΔT) were obtained for a set of incident EM fields with different spatial distributions. A reciprocity approach was used to determine a TF for each electrode based on the results of the computational model. The evaluation of the calibration factors and the TF validation were performed using the linear regression of P versus the LEM predictions.

Results

P and ΔT were investigated for four multi-electrode leads and four single-electrode leads containing either helical or straight wires. All electrodes of the multi-electrode lead were found to be points of high power deposition and temperature rise. The LEMs for the individual electrodes varied substantially. A significant dependence of the calibration factors on the surrounding tissue medium was also found. Finally, the model showed that the TF, the calibration factor, P and ΔT for multi-electrode leads differ significantly from those for single-electrode leads.

Conclusion

These results highlight the need to evaluate a LEM for each electrode of a multi-electrode lead as well as for each possible surrounding medium. It is also shown that the results derived from simulations based on simplified single-electrode leads can significantly mislead multi-electrode lead analyses.

MRI-Induced Heating of Coils for Microscopic Magnetic Stimulation at 1.5 Tesla: An Initial Study

Purpose

Deep brain stimulation (DBS) has proved to be effective in the treatment of movement disorders. However, the direct contact between the metal contacts of the DBS electrode and the brain can cause RF heating in magnetic resonance imaging (MRI) scanning, due to an increase of local specific absorption rate (SAR). Recently, micro coils (μMS) have demonstrated excitation of neuronal tissue through the electromagnetic induction both in vitro and in vivo experiments. In contrast to electrical stimulation, in μMS, there is no direct contact between the metal and the biological tissue.

Methods

We compared the heating of a μMS coil with a control case of a metal wire. The heating was induced by RF fields in a 1.5 T MRI head birdcage coil (often used for imaging patients with implants) at 64 MHz, and normalized results to 3.2 W/kg whole head average SAR.

Results

The μMS coil or wire implants were placed inside an anatomically accurate head saline-gel filled phantom inserted in the RF coil, and we observed approximately 1°C initial temperature rise at the μMS coil, while the wire exhibited a 10°C temperature rise in the proximity of the exposed end. The numerical simulations showed a 32-times increase of local SAR induced at the tips of the metal wire compared to the μMS.

Conclusion

In this work, we show with measurements and electromagnetic numerical simulations that the RF-induced increase in local SAR and induced heating during MRI scanning can be greatly reduced by using magnetic stimulation with the proposed μMS technology.

MRI-based transfer function determination through the transfer matrix by jointly fitting the incident and scattered B1+ field

PURPOSE

A purely experimental method for MRI-based transfer function (TF) determination is presented. A TF characterizes the potential for radiofrequency heating of a linear implant by relating the incident tangential electric field to a scattered electric field at its tip. We utilize the previously introduced transfer matrix (TM) to determine transfer functions solely from the MR measurable quantities, that is, the B 1 + and transceive phase distributions. This technique can extend the current practice of phantom-based TF assessment with dedicated experimental setup toward MR-based methods that have the potential to assess the TF in more realistic situations.

THEORY AND METHODS

An analytical description of the B 1 + magnitude and transceive phase distribution around a wire-like implant was derived based on the TM. In this model, the background field is described using a superposition of spherical and cylindrical harmonics while the transfer matrix is parameterized using a previously introduced attenuated wave model. This analytical description can be used to estimate the transfer matrix and transfer function based on the measured B 1 + distribution.

RESULTS

The TF was successfully determined for 2 mock-up implants: a 20-cm bare copper wire and a 20-cm insulated copper wire with 10 mm of insulation stripped at both endings in respectively 4 and 3 different trajectories. The measured TFs show a strong correlation with a reference determined from simulations and between the separate experiments with correlation coefficients above 0.96 between all TFs. Compared to the simulated TF, the maximum deviation in the estimated tip field is 9.4% and 12.2% for the bare and insulated wire, respectively.

CONCLUSIONS

A method has been developed to measure the TF of medical implants using MRI experiments. Jointly fitting the incident and scattered B 1 + distributions with an analytical description based on the transfer matrix enables accurate determination of the TF of 2 test implants. The presented method no longer needs input from simulated data and can therefore, in principle, be used to measure TF's in test animals or corpses.

Accelerating implant RF safety assessment using a low-rank inverse update method

Purpose

Patients who have medical metallic implants, e.g. orthopaedic implants and pacemakers, often cannot undergo an MRI exam. One of the largest risks is tissue heating due to the radio frequency (RF) fields. The RF safety assessment of implants is computationally demanding. This is due to the large dimensions of the transmit coil compared to the very detailed geometry of an implant.

Methods

In this work, we explore a faster computational method for the RF safety assessment of implants that exploits the small geometry. The method requires the RF field without an implant as a basis and calculates the perturbation that the implant induces. The inputs for this method are the incident fields and a library matrix that contains the RF field response of every edge an implant can occupy. Through a low‐rank inverse update, using the Sherman–Woodbury–Morrison matrix identity, the EM response of arbitrary implants can be computed within seconds. We compare the solution from full‐wave simulations with the results from the presented method, for two implant geometries.

Results

From the comparison, we found that the resulting electric and magnetic fields are numerically equivalent (maximum error of 1.35%). However, the computation was between 171 to 2478 times faster than the corresponding GPU accelerated full‐wave simulation.

Conclusions

The presented method enables for rapid and efficient evaluation of the RF fields near implants and might enable situation‐specific scanning conditions.

MRI-based, wireless determination of the transfer function of a linear implant: Introduction of the transfer matrix

PURPOSE

We introduce the transfer matrix (TM) that makes MR-based wireless determination of transfer functions (TFs) possible. TFs are implant specific measures for RF-safety assessment of linear implants. The TF relates an incident tangential electric field on an implant to a scattered electric field at its tip that generally governs local heating. The TM extends this concept and relates an incident tangential electric field to a current distribution in the implant therewith characterizing the RF response along the entire implant. The TM is exploited to measure TFs with MRI without hardware alterations.

THEORY AND METHODS

A model of rightward and leftward propagating attenuated waves undergoing multiple reflections is used to derive an analytical expression for the TM. This allows parameterization of the TM of generic implants, e.g., (partially) insulated single wires, in a homogeneous medium in a few unknowns that simultaneously describe the TF. These unknowns can be determined with MRI making it possible to measure the TM and, therefore, also the TF.

RESULTS

The TM is able to predict an induced current due to an incident electric field and can be accurately parameterized with a limited number of unknowns. Using this description the TF is determined accurately (with a Pearson correlation coefficient R ≥ 0.9 between measurements and simulations) from MRI acquisitions.

CONCLUSION

The TM enables measuring of TFs with MRI of the tested generic implant models. The MR-based method does not need hardware alterations and is wireless hence making TF determination in more realistic scenarios conceivable.