Synopsis

The purpose of this work is to provide a quantitative understanding of how a conducting metallic shield over a lead will reduce RF heating at the electrode during MRI scans. A physical model and equations for reduction of RF heating by a shielded lead are presented. Temperature rise were calculated for different lengths of shielded and unshielded leads. Confirming measurements were made for a quarter wavelength coaxial cable model of the lead. Measured temperature rise and transfer function depended on terminations conditions, with the open lead exhibiting a temperature rise approximately 10 times greater than the shorted lead.

Motivation and Purpose:

Physical description for reduction of RF induced heating by shielding a lead wire:

Figure 1 shows a representation of an implanted electrical stimulation system with a generator and a lead wire with an electrode. The background electric field will induce currents and electric charge on the shield. These will produce a scattered electric field E_s at the edges of the shield. The tangential component of the scattered field will induce propagating currents on the central conductor. The current that is transmitted from the electrode will induce power in the surrounding tissue.

Let $$$\tau$$$ represent parametric distance along the lead and let $$$\tau=0$$$ at the distal end of the electrode, $$$\tau=\tau_{d}$$$ at the distal end of the shield, $$$\tau=\tau_{p}$$$ at the proximal end of the shield, and $$$\tau=L$$$ where the lead enters the generator. With the shield, the temperature rise $$$\triangle T_{shield}$$$ at electrode is
$$\triangle T_{shield}=|\int_{0}^{\tau_d}S_E^s(\tau)E_{tan}(\tau)d{\tau}+\int_{\tau_p}^{L}S_E^s(\tau)E_{tan}(\tau)d{\tau}+S_E^s(L)\triangle{V_{gen}} |^{2}............................(1)$$
where $$$S_E^s$$$ is the electric field transfer function for the shielded lead, and $$$\triangle V_{gen}$$$ is an effective voltage that is developed across the generator due to the background tangential electric field. We expect that the magnitude of $$$\triangle V_{gen}$$$ to be about $$$|E_{tan}|L_{gen}/2$$$ where E_tan is the background electric field at the location of the generator and is the length of the generator.

Equation (1) is integrated along the portion of the lead outside the shield as E_tan is zero under the shield. In the absence of the shield, the temperature rise is
$$\triangle T_{noshield}=|\int_{0}^{L}S_E^b(\tau)E_{tan}(\tau)d{\tau}+S_E^b(L)\triangle{V_{gen}} |^{2}$$ where $$$S_E^b$$$ is the electrode transfer function without the shield.

Methods for Calculations and Measurements in Phantom

To quantitatively test the model, temperature rise for shielded and unshielded model leads were calculated with FDTD method and measured (Figure 2) in an ASTM rectangular phantom. The model lead is quarter wave length coaxial cable RG 316. An Electrode was formed by removing 6 mm insulation from distal end and proximal end is either shorted or open.The phantom was placed in a GE Signa 1.5T coil and RF power averaging about 3 W/kg over the entire phantom was applied CW. Local SAR at the location of the wire during the tests was 7.1 W/kg. In the simulation, a plane-wave electric field with polarization parallel to the length of the model was applied.

Figure 2(d) illustrates the measurement of transfer function parameter, S_E. A tangential electric field is applied over a short length of the lead with a E_tan coupler which is translated along the length of the model lead.⁴ The scattered electric field at the end of the electrode is proportional to the voltage measured with a sensor.

Results of Calculations and Measurements:

Figure 3 shows the calculated temperature rises vs. lead length at 128 MHz for different configurations of lead. Lowest rises occur for the shielded leads with generator.

Figure 4 shows the measured electric field transfer function $$$S_E^b$$$ plot for 80 cm shielded lead at 64 MHz. Magnitude of transfer function along the shield is less for the shorted lead as compared to open lead.

Figure 5 shows the measured scaled temperature rises vs. time for open and short condition for 80 cm shielded lead at 64 MHz. The greatest temperature rise occurs for the open-ended cable.

Conclusions

The temperature rise at the electrode with shield $$$\triangle T_{shield}$$$ will differ from the temperature rise for the unshielded $$$\triangle T_{noshield}$$$ for the following reasons.

1) The tangential electric field under the shield will be minimal whereas tangential electric field is equal to the background value for the unshielded lead.

2)The tangential component of the scattered electric field at the edges of the shield will be different, and likely larger in magnitude, compared to background E_tan.

3) The electric field transfer function $$$S_E^s$$$ with the shield will differ from the electric field transfer function $$$S_E^b$$$ without shield. This is because the effective wavelength and damping factors for current waves on the lead are different when the insulation is surrounded by body tissues compared to when it is surrounded by the metal shield.

A strategy to minimize temperature rise might involve placing the edges of the shield at locations where $$$S_E^b$$$ is smallest.

Acknowledgements

References

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