Mikhail Kozlov^{1} and Wolfgang Kainz^{2}

This case study investigated RF-induced heating of straight and helix leads at 127.7 MHz obtained with the lead electromagnetic model (LEM) and direct 3D electromagnetic and thermal co-simulations. A large set of incident electric fields was generated in a phantom by an array of four antennas with varying spatial positions and sources. LEM was a suitable approach for predicting temperature in close proximity to the end face of lead tip. However the variance of the fitted values and observed values was rather high for temperature at other locations around the lead tip.

One
approach to evaluate RF-induced heating near an active implantable medical device (AIMD) lead is the lead
electromagnetic model (LEM) prescribed in Clause#8 of ISO/TS_10974_Ed2 [1]. Using
the transfer function (*S*(*l*)) [2] the LEM relates the incident tangential electric
field (*E*_{tan}) along lead trajectory to the RF power deposition (*P*) and temperature rise at a given point in space (ΔTp) due to presence of the lead. In the LEM

$$P = A\cdot\left[\int_{0}^{L} S(l)\cdot E_{tan}\cdot dl \right]^{2}$$

$$\triangle T_{p} = A_{T_{p}}\cdot\left[\int_{0}^{L} S(l)\cdot E_{tan}\cdot dl \right]^{2}$$

where: *A* and
*A*_{Tp} are the calibration
factors of the LEM for *P* and ΔT_{p}, respectively, and *L* is the lead length.
Both calibration
factors can be assessed using a linear regression analysis
of *P* and ΔT_{p} versus $$$P_{lem} = \left[\int_{0}^{L} S(l)\cdot E_{tan}\cdot dl \right]^{2}$$$ obtained for a set of
diverse non-uniform *E*_{tan}(*l*). The associated regression coefficients *R*^{2}_{A}
and *R*^{2}_{ATp} are the quotient of the variances of the fitted
values and the observed values of the dependent variable. *E*_{tan}(*l*) disturbance depends on the proximity between the
implant segments and the construction of the implant. The smallest disturbance
of *E*_{tan}(*l*) occurs for the straight lead trajectory allowed the most reliable estimation of *A* and *A*_{Tp}.

[1] Technical specification ISO/TS 10974, “Assessment of the safety of magnetic resonance imaging for patients with an active implantable medical device”, 1st edition 2012.

[2] S-M. Park, K. Kamondetdacha, and J. A. Nyenhuis, “Calculation of MRI-induced heating of an implanted medical lead wire with an electric field transfer function”, J. Magn. Reson. Imaging, 26(5), 2007, 1278–1285.

[3] S. Feng, R. Qiang, W. Kainz, and J. Chen, “A technique to evaluate MRI-Induced electric fields at the ends of practical implanted lead,” IEEE Transactions on Microwave Theory and Techniques, 63(1), 2015, 305-313.

Figure 1. a) and b) Straight and helix lead geometry zoomed for
lead tip showing the hot spot
integration volume. The other lead end was capped. S1-S14 are positions of temperature sensors. c) 3D-EM simulation setup.
The leads were positioned in the middle of a box (600×600×2400mm^{3}) filled with a medium ε_{r}=78 and σ=1.2S/m, thermal properties: specific heat 4181J/kg/K, isotropic thermal conductivity 0.6W/m/K, and density 1001kg/m^{3}. Titanium alloy properties: σ=595238S/m, specific heat 526.3J/kg/K,
isotropic thermal conductivity 6.7W/m/K and density 4430kg/m^{3}. Insulation material properties: σ=24mS/m, ε_{r}=2.7, specific heat 1000J/kg/K, isotropic thermal conductivity 0.2W/m/K and density 1350kg/m^{3}.

Figure 2. a) and
b) Amplitudes and phases of *S*(*l*) for straight and helix lead, respectively;
c) and d) ||*E*_{tan}(*l*)|| and φ(*E*_{tan}(*l*)) for excitations: Ex1, Ex2, Ex3, Ex4 (generated by the single 1,
2, 3, or 4 antennas, respectively), Ex5, and Ex6 (generated by all
antennas simultaneously with the same source amplitudes, but different phases);
e) and f) estimation of the calibration factor *A* for
straight and helix lead, respectively; g) and h) estimation of the calibration factor *A*_{VLD} for point VLD values
(calculated at axial location 1mm from the tip) obtained from linear regression analysis: *VLD*_{3D_EM} versus *P*_{lem}.

Figure 3. Helix lead results for different excitations and
temperature transient time steps. a) Volume loss density profiles rescaled to
local maximum; b) temperature profiles rescaled to local maximum for
temperature transient at 1s; c) temperature profiles rescaled to local maximum
for temperature transient at 10s; d) temperature profiles rescaled to local
maximum for temperature transient at 60s; e) temperature profiles rescaled to
local maximum for temperature transient at 360s.

Figure 4. Estimation
of the calibration factor *A*_{Tp}
for straight lead at
different location and time step of transient temperature rise.

Figure 5. Estimation
of the calibration factor ATp
for helix lead at different
location and time step of transient temperature rise.