An Evaluation of Radio Frequency Induced Power Deposition of Coaxial Leads with an Implant Model
Mikhail Kozlov1,2 and Gregor Schaefers1,3

1MR:comp GmbH, Gelsenkirchen, Germany, 2Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany, 3Magnetic Resonance Institute for Safety, Technology and Research GmbH, Gelsenkirchen, Germany


We performed 3-D electromagnetic simulations of coaxial leads and numerically obtained the lead models to evaluate power deposition and the voltage induced at the lead proximal end with the lead models. No correlation between peak volume loss density and deposited powers at the tip and the ring was observed. In some cases deposited power at the ring exceeded deposited power at the tip. However further extensive simulations of induced heating behavior should be done before final conclusions regarding coax lead design preferences are made.


In some bipolar leads significant RF induced heating can appear not only at the wire tips, but also in a comparable level at the ring electrodes [1]. Numerical simulations of leads are useful for understanding the complex interaction between the incident RF field and a lead, which is important for reliably designing MR Conditional leads. The ISO/TS 10974 Tier 3 procedure [2] separates analysis of clinically relevant incident tangential electric fields (Etan(z)) along the lead pathways from calculations of the lead responses to these Etan(z) using a lead (implant) model expressed as: $$$p = A \times\ |\int_{0}^{L}S(z)\cdot E_{tan}(z)\cdot dz|^2 $$$, where p is power deposited at a hot spot, A is the calibration factor, L is lead length, complex S(z) is the transfer function (TF). Similar expression is used to model voltage (Vp) induced at the lead proximal end. TF based numerical analysis of coax leads has not been published yet. It is still a challenge to simulate some commercial bipolar leads that consist of helical inner and outer conductors. Simulations of generic RF coaxial cable structures not only allow to gather experience in analysis of a rather complex coaxial geometry but also provides results for design optimization of some medical surgery instruments that can be represented as a coaxial structure from an RF point of view. Our goals in this study were: 1) to perform 3-D electromagnetic simulation of coaxial leads; 2) to numerically obtain the lead models; 3) to calculate the largest p and Vp for uniform RF excitations using the lead models.


The leads were coaxial titanium alloy structures: straight inner wire of 1.5 mm in diameter with insulation thickness of 0.5 mm, straight outer tube of 3 mm in outer diameter with outer insulation thickness of 0.25 mm. L was varied from 40 mm to 800 mm in steps of 10 mm. At the proximal end the lead was capped and inner wire and outer tube were connected via a resistor Rproximal. At the distal end, wire tip and ring electrode lengths were 10 mm long (Fig.1a). Electrical properties of both insulators were εr = 2.7 and σ = 0.000024 S/m. Rproximal = {10-6, 1.25, 2.5, 50, 106} Ohm. S(z) for p of tip, ring and Vp were calculated using the reciprocity approach described in [3]. The calibration factors for the tip and the ring were calculated from p (p_uf), obtained for the leads excited from one side by a uniform 64 MHz source. The same simulations that provided p_uf were used to calculate calibration factors for the Vp model. Hot spot integration volumes (Fig. 1b) enveloped an area where the volume loss density (VLD) decayed more than 30 dB. |Etan(z)| being constant, the largest p (p_wc) was generated if φ(Etan(z)) = - φ(S(z)).

Results and discussion

VLD distribution in proximity of the wire tip and ring depended significantly on length of the coaxial structure (Fig. 1b – 1g). Despite significantly large VLD peak value in proximity of the wire tip, p values at the tip and ring were of the same order of magnitude. For Rproximal=1 GOhm, ring p values were even larger than tip p values (Fig. 2a and 2b). Tip and ring p values, Vp (Fig 2.c), and S(z) for both the tip and the ring (Fig. 3 and 4) significantly depended on Rproximal. For Rproximal = {10-6, 1.25, 2.5}, tip φ(S(z)) varied significantly depending on distance from the distal end. The large variation of φ(S(z)) near the proximal end was due to a sharp drop to zero of |S(z)|. Coaxial structures properties were Z0 = 18.6 Ohm, λ/4 = 712 mm. The λ/4 impedance transformation resulted in an effective high impedance between the tip and the ring for L ≈ 700 mm and even significantly (close to zero) decreased values of tip p_wc (Fig. 5). However, ring p_wc value decrease was noticeably smaller.


Numerical simulation of coaxial structures can provide important requirements for experimental validation of TF, for example, maximum acceptable distance between measurement points for proper determination of spatial TF variations and required precision of Rproximal. Correlations existed neither between peak VLD and p at the tip and the ring nor between Rproximal and p at the tip and the ring. Larger p at the ring was observed for Rproximal equal to 50 and 106 Ohm. However p results cannot be simply extrapolated to induced heating evaluation. Further extensive thermal simulations should be conducted to obtain dependences of induced heating at the tip and rings on coaxial structure geometry and material electrical and thermal properties.


This work was supported by the German Federal Ministry of Education and Research (BMBF) and within the European Joint Undertakings ENIAC JU, grant # 16ES0028, DeNeCoR.


[1] P. Nordbeck, et al. MRM 68:1963–1972 (2012).

[2] Technical specification ISO/TS 10974 1st edition 2012.

[3] Shi Feng et al. MTT, Vol.63,No.1,305-313,2015.


Fig.1. a) Sketch of coaxial line at the distal end.

VLD profiles at the distal end for Rproximal = 10-6 Ohm.

b) L = 40 mm. c) L = 100 mm. d) L = 150 mm. e) L = 200 mm. f) L = 260 mm. g) L = 400 mm.

Fig. 2. 3-D electromagnetic simulation results. a) power deposited at the tip hot spot. b) power deposited at the ring hot spot. c) the voltage induced at the lead proximal end.

Fig. 3. Transfer function for the lead tip. a) and d) Rproximal = 106 Ohm, b) and e) Rproximal = 10-6 Ohm, c) and f) Rproximal = 1.25 Ohm

Fig. 4. Transfer function for the lead ring. a) and d) Rproximal = 106 Ohm, b) and e) Rproximal = 10-6 Ohm, c) and f) Rproximal = 1.25 Ohm.

Fig. 5. Results of deposited power calculated with the implant model for the case φ(Etan(z)) = - φ(S(z)). a) tip, b) ring.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)