Synopsis
We
evaluated the
dependence of RF-induced power deposited at a hot spot (p) on insulating electrical properties for insulated stainless steel wires of 1.5 mm in diameter with insulation thickness of
0.5 mm. Lead transfer functions (TF) were obtained by 3-D electromagnetic simulations. TF and p depended
significantly on electrical properties of insulation. Increased insulator conductivity resulted in decreased p. For all insulated wires investigated non-uniform
RF excitation resulted in higher power deposition than uniform RF excitation.Introduction
It was experimentally
discovered that addition of conductive material to lead insulation resulted in
a reduction of radio frequency (RF) induced heating at the lead tip (hot spot)
up to 60% [1]. In that experiment the leads were placed in a rectangular phantom
so that the tangential electric field along the lead pathway
(
Etan(
z))
varied significantly. ISO/TS 10974 Tier 3 [2] requires the assessment of power deposited at a hot spot (
p). Tier
3 separates analysis
of clinically relevant
Etan(
z)
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
A is the calibration factor,
L
is lead length, complex
S(
z) is the transfer function (TF).
TF
for an insulated lead was published in [3] but electrical properties of the insulator
were not provided. If |
Etan(
z)| is constant the
largest
p (
p_
WC_uf) is generated, if phase distribution φ(
Etan(
z))=-φ(
S(
z)) [4]. However clinically
relevant
Etan(
z) can be non-uniform. Thus
p_
WC_uf
cannot be considered as the worst-case power deposition. Our goals in this
study were: 1) to perform electromagnetic simulation of insulated leads, the
insulation electrical properties of which varied, and to calculate
p
(
EM_
p);
2) to numerically obtain the lead models; 3) to calculate the largest
p
for uniform and non-uniform RF excitations using the lead models.
Method
The leads were insulated
stainless steel wires of
L={40:800:10} mm, ∅1.5 mm with insulation thickness of
0.5 mm. The
wire was capped at one end and had a 10 mm long bare segment at the other end. A
sensitivity study of insulator electrical properties was performed for a parameter matrix formed by
ε
r={2.7,4}, and σ={0.007,0.000024} S/m.
S(
z) was
calculated using the reciprocity approach [5]. The calibration
factor was calculated from
EM_
p obtained for the leads excited from one side by
an ideal 64 MHz uniform source. Hot spot integration volume (Fig. 1a) enveloped an area where the
power deposition decayed more than 30 dB. For
quantitative comparison all results were rescaled to
Etan(
z) equal to 1 V/m (peak-to-peak). Non-uniform linearly decayed
Etan(
z)=(-2/
L)×z+2.
p_
WC_lr was calculated for φ(
Etan(
z))=-φ(
S(
z)).
Results and discussion
Two highest
VLD areas
were observed: one near the lead tip and one near the insulator end face (Fig.
1b). They are considered as one hot spot because one continuous area was
visible from the temperature rise (
Trise) profile (Fig. 1c).
For
L=400 mm there is significant
discrepancy between the TF previously published [2] and TF
calculated in our study (Fig. 2a). Taking into account TF
for bare rod [3], it seems that the piece-wise excitation approach used in [2]
is not robust at locations close to the lead tip. TF,
EM_
p (Fig. 3a), and
p_
WC_uf (Fig. 3b) depended significantly on electrical properties of insulation. The lead length, which
resulted in the highest
EM_
p for plane wave
excitation, was essentially shorter for ε
r=4. However for σ=0.000024 S/m,
p_
WC_uf(ε
r=4) was smaller than
p_
WC_uf(ε
r=2.7) only for
L={360:600} mm and {760:800} mm. For
a lead with
L>200 mm located symmetrically about the
Z axis in the ASTM
phantom,
p and
Trise are essentially smaller than respective values for
plane wave excitation due to: a)
Etan(
z) being
essentially reduced at the lead ends in comparison with the value at the center,
b)
S(
z) being significantly reduced along the lead pathway. For
all
L
investigated non-uniform excitation resulted in higher power deposition than
uniform excitation (Fig. 4a). The ratio
p_
WC_lr/
p_
WC_uf
depended on lead length and the insulator conductivity (Fig. 4c). Thus even for
electrically short implants, worst case analysis based on results obtained only
for uniform
Etan(
z)
can lead to significant underestimation. Increased insulator conductivity from σ=0.000024 S/m to σ=0.007 S/m resulted in significant reduction
of
EM_
p
for
L<500 mm,
p_
WC_uf and
p_
WC_lr for all
L.
Conclusion
Hot spot counting
based on
VLD or
SAR data could result in an improper number of hot spots
because thermal heating could merge several separated high-value
VLD areas into
one thermal hot spot. Electrical properties of lead insulator and clinically
relevant
Etan(
z) are important initial implant data for RF-induced heating analysis. However, the specific results of this study, e.g., increased
insulator conductivity resulted in decreased
power deposition, cannot be simply extrapolated to other leads. A
further extensive analysis should be conducted to cover different lead constructions.
Acknowledgements
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.References
[1]
P. Nordbeck, et al.
MRM 68:1963–1972 (2012).
[2] Technical specification ISO/TS 10974 1st edition 2012.
[3] E. Zastrow, et al. EMC 2014, Tokio.
[4] S-M.
Park et al. JMRI, 26(5), 1278–1285. 2007.
[5] Shi Feng et al.
MTT, Vol.63,No.1,305-313,2015.