MRI presents several potential risks for patients with implanted devices and one of the main concerns is RF induced heating of devices and nearby tissues. The aim of this study was to compare 1.5T and 3T RF induced heating at the tip of a wire as a surrogate for an implanted medical device.

The temperature increase at the wire-tip is related to the tangential component of the incident E-field along the wire path. For a uniform incident E-field, wire-tip heating has previously been formulated using the Modified Transmission Line Method (MoTLiM)[1]:

$$\Delta T \approx C |\frac{E_0}{k_t} tan(k_t l_w /2 )|^2 \quad \quad \ \ \ \ \ [1]$$

where k_t is the wavenumber, l_w is the lead length, E₀ is the incident E-field, and C is the constant for EM and thermal calculations needed to find the E-field from hypothetical voltage (V_Hyp) and temperature from the SAR. Note that Equation 1 comes from V_Hyp, which is a scaled version of the charge distribution along the lead, defined by MoTLiM and assumes scattered fields decay fast and establish a quadratic relationship between V_Hyp at the wire-tip and the temperature rise (∆T). For straight wires the wavenumber is a linear function of frequency. Consequently, higher field strengths may cause lower temperature increases when the E-field is kept constant. To better understand the potential for temperature increases (∆T) the constant C (Eqn. 1) was set to unity and the frequency range was evaluated between 64MHz and 128MHz (equivalent to exposure at 1.5T to 3T) square of the V_Hyp is plotted. Bare copper wires (1cm to 40cm and 0.5mm radius) were used to evaluate the resonance behavior of the wire and compared with computational electromagnetics simulations using the Method of Moments (MoM) (FEKO, Altair Engineering) and a 1V/m incident E-field. For the simulations and MoTLiM comparisons the relative permittivity and conductivity of the medium was 70 and 0.42S/m, respectively, for all frequencies. The temperature rise at the wire-tip was also tested with MRI experiments at both 1.5T (Avanto, Siemens) and 3T (Prisma, Siemens). A bare wire with radius 0.4mm was used to achieve resonance behavior at a shorter length, and immersed in an aqueous solution (14g/L HEC). In order to achieve a relatively uniform E-field distribution along the wire, the wire was placed on a circular path with radius 12.5cm inside a circular phantom with radius 16cm. The length of the wire length was changed from 14cm-40cm (2cm increments) at 1.5T and 7cm-22cm (1cm increments) at 3T. Each wire was exposed to 4 W/kg whole-body SAR for a duration of 10-minutes. The temperature rise at the wire-tip was measured directly with a fiber optic temperature probe. SAR at the wire-tip (SAR_w) was calculated from the initial slope of the temperature data. After measuring temperature rise for each wire length, a reference temperature measurement was acquired without the wire and the incident SAR (SAR_i) was calculated from the slope of the reference temperature rise. The calculated SAR-gain due to the wire was found as the ratio of SAR_w/SAR_i.

Figure 1 shows a comparison of SAR-gain at the wire-tip obtained from MoM (red circles) compared to calculations made with MoTLiM (black circles). Results are plotted by normalizing to their maximum values. The results show excellent agreement between MoM and MoTLiM over a wide range of wire lengths and field strengths. The results also highlight that greater heating (SAR-gain) can be observed at lower field strengths for longer wires. In Figure 2 the SAR-gain measured during the MRI experiments is shown for both 1.5T (blue stars) and 3T (red squares). The results show the maximum SAR-gain is higher (~1300) at 1.5T for longer wires (26cm) compared to a maximum SAR-gain of 750 at 14cm at 3T. Note that the SAR-gain at 1.5T is higher than 3T for all wires >16cm. Note the excellent agreement between simulation and experimental results.RF induced wire-tip heating at 1.5T and 3T field strengths were compared. To understand the wire-tip heating (SAR-gain) results the resonance length of the wires must be considered. While keeping the wire length constant as the frequency increases, the SAR-gain can increase or decrease depending on the resonance behavior of the wire. However, when the temperature rise for different field strengths is compared at the resonance peaks (different wire lengths), it can be seen that SAR-gain decreases with the frequency. Greater heating (SAR-gain) can be observed at lower field strengths for longer wires as evident in both simulations and direct measurements at 1.5T and 3T.