MR/PET can have a significant role in medical diagnosis because it combines the high resolution and soft tissue contrast of MRI with the ability of PET to provide information about metabolic rate and other molecular events, depending on the radiopharmaceutical used. The RF energy applied to the body in MRI can cause temperature increase in the body tissues which can, in turn, influence the metabolic rate¹. In this work we propose a simple method to estimate the effect of temperature increase on the PET images acquired during an MR/PET scan.

A human body was modeled in a body-sized birdcage coil operating at 128 MHz with the heart near the center of the coil. The electromagnetic fields throughout the body were computed with a commercially available 3D simulator (XFDTD, Remcom). After the simulation all electromagnetic fields were normalized so that the average SAR absorbed in the whole body was 2W/kg, corresponding to the maximum value recommended under the IEC guidelines for normal mode operation².

For a given SAR distribution, temperature increase can be estimated using the Pennes Bioheat Equation:$$\rho c\frac{\partial T}{\partial t} = \nabla\cdot(k\nabla T)-W\rho_{bl}c_{bl}(T-T_{bl})+Q+\rho SAR\;[1]$$where c is heat capacity, W is blood perfusion rate, k is thermal conductivity, ρ is material density, the subscript bl indicates values for blood, and Q is the heat generated by metabolism. The temperature T was computed with a home-built Finite Difference implementation of Eq. [1] for an exposure of 60 minutes at the above-mentioned SAR levels. At the end of each timestep the values of metabolic rate Q were updated according to the relation³$$Q=Q_0(1.1)^{T-T_0}\;[2]$$where Q₀ and T₀ represent respectively the value of metabolic rate and the temperature at equilibrium before beginning the MR exam. The core body temperature (seen as blood temperature, T_bl, in Eq. [1]) was allowed to increase according to the total energy absorbed by the body considering whole-body SAR, respiration, conduction to the patient table, convection⁴, and the blood perfusion W was allowed to change according to a previously-published model⁵.The FDG uptake was calculated with a simple two-compartment model considering the FDG concentration in the blood ([FDG]_b), and the concentration in the tissue ([FDG]_t). The concentrations were estimated with the following differential equations:$$\begin{cases}\frac{\partial [FDG]_b}{\partial t}=-\lambda [FDG]_b+\delta (t-t_i)\\\frac{\partial [FDG]_t}{\partial t}=-\lambda [FDG]_t+Q[FDG]_b\end{cases}\;[3]$$where the decay constant λ is equal to $$$\lambda=\ln(2)/t_{1/2}\;[4]$$$ where $$$t_{1/2}$$$ is the half-life of FDG, estimated to be 110 minutes. The delta function δ indicates a sudden increase in [FDG]_b at the time of injection, t_i. Two different timecourses were considered with respect to the time of FDG injection, one where the imaging period began immediately after the injection of the FDG agent, and one where the imaging period began one hour after the injection. The PET signal was calculated as the local [FDG]_t integrated through the entire 60 minute imaging period projected along the anterior-posterior direction. For comparison, the PET signal was also calculated for zero SAR, such that T=T₀ and Q=Q₀ throughout time and space.

Fig. 2 shows the simulated PET images both in the case of maximum allowable SAR and no SAR applied throughout the imaging period. Fig. 3 shows both the temperature distributions and the percent increase of the signal intensity with maximum allowable SAR. The maximum temperature increase is equal to 6.1 °C and it is located in the shoulder: for this temperature increase, the corresponding local metabolic rate increase is equal to 77.6%. The maximum signal intensity increase in the simulated PET images is 23% in case the imaging time starts immediately after the FDG injection, while it is equal to 7.4% in case the imaging time starts one hour after the FDG injection. However, these maximum changes occur in regions where baseline metabolic rate is inherently low, such that differences are not easily visible (Fig. 2).The images in Fig. 2 show that the simulated PET images are not significantly affected by the increase of the metabolic rate during the MRI exam, although the relative increase of metabolic rate is significant in some tissues (Fig. 3). In addition, the simulations have been performed in a conservative scenario, because SAR levels during an actual MRI exam are not at the maximum allowable levels for longer than a few minutes. In practice, any effects on PET signal should be significantly less than those seen here. The observed differences should not affect most clinical studies (such as for detection of malignant tumors), but may potentially affect the results of sensitive quantitative, dynamic MR-PET studies if SAR levels are very high for a prolonged period of time.