Predicting peak local SAR (pSAR) in a standard MR experiment is a difficult task due to a variety of factors including anatomical variation. Parallel transmit (PTx) further complicates pSAR prediction because simulated SAR values are also dependent on array coupling. While the effect of subject variability on pSAR has been investigated¹, there has been little attention to the effect of array coupling on pSAR predictions. Due to all these unknowns, pSAR predictions are often based on a conservative worst case setting. Understanding how SAR is related to coupling, combined with more accurate subject-specific body models, will reduce the overly conservative B1+ and duty cycle restrictions on pTx arrays.

The current practice in PTx SAR prediction is to rely on numerical FDTD simulations. Circuit co-simulation^2,3 has been introduced as a way to quickly achieve optimal tuning, matching, and coupling of an array in the simulation environment with a given load. However, real physical array coupling is rarely optimal and is also load dependent. PTx simulations where the coupling does not match the physical coupling are, in most cases, incorrectly estimating pSAR. We propose a technique to measure the real S-matrix of the in-situ array/subject setup and then match it in simulation using circuit co-simulation with a modified cost function.

The proposed method was tested at 7T using a 4-ch Tx/Rx head array consisting of four rectangular loop coils distributed 90° apart (modeled in Fig.1). The array was loaded with a 10 cm diameter spherical phantom with known dielectric properties.

Directional couplers were installed in the transmit path of a Philips 7T MRI. The couplers were calibrated to measure the forward and reflected propagating waves at the coil connection plane. The S-matrix is computed from a quick dynamic sequence where forward power is delivered to one channel at a time and the reflections are monitored on all channels.

The experimental setup was modeled and simulated using Sim4Life (ZMT AG, Zurich). For co-simulation, all capacitors and sources were simulated as transmitting ports while the remaining ports were terminated with 50 ohms.

In co-simulation, the ideal capacitor values are found through optimizing the S-matrix based on a target cost function. A typical cost function for optimal array tuning is the 2-norm of the simulated S-matrix (i.e. minimum reflected power). Here we define a modified cost function as the 2-norm of the difference between the simulation output S-matrix ($$$S_{out}$$$) and the measured S-matrix.

$$cost=\|S_{out}(C)-S_{measured}\|$$

The optimization returns a vector of capacitor values, C, such that the complex difference between measured and simulated S-matrix is minimized. Co-simulation was implemented using python scripting in conjunction with Sim4Life.

Simulations were compared to measured B1+ maps. B1+ was calculated using low flip angle gradient echo (low FA GE) images for good dynamic range. The sequence used a sufficiently long TR (50ms) and a 10° flip angle to ensure signal intensity is proportional to B1+. B1- was divided out after determining B1- as the ratio of a quadrature dual TR B1+ map⁴ and quadrature low FA GE image.

The realistic co-simulation method approximates the measured S-matrix with good agreement - All entries of the simulated S-matrix differ from the measured S-matrix by less than -19.5 dB (negligible difference in power coupling). In contrast, using co-simulation to simulate an array tuned for minimum reflected power produces a noticeably different S-matrix.

Fig.3 shows the measured B1+ maps compared to simulated B1+ maps using both co-simulated S-matrices. The simulated B1+ maps include pSAR calculated for the corresponding drive configuration.

Although the B1+ pattern looks relatively similar for each drive, there is a difference in pSAR values of up to 43%, highlighting the effect of coupling on pSAR prediction. Based on the similarity of the B1+ measurements compared to realistically tuned simulation (Fig.3), we confirm that matching simulated and physical array coupling tends to improve simulation accuracy.

In this example, the physical array is fairly well tuned (i.e. similar to the minimum reflection case). However, manufacturing error or uneven loading could potentially lead to less ideal coupling. To demonstrate this situation, we performed the proposed method with an S-matrix measured during array assembly, when one element was still poorly tuned (Fig.4a). This coupling condition yields pSAR that exceed that of the ideally coupled array in one case by over 40% (Fig.4b).

Using this modified circuit co-simulation method, SAR can be re-evaluated before every scan session based on a measured S-matrix in under a couple minutes. This method, used in conjunction with detailed, subject specific body models¹, would facilitate accurate pSAR predictions in pTx experiments.