Experimental (blue) and simulated (red) PNS threshold curves with varying pulse durations for trapezoidal and sinusoidal current waveforms applied to BG1 gradient coils in the imaged subject position. The PNS threshold is denoted as the minimum magnetic field gradient strength capable of inducing a PNS

Figure 3 illustrates the experimental and simulated PNS thresholds as they relate to pulse duration (\(\tau\)) for both trapezoidal and sinusoidal gradient waveforms when applied to BG1 gradient coils. In this figure, the blue curves denote experimental data, whereas the red curves indicate simulation outcomes. The simulated thresholds for the female model were consistently higher than those for the male model at the same pulse duration. In terms of accuracy, compared to the average experimental findings, the female and male models’ average thresholds displayed normalized root-mean-square errors (NRMSE) of 13.6%, 21.3%, 28.6%, and 15.7% for the Y-axis trapezoidal, Y-axis sinusoidal, combined X+Y axes, and combined X+Y+Z axes respectively. However, the experimental results were more closely aligned with the thresholds of the female model, showing NRMSEs of 6.38%, 7.47%, 10%, and 5.27% for these respective cases.

Electric fields (maximum intensity projection) generated by the BG1 y-gradient coil for female (a) and male (b) models in the imaged subject position, respectively. To enhance visibility of electric field distribution in other body regions, the electric field within the bones was set to 0, as it is typically very high. The stimulated nerves and the first stimulated sites were also indicated with light green curves and dark green squares, respectively

Figure 4 depicts the electric field magnitudes observed in the two human body models positioned as a typical imaged subject, generated by the Gy channel of the BG1 gradient coil. The head of the subject being measured was located within the imaging FOV as shown in Fig. 1a. Areas in proximity to the shoulders, ribs, and hipbones were notable for their high electric field magnitudes. Additionally, the male and female models demonstrated subtle differences in the distribution of these electric fields. Specifically, the shoulder region of the male model exhibited a significantly higher electric field compared to the female model. Conversely, in certain areas around the ribs and the lower body, the female model experienced higher electric fields than the male model. Figure 4 also identifies the stimulated sites in both the female and male human body models for the BG1 Gy gradient coil, with primary stimulation occurring at the suprascapular nerves.

Comparison of PNS thresholds between the imaged subject and interventionalist positions for AG gradient coils. Here, the configurations labeled as ’Female Head,’ ’Average Head,’ and ’Male Head’ correspond to the case of the imaged subject’s position. Various rotational positions of the arm were considered, including Arm0, Arm-15, and Arm15, as shown in Fig. 2. Four different combined axes modes (X+Y+Z, X-Y+Z, X-Y-Z, and X+Y-Z) were investigated, employing three directional gradients generated by AG Gx, Gy, and Gz coils

Figure 5 displays the PNS threshold curves for both the patient position, serving as a reference, and various interventionalist positions with differing arm rotations. In comparison to the imaged subject position, the average thresholds for all interventionalist positions increased by a factor of at least 3.63, 2.69, 2.4, and 4.48 times in the combined axes modes of X+Y+Z, X-Y+Z, X-Y-Z, and X+Y-Z, respectively. Notably, in the X-Y-Z mode for the male model, the lowest among all modes evaluated for the interventionalist, the thresholds were at least double that of the average patient position threshold.

As illustrated in Fig. 5, variations in an interventionalist’s arm rotation induced differing changes in PNS thresholds across various combined axes modes, depending on the body model. For the female interventionalist model, arm rotations of ±15\(^\) from the middle position resulted in PNS threshold fluctuations of up to 25.4%, 4.8%, 18.1%, and 8.1% in the X+Y+Z, X-Y+Z, X-Y-Z, and X+Y-Z modes, respectively. In the case of the male model, similar arm rotations led to threshold variations of up to 13.5%, 9.22%, 15%, and 13% in these respective modes.

The same figure also reveals that the female interventionalist consistently exhibited higher average PNS thresholds than the male counterpart, by at least factors of 1.07, 1.48, 1.14, and 1.61 in the X+Y+Z, X-Y+Z, X-Y-Z, and X+Y-Z modes, respectively. However, an exception was observed in the X-Y-Z mode, where the threshold for a female interventionalist with a 15-degree arm rotation was marginally lower than that of a male with the same arm rotation. Additionally, in the X+Y+Z mode, a −15-degree arm rotation by the female interventionalist led to a decrease in threshold by at least 1.45 times compared to the male interventionalist in the same posture.

Figure 5 also indicates that interventionalists are likely to experience nerve stimulation with various arm rotations in certain combined modes despite hardware constraints imposed by the gradient amplifiers. For instance, in the X-Y-Z mode, the calculated PNS thresholds for male interventionalists, across all three arm rotation scenarios, were within the operational region of the coils when the pulse duration ranged from 0.4 to 0.6 ms. These results can be used to guide experiments aimed at stimulating interventionalists.

Moreover, Fig. 5 highlights that male and female interventionalist thresholds can exhibit divergent trends as arm rotation angles vary, particularly in relation to the combined-axes modes. For instance, in the X-Y+Z mode, both male and female threshold levels increased as the arm rotation shifted from – 15\(^\) to 0\(^\), and further to 15\(^\). Conversely, in the X+Y-Z mode, threshold levels decreased with these angle changes for both models. However, in the X-Y-Z mode, female thresholds decreased while male thresholds increased with the change in arm angle.

Electric fields (maximum intensity projection) generated by the combined X+Y+Z gradient of AG gradient coils for female (a–\(^\)) and male (d–\(^\)) models, respectively. The first PNS stimulated sites and the located neuron were identified by dark green squares and light green curves, respectively. Since the first stimulated sites were in the arm regions, only the electric fields in those regions were presented. To better show the electric field distribution in other parts of the arm, the electric field in the bones was set to 0 since that in the bones is usually very high

Electric fields (maximum intensity projection) generated by the combined X-Y+Z gradient of AG gradient coils for female (a–c) and male (d–f) arm models, respectively. To better show the electric field distribution in other parts of the body, the electric field in the bones was set to 0 since that in the bones is usually very high

Figures 6, 7, 8, and 9 present the electric field distributions corresponding to the X+Y+Z, X-Y+Z, X-Y-Z, and X+Y-Z combined gradient modes, respectively. Notably, the X-Y-Z combined gradient mode is characterized by a comparatively higher electric field distribution than the other three combined gradient modes.

Electric fields (maximum intensity projection) generated by the combined X-Y-Z gradient of AG gradient coils for female arm models (a–c) and male arm models (d–f) as illustrated in (Fig. 2). To enhance the visualization of electric field distribution in other body parts, the electric field within the bones was set to 0 as it is typically very high. The stimulated nerves and the first stimulated sites were indicated with light green curves and dark green squares, respectively

Figures 6, 7, 8, and 9 additionally illustrate the primary PNS sites, marked by dark gray squares, along the nerve tracks in the arm regions for the X+Y+Z, X-Y+Z, X-Y-Z, and X+Y-Z combined gradient modes, respectively. These figures indicate that the location of stimulated sites varies between male and female models within the same gradient mode. For instance, in the X+Y+Z mode, the stimulation site for a female interventionalist is typically near the wrist, while for a male, it is closer to the elbow as depicted in Fig. 6. Additionally, the position of these stimulation sites can be influenced by arm movements as demonstrated in Fig. 8e, f.