Current MR safety standards significantly limit the use of some MRI gradient systems to prevent cardiac stimulation, even though there is suspicion that these limits are too restrictive. This work combines a recently developed simulation framework for Peripheral Nerve Stimulation (PNS) with electrical models of excitable cardiac tissue (ventricular muscle and Purkinje fibers) to investigate the relationship between PNS and cardiac stimulation thresholds. Considering the lack of experimental data on gradient-induced cardiac stimulation in humans, the presented simulation approach could provide valuable new insights on the mechanisms behind cardiac magnetostimulation and might eventually help to determine appropriate safety limits.
Cardiac fiber models: We add manually drawn fiber pathways that are representative of the ventricular muscle fibers and the Purkinje fibers in the normal heart (Fig. 1) to a detailed electromagnetic/nerve female body model. We model two Purkinje fiber branches that innervate the LV and RV. For the ventricular muscle fibers, we reproduce the well-known helicoidal structure by modeling ten clockwise (endocardium) and ten counterclockwise (epicardium) fiber paths.
Stimulation threshold simulation: We simulate the stimulation thresholds induced by a commercial whole-body gradient system (Siemens Sonata, three axes modeled) in our female body model following a simulation workflow described previously5. Briefly, we 1) compute the E-field induced in the body using a hexahedral magneto-quasistatic FEM solver (Sim4Life, Zurich MedTech, Switzerland), 2) project the E-field onto the nerve/cardiac fibers, and 3) compute the electrical response of the fibers to this stimulus. We model cardiac muscle fibers using the Luo-Rudy model of ventricular cells with gap-junctional coupling7,8. For the Purkinje fibers, we use the McAllister-Noble-Tsien model9 in combination with the cable equation10. Peripheral nerves are modeled using the McIntyre-Richardson-Grill model11 (Fig. 2). We compute PNS and cardiac stimulation thresholds by increasing the gradient waveform amplitude at a given frequency and for a given gradient axis until an AP is observed (“titration”). We repeat this process for frequencies in the (50–2500) Hz range.
Figure 3 shows the E-field produced by the Z-gradient in the female body model at a slew rate of 100 T/m/s. The heart zoom insert shows that the peak E-field induced on the myocardial surface is much smaller (1 V/m) than in the periphery (13 V/m peak E-field in the whole torso). Thus, the heart is electrically shielded by the rest of the body. Moreover, Fig. 3 shows that the E-field distribution on the myocardium is highly non-uniform, with a 2-fold E-field magnitude variation from apex to base.
Figure 4 shows the cardiac and PNS thresholds for the three gradient axes. In our simulations, the practical cardiac threshold is set by the ventricular muscle fibers (the Purkinje fibers are harder to stimulate). For a rise time of t=1 ms, the cardiac thresholds are 540-fold, 2740-fold and 610-fold greater than the PNS thresholds for the X-, Y-, and Z-axis, respectively. Figure 5 shows the same results translated to dB/dt units, in comparison to the IEC safety limits.
Lack of experimental data on gradient-induced cardiac stimulation makes it difficult to validate the simulation results. However, measurements from cardiac pacemaker studies might be used to this purpose. Moreover, including an automatic definition of realistic ventricular and Purkinje fiber paths12,13 might extend the number of cardiac muscle fibers evaluated.
Despite these current limitations, the preliminary simulations reproduced important theoretical predictions such as the expected large margin between the cardiac thresholds and PNS thresholds4,14 which decreases for long rise times3. The simulated cardiac thresholds are significantly higher (by at least two orders of magnitude) than the IEC safety limits for all investigated frequencies. While preliminary, our findings suggest that simulation tools might play an important role in determining appropriate safety regulations in the future.
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