Derivation and properties of the convolution model for MRI gradient-induced cardiac stimulation

<i>Objective.</i>Reliable prediction of gradient-induced peripheral nerve stimulation (PNS) and cardiac stimulation (CS) is important to ensure patient safety and maximize imaging performance in modern MRI scanners. Here we extend the dynamic convolution-based PNS prediction model to CS, and present theoretical analysis and numerical survey of general properties of the convolution model.<i>Approach.</i>CS convolution kernel was derived from the exponential model of the strength-duration curve of excitable tissue stimulation with representative stimulation parameters for a whole-body gradient coil. Self-consistency of the convolution method and the properties of the convolution output (response function) for a periodic trapezoidal wave were theoretically analyzed. PNS and CS response functions were computed for clinical 3T brain and pelvic imaging sequences for comparison.<i>Main results.</i>CS convolution kernel takes the form of a simple, decaying exponential function. For both PNS and CS kernels, the convolution model is consistent with the strength-duration curve when applied to a rectangular d<i>G</i>/d<i>t</i>pulse. The long time constant of a CS kernel tends to suppress stimulation by short d<i>G</i>/d<i>t</i>pulses, and makes dynamic CS response correlate more with gradient amplitude than slew rate. On a trapezoidal gradient pulse train, the maximum PNS or CS occurs at the end of the first full slope of the waveform, independent of the number of cycles. In light of the available evidence to the contrary, such independence indicates limitation of the convolution model which is strictly linear.<i>Significance.</i>The proposed CS convolution model can supplement existing PNS models to better assess patient safety of arbitrary gradient waveforms. General theoretical properties of the convolution model can help guide waveform design to minimize risks. While our method was demonstrated primarily on whole-body gradient systems, it can also inform PNS and CS prediction for anatomy-specific scanners employing fast and strong gradient fields.