Simple linear formulation for magnetostimulation specific to MRI gradient coils

A simple linear formulation for magnetostimulation thresholds specific to MRI gradient coils is derived based on established hyperbolic electrostimulation strength vs. duration relations. Thresholds are derived in terms of the gradient excursion required to cause stimulation, and it is demonstrated that the threshold curve is a linear function of the gradient switching time. A parameter beta is introduced as being fundamental in the evaluation of gradient coil stimulation. beta is a map of the induced electric field per unit gradient slew rate, and can be calculated directly from the gradient coil wire pattern. Consideration of beta alone is sufficient to compare stimulation thresholds between different gradient coil designs, as well as to evaluate the expected dependency of stimulation threshold on position within the gradient coil. The linear gradient threshold curve is characterized by two parameters: SR(min) and DeltaG(min). SR(min) is the slope of the threshold curve and represents the minimum slew rate required to cause stimulation in the limit of infinite gradient strength. DeltaG(min) is the vertical axis intercept of the curve and represents the minimum gradient excursion required to cause stimulation in the limit of infinite slew rate. Both SR(min) and DeltaG(min) are functions of both beta and the standard tissue parameters E(r) (rheobase) and tau(c) (chronaxie time). The ease with which both the gradient system performance and the stimulation thresholds can be plotted on the same axes is noted and is used to introduce the concept of a piece-wise linear operational limit curve for a gradient system.