Liquid infusion apparatus includes non-magnetic materials in a pumping structure and ultrasonic drive motor therefor, and in a controller that supplies drive signals to the motor to facilitate convenient operation in intense magnetic fields without distorting the magnetic fields and without radiating objectionable radio-frequency interference. A non-MRI-compatible liquid infusion apparatus is temporarily replaced with MRI-compatible, non-magnetic liquid infusion apparatus without disconnecting a patient from an installed intravenous infusion set to continue infusing liquid within the MRI environment. The pumping apparatus operates on a segment of a liquid conduit that is mounted in tension between a linear peristaltic pump and platen, with associated safety interlocks to assure proper operation of infusing liquid into a patient compatibly with conditions in an MRI environment. Drive circuitry generates low-harmonic signals for operating the ultrasonic motor at variable speeds to compensate for flow rate discontinuities through the peristaltic pumping cycles.