The MRI Heating Bound: Specific Absorption Rate as the Wall Behind Field Strength

Magnetic resonance imaging gains signal with static field strength, but the radiofrequency power deposited in a conducting body grows faster than the signal. From Faraday's law for a cylindrical body model (radius 0.15 m, conductivity 0.50 S/m), the volume-averaged specific absorption rate (SAR) during a pulse is proportional to B0 squared at fixed pulse duration, and to B0 to the fourth power when pulse bandwidth in parts per million is preserved (so duration falls as 1/B0 and B1 rises as B0). Against a whole-body ceiling of 4.0 W/kg, the allowed number of canonical 180-degree, 1.0 ms pulses per second falls from 256.18 at 1.5 T to 64.04 at 3.0 T, 11.76 at 7.0 T and 5.23 at 10.5 T in the fixed-duration regime, and to 32.02, 2.52 and 0.75 in the fixed-bandwidth regime. At a fixed duty cycle of 0.10 the largest permitted flip angle falls from 288.1 degrees at 1.5 T to 41.2 degrees at 10.5 T (5.9 degrees in the stricter regime). At the ceiling, poorly perfused tissue warms adiabatically at 0.0686 K/min, reaching 1.029 K in 15 minutes. The field-strength ladder is thus repriced as a heating budget: SAR, not signal-to-noise ratio, is the binding constraint on refocusing-heavy sequence design from 3 T upward. All numbers are produced by the deposited compute.py. This is a physics bound only, not clinical guidance. AI use is disclosed: this paper was prepared with the assistance of Dave, an AI system, which carried out the derivation, computation and drafting under the direction of the named author. William Alexander Aldred is sole author of record.