Combined use of transcranial magnetic stimulation and metal electrode implants: a theoretical assessment of safety considerations

This paper provides a theoretical assessment of the safety considerations encountered in the simultaneous use of transcranial magnetic stimulation (TMS) and neurological interventions involving implanted metallic electrodes, such as electrocorticography. Metal implants are subject to magnetic forces due to fast alternating magnetic fields produced by the TMS coil. The question of whether the mechanical movement of the implants leads to irreversible damage of brain tissue is addressed by an electromagnetic simulation which quantifies the magnitude of imposed magnetic forces. The assessment is followed by a careful mechanical analysis determining the maximum tolerable force which does not cause irreversible tissue damage. Results of this investigation provide useful information on the range of TMS stimulator output powers which can be safely used in patients having metallic implants. It is shown that conventional TMS applications can be considered safe when applied on patients with typical electrode implants as the induced stress in the brain tissue remains well below the limit of tissue damage.

Lower complexity bounds in justification logic

Justification Logic studies epistemic and provability phenomena by introducing justifications/proofs into the language in the form of justification terms. Pure justification logics serve as counterparts of traditional modal epistemic logics, and hybrid logics combine epistemic modalities with justification terms. The computational complexity of pure justification logics is typically lower than that of the corresponding modal logics. Moreover, the so-called reflected fragments, which still contain complete information about the respective justification logics, are known to be in~NP for a wide range of justification logics, pure and hybrid alike. This paper shows that, under reasonable additional restrictions, these reflected fragments are NP-complete, thereby proving a matching lower bound. The proof method is then extended to provide a uniform proof that the corresponding full pure justification logics are $\Pi^p_2$-hard, reproving and generalizing an earlier result by Milnikel.