Gaussian Process–Based Bayesian Optimization of Lower-Limb PNS–TMS Interstimulus Intervals in Adults and Children: A Proof-of-Concept Toward a Personalized Framework

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Abstract Background Peripheral nerve stimulation (PNS) before transcranial magnetic stimulation (TMS) can modulate lower-limb motor evoked potentials (MEPs), but individualized interstimulus interval (ISI) selection remains unclear, particularly in children. Methods Ten adults and eight children were tested. Common peroneal nerve PNS preceded TMS of the tibialis anterior (TA) hotspot at 26 latency-referenced ISIs. Adults completed sensory- and motor-threshold PNS; children completed motor-threshold PNS only. Gaussian process (GP) regression modeled ISI–response profiles, and retrospective GP-based Bayesian optimization (GPBO) was benchmarked against random sampling, with population-informed initialization evaluated separately. Results In adults, PNS condition, ISI, and their interaction significantly affected TA, soleus, and gastrocnemius responses (all p < 0.001); in children, ISI significantly affected all three muscles. GP regression reproduced motor-threshold TA profiles with mean R² values of 0.91 in adults and 0.66 in children, with leave-one-ISI-out R² values of 0.71 and 0.18. GP regression improved profile recovery with one repetition per ISI. In adults, GPBO reached threshold in 9/10 participants with a median of 10 [IQR: 8–17] stimulations versus 20 [13–66] with random sampling (9/10). In children, corresponding values were 45 [24–60] in 5/8 versus 56 [35–79] in 4/8. Population-informed initialization provided no consistent benefit. Conclusion Lower-limb PNS–TMS responses are timing dependent and individualized. GP modeling and GPBO may support efficient individualized ISI characterization, particularly in adults. Greater pediatric response variability and weaker predictability may make reliable identification of a consistently high-performing ISI more difficult.