The glutamatergic modulator ketamine has been shown to rapidly reduce depressive symptoms in patients with treatment-resistant major depressive disorder (TRD). Although its mechanisms of action are not fully understood, changes in cortical excitation/inhibition (E/I) following ketamine administration are well documented in animal models and could represent a potential biomarker of treatment response. Here, we analyse neuromagnetic virtual electrode timeseries collected from the primary somatosensory cortex in 18 unmedicated patients with TRD and in an equal number of age-matched healthy controls during a somatosensory 'airpuff' stimulation task. These two groups were scanned as part of a clinical trial of ketamine efficacy under three conditions: a) baseline; b) 6-9 hours following subanesthetic ketamine infusion; and c) 6-9 hours following placebo-saline infusion. We obtained estimates of E/I interaction strengths by using Dynamic Causal Modelling (DCM) on the timeseries, thereby allowing us to pinpoint, under each scanning condition, where each subject's dynamics lie within the Poincar\'e diagram - as defined in dynamical systems theory. We demonstrate that the Poincar\'e diagram offers classification capability for TRD patients, in that the further the patients' coordinates were shifted (by virtue of ketamine) toward the stable (top-left) quadrant of the Poincar\'e diagram, the more their depressive symptoms improved. The same relationship was not observed by virtue of a placebo effect - thereby verifying the drug-specific nature of the results. We show that the shift in neural dynamics required for symptom improvement necessitates an increase in both excitatory and inhibitory coupling. We present accompanying MATLAB code made available in a public repository, thereby allowing for future studies to assess individually-tailored treatments of TRD.
