  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.
