Face to phase: pitfalls in time delay estimation from coherency phase

Abstract

Coherency phase is often interpreted as a time delay reflecting a transmission delay between spatially separated neural populations. However, time delays estimated from corticomuscular coherency are conflicting and often shorter than expected physiologically. Recent work suggests that corticomuscular coherence is influenced by afferent sensory feedback and bidirectional interactions. We investigated how bidirectional interaction affects time delay estimated from coherency, using a feedback model of the corticomuscular system. We also evaluated the effect of bidirectional interaction on two popular directed connectivity measures: directed transfer function (DTF) and partial directed coherence (PDC). The model is able to reproduce the range of time delays found experimentally from coherency phase by varying the strengths of the efferent and afferent pathways and the recording of sensory feedback in the cortical signal. Both coherency phase and DTF phase were affected by sensory feedback, resulting in an underestimation of the transmission delay. Coherency phase was altered by the recording of sensory feedback in the cortical signals and both measures were affected by the presence of a closed loop feedback system. Only PDC phase led to the correct estimation of efferent transmission delay in all simulated model configurations. Coherency and DTF phase should not be used to estimate transmission delays in neural networks as the estimated time delays are meaningless in the presence of sensory feedback and closed feedback loops.

Nonlinear Coupling between Cortical Oscillations and Muscle Activity during Isotonic Wrist Flexion

“…The nonlinear coupling was shown in the similar ratios as previously reported in the somatosensory studies with both integer multiples and the 2:3 non-integer multiple. Since there is no significant “asymmetry” effect, we suggest that the ratios of n:m and m:n likely come from the same type of nonlinearity but appear in a reciprocal to each other due to the closed-loop effect of sensorimotor system (Schouten and Campfens, 2012; Campfens et al, 2014). …”

“…Thereby, coupled oscillations have also been detected in the somatosensory cortex and sensory association areas such as posterior parietal cortex (PPC; Witham et al, 2007, 2010; Meng et al, 2008). Thus, corticomuscular coupling is mediated in a closed-loop (Schouten and Campfens, 2012; van Wijk et al, 2012; Campfens et al, 2014). …”

Unveiling neural coupling within the sensorimotor system: directionality and nonlinearity

“…Voluntary movement control is initiated in the brain but also involves somatosensory feedback. Abundant evidence indicates that the oscillatory corticomuscular interactions originate not only from descending motor command but also is affected by ascending somatosensory feedback (Baker et al ., ; Baker, ; Witham et al ., ; Campfens et al ., , ). However, CMC cannot separate this bidirectionality in corticomuscular interaction; and more advanced measures are necessary to assess directionality (Witham et al ., ; Campfens et al ., ).…”

Cortico-Muscular Coherence with Time Lag with Application to Delay Estimation

“…Unfortunately, their work has rarely been used in physiological studies, which could be due to its technical sophistication and underlying assumptions which are difficult to verify in practice. Further, there is evidence of bidirectional connectivity in the motor control system [15]- [17] and the delay estimated from phase spectrum is subject to errors if the coupling is bidirectional in the estimated period [18], [19]. Although some groups have considered directed coherence based on the Granger causality [15], [20]- [22] which in principle can discern different propagation directions, the results vary much from individual to individual.…”