Dynamic causal modelling of phase-amplitude interactions

Abstract

Models of coupled oscillators are used to describe a wide variety of phenomena in neuroimaging. These models typically rest on the premise that oscillator dynamics do not evolve beyond their respective limit cycles, and hence that interactions can be described purely in terms of phase differences. Whilst mathematically convenient, the restrictive nature of phase-only models can limit their explanatory power. We therefore propose a generalisation of dynamic causal modelling that incorporates both phase and amplitude. This allows for the separate quantifications of phase and amplitude contributions to the connectivity between neural regions. We establish, using model-generated data and simulations of coupled pendula, that phase-only models perform well only under weak coupling conditions. We also show that, despite their higher complexity, phase-amplitude models can describe strongly coupled systems more effectively than their phase-only counterparts. We relate our findings to four metrics commonly used in neuroimaging: the Kuramoto order parameter, crosscorrelation, phase-lag index, and spectral entropy. We find that, with the exception of spectral entropy, the phase-amplitude model is able to capture all metrics more effectively than the phase-only model. We then demonstrate, using local field potential recordings in rodents and functional magnetic resonance imaging in macaque monkeys, that amplitudes in oscillator models play an important role in describing neural dynamics in anaesthetised brain states.

Conservation laws by virtue of scale symmetries in neural systems

“…In fact, as we show in Eqs (28) to (30) (see Materials and Methods), the only way for a classical 1D time-independent Lagrangian to qualify as scale-symmetric is if its potential energy term varies as the inverse square of position. More generally, we show that a scale-free dynamical system that follows the principle of stationary action is only scale-symmetric in the special case that its Lagrangian scales inversely with time (see Eq (12) in Materials and Methods).…”

“…The macaque monkey was sedated with dexdomitor (0.02 mg/kg IM), ketamine (8 mg/kg IM), atropine (0.05 mg/kg IM), and maintained at an isoflurane level of 0.75% following intubation. Pre-processing of the murine calcium imaging [11] and macaque monkey fMRI [12] datasets were carried out as described previously. We show all results obtained for the resting states in Fig 2. The calcium imaging data were collected across an entire hemisphere of mouse cortex (Fig 2A & 2B).…”

“…where x, y and z are constants and C xyz is an arbitrary expansion coefficient. Using (12) we see that (13) is scale-symmetric if:…”

“…From (12) we know that a scale symmetry exists if and only if L s ¼ l À a L, implying that 2(1 −α) = p = −α and hence that α = 2 and p = −2.…”

Perinatal Inflammation: Could Partial Blocking of Cell Adhesion Molecule Function Be a Solution?

“…This disease clinically presents with epistaxis, purpura, and bleeding as a result of an either qualitative or quantitative defect on platelets and recurrent infections without abscesses or leykocytosis. There are also reported cases of osteopetrosis due to the impact of gene mutations on osteoclast function [ 74 , 75 , 76 ]. Whereas the expression of LFA-1 and Mac-1 remains normal, these ligands function defectively [ 77 ].…”