A neural mass model of cross frequency coupling

Abstract

Electrophysiological signals of cortical activity show a range of possible frequency and amplitude modulations, both within and across regions, collectively known as cross-frequency coupling. To investigate whether these modulations could be considered as manifestations of the same underlying mechanism, we developed a neural mass model. The model provides five out of the theoretically proposed six different coupling types. Within model components, slow and fast activity engage in phase-frequency coupling in conditions of low ambient noise level and with high noise level engage in phase-amplitude coupling. Between model components, these couplings can be coordinated via slow activity, giving rise to more complex modulations. The model, thus, provides a coherent account of cross-frequency coupling, both within and between components, with which regional and cross-regional frequency and amplitude modulations could be addressed.

Fig 1. Schematic diagram of the proposed model.

Each node is comprised of four neural population units: pyramidal neurons, excitatory interneurons, slow inhibtory interneurons and fast ihbitory internneurons. Each node is identical to the NMM in [36]. The nodes are mutually connected by the dynamics of the pyramidal neurons. Two independent Gaussian noise sources drive the NMM nodes.

Fig 2. Phase-Frequency Coupling (PFC) simulation.

Time domain signals are shown for visual inspection of each CFC. FO₁, SO₁, FO₂ and SO₂ are the filtered output of the Node 1 and Node 2 respectively. The frequency of FO₁ varies between positive (yellow stripes) and negative (green stripes) phases of SO₁. SO₁ and SO₂ are synchronized (i.e., cross-node PPC). Integers below the FO time waves are average numbers of FO zero crossings, which is used as an index of average frequency of each phase. Local PFC between FO₁ and SO₁ and cross-node PFC between FO₁ and SO₂ are observed.

Fig 3. Phase-Amplitude Coupling (PAC) simulation.

The instantaneous amplitude of FO₁ correlates with the synchronized SO₁ and SO₂. Local PAC between FO₁ and SO₁ and cross-node PAC between FO₁ and SO₂ are observable. Integers below the FO time waves indicate average number of zero crossings of FOs.

Fig 4. Frequency-Frequency Coupling (FFC) simulation.

The frequency of FO₁ and FO₂ varies for the synchronized SO₁ and SO₂. Integers below the FO time waves are the average number of zero crossings, which is an index of average frequency of each phase. The numbers change between positive and negative phases of synchronized SO₁ and SO₂. Local PFC between FO₁ and SO₁, and between FO₂ and SO₂ are also observed.

Fig 5. Amplitude-Amplitude Coupling (AAC) simulation.

The instantaneous amplitude of FO₁ and FO₂ correlate with the synchronized SO₁ and SO₂. Integers below the FO time waves indicate average number of zero crossings of FOs.

Fig 6. Amplitude-Frequency Coupling (AFC) simulation.

The instantaneous amplitude of FO₁ correlates with the synchronized SO₁ and SO₂. The frequency of FO₂ is about constant while the frequency of FO₁ varies for the synchronized SO₁ and SO₂. See average number of zero crossings in FOs, indicated as integers below the FO time waves.

Fig 7. The comparison of PSDs in different forms of CFC.

PFC: Phase-Frequency Coupling, PAC: Phase-Amplitude Coupling, FFC: Frequency-Frequency Coupling, AAC: Amplitude-Amplitude Coupling, AFC: Amplitude-Frequency Coupling.