Neural Geometrodynamics, Complexity, and Plasticity: A Psychedelics Perspective

Abstract

We explore the intersection of neural dynamics and the effects of psychedelics in light of distinct timescales in a framework integrating concepts from dynamics, complexity, and plasticity. We call this framework neural geometrodynamics for its parallels with general relativity's description of the interplay of spacetime and matter. The geometry of trajectories within the dynamical landscape of "fast time" dynamics are shaped by the structure of a differential equation and its connectivity parameters, which themselves evolve over "slow time" driven by state-dependent and state-independent plasticity mechanisms. Finally, the adjustment of plasticity processes (metaplasticity) takes place in an "ultraslow" time scale. Psychedelics flatten the neural landscape, leading to heightened entropy and complexity of neural dynamics, as observed in neuroimaging and modeling studies linking increases in complexity with a disruption of functional integration. We highlight the relationship between criticality, the complexity of fast neural dynamics, and synaptic plasticity. Pathological, rigid, or "canalized" neural dynamics result in an ultrastable confined repertoire, allowing slower plastic changes to consolidate them further. However, under the influence of psychedelics, the destabilizing emergence of complex dynamics leads to a more fluid and adaptable neural state in a process that is amplified by the plasticity-enhancing effects of psychedelics. This shift manifests as an acute systemic increase of disorder and a possibly longer-lasting increase in complexity affecting both short-term dynamics and long-term plastic processes. Our framework offers a holistic perspective on the acute effects of these substances and their potential long-term impacts on neural structure and function.

Keywords: complexity; plasticity; psychedelics.

Figure A1

Conceptual funnel of terms between the NGD (neural geometrodynamics), Deep CANAL [48], CANAL [11], and REBUS [12] frameworks. The figure provides an overview of the different frameworks discussed in the paper and how the concepts in each relate to each other, including their chronological evolution. We wish to stress that there is no one-to-one mapping between the concepts as different frameworks build and expand on the previous work in a non-trivial way. In red, we highlight the main conceptual leaps between the frameworks. See the main text or the references for a definition of all the terms, variables, and acronyms used.

Figure 1

Neural Geometrodynamics: a dynamic interplay between brain states and connectivity. A central element in the discussion is the dynamic interplay between brain state (x) and connectivity (w), where the dynamics of brain states is driven by neural connectivity while, simultaneously, state dynamics influence and reshape connectivity through neural plasticity mechanisms. The central arrow represents the passage of time and the effects of external forcing (from, e.g., drugs, brain stimulation, or sensory inputs), with plastic effects that alter connectivity ( $\dot{w}$ , with the overdot standing for the time derivative).

Figure 2

Dynamics of a pendulum with friction. Time series, phase space, and energy landscape. Attractors in phase space are sets to which the system evolves after a long enough time. In the case of the pendulum with friction, it is a point in the valley in the “energy” landscape (more generally, defined by the level sets of a Lyapunov function).

Figure 3

Geometrodynamics of the acute and post-acute plastic effects of psychedelics. The acute plastic effects can be represented by rapid state-independent changes in connectivity parameters, i.e., the term $\psi (w;\gamma )$ in Equation (3). This results in the flattening or de-weighting of the dynamical landscape. Such flattening allows for the exploration of a wider range of states, eventually creating new minima through state-dependent plasticity, represented by the term $h(x,w;\alpha )$ in Equation (3). As the psychedelic action fades out, the landscape gradually transitions towards its initial state, though with lasting changes due to the creation of new attractors during the acute state. The post-acute plastic effects can be described as a “window of enhanced plasticity”. These transitions are brought about by changes of the parameters $\gamma$ and $\alpha$ , each controlling the behavior of state-independent and state-dependent plasticity, respectively. In this post-acute phase, the landscape is more malleable to internal and external influences.

Figure 4

Psychedelics and psychopathology: a dynamical systems perspective. From left to right, we provide three views of the transition from health to canalization following a traumatic event and back to a healthy state following the acute effects and post-acute effects of psychedelics and psychotherapy. The top row provides the neural network (NN) and effective connectivity (EC) view. The circles represent nodes in the network and the edge connectivity between them, with the edge thickness representing the connectivity strength between the nodes. The middle row provides the landscape view, with three schematic minima and colors depicting the valence of each corresponding state (positive, neutral, or negative). The bottom row represents the transition probabilities across states and how they change across the different phases. Due to traumatic events, excessive canalization may result in a pathological landscape, reflected as deepening of a negative valence minimum in which the state may become trapped. During the acute psychedelic state, this landscape becomes deformed, enabling the state to escape. Moreover, plasticity is enhanced during the acute and post-acute phases, benefiting interventions such as psychotherapy and brain stimulation (i.e., changes in effective connectivity). Not shown here is the possibility that a deeper transformation of the landscape may take place during the acute phase (see the discussion on the wormhole analogy in Section 4).

Figure 5

General Relativity and Neural Geometrodynamics. Left: Equations for general relativity (the original geometrodynamics), coupling the dynamics of matter with those of spacetime. Right: Equations for neural geometrodynamics, coupling neural state and connectivity. Only the fast time and slow time equations are shown (ultraslow time endows the “constants” appearing in these equations with dynamics).

Figure 6

A hypothetical psychedelic wormhole. On the left, the landscape is characterized by a deep pathological attractor which leads the neural state to become trapped. After ingestion of psychedelics (middle) a radical transformation of the neural landscape takes place, with the formation of a wormhole connecting the pathological attractor to another healthier attractor location and allowing the neural state to tunnel out. After the acute effects wear off (right panel), the landscape returns near to its original topology and geometry, but the activity-dependent plasticity reshapes it into a less pathological geometry.