Proposed framework:

A) Large-scale brain dynamics are constrained by energy balance and ongoing physiological inputs.

B) Cognitive performance depends on the alignment between neural metastability and fluctuations in peripheral energy, a relationship conceptualized here as Body Energy Coupling. Within this framework, metabolism is not merely a constraining variable; rather, it reflects a regulated and coordinated interaction between brain and body oscillatory processes. Cognition can thus be understood as an emergent property—or rebound—of metabolic homeostasis.

From this perspective, vulnerability arises from a disequilibrium between predictive (or active inference) processes and energy homeostasis mechanisms, leading to maladaptive system dynamics.

This view is still preliminary and exploratory, as there is currently no empirical evidence supporting this theory; rather, it serves as a proof of concept.

Diego Lombardo. Cross-Scale Energy Coordination in Brain–Body Systems Supports Cognitive Function Across the Lifespan, 31 March 2026, PREPRINT (Version 1) available at Research Square [https://doi.org/10.21203/rs.3.rs-9279633/v1]

Model Architecture

1. Structural Brain Networks

Brain structure is modeled using small-world networks, which capture key properties of biological brain connectivity.

Networks are generated using a Watts–Strogatz procedure with sizes:

• 40 nodes

• 80 nodes

• 120 nodes

Edges are partially rewired to introduce long-range connections.
Connectivity matrices are normalized by their largest eigenvalue to maintain stable dynamics across network sizes.

2. Peripheral Physiology

Two physiological oscillators are simulated:

• Cardiac rhythm

• Respiratory rhythm

These signals:

• act as external modulatory inputs to the neural network

• contribute to metabolic energy production

The oscillators evolve with stochastic phase noise to mimic physiological variability.

3. Neural Dynamics

Each node in the network follows a Stuart–Landau oscillator equation, a standard model for neural population dynamics.

Neural activity evolves according to:

• intrinsic oscillatory frequency

• network coupling

• physiological inputs

• metabolic energy feedback

• stochastic noise

This produces complex large-scale neural coordination patterns similar to those observed in resting-state brain activity.

Neural power is defined as the squared amplitude of oscillator activity, and the global brain signal is the average power across nodes.

4. Metabolic Energy Dynamics

A dynamic energy variable represents metabolic resource availability.

Energy evolves as a balance between:

Production

• driven by cardiac and respiratory signals

Consumption

• proportional to neural activity

Decay

• representing metabolic dissipation

This creates bidirectional coupling:

• neural activity consumes energy

• energy availability feeds back into neural dynamics

Extracted Dynamical Metrics

Several system-level metrics are computed from the simulations:

Metastability

Temporal variability of global neural synchronization.

Brain–Heart Coherence

Phase coherence between the global neural signal and the cardiac rhythm.

Forward Modeling

A measure of the temporal responsiveness of the neural system, defined as the root-mean-square change in neural activity.

Energy Stability

Variability of the energy time series.

Energy Efficiency

Mean energy level maintained by the system.

Synthetic Cognition

To approximate an emergent cognitive outcome, the model defines a synthetic cognition variable:

Csyn=w1FM+w2M+w3C+ϵC_{syn} = w_1 FM + w_2 M + w_3 C + \epsilonCsyn=w1FM+w2M+w3C+ϵ

where

• FM = forward modeling

• M = metastability

This variable represents a computational proxy of cognitive function emerging from system dynamics.

To avoid circularity, a separate model was used to test mediation effects (sup matieral). GlobalCognition is a synthetic proxy of a general cognitive factor (G-like construct), combining structural integration and predictive neural dynamics. It is independent of the predictors, ensuring that no circularity arises in these analyses.

Formaly here: GlobalCognition = 0.6*G + 0.4*predictive_metric(power)

Dataset Generation

The simulation generates large synthetic populations of subjects.

For each network:

• 50 random seeds

• 200 simulated subjects per seed

Subject-level parameters include:

• age (20–80 years)

• neural coupling strength

• neural noise amplitude

Each simulation produces:

• neural dynamical metrics

• physiological summaries

• energy measures

• synthetic cognition values

To handle the large dataset, results are saved incrementally to disk.

Statistical Analysis

The code evaluates whether neural dynamical metrics predict energy and cognition outcomes.

Cross-validated regression

Predictive models use 10-fold cross-validation controlling for age.

Performance is quantified with:

Cross-validated R²

Permutation testing

Statistical significance is assessed using 100 permutation tests to generate null distributions.

Multiple comparison correction

P-values are corrected using:

• Bonferroni correction

• False Discovery Rate (FDR)

Figures Generated by the Code

The script automatically produces publication-quality figures used in the paper.

Figure 1 — Predictors of Energy Stability and Efficiency

Bar plots comparing predictive power of:

• Metastability

• Brain–Heart Coherence

• Forward Modeling

• Null Model

for predicting:

• energy stability

• energy efficiency

These results correspond to Table 2 in the paper.

The figure demonstrates that:

• Brain–Heart Coherence

• Forward Modeling

significantly predict energy outcomes.

Figure 2 — Predictors of Synthetic Cognition

Bar plot showing cross-validated R² values for predicting the synthetic cognition variable.

This corresponds to Table 1 in the paper and demonstrates that:

• Brain–Heart Coherence

• Forward Modeling

predict cognitive outcomes, whereas metastability does not.

Figure 3 — Correlation Structure of Brain–Body Metrics

A heatmap visualizing correlations between:

• metastability

• brain–heart coherence

• forward modeling

• synthetic cognition

This illustrates the relationship structure among dynamical predictors.

Figure 4 — Lifespan Trajectories

Age-binned correlations show how the relationship between neural metrics and energy outcomes changes across the simulated lifespan.

This analysis supports the paper's claim that:

brain–body coordination may reflect vulnerability trajectories across the lifespan.

Figure 5 — Peripheral Physiology and Energy Efficiency

Scatter plots showing associations between:

• cardiac activity

• respiratory activity

and energy efficiency.

This demonstrates how peripheral physiology contributes to metabolic regulation in the simulated system.

Key Findings Reproduced by the Code

The simulations reproduce several core results reported in the paper:

1. Brain–heart coupling predicts energy efficiency

2. Forward modeling predicts synthetic cognition

3. Metastability alone has limited predictive value

4. Age-related changes in brain–body coordination correspond to reduced energetic stability

These findings suggest that cognitive outcomes emerge from energy-constrained brain–body dynamics rather than neural coordination alone.

Output Files

Running the script produces:

Purpose of the Repository

This code provides a reproducible computational framework for studying:

• brain–body interactions

• metabolic constraints on neural dynamics

• emergent cognition in complex systems

The model can serve as a testbed for theoretical neuroscience, computational psychiatry, and brain–body medicine.

References:

Attwell D, Laughlin SB. An energy budget for signaling in the grey matter of the brain. J Cereb Blood Flow Metab. 2001 Oct;21(10):1133-45. doi: 10.1097/00004647-200110000-00001. PMID: 11598490.

Raichle, M. E., MacLeod, A. M., Snyder, A. Z., Powers, W. J., Gusnard, D. A., & Shulman, G. L. (2001). A default mode of brain function. Proceedings of the National Academy of Sciences of the United States of America, 98(2), 676–682.

Magistretti, P., & Allaman, I. (2018). Lactate in the brain: from metabolic end‑product to signalling molecule. Nature Reviews Neuroscience, 19, 235–249.

Critchley, H. D., & Harrison, N. A. (2013). Visceral influences on brain and behavior. Neuron, 77(4), 624–638. https://doi.org/10.1016/j.neuron.2013.02.008