PhysBrain: Physical Principles in Brain Modeling

• PhysBrain is a computational framework that bridges physical principles with brain dynamics through multi-scale biophysical modeling and statistical energy landscapes.
• It employs delayed nonlinear network interactions and advanced neural models, such as the IPF brain model and Hodgkin–Huxley architectures, to capture neuro-mechanical behavior.
• The framework enables personalized brain simulations and digital twins with applications ranging from drug transport inference to embodied AI through differentiable simulation.

PhysBrain refers to a set of modeling and computational frameworks that aim to explicitly bridge physical principles, biophysical realism, and system-level dynamics in the study and simulation of human brains and brain-inspired systems. The PhysBrain paradigm encompasses multi-scale biophysical modeling, energy-based statistical descriptions, neuro-mechanical characterization, personalized simulation, and the extraction of physical intelligence from observation and interaction, extending to embodied artificial intelligence. It supports both mechanistic simulation and inference, leveraging physical constraints and heterogeneity across the anatomical, dynamical, and cognitive domains.

1. Conceptual Scope and Motivation

PhysBrain frameworks are unified by the goal of linking macro-level brain function, structure, and energetics to underlying physical mechanisms, measurable at the molecular, cellular, network, and tissue levels. Key motivations include:

• Capturing the high-dimensional, heterogeneous, and dissipative nature of real brains
• Enabling translation between biophysical simulation and functional/task-level prediction
• Quantifying energy usage and the efficiency of neural computations
• Providing scalable, physically-constrained models for both scientific discovery and engineered systems

The PhysBrain paradigm encompasses both forward simulation (e.g., whole-brain spiking networks, multi-physics flow models, viscoelastic finite elements) and inverse modeling (e.g., PINN-based pharmacokinetics, statistical inference of energy landscapes and probability fluxes) (Bader, 2022, Lu et al., 2023, Eliasmith et al., 2016, Horiike et al., 28 Aug 2025, Wickramasinghe et al., 16 Sep 2025, Wang et al., 2023, Morrison et al., 2023, Fumagalli et al., 2023, Chung et al., 2022, Lin et al., 18 Dec 2025).

2. Discrete Dynamical Network Models

Several core PhysBrain frameworks formulate brain activity as the evolution of a set of delayed, nonlinear interactions among network nodes, governed by physical reflection, damping, and plasticity principles.

Impulse Pattern Formulation (IPF) Brain Model

The IPF model posits that a single "viewpoint" neuron emits bursts (impulses) reflected off a network of $N-1$ reflection nodes. Each node is characterized by:

• A damping factor $\alpha_i$
• A polarization $P_i = \pm 1$ (excitatory/inhibitory)

The central system variable, $g_t$, models the inter-spike interval or burst amplitude, evolving recursively as:

$$g_t = g_{t-1} - \frac{1}{N} \Big| \sum_{i=2}^N P_i \ln(\alpha_t^i) g_{t-i} \Big| + w_2 g_t^I$$

where $w_2$ is the coupling to an external input pattern $g_t^I$. Plasticity (synaptic adaptation) is modeled by log-type updates to $\alpha_i$, reflecting spike-timing-dependent changes:

$$\alpha_t^i = \Big| \alpha_{t-1}^i + w_1 \ln[1 + (g_{t-i} - g_t)] \Big|$$

Parameter sweeps over the inhibitory/excitatory ratio $C_{in/ex}$ reveal optimal adaptation at physiological ratios (10–20% inhibitory), with convergence times matching short-term memory and ERP-relevant delays (Bader, 2022).

3. Biophysical and Statistical Mechanistic Frameworks

PhysBrain integrates biophysical realism at the neuron and network level with large-scale statistical modeling of state evolution and energy landscapes.

Conductance-based and Compartmental Neuron Models

The BioSpaun approach embeds Hodgkin–Huxley or reduced-morphology compartmental models into large-scale brain simulations (2.5 million neurons, 8 billion synapses), preserving correspondence between molecular-level perturbations (e.g., TTX sodium-channel blockade) and behavioral task output across visual, memory, and motor domains (Eliasmith et al., 2016). This architecture enables direct mapping between changes in conductance parameters and system-level behavior, a prerequisite for causal PhysBrain inference.

Statistical Energy Landscapes and Probability Flux

PhysBrain models also utilize high-dimensional Ising-type statistical mechanics frameworks, fitting asymmetric interaction matrices $J_{ij}$ to empirical transition rates among coarse-grained brain states. The decomposition:

$J_{ij} = J^{(\text{sym})}_{ij} + A_{ij}$

isolates symmetric ("energy landscape"/equilibrium) and antisymmetric ("probability flux"/nonequilibrium) components. Task-induced brain function manifests as subtle rewirings in the antisymmetric sector, shifting the pattern of irreversible probability fluxes ($\mathcal{J}_{\mu\nu}$) while leaving the symmetric energy scaffold largely invariant. The incremental metabolic cost of function-specific computation is thus minimized, consistent with measured negligible increases ($\lesssim 1\%$) in brain energy consumption across cognitive states (Horiike et al., 28 Aug 2025).

4. Multiphysics and Mechanical Characterization

PhysBrain encompasses models of tissue mechanics, fluid transport, and viscoelastic response, enabling the study of injury, transport, and dynamic interactions.

Heterogeneous Viscoelasticity

Comprehensive regional viscoelastic models represent the brain as a spatially heterogeneous medium with Prony-series–type relaxation spectra:

$G(t) = G_\infty + \sum_{i=1}^N G_i e^{-t/\tau_i}$

with empirically derived parameters (relaxation times, amplitudes, instantaneous modulus $G_0$) for cortex, white matter, hippocampus, etc. Attenuation follows fractional power laws ($\alpha(\omega) = A \omega^\gamma$) with exponents $0.77 < \gamma < 0.97$, and all relevant dispersion and stiffness parameters mapped per region and species (Morrison et al., 2023). Applications include trauma and shock formation modeling.

Multiphysics Flow and Fluid–Structure Interaction

Coupled multiphysics models, such as those discretized by high-order polytopal DG schemes, integrate multi-compartment poroelasticity and Stokes flow for blood, CSF, and tissue deformation. Interface conditions (normal-stress, flux, pressure continuity) are rigorously enforced, and the framework supports scalable, robust computations on subject-specific brain geometries reconstructed from imaging (Fumagalli et al., 2023). This modeling supports analysis of clearance, pulsatility, and neurodegenerative processes.

5. Inverse and Differentiable Modeling

PhysBrain approaches leverage differentiable programming and neural network–based inverse modeling to estimate functional and physiological parameters from sparse, noisy, or indirect measurements.

Physics-Informed Neural Networks for PBPK

Inverse PINN frameworks for physiologically based pharmacokinetics (PBPK-iPINN) encode multi-compartment brain drug transport as ODE systems, using deep networks trained to satisfy data, ODE, and initial condition constraints:

$$\mathcal{L}(\theta, p) = \lambda_\text{data} \mathcal{L}_\text{data} + \lambda_\text{ODE} \mathcal{L}_\text{ODE} + \lambda_\text{IC} \mathcal{L}_\text{IC}$$

With automatic differentiation, PINNs recover patient/drug-specific parameters and concentration–time curves with performance matching or exceeding maximum-likelihood and evolutionary optimization methods, automatically respecting mass-balance and ODE structure (Wickramasinghe et al., 16 Sep 2025).

Differentiable Simulation and Training

Platforms such as BrainPy enable automatic gradient computation through large-scale spiking simulations, supporting BPTT and surrogate gradients for training both physical (GIF/LIF, HH) and hybrid network models. Event-driven and JIT operators provide computational scalability, while the class–function abstraction allows seamless construction of multi-scale PhysBrain models (neurons, synapses, populations) (Wang et al., 2023).

6. Embodied and Physical Intelligence Extraction

PhysBrain applies not only to mechanistic/biomedical modeling but also to the extraction of physical intelligence from human egocentric data, supporting embodied artificial agents.

Egocentric2Embodiment Pipelines

Egocentric video is segmented, annotated, and validated with schema-driven, evidence-grounded VQA to produce large-scale datasets (E2E-3M) capturing multi-level interaction and planning structure. PhysBrain models derived from such data—using VLM fine-tuning—demonstrate improved planning, compositional reasoning, and sample-efficient transfer in vision–language–action downstream tasks (EgoThink, SimplerEnv), outperforming VLMs trained solely on third-person perspectives (Lin et al., 18 Dec 2025). Structured annotation enforces temporal, causal, and viewpoint consistency, critical for mapping visual perception to physical action and reasoning.

7. Large-Scale Personalization and Digital Twins

Whole-brain digital twins integrate multi-modal anatomical and physiological data (sMRI, DTI, PET), inferring individualized microcircuit parameters and simulating subject-specific BOLD/fMRI and behavior. Platforms such as Digital Twin Brain (DTB) implement data assimilation at the mesoscopic scale, GPU-optimized graph partitioning for multi-billion neuron simulations, and scaling protocols to bridge individual neuroimaging, brain–machine interfaces, and in silico experimentation (Lu et al., 2023).

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PhysBrain, in summary, unifies mechanistic, statistical, and embodied modeling paradigms under physically principled, scalable, and data-assimilative frameworks, generating a substrate for personalized simulation, multi-scale inference, neuro-mechanical design, and transfer of physical intelligence in both biological and artificial systems.