Vortical Dynamics of CSF: The Mechanical Model — A Distributed Mechanical Framework for Human Cerebrospinal Fluid Dynamics (Version 5.4)

Description Cerebrospinal fluid (CSF) dynamics are governed by the interaction between physiological forcing and the heterogeneous mechanical architecture of the craniospinal system. Vortical Dynamics of CSF: The Mechanical Model proposes a unified distributed mechanical description of this system, integrating physiological forcing, anatomical geometry, mechanical constraints, flow asymmetry, rotational flow organization, impedance, and dynamic coherence within a single framework. The model is centered on four principal physical quantities: 3D CSF velocity field — v(x,t)v(x,t) Distributed flow-asymmetry field — A(x,t)A(x,t) Vorticity field — ω(x,t)=∇×v(x,t)\omega(x,t)=\nabla\times v(x,t) Frequency-dependent mechanical impedance — Z(ω)Z(\omega), with a real-valued effective representation ZeffZ_{\mathrm{eff}} A derived coherence index CC and a dimensionally consistent normalized dynamic state variable Ψ(τ)\Psi(\tau) complete the mathematical representation. The central mechanical proposition of the model is that distributed anatomical and mechanical asymmetries generate spatially organized velocity asymmetries which, where permitted by geometry and boundary conditions, generate secondary rotational flow organization. This framework provides a unified explanation for phenomena that are otherwise generally described as separate components of CSF dynamics, including oscillatory forcing, spatially heterogeneous flow, phase-dependent behavior, recirculation, vortical structures, anatomical asymmetry, and mechanical impedance. The model therefore does not treat CSF motion as a simple one-dimensional oscillatory or bulk-flow phenomenon. It describes CSF dynamics as a distributed mechanical system whose observed behavior emerges from the interaction between forcing, geometry, compliance, resistance, asymmetry, and spatial organization. A specific anatomical hypothesis developed within the framework concerns right-dominant thoraco-abdominal anatomy, including the liver and right subdiaphragmatic region, as a potential contributor to the observed spatial organization of CSF dynamics. This hypothesis is explicitly formulated as a consequence of the mechanical model and is subject to direct empirical testing. The framework defines nine pre-specified testable predictions (P1–P9). These predictions provide direct criteria by which the model can be confirmed, refined, or falsified. Scientific Position The purpose of this work is not to propose another isolated mechanism for CSF motion, but to provide a single distributed mechanical model capable of accounting for the interaction of the principal physical determinants of CSF dynamics within one coherent mathematical architecture. Existing observations concerning respiratory and cardiac forcing, vascular coupling, anatomical heterogeneity, spinal geometry, vortical structures, recirculation, compliance, and pressure-flow relationships are incorporated into this unified representation rather than treated as independent phenomena. To the authors' knowledge, no existing CSF model currently provides an equivalent integration of these mechanisms into a single distributed framework with explicit velocity asymmetry, independently computed vorticity, frequency-dependent mechanical impedance, coherence, dynamic state representation, and pre-specified testable predictions. The model is therefore proposed as the current mechanical representation of CSF dynamics, pending evidence capable of demonstrating that another framework explains the same observations with greater completeness, predictive power, or mechanical consistency. The burden of proof is consequently placed on experimental evidence: if the predicted relationships fail systematically, the model must be revised or rejected; if they are repeatedly observed, the model gains empirical support. Key Features & Deposit Contents Theoretical frameworkComplete mathematical formulation of the distributed mechanical model and its principal relationships. Python computational pipeline (pipeline_v54.py)Reference implementation for processing time-resolved 3D velocity data, calculating distributed flow asymmetry and vorticity, estimating effective mechanical impedance, computing the coherence index CC, and evaluating the normalized dynamic state variable Ψ\Psi. Pre-specified analytical protocol (protocol_v54.txt)Defines analytical procedures, parameters, thresholds, and decision rules prior to pathological cohort inspection. High-resolution vector diagramsVisual representation of the mechanical architecture, anatomical organization, and prediction matrix. Synthetic validation testsComputational tests covering mathematical bounds, vorticity behavior, impedance representation, and dynamic-state formulation. Model Architecture The complete framework follows the sequence: physiological forcing → anatomical/mechanical heterogeneity → velocity asymmetry → rotational flow organization → mechanical impedance → coherence → dynamic state The architecture is designed to connect measurable physical quantities directly to mathematical representations and testable predictions. The distinction between velocity asymmetry and true vorticity is maintained explicitly: asymmetry describes spatial organization of the velocity field, whereas vorticity quantifies its local rotational component. Scientific Scope This deposit presents the Vortical Dynamics of CSF model as a unified mechanical explanation of cerebrospinal fluid dynamics. The framework distinguishes established observations from mathematical derivations and identifies specific propositions whose validity can be directly tested against measurements. The model is deliberately constructed to remain falsifiable. Its strength does not depend on treating its propositions as unquestionable, but on whether its predicted mechanical relationships are supported by independent measurements. The complete reference architecture is: mechanical model → measurable variables → mathematical formulation → computational implementation → pre-specified protocol → predictions → falsification criteria Version & Reference Version: 5.4Current DOI: 10.5281/zenodo.22229743Previous reference / historical anchor: 10.5281/zenodo.20323393INPI Reference: AxeSaros V024022026 © August 2026 — Karl Julien Iaiche Achour & Julien Karlia [email protected]