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A rational extended thermodynamic model for dopamine diffusion and uptake

Author

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  • Barbera, E.
  • Desiderio, L.
  • Fazio, C.

Abstract

In this work, a hyperbolic model is proposed within the framework of Rational Extended Thermodynamics to study dopamine diffusion in the striatum. The model incorporates a nonlinear uptake mechanism described by Michaelis–Menten kinetics. While it has the main characteristics of the classical parabolic Nicholson model, it also introduces key features typical of hyperbolic systems. Analytical solutions are derived for some particular cases, enabling a direct comparison between the hyperbolic and parabolic formulations. The analytical solutions obtained through the Laplace Transform method, is validated with numerical simulations carried out using the Taylor–Galerkin Finite Element Method (TG-FEM). These two different approaches provide a comprehensive insight of the model and highlight the differences with the parabolic case. Finally, the propagation of acceleration waves is studied to analyze the system’s response to specific perturbations. The temporal evolution of such disturbances is examined in detail, and the critical time at which derivative discontinuities evolve into shock waves is identified.

Suggested Citation

  • Barbera, E. & Desiderio, L. & Fazio, C., 2026. "A rational extended thermodynamic model for dopamine diffusion and uptake," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 247(C), pages 574-586.
    • Handle: RePEc:eee:matcom:v:247:y:2026:i:c:p:574-586
    DOI: 10.1016/j.matcom.2026.03.032
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    References listed on IDEAS

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    1. Tommaso Ruggeri & Masaru Sugiyama, 2015. "Rational Extended Thermodynamics beyond the Monatomic Gas," Springer Books, Springer, edition 1, number 978-3-319-13341-6, January.
    2. Tommaso Ruggeri & Masaru Sugiyama, 2021. "Classical and Relativistic Rational Extended Thermodynamics of Gases," Springer Books, Springer, number 978-3-030-59144-1, January.
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