Thermodynamic derivation of a non-linear poroelastic model describing hemodynamicsmechanics interplay in the lamina cribrosa

How to Cite

Recrosi F, Repetto R, Tatone A, Guidoboni G. Thermodynamic derivation of a non-linear poroelastic model describing hemodynamicsmechanics interplay in the lamina cribrosa. MAIO [Internet]. 2018 Jun. 18 [cited 2022 Jun. 25];2(2):80-5. Available from:

Copyright notice

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication, with the work twelve (12) months after publication simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work’s authorship and initial publication in this journal.

  2. After 12 months from the date of publication, authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.


blood perfusion; large deformations; poroelasticity; species diffusion


In this paper we formulate a poroelastic model starting from a model of species diffusion in an elastic material. The model is applied to study the mechanics of the lamina cribrosa (LC) in the eye. The LC is a porous tissue at the head of the optic nerve. Deformation of this tissue and impairment of blood flow induced by tissue deformation are considered to be related to the pathogenesis of glaucoma.

The governing equations are derived from general thermomechanical principles. We carefully revise the role of the energy-stress Eshelby tensor, mutuated from the framework of tissue growth, in describing the hemo-mechanical behaviour of the tissue.

The model accounts for non-linear deformations of the solid matrix and deformation-induced changes in porosity and permeability. The model provides a qualitative better undertanding of the phatophysiology and pathogenesis of glaucoma in terms of coupling between tissue deformation and the resulting impaired hemodynamics inside the LC.


Sigal IA, Flanagan JG, Tertinegg I, Ethier CR. finite element modeling in optic nerve. Invest Ophthalmol Vis Sci. 2004;45(12):4378–4387.

Sigal IA, Hongli Y, Roberts MD, Burgoyne CF, Downs CJ. IOP-induced lamina cribrosa displacement and scleral canal expansion: an analysis of factor interactions using parameterized eye-specific models. Invest Ophthalmol Vis Sci. 2011;52(3):1896–1907.

Sigal IA, Grimm JL, Jan NJ, Reid K, Minckler DS, Brown DJ. Eye-specific IOP-induced displacements and deformations of human lamina cribrosa. Invest Ophthalmol Vis Sci. 2011;55(1):1–15.

Causin P, Guidoboni G, Harris A, Prada D, Sacco R, Terragni S. A poroelastic model for the perfusion of the lamina cribrosa in the optic nerve head. Math Biosci. 2014;(257):33–41.

Guidoboni G, Harris A, Carichino L, Arieli Y, Siesky BA. Effect of intraocular pressure on the hemodynamics of the central retinal artery: a mathematical model. Math Biosci Eng. 2014;(11):523–546.

Biot MA. General theory of of three-dimensional consolidation. J Appl Phys. 1941;(12):155–164.

Biot MA. Theory of finite deformations of porous solids. Ind Univ Math J. 1972;21:597–620.

Larchè F, Cahn JW. Linear theory of thermomechanical equilibrium solids under stress. Acta. Metall. 1973;21:1051–1063.

Larchè F, Cahn JW. The interactions of composition and stress in crystalline solids. J Res Natl Bur Stand. 1984;89:467–500.

Honga W, Zhaoa X, Zhoua J, Suo Z. A theory of coupled diusion and large deformation in polymeric gels. J Mechan Phys Solids. 2008;56:1779–1793.

Eshelby JD. Elastic energy momentum tensor. J Elasticity. 1975;5:331–335.