An extended biphasic model for charged hydrated tissues with application to the intervertebral disc

Area of Science:

• Computational mechanics
• Biomaterials science
• Tissue engineering

Background:

• Existing finite element models for soft biological tissues often fail to accurately capture mechanical and electro-chemical responses.
• Single-phasic models cannot predict interstitial fluid flow or osmotic effects.
• Multi-phasic models are frequently limited to small strains, lack intrinsic viscoelasticity, or do not incorporate collagen fiber reinforcement.

Purpose of the Study:

• To develop a thermodynamically consistent and general finite element model for hydrated soft biological tissues.
• To overcome the deficiencies of existing models in reproducing mechanical and electro-chemical behaviors.
• To accurately simulate complex tissue responses, including fluid flow, viscoelasticity, and fiber reinforcement.

Main Methods:

• Application of the Theory of Porous Media (TPM).
• Incorporation of polyconvex Ogden-type material laws for anisotropic and intrinsically viscoelastic solid matrix behavior using a generalized Maxwell model.
• Inclusion of deformation-dependent permeability, inhomogeneities (e.g., fiber alignment), and osmotic effects (Lanir's assumption).

Main Results:

• A generalized finite element model capable of reproducing complex hydrated soft tissue behavior was developed.
• The model successfully integrates multiple essential features often lacking in previous models.
• Numerical examples using the human intervertebral disc demonstrate the model's capacity for simulating viscoelastic and osmotic effects.

Conclusions:

• The presented model offers a significant advancement in simulating hydrated soft biological tissues.
• It provides a robust framework for analyzing complex behaviors like viscoelasticity and osmosis in tissues.
• This generalized approach has broad applicability for various charged hydrated tissues, with the human intervertebral disc serving as a key example.