During the past decades, hydrogels have been introduced suitable as novelmaterials for a variety of applications such as biomedical engineering, sanitaryproducts, agriculture, bioseparation, enhanced oil recovery, etc. They havebeen successfully used as superabsorbent materials and in drug delivery, cellencapsulation and tissue repair due to their high water content and consequentbiocompatibility. Considering the fact that water retention in the hydrogels provides asuitable drug diffusion pathway; many hydrogel-based networks have been designedand fabricated as intelligent carriers of drugs. The rate and degree of hydrogel swellingare the most important parameters which control the release patterns of solvents anddrugs from these polymeric networks. Therefore, the precise account of hydrogelbehaviour as well as mathematical description of equilibrium swelling, dimensionalchanges due to solvent uptake, desorption and drug release profiles were the mainobjectives in many investigations. The objective of this manuscript is to give a briefreview on existing mathematical models and theories in the field of hydrogel swellingas well as the description of the drug release mechanism from swelling-controllednetworks. The most important properties of hydrogels relevant to their swellingbehaviour as well as kinetics and thermodynamic of swelling are also presented.

Theoretical Description of Hydrogel Swelling: A Review

In this chapter, the recent advances in cartilage biomechanics and electromechanics are reviewed and summarized. Our emphasis is on the new experimental techniques in cartilage mechanical testing, new experimental and theoretical findings in cartilage biomechanics and electromechanics, and emerging theories and computational modeling of articular cartilage. The charged nature and depth-dependent inhomogeneity in mechano-electrochemical properties of articular cartilage are examined, and their importance in the normal and/or pathological structure-function relationships with cartilage is discussed, along with their pathophysiological implications. Developments in theoretical and computational models of articular cartilage are summarized, and their application in cartilage biomechanics and biology is reviewed. Future directions in cartilage biomechanics and mechano-biology research are proposed.

Mechano-electrochemical properties of articular cartilage: their inhomogeneities and anisotropies.

MECHANO-ELECTROCHEMICAL PROPERTIES OF ARTICULAR CARTILAGE: Their Inhomogeneities

A fibril-reinforced poroviscoelastic swelling model for articular cartilage

This paper outlines the framework of a porous flow mixture theory for the mathematical modelling of in vitro tissue growth, and gives an application of this theory to an aspect of tissue engineering. The problem is formulated as a set of partial differential equations governing the space and time dependence of the amounts of each component of the tissue (phase), together with the physical stresses in each component. The theory requires constitutive relations to specify the material properties of each phase, and also requires relations to specify the stresses developed due to mechanical interactions, both within each phase and between different phases. An application of the theory is given to the study of the mobility and aggregation of a population of cells seeded into an artificial polymeric scaffold. Stability analysis techniques show that the interplay of the forces between the tissue constituents results in two different regimes: either the cells form aggregates or disperse through the scaffold.

Mathematical modelling of engineered tissue growth using a multiphase porous flow mixture theory

An equivalent new expression of the triphasic mechano-electrochemical theory [9] is presented and a mixed finite element formulation is developed using the standard Galerkin weighted residual method. Solid displacement us, modified electrochemical/chemical potentials ϵw, ϵ+and ϵ− (with dimensions of concentration) for water, cation and anion are chosen as the four primary degrees of freedom (DOFs) and are independently interpolated. The modified Newton–Raphson iterative procedure is employed to handle the non-linear terms. The resulting first-order Ordinary Differential Equations (ODEs) with respect to time are solved using the implicit Euler backward scheme which is unconditionally stable. One-dimensional (1-D) linear isoparametric element is developed. The final algebraic equations form a non-symmetric but sparse matrix system. With the current choice of primary DOFs, the formulation has the advantage of small amount of storage, and the jump conditions between elements and across the interface boundary are satisfied automatically. The finite element formulation has been used to investigate a 1-D triphasic stress relaxation problem in the confined compression configuration and a 1-D triphasic free swelling problem. The formulation accuracy and convergence for 1-D cases are examined with independent finite difference methods. The FEM results are in excellent agreement with those obtained from the other methods. Copyright © 1999 John Wiley & Sons, Ltd.

A mixed finite element formulation of triphasic mechano-electrochemical theory for charged, hydrated biological soft tissues

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A mixed finite element formulation of triphasic mechano-electrochemical theory for charged, hydrated biological soft tissues