Mixed finite element modelling of cartilaginous tissues

Swelling and shrinking of cartilaginous tissues is modelled by a four-component mixture theory. This theory results in a set of coupled non-linear partial differential equations for the electro-chemical potentials and the displacement. For the sake of local mass conservation these equations are discretised in space by a mixed finite element method. Integration in time by backward Euler leads to...

متن کامل

Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part II: Mixed-hybrid finite element solution

The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory. This theory results in a coupled system of nonlinear parabolic differential equations together with an algebraic constraint for electroneutrality. In this model, it is desirable to obtain accurate approximations of the fluid flow and ions flow. Such accurate approximations can be determined by the ...

متن کامل

CASA Report, Thechnische Universiteit Eindhoven MATHEMATICAL MODELLING AND NUMERICAL SOLUTION OF SWELLING OF CARTILAGINOUS TISSUES. PART II: MIXED-HYBRID FINITE ELEMENT SOLUTION

The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory. This theory results in a coupled system of nonlinear parabolic differential equations together with an algebraic constraint for electroneutrality. In this model, it is desirable to obtain accurate approximations of the fluid flow and ions flow. Such accurate approximations can be determined by the ...

متن کامل

Three-dimensional finite element modelling for soft tissues surgery

Laparoscopy is a surgical technique that requires fine control from the surgeon point of view. Up to this day, this experience can only be obtained by intensive training. That is why a lot of training simulators have been developed in the medical area. We present here a new approach based on a three-dimensional finite element software and an elastic constitutive equation, able to predict realis...

متن کامل

Mixed Finite Element Methods

A new mixed nite element method on totally distorted rectangular meshes is introduced with optimal error estimates for both pressure and velocity. This new mixed discretization ts the geometric shapes of the discontinuity of the rough coeecients and domain boundaries well. This new mixed method also enables us to derive the optimal error estimates and existence and uniqueness of Thomas's mixed ...

متن کامل

Mixed finite element modelling of cartilaginous tissues

نویسندگان

چکیده

منابع مشابه