Flow-induced deformation from pressurized cavities in absorbing porous tissues

Abstract

The behaviour of a cavity during an injection of fluid into biological tissue is considered. High cavity pressure drives fluid into the neighbouring tissue where it is absorbed by capillaries and lymphatics. The tissue is modelled as a nonlinear deformable porous medium with the injected fluid absorbed by the tissue at a rate proportional to the local pressure. A model with a spherical cavity in an infinite medium is used to find the pressure and displacement of the tissue as a function of time and radial distance. Analytical and numerical solutions for a step change in cavity pressure show that the flow induces a radial compression in the medium together with an annular expansion, the net result being an overall expansion of the medium. Thus any flow induced deformation of the material will aid in the absorption of fluid.

Brain mechanics For neurosurgery: modeling issues

“…On a similar note, it has been postulated that many viscoelastic phenomena like creep and stress left, but for stress relaxation. Both plots show quite a different compressibility behavior: in particular, the relaxation behavior is totally different with the poroelastic model having a logarithmic-type compressibility while the viscoelastic model has more of a relaxation behavior, with a spike at the origin and then a smoothly converging reduction relaxation can be reproduced using a poroelastic theory (Barry and Aldis 1992). Yang and Taber (1991) advocate the use of poroelasticity (together with some viscoelastic elements) in modeling the passive cardiac muscle.…”

“…The use of constant permeability may thus be an important source of error and indicates that further evaluation would be of value. The need for a variable permeability in the poroelastic formulation has also been discussed extensively before (Kaczmarek et al 1997;Barry and Aldis 1992).…”

A Review of Mixture Theory for Deformable Porous Media and Applications

“…Number of authors [11,[15][16][17][18][19][20][21] have used different forms of permeability functions while analyzing the specifics of their research.…”

“…Only necessary details are provided rather than complete mathematical model and solution procedure. It is important to note that all the graphical results shown below are for non-dimensional systems and details are not shown here (Barry and Aldis [16], Siddique and Anderson [19] and Farina et al [22]). …”

“…The modeling details of flow induced deformation from pressurized cavities in absorbing porous tissue (as presented by Barry and Aldis [16]) are reproduced in this section. The schematic diagram of the mathematical model under consideration is presented in Figure 1.…”