Pitt | Swanson Engineering
Growth and Remodeling of Fully Saturated Porous Media
  • Growth and Remodeling of Fully Saturated Porous Media

The purpose of this research is to establish a unified theory of growth and remodeling that includes contributions from the solid, fluid, and mobile species constituents of soft tissues. Towards this end our laboratory has combined theories of volumetric growth and mixed porohyperelasticity with transport and swelling (MPHETS) to derive a new approach to modeling the growth and remodeling of biological soft tissues (GMPHETS). The developed theoretical and computational approach is flexible in that it is capable of modeling tissue growth from stimuli in all phases - fluid, solid, and species. This will allow computational simulation of soft tissues whose extracellular matrix remodeling is influenced not only by mechanical stimuli (stretch, stress) but also tissue fluid pressure/shear in addition to convecting and diffusing mobile species (e.g., growth factors, cytokines). The interested reader can find further detail on the theoretical and computational methods in Harper et al. 2014 and Armstrong MH et al. 2016.

armstrong fig 10 
Displacement, pore fluid pressure, concentration, and growth stretch for nonlinear concentration-driven growth in an internally pressurized cylinder. Values plotted for the case of larger Péclet-like number. (A) Displacement in time. Note that displacement initially increases a very small amount due to the pressurization of the vessel, then decreases for all elements due to resorption, followed by an increase due to growth. (B) Pore fluid pressure during growth. (C) Concentration during growth. For comparison, (C) has a transparent red plane that shows the level of the concentration threshold for all time. (D) Growth of three specific elements located near the middle of the material are tracked in time. All three elements experience a small amount of resorption at the beginning of growth time, because the concentration is initially below the threshold value. Note that after this initial dip, the innermost element (blue) experiences growth, the outermost element (red) experiences resorption for the entire time, and the middle element (green) experiences resorption followed by growth, ultimately experiencing net growth.