In a series of recent papers, J.~D.~Humphrey and K.~R.~Rajagopal introduce and illustrate the use of an approach to modeling the growth and adaptation of soft biological tissue to a changing mechanical environment that utilizes the construct of continuously evolving natural configurations for determining the mechanical response of the tissue. In particular, they consider the thickening response of an arterial wall to a hypertensive environment. Their studies focus attention upon three constituents of the medial (muscular) layer of an arterial wall:\ \ smooth muscle cells and the structural proteins elastin and collagen. The smooth muscle cells play two vital roles in the mechanical response of the arterial wall. Firstly they add to the structural integrity of the tissue and secondly they manufacture the collagenous structural proteins. The principle issue addressed by Humphrey and Rajagopal was how to model the growth of tissue in response to a sustained hypertensive environment. In their model for growth, they do not differentiate increase of smooth muscle cell biomass due to cell division (hyperplasia) and mass increase due to individual cell growth (hypertrophy). In this talk, a generalization of their modeling approach is described that accounts for both aspects of smooth muscle cell mass increase. The trigger for hypertrophy is taken to be a threshold hoop stress while for hyperplasia it is a threshold mass per individual cell. The coupled growth and momentum balanced system is studied for two dimensional, radially symmetric boundary value problems.
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