Theoretical Modeling of Cyclically Loaded, Biodegradable Cylinders
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© 2007, Birkhäuser Boston. The adaptation of fully biodegradable stents, thought to be the next revolution in minimally invasive cardiovascular interventions, is supported by recent findings in cardiovascular medicine concerning human coronaries and the likelihood of their deployment has been made possible by advances in polymer engineering. The main potential advantages of biodegradable polymeric stents are: (1) the stent can degrade and transfer the load to the healing artery wall which allows favorable remodeling, and (2) the size of the drug reservoir is dramatically increased. The in-stent restenotic response usually happens within the first six months, thus a fully biodegradable stent can fulfill the mission of restoring flow while mitigating the probability of long-term complications. However, it is a key concern that the stent not degrade away too soon, or develop structural instabilities due to faster degradation in key portions of the stent. We present here a preliminary model of the mechanics of a loaded, biodegradable cylindrical structure. The eventual goal of this research is to provide a means of predicting the structural stability of biodegradable stents As a first step towards a fully nonlinear model, biodegradable polymers are modeled as a class of linearized materials. An inhomogeneous field that reflects the degradation, which we henceforth refer to as degradation, and a partial differential equation governing the degradation are defined. They express the local degradation of the material and its relationship to the strain field. The impact of degradation on the material is accomplished by introducing a time-dependent Young’s modulus function that is influenced by the degradation field. In the absence of degradation, one recovers the classical linearized elastic model. The rate of increase of degradation was assumed to be dependent on time and linearized strain with the following characteristics: (1) a material degrades faster when it is exposed to higher strains, and (2) a material that is strained for a longer period of time degrades more rapidly than a material that has been strained by the same amount for a shorter period of time The initial boundary value problem considered is that of an infinitely long, isotropic, nearly incompressible, homogeneous, and strain-degradable cylindrical annulus subjected to radial stresses at its boundaries. A semiinverse method assuming a specific form of the displacement field was employed and the problem reduced to two coupled nonlinear partial differential equations for a single spatial coordinate and time. These equations were solved simultaneously for the displacement and degradation fields using a time marching finite element formulation with a set of nonlinear iterations for each time step The main features that were observed were: (1) strain-induced degradation showed acceptable phenomenological characteristics (i.e. progressive failure of the material and parametric coherence with the defined constants); (2) an inhomogeneous deformation leads to inhomogeneous degradation and therefore in an initially homogeneous body the properties vary with the current location of the particles; and (3) the linearized model, in virtue of degradation, exhibits creep, stress relaxation, and hysteresis, but this is markedly different from the similar phenomena exhibited by viscoelastic materials.
author list (cited authors)
Soares, J. S., Moore, J. E., & Rajagopal, K. R.
Modeling of Biological Materials