A model for simultaneous crystallisation and biodegradation of biodegradable polymers.

This paper completes the model of biodegradation for biodegradable polymers that was previously developed by Wang et al. (Wang Y, Pan J, Han X, Sinka, Ding L. A phenomenological model for the degradation of biodegradable polymers. Biomaterials 2008;29:3393-401). Crystallisation during biodegradation was not considered in the previous work which is the topic of the current paper. For many commonly used biodegradable polymers, there is a strong interplay between crystallisation and hydrolysis reaction during biodegradation - the chain cleavage caused by the hydrolysis reaction provides an extra mobility for the polymer chains to crystallise and the resulting crystalline phase becomes more resistant to further hydrolysis reaction. This paper presents a complete theory to describe this interplay. The fundamental equations in the Avrami's theory for crystallisation are modified and coupled to the diffusion-reaction equations that were developed in our previous work. The mathematical equations are then applied to three biodegradable polymers for which long term degradation data are available in the literature. It is shown that the model can capture the behavior of the major biodegradable polymers very well.

[1]  A T Florence,et al.  Local controlled drug delivery to the brain: mathematical modeling of the underlying mass transport mechanisms. , 2006, International journal of pharmaceutics.

[2]  M. Muthukumar,et al.  Molecular modelling of nucleation in polymers , 2003, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[3]  Suming Li,et al.  Hydrolytic degradation of devices based on poly(DL-lactic acid) size-dependence. , 1995, Biomaterials.

[4]  M. Avrami.  Kinetics of Phase Change. I General Theory , 1939 .

[5]  M. Avrami.  Granulation, Phase Change, and Microstructure Kinetics of Phase Change. III , 1941 .

[6]  H. Tsuji,et al.  Blends of aliphatic polyesters: V non-enzymatic and enzymatic hydrolysis of blends from hydrophobic poly(l-lactide) and hydrophilic poly(vinyl alcohol) , 2001 .

[7]  Yoshito Ikada,et al.  Properties and morphology of poly(L-lactide). 4. Effects of structural parameters on long-term hydrolysis of poly(L-lactide) in phosphate-buffered solution , 2000 .

[8]  G. D. Wood.  Inion biodegradable plates: the first century. , 2006, The British journal of oral & maxillofacial surgery.

[9]  M. Avrami.  Kinetics of Phase Change. II Transformation‐Time Relations for Random Distribution of Nuclei , 1940 .

[10]  Kent J. Voorhees,et al.  Hydrolysis of Polylactic Acid (PLA) and Polycaprolactone (PCL) in Aqueous Acetonitrile Solutions: Autocatalysis , 1998 .

[11]  M. Starink.  On the meaning of the impingement parameter in kinetic equations for nucleation and growth reactions , 2001 .

[12]  Jingzhe Pan,et al.  A phenomenological model for the degradation of biodegradable polymers. , 2008, Biomaterials.

[13]  R. Bell,et al.  The use of biodegradable plates and screws to stabilize facial fractures. , 2006, Journal of oral and maxillofacial surgery : official journal of the American Association of Oral and Maxillofacial Surgeons.

[14]  R. Drew,et al.  Wettability and spreading kinetics of molten aluminum on copper-coated ceramics , 2006 .

[15]  Z. Stachurski,et al.  Kinetics of polymer crystallisation , 1995 .

[16]  Jack G. Zhou,et al.  Structure and morphology changes in absorbable poly(glycolide) and poly(glycolide-co-lactide) during in vitro degradation , 1999 .

[17]  A. Södergård,et al.  Properties of lactic acid based polymers and their correlation with composition , 2002 .

[18]  Mark Taylor,et al.  Computational modelling of cell spreading and tissue regeneration in porous scaffolds. , 2007, Biomaterials.