Physics-Based Models of Extraction Kinetics in Solvent-Swollen Polymers: Using Non-Exhaustive Extractions to Estimate Total Extractable Quantities.

Abstract

Leachables from polymeric medical devices can migrate into the body, potentially impacting patient health. Physics-based mass-transport models can estimate patient exposure but require knowledge of the initial leachable amount, <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> <mrow><msub><mi>M</mi> <mn>0</mn></msub> </mrow> <annotation>$$ {M}_0 $$</annotation></semantics> </math> . Although <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> <mrow><msub><mi>M</mi> <mn>0</mn></msub> </mrow> <annotation>$$ {M}_0 $$</annotation></semantics> </math> can be determined through exhaustive extraction testing, this may be impractical for some solutes due to kinetic or thermodynamic limitations. We developed a free-volume model to estimate <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> <mrow><msub><mi>M</mi> <mn>0</mn></msub> </mrow> <annotation>$$ {M}_0 $$</annotation></semantics> </math> from non-exhaustive extractions, accounting for solvent-swelling effects on solute diffusivity, <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics><mrow><mi>D</mi></mrow> <annotation>$$ D $$</annotation></semantics> </math> , in polymers. Based on an analysis of polymer/solvent partition coefficients, we also propose a limiting value for the partition coefficient <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics><mrow><mi>K</mi></mrow> <annotation>$$ K $$</annotation></semantics> </math> . We couple this model to a mass-transport equation to predict <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> <mrow><msub><mi>M</mi> <mn>0</mn></msub> </mrow> <annotation>$$ {M}_0 $$</annotation></semantics> </math> . Validation against experimental data demonstrates order-of-magnitude accuracy for both <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics><mrow><mi>D</mi></mrow> <annotation>$$ D $$</annotation></semantics> </math> and <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> <mrow><msub><mi>M</mi> <mn>0</mn></msub> </mrow> <annotation>$$ {M}_0 $$</annotation></semantics> </math> . The model is applicable only to rubbery polymers and systems involving relatively hydrophobic polymers, solvents, and solutes. Using the predicted <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> <mrow><msub><mi>M</mi> <mn>0</mn></msub> </mrow> <annotation>$$ {M}_0 $$</annotation></semantics> </math> with a transport model for in vivo exposure yields results similar to those obtained when <math xmlns="http://www.w3.org/1998/Math/MathML"> <semantics> <mrow><msub><mi>M</mi> <mn>0</mn></msub> </mrow> <annotation>$$ {M}_0 $$</annotation></semantics> </math> is known a priori. Our work shows that non-exhaustive extractions can be used to infer total extractable quantities and conservatively estimate patient exposure.