Mechanical properties of single alginate microspheres determined by microcompression and finite element modelling

Calcium alginate microspheres have been studied extensively as carriers in drug delivery systems, for encapsulation of biological materials such as biocatalysts, and as matrices in tissue engineering. Understanding the mechanical properties of such microspheres is essential because they may be exposed to mechanical forces during processing and in end applications. In order to characterise their mechanical properties, microspheres may be compressed between two flat surfaces, and a theoretical model applied to the force–displacement and force–time data to extract mechanical property parameters. In previous work, single calcium alginate microspheres were compressed and then held at constant deformation, and the force being imposed on them was measured. It was found that the force increased with deformation, as expected, and that there was significant force relaxation during holding. In this work, force versus displacement/time data corresponding to compression and holding of a single (102 μm) calcium alginate microsphere were modelled by finite element analysis. Since the force relaxation might be due to water loss or microsphere viscoelasticity, a poroelastic material model was first used to assess the potential effect of water loss from the microsphere solid matrix during holding. Using image analysis, the volume loss during compression and relaxation of the microsphere was determined. Assuming all the change in volume was due to water loss, and assuming a literature value of alginate permeability, the poroelastic material model showed that the effect of water loss on the force behaviour was small enough during relaxation that it might be neglected. This allowed a compressible, isotropic and homogeneous linear viscoelastic material model to be evaluated against experimental relaxation data to obtain viscoelastic property parameters of the microsphere. A viscoelastic material model with two relaxation times showed excellent capability in modelling both compression and relaxation. The instantaneous elastic modulus, long-term elastic modulus and the two relaxation times were found to be 490, 68.6 kPa, and 0.013 and 0.085 s, respectively. Deformation parameters of the compressed microsphere such as the contact radius and central lateral extension were also obtained from finite element modelling, and were compared with experimental data, showing good agreement and confirming the validity of the model at least for the microsphere under test.