Analysis of Stiffness in Extracellular Matrix Embedded with Bio-Conjugated Magnetic Beads in a Magnetic Field

Abstract

In this paper we present a new model for determining the local stiffness of an extracellular matrix (ECM) sample embedded with bio-conjugated magnetic beads under the influence of an external magnetic field. In this model, the viscoelastic deformation of such ECM samples is analyzed using the finite element method. We report results from numerical simulations using our model on two typical scenarios for studying the pre-tension in the ECM caused by beads under a magnetic field. The analytical results are in close agreement with that obtained from COMSOL. We also applied our model on an actual ECM sample embedded with bio-conjugated beads and compared our analytical results with that obtained from stretch tests done on that sample. These results are comparable to that from the stretching tests. In this paper, we present a finite-element model for determining the local stiffness of an ECM sample embedded with bio-conjugated beads under the influence of an external magnetic field. Section II discusses the modification of ECM for manipulating the stiffness of ECM. Section III describes our finite-element method for analyzing viscoelastic deformation of ECM gel embedded with bio-conjugated beads, while Section IV discusses the calculation of magnetic force induced on the beads in the magnetic field generated by a permanent magnet. In Section V we apply this finite-element model to simulate the pre-tension generated in ECM by (i) a single bead, and (ii) two columns of aligned beads, and compare the results to that obtained using COMSOL. We also apply our finite-element model to an ECM sample with randomly distributed beads, and compare the analytical results (in terms of the percentage change in ECM stiffness) with experimental results obtained from a stretch test done on an actual ECM sample. Simulations are also conducted to reveal the influence of the size and concentration of beads on the change in ECM stiffness. We discuss possible improvements for this proposed model in Section VI.