Theoretical evaluation of the magnetic force bioreactor

A problem presented at the UK MMSG Nottingham 2001.

Presented by:
Dr Jon Dobson (Centre for Science and Technology in Medicine, Keele University)
Prof Alicia El-Haj (Centre for Science and Technology in Medicine, Keele University)
J Dobson, A El-Haj, A Grief, G Richardson

Problem Description

A novel bioreactor has been designed to overcome problems with the ex vivo growth of mechanically stable, functional connective tissue. Current bioreactors face limitations due to the fact that biochemical reactions must be initiated in cells growing on biodegradable scaffolds within the bioreactor by the application of mechanical forces to the cell membrane. Up to now, systems which have been designed to overcome this limitation face other problems [e.g. the bioreactor environment must be completely sterile; the scaffold materials are mechanically weak and cannot withstand the stresses; the production of complex, three-dimensional tissue structures is not possible].

The magnetic force bioreactor is designed to apply forces directly to the cell membrane by coupling biocompatible magnetic nano- and microparticles to the membrane surface and receptor sites. Forces on the order of a few picoNewtons are required to deform the cell membrane and activate mechanosensitive transmembrane ion channels. The activation of these ion channels and deformation of the membrane initiates the biochemical reaction cascades necessary for functional tissue growth. By applying such small forces directly to the membrane, mechanically weak scaffold materials may be used and, as the applied forces are produced remotely by coupling the particles to external fields, the system can be closed, preventing infection. In addition, forces applied to the scaffolds can be varied spatially in three dimensions by varying the distance of different regions of the scaffold to the field source or by changing the magnetic particle properties in different regions of the scaffold. This should allow for the production of complex 3-D tissue structures (i.e. bone/interface/cartilage composites).

For this project, an understanding of the spatial variation of the forces (translational and, in magnetically blocked particles, torque) which may be produced and factors affecting the interaction of the particles with the cell membrane is required to optimize the bioreactor design. In addition, the interaction of adjacent fields in an array of magnets must be understood in order to grow tissue on more than one scaffold in the bioreactor. These problems will be addressed in this workshop.

Study Group Report

The aim of this report is twofold: firstly to determine the force or torque exerted on a particle of given size by a magnet and secondly to derive models for the transmission of stress in osteoblasts (bone cell) and chondrocytes (cartilage cell).

The properties of the magnetic particles used in this process depend greatly upon their size. Particles with diameter below about 50nm behave as superparamagnets, that is as a paramagnetic material but with large susceptibility , whereas particles with diameter much above 50nm behave as permanent magnetic dipoles. In the first part of the report we calculate the forces and moments exerted on these different types of particle in a magnetic field generated by a disc magnet with uniform magnetisation aligned along its axis.

In the second part of the report we model the transmission of stresses in osteoblasts and chondrocytes. A reasonable amount of experimental evidence is available to support the modelling of chondrocytes and this tends to suggest that they should be modelled, over a short time-scale at least, as an elastic ball. There is, however, much less data available on osteoblasts, so following suggestion from the experimentalists (who brought the problem), we modelled these as a fluid filled sac enclosed by a taught elastic membrane. There needs to be further experimental work to determine the properties of this membrane. A linear model using known cell data leads to the conclusion that geometrically nonlinear effects need to be incorporated into the model.

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