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2011, 8(4): 1061-1083. doi: 10.3934/mbe.2011.8.1061

## A mathematical model of the compression of a spinal disc

 1 Calgary Board of Education, Calgary, AB T2G 2L9, Canada 2 School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623-5801, United States

Received  January 2010 Revised  April 2011 Published  August 2011

A model is developed of the stress-strain response of an intervertebral disc to axial compression. This is based on a balance of increased intradiscal pressure, resulting from the compression of the disc, and the restraining forces generated by the collagen fibres within the annulus fibrosus. A formula is derived for predicting the loading force on a disc once the nucleus pressure is known. Measured material values of L3 and L4 discs are used to make quantitative predictions. The results compare reasonably well with experimental results.
Citation: Matthias Ngwa, Ephraim Agyingi. A mathematical model of the compression of a spinal disc. Mathematical Biosciences & Engineering, 2011, 8 (4) : 1061-1083. doi: 10.3934/mbe.2011.8.1061
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