European Journal of Applied Mathematics

Free boundary value problems associated with the growth and development of multicellular spheroids

H. M. BYRNE a1 and M. A. J. CHAPLAIN a2
a1 Department of Mathematics, UMIST, PO Box 88, Manchester M60 1QD, UK (email:
a2 Department of Mathematics and Computer Science, University of Dundee, Dundee DD1 4HN, UK (email:


In this paper a generalized model for the growth of avascular tumours is presented. The formulation leads naturally to the incorporation of free boundaries which define the outer tumour surface explicitly and various inner surfaces implicitly. A combination of numerical simulations, asymptotic analysis and perturbation techniques is used to study the model and yields results, which agree well with experimentally-observed phenomena.

(Received August 30 1996)
(Revised March 5 1997)