A diffusion-limited-aggregation (DLA) model of human breast lobe growth

The Centenary (190th) Meeting of the Pathological Society of Great Britain and Ireland
The Journal of Pathology
4 – 7 July 2006
DOI: 10.1002/path.2052

J.J. Going1, P. Bourke2

1 University of Glasgow, Glasgow, United Kingdom
2 Swinburne University, Melbourne, Australia

Background. The ‘sick lobe’ hypothesis emphasizes a lobar dimension in breast intraepithelial neoplasia. Separate parenchymal lobes differ greatly in size, but it is not known whether this variation is random, or deterministic. ‘Virtual lobes’ were grown ‘in silico’ to explore size variation in a model of breast lobe growth. Methods. The virtual lobes were grown inside an ‘envelope’ bounded by a 3D breast surface scan and a plane representing the chest wall. 3D diffusion-limited aggregation (DLA) used seed points representing lobar anlagen of the breast bud with visualisation in POV-Ray. Results. Branching lobe-like structures were created, with striking similarities and differences from real breast structure. Highly variable lobe size mirrored the in vivo situation, but long unbranched central ducts, which occur in human breast, did not appear. Conclusions. Highly variable lobe size emerges readily in a random model of breast lobe growth. It is certainly possible, therefore, that variable lobe volume in human breasts could arise by stochastic processes. However, differences between virtual and real lobe branching emphasize that DLA modelling over- simplifies actual human breast growth, and lobe-size determining events such (hypothetical) growth promoting mutations prior to thelarche are not excluded.