In vitro researches on rat cells exposed to several types of thin asbestos fibres show a saturation in cytotoxicity as one increases the fibre concentration n on the cell surface. For given average fibre lengths, the saturation occurs at values that are 2-3 times the critical concentration nc for a percolative arrangement of randomly thrown sticks on a surface. Measurements of the threshold for genotoxic damage give concentrations that are about 0.1nc. One expects that, somewhere between these concentrations, large scale "critical fluctuations" will be observed in the data. These fluctuations are indeed seen in chrysotile treated rat pleural mesothelial cells, exhibiting DNA damage and chromosomal-number aberrations. We hypothesize that at such concentrations that fibre-clustering occurs, the fibres lock together and are hindered from traversing the cell membranes and internalizing. Some damage processes are thereby impeded. The kinetics of internalization is worked out with models involving continuum percolation. Pieces of evidence from in vivo results that support the theory are noted.