Relative Biological Effectiveness (RBE) and Quality Factor (Q) at extreme values of Linear Energy Transfer (LET) have been determined on the basis of experiments with single-cell systems and specific tissue responses. In typical single cell systems, each heavy particle (Ar or Fe) passes through a single cell or no cell. In tissue end-point experiments each heavy particle passes through several cells, and the LET can exceed 200 keV/micrometer in every cell. In most laboratory animal tissue systems, however, only a small portion of the hit cells are capable of expressing the end-point of interest to the investigator, such as cell killing, mutation or carcinogenesis. The following question must therefore be addressed: Do RBE's and Q factors derived from single-cell experiments properly account for the increased probability of multiple-cell damage by HZE tracks? A model is offered in which measured radiation effects and known tissue properties are combined to estimate the value of a multiplier of damage effectiveness on the basis of number of cells at risk, p3n, per track containing a hit cell, where n is the number of cells per track, based on tissue and organ geometry, and P3 is the probability that a cell in the track is capable of expressing the experimental end-point.