Mathematical assessment of the spatial distribution of Langerhans cells in guinea pig epidermis.

Two mathematical indexes, Hopkins-Skellam index (HSI) and Morisita index (MI), were applied to assess the distribution of ATPase-stained epidermal Langerhans cells (ELC) in the guinea pig skin. To our knowledge, this is the first report in which the degree of regularity has been expressed numerically by computation based on theoretical equations. The regularity of ELC in the normal skin was confirmed by the value of HSI (P < 0.0001). In the topical steroid applied skin, the number of ELC decreased significantly but the value of HSI was similar to that of the normal skin; while in the ultraviolet B (UVB) exposed skin, both number of ELC and regularity of ELC distribution decreased significantly. The graph of MI for the UVB exposed skin clearly showed that the distribution of ELC had local clumps. The two indexes, HSI and MI have been quite useful for determining the regularity of ELC. These indexes may have a wide application to other cells.