Definition of a simple statistical parameter for the quantification of orientation in two dimensions: Application to cells on grooves of nanometric depths

Contact guidance is generally evaluated by measuring the orientation angle of cells. However, statistical analyses are rarely performed on these parameters. Here we propose a statistical analysis based on a new parameter σ, the orientation parameter, defined as the dispersion of the distribution of orientation angles. This parameter can be used to obtain a truncated Gaussian distribution that models the distribution of the data between −90° and +90°. We established a threshold value of the orientation parameter below which the data can be considered to be aligned within a 95% confidence interval. Applying our orientation parameter to cells on grooves and using a modelling approach, we established the relationship σ = αmeas + (52° − αmeas)/(1 + CGDER) where the parameter CGDE represents the sensitivity of cells to groove depth, and R the groove depth. The values of CGDE obtained allowed us to compare the contact guidance of human osteoprogenitor (HOP) cells across experiments involving different groove depths, times in culture and inoculation densities. We demonstrate that HOP cells are able to identify and respond to the presence of grooves 30, 100, 200 and 500 nm deep and that the deeper the grooves, the higher the cell orientation. The evolution of the sensitivity (CGDE) with culture time is roughly sigmoidal with an asymptote, which is a function of inoculation density. The σ parameter defined here is a universal parameter that can be applied to all orientation measurements and does not require a mathematical background or knowledge of directional statistics.