Development of a diffusion-weighed mathematical model for intradermal drainage quantification

The quantitative assessment of lymphatic dermal clearance using NIR fluorescent tracers is particularly important for the early diagnosis of several potential disabling diseases. Currently, half-life values are computed using a mono-exponential mathematical model, neglecting diffusion of the tracer within the dermis after injection. The size and position of the region of interest are subjectively manually selected around the point of injection on the skin surface where the fluorescence signal intensity is averaged, neglecting any spatial information contained in the image. In this study we present and test a novel mathematical model allowing the objective quantification of dermal clearance, taking into consideration potential dermal diffusion. With only two parameters, this “clearance-diffusion” model is simple enough to be applied in a variety of settings and requires almost no prior information about the system. We demonstrate that if dermal diffusion is low, the mono-exponential approach is suitable but still lacking objectivity. However, if dermal diffusion is substantial, the clearance-diffusion model is superior and allows the accurate calculation of half-life values. Graphic Abstract