  The mixing problem is classically encountered in the study of differential
equations applied to fluid dynamics. An understanding of fluid movement under
constraints is particularly important in the field of medicine as many
therapeutics and biologic molecules are dissolved in bodily fluids. Many areas
of biomedical research and diagnostics also rely on fluid sampling to obtain
accurate measurements of biologic markers. We present in this manuscript the
general solution to the mixing problem in the context of studying physiological
phenomena based on the movement of fluid acting as a carrier for medically
relevant molecules/solutes. We also expanded the general solution to become
more compatible with areas of biomedical research and diagnostics that seek to
characterize bodily fluids located in areas that are difficult to sample.
