DGT (Diffusion Gradients in Thin films) was designed to sample trace metals in situ at their natural concentrations. The setup and the experimental deployment conditions were established to allow interpretation of a linear accumulation of metal with time, using a simple expression based on a steady-state flux under perfect sink conditions. However, the extension of DGT to a wide range of analytes and its use under varied conditions has shown that, in some situations, these conditions are not fulfilled, so that accumulations with time are nonlinear. Previously, when such curvature was observed, concentrations in solution could not be reliably calculated. Here, we present fundamentally derived equations that reproduce the time accumulation for three situations: (i) kinetic limitations in the binding to the resin, (ii) saturation or equilibrium effects, or (iii) non-negligible competitive effects. We show how the accumulations can be quantified, in terms of the required kinetic and thermodynamic constants, and provide practical guidance for their use to obtain reliable estimates of solution concentrations. Solutions containing Mg or Mn, where all three situations can prevail, are used as examples. Calculated concentrations show reasonable agreement with the experimentally known values and with the results of a numerical model of the system, significantly improving, the estimations based on perfect sink conditions., Such an approach opens up the possibility of using DGT more widely in challenging systems and allows DGT data to be interpreted more fully.