Diffusion dimensionality modeling of subcutaneous/intramuscular absorption of antibodies and long-acting injectables

To evaluate the role of diffusion process dimensionality in drug absorption following subcutaneous or intramuscular administration. The diffusion dimensionality model is based on analytical solutions of the 1-, 2- or 3-dimensional diffusion equations for a bolus input linked to a central compartment with first-order elimination. The model equations were reparameterized to contain three parameters for the time needed for the drug diffusion from the administration site, drug absorption into the central compartment, and the elimination rate constant. The diffusion dimensionality models were challenged with previously published subcutaneous absorption data for 13 antibody drugs and insulin lispro, and the long-acting injectable antipsychotic drugs: subcutaneous Perseris™, intramuscular Invega Sustenna®, Risperdal Consta®, and olanzapine. The Bayesian information criterion was used for model selection. The solution to the diffusion equation for a bolus dose administration is strongly dependent on the number of dimensions. The maximal concentration is lowest for the 3-dimensional diffusion equation. The pharmacokinetic profiles of all 13 antibodies were satisfactorily approximated by a diffusion dimensionality model. Three antibodies (CNTO5825, ACE910 and ustekinumab) were best described by the 2-dimensional diffusion equation. The 2- and 3-dimensional diffusion equations were equivalent for ABT981, guselkumab, adalimumab, nemolizumab, omalizumab, and secukinumab. Golimumab, DX2930, AMG139, and mepolizumab were best described by the 3-dimensional diffusion equation. All the long-acting antipsychotic dosage forms except Risperdal Consta were modeled satisfactorily. Diffusion dimensionality models are a parsimonious and effective approach for modeling drug absorption profiles of subcutaneously and intramuscularly administered small molecule and protein drugs and their dosage forms.