Practical Recoverability and Numerical Identifiability of Kinetic Rate Constants from Noisy Time-Activity Curves in a Patient-Derived Renogram Model

Close agreement between modeled and observed time-activity curves (TACs) does not necessarily imply accurate recovery of the underlying kinetic parameters. We evaluated this distinction using a partially observed four-compartment renogram model with a latent reservoir and observed left kidney, right kidney, and bladder TACs. Six de-identified renograms provided patient-derived reference parameter vectors for synthetic recovery experiments with added noise, together with analyses of temporal sampling, optimizer behavior, initialization, and numerical identifiability. Median total NRMSE values relative to the clean synthetic TACs were on the order of 10 − 3 , indicating excellent TAC reconstruction. Parameter recovery was substantially less uniform: some rate constants were recovered accurately, whereas others exhibited multiplicative errors of tens to hundreds, repeated boundary contact, or compensation involving the latent reservoir. Repeated optimizations also converged consistently to incorrect parameter vectors while preserving excellent TAC fits. The scaled residual Jacobian was numerically full rank but severely ill-conditioned, and several 95% profile likelihood intervals remained open at the optimization bounds. These findings demonstrate that TAC fit quality alone is insufficient to assess parameter reliability. TAC reconstruction, parameter recovery, numerical rank, boundary behavior, optimizer stability, and profile likelihoods provide complementary evidence and should be interpreted together when evaluating partially observed kinetic models.