Tikhonov Regularization and Perturbation-Level Tuning for the CNM in Pharmacokinetics

Abstract

In pharmacokinetics, the clinical information collected from the patient is often much less than the complexity of the patient’s internal operations, hence the undetermined inverse problem has emerged as a challenge to solve it and find multiple possible point sets for considering the many possible implications of drug kinetics in the patient’s body. This paper suggests two enhanced schemes for the early cluster Newton method (CNM) to concomitantly explore a great solutions number for the inverse parameter determination in pharmacokinetics. The first scheme is the application of Tikhonov regularization to deal with the overdetermined system for hyperplane fitting in the CNM, and the second is an effective iterative strategy by tuning perturbation-level for the CNM. As a result of Tikhonov’s filtering operation, lower order singular values than the regularization parameter, that are to blame for the instability of the matrix equation, are efficiently eliminated. With perturbation-level tuning, following every iteration, as the point cluster (PoC) gets near the solution manifold (SoM), it is essential to lessen the level of perturbation in the patient’s clinical measurement data and this is suited for a numerical stabilization. Numerical simulation scenarios of two schemes have revealed that these suggested schemes can lower the iterations number and computed time, and PoC move more steadily towards the solutions manifold.

Keywords

• Tikhonov regularization
• physiologically based pharmacokinetics
• pharmacokinetics
• cluster Newton method
• inverse problem