Constraint-based perturbation analysis with cluster Newton method: a case study of personalized parameter estimations with irinotecan whole-body physiologically based pharmacokinetic model

Background: Drug development considering individual varieties among patients becomes crucial to improve clinical development success rates and save healthcare costs. As a useful tool to predict individual phenomena and correlations among drug characteristics and individual varieties, recently, whole-body physiologically based pharmacokinetic (WB-PBPK) models are getting more attention. WB-PBPK models generally have a lot of drug-related parameters that need to be estimated, and the estimations are difficult because the observed data are limited. Furthermore, parameter estimation in WB-PBPK models may cause overfitting when applying to individual clinical data such as urine/feces drug excretion for each patient in which Cluster Newton Method (CNM) is applicable for parameter estimation. In order to solve this issue, we came up with the idea of constraint-based perturbation analysis of the CNM. The effectiveness of our approach is demonstrated in the case of irinotecan WB-PBPK model using common organ-specific tissue-plasma partition coefficients (Kp) among the patients as constraints in WB-PBPK parameter estimation. Results: We find strong correlations between age, renal clearance and liver functions in irinotecan WB-PBPK model with personalized physiological parameters by observing the distributions of optimized values of strong convergence drug-related parameters using constraint-based perturbation analysis on CNM. The constraint-based perturbation analysis consists of the following three steps: (1) Estimation of all drug-related parameters for each patient; the parameters include organ-specific Kp. (2) Fixing suitable values of Kp for each organ among all patients identically. (3) Re-estimation of all drug-related parameters other than Kp by using the fixed values of Kp as constraints of CNM. Conclusions: Constraint-based perturbation analysis could yield new findings when using CNM with appropriate constraints. This method is a new technique to find suitable values and important insights that are masked by CNM without constraints.