Identiﬁability of parameters in PBPK models - Watanabe, Simon Berglund (My University, 2019)
Intheﬁeldofpharmacologics,physiologically-basedpharmacokinetic(PBPK)models can be used for predicting the pharmacokinetics of a drug compound in the body. These models are often a system of ordinary diﬀerential equations (ODEs) that describe the transport of a drug between diﬀerent compartments of the body. The models depend on several parameters, some of which cannot be measured experimentally and instead these parameters are often estimated from experimental data using maximum likelihood. However, in many applications in systems biology, estimates will suﬀer from unidentiﬁability issues, meaning that well-determined estimates cannot be inferred from the data [17]. Thisproblemcomesintwoforms,structuralunidentiﬁabilityandpracticalunidentiﬁability,bothofwhichcanbeanalyzedwiththeproﬁlelikelihoodmethoddeveloped by Raue et.al [14]. The proﬁle likelihood method is a numerical method for calculating likelihood-based conﬁdence intervals of the parameters, which are then used to assess identiﬁability. In this project the proﬁle likelihood method is implemented in MATLAB and used to perform identiﬁability analysis on key model parameters for three PBPK models using simulated data. Thus, the results of this project are both a showcase of the proﬁlelikelihoodmethodandananalysisoftheidentiﬁabilityofparametersinsome speciﬁc models used for pulmonary drug delivery. The results indicate that if very precise measurements could be taken then all parameters considered would be identiﬁable. When a reasonable measurement error is applied on the simulated data the same is not true. Some parameters, such as the in-vivo pulmonary permeability and deposition fraction will remain identiﬁable, but most other parameters will suﬀer from practical unidentiﬁability. With a reasonable measurement error the identiﬁability of most model parameters will also be dependent on the particular error realization. To address these issues, additional dataisconsideredbyobservinghowtheuncertaintyinparameterestimatesimpacts observables. Bythismethod(alsosuggestedbyRaue[14])additionalmeasurements are introduced in an eﬀective manner to potentially resolve unidentiﬁabilities. Keywords: structural unidentiﬁability, practical unidentiﬁability, pulmonary drug delivery, maximum likelihood estimation.
Keywords: Matematik; Mathematics