Optimizing circadian drug infusion schedules towards personalized cancer chronotherapy

Precision medicine requires accurate technologies for drug administration and proper systems pharmacology approaches for patient data analysis. Here, plasma pharmacokinetics (PK) data of the OPTILIV trial in which cancer patients received oxaliplatin, 5-fluorouracil and irinotecan via chronomodulated schedules delivered by an infusion pump into the hepatic artery were mathematically investigated. A pump-to-patient model was designed in order to accurately represent the drug solution dynamics from the pump to the patient blood. It was connected to semi-mechanistic PK models to analyse inter-patient variability in PK parameters. Large time delays of up to 1h41 between the actual pump start and the time of drug detection in patient blood was predicted by the model and confirmed by PK data. Sudden delivery spike in the patient artery due to glucose rinse after drug administration accounted for up to 10.7% of the total drug dose. New model-guided delivery profiles were designed to precisely lead to the drug exposure intended by clinicians. Next, the complete mathematical framework achieved a very good fit to individual time-concentration PK profiles and concluded that inter-subject differences in PK parameters was the lowest for irinotecan, intermediate for oxaliplatin and the largest for 5-fluorouracil. Clustering patients according to their PK parameter values revealed patient subgroups for each drug in which inter-patient variability was largely decreased compared to that in the total population. This study provides a complete mathematical framework to optimize drug infusion pumps and inform on inter-patient PK variability, a step towards precise and personalized cancer chronotherapy.

− (V max cp * L cpt )/(Kcp + L cpt ))/V l (1) dL sn dt = (−C sn l * L sn − Ef l * L sn + U p l * B sn where L i , B i and O i represent the concentration in the Liver, Blood and Organs respectively, with cpt representing CPT-11, and sn standing for SN38.
Parameters estimates for individual patients are presented in Table A and parameter mean and CV are in Table B. Model fit was assessed through Sum of Squared Residuals (SSR) ( Table C) and R 2 values (Table D). To test the validity of the PDE-based pump-to-patient model, we compared the goodness of this fit with that of the PK model with drug infusion rate equal to the infusion profile programmed in to the pump. Using the PDE to account for the properties of the system largely increased the model validity (

Oxaliplatin
The equations for oxaliplatin PK model are: where L i , B i and O i represent the concentration in the Liver, Blood and Organs respectively, with i representing either the the bound drug b or the free drug f . Parameters estimates for individual patients and mean and CV over the patient population are presented in Table E. Model fit was assessed through Sum of Squared Residuals (SSR) ( Table F) and R 2 values (Table G). To test the validity of the PDE-based pump-to-patient model, we compared the goodness of this fit with that of the PK model with drug infusion rate equal to the infusion profile programmed in to the pump. Using the PDE to account for the properties of the system largely increased the model validity (Table  F,    (10)

5-fluorouracil
The equations for 5-fluorouracil PK model are: where L i , B i and O i represent the concentrations of 5-fluorouracil in the Liver, Blood and Organs respectively. Parameters estimates for individual patients and Mean and CV over the patient population are presented in Table H. Model fit was assessed through Sum of Squared Residuals (SSR) ( Table I) and R 2 values (Table J). To test the validity of the pump-to-patient model, we compared the goodness of this fit with that of the PK model with drug infusion rate equal to the infusion profile programmed in to the pump. Using the PDE to account for the properties of the system largely increased the model validity (Table I,

Identifiability
Parameter identifiability was checked for irinotecan, oxaliplatin and 5-fluorouracil model using the method of likelihood profiles (reference [23] of main text). Briefly, the distance between the experimental data and the model is computed by an objective function, here the weighted sum of squared residuals: where y i are the data points at the corresponding time points t i , f (t i , θ) are the model values at t i with parameters θ, and σ i the data standard deviations. Minimizing this objective function over parameter values is equivalent to maximizing the likelyhood estimator for normally distributed datasets. For each parameter θ j , the likelihood profile C P L (θ j ) is defined as: The pointwise confidence interval of parameter θ j is defined as: where θ * j is the parameter optimal value which minimizes C(θ) . ∆ α is the χ 2 distribution value for 0.95 confidence α and one degree of freedom df = 1: A parameter is identifiable if its pointwise confidence interval is finite ([23] in main text). In other words, if the likelihood profile crosses the threshold value C P L (θ * j ) + ∆ α twice (i.e. when increasing and decreasing parameter value starting from optimal value), this proves parameter identifiability. The points at which the likelihood profile crosses the threshold are the ranges of the parameter confidence interval.
The study was done using Patient 1 parameter estimates as starting points. All model parameters were identifiable for all three drugs ( Figure  IV, V, VI).

Clustering
Clustering was done using fuzzy c-means clustering as described in the Methods section of main text. The validity function V F S as proposed by Fukuyama and Sugeno was used to determine the number of clusters for each drug. The optimal cluster number is defined as the one minimizing V F S . Results ares shown in Figures