A general model-based design of experiments approach to achieve practical identifiability of pharmacokinetic and pharmacodynamic models

Evolving Improved Sampling Protocols for Dose-Response Modelling Using Genetic Algorithms with a Profile-Likelihood Metric

Practical limitations of quality and quantity of data can limit the precision of parameter identification in mathematical models. Model-based experimental design approaches have been developed to minimise parameter uncertainty, but the majority of these approaches have relied on first-order approximations of model sensitivity at a local point in parameter space. Practical identifiability approaches such as profile-likelihood have shown potential for quantifying parameter uncertainty beyond linear approximations. This research presents a genetic algorithm approach to optimise sample timing across various parameterisations of a demonstrative PK-PD model with the goal of aiding experimental design. The optimisation relies on a chosen metric of parameter uncertainty that is based on the profile-likelihood method. Additionally, the approach considers cases where multiple parameter scenarios may require simultaneous optimisation. The genetic algorithm approach was able to locate near-optimal sampling protocols for a wide range of sample number (n = 3-20), and it reduced the parameter variance metric by 33-37% on average. The profile-likelihood metric also correlated well with an existing Monte Carlo-based metric (with a worst-case r > 0.89), while reducing computational cost by an order of magnitude. The combination of the new profile-likelihood metric and the genetic algorithm demonstrate the feasibility of considering the nonlinear nature of models in optimal experimental design at a reasonable computational cost. The outputs of such a process could allow for experimenters to either improve parameter certainty given a fixed number of samples, or reduce sample quantity while retaining the same level of parameter certainty.

Streamlining tablet lubrication design via model-based design of experiments

In oral solid dosage production through direct compression powder lubrication must be carefully selected to facilitate the manufacturing of tablets without degrading product manufacturability and quality (e.g. dissolution). To do so, several semi-empirical models relating compression performance to process operating conditions have been developed. Among them, we consider an extension of the Kushner and Moore model (Kushner and Moore, 2010, International Journal Pharmaceutics, 399:19) that is useful for the purpose, but requires an extensive experimental campaign for parameters identification. This implies the preparation and compression of multiple powder blends, each one with a different lubrication extent. In turn, this translates into a considerable consumption of Active Pharmaceutical Ingredient (API), and into time-consuming experiments. We tackled this issue by proposing a novel model-based design of experiments (MBDoE) approach, which minimizes the number of optimal blends for model calibration, while obtaining statistically sound parameters estimates and model predictions. Both sequential and parallel MBDoE configurations were compared. Experimental results involving two placebo blends with different lubrication sensitivity showed that this methodology is able to reduce the experimental effort by 60-70% with respect to the standard industrial practice independently of the formulation considered and configuration (i.e. parallel vs. sequential) adopted.

Kinetic analysis of the partial synthesis of artemisinin: Photooxygenation to the intermediate hydroperoxide

The price of the currently best available antimalarial treatment is driven in large part by the limited availability of its base drug compound artemisinin. One approach to reduce the artemisinin cost is to efficiently integrate the partial synthesis of artemisinin starting from its biological precursor dihydroartemisinic acid (DHAA) into the production process. The optimal design of such an integrated process is a complex task that is easier to solve through simulations studies and process modelling. In this article, we present a quantitative kinetic model for the photooxygenation of DHAA to an hydroperoxide, the essential initial step of the partial synthesis to artemisinin. The photooxygenation reactions were studied in a two-phase photo-flow reactor utilizing Taylor flow for enhanced mixing and fast gas-liquid mass transfer. A good agreement of the model and the experimental data was achieved for all combinations of photosensitizer concentration, photon flux, fluid velocity and both liquid and gas phase compositions. Deviations between simulated predictions and measurements for the amount of hydroperoxide formed are 7.1 % on average. Consequently, the identified and parameterized kinetic model is exploited to investigate different behaviors of the reactor under study. In a final step, the kinetic model is utilized to suggest attractive operating windows for future applications of the photooxygenation of DHAA exploiting reaction rates that are not affected by mass transfer limitations.

A framework for the optimal design of a minimum set of clinical trials to characterize von Willebrand disease

BACKGROUND AND OBJECTIVE

Von Willebrand disease (VWD) is one of the most severe inherited bleeding disorder in humans, and it is associated with a qualitative and/or quantitative deficiency of von Willebrand factor, a multimeric glycoprotein fundamental in the coagulation process. At present, the diagnosis of VWD is extremely challenging and mostly based on clinical experience. Kinetic models have been recently proposed and applied to help in the diagnosis and characterization of VWD, but the complexity of these models is such that they requires long and stressful clinical tests, such as the desmopressin response test (DDAVP), to achieve a satisfactory estimation of the individual haemostatic parameters. The goal of this paper is to design a minimal set of clinical tests for the identification of akinetic model to decrease the required time and effort for the characterization and diagnosis of VWD.

METHODS

A model proposed in the literature is used as a building block to develop a new model, where response surface methodologies have been applied to determine a set of explicit correlations linkingkinetic model parameters to basal clinical trials data. Model-based design of experiments techniques are then used to devise optimally informative tests for model validation which are shorter and easier to implement.

RESULTS

Results show an excellent agreement between the original model for VWD and the new proposed model on representing healthy and VWD subjects. The application of experimental design techniques for model validation shows the possibility to drastically reduce the duration of DDAVP tests from 24 h-3 h by exploiting complementary information from basal clinical tests.

CONCLUSIONS

Basal clinical tests can be used alongside a time-reduced DDAVP test to validate pharmacokinetic models for a quantitative characterisation of subjects affected by VWD and for a quicker and easier diagnosis of the disease.

Successive complementary model-based experimental designs for parameter estimation of fed-batch bioreactors

When a dynamic model is used for the description of (fed-)batch bioreactors, it is typical that the model parameters are highly correlated to each other. In this case, it is important to keep the parameter correlation as small as possible to obtain a reliable set of parameter estimates. In this study, we propose an anticorrelation parameter estimation scheme that can be best utilized when a number of different batch experiments are sequentially processed. The scheme iteratively performs parameter estimation and model-based design of experiment (MBDOE) at the beginning and between the batches. The important difference from the existing approaches is that the MBDOE objective is defined according to the system analysis performed a priori, so that each new batch supplements what is lacking from the previous batches combined, in terms of information. The use of the scheme is illustrated on a fed-batch bioreactor model.

Assessing the relative potency of (S)- and (R)-warfarin with a new PK-PD model, in relation to VKORC1 genotypes

PURPOSE

The purpose of this study is to develop a new pharmacokinetic-pharmacodynamic (PK-PD) model to characterise the contribution of (S)- and (R)-warfarin to the anticoagulant effect on patients in treatment with rac-warfarin.

METHODS

Fifty-seven patients starting warfarin (W) therapy were studied, from the first dose and during chronic treatment at INR stabilization. Plasma concentrations of (S)- and (R)-W and INRs were measured 12, 36 and 60 h after the first dose and at steady state 12-14 h after dosing. Patients were also genotyped for the G>A VKORC1 polymorphism. The PK-PD model assumed a linear relationship between W enantiomer concentration and INR and included a scaling factor k to account for a different potency of (R)-W. Two parallel compartment chains with different transit times (MTT₁ and MTT₂) were used to model the delay in the W effect. PD parameters were estimated with the maximum likelihood approach.

RESULTS

The model satisfactorily described the mean time-course of INR, both after the initial dose and during long-term treatment. (R)-W contributed to the rac-W anticoagulant effect with a potency of about 27% that of (S)-W. This effect was independent of VKORC1 genotype. As expected, the slope of the PK/PD linear correlation increased stepwise from GG to GA and from GA to AA VKORC1 genotype (0.71, 0.90 and 1.49, respectively).

CONCLUSIONS

Our PK-PD linear model can quantify the partial pharmacodynamic activity of (R)-W in patients contemporaneously exposed to therapeutic (S)-W plasma levels. This concept may be useful in improving the performance of future algorithms aiming at identifying the most appropriate W maintenance dose.

Self-optimisation and model-based design of experiments for developing a C-H activation flow process

A recently described C(sp3)-H activation reaction to synthesise aziridines was used as a model reaction to demonstrate the methodology of developing a process model using model-based design of experiments (MBDoE) and self-optimisation approaches in flow. The two approaches are compared in terms of experimental efficiency. The self-optimisation approach required the least number of experiments to reach the specified objectives of cost and product yield, whereas the MBDoE approach enabled a rapid generation of a process model.

High-Fidelity Modelling Methodology of Light-Limited Photosynthetic Production in Microalgae

Reliable quantitative description of light-limited growth in microalgae is key to improving the design and operation of industrial production systems. This article shows how the capability to predict photosynthetic processes can benefit from a synergy between mathematical modelling and lab-scale experiments using systematic design of experiment techniques. A model of chlorophyll fluorescence developed by the authors [Nikolaou et al., J Biotechnol 194:91-99, 2015] is used as starting point, whereby the representation of non-photochemical-quenching (NPQ) process is refined for biological consistency. This model spans multiple time scales ranging from milliseconds to hours, thus calling for a combination of various experimental techniques in order to arrive at a sufficiently rich data set and determine statistically meaningful estimates for the model parameters. The methodology is demonstrated for the microalga Nannochloropsis gaditana by combining pulse amplitude modulation (PAM) fluorescence, photosynthesis rate and antenna size measurements. The results show that the calibrated model is capable of accurate quantitative predictions under a wide range of transient light conditions. Moreover, this work provides an experimental validation of the link between fluorescence and photosynthesis-irradiance (PI) curves which had been theoricized.

An Identifiable State Model To Describe Light Intensity Influence on Microalgae Growth

Despite the high potential as feedstock for the production of fuels and chemicals, the industrial cultivation of microalgae still exhibits many issues. Yield in microalgae cultivation systems is limited by the solar energy that can be harvested. The availability of reliable models representing key phenomena affecting algae growth may help designing and optimizing effective production systems at an industrial level. In this work the complex influence of different light regimes on seawater alga Nannochloropsis salina growth is represented by first principles models. Experimental data such as in vivo fluorescence measurements are employed to develop the model. The proposed model allows description of all growth curves and fluorescence data in a reliable way. The model structure is assessed and modified in order to guarantee the model identifiability and the estimation of its parametric set in a robust and reliable way.