Federico Galvanin

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

The use of pharmacokinetic (PK) and pharmacodynamic (PD) models is a common and widespread practice in the preliminary stages of drug development. However, PK–PD models may be affected by structural identifiability issues intrinsically related to their mathematical formulation. A preliminary structural identifiability analysis is usually carried out to check if the set of model parameters can be uniquely determined from experimental observations under the ideal assumptions of noise-free data and no model uncertainty. However, even for structurally identifiable models, real-life experimental conditions and model uncertainty may strongly affect the practical possibility to estimate the model parameters in a statistically sound way. A systematic procedure coupling the numerical assessment of structural identifiability with advanced model-based design of experiments formulations is presented in this paper. The objective is to propose a general approach to design experiments in an optimal way, detecting a proper set of experimental settings that ensure the practical identifiability of PK–PD models. Two simulated case studies based on in vitro bacterial growth and killing models are presented to demonstrate the applicability and generality of the methodology to tackle model identifiability issues effectively, through the design of feasible and highly informative experiments.

Optimal design of clinical tests for the identification of physiological models of type 1 diabetes in the presence of model mismatch

How to design a clinical test aimed at identifying in the safest, most precise and quickest way the subject-specific parameters of a detailed model of glucose homeostasis in type 1 diabetes is the topic of this article. Recently, standard techniques of model-based design of experiments (MBDoE) for parameter identification have been proposed to design clinical tests for the identification of the model parameters for a single type 1 diabetic individual. However, standard MBDoE is affected by some limitations. In particular, the existence of a structural mismatch between the responses of the subject and that of the model to be identified, together with initial uncertainty in the model parameters may lead to design clinical tests that are sub-optimal (scarcely informative) or even unsafe (the actual response of the subject might be hypoglycaemic or strongly hyperglycaemic). The integrated use of two advanced MBDoE techniques (online model-based redesign of experiments and backoff-based MBDoE) is proposed in this article as a way to effectively tackle the above issue. Online model-based experiment redesign is utilised to exploit the information embedded in the experimental data as soon as the data become available, and to adjust the clinical test accordingly whilst the test is running. Backoff-based MBDoE explicitly accounts for model parameter uncertainty, and allows one to plan a test that is both optimally informative and safe by design. The effectiveness and features of the proposed approach are assessed and critically discussed via a simulated case study based on state-of-the-art detailed models of glucose homeostasis. It is shown that the proposed approach based on advanced MBDoE techniques allows defining safe, informative and subject-tailored clinical tests for model identification, with limited experimental effort.

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.

Online model-based redesign of experiments with erratic models: A disturbance estimation approach

Abstract Model-based design of experiment (MBDoE) techniques are a useful tool to maximise the information content of experimental trials when the purpose is identifying the set of parameters of a deterministic model in a statistically sound way. In a conventional MBDoE procedure, the information gathered during the evolution of an experiment is exploited only at the end of the experiment itself. Conversely, online model-based redesign of experiment (OMBRE) techniques have been recently proposed to exploit the information as soon as it is generated by the running experiment, allowing for the dynamic update of the experimental conditions to yield the most informative data in order to improve the parameter identification task. However, the effectiveness of MBDoE strategies (including OMBRE) may be severely affected by the presence of systematic modelling errors as well as by disturbances acting on the system. In this paper, a novel experiment design approach (DE-OMBRE) is presented, where a model updating policy including disturbance estimation (DE) is embedded within an OMBRE strategy in order to achieve a statistically satisfactory estimation of the model parameters as well as to estimate the possible discrepancy between the real system and the model being identified. The procedure allows reducing (or even avoiding) constraint violations, preserving the optimality of the redesign even in the presence of systematic errors and/or unknown disturbances acting on the system. Two simulated case studies of different levels of complexity are used to illustrate the benefits of the novel approach.

A joint model-based experimental design approach for the identification of kinetic models in continuous flow laboratory reactors

Continuous flow laboratory reactors are typically used for the development of kinetic models for catalytic reactions. Sequential model-based design of experiments (MBDoE) procedures have been proposed in literature where experiments are optimally designed for discriminating amongst candidate models or for improving the estimation of kinetic parameters. However, the effectiveness of these procedures is strongly affected by the initial model uncertainty, leading to suboptimal design solutions and higher number of experiments to be executed. A joint model-based design of experiments (j-MBDoE) technique, based on multi-objective optimization, is proposed in this paper for the simultaneous solution of the dual problem of discriminating among competitive kinetic models and improving the estimation of the model parameters. The effectiveness of the proposed design methodology is tested and discussed through a simulated case study for the identification of kinetic models of methanol oxidation over silver catalyst.

Towards on-line model-based design of experiments

Abstract Model-based experiment design aims at detecting a set of experimental conditions yielding the most informative process data to be used for the estimation of the process model parameters. In this paper, a novel on-line strategy for the optimal model-based re-design of experiments is presented and discussed. The novel technique allows the dynamic update of the control variable profiles while an experiment is still running, and can embody a dynamic investigation of different directions of information through the adoption of modified design criteria. A case study illustrates the benefits of the new approach when compared to a conventional design.

Towards Model-Based Diagnosis of von Willebrand Disease

Von Willebrand disease (VWD) is the most common inherited coagulation disorder to be seen in humans. It originates from a deficiency and/or dysfunction of the von Willebrand factor (VWF), a large multimeric glycoprotein playing a central role in the hemostasis process. Diagnosing VWD may be complicated because of the heterogeneous nature of the disorder. A new mechanistic model of VWD, identified from clinical data, is presented in this paper. The model allows for the automatic detection of VWD variants, elucidating the critical pathways involved in the disease recognition and characterisation.

On the use of continuous glucose monitoring systems to design optimal clinical tests for the identification of type 1 diabetes models

The identification of individual parameters of detailed physiological models of type 1 diabetes can be carried out by clinical tests designed optimally through model-based design of experiments (MBDoE) techniques. So far, MBDoE for diabetes models has been considered for discrete glucose measurement systems only. However, recent advances on sensor technology allowed for the development of continuous glucose monitoring systems (CGMSs), where glucose measurements can be collected with a frequency that is practically equivalent to continuous sampling. To specifically address the features of CGMSs, in this paper the optimal clinical test design problem is formulated and solved through a continuous, rather than discrete, approach. A simulated case study is used to assess the impact of CGMSs both in the optimal clinical test design problem and in the subsequent parameter estimation for the identification of a complex physiological model of glucose homeostasis. The results suggest that, although the optimal design of a clinical test is simpler if continuous glucose measurements are made available through a CGMS, the noise level and formulation may make continuous measurements less suitable for model identification than their discrete counterparts.

A framework for model-based design of parallel experiments in dynamic systems

Abstract Advanced model-based experiment design techniques are essential for rapid development, refinement and statistical assessment of deterministic process models. One objective of experiment design is to devise experiments yielding the most informative data for use in the estimation of the model parameters. Current techniques assume the multiple experiments are designed in a sequential manner. The concept of model-based design of parallel experiments design is presented in this paper. A novel approach, viable for sequential, parallel and sequential-parallel design isproposed and evaluated through an illustrative case study.

A methodology for direct exploitation of available information in the online model-based redesign of experiments

Online model-based design of experiments techniques were proposed to exploit the progressive increase of the information resulting from the running experiment, but they currently exhibit some limitations: the redesign time points are chosen “a-priori” and the first design may be heavily affected by the initial parametric mismatch. In order to face such issues an information driven redesign optimisation (IDRO) strategy is here proposed: a robust approach is adopted and a new design criterion based on the maximisation of a target profile of dynamic information is introduced. The methodology allows determining when to redesign the experiment in an automatic way, thus guaranteeing that an acceptable increase in the information content has been achieved before proceeding with the intermediate estimation of the parameters and the subsequent redesign of the experiment. The effectiveness of the new experiment design technique is demonstrated through two simulated case studies.