Optimal Design of Dynamic Experiments in Bioscience Engineering

Living systems are rife with variability. Well-chosen experimental designs are necessary to deal with this variability when modeling such systems. Models for living systems often rely on knowledge of physical, chemical and biological laws, such as mass balances, transport phenomena and reaction kinetics, and are often described by a system of non-linear differential equations. So, the structure of a model can often be determined from first principles. However, the model will generally also rely on parameters whose numerical values cannot be determined from physical laws. These parameters must then be inferred from experimental data before the model can be put to use. A well-chosen experiment can greatly improve the estimation of the model parameters. However, there exist several challenges for constructing such informative experiments for dynamic systems. One challenge is the dependence of the optimal experiment on the true model parameters, making it difficult to perform robust experiments that work well regardless of the specific model parameter values. Another challenge is the correlation of the observations due to the presence of process noise. The central research topic of this thesis revolves around solving these challenges by developing robust experimental design methodology for noisy dynamic systems. My novel methodology is developed to improve postharvest and other bio-science engineering applications, and is mainly applied to the estimation of respiration and fermentation parameters of pear fruit. Experiments that precisely estimate the model parameters of spring-mass-damper systems and compartment systems are also constructed. After a brief introduction on dynamic design of experiments and its application areas, this PhD thesis deals with the estimation of respiration parameters of pear fruit inside a jar, modeled by Michaelis-Menten kinetics. Air flowing into the jar has to be controlled so that the parameters of the Michaelis-Menten model can be estimated as precisely as possible. The quality of this parameter estimation, and thus of the experimental design, is quantified using the determinant of the Fisher information matrix, which is inversely related to the area of the confidence ellipse of the two Michaelis-Menten model parameters. The air flowing into the jar must thus be optimized so that the determinant of the Fisher information matrix is as large as possible. One major challenge here is the dependence of this Fisher information matrix on the true, but unknown, parameters of the system. The most commonly used method in the literature to deal with this issue is locally optimal design, where a single initial guess is used for the true parameter. One main conclusion from my work is that this optimal experimental design technique outperforms several commonly used heuristic experimental techniques. Subsequently, also fermentation of the pear fruit is taken into account. The locally optimal design method only takes into account a single initial guess, and may not perform well if this guess deviates substantially from the true parameter values. Instead of a single initial guess, an entire distribution could be used to quantify the prior knowledge and uncertainty on the unknown parameters. Because of the use of a prior distribution, this method is called Bayesian experimental design. Most current techniques in the literature only allow for parametric prior distributions, such as normal distributions. The prior information about respiration and fermentation, coming from a previously gathered dataset, could not be summarized by any parametric distribution. For this reason, I developed a novel experimental design technique based on a Markov-chain Monte-Carlo (MCMC) analysis of this previously gathered data. This method is thus able to approximate arbitrary distributions. I found that this flexible experimental design technique is more robust than the commonly used locally optimal design method and other robust methods. The final part of the thesis focuses on robust and adaptive experimental design techniques for dynamic systems with process noise. Current experimental design techniques for dynamic systems generally only incorporate measurement noise, but biological systems also often involve process noise. Calculating the Fisher information matrix for such systems requires estimating the uncertain dynamic states, using Bayesian filtering techniques. For linear dynamical systems, the optimal filter is the Kalman filter. However, deriving the Fisher information matrix for dynamic systems under process noise greatly improves the quality of the experiment.

Jaar van publicatie:2021

Toegankelijkheid:Open