Estimating parameters in unstructured models of biological systems

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Biomedical and Chemical Engineering


Philip A. Rice


Fermentation, Ethanol, Optimal control, Parameter estimation, Unstructured models

Subject Categories

Biomedical Engineering and Bioengineering | Chemical Engineering | Computer Sciences | Engineering | Physical Sciences and Mathematics


In this study, an infeasible path optimization algorithm was developed to estimate parameters in unstructured growth models of fermentation systems. Optimum values of the kinetic parameters were evaluated for a growth-associated product formation system and a non growth-associated product formation system. Ethanol synthesis, which occurs during growth of yeast under anaerobic conditions, was the growth associated product formation process studied. To describe the specific growth rate of microorganisms and the product inhibition of the growth, two unstructured models (linear and exponential) were used. Optimum values of the kinetic constants in these two different models were evaluated for each experiment. Experiments were carried out with different initial conditions to study any variation in the values of the kinetic parameters.

The aerobic fermentation of penicillin with an induction of metabolite production, was the non-growth associated product formation studied. The mathematical model, developed by Bajpai and Reub (1981) for production of penicillin, and the Contois kinetics for the specific rate of the mycelial growth, were used in this research. Experiments under different fed-batch conditions were carried out, and the optimum values of the kinetic parameters were evaluated from each experiment. However, because of the characteristics of the fermentation system, different sets of parameters were evaluated from the different parts of the experiment.

Usually, optimal control and estimation problems are solved by embedding a differential equation solver into the optimization strategy. The optimization algorithm requires solving the differential equations of the system and evaluating the objective function and constraints at each iteration, which can be time consuming and not robust even for small problems. In this study, an infeasible path algorithm was implemented which avoids the above requirement by simultaneously converging to the optimal parameters values, while solving the differential equations. To do this, the constraints, which are the state-space representation of the system (differential equations), are converted to algebraic equations by using orthogonal collocation [Finlayson (1980)]. The objective function for the parameter estimation was based on the least square formulation. Successive Quadratic Programming (SQP), was the algorithm used to perform the parameter estimation.


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