Model based optimal control of gene delivery systems

After more than two decades of intensive investigations, gene therapy has made impressive recent progress and is now among the most promising strategies for treating genetic disorders. However, a major challenge currently facing a clinical translation of gene-based therapy is the lack of an optimal gene delivery vector. This PhD thesis aims to investigate the application of mathematical modelling techniques, coupled with the optimal control theory, in gene delivery systems in order to improve the pharmacological effects while minimising the toxicological responses. The first contribution of this work presents an innovative approach based on the optimal control strategy for optimising the process of gene delivery. The methodology developed in this work highlights the advantages of process modelling and model analysis, contributing towards a detailed quantitative understanding of the system, while aiming for the optimal control of such systems. An integrated pharmacokinetic/pharmacodynamic (PK/PD) model-based optimal control algorithm was developed for non-viral siRNA delivery. This aims at incorporating the dynamics of the delivery process while simultaneously considering the main multi-objective optimisation issues, such as efficacy and toxicity. The framework presented in this thesis provides an efficient model-based platform for making decisions under uncertainty, which is lacking for gene delivery systems. As part of the presented approach, the model uncertainty that comes from variability in cell division time was analysed and the developed control strategy was tested in the presence of uncertainty. The proposed methodology was also tested by using in vivo clinical data for gene therapy in patients with haemophilia B. Haemophilia B is a genetic bleeding disorder resulting from a deficiency or dysfunction of a protein called factor IX, which is critical for blood-clotting. In this work, a modelling framework is proposed to predict the physiological response of a subject affected by type B haemophilia to a dose of vector. The results from this study demonstrate a good prediction of the model. The PK/PD parameters were individually estimated for each patient in a dose-independent manner for a personalised gene therapy, while a population modelling approach was investigated to guide initial dose selection. The modelling framework being developed in this thesis should be extended in the future to include the spatial distribution of the genetic materials resulting in a system of reaction-diffusion partial differential equations (PDEs). To this end, the last part of the thesis presents a novel theoretical framework for parameter estimation of partial differential equations in a complex geometrical domain using an artificial neural network (ANN) algorithm. This work will provide a stepping stone on the pathway for developing a reaction-diffusion model paving the way for further investigation of the effect of cellular geometry in the diffusion of genetic materials by taking into account the cellular architectures.