Por favor, use este identificador para citar o enlazar este ítem:
http://cimat.repositorioinstitucional.mx/jspui/handle/1008/999| BONE METASTASIS TREATMENTS BASED ON OPTIMAL CONTROL | |
| JOSE ARIEL CAMACHO GUTIERREZ | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| Metastatic disease is a lethal stage of cancer progression, characterized by the spread of aberrant cells from a primary tumor to distant tissues in the body. In recent years, there has been a multidisciplinary effort by the scientific community to understand the mechanisms of bone metastasis. Several treatments are used to deal with bone metastases formation. Unfortunately, they are mainly palliative as the disease is considered incurable. We devote this Thesis to the mathematical modeling of bone metastasis with the objective of gaining more insight about this biological process while exploring the optimization of treatments. In this Thesis, we first propose a nonlinear differential model to describe the dynamics between tumor cells and bone cells, osteoclasts and osteoblasts. The model is based on a power law functional that represents and simplify the paracrine signaling between the BMU cells along with a logistic growth for cancer cells. This model allows us to explore different metastatic scenarios and to identify potential factors that may aid cancer cells in the colonization of bone. We then explore the effects of TGF_ andWnt on bone dynamics with an extended mathematical model, and thereby study different disease control strategies. For these models, we present the corresponding stability analysis, deduce biological implications of these theoretical results, and show numerical simulations. This allows us to gain biological information regarding the success or failure of the invasion of bone metastasis, as well as to acknowledge a crucial interplay between TGF-beta and Wnt in the bone remodeling process, both in health and in disease. As a second step, in this Thesis we present an optimal control approach to explore treatment strategies for bone diseases with a main focus on bone metastasis. We first focus on denosumab and radiotherapy treatments through optimal control problems with L2 cost functionals, obtaining continuous optimal control solutions. We provide proofs of existence and uniqueness of solutions to the corresponding optimal control problems for each treatment and present numerical simulations to analyze the effectiveness of both treatments under different metastatic invasion scenarios. We next focus on employing optimal control for the TGF-beta/Wnt model. Clinically, optimal solutions may be more relevant if they only present ’off’ and ’on’ states, and that is why we propose in this case a L1 cost functional to potentially obtain p | |
| 23-08-2019 | |
| Tesis de doctorado | |
| OTRAS | |
| Versión aceptada | |
| acceptedVersion - Versión aceptada | |
| Aparece en las colecciones: | Tesis del CIMAT |
Cargar archivos:
| Fichero | Descripción | Tamaño | Formato | |
|---|---|---|---|---|
| TE 722.pdf | 4 MB | Adobe PDF | Visualizar/Abrir |