title: Enhancing dendritic cell immunotherapy for melanoma using a simple mathematical model.
abstract: BACKGROUND
  The immunotherapy using dendritic cells (DCs) against different varieties of cancer is an approach that has been previously explored which induces a specific immune response. This work presents a mathematical model of DCs immunotherapy for melanoma in mice based on work by Experimental Immunotherapy Laboratory of the Medicine Faculty in the Universidad Autonoma de Mexico (UNAM).
  
  
  METHODS
  The model is a five delay differential equation (DDEs) which represents a simplified view of the immunotherapy mechanisms. The mathematical model takes into account the interactions between tumor cells, dendritic cells, naive cytotoxic T lymphocytes cells (inactivated cytotoxic cells), effector cells (cytotoxic T activated cytotoxic cells) and transforming growth factor β cytokine (T G F-β). The model is validated comparing the computer simulation results with biological trial results of the immunotherapy developed by the research group of UNAM.
  
  
  RESULTS
  The results of the growth of tumor cells obtained by the control immunotherapy simulation show a similar amount of tumor cell population than the biological data of the control immunotherapy. Moreover, comparing the increase of tumor cells obtained from the immunotherapy simulation and the biological data of the immunotherapy applied by the UNAM researchers obtained errors of approximately 10 %. This allowed us to use the model as a framework to test hypothetical treatments. The numerical simulations suggest that by using more doses of DCs and changing the infusion time, the tumor growth decays compared with the current immunotherapy. In addition, a local sensitivity analysis is performed; the results show that the delay in time " τ", the maximal growth rate of tumor "r" and the maximal efficiency of tumor cytotoxic cells rate "aT" are the most sensitive model parameters.
  
  
  CONCLUSIONS
  By using this mathematical model it is possible to simulate the growth of the tumor cells with or without immunotherapy using the infusion protocol of the UNAM researchers, to obtain a good approximation of the biological trials data. It is worth mentioning that by manipulating the different parameters of the model the effectiveness of the immunotherapy may increase. This last suggests that different protocols could be implemented by the Immunotherapy Laboratory of UNAM in order to improve their results.
authors.affiliation: Laboratorio de Modelación y Simulación, Centro de Investigación en Computación, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz, Esq. Miguel Othón de Mendizábal, Del. Gustavo A. Madero, México City, 07738, México. erandicm@sagitario.cic.ipn.mx.
authors.forename: E
authors.initials: E
authors.lastname: Castillo-Montiel
authors.affiliation: Laboratorio de Modelación y Simulación, Centro de Investigación en Computación, Instituto Politécnico Nacional, Av. Juan de Dios Bátiz, Esq. Miguel Othón de Mendizábal, Del. Gustavo A. Madero, México City, 07738, México. jchimale@ipn.mx.
authors.forename: J C
authors.initials: JC
authors.lastname: Chimal-Eguía
authors.affiliation: Departamento de Matemática Aplicada a las Tecnologías de la Información y las Telecomunicaciones, E.T.S.I. Sistemas Informáticos, Universidad Politécnica de Madrid, Ctral. de Valencia. Km. 7, Madrid, 28031, Spain. jtello@upm.es.
authors.forename: J Ignacio
authors.initials: JI
authors.lastname: Tello
authors.affiliation: Laboratorio de Inmunoterapia e Ingeniería de Tejidos, Departamento de Biológia Celular y Tisular, Facultad de Medicina, Universidad Nacional Autónoma de México, Edificio A, Sexto Piso, Ciudad Universitaria, Av. Universidad No. 3000, México City, 04510, México. gabrielapinon@hotmail.com.
authors.forename: G
authors.initials: G
authors.lastname: Piñon-Zaráte
authors.affiliation: Laboratorio de Inmunoterapia e Ingeniería de Tejidos, Departamento de Biológia Celular y Tisular, Facultad de Medicina, Universidad Nacional Autónoma de México, Edificio A, Sexto Piso, Ciudad Universitaria, Av. Universidad No. 3000, México City, 04510, México. mikeh@unam.mx.
authors.forename: M
authors.initials: M
authors.lastname: Herrera-Enríquez
authors.affiliation: Laboratorio de Inmunoterapia e Ingeniería de Tejidos, Departamento de Biológia Celular y Tisular, Facultad de Medicina, Universidad Nacional Autónoma de México, Edificio A, Sexto Piso, Ciudad Universitaria, Av. Universidad No. 3000, México City, 04510, México. castell@unam.mx.
authors.forename: A E
authors.initials: AE
authors.lastname: Castell-Rodríguez
mesh_terms: D000818:Animals; D003198:Computer Simulation; D003713:Dendritic Cells; D007167:Immunotherapy; D008545:Melanoma / Q000628:therapy*; D051379:Mice; D008954:Models, Biological