BackgroundThe 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).MethodThe 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 (TGF−β). The model is validated comparing the computer simulation results with biological trial results of the immunotherapy developed by the research group of UNAM.ResultsThe 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.ConclusionBy 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.Electronic supplementary materialThe online version of this article (doi:10.1186/s12976-015-0007-0) contains supplementary material, which is available to authorized users.

This work presents an analysis for real and synthetic angiogenic networks using a tomography image that obtains a portrait of a vascular network. After the image conversion into a binary format it is possible to measure various network properties, which includes the average path length, the clustering coefficient, the degree distribution and the fractal dimension. When comparing the observed properties with that produced by the Invasion Percolation algorithm (IPA), we observe that there exist differences between the properties obtained by the real and the synthetic networks produced by the IPA algorithm. Taking into account the former, a new algorithm which models the expansion of an angiogenic network through randomly heuristic rules is proposed. When comparing this new algorithm with the real networks it is observed that now both share some properties. Once creating synthetic networks, we prove the robustness of the network by subjecting the original angiogenic and the synthetic networks to the removal of the most connected nodes, and see to what extent the properties changed. Using this concept of robustness, in a very naive fashion it is possible to launch a hypothetical proposal for a therapeutic treatment based on the robustness of the network.

Therapeutic protocols in immunotherapy are usually proposed following the intuition and experience of the therapist. In order to deduce such protocols mathematical modeling, optimal control and simulations are used instead of the therapist's experience. Clinical efficacy of dendritic cell (DC) vaccines to cancer treatment is still unclear, since dendritic cells face several obstacles in the host environment, such as immunosuppression and poor transference to the lymph nodes reducing the vaccine effect. In view of that, we have created a mathematical murine model to measure the effects of dendritic cell injections admitting such obstacles. In addition, the model considers a therapy given by bolus injections of small duration as opposed to a continual dose. Doses timing defines the therapeutic protocols, which in turn are improved to minimize the tumor mass by an optimal control algorithm. We intend to supplement therapist's experience and intuition in the protocol's implementation. Experimental results made on mice infected with melanoma with and without therapy agree with the model. It is shown that the dendritic cells' percentage that manages to reach the lymph nodes has a crucial impact on the therapy outcome. This suggests that efforts in finding better methods to deliver DC vaccines should be pursued.

Nowadays, immunotherapy has become an important alternative to fight cancer. One way in which biologists and medics use immunotherapy is by injecting antigen-incubated Dendritic Cells (DCs) into mice to stimulate an immune response. The DCs optimal quantities and infusion times for a successful cancer eradication are often unknown to the therapists; usually, these quantities are obtained by testing various protocols. The article shows a model of five differential equations which represents some interactions between some cells of the immune system and tumor cells which is used to test different infusion protocols of Dendritic Cells. This study aims to find operation ranges to DCs quantities and injection times for which the therapy reduces the tumor significantly. To that end, an exhaustive search of operative protocols is performed using simulations of a mathematical model. Furthermore, nonlinear analysis of the model reveals that without the DC therapy tumor cells cannot stay under non-lethal bounds. Finally, we show that a pulsed periodic therapy can prevent tumor relapsing when the doses and period times lie within a certain range.

Resumen. Las mitocondrias son organelos dinámicos involucrados en diversos procesos celulares, sus funciones están relacionadas a su morfología. Las alteraciones en la dinámica mitocondrial se han asociado como biomarcadores a diversas enfermedades incluyendo el cáncer de mama. En este trabajo presentamos un método de clasificación para imágenes de redes mitocondriales extraídas de distintas líneas celulares (MCF10A, BT549, MDAMB23 y CMF) pertenecientes a distintos subtipos del cáncer de mama. El método se basa en tres etapas: en la primera se aplica un algoritmo de procesamiento morfológico y de segmentación, en la segunda se extraen características usando medidas empleadas comunmente en redes complejas, finalmente se emplea el algoritmo no supervisado K-means para el proceso de clasificación. Los resultados indican una diferencia de las medidas obtenidas en cada subconjunto o clase, obteniendo una exactitud de 63.33 % con 30 imágenes muestra.Abstract. Mitochondria are involved in a variety of cellular functions, which are related to their morphology. The disturbance in mitochondria dynamics has been associated to biomarkers for assessing breast cancer. In this work, we present a method for classification of mitochondrial morphology images, the set of images belongs to cell lines: (MCF10A, BT549, MDAMB23 y CMF) which are subtypes of breast cancer. The proposed method is based on the following image processing algorithms: segmentation (Otsu's method), features extraction (based on graph measures), and clustering algorithm (K-means). The study reveals a remarkable difference between the graph measures applied in features extraction. We obtain an accuracy of 63.33