Computational Simulation of Tumor Surgical Resection Coupled with the Immune System Response to Neoplastic Cells

Numerous mathematical and computational models have arisen to study and predict the effects of diverse therapies against cancer (e.g., chemotherapy, immunotherapy, and even therapies under research with oncolytic viruses) but, unfortunately, few efforts have been directed towards development of tumor resection models, the first therapy against cancer. The model hereby presented was stated upon fundamental assumptions to produce a predictor of the clinical outcomes of patients undergoing a tumor resection. It uses ordinary differential equations validated for predicting the immune system response and the tumor growth in oncologic patients. This model could be further extended to a personalized prognosis predictor and tools for improving therapeutic strategies. 1. Introduction The most recent mathematical models are relegating Gompertzian growth curves out of tumor growth modeling. Gompertzian growth strongly depends on time [1], and it can be demonstrated that this leads to artifacts in tumor growth models working with external perturbations, that is, any given therapy. Thus, ordinary differential equations (ODEs) that resemble more the behavior of perturbed tumors [2–4] also share more similarities with the ODEs from the Lotka-Volterra predator-prey model and with the logistic curve described by Verhulst. These ODEs are less time-dependent and focus on interactions among different populations and the carrying capacity of the system [5]. Other approaches for modeling tumor growth use complexity models [6, 7] or physically based models [8, 9], although they have been applied less on therapeutic models than ODEs. Metastasis, the spread of the malignant cells through the body, causes the degeneration of different body functions, depending on the systems affected. Some of the computational models for metastasis are (a) those belonging to the field of complexity—where discrete models based on single cell interactions have been developed [10]—and (b) models with ODEs [11, 12]. These models are useful for predicting outcomes for patients under antimetastatic drugs therapies. Another important factor affecting the dynamics of the tumor is the immune system. De Pillis et al. developed a model that includes as input some features of natural killer cells (NK) and T CD8+ cells (TCD8), as well as the tumor growth rate. NK and TCD8 cells mediate most of the immune response against tumor growth. This model was incorporated into another one that was able to predict clinical outcomes in patients receiving immunotherapy. Interestingly, this model neglects metastasis but