A PDE Model of Breast Tumor Progression in MMTV-PyMT Mice

Modeling cancer progression: an integrated workflow extending data-driven kinetic models to bio-mechanical PDE models

Computational modeling of cancer can help unveil dynamics and interactions that are hard to replicate experimentally. Thanks to the advancement in cancer databases and data analysis technologies, these models have become more robust than ever. There are many mathematical models which investigate cancer through different approaches, from sub-cellular to tissue scale, and from treatment to diagnostic points of view. In this study, we lay out a step-by-step methodology for a data-driven mechanistic model of the tumor microenvironment. We discuss data acquisition strategies, data preparation, parameter estimation, and sensitivity analysis techniques. Furthermore, we propose a possible approach to extend mechanistic ordinary differential equation models to PDE models coupled with mechanical growth. The workflow discussed in this article can help understand the complex temporal and spatial interactions between cells and cytokines in the tumor microenvironment and their effect on tumor growth.

Mathematical and Machine Learning Models of Renal Cell Carcinoma: A Review

This review explores the multifaceted landscape of renal cell carcinoma (RCC) by delving into both mechanistic and machine learning models. While machine learning models leverage patients' gene expression and clinical data through a variety of techniques to predict patients' outcomes, mechanistic models focus on investigating cells' and molecules' interactions within RCC tumors. These interactions are notably centered around immune cells, cytokines, tumor cells, and the development of lung metastases. The insights gained from both machine learning and mechanistic models encompass critical aspects such as signature gene identification, sensitive interactions in the tumors' microenvironments, metastasis development in other organs, and the assessment of survival probabilities. By reviewing the models of RCC, this study aims to shed light on opportunities for the integration of machine learning and mechanistic modeling approaches for treatment optimization and the identification of specific targets, all of which are essential for enhancing patient outcomes.

Investigating the spatial interaction of immune cells in colon cancer

The intricate network of interactions between cells and molecules in the tumor microenvironment creates a heterogeneous ecosystem. The proximity of the cells and molecules to their activators and inhibitors is essential in the progression of tumors. Here, we develop a system of partial differential equations coupled with linear elasticity to investigate the effects of spatial interactions on the tumor microenvironment. We observe interesting cell and cytokine distribution patterns, which are heavily affected by macrophages. We also see that cytotoxic T cells get recruited and suppressed at the site of macrophages. Moreover, we observe that anti-tumor macrophages reorganize the patterns in favor of a more spatially restricted cancer and necrotic core. Furthermore, the adjoint-based sensitivity analysis indicates that the most sensitive model's parameters are directly related to macrophages. The results emphasize the widely acknowledged effect of macrophages in controlling cancer cells population and spatially arranging cells in the tumor microenvironment.

Infantile hemangioma models: is the needle in a haystack?

Infantile hemangioma (IH) is the most prevalent benign vascular tumor in infants, with distinct disease stages and durations. Despite the fact that the majority of IHs can regress spontaneously, a small percentage can cause disfigurement or even be fatal. The mechanisms underlying the development of IH have not been fully elucidated. Establishing stable and reliable IH models provides a standardized experimental platform for elucidating its pathogenesis, thereby facilitating the development of new drugs and the identification of effective treatments. Common IH models include the cell suspension implantation model, the viral gene transfer model, the tissue block transplantation model, and the most recent three-dimensional (3D) microtumor model. This article summarizes the research progress and clinical utility of various IH models, as well as the benefits and drawbacks of each. Researchers should select distinct IH models based on their individual research objectives to achieve their anticipated experimental objectives, thereby increasing the clinical relevance of their findings.

Bio-Mechanical Model of Osteosarcoma Tumor Microenvironment: A Porous Media Approach

Osteosarcoma is the most common malignant bone tumor in children and adolescents with a poor prognosis. To describe the progression of osteosarcoma, we expanded a system of data-driven ODE from a previous study into a system of Reaction-Diffusion-Advection (RDA) equations and coupled it with Biot equations of poroelasticity to form a bio-mechanical model. The RDA system includes the spatio-temporal information of the key components of the tumor microenvironment. The Biot equations are comprised of an equation for the solid phase, which governs the movement of the solid tumor, and an equation for the fluid phase, which relates to the motion of cells. The model predicts the total number of cells and cytokines of the tumor microenvironment and simulates the tumor's size growth. We simulated different scenarios using this model to investigate the impact of several biomedical settings on tumors' growth. The results indicate the importance of macrophages in tumors' growth. Particularly, we have observed a high co-localization of macrophages and cancer cells, and the concentration of tumor cells increases as the number of macrophages increases.

Patient-Specific Mathematical Model of the Clear Cell Renal Cell Carcinoma Microenvironment

The interactions between cells and molecules in the tumor microenvironment can give insight into the initiation and progression of tumors and their optimal treatment options. In this paper, we developed an ordinary differential equation (ODE) mathematical model of the interaction network of key players in the clear cell renal cell carcinoma (ccRCC) microenvironment. We then performed a global gradient-based sensitivity analysis to investigate the effects of the most sensitive parameters of the model on the number of cancer cells. The results indicate that parameters related to IL-6 have high a impact on cancer cell growth, such that decreasing the level of IL-6 can remarkably slow the tumor's growth.

Exploring approaches for predictive cancer patient digital twins: Opportunities for collaboration and innovation

We are rapidly approaching a future in which cancer patient digital twins will reach their potential to predict cancer prevention, diagnosis, and treatment in individual patients. This will be realized based on advances in high performance computing, computational modeling, and an expanding repertoire of observational data across multiple scales and modalities. In 2020, the US National Cancer Institute, and the US Department of Energy, through a trans-disciplinary research community at the intersection of advanced computing and cancer research, initiated team science collaborative projects to explore the development and implementation of predictive Cancer Patient Digital Twins. Several diverse pilot projects were launched to provide key insights into important features of this emerging landscape and to determine the requirements for the development and adoption of cancer patient digital twins. Projects included exploring approaches to using a large cohort of digital twins to perform deep phenotyping and plan treatments at the individual level, prototyping self-learning digital twin platforms, using adaptive digital twin approaches to monitor treatment response and resistance, developing methods to integrate and fuse data and observations across multiple scales, and personalizing treatment based on cancer type. Collectively these efforts have yielded increased insights into the opportunities and challenges facing cancer patient digital twin approaches and helped define a path forward. Given the rapidly growing interest in patient digital twins, this manuscript provides a valuable early progress report of several CPDT pilot projects commenced in common, their overall aims, early progress, lessons learned and future directions that will increasingly involve the broader research community.