"Invasion of homogeneous and polyploid populations in nutrient-limiting environments?"
Breast cancer progresses in a multistep process from primary tumor growth and stroma invasion to metastasis. Progression is accompanied by a switch to an invasive cell phenotype. Nutrient-limiting environments promote chemotaxis with aggressive morphologies characteristic of invasion. It is unknown how co-existing cells differ in their response to nutrient limitations and how this impacts invasion of the metapopulation as a whole. We integrate mathematical modeling with microenvironmental perturbation-data to investigate invasion in nutrient-limiting environments inhabited by one or two cancer cell subpopulations. Hereby, subpopulations are defined by their energy efficiency and chemotactic ability. We estimate the invasion-distance traveled by a homogeneous population. For heterogeneous populations, our results suggest that an imbalance between nutrient efficacy and chemotactic superiority accelerates invasion. Such imbalance will spatially segregate the two populations and only one type will dominate at the invasion front. Only if these two phenotypes are balanced do the two subpopulations compete for the same space, which decelerates invasion. We investigate ploidy as a candidate biomarker of this phenotypic heterogeneity to discern circumstances when inhibiting chemotaxis amplifies internal competition and decelerates tumor progression, from circumstances that render clinical consequences of chemotactic inhibition unfavorable.
IIEST, SHIBPUR, India
"Optimal treatment strategies with multiple therapeutic approach in Cancer remission: A model based study"
In this talk, a delayed tumor-immune model is proposed and analyzed in the presence of a multi-therapeutic drug. Local dynamics of drug-free steady states are studied and Hopf-bifurcation is observed with delay bifurcation parameter. By formulating a quadratic control based functional, an optimal control problem is constructed with treatments as control variables. The formulation of the functional is aimed at minimizing the proliferation rate of tumor cells and the detrimental effects of injected drugs. Additionally, maximizing the effector cells and maintaining an attributed level of normal cells are also a priority. By applying Pontryagin’s maximum principle, the sufficient and necessary conditions of optimality system are established. The sensitivity analysis of cost functional is performed with different combinations of control variables. The cost-effectiveness analysis is carried out to determine the most cost-effective strategy. The numerical results verify analytical findings and demonstrate that a multi-therapeutic treatment protocol can alleviate tumor burden within a few months of drug administration.
Anna K. Miller
H. Lee Moffitt Cancer Center, Tampa USA
"Modeling the spatiotemporal dynamics of the vicious cycle in multiple myeloma"
Multiple myeloma is a cancer characterized by the expansion of plasma cells in the bone marrow and causes bone pain in over 80% of patients. Bone pain occurs as a result of the interaction between myeloma cells and the trabecular bone microenvironment. Bone is a highly dynamic tissue that is maintained in homeostasis through a balance between bone resorption and bone formation. Multiple myeloma tips the balance in favor of bone resorption, creating a “vicious cycle” in which growth factors released by bone resorption leads to increased survival of multiple myeloma cells, which in turn results in more bone destruction. Multiple myeloma is treatable but largely incurable due to the failure of treatment to completely eradicate the disease. Because the interactions between multiple myeloma and the bone microenvironment contribute to the progression of the disease, it is essential to understand the spatiotemporal dynamics of the vicious cycle to improve treatment response. To explore these dynamics, we developed a hybrid agent-based model that is integrated with published data and data generated by the Lynch lab. We simulate the progression of myeloma growth and bone disease, starting from normal bone remodeling dynamics. To test the assumptions of the normal bone model, we perturb model parameters and show that the model is consistent with data from similar in-vivo experiments. We discuss which model assumptions and parameters are necessary to drive the vicious cycle and capture the data from an in-vivo model of multiple myeloma. This computational model provides a foundation to explore how spatiotemporal dynamics between multiple myeloma and bone microenvironment contribute to drug resistance and tumor growth which ultimately has the potential to help improve treatment strategies.
Fabio A. Milner
Arizona State University
"A model for acute myeloid leukemia (AML)"
Idasanutlin (RG7388) is a selective MDM2 antagonist showing promising responses in phase 1 studies of relapsed AML. The drug is presently undergoing Phase I and II clinical trials. RG7388 was generally well tolerated, with GI toxicity being the most commonly reported adverse event. In laboratory cultures of MOLM-13 wild type cells it was observed that using increasing dosages of RG7388 led, within 3 months, to a complete replacement of wild type (drug-sensitive) cells by mutant (drug-resistant) cells. We propose a model for the growth of the two strains of cells in such cultures that is designed to elucidate whether the replacement is due to the RG7388 selecting for mutant type cells or rather generating the mutants the TP53 mutant clones.
Inmaculada C. Sorribes
"Detailed quantitative framework of in silico xenografts implanted with high-grade gliomas reveals novel dosage schedule of several chemotherapeutic agents"
Glioblastoma multiforme (GBM) is one of the most lethal cancers, with a 5-year survival rate below 25%. GBM-associated death rates remain high, in part because the last few decades have produced only modest advances in treatment. Consequently, the standard therapy for GBM remains palliative, rather than curative, and patients ultimately die from this disease. Chemotherapy has proven to be effective against cancers in general; however, in the case of brain tumors, it has failed to produce sustained remission. Developed in collaboration with experimentalists we present a quantitative framework that captures the specific pharmacokinetics and pharmacodynamics of three different chemotherapeutic agents: temozolomide, Avastin, and vincristine. The effect of these drugs is incorporated into a simple tumor growth model and parametrized using clinical data. The resulting models are used to virtually simulate novel dosage schedules for these drugs and predict their potential in improving survival times.
School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, Scotland
"Bridging in vitro and in vivo research via an agent-based modelling approach"
Translating quantitative information between in vitro and in vivo research remains a scientifically and financially challenging step in preclinical drug development processes. However, well-developed in silico tools can be used to facilitate this in vitro to in vivo translation, and we here propose using an agent-based model to bridge the gap between in vitro and in vivo research. In order to capture the multi-scale nature of cancer, when simulating cancer growth and treatment re- sponses, we use a multi-scale, agent-based model that links individual cell behaviour with the macroscopic behaviour of cell organisation and the microenvironment. We highlight how agent-based models, that are currently underutilised in pharmaceutical contexts, can be used in preclinical drug development and in finding optimal treatment schedules. In pursuit of hindering the onset of drug resistance in melanoma, we investigate various targeted drug dosing regimens in silico.