Intra-tumoral heterogeneity (ITH) could represent clonal evolution where subclones with greater fitness confer more malignant phenotypes and invasion constitutes an evolutionary bottleneck. Alternatively, ITH could represent branching evolution with invasion of multiple subclones. The two models respectively predict a hierarchy of subclones arranged by phenotype, or multiple subclones with shared phenotypes. We delineate these modes of invasion by merging ancestral, topographic, and phenotypic information from 12 human colorectal tumors (11 carcinomas, 1 adenoma) obtained through saturation microdissection of 325 small tumor regions. The majority of subclones (29/46, 60%) share superficial and invasive phenotypes. Of 11 carcinomas, 9 show evidence of multiclonal invasion, and invasive and metastatic subclones arise early along the ancestral trees. Early multiclonal invasion in the majority of these tumors indicates the expansion of co-evolving subclones with similar malignant potential in absence of late bottlenecks and suggests that barriers to invasion are minimal during colorectal cancer growth.

Brain tumor growth and tumor-induced edema result in increased intracranial pressure (ICP), which, in turn, is responsible for conditions as benign as headaches and vomiting or as severe as seizures, neurological damage, or even death. Therefore, it has been hypothesized that tracking ICP dynamics may offer improved prognostic potential in terms of early detection of brain cancer and better delimitation of the tumor boundary. However, translating such theory into clinical practice remains a challenge, in part because of an incomplete understanding of how ICP correlates with tumor grade. Here, we propose a multiphase mixture model that describes the biomechanical response of healthy brain tissue-in terms of changes in ICP and edema-to a growing tumor. The model captures ICP dynamics within the diseased brain and accounts for the ability/inability of healthy tissue to compensate for this pressure. We propose parameter regimes that distinguish brain tumors by grade, thereby providing critical insight into how ICP dynamics vary by severity of disease. In particular, we offer an explanation for clinically observed phenomena, such as a lack of symptoms in low-grade glioma patients versus a rapid onset of symptoms in those with malignant tumors. Our model also takes into account the effects tumor-derived proteases may have on ICP levels and the extent of tumor invasion. This work represents an important first step toward understanding the mechanisms that underlie the onset of edema and ICP in cancer-afflicted brains. Continued modeling effort in this direction has the potential to make an impact in the field of brain cancer diagnostics.

Sipuleucel-T (Provenge) is the first live cell vaccine approved for advanced, hormonally refractive prostate cancer. However, survival benefit is modest and the optimal combination or schedule of sipuleucel-T with androgen depletion remains unknown. We employ a nonlinear dynamical systems approach to modeling the response of hormonally refractive prostate cancer to sipuleucel-T. Our mechanistic model incorporates the immune response to the cancer elicited by vaccination, and the effect of androgen depletion therapy. Because only a fraction of patients benefit from sipuleucel-T treatment, inter-individual heterogeneity is clearly crucial. Therefore, we introduce our novel approach, Standing Variations Modeling, which exploits inestimability of model parameters to capture heterogeneity in a deterministic model. We use data from mouse xenograft experiments to infer distributions on parameters critical to tumor growth and to the resultant immune response. Sampling model parameters from these distributions allows us to represent heterogeneity, both at the level of the tumor cells and the individual (mouse) being treated. Our model simulations explain the limited success of sipuleucel-T observed in practice, and predict an optimal combination regime that maximizes predicted efficacy. This approach will generalize to a range of emerging cancer immunotherapies.

Brain tumor growth and tumor-induced edema result in increased intracranial pressure (ICP), which, in turn, is responsible for conditions as benign as headaches and vomiting, or as severe as seizures, neurological damage, or even death. Therefore, it has been hypothesized that tracking ICP dynamics may offer improved prognostic potential in terms of early detection of brain cancer and better delimitation of the tumor boundary. However, translating such theory into clinical practice remains a challenge, in part, due to an incomplete understanding of how ICP correlates with tumor grade. Here, we propose a multiphase mixture model that describes the biomechanical response of healthy brain tissue -in terms of changes in ICP and edema -to a growing tumor. The model captures ICP dynamics within the diseased brain and accounts for the ability/inability of healthy tissue to compensate for this pressure. We propose parameter regimes that distinguish brain tumors by grade thereby providing critical insight into how ICP dynamics vary by severity of disease. In particular, we offer an explanation for clinically observed phenomena such as lack of symptoms in low grade glioma patients versus a rapid onset of symptoms in those with malignant tumors. Our model also takes into account the effects tumor-derived proteases may have on ICP levels and extent of tumor invasion. This work represents an important first step towards understanding the mechanisms that underlie the onset of edema and ICP in cancer-afflicted brains. Continued modeling effort in this direction has the potential to make an impact in the field of brain cancer diagnostics.

Glioblastomas are among the most lethal cancers, with a 5 year survival rate below 25%. Temozolomide is typically used in glioblastoma treatment; however, the enzymes alkylpurine-DNA- N -glycosylase (APNG) and methylguanine-DNA-methyltransferase (MGMT) efficiently mediate the repair of DNA damage caused by temozolomide, reducing treatment efficacy. Consequently, APNG and MGMT inhibition has been proposed as a way of overcoming chemotherapy resistance. Here, we develop a mechanistic mathematical model that explicitly incorporates the effects of chemotherapy on tumour cells, including the processes of DNA damage induction, cell arrest and DNA repair. Our model is carefully parametrized and validated, and then used to virtually recreate the response of heteroclonal glioblastomas to dual treatment with temozolomide and inhibitors of APNG/MGMT. Using our mechanistic model, we identify four combination treatment strategies optimized by tumour cell phenotype, and isolate the strategy most likely to succeed in a pre-clinical and clinical setting. If confirmed in clinical trials, these strategies have the potential to offset chemotherapy resistance in patients with glioblastoma and improve overall survival.