Narrow Results

A mathematical model for cancer chemotherapy of heterogeneous tumor populations is considered as an optimal control problem with the objective to minimize the tumor burden over a prescribed therapy horizon. While an upfront maximum tolerated dose (MTD) regimen with rest-period has been confirmed as mathematically optimal for models when the tumor population is homogeneous, in the presence of partially sensitive or even resistant cells, protocols that administer the therapeutic agents at lower dose rates described by so-called singular controls become a viable alternative. In this paper, the structure of protocols that follow an initial upfront maximum dose treatment with reduced dose rate singular controls is investigated. Such protocols reflect structures which in the medical literature sometimes are called chemo-switch protocols.

The detection, in a wide variety of cancer types, of a population of highly tumorigenic cells that exhibit self-renewal and multipotency, which are hallmarks of stem cells, has transformed the current view of tumor initiation, progression, and treatment. Here, we develop and analyze a mathematical model for tumor growth that is based on the current biological understanding of the processes that underlie cellular expansion under the hierarchical guidelines of the cancer stem cell (CSC) hypothesis. Important features of the model include (i) a nonlinear probability of CSC self-renewal that reflects the fact that this key type of stem cell division can be regulated by extrinsic and intrinsic chemical signaling as well as environmental (niche) constraints and (ii) an amplification factor that captures the transient amplifying divisions that are a defining characteristic of progenitor cells. We present a thorough mathematical analysis of the model and highlight the conditions required for tumors to evolve toward either bounded or exponential growth. Numerical simulations further illustrate the impact of the various parameters on the tumor growth rate and on the heterogeneous cellular composition, which varies during progression.

In this paper, we present a novel feature allocation model to describe tumor heterogeneity (TH) using next-generation sequencing (NGS) data. Taking a Bayesian approach, we extend the Indian buffet process (IBP) to define a class of nonparametric models, the categorical IBP (cIBP). A cIBP takes categorical values to denote homozygous or heterozygous genotypes at each SNV. We define a subclone as a vector of these categorical values, each corresponding to an SNV. Instead of partitioning somatic mutations into non-overlapping clusters with similar cellular prevalences, we took a different approach using feature allocation. Importantly, we do not assume somatic mutations with similar cellular prevalence must be from the same subclone and allow overlapping mutations shared across subclones. We argue that this is closer to the underlying theory of phylogenetic clonal expansion, as somatic mutations occurred in parent subclones should be shared across the parent and child subclones. Bayesian inference yields posterior probabilities of the number, genotypes, and proportions of subclones in a tumor sample, thereby providing point estimates as well as variabilities of the estimates for each subclone. We report results on both simulated and real data. BayClone is available at http://health.bsd.uchicago.edu/yji/soft.html.

We present a feature allocation model to reconstruct tumor subclones based on mutation pairs. The key innovation lies in the use of a pair of proximal single nucleotide variants (SNVs) for the subclone reconstruction as opposed to a single SNV. Using the categorical extension of the Indian buffet process (cIBP) we define the subclones as a vector of categorical matrices corresponding to a set of mutation pairs. Through Bayesian inference we report posterior probabilities of the number, genotypes and population frequencies of subclones in one or more tumor sample. We demonstrate the proposed methods using simulated and real-world data. A free software package is available at http://www.compgenome.org/pairclone.