We describe a cell-molecular based evolutionary mathematical model of tumor development driven by a stochastic Moran birth-death process. The cells in the tumor carry molecular information in the form of a numerical genome which we represent as a four-digit binary string used to differentiate cells into 16 molecular types. The binary string is able to undergo stochastic point mutations that are passed to a daughter cell after each birth event. The value of the binary string determines the cell fitness, with lower fit cells (e.g. 0000) defined as healthy phenotypes, and higher fit cells (e.g. 1111) defined as malignant phenotypes. At each step of the birth-death process, the two phenotypic sub-populations compete in a prisoner’s dilemma evolutionary game with the healthy cells playing the role of cooperators, and the cancer cells playing the role of defectors. Fitness, birth-death rates of the cell populations, and overall tumor fitness are defined via the prisoner’s dilemma payoff matrix. Mutation parameters include passenger mutations (mutations conferring no fitness advantage) and driver mutations (mutations which increase cell fitness). The model is used to explore key emergent features associated with tumor development, including tumor growth rates as it relates to intratumor molecular heterogeneity. The tumor growth equation states that the growth rate is proportional to the logarithm of cellular diversity/heterogeneity. The Shannon entropy from information theory is used as a quantitative measure of heterogeneity and tumor complexity based on the distribution of the 4-digit binary sequences produced by the cell population. To track the development of heterogeneity from an initial population of healthy cells (0000), we use dynamic phylogenetic trees which show clonal and sub-clonal expansions of cancer cell sub-populations from an initial malignant cell. We show tumor growth rates are not constant throughout tumor development, and are generally much higher in the subclinical range than in later stages of development, which leads to a Gompertzian growth curve. We explain the early exponential growth of the tumor and the later saturation associated with the Gompertzian curve which results from our evolutionary simulations using simple statistical mechanics principles related to the degree of functional coupling of the cell states. We then compare dosing strategies at early stage development, mid-stage (clinical stage), and late stage development of the tumor. If used early during tumor development in the subclinical stage, well before the cancer cell population is selected for growth, therapy is most effective at disrupting key emergent features of tumor development.

Tumor development is an evolutionary process in which a heterogeneous population of cells with different growth capabilities compete for resources in order to gain a proliferative advantage. What are the minimal ingredients needed to recreate some of the emergent features of such a developing complex ecosystem? What is a tumor doing before we can detect it? We outline a mathematical model, driven by a stochastic Moran process, in which cancer cells and healthy cells compete for dominance in the population. Each are assigned payoffs according to a Prisoner’s Dilemma evolutionary game where the healthy cells are the cooperators and the cancer cells are the defectors. With point mutational dynamics, heredity, and a fitness landscape controlling birth and death rates, natural selection acts on the cell population and simulated ‘cancer-like’ features emerge, such as Gompertzian tumor growth driven by heterogeneity, the log-kill law which (linearly) relates therapeutic dose density to the (log) probability of cancer cell survival, and the Norton-Simon hypothesis which (linearly) relates tumor regression rates to tumor growth rates. We highlight the utility, clarity, and power that such models provide, despite (and because of) their simplicity and built-in assumptions.

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Currently in patients with bladder cancer, various clinical evaluations (imaging, operative findings at transurethral resection and radical cystectomy, pathology) are collectively used to determine disease status and prognosis, and recommend neoadjuvant, definitive and adjuvant treatments. We analyze the predictive power of these measurements in forecasting two key long-term outcomes following radical cystectomy, i.e., cancer recurrence and survival. Information theory and machine learning algorithms are employed to create predictive models using a large prospective, continuously collected, temporally resolved, primary bladder cancer dataset comprised of 3503 patients (1971-2016). Patient recurrence and survival one, three, and five years after cystectomy can be predicted with greater than 70% sensitivity and specificity. Such predictions may inform patient monitoring schedules and post-cystectomy treatments. The machine learning models provide a benchmark for predicting oncologic outcomes in patients undergoing radical cystectomy and highlight opportunities for improving care using optimal preoperative and operative data collection.

This paper presents a new fabrication technique capable of creating three-dimensional (3D) buried microchannels in a silicon substrate. With a single mask and a single etch of the substrate, silicon microstructures are created with control in all three dimensions by utilizing reactive ion etch (RIE) lag. The microstructures are then sealed with plasma enhanced chemical vapor deposition (PECVD) dielectrics. By depositing up to 6.3 μm of PECVD oxide, rectangular openings in the masking layer ranging in size from 2 μm × 2 μm to 4 μm × 10 μm microchannels were sealed. Using these mask openings, microchannels were created with depths ranging from 4 μm to 200 μm. In addition channels with controlled transition between depths and transition slopes ranging from 40 • and 60 • were created. Furthermore, the flexibility of this technique allows for the creation of predictable nano-scaled holes on the substrate surface. The entire process is fabricated on silicon and CMOS compatible, thus allowing for 3D buried channel devices to be integrated with microelectronics. To show the impact of this technique, practical microfluidic devices with a wide range of applications are demonstrated.