Number and Size Distribution of Colorectal Adenomas under the Multistage Clonal Expansion Model of Cancer

Colorectal cancer (CRC) is believed to arise from mutant stem cells in colonic crypts that undergo a well-characterized progression involving benign adenoma, the precursor to invasive carcinoma. Although a number of (epi)genetic events have been identified as drivers of this process, little is known about the dynamics involved in the stage-wise progression from the first appearance of an adenoma to its ultimate conversion to malignant cancer. By the time adenomas become endoscopically detectable (i.e., are in the range of 1–2 mm in diameter), adenomas are already comprised of hundreds of thousands of cells and may have been in existence for several years if not decades. Thus, a large fraction of adenomas may actually remain undetected during endoscopic screening and, at least in principle, could give rise to cancer before they are detected. It is therefore of importance to establish what fraction of adenomas is detectable, both as a function of when the colon is screened for neoplasia and as a function of the achievable detection limit. To this end, we have derived mathematical expressions for the detectable adenoma number and size distributions based on a recently developed stochastic model of CRC. Our results and illustrations using these expressions suggest (1) that screening efficacy is critically dependent on the detection threshold and implicit knowledge of the relevant stem cell fraction in adenomas, (2) that a large fraction of non-extinct adenomas remains likely undetected assuming plausible detection thresholds and cell division rates, and (3), under a realistic description of adenoma initiation, growth and progression to CRC, the empirical prevalence of adenomas is likely inflated with lesions that are not on the pathway to cancer

Models of HPV as an Infectious Disease and as an Etiological Agent of Cancer.

The human papillomavirus (HPV) infects multiple sites in the human epithelium and is the etiological agent for over 90% of anogenital cancers and an increasing percentage of oropharyngeal cancers. HPV presents an inherently multiscale problem: disease prevalence is known at the population level, infection and disease progression occur within an individual, and cancer incidence is given again for the population. This dissertation uses several mathematical models (of prevalence, transmission, and the progression to oral cancer) to address HPV at different levels. Using data from the National Health and Nutrition Examination Survey, I assess trends in prevalence of cervical HPV and seroprevalence of HPV antibodies using age-period-cohort (APC) epidemiological models that seek to differentiate between the temporal effects of age, period, and birth cohort. Additionally, I consider demographic (age, race) variation in concurrence and type-concordance of genital and oral infections and serum antibodies and the impact of vaccination on seroprevalence and genital prevalence among women. To study the dynamics of HPV transmission and infection, I develop a multisite transmission model that includes consideration of autoinoculation. Assuming homogeneous contacts, I analyze the basic reproductive number R0, as well as type and target reproduction numbers, for a two-site model. I find R0 takes the maximum of certain next generation matrix terms or takes their geometric average in certain limiting cases, and heterogeneity in the same-site terms increases R0 while heterogeneity in the cross-site terms decreases it. I extend this analysis to a heterosexual population, which yields dynamics analogous to those of vector-host models. Finally, I leverage multistage clonal expansion (MSCE) models of cancer biology coupled with APC models to analyze oral squamous cell carcinoma data in the Surveillance, Epidemiology, and End Results cancer registry. MSCE models are based on the initiation-promotion-malignant conversion paradigm in carcinogenesis. I find that HPV-related, HPV-unrelated, and oral tongue sites are best described by placing period and cohort effects on the initiation rate. Racial differences in estimated biological parameters as well as period and cohort trends are considered. To connect HPV prevalence to incidence of oral cancer, I develop MSCE models that use initiation rates dependent on HPV prevalence.PhDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111523/1/brouweaf_1.pd