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

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Abstract
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. The adenomatous polyp (or adenoma) is considered the common precursor lesion for colorectal cancer (CRC). Although the natural history of adenomas is well-characterized in terms of their histopathology and (epi)genomic changes, little is known about their dynamics in the stage-wise progression from the first appearance of an adenoma to its 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. A large fraction of adenomas may therefore remain undetected during screening and, in spite of their small (subthreshold) size, could give rise to cancer prior to being detected. It is therefore of importance to establish what fraction of adenomas is detectable, both as a function of the age at screening for colorectal neoplasia and the size (threshold) above which adenomas can be detected reliably. Here we derive mathematical expressions for the distribution of adenoma number and sizes based on a recently developed stochastic model for CRC, which has previously been calibrated and validated against age-specific CRC incidence data.

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