Wavelet-Based Nonparametric Modeling of Hierarchical Functions in Colon Carcinogenesis

Article excerpt

1. INTRODUCTION

1.1 Colon Carcinogenesis Studies

Colorectal cancer is a major international health problem. It is the third most common cancer worldwide and the second-leading cause of cancer deaths in the United States. Because colon cancer is often asymptomatic until it is advanced, and current treatment of advanced disease has limited effectiveness, the development of preventive approaches is crucial in fighting this disease. A large part of this effort entails gaining a better understanding of the mechanisms underlying colon carcinogenesis, identifying important risk factors, and understanding how they operate.

There are indications that environmental factors (most notably, diet) play a primary role in the development of colon cancer (see, e.g., Giovannucci and Willet 1994). Carcinogen-induced colon cancer in rodent models are extensively used to delineate mechanisms in colon carcinogenesis. In these models, rodents are fed particular diets of interest for a specific period, exposed to a carcinogen known to induce colon cancer, and then later euthanized, with their colons removed and examined for carcinogenic responses.

In modeling biological mechanisms in the colon, it is important to consider the special architecture of cells within the colon. Colon cells replicate and spend their entire life cycles within crypts, fingerlike structures that grow into the wall of the colon. An individual cell is "born" in a region known as the stem cell region, toward the bottom of the crypt, and moves up the crypt wall as it matures and differentiates, until it is finally exfoliated out into the lumen at the end of its natural life cycle. This special cell-life sequence in the crypts suggests two important facts. First, cells at the same relative depths within different crypts will tend to share common biological characteristics. Second, cells at different depths of a given crypt are at different stages of maturity and could in principle react differently to carcinogens and other stimuli. As a result, it is important to study biological measurements in the colon as a function of relative cell position, because averaging over all crypt cells obscures any potential depth-specific effects. The relative cell position t is defined such that the bottom of each crypt has t = 0 and the top has t = 1, with positions in between coded proportionally.

1.2 Application

Epidemiologic and animal studies have suggested that diets high in fish oil fats, or n-3 polyunsaturated fatty acids, have a protective effect against colon cancer when compared with diets high in corn oil fats (e.g., Boyle, Zaridze, and Smans 1985). However, the biological mechanisms behind this observed effect remain unknown and are of considerable interest. Nutrition researchers at Texas A & M University (Hong et al. 2001) investigated how dietary fat type affects the initiation stage of colon carcinogenesis (the first few hours after exposure to a carcinogen). During this stage, the carcinogen exposure leads to damage to the cells' DNA, which, if not either repaired or removed, may eventually lead to cancer. The biological responses of interest in this study include DNA adduct levels, which quantify the amount of carcinogen-induced damage; [O.sup.6]-methylguanine-DNA-methyltransferase (MGMT), measuring the amount of an enzyme that can repair this damage; apoptosis, the elimination of damaged cells; and BCL2, a protein related to apoptosis.

In this study, 30 rats were randomized to a diet high in either fish oil or corn oil. After being fed these diets for 2 weeks, each rat was exposed to the carcinogen azoxymethane (AOM) and euthanized at one of five randomly chosen time points: 0, 3, 6, 9, or 12 hours after exposure to the carcinogen. For each response, 20-25 crypts were selected from each rat, and the response was quantified at fixed units of distance (pixel) along the left side of each selected crypt using immunhistochemical staining. …