Using mathematical models to understand the time dependence of the growth of ductal carcinoma in situ.

Abstract

#1165 Background: Models of cancer growth have been developed that predict tumor size and growth dynamics for invasive tumors. However, it has been difficult to model ductal carcinoma in situ (DCIS) because of the constraints introduced by its containment within the duct system.
 Materials and Methods: We have developed a spherical model of growth of solid type DCIS using chemical engineering models of reaction and diffusion in porous media to represent the spread of DCIS in the duct systems. The model predicts tumor diameter based on four input parameters: the ratio of the apoptosis rate to the proliferation rate (A), the diffusion penetration length for nutrient to sustain the tumor growth (L), the volume fraction that tumor cells occupied within the involved breast tissue (V), and the time taken for a cell to complete mitosis(T). We have estimated L, V, and T from the literature, and then back-calcuated A for a range of diameters. We have used these four parameters as inputs and studied the time dependence of the evolution of DCIS.
 Results: We have found that the range of the values of A that we determined are within an adeqaute physiological range based on rates of proliferation and apoptosis taken from the literature. Using the model, the time to reach at least 95% of the maximum size ranges from less than 30 days for DCIS measuring 0.5 cm to almost 80 days for DCIS measuring 6 cm in diameter.
 
 Discussion: There has been little understanding of how long it takes for DCIS to grow, and whether it reaches a steady state size. Our simulations show that DCIS can grow to sizes as large as 6 cm in less than 3 months if it has the correct properties, including a high proliferation rate relative to the apoptosis rate and appropriate access to nutrients. This finding may help to explain why many cases of DCIS are not diagnosed before they progress to invasive carcinoma. Citation Information: Cancer Res 2009;69(2 Suppl):Abstract nr 1165.

A Novel, Patient-Specific Mathematical Pathology Approach for Assessment of Surgical Volume: Application to Ductal Carcinomain situof The Breast

“…Specifically, a rapid growth phase (on a time scale of 2-3 months) is followed by a prolonged phase of slow growth (on a time scale of years) as tumor growth becomes hampered by diffusion gradients of cell nutrients. Using input parameters that represent a physiological range seen in DCIS tumors excised at the University of Texas MD Anderson Cancer Center, the model predicts that DCIS tumors will have reached a stationary volume within approximately three months [32]. Thus, within a year's time most of the in situ tumors will have reached their steady-state volume.…”

“…Analysis [1] of the model reveals that the geometric mean of the tumor dimensions (i.e., the cube-root of the surgical volume or, as expressed in our model, the diameter 2R) reaches a (nearly) stationary value, which is set by an overall balance of mass gain from proliferation in well oxygenated areas and mass loss from cell death in hypoxic or nutrient-depleted areas. Our simulations using a range of physiological input values (as described below) show that DCIS tumors reach nearly stationary sizes following a short period of fast growth which may last as little as about two months [31,32]. Given such short growth time compared to yearly screenings by mammogram, we may expect most DCIS tumors to be near their stationary size at the time of diagnosis.…”