Patient-calibrated agent-based modelling of ductal carcinoma in situ (DCIS): From microscopic measurements to macroscopic predictions of clinical progression

Abstract

Ductal carcinoma in situ (DCIS)—a significant precursor to invasive breast cancer—is typically diagnosed as microcalcifications in mammograms. However, the effective use of mammograms and other patient data to plan treatment has been restricted by our limited understanding of DCIS growth and calcification. We develop a mechanistic, agent-based cell model and apply it to DCIS. Cell motion is determined by a balance of biomechanical forces. We use potential functions to model interactions with the basement membrane and amongst cells of unequal size and phenotype. Each cell’s phenotype is determined by genomic/proteomic- and microenvironment-dependent stochastic processes. Detailed “sub-models” describe cell volume changes during proliferation and necrosis; we are the first to account for cell calcification. We introduce the first patient-specific calibration method to fully constrain the model based upon clinically-accessible histopathology data. After simulating 45 days of solid-type DCIS with comedonecrosis, the model predicts: necrotic cell lysis acts as a biomechanical stress relief, and is responsible for the linear DCIS growth observed in mammography; the rate of DCIS advance varies with the duct radius; the tumour grows 7 to 10 mm per year—consistent with mammographic data; and the mammographic and (post-operative) pathologic sizes are linearly correlated—in quantitative agreement with the clinical literature. Patient histopathology matches the predicted DCIS microstructure: an outer proliferative rim surrounds a stratified necrotic core with nuclear debris on its outer edge and calcification in the centre. This work illustrates that computational modelling can provide new insight on the biophysical underpinnings of cancer. It may one day be possible to augment a patient’s mammography and other imaging with rigorously-calibrated models that help select optimal surgical margins based upon the patient’s histopathologic data.

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

“…We set τ P = 18 hours to complete a cell cycle and proliferate [37]. We set τ A = 6.6 hours [24,30,33] by applying the population model to (benign) breast epithelium [38] and correcting for the early portion of apoptosis that cannot be detected by TUNEL assay but is detected by cleaved caspase-3 [39]; this estimate is consistent with the experimental literature (e.g., [40,41]). The diffusion penetration length L is calculated from Eq.…”

“…Previous mathematical and computational models of DCIS have focused on a single breast duct and have been successful in recapitulating certain features of the spatio-temporal dynamics of proliferating and motile tumor cells at this microscale [18][19][20][21][22][23][24][25][26][27][28][29], and have even, in some cases, been capable of extrapolating their results to predictions of macroscopic growth features [24] or invasive potentials as a function of grade [29]. Here we adopt a multiscale approach to predict growth and size of the volume of breast containing ducts with DCIS based on molecular measurements from histopathology of individual patient tumors.…”

“…We thus aim not at predicting tumor volume within a single duct, but rather the gross volume of a breast lesion (herein denoted as surgical volume), which is currently the subject of mammographic imaging, and contains, among the various tissues: breast stroma, endothelium, fat, and ducts with DCIS within. Immunohistochemistry (i.e., Ki-67 and cleaved caspase-3 staining) and morphometric measurements (e.g., duct radius and thickness of viable rim of tumor cells within) are used to calibrate a cell-scale population dynamics model [24]. This information is then upscaled to a continuum, tissue-scale model [1] to estimate (surgical) tumor volumes.…”

“…By volume averaging, we set the rates of mass growth (due to DCIS cell mitosis) and decrease (death) within the surgical volume by averaging over corresponding proliferation rates in a cell population model [24,30,33]:…”

Model Prediction and Validation of an Order Mechanism Controlling the Spatiotemporal Phenotype of Early Hepatocellular Carcinoma

“…The movement of each cell was calculated from all forces exerted on that cell including its own micro-motility using an equation of motion. Agent-based models in which an individual agent represents each cell have been extensively used to mimic the emergence of spatial tumor phenotypes in tumor development and evolution as they are perfectly suited to represent heterogeneity at cellular resolution (e.g., Anderson et al 2006;Tang et al 2011;Macklin et al 2012). They are equally well able to display spatial tissue structures on scales of individual cells, as they occur on the level of liver micro-architecture, and permit the direct display and fate tracking of each individual cell and vessel at the scale of liver lobules.…”