I am pleased to report that our paper has now been accepted. You can download the accepted preprint here. We also have a lot of supplementary material, including simulation movies, simulation datasets (for 0, 15, 30, adn 45 days of growth), and open source C++ code for postprocessing and visualization.
I discussed the results in detail here, but here’s the short version:
- We use a mechanistic, agent-based model of individual cancer cells growing in a duct. Cells are moved by adhesive and repulsive forces exchanged with other cells and the basement membrane. Cell phenotype is controlled by stochastic processes.
- We constrained all parameter expected to be relatively independent of patients by a careful analysis of the experimental biological and clinical literature.
- We developed the very first patient-specific calibration method, using clinically-accessible pathology. This is a key point in future patient-tailored predictions and surgical/therapeutic planning.
- The model made numerous quantitative predictions, such as:
- The tumor grows at a constant rate, between 7 to 10 mm/year. This is right in the middle of the range reported in the clinic.
- The tumor’s size in mammgraphy is linearly correlated with the post-surgical pathology size. When we linearly extrapolate our correlation across two orders of magnitude, it goes right through the middle of a cluster of 87 clinical data points.
- The tumor necrotic core has an age structuring: with oldest, calcified material in the center, and newest, most intact necrotic cells at the outer edge.
- The appearance of a “typical” DCIS duct cross-section varies with distance from the leading edge; all types of cross-sections predicted by our model are observed in patient pathology.
- The model also gave new insight on the underlying biology of breast cancer, such as:
- The split between the viable rim and necrotic core (observed almost universally in pathology) is not just an artifact, but an actual biomechanical effect from fast necrotic cell lysis.
- The constant rate of tumor growth arises from the biomechanical stress relief provided by lysing necrotic cells. This points to the critical role of intracellular and intra-tumoral water transport in determining the qualitative and quantitative behavior of tumors.
- Pyknosis (nuclear degradation in necrotic cells), must occur at a time scale between that of cell lysis (on the order of hours) and cell calcification (on the order of weeks).
- The current model cannot explain the full spectrum of calcification types; other biophysics, such as degradation over a long, 1-2 month time scale, must be at play.
After a lot of revision, I have merged my two papers on ductal carcinoma in situ (DCIS) in to a single manuscript and resubmitted to the Journal of Theoretical Biology for final review. A preprint is posted at my website, along with considerable supplementary material (data sets and source code, and animations). Thanks to my co-authors and other friends for all the help in the revisions. Thanks also the reviewers for insightful comments. I think this revised manuscript is all the better for it.
DCIS is a precursor to invasive breast cancer, and it is generally detected by annual mammographic screening. More advanced DCIS (with greater risk) tends to have comedonecrosis–a type of cell death that leaves calcium phosphate deposits in the centers of the ducts. In fact, this is generally what’s detected in mammograms. DCIS is usually surgically removed by cutting out a small ball of tissue around what’s found in the mammograms (breast-conserving surgery, or lumpectomy). But current planning isn’t so great. Even with the state-of-the-art in patient imaging and surgical planning, about 20%-50% of women need to get a second surgery because the first one didn’t get the entire tumor.
So, there’s great need to understand calcifications, and how what you see in mammography relates to the actual tumor size and shape. And if you do have a model to do this, there’s great need to calibrate it to patient pathology data (the stuff you get from your biopsies) so that the models say something meaningful about individual patients. And there has been no method to do that. Until now.
(As far as I know), this paper is the first to calibrate to individual patient immunohistochemistry and histopathology. This, along with some parameter estimates to the theoretical and experimental biology literature, allows us to fully constrain the model. No free parameters to play with until it looks right. Any results are fully emergent from a mechanistic model and realistic parameter estimates rooted in the biology.
This model also includes the most detailed description of necrosis–the type of cell death that results in the comedonecrosis seen in mammograms. We include cell swelling, cell bursting, gradual loss of fluid, and the very first model of calcification.
Clinical predictions, with lots of validation:
All said and done, the model gives some big (and validated!) predictions:
- The model predicts that a tumor grows through the duct at a constant rate. This is consistent with what’s actually seen in mammography.
- The model gives a new explanation for the known trend: when necrotic cells burst and lose fluid, it makes it more mechanically favorable for proliferating cells to push into the center of the duct, rather than along the duct. For this reason the model predicts faster growth in smaller ducts, and slower growth in larger ducts.
- The model predicts growth rates between 7.5 and 10 mm per year. This is quantitatively consistent with published values in the clinical literature.
- The model predicts the difference between the size in a mammogram and the actual size (as measured by a pathologist after surgery) grows in time. This unfortunately means that it’s unlikely that there is some “fixed” safe distance to cut around the mammographic findings.
- On the other hand, the model predicts that there is a linear correlation between the size in a mammogram and the actual (pathology) tumor size. This bodes well for future surgical planning.
- Better still, the linear correlation we found quantitatively fits through 87 published patients, spanning two orders of magnitude.
The model also makes several key predictions on the smaller-scale biology:
- The model predicts that fast swelling of necrotic cells (on the order of 6 hours) is responsible for the tear between the viable rim and necrotic core seen in just about every pathology image of DCIS.
- The model predicts that the necrotic core is “age structured”, with newly necrotic cells (with relatively intact nuclei) on the outer edge, and interior band of mostly degraded but noncalcified cells, and a central core of oldest, calcified material. This compares well with patient histopathology.
- Comparing the model-predicted age structuring to histopathology predicts a sharper estimate on the various necrosis time scales: swelling and lysis (~6 h) < slow fluid loss (~days to a week) < pyknosis (~10+ days) < calcification (~2 weeks).
- Because the model only predicts linear / casting-type calcifications (long “plugs” of calcification), other biophysics must be responsible for the variety of calcification types seen in mammography.
- Among other mechanisms, we postulate a very long-timescale (1-2 months) process of degradation of the phospholipid “backbone” of the calcifications, resulting in degradation of the calcifications. The cracks seen in the central portions of calcifications (in histopathology) supports this view.