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.
This is really exciting–I’ll be giving a talk at the weekly applied math seminar at the University of California at Irvine in November. (4:00 pm on November 21, 2011) This will be a fun homecoming, and I can’t wait to catch up with old friends (and potential collaborators)! Many thanks to John Lowengrub for the invitation!
Here is my current list of upcoming talks in 2011-2012:
- September 30, 2011 (noon): Millind Tambe’s Teamcore group, University of Southern California (not a public talk)
- October 17, 2011 (Session II): USC PSOC short course: “physical sciences approach to understanding cancer”, University of Southern California
- November 21, 2011 (4:00 pm): Applied Mathematics Seminar, Department of Mathematics, University of California at Irvine
- Spring 2012: Mathematics Biology and Ecology Seminar, Centre for Mathematical Biology, University of Oxford (UK)
- May 18, 2012: USC PSOC seminar, Center for Applied Molecular Medicine, University of Southern California
David Agus sent word that there will be a special Halloween / Ramone’s Benefit for our cancer research center. The proceeds will benefit the Westside Cancer Center and the Center for Applied Molecular Medicine.
Drop in if you’re in the Los Angeles area–it should be a lot of fun, and the proceeds will help our research towards patient-calibrated cancer modeling!
- We used my agent model calibration technique, plus a volume-averaging upscaling to calibrate a simplified continuum model of DCIS growth in the breast.
- We used the steady-state approximation of the continuum model to estimate the DCIS volume.
- We applied this technique to 17 cases and found a very good match in predicted vs. pathology volume in 14 of 17 cases.
- We also found that the model was a much better predictor of volume than mammographic estimates (although this can vary with how the mammography is processed).
- We found that the mathematical theory predicted that a single variable A–a ratio of the apoptotic index, the proliferative index, and the estimated intraductal oxygenation–is a better predictor of tumor volume than grade, PI, or AI alone.
Edit on Sept. 8, 2011 at 11:22 am PDT:
Preprint is now online: