(41f) The Effect of Metastasis Merging on Tumor Spread in the EMT6 Mouse Model

Cancers kill over 600,000 Americans every year. Breast cancer is the fourth leading cause of cancer death overall and the second among US women. Thus, it is crucial to study cancer growth in both clinical and laboratory settings and, when possible, complemented by theory that expands understanding. In both observational paradigms, medical imaging is one of the most important non-invasive tools we use to detect and track the progression of cancer. Especially in the case of metastatic disease, these images can be complicated to interpret. Moreover imaging in mice, the go-to model for many cancers, has proven unsuccessful thus far in yielding accurate imaging of small tumors, partly due to the lack of contrast agents that work in this model. When imaging human cancers, one difficult aspect of imaging is interpreting tumor clusters that fragment or merge. The RECIST 1.1 guidelines, which judge the effectiveness of treatments through interpreting radiology images, take a practical approach to accounting for merging and splitting events. The long axis of coalesced tumors or the sum of the lengths of tumor fragments are measured and used as indicators of tumor burden. But this surface interpretation does not account for all the potential consequences of merging events.

In this study, we use an EMT6 syngeneic breast cancer/ baln/c mouse model. We inoculate EMT6 cells into the mammary fat pad of the female mouse that grow into an apparent primary tumor and throw off metastases to the lungs. These lung metastases grow and tend to kill the mouse before one detects any metastases elsewhere. Whereas we are developing improved non-invasive imaging techniques to detect numbers and sizes of lung metastases, in this talk we opt for a time-tested method. For decades, the gold standard for accurate post-mortem tumor characterization has been tissue histology using H&E staining and microscopic evaluation of several sample ~5micron sections through the tumor-bearing tissue. Since these sections represent a few two-dimensional slices - information - through a three-dimensional tissue or organ, they represent limited information since a random section of a tumor is unlikely to give its maximum width of that tumor and other tumors may escape sectioning if they lie completely between sections taken. As such, stereology utilizes probability arguments to infer the most likely tumor size distribution from the sizes of the tumor sections in the examined tissue slices. We worked with 30 mice, sacrificed groups of them at four different time points, examined five roughly equally-spaced tissue sections of each mouse’s lungs, and used a stereology algorithm that assumes spherical tumors that we modified by assuming equally-spaced sections to extract a distribution of likely lung tumor sizes at each of these four times. We also measured primary tumor sizes in all the mice three-times per week using calipers and calibrated these measurements by weighing the primary tumors at sacrifice.

We then used these data to find parameters for this cancer in our (continuous time and tumor-size) mathematical tumor population balance model that describes the change with time of the size distribution of a large population of tumors subject to growth (via mitosis), size reduction (via apoptosis, necrosis, treatment, etc. when tumors are non-syngeneic) and shedding and metastasis, a theory that we have presented in the past. The model easily describes the growth of the primary tumor but, absent merging, only describes the metastasis size distribution at the two earlier times well. At the later times, it overestimates the numbers of medium-sized and under-estimates the numbers of large tumors, strongly suggesting that tumors are merging at these later times. Merging is also consistent with the appearance of the lungs at long times of sacrifice, which are visibly filled with tumors.

The supposition of merging's importance is consistent with recent work by a group in Bordeaux (Baratchart et al. PLOS Computational Biology. 2015) that used unsharp MRI images of lung metastases from an inoculated renal tumor in a single mouse to argue that accounting for merging is necessary. They studied the likelihood of merging of two tumors by assuming a high pressure inside a tumor that drives cells outward and a proliferation rate that decreases with increasing pressure; it introduces several new parameters. In contrast, we invoke a much simpler geographic and growth argument to generate merging. To account for merging and to account for the uncertainty in parameter values, we shift from a continuous to a discrete version of our model that views each of the three above-mentioned processes as Markov processes each of whose parameter is known statistically with a mean and standard deviation. Rather than trying to include a non-linear merging process that would necessitate the introduction of a new parameter, each time the model produces a metastasis, it places that tumor randomly inside a 3D model of the lungs, where it can grow. When growing tumors impinge on each other via growth, we combine them in a merging event. Naturally this model does not describe the fate of the normal cells that lie between the about-to-merge tumors as they grow. This analysis clearly provides that merging increases the size of the largest apparent metastasis observed while decreasing the observed number of metastases. In this manner, we significantly improve the agreement of model and stereologically inferred H&E data.

Clearly histology and stereological inference, being indirect and probabilistic and using measurements on different animals at each time point since measurement requires animal sacrifice, pale in comparison with the possibility of directly imaging the tumor size distribution on the same animals at multiple times. In parallel with this work, we are developing such methods to measure the needed histograms noninvasively using both CT and MRI, and will report on them in a future meeting.