Spatiotemporal progression of metastatic breast cancer: a Markov chain model highlighting the role of early metastatic sites

Abstract

Background: Cancer cell migration patterns are critical for understanding metastases and clinical evolution. Breast cancer spreads from one organ system to another via hematogenous and lymphatic routes. Although patterns of spread may superficially seem random and unpredictable, we explored the possibility that this is not the case.

Aims: Develop a Markov based model of breast cancer progression that has predictive capability.

Methods: On the basis of a longitudinal data set of 446 breast cancer patients, we created a Markov chain model of metastasis that describes the probabilities of metastasis occurring at a given anatomic site together with the probability of spread to additional sites. Progression is modeled as a random walk on a directed graph, where nodes represent anatomical sites where tumors can develop.

Results: We quantify how survival depends on the location of the first metastatic site for different patient subcategories. In addition, we classify metastatic sites as "sponges" or "spreaders" with implications regarding anatomical pathway prediction and long-term survival. As metastatic tumors to the bone (main spreader) are most prominent, we focus in more detail on differences between groups of patients who form subsequent metastases to the lung as compared with the liver.

Conclusions: We have found that spatiotemporal patterns of metastatic spread in breast cancer are neither random nor unpredictable. Furthermore, the novel concept of classifying organ sites as sponges or spreaders may motivate experiments seeking a biological basis for these phenomena and allow us to quantify the potential consequences of therapeutic targeting of sites in the oligometastatic setting and shed light on organotropic aspects of the disease.

Figure 1

Spatiotemporal progression diagram over a 10-year period of subsets of breast cancer patients. The innermost to outermost rings show progression patterns of primary breast cancer patients (pink ring) and formation of metastases (subsequent rings). Circular arc length of each sector represents the percentage of patients with a metastatic tumor in that location. Bone (yellow) is the most common first metastatic site (first ring outside pink). (a) All Patients, (b) ER+/HER2−, (c) ER−/HER2−, and (d) HER2+.

Figure 2

Kaplan–Meier curves showing the survival of breast cancer patients when they initially have no evidence of metastasis to when they progress through their metastatic disease. (a) Comparison of ER+/HER2−, ER−/HER2−, and HER2+ patients, (b) patients with a solitary first metastatic site at bone, chest wall, liver, or brain, and (c) subsets of patients with different numbers of first relapse metastases.

Figure 3

Markov chain networks of metastatic breast cancer shown as circular chord diagrams. Chord widths at their respective starting locations represent one-step transition probabilities between two sites. Primary breast cancer is located on top with metastatic sites ordered clockwise in decreasing order according to transition probability from primary. (a) All patients’ network, (b) all patients’ network highlighting paths connected to the breast, (c) all patients’ network highlighting paths connected to the bone, and (d) all patients’ network highlighting paths connected to deceased.

Figure 4

Pathway diagrams showing top 30 two-step pathways emanating from breast (pink ring). Nodes are classified as a “spreader” (red) or “sponge” (blue) based on the ratio of the incoming and outgoing two-step probabilities (spreader and sponge factor listed in respective ovals). (a) All patients’ pathway diagram representing 79.8% of total pathways, (b) ER+/HER2− pathway diagram representing 83.0% of total pathways, (c) ER−/HER2− pathway diagram representing 81.9% of total pathways, and (d) HER2+ pathway diagram representing 85.5% of total pathways.

Figure 5

Spreader/sponge diagrams for all patients showing one-step transition probability from (a) bone, (b) chest wall, (c) LN (mam), (d) lung/pleura, (e) LN (dist), and (f) liver to the top nine sites in the network. Sites are ordered in decreasing order, clockwise, with the spreader/sponge in question located at 12:00. Outer pink ring represents primary breast cancer and shows the percentage of total transition probability it represents. dist, distant; LN, lymph node; mam, mammary.

Figure 6

Histograms showing average time from diagnosis to (a) first metastatic site, (b) second metastatic site, (c) bone metastasis, (d) chest wall metastasis, (e) lung metastasis, and (f) liver metastasis. Graphs are color coded for specific metastases (a and b) or met relapse number (c–f). A two-parameter Weibull distribution is used as a curve fit.