Original Scientific Reports Functional Maps of Metastases from Breast Cancers: Proof of the Principle that Multidimensional Scaling Can Summarize Disease Progression Lincoln C. Gray, Ph.D., 1 Jayant S. Vaidya, M.D., Ph.D., 2 Michael Baum, M.D., 2 Rajendra A. Badwe, M.D., 3 Indraneel Mittra, M.D., 3 Tariq Siddiqui, M.D., 4 Dorothea Wiarda, Ph.D. 5 1 School of Health Information Sciences, University of Texas Health Science Center, 7000 Fannin Street, Suite 600, Houston, Texas 77030, USA 2 Department of Surgery, University College London, 67-73 Riding House Street, W1W7EJ London, UK 3 Tata Memorial Cancer Center, Dr. E. Borges Marg, 400 012 Parel, Mumbai, India 4 Aga Khan University Hospital, Stadium Road, PO Box 3500 74800 Karachi, Pakistan 5 7520 Wickam Road, Knoxville, Tennessee 37931, USA Published Online: June 8, 2004 Abstract. The mathematic technique of multidimensional scaling can cre- ate “functional maps” of metastases from breast cancer such that positions of organs in these maps are proportional to the probability of metastases. Areas that are likely to share disease are close together in a functional map, even though they may be physically distant, and vice versa. Two functional maps of breast cancers—one of local metastases to axillary levels I to III and another of distant metastases—are statistically significant and clini- cally meaningful. The maps accurately reflect the clinical data (r > 0.97, p < 0.01), and so the progression of disease is revealed in simple visual sum- maries. As an analogy, the metastatic sites are like buoys on a fluid surface, and cancer spreads from a primary tumor like waves emanating from a point of impact on that surface. Metastases are predicted when the waves swamp the buoys. Because breast cancers do not always spread to the next nearest site, these functional maps do not resemble anatomic maps. The maps are a view of the body as “seen” by the tumor. Several well known clinical features are seen in these maps: most local metastases are to axil- lary level I; upper-inner primaries spread equally to levels II and III; in- transit metastases in the lymph and blood vessels do not follow the pattern of other distant metastases. Future functional maps can expand these sum- mary diagrams to include biologic parameters (gene-expression profiles or endocrine response) and give valuable insights into patterns of recurrence in different populations. “The ultimate event that leads to the mortality of breast cancer is metastasis” [1]. Knowledge of the likelihood of metastases is im- portant for staging and planning treatment for patients with breast cancer [2]. The cellular changes that lead to metastases have been well studied [3], but difficult questions remain about the pattern of metastasis [4–6]. Various authors have debated the relative probability of metas- tases in different populations of patients [7, 8] and have reported their findings in different ways [5, 9–11]. Underlying trends can be difficult to compare when the data are described in text form or are presented in complex tables. A simple, graphic, universally appli- cable method for displaying patterns of metastases would help summarize and compare data from around the world. Using multidimensional scaling (MDS) it is possible to create what we call “functional maps” of the body such that distances in the map represent probabilities of metastatic spread [12]. Sites that are equally likely to share metastases are close together in such a map, even though they may be physically distant. Conversely, sites that have different probabilities of metastases are far apart in a functional map, even though they may be physically adjacent. Thus a functional map may bear little resemblance to an anatomic map. For example, if the brain and liver had similar probabilities of me- tastases, these regions would be close together in a functional map. If a disease, such as basal cell carcinoma of the skin, were to spread simply to the next nearest area, the functional map would resemble a map of the local anatomy. Treatment in such a situation is relatively easy: Expand the area of resection from the primary tumor until the margins are clear and then stop. Of course, breast cancer does not behave in this manner. The disease spreads and recurs in complex patterns, usually not in tissue immediately adja- cent to the primary tumor. Therefore we ask a computer to redraw relevant areas of the body into a space of the computers devising such that the disease does spread to the next nearest area—within a mathematically defined landscape. Patterns of progression are then easily seen in a map that represents this result. The goal of this article is to show that functional maps can be constructed from data on breast cancer metastases. This is demon- strated twice: with clinical data on local metastases and distant me- tastases. These maps are both statistically significant and clinically meaningful. This proves the principle that complex patterns for clinical data can be objectively summarized in simple pictures—the output of multidimensional scaling. The functional map is a suc- cinct depiction of tumors’ behavior. Future maps can thus depict the divergent behaviors of tumors that differ in endocrine response or gene expression, for example. Correspondence to: Lincoln C. Gray, Ph.D., e-mail: lgray@uth.tmc.edu WORLD Journal of SURGERY © 2004 by the Socie ´te ´ Internationale de Chirurgie World J. Surg. 28, 646–651, 2004 DOI: 10.1007/s00268-004-7207-9