Skip to main content


Recent translational research: computational studies of breast cancer

  • 5312 Accesses

  • 5 Citations


The combination of mathematics – queen of sciences – and the general utility of computers has been used to make important inroads into insight-providing breast cancer research and clinical aids. These developments are in two broad areas. First, they provide useful prognostic guidelines for individual patients based on historic evidence. Second, by suggesting numeric tumor growth laws that are correlated to clinical parameters, they permit development of biologically relevant theories and comparison with patient data to help us understand complex biologic processes. These latter studies have produced many new ideas that are testable in clinical trials. In this review we discuss these developments from a clinical perspective, and ask whether and how they translate into useful tools for patient treatment.


We selectively and briefly review the recent literature describing mathematical modeling and computer simulation of breast cancer biology, as well as how this work might ultimately aid patient care. The first group of papers provide a basis for measuring prognosis among individual patients after therapy, employing neural network or statistical regression tools. The second set of papers use simulations of the growth and/or spread of tumors and, on this basis, predict clinically relevant results.

Prognostic assessment by neural net or regression analysis

In a report published in 1989, Gail and coworkers [1] discussed the risk for developing breast cancer using family history. The proposed model was validated and variously modified by other researchers, who incorporated genetic risks but not hormonal factors. Tyrer and coworkers [2] attempted to include most known predictive factors and proposed a model for calculating the risk for breast cancer based on a knowledge of individual genetic markers such as BRCA, family factors, and personal history data. It requires verification, however.

The need to take into account multiple clinical and prognostic factors, the limitations of traditional mathematical models, and the effort needed to apply inferences to individuals rather than to populations has fueled the development of artificial neural network (ANN) methods. An ANN is an information-processing paradigm that is inspired by the way in which biologic nervous systems, such as the brain, process information. The structure consists of a large number of highly interconnected processing elements working in unison to recognize patterns. ANNs, like people, learn by example. Learning in biologic systems and ANNs involves successive adjustments to the synaptic connections [3] using a training set. ANNs may be used in the process of therapeutic decision making and as exploratory tools for studies of disease dynamics. Although all ANNs require both a training set and a validation set of data, their true performance should be tested on a separate verification set.

The most important of the ANN programs is that developed by Ravdin [4], termed 'Adjuvant!', which is used to provide prognosis of early stage breast cancer patients after various modes of standard adjuvant therapy. This program is available online and has recently been independently verified to predict recurrence and survival to within 2% of actual observed outcomes. It will probably be widely used by clinicians to make treatment decisions in concert with patients, and it may eventually supplant TNM as a staging system. Like all neural network methods, however, it is not useful for new therapies, such as the forthcoming adjuvant antiangiogenic and targeted pathway modalities, because it depends on mature clinical data. That is the one drawback to Adjuvant! that we can identify.

Other tools are under development that are based on ANN, fuzzy logic, linear regression, and partial logistic ANN [510]. These have important potential for clinical applications because there are many clear needs. However, none of these mathematical tools are at the mature level or as valuable as Adjuvant!

Mathematical and computer models of breast cancer growth

Before publication of a report by Collins and coworkers in 1956 [11], tumors were said to grow fast or slow. Those investigators introduced tumor volume doubling time to quantitatively describe the rate at which a tumor grew and assumed that the doubling time was constant (exponential growth) and that tumors grew continually. The spontaneous mutation model of acquired drug resistance based on exponential kinetics by Coldman and Goldie [12] was an important theoretical development in our understanding of adjuvant chemotherapy.

It was observed, however, that exponential growth could only fit data for some particular conditions, such as multipassaged animal models [13] and when a limited life span of the tumor was studied. These difficulties prompted the next step in the evolution of mathematical models, which is the use of Gompertzian or damped exponential kinetics, in which growth is approximately exponential in its early stages before gradually slowing and asymptotically approaching zero.

Laird [14], who first proposed that Gompertzian growth (formerly used for population kinetics) applies to tumors, measured the growth of '19 examples of 12 different tumors of the rat, mouse, and rabbit' and concluded that 'The pattern of growth defined by the Gompertz equation appears to be a general biological characteristic of tumor growth.' That is a far-reaching statement based on only 18 rodents and one rabbit. The Gompertzian model proved better than the exponential model in describing tumor growth and became widely used. These early models are 'continuous growth' models and, for breast cancer in particular, they are unable to account for the long-lasting recurrence risk (metastasis appearance even more than 30 years after curative primary tumor removal) and many observations of temporary dormancy [1526]. This major discrepancy between theory and observation leads us to reject the continuous growth assumption of Collins and coworkers.

In addition to temporary dormancy, there are other striking aspects of breast cancer that must be addressed. A double-peaked hazard of relapse with menopausal status dependent features has been reported for early stage breast cancer patients undergoing resection of the primary tumor. Distinct peaks at 1–2 years and at 5–6 years appear in several large and mature databases [7, 2734]. Moreover, a screening paradox has resulted for women aged 40–49 years. As reported by eight randomized trials of breast cancer screening, women aged 50–59 years who are invited to screening have a 20–30% mortality advantage as compared with control women. However, when women aged 40–49 years are screened, there is either no advantage or a slight disadvantage for the first 6–8 years in individual trials, meta-analyses, and overviews of all trials. After that, an advantage begins to appear [3542]. Clearly, models incorporating more biology and possessing more general growth patterns than exponential or Gompertz dynamics are required to explain such phenomena.

The Norton–Simon [43] model assumes Gompertzian growth kinetics and has played an important 'cultural' role [4447], although it suffers from the continuous growth flaw. It has nonetheless aided the recent development of dose-dense adjuvant chemotherapy and significant survival gains for certain patient subsets.

A paper by Guiot and coworkers [48] proposed application to tumors of the general model of ontogenic growth proposed by West – that is, a scaled variation of Gompertz growth derived from basic principles for the allocation of metabolic energy between maintenance of existing tissue and production of new biomass. It does not address points in the continuous growth crisis, and the conclusions should therefore be used with caution to help design therapies for clinical evaluation [49].

Plevritis [50] presented a growth model incorporating exponential growth to analyze screening data. Interestingly, despite the use of exponential growth, that author calculated a histogram of primary tumor doubling time distribution that agrees remarkably with stochastic dormancy model results.

The biology-based model for breast cancer growth and metastases development by Retsky, Demicheli and coworkers [5153] incorporates tumor dormancy, transitions between micrometastatic phases, and metastasis acceleration by surgery. The computer simulation proposed an explanation of the various peaks in relapse hazard and predicted that more than half of all relapses in breast cancer are accelerated. The model quantitatively describes tumor dormancy, the mammography paradox and the bimodal relapse pattern, and it gives clues as to why adjuvant chemotherapy works best in premenopausal node-positive patients [53]. It suggests that an antiangiogenic drug given before surgery or timing surgery to the menstrual cycle for young women will reduce growth stimulation from surgery. This model has spawned a few clinical trials and logically could lead to metronomic therapy protocols [5460]. The fundamental difference in this approach is that it specifies and quantifies the inherently intermittent or saltatory nature of tumor growth. Consideration of the duration, timing, and frequency of dormant spans is a unique attribute of this model. The dynamics of the dormancy–growth pattern are determined, over time, by the balance between tumor-based and host-based factors.

Objectively speaking, the weakness in this model is that it is based on only one database and is the product of one group. Although it is perhaps unlikely that the computer simulation will be duplicated by others, independent verification of the bimodal relapse pattern plus supportive reactions from breast cancer clinicians and researchers in the inevitable debate is needed before acceptance should be considered.


Medical science has long relied on empirical methods to learn how to successfully treat disease. However, that strategy does not work well with a disease like breast cancer with over 10 years between application of treatment and ultimate determination of outcome. It is primarily for this reason that computational methods have played an important historical role in the very long struggle to understand breast cancer – a still elusive goal. Perhaps recent computational efforts are making some progress in that direction. We are also reminded by this study (the mammography paradox in particular) that according to the scientific method when theory and experiment disagree, we are compelled to revisit the theory.



artificial neural network.


  1. 1.

    Gail MH, Brinton LA, Byar DP, Corle DK, Green SB, Schairer C, Mulvihill JJ: Projecting individualized probabilities of developing breast cancer for white females who are being examined annually. J Natl Cancer Inst. 1989, 81: 1879-1886.

  2. 2.

    Tyrer J, Duffy SW, Cuzick J: A breast cancer prediction model incorporating familial and personal risk factors. Stat Med. 2004, 23: 1111-1130. 10.1002/sim.1668.

  3. 3.

    Lisboa PJ: A review of evidence of health benefit from artificial neural networks in medical intervention. Neural Netw. 2002, 15: 11-39. 10.1016/S0893-6080(01)00111-3.

  4. 4.

    Ravdin PM, Siminoff LA, Davis GJ, Mercer MB, Hewlett J, Gerson N, Parker HL: Computer program to assist in making decisions about adjuvant therapy for women with early breast cancer. J Clin Oncol. 2001, 19: 980-991.

  5. 5.

    Jerez-Aragones JM, Gomez-Ruiz JA, Ramos-Jimenez G, Munoz-Perez J, Alba-Conejo E: A combined neural network and decision trees model for prognosis of breast cancer relapse. Artif Intell Med. 2003, 27: 45-63. 10.1016/S0933-3657(02)00086-6.

  6. 6.

    Seker H, Odetayo MO, Petrovic D, Naguib RN: A fuzzy logic based-method for prognostic decision making in breast and prostate cancers. IEEE Trans Inf Technol Biomed. 2003, 7: 114-122. 10.1109/TITB.2003.811876.

  7. 7.

    Ripley RM, Harris AL, Tarassenko L: Non-linear survival analysis using neural networks. Stat Med. 2004, 23: 825-842. 10.1002/sim.1655.

  8. 8.

    Biganzoli E, Boracchi P, Coradini D, Grazia Daidone M, Marubini E: Prognosis in node-negative primary breast cancer: a neural network analysis of risk profiles using routinely assessed factors. Ann Oncol. 2003, 14: 1484-1493. 10.1093/annonc/mdg422.

  9. 9.

    Lisboa PJ, Wong H, Harris P, Swindell R: A Bayesian neural network approach for modelling censored data with an application to prognosis after surgery for breast cancer. Artif Intell Med. 2003, 28: 1-25. 10.1016/S0933-3657(03)00033-2.

  10. 10.

    Orbe J, Ferreira E, Nunez-Anton V: Comparing proportional hazards and accelerated failure time models for survival analysis. Stat Med. 2002, 21: 3493-3510. 10.1002/sim.1251.

  11. 11.

    Collins VP, Loeffler RK, Tivey H: Observations on growth rates of human tumors. Am J Roentgenol Radium Ther Nucl Med. 1956, 76: 988-1000.

  12. 12.

    Coldman AJ, Goldie JH: Role of mathematical modeling in protocol formulation in cancer chemotherapy. Cancer Treat Rep. 1985, 69: 1041-1048.

  13. 13.

    Steel GG: Growth Kinetics of Tumours. 1977, Oxford: Clarendon Press

  14. 14.

    Laird AK: Dynamics of tumor growth. Br J Cancer. 1964, 18: 490-502.

  15. 15.

    Demicheli R, Terenziani M, Valagussa P, Moliterni A, Zambetti M, Bonadonna G: Local recurrences following mastectomy: support for the concept of tumor dormancy. J Natl Cancer Inst. 1994, 86: 45-48.

  16. 16.

    Goodison S, Kawai K, Hihara J, Jiang P, Yang M, Urquidi V, Hoffman RM, Tarin D: Prolonged dormancy and site-specific growth potential of cancer cells spontaneously disseminated from nonmetastatic breast tumors as revealed by labeling with green fluorescent protein. Clin Cancer Res. 2003, 9: 3808-3814.

  17. 17.

    Chambers AF, Groom AC, MacDonald IC: Dissemination and growth of cancer cells in metastatic sites. Nat Rev Cancer. 2002, 2: 563-572. 10.1038/nrc865.

  18. 18.

    Stoll BA: Prolonged survival in breast cancer. In Prolonged Arrest of Cancer. 1982, New York: John Wiley & Sons, 1: 59-86.

  19. 19.

    Udagawa T, Fernandez A, Achilles EG, Folkman J, D'Amato RJ: Persistence of microscopic human cancers in mice: alterations in the angiogenic balance accompanies loss of tumor dormancy. FASEB J. 2002, 16: 1361-1370. 10.1096/fj.01-0813com.

  20. 20.

    Hart IR: Perspective: tumour spread – the problems of latency. J Pathol. 1999, 187: 91-94. 10.1002/(SICI)1096-9896(199901)187:1<91::AID-PATH234>3.0.CO;2-J.

  21. 21.

    Naumov GN, Townson JL, MacDonald IC, Wilson SM, Bramwell VH, Groom AC, Chambers AF: Ineffectiveness of doxorubicin treatment on solitary dormant mammary carcinoma cells or late-developing metastases. Breast Cancer Res Treat. 2003, 82: 199-206. 10.1023/B:BREA.0000004377.12288.3c.

  22. 22.

    Klauber-DeMore N, Van Zee KJ, Linkov I, Borgen PI, Gerald WL: Biological behavior of human breast cancer micrometastases. Clin Cancer Res. 2001, 7: 2434-2439.

  23. 23.

    Meltzer A: Dormancy and breast cancer. J Surg Oncol. 1990, 43: 181-188.

  24. 24.

    Uhr JW, Scheuermann RH, Street NE, Vitetta ES: Cancer dormancy: opportunities for new therapeutic approaches. Nat Med. 1997, 3: 505-509. 10.1038/nm0597-505.

  25. 25.

    Kuznetsov VA, Knott GD: Modeling tumor regrowth and immunotherapy. Math Comp Modelling. 2001, 33: 1275-1287. 10.1016/S0895-7177(00)00314-9.

  26. 26.

    Hahnfeldt P, Panigrahy D, Folkman J, Hlatky L: Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response and postvascular dormancy. Cancer Res. 1999, 59: 4770-4775.

  27. 27.

    Fisher ER, Sass R, Fisher B: Pathologic findings from the National Adjuvant Project for Breast Cancers (protocol no. 4). Cancer. 1984, 712-723. Suppl

  28. 28.

    Saphner T, Tormey DC, Gray R: Annual hazard rates of recurrence for breast cancer after primary therapy. J Clin Oncol. 1996, 14: 2738-2746.

  29. 29.

    Baum M, Badwe RA: Does surgery influence the natural history of breast cancer?. In Breast Cancer: Controversies in Management. Edited by: Wise H, Johnson HJ. 1994, Armonk, NY: Futura;, 61-69.

  30. 30.

    Bedwinek J: Adjuvant irradiation for early breast cancer. An ongoing controversy. Cancer. 1984, 729-739. Suppl

  31. 31.

    de la Rochefordiere A, Asselain B, Campana F, Scholl SM, Fenton J, Vilcoq JR, Durand JC, Pouillart P, Magdelenat H, Fourquet A: Age as prognostic factor in premenopausal breast carcinoma. Lancet. 1993, 341: 1039-1043. 10.1016/0140-6736(93)92407-K.

  32. 32.

    Veronesi U, Marubini E, Del Vecchio M, Manzari A, Andreola S, Greco M, Luini A, Merson M, Saccozzi R, Rilke F, et al: Local recurrences and distant metastases after conservative breast cancer treatments: partly independent events. J Natl Cancer Inst. 1995, 87: 19-27.

  33. 33.

    Fortin A, Larochelle M, Laverdiere J, Lavertu S, Tremblay D: Local failure is responsible for the decrease in survival for patients with breast cancer treated with conservative surgery and postoperative radiotherapy. J Clin Oncol. 1999, 17: 101-109.

  34. 34.

    Demicheli R, Abbattista A, Miceli R, Valagussa P, Bonadonna G: Time distribution of the recurrence risk for breast cancer patients undergoing mastectomy: further support about the concept of tumor dormancy. Breast Cancer Res Treat. 1996, 41: 177-185.

  35. 35.

    Retsky M, Demicheli R, Hrushesky W: Premenopausal status accelerates relapse in node positive breast cancer: hypothesis links angiogenesis, screening controversy. Breast Cancer Res Treat. 2001, 65: 217-224. 10.1023/A:1010626302152.

  36. 36.

    Retsky M, Demicheli R, Hrushesky W: Breast cancer screening: controversies and future directions. Curr Opin Obstet Gynecol. 2003, 15: 1-8. 10.1097/00001703-200302000-00001.

  37. 37.

    Demicheli R, Bonadonna G, Hrushesky WJ, Retsky MW, Valagussa P: Menopausal status dependence of early mortality reduction due to diagnosis of smaller breast cancers (T1 v T2-T3): relevance to screening. J Clin Oncol. 2004, 22: 102-107. 10.1200/JCO.2004.12.139.

  38. 38.

    Baines CJ: Mammography screening: are women really giving informed consent?. J Natl Cancer Inst. 2003, 95: 1508-1511.

  39. 39.

    Cox B: Variation in the effectiveness of breast screening by year of follow-up. J Natl Cancer Inst Monogr. 1997, 22: 69-72.

  40. 40.

    Maranto G: Should women in their 40s have mammograms?. Sci Am. 1996, 275: 113-

  41. 41.

    NIH Consensus Development Panel: Consensus statement. J Natl Cancer Inst Monogr. 1997, 22: vii-

  42. 42.

    Fletcher SW: Whither scientific deliberation in health policy recommendations? Alice in the Wonderland of breast-cancer screening. N Engl J Med. 1997, 336: 1180-1183. 10.1056/NEJM199704173361612.

  43. 43.

    Norton L: Karnofsky Memorial Lecture: ignorato motu, ignoratur natura. In American Society of Clinical Oncology virtual meeting. 2004, []

  44. 44.

    Hellman S, DeVita VT: Principles of cancer biology: kinetics of cellular proliferation. In Cancer: Principles and Practices of Oncology. Edited by: DeVita Jr, Hellman S, Rosenberg S. 1982, Philadelphia: Lippincott, 13-

  45. 45.

    Cooper MR, Cooper MR: Principles of medical oncology. In American Cancer Society Textbook of Clinical Oncology. Edited by: Holleb AI, Fink DJ, Murphy GP. 1991, Atlanta: American Cancer Society, 47-68.

  46. 46.

    Prehn RT: The inhibition of tumor growth by tumor mass. Cancer Res. 1991, 51: 2-4.

  47. 47.

    Norton L: A Gompertzian model of human breast cancer growth. Cancer Res. 1988, 48: 7067-7071.

  48. 48.

    Guiot C, Degiorgis PG, Delsanto PP, Gabriele P, Deisboeck TS: Does tumor growth follow a 'universal law'?. J Theor Biol. 2003, 225: 147-151. 10.1016/S0022-5193(03)00221-2.

  49. 49.

    Retsky M: Universal law of tumor growth [letter]. J Theor Biol. 2004, 229: 289-10.1016/j.jtbi.2004.04.008.

  50. 50.

    Plevritis SK: A mathematical algorithm that computes breast cancer sizes and doubling times detected by screening. Math Biosci. 2001, 171: 155-178. 10.1016/S0025-5564(01)00054-2.

  51. 51.

    Retsky MW, Demicheli R, Swartzendruber DE, Bame PD, Wardwell RH, Bonadonna G, Speer JF, Valagussa P: Computer simulation of a breast cancer metastasis model. Breast Cancer Res Treat. 1997, 45: 193-202. 10.1023/A:1005849301420.

  52. 52.

    Demicheli R, Retsky MW, Swartzendruber DE, Bonadonna G: Proposal for a new model of breast cancer metastatic development. Ann Oncol. 1997, 8: 1075-1080. 10.1023/A:1008263116022.

  53. 53.

    Retsky M, Bonadonna G, Demicheli R, Folkman J, Hrushesky W, Valagussa P: Hypothesis: induced angiogenesis after surgery in premenopausal node-positive breast cancer patients is a major underlying reason why adjuvant chemotherapy works particularly well for those patients. Breast Cancer Res. 2004, 6: R372-R374. 10.1186/bcr804.

  54. 54.

    Castiglione-Gertsch M, Gelber R, Goldhirsch A: Adjuvant systemic therapy: the issues of timing and sequence. Recent Results Cancer Res. 1996, 140: 201-213.

  55. 55.

    Frei E, Richardson P, Avigan D, Bunnell C, Wheeler C, Elias A: The interval between courses of high dose chemotherapy with stem cell rescue: therapeutic hypothesis. Bone Marrow Transplant. 1999, 24: 939-945. 10.1038/sj.bmt.1702012.

  56. 56.

    Cooke R: Dr. Folkman's War: Angiogenesis and the Struggle to Defeat Cancer. 2000, New York: Random House, 328-350.

  57. 57.

    Browder T, Butterfield CE, Kraling BM, Shi B, Marshall B, O'Reilly MS, Folkman J: Antiangiogenic scheduling of chemotherapy improves efficacy against experimental drug-resistant cancer. Cancer Res. 2000, 60: 1878-1886.

  58. 58.

    Kerbel RS, Kamen BA: The anti-angiogenic basis of metronomic chemotherapy. Nat Rev Cancer. 2004, 4: 423-436. 10.1038/nrc1369.

  59. 59.

    Retsky M, Swartzendruber D, Wardwell R, Bame P: Computer model challenges breast cancer treatment strategy. Cancer Invest. 1994, 12: 559-567.

  60. 60.

    Clare SE, Nakhlis F, Panetta JC: Review: molecular biology of breast cancer metastasis: the use of mathematical models to determine relapse and to predict response to chemotherapy in breast cancer. Breast Cancer Res. 2000, 2: 430-435. 10.1186/bcr90.

Download references

Author information

Correspondence to Michael Retsky.

Additional information

Competing interests

The author(s) declare that they have no competing interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Retsky, M., Demicheli, R., Hrushesky, W. et al. Recent translational research: computational studies of breast cancer. Breast Cancer Res 7, 37 (2004).

Download citation


  • breast cancer
  • computer models
  • dormancy
  • early detection
  • exponential growth
  • Gompertzian growth
  • risk