NCI U01 CA-202144: Multi-Tensor Decompositions for Personalized Cancer Diagnostics and Prognostics1,2,3

This Physical Sciences in Oncology project is developing new mathematical frameworks to do what no others currently can, that is, create a single coherent model from multiple high-dimensional datasets, known as tensors. The frameworks – comparative spectral decompositions – generalize those that underlie the theoretical description of the physical world. We are using the frameworks to compare and contrast datasets recording different aspects of a single disease, such as genomic profiles of multiple cell types from the same set of patients, measured more than once by several different methods. By using the complex structure of the datasets, rather than simplifying them as is commonly done, the frameworks enable the separation of patterns of DNA alterations – which occur only in the tumor genomes – from those that occur in the genomes of normal cells in the body, and from variations caused by experimental inconsistencies. The patterns that we uncover in the data are expected to offer answers to the open question of the relation between a tumor's genome and a patient's outcome.

For example, recent comparisons of the genomes of tumor and normal cells from the same sets of ovarian and, separately, glioblastoma brain cancer patients uncovered patterns of DNA copy-number alterations that were found to be correlated with a patient's survival and response to chemotherapy. For three decades prior, the best predictor of ovarian cancer survival was the tumor's stage; more than a quarter of ovarian tumors are resistant to the platinum-based chemotherapy, the first-line treatment, yet no diagnostic existed to distinguish resistant from sensitive tumors before the treatment. For five decades prior, the best prognostic indicator of glioblastoma was the patient's age at diagnosis. The ovarian and brain cancer data were published, but the patterns remained unknown until we applied our comparative spectral decompositions.

Pending experimental revalidation, we will bring the patterns that we uncover to the clinic, to be used in personalized diagnostic and prognostic pathology laboratory tests. The tests would predict a patient's survival and response to therapy, and doctors could tailor treatment accordingly.


Physics-inspired mathematical frameworks. We develop mathematical frameworks to uncover patterns in datasets arranged in two or more third- or higher-dimensional tables, known as tensors. Rather than simplifying the datasets, as is commonly done, the frameworks make use of their complex structure in order to tease out the patterns within them.


Genomic predictors of a patient's outcome. A recent comparison of the genomes of tumor and normal cells from the same sets of ovarian serous cystadenocarcinoma patients uncovered patterns of DNA copy-number alterations that were found to be correlated with a patient's survival and response to platinum-based chemotherapy. Among patients that were diagnosed at late stages, the DNA patterns distinguished short-term survivors, with a median survival time of three years, from long-term survivors, with a median survival time almost twice as long. Among patients treated with platinum, the DNA patterns distinguished those with platinum-resistant tumors, with a median survival time of three years, from those with platinum-sensitive tumors, with a median survival time of more than seven years.


Patterns of DNA copy-number alterations in personalized diagnostic and prognostic tests. Pending experimental revalidation, we will bring the patterns that we uncover to the clinic, to be used in personalized diagnostic and prognostic pathology laboratory tests. The tests would predict a patient's survival and response to therapy, and doctors could tailor treatment accordingly. The specific genes found to be perturbed may be actively involved in cancer development and progression, and could be the basis for drug therapies.

    In the News

  1. Mention: Among the most shared Applied Physics Letters (APL) Bioengineering research as of 2021.
  2. Press Release: J. Kiefer, "Genome-Wide Pattern Found in Tumors from Brain Cancer Patients Predicts Life Expectancy," American Association for the Advancement of Science (AAAS) EurekAlert! (May 15, 2020).
  3. Mention: Among the top 10 most downloaded Applied Physics Letters (APL) Bioengineering articles as of 2019.
  4. Feature: A. J. Engler and D. E. Discher, "Rationally Engineered Advances in Cancer Research," Applied Physics Letters (APL) Bioengineering 2 (3), Special Topic: Bioengineering of Cancer preface 031601 (September 2018).
  5. Mention: Among the top 10% most cited Public Library of Science (PLoS) One articles as of 2017.
  6. Feature: F. Pavlou, "Big Data, Hidden Knowledge," The Pathologist (June 15, 2015).4
  7. Feature: R. Atkins, "Calculating Cancer Cures," National Academy of Engineering (NAE) Innovation Podcast and Radio Series (April 19, 2015).5
  8. Press Release: J. Kiefer, "New Method Increases Accuracy of Ovarian Cancer Prognosis and Diagnosis," American Association for the Advancement of Science (AAAS) EurekAlert! (April 15, 2015).