ArticleNPJ breast cancer2015
Spatiotemporal progression of metastatic breast cancer: a Markov chain model highlighting the role of early metastatic sites.
Article in NPJ breast cancer, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 23 papers.
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Who cites it
23 citing papers in PubMed.
- Mechanisms of breast cancer dormancy in bone metastasis.Clinical & experimental metastasis · 2026Review
- Νovel methylation biomarkers in liquid biopsy and classifying biosignatures for the clinical management of breast cancer.Breast cancer research : BCR · 2026Article
- Accuracy of an Automated Bone Scan Index Measurement System Enhanced by Deep Learning of the Female Skeletal Structure in Patients with Breast Cancer.Nuclear medicine and molecular imaging · 2025Article
- How modulation of the tumor microenvironment drives cancer immune escape dynamics.Scientific reports · 2025Article
- Article
- Reuniting philosophy and science to advance cancer research.Biological reviews of the Cambridge Philosophical Society · 2023Article
- Modeling cancer immunoediting in tumor microenvironment with system characterization through the ising-model Hamiltonian.BMC bioinformatics · 2022Article
- Prediction of Metastatic Patterns in Bladder Cancer: Spatiotemporal Progression and Development of a Novel, Web-based Platform for Clinical Utility.European urology open science · 2021Article
- Article
- Impact of tumor-parenchyma biomechanics on liver metastatic progression: a multi-model approach.Scientific reports · 2021Article
- Uncertainty quantification on a spatial Markov-chain model for the progression of skin cancer.Journal of mathematical biology · 2020Article
- Survival Rate and Prognostic Factors among Iranian Breast Cancer Patients.Iranian journal of public health · 2020Article
- Modeling the Onset of Symptoms of COVID-19.Frontiers in public health · 2020Article
- Prediction of Bone Metastasis in Inflammatory Breast Cancer Using a Markov Chain Model.The oncologist · 2019Article
- Integrated molecular and clinical staging defines the spectrum of metastatic cancer.Nature reviews. Clinical oncology · 2019Review
- A Mathematical Framework for Modelling the Metastatic Spread of Cancer.Bulletin of mathematical biology · 2019Article
- A copula model for joint modeling of longitudinal and time-invariant mixed outcomes.Statistics in medicine · 2018Article
- Emerging and Established Models of Bone Metastasis.Cancers · 2018Review
- Implicating anaesthesia and the perioperative period in cancer recurrence and metastasis.Clinical & experimental metastasis · 2018Review
- Bisphosphonate Use and Risk of Recurrence, Second Primary Breast Cancer, and Breast Cancer Mortality in a Population-Based Cohort of Breast Cancer Patients.Cancer epidemiology, biomarkers & prevention : a publication of the American Association for Cancer Research, cosponsored by the American Society of Preventive Oncology · 2018Article
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Authors and funding
9 authors.
Funding
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Abstract
backgroundCancer 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.
aimsDevelop a Markov based model of breast cancer progression that has predictive capability.
methodsOn 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.
resultsWe 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.
conclusionsWe 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.
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