Jain, R. K. Normalizing tumor microenvironment to treat cancer: bench to bedside to biomarkers. J. Clin. Oncol. 31, 2205–2218 (2013). This review article describes how different components of the TME are abnormal, how these abnormalities contribute to resistance to drug delivery and efficacy, and how repairing these abnormalities can improve drug delivery and efficacy.

Article  CAS  PubMed  PubMed Central  Google Scholar 

Jain, R. K. Determinants of tumor blood flow: a review. Cancer Res. 48, 2641–2658 (1988).

CAS  PubMed  Google Scholar 

Nagy, J., Chang, S.-H., Shih, S.-C., Dvorak, A. & Dvorak, H. Heterogeneity of the tumor vasculature. Semin. Thromb. Hemost. 36, 321–331 (2010).

Article  CAS  PubMed  PubMed Central  Google Scholar 

Jain, R. K. Antiangiogenesis strategies revisited: from starving tumors to alleviating hypoxia. Cancer Cell 26, 605–622 (2014).

Article  CAS  PubMed  PubMed Central  Google Scholar 

Mitchell, M. J., Jain, R. K. & Langer, R. Engineering and physical sciences in oncology: challenges and opportunities. Nat. Rev. Cancer 17, 659–675 (2017).

Article  CAS  PubMed  PubMed Central  Google Scholar 

Nia, H. T., Munn, L. L. & Jain, R. K. Probing the physical hallmarks of cancer. Nat. Methods https://doi.org/10.1038/s41592-024-02564-4 (2025). This review article describes different types of physical forces in tumours, how to measure them, how to overcome the challenges posed by these physical constraints in tumours and how mathematical modelling has helped measure these forces.

Stylianopoulos, T. et al. Causes, consequences, and remedies for growth-induced solid stress in murine and human tumors. Proc. Natl Acad. Sci. USA 109, 15101–15108 (2012).

Article  CAS  PubMed  PubMed Central  Google Scholar 

Voutouri, C. & Stylianopoulos, T. Accumulation of mechanical forces in tumors is related to hyaluronan content and tissue stiffness. PLoS ONE 13, e0193801 (2018).

Article  PubMed  PubMed Central  Google Scholar 

Linke, J. A., Munn, L. L. & Jain, R. K. Compressive stresses in cancer: characterization and implications for tumour progression and treatment. Nat. Rev. Cancer 24, 768–791 (2024).

Article  CAS  PubMed  Google Scholar 

Padera, T. P. et al. Cancer cells compress intratumour vessels. Nature 427, 695–695 (2004).

Article  CAS  PubMed  Google Scholar 

Stylianopoulos, T., Munn, L. L. & Jain, R. K. Reengineering the physical microenvironment of tumors to improve drug delivery and efficacy: from mathematical modeling to bench to bedside. Trends Cancer 4, 292–319 (2018). This review describes the barriers posed by the physical microenvironment of tumours to effective drug delivery and provides evidence that reengineering the tumour microenvironment can enhance treatment efficacy.

Article  CAS  PubMed  PubMed Central  Google Scholar 

Jain, R. K. & Baxter, L. T. Mechanisms of heterogeneous distribution of monoclonal antibodies and other macromolecules in tumors: significance of elevated interstitial pressure. Cancer Res. 48, 7022–7032 (1988). This paper presented the first mathematical model for the transport of fluid and macromolecules in tumours and predicted the spatial profile of interstitial fluid pressure in tumours subsequently confirmed by direct measurements in tumours in rats.

CAS  PubMed  Google Scholar 

Jain, R. K., Tong, R. T. & Munn, L. L. Effect of vascular normalization by antiangiogenic therapy on interstitial hypertension, peritumor edema, and lymphatic metastasis: insights from a mathematical model. Cancer Res. 67, 2729–2735 (2007).

Article  CAS  PubMed  PubMed Central  Google Scholar 

McDonald, T. O. et al. Computational approaches to modelling and optimizing cancer treatment. Nat. Rev. Bioeng. 1, 695–711 (2023).

Article  CAS  Google Scholar 

Nikmaneshi, M. R., Jain, R. K. & Munn, L. L. Computational simulations of tumor growth and treatment response: benefits of high-frequency, low-dose drug regimens and concurrent vascular normalization. PLoS Comput. Biol. 19, e1011131 (2023). This paper developed a hybrid continuous–discrete model that simulates the TME, showing that metronomic therapy improves drug delivery, especially when combined with anti-angiogenic treatments.

Article  CAS  PubMed  PubMed Central  Google Scholar 

Vavourakis, V. et al. A validated multiscale in-silico model for mechano-sensitive tumour angiogenesis and growth. PLoS Comput. Biol. 13, e1005259 (2017).

Article  PubMed  PubMed Central  Google Scholar 

Yanagisawa, H., Sugimoto, M. & Miyashita, T. Mathematical simulation of tumour angiogenesis: angiopoietin balance is a key factor in vessel growth and regression. Sci. Rep. 11, 419 (2021).

Article  CAS  PubMed  PubMed Central  Google Scholar 

Slavkova, K. P. et al. Mathematical modelling of the dynamics of image-informed tumor habitats in a murine model of glioma. Sci. Rep. 13, 2916 (2023).

Article  CAS  PubMed  PubMed Central  Google Scholar 

Mirramezani, M. & Shadden, S. C. A distributed lumped parameter model of blood flow. Ann. Biomed. Eng. 48, 2870–2886 (2020).

Article  PubMed  PubMed Central  Google Scholar 

Zhu, J. et al. Translational pharmacokinetic/pharmacodynamic modeling and simulation of oxaliplatin and irinotecan in colorectal cancer. Pharmaceutics 15, 2274 (2023).

Article  CAS  PubMed  PubMed Central  Google Scholar 

Michor, F. & Beal, K. Improving cancer treatment via mathematical modeling: surmounting the challenges is worth the effort. Cell 163, 1059–1063 (2015).

Article  CAS  PubMed  PubMed Central  Google Scholar 

Malinzi, J., Basita, K. B., Padidar, S. & Adeola, H. A. Prospect for application of mathematical models in combination cancer treatments. Inform. Med. Unlocked 23, 100534 (2021).

Article  Google Scholar 

Baxter, L. T., Zhu, H., Mackensen, D. G. & Jain, R. K. Physiologically based pharmacokinetic model for specific and nonspecific monoclonal antibodies and fragments in normal tissues and human tumor xenografts in nude mice. Cancer Res. 54, 1517–1528 (1994).

CAS  PubMed  Google Scholar 

De Montigny, J. et al. An in silico hybrid continuum-/agent-based procedure to modelling cancer development: interrogating the interplay amongst glioma invasion, vascularity and necrosis. Methods 185, 94–104 (2021).

Article  PubMed  Google Scholar 

Vavourakis, V., Stylianopoulos, T. & Wijeratne, P. A. In-silico dynamic analysis of cytotoxic drug administration to solid tumours: effect of binding affinity and vessel permeability. PLoS Comput. Biol. 14, e1006460 (2018).

Article  PubMed  PubMed Central  Google Scholar 

Moradi Kashkooli, F. & Soltani, M. Evaluation of solid tumor response to sequential treatment cycles via a new computational hybrid approach. Sci. Rep. 11, 21475 (2021).

Article  CAS  PubMed  PubMed Central  Google Scholar 

Ocaña-Tienda, B. & Pérez-García, V. M. Mathematical modeling of brain metastases growth and response to therapies: a review. Math. Biosci. 373, 109207 (2024).

Article  PubMed  Google Scholar 

Cogno, N., Axenie, C., Bauer, R. & Vavourakis, V. Agent-based modeling in cancer biomedicine: applications and tools for calibration and validation. Cancer Biol. Ther. 25, 2344600 (2024).

Article  PubMed  PubMed Central  Google Scholar 

Dewhirst, M. W. & Secomb, T. W. Transport of drugs from blood vessels to tumour tissue. Nat. Rev. Cancer 17, 738–750 (2017).

Article  CAS  PubMed  PubMed Central  Google Scholar 

Butner, J. D. et al. Mathematical modeling of cancer immunotherapy for personalized clinical translation. Nat. Comput. Sci. 2, 785–796 (2022).

Article  PubMed  PubMed Central  Google Scholar 

Luchini, C., Pea, A. & Scarpa, A. Artificial intelligence in oncology: current applications and future perspectives. Br. J. Cancer 126, 4–9 (2022).

Article  PubMed