Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

Using mathematical modelling and AI to improve delivery and efficacy of therapies in cancer

Nature Reviews Cancer volume 25, pages 324–340 (2025)Cite this article

Subjects

Abstract

Mathematical modelling has proven to be a valuable tool in predicting the delivery and efficacy of molecular, antibody-based, nano and cellular therapy in solid tumours. Mathematical models based on our understanding of the biological processes at subcellular, cellular and tissue level are known as mechanistic models that, in turn, are divided into continuous and discrete models. Continuous models are further divided into lumped parameter models — for describing the temporal distribution of medicine in tumours and normal organs — and distributed parameter models — for studying the spatiotemporal distribution of therapy in tumours. Discrete models capture interactions at the cellular and subcellular levels. Collectively, these models are useful for optimizing the delivery and efficacy of molecular, nanoscale and cellular therapy in tumours by incorporating the biological characteristics of tumours, the physicochemical properties of drugs, the interactions among drugs, cancer cells and various components of the tumour microenvironment, and for enabling patient-specific predictions when combined with medical imaging. Artificial intelligence-based methods, such as machine learning, have ushered in a new era in oncology. These data-driven approaches complement mechanistic models and have immense potential for improving cancer detection, treatment and drug discovery. Here we review these diverse approaches and suggest ways to combine mechanistic and artificial intelligence-based models to further improve patient treatment outcomes.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to the full article PDF.

USD 39.95

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Mechanisms of transport of low-molecular-weight agents, nanoparticles, antibodies and cell therapies from the tumour vessel across the tumour vessel walls and within the tumour interstitial space.
Fig. 2: Lumped parameter physiologically based pharmacokinetic models can be used to calculate the time-dependent behaviour of the average drug concentration and cell density in different compartments.
Fig. 3: Distributed parameter models predict the spatiotemporal changes in the tumour and the surrounding normal tissue.
Fig. 4: Discrete modelling approaches are used to calculate the cellular heterogeneity and stochastic response of cells.
Fig. 5: Artificial intelligence models are data driven, finding patterns within the data without an understanding of the underlying biological mechanisms.

Similar content being viewed by others

References

  1. 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 

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

    CAS  PubMed  Google Scholar 

  3. 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 

  4. 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 

  5. 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 

  6. 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.

  7. 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 

  8. 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 

  9. 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 

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

    Article  CAS  PubMed  Google Scholar 

  11. 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 

  12. 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 

  13. 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 

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

    Article  CAS  Google Scholar 

  15. 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 

  16. 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 

  17. 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 

  18. 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 

  19. 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 

  20. 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 

  21. 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 

  22. 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 

  23. 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 

  24. 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 

  25. 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 

  26. 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 

  27. 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 

  28. 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 

  29. 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 

  30. 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 

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

    Article  PubMed  Google Scholar 

  32. Rösler, W. et al. An overview and a roadmap for artificial intelligence in hematology and oncology. J. Cancer Res. Clin. Oncol. 149, 7997–8006 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  33. Lorenzo, G. et al. Patient-specific, mechanistic models of tumor growth incorporating artificial intelligence and big data. Annu. Rev. Biomed. Eng. 26, 529–560 (2024).

    Article  CAS  PubMed  Google Scholar 

  34. Lotter, W. et al. Artificial intelligence in oncology: current landscape, challenges, and future directions. Cancer Discov. 14, 711–726 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  35. Gerlowski, L. E. & Jain, R. K. Physiologically based pharmacokinetic modeling: principles and applications. J. Pharm. Sci. 72, 1103–1127 (1983). This comprehensive review article summarized how pharmacokinetic models can describe the distribution and disposition of drugs in living systems, helping the design of preclinical and clinical studies.

    Article  CAS  PubMed  Google Scholar 

  36. Weissbrod, J. M., Jain, R. K. & Sirotnak, F. M. Pharmacokinetics of methotrexate in leukemia cells: effect of dose and mode of injection. J. Pharmacokinet. Biopharm. 6, 487–503 (1978).

    Article  CAS  PubMed  Google Scholar 

  37. Jayachandran, P., Knox, S. J., Garcia-Cremades, M. & Savić, R. M. Clinical pharmacokinetics of oral sodium selenite and dosing implications in the treatment of patients with metastatic cancer. Drugs R D 21, 169–178 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  38. Jain, R. K., Wei, J. & Gullino, P. M. Pharmacokinetics of methotrexate in solid tumors. J. Pharmacokinet. Biopharm. 7, 181–194 (1979).

    Article  CAS  PubMed  Google Scholar 

  39. McKenna, M. T. et al. A predictive mathematical modeling approach for the study of doxorubicin treatment in triple negative breast cancer. Sci. Rep. 7, 5725 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  40. Ciccolini, J. et al. Pharmacokinetics and pharmacodynamics-based mathematical modeling identifies an optimal protocol for metronomic chemotherapy. Cancer Res. 77, 4723–4733 (2017).

    Article  CAS  PubMed  Google Scholar 

  41. Clewell, R. A. & Clewell, H. J. Development and specification of physiologically based pharmacokinetic models for use in risk assessment. Regul. Toxicol. Pharmacol. 50, 129–143 (2008).

    Article  CAS  PubMed  Google Scholar 

  42. Zang, X. & Kagan, L. Physiologically-based modeling and interspecies prediction of paclitaxel pharmacokinetics. J. Pharmacokinet. Pharmacodyn. 45, 577–592 (2018).

    Article  CAS  PubMed  Google Scholar 

  43. Dumontet, C., Reichert, J. M., Senter, P. D., Lambert, J. M. & Beck, A. Antibody–drug conjugates come of age in oncology. Nat. Rev. Drug Discov. 22, 641–661 (2023).

    Article  CAS  PubMed  Google Scholar 

  44. Klein, C., Brinkmann, U., Reichert, J. M. & Kontermann, R. E. The present and future of bispecific antibodies for cancer therapy. Nat. Rev. Drug Discov. 23, 301–319 (2024).

    Article  CAS  PubMed  Google Scholar 

  45. Drago, J. Z., Modi, S. & Chandarlapaty, S. Unlocking the potential of antibody–drug conjugates for cancer therapy. Nat. Rev. Clin. Oncol. 18, 327–344 (2021).

    Article  PubMed  PubMed Central  Google Scholar 

  46. Ray, C. M. P., Yang, H., Spangler, J. B. & Mac Gabhann, F. Mechanistic computational modeling of monospecific and bispecific antibodies targeting interleukin-6/8 receptors. PLoS Comput. Biol. 20, e1012157 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  47. Yang, H. et al. Engineered bispecific antibodies targeting the interleukin-6 and -8 receptors potently inhibit cancer cell migration and tumor metastasis. Mol. Ther. 30, 3430–3449 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  48. Shah, D. K., Haddish-Berhane, N. & Betts, A. Bench to bedside translation of antibody drug conjugates using a multiscale mechanistic PK/PD model: a case study with brentuximab–vedotin. J. Pharmacokinet. Pharmacodyn. 39, 643–659 (2012).

    Article  PubMed  Google Scholar 

  49. Chudasama, V. L. et al. Semi-mechanistic population pharmacokinetic model of multivalent trastuzumab emtansine in patients with metastatic breast cancer. Clin. Pharmacol. Ther. 92, 520–527 (2012).

    Article  CAS  PubMed  Google Scholar 

  50. Lu, D. et al. Semi-mechanistic multiple-analyte pharmacokinetic model for an antibody–drug-conjugate in cynomolgus monkeys. Pharm. Res. 32, 1907–1919 (2015).

    Article  CAS  PubMed  Google Scholar 

  51. Betts, A. M. et al. Preclinical to clinical translation of antibody–drug conjugates using PK/PD modeling: a retrospective analysis of inotuzumab ozogamicin. AAPS J. 18, 1101–1116 (2016).

    Article  CAS  PubMed  Google Scholar 

  52. Singh, A. & Shah, D. in Innovations for Next-Generation Antibody–Drug Conjugates (ed. Demelin, M.) 73–97 (Springer, 2018).

  53. Scheuher, B. et al. Towards a platform quantitative systems pharmacology (QSP) model for preclinical to clinical translation of antibody drug conjugates (ADCs). J. Pharmacokinet. Pharmacodyn. 51, 429–447 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  54. Singh, A. P. & Shah, D. K. Application of a PK–PD modeling and simulation-based strategy for clinical translation of antibody–drug conjugates: a case study with trastuzumab emtansine (T-DM1). AAPS J. 19, 1054–1070 (2017).

    Article  CAS  PubMed  Google Scholar 

  55. Nicolò, E. et al. Combining antibody–drug conjugates with immunotherapy in solid tumors: current landscape and future perspectives. Cancer Treat. Rev. 106, 102395 (2022).

    Article  PubMed  Google Scholar 

  56. Jain, R. K. & Stylianopoulos, T. Delivering nanomedicine to solid tumors. Nat. Rev. Clin. Oncol. 7, 653–664 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  57. Nirmala, M. J. et al. Cancer nanomedicine: a review of nano-therapeutics and challenges ahead. RSC Adv. 13, 8606–8629 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  58. Li, M., Al-Jamal, K. T., Kostarelos, K. & Reineke, J. Physiologically based pharmacokinetic modeling of nanoparticles. ACS Nano 4, 6303–6317 (2010).

    Article  CAS  PubMed  Google Scholar 

  59. Kutumova, E. O. et al. Physiologically based pharmacokinetic modeling of nanoparticle biodistribution: a review of existing models, simulation software, and data analysis tools. Int. J. Mol. Sci. 23, 12560 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  60. Dogra, P. et al. A mathematical model to predict nanomedicine pharmacokinetics and tumor delivery. Comput. Struct. Biotechnol. J. 18, 518–531 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  61. Patnaik, A. et al. Phase I study of pembrolizumab (MK-3475; anti–PD-1 monoclonal antibody) in patients with advanced solid tumors. Clin. Cancer Res. 21, 4286–4293 (2015).

    Article  CAS  PubMed  Google Scholar 

  62. Elassaiss-Schaap, J. et al. Using model-based ‘Learn and Confirm’ to reveal the pharmacokinetics–pharmacodynamics relationship of pembrolizumab in the KEYNOTE-001 trial: modeling of the PK/PD of Pembro in KEYNOTE-001. CPT Pharmacomet. Syst. Pharmacol. 6, 21–28 (2017).

    Article  CAS  Google Scholar 

  63. Ahamadi, M. et al. Model-based characterization of the pharmacokinetics of pembrolizumab: a humanized anti-PD-1 monoclonal antibody in advanced solid tumors: pharmacokinetics of pembro in solid tumors. CPT Pharmacomet. Syst. Pharmacol. 6, 49–57 (2017).

    Article  CAS  Google Scholar 

  64. Lala, M. et al. A six-weekly dosing schedule for pembrolizumab in patients with cancer based on evaluation using modelling and simulation. Eur. J. Cancer 131, 68–75 (2020).

    Article  CAS  PubMed  Google Scholar 

  65. Tao, Z. et al. Impact of T cell characteristics on CAR-T cell therapy in hematological malignancies. Blood Cancer J. 14, 213 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  66. US Food and Drug Administration. FDA approves first cellular therapy to treat patients with unresectable or metastatic melanoma (FDA, 2024).

  67. Chen, T., Wang, M., Chen, Y. & Liu, Y. Current challenges and therapeutic advances of CAR-T cell therapy for solid tumors. Cancer Cell Int. 24, 133 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  68. Zhu, H., Melder, R. J., Baxter, L. T. & Jain, R. K. Physiologically based kinetic model of effector cell biodistribution in mammals: implications for adoptive immunotherapy. Cancer Res. 56, 3771–3781 (1996). This paper presented the first mathematical model of adoptively transferred immune cells in tumours and normal tissues and suggested ways to improve the improve their delivery of tumours — confirmed later in CAR T cells in clinical trials.

    CAS  PubMed  Google Scholar 

  69. Choi, B. D. et al. Intraventricular CARv3-TEAM-E T cells in recurrent glioblastoma. N. Engl. J. Med. 390, 1290–1298 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  70. Nikitich, A., Helmlinger, G., Peskov, K. & Bocharov, G. Mathematical modeling of endogenous and exogenously administered T cell recirculation in mouse and its application to pharmacokinetic studies of cell therapies. Front. Immunol. 15, 1357706 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  71. Adhikarla, V. et al. Designing combination therapies for cancer treatment: application of a mathematical framework combining CAR T-cell immunotherapy and targeted radionuclide therapy. Front. Immunol. 15, 1358478 (2024). This mathematical model showed how combination treatment with CAR T cell therapy and targeted radionuclide therapy can be optimized.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  72. Jafarnejad, M. et al. A computational model of neoadjuvant PD-1 inhibition in non-small cell lung cancer. AAPS J. 21, 79 (2019).

    Article  PubMed  Google Scholar 

  73. Arulraj, T. et al. Virtual patient analysis identifies strategies to improve the performance of predictive biomarkers for PD-1 blockade. Proc. Natl Acad. Sci. USA 121, e2410911121 (2024).

    Article  CAS  PubMed  Google Scholar 

  74. Ma, H. et al. Combination therapy with T cell engager and PD-L1 blockade enhances the antitumor potency of T cells as predicted by a QSP model. J. Immunother. Cancer 8, e001141 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  75. Milberg, O. et al. A QSP model for predicting clinical responses to monotherapy, combination and sequential therapy following CTLA-4, PD-1, and PD-L1 checkpoint blockade. Sci. Rep. 9, 11286 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  76. Wang, H. et al. Conducting a virtual clinical trial in HER2-negative breast cancer using a quantitative systems pharmacology model with an epigenetic modulator and immune checkpoint inhibitors. Front. Bioeng. Biotechnol. 8, 141 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  77. Hardiansyah, D. & Ng, C. M. Quantitative systems pharmacology model of chimeric antigen receptor T‐cell therapy. Clin. Transl. Sci. 12, 343–349 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  78. Huitema, A. D. R. et al. Relationship between exposure and toxicity in high-dose chemotherapy with cyclophosphamide, thiotepa and carboplatin. Ann. Oncol. 13, 374–384 (2002).

    Article  CAS  PubMed  Google Scholar 

  79. Harkos, C., Svensson, S. F., Emblem, K. E. & Stylianopoulos, T. Inducing biomechanical heterogeneity in brain tumor modeling by MR elastography: effects on tumor growth, vascular density and delivery of therapeutics. Cancers 14, 884 (2022). This paper demonstrated that integrating patient-specific biomechanical properties with magnetic resonance elastography can improve mathematical models of glioblastoma, enabling more realistic simulations of tumour growth, vascular changes and drug delivery.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  80. Jain, R. K. & Wei, J. Dynamics of drug transport in solid tumors: distributed parameter model. J. Bioeng. 1, 313–329 (1977). The first distributed parameter mathematical model to describe the non-uniform distribution of methotrexate — a widely prescribed cancer drug — in solid tumours grown in rats, and identified poor and heterogeneous blood supply as a challenge in drug delivery to tumours.

    Google Scholar 

  81. Baxter, L. T. & Jain, R. K. Transport of fluid and macromolecules in tumors. I. Role of interstitial pressure and convection. Microvasc. Res. 37, 77–104 (1989).

    Article  CAS  PubMed  Google Scholar 

  82. Baxter, L. T. & Jain, R. K. Transport of fluid and macromolecules in tumors: III. Role of binding and metabolism. Microvasc. Res. 41, 5–23 (1991).

    Article  CAS  PubMed  Google Scholar 

  83. Baxter, L. T. & Jain, R. K. Transport of fluid and macromolecules in tumors. II. Role of heterogeneous perfusion and lymphatics. Microvasc. Res. 40, 246–263 (1990).

    Article  CAS  PubMed  Google Scholar 

  84. Baxter, L. T. & Jain, R. K. Transport of fluid and macromolecules in tumors. IV. A microscopic model of the perivascular distribution. Microvasc. Res. 41, 252–272 (1991).

    Article  CAS  PubMed  Google Scholar 

  85. Boucher, Y., Baxter, L. T. & Jain, R. K. Interstitial pressure gradients in tissue-isolated and subcutaneous tumors: implications for therapy. Cancer Res. 50, 4478–4484 (1990).

    CAS  PubMed  Google Scholar 

  86. Boucher, Y., Salehi, H., Witwer, B., Harsh, G. & Jain, R. Interstitial fluid pressure in intracranial tumours in patients and in rodents. Br. J. Cancer 75, 829–836 (1997).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  87. Goel, S. et al. Normalization of the vasculature for treatment of cancer and other diseases. Physiol. Rev. 91, 1071–1121 (2011).

    Article  CAS  PubMed  Google Scholar 

  88. Nia, H. T., Munn, L. L. & Jain, R. K. Physical traits of cancer. Science 370, eaaz0868 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  89. Helmlinger, G., Netti, P. A., Lichtenbeld, H. C., Melder, R. J. & Jain, R. K. Solid stress inhibits the growth of multicellular tumor spheroids. Nat. Biotechnol. 15, 778–783 (1997).

    Article  CAS  PubMed  Google Scholar 

  90. Netti, P. A., Baxter, L. T., Boucher, Y., Skalak, R. & Jain, R. K. Time-dependent behavior of interstitial fluid pressure in solid tumors: implications for drug delivery. Cancer Res. 55, 5451–5458 (1995).

    CAS  PubMed  Google Scholar 

  91. Skalak, R., Zargaryan, S., Jain, R. K., Netti, P. A. & Hoger, A. Compatibility and the genesis of residual stress by volumetric growth. J. Math. Biol. 34, 889–914 (1996).

    Article  CAS  PubMed  Google Scholar 

  92. Swartz, M. A. et al. Mechanics of interstitial–lymphatic fluid transport: theoretical foundation and experimental validation. J. Biomech. 32, 1297–1307 (1999).

    Article  CAS  PubMed  Google Scholar 

  93. Roose, T., Netti, P. A., Munn, L. L., Boucher, Y. & Jain, R. K. Solid stress generated by spheroid growth estimated using a linear poroelasticity model. Microvasc. Res. 66, 204–212 (2003).

    Article  PubMed  Google Scholar 

  94. Stylianopoulos, T. et al. Coevolution of solid stress and interstitial fluid pressure in tumors during progression: implications for vascular collapse. Cancer Res. 73, 3833–3841 (2013). The first mathematical model to calculate the increase in both solid stress and interstitial fluid pressure and their implications in drug delivery.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  95. Mpekris, F., Angeli, S., Pirentis, A. P. & Stylianopoulos, T. Stress-mediated progression of solid tumors: effect of mechanical stress on tissue oxygenation, cancer cell proliferation, and drug delivery. Biomech. Model. Mechanobiol. 14, 1391–1402 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  96. Mpekris, F., Baish, J. W., Stylianopoulos, T. & Jain, R. K. Role of vascular normalization in benefit from metronomic chemotherapy. Proc. Natl Acad. Sci. USA 114, 1994–1999 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  97. Seano, G. et al. Solid stress in brain tumours causes neuronal loss and neurological dysfunction and can be reversed by lithium. Nat. Biomed. Eng. 3, 230–245 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  98. Nia, H. T. et al. Solid stress estimation via intraoperative 3D navigation in patients with brain tumors. Preprint at medRxiv https://doi.org/10.1101/2024.11.28.24318104 (2024).

  99. Papageorgis, P. et al. Tranilast-induced stress alleviation in solid tumors improves the efficacy of chemo- and nanotherapeutics in a size-independent manner. Sci. Rep. 7, 46140 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  100. Voutouri, C. et al. Ultrasound stiffness and perfusion markers correlate with tumor volume responses to immunotherapy. Acta Biomater. 167, 121–134 (2023).

    Article  CAS  PubMed  Google Scholar 

  101. Angeli, S., Emblem, K. E., Due-Tonnessen, P. & Stylianopoulos, T. Towards patient-specific modeling of brain tumor growth and formation of secondary nodes guided by DTI-MRI. Neuroimage Clin. 20, 664–673 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  102. Swanson, K. R., Alvord, E. C. & Murray, J. D. Virtual brain tumours (gliomas) enhance the reality of medical imaging and highlight inadequacies of current therapy. Br. J. Cancer 86, 14–18 (2002).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  103. Hadjigeorgiou, A. G. & Stylianopoulos, T. Evaluation of growth-induced, mechanical stress in solid tumors and spatial association with extracellular matrix content. Biomech. Model. Mechanobiol. 22, 1625–1643 (2023).

    Article  PubMed  Google Scholar 

  104. Swanson, K. R., Alvord, E. C. & Murray, J. D. A quantitative model for differential motility of gliomas in grey and white matter. Cell Prolif. 33, 317–329 (2000).

    Article  CAS  PubMed  Google Scholar 

  105. Swanson, K. R., Bridge, C., Murray, J. D. & Alvord, E. C. Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. J. Neurol. Sci. 216, 1–10 (2003).

    Article  PubMed  Google Scholar 

  106. Jbabdi, S. et al. Simulation of anisotropic growth of low‐grade gliomas using diffusion tensor imaging. Magn. Reson. Med. 54, 616–624 (2005).

    Article  PubMed  Google Scholar 

  107. Katsamba, I. et al. Biomechanical modelling of spinal tumour anisotropic growth. Proc. R. Soc. A 476, 20190364 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  108. Kolokotroni, E. et al. A multidisciplinary hyper-modeling scheme in personalized in silico oncology: coupling cell kinetics with metabolism, signaling networks, and biomechanics as plug-in component models of a cancer digital twin. J. Pers. Med. 14, 475 (2024). This paper developed a modeling scheme for personalized simulations for Wilms tumour and non-small-cell lung cancer that predicts treatment responses and promising future applications in clinical decision support and in silico trials.

    Article  PubMed  PubMed Central  Google Scholar 

  109. Bodei, L., Herrmann, K., Schöder, H., Scott, A. M. & Lewis, J. S. Radiotheranostics in oncology: current challenges and emerging opportunities. Nat. Rev. Clin. Oncol. 19, 534–550 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  110. Piranfar, A. et al. Radiopharmaceutical transport in solid tumors via a 3-dimensional image-based spatiotemporal model. npj Syst. Biol. Appl. 10, 39 (2024). This paper presented a model based on clinical imaging that simulates the pharmacokinetics of 177Lu-PSMA in prostate tumours, offering insights for personalizing treatment for metastatic prostate cancer.

    Article  PubMed  PubMed Central  Google Scholar 

  111. Walker, C. R. & Angelo, M. Insights and opportunity costs in applying spatial biology to study the tumor microenvironment. Cancer Discov. 14, 707–710 (2024).

    Article  PubMed  Google Scholar 

  112. Lai, X. & Friedman, A. Combination therapy of cancer with cancer vaccine and immune checkpoint inhibitors: a mathematical model. PLoS ONE 12, e0178479 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  113. Friedman, A. & Hao, W. The role of exosomes in pancreatic cancer microenvironment. Bull. Math. Biol. 80, 1111–1133 (2018).

    Article  CAS  PubMed  Google Scholar 

  114. Mpekris, F. et al. Combining microenvironment normalization strategies to improve cancer immunotherapy. Proc. Natl Acad. Sci. USA 117, 3728–3737 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  115. Harkos, C. & Stylianopoulos, T. Investigating the synergistic effects of immunotherapy and normalization treatment in modulating tumor microenvironment and enhancing treatment efficacy. J. Theor. Biol. 583, 111768 (2024).

    Article  CAS  PubMed  Google Scholar 

  116. Harkos, C., Stylianopoulos, T. & Jain, R. K. Mathematical modeling of intratumoral immunotherapy yields strategies to improve the treatment outcomes. PLoS Comput. Biol. 19, e1011740 (2023). This paper presented a mechanistic mathematical model for optimizing intratumoral immunotherapy that revealed how the tumour microenvironment and conjugated cytokine properties influence treatment outcome.

    Article  PubMed  PubMed Central  Google Scholar 

  117. Anderson, A. R. A. & Chaplain, M. A. J. Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull. Math. Biol. 60, 857–899 (1998). The first discrete model of tumour angiogenesis.

    Article  CAS  PubMed  Google Scholar 

  118. Anderson, A. R. A., Chaplain, M. A. J. & McDougall, S. in Modeling Tumor Vasculature: Molecular, Cellular, and Tissue Level Aspects and Implications (ed. Jackson, T. L. L.) 105–133 (Springer, 2012).

  119. Valentim, C. A., Rabi, J. A. & David, S. A. Cellular-automaton model for tumor growth dynamics: virtualization of different scenarios. Comput. Biol. Med. 153, 106481 (2023).

    Article  PubMed  Google Scholar 

  120. Chauhan, V. P. et al. Normalization of tumour blood vessels improves the delivery of nanomedicines in a size-dependent manner. Nat. Nanotechnol. 7, 383–388 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  121. Stylianopoulos, T., Soteriou, K., Fukumura, D. & Jain, R. K. Cationic nanoparticles have superior transvascular flux into solid tumors: insights from a mathematical model. Ann. Biomed. Eng. 41, 68–77 (2013).

    Article  PubMed  Google Scholar 

  122. Stylianopoulos, T., Economides, E.-A., Baish, J. W., Fukumura, D. & Jain, R. K. Towards optimal design of cancer nanomedicines: multi-stage nanoparticles for the treatment of solid tumors. Ann. Biomed. Eng. 43, 2291–2300 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  123. Rejniak, K. A. et al. The role of tumor tissue architecture in treatment penetration and efficacy: an integrative study. Front. Oncol. 3, 111 (2013).

    Article  PubMed  PubMed Central  Google Scholar 

  124. Kingsley, J. L., Costello, J. R., Raghunand, N. & Rejniak, K. A. Bridging cell-scale simulations and radiologic images to explain short-time intratumoral oxygen fluctuations. PLoS Comput. Biol. 17, e1009206 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  125. Shields, J. D. et al. Autologous chemotaxis as a mechanism of tumor cell homing to lymphatics via interstitial flow and autocrine CCR7 signaling. Cancer Cell 11, 526–538 (2007).

    Article  CAS  PubMed  Google Scholar 

  126. Ben-Ami, Y., Pitt-Francis, J. M., Maini, P. K. & Byrne, H. M. Using a probabilistic approach to derive a two-phase model of flow-induced cell migration. Biophys. J. 123, 799–813 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  127. Kecman, V. in Real World Applications of Computational Intelligence Vol. 179 (eds Gh. Negoita, M. & Reusch, B.) 49–103 (Springer, 2005). This paper described an AI-powered analyser for whole-slide images of tumour-infiltrating lymphocytes that identified three immune phenotypes that correlate with tumour response and survival in advanced non-small-cell lung cancer.

  128. Voutouri, C. et al. A convolutional attention model for predicting response to chemo-immunotherapy from ultrasound elastography in mouse tumor models. Commun. Med. 4, 203 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  129. Englezos, D., Voutouri, C. & Stylianopoulos, T. Machine learning analysis reveals tumor stiffness and hypoperfusion as biomarkers predictive of cancer treatment efficacy. Transl. Oncol. 44, 101944 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  130. Rumelhart, D. E., Hinton, G. E. & Williams, R. J. Learning representations by back-propagating errors. Nature 323, 533–536 (1986).

    Article  Google Scholar 

  131. Esteva, A. et al. Dermatologist-level classification of skin cancer with deep neural networks. Nature 542, 115–118 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  132. Malibari, A. A. et al. Optimal deep neural network-driven computer aided diagnosis model for skin cancer. Comput. Electr. Eng. 103, 108318 (2022).

    Article  Google Scholar 

  133. Krakowski, I. et al. Human-AI interaction in skin cancer diagnosis: a systematic review and meta-analysis. npj Digital Med. 7, 78 (2024).

    Article  Google Scholar 

  134. Setio, A. A. A. et al. Pulmonary nodule detection in CT images: false positive reduction using multi-view convolutional networks. IEEE Trans. Med. Imaging 35, 1160–1169 (2016).

    Article  PubMed  Google Scholar 

  135. Ma, L., Li, G., Feng, X., Fan, Q. & Liu, L. TiCNet: transformer in convolutional neural network for pulmonary nodule detection on CT images. J. Imaging Inform. Med. 37, 196–208 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  136. Wakili, M. A. et al. Classification of breast cancer histopathological images using DenseNet and transfer learning. Comput. Intell. Neurosci. 2022, 1–31 (2022).

    Article  Google Scholar 

  137. Falou, O., Sannachi, L., Haque, M., Czarnota, G. J. & Kolios, M. C. Transfer learning of pre-treatment quantitative ultrasound multi-parametric images for the prediction of breast cancer response to neoadjuvant chemotherapy. Sci. Rep. 14, 2340 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  138. Stashko, C. et al. A convolutional neural network STIFMap reveals associations between stromal stiffness and EMT in breast cancer. Nat. Commun. 14, 3561 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  139. Jumper, J. et al. Highly accurate protein structure prediction with AlphaFold. Nature 596, 583–589 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  140. Ekins, S. et al. Exploiting machine learning for end-to-end drug discovery and development. Nat. Mater. 18, 435–441 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  141. Stokes, J. M. et al. A deep learning approach to antibiotic discovery. Cell 180, 688–702.e13 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  142. Mongia, M., Guler, M. & Mohimani, H. An interpretable machine learning approach to identify mechanism of action of antibiotics. Sci. Rep. 12, 10342 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  143. You, Y. et al. Artificial intelligence in cancer target identification and drug discovery. Signal Transduct. Target. Ther. 7, 156 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  144. Campana, P. A. et al. Cancer drug sensitivity estimation using modular deep Graph Neural Networks. NAR Genom. Bioinform. 6, lqae043 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  145. Stärk, H., Ganea, O.-E., Pattanaik, L., Barzilay, R. & Jaakkola, T. EquiBind: geometric deep learning for drug binding structure prediction. Preprint at arXiv https://doi.org/10.48550/ARXIV.2202.05146 (2022).

  146. Boehm, K. M. et al. Multimodal data integration using machine learning improves risk stratification of high-grade serous ovarian cancer. Nat. Cancer 3, 723–733 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  147. Cheerla, A. & Gevaert, O. Deep learning with multimodal representation for pancancer prognosis prediction. Bioinformatics 35, i446–i454 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  148. Carrillo-Perez, F. et al. Machine-learning-based late fusion on multi-omics and multi-scale data for non-small-cell lung cancer diagnosis. J. Pers. Med. 12, 601 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  149. Vaswani, A. et al. in Advances in Neural Information Processing Systems Vol. 30 (eds Guyon, I. et al.) (Curran Associates, 2017).

  150. Wang, L. et al. Transformer-based deep learning model for the diagnosis of suspected lung cancer in primary care based on electronic health record data. eBioMedicine 110, 105442 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  151. Wagner, S. J. et al. Transformer-based biomarker prediction from colorectal cancer histology: a large-scale multicentric study. Cancer Cell 41, 1650–1661.e4 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  152. Cai, Z. et al. DeePathNet: a transformer-based deep learning model integrating multi-omic data with cancer pathways. Cancer Res. Commun. 4, 3151–3164 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  153. Raissi, M., Perdikaris, P. & Karniadakis, G. E. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707 (2019).

    Article  Google Scholar 

  154. Sarabian, M., Babaee, H. & Laksari, K. Physics-informed neural networks for brain hemodynamic predictions using medical imaging. IEEE Trans. Med. Imaging 41, 2285–2303 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  155. Sel, K., Mohammadi, A., Pettigrew, R. I. & Jafari, R. Physics-informed neural networks for modeling physiological time series for cuffless blood pressure estimation. npj Digit. Med. 6, 110 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  156. Ragoza, M. & Batmanghelich, K. in Medical Image Computing and Computer Assisted Intervention — MICCAI 2023 Vol. 14229 (eds Greenspan, H. et al.) 333–343 (Springer, 2023).

  157. Rodrigues, J. A. Using physics-informed neural networks (PINNs) for tumor cell growth modeling. Mathematics 12, 1195 (2024).

    Article  Google Scholar 

  158. Mukhmetov, O. et al. Physics-informed neural network for fast prediction of temperature distributions in cancerous breasts as a potential efficient portable AI-based diagnostic tool. Comput. Methods Prog. Biomed. 242, 107834 (2023).

    Article  Google Scholar 

  159. Metzcar, J., Jutzeler, C. R., Macklin, P., Köhn-Luque, A. & Brüningk, S. C. A review of mechanistic learning in mathematical oncology. Front. Immunol. 15, 1363144 (2024).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  160. Gu, Y. & Ng, M. K. Deep neural networks for solving large linear systems arising from high-dimensional problems. SIAM J. Sci. Comput. 45, A2356–A2381 (2023).

    Article  Google Scholar 

  161. Ghaffarizadeh, A., Heiland, R., Friedman, S. H., Mumenthaler, S. M. & Macklin, P. PhysiCell: an open source physics-based cell simulator for 3-D multicellular systems. PLoS Comput. Biol. 14, e1005991 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  162. Fernandes, M. R., Aggarwal, P., Costa, R. G. F., Cole, A. M. & Trinchieri, G. Targeting the gut microbiota for cancer therapy. Nat. Rev. Cancer 22, 703–722 (2022).

    Article  CAS  PubMed  Google Scholar 

  163. Park, E. M. et al. Targeting the gut and tumor microbiota in cancer. Nat. Med. 28, 690–703 (2022).

    Article  CAS  PubMed  Google Scholar 

  164. Battaglia, T. W. et al. A pan-cancer analysis of the microbiome in metastatic cancer. Cell 187, 2324–2335.e19 (2024).

    Article  CAS  PubMed  Google Scholar 

  165. Davar, D. et al. Fecal microbiota transplant overcomes resistance to anti-PD-1 therapy in melanoma patients. Science 371, 595–602 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  166. Baruch, E. N. et al. Fecal microbiota transplant promotes response in immunotherapy-refractory melanoma patients. Science 371, 602–609 (2021).

    Article  CAS  PubMed  Google Scholar 

  167. Liang, H. et al. Predicting cancer immunotherapy response from gut microbiomes using machine learning models. Oncotarget 13, 876–889 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  168. Marino, S., Baxter, N. T., Huffnagle, G. B., Petrosino, J. F. & Schloss, P. D. Mathematical modeling of primary succession of murine intestinal microbiota. Proc. Natl Acad. Sci. USA 111, 439–444 (2014).

    Article  CAS  PubMed  Google Scholar 

  169. Bucci, V. et al. MDSINE: microbial dynamical systems inference engine for microbiome time-series analyses. Genome Biol. 17, 121 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  170. Rolig, A. S., Parthasarathy, R., Burns, A. R., Bohannan, B. J. M. & Guillemin, K. Individual members of the microbiota disproportionately modulate host innate immune responses. Cell Host Microbe 18, 613–620 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  171. Stein, R. R. et al. Computer-guided design of optimal microbial consortia for immune system modulation. eLife 7, e30916 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  172. Hadjigeorgiou, A.G. et al. Dissecting the impact of the gut microbiome on cancer immunotherapy. Preprint at Research Square https://doi.org/10.21203/rs.3.rs-3647386/v1 (2023).

  173. Meng, X. et al. The application of large language models in medicine: a scoping review. iScience 27, 109713 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  174. Rao, A. et al. Evaluating GPT as an adjunct for radiologic decision making: GPT-4 versus GPT-3.5 in a breast imaging pilot. J. Am. Coll. Radiol. 20, 990–997 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  175. Rao, A. et al. Assessing the utility of ChatGPT throughout the entire clinical workflow: development and usability study. J. Med. Internet Res. 25, e48659 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  176. Lawson McLean, A., Wu, Y., Lawson McLean, A. C. & Hristidis, V. Large language models as decision aids in neuro-oncology: a review of shared decision-making applications. J. Cancer Res. Clin. Oncol. 150, 139 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  177. Longwell, J. B. et al. Performance of large language models on medical oncology examination questions. JAMA Netw. Open 7, e2417641 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

Download references

Acknowledgements

We would like to thank J. Baish, L.L. Munn, F. Yuan and W. Lotter for their helpful comments during the preparation of this article. This work was supported through NIH grant R35-CA197743, and in part through grants R01CA259253, R01-CA269672, R01-NS118929, U01-CA224348 and U01-CA261842 and by the National Foundation for Cancer Research, Harvard Ludwig Cancer Center, Nile Albright Research Foundation and Jane’s Trust Foundation (to R.K.J.). Also, this work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 863955 to T.S.).

Author information

Author notes

  1. These authors contributed equally: Constantinos Harkos, Andreas G. Hadjigeorgiou.

Authors and Affiliations

  1. Cancer Biophysics Laboratory, Department of Mechanical and Manufacturing Engineering, University of Cyprus, Nicosia, Cyprus

    Constantinos Harkos, Andreas G. Hadjigeorgiou, Chrysovalantis Voutouri & Triantafyllos Stylianopoulos

  2. Edwin L. Steele Laboratories, Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, MA, USA

    Ashwin S. Kumar & Rakesh K. Jain

Authors
  1. Constantinos Harkos
    View author publications

    Search author on:PubMed Google Scholar

  2. Andreas G. Hadjigeorgiou
    View author publications

    Search author on:PubMed Google Scholar

  3. Chrysovalantis Voutouri
    View author publications

    Search author on:PubMed Google Scholar

  4. Ashwin S. Kumar
    View author publications

    Search author on:PubMed Google Scholar

  5. Triantafyllos Stylianopoulos
    View author publications

    Search author on:PubMed Google Scholar

  6. Rakesh K. Jain
    View author publications

    Search author on:PubMed Google Scholar

Contributions

C.H., A.G.H., C.V., A.S.K., T.S. and R.K.J. researched data for the article. C.H., A.G.H., C.V., A.S.K., T.S. and R.K.J. contributed substantially to discussion of the content. All authors wrote the article.

Corresponding authors

Correspondence to Triantafyllos Stylianopoulos or Rakesh K. Jain.

Ethics declarations

Competing interests

R.K.J. received consultant fees from DynamiCure, SPARC and SynDevRx; owns equity in Accurius, Enlight, SynDevRx; and served on the Boards of Trustees of Tekla Healthcare Investors, Tekla Life Sciences Investors, Tekla Healthcare Opportunities Fund and Tekla World Healthcare Fund; and received grants from Boehringer Ingelheim and Sanofi. Neither any reagent nor any funding from these organizations was used in this study. Other co-authors have no conflict of interests to declare.

Peer review

Peer review information

Nature Reviews Cancer thanks Georgios Lolas, Aleksander Popel who co-reviewed with Theinmozhi Arulraj and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Glossary

Anastomosis

The process of joining of two blood vessels.

Autologous chemotaxis

The process whereby a cell can receive directional cues while at the same time be the source of such cues.

Convection

The bulk motion of agents driven by the fluid velocity, which is proportional to fluid pressure gradient.

Finite element modelling

A computational numerical method used to solve partial differential equations by discretizing a structure into smaller parts called finite elements.

Hypoperfusion

Insufficient blood supply to tissues.

Immune checkpoint inhibitors

Therapeutic antibodies that inhibit regulators of the immune system, immune checkpoint proteins, that when stimulated suppress immune cell.

Interstitial fluid pressure

The pressure exerted by the fluid present in the spaces between cells in a tissue.

Pharmacodynamics

The study of the effect of the drug at the site of action.

Pharmacokinetics

The study of how drugs are absorbed, distributed, metabolized and eliminated in the body.

Random-walk model

A stochastic model that simulates the behaviour of cells, including cancer and endothelial cells, by capturing probabilistic processes such as cell migration, proliferation and the formation of new blood vessels.

Solid stresses

The mechanical forces (per unit area), in the context of tumour biology, refers to the mechanical stresses generated during tumour growth due to the deformation of the structural components of the tissue.

Targeted radionucleotide therapy

A systemic treatment that uses radiolabeled drugs (for example, antibodies, antibody fragments, proteins and peptides) that are cancer specific to deliver cytotoxic doses of radiation to kill cancer cells.

Tensotaxis

The migration of cells in response to mechanical stress.

Vascular normalization

Restoring normal structure and function of blood vessels in tumours (for example, with judicious use of anti-angiogenic agents).

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Harkos, C., Hadjigeorgiou, A.G., Voutouri, C. et al. Using mathematical modelling and AI to improve delivery and efficacy of therapies in cancer. Nat Rev Cancer 25, 324–340 (2025). https://doi.org/10.1038/s41568-025-00796-w

Download citation

  • Accepted:

  • Published:

  • Version of record:

  • Issue date:

  • DOI: https://doi.org/10.1038/s41568-025-00796-w

This article is cited by

Search

Advanced search

Quick links

Nature Briefing: Cancer

Sign up for the Nature Briefing: Cancer newsletter — what matters in cancer research, free to your inbox weekly.

Get what matters in cancer research, free to your inbox weekly. Sign up for Nature Briefing: Cancer