Skip to main content

Advertisement

Log in

Computational approaches to modelling and optimizing cancer treatment

  • Review Article
  • Published:

From Nature Reviews Bioengineering

View current issue Sign up to alerts

Abstract

Computational models can be applied to optimize treatment schedules and model treatment responses in cancer therapy. In this Review, we provide an overview of such computational approaches, including deterministic models, such as those based on ordinary and partial differential equations, stochastic models, spatially explicit agent-based approaches as well as control theory and machine learning methods. We discuss their advantages and current limitations in different scenarios. We outline how therapeutic decision-making can be aided by mathematical and computational approaches and how patient-specific responses can be assessed and incorporated into such methods. We also survey models that can incorporate adaptive changes throughout the course of treatment and discuss data and parameter estimation approaches. Finally, we highlight how such methods can lead to the identification of optimum treatment options for individual cancer and treatment types, and examine the challenges that remain to be addressed to enable the clinical translation of computational models in cancer therapy.

Key points

  • Computational approaches can be applied to describe the response of tumour cells to cancer treatment.

  • Such computational methods can be based on ordinary and partial differential equation modelling, stochastic modelling and spatially explicit agent-based models.

  • Adaptive treatment schedules and incorporation of patient-specific responses allow a personalized assessment of treatment options.

  • Control theory and machine learning methods, such as reinforcement learning, can be applied to design cancer treatment schedules.

  • Multimodal and longitudinal data sets could be integrated into patient-specific models to identify the best therapeutic options for individual patients.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1: ODE-based models.
Fig. 2: PDE models.
Fig. 3: Stochastic models.
Fig. 4: ABMs.
Fig. 5: OCT.

Similar content being viewed by others

References

  1. Jiang, P. et al. Big data in basic and translational cancer research. Nat. Rev. Cancer 22, 625–639 (2022).

    Article  Google Scholar 

  2. Basu, A. et al. An interactive resource to identify cancer genetic and lineage dependencies targeted by small molecules. Cell 154, 1151–1161 (2013).

    Article  Google Scholar 

  3. Van Allen, E. M. et al. Whole-exome sequencing and clinical interpretation of formalin-fixed, paraffin-embedded tumor samples to guide precision cancer medicine. Nat. Med. 20, 682–688 (2014).

    Article  Google Scholar 

  4. Xue, J.-M., Liu, Y., Wan, L.-H. & Zhu, Y.-X. Comprehensive analysis of differential gene expression to identify common gene signatures in multiple cancers. Med. Sci. Monit. 26, e919953 (2020).

    Article  Google Scholar 

  5. Song, Q. et al. Proteomic analysis reveals key differences between squamous cell carcinomas and adenocarcinomas across multiple tissues. Nat. Commun. 13, 4167 (2022).

    Article  Google Scholar 

  6. Reznik, E. et al. A landscape of metabolic variation across tumor types. Cell Syst. 6, 301–313.e3 (2018).

    Article  Google Scholar 

  7. Büttner, M., Miao, Z., Wolf, F. A., Teichmann, S. A. & Theis, F. J. A test metric for assessing single-cell RNA-seq batch correction. Nat. Methods 16, 43–49 (2019).

    Article  Google Scholar 

  8. Sammut, S.-J. et al. Multi-omic machine learning predictor of breast cancer therapy response. Nature 601, 623–629 (2022).

    Article  Google Scholar 

  9. Gallasch, R., Efremova, M., Charoentong, P., Hackl, H. & Trajanoski, Z. Mathematical models for translational and clinical oncology. J. Clin. Bioinform. 3, 23 (2013).

    Article  Google Scholar 

  10. Altrock, P. M., Liu, L. L. & Michor, F. The mathematics of cancer: integrating quantitative models. Nat. Rev. Cancer 15, 730–745 (2015).

    Article  Google Scholar 

  11. Foo, J. & Michor, F. Evolution of resistance to targeted anti-cancer therapies during continuous and pulsed administration strategies. PLoS Comput. Biol. 5, e1000557 (2009).

    Article  MathSciNet  Google Scholar 

  12. Yang, J., Lindström, H. J. G. & Friedman, R. Combating drug resistance in acute myeloid leukaemia by drug rotations: the effects of quizartinib and pexidartinib. Cancer Cell Int. 21, 198 (2021).

    Article  Google Scholar 

  13. Poels, K. E. et al. Identification of optimal dosing schedules of dacomitinib and osimertinib for a phase I/II trial in advanced EGFR-mutant non-small cell lung cancer. Nat. Commun. 12, 3697 (2021).

    Article  Google Scholar 

  14. Gatenby, R. A., Silva, A. S., Gillies, R. J. & Frieden, B. R. Adaptive therapy. Cancer Res. 69, 4894–4903 (2009).

    Article  Google Scholar 

  15. Zhang, J., Cunningham, J. J., Brown, J. S. & Gatenby, R. A. Integrating evolutionary dynamics into treatment of metastatic castrate-resistant prostate cancer. Nat. Commun. 8, 1816 (2017).

    Article  Google Scholar 

  16. Luria, S. E. & Delbrück, M. Mutations of bacteria from virus sensitivity to virus resistance. Genetics 28, 491–511 (1943).

    Article  Google Scholar 

  17. Gardner, S. N. Modeling multi-drug chemotherapy: tailoring treatment to individuals. J. Theor. Biol. 214, 181–207 (2002).

    Article  Google Scholar 

  18. Michelson, S. & Leith, J. T. Effects of differential cell kill on the dynamic composition of heterogeneous tumors. Comput. Math. Appl. 20, 149–159 (1990).

    Google Scholar 

  19. Leder, K. et al. Mathematical modeling of PDGF-driven glioblastoma reveals optimized radiation dosing schedules. Cell 156, 603–616 (2014).

    Article  Google Scholar 

  20. Paryad-Zanjani, S., Saint-Antoine, M. M. & Singh, A. Optimal scheduling of therapy to delay cancer drug resistance. IFAC-Pap. 54, 239–244 (2021).

    Google Scholar 

  21. Lea, D. E. & Catcheside, D. G. The mechanism of the induction by radiation of chromosome aberrations in Tradescantia. J. Genet. 44, 216–245 (1942).

    Article  Google Scholar 

  22. Pisco, A. O. et al. Non-Darwinian dynamics in therapy-induced cancer drug resistance. Nat. Commun. 4, 2467 (2013).

    Article  Google Scholar 

  23. Greene, J. M., Gevertz, J. L. & Sontag, E. D. Mathematical approach to differentiate spontaneous and induced evolution to drug resistance during cancer treatment. JCO Clin. Cancer Inform. 3, 1–20 (2019).

    Article  Google Scholar 

  24. Greene, J. M., Sanchez-Tapia, C. & Sontag, E. D. Mathematical details on a cancer resistance model. Front. Bioeng. Biotechnol. 8, 501 (2020).

    Article  Google Scholar 

  25. Johnson, K. E. et al. Integrating transcriptomics and bulk time course data into a mathematical framework to describe and predict therapeutic resistance in cancer. Phys. Biol. 18, 016001 (2020).

    Article  Google Scholar 

  26. Owolabi, K. M. & Shikongo, A. Mathematical modelling of multi-mutation and drug resistance model with fractional derivative. Alex. Eng. J. 59, 2291–2304 (2020).

    Article  Google Scholar 

  27. Strobl, M. A. R. et al. Turnover modulates the need for a cost of resistance in adaptive therapy. Cancer Res. 81, 1135–1147 (2021).

    Article  Google Scholar 

  28. Kim, E., Brown, J. S., Eroglu, Z. & Anderson, A. R. A. Adaptive therapy for metastatic melanoma: predictions from patient calibrated mathematical models. Cancers 13, 823 (2021).

    Article  Google Scholar 

  29. Angelini, E., Wang, Y., Zhou, J. X., Qian, H. & Huang, S. A model for the intrinsic limit of cancer therapy: duality of treatment-induced cell death and treatment-induced stemness. PLoS Comput. Biol. 18, e1010319 (2022).

    Article  Google Scholar 

  30. Fröhlich, F. et al. Efficient parameter estimation enables the prediction of drug response using a mechanistic pan-cancer pathway model. Cell Syst. 7, 567–579.e6 (2018).

    Article  Google Scholar 

  31. Aghamiri, S. S., Amin, R. & Helikar, T. Recent applications of quantitative systems pharmacology and machine learning models across diseases. J. Pharmacokinet. Pharmacodyn. 49, 19–37 (2022).

    Article  Google Scholar 

  32. Neftel, C. et al. An integrative model of cellular states, plasticity, and genetics for glioblastoma. Cell 178, 835–849.e21 (2019).

    Article  Google Scholar 

  33. Shaffer, S. M. et al. Memory sequencing reveals heritable single-cell gene expression programs associated with distinct cellular behaviors. Cell 182, 947–959.e17 (2020).

    Article  Google Scholar 

  34. Rambow, F., Marine, J.-C. & Goding, C. R. Melanoma plasticity and phenotypic diversity: therapeutic barriers and opportunities. Genes Dev. 33, 1295–1318 (2019).

    Article  Google Scholar 

  35. Fukui, R. et al. Tumor radioresistance caused by radiation-induced changes of stem-like cell content and sub-lethal damage repair capability. Sci. Rep. 12, 1056 (2022).

    Article  Google Scholar 

  36. Stein, S., Zhao, R., Haeno, H., Vivanco, I. & Michor, F. Mathematical modeling identifies optimum lapatinib dosing schedules for the treatment of glioblastoma patients. PLoS Comput. Biol. 14, e1005924 (2018).

    Article  Google Scholar 

  37. Gillies, R. J., Verduzco, D. & Gatenby, R. A. Evolutionary dynamics of carcinogenesis and why targeted therapy does not work. Nat. Rev. Cancer 12, 487–493 (2012).

    Article  Google Scholar 

  38. Smith, J. M. & Price, G. R. The logic of animal conflict. Nature 246, 15–18 (1973).

    Article  MATH  Google Scholar 

  39. Basanta, D., Gatenby, R. A. & Anderson, A. R. A. Exploiting evolution to treat drug resistance: combination therapy and the double bind. Mol. Pharm. 9, 914–921 (2012).

    Article  Google Scholar 

  40. Orlando, P. A., Gatenby, R. A. & Brown, J. S. Cancer treatment as a game: integrating evolutionary game theory into the optimal control of chemotherapy. Phys. Biol. 9, 065007 (2012).

    Article  Google Scholar 

  41. West, J. B. et al. Multidrug cancer therapy in metastatic castrate-resistant prostate cancer: an evolution-based strategy. Clin. Cancer Res. 25, 4413–4421 (2019).

    Article  Google Scholar 

  42. Gluzman, M., Scott, J. G. & Vladimirsky, A. Optimizing adaptive cancer therapy: dynamic programming and evolutionary game theory. Proc. Biol. Sci. 287, 20192454 (2020).

    Google Scholar 

  43. Stanková, K., Brown, J. S., Dalton, W. S. & Gatenby, R. A. Optimizing cancer treatment using game theory: a review. JAMA Oncol. 5, 96–103 (2019).

    Article  Google Scholar 

  44. West, J. et al. Towards multidrug adaptive therapy. Cancer Res. 80, 1578–1589 (2020).

    Article  Google Scholar 

  45. Roy, M. & Finley, S. D. Computational model predicts the effects of targeting cellular metabolism in pancreatic cancer. Front. Physiol. 8, 217 (2017).

    Article  Google Scholar 

  46. Yu, L. et al. Modeling the genetic regulation of cancer metabolism: interplay between glycolysis and oxidative phosphorylation. Cancer Res. 77, 1564–1574 (2017).

    Article  Google Scholar 

  47. Jia, D. et al. Elucidating cancer metabolic plasticity by coupling gene regulation with metabolic pathways. Proc. Natl Acad. Sci. USA 116, 3909–3918 (2019).

    Article  Google Scholar 

  48. Shan, M., Dai, D., Vudem, A., Varner, J. D. & Stroock, A. D. Multi-scale computational study of the Warburg effect, reverse Warburg effect and glutamine addiction in solid tumors. PLoS Comput. Biol. 14, e1006584 (2018).

    Article  Google Scholar 

  49. Li, W. & Wang, J. Uncovering the underlying mechanisms of cancer metabolism through the landscapes and probability flux quantifications. iScience 23, 101002 (2020).

    Article  Google Scholar 

  50. Tripathi, S. et al. A mechanistic modeling framework reveals the key principles underlying tumor metabolism. PLoS Comput. Biol. 18, e1009841 (2022).

    Article  Google Scholar 

  51. Vernieri, C. et al. Targeting cancer metabolism: dietary and pharmacologic interventions. Cancer Discov. 6, 1315–1333 (2016).

    Article  Google Scholar 

  52. Stine, Z. E., Schug, Z. T., Salvino, J. M. & Dang, C. V. Targeting cancer metabolism in the era of precision oncology. Nat. Rev. Drug Discov. 21, 141–162 (2022).

    Article  Google Scholar 

  53. Sun, X., Bao, J. & Shao, Y. Mathematical modeling of therapy-induced cancer drug resistance: connecting cancer mechanisms to population survival rates. Sci. Rep. 6, 22498 (2016).

    Article  Google Scholar 

  54. Jackson, T. L. & Byrne, H. M. A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy. Math. Biosci. 164, 17–38 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  55. Hamis, S., Nithiarasu, P. & Powathil, G. G. What does not kill a tumour may make it stronger: in silico insights into chemotherapeutic drug resistance. J. Theor. Biol. 454, 253–267 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  56. 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  Google Scholar 

  57. Zheng, X. et al. A continuous model of angiogenesis: initiation, extension, and maturation of new blood vessels modulated by vascular endothelial growth factor, angiopoietins, platelet-derived growth factor-B, and pericytes. Discret. Contin. Dyn. Syst. B 18, 1109–1154 (2013).

    MathSciNet  MATH  Google Scholar 

  58. Voutouri, C. et al. Experimental and computational analyses reveal dynamics of tumor vessel cooption and optimal treatment strategies. Proc. Natl Acad. Sci. USA 116, 2662–2671 (2019).

    Article  Google Scholar 

  59. De Palma, M., Biziato, D. & Petrova, T. V. Microenvironmental regulation of tumour angiogenesis. Nat. Rev. Cancer 17, 457–474 (2017).

    Article  Google Scholar 

  60. Lugano, R., Ramachandran, M. & Dimberg, A. Tumor angiogenesis: causes, consequences, challenges and opportunities. Cell. Mol. Life Sci. 77, 1745–1770 (2020).

    Article  Google Scholar 

  61. Stylianopoulos, T. The solid mechanics of cancer and strategies for improved therapy. J. Biomech. Eng. 139, 4034991 (2017).

    Article  Google Scholar 

  62. Sefidgar, M. et al. Numerical modeling of drug delivery in a dynamic solid tumor microvasculature. Microvasc. Res. 99, 43–56 (2015).

    Article  Google Scholar 

  63. Arvanitis, C. D. et al. Mechanisms of enhanced drug delivery in brain metastases with focused ultrasound-induced blood–tumor barrier disruption. Proc. Natl Acad. Sci. USA 115, E8717–E8726 (2018).

    Article  Google Scholar 

  64. Mainprize, T. et al. Blood–brain barrier opening in primary brain tumors with non-invasive MR-guided focused ultrasound: a clinical safety and feasibility study. Sci. Rep. 9, 321 (2019).

    Article  Google Scholar 

  65. Ischenko, I., Seeliger, H., Schaffer, M., Jauch, K.-W. & Bruns, C. J. Cancer stem cells: how can we target them? Curr. Med. Chem. 15, 3171–3184 (2008).

    Article  Google Scholar 

  66. Anderson, K. C. et al. The role of minimal residual disease testing in myeloma treatment selection and drug development: current value and future applications. Clin. Cancer Res. 23, 3980–3993 (2017).

    Article  Google Scholar 

  67. da Silva-Diz, V., Lorenzo-Sanz, L., Bernat-Peguera, A., Lopez-Cerda, M. & Muñoz, P. Cancer cell plasticity: impact on tumor progression and therapy response. Semin. Cancer Biol. 53, 48–58 (2018).

    Article  Google Scholar 

  68. Hinohara, K. et al. KDM5 histone demethylase activity links cellular transcriptomic heterogeneity to therapeutic resistance. Cancer Cell 34, 939–953.e9 (2018).

    Article  Google Scholar 

  69. Kimmel, M. & Axelrod, D. E. Branching Processes in Biology (Springer, 2015).

  70. Bozic, I. et al. Accumulation of driver and passenger mutations during tumor progression. Proc. Natl Acad. Sci. USA 107, 18545–18550 (2010).

    Article  Google Scholar 

  71. Bauer, B., Siebert, R. & Traulsen, A. Cancer initiation with epistatic interactions between driver and passenger mutations. J. Theor. Biol. 358, 52–60 (2014).

    Article  MATH  Google Scholar 

  72. Yakovlev, A. Y. & Yanev, N. M. Relative frequencies in multitype branching processes. Ann. Appl. Probab. 19, 1–14 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  73. Roney, J. P., Ferlic, J., Michor, F. & McDonald, T. O. ESTIpop: a computational tool to simulate and estimate parameters for continuous-time Markov branching processes. Bioinformatics 36, 4372–4373 (2020).

    Article  Google Scholar 

  74. Komarova, N. L. & Wodarz, D. Stochastic modeling of cellular colonies with quiescence: an application to drug resistance in cancer. Theor. Popul. Biol. 72, 523–538 (2007).

    Article  MATH  Google Scholar 

  75. Chmielecki, J. et al. Optimization of dosing for EGFR-mutant non-small cell lung cancer with evolutionary cancer modeling. Sci. Transl Med. 3, 90ra59 (2011).

    Article  Google Scholar 

  76. Yu, H. A. et al. Phase 1 study of twice weekly pulse dose and daily low-dose erlotinib as initial treatment for patients with EGFR-mutant lung cancers. Ann. Oncol. 28, 278–284 (2017).

    Article  Google Scholar 

  77. Haeno, H. et al. Computational modeling of pancreatic cancer reveals kinetics of metastasis suggesting optimum treatment strategies. Cell 148, 362–375 (2012).

    Article  Google Scholar 

  78. Lindström, H. J. G., de Wijn, A. S. & Friedman, R. Stochastic modelling of tyrosine kinase inhibitor rotation therapy in chronic myeloid leukaemia. BMC Cancer 19, 508 (2019).

    Article  Google Scholar 

  79. Danesh, K., Durrett, R., Havrilesky, L. J. & Myers, E. A branching process model of ovarian cancer. J. Theor. Biol. 314, 10–15 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  80. Dean, J., Goldberg, E. & Michor, F. Designing optimal allocations for cancer screening using queuing network models. PLoS Comput. Biol. 18, e1010179 (2022).

    Article  Google Scholar 

  81. Chakrabarti, S. & Michor, F. Pharmacokinetics and drug interactions determine optimum combination strategies in computational models of cancer evolution. Cancer Res. 77, 3908–3921 (2017).

    Article  Google Scholar 

  82. US National Library of Medicine. ClinicalTrials.gov https://clinicaltrials.gov/ct2/show/NCT03810807 (2023).

  83. Baar, M. et al. A stochastic model for immunotherapy of cancer. Sci. Rep. 6, 24169 (2016).

    Article  Google Scholar 

  84. Yamamoto, K. N. et al. Computational modeling of pancreatic cancer patients receiving FOLFIRINOX and gemcitabine-based therapies identifies optimum intervention strategies. PLoS ONE 14, e0215409 (2019).

    Article  Google Scholar 

  85. Yamamoto, K. N., Liu, L. L., Nakamura, A., Haeno, H. & Michor, F. Stochastic evolution of pancreatic cancer metastases during logistic clonal expansion. JCO Clin. Cancer Inf. 3, 1–11 (2019).

    Google Scholar 

  86. Moran, P. A. P. The Statistical Processes Of Evolutionary Theory (Clarendon Press, 1962).

  87. Michor, F., Iwasa, Y. & Nowak, M. A. Dynamics of cancer progression. Nat. Rev. Cancer 4, 197–205 (2004).

    Article  Google Scholar 

  88. Beerenwinkel, N. et al. Genetic progression and the waiting time to cancer. PLoS Comput. Biol. 3, e225 (2007).

    Article  MathSciNet  Google Scholar 

  89. Park, J. & Newton, P. K. Stochastic competitive release and adaptive chemotherapy. Preprint at bioRxiv https://doi.org/10.1101/2022.06.17.496594 (2022).

    Article  Google Scholar 

  90. Fischer, A., Vázquez-García, I. & Mustonen, V. The value of monitoring to control evolving populations. Proc. Natl Acad. Sci. USA 112, 1007–1012 (2015).

    Article  Google Scholar 

  91. Chen, L., Yang, J., Tan, Y., Liu, Z. & Cheke, R. A. Threshold dynamics of a stochastic model of intermittent androgen deprivation therapy for prostate cancer. Commun. Nonlinear Sci. Numer. Simul. 100, 105856 (2021).

    Article  MathSciNet  MATH  Google Scholar 

  92. Camara, B. I., Mokrani, H., Diouf, A., Sané, I. & Diallo, A. S. Stochastic model analysis of cancer oncolytic virus therapy: estimation of the extinction mean times and their probabilities. Nonlinear Dyn. 107, 2819–2846 (2022).

    Article  Google Scholar 

  93. US National Library of Medicine. ClinicalTrials.gov https://clinicaltrials.gov/ct2/show/NCT03557372 (2021).

  94. Tanaka, G., Hirata, Y., Goldenberg, S. L., Bruchovsky, N. & Aihara, K. Mathematical modelling of prostate cancer growth and its application to hormone therapy. Phil. Trans. R. Soc. A 368, 5029–5044 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  95. Albano, G., Giorno, V., Román-Román, P., Román-Román, S. & Torres-Ruiz, F. Estimating and determining the effect of a therapy on tumor dynamics by means of a modified Gompertz diffusion process. J. Theor. Biol. 364, 206–219 (2015).

    Article  MATH  Google Scholar 

  96. Sfakianakis, N., Madzvamuse, A. & Chaplain, M. A. J. A hybrid multiscale model for cancer invasion of the extracellular matrix. Multiscale Model. Simul. 18, 824–850 (2020).

    Article  MathSciNet  MATH  Google Scholar 

  97. Mirams, G. R. et al. Chaste: an open source C++ library for computational physiology and biology. PLoS Comput. Biol. 9, e1002970 (2013).

    Article  MathSciNet  Google Scholar 

  98. Chamseddine, I. M. & Rejniak, K. A. Hybrid modeling frameworks of tumor development and treatment. Wiley Interdisc. Rev. Syst. Biol. Med. 12, e1461 (2020).

    Article  Google Scholar 

  99. Olsen, M. M. & Siegelmann, H. T. Multiscale agent-based model of tumor angiogenesis. Proc. Comput. Sci. 18, 1016–1025 (2013).

    Article  Google Scholar 

  100. Noble, R. et al. Spatial structure governs the mode of tumour evolution. Nat. Ecol. Evol. 6, 207–217 (2022).

    Article  Google Scholar 

  101. Beerenwinkel, N., Schwarz, R. F., Gerstung, M. & Markowetz, F. Cancer evolution: mathematical models and computational inference. Syst. Biol. 64, e1–e25 (2015).

    Article  Google Scholar 

  102. Swanton, C. Intratumor heterogeneity: evolution through space and time. Cancer Res. 72, 4875–4882 (2012).

    Article  Google Scholar 

  103. Wu, H.-J. et al. Spatial intra-tumor heterogeneity is associated with survival of lung adenocarcinoma patients. Cell Genom. 2, 100165 (2022).

    Article  Google Scholar 

  104. Zhang, L., Wang, Z., Sagotsky, J. A. & Deisboeck, T. S. Multiscale agent-based cancer modeling. J. Math. Biol. 58, 545–559 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  105. Fusco, D., Gralka, M., Kayser, J., Anderson, A. & Hallatschek, O. Excess of mutational jackpot events in expanding populations revealed by spatial Luria–Delbrück experiments. Nat. Commun. 7, 12760 (2016).

    Article  Google Scholar 

  106. Paterson, C., Nowak, M. A. & Waclaw, B. An exactly solvable, spatial model of mutation accumulation in cancer. Sci. Rep. 6, 39511 (2016).

    Article  Google Scholar 

  107. Randles, A. et al. Computational modelling of perivascular-niche dynamics for the optimization of treatment schedules for glioblastoma. Nat. Biomed. Eng. 5, 346–359 (2021).

    Article  Google Scholar 

  108. Waclaw, B. et al. A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity. Nature 525, 261–264 (2015).

    Article  Google Scholar 

  109. Chkhaidze, K. et al. Spatially constrained tumour growth affects the patterns of clonal selection and neutral drift in cancer genomic data. PLoS Comput. Biol. 15, e1007243 (2019).

    Article  Google Scholar 

  110. Liggett, T. M. Interacting Particle Systems (Springer, 2005).

  111. Nicol, P. B., Barabási, D. L., Coombes, K. R. & Asiaee, A. SITH: an R package for visualizing and analyzing a spatial model of intratumor heterogeneity. Comput. Syst. Oncol. 2, e1033 (2022).

    Article  Google Scholar 

  112. Angaroni, F. et al. J-SPACE: a Julia package for the simulation of spatial models of cancer evolution and of sequencing experiments. BMC Bioinformatics 23, 269 (2022).

    Article  Google Scholar 

  113. Opasic, L., Scott, J., Traulsen, A. & Fortmann-Grote, C. CancerSim: a cancer simulation package for Python 3. J. Open Source Softw. 5, 2436 (2020).

    Article  Google Scholar 

  114. Van Liedekerke, P., Palm, M. M., Jagiella, N. & Drasdo, D. Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results. Comp. Part. Mech. 2, 401–444 (2015).

    Article  Google Scholar 

  115. van Leeuwen, I. M. M. et al. An integrative computational model for intestinal tissue renewal. Cell Prolif. 42, 617–636 (2009).

    Article  Google Scholar 

  116. 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  Google Scholar 

  117. Gallaher, J. A., Enriquez-Navas, P. M., Luddy, K. A., Gatenby, R. A. & Anderson, A. R. A. Spatial heterogeneity and evolutionary dynamics modulate time to recurrence in continuous and adaptive cancer therapies. Cancer Res. 78, 2127–2139 (2018).

    Article  Google Scholar 

  118. Thomas, D. S., Cisneros, L. H., Anderson, A. R. A. & Maley, C. C. In silico investigations of multi-drug adaptive therapy protocols. Cancers 14, 2699 (2022).

    Article  Google Scholar 

  119. Strobl, M. A. R. et al. Spatial structure impacts adaptive therapy by shaping intra-tumoral competition. Commun. Med. 2, 46 (2022).

    Article  Google Scholar 

  120. Rejniak, K. A. & Anderson, A. R. A. Hybrid models of tumor growth. Wiley Interdisc. Rev. Syst. Biol. Med. 3, 115–125 (2011).

    Article  Google Scholar 

  121. Bacevic, K. et al. Spatial competition constrains resistance to targeted cancer therapy. Nat. Commun. 8, 1995 (2017).

    Article  Google Scholar 

  122. Bergman, D. et al. PhysiPKPD: a pharmacokinetics and pharmacodynamics module for PhysiCell. Gigabyte 2022, gigabyte72 (2022).

    Google Scholar 

  123. Almendro, V. et al. Inference of tumor evolution during chemotherapy by computational modeling and in situ analysis of genetic and phenotypic cellular diversity. Cell Rep. 6, 514–527 (2014).

    Article  Google Scholar 

  124. Sutton, R. S. & Barto, A. G. Reinforcement Learning: An Introduction (MIT Press, 2018).

  125. Schättler, H. M. & Ledzewicz, U. Optimal Control for Mathematical Models of Cancer Therapies: An Application of Geometric Methods (Springer, 2015).

  126. Jarrett, A. M. et al. Optimal control theory for personalized therapeutic regimens in oncology: background, history, challenges, and opportunities. J. Clin. Med. 9, 1314 (2020).

    Article  Google Scholar 

  127. Swan, G. W. & Vincent, T. L. Optimal control analysis in the chemotherapy of IgG multiple myeloma. Bull. Math. Biol. 39, 317–337 (1977).

    Article  MATH  Google Scholar 

  128. Kuosmanen, T. et al. Drug-induced resistance evolution necessitates less aggressive treatment. PLoS Comput. Biol. 17, e1009418 (2021).

    Article  Google Scholar 

  129. Jerez, S., Pliego, E., Solis, F. J. & Miller, A. K. Antigen receptor therapy in bone metastasis via optimal control for different human life stages. J. Math. Biol. 83, 44 (2021).

    Article  MathSciNet  MATH  Google Scholar 

  130. Hu, X., Ke, G. & Jang, S. R.-J. Modeling pancreatic cancer dynamics with immunotherapy. Bull. Math. Biol. 81, 1885–1915 (2019).

    Article  MathSciNet  MATH  Google Scholar 

  131. de Los Reyes, A. A. & Kim, Y. Optimal regulation of tumour-associated neutrophils in cancer progression. R. Soc. Open. Sci. 9, 210705 (2022).

    Article  Google Scholar 

  132. Lee, T., Jenner, A. L., Kim, P. S. & Lee, J. Application of control theory in a delayed-infection and immune-evading oncolytic virotherapy. Math. Biosci. Eng. 17, 2361–2383 (2020).

    Article  MathSciNet  MATH  Google Scholar 

  133. Aspirin, A. P., de Los Reyes V, A. A. & Kim, Y. Polytherapeutic strategies with oncolytic virus-bortezomib and adjuvant NK cells in cancer treatment. J. R. Soc. Interf. 18, 20200669 (2021).

    Article  Google Scholar 

  134. Anelone, A. J. N., Villa-Tamayo, M. F. & Rivadeneira, P. S. Oncolytic virus therapy benefits from control theory. R. Soc. Open. Sci. 7, 200473 (2020).

    Article  Google Scholar 

  135. Cunningham, J. et al. Optimal control to reach eco-evolutionary stability in metastatic castrate-resistant prostate cancer. PLoS ONE 15, e0243386 (2020).

    Article  Google Scholar 

  136. Wu, C. et al. Towards patient-specific optimization of neoadjuvant treatment protocols for breast cancer based on image-guided fluid dynamics. IEEE Trans. Biomed. Eng. 69, 3334–3344 (2022).

    Article  Google Scholar 

  137. Angaroni, F. et al. An optimal control framework for the automated design of personalized cancer treatments. Front. Bioeng. Biotechnol. 8, 523 (2020).

    Article  Google Scholar 

  138. Lee, J., Lee, D. & Kim, Y. Mathematical model of STAT signalling pathways in cancer development and optimal control approaches. R. Soc. Open Sci. 8, 210594 (2021).

    Article  Google Scholar 

  139. Martin, R. B., Fisher, M. E., Minchin, R. F. & Teo, K. L. Optimal control of tumor size used to maximize survival time when cells are resistant to chemotherapy. Math. Biosci. 110, 201–219 (1992).

    Article  MATH  Google Scholar 

  140. François-Lavet, V., Henderson, P., Islam, R., Bellemare, M. G. & Pineau, J. An introduction to deep reinforcement learning. Found. Trends Mach. Learn. 11, 219–354 (2018).

    Article  MATH  Google Scholar 

  141. Engelhardt, D. Dynamic control of stochastic evolution: a deep reinforcement learning approach to adaptively targeting emergent drug resistance. J. Mach. Learn. Res. 21, 1–30 (2020).

    MathSciNet  MATH  Google Scholar 

  142. Eastman, B., Przedborski, M. & Kohandel, M. Reinforcement learning derived chemotherapeutic schedules for robust patient-specific therapy. Sci. Rep. 11, 17882 (2021).

    Article  Google Scholar 

  143. Ebrahimi Zade, A., Shahabi Haghighi, S. & Soltani, M. Deep neural networks for neuro-oncology: towards patient individualized design of chemo-radiation therapy for glioblastoma patients. J. Biomed. Inf. 127, 104006 (2022).

    Article  Google Scholar 

  144. Moreau, G., François-Lavet, V., Desbordes, P. & Macq, B. Reinforcement learning for radiotherapy dose fractioning automation. Biomedicines 9, 214 (2021).

    Article  Google Scholar 

  145. Tortora, M. et al. Deep reinforcement learning for fractionated radiotherapy in non-small cell lung carcinoma. Artif. Intell. Med. 119, 102137 (2021).

    Article  Google Scholar 

  146. Yauney, G. & Shah, P. in Proc. 3rd Machine Learning Healthcare Conf. Vol. 85 161–226 (PMLR, 2018).

  147. Padmanabhan, R., Meskin, N. & Haddad, W. M. Reinforcement learning-based control of drug dosing for cancer chemotherapy treatment. Math. Biosci. 293, 11–20 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  148. Wang, M., Scott, J. G. & Vladimirsky, A. Stochastic optimal control to guide adaptive cancer therapy. Preprint at bioRxiv https://doi.org/10.1101/2022.06.17.496649 (2022).

    Article  Google Scholar 

  149. Tseng, H.-H. et al. Deep reinforcement learning for automated radiation adaptation in lung cancer. Med. Phys. 44, 6690–6705 (2017).

    Article  Google Scholar 

  150. Tardini, E. et al. Optimal treatment selection in sequential systemic and locoregional therapy of oropharyngeal squamous carcinomas: deep Q-learning with a patient–physician digital twin dyad. J. Med. Internet Res. 24, e29455 (2022).

    Article  Google Scholar 

  151. Niraula, D., Jamaluddin, J., Matuszak, M. M., Haken, R. K. T. & Naqa, I. E. Quantum deep reinforcement learning for clinical decision support in oncology: application to adaptive radiotherapy. Sci. Rep. 11, 23545 (2021).

    Article  Google Scholar 

  152. US National Library of Medicine. ClinicalTrials.gov https://clinicaltrials.gov/ct2/show/NCT02415621 (2023).

  153. US National Library of Medicine. ClinicalTrials.gov https://clinicaltrials.gov/ct2/show/NCT03543969 (2023).

  154. US National Library of Medicine. Pilot study of adaptive BRAF-MEK inhibitor therapy for advanced BRAF mutant melanoma. ClinicalTrials.gov https://clinicaltrials.gov/ct2/show/NCT03543969 (2018).

  155. US National Library of Medicine. ClinicalTrials.gov https://clinicaltrials.gov/ct2/show/NCT03630120 (2021).

  156. Smalley, I. et al. Leveraging transcriptional dynamics to improve BRAF inhibitor responses in melanoma. EBioMedicine 48, 178–190 (2019).

    Article  Google Scholar 

  157. Komorowski, M., Celi, L. A., Badawi, O., Gordon, A. C. & Faisal, A. A. The Artificial Intelligence Clinician learns optimal treatment strategies for sepsis in intensive care. Nat. Med. 24, 1716–1720 (2018).

    Article  Google Scholar 

  158. Dean, J. A. et al. Phase I study of a novel glioblastoma radiation therapy schedule exploiting cell-state plasticity. Neuro Oncol. 25, 1100–1112 (2022).

    Article  Google Scholar 

  159. Zhang, J. et al. A phase 1b adaptive androgen deprivation therapy trial in metastatic castration sensitive prostate cancer. J. Clin. Oncol. 40, 5075 (2022).

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge support from the Dana-Farber Cancer Institute’s Center for Cancer Evolution.

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed equally to the preparation of this manuscript.

Corresponding author

Correspondence to Franziska Michor.

Ethics declarations

Competing interests

F.M. is a co-founder of and has equity in Harbinger Health, has equity in Zephyr AI, serves as a consultant for Harbinger Health and Zephyr AI and is on the board of directors of Exscientia Plc. F.M. declares that none of these relationships are directly or indirectly related to the content of this manuscript. All other authors declare no competing interests.

Peer review

Peer review information

Nature Reviews Bioengineering thanks Robert Noble, Blair Colyer 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.

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

McDonald, T.O., Cheng, YC., Graser, C. et al. Computational approaches to modelling and optimizing cancer treatment. Nat Rev Bioeng 1, 695–711 (2023). https://doi.org/10.1038/s44222-023-00089-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s44222-023-00089-7

  • Springer Nature Limited

Navigation