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Second-Order Effects of Chemotherapy Pharmacodynamics and Pharmacokinetics on Tumor Regression and Cachexia

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Abstract

Drug dose response curves are ubiquitous in cancer biology, but these curves are often used to measure differential response in first-order effects: the effectiveness of increasing the cumulative dose delivered. In contrast, second-order effects (the variance of drug dose) are often ignored. Knowledge of second-order effects may improve the design of chemotherapy scheduling protocols, leading to improvements in tumor response without changing the total dose delivered. By considering treatment schedules with identical cumulative dose delivered, we characterize differential treatment outcomes resulting from high variance schedules (e.g. high dose, low dose) and low variance schedules (constant dose). We extend a previous framework used to quantify second-order effects, known as antifragility theory, to investigate the role of drug pharmacokinetics. Using a simple one-compartment model, we find that high variance schedules are effective for a wide range of cumulative dose values. Next, using a mouse-parameterized two-compartment model of 5-fluorouracil, we show that schedule viability depends on initial tumor volume. Finally, we illustrate the trade-off between tumor response and lean mass preservation. Mathematical modeling indicates that high variance dose schedules provide a potential path forward in mitigating the risk of chemotherapy-associated cachexia by preserving lean mass without sacrificing tumor response.

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References

  • Altrock PM, Liu LL, Michor F (2015) The mathematics of cancer: integrating quantitative models. Nat Rev Cancer 15:730–745

    Article  Google Scholar 

  • Anderson AR, Quaranta V (2008) Integrative mathematical oncology. Nat Rev Cancer 8:227–234

    Article  Google Scholar 

  • Axenie C et al (2023) Antifragility as a complex system’s response to perturbations, volatility, and time. arXiv preprint arXiv:2312.13991

  • Axenie C, Kurz D, Saveriano M (2022) Antifragile control systems: the case of an anti-symmetric network model of the tumor-immune-drug interactions. Symmetry 14:2034

    Article  Google Scholar 

  • Barreto R et al (2016) Chemotherapy-related cachexia is associated with mitochondrial depletion and the activation of erk1/2 and p38 mapks

  • Bayer P, West J (2023) Games and the treatment convexity of cancer. Dyn Games Appl 13(4):1088–1105

    Article  MathSciNet  Google Scholar 

  • Citron ML (2008) Dose-dense chemotherapy: principles, clinical results and future perspectives. Breast Care 3:251–255

    Article  Google Scholar 

  • Danchin A, Binder PM, Noria S (2011) Antifragility and tinkering in biology (and in business) flexibility provides an efficient epigenetic way to manage risk. Genes 2:998–1016

    Article  Google Scholar 

  • Farhang-Sardroodi S, Wilkie KP (2020) Mathematical model of muscle wasting in cancer cachexia. J Clin Med 9:2029

    Article  Google Scholar 

  • Farhang-Sardroodi S, La Croix MA, Wilkie KP (2022) Chemotherapy-induced cachexia and model-informed dosing to preserve lean mass in cancer treatment. PLoS Comput Biol 18:e1009505

    Article  Google Scholar 

  • Fearon K et al (2011) Definition and classification of cancer cachexia: an international consensus. Lancet Oncol 12:489–495

    Article  Google Scholar 

  • Harris LA et al (2016) An unbiased metric of antiproliferative drug effect in vitro. Nat Methods 13:497–500

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Köhn-Luque A et al (2023) Phenotypic deconvolution in heterogeneous cancer cell populations using drug-screening data. Cell Rep Methods 3

  • Meyer CT et al (2019) Quantifying drug combination synergy along potency and efficacy axes. Cell Syst 8:97–108

    Article  Google Scholar 

  • Naito T et al (2017) Skeletal muscle depletion during chemotherapy has a large impact on physical function in elderly Japanese patients with advanced non-small-cell lung cancer. BMC Cancer 17:1–9

    Article  Google Scholar 

  • Phoenix WinNonlin User’s Guide (2020)

  • Piccart M, Biganzoli L, Di Leo A (2000) The impact of chemotherapy dose density and dose intensity on breast cancer outcome: what have we learned? Eur J Cancer 36:4–10

    Article  Google Scholar 

  • Pin F, Couch ME, Bonetto A (2018) Preservation of muscle mass as a strategy to reduce the toxic effects of cancer chemotherapy on body composition. Curr Opin Support Palliat Care 12:420

    Article  Google Scholar 

  • Pin F, Barreto R, Couch ME, Bonetto A, O’Connell TM (2019) Cachexia induced by cancer and chemotherapy yield distinct perturbations to energy metabolism. J Cachexia Sarcopenia Muscle 10:140–154

    Article  Google Scholar 

  • Pineda OK, Kim H, Gershenson C (2019) A novel antifragility measure based on satisfaction and its application to random and biological boolean networks. Complexity 2019

  • Poterucha T, Burnette B, Jatoi A (2012) A decline in weight and attrition of muscle in colorectal cancer patients receiving chemotherapy with bevacizumab. Med Oncol 29:1005–1009

    Article  Google Scholar 

  • Sbeity H, Younes R (2015) Review of optimization methods for cancer chemotherapy treatment planning. J Comput Sci Syst Biol 8:74

    Article  Google Scholar 

  • Schättler H, Ledzewicz U (2015) Optimal control for mathematical models of cancer therapies. An Application of Geometric Methods

  • Taleb NN (2012) Antifragile: things that gain from disorder, vol 3 (Random House, 2012)

  • Taleb NN, Douady R (2013) Mathematical definition, mapping, and detection of (anti) fragility. Quant Finance 13:1677–1689

    Article  MathSciNet  Google Scholar 

  • Taleb NN, West J (2023) Working with convex responses: Antifragility from finance to oncology. Entropy 25:343

    Article  MathSciNet  Google Scholar 

  • Vakil V, Trappe W (2021) Dosage strategies for delaying resistance emergence in heterogeneous tumors. FEBS Open Bio 11:1322–1331

    Article  Google Scholar 

  • West J et al (2021) Antifragile therapy. bioRxiv 2020–10

  • Wooten DJ, Meyer CT, Lubbock AL, Quaranta V, Lopez CF (2021) Musyc is a consensus framework that unifies multi-drug synergy metrics for combinatorial drug discovery. Nat Commun 12:4607

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge funding by the National Cancer Institute via the Cancer Systems Biology Consortium (CSBC) U01CA232382, U54CA274507; the Physical Sciences Oncology Network (PSON) U54CA193489; and support from the Moffitt Center of Excellence for Evolutionary Therapy.

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Correspondence to Alexander R. A. Anderson or Jeffrey West.

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Pierik, L., McDonald, P., Anderson, A.R.A. et al. Second-Order Effects of Chemotherapy Pharmacodynamics and Pharmacokinetics on Tumor Regression and Cachexia. Bull Math Biol 86, 47 (2024). https://doi.org/10.1007/s11538-024-01278-0

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