Introduction to Mathematical Oncology

Rockne, Russell C.; Scott, Jacob G.

doi:10.1200/cci.19.00010

Cited by 26 publications

(23 citation statements)

References 24 publications

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“…This example clearly shows benefits of understanding the cancer cell dependencies and their combinations in improving efficacy of treatments for heterogeneous tumors. Mathematical modeling can also help with predicting optimal drug combinations and treatment schedules that are most likely to work in heterogeneous tumors (Rockne and Scott , 2019;Chakrabarti and Michor, 2017;Gallaher et al, 2018;Leder et al, 2014). Indeed, several clinical trials have been designed based on these models and following evolutionary principles and some have shown promising results (Zhang et al, 2017).…”

Section: Accounting For Heterogeneity In Therapeutic Decision Makingmentioning

confidence: 99%

Intratumor Heterogeneity: The Rosetta Stone of Therapy Resistance

2020

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Advances in our understanding of molecular mechanisms of tumorigenesis have translated into knowledgebased therapies directed against specific oncogenic signaling targets. These therapies often induce dramatic responses in susceptible tumors. Unfortunately, most advanced cancers, including those with robust initial responses, eventually acquire resistance to targeted therapies and relapse. Even though immunebased therapies are more likely to achieve complete cures, acquired resistance remains an obstacle to their success as well. Acquired resistance is the direct consequence of pre-existing intratumor heterogeneity and ongoing diversification during therapy, which enables some tumor cells to survive treatment and facilitates the development of new therapy-resistant phenotypes. In this review, we discuss the sources of intratumor heterogeneity and approaches to capture and account for it during clinical decision making. Finally, we outline potential strategies to improve therapeutic outcomes by directly targeting intratumor heterogeneity.

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Section: Accounting For Heterogeneity In Therapeutic Decision Makingmentioning

confidence: 99%

Intratumor Heterogeneity: The Rosetta Stone of Therapy Resistance

2020

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“…The growth of solid tumors and their response to therapy is hard to predict on the level of individual patients. Similar to other complex systems such as the climate [ 1 , 2 ] or stock markets [ 3 ], quantitative mathematical models can be used to describe and forecast the behavior of cancer: this is one of the main objectives of “mathematical oncology” [ 4 , 5 ]. Mathematical models of tumor growth kinetics have improved the understanding of underlying biological mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Classical mathematical models for prediction of response to chemotherapy and immunotherapy

et al. 2022

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Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage. However, even the simplest textbook models have been barely validated in real world-data of human patients. In this study, we fitted a range of differential equation models to tumor volume measurements of patients undergoing chemotherapy or cancer immunotherapy for solid tumors. We used a large dataset of 1472 patients with three or more measurements per target lesion, of which 652 patients had six or more data points. We show that the early treatment response shows only moderate correlation with the final treatment response, demonstrating the need for nuanced models. We then perform a head-to-head comparison of six classical models which are widely used in the field: the Exponential, Logistic, Classic Bertalanffy, General Bertalanffy, Classic Gompertz and General Gompertz model. Several models provide a good fit to tumor volume measurements, with the Gompertz model providing the best balance between goodness of fit and number of parameters. Similarly, when fitting to early treatment data, the general Bertalanffy and Gompertz models yield the lowest mean absolute error to forecasted data, indicating that these models could potentially be effective at predicting treatment outcome. In summary, we provide a quantitative benchmark for classical textbook models and state-of-the art models of human tumor growth. We publicly release an anonymized version of our original data, providing the first benchmark set of human tumor growth data for evaluation of mathematical models.

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“…How do we deviate from fractionation dogma that has stood the test of time? The field of mathematical oncology provides an excellent platform to tackle these questions through in silico analysis [21][22][23][24][25]. Mathematical frameworks can efficiently mine and optimize this parameter space, and, hence, could pave the way towards clinical testing of the most promising approaches.…”

Section: Introductionmentioning

confidence: 99%

A Century of Fractionated Radiotherapy: How Mathematical Oncology Can Break the Rules

Ghaderi

Jung

Brüningk

et al. 2022

IJMS

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Radiotherapy is involved in 50% of all cancer treatments and 40% of cancer cures. Most of these treatments are delivered in fractions of equal doses of radiation (Fractional Equivalent Dosing (FED)) in days to weeks. This treatment paradigm has remained unchanged in the past century and does not account for the development of radioresistance during treatment. Even if under-optimized, deviating from a century of successful therapy delivered in FED can be difficult. One way of exploring the infinite space of fraction size and scheduling to identify optimal fractionation schedules is through mathematical oncology simulations that allow for in silico evaluation. This review article explores the evidence that current fractionation promotes the development of radioresistance, summarizes mathematical solutions to account for radioresistance, both in the curative and non-curative setting, and reviews current clinical data investigating non-FED fractionated radiotherapy.

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Introduction to Mathematical Oncology

Cited by 26 publications

References 24 publications

Intratumor Heterogeneity: The Rosetta Stone of Therapy Resistance

Intratumor Heterogeneity: The Rosetta Stone of Therapy Resistance

Classical mathematical models for prediction of response to chemotherapy and immunotherapy

A Century of Fractionated Radiotherapy: How Mathematical Oncology Can Break the Rules

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