ArticlePLoS computational biology2022
Classical mathematical models for prediction of response to chemotherapy and immunotherapy.
Article in PLoS computational biology, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 49 papers.
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Who cites it
49 citing papers in PubMed.
- Systematic modeling of phenotypic drug response profiles in patient-derived organoids.bioRxiv : the preprint server for biology · 2026Article
- Internet of Things-Enhanced Mathematical Oncology: Conceptual Framework for Adaptive Cancer Care Modeling.JMIR cancer · 2026Article
- In silico clinical trials of BiTE expression by oncolytic viruses reveal the impact of patient heterogeneity on dosage protocol.PLoS computational biology · 2026Article
- Mathematical modeling of immune counter-regulation predicts efficacy of fractionated CD8Scientific reports · 2026Article
- Simulating Cancer Recurrence Patterns From Post-Treatment Viable Tumor Burden Distributions.JCO clinical cancer informatics · 2026Article
- Gompertz growth with a shared carrying capacity optimally simulates primary and metastatic tumor growth dynamics.British journal of cancer · 2026Article
- Follow-Up Bias in Tumor Dynamic Modeling: A Comparison of Classical and Neural-ODE Approaches.CPT: pharmacometrics & systems pharmacology · 2026Article
- Can evolutionary therapy be applied in non-small cell lung cancer?Scientific reports · 2026Article
- Mathematical analysis of metronomic chemotherapy response in metastatic gastrointestinal cancer: identifying critical parameters from clinical data.Scientific reports · 2026Article
- Migrastatic therapy as a potential game-changer in adaptive cancer treatment.Scientific reports · 2026Article
- Article
- Continuous adaptive chemotherapy dosing by using planet-formation-inspired dynamics: analytical andFrontiers in oncology · 2026Article
- An accurate analytical modeling method for microwave-based breast tumor detection and phantom manufacturing.Biomedical engineering letters · 2026Article
- Navigating the landscape of personalized oncology: overcoming challenges and expanding horizons with computational modeling.Journal of the American Medical Informatics Association : JAMIA · 2026Article
- Impact of mild hyperthermia on tumor-immune dynamics explored through mathematical modeling.Scientific reports · 2025Article
- An efficient and flexible framework for inferring global sensitivity of agent-based model parameters.PLoS computational biology · 2025Article
- Beyond RECIST: mathematical modeling and Bayesian inference reveal the importance of immune parameters in metastatic breast cancer.bioRxiv : the preprint server for biology · 2025Article
- Quantitative Method for Monitoring Tumor Evolution During and After Therapy.Journal of personalized medicine · 2025Article
- Bringing evolutionary cancer therapy to the clinic: a systems approach.NPJ systems biology and applications · 2025Review
- Validating the predictions of mathematical models describing tumor growth and treatment response.ArXiv · 2025Article
Corrections and comments
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Authors and funding
10 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
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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