Fractional calculus in mathematical oncology

Scientific Reports, Journal Year: 2023, Volume and Issue: 13(1)

Published: June 21, 2023

Abstract Even though, nowadays, cancer is one of the leading causes death, too little known about behavior this disease due to its unpredictability from patient another. Classical mathematical models tumor growth have shaped our understanding and broad practical implications for treatment scheduling dosage. However, improvements are still necessary on these models. The primary objective present research prove efficiency fractional order calculus in oncology, more specifically modeling. For this, a generalization four most used differential equation volume measurements fitting realized, using corresponding equivalent. Are established Exponential, Logistic, Gompertz, General Bertalanffy-Pütter treated untreated dataset. obtained results compared by Mean Squared Error (MSE) with integer correspondent each model. superiority MSE reduced at least half comparison It demonstrated way that deterministic can offer good starting point finding proper model evolution prediction. Fractional suitable method case memory property, aspect particularly characterizes biological processes.

Language: Английский

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Generating immunogenomic data-guided virtual patients using a QSP model to predict response of advanced NSCLC to PD-L1 inhibition

npj Precision Oncology, Journal Year: 2023, Volume and Issue: 7(1)

Published: June 8, 2023

Generating realistic virtual patients from a limited amount of patient data is one the major challenges for quantitative systems pharmacology modeling in immuno-oncology. Quantitative (QSP) mathematical methodology that integrates mechanistic knowledge biological to investigate dynamics whole system during disease progression and drug treatment. In present analysis, we parameterized our previously published QSP model cancer-immunity cycle non-small cell lung cancer (NSCLC) generated cohort predict clinical response PD-L1 inhibition NSCLC. The generation was guided by immunogenomic iAtlas portal population pharmacokinetic durvalumab, inhibitor. With following distribution, predicted rate 18.6% (95% bootstrap confidence interval: 13.3-24.2%) identified CD8/Treg ratio as potential predictive biomarker addition expression tumor mutational burden. We demonstrated omics served reliable resource techniques immuno-oncology using models.

Language: Английский

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Geometric analysis enables biological insight from complex non-identifiable models using simple surrogates

PLoS Computational Biology, Journal Year: 2023, Volume and Issue: 19(1), P. e1010844 - e1010844

Published: Jan. 20, 2023

An enduring challenge in computational biology is to balance data quality and quantity with model complexity. Tools such as identifiability analysis information criterion have been developed harmonise this juxtaposition, yet cannot always resolve the mismatch between available granularity required mathematical models answer important biological questions. Often, it only simple phenomenological models, logistic Gompertz growth that are identifiable from standard experimental measurements. To draw insights complex, non-identifiable incorporate key mechanisms of interest, we study geometry a map parameter space complex simple, identifiable, surrogate model. By studying how parameters quantitatively relate surrogate, introduce exploit layer interpretation set goodness-of-fit metric or likelihood studied typical analysis. We demonstrate our approach by analysing hierarchy for multicellular tumour spheroid experiments. Typical experiments limited noisy, corresponding very often made arbitrarily complex. Our geometric able predict non-identifiabilities, classify spaces into combinations features characterised model, overall provide additional insight models.

Language: Английский

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Optimization of chemotherapy regimens using mathematical programming

Computers & Industrial Engineering, Journal Year: 2024, Volume and Issue: 191, P. 110078 - 110078

Published: March 24, 2024

Cancer is a leading cause of death and cost burden on healthcare systems worldwide. The mainstay treatment chemotherapy which most often administered empirically. Optimizing the frequency drug administration would benefit patients by avoiding overtreatment reducing costs. In this work, optimization regimens using mathematical programming techniques demonstrated developing simple model for fictitious drug. question to be answered solution how should so that tumor size does not exceed predefined reaches minimum value. proposed computer-implemented well-established system, thus keeping effort obtaining results low. An example used demonstrate superiority approach over approach.

Language: Английский

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A mathematical model for predicting the spatiotemporal response of breast cancer cells treated with doxorubicin

Cancer Biology & Therapy, Journal Year: 2024, Volume and Issue: 25(1)

Published: Feb. 27, 2024

Tumor heterogeneity contributes significantly to chemoresistance, a leading cause of treatment failure. To better personalize therapies, it is essential develop tools capable identifying and predicting intra- inter-tumor heterogeneities. Biology-inspired mathematical models are attacking this problem, but tumor often overlooked in

Language: Английский

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Theoretical and Experimental Approaches to Study of Biological Objects by Mathematical Methods Using the Example of Hormone Production in the Thyroid Gland

SSP Modern Pharmacy and Medicine, Journal Year: 2024, Volume and Issue: 4(3), P. 1 - 14

Published: July 10, 2024

The study of any biological object is a complex process that involves number successive stages, one which tools can be specially created expert system. It advisable to present the conclusion about studied in clear forms expression – quantitative or binary, are results practical application principles absorption by some researched factors others, compromise between them prevailing alternative properties. involvement mathematical technologies identification and explanation regularities activity objects requires display their research using language. This makes it possible establish course processes predict consequences. Since living system formed from large elements, organism has hierarchy structural functional levels organization. A mandatory prerequisite for variety states, each being characterized its own characteristics markers change, which, according degree completeness state transformation into another, should divided primary changes, majority final changes. Comprehensive Semi-quantitative analysis electronograms Ryabukha O. (2000) her method determining profiles hormonopoietic cells’ special capacities (2003) when studying cytophysiology thyroid gland normal pathological conditions, determine specific link follicular cell’s specialized activity, there was violation hormonopoiesis, assess intensity. developed Conceptual apparatus connections organelles hormone-producing cells Method correlation creating intra- intersystem portraits reflects features mutual influences interdependencies, deepens understanding intimate mechanisms hormonopoiesis.

Language: Английский

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Myeloid-Derived Suppressor–Cell Dynamics Control Outcomes in the Metastatic Niche

Cancer Immunology Research, Journal Year: 2023, Volume and Issue: 11(5), P. 614 - 628

Published: Feb. 27, 2023

Abstract Myeloid-derived suppressor cells (MDSC) play a prominent role in the tumor microenvironment. A quantitative understanding of tumor–MDSC interactions that influence disease progression is critical, and currently lacking. We developed mathematical model metastatic growth immune-rich microenvironments. modeled tumor–immune dynamics with stochastic delay differential equations studied impact delays MDSC activation/recruitment on outcomes. In lung environment, when circulating level MDSCs was low, had pronounced probability new establishment: blocking recruitment could reduce metastasis by as much 50%. To predict patient-specific responses, we fit to individual tumors treated immune checkpoint inhibitors via Bayesian parameter inference. reveal control inhibition rate natural killer (NK) larger outcomes than controlling directly. Posterior classification demonstrates incorporating knowledge responses improved predictive accuracy from 63% 82%. Investigation an environment low NK abundant cytotoxic T revealed, contrast, small no longer impacted dynamics. Our results illustrate importance microenvironment overall interventions promoting shifts toward less immune-suppressed states. propose there pressing need consider more often analyses

Language: Английский

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Validation of polymorphic Gompertzian model of cancer through in vitro and in vivo data

PLoS ONE, Journal Year: 2025, Volume and Issue: 20(1), P. e0310844 - e0310844

Published: Jan. 9, 2025

Mathematical modeling plays an important role in our understanding and targeting therapy resistance mechanisms cancer. The polymorphic Gompertzian model, analyzed theoretically numerically by Viossat Noble to demonstrate the benefits of adaptive metastatic cancer, describes a heterogeneous cancer population consisting therapy-sensitive therapy-resistant cells. In this study, we that model successfully captures trends both vitro vivo data on non-small cell lung (NSCLC) dynamics under treatment. Additionally, for tumor patients undergoing treatment, compare goodness fit classical oncologic models, which were previously identified as models best. We show can capture U-shape trend size during relapse, not be fitted with models. general, corresponds well real-world data, suggesting it candidate improving efficacy therapy, example, through evolutionary/adaptive therapies.

Language: Английский

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Dynamic Behaviors of a Periodic System with Threshold Policy-Guided Periodic and Intermittent Therapy of Tumor

SIAM Journal on Applied Mathematics, Journal Year: 2025, Volume and Issue: 85(1), P. 366 - 392

Published: Feb. 18, 2025

Language: Английский

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Assessing the role of model choice in parameter identifiability of cancer treatment efficacy

Frontiers in Applied Mathematics and Statistics, Journal Year: 2025, Volume and Issue: 11

Published: March 24, 2025

Several mathematical models are commonly used to describe cancer growth dynamics. Fitting of these experimental data has not yet determined which particular model best describes growth. Unfortunately, choice is known drastically alter the predictions both future tumor and effectiveness applied treatment. Since there growing interest in using help predict chemotherapy, we need determine if affects estimates chemotherapy efficacy. Here, simulate an vitro study by creating synthetic treatment each seven fit sets other (“wrong”) models. We estimate ε max (the maximum efficacy drug) IC 50 drug concentration at half effect achieved) effort whether use incorrect changes parameters. find that largely weakly practically identifiable no matter generate or data. The more likely be identifiable, but sensitive model, showing poor identifiability when Bertalanffy either

Language: Английский

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