Fractional calculus in mathematical oncology

Scientific Reports, Год журнала: 2023, Номер 13(1)

Опубликована: Июнь 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.

Язык: 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, Год журнала: 2023, Номер 7(1)

Опубликована: Июнь 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.

Язык: Английский

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

PLoS ONE, Год журнала: 2025, Номер 20(1), С. e0310844 - e0310844

Опубликована: Янв. 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.

Язык: Английский

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

PLoS Computational Biology, Год журнала: 2023, Номер 19(1), С. e1010844 - e1010844

Опубликована: Янв. 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.

Язык: Английский

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

Cancer Biology & Therapy, Год журнала: 2024, Номер 25(1)

Опубликована: Фев. 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

Язык: Английский

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Optimization of chemotherapy regimens using mathematical programming

Computers & Industrial Engineering, Год журнала: 2024, Номер 191, С. 110078 - 110078

Опубликована: Март 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.

Язык: Английский

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

Cancer Immunology Research, Год журнала: 2023, Номер 11(5), С. 614 - 628

Опубликована: Фев. 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

Язык: 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, Год журнала: 2024, Номер 4(3), С. 1 - 14

Опубликована: Июль 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.

Язык: Английский

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Solvability and Ulam-Hyers stability analysis for nonlinear piecewise fractional cancer dynamic systems

Physica Scripta, Год журнала: 2023, Номер 99(2), С. 025225 - 025225

Опубликована: Дек. 28, 2023

Abstract We examine a nonlinear dynamical model that depicts the interaction between cancerous cells and an oncolytic virus. For best modelling disease, we use Caputo fractional derivative in piecewise approaches. By employing piecemeal techniques, treat compartment body contains infectious non-infectious cells. More precisely, solvability Ulam-Hyers (U-H) stability results are considered using standard concepts. Further, to support our investigation with numerical results, apply Euler method develop approximation solution. It connected numerous graphical representations of system various arbitrary ordering varying values isolation parameters. Here remark multi-step behavior certain problems exhibit, is one important issues naturally. This paper introduces idea goal modeling real-world follow multiples processes. With help used approach, investigate cancer disease its transmission crossover effect.

Язык: Английский

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

Frontiers in Applied Mathematics and Statistics, Год журнала: 2025, Номер 11

Опубликована: Март 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

Язык: Английский

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