Bulletin of Mathematical Biology最新文献_第2页

Characterising the Behaviour of a Structured PDE Model of the Cell Cycle in Contrast to a Corresponding ODE System. 细胞周期的结构化PDE模型的行为特征与相应的ODE系统的对比。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-06-08 DOI: 10.1007/s11538-025-01472-8

Ruby E Nixson, Helen M Byrne, Joe M Pitt-Francis, Philip K Maini

{"title":"Characterising the Behaviour of a Structured PDE Model of the Cell Cycle in Contrast to a Corresponding ODE System.","authors":"Ruby E Nixson, Helen M Byrne, Joe M Pitt-Francis, Philip K Maini","doi":"10.1007/s11538-025-01472-8","DOIUrl":"10.1007/s11538-025-01472-8","url":null,"abstract":"Experimental results have shown that anti-cancer therapies, such as radiotherapy and chemotherapy, can modulate the cell cycle and generate cell cycle phase-dependent responses. As a result, obtaining a detailed understanding of the cell cycle is one possible path towards improving the efficacy of many of these therapies. Here, we consider a basic structured partial differential equation (PDE) model for cell progression through the cell cycle, and derive expressions for key quantities, such as the population growth rate and cell phase proportions. These quantities are shown to be periodic and, as such, we compare the PDE model to a corresponding ordinary differential equation (ODE) model in which the parameters are linked by ensuring that the long-term ODE behaviour agrees with the average PDE behaviour. By design, we find that the ODE model does an excellent job of representing the mean dynamics of the PDE model within just a few cell cycles. However, by probing the parameter space we find cases in which this mean behaviour is not a good measure of the PDE population growth. Our analytical comparison of two caricature models (one PDE and one ODE system) provides insight into cases in which the simple ODE model is an appropriate approximation to the PDE model.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 7","pages":"93"},"PeriodicalIF":2.0,"publicationDate":"2025-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12146229/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144246501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Spatio-Temporal Dynamics of M₁ and M₂ Macrophages in a Multiphase Model of Tumor Growth. M1和M2巨噬细胞在肿瘤生长多期模型中的时空动态。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-06-04 DOI: 10.1007/s11538-025-01466-6

Ioannis Lampropoulos, Panayotis G Kevrekidis, Christos E Zois, Helen Byrne, Michail Kavousanakis

{"title":"Spatio-Temporal Dynamics of M1 and M2 Macrophages in a Multiphase Model of Tumor Growth.","authors":"Ioannis Lampropoulos, Panayotis G Kevrekidis, Christos E Zois, Helen Byrne, Michail Kavousanakis","doi":"10.1007/s11538-025-01466-6","DOIUrl":"10.1007/s11538-025-01466-6","url":null,"abstract":"This study investigates the complex dynamics of vascular tumors and their interplay with macrophages, key agents of the innate immune response. We model the tumor microenvironment as a multiphase fluid, with each cellular population treated as a distinct, non-mixing phase. The framework also incorporates diffusible species that are critical for processes such as nutrient transport, angiogenesis, chemotaxis, and macrophage activation. A central contribution of this work is the explicit modeling of macrophage infiltration and polarization within the tumor microenvironment. The model captures the divergent roles of <math><msub><mtext>M</mtext> <mn>1</mn></msub> </math> (anti-tumor) and <math><msub><mtext>M</mtext> <mn>2</mn></msub> </math> (pro-tumor) macrophages and their influence on tumor aggressiveness and progression. Through numerical simulations, we demonstrate the emergence of both spatial and phenotypic heterogeneity in the macrophage population, including their peripheral localization and limited core infiltration -patterns consistent with experimental observations. Furthermore, this is the first multiphase model to incorporate the effects of TGF- <math><mi>β</mi></math> -targeting immunotherapy using vactosertib. Our simulations demonstrate that treatment initially enhances the presence of anti-tumor macrophages, followed by a relapse period where tumor dynamics returns to pre-treatment trends. Model parameters are grounded in experimental data and clinically relevant dosage protocols.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 7","pages":"92"},"PeriodicalIF":2.0,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12137437/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144215002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Effect of Disease Stage on Melanoma Treatment Efficacy: Insights from Mathematical Modeling and In vivo Clinical Data. 疾病分期对黑色素瘤治疗效果的影响：来自数学模型和体内临床数据的见解。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-06-03 DOI: 10.1007/s11538-025-01458-6

Mohammad Amini, Ramin Vatankhah

{"title":"The Effect of Disease Stage on Melanoma Treatment Efficacy: Insights from Mathematical Modeling and In vivo Clinical Data.","authors":"Mohammad Amini, Ramin Vatankhah","doi":"10.1007/s11538-025-01458-6","DOIUrl":"https://doi.org/10.1007/s11538-025-01458-6","url":null,"abstract":"Melanoma progression can be effectively modeled through mathematical frameworks, making it a pivotal focus for enhancing our understanding of cancer dynamics and informing personalized treatment strategies. The present research investigates the growth dynamics of melanoma by analyzing 16 individual melanoma cell lines, utilizing in vivo clinical data that spans a range of metastatic stages from primary melanoma to stage IV. The study estimates growth rates across these cell lines by implementing a power law model through nonlinear least squares, uncovering distinct mathematical patterns linked to melanoma stages. Furthermore, the research evaluates the efficacy of various treatment strategies tailored to each disease stage through a chemoimmunotherapy mathematical model. For primary and early-stage melanoma, where tumors are localized, surgical excision is identified as the most effective intervention, often enhanced by CD4+T cell immunotherapy. In cases of low to moderately metastatic melanoma, a combination of low-dose chemotherapy with CD8+T cell immunotherapy effectively targets metastatic lesions, reducing systemic toxicity while promoting a strong immune response. For highly metastatic melanoma, which presents significant treatment challenges, a combination therapy involving both CD8+T and CD4+T cell immunotherapy is recommended. This dual approach utilizes the direct tumor-killing effects of CD8+T cells alongside the supportive actions of CD4+T cells, resulting in improved treatment efficacy and survival outcomes. Overall, this research provides a comprehensive analysis of melanoma cell lines at various stages, integrating mathematical modeling with treatment efficacy to enhance personalized treatment strategies in melanoma management.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 7","pages":"90"},"PeriodicalIF":2.0,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144207807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Finding Reproduction Numbers for Epidemic Models and Predator-Prey Models of Arbitrary Finite Dimension Using the Generalized Linear Chain Trick. 用广义线性链技巧求流行病模型和任意有限维捕食者-猎物模型的繁殖数。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-06-03 DOI: 10.1007/s11538-025-01467-5

Paul J Hurtado, Cameron Richards

{"title":"Finding Reproduction Numbers for Epidemic Models and Predator-Prey Models of Arbitrary Finite Dimension Using the Generalized Linear Chain Trick.","authors":"Paul J Hurtado, Cameron Richards","doi":"10.1007/s11538-025-01467-5","DOIUrl":"10.1007/s11538-025-01467-5","url":null,"abstract":"Reproduction numbers, like the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> , play an important role in the analysis and application of dynamic models, including contagion models and ecological population models. One difficulty in deriving these quantities is that they must be computed on a model-by-model basis, since it is typically impractical to obtain general reproduction number expressions applicable to a family of related models, especially if these are of different dimensions (i.e., differing numbers of state variables). For example, this is typically the case for SIR-type infectious disease models derived using the linear chain trick. Here we show how to find general reproduction number expressions for such model families (which vary in their number of state variables) using the next generation operator approach in conjunction with the generalized linear chain trick (GLCT). We further show how the GLCT enables modelers to draw insights from these results by leveraging theory and intuition from continuous time Markov chains (CTMCs) and their absorption time distributions (i.e., phase-type probability distributions). To do this, we first review the GLCT and other connections between mean-field ODE model assumptions, CTMCs, and phase-type distributions. We then apply this technique to find reproduction numbers for two sets of models: a family of generalized SEIRS models of arbitrary finite dimension, and a generalized family of finite dimensional predator-prey (Rosenzweig-MacArthur type) models. These results highlight the utility of the GLCT for the derivation and analysis of mean field ODE models, especially when used in conjunction with theory from CTMCs and their associated phase-type distributions.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 7","pages":"89"},"PeriodicalIF":2.0,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12133974/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144207806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Modular Control of Boolean Network Models. 布尔网络模型的模块化控制。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-06-03 DOI: 10.1007/s11538-025-01471-9

David Murrugarra, Alan Veliz-Cuba, Elena Dimitrova, Claus Kadelka, Matthew Wheeler, Reinhard Laubenbacher

{"title":"Modular Control of Boolean Network Models.","authors":"David Murrugarra, Alan Veliz-Cuba, Elena Dimitrova, Claus Kadelka, Matthew Wheeler, Reinhard Laubenbacher","doi":"10.1007/s11538-025-01471-9","DOIUrl":"10.1007/s11538-025-01471-9","url":null,"abstract":"The concept of control is crucial for effectively understanding and applying biological network models. Key structural features relate to control functions through gene regulation, signaling, or metabolic mechanisms, and computational models need to encode these. Applications often focus on model-based control, such as in biomedicine or metabolic engineering. In a recent paper, the authors developed a theoretical framework of modularity in Boolean networks, which led to a canonical semidirect product decomposition of these systems. In this paper, we present an approach to model-based control that exploits this modular structure, as well as the canalizing features of the regulatory mechanisms. We show how to identify control strategies from the individual modules, and we present a criterion based on canalizing features of the regulatory rules to identify modules that do not contribute to network control and can be excluded. For even moderately sized networks, finding global control inputs is computationally challenging. Our modular approach leads to an efficient approach to solving this problem. We apply it to a published Boolean network model of blood cancer large granular lymphocyte (T-LGL) leukemia to identify a minimal control set that achieves a desired control objective.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 7","pages":"91"},"PeriodicalIF":2.0,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12133937/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144215001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mathematical Modelling and Optimization of Medication Regimens for Combination Immunotherapy of Breast Cancer. 乳腺癌联合免疫治疗方案的数学建模与优化。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-06-02 DOI: 10.1007/s11538-025-01459-5

Zixiao Xiong, Yunfei Xia, Ling Xue, Jinzhi Lei

{"title":"Mathematical Modelling and Optimization of Medication Regimens for Combination Immunotherapy of Breast Cancer.","authors":"Zixiao Xiong, Yunfei Xia, Ling Xue, Jinzhi Lei","doi":"10.1007/s11538-025-01459-5","DOIUrl":"https://doi.org/10.1007/s11538-025-01459-5","url":null,"abstract":"Immunotherapy is an emerging and effective treatment for cancer. The mRNA-based cancer vaccines enhance the immune response to cancer cells by activating T cells. However, the cytotoxic T-lymphocyte antigen (CTLA-4) receptor signaling inhibits T-cell activation, thereby reducing the effectiveness of the mRNA-based vaccines. Fortunately, the anti-CTLA-4 monoclonal antibody therapy can block CTLA-4 signaling. Nevertheless, the use of anti-CTLA-4 antibodies is also accompanied by immunotoxic side effects. Therefore, an effective and safe medication regimen plays an essential role in the treatment of cancer. First, we develop a mathematical model to describe the interaction of mRNA-based cancer vaccines and anti-CTLA-4 antibodies under the tumor immune microenvironment. Secondly, by employing the method of Markov Chain Monte Carlo (MCMC), the model is parameterized using experimental data, and the simulations are in agreement with experimental results. Finally, the gradient descent method is designed to optimize the medication regimens to inhibit tumor growth and reduce the side effects. Additionally, we find that the anti-CTLA-4 antibody should be administered following vaccination, and the dose of the antibody should positively correlate with the dose of vaccine within a safe range. Our study provides a theoretical basis for the selection of treatment regimens for clinical trials from a mathematical perspective.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 7","pages":"88"},"PeriodicalIF":2.0,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144198296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Transmission of Multiple Pathogens Across Species. 多种病原体的跨物种传播。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-05-28 DOI: 10.1007/s11538-025-01469-3

Clotilde Djuikem, Julien Arino

引用次数: 0

Optimizing the Efficacy of Vaccine-Induced Immunotherapy in Melanomas. 优化疫苗诱导免疫治疗黑素瘤的疗效。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-05-28 DOI: 10.1007/s11538-025-01462-w

Ibrahim Chamseddine, Manoj Kambara, Priya Bhatt, Shari Pilon-Thomas, Katarzyna A Rejniak

{"title":"Optimizing the Efficacy of Vaccine-Induced Immunotherapy in Melanomas.","authors":"Ibrahim Chamseddine, Manoj Kambara, Priya Bhatt, Shari Pilon-Thomas, Katarzyna A Rejniak","doi":"10.1007/s11538-025-01462-w","DOIUrl":"10.1007/s11538-025-01462-w","url":null,"abstract":"Cancer therapeutic vaccines are used to strengthen a patient's own immune system by amplifying existing immune responses. Intralesional administration of the bacteria-based emm55 vaccine together with the PD1 checkpoint inhibitor produced a strong anti-tumor effect against the B16 melanoma murine model. However, it is not trivial to design an optimal order and frequency of injections for combination therapies. Here, we developed a coupled ordinary differential equations model calibrated to experimental data and used the mesh adaptive direct search method to optimize the treatment protocols of the emm55 vaccine and anti-PD1 combined therapy. This method determined that early consecutive vaccine injections combined with distributed anti-PD1 injections of decreasing separation time yielded the best tumor size reduction. The optimized protocols led to a twofold decrease in tumor area for the vaccine-alone treatment, and a fourfold decrease for the combined therapy. Our results reveal the tumor subpopulation dynamics in the optimal treatment condition, defining the path for efficacious treatment design. Similar computational frameworks can be applied to other tumors and other combination therapies to generate experimentally testable hypotheses in a fairly unrestricted and inexpensive setting.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 7","pages":"86"},"PeriodicalIF":2.0,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144157042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Quantitative Pharmacology Methods for Bispecific T Cell Engagers. 双特异性T细胞接合物的定量药理学方法。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-05-24 DOI: 10.1007/s11538-025-01455-9

Mahdiar Sadeghi, Irina Kareva, Gleb Pogudin, Eduardo D Sontag

{"title":"Quantitative Pharmacology Methods for Bispecific T Cell Engagers.","authors":"Mahdiar Sadeghi, Irina Kareva, Gleb Pogudin, Eduardo D Sontag","doi":"10.1007/s11538-025-01455-9","DOIUrl":"https://doi.org/10.1007/s11538-025-01455-9","url":null,"abstract":"T Cell Engager (TCE)s are an exciting therapeutic modality in immuno-oncology that acts to bypass antigen presentation and forms a direct link between cancer and immune cells in the Tumor Microenvironment (TME). TCEs are efficacious only when the drug is bound to both immune and cancer cell targets. Therefore, approaches that maximize the formation of the drug-target trimer in the TME are expected to increase the drug's efficacy. In this study, we quantitatively investigate how the concentration of ternary complex and its biodistribution depend on both the targets' specific properties and the design characteristics of the TCE, and specifically on the binding kinetics of the drug to its targets. A simplified mathematical model of drug-target interactions is considered here, with insights from the \"three-body\" problem applied to the model. Parameter identifiability analysis performed on the model demonstrates that steady state data, which is often available at the early pre-clinical stages, is sufficient to estimate the binding affinity of the TCE molecule to both targets. We used the model to analyze several existing antibodies, both clinically approved and under development, to explore their common kinetic features. The manuscript concludes with an assessment of a full quantitative pharmacology model that accounts for drug disposition into the peripheral compartment.","PeriodicalId":9372,"journal":{"name":"Bulletin of Mathematical Biology","volume":"87 7","pages":"85"},"PeriodicalIF":2.0,"publicationDate":"2025-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144141399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fast simulation of identity-by-descent segments. 快速模拟身份的下降段。

IF 2 4区数学

Bulletin of Mathematical Biology Pub Date : 2025-05-23 DOI: 10.1007/s11538-025-01464-8

Seth D Temple, Sharon R Browning, Elizabeth A Thompson

引用次数: 0