Mathematical Medicine and Biology-A Journal of the Ima最新文献_第7页

An evaluation of some assumptions underpinning the bidomain equations of electrophysiology. 对支持电生理学双域方程的一些假设的评价。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2019-11-01 DOI: 10.1093/imammb/dqz014

J. Whiteley

{"title":"An evaluation of some assumptions underpinning the bidomain equations of electrophysiology.","authors":"J. Whiteley","doi":"10.1093/imammb/dqz014","DOIUrl":"https://doi.org/10.1093/imammb/dqz014","url":null,"abstract":"Tissue level cardiac electrophysiology is usually modelled by the bidomain equations, or the monodomain simplification of the bidomain equations. One assumption made when deriving the bidomain equations is that both the intracellular and extracellular spaces are in electrical equilibrium. This assumption neglects the disturbance of this equilibrium in thin regions close to the cell membrane known as Debye layers. We first demonstrate that the governing equations at the cell, or microscale, level may be adapted to take account of these Debye layers with little additional complexity, provided the permittivity within the Debye layers satisfies certain conditions that are believed to be satisfied for biological cells. We then homogenize the microscale equations using a technique developed for an almost periodic microstructure. Cardiac tissue is usually modelled as sheets of cardiac fibres stacked on top of one another. A common assumption is that an orthogonal coordinate system can be defined at each point of cardiac tissue, where the first axis is in the fibre direction, the second axis is orthogonal to the first axis but lies in the sheet of cardiac fibres and the third axis is orthogonal to the cardiac sheet. It is assumed further that both the intracellular and extracellular conductivity tensors are diagonal with respect to these axes and that the diagonal entries of these tensors are constant across the whole tissue. Using the homogenization technique we find that this assumption is usually valid for cardiac tissue, but highlight situations where the assumption may not be valid.","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"70 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79970323","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: 2

Mathematical modelling of trastuzumab-induced immune response in an in vivo murine model of HER2+ breast cancer. 曲妥珠单抗诱导的HER2+乳腺癌小鼠体内模型免疫反应的数学建模

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2019-09-02 DOI: 10.1093/imammb/dqy014

Angela M Jarrett, Meghan J Bloom, Wesley Godfrey, Anum K Syed, David A Ekrut, Lauren I Ehrlich, Thomas E Yankeelov, Anna G Sorace

{"title":"Mathematical modelling of trastuzumab-induced immune response in an in vivo murine model of HER2+ breast cancer.","authors":"Angela M Jarrett, Meghan J Bloom, Wesley Godfrey, Anum K Syed, David A Ekrut, Lauren I Ehrlich, Thomas E Yankeelov, Anna G Sorace","doi":"10.1093/imammb/dqy014","DOIUrl":"https://doi.org/10.1093/imammb/dqy014","url":null,"abstract":"The goal of this study is to develop an integrated, mathematical-experimental approach for understanding the interactions between the immune system and the effects of trastuzumab on breast cancer that overexpresses the human epidermal growth factor receptor 2 (HER2+). A system of coupled, ordinary differential equations was constructed to describe the temporal changes in tumour growth, along with intratumoural changes in the immune response, vascularity, necrosis and hypoxia. The mathematical model is calibrated with serially acquired experimental data of tumour volume, vascularity, necrosis and hypoxia obtained from either imaging or histology from a murine model of HER2+ breast cancer. Sensitivity analysis shows that model components are sensitive for 12 of 13 parameters, but accounting for uncertainty in the parameter values, model simulations still agree with the experimental data. Given theinitial conditions, the mathematical model predicts an increase in the immune infiltrates over time in the treated animals. Immunofluorescent staining results are presented that validate this prediction by showing an increased co-staining of CD11c and F4/80 (proteins expressed by dendritic cells and/or macrophages) in the total tissue for the treated tumours compared to the controls ($p < 0.03$). We posit that the proposed mathematical-experimental approach can be used to elucidate driving interactions between the trastuzumab-induced responses in the tumour and the immune system that drive the stabilization of vasculature while simultaneously decreasing tumour growth-conclusions revealed by the mathematical model that were not deducible from the experimental data alone.","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"36 3","pages":"381-410"},"PeriodicalIF":1.1,"publicationDate":"2019-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqy014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36510687","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: 26

Optimal public health intervention in a behavioural vaccination model: the interplay between seasonality, behaviour and latency period. 行为疫苗模型中的最佳公共卫生干预:季节性、行为和潜伏期之间的相互作用。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2019-09-02 DOI: 10.1093/imammb/dqy011

Bruno Buonomo, Rossella Della Marca, Alberto d'Onofrio

{"title":"Optimal public health intervention in a behavioural vaccination model: the interplay between seasonality, behaviour and latency period.","authors":"Bruno Buonomo, Rossella Della Marca, Alberto d'Onofrio","doi":"10.1093/imammb/dqy011","DOIUrl":"https://doi.org/10.1093/imammb/dqy011","url":null,"abstract":"Hesitancy and refusal of vaccines preventing childhood diseases are spreading due to 'pseudo-rational' behaviours: parents overweigh real and imaginary side effects of vaccines. Nonetheless, the 'Public Health System' (PHS) may enact public campaigns to favour vaccine uptake. To determine the optimal time profiles for such campaigns, we apply the optimal control theory to an extension of the susceptible-infectious-removed (SIR)-based behavioural vaccination model by d'Onofrio et al. (2012, PLoS ONE, 7, e45653). The new model is of susceptible-exposed-infectious-removed (SEIR) type under seasonal fluctuations of the transmission rate. Our objective is to minimize the total costs of the disease: the disease burden, the vaccination costs and a less usual cost: the economic burden to enact the PHS campaigns. We apply the Pontryagin minimum principle and numerically explore the impact of seasonality, human behaviour and latency rate on the control and spread of the target disease. We focus on two noteworthy case studies: the low (resp. intermediate) relative perceived risk of vaccine side effects and relatively low (resp. very low) speed of imitation. One general result is that seasonality may produce a remarkable impact on PHS campaigns aimed at controlling, via an increase of the vaccination uptake, the spread of a target infectious disease. In particular, a higher amplitude of the seasonal variation produces a higher effort and this, in turn, beneficially impacts the induced vaccine uptake since the larger is the strength of seasonality, the longer the vaccine propensity remains large. However, such increased effort is not able to fully compensate the action of seasonality on the prevalence.","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"36 3","pages":"297-324"},"PeriodicalIF":1.1,"publicationDate":"2019-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqy011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36356271","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: 11

Models of cytokine dynamics in the inflammatory response of viral zoonotic infectious diseases. 病毒性人畜共患传染病炎症反应中的细胞因子动态模型。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2019-09-02 DOI: 10.1093/imammb/dqy009

Wenjing Zhang, Sophia Jang, Colleen B Jonsson, Linda J S Allen

{"title":"Models of cytokine dynamics in the inflammatory response of viral zoonotic infectious diseases.","authors":"Wenjing Zhang, Sophia Jang, Colleen B Jonsson, Linda J S Allen","doi":"10.1093/imammb/dqy009","DOIUrl":"10.1093/imammb/dqy009","url":null,"abstract":"Inflammatory responses to an infection from a zoonotic pathogen, such as avian influenza viruses, hantaviruses and some coronaviruses, are distinctly different in their natural reservoir versus human host. While not as well studied in the natural reservoirs, the pro-inflammatory response and viral replication appear controlled and show no obvious pathology. In contrast, infection in humans results in an initial high viral load marked by an aggressive pro-inflammatory response known as a cytokine storm. The key difference in the course of the infection between the reservoir and human host is the inflammatory response. In this investigation, we apply a simple two-component differential equation model for pro-inflammatory and anti-inflammatory responses and a detailed mathematical analysis to identify specific regions in parameter space for single stable endemic equilibrium, bistability or periodic solutions. The extensions of the deterministic model to two stochastic models account for variability in responses seen at the cell (local) or tissue (global) levels. Numerical solutions of the stochastic models exhibit outcomes that are typical of a chronic infection in the natural reservoir or a cytokine storm in human infection. In the chronic infection, occasional flare-ups between high and low responses occur when model parameters are in a region of bistability or periodic solutions. The cytokine storm with a vigorous pro-inflammatory response and less vigorous anti-inflammatory response occurs in the parameter region for a single stable endemic equilibrium with a strong pro-inflammatory response. The results of the model analyses and the simulations are interpreted in terms of the functional role of the cytokines and the inflammatory responses seen in infection of the natural reservoir or of the human host.","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"36 3","pages":"269-295"},"PeriodicalIF":1.1,"publicationDate":"2019-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7108568/pdf/dqy009.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36274039","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

Lattice and continuum modelling of a bioactive porous tissue scaffold. 生物活性多孔组织支架的晶格和连续体建模。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2019-09-02 DOI: 10.1093/imammb/dqy012

Andrew L Krause, Dmitry Beliaev, Robert A Van Gorder, Sarah L Waters

{"title":"Lattice and continuum modelling of a bioactive porous tissue scaffold.","authors":"Andrew L Krause, Dmitry Beliaev, Robert A Van Gorder, Sarah L Waters","doi":"10.1093/imammb/dqy012","DOIUrl":"https://doi.org/10.1093/imammb/dqy012","url":null,"abstract":"A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport and their interactions. The network structure of the physical porous scaffold is often incorporated through parameters in these models, either phenomenologically or through techniques like mathematical homogenization. We derive a model on a square grid lattice to demonstrate the importance of explicitly modelling the network structure of the porous scaffold and compare results from this model with those from a modified continuum model from the literature. We capture two-way coupling between cell growth and fluid flow by allowing cells to block pores, and by allowing the shear stress of the fluid to affect cell growth and death. We explore a range of parameters for both models and demonstrate quantitative and qualitative differences between predictions from each of these approaches, including spatial pattern formation and local oscillations in cell density present only in the lattice model. These differences suggest that for some parameter regimes, corresponding to specific cell types and scaffold geometries, the lattice model gives qualitatively different model predictions than typical continuum models. Our results inform model selection for bioactive porous tissue scaffolds, aiding in the development of successful tissue engineering experiments and eventually clinically successful technologies.","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"36 3","pages":"325-360"},"PeriodicalIF":1.1,"publicationDate":"2019-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqy012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36397414","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: 5

Optimal modality selection in external beam radiotherapy. 体外放射治疗的最佳模式选择。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2019-09-02 DOI: 10.1093/imammb/dqy013

Sevnaz Nourollahi, Archis Ghate, Minsun Kim

引用次数: 4

Analyzing the effects of instillation volume on intravesical delivery using biphasic solute transport in a deformable geometry. 分析注射体积对在可变形几何结构中使用双相溶质输送的膀胱内输送的影响。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2019-06-13 DOI: 10.1093/imammb/dqy004

Sean G Smith, Boyce E Griffith, David A Zaharoff

{"title":"Analyzing the effects of instillation volume on intravesical delivery using biphasic solute transport in a deformable geometry.","authors":"Sean G Smith, Boyce E Griffith, David A Zaharoff","doi":"10.1093/imammb/dqy004","DOIUrl":"https://doi.org/10.1093/imammb/dqy004","url":null,"abstract":"Ailments of the bladder are often treated via intravesical delivery-direct application of therapeutic into the bladder through a catheter. This technique is employed hundreds of thousands of times every year, but protocol development has largely been limited to empirical determination. Furthermore, the numerical analyses of intravesical delivery performed to date have been restricted to static geometries and have not accounted for bladder deformation. This study uses a finite element analysis approach with biphasic solute transport to investigate several parameters pertinent to intravesical delivery including solute concentration, solute transport properties and instillation volume. The volume of instillation was found to have a substantial impact on the exposure of solute to the deeper muscle layers of the bladder, which are typically more difficult to reach. Indeed, increasing the instillation volume from 50-100 ml raised the muscle solute exposure as a percentage of overall bladder exposure from 60-70% with higher levels achieved for larger instillation volumes. Similar increases were not seen for changes in solute concentration or solute transport properties. These results indicate the role that instillation volume may play in targeting particular layers of the bladder during an intravesical delivery.","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"36 2","pages":"139-156"},"PeriodicalIF":1.1,"publicationDate":"2019-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqy004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36013705","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: 3

Why, when and how should exposure be considered at the within-host scale? A modelling contribution to PRRSv infection. 为什么，何时以及如何在宿主内尺度上考虑暴露?对PRRSv感染的建模贡献。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2019-06-13 DOI: 10.1093/imammb/dqy005

Natacha Go, Catherine Belloc, Caroline Bidot, Suzanne Touzeau

{"title":"Why, when and how should exposure be considered at the within-host scale? A modelling contribution to PRRSv infection.","authors":"Natacha Go, Catherine Belloc, Caroline Bidot, Suzanne Touzeau","doi":"10.1093/imammb/dqy005","DOIUrl":"https://doi.org/10.1093/imammb/dqy005","url":null,"abstract":"Understanding the impact of pathogen exposure on the within-host dynamics and its outcome in terms of infectiousness is a key issue to better understand and control the infection spread. Most experimental and modelling studies tackling this issue looked at the impact of the exposure dose on the infection probability and pathogen load, very few on the within-host immune response. Our aim was to explore the impact on the within-host response not only of the exposure dose, but also of its duration and peak, for contrasted virulence levels. We used an integrative modelling approach of the within-host dynamics at the between-cell level. We focused on the porcine reproductive and respiratory syndrome virus, a major concern for the swine industry. We quantified the impact of exposure and virulence on the viral dynamics and immune response by global sensitivity analyses and descriptive statistics. We found that the area under the viral curve, an indicator of the infection severity, was fully determined by the exposure intensity. The infection duration increased with the strain virulence and, for a given strain, exhibited a positive linear correlation with the exposure intensity logarithm and the exposure duration. Taking into account the exposure intensity is hence necessary. Besides, representing the exposure due to contacts by a single punctual dose would tend to underestimate the infection duration. As the infection severity and duration both contribute to the pig infectiousness, a prolonged exposure of the adequate intensity would be recommended in an immuno-epidemiological context.","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"36 2","pages":"179-206"},"PeriodicalIF":1.1,"publicationDate":"2019-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqy005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36122591","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: 5

A unidimensional diffusion model applied to uremic toxin kinetics in haemodiafiltration treatments. 一维扩散模型应用于血液滤过处理中的尿毒症毒素动力学。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2019-06-13 DOI: 10.1093/imammb/dqy008

Miquel Gomez, Francisco Maduell

引用次数: 0

The ups and downs of S. aureus nasal carriage. 金黄色葡萄球菌鼻腔运载的起伏。

IF 1.1 4区数学

Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2019-06-13 DOI: 10.1093/imammb/dqy006

Angela M Jarrett, Nicholas G Cogan

{"title":"The ups and downs of S. aureus nasal carriage.","authors":"Angela M Jarrett, Nicholas G Cogan","doi":"10.1093/imammb/dqy006","DOIUrl":"https://doi.org/10.1093/imammb/dqy006","url":null,"abstract":"Staphylococcus aureus infections are a growing concern worldwide due to the increasing number of strains that exhibit antibiotic resistance. Recent studies have indicated that some percentage of people carry the bacteria in the nasal cavity and therefore are at a higher risk of subsequent, and more serious, infections in other parts of the body. However, individuals carrying the infection can be classified as only intermittent carriers versus persistent carriers, being able to eliminate the bacteria and later colonized again. Using a model of bacterial colonization of the anterior nares, we investigate oscillatory patterns related to intermittent carriage of S. aureus. Following several studies using global sensitivity analysis techniques, various insights into the model's behaviour were made including interacting effects of the bacteria's growth rate and movement in the mucus, suggesting parameter connections associated with biofilm-like behaviour. Here the bacterial growth rate and bacterial movement are explicitly connected, leading to expanded oscillatory behaviour in the model. We suggest possible implications that this oscillatory behaviour can have on the definition of intermittent carriage and discuss differences in the bacterial virulence dependent upon individual host health. Furthermore, we show that connecting the bacterial growth and movement also expands the region of the parameter space for which the bacteria are able to survive and persist.","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"36 2","pages":"157-177"},"PeriodicalIF":1.1,"publicationDate":"2019-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqy006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36103911","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: 4