Mathematical medicine and biology : a journal of the IMA最新文献_第9页

Revisiting a two-patch SIS model with infection during transport 重新审视运输过程中感染的双补丁SIS模型

Mathematical medicine and biology : a journal of the IMA Pub Date : 2016-03-01 DOI: 10.1093/imammb/dqv001

Julien Arino;Chengjun Sun;Wei Yang

引用次数: 16

Front matter 前页

Mathematical medicine and biology : a journal of the IMA Pub Date : 2016-03-01

引用次数: 0

Modelling cholesterol effects on the dynamics of the hypothalamic–pituitary–adrenal (HPA) axis 模拟胆固醇对下丘脑-垂体-肾上腺(HPA)轴动力学的影响

Mathematical medicine and biology : a journal of the IMA Pub Date : 2016-03-01 DOI: 10.1093/imammb/dqu020

Vladimir M. Marković;Željko Čupić;Stevan Maćešić;Stevan Maćešić;Vladana Vukojević;Ljiljana Kolar-Anić

{"title":"Modelling cholesterol effects on the dynamics of the hypothalamic–pituitary–adrenal (HPA) axis","authors":"Vladimir M. Marković;Željko Čupić;Stevan Maćešić;Stevan Maćešić;Vladana Vukojević;Ljiljana Kolar-Anić","doi":"10.1093/imammb/dqu020","DOIUrl":"10.1093/imammb/dqu020","url":null,"abstract":"A mathematical model of the hypothalamic–pituitary–adrenal (HPA) axis with cholesterol as a dynamical variable was derived to investigate the effects of cholesterol, the primary precursor of all steroid hormones, on the ultradian and circadian HPA axis activity. To develop the model, the parameter space was systematically examined by stoichiometric network analysis to identify conditions for ultradian oscillations, determine conditions under which dynamic transitions, i.e. bifurcations occur and identify bifurcation types. The bifurcations were further characterized using numerical simulations. Model predictions agree well with empirical findings reported in the literature, indicating that cholesterol levels may critically affect the global dynamics of the HPA axis. The proposed model provides a base for better understanding of experimental observations, it may be used as a tool for designing experiments and offers useful insights into the characteristics of basic dynamic regulatory mechanisms that, when impaired, may lead to the development of some modern-lifestyle-associated diseases.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"33 1","pages":"1-28"},"PeriodicalIF":0.0,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqu020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32761440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 27

Numerical resolution of a model of tumour growth 肿瘤生长模型的数值分辨率

Mathematical medicine and biology : a journal of the IMA Pub Date : 2016-03-01 DOI: 10.1093/imammb/dqv004

Ana I. Muñoz

{"title":"Numerical resolution of a model of tumour growth","authors":"Ana I. Muñoz","doi":"10.1093/imammb/dqv004","DOIUrl":"10.1093/imammb/dqv004","url":null,"abstract":"We consider and solve numerically a mathematical model of tumour growth based on cancer stem cells (CSC) hypothesis with the aim of gaining some insight into the relation of different processes leading to exponential growth in solid tumours and into the evolution of different subpopulations of cells. The model consists of four hyperbolic equations of first order to describe the evolution of four subpopulations of cells. A fifth equation is introduced to model the evolution of the moving boundary. The coefficients of the model represent the rates at which reactions occur. In order to integrate numerically the four hyperbolic equations, a formulation in terms of the total derivatives is posed. A finite element discretization is applied to integrate the model equations in space. Our numerical results suggest the existence of a pseudo-equilibrium state reached at the early stage of the tumour, for which the fraction of CSC remains small. We include the study of the behaviour of the solutions for longer times and we obtain that the solutions to the system of partial differential equations stabilize to homogeneous steady states whose values depend only on the values of the parameters. We show that CSC may comprise different proportions of the tumour, becoming, in some cases, the predominant type of cells within the tumour. We also obtain that possible effective measure to detain tumour progression should combine the targeting of CSC with the targeting of progenitor cells.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"33 1","pages":"57-85"},"PeriodicalIF":0.0,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqv004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33051959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Back matter 背景材料

Mathematical medicine and biology : a journal of the IMA Pub Date : 2016-03-01

引用次数: 0

Mathematical modelling of decline in follicle pool during female reproductive ageing 女性生殖老化过程中卵泡池下降的数学模型

Mathematical medicine and biology : a journal of the IMA Pub Date : 2016-03-01 DOI: 10.1093/imammb/dqv006

Alagu Thilagam

{"title":"Mathematical modelling of decline in follicle pool during female reproductive ageing","authors":"Alagu Thilagam","doi":"10.1093/imammb/dqv006","DOIUrl":"10.1093/imammb/dqv006","url":null,"abstract":"The factors which govern the subtle links between follicle loss and mammalian female reproductive ageing remain unclear despite extensive studies undertaken to understand the critical physiological and biochemical mechanisms that underly the accelerated decline in follicle numbers in women older than 37 years. It is not certain whether there is a sole control by the ovary or whether other factors which affect ageing also intersect with the ovarian effect. There is convincing experimental evidence for an interplay of several processes that seem to influence the follicle loss-female reproductive ageing links, with specific hormones (follicle-stimulating hormone, anti-Müllerian hormone, dehydroepiandrosterone) noted to play important roles in follicular dynamics and ovarian ageing. In this work, we examine the subtle links between the rate of follicular decline with ageing and the role of hormones via a series of non-autonomous equations. Simulation results based on the time evolution of the number of ovarian follicles and biochemical changes in the ovarian environment influenced by hormone levels is compared with empirical data based on follicle loss-reproductive ageing correlation studies.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"33 1","pages":"107-121"},"PeriodicalIF":0.0,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqv006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33025585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

Conduction of feedback-mediated signal in a computational model of coupled nephrons 耦合肾元计算模型中反馈介导信号的传导

Mathematical medicine and biology : a journal of the IMA Pub Date : 2016-03-01 DOI: 10.1093/imammb/dqv005

Ioannis Sgouralis;Anita T. Layton

{"title":"Conduction of feedback-mediated signal in a computational model of coupled nephrons","authors":"Ioannis Sgouralis;Anita T. Layton","doi":"10.1093/imammb/dqv005","DOIUrl":"10.1093/imammb/dqv005","url":null,"abstract":"The nephron in the kidney regulates its fluid flow by several autoregulatory mechanisms. Two primary mechanisms are the myogenic response and the tubuloglomerular feedback (TGF). The myogenic response is a property of the pre-glomerular vasculature in which a rise in intravascular pressure elicits vasoconstriction that generates a compensatory increase in vascular resistance. TGF is a negative feedback response that balances glomerular filtration with tubular reabsorptive capacity. While each nephron has its own autoregulatory response, the responses of the kidney's many nephrons do not act autonomously but are instead coupled through the pre-glomerular vasculature. To better understand the conduction of these signals along the pre-glomerular arterioles and the impacts of internephron coupling on nephron flow dynamics, we developed a mathematical model of renal haemodynamics of two neighbouring nephrons that are coupled in that their afferent arterioles arise from a common cortical radial artery. Simulations were conducted to estimate internephron coupling strength, determine its dependence on vascular properties and to investigate the effect of coupling on TGF-mediated flow oscillations. Simulation results suggest that reduced gap-junctional conductances may yield stronger internephron TGF coupling and highly irregular TGF-mediated oscillations in nephron dynamics, both of which experimentally have been associated with hypertensive rats.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"33 1","pages":"87-106"},"PeriodicalIF":0.0,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqv005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33148701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

A receptor state space model of the insulin signalling system in glucose transport 葡萄糖转运中胰岛素信号系统的受体状态空间模型

Mathematical medicine and biology : a journal of the IMA Pub Date : 2015-12-01 DOI: 10.1093/imammb/dqv003

Catheryn W. Gray;Adelle C.F. Coster

{"title":"A receptor state space model of the insulin signalling system in glucose transport","authors":"Catheryn W. Gray;Adelle C.F. Coster","doi":"10.1093/imammb/dqv003","DOIUrl":"10.1093/imammb/dqv003","url":null,"abstract":"Insulin is a potent peptide hormone that regulates glucose levels in the blood. Insulin-sensitive cells respond to insulin stimulation with the translocation of glucose transporter 4 (GLUT4) to the plasma membrane (PM), enabling the clearance of glucose from the blood. Defects in this process can give rise to insulin resistance and ultimately diabetes. One widely cited model of insulin signalling leading to glucose transport is that of Sedaghat et al. (2002) Am. J. Physiol. Endocrinol. Metab.283, E1084–E1101. Consisting of 20 deterministic ordinary differential equations (ODEs), it is the most comprehensive model of insulin signalling to date. However, the model possesses some major limitations, including the non-conservation of key components. In the current work, we detail mathematical and sensitivity analyses of the Sedaghat model. Based on the results of these analyses, we propose a reduced state space model of the insulin receptor subsystem. This reduced model maintains the input–output relation of the original model but is computationally more efficient, analytically tractable and resolves some of the limitations of the Sedaghat model.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"32 4","pages":"457-473"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqv003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33046889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Synchronization in stress p53 network 应激p53网络的同步性

Mathematical medicine and biology : a journal of the IMA Pub Date : 2015-12-01 DOI: 10.1093/imammb/dqv002

Gurumayum Reenaroy Devi;Md. Jahoor Alam;R.K. Brojen Singh

{"title":"Synchronization in stress p53 network","authors":"Gurumayum Reenaroy Devi;Md. Jahoor Alam;R.K. Brojen Singh","doi":"10.1093/imammb/dqv002","DOIUrl":"10.1093/imammb/dqv002","url":null,"abstract":"We study transition of the temporal behaviours of \u0000<tex>$p53$</tex>\u0000 and \u0000<tex>$MDM2$</tex>\u0000 in a stress p53-MDM2-NO regulatory network induced by a bioactive molecule \u0000<tex>$NO$</tex>\u0000 (Nitric Oxide). We further study synchronization among a group of identical stress systems arranged in a 3D array with nearest neighbour diffusive coupling. The role of \u0000<tex>$NO$</tex>\u0000 and the effect of noise are investigated. In the single system study, we found three distinct types of temporal behaviour of \u0000<tex>$p53$</tex>\u0000, namely oscillation death, damped oscillation and sustained oscillation, depending on the amount of stress induced by \u0000<tex>$NO$</tex>\u0000, indicating how \u0000<tex>$p53$</tex>\u0000 responds to incoming stress. The correlation among coupled systems increases as the value of the coupling constant (\u0000<tex>$epsilon$</tex>\u0000) is increased (\u0000<tex>$gamma$</tex>\u0000 increases) and becomes constant after a certain value of \u0000<tex>$epsilon$</tex>\u0000. The permutation entropy spectra \u0000<tex>$H(epsilon )$</tex>\u0000 for \u0000<tex>$p53$</tex>\u0000 and \u0000<tex>$MDM2$</tex>\u0000 as a function of \u0000<tex>$epsilon$</tex>\u0000 are found to be different due to direct and indirect interaction of \u0000<tex>$NO$</tex>\u0000 with respective proteins. We find \u0000<tex>$gamma$</tex>\u0000 versus \u0000<tex>$epsilon$</tex>\u0000 for \u0000<tex>$p53$</tex>\u0000 and \u0000<tex>$MDM2$</tex>\u0000 to be similar in a deterministic approach but different in a stochastic approach, and the separation between \u0000<tex>$gamma$</tex>\u0000 of the respective proteins as a function of \u0000<tex>$epsilon$</tex>\u0000 decreases as system size increases. The role of \u0000<tex>$NO$</tex>\u0000 is found to be two-fold: stress induced by NO is prominent at small and large values of \u0000<tex>$epsilon$</tex>\u0000 but synchrony induced by it dominates in the moderate range of \u0000<tex>$epsilon$</tex>\u0000. Excess stress induces apoptosis.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"32 4","pages":"437-456"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqv002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33081827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

A theoretical study of the initiation, maintenance and termination of gastric slow wave re-entry 胃慢波再入的起始、维持和终止的理论研究

Mathematical medicine and biology : a journal of the IMA Pub Date : 2015-12-01 DOI: 10.1093/imammb/dqu023

Peng Du;Niranchan Paskaranandavadivel;Greg O'Grady;Shou-Jiang Tang;Leo K. Cheng

{"title":"A theoretical study of the initiation, maintenance and termination of gastric slow wave re-entry","authors":"Peng Du;Niranchan Paskaranandavadivel;Greg O'Grady;Shou-Jiang Tang;Leo K. Cheng","doi":"10.1093/imammb/dqu023","DOIUrl":"10.1093/imammb/dqu023","url":null,"abstract":"Gastric slow wave dysrhythmias are associated with motility disorders. Periods of tachygastria associated with slow wave re-entry were recently recognized as one important dysrhythmia mechanism, but factors promoting and sustaining gastric re-entry are currently unknown. This study reports two experimental forms of gastric re-entry and presents a series of multi-scale models that define criteria for slow wave re-entry initiation, maintenance and termination. High-resolution electrical mapping was conducted in porcine and canine models and two spatiotemporal patterns of re-entrant activities were captured: single-loop rotor and double-loop figure-of-eight. Two separate multi-scale mathematical models were developed to reproduce the velocity and entrainment frequency of these experimental recordings. A single-pulse stimulus was used to invoke a rotor re-entry in the porcine model and a figure-of-eight re-entry in the canine model. In both cases, the simulated re-entrant activities were found to be perpetuated by tachygastria that was accompanied by a reduction in the propagation velocity in the re-entrant pathways. The simulated re-entrant activities were terminated by a single-pulse stimulus targeted at the tip of re-entrant wave, after which normal antegrade propagation was restored by the underlying intrinsic frequency gradient. Main findings: (i) the stability of re-entry is regulated by stimulus timing, intrinsic frequency gradient and conductivity; (ii) tachygastria due to re-entry increases the frequency gradient while showing decreased propagation velocity; (iii) re-entry may be effectively terminated by a targeted stimulus at the core, allowing the intrinsic slow wave conduction system to re-establish itself.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"32 4","pages":"405-423"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqu023","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32944628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 23