IMA journal of mathematics applied in medicine and biology最新文献

{"title":"Tumour dynamics and necrosis: surface tension and stability.","authors":"K. Landman, C. Please","doi":"10.1093/IMAMMB/18.2.131","DOIUrl":"https://doi.org/10.1093/IMAMMB/18.2.131","url":null,"abstract":"A model is developed for the motion of cells within a multicell spherical tumour. The model allows either for the intercellular forces to be in compression and cells to be compacted to a fixed number density, or for the cell number density to fall and cells to become isolated from each other. The model develops necrotic regions naturally due to force balances rather than being directly attributable to a critical oxygen concentration. These necrotic regions may result in a gradual reduction in local cell density rather than jump to a completely dead region. Numerical and analytical analysis of the spherically symmetric model shows that the long time behaviour of the spheroid depends on any surface tension effects created by cells on the outer surface. For small surface tension the spheroid grows linearly in time developing a large necrotic region, while for larger surface tension the growth can be halted. The linear stability to spherically symmetric perturbations of all the possible resulting steady states is revealed.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"18 2 1","pages":"131-58"},"PeriodicalIF":0.0,"publicationDate":"2001-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/18.2.131","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61181898","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}

{"title":"The use of multistate life-table models for improving population health.","authors":"M. Roberts, M. Tobias","doi":"10.1093/IMAMMB/18.2.119","DOIUrl":"https://doi.org/10.1093/IMAMMB/18.2.119","url":null,"abstract":"We demonstrate how incidence, prevalence, remission, mortality (IPRM) models may be constructed on population life-tables, how the incidence of a condition may be calculated, and how the consequences of demographic changes and public health interventions may be predicted. We illustrate the methodology by applying it to the epidemiology of diabetes, physical inactivity and obesity in New Zealand.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"18 2 1","pages":"119-30"},"PeriodicalIF":0.0,"publicationDate":"2001-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/18.2.119","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61181807","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}

{"title":"Pro-inflammatory--anti-inflammatory cytokine dynamics mediated by cytokine-receptor dynamics in monocytes.","authors":"R. Seymour, B. Henderson","doi":"10.1093/IMAMMB/18.2.159","DOIUrl":"https://doi.org/10.1093/IMAMMB/18.2.159","url":null,"abstract":"Many of the major human diseases, both infectious (septic shock syndromes) and idiopathic (for example, rheumatoid arthritis), are driven by the production of the pro-inflammatory cytokines interleukin-1 (IL-1) and tumour necrosis factor-alpha (TNF-alpha) produced by monocytes and macrophages. These key pro-inflammatory cytokines can, in turn, stimulate the production of additional cytokines which, in totality, generate tissue pathology. A major deactivator of activated, cytokine-producing monocytes and macrophages is the anti-inflammatory cytokine interleukin-10 (IL-10). It is known that the interactions between these three cytokines are pivotal in terms of health and pathology, but almost nothing is known of the dynamics of these interactions. In this study we have modelled the autocrine interactions of TNF-alpha, IL-1 and IL-10 with monocytes. The model constructed is a six-dimensional, continuous-time dynamical system, with free IL-1 and IL- 10 concentrations in the cell's vicinity, and the proportions of bound and free IL-1 and IL-10 cell-surface receptors, which transduce the cell's response to stimulation, as the state variables. The monocyte is assumed to be initially in a quiescent state, and it is stimulated to produce IL-1 by an external stimulus (e.g. exposure to TNF-alpha or lipopolysaccharide, LPS). This in turn invokes an autocrine IL-1 response, and also induces the production of the anti-inflammatory cytokine IL-10, which acts to downregulate IL-1 production. These responses are mediated by specific cell-surface receptors, the concentrations of which may also be subject to stimulated upregulation. We analyse a reduced, four-dimensional version of the model, and explore its asymptotic states. We find a variety of possible outcomes: runaway IL-1 production, multiple stable equilibria, stable limit cycles, and, exceptionally, quasi-periodic behaviour. These behaviours depend crucially on the form of the cell's response functions. The possible biological implications of these phenomena are discussed.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"18 2 1","pages":"159-92"},"PeriodicalIF":0.0,"publicationDate":"2001-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/18.2.159","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61181536","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}

{"title":"Control analysis of the Rose-Hindmarsh model for neural activity.","authors":"A. Milne, Z. Chalabi","doi":"10.1093/IMAMMB/18.1.53","DOIUrl":"https://doi.org/10.1093/IMAMMB/18.1.53","url":null,"abstract":"It is well known that vasopressin cells fire action potentials in bursts, but also have the ability to continuously discharge or have long periods of silence. Experimentally, various external stimuli can be applied to the vasopressin cell in order to manipulate the patterns of discharge observed. In this paper, the Rose-Hindmarsh model is used to describe the discharging of a single vasopressin cell. The range of parameter values which makes the model display the various patterns observed in vivo are described. It is shown that the model can be controlled to follow desired patterns of discharge and thus mimic external stimulation.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"19 1","pages":"53-75"},"PeriodicalIF":0.0,"publicationDate":"2001-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/18.1.53","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61181525","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}

{"title":"A control theoretic approach to containing the spread of rabies.","authors":"N. Evans, A. Pritchard","doi":"10.1093/IMAMMB/18.1.1","DOIUrl":"https://doi.org/10.1093/IMAMMB/18.1.1","url":null,"abstract":"Many problems in medicine and biology involve some kind of spatial spread, and quite often the need to control it. A large proportion of medical and biological systems distinguish themselves from those found in engineering by the way the control acts. We illustrate this by considering the specific example of the spread of rabies among foxes. We first give a brief description of a model proposed by Murray et al. (Murray, J. D., Stanley, E. A. & Brown, D. L., Proc. R. Soc. Lond., B 229, 111-150 (1986)), which we extend to include the control mechanism. The problem is to prevent the spread of rabies by vaccinating foxes via the distribution of bait in a region around an observed outbreak. The extended model can be formulated as a nonlinear time-varying control system described by partial differential equations. In contrast to most engineering type control problems, the control does not continuously affect the system but only acts through the initial distributions. We briefly outline a general theory developed for dealing with such nonlinear systems by the use of a fixed point theorem. The problem and the theory are illustrated by some numerical simulations.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"18 1 1","pages":"1-23"},"PeriodicalIF":0.0,"publicationDate":"2001-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/18.1.1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61181244","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}

{"title":"Physiological flow waveform in a rigid elliptical vessel.","authors":"M. Robertson, U. Köhler","doi":"10.1093/IMAMMB/18.1.77","DOIUrl":"https://doi.org/10.1093/IMAMMB/18.1.77","url":null,"abstract":"A procedure to model the velocity and wall shear stress for a physiological flow in a non-cylindrical vessel is presented. The work describes how a vessel with an elliptical cross section may be used to represent flow in compressed or partially occluded arteries and veins. The procedure was applied to produce a simulation of a physiological flow in a straight rigid vessel with a slightly elliptical cross section (ellipticity, epsilon = 0.8). Fourier analysis was performed on a physiological flow waveform. Flow in the common carotid artery was satisfactorily represented (Pearson correlation coefficient, r > 95%) with a series of five harmonic terms. Expressions involving a linear combination of ordinary and modified Mathieu functions were used to describe the velocity and wall shear stress for each harmonic. An outline of the procedure, and the expressions, which were used to compute the characteristic Mathieu numbers and coefficients is illustrated with their behaviour at the fundamental and Nyquist frequencies. Superposition of the individual contributions to the velocity and wall shear stress allowed the calculation of the overall properties of the flow.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"26 3 1","pages":"77-98"},"PeriodicalIF":0.0,"publicationDate":"2001-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/18.1.77","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61181739","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}

{"title":"On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion.","authors":"S. Ruan, Junjie Wei","doi":"10.1093/IMAMMB/18.1.41","DOIUrl":"https://doi.org/10.1093/IMAMMB/18.1.41","url":null,"abstract":"In this paper, we first study the distribution of the zeros of a third degree exponential polynomial. Then we apply the obtained results to a delay model for the control of testosterone secretion. It is shown that under certain assumptions on the coefficients the steady state of the delay model is asymptotically stable for all delay values. Under another set of conditions, there is a critical delay value, the steady state is stable when the delay is less than the critical value and unstable when the delay is greater than the critical value. Thus, oscillations via Hopf bifurcation occur at the steady state when the delay passes through the critical value. Numerical simulations are presented to illustrate the results.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"18 1 1","pages":"41-52"},"PeriodicalIF":0.0,"publicationDate":"2001-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/18.1.41","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61181341","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}

{"title":"Optimal chemotherapy regimens: influence of tumours on normal cells and several toxicity constraints.","authors":"A. Matveev, A. Savkin","doi":"10.1093/IMAMMB/18.1.25","DOIUrl":"https://doi.org/10.1093/IMAMMB/18.1.25","url":null,"abstract":"Cancer chemotherapy for the case of one drug is studied. The negative and inhibiting effect of the tumour on normal cells is taken into account. Under certain assumptions, we determine the optimal regimen that minimizes the tumour burden at the end of a fixed period of therapy while maintaining certain normal cell populations above prescribed levels. More precisely, it is demonstrated that the optimal strategy corresponds to injection of the drug at the maximal rate.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"18 1 1","pages":"25-40"},"PeriodicalIF":0.0,"publicationDate":"2001-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/18.1.25","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61181305","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}

{"title":"Modelling the growth of soil-borne fungi in response to carbon and nitrogen.","authors":"A. Lamour, F. C. van den Bosch, A. Termorshuizen, M. Jeger","doi":"10.1093/imamci/17.4.329","DOIUrl":"https://doi.org/10.1093/imamci/17.4.329","url":null,"abstract":"Growth of soil-borne fungi is poorly described and understood, largely because non-destructive observations on hyphae in soil are difficult to make. Mathematical modelling can help in the understanding of fungal growth. Except for a model by Paustian & Schnürer (1987a), fungal growth models do not consider carbon and nitrogen contents of the supplied substrate, although these nutrients have considerable effects on hyphal extension in soil. We introduce a fungal growth model in relation to soil organic matter decomposition dealing with the detailed dynamics of carbon and nitrogen. Substrate with a certain carbon : nitrogen ratio is supplied at a constant rate, broken down and then taken up by fungal mycelium. The nutrients are first stored internally in metabolic pools and then incorporated into structural fungal biomass. Standard mathematical procedures were used to obtain overall-steady states of the variables (implicitly from a cubic equation) and the conditions for existence. Numerical computations for a wide range of parameter combinations show that at most one solution for the steady state is biologically meaningful, specified by the conditions for existence. These conditions specify a constraint, namely that the 'energy' (in terms of carbon) invested in breakdown of substrate should be less than the 'energy' resulting from breakdown of substrate, leading to a positive carbon balance. The biological interpretation of the conditions for existence is that for growth the 'energy' necessary for production of structural fungal biomass and for maintenance should be less than the mentioned positive carbon balance in the situation where all substrate is colonized. In summary, the analysis of this complicated fungal growth model gave results with a clear biological interpretation.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"18 2 1","pages":"329-46"},"PeriodicalIF":0.0,"publicationDate":"2001-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61161679","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}

{"title":"Enhanced efficiency of feeding and mixing due to chaotic flow patterns around choanoflagellates.","authors":"B. Orme, S. Otto, J. Blake","doi":"10.1093/IMAMMB/18.3.293","DOIUrl":"https://doi.org/10.1093/IMAMMB/18.3.293","url":null,"abstract":"The motion of particles and feeding currents created by micro-organisms due to a flagellum are considered. The calculations are pertinent to a range of sessile organisms, but we concentrate on a particular organism, namely Salpingoeca amphoridium (SA) (a choanoflagellate), due to the availability of experimental data (Pettitt, 2000). These flow fields are characterized as having very small Reynolds numbers, which implies that viscous forces dominate over inertial ones consistent with using the Stokes flow equations. The flow generated by the flagellum is modelled via the consideration of a point force known as a stokeslet. The interaction between the boundary, to which the organism is attached, and its flagellum leads to toroidal eddies, which serve to transport particles towards the micro-organism, promoting filtering of nutrients by the microvilli which constitute the cell's collar (the filtering mechanism in SA). It is our conjecture that the interaction of multiple toroidal eddies will lead to chaotic advection and hence enhance the domain of feeding for these organisms. The degree of mixing in the region around SA is investigated using chaotic and statistical measures to study the influence the flagellum has on the surrounding fluid. The three-dimensional particle paths around such organisms are also considered with the aim of showing that the plane within which they are situated is an attractor.","PeriodicalId":77168,"journal":{"name":"IMA journal of mathematics applied in medicine and biology","volume":"18 3 1","pages":"293-325"},"PeriodicalIF":0.0,"publicationDate":"2000-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/IMAMMB/18.3.293","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61182051","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}