Abstract：
:A mathematical model is presented for the growth of a multicellular spheroid that comprises a central core of necrotic cells surrounded by an outer annulus of proliferating cells. The model distinguishes two mechanisms for cell loss: apoptosis and necrosis. Cell loss due to apoptosis is defined to be programmed cell death, occurring, for example, when a cell exceeds its natural lifespan, whereas cell death due to necrosis is induced by changes in the cell's microenvironment, occurring, for example, in nutrient-depleted regions. Mathematically, the problem involves tracking two free boundaries, one for the outer tumor radius, the other for the inner necrotic radius. Numerical simulations of the model are presented in an inhibitor-free setting and an inhibitor-present setting for various parameter values. The effects of nutrients and inhibitors on the existence and stability of the time-independent solutions of the model are studied using a combination of numerical and asymptotic techniques.
journal_name
Math Bioscijournal_title
Mathematical biosciencesauthors
Byrne HM,Chaplin MAdoi
10.1016/0025-5564(96)00023-5subject
Has Abstractpub_date
1996-07-15 00:00:00pages
187-216issue
2eissn
0025-5564issn
1879-3134pii
0025556496000235journal_volume
135pub_type
杂志文章abstract：:The problem of testing for treatment effect when some subjects in the treatment group may be unaffected by the treatment is considered. A form of the Lehmann alternative suggested by Conover and Salsburg is used that assumes that each control score has the same distribution as the minimum of the known number of respon...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(92)90052-x
更新日期：1992-04-01 00:00:00
abstract：:A significant consideration in modeling systems with stages is to obtain models for the individual stages that have probability density functions (pdfs) of residence times that are close to those of the real system. Consequently, the theory of residence time distributions is important for modeling. Here I show first t...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(02)00110-4
更新日期：2002-11-01 00:00:00
abstract：:The article theoretically regards probability density functions (PDFs) for axial ratio (X/Y) of sectioning profiles of elliptical microvessels (MVs) arranged with anisotropy in a biological tissue volume. A technique for the PDF(X/Y) calculations in anisotropy of the elliptical MVs is described. The essence of this te...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2009.03.001
更新日期：2009-06-01 00:00:00
abstract：:In this paper, two cancer therapies are investigated through their mathematical models. Namely, angiogenesis inhibition (P. Hahndfeldt, D. Panigrahy, J. Folkman, L. Hlatky, Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy, Cancer Res. 59, 1...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2011.02.010
更新日期：2011-06-01 00:00:00
abstract：:A structure for representing problems in decision analysis and in expert systems, which reason under uncertainty, is the influence diagram or causal network. A causal network consists of an underlying joint probability distribution and a directed acyclic graph in which a propositional variable that represents a margin...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(91)90089-2
更新日期：1991-02-01 00:00:00
abstract：:We discuss an N-dimensional model for diffusion of age dependent populations. Let rho(x, t, a) be the population density at time t, age a and spatial position x, and let u(x, t) = [formula: see text] rho(x, t, a) da be the total population at t and x. The directed dispersal model to be discussed, with diffusion depend...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(97)10014-1
更新日期：1998-04-01 00:00:00
abstract：:In a previous paper we studied the spread of excitation in a simplified model of the left ventricle, affected by fiber structure and obliqueness, curvature of the wall and Purkinje network. In the present paper we investigate the extracellular potential distribution u in the same ventricular model. Given the transmemb...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(98)10004-4
更新日期：1998-07-01 00:00:00
abstract：:In this paper, we consider a deterministic malaria transmission model with standard incidence rate and treatment. Human population is divided into susceptible, infectious and recovered subclasses, and mosquito population is split into susceptible and infectious classes. It is assumed that, among individuals with malar...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2015.05.005
更新日期：2015-08-01 00:00:00
abstract：:A mathematical analysis of the stability in human respiration, based on the tau-decomposition method, is conducted on a simple, but realistic CO2 model of the respiratory system. This model incorporates a two-compartment representation (lungs and tissues) for the plant and a very general class of controller. By derivi...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(98)10028-7
更新日期：1998-09-01 00:00:00
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journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/s0025-5564(02)00149-9
更新日期：2003-01-01 00:00:00
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journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2013.04.011
更新日期：2013-08-01 00:00:00
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journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2007.04.008
更新日期：2007-11-01 00:00:00
abstract：:Modeling a cell's response to encroaching ice has informed the development of cryopreservation protocols for four decades. It has been well documented that knowledge of the cellular state as a function of media and cooling rate faciliate informed cryopreservation protocol design and explain mechanisms of damage. Howev...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2019.108240
更新日期：2019-10-01 00:00:00
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journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2018.02.006
更新日期：2018-04-01 00:00:00
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journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2018.03.013
更新日期：2018-05-01 00:00:00
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journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2019.02.003
更新日期：2019-05-01 00:00:00
abstract：:The problem addressed is that of finding the harvesting policy that will maximize the yield and maintain a given population in a steady state. It is assumed that the equations describing the evolution of the population and the yield are linear but that the equation describing reproduction is nonlinear (density depende...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(94)90039-6
更新日期：1994-03-01 00:00:00
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journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(94)90031-0
更新日期：1994-05-01 00:00:00
abstract：:Cooperating behaviors abound across all domains of life, but are vulnerable to invasion by cheaters. An important evolutionary question is to determine mechanisms that stabilize and maintain cooperation levels and prevent population collapse. Policing is one strategy populations may employ to achieve this goal, and it...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2019.108257
更新日期：2019-10-01 00:00:00
abstract：:The interrelationship between pathogen infection and host mobility is of great importance for successful spread of disease in spatial pest population. As spread of infection depends on horizontal transmission of pathogen, there are numerous factors like susceptibility, latent period, host movement that influence overa...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2013.03.009
更新日期：2013-07-01 00:00:00
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journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2013.08.008
更新日期：2013-11-01 00:00:00
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journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2020.108346
更新日期：2020-06-01 00:00:00
abstract：:Half-sib, first cousin, half nth cousin, and nth cousin mating systems are robust in that small deviations from the mating structure will not significantly alter the levels of genetic identity or effect qualitative distinctions between the models. Substitution of nearest kin in matings may either increase or decrease ...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(91)90026-f
更新日期：1991-04-01 00:00:00
abstract：:Habitat heterogeneity can have profound effects on the spreading dynamics of invasive species. Using integro-difference equations, we investigate the spreading dynamics in a one-dimensional heterogeneous landscape comprising alternating favourable and unfavourable habitat patches or randomly generated habitat patches ...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2016.02.013
更新日期：2016-05-01 00:00:00
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journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(94)90012-4
更新日期：1994-10-01 00:00:00
abstract：:Frailty models are becoming increasingly popular in multivariate survival analysis. Shared frailty models in particular are often used despite their limitations. To overcome their disadvantages numerous correlated frailty models were established during the last decade. In the present study, we examine bivariate correl...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2004.11.010
更新日期：2005-11-01 00:00:00
abstract：:Bacterial biofilms are complex microbial depositions on immersed interfaces that form wherever the environmental conditions sustain microbial growth. Despite their name, biofilms can develop in highly irregular structures. Recently several mathematical concepts have been introduced to model these spatially structured ...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2011.05.006
更新日期：2011-09-01 00:00:00
abstract：:The high failure rates encountered in the chemotherapy of some cancers suggest that drug resistance is a common phenomenon. In the current study, the tumor burden during therapy is used to slow the growth of the drug-resistant cells, thereby maximizing the survival time of the host. Three types of tumor growth model a...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/0025-5564(92)90038-x
更新日期：1992-07-01 00:00:00
abstract：:The methods of Laplace transform were used to solve a mathematical model developed for percutaneous drug absorption. This model includes application and removal of the vehicle from the skin. A system of two linear partial differential equations was solved for the application period. The concentration of the medicinal ...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2005.07.002
更新日期：2005-10-01 00:00:00
abstract：:We present a theoretical model for steady-state radial and longitudinal oxygen transport in arterioles containing flowing blood (plasma and red blood cells) and surrounded by living tissue. This model combines a detailed description of convective and diffusive oxygen transport inside the arteriole with a novel boundar...
journal_title：Mathematical biosciences
pub_type： 杂志文章
doi：10.1016/j.mbs.2011.03.010
更新日期：2011-07-01 00:00:00
