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1.
Pedro Freitas 《Biomechanics and modeling in mechanobiology》2009,8(6):457-471
We consider the model originally proposed by Shah and Humphrey (J Biomech 32:593–599, 1999) for a class of intracranial saccular
aneurysms and show that for constant pressure the addition of the viscoelastic term corresponding to the presence of cerebral
spinal fluid outside the membrane, no matter how small, does ensure convergence to an equilibrium. Our arguments apply to
a general equation of this type, and thus also hold for variations of this model such as that proposed by David and Humphrey
(J Biomech 36:1143–1150, 2003). On the other hand, it is known that the presence of damping may destabilize periodic orbits
of periodically forced systems or even prevent them from existing altogether. We present numerical simulations showing that
for some forcing terms the high-frequency oscillations do not die out with time, and a much more complex behaviour may emerge
as a discontinuous forcing term is approached. The key point for this situation to occur is related to the derivative of the
forcing term, supporting the hypothesis that sharper rises (or falls) in blood pressure may increase the risk of aneurysm
rupture. 相似文献
2.
We introduce inhomogeneous, substrate dependent cell division in a time discrete, nonlinear matrix model of size-structured
population growth in the chemostat, first introduced by Gage et al. [8] and later analysed by Smith [13]. We show that mass conservation is verified, and conclude that our system admits one
non zero globally stable equilibrium, which we express explicitly. Then we run numerical simulations of the system, and compare
the predictions of the model to data related to phytoplankton growth, whose obtention we discuss. We end with the identification
of several parameters of the system.
Received: 9 February 2000 / Revised version: 10 October 2001 / Published online: 23 August 2002
RID="*"
ID="*" Present address: Department of Mathematics and Statistics, University of Victoria, B.C., Canada. e-mail: jarino@math.uvic.ca
Key words or phrases: Chemostat – Structured population models – Discrete model – Inhomogeneous division size 相似文献
3.
We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion
system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent
to heteroclinic orbits in R
4
and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R
4
. The methods used to prove the results are the shooting argument and the Hopf bifurcation theorem.
Received: 25 May 2001 / Revised version: 5 August 2002 / Published online: 19 November 2002
RID="*"
ID="*" Research was supported by the National Natural Science Foundations (NNSF) of China.
RID="*"
ID="*" Research was partially supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. On leave
from the Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia B3H 3J5, Canada.
Mathematics Subject Classification (2000): 34C35, 35K57
Key words or phrases: Traveling wave solution – Wazewski set – Shooting argument – Hopf bifurcation
Acknowledgements. We would like to thank the two referees for their careful reading and helpful comments. 相似文献
4.
Exact formulas for the mean and variance of the proportion of different types in a fixed generation of a multi-type Galton-Watson
process are derived. The formulas are given in terms of iterates of the probability generating function of the offspring distribution.
It is also shown that the sequence of types backwards from a randomly sampled particle in a fixed generation is a non-homogeneous
Markov chain where the transition probabilities can be given explicitly, again in terms of probability generating functions.
Two biological applications are considered: mutations in mitochondrial DNA and the polymerase chain reaction.
Received: 10 June 2001 / Revised version: 21 November 2001 / Published online: 23 August 2002
Mathematics Subject Classification (2000): Primary 60J80, Secondary 92D10, 92D25
Key words or phrases: Multi-type Galton-Watson process – sampling formula – PCR – mitochondrial DNA 相似文献
5.
Weinberger HF 《Journal of mathematical biology》2002,45(6):511-548
It is shown that the methods previously used by the author [Wei82] and by R. Lui [Lui89] to obtain asymptotic spreading results
and sometimes the existence of traveling waves for a discrete-time recursion with a translation invariant order preserving
operator can be extended to a recursion with a periodic order preserving operator. The operator can be taken to be the time-one
map of a continuous time reaction-diffusion model, or it can be a more general model of time evolution in population genetics
or population ecology in a periodic habitat. Methods of estimating the speeds of spreading in various directions will also
be presented.
Received: 12 July 2001 / Revised version: 19 July 2002 / Published online: 17 October 2002
Mathematics Subject Classification (2000): 92D40, 92D25, 35K55, 35K57, 35B40
Keywords or phrases: Periodic – Spreading speed – Traveling wave 相似文献
6.
Complex nonlinear dynamics of the Hodgkin-Huxley equations induced by time scale changes 总被引:3,自引:0,他引:3
The Hodgkin–Huxley equations with a slight modification are investigated, in which the inactivation process (h) of sodium channels or the activation process of potassium channels (n) is slowed down. We show that the equations produce a variety of action potential waveforms ranging from a plateau potential,
such as in heart muscle cells, to chaotic bursting firings. When h is slowed down – differently from the case of n variable being slow – chaotic bursting oscillations are observed for a wide range of parameter values although both variables
cause a decrease in the membrane potential. The underlying nonlinear dynamics of various action potentials are analyzed using
bifurcation theory and a so-called slow–fast decomposition analysis. It is shown that a simple topological property of the
equilibrium curves of slow and fast subsystems is essential to the production of chaotic oscillations, and this is the cause
of the large difference in global firing characteristics between the h-slow and n-slow cases.
Received: 9 August 2000 / Accepted in revised form: 10 January 2001 相似文献
7.
We consider a partially coupled diffusive population model in which the state variables represent the densities of the immature
and mature population of a single species. The equation for the mature population can be considered on its own, and is a delay
differential equation with a delay-dependent coefficient. For the case when the immatures are immobile, we prove that travelling
wavefront solutions exist connecting the zero solution of the equation for the matures with the delay-dependent positive equilibrium
state. As a perturbation of this case we then consider the case of low immature diffusivity showing that the travelling front
solutions continue to persist. Our findings are contrasted with recent studies of the delayed Fisher equation. Travelling
fronts of the latter are known to lose monotonicity for sufficiently large delays. In contrast, travelling fronts of our equation
appear to remain monotone for all values of the delay.
Received: 1 November 2001 / Revised version: 10 May 2002 / Published online: 23 August 2002
Mathematics Subject Classification (2000): 35K57, 92D25
Key words or phrases: Age-structure – Time-delay – Travelling Fronts – Reaction-diffusion 相似文献
8.
Lindström T 《Journal of mathematical biology》2002,45(5):396-418
In this paper we derive and analyze a discrete version of Rosenzweig's (Am. Nat. 1973) food-chain model. We provide substantial
analytical and numerical evidence for the general dynamical patterns of food chains predicted by De Feo and Rinaldi (Am. Nat.
1997) remaining largely unaffected by this discretization. Our theoretical analysis gives rise to a classification of the
parameter space into various regions describing distinct governing dynamical behaviors. Predator abundance has a local optimum
at the edge of chaos.
Received: 13 August 1999 / Revised version: 12 March 2002 / Published online: 17 October 2002
Mathematics Subject Classification (1991): 92D40
Keywords or phrases: Discrete food-chain – Discrete Hopf (Neimark-Sacker) bifurcation – Pulsewise birth processes – Mean yield maximization –
Nicholson-Bailey model 相似文献
9.
It is shown that a chemostat with two organisms can be made coexistent by means of feedback control of the dilution rate.
Remaining freedom in the feedback law can be used to guarantee robustness or improve particular performance indices. Unfortunately
a topological property prevents coexistence by feedback control for chemostats with more than two organisms. We apply our
results to control bioreactors aimed at producing commercial products through genetically altered organisms. In all our results
the coexistence takes its simplest form: a global asymptotically stable equilibrium point in the interior of the non-negative
orthant.
Received: 1 November 2001 / Revised version: 19 August 2002 / Published online: 19 November 2002
Mathematics Subject Classification (2000): 34H05, 34D23, 93C10
Keywords or phrases: Chemostat – Feedback control – Coexistence 相似文献
10.
Morphogenesis and regeneration from stomatal guard cell complexes of cotton (Gossypium hirsutum L.) 总被引:1,自引:0,他引:1
The development of a regeneration system from cotton stomatal guard cells directly on epidermal strips is described. The
most important factors affecting embryogenic callus initiation in both of the varieties tested (Coker 312 and 315) were the
source of the epidermal tissue, including plant age (4–5 months old), the developmental stage of the flower (opening flower
stage) from which bracts were obtained, the composition of the culture medium and light irradiance. The flower developmental
stage was critical for callus formation, which was observed only from bracts obtained from opening flowers. In addition, epidermal
strips excised from the bract basal region were more responsive in culture than those obtained from the top region. Improved
callus initiation was obtained on epidermal strips which had their cuticle in contact with the culture medium. Light irradiance
was a limiting factor for embryogenic callus formation, which was observed only in calluses cultured under the lower light
irradiance (15.8 μmol m–2 s–1). Somatic embryogenesis was observed on callus cultures subcultured consecutively to a culture medium containing naphthalene
acetic acid (10.7 μM) and isopentenyladenine (4.9 μM). Histodifferentiation of somatic embryos was improved on a medium containing naphthaleneacetic acid (8.1 μM)+isopentenyladenine (2.5 μM) and abscisic acid (0.19–0.38 μM). Somatic embryo germination and plantlet development were obtained using established protocols with few modifications. On
average, one fully developed plant was obtained from the culture of circa 100 epidermal strips in both cultivars.
Received: 19 May 2000 / Revision received: 25 August 2000 / Accepted: 29 August 2000 相似文献
11.
We start from a stochastic SIS model for the spread of epidemics among a population partitioned into M sites, each containing
N individuals; epidemic spread occurs through within-site (`local') contacts and global contacts. We analyse the limit behaviour
of the system as M and N increase to ∞. Two limit procedures are considered, according to the order in which M and N go to ∞; independently of the order, the limiting distribution of infected individuals across sites is a probability measure,
whose evolution in time is governed by the weak form of a PDE. Existence and uniqueness of the solutions to this problem is
shown. Finally, it is shown that the infected distribution converges, as time goes to infinity, to a Dirac measure at the
value x
*
, the equilibrium of a single-patch SIS model with contact rate equal to the sum of local and global contacts.
Received: 18 July 2001 / Revised version: 16 March 2002 / Published online: 26 September 2002
Mathematics Subject Classification (2000): 92D30, 60F99
Key words or phrases: SIS epidemic – Metapopulation – Markov population processes – Weak convergence of measures 相似文献
12.
Ottesen JT 《Journal of mathematical biology》2003,46(4):309-332
An elastic rubber tube is connected with a stiffer rubber tube forming two halves of a torus and filled with water. Compressing
one of the rubber tubes symmetrically and periodic at a point of asymmetry creates a remarkable unidirectional mean flow in
the system. The size and the direction of the mean flow depend on the frequency of compression, the elasticity of the tubes,
the compression ratio, and the type of compression with respect to time in a complicated manner. The system is modelled using
a one-dimensional theory derived by averaging the Navier-Stokes equations ignoring higher order terms in a certain small quantity.
The one-dimensional model is analysed partly analytically and partly numerically. A series of experiments on a physical realisation
of the system are described. The theoretical findings and experimental results are compared; They show a remarkable agreement
between the experiments and the predictions of the model. Frequencies at which the mean flow change direction are predicted
numerically as well as analytically and the two results are compared.
Received: 21 February 2002 / Revised version: 30 August 2002 / Published online: 17 January 2003
Key words or phrases: Flow – Elastic tubes – Valveless pumping – Navier-Stokes equations – Frequency dependent – One-dimensional model – Experimental
validation 相似文献
13.
We derive models for chemosensitive movement based on Cattaneo's law of heat propagation with finite speed. We apply the
model to pattern formation as observed in experiments with Dictyostelium discoideum, with Salmonella typhimurium and with Escherichia coli. For Salmonella typhimurium we make predictions on pattern formation which can be tested in experiments. We discuss the relations of the Cattaneo models
to classical models and we develop an effective numerical scheme.
Received: 8 October 2001 / Revised version: 2 August 2002 / Published online: 19 November 2002
Key words or phrases: Chemotaxis – Aggregation – Cattaneo model – Numerical schemes
Acknowledgements. We are very grateful for comments of S. Noelle concerning the numerical scheme. We thank K.P. Hadeler and C. Schmeiser for
helpful remarks. The research was supported by the Deutsche Forschungsgemeinschaft, research project ANumE and the Austrian Science Foundation, grant no. W008. 相似文献
14.
15.
H. A. Richards V. A. Rudas H. Sun J. K. McDaniel Z. Tomaszewski B. V. Conger 《Plant cell reports》2001,20(1):48-54
A dual marker plasmid comprising the reporter gene sgfp (green fluorescent protein) and the selectable bar gene (Basta tolerance) was constructed by replacing the uidA (β-glucuronidase, GUS) gene in a uidA-bar construct with sgfp. A particle inflow gun was used to propel tungsten particles coated with this plasmid into immature inflorescence-derived
embryogenic callus of switchgrass (Panicum virgatum L.). GFP was observed in leaf tissue and pollen of transgenic plants. Nearly 100 plants tolerant to Basta were obtained from
the experiments, and Southern blot hybridization confirmed the presence of both the bar and sgfp genes. Plants regenerated from in vitro cultures of transgenic plants grew on medium with 10 mg l–1 bialaphos. When the pH indicator chlorophenol red was in the medium, the transgenic plantlets changed the medium from red
to yellow. Basta tolerance was observed in T1 plants resulting from crosses between transgenic and nontransgenic control plants, indicating inheritance of the bar transgene.
Received: 11 May 2000 / Revision received: 21 August 2000 / Accepted: 22 August 2000 相似文献
16.
Intracranial aneurysms (ICA) are abnormal saccular dilations of cerebral arteries, commonly found at apices of arterial bifurcations
and outer walls of curved arterial segments. Histological evidence suggests the stages in ICA development include the deformation
of a segment of arterial wall into a “bleb” with no identifiable neck region followed by the development of an aneurysm with
a clear neck. Afterwards, the aneurysm may undergo further enlargement, possibly with significant biological response including
calcification and thrombosis. Past studies of the biomechanics of cerebral aneurysm tissue have been directed at modeling
elastic deformations of pre-existing aneurysms. Taking this approach, the aneurysm wall is treated as a different entity than
the arterial tissue from which it developed. In the current work, a nonlinear, inelastic, dual-mechanism constitutive equation
for cerebral arterial tissue is developed. It is the first to model the recruitment of collagen fibers and degradation of
the internal elastic lamina, two important characteristics of early stage aneurysm formation. 相似文献
17.
Schliekelman P 《Journal of mathematical biology》2003,46(2):171-188
With recent advances in molecular genetics, it is likely that releases of genetically modified organisms will be used for
a variety of purposes. In many cases, such systems would utilize organisms that have been modified on multiple genetic loci.
Predicting the effect of such releases will require an understanding of the transient dynamics in the system. However, theoretical
understanding of transient dynamics in multilocus systems is limited, particularly for early generations when gametic disequilibrium
is still high. I derive approximate expressions for marginal allele frequency and marginal two-locus disequilibrium that are
applicable in this initial period, assuming infinite population size, two alleles per locus, and weak viability selection.
I then apply these results to exploring the effect of parameters on the frequency of the resident gamete type in a release
of organisms carrying an autocidal allele on multiple loci. This leads to simple approximate expressions for the optimal number
of loci carrying the autocidal allele (as a function of release size and the degree of natural selection against the alleles)
and the size of release needed to overcome a given level of selection against the released alleles.
Received: 5 March 2001 / Revised version: 10 July 2002 / Published online: 18 December 2002
Current address: Department of Statistics, 204 Statistics Building, University of Georgia, Athens, GA 30602-1952, USA. e-mail:
pdschlie@stat.uga.edu
Key words or phrases: Multilocus – Selection – Transgenic – Pest control – Genetic control
Acknowledgements. I thank Steve Ellner for insight and guidance throughout this project. This research was partially funded by a fellowship
from the College of Agricultural and Life Sciences Foundation of North Carolina State University. 相似文献
18.
This study presents a computational framework that capitalizes on known human neuromechanical characteristics during limb
movements in order to predict human–machine interactions. A parallel–distributed approach, the mixture of nonlinear models, fits the relationship between the measured kinematics and kinetics at the handle of a robot. Each element of the mixture
represented the arm and its controller as a feedforward nonlinear model of inverse dynamics plus a linear approximation of
musculotendonous impedance. We evaluated this approach with data from experiments where subjects held the handle of a planar
manipulandum robot and attempted to make point-to-point reaching movements. We compared the performance to the more conventional
approach of a constrained, nonlinear optimization of the parameters. The mixture of nonlinear models accounted for 79±11%
(mean ±SD) of the variance in measured force, and force errors were 0.73 ± 0.20% of the maximum exerted force. Solutions were
acquired in half the time with a significantly better fit. However, both approaches suffered equally from the simplifying
assumptions, namely that the human neuromechanical system consisted of a feedforward controller coupled with linear impedances
and a moving state equilibrium. Hence, predictability was best limited to the first half of the movement. The mixture of nonlinear models may be useful in human–machine tasks such as in telerobotics, fly-by-wire vehicles, robotic training, and rehabilitation.
Received: 20 October 2000 / Accepted in revised form: 8 May 2001 相似文献
19.
The urine concentrating mechanism of mammals and birds depends on a counterflow configuration of thousands of nearly parallel
tubules in the medulla of the kidney. Along the course of a renal tubule, cell type may change abruptly, resulting in abrupt
changes in the physical characteristics and transmural transport properties of the tubule. A mathematical model that faithfully
represents these abrupt changes will have jump discontinuities in model parameters. Without proper treatment, such discontinuities
may cause unrealistic transmural fluxes and introduce suboptimal spatial convergence in the numerical solution to the model
equations. In this study, we show how to treat discontinuous parameters in the context of a previously developed numerical
method that is based on the semi-Lagrangian semi-implicit method and Newton's method. The numerical solutions have physically
plausible fluxes at the discontinuities and the solutions converge at second order, as is appropriate for the method.
Received: 13 November 2001 / Revised version: 28 June 2002 / Published online: 26 September 2002
This work was supported in part by the National Institutes of Health (National Institute of Diabetes and Digestive and Kidney
Diseases, grant DK-42091.)
Mathematics Subject Classification (2000): 65-04, 65M12, 65M25, 92-04, 92C35, 35-04, 35L45
Keywords or phrases: Mathematical models – Differential equations – Mathematical biology – Kidney – Renal medulla – Semi-Lagrangian semi-implicit 相似文献
20.
R. W. Herzog H. Daniell N. K. Singh P. A. Lemke 《Applied microbiology and biotechnology》1996,45(3):333-337
An Aspergillus nidulans strain, auxotrophic for pyrimidine, was transformed to prototrophy by means of microprojectile bombardment. The transformation
frequency was somewhat lower than conventional polyethyleneglycol-mediated transformation of protoplasts. However, the percentage
of stable transformants was considerably higher with the biolistic approach. Typically, integrations of several copies of
the plasmid introduced into chromosomal DNA were observed. The effect of several parameters, like the concentration of conidia,
chamber pressure during bombardment and size of microprojectiles, on transformation frequencies were investigated and compared
to previously published data on microprojectile bombardment of fungal conidia. Optimum results (6 transformants/μg plasmid
DNA) were obtained when 108 conidia were bombarded with a helium pressure of 5.5–8.3 MPa (800–1200 lb/in2). M5, M10 and M17 tungsten particles were equally efficient.
Received: 9 August 1995/Received revision: 27 September 1995/Accepted: 4 October 1995 相似文献