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1.
Torcasio A Zhang X Van Oosterwyck H Duyck J van Lenthe GH 《Biomechanics and modeling in mechanobiology》2012,11(5):743-750
Although research has been addressed at investigating the effect of specific loading regimes on bone response around the implant,
a precise quantitative understanding of the local mechanical response close to the implant site is still lacking. This study
was aimed at validating micro-CT-based finite element (μFE) models to assess tissue strains after implant placement in a rat
tibia. Small implants were inserted at the medio-proximal site of 8 rat tibiae. The limbs were subjected to axial compression
loading; strain close to the implant was measured by means of strain gauges. Specimen-specific μFE models were created and
analyzed. For each specimen, 4 different models were created corresponding to different representations of the bone–implant
interface: bone and implant were assumed fully osseointegrated (A); a low stiffness interface zone was assumed with thickness
of 40 μm (B), 80 μm (C), and 160 μm (D). In all cases, measured and computational strains correlated highly (R
2 = 0.95, 0.92, 0.93, and 0.95 in A, B, C, and D, respectively). The averaged calculated strains were 1.69, 1.34, and 1.15
times higher than the measured strains for A, B, and C, respectively, and lower than the experimental strains for D (factor
= 0.91). In conclusion, we demonstrated that specimen-specific FE analyses provide accurate estimates of peri-implant bone
strains in the rat tibia loading model. Further investigations of the bone-implant interface are needed to quantify implant
osseointegration. 相似文献
2.
A number of mechano-regulation theories have been proposed that relate the differentiation pathway of mesenchymal stem cells
(MSCs) to their local biomechanical environment. During spontaneous repair processes in skeletal tissues, the organisation
of the extracellular matrix is a key determinant of its mechanical fitness. In this paper, we extend the mechano-regulation
theory proposed by Prendergast et al. (J Biomech 30(6):539–548, 1997) to include the role of the mechanical environment on
the collagen architecture in regenerating soft tissues. A large strain anisotropic poroelastic material model is used in a
simulation of tissue differentiation in a fracture subject to cyclic bending (Cullinane et al. in J Orthop Res 20(3):579–586,
2002). The model predicts non-union with cartilage and fibrous tissue formation in the defect. Predicted collagen fibre angles,
as determined by the principal decomposition of strain- and stress-type tensors, are similar to the architecture seen in native
articular cartilage and neoarthroses induced by bending of mid-femoral defects in rats. Both stress and strain-based remodelling
stimuli successfully predicted the general patterns of collagen fibre organisation observed in vivo. This provides further
evidence that collagen organisation during tissue differentiation is determined by the mechanical environment. It is envisioned
that such predictive models can play a key role in optimising MSC-based skeletal repair therapies where recapitulation of
the normal tissue architecture is critical to successful repair. 相似文献
3.
A mathematical model is developed with a highly controlled birth and death process for precursor cells. This model is both
biologically- and statistically-based. The controlled growth and differentiation (CGD) model limits the number of replications
allowed in the development of a tissue or organ and thus, more closely reflects the presence of a true stem cell population.
Leroux et al. (1996) presented a biologically-based dose-response model for developmental toxicology that was derived from a partial differential
equation for the generating function. This formulation limits further expansion into more realistic models of mammalian development.
The same formulae for the probability of a defect (a system of ordinary differential equations) can be derived through the
Kolmogorov forward equations due to the nature of this Markov process. This modified approach is easily amenable to the expansion
of more complicated models of the developmental process such as the one presented here. Comparisons between the Leroux et al. (1996) model and the controlled growth and differentiation (CGD) model as developed in this paper are also discussed.
Received: 8 June 2001 / Revised version: 15 June 2002 / Published online: 26 September 2002
Keywords or phrases: Teratology – Multistate process – Cellular kinetics – Numerical simulation 相似文献
4.
Victor D. Hosfeld Steffan Puwal Keith Jankowski Bradley J. Roth 《Journal of biological physics》2007,33(2):145-153
Traditionally, cardiac defibrillation requires a strong electric shock. Many unwanted side effects of this shock could be
eliminated if defibrillation were performed using weak stimuli applied to several locations throughout the heart. Such multi-site
pacing algorithms have been shown to defibrillate both experimentally (Pak et al., Am J Physiol 285:H2704–H2711, 2003) and
theoretically (Puwal and Roth, J Biol Systems 14:101–112, 2006). Gauthier et al. (Chaos, 12:952–961, 2002) proposed a method
to pace the heart using an algorithm based on nonlinear dynamics feedback applied through a single electrode. Our study applies
a related but simpler algorithm, which essentially configures each electrode as a demand pacemaker, to simulate the multi-site
pacing of fibrillating cardiac tissue. We use the numerical model developed by Fenton et al. (Chaos, 12:852–892, 2002) as
the reaction term in a reaction–diffusion equation that we solve over a two-dimensional sheet of tissue. The defibrillation
rate after pacing for 3 s is about 30%, which is significantly higher than the spontaneous defibrillation rate and is higher
than observed in previous experimental and theoretical studies. Tuning the algorithm period can increase this rate to 45%.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. 相似文献
5.
6.
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
7.
The equations governing oxygen transport from blood to tissue are presented for a cylindrical tissue compartment, with blood
flowing along a co–axial cylindrical capillary inside the tissue. These governing equations take account of: (i) the non–linear
reactions between oxygen and haemoglobin in blood and between oxygen and myoglobin in tissue; (ii) diffusion of oxygen in
both the axial and radial directions; and (iii) convection of haemoglobin and plasma in the capillary. A non–dimensional analysis
is carried out to assess some assumptions made in previous studies. It is predicted that: (i) there is a boundary layer for
oxygen partial pressure but not for haemoglobin or myoglobin oxygen saturation close to the inflow boundary in the capillary;
(ii) axial diffusion may not be neglected everywhere in the model; (iii) the reaction between oxygen and both haemoglobin
and myoglobin may be assumed to be instantaneous in nearly all cases; and (iv) the effect of myoglobin is only significant
for tissue with a low oxygen partial pressure. These predictions are validated by solving the full equations numerically and
are then interpreted physically.
Received: 13 October 2000 / Revised version: 12 June 2001 / Published online: 17 May 2002 相似文献
8.
Lauren Nicole Miller Hayward Elise F. Morgan 《Biomechanics and modeling in mechanobiology》2009,8(6):447-455
Mechanical cues are known to regulate tissue differentiation during skeletal healing. Quantitative characterization of this
mechano-regulatory effect has great therapeutic potential. This study tested an existing theory that shear strain and interstitial
fluid flow govern skeletal tissue differentiation by applying this theory to a scenario in which a bending motion applied
to a healing transverse osteotomy results in cartilage, rather than bone, formation. A 3-D finite element mesh was created
from micro-computed tomography images of a bending-stimulated callus and was used to estimate the mechanical conditions present
in the callus during the mechanical stimulation. Predictions regarding the patterns of tissues—cartilage, fibrous tissue,
and bone—that formed were made based on the distributions of fluid velocity and octahedral shear strain. These predictions
were compared to histological sections obtained from a previous study. The mechano-regulation theory correctly predicted formation
of large volumes of cartilage within the osteotomy gap and many, though not all patterns of tissue formation observed throughout
the callus. The results support the concept that interstitial fluid velocity and tissue shear strain are key mec- hanical
stimuli for the differentiation of skeletal tissues. 相似文献
9.
We examine a generalised SIR model for the infection dynamics of four competing disease strains. This model contains four
previously-studied models as special cases. The different strains interact indirectly by the mechanism of cross-immunity;
individuals in the host population may become immune to infection by a particular strain even if they have only been infected
with different but closely related strains. Several different models of cross-immunity are compared in the limit where the
death rate is much smaller than the rate of recovery from infection. In this limit an asymptotic analysis of the dynamics
of the models is possible, and we are able to compute the location and nature of the Takens–Bogdanov bifurcation associated
with the presence of oscillatory dynamics observed by previous authors.
Received: 5 December 2001 / Revised version: 5 May 2002 / Published online: 17 October 2002
Keywords or phrases: Infection – Pathogen – Epidemiology – Multiple strains – Cross-immunity – Oscillations – Dynamics – Bifurcations 相似文献
10.
Alber M Glimm T Hentschel HG Kazmierczak B Zhang YT Zhu J Newman SA 《Bulletin of mathematical biology》2008,70(2):460-483
A recently proposed mathematical model of a “core” set of cellular and molecular interactions present in the developing vertebrate
limb was shown to exhibit pattern-forming instabilities and limb skeleton-like patterns under certain restrictive conditions,
suggesting that it may authentically represent the underlying embryonic process (Hentschel et al., Proc. R. Soc. B 271, 1713–1722, 2004). The model, an eight-equation system of partial differential equations, incorporates the behavior of mesenchymal cells as
“reactors,” both participating in the generation of morphogen patterns and changing their state and position in response to
them. The full system, which has smooth solutions that exist globally in time, is nonetheless highly complex and difficult
to handle analytically or numerically. According to a recent classification of developmental mechanisms (Salazar-Ciudad et
al., Development 130, 2027–2037, 2003), the limb model of Hentschel et al. is “morphodynamic,” since differentiation of new cell types occurs simultaneously with
cell rearrangement. This contrasts with “morphostatic” mechanisms, in which cell identity becomes established independently
of cell rearrangement. Under the hypothesis that development of some vertebrate limbs employs the core mechanism in a morphostatic
fashion, we derive in an analytically rigorous fashion a pair of equations representing the spatiotemporal evolution of the
morphogen fields under the assumption that cell differentiation relaxes faster than the evolution of the overall cell density
(i.e., the morphostatic limit of the full system). This simple reaction–diffusion system is unique in having been derived
analytically from a substantially more complex system involving multiple morphogens, extracellular matrix deposition, haptotaxis,
and cell translocation. We identify regions in the parameter space of the reduced system where Turing-type pattern formation
is possible, which we refer to as its “Turing space.” Obtained values of the parameters are used in numerical simulations
of the reduced system, using a new Galerkin finite element method, in tissue domains with nonstandard geometry. The reduced
system exhibits patterns of spots and stripes like those seen in developing limbs, indicating its potential utility in hybrid
continuum-discrete stochastic modeling of limb development. Lastly, we discuss the possible role in limb evolution of selection
for increasingly morphostatic developmental mechanisms. 相似文献
11.
Early development and quorum sensing in bacterial biofilms 总被引:3,自引:0,他引:3
Ward JP King JR Koerber AJ Croft JM Sockett RE Williams P 《Journal of mathematical biology》2003,47(1):23-55
We develop mathematical models to examine the formation, growth and quorum sensing activity of bacterial biofilms. The growth
aspects of the model are based on the assumption of a continuum of bacterial cells whose growth generates movement, within
the developing biofilm, described by a velocity field. A model proposed in Ward et al. (2001) to describe quorum sensing, a process by which bacteria monitor their own population density by the use of quorum
sensing molecules (QSMs), is coupled with the growth model. The resulting system of nonlinear partial differential equations
is solved numerically, revealing results which are qualitatively consistent with experimental ones. Analytical solutions derived
by assuming uniform initial conditions demonstrate that, for large time, a biofilm grows algebraically with time; criteria
for linear growth of the biofilm biomass, consistent with experimental data, are established. The analysis reveals, for a
biologically realistic limit, the existence of a bifurcation between non-active and active quorum sensing in the biofilm.
The model also predicts that travelling waves of quorum sensing behaviour can occur within a certain time frame; while the
travelling wave analysis reveals a range of possible travelling wave speeds, numerical solutions suggest that the minimum
wave speed, determined by linearisation, is realised for a wide class of initial conditions.
Received: 10 February 2002 / Revised version: 29 October 2002 /
Published online: 19 March 2003
Key words or phrases: Bacterial biofilm – Quorum sensing – Mathematical modelling – Numerical solution – Asymptotic analysis – Travelling wave
analysis 相似文献
12.
A simple structured model for biomass and extracellular enzyme production with recombinant Saccharomyces cerevisiae YPB-G 总被引:1,自引:0,他引:1
A simple structured model is proposed for simulating batch cultivation data on growth, substrate utilization, and heterologous
enzyme production of recombinant Saccharomyces cerevisiae YPB-G. The enzyme is a fusion protein displaying α-amylase and glucoamylase activities. Cell growth is modulated mainly by
intracellular substrate and ethanol concentrations. Intracellular substrate concentration is evaluated by means of the extracellular
substrate and biomass concentrations. Extracellular α-amylase and glucoamylase activities are taken to depend on biomass concentration.
The nine parameters of the proposed model are determined using nonlinear estimation techniques, and the model is validated
against experiments not used in parameter determination. The model developed simulates glucose consumption, cell mass, α-amylase
and glucoamylase production in a batch system. Simulation and experimental results are found to be in good agreement. Journal of Industrial Microbiology & Biotechnology (2002) 29, 111–116 doi:10.1038/sj.jim.7000281
Received 07 January 2002/ Accepted in revised form 22 May 2002 相似文献
13.
Temperature is the most important factor affecting growth at high altitudes. As trees use much of the allocated carbon gained
from photosynthesis to produce branches and stems, information on the timing and dynamics of secondary wood growth is crucial
to assessing temperature thresholds for xylogenesis. We have carried out histological analyses to determine cambial activity
and xylem cell differentiation in conifers growing at the treeline on the eastern Alps in two sites during 2002–2004 with
the aim of linking the growth process with temperature and, consequently, of defining thresholds for xylogenesis. Cambial
activity occurred from May to July–August and cell differentiation from May–June to September–October. The earliest start
of radial enlargement was observed in stone pine in mid-May, while Norway spruce was the last species to begin tracheid differentiation.
The duration of wood formation varied from 90 to 137 days, depending on year and site, with no difference between species.
Longer durations were observed in trees on the south-facing site because of the earlier onset and later ending of cell production
and differentiation. The threshold temperatures at which xylogenesis had a 0.5 probability of being active were calculated
by logistic regressions. Xylogenesis was active when the mean daily air temperature was 5.6–8.5°C and mean stem temperature
was 7.2–9°C. The similar thresholds among all trees suggested the existence of thermal limits in wood formation that correspond
with temperatures of 6–8°C that are supposed to limit growth at the treeline. Different soil temperature thresholds between
sites indicated that soil temperature may not be the main factor limiting xylogenesis. This study represents the first attempt
to define a threshold through comparative assessment of xylem growth and tissue temperatures in stem meristems at high altitudes. 相似文献
14.
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
15.
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
16.
We formulate a non–linear system of differential equations that models the dynamics of dengue fever. This disease is produced
by any of the four serotypes of dengue arbovirus. Each serotype produces permanent immunity to it, but only a certain degree
of cross–immunity to heterologous serotypes. In our model we consider the relation between two serotypes. Our interest is
to analyze the factors that allow the invasion and persistence of different serotypes in the human population. Analysis of
the model reveals the existence of four equilibrium points, which belong to the region of biological interest. One of the
equilibrium points corresponds to the disease–free state, the other three equilibria correspond to the two states where just
one serotype is present, and the state where both serotypes coexist, respectively. We discuss conditions for the asymptotic
stability of equilibria, supported by analytical and numerical methods. We find that coexistence of both serotypes is possible
for a large range of parameters.
Received: 7 July 1998 / Revised version: 12 July 2002 / Published online: 26 September 2002
Keywords or phrases: Dengue fever – Primary and secondary infections – Serotype – Coexistence – Threshold – Basic reproduction number – Persistence 相似文献
17.
Somites are condensations of mesodermal cells that form along the two sides of the neural tube during early vertebrate development.
They are one of the first instances of a periodic pattern, and give rise to repeated structures such as the vertebrae. A number
of theories for the mechanisms underpinning somite formation have been proposed. For example, in the “clock and wavefront”
model (Cooke and Zeeman in J. Theor. Biol. 58:455–476, 1976), a cellular oscillator coupled to a determination wave progressing along the anterior-posterior axis serves to group cells
into a presumptive somite. More recently, a chemical signaling model has been developed and analyzed by Maini and coworkers
(Collier et al. in J. Theor. Biol. 207:305–316, 2000; Schnell et al. in C. R. Biol. 325:179–189, 2002; McInerney et al. in Math. Med. Biol. 21:85–113, 2004), with equations for two chemical regulators with entrained dynamics. One of the chemicals is identified as a somitic factor,
which is assumed to translate into a pattern of cellular aggregations via its effect on cell–cell adhesion. Here, the authors
propose an extension to this model that includes an explicit equation for an adhesive cell population. They represent cell
adhesion via an integral over the sensing region of the cell, based on a model developed previously for adhesion driven cell
sorting (Armstrong et al. in J. Theor. Biol. 243:98–113, 2006). The expanded model is able to reproduce the observed pattern of cellular aggregates, but only under certain parameter restrictions.
This provides a fuller understanding of the conditions required for the chemical model to be applicable. Moreover, a further
extension of the model to include separate subpopulations of cells is able to reproduce the observed differentiation of the
somite into separate anterior and posterior halves.
N.J. Armstrong was supported by a Doctoral Training Account Studentship from EPSRC. K.J. Painter and J.A. Sherratt were supported
in part by Integrative Cancer Biology Program Grant CA113004 from the US National Institute of Health and in part by BBSRC
grant BB/D019621/1 for the Centre for Systems Biology at Edinburgh. 相似文献
18.
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
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.
Jean-Louis Milan Josep A. Planell Damien Lacroix 《Biomechanics and modeling in mechanobiology》2010,9(5):583-596
A computational model of mechanoregulation is proposed to predict bone tissue formation stimulated mechanically by overall
dynamical compression within a porous polymeric scaffold rendered by micro-CT. Dynamic compressions of 0.5–5% at 0.0025–0.025
s−1 were simulated. A force-controlled dynamic compression was also performed by imposing a ramp of force from 1 to 70 N. The
model predicts homogeneous mature bone tissue formation under strain levels of 0.5–1% at strain rates of 0.0025–0.005 s−1. Under higher levels of strain and strain rates, the scaffold shows heterogeneous mechanical behaviour which leads to the
formation of a heterogeneous tissue with a mixture of mature bone and fibrous tissue. A fibrous tissue layer was also predicted
under the force-controlled dynamic compression, although the same force magnitude was found promoting only mature bone during
a strain-controlled compression. The model shows that the mechanical stimulation of bone tissue formation within a porous
scaffold closely depends on the loading history and on the mechanical behaviour of the scaffold at local and global scales. 相似文献