657 research outputs found
Osteocytes as a record of bone formation dynamics: A mathematical model of osteocyte generation in bone matrix
The formation of new bone involves both the deposition of bone matrix, and
the formation of a network of cells embedded within the bone matrix, called
osteocytes. Osteocytes derive from bone-synthesising cells (osteoblasts) that
become buried in bone matrix during bone deposition. The generation of
osteocytes is a complex process that remains incompletely understood. Whilst
osteoblast burial determines the density of osteocytes, the expanding network
of osteocytes regulates in turn osteoblast activity and osteoblast burial. In
this paper, a spatiotemporal continuous model is proposed to investigate the
osteoblast-to-osteocyte transition. The aims of the model are (i) to link
dynamic properties of osteocyte generation with properties of the osteocyte
network imprinted in bone, and (ii) to investigate Marotti's hypothesis that
osteocytes prompt the burial of osteoblasts when they become covered with
sufficient bone matrix. Osteocyte density is assumed in the model to be
generated at the moving bone surface by a combination of osteoblast density,
matrix secretory rate, rate of entrapment, and curvature of the bone substrate,
but is found to be determined solely by the ratio of the instantaneous burial
rate and matrix secretory rate. Osteocyte density does not explicitly depend on
osteoblast density nor curvature. Osteocyte apoptosis is also included to
distinguish between the density of osteocyte lacuna and the density of live
osteocytes. Experimental measurements of osteocyte lacuna densities are used to
estimate the rate of burial of osteoblasts in bone matrix. These results
suggest that: (i) burial rate decreases during osteonal infilling, and (ii) the
control of osteoblast burial by osteocytes is likely to emanate as a collective
signal from a large group of osteocytes, rather than from the osteocytes
closest to the bone deposition front.Comment: 11 pages, 6 figures. V2: substantially augmented version. Addition of
Section 4 (osteocyte apoptosis
Governing equations of tissue modelling and remodelling: A unified generalised description of surface and bulk balance
Several biological tissues undergo changes in their geometry and in their
bulk material properties by modelling and remodelling processes. Modelling
synthesises tissue in some regions and removes tissue in others. Remodelling
overwrites old tissue material properties with newly formed, immature tissue
properties. As a result, tissues are made up of different "patches", i.e.,
adjacent tissue regions of different ages and different material properties,
within evolving boundaries. In this paper, generalised equations governing the
spatio-temporal evolution of such tissues are developed within the continuum
model. These equations take into account nonconservative, discontinuous surface
mass balance due to creation and destruction of material at moving interfaces,
and bulk balance due to tissue maturation. These equations make it possible to
model patchy tissue states and their evolution without explicitly maintaining a
record of when/where resorption and formation processes occurred. The time
evolution of spatially averaged tissue properties is derived systematically by
integration. These spatially-averaged equations cannot be written in closed
form as they retain traces that tissue destruction is localised at tissue
boundaries.
The formalism developed in this paper is applied to bone tissues, which
exhibit strong material heterogeneities due to their slow mineralisation and
remodelling processes. Evolution equations are proposed in particular for
osteocyte density and bone mineral density. Effective average equations for
bone mineral density (BMD) and tissue mineral density (TMD) are derived using a
mean-field approximation. The error made by this approximation when remodelling
patchy tissue is investigated. The specific time signatures of BMD or TMD
during remodelling events may provide a way to detect these events occurring at
lower, unseen spatial resolutions from microCT scans.Comment: 14 pages, 8 figures. V2: minor stylistic changes, more detailed
derivation of Eqs (30)-(31), additional comments on implication of BMD and
TMD signatures for microCT scan
The Casimir Effect
After a review of the standard calculation of the Casimir force between two
metallic plates at zero and non-zero temperatures, we present the study of
microscopic models to determine the large-distance asymptotic force in the
high-temperature regime. Casimir's conducting plates are modelized by plasmas
of interacting charges at temperature T. The charges are either classical, or
quantum-mechanical and coupled to a (classical) radiation field. In these
models, the force obtained is twice weaker than that arising from standard
treatments neglecting the microscopic charge fluctutations inside the bodies.
The enforcement of inert boundary conditions on the field in the usual
calculations turns out to be inadequate in this regime.
Other aspects of dispersion forces are also reviewed. The status of
(non-retarded) van der Waals-London forces in a dilute medium of non-zero
temperature and density is investigated. In a proper scaling regime called the
atomic limit (high dilution and low temperature), one is able to give the exact
large-distance atomic correlations up to exponentially small terms as T->0.
Retarded van der Waals forces and forces between dielectric bodies are also
reviewed.
Finally, the Casimir effect in critical phenomena is addressed by considering
the free Bose gas. It is shown that the grand-canonical potential of the gas in
a slab at the critical value of the chemical potential has finite size
corrections of the standard Casimir type. They can be attributed to the
existence of long-range order generated by gapless excitations in the phase
with broken continuous symmetry.Comment: Lecture notes prepared for the proceedings of the 1st Warsaw School
of Statistical Physics, Kazimierz, Poland, June 2005. To appear in Acta
Physica Polonica (2006). 52 pages, 0 figures. Available at
http://th-www.if.uj.edu.pl/acta/vol37/pdf/v37p2503.pd
Osteoblasts infill irregular pores under curvature and porosity controls: A hypothesis-testing analysis of cell behaviours
The geometric control of bone tissue growth plays a significant role in bone
remodelling, age-related bone loss, and tissue engineering. However, how
exactly geometry influences the behaviour of bone-forming cells remains
elusive. Geometry modulates cell populations collectively through the evolving
space available to the cells, but it may also modulate the individual
behaviours of cells. To factor out the collective influence of geometry and
gain access to the geometric regulation of individual cell behaviours, we
develop a mathematical model of the infilling of cortical bone pores and use it
with available experimental data on cortical infilling rates. Testing different
possible modes of geometric controls of individual cell behaviours consistent
with the experimental data, we find that efficient smoothing of irregular pores
only occurs when cell secretory rate is controlled by porosity rather than
curvature. This porosity control suggests the convergence of a large scale of
intercellular signalling to single bone-forming cells, consistent with that
provided by the osteocyte network in response to mechanical stimulus. After
validating the mathematical model with the histological record of a real
cortical pore infilling, we explore the infilling of a population of randomly
generated initial pore shapes. We find that amongst all the geometric
regulations considered, the collective influence of curvature on cell crowding
is a dominant factor for how fast cortical bone pores infill, and we suggest
that the irregularity of cement lines thereby explains some of the variability
in double labelling data as well as the overall speed of osteon infilling.Comment: 14 pages, 11 figures, Appendi
HST observations of the limb polarization of Titan
Titan is an excellent test case for detailed studies of the scattering
polarization from thick hazy atmospheres. We present the first limb
polarization measurements of Titan, which are compared as a test to our limb
polarization models. Previously unpublished imaging polarimetry from the HST
archive is presented which resolves the disk of Titan. We determine
flux-weighted averages of the limb polarization and radial limb polarization
profiles, and investigate the degradation and cancelation effects in the
polarization signal due to the limited spatial resolution of our observations.
Taking this into account we derive corrected values for the limb polarization
in Titan. The results are compared with limb polarization models, using
atmosphere and haze scattering parameters from the literature.
In the wavelength bands between 250 nm and 2000 nm a strong limb polarization
of about 2-7 % is detected with a position angle perpendicular to the limb. The
fractional polarization is highest around 1 micron. As a first approximation,
the polarization seems to be equally strong along the entire limb. The detected
polarization is compatible with expectations from previous polarimetric
observations taken with Voyager 2, Pioneer 11, and the Huygens probe.
Our results indicate that ground-based monitoring measurements of the
limb-polarization of Titan could be useful for investigating local haze
properties and the impact of short-term and seasonal variations of the hazy
atmosphere of Titan. Planets with hazy atmospheres similar to Titan are
particularly good candidates for detection with the polarimetric mode of the
upcoming planet finder instrument at the VLT. Therefore, a good knowledge of
the polarization properties of Titan is also important for the search and
investigation of extra-solar planets.Comment: 13 pages, 13 figures, accepted for publication in Astronomy &
Astrophysic
A van der Waals free energy in electrolytes revisited
A system of three electrolytes separated by two parallel planes is
considered. Each region is described by a dielectric constant and a Coulomb
fluid in the Debye-H\"uckel regime. In their book Dispersion Forces, Mahanty
and Ninham have given the van der Waals free energy of this system. We rederive
this free energy by a different method, using linear response theory and the
electrostatic Maxwell stress tensor for obtaining the dispersion force.Comment: 7 pages. PACS numbers updated. References update
A multiscale mechanobiological model of bone remodelling predicts site-specific bone loss in the femur during osteoporosis and mechanical disuse
We propose a multiscale mechanobiological model of bone remodelling to
investigate the site-specific evolution of bone volume fraction across the
midshaft of a femur. The model includes hormonal regulation and biochemical
coupling of bone cell populations, the influence of the microstructure on bone
turnover rate, and mechanical adaptation of the tissue. Both microscopic and
tissue-scale stress/strain states of the tissue are calculated from macroscopic
loads by a combination of beam theory and micromechanical homogenisation.
This model is applied to simulate the spatio-temporal evolution of a human
midshaft femur scan subjected to two deregulating circumstances: (i)
osteoporosis and (ii) mechanical disuse. Both simulated deregulations led to
endocortical bone loss, cortical wall thinning and expansion of the medullary
cavity, in accordance with experimental findings. Our model suggests that these
observations are attributable to a large extent to the influence of the
microstructure on bone turnover rate. Mechanical adaptation is found to help
preserve intracortical bone matrix near the periosteum. Moreover, it leads to
non-uniform cortical wall thickness due to the asymmetry of macroscopic loads
introduced by the bending moment. The effect of mechanical adaptation near the
endosteum can be greatly affected by whether the mechanical stimulus includes
stress concentration effects or not.Comment: 25 pages, 10 figure
Microscopic Origin of Universality in Casimir Forces
The microscopic mechanisms for universality of Casimir forces between macroscopic conductors are displayed in a model of classical charged fluids. The model consists of two slabs in empty space at distance d containing classical charged particles in thermal equilibrium (plasma, electrolyte). A direct computation of the average force per unit surface yields, at large distance, the usual form of the Casimir force in the classical limit (up to a factor 2 due to the fact that the model does not incorporate the magnetic part of the force). Universality originates from perfect screening sum rules obeyed by the microscopic charge correlations in conductors. If one of the slabs is replaced by a macroscopic dielectric medium, the result of Lifshitz theory for the force is retrieved. The techniques used are Mayer expansions and integral equations for charged fluid
- …