A Multiscale Theoretical Investigation of Electric Measurements in Living Bone

This paper presents a theoretical investigation of the multiphysical phenomena that govern cortical bone behaviour. Taking into account the piezoelectricity of the collagen–apatite matrix and the electrokinetics governing the interstitial fluid movement, we adopt a multiscale approach to derive a coupled poroelastic model of cortical tissue. Following how the phenomena propagate from the microscale to the tissue scale, we are able to determine the nature of macroscopically observed electric phenomena in bone.     

Fusion induced aggregation of model vesicles studied by dynamic and static light scattering

Membrane fusion is a key step in the virus mediated cell fusion. The vesicular dispersion serves as a model system to study the membrane fusion. We employed dynamic and static light scattering to study the fusion of phosphatidylcholine vesicles in the presence of model fusion peptide fragments from the hemagglutinin HA2 protein. The fusion-induced aggregation under the present experimental setup exhibited strong pH dependence, similar to the parental viral protein. Replacement of the glycine residue at the extreme amino terminus by glutamic acid (G1E) abolished fusion activity. The average molecular mass and diameter of vesicular dispersion obtained from static and dynamic light scattering measurements respectively at neutral and acidic pH showed about three fold increase in acidic solution containing wild type fusion peptide. The light scattering data are consistent with lipid mixing results. The present work demonstrates the utility of light scattering as a facile means to monitor the fusion process.     

Micro-Brillouin scattering measurements in mature and newly formed bone tissue surrounding an implant

The evolution of implant stability in bone tissue remains difficult to assess because remodeling phenomena at the bone-implant interface are still poorly understood. The characterization of the biomechanical properties of newly formed bone tissue in the vicinity of implants at the microscopic scale is of importance in order to better understand the osseointegration process. The objective of this study is to investigate the potentiality of micro-Brillouin scattering techniques to differentiate mature and newly formed bone elastic properties following a multimodality approach using histological analysis. Coin-shaped Ti-6Al-4V implants were placed in vivo at a distance of 200?μm from rabbit tibia leveled cortical bone surface, leading to an initially empty cavity of 200?μm×4.4?mm. After 7 weeks of implantation, the bone samples were removed, fixed, dehydrated, embedded in methyl methacrylate, and sliced into 190?μm thick sections. Ultrasonic velocity measurements were performed using a micro-Brillouin scattering device within regions of interest (ROIs) of 10?μm diameter. The ROIs were located in newly formed bone tissue (within the 200?μm gap) and in mature bone tissue (in the cortical layer of the bone sample). The same section was then stained for histological analysis of the mineral content of the bone sample. The mean values of the ultrasonic velocities were equal to 4.97×10(-3)?m/s in newly formed bone tissue and 5.31×10(-3)?m/s in mature bone. Analysis of variance (p=2.42×10(-4)) tests revealed significant differences between the two groups of measurements. The standard deviation of the velocities was significantly higher in newly formed bone than in mature bone. Histological observations allow to confirm the accurate locations of the velocity measurements and showed a lower degree of mineralization in newly formed bone than in the mature cortical bone. The higher ultrasonic velocity measured in newly formed bone tissue compared with mature bone might be explained by the higher mineral content in mature bone, which was confirmed by histology. The heterogeneity of biomechanical properties of newly formed bone at the micrometer scale may explain the higher standard deviation of velocity measurements in newly formed bone compared with mature bone. The results demonstrate the feasibility of micro-Brillouin scattering technique to investigate the elastic properties of newly formed bone tissue.     

A simplified model of hydrodynamics in airlift loop reactors

As a function of the gas throughput the following parameters were measured in an external loop reactor with a riser diameter of 0.6 m and a gassed liquid height of 8.6 m: integral and local values of gas hold-up; liquid velocities; mixing times and axial dispersion coefficients of the liquid phase. The height of the reactor could be altered by reconstruction. Measurements were also carried out with lower heights than 8.6 m. Besides pure water, aqueous solutions of coalescing, non-coalescing and viscosity-increasing substances were used as model systems. With the results a general relationship between superficial gas velocity, gas hold-up and liquid velocity was established. This hydrodynamic model uses the relative velocity between gas and liquid phase as the fundamental parameter. The generally valid model consists of one term for the homogeneous and of two additional terms for the heterogeneous flow regime.     

Partitioning particulate scattering and absorption into contributions of phytoplankton and non-algal particles in winter in Lake Taihu (China)

Light scattering, backscattering, and absorption coefficients of particles were observed at 62 locations in Lake Taihu (China) in November 2008. A method using a priori knowledge and the measured data was proposed to partition particulate scattering and absorption into contributions of phytoplankton and non-algal particles. The results showed that phytoplankton weakly contributed to the particulate scattering and backscattering with the mean b _ph/b _p values usually below 10% and b _bph/b _bt values of 0.3–3.9% in the whole visible light spectrum, and an approximate relationship of b _bt ≈ b _bp ≈ b _bnap was regarded as reasonable in Lake Taihu. In contrast with scattering and backscattering, phytoplankton made more contributions to the particulate absorption with the mean a _ph/a _p values varying in a wide range of about 20–70%. Both the scattering and absorption spectra of non-algal particles can be modeled well by corresponding methods. A power function model was used to simulate the scattering spectra, which presented high predictive accuracies with MAPE values usually below 5% and RMSE values below 1.5 m⁻¹, while the spectral absorption model also performed well with mean S _nap being 0.0052 nm⁻¹ (standard deviation, SD = 0.0010 nm⁻¹). As to the phytoplankton absorption, a quadratic function model used was considered to have a good performance with corresponding parameters being supported at each wavelength in the spectral range of 400–700 nm. Additionally, two basic bio-optical parameters were determined, that is, b _nap^*(550) = 0.604 m² g⁻¹ and a _ph^*(675) = 0.0288 m² mg⁻¹. Overall, these results obtained in the present study supply us with new knowledge about optical properties of suspended particulates in an inland and highly turbid lake (Lake Taihu), which are beneficial to the development of analytical models of water color remote sensing.     

The Lagrangian stochastic model for estimating footprint and water vapor fluxes over inhomogeneous surfaces

This study investigated a two-dimensional Lagrangian stochastic dispersion model for estimating water vapor fluxes and footprint over homogeneous and inhomogeneous surfaces. Over the homogeneous surface, particle trajectories were computed from a 2-D Lagrangian model forced by Eulerian velocity statistics determined by Monin–Obukhov similarity theory (MOST). For an inhomogeneous surface, the velocity and atmospheric stability profiles were computed using a second-order Eulerian closure model, and these local profiles were then used to drive the Lagrangian model. The model simulations were compared with water vapor flux measurements carried out above an irrigated bare soil site and an irrigated potato site. The inhomogeneity involved a step change in surface roughness, humidity, and temperature. Good agreement between eddy-correlation-measured and Lagrangian-model-predicted water vapor fluxes was found for both sites. Hence, this analysis demonstrates the practical utility of second-order closure models in conjunction with Lagrangian analysis to estimate the scalar footprint in planar inhomogeneous flows.     

Multiscale methodology for bone remodelling simulation using coupled finite element and neural network computation

The aim of this paper is to develop a multiscale hierarchical hybrid model based on finite element analysis and neural network computation to link mesoscopic scale (trabecular network level) and macroscopic (whole bone level) to simulate the process of bone remodelling. As whole bone simulation, including the 3D reconstruction of trabecular level bone, is time consuming, finite element calculation is only performed at the macroscopic level, whilst trained neural networks are employed as numerical substitutes for the finite element code needed for the mesoscale prediction. The bone mechanical properties are updated at the macroscopic scale depending on the morphological and mechanical adaptation at the mesoscopic scale computed by the trained neural network. The digital image-based modelling technique using μ-CT and voxel finite element analysis is used to capture volume elements representativeof 2 mm³ at the mesoscale level of the femoral head. The input data for the artificial neural network are a set of bone material parameters, boundary conditions and the applied stress. The output data are the updated bone properties and some trabecular bone factors. The current approach is the first model, to our knowledge, that incorporates both finite element analysis and neural network computation to rapidly simulate multilevel bone adaptation.     

Multiscale modeling of skeletal muscle properties and experimental validations in isometric conditions

In this article, we describe an approach to model the electromechanical behavior of the skeletal muscle based on the Huxley formulation. We propose a model that complies with a well established macroscopic behavior of striated muscles where force-length, force–velocity, and Mirsky–Parmley properties are taken into account. These properties are introduced at the microscopic scale and related to a tentative explanation of the phenomena. The method used integrates behavior ranging from the microscopic to the macroscopic scale, and allows the computation of the dynamics of the output force and stiffness controlled by EMG or stimulation parameters. The model can thus be used to simulate and carry out research to develop control strategies using electrical stimulation in the context of rehabilitation. Finally, through animal experiments, we estimated model parameters using a Sigma Point Kalman Filtering technique and dedicated experimental protocols in isometric conditions and demonstrated that the model can accurately simulate individual variations and thus take into account subject dependent behavior.     

Culture and behavior of osteoblastic cells isolated from normal trabecular bone surfaces

Summary We report the characterization of human osteoblastic cells that were derived from the surface of trabecular bone fragments. After removal of bone marrow cells, the bone lining osteoblastic cells lining the bone surface were obtained by migration and proliferation from the trabecular surface onto a nylon mesh. The isolated population proliferated in culture and exhibited osteoblastic phenotype. Cultured cells show a regular arrangment in vitro and exhibited multiple interconnecting junctions on scanning electron microscopic examination. Immunocytochemical staining showed that the cells produced almost exclusively type I collagen. Bone-surface-derived cells responded to 1–34 human parathyroid hormone by increasing intracellular cyclic AMP. Cell cultures exhibited high alkaline phosphatase activity, which was unaffected by 1,25 (OH)₂ vitamin D. Untreated cells produced high levels of osteocalcin, a bone-specific protein, and they responded to 1,25(OH) vitamin D by increasing osteocalcin synthesis in a dose-dependent manner. Although cells cultured for up to 5 mo. still produced osteocalcin, the response to 1,25(OH)₂D decreased after multiple passages. This study shows that the bone cell populations isolated from trabecular bone surface are enriched in osteoblast precursors and mature osteoblstic cells.     

Kappa-casein micelles: structure, interaction and gelling studied by small-angle neutron scattering

Small-angle neutron scattering (SANS) measurements on dilute and concentrated dispersions of kappa-casein micelles in a buffer at pH = 6.7 were made using the D11 diffractometer in Grenoble. Results indicate that the micelles have a dense core with a fluffy outer layer. This outer layer appears to give rise to a steeply repulsive interaction on contact. In fact, the hard-sphere model best fits the measured scattering intensities. Adding chymosin to the dispersion initiated a fractal flocculation of the micelles and consecutively a coalescence of the micelles. This unexpected second process resembled that of spinodal demixing. The dispersion phase thus separates into a water and a protein phase on a time scale of hours. The observed phenomona contribute to the understanding of the cheese-making process.     

The specific inherent optical properties of three sub-tropical and tropical water reservoirs in Queensland, Australia

The underwater light climate, which is a major influence on the ecology of aquatic systems, is affected by the absorption and scattering processes that take place within the water column. Knowledge of the specific inherent optical properties (SIOPs) of water quality parameters and their spatial variation is essential for the modelling of underwater light fields and remote sensing applications. We measured the SIOPs and water quality parameter concentrations of three large inland water impoundments in Queensland, Australia. The measurements ranged from 0.9 to 42.7 μg l⁻¹ for chlorophyll a concentration, 0.9–170.4 mg l⁻¹ for tripton concentration, 0.36–1.59 m⁻¹ for a _CDOM(440) and 0.15–2.5 m for Secchi depth. The SIOP measurements showed that there is sufficient intra-impoundment variation in the specific absorption and specific scattering of phytoplankton and tripton to require a well distributed network of measurement stations to fully characterise the SIOPs of the optical water quality parameters. While significantly different SIOP sets were measured for each of the study sites the measurements were consistent with published values in other inland waters. The multiple measurement stations were allocated into optical domains as a necessary step to parameterise a semi-analytical inversion remote sensing algorithm. This article also addresses the paucity of published global inland water SIOP sets by contributing Australian SIOP sets to allow international and national comparison.     

A calcium-based phantom bursting model for pancreatic islets

Insulin-secreting β-cells, located within the pancreatic islets of Langerhans, are excitable cells that produce regular bursts of action potentials when stimulated by glucose. This system has been the focus of mathematical investigation for two decades, spawning an array of mathematical models. Recently, a new class of models has been introduced called ‘phantom bursters’ [Bertram et al. (2000) Biophys. J. 79, 2880–2892], which accounts for the wide range of burst frequencies exhibited by islets via the interaction of more than one slow process. Here, we describe one implementation of the phantom bursting mechanism in which intracellular Ca²⁺ controls the oscillations through both direct and indirect negative feedback pathways. We show how the model dynamics can be understood through an extension of the fast/slow analysis that is typically employed for bursting oscillations. From this perspective, the model makes use of multiple degrees of freedom to generate the full range of bursting oscillations exhibited by β-cells. The model also accounts for a wide range of experimental phenomena, including the ubiquitous triphasic response to the step elevation of glucose and responses to perturbations of internal Ca²⁺ stores. Although it is not presently a complete model of all β-cell properties, it demonstrates the design principles that we anticipate will underlie future progress in β-cell modeling.     

Effects of arm and leg loading on sprint performance

The effects of loading on sprint kinematics were examined in 24 male students. The moment of inertia of either the arms or legs was increased by up to 50% of their unloaded values and the time for distances of 0.5–15 m and 15–30 m from a sprint start was measured. An increase in leg loading was associated with a gradual decrease in velocity of both sprint phases, while the change associated with arm loading was modest and significant only in the second phase. The decrease in sprint velocity was predominantly due to a reduction in stride rate, while the stride length remained almost unchanged. It was concluded that leg loading affected sprint velocity more than arm loading, and also that the velocity was reduced due to a decrease in the stride rate rather than in the stride length. Accepted: 10 November 1997     

Comparing PAR transmission models for forest understorey vegetation

Question: Do Beer's Law models, multi‐layer scattering models, and a semi‐empirical model for predicting PAR transmission through understorey vegetation give comparable results? Do different driving variables (LAI, PLAI and percentage cover) give different results? How do the models vary when fit with species‐specific, species‐average and the ‘default’ parameters recommended in the literature? Location: Upland boreal forests of western North America. Methods: In calibration and validation plots, PAR transmission was measured, total cover visually estimated, and leaf dispersion, PLAI and cover estimated for each species using a point‐frame. Leaf inclination was measured by clinometer. PAR transmission was modelled using empirically‐fit Beer's Law models, a semi‐empirical model based on hemispherical gap fraction and first‐order scattering, and a multi‐layer model allowing multiple scattering. All models were modified to use leaf area index (LAI), vertically projected leaf area index (PLAI), or percentage cover data. Results: The empirical Beer's Law models had the least bias and best precision in predicting PAR transmission. The semi‐empirical model also had little bias and good precision, since the scattering coefficient compensated for problems in the estimation of gap fraction. The multi‐layer model consistently underestimated transmission. There was little benefit in accounting for species separately. LAI and PLAI‐based models were the most precise, but percentage cover models also provided reasonable predictions of PAR transmission. Conclusions: PAR transmission through forest understories can be simply modelled with Beer's Law using one empirical coefficient representing the average understorey species. More complex scattering models are less effective, likely because they fail to account for the complexity of the dispersion of this vegetation layer and its effect on radiation scattering.     

A two-dimensional many-body system with competing interactions as a model for segregation of photosystems in thylakoids of green plants

 We address the segregation of photosystems I (PSI) and II (PSII) in thylakoid membranes by means of a molecular dynamics method. We assume a two-dimensional (in-plane) problem with PSI and PSII being represented by particles with different values of negative charge. The pair interactions between particles include a screened Coulomb repulsive part and am exponentially decaying attractive part. Our modeling results suggest that the system may have a complicated phase behavior, including a quasi-crystalline phase at low ionic screening, a disordered phase and, in addition, a possible “clotting” agglomerate phase at high screening where the photosystems tend to clot together. The relevance of the observed phenomena to the stacking of thylakoid membranes is discussed. Received: 14 October 1999 / Revised version: 30 March 2000 / Accepted: 30 March 2000     

Protein interactions in solution characterized by light and neutron scattering: comparison of lysozyme and chymotrypsinogen.

The effects of pH and electrolyte concentration on protein-protein interactions in lysozyme and chymotrypsinogen solutions were investigated by static light scattering (SLS) and small-angle neutron scattering (SANS). Very good agreement between the values of the virial coefficients measured by SLS and SANS was obtained without use of adjustable parameters. At low electrolyte concentration, the virial coefficients depend strongly on pH and change from positive to negative as the pH increases. All coefficients at high salt concentration are slightly negative and depend weakly on pH. For lysozyme, the coefficients always decrease with increasing electrolyte concentration. However, for chymotrypsinogen there is a cross-over point around pH 5.2, above which the virial coefficients decrease with increasing ionic strength, indicating the presence of attractive electrostatic interactions. The data are in agreement with Derjaguin-Landau-Verwey-Overbeek (DLVO)-type modeling, accounting for the repulsive and attractive electrostatic, van der Waals, and excluded volume interactions of equivalent colloid spheres. This model, however, is unable to resolve the complex short-ranged orientational interactions. The results of protein precipitation and crystallization experiments are in qualitative correlation with the patterns of the virial coefficients and demonstrate that interaction mapping could help outline new crystallization regions.     

Force–velocity relationship for multiple kinesin motors pulling a magnetic bead

Although the velocity of single kinesin motors against an opposing force F of 0–10 pN is well known, the behavior of multiple kinesin motors working to overcome a larger load is still poorly understood. We have carried out gliding assays in which 3–7 Drosophila kinesin-1 motors moved a microtubule at 200–700 μm/s against a 0–31 pN load at saturating [ATP]. The load F was generated by applying a spatially uniform magnetic field gradient to a superparamagnetic bead attached to the (+) end of the microtubule. When F was scaled by the average number of motors 〈n〉, the force–velocity relationship for multiple motors was similar to the force–velocity relationship for a single motor, supporting a minimal load-sharing model. The velocity distribution at low load has a single mode consistent with rapid fluctuations of n. However, against a load of 2.5–4.7 pN/motor, additional modes appeared at lower velocity. These observations support the Klumpp–Lipowsky model of multimotor transport [Proc Natl Acad Sci USA 102. 17284–17289 (2005)].     

Infrared spectroscopic assessment of the inflammation-mediated osteoporosis (IMO) model applied to rabbit bone

A model of osteoporosis based on induced inflammation (IMO) was applied on rabbit bones. The structural heterogeneity and molecular complexity of bone significantly affect bone mechanical properties. A tool like Fourier transform infrared spectroscopy, able to analyze both the inorganic and organic phase simultaneously, could provide compositional information regarding cortical and trabecular sections under normal and osteoporotic conditions. In this study, we assessed the mineral/matrix ratio, carbonate and phosphate content and labile (i.e., non-apatitic) species contribution to bone mineral and collagen cross-linking patterns. Clear differences were observed between cortical and trabecular bone regarding mineral and carbonate content. Induced inflammation lowers the mineral/matrix ratio and increases the overall carbonate accumulation. Elevated concentrations of labile species were detected in osteoporotic samples, especially in the trabecular sections. Collagen cross-linking patterns were indirectly observed through the 1660/1690 cm^− 1 ratio in the amide I band and a positive correlation was found with the mineralization index. Principal component analysis (PCA) applied to female samples successfully clustered trabecular and osteoporotic cases. The important role played by the phosphate ions was confirmed by corresponding loadings plots. The results suggest that the application of the IMO model to rabbit bones effectively alters bone remodeling and forms an osteoporotic bone matrix with a dissimilar composition compared to the normal one.     

Trabecular bone adaptation with an orthotropic material model.

Most bone adaptation algorithms, that attempt to explain the connection between bone morphology and loads, assume that bone is effectively isotropic. An isotropic material model can explain the bone density distribution, but not the structure and pattern of trabecular bone, which clearly has a mechanical significance. In this paper, an orthotropic material model is utilized to predict the proximal femur trabecular structure. Two hypotheses are combined to determine the local orientation and material properties of each element in the model. First, it is suggested that trabecular directions, which correspond to the orthotropic material axes, are determined locally by the maximal principal stress directions due to the multiple load cases (MLC) the femur is subject to. The second hypothesis is that material properties in each material direction can be determined using directional stimuli, thus extending existing adaptation algorithms to include directionality. An algorithm is utilized, where each iteration comprises of two stages. First, material axes are rotated to the direction of the largest principal stress that occurs from a multiple load scheme applied to the proximal femur. Next, material properties are modified in each material direction, according to a directional stimulus. Results show that local material directions correspond with known trabecular patterns, reproducing all main groups of trabeculae very well. The local directional stiffnesses, degree of anisotropy and density distribution are shown to conform to real femur morphology.     

Comparison of acoustic characteristics predicted by Biot's theory and the modified Biot-Attenborough model in cancellous bone

Biot's theory and the modified Biot-Attenborough (MBA) model are applied to predict the dependences of acoustic characteristics on frequency and on porosity in cancellous bone. The phase velocities and the attenuation coefficients predicted by both theories are compared with the experimental data of bovine cancellous bone specimens published in the literature. Biot's theory successfully predicts the dependences of the phase velocity on frequency and on porosity in cancellous bone, whereas a significant discrepancy is observed between the predicted and the measured attenuation coefficients. The MBA model agrees well with the frequency and the porosity dependences of the phase velocity and the attenuation coefficient experimentally measured in bovine bones. Although the MBA model relies on phenomenological parameters derived from the experimental data, its approach to cancellous bone can be usefully employed in the field of clinical ultrasonic bone assessment.