Effects of collagen deposition on passive and active mechanical properties of large pulmonary arteries in hypoxic pulmonary hypertension

Proximal pulmonary artery (PA) stiffening is a strong predictor of mortality in pulmonary hypertension. Collagen accumulation is mainly responsible for PA stiffening in hypoxia-induced pulmonary hypertension (HPH) in mouse models. We hypothesized that collagen cross-linking and the type I isoform are the main determinants of large PA mechanical changes during HPH, which we tested by exposing mice that resist type I collagen degradation (Col1a1 $^\mathrm{R/R})$ and littermate controls (Col1a1 $^{+/+})$ to hypoxia for 10 days with or without $\beta $ -aminopropionitrile (BAPN) treatment to prevent cross-link formation. Static and dynamic mechanical tests were performed on isolated PAs with smooth muscle cells (SMC) in passive and active states. Percentages of type I and III collagen were quantified by histology; total collagen content and cross-linking were measured biochemically. In the SMC passive state, for both genotypes, hypoxia tended to increase PA stiffness and damping capacity, and BAPN treatment limited these increases. These changes were correlated with collagen cross-linking ( $p<0.05$ ). In the SMC active state, hypoxia increased PA dynamic stiffness and BAPN had no effect in Col1a1 $^{+/+}$ mice ( $p<0.05$ ). PA stiffness did not change in Col1a1 $^\mathrm{R/R}$ mice. Similarly, damping capacity did not change for either genotype. Type I collagen accumulated more in Col1a1 $^{+/+}$ mice, whereas type III collagen increased more in Col1a1 $^\mathrm{R/R}$ mice during HPH. In summary, PA passive mechanical properties (both static and dynamic) are related to collagen cross-linking. Type I collagen turnover is critical to large PA remodeling during HPH when collagen metabolism is not mutated and type III collagen may serve as a reserve.     

The average local ionization energy as a tool for identifying reactive sites on defect-containing model graphene systems

In a continuing effort to further explore the use of the average local ionization energy $ \overline{\mathrm{I}}\left( \mathbf{r} \right) $ as a computational tool, we have investigated how well $ \overline{\mathrm{I}}\left( \mathbf{r} \right) $ computed on molecular surfaces serves as a predictive tool for identifying the sites of the more reactive electrons in several nonplanar defect-containing model graphene systems, each containing one or more pentagons. They include corannulene (C₂₀H₁₀), two inverse Stone-Thrower-Wales defect-containing structures C₂₆H₁₂ and C₄₂H₁₆, and a nanotube cap model C₂₂H₆, whose end is formed by three fused pentagons. Coronene (C₂₄H₁₂) has been included as a reference planar defect-free graphene model. We have optimized the structures of these systems as well as several monohydrogenated derivatives at the B3PW91/6-31G* level, and have computed their $ \overline{\mathrm{I}}\left( \mathbf{r} \right) $ on molecular surfaces corresponding to the 0.001 au, 0.003 au and 0.005 au contours of the electronic density. We find that (1) the convex sides of the interior carbons of the nonplanar models are more reactive than the concave sides, and (2) the magnitudes of the lowest $ \overline{\mathrm{I}}\left( \mathbf{r} \right) $ surface minima (the $ {{\overline{\mathrm{I}}}_{{\mathrm{S}\text{,}\min }}} $ ) correlate well with the interaction energies for hydrogenation at these sites. These $ {{\overline{\mathrm{I}}}_{{\mathrm{S}\text{,}\min }}} $ values decrease in magnitude as the nonplanarity of the site increases, consistent with earlier studies. A practical benefit of the use of $ \overline{\mathrm{I}}\left( \mathbf{r} \right) $ is that a single calculation suffices to characterize the numerous sites on a large molecular system, such as graphene and defect-containing graphene models.

Sensory uncertainty and stick balancing at the fingertip

The effects of sensory input uncertainty, $\varepsilon $ , on the stability of time-delayed human motor control are investigated by calculating the minimum stick length, $\ell _\mathrm{crit}$ , that can be stabilized in the inverted position for a given time delay, $\tau $ . Five control strategies often discussed in the context of human motor control are examined: three time-invariant controllers [proportional–derivative, proportional–derivative–acceleration (PDA), model predictive (MP) controllers] and two time-varying controllers [act-and-wait (AAW) and intermittent predictive controllers]. The uncertainties of the sensory input are modeled as a multiplicative term in the system output. Estimates based on the variability of neural spike trains and neural population responses suggest that $\varepsilon \approx 7$ –13 %. It is found that for this range of uncertainty, a tapped delay-line type of MP controller is the most robust controller. In particular, this controller can stabilize inverted sticks of the length balanced by expert stick balancers (0.25–0.5 m when $\tau \approx 0.08$  s). However, a PDA controller becomes more effective when $\varepsilon > 15\,\%$ . A comparison between $\ell _\mathrm{crit}$ for human stick balancing at the fingertip and balancing on the rubberized surface of a table tennis racket suggest that friction likely plays a role in balance control. Measurements of $\ell _\mathrm{crit},\,\tau $ , and a variability of the fluctuations in the vertical displacement angle, an estimate of $\varepsilon $ , may make it possible to study the changes in control strategy as motor skill develops.     

Integrating qPLM and biomechanical test data with an anisotropic fiber distribution model and predictions of TGF-\upbeta 1 and IGF-1 regulation of articular cartilage fiber modulus

A continuum mixture model with distinct collagen (COL) and glycosaminoglycan elastic constituents was developed for the solid matrix of immature bovine articular cartilage. A continuous COL fiber volume fraction distribution function and a true COL fiber elastic modulus ( $E^\mathrm{f})$ were used. Quantitative polarized light microscopy (qPLM) methods were developed to account for the relatively high cell density of immature articular cartilage and used with a novel algorithm that constructs a 3D distribution function from 2D qPLM data. For specimens untreated and cultured in vitro, most model parameters were specified from qPLM analysis and biochemical assay results; consequently, $E^\mathrm{f}$ was predicted using an optimization to measured mechanical properties in uniaxial tension and unconfined compression. Analysis of qPLM data revealed a highly anisotropic fiber distribution, with principal fiber orientation parallel to the surface layer. For untreated samples, predicted $E^\mathrm{f}$ values were 175 and 422 MPa for superficial (S) and middle (M) zone layers, respectively. TGF- $\upbeta $ 1 treatment was predicted to increase and decrease $E^\mathrm{f}$ values for the S and M layers to 281 and 309 MPa, respectively. IGF-1 treatment was predicted to decrease $E^\mathrm{f}$ values for the S and M layers to 22 and 26 MPa, respectively. A novel finding was that distinct native depth-dependent fiber modulus properties were modulated to nearly homogeneous values by TGF- $\upbeta $ 1 and IGF-1 treatments, with modulated values strongly dependent on treatment.     

Topological classification and enumeration of RNA structures by genus

To an RNA pseudoknot structure is naturally associated a topological surface, which has its associated genus, and structures can thus be classified by the genus. Based on earlier work of Harer–Zagier, we compute the generating function $\mathbf{D}_{g,\sigma }(z)=\sum _{n}\mathbf{d}_{g,\sigma }(n)z^n$ for the number $\mathbf{d}_{g,\sigma }(n)$ of those structures of fixed genus $g$ and minimum stack size $\sigma $ with $n$ nucleotides so that no two consecutive nucleotides are basepaired and show that $\mathbf{D}_{g,\sigma }(z)$ is algebraic. In particular, we prove that $\mathbf{d}_{g,2}(n)\sim k_g\,n^{3(g-\frac{1}{2})} \gamma _2^n$ , where $\gamma _2\approx 1.9685$ . Thus, for stack size at least two, the genus only enters through the sub-exponential factor, and the slow growth rate compared to the number of RNA molecules implies the existence of neutral networks of distinct molecules with the same structure of any genus. Certain RNA structures called shapes are shown to be in natural one-to-one correspondence with the cells in the Penner–Strebel decomposition of Riemann’s moduli space of a surface of genus $g$ with one boundary component, thus providing a link between RNA enumerative problems and the geometry of Riemann’s moduli space.     

Pareto genealogies arising from a Poisson branching evolution model with selection

We study a class of coalescents derived from a sampling procedure out of $N$ i.i.d. Pareto $\left( \alpha \right) $ random variables, normalized by their sum, including $\beta $ –size-biasing on total length effects ( $\beta <\alpha $ ). Depending on the range of $\alpha ,$ we derive the large $N$ limit coalescents structure, leading either to a discrete-time Poisson-Dirichlet $ \left(\alpha ,-\beta \right) \Xi -$ coalescent ( $\alpha \in \left[ 0,1\right) $ ), or to a family of continuous-time Beta $\left( 2-\alpha ,\alpha -\beta \right) \Lambda -$ coalescents ( $\alpha \in \left[ 1,2\right) $ ), or to the Kingman coalescent ( $\alpha \ge 2$ ). We indicate that this class of coalescent processes (and their scaling limits) may be viewed as the genealogical processes of some forward in time evolving branching population models including selection effects. In such constant-size population models, the reproduction step, which is based on a fitness-dependent Poisson Point Process with scaling power-law $\left( \alpha \right) $ intensity, is coupled to a selection step consisting of sorting out the $N$ fittest individuals issued from the reproduction step.     

Modeling analysis of the lipid bilayer–cytoskeleton coupling in erythrocyte membrane

Studies of thermal fluctuations in discocytes, echinocytes, and spherocytes suggest that the coupling between lipid bilayer and cytoskeleton can affect viscoelastic behavior of single erythrocyte membranes. To test this hypothesis, we developed a 3D constitutive model describing viscoelastic behavior of erythrocyte membranes, at long relaxation times \(t \in [0.20\,\mathrm {s}, 1.05\,\mathrm {s}]\) and short relaxation times \(t \in [0.03\,\mathrm {s}, 0.20\,\mathrm {s}]\) . The model was constructed using combination of spring and spring pot rheological elements arranged in parallel. The rearrangement of cytoskeleton induced by changing the bending state of lipid bilayer was described by a modified Eyring model. The model predictions point to an anomalous nature of energy dissipation and an ordered harmonic nature of the coupling mechanism described by a series of fractional derivatives of the order n \(\alpha \) (where \( n \in [- 1, 2]\) ). As a result, the stress generated within the lipid bilayer is related to the rate of change of the irreversible stress within the cytoskeleton.     

When does pathogen evolution maximize the basic reproductive number in well-mixed host–pathogen systems?

Pathogen evolution towards the largest basic reproductive number, $\mathcal R _0$ , has been observed in many theoretical models, but this conclusion does not hold universally. Previous studies of host–pathogen systems have defined general conditions under which $\mathcal R _0$ maximization occurs in terms of $\mathcal R _0$ itself. However, it is unclear what constraints these conditions impose on the functional forms of pathogen related processes (e.g. transmission, recover, or mortality) and how those constraints relate to the characteristics of natural systems. Here we focus on well-mixed SIR-type host–pathogen systems and, via a synthesis of results from the literature, we present a set of sufficient mathematical conditions under which evolution maximizes $\mathcal R _0$ . Our conditions are in terms of the functional responses of the system and yield three general biological constraints on when $\mathcal R _0$ maximization will occur. First, there are no genotype-by-environment interactions. Second, the pathogen utilizes a single transmission pathway (i.e. either horizontal, vertical, or vector transmission). Third, when mortality is density dependent: (i) there is a single infectious class that individuals cannot recover from, (ii) mortality in the infectious class is entirely density dependent, and (iii) the rates of recovery, infection progression, and mortality in the exposed classes are independent of the pathogen trait. We discuss how this approach identifies the biological mechanisms that increase the dimension of the environmental feedback and prevent $\mathcal R _0$ maximization.     

Estimation of viscosity from passage time of liquids flowing through a microchannel array

Recently, a microchannel flow analyzer (MC-FAN) has been used to study the flow properties of blood. However, the correlation between blood passage time measured by use of the MC-FAN and hemorheology has not been clarified. In this study, a simple model is proposed for estimation of liquid viscosity from the passage time t _p of liquids. The t _p data for physiological saline were well represented by the model. According to the model, the viscosity of Newtonian fluids was estimated reasonably well from the t _p data. For blood samples, although the viscosity $ \eta_{\text{mc}} $ estimated from t _p was shown to be smaller than the viscosity $ \eta_{{450{\text{s}}^{ - 1} }} $ measured by use of a rotatory viscometer at a shear rate of 450 s^?1, $ \eta_{\text{mc}} $ was correlated with $ \eta_{{450{\text{s}}^{ - 1} }} $ . An empirical equation for estimation of $ \eta_{{450{\text{s}}^{ - 1} }} $ from $ \eta_{\text{mc}} $ of blood samples is proposed.     

A thermomechanical framework for reconciling the effects of ultraviolet radiation exposure time and wavelength on connective tissue elasticity

Augmentation of the mechanical properties of connective tissue using ultraviolet (UV) radiation—by targeting collagen cross-linking in the tissue at predetermined UV exposure time \((t)\) and wavelength \((\lambda )\) —has been proposed as a therapeutic method for supporting the treatment for structural-related injuries and pathologies. However, the effects of \(\lambda \) and \(t\) on the tissue elasticity, namely elastic modulus \((E)\) and modulus of resilience \((u_\mathrm{Y})\) , are not entirely clear. We present a thermomechanical framework to reconcile the \(t\) - and \(\lambda \) -related effects on \(E\) and \(u_\mathrm{Y}\) . The framework addresses (1) an energy transfer model to describe the dependence of the absorbed UV photon energy, \(\xi \) , per unit mass of the tissue on \(t\) and \(\lambda \) , (2) an intervening thermodynamic shear-related parameter, \(G\) , to quantify the extent of UV-induced cross-linking in the tissue, (3) a threshold model for the \(G\) versus \(\xi \) relationship, characterized by   \(t_\mathrm{C}\) —the critical \(t\) underpinning the association of \(\xi \) with \(G\) —and (4) the role of \(G\) in the tissue elasticity. We hypothesized that \(G\) regulates \(E\) (UV-stiffening hypothesis) and \(u_\mathrm{Y}\) (UV-resilience hypothesis). The framework was evaluated with the support from data derived from tensile testing on isolated ligament fascicles, treated with two levels of \(\lambda \) (365 and 254 nm) and three levels of \(t\) (15, 30 and 60 min). Predictions from the energy transfer model corroborated the findings from a two-factor analysis of variance of the effects of \(t\) and \(\lambda \) treatments. Student’s t test revealed positive change in \(E\) and \(u_\mathrm{Y}\) with increases in \(G\) —the findings lend support to the hypotheses, implicating the implicit dependence of UV-induced cross-links on \(t\) and \(\lambda \) for directing tissue stiffness and resilience. From a practical perspective, the study is a step in the direction to establish a UV irradiation treatment protocol for effective control of exogenous cross-linking in connective tissues.     

Do calcium buffers always slow down the propagation of calcium waves?

Calcium buffers are large proteins that act as binding sites for free cytosolic calcium. Since a large fraction of cytosolic calcium is bound to calcium buffers, calcium waves are widely observed under the condition that free cytosolic calcium is heavily buffered. In addition, all physiological buffered excitable systems contain multiple buffers with different affinities. It is thus important to understand the properties of waves in excitable systems with the inclusion of buffers. There is an ongoing controversy about whether or not the addition of calcium buffers into the system always slows down the propagation of calcium waves. To solve this controversy, we incorporate the buffering effect into the generic excitable system, the FitzHugh–Nagumo model, to get the buffered FitzHugh–Nagumo model, and then to study the effect of the added buffer with large diffusivity on traveling waves of such a model in one spatial dimension. We can find a critical dissociation constant ( $K=K(a)$ ) characterized by system excitability parameter $a$ such that calcium buffers can be classified into two types: weak buffers ( $K\in (K(a),\infty )$ ) and strong buffers ( $K\in (0,K(a))$ ). We analytically show that the addition of weak buffers or strong buffers but with its total concentration $b_0^1$ below some critical total concentration $b_{0,c}^1$ into the system can generate a traveling wave of the resulting system which propagates faster than that of the origin system, provided that the diffusivity $D_1$ of the added buffers is sufficiently large. Further, the magnitude of the wave speed of traveling waves of the resulting system is proportional to $\sqrt{D_1}$ as $D_1\rightarrow \infty $ . In contrast, the addition of strong buffers with the total concentration $b_0^1>b_{0,c}^1$ into the system may not be able to support the formation of a biologically acceptable wave provided that the diffusivity $D_1$ of the added buffers is sufficiently large.     

Obtain Quadruple Intense Plasmonic Resonances from Multilayered Gold Nanoshells by Silver Coating: Application in Multiplex Sensing

Four intense and separate localized surface plasmon resonance (LSPR) absorption peaks have been obtained in the gold-dielectric–gold–silver multilayer nanoshells. The silver coating on the gold shell results in a new LSPR peak at about 400 nm corresponding to the $ {{\left| {\omega_{+}^{-}} \right\rangle}_{Ag }} $ mode. The intense local electric field concentrated in the silver shell at the wavelength of 400 nm indicates that this new plasmonic band is coming from the symmetric coupling between the antibonding silver shell plasmon mode and the inner sphere plasmon. Increasing the silver shell thickness also leads to the intensity increasing of the $ {{\left| {\omega_{+}^{-}} \right\rangle}_{Au }} $ mode and blue shift of $ \left| {\omega_{-}^{+}} \right\rangle $ and $ \left| {\omega_{-}^{-}} \right\rangle $ modes. Therefore, quadruple intense plasmonic resonances in the visible region could be achieved in gold-dielectric–gold–silver multilayer nanoshells by tuning the geometrical parameters. And the quadruple intense plasmonic resonances in the visible region provide well potential for multiplex biosensing based on LSPR.     

Towards a conceptualization of ETL and physical storage of semantic data warehouses as a service

The data warehouse technology has become the incontestable tool for businesses and organizations to make strategic decisions to ensure their competitively. The construction of a data warehouse ( $\mathcal{D}\mathcal{W}$ ) passes by selecting relevant information sources, extracting relevant data and loading them into the $\mathcal{D}\mathcal{W}$ . These processes require a precise expertise from designers related to logical and physical implementations of information sources, which is not usually an easy task. The diversity and heterogeneity of information sources makes the construction process of the $\mathcal{D}\mathcal{W}$ complex and time consuming. Domain ontologies have been proposed to reduce heterogeneity between sources, platforms, services, etc. They resolve syntax and semantic conflicts. The phenomenon of adopting domain ontologies by organizations creates a new type of databases, called semantic databases ( $\mathcal{S}\mathcal{D}\mathcal{B}$ ). As a consequence, they become a candidate for building the semantic $\mathcal{D}\mathcal{W}$ ( $\mathcal{S}\mathcal{D}\mathcal{W}$ ). To handle the diversity of information sources and hide the implementations aspects of sources, proposing a generic framework for constructing $\mathcal{D}\mathcal{W}$ becomes a necessity. In this paper, we first proposed an ontology-based approach for designing $\mathcal{S}\mathcal {D}\mathcal{B}$ . Secondly, ETL phases are defined at ontological level to hide the implementation details. Thirdly, a storage service for ontologies and its associated data is given. Finally, our proposal is validated through a case study and a tool.     

Head impact accelerations for brain strain-related responses in contact sports: a model-based investigation

Both linear \((\mathbf{a}_{\mathrm{lin}})\) and rotational \((\mathbf{a}_{\mathrm{rot}} )\) accelerations contribute to head impacts on the field in contact sports; however, they are often isolated in injury studies. It is critical to evaluate the feasibility of estimating brain responses using isolated instead of full degrees-of-freedom (DOFs) accelerations. In this study, we investigated the sensitivities of regional brain strain-related responses to resultant \(\mathbf{a}_{\mathrm{lin}}\) and \(\mathbf{a}_{\mathrm{rot}}\) as well as the relative contributions of these acceleration components to the responses via random sampling and linear regression using parameterized, triangulated head impacts with kinematic variable values based on on-field measurements. Two independently established and validated finite element models of the human head were employed to evaluate model-consistency and dependency in results: the Dartmouth Head Injury Model and Simulated Injury Monitor. For the majority of the brain, volume-weighted regional peak strain, strain rate, and von Mises stress accumulated from the simulation significantly correlated with the product of the magnitude and duration of \(\mathbf{a}_{\mathrm{rot}}\) , or effectively, the rotational velocity, but not to \(\mathbf{a}_{\mathrm{lin}}\) . Responses from \(\mathbf{a}_{\mathrm{rot}}\) -only were comparable to the full-DOF counterparts especially when normalized by injury-causing thresholds (e.g., volume fractions of large differences virtually diminished (i.e., \(<\) 1 %) at typical difference percentage levels of 1–4 % on average). These model-consistent results support the inclusion of both rotational acceleration magnitude and duration into kinematics-based injury metrics and demonstrate the feasibility of estimating strain-related responses from isolated \(\mathbf{a}_{\mathrm{rot}}\) for analyses of strain-induced injury relevant to contact sports without significant loss of accuracy, especially for the cerebrum.     

Studies on mass attenuation coefficient, effective atomic number and electron density of some vitamins

Mass attenuation coefficient, $ \mu_{m} $ , atomic cross-section, $ \sigma_{i} $ , electronic cross-section, $ \sigma_{e} $ , effective atomic number, $ Z_{\text{eff}} $ and effective electron density, $ N_{\text{el}} $ , were determined experimentally and theoretically for some vitamins (retinol, beta-carotene, thiamine, riboflavin, niacinamide, pantothenic acid, pyridoxine, biotin, folic acid, cyanocobalamin, ascorbic acid, cholecalciferol, alpha-tocopherol, ketamine, hesperidin) at 30.82, 59.54, 80.99, 356.61, 661.66 and 1,408.01?keV photon energies using a NaI(Tl) scintillation detector. The theoretical mass attenuation coefficients were estimated using mixture rules. The calculated values were compared with the experimental values for all vitamins.     

Enhanced accuracy of kinetic information from CT-CPMG experiments by transverse rotating-frame spectroscopy

Micro-to-millisecond motions of proteins transmit pivotal signals for protein function. A powerful technique for the measurement of these motions is nuclear magnetic resonance spectroscopy. One of the most widely used methodologies for this purpose is the constant-time Carr–Purcell–Meiboom–Gill (CT-CPMG) relaxation dispersion experiment where kinetic and structural information can be obtained at atomic resolution. Extraction of accurate kinetics determined from CT-CPMG data requires refocusing frequencies that are much larger than the nuclei’s exchange rate between states. We investigated the effect when fast processes are probed by CT-CPMG experiments via simulation and show that if the intrinsic relaxation rate $ \left( {R_{2,0}^{CT - CPMG} } \right) $ ( R 2 , 0 CT ? CPMG ) is not known a priori the extraction of accurate kinetics is hindered. Errors on the order of 50 % in the exchange rate are attained when processes become fast, but are minimized to 5 % with a priori $ R_{2,0}^{CT - CPMG} $ R 2 , 0 CT ? CPMG information. To alleviate this shortcoming, we developed an experimental scheme probing $ R_{2,0}^{CT - CPMG} $ R 2 , 0 CT ? CPMG with large amplitude spin-lock fields, which specifically contains the intrinsic proton longitudinal Eigenrelaxation rate. Our approach was validated with ubiquitin and the Oscillatoria agardhii agglutinin (OAA). For OAA, an underestimation of 66 % in the kinetic rates was observed if $ R_{2,0}^{CT - CPMG}\, $ R 2 , 0 CT ? CPMG is not included during the analysis of CT-CPMG data and result in incorrect kinetics and imprecise amplitude information. This was overcome by combining CT-CPMG with $ R_{2,0}^{CT - CPMG} $ R 2 , 0 CT ? CPMG measured with a high power R_1ρ experiment. In addition, the measurement of $ R_{2,0}^{CT - CPMG} $ R 2 , 0 CT ? CPMG removes the ambiguities in choosing between different models that describe CT-CPMG data.     

Bone refilling in cortical basic multicellular units: insights into tetracycline double labelling from a computational model

Bone remodelling is carried out by ‘bone multicellular units’ ( $\text{ BMU }$ s) in which active osteoclasts and active osteoblasts are spatially and temporally coupled. The refilling of new bone by osteoblasts towards the back of the $\text{ BMU }$ occurs at a rate that depends both on the number of osteoblasts and on their secretory activity. In cortical bone, a linear phenomenological relationship between matrix apposition rate and $\text{ BMU }$ cavity radius is found experimentally. How this relationship emerges from the combination of complex, nonlinear regulations of osteoblast number and secretory activity is unknown. Here, we extend our previous mathematical model of cell development within a single cortical $\text{ BMU }$ to investigate how osteoblast number and osteoblast secretory activity vary along the $\text{ BMU }$ ’s closing cone. The mathematical model is based on biochemical coupling between osteoclasts and osteoblasts of various maturity and includes the differentiation of osteoblasts into osteocytes and bone lining cells, as well as the influence of $\text{ BMU }$ cavity shrinkage on osteoblast development and activity. Matrix apposition rates predicted by the model are compared with data from tetracycline double labelling experiments. We find that the linear phenomenological relationship observed in these experiments between matrix apposition rate and $\text{ BMU }$ cavity radius holds for most of the refilling phase simulated by our model, but not near the start and end of refilling. This suggests that at a particular bone site undergoing remodelling, bone formation starts and ends rapidly, supporting the hypothesis that osteoblasts behave synchronously. Our model also suggests that part of the observed cross-sectional variability in tetracycline data may be due to different bone sites being refilled by $\text{ BMU }$ s at different stages of their lifetime. The different stages of a $\text{ BMU }$ ’s lifetime (such as initiation stage, progression stage, and termination stage) depend on whether the cell populations within the $\text{ BMU }$ are still developing or have reached a quasi-steady state whilst travelling through bone. We find that due to their longer lifespan, active osteoblasts reach a quasi-steady distribution more slowly than active osteoclasts. We suggest that this fact may locally enlarge the Haversian canal diameter (due to a local lack of osteoblasts compared to osteoclasts) near the $\text{ BMU }$ ’s point of origin.     

A network with tunable clustering, degree correlation and degree distribution, and an epidemic thereon

A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form a network. Clustering is obtained by forming small completely connected subgroups, and positive (negative) degree correlation is obtained by connecting a fraction of the stubs with stubs of similar (dissimilar) degree. An SIR (Susceptible $\rightarrow $ Infective $\rightarrow $ Recovered) epidemic model is defined on this network. Asymptotic properties of both the network and the epidemic, as the population size tends to infinity, are derived: the degree distribution, degree correlation and clustering coefficient, as well as a reproduction number $R_*$ , the probability of a major outbreak and the relative size of such an outbreak. The theory is illustrated by Monte Carlo simulations and numerical examples. The main findings are that (1) clustering tends to decrease the spread of disease, (2) the effect of degree correlation is appreciably greater when the disease is close to threshold than when it is well above threshold and (3) disease spread broadly increases with degree correlation $\rho $ when $R_*$ is just above its threshold value of one and decreases with $\rho $ when $R_*$ is well above one.     

Dynamic permeability of the lacunar–canalicular system in human cortical bone

A new method for the experimental determination of the permeability of a small sample of a fluid-saturated hierarchically structured porous material is described and applied to the determination of the lacunar–canalicular permeability \((K_\mathrm{LC})\) in bone. The interest in the permeability of the lacunar–canalicular pore system (LCS) is due to the fact that the LCS is considered to be the site of bone mechanotransduction due to the loading-driven fluid flow over cellular structures. The permeability of this space has been estimated to be anywhere from \(10^{-17}\;\) to \(10^{-25}\; \hbox {m}^{2}\) . However, the vascular pore system and LCS are intertwined, rendering the permeability of the much smaller-dimensioned LCS challenging to measure. In this study, we report a combined experimental and analytical approach that allowed the accurate determination of the \(K_\mathrm{LC}\) to be on the order of \(10^{-22}\; \hbox {m}^{2}\) for human osteonal bone. It was found that the \(K_\mathrm{LC}\) has a linear dependence on loading frequency, decreasing at a rate of \(2 \times 10^{-24}\; \hbox {m}^{2}\) /Hz from 1 to 100 Hz, and using the proposed model, the porosity alone was able to explain 86 % of the \(K_\mathrm{LC}\) variability.     

Release of non-exchangeable {}^{{{\text{15}}}}{\text{NH}}^{{\text{ + }}}_{{\text{4}}} from subgrade, decomposed granite substrates and uptake by non-mycorrhizal and mycorrhizal California native annual grass, Vulpia microstachys

Release rates of recently fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ from non-exchangeable interlayer sites in 2:1 silicate minerals were determined for decomposed granite (DG) saprolites from three locations in California, USA. Recently-fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ release from the DG substrate was quantified by extracting diffused $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ with H-resin, as well as a native, annual grass Vulpia microstachys. The $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ release data varied with via the method of extraction, which included H-resin pre-treatments (Na⁺ or H⁺) and V. microstachys uptake (mycorrhizal inoculated or uninoculated). After 6 weeks (1008 h), more $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ was recovered from fixed interlayer positions by the H-resins as compared to uptake by V. microstachys. The H⁺ treated H-resins recovered more released $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ (≈94 mg ${\text{NH}}^{{\text{ + }}}_{{\text{4}}} - {\text{N}}\;{\text{kg}}^{1} $ or (12%) of total fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ ) in two of the three DG samples as compared to the Na⁺ treated resins, (which recovered ≈70–78 mg ${\text{NH}}^{{\text{ + }}}_{{\text{4}}} - {\text{N}}\;{\text{kg}}^{{{\text{ - 1}}}} $ (or 9–10%) of the total fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ ). The V. microstachys assimilated 8–9% of the total fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ with mycorrhizal inoculum as compared to only 2% without a mycorrhizal inoculum, over the same time period. The fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ release kinetics from the H-resin experiments were most accurately described by first order and power function models, and can be characterized as biphasic using a heterogeneous diffusion model. Uptake of both the ¹⁵N and ambient, unlabelled N from the soils was closely related to plant biomass. There was no significant difference in percent of N per unit of biomass between the control and mycorrhizal treatments. The findings presented here indicate that observed, long-term $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ release rates from DG in studies utilizing resins, may overestimate the levels of fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ made available to plants and microorganisms. Additionally, the study suggested that mycorrhizae facilitate the acquisition and plant uptake of fixed $ {\text{NH}}^{{\text{ + }}}_{{\text{4}}} $ , resulting in markedly increased plant biomass production.