Intra-abdominal pressure mechanism for stabilizing the lumbar spine

Currently, intra-abdominal pressure (IAP) is thought to provide stability to the lumbar spine but the exact principles have yet to be specified. A simplified physical model was constructed and theoretical calculations performed to illustrate a possible intra-abdominal pressure mechanism for stabilizing the spine. The model consisted of an inverted pendulum with linear springs representing abdominal and erector spinae muscle groups. The IAP force was simulated with a pneumatic piston activated with compressed air. The critical load of the model was calculated theoretically based on the minimum potential energy principle and obtained experimentally by increasing weight on the model until the point of buckling. Two distinct mechanisms were simulated separately and in combination. One was antagonistic flexor extensor muscle coactivation and the second was abdominal muscle activation along with generation of IAP. Both mechanisms were effective in stabilizing the model of a lumbar spine. The critical load and therefore the stability of the spine model increased with either increased antagonistic muscle coactivation forces or increased IAP along with increased abdominal spring force. Both mechanisms were also effective in providing mechanical stability to the spine model when activated simultaneously. Theoretical calculation of the critical load agreed very well with experimental results (95.5% average error). The IAP mechanism for stabilizing the lumbar spine appears preferable in tasks that demand trunk extensor moment such as lifting or jumping. This mechanism can increase spine stability without the additional coactivation of erector spinae muscles.     

Influence of ligament stiffness on the mechanical behavior of a functional spinal unit

Data on the stiffnesses of spinal ligaments are required for analytical studies on the mechanical behavior of spinal segments. Values obtained experimentally vary widely in the literature. A finite element model of an L3/L4 functional spinal unit was used to determine the influence of ligament stiffness on intersegmental rotation and forces in the ligaments. The lowest values for ligament stiffness selected from the literature were used in one set of calculations, and the highest values were simulated in a second set. The nonlinear model was loaded with pure moments of 7.5 and 15 Nm in the three main anatomical planes. The mechanical behavior of the functional spinal unit was strongly influenced by ligament stiffness. In some cases, a ligament with low stiffness does not carry any load, while the same ligament with high stiffness has to carry a high load. This indicates that finite element models of spinal segments have to be validated and that a realistic quantitative prediction of ligament forces is extremely difficult.     

Effect of the shape of the electron energy distribution function on the dust grain charge and its screening in glow discharge plasmas

The dust grain charge in the plasma of a glow discharge in noble gases and nitrogen is calculated in the orbit motion limited model for reduced fields in the range of E/N = 1–20 Td. The calculations were performed using the electron energy distribution functions (EEDFs) obtained by solving the Boltzmann equation numerically with allowance for elastic and inelastic electron scattering and analytically with allowance for only elastic scattering and (for nitrogen) excitation of rotational levels, as well as using a Maxwellian EEDF. In the latter case, either the characteristic electron energy or mean electron energy multiplied by two thirds was used as the electron temperature. It is shown that the calculations with the use of a Maxwellian EEDF yield larger values of the grain charge as compared to those calculated with EEDFs obtained by solving the Boltzmann equation. The range of E/N values is determined in which analytical expressions for the EEDF obtained with allowance for elastic scattering and excitation of rotational levels are applicable to calculating the grain charge. The effect of the EEDF shape on the screening of the dust grain charge in plasma is investigated. The Debye screening length in case of a Maxwellian EEDF is shown to be shorter than that obtained with EEDFs calculated by numerically solving the Boltzmann equation.     

Stochastic epidemics: major outbreaks and the duration of the endemic period

A study is made of a two-dimensional stochastic system that models the spread of an infectious disease in a population. An asymptotic expression is derived for the probability that a major outbreak of the disease will occur in case the number of infectives is small. For the case that a major outbreak has occurred, an asymptotic approximation is derived for the expected time that the disease is in the population. The analytical expressions are obtained by asymptotically solving Dirichlet problems based on the Fokker-Planck equation for the stochastic system. Results of numerical calculations for the analytical expressions are compared with simulation results.     

A theoretical model study of the influence of fluid stresses on a cell adhering to a microchannel wall.

We predict the amplification of mechanical stress, force, and torque on an adherent cell due to flow within a narrow microchannel. We model this system as a semicircular bulge on a microchannel wall, with pressure-driven flow. This two-dimensional model is solved computationally by the boundary element method. Algebraic expressions are developed by using forms suggested by lubrication theory that can be used simply and accurately to predict the fluid stress, force, and torque based upon the fluid viscosity, muoffhannel height, H, cell size, R, and flow rate per unit width, Q2-d. This study shows that even for the smallest cells (gamma = R/H << 1), the stress, force, and torque can be significantly greater than that predicted based on flow in a cell-free system. Increased flow resistance and fluid stress amplification occur with bigger cells (gamma > 0.25), because of constraints by the channel wall. In these cases we find that the shear stress amplification is proportional to Q2-d(1-gamma)-2, and the force and torque are proportional to Q2-d(1-gamma2)-5/2. Finally, we predict the fluid mechanical influence on three-dimensional immersed objects. These algebraic expressions have an accuracy of approximately 10% for flow in channels and thus are useful for the analysis of cells in flow chambers. For cell adhesion in tubes, the approximations are accurate to approximately 25% when gamma > 0.5. These calculations may thus be used to simply predict fluid mechanical interactions with cells in these constrained settings. Furthermore, the modeling approach may be useful in understanding more complex systems that include cell deformability and cell-cell interactions.     

A united residue force-field for calcium-protein interactions

United-residue potentials are derived for interactions of the calcium cation with polypeptide chains in energy-based prediction of protein structure with a united-residue (UNRES) force-field. Specific potentials were derived for the interaction of the calcium cation with the Asp, Glu, Asn, and Gln side chains and the peptide group. The analytical expressions for the interaction energies for each of these amino acids were obtained by averaging the electrostatic interaction energy, expressed by a multipole series over the dihedral angles not considered in the united-residue model, that is, the side-chain dihedral angles chi and the dihedral angles lambda for the rotation of peptide groups about the C(alpha)...C(alpha) virtual-bond axes. For the side-chains that do not interact favorably with calcium, simple excluded-volume potentials were introduced. The parameters of the potentials were obtained from ab initio quantum mechanical calculations of model systems at the Restricted Hartree-Fock (RHF) level with the 6-31G(d,p) basis set. The energy surfaces of pairs consisting of Ca(2+)-acetate, Ca(2+)-propionate, Ca(2+)-acetamide, Ca(2+)-propionamide, and Ca(2+)-N-methylacetamide systems (modeling the Ca(2+)-Asp(-), Ca(2+)-Glu(-), Ca(2+)-Asn, Ca(2+)-Gln, and Ca(2+)-peptide group interactions) at different distances and orientations were calculated. For each pair, the restricted free energy (RFE) surfaces were calculated by numerical integration over the degrees of freedom lost when switching from the all-atom model to the united-residue model. Finally, the analytical expressions for each pair were fitted to the RFE surfaces. This force-field was able to distinguish the EF-hand motif from all potential binding sites in the crystal structures of bovine alpha-lactalbumin, whiting parvalbumin, calbindin D9K, and apo-calbindin D9K.     

Microstructural mechanics of collagen gels in confined compression: poroelasticity, viscoelasticity, and collapse

BACKGROUND: Collagen gels are important as platforms for in vitro study of cell behavior and as prototypical bioartificial tissues, but their mechanical behavior, particularly on the microscopic scale, is still poorly understood. METHOD OF APPROACH: Collagen gels were studied in step (10% strain in 0.05 s) and ramp (0.1%/s strain rate for 100 s) confined compression. Real-time birefringence mapping gave the local collagen concentration and orientation along with piston stress. Variations in the retardation allowed material-point tracking and qualitative determination of the strain distribution. RESULTS: Ramp tests showed classical poroelastic behavior: compression near the piston and relaxation to a uniform state. Step tests, however, showed an irreversibly collapsed region near the piston. CONCLUSIONS: Our results suggest that interstitial flow and fibril bending at crosslinks are the dominant mechanical processes during compression, and that fibril bending is reversible before collapse.     

Design parameters of the fan-out phase of sensory systems

This paper focuses on the calculation of boundary values for the design parameters in the fan-out phase of the olfactory system of insects. Three main criteria are taken into account to determine the boundaries of the parameters: (i) information conservation, (ii) low energy costs and (iii) full involvement of all the neurons. These criteria serve to determine the structural parameters that produce a sufficient minimal response. Analytical calculations lead to a few general expressions which show how the main internal parameters can be obtained for any system with similar characteristics. We calculate the optimal threshold for coincidence detection, connectivity and output activity values that verify criteria (i), (ii) and (iii). The range of parameter values obtained by these calculations include those observed in the olfactory system of the locust.     

Effect of anisotropic reactivity on the rate of diffusion-controlled reactions: comparative analysis of the models of patches and hemispheres

A comparative analysis of two models of anisotropic reactivity in bimolecular diffusion-controlled reaction kinetics is presented. One is the conventional model of reactive patches (MRP), where the surface of a molecule is assumed to be reactive over a certain region (circular patch) with the rest of the surface being inert. Another one is the model of reactive hemispheres (MRH), assuming that a molecule is reactive within a certain distance from a point on its surface. The accuracy of the known and newly derived simple analytical expressions for the reaction rate is tested by comparison with the simulation results obtained by the original Brownian dynamics method. These formulas prove to be quite accurate in the practically important limit of strong anisotropy corresponding to small size of the reactive patches or hemispheres. Numerical calculations confirm earlier predictions that the MRP rates are much smaller than the MRH rates for the same radii of the reactive regions, especially in the case where both reacting molecules are anisotropic.     

MINDO/3 calculations of the conformation and carcinogenicity of epoxy-metabolites of aromatic hydrocarbons: 7,8-dihydroxy-9,10-oxy-7,8,9,10-tetrahydrobenzo(a)pyrene

Quantum mechanical calculations in the MINDO/3 approximation were performed on the four conformations of the alicyclic moiety of 7,8-dihydroxy-9,10-epoxy-7,8,9,10-tetrahydrobenzo(a)pyrene.Total charge and frontier orbital densities show that attack by nucleophiles will occur predominantly at Position 10 of all configurations of the dihydroxyepoxybenzo(a)pyrene.The calculations show the cis diastereomer to be more stable than the trans, although no evidence for hydrogen bonding in the (ax, ax′) conformer was found.On the basis of the results obtained for the stability of the various conformers, a model is proposed to explain the higher carcinogenicity of the trans isomer as compared to the cis. Such a model implies the formation of an intercalation complex between the diol epoxide metabolite and nucleic acids.     

Survival of bone tissue in organotypic culture under intermittent mechanical loading. Preliminary results

With the aim to study the mechanism of transduction of mechanical stimuli in biological ones we have realized an experimental device for the application of intermittent mechanical forces on bone specimens in vitro. The scheme of the device is reported in Fig. 1. It is constituted by a drive shaft which rotates on eccentric axis (1) supporting a longitudinal bar (2) with the load (3). The latter rests on a piston (4) only during a limited period of every shaft revolution, so that the load becomes intermittent. The bone specimen (5) is placed under the piston and the two are placed in a tube containing the culture medium. This latter is BGJ mod. Fitton-Jackson (Gibco), enriched with fetal calf serum (10%) and ascorbic acid (70 microliters/ml). Right metatarsi from 18-day-old rats were removed aseptically and placed under the piston for 2-6 days after resection of both ends. The homotypic ones, unloaded, were placed in 30 mm Petri dishes, and used as a control. The incubator environment was 5% CO2 in air (A group), or enriched with O2 (25-35%) (B group). At the end of the experimental period the bone specimens were fixed in 4% formalin buffered and treated for conventional histologic methods. In the A group most of the osteocytic lacunae were empty. The osteoblasts disappeared already at the 2nd day; the periosteal fibroblast dedifferentiated and multiplied. The deposition or calcification of osteoid were completely lacking. The application of mechanical load promoted deposition of granular degenerative material around the bone, and the periosteal cells, well differentiated, were surrounded by metachromatic material, which resembles cartilage matrix.(ABSTRACT TRUNCATED AT 250 WORDS)     

The impact of the parameters of the constitutive model on the distribution of strain in the femoral head

The rapid spread of the finite element method has caused that it has become, among other methods, the standard tool for pre-clinical estimates of bone properties. This paper presents an application of this method for the calculation and prediction of strain and stress fields in the femoral head. The aim of the work is to study the influence of the considered anisotropy and heterogeneity of the modeled bone on the mechanical fields during a typical gait cycle. Three material models were tested with different properties of porous bone carried out in literature: a homogeneous isotropic model, a heterogeneous isotropic model, and a heterogeneous anisotropic model. In three cases studied, the elastic properties of the bone were determined basing on the Zysset-Curnier approach. The tensor of elastic constants defining the local properties of porous bone is correlated with a local porosity and a second order fabric tensor describing the bone microstructure. In the calculations, a model of the femoral head generated from high-resolution tomographic scans was used. Experimental data were drawn from publicly available database “Osteoporotic Virtual Physiological Human Project.” To realistically reflect the load on the femoral head, main muscles were considered, and their contraction forces were determined based on inverse kinematics. For this purpose, the results from OpenSim packet were used. The simulations demonstrated that differences between the results predicted by these material models are significant. Only the anisotropic model allowed for the plausible distribution of stresses along the main trabecular groups. The outcomes also showed that the precise evaluation of the mechanical fields is critical in the context of bone tissue remodeling under mechanical stimulations.

     

On the nonlinear dynamic plane base-rotator models of DNA: Base-base interaction and dissipation

Nonlinear mechanical plane base-rotator models of DNA are considered. Various expressions for the potential energy of interaction between complementary bases are analyzed. Dissipative functions are introduced into these models: the external function describing the motion of the bases in a solvent and the function describing the internal friction in the molecule. Particle-like solutions of the model without dissipation are obtained and the influence of dissipation on these (soliton) excitations is studied.     

DNA bis-intercalation: Application of theory to the binding of echinomycin to DNA

The statistical mechanical model for the binding of bifunctional intercalating ligands to duplex DNA described in the preceding paper is applied to the example of echinomycin–DNA interactions. This is the only system for which binding curves have been obtained under conditions leading to binding by both bis-intercalation and mono-intercalation simultaneously. Binding parameters and Scatchard plots are calculated for a variety of conditions. A detailed comparison of these calculations with the results from the previous analysis of the same binding data in terms of the McGhee-Von Hippel theory, assuming only one mode of binding, is presented. The results of our calculations are consistent with the model of bis-intercalation requiring the two bound chromophores of a bifunctional ligand to be separated by two base pairs. It is not necessary to assume violation of the nearest-neighbor exclusion principle, as occurred in the original analysis.     

Simple and accurate correlation of experimental redox potentials and DFT-calculated HOMO/LUMO energies of polycyclic aromatic hydrocarbons

The ability to accurately predict the oxidation and reduction potentials of molecules is very useful in various fields and applications. Quantum mechanical calculations can be used to access this information, yet sometimes the usefulness of these calculations can be limited because of the computational requirements for large systems. Methodologies that yield strong linear correlations between calculations and experimental data have been reported, however the balance between accuracy and computational cost is always a major issue. In this work, linear correlations (with an R² value of up to 0.9990) between DFT-calculated HOMO/LUMO energies and 70 redox potentials from a series of 51 polycyclic aromatic hydrocarbons (obtained from the literature) are presented. The results are compared to previously reported linear correlations that were obtained with a more expensive computational methodology based on a Born-Haber thermodynamic cycle. It is shown in this article that similar or better correlations can be obtained with a simple and cheaper calculation.     

Backmixing and mass transfer in the design of immobilized-enzyme reactors

The effects of dispersion and mass transfer resistance on the degree of conversion in an immobilized-enzyme reactor have been considered theoretically. It is assumed that the immobilized enzymes obey a Michaelis–Menten relationship and backmixing can be characterized by a dispersion model. For two extreme cases (perfect mixing and piston flow), approximate equations are obtained, which can be readily used to evaluate the effect of mass transfer on degree of conversion. Numerical solutions are obtained for other intermediate cases. Design charts are given which set practical limits of enzyme reactor design.     

An electromechanical theory of permeability during nerve action

In this paper is presented a model displaying a cooperative phenomenon between an electrical and a mechanical wave during nerve action. The action potential utilizes the elastic properties and the surface tension of the membrane to generate a nonlinear mechanical wave. This stable mechanical wave, upon interacting with the protein domain, places the latter into a conducing conformation which is then used as a gate by the potential wave.The conformation state of the protein domain is described in terms of Ca²⁺ linkages for which a simple Ising model with nearest-neighbor interactions has been selected. The spin variables of this model describe the two states of the Ca²⁺ linkages and the mechanical wave plays the role of the external field.From these calculations a threshold is obtained for the axon in terms of the structural properties of the membrane and the allosteric nature of the protein domain is expressed by the dynamics of the average number of Ca²⁺ linkages. In addition, the formula obtained for the membrane conductance shows good agreement with experimental data.     

The structure and mechanical properties of the proteins of lamprey cartilage

The cyanogen bromide‐resistant proteins of lamprey cartilage are biochemically related to the mammalian elastic protein, elastin. This study investigates their mechanical properties and enquires whether, like elastin, long‐range elasticity arises in them from a combination of entropic and hydrophobic mechanisms. Branchial and pericardial proteins resembled elastin mechanically, with elastic moduli of 0.13–0.35 MPa, breaking strains of 50%, and low hysteresis. Annular and piston proteins had higher elastic moduli (0.27–0.75 MPa) and larger hysteresis. Exchanging solvent water for trifluoroethanol increased the elastic moduli, whereas increasing temperature lowered the elastic moduli. Raman microspectrometry showed small differences in side‐chain modes consistent with reported biochemical differences. Decomposition of the amide I band indicated that the secondary structures were like those of elastin, preponderantly unordered, which probably confer the conformational flexibility necessary for entropy elasticity. Piston and annular proteins showed the strongest interactions with water, suggesting, together with the mechanical testing data, a greater role of hydrophobic interactions in their mechanics. Two‐photon imaging of intrinsic fluorescence and dye injection experiments showed that annular and piston proteins formed closed‐cell honeycomb structures, whereas the branchial and pericardial proteins formed open‐cell structures, which may account for the differences in mechanical properties. © 2014 Wiley Periodicals, Inc. Biopolymers 103: 187–202, 2015.     

Mechanics of root growth

Summary A model is developed for the rate of elongation of a root tip in terms of the balance of pressures acting on the root. Differentials of this equation give expressions for the changes in root elongation rate with respect to soil water potential and soil mechanical resistance. The model predicts that root cells osmoregulate against both water stress and soil mechanical resistance with predicts that root cells osmoregulate against both water stress and soil mechanical resistance with similar efficiencies which are less than 100%. Analysis of published data leads to the conclusion that root tips of pea osmoregulate with 70% efficiency. A working equation is developed for the elongation rate of roots in conditions of combined water stress and mechanical resistance.     

Potential of Raloxifene in reversing osteoarthritis-like alterations in rat chondrocytes: An in vitro model study

The aim of this study was to investigate the effects of Raloxifene (Ral) on degeneration-related changes in osteoarthritis (OA)-like chondrocytes using two- and three-dimensional models. Five-azacytidine (Aza-C) was used to induce OA-like alterations in rat articular chondrocytes and the model was verified at molecular and macrolevels. Chondrocytes were treated with Ral (1, 5 and 10 μM) for 10 days. Caspase-3 activity, gene expressions of aggrecan, collagen II, alkaline phosphatase (ALP), collagen X, matrix metalloproteinases (MMP-13, MMP-3 and MMP-2), and MMP-13, MMP-3 and MMP-2 protein expressions were studied in two-dimensional model. Matrix deposition and mechanical properties of agarose-chondrocyte discs were evaluated in three-dimensional model. One μM Ral reduced expression of OA-related genes, decreased apoptosis, and MMP-13 and MMP-3 protein expressions. It also increased aggrecan and collagen II gene expressions relative to untreated OA-like chondrocytes. In three-dimensional model, 1 μM Ral treatment resulted in increased collagen deposition and improved mechanical properties, although a significant increase for sGAG was not observed. In summation, 1 μM Ral improved matrix-related activities, whereas dose increment reversed these effects except ALP gene expression and sGAG deposition. These results provide evidence that low-dose Ral has the potential to cease or reduce the matrix degeneration in OA.