Size effects in the elasticity and viscoelasticity of bone

 Size effects of large magnitude are observed in the torsional shear modulus and damping of bovine plexiform bone. Damping increases and stiffness decreases with specimen size over all sizes studied. Measurements were conducted in torsion using a laser-based micromechanics apparatus capable of viscoelastic studies over a range of frequencies up to 100 kHz, upon samples of various size, with no parasitic friction or other errors that could mimic any size effect. Torsional tan δ at 1 Hz varies by about a factor of five over the size range 2.8–6.2 mm thick, and is more dependent on specimen thickness at 1 Hz than it is at higher frequency. The size effects are attributed to compliance and viscoelasticity of the interfaces between laminae. These laminae must be substantially stiffer than whole bone. Observed size effects are likely to play a role in understanding scaling laws of bones in living organisms. Received: 12 February 2002 / Accepted: 22 November 2002 R.S. Lakes is also at the Department of Biomedical Engineering, Department of Engineering Physics, Materials Science Program and Rheology Research Center all at the University of Wisconsin. We thank the Whitaker foundation for their support of this work.     

Biochemical anatomy of human bone: comparative study of compact and spongy bone in femur, rib and iliac crest

Using EDTA extraction procedure, compact and spongy bone from human femur, rib and iliac crest were compared in terms of their content in collagen, sialoprotein, proteoglycan and carbohydrate. The bone matrix sizes displayed significant variations, the femur having the smallest size and iliac crest the largest one. No significant difference in the matrix size has been found between the spongy and compact bone. The EDTA extractability of the spongy bone was higher than that of the compact bone, with femur showing the lowest extractability. The collagen content of the 3 bones studied was similar although the femur had slightly lower values. The sialic and uronic acids and hexose contents were higher in the femur than in the rib and iliac crest. The collagen/hexose, collagen/sialic acid and collagen/uronic acid ratios in the bone matrix were highest in the iliac crest and lowest in the femur, suggesting that alterations in the amounts of bone matrix can affect the mechanical properties of different parts of the bony skeleton and vice versa.     

On the mechanical characterization of compact bone structure using the homogenization theory

In a previous paper (Crolet et al., 1993, J. Biomechanics 26, 677–687), a modelling of the mechanical behavior of compact bone was presented, in which the homogenization theory was the basic tool of computation. In this simulation, approximations were used for the modelling of the lamellae and the osteons: the lamella and the osteon were divided into cylindrical sectors, each sector being approximated as a parallelepiped having a periodic structure (fibrous composite for the lamella, superimposition of plates for the osteon). The present study deals with a new model without these approximations. First, it can be proved that the homogenized elasticity tensor for a lamella, which has a non-periodic structure, is obtained at each geometrical point as a homogenized tensor of a periodic problem. Similarly, for the osteonal structure, the components of the homogenized tensor are determined at each point as the result of a periodic homogenization.

The software OSTEON, which is the computational method associated with this model, allows one to obtain a better understanding of the effects of many bony parameters. The obtained results are in accordance with experimental data.     

The effect of porosity and mineral content on the Young's modulus of elasticity of compact bone

The Young's modulus of elasticity, the calcium content and the volume fraction (1-porosity) of 23 tension specimens and 80 bending specimens, taken from compact bone of 18 species of mammal, bird and reptile, were determined. There was a strong positive relationship between Young's modulus and both calcium content and volume fraction. A power law model fits the data better than a linear model. Young's modulus has a roughly cubic relationship with both calcium content and volume fraction. Over 80% of the total variation in Young's modulus in this data set is explained by these two variables.     

An experimental model of apneusis and periodic respiration]

In experiments on sodium pentobarbital (40 mg/kg, i. p.) anesthetized mongrel cats of either sex weighting from 2.0 to 4.0 kg, it was stated, that sodium or lithium hydroxybutyrate (HOB) (200 mg/kg, i. v.) effectively slowed down breathing with inspiratory holdings. Thus 3-5 minutes after HOB administration, eupneic pattern of respiration was changed firstly to inspiratory apneustic one (100% of cats), and then to periodic one (80% of cats). This pattern persisted for 60-90 minutes, and after that the respiratory pattern usually changed its direction to the opposite one. In these conditions alterations of arterial blood composition (pH, pO2, pCO2, SO2) and hemodynamic variables (heart rate, arterial pressure) can not be considered as the cause of apneustic pattern of respiration. It is suggested, that HOB can be used for simulating such terminal respiratory patterns as apneustic and periodic ones.     

Blood supply of the compact and spongy myocardium of fish, amphibia and reptiles]

Coronal arteries were injected with lead carbonate suspension and with Indian ink and cleared preparations 150--300 mkm thick were made in 195 hearts of fish, amphibians and reptiles and studied roentgenographically. It was stated that in Chondrichthyes (shark, skate) and in Chondrostei (beluga, stellate sturgeon, sturgeon), as well as in alligator both compact and spongy myocardium of the cardiac ventricle possess blood vessels. In teleostei, amphibians and reptiles (except alligator) spongy myocardium is avascular and receives its nutrition from the ventricle. In view of the data on the presence of blood vessels in the spongy myocardium in some vertebrates, it is impossible to accept the theory suggested by Grant and Regnier according to which vessels in the heart walls appear only in connection with compactization of the myocardium. Vascularization of the spongy myocardium is closely connected with oxygen saturation of the blood flowing through the heart. When this saturation is not satisfactory, the spongy myocardium has blood vessels. In alligator, vascularization of the spongy myocardium is connected with the fact that the heart has four chambers and there are arterial and venous blood streams.     

An experimental and theoretical approach to determining linkages between geochemical variability and microbial biodiversity in seafloor hydrothermal chimneys

New experimental results of fluid–mineral reactions at hydrothermal conditions relevant to life demonstrate that key redox reactions involving iron, sulfur, and hydrogen remain at disequilibrium at 100 °C, even in a heterogeneous system and thus are energetically favorable for microbial metabolism. Predictions from geochemical models utilizing the experimental results and specific to two contrasting case studies from the East Pacific Rise were statistically characterized and correlated to the energetics of redox reactions available for intra‐chimney microbial populations. In general, predictions of available energy for autotrophic metabolism are largely similar between the mature and the nascent chimneys, although important differences still exist. Metabolic processes predicted by energetics exhibit the same trends observed in the field data for the mature chimney, but overestimate the diversity observed in the nascent chimney. Several combinations of redox reaction pairs are predicted to support mixed consortia, while some combinations appear to favor more versatile microbes capable of utilizing several reactions under rapidly changing environmental conditions within chimney walls. In addition, conditions favorable to elemental sulfur reduction and methanogenesis exhibit a negative control on the diversity of microbial populations within these chimney walls, whereas H₂S oxidation, elemental sulfur oxidation and the knallgas reaction are positively correlated with both abundance and diversity of micro‐organisms. Coupling field observations of both microbial diversity and geochemical heterogeneity with lab‐based experimental and theoretical modeling can facilitate translation of the observed genetic diversity into physiological diversity, thus enhancing understanding of linked phenomena of microbially induced biogeochemical transformations in complex heterogeneous systems.     

An experimental and theoretical analysis of ultrasound-induced permeabilization of cell membranes

Application of ultrasound transiently permeabilizes cell membranes and offers a nonchemical, nonviral, and noninvasive method for cellular drug delivery. Although the ability of ultrasound to increase transmembrane transport has been well demonstrated, a systematic dependence of transport on ultrasound parameters is not known. This study examined cell viability and cellular uptake of calcein using 3T3 mouse cell suspension as a model system. Cells were exposed to varying acoustic energy doses at four different frequencies in the low frequency regime (20-100 kHz). At all frequencies, cell viability decreased with increasing acoustic energy dose, while the fraction of cells exhibiting uptake of calcein showed a maximum at an intermediate energy dose. Acoustic spectra under various ultrasound conditions were also collected and assessed for the magnitude of broadband noise and subharmonic peaks. While the cell viability and transport data did not show any correlation with subharmonic (f/2) emission, they correlated with the broadband noise, suggesting a dominant contribution of transient cavitation. A theoretical model was developed to relate reversible and irreversible membrane permeabilization to the number of transient cavitation events. The model showed that nearly every stage of transient cavitation, including bubble expansion, collapse, and subsequent shock waves may contribute to membrane permeabilization. For each mechanism, the volume around the bubble within which bubbles induce reversible and irreversible membrane permeabilization was determined. Predictions of the model are consistent with experimental data.     

A theoretical and experimental approach to the use of single wavelength calcium indicators

Fluorescent Ca(2+) indicators have been extremely valuable in understanding the role of intracellular Ca(2+). However, the presence of extracellular dye can confound interpretation of data due to indicator accumulation in the Ca(2+)-rich medium, which induces an increase in the fluorescence signal. By using a mathematical approach, we show that overlooking extracellular dye usually leads to overestimating cytosolic Ca(2+) ([Ca(2+)]) levels. We propose an experimental design and provide mathematical formulations to make the appropriate correction. We applied our model to determine [Ca(2+)] in Fluo-3-loaded bovine aortic endothelial cells (BAECs). Our results indicate that for basal level Ca(2+), the uncorrected value overestimates by a factor of 2.7 the result obtained when extracellular dye was accounted for. We also showed that both bradykinin (BK) and ATP significantly increase [Ca(2+)] in BAECs. For the uncorrected values, BK and ATP induced 2.3- and 3.3-fold apparent increases in [Ca(2+)], respectively. When applying the correction, there was a 4.5- and 5.4-fold induction of [Ca(2+)] for BK and ATP, respectively. Our theoretical and experimental models provide explanations and, at least in part, solutions to the dye leakage problem, and should thus be a valuable tool in clarifying the proper usage of fluorescent dyes for Ca(2+) measurements.     

Conformational analysis of dolastatin 10: An nmr and theoretical approach

A solution conformational analysis of dolastatin 10, a powerful antineoplaslic agent, has been carried out by means of nmr techniques and theoretical calculations. ¹H mono- and bidimensional nmr experiments, as well as ¹H-¹³C heterocorrelated spectra, have been performed on CD₂Cl₁₂ solutions. The most interesting nmr data is a huge shielding of the aCH (25) proton of the Dov residue, suggesting the presence of an interaction between the N-terminal and the aromatic C-terminal ends of the molecule. The possibility of a head-to-tail intermolecular association having been discarded, the presence of a series of preferred folded conformation has been hypothesized. Conformational theoretical analysis supports the nmr hypothesis of a folded peptide-like molecule, and a series of possible conformers in good agreement with the experimental data have been analyzed. © 1995 John Wiley & Sons, Inc.     

RNA accessibility prediction: a theoretical approach is consistent with experimental studies in cell extracts

The use of antisense oligodeoxyribonucleotides (ODN) or ribozymes to specifically suppress gene expression is simple in concept and relies on efficient binding of the antisense strand to the target RNA. Although the identification of target sites accessible to base pairing is gradually being overcome by different techniques, it remains a major problem in the antisense and ribozyme approaches. In this study we have investigated the potential of a recent experimental and theoretical approach to predict the local accessibility of murine DNA-methyltransferase (MTase) mRNA in a comparative way. The accessibility of the native target RNA was probed with antisense ODN in cellular extracts. The results strongly correlated with the theoretically predicted target accessibility. This work suggests an effective two-step procedure for predicting RNA accessibility: first, computer-aided selection of ODN binding sites defined by an accessibility score followed by a more detailed experimental procedure to derive information about target accessibility at the single nucleotide level.     

Nutrient utilization by bovine articular chondrocytes: a combined experimental and theoretical approach

A combined experimental-numerical approach was adopted to characterize glucose and oxygen uptake and lactate production by bovine articular chondrocytes in a model system. For a wide range of cell concentrations, cells in agarose were supplemented with either low or high glucose medium. During an initial culture phase of 48 h, oxygen was monitored noninvasively using a biosensor system. Glucose and lactate were determined by medium sampling. In order to quantify glucose and oxygen uptake, a finite element approach was adopted to describe diffusion and uptake in the experimental model. Numerical predictions of lactate, based on simple relations for cell metabolism, were found to agree well for low glucose, but not for high glucose medium. Oxygen did not play a role in either case. Given the close association between chondrocyte energy metabolism and matrix synthesis, a quantifiable prediction of utilization can present a valuable contribution in the optimization of tissue engineering conditions.     

An approach to the mechanical constitutive modelling of arterial tissue based on homogenization and optimization

This paper is concerned with characterizing the quasistatic mechanical behaviour of arterial tissue undergoing finite deformation through hyperelastic constitutive functions. Commonly the parameters of constitutive functions are established by a process of optimization based on experimental data. Instead we construct a finite element model of a representative volume element of the material and compute its homogenized response to a range of deformations. These data are then used to provide objective functions for optimizing the parameters of two analytical models from the literature.     

26 Inversion approach to the origin of life: theoretical notions and experimental data

The essence of the inversion concept of the origin of life can be narrowed down to the following theses: (1) thermodynamic inversion is the key transformation of prebiotic microsystems leading to their transition into primary forms of life; (2) this transformation might occur only in the microsystems oscillating around the bifurcation point under far-from-equilibrium conditions. The transformation consists in the inversion of the balance “free energy contribution entropy contribution” (as well as “information contribution informational entropy contribution”), from negative to positive values. At the inversion moment, the microsystem radically reorganizes in accordance with the new negentropy (i.e. biological) way of organization. According to this concept, the origin-of-life process on the early Earth took place in oscillating hydrothermal medium. The process was taking two successive stages: (1) spontaneous self-assembly of initial three-dimensional prebiotic microsystems composed mainly of hydrocarbons, lipids, and simple amino acids, or their precursors, within the temperature interval of 100–300?°C (prebiotic stage); (2) nonspontaneous synthesis of sugars, ATP, and nucleic acids started at the inversion moment under the temperature 70–100?°C (biotic stage). Macro and microfluctuations of thermodynamic and physicochemical parameters able to sustain this way of chemical conversion have been detected in several contemporary hydrothermal systems (Kompanichenko, 2012). Conditions in potential hydrothermal medium for the origin of life were explored on the examples of several hydrothermal systems in Kamchatka peninsula. Temperature of water in hot springs ranges from?<?60 to 98?°C, in the bore holes water-steam temperature varies from?<?100 to 239?°C, and pressure from?<?1 to 35 bars at the wellheads; pH is within the interval 2.5–9.0. Pressure monitoring at the depth 950?meters in the borehole No. 30 (Mutnovsky field) has revealed high-amplitude (up to 1–2 bars) irregular macrofluctuations and low-amplitude quite regular microoscillations of pressure (amplitudes 0.1–0.3 bars). Hydrocarbons, lipid precursors, and simple amino acids are available in the fluid. The lifeless condensate of water-steam mixture (temperature 108–175?°C) contains aromatic hydrocarbons, n-alkanes, ketons, alcohols, and aldehydes. In addition to those, cycloalkanes, alkenes, dietoxyalkanes, naphtenes, fatty acids, ethyl ethers of fatty acids, and monoglycerides have been detected in hot solutions inhabited by thermophiles and hyperthermophiles (temperature 70–98?°C). According to Mukhin et al. (1979), glycine of probably abiotic origination was detected in lifeless condensate.     

An experimental and theoretical approach to 5alpha-cholestan-6-spiro-1',2',4'-triazolidine-3'-one

The 5alpha-cholestan-6-one semicarbazone (1) on reaction with hydrogen peroxide at 0 degrees C affords selectively 5alpha-cholestan-6-spiro-1',2',4'-triazolidine-3'-one. (2) The structural assignment of the product was confirmed on the basis of its elemental, analytical and spectral analysis. The Hartree-Fock method using 6-31G* basis set was employed in order to explore the reaction mechanism. The results of the computational study show that the reaction proceeds through two radical intermediates formation. The different characteristics involved during the reaction were explained, firstly, the lower energy conformation of each molecule using total energy, hardness and dipole moment, and secondly, the explanation of the free radical mechanism, using frontier molecular orbital (FMO) theory, encoded electrostatic potential, spin electronic density and atomic charges. The localization of highest occupied molecular orbital (HOMO) or alpha-HOMO, lowest unoccupied molecular orbital (LUMO) or alpha-LUMO and the flow of atomic charges are in good agreement to support the present mechanism of the reaction. Stability and feasibility of all the optimized structures were supported by their respective fundamental frequencies and energy minima.     

The effects of non-Newtonian viscoelasticity and wall elasticity on flow at a 90 degrees bifurcation

To study the fundamentals of hemodynamics in arteries, the flow parameters: pulsatility, elasticity and non-Newtonian viscoelasticity were considered in detail in a 90 degrees-T-bifurcation of a rigid and elastic model. The velocity distribution 2.5 mm behind the bifurcation in the straight tube was measured with a laser-Doppler-anemometer. The fluid used was an aqueous glycerine solution and a viscoelastic Separan mixture. Flow visualization studies were done with a sheet of laser light in the plane of the bifurcation. The velocity distribution was measured for both steady and pulsatile flows with a laser-Doppler-anemometer in a backward scattered way. From the velocity measurements the shear gradients were calculated. Substantial differences were found in the flow behavior of Newtonian and non-Newtonian fluids, especially behind the bifurcation in the main tube, where secondary flows and flow separation started. Also, differences due to the elastic and rigid wall could be seen. Very high shear gradients were found in the flow between main flow and the separation zone which can lead to a damage of the blood cells.     

On a new law of bone remodeling based on damage elasticity: a thermodynamic approach

Background

Bone tissue is the main element of the human skeleton and is a dynamic tissue that is continuously renewed by bone-resorbing osteoclasts and bone-forming osteoblasts.The bone is also capable of repairing itself and adapting its structure to changes in its load environment through the process of bone remodeling.Therefore, this phenomenon has been gaining increasing interest in the last years and many laws have been developed in order to simulate this process.

Results

In this paper, we develop a new law of bone remodeling in the context of damaged elastic by applying the thermodynamic approach in the case of small perturbations.The model is solved numerically by a finite difference method in the one-dimensional bone structure of a n-unit elements model.

Conclusion

In addition, several numerical simulations are presented that confirm the accuracy and effectiveness of the model.