Effect of the trabecular bone microstructure on measuring its thermal conductivity: A computer modeling-based study.

The objective of this work is to quantify the relation between the value of the effective thermal conductivity of trabecular bone and its microstructure and marrow content. The thermal conductivity of twenty bovine trabecular bone samples was measured prior to and after defatting at 37, 47, and 57 °C. Computer models were built including the microstructure geometry and the gap between the tissue and measurement probe. The thermal conductivity (k) measured was 0.39 ±â€¯0.06 W m-1 K-1 at 37 °C, with a temperature dependence of + 0.2%°C-1. Replacing marrow by phosphate-buffered saline (defatting) increased both the computer simulations and measurement results by 0.04 W m-1 K-1. The computer simulations showed that k increases by 0.02-0.04 W m-1 K-1 when the model includes a gap filled by phosphate-buffered saline between the tissue and measurement probe. In the presence of microstructure and fatty red marrow, k varies by ±â€¯0.01 W m-1 K-1 compared with the case considering matrix only, which suggests that there are no significant differences between cortical and trabecular bone in terms of k. The computer results showed that the presence of a gap filled by phosphate-buffered saline around the energy applicator changes maximum temperature by < 0.7 °C, while including the bone microstructure involved a variation of < 0.2 mm in the isotherm location. Future experimental studies on measuring the value of k involving the insertion of a probe into the bone through a drill hole should consider the bias found in the simulations. Thermal models based on a homogeneous geometry (i.e. ignoring the microstructure) could provide sufficient accuracy.

Chirality in a quaternionic representation of the genetic code.

A quaternionic representation of the genetic code, previously reported by the authors (BioSystems 141 (10-19), 2016), is updated in order to incorporate chirality of nucleotide bases and amino acids. The original representation associates with each nucleotide base a prime integer quaternion of norm 7 and involves a function that assigns to each codon, represented by three of these quaternions, another integer quaternion (amino acid type quaternion). The assignation is such that the essentials of the standard genetic code (particularly its degeneration) are preserved. To show the advantages of such a quaternionic representation we have designed an algorithm to go from the primary to the tertiary structure of the protein. The algorithm uses, besides of the type quaternions, a second kind of quaternions with real components that we additionally associate with the amino acids according to their order along the proteins (order quaternions). In this context, we incorporate chirality in our representation by observing that the set of eight integer quaternions of norm 7 can be partitioned into a pair of subsets of cardinality four each with their elements mutually conjugate and by putting them into correspondence one to one with the two sets of enantiomers (D and L) of the four nucleotide bases adenine, cytosine, guanine and uracil, respectively. We then propose two diagrams in order to describe the hypothetical evolution of the genetic codes corresponding to both of the chiral systems of affinities: D-nucleotide bases/L-amino acids and L-nucleotide bases/D-amino acids at reading frames 5'→3' and 3'→5', respectively. Guided by these diagrams we define functions that in each case assign to the triplets of D- (L-) bases a L- (D-) amino acid type integer quaternion. Specifically, the integer quaternion associated with a given D-amino acid is the conjugate of that one corresponding to the enantiomer L. The chiral type quaternions obtained for the amino acids are used, together with a common set of order quaternions, to describe the folding of the two classes, L and D, of homochiral proteins.

Quaternionic representation of the genetic code.

A heuristic diagram of the evolution of the standard genetic code is presented. It incorporates, in a way that resembles the energy levels of an atom, the physical notion of broken symmetry and it is consistent with original ideas by Crick on the origin and evolution of the code as well as with the chronological order of appearance of the amino acids along the evolution as inferred from work that mixtures known experimental results with theoretical speculations. Suggested by the diagram we propose a Hamilton quaternions based mathematical representation of the code as it stands now-a-days. The central object in the description is a codon function that assigns to each amino acid an integer quaternion in such a way that the observed code degeneration is preserved. We emphasize the advantages of a quaternionic representation of amino acids taking as an example the folding of proteins. With this aim we propose an algorithm to go from the quaternions sequence to the protein three dimensional structure which can be compared with the corresponding experimental one stored at the Protein Data Bank. In our criterion the mathematical representation of the genetic code in terms of quaternions merits to be taken into account because it describes not only most of the known properties of the genetic code but also opens new perspectives that are mainly derived from the close relationship between quaternions and rotations.

Modeling of the dielectric properties of trabecular bone samples at microwave frequency.

In this paper, the dielectric properties of human trabecular bone are evaluated under physiological condition in the microwave range. Assuming a two components medium, simulation and experimental data are presented and discussed. A special experimental setup is developed in order to deal with inhomogeneous samples. Simulation data are obtained using finite difference time domain from a realistic sample. The bone mineral density of the samples are also measured. The simulation and experimental results of the present study suggest that there is a negative relation between bone volume fraction (BV/TV) and permittivity/conductivity: the higher the BV/TV, the lower the permittivity/conductivity. This is in agreement with the recently published in vivo data.

Genetic algorithm for the pair distribution function of the electron gas.

The pair distribution function of the electron gas is calculated using a parameterized generalization of hypernetted chain approximation with the parameters being obtained by optimizing the system energy with a genetic algorithm. The functions so obtained are compared with Monte Carlo simulations performed by other authors in its variational and di_usion versions showing a very good agreement especially with the di_usion Monte Carlo results.

Nonmonotonic reversible branch in four model granular beds subjected to vertical vibration.

We present results from four independent models of a granular assembly subjected to tapping. We find that the steady-state packing fraction as a function of the tapping intensity is nonmonotonic. In particular, for high tapping intensities, we observe an increase of the packing fraction with tapping strength. This finding challenges the current understanding of compaction of granular media since the steady-state packing fraction is believed to decrease monotonically with increasing tapping intensity. We propose an explanation of our results based on the properties of the arches formed by the particles.

Continuum percolation of long lifespan clusters in a simple fluid.

We present results on the percolation loci for chemical clusters and physical clusters of long lifespan. Chemical clusters are defined as sets of particles connected through particle-particle bonds that last for a given time tau. Physical clusters are sets of particles that remain close together at every instant for a given period of time tau. By using molecular dynamics simulations of a Lennard-Jones system we obtain the percolation loci at different values of tau as the lines in the temperature-density plane at which the system presents a spanning cluster in 50% of the configurations. We find that the percolation loci for chemical clusters shifts rapidly toward high densities as tau is increased. For moderate values of tau this line converges to the low-density branch of the liquid-solid coexistence curve. This implies that no stable chemical clusters can be found in the fluid phase. In contrast, the percolation loci for physical clusters tend to a limiting line, as tau tends to infinity, which is far from the liquid-solid transition line.

Cluster pair correlation function of simple fluids: energetic connectivity criteria.

We consider the clustering of Lennard-Jones particles by using an energetic connectivity criterion proposed long ago by Hill [J. Chem. Phys. 32, 617 (1955)] for the bond between pairs of particles. The criterion establishes that two particles are bonded (directly connected) if their relative kinetic energy is less than minus their relative potential energy. Thus, in general, it depends on the direction as well as on the magnitude of the velocities and positions of the particles. An integral equation for the pair connectedness function, proposed by two of the authors [Phys. Rev. E 61, R6067 (2000)], is solved for this criterion and the results are compared with those obtained from molecular dynamics simulations and from a connectedness Percus-Yevick-type integral equation for a velocity-averaged version of Hill's energetic criterion.

Hydration properties and potentials of mean force of nonpolar amino acid residues in water: a pertubation theoretic approach.

We use a perturbation approach to calculate the solute-solvent and solute-solute pair correlations for infinitely dilute solutions of nonpolar amino acid side chains in water. In particular, from the solute-solute correlations we derive potentials of mean force for all the distances between different residues of amino acids. Comparison with molecular dynamics simulations performed using GROMOS package shows that the goodness of the approximation varies with the amino acid considered. We discuss in terms of hydrophobicity the different effect that the inclusion of the attractions causes on the solute-water and solute-solute correlations.

Percolation of clusters with a residence time in the bond definition: Integral equation theory.

We consider the clustering and percolation of continuum systems whose particles interact via the Lennard-Jones pair potential. A cluster definition is used according to which two particles are considered directly connected (bonded) at time t if they remain within a distance d, the connectivity distance, during at least a time of duration tau, the residence time. An integral equation for the corresponding pair connectedness function, recently proposed by two of the authors [Phys. Rev. E 61, R6067 (2000)], is solved using the orthogonal polynomial approach developed by another of the authors [Phys. Rev. E 55, 426 (1997)]. We compare our results with those obtained by molecular dynamics simulations.