Langevin dynamics modeling of the water diffusion tensor in partially aligned collagen networks

In this work, a Langevin dynamics model of the diffusion of water in articular cartilage was developed. Numerical simulations of the translational dynamics of water molecules and their interaction with collagen fibers were used to study the quantitative relationship between the organization of the collagen fiber network and the diffusion tensor of water in model cartilage. Langevin dynamics was used to simulate water diffusion in both ordered and partially disordered cartilage models. In addition, an analytical approach was developed to estimate the diffusion tensor for a network comprising a given distribution of fiber orientations. The key findings are that (1) an approximately linear relationship was observed between collagen volume fraction and the fractional anisotropy of the diffusion tensor in fiber networks of a given degree of alignment, (2) for any given fiber volume fraction, fractional anisotropy follows a fiber alignment dependency similar to the square of the second Legendre polynomial of cos(θ), with the minimum anisotropy occurring at approximately the magic angle (θMA), and (3) a decrease in the principal eigenvalue and an increase in the transverse eigenvalues is observed as the fiber orientation angle θ progresses from 0◦ to 90◦. The corresponding diffusion ellipsoids are prolate for θ < θMA, spherical for θ ≈ θMA, and oblate for θ > θMA. Expansion of the model to include discrimination between the combined effects of alignment disorder and collagen fiber volume fraction on the diffusion tensor is discussed.

Use of vibration characteristics to predict the axial deformation of columns

Vibration characteristics of columns are influenced by their axial loads. Numerous methods have been developed to quantify axial load and deformation in individual columns based on their natural frequencies. However, these methods cannot be applied to columns in a structural framing system as the natural frequency is a global parameter of the entire framing system. This paper presents an innovative method to quantify axial deformations of columns in a structural framing system using its vibration characteristics, incorporating the influence of load tributary areas, boundary conditions and load migration among the columns.

Characterisation of the micro-architecture of direct writing melt electrospun tissue engineering scaffolds using diffusion tensor and computed tomography microimaging

This article describes the first steps toward comprehensive characterization of molecular transport within scaffolds for tissue engineering. The scaffolds were fabricated using a novel melt electrospinning technique capable of constructing 3D lattices of layered polymer fibers with well - defined internal microarchitectures. The general morphology and structure order was then determined using T 2 - weighted magnetic resonance imaging and X - ray microcomputed tomography. Diffusion tensor microimaging was used to measure the time - dependent diffusivity and diffusion anisotropy within the scaffolds. The measured diffusion tensors were anisotropic and consistent with the cross - hatched geometry of the scaffolds: diffusion was least restricted in the direction perpendicular to the fiber layers. The results demonstrate that the cross - hatched scaffold structure preferentially promotes molecular transport vertically through the layers ( z - axis), with more restricted diffusion in the directions of the fiber layers ( x – y plane). Diffusivity in the x – y plane was observed to be invariant to the fiber thickness. The characteristic pore size of the fiber scaffolds can be probed by sampling the diffusion tensor at multiple diffusion times. Prospective application of diffusion tensor imaging for the real - time monitoring of tissue maturation and nutrient transport pathways within tissue engineering scaffolds is discussed.

Force-deformation properties of the human heel pad during barefoot walking

Introduction: The plantar heel pad is a specialized fibroadipose tissue that attenuates and, in part, dissipates the impact energy associated with heel strike. Although near maximal deformation of the heel pad has been shown during running, in vivo measurement of the deformation and structural properties of the heel pad during walking remains largely unexplored. This study employed a fluoroscope, synchronized with a pressure platform, to obtain force–deformation data for the heel pad during walking. Methods: Dynamic lateral foot radiographs were acquired from 6 male and 10 female adults (age, 45 ± 10 yrs; height, 1.66 ± 0.10 m; and weight, 80.7 ± 10.8 kg), while walking barefoot at preferred speeds. The inferior aspect of the calcaneus was digitized and the sagittal thickness and deformation of the heel pad relative to the support surface calculated. Simultaneous measurement of the peak force beneath the heel was used to estimate the principal structural properties of the heel pad. Results: Transient loading profiles associated with walking induced rapidly changing deformation rates in the heel pad and resulted in irregular load–deformation curves. The initial stiffness (32 ± 11 N.mm-1) of the heel pad was an order of magnitude lower than its final stiffness (212 ± 125 N.mm-1) and on average, only 1.0 J of energy was dissipated by the heel pad with each step during walking. Peak deformation (10.3 mm) approached that predicted for the limit of pain tolerance (10.7 mm). Conclusion: These findings suggest the heel pad operates close to its pain threshold even at speeds encountered during barefoot walking and provides insight as to why barefoot runners may adopt ‘forefoot’ strike patterns that minimize heel loading.

Raman spectroscopy of the molybdate minerals chillagite (tungsteinian wulfenite-I4), stolzite, scheelite, wolframite and wulfenite

Raman spectra of chillagite, wulfenite, stolzite, scheelite and wolframite were obtained at 298 and 77 K using a Raman microprobe in combination with a thermal stage. Chillagite is a solid solution of wulfenite and stolzite. The spectra of these molybdate minerals are orientation dependent. The band at 695 cm-1 is interpreted as an antisymmetric bridging mode associated with the tungstate chain. The bands at 790 and 881 cm-1 are associated with the antisymmetric and symmetric Ag modes of terminal WO2 whereas the origin of the 806 cm-1 band remains unclear. The 4(Eg) band was absent for scheelite. The bands at 353 and 401 cm-1 are assigned as either deformation modes or as r(Bg) and (Ag) modes of terminal WO2. The band at 462 cm-1 has an equivalent band in the infrared at 455 cm-1 assigned as as(Au) of the (W2O4)n chain. The band at 508 cm-1 is assigned as sym(Bg) of the (W2O4)n chain.

Raman microscopic study of the Li amphibole holmquistite, from the Martin Marietta Quarry, Bessemer City, NC, USA

The Raman spectrum of holmquistite, a Li-containing orthorhombic amphibole from Bessemer City, USA has been measured. The OH-stretching region is characterized by bands at 3661, 3646, 3634 and 3614 cm–1 assigned to 3 Mg–OH, 2 Mg + Fe2+–OH, Mg + 2Fe2+–OH and 3 Fe2+–OH, respectively. These Mg and Fe2+ cations are located at the M1 and M3 sites and have a Fe2+/(Fe2+ + Mg) ratio of 0.35. The 960–1110 cm–1 region represents the antisymmetric Si–O–Si and O–Si–O stretching vibrations. For holmquistite, strong bands are observed around 1022 and 1085 cm–1 with a shoulder at 1127 cm–1 and minor bands at 1045 and 1102 cm–1. In the region 650–800 cm–1 bands are observed at 679, 753 and 791 cm–1 with a minor band around 694 cm–1 attributed to the symmetrical Si–O–Si and Si–O vibrations. The region below 625 cm–1 is characterized by 14 vibrations related to the deformation modes of the silicate double chain and vibrations involving Mg, Fe, Al and Li in the various M sites. The 502 cm–1 band is a Li–O deformation mode while the 456, 551 and 565 cm–1 bands are Al–O deformation modes.

Raman spectroscopy of the copper chloride minerals nantokite, eriochalcite and claringbullite - implications for copper corrosion

The application of Raman spectroscopy to the study of the copper chloride minerals nantokite, eriochalcite and claringbullite has enabled the vibrational modes for the CuCl, CuOH and CuOH2 to be determined. Nantokite is characterised by bands at 205 and 155 cm-1 attributed to the transverse and longitudinal optic vibrations. Nantokite also has an intense band at 463 cm-1, eriochalcite at 405 and 390 cm-1 and claringbullite at 511 cm-1. These bands are attributed to CuO stretching modes. Water librational bands at around 672 cm-1 for eriochalcite have been identified and hydroxyl deformation modes of claringbullite at 970, 906 and 815 cm-1 are observed. Spectra of the three minerals are so characteristically different that the minerals are readily identified by Raman spectroscopy. The minerals are often determined in copper corrosion products by X-ray diffraction. Raman spectroscopy offers a rapid, in-situ technique for the identification of these corrosion products.

Comparison of 3D finite element analysis derived stiffness and BMD to determine the failure load of the excised proximal femur

Introduction: Bone mineral density (BMD) is currently the preferred surrogate for bone strength in clinical practice. Finite element analysis (FEA) is a computer simulation technique that can predict the deformation of a structure when a load is applied, providing a measure of stiffness (Nmm−1). Finite element analysis of X-ray images (3D-FEXI) is a FEA technique whose analysis is derived froma single 2D radiographic image. Methods: 18 excised human femora had previously been quantitative computed tomography scanned, from which 2D BMD-equivalent radiographic images were derived, and mechanically tested to failure in a stance-loading configuration. A 3D proximal femur shape was generated from each 2D radiographic image and used to construct 3D-FEA models. Results: The coefficient of determination (R2%) to predict failure load was 54.5% for BMD and 80.4% for 3D-FEXI. Conclusions: This ex vivo study demonstrates that 3D-FEXI derived from a conventional 2D radiographic image has the potential to significantly increase the accuracy of failure load assessment of the proximal femur compared with that currently achieved with BMD. This approach may be readily extended to routine clinical BMD images derived by dual energy X-ray absorptiometry. Crown Copyright © 2009 Published by Elsevier Ltd on behalf of IPEM. All rights reserved

Comparison of 3D finite element analysis derived stiffness and BMD to determine the failure load of the excised proximal femur

Bone mineral density (BMD) is currently the preferred surrogate for bone strength in clinical practice. Finite element analysis (FEA) is a computer simulation technique that can predict the deformation of a structure when a load is applied, providing a measure of stiffness (N mm− 1). Finite element analysis of X-ray images (3D-FEXI) is a FEA technique whose analysis is derived from a single 2D radiographic image. This ex-vivo study demonstrates that 3D-FEXI derived from a conventional 2D radiographic image has the potential to significantly increase the accuracy of failure load assessment of the proximal femur compared with that currently achieved with BMD.

Raman spectroscopic study of the antimonate mineral brandholzite Mg[Sb(OH)12].6H2O

Raman spectra of brandholzite Mg[Sb(OH)6].6H2O were studied, complemented with infrared spectra, and related to the structure of the mineral. An intense Raman sharp band at 618 cm-1 is attributed to the SbO symmetric stretching mode. The low intensity band at 730 cm-1 is ascribed to the SbO antisymmetric stretching vibration. Low intensity Raman bands were found at 503, 526 and 578 cm-1. Corresponding infrared bands were observed at 527, 600, 637, 693, 741 and 788 cm-1. Four Raman bands observed at 1043, 1092, 1160 and 1189 cm-1 and eight infrared bands at 963, 1027, 1055, 1075, 1108, 1128, 1156 and 1196 cm-1 are assigned to δ SbOH deformation modes. A complex pattern resulting from the overlapping band of the water and hydroxyl units is observed. Raman bands are observed at 3240, 3383, 3466, 3483 and 3552 cm-1, infrared bands at 3248, 3434 and 3565 cm-1. The first two Raman bands and the first infrared band are assigned to water stretching vibrations. The two higher wavenumber Raman bands observed at 3466 and 3552 cm-1 and two infrared bands at 3434 and 3565 cm-1 are assigned to the stretching vibrations of the hydroxyl units. Observed Raman and infrared bands are connected with O-H…O hydrogen bonds and their lengths 2.72, 2.79, 2.86, 2.88 and 3.0 Å (Raman) and 2.73, 2.83 and 3.07 Å (infrared).

Raman spectroscopic study of the antimonate mineral bahianite Al5Sb35+O14(OH)2

Raman spectroscopy has been used to characterise the antimonate mineral bahianite Al5Sb35+O14(OH)2 , a semi-precious gem stone. The mineral is characterised by an intense Raman band at 818 cm-1 assigned to Sb3O1413- stretching vibrations. Other lower intensity bands at 843 and 856 cm-1 are also assigned to this vibration and this concept suggests the non-equivalence of SbO units in the structure. Low intensity Raman bands at 669 and 682 cm-1 are probably assignable to the OSbO antisymmetric stretching vibrations. Raman bands at 1756, 1808 and 1929 cm-1 may be assigned to δ SbOH deformation modes, whilst Raman bands at 3462 and 3495 cm-1 are assigned to AlOH stretching vibrations. Complexity in the low wave number region is attributed to the composition of the mineral.

Raman spectroscopic study of the mineral finnemanite Pb5(As3+O3)3Cl

The arsenite minerals finnemanite Pb5(As3+O3)3Cl been studied by Raman spectroscopy. The most intense Raman band at 871 cm-1 is assigned to the ν1 (AsO3)3- symmetric stretching vibration. Three Raman bands at 898, 908 and 947 cm-1 are assigned to the ν3 (AsO3)3- antisymmetric stretching vibration. The observation of multiple antisymmetric stretching vibrations suggest that the (AsO3)3- units are not equivalent in the molecular structure of finnemanite. Two Raman bands at 383 and 399 cm-1 are assigned to the ν2 (AsO3)3- bending modes. DFT calculations enabled the position of AsO32- symmetric stretching mode at 839 cm-1, the antisymmetric stretching mode at 813 cm-1, and the deformation mode at 449 cm-1 to be calculated. Raman bands are observed at 115, 145, 162, 176, 192, 216 and 234 cm-1 as well. The two most intense bands are observed at 176 and 192 cm-1. These bands are assigned to PbCl stretching vibrations and result from transverse/ longitudinal splitting. The bands at 145 and 162 cm-1 may be assigned to Cl-Pb-Cl bending modes.

Raman spectroscopic study of the arsenite minerals leiteite ZnAs2O4 , reinerite Zn3(AsO3)2 and cafarsite Ca5(Ti,Fe,Mn)7(AsO3)12.4H2O

The selected arsenite minerals leiteite, reinerite and cafarsite have been studied by Raman spectroscopy. DFT calculations enabled the position of AsO22- symmetric stretching mode at 839 cm-1, the antisymmetric stretching mode at 813 cm-1, and the deformation mode at 449 cm-1 to be calculated. The Raman spectrum of leiteite shows bands at 804 and 763 cm-1 assigned to the As2O42- symmetric and antisymmetric stretching modes. The most intense Raman band of leiteite is the band at 457 cm-1 and is assigned to the ν2 As2O42- bending mode. A comparison of the Raman spectrum of leiteite is made with the arsenite minerals reinerite and cafarsite.

Raman spectroscopic study of the antimony containing mineral partzite Cu2Sb2(O,OH)7

Raman spectroscopy of the mineral partzite Cu2Sb2(O,OH)7 complimented with infrared spectroscopy were studied and related to the structure of the mineral. The Raman spectrum shows some considerable complexity with a number of overlapping bands observed at 479, 520, 594, 607 and 620 cm-1 with additional low intensity bands found at 675, 730, 777 and 837 cm-1. Raman bands of partzite in the spectral region 590 to 675 cm-1 are attributable the ν1 symmetric stretching modes. The Raman bands at 479 and 520 cm-1 are assigned to the ν3 antisymmetric stretching modes. Raman bands at 1396 and 1455 cm-1 are attributed to SbOH deformation modes. A complex pattern resulting from the overlapping band of the water and OH units is found. Raman bands are observed at 3266, 3376, 3407, 3563, 3586 and 3622 cm-1. The first three bands are assigned to water stretching vibrations. The three higher wavenumber bands are assigned to the stretching vibrations of the OH units. It is proposed that based upon observation of the Raman spectra that water is involved in the structure of partzite. Thus the formula Cu2Sb2(O,OH)7 may be better written as Cu2Sb2(O,OH)7 •xH2O

Raman spectroscopic study of the multi-anion mineral dixenite CuMn2+14Fe3+(AsO3)5(SiO4)2(AsO4)(OH)6

The mixed anion mineral dixenite has been studied by Raman spectroscopy, complimented with infrared spectroscopy. The Raman spectrum of dixenite shows bands at 839 and 813 cm-1 assigned to the (AsO3)3- symmetric and antisymmetric stretching modes. The most intense Raman band of dixenite is the band at 526 cm-1 and is assigned to the ν2 AsO33- bending mode. DFT calculations enabled the position of AsO22- symmetric stretching mode at 839 cm-1, the antisymmetric stretching mode at 813 cm-1, and the deformation mode at 449 cm-1 to be calculated. Raman bands at 1026 and 1057 cm-1 are assigned to the SiO42- symmetric stretching vibrations and at 1349 and 1386 cm-1 to the SiO42- antisymmetric stretching vibrations. Both Raman and infrared spectra indicate the presence of water in the structure of dixenite. This brings into question the commonly accepted formula of dixenite as CuMn2+14Fe3+(AsO3)5(SiO4)2(AsO4)(OH)6. The formula may be better written as CuMn2+14Fe3+(AsO3)5(SiO4)2(AsO4)(OH)6•xH2O.