Travelling waves for a velocity–jump model of cell migration and proliferation

Cell invasion, characterised by moving fronts of cells, is an essential aspect of development, repair and disease. Typically, mathematical models of cell invasion are based on the Fisher–Kolmogorov equation. These traditional parabolic models can not be used to represent experimental measurements of individual cell velocities within the invading population since they imply that information propagates with infinite speed. To overcome this limitation we study combined cell motility and proliferation based on a velocity–jump process where information propagates with finite speed. The model treats the total population of cells as two interacting subpopulations: a subpopulation of left–moving cells, $L(x,t)$, and a subpopulation of right–moving cells, $R(x,t)$. This leads to a system of hyperbolic partial differential equations that includes a turning rate, $\Lambda \ge 0$, describing the rate at which individuals in the population change direction of movement. We present exact travelling wave solutions of the system of partial differential equations for the special case where $\Lambda = 0$ and in the limit that $\Lambda \to \infty$. For intermediate turning rates, $0 < \Lambda < \infty$, we analyse the travelling waves using the phase plane and we demonstrate a transition from smooth monotone travelling waves to smooth nonmonotone travelling waves as $\Lambda$ decreases through a critical value $\Lambda_{crit}$. We conclude by providing a qualitative comparison between the travelling wave solutions of our model and experimental observations of cell invasion. This comparison indicates that the small $\Lambda$ limit produces results that are consistent with experimental observations.

Sole depth and weight-bearing characteristics of the palmar surface of the feet of feral horses and domestic Thoroughbreds

Objective: To determine solar load-bearing structures in the feet of feral horses and investigate morphological characteristics of the sole in feral horses and domestic Thoroughbreds. Sample: Forelimbs from cadavers of 70 feral horses and 20 domestic Thoroughbreds in Australia. Procedures: Left forefeet were obtained from 3 feral horse populations from habitats of soft substrate (SS [n = 10 horses]), hard substrate (HS [10]), and a combination of SS and HS (10) and loaded in vitro. Pressure distribution was measured with a pressure plate. Sole depth was measured at 12 points across the solar plane in feet obtained from feral horses from SS (n = 20 horses) and HS (20) habitats and domestic Thoroughbreds (20). Results: Feet of feral horses from HS habitats loaded the periphery of the sole and hoof wall on a flat surface. Feral horses from HS or SS habitats had greater mean sole depth than did domestic Thoroughbreds. Sole depth was greatest peripherally and was correlated with the loading pattern. Conclusions and Clinical Relevance: The peripheral aspect of the sole in the feet of feral horses had a load-bearing function. Because of the robust nature of the tissue architecture, the hoof capsule of feral horses may be less flexible than that of typical domestic horses. The application of narrow-web horseshoes may not take full advantage of the load-bearing and force-dissipating properties of the peripheral aspect of the sole. Further studies are required to understand the effects of biomechanical stimulation on the adaptive responses of equine feet.

Gravity-driven fingering simulations for a thin liquid film flowing down the outside of a vertical cylinder

A numerical study is presented to examine the fingering instability of a gravity-driven thin liquid film flowing down the outer wall of a vertical cylinder. The lubrication approximation is employed to derive an evolution equation for the height of the film, which is dependent on a single parameter, the dimensionless cylinder radius. This equation is identified as a special case of that which describes thin film flow down an inclined plane. Fully three-dimensional simulations of the film depict a fingering pattern at the advancing contact line. We find the number of fingers observed in our simulations to be in excellent agreement with experimental observations and a linear stability analysis reported recently by Smolka & SeGall (Phys Fluids 23, 092103 (2011)). As the radius of the cylinder decreases, the modes of perturbation have an increased growth rate, thus increasing cylinder curvature partially acts to encourage the contact line instability. In direct competition with this behaviour, a decrease in cylinder radius means that fewer fingers are able to form around the circumference of the cylinder. Indeed, for a sufficiently small radius, a transition is observed, at which point the contact line is stable to transverse perturbations of all wavenumbers. In this regime, free surface instabilities lead to the development of wave patterns in the axial direction, and the flow features become perfectly analogous to the two-dimensional flow of a thin film down an inverted plane as studied by Lin & Kondic (Phys Fluids 22, 052105 (2010)). Finally, we simulate the flow of a single drop down the outside of the cylinder. Our results show that for drops with low volume, the cylinder curvature has the effect of increasing drop speed and hence promoting the phenomenon of pearling. On the other hand, drops with much larger volume evolve to form single long rivulets with a similar shape to a finger formed in the aforementioned simulations.

An FE investigation simulating intra-operative corrective forces applied to correct scoliosis deformity

Background: Adolescent idiopathic scoliosis (AIS) is a deformity of the spine, which may 34 require surgical correction by attaching a rod to the patient’s spine using screws 35 implanted in the vertebral bodies. Surgeons achieve an intra-operative reduction in the 36 deformity by applying compressive forces across the intervertebral disc spaces while 37 they secure the rod to the vertebra. We were interested to understand how the 38 deformity correction is influenced by increasing magnitudes of surgical corrective forces 39 and what tissue level stresses are predicted at the vertebral endplates due to the 40 surgical correction. 41 Methods: Patient-specific finite element models of the osseoligamentous spine and 42 ribcage of eight AIS patients who underwent single rod anterior scoliosis surgery were 43 created using pre-operative computed tomography (CT) scans. The surgically altered 44 spine, including titanium rod and vertebral screws, was simulated. The models were 45 analysed using data for intra-operatively measured compressive forces – three load 46 profiles representing the mean and upper and lower standard deviation of this data 47 were analysed. Data for the clinically observed deformity correction (Cobb angle) were 48 compared with the model-predicted correction and the model results investigated to 49 better understand the influence of increased compressive forces on the biomechanics of 50 the instrumented joints. 51 Results: The predicted corrected Cobb angle for seven of the eight FE models were 52 within the 5° clinical Cobb measurement variability for at least one of the force profiles. 53 The largest portion of overall correction was predicted at or near the apical 54 intervertebral disc for all load profiles. Model predictions for four of the eight patients 55 showed endplate-to-endplate contact was occurring on adjacent endplates of one or 56 more intervertebral disc spaces in the instrumented curve following the surgical loading 57 steps. 58 Conclusion: This study demonstrated there is a direct relationship between intra-59 operative joint compressive forces and the degree of deformity correction achieved. The 60 majority of the deformity correction will occur at or in adjacent spinal levels to the apex 61 of the deformity. This study highlighted the importance of the intervertebral disc space 62 anatomy in governing the coronal plane deformity correction and the limit of this 63 correction will be when bone-to-bone contact of the opposing vertebral endplates 64 occurs.

Changes in Knee Biomechanics After a Hip-Abductor Strengthening Protocol for Runners With Patellofemoral Pain Syndrome

Context: Very few authors have investigated the relationship between hip-abductor muscle strength and frontal-plane knee mechanics during running. Objective: To investigate this relationship using a 3-week hip-abductor muscle-strengthening program to identify changes in strength, pain, and biomechanics in runners with patellofemoral pain syndrome (PFPS). Design: Cohort study. Setting: University-based clinical research laboratory. Patients or Other Participants: Fifteen individuals (5 men, 10 women) with PFPS and 10 individuals without PFPS (4 men, 6 women) participated. Intervention(s): The patients with PFPS completed a 3-week hip-abductor strengthening protocol; control participants did not. Main Outcome Measure(s): The dependent variables of interest were maximal isometric hip-abductor muscle strength, 2-dimensional peak knee genu valgum angle, and stride-to-stride knee-joint variability. All measures were recorded at baseline and 3 weeks later. Between-groups differences were compared using repeated-measures analyses of variance. Results: At baseline, the PFPS group exhibited reduced strength, no difference in peak genu valgum angle, and increased stride-to-stride knee-joint variability compared with the control group. After the 3-week protocol, the PFPS group demonstrated increased strength, less pain, no change in peak genu valgum angle, and reduced stride-to-stride knee-joint variability compared with baseline. Conclusions: A 3-week hip-abductor muscle-strengthening protocol was effective in increasing muscle strength and decreasing pain and stride-to-stride knee-joint variability in individuals with PFPS. However, concomitant changes in peak knee genu valgum angle were not observed.

The relationship between hip-abductor strength and the magnitude of pelvic drop in patients with low back pain

Context: It has been theorized that a positive Trendelenburg test (TT) indicates weakness of the stance hip-abductor (HABD) musculature, results in contralateral pelvic drop, and represents impaired load transfer, which may contribute to low back pain. Few studies have tested whether weakness of the HABDs is directly related to the magnitude of pelvic drop (MPD). Objective: To examine the relationship between HABD strength and MPD during the static TT and during walking for patients with nonspecific low back pain (NSLBP) and healthy controls (CON). A secondary purpose was to examine this relationship in NSLBP after a 3-wk HABD-strengthening program. Design: Quasi-experimental. Setting: Clinical research laboratory. Participants: 20 (10 NSLBP and 10 CON). Intervention: HABD strengthening. Main Outcome Measures: Normalized HABD strength, MPD during TT, and maximal pelvic frontal-plane excursion during walking. Results: At baseline, the NSLBP subjects were significantly weaker (31%; P = .03) than CON. No differences in maximal pelvic frontal-plane excursion (P = .72), right MPD (P = 1.00), or left MPD (P = .40) were measured between groups. During the static TT, nonsignificant correlations were found between left HABD strength and right MPD for NSLBP (r = -.32, P = .36) and CON (r = -.24, P = .48) and between right HABD strength and left MPD for NSLBP (r = -.24, P = .50) and CON (r = -.41, P = .22). Nonsignificant correlations were found between HABD strength and maximal pelvic frontal-plane excursion for NSLBP (r = -.04, P = .90) and CON (r = -.14, P = .68). After strengthening, NSLBP demonstrated significant increases in HABD strength (12%; P = .02), 48% reduction in pain, and no differences in MPD during static TT and maximal pelvic frontal-plane excursion compared with baseline. Conclusions: HABD strength was poorly correlated to MPD during the static TT and during walking in CON and NSLBP. The results suggest that HABD strength may not be the only contributing factor in controlling pelvic stability, and the static TT has limited use as a measure of HABD function.

The relationship between hip abductor muscle strength and magnitude of pelvic drop following a 3 week strengthening protocol in non-specific low back pain patients.

Purpose: To examine the relationship between hip abductor muscle (HABD) strength and the magnitude of pelvic drop (MPD) for patients with non-specific low back pain (NSLBP) and controls (CON) prior to and following a 3-week HABD strengthening protocol. At baseline, we hypothesized that NSLBP patients would exhibit reduced HABD strength and greater MPD compared to CON. Following the protocol, we hypothesized that strength would increase and MPD would decrease. Relevance: The Trendelenburg test (TT) is a common clinical test used to examine the ability of the HABD to maintain horizontal pelvic position during single limb stance. However, no study has specifically tested this theory. Moreover, no study has investigated the relationship between HABD strength and pelvic motion during walking or tested whether increased HABD strength would reduce the MPD. Methods: Quasi-experimental with 3-week exercise intervention. Fifteen NSLBP patients (32.5yrs,range 21-51yrs; VAS baseline: 5.3cm) and 10 CON (29.5yrs,range 22-47yrs) were recruited. Isometric HABD strength was measured using a force dynamometer and the average of three maximal voluntary contractions were normalized to body mass (N/kg). Two-dimensional MPD (degrees) was measured using a 60 Hz camera and was derived from two retroreflective-markers placed on the posterior superior iliac spines. MPD was measured while performing the static TT and while walking and averaged over 10 consecutive footfalls. NSLBP patients completed a 3-week HABD strengthening protocol consisting of 2 open-kinetic-chain exercises then all measures were repeated. Non-parametric analysis was used for group comparisons and correlation analysis. Results: At baseline, the NSLBP patients demonstrated 31% reduced HABD strength (mean=6.6 N/kg) compared to CON (mean=9.5 N/kg: p=0.03) and no significant differences in maximal pelvic frontal plane excursion while walking (NSLBP:mean=8.1°, CON:mean=7.1°: p=0.72). No significant correlations were measured between left HABD strength and right MPD (r=-0.37, p=0.11), or between right HABD strength and left MPD (r=-0.04, p=0.84) while performing the static TT. Following the 3-week strengthening protocol, NSLBP patients demonstrated a 12% improvement in strength (Post:mean=7.4 N/kg: p=0.02), a reduction in pain (VAS followup: 2.8cm), but no significant decreases in MPD while walking (p=0.92). Conclusions: NSLBP patients demonstrated reduced HABD strength at baseline and were able to increase strength and reduce pain in a 3-week period. However, despite increases in HABD strength, the NSLBP group exhibited similar MPD motion during the static TT and while walking compared to baseline and controls. Implications: The results suggest that the HABD alone may not be primarily responsible for controlling a horizontal pelvic position during static and dynamic conditions. Increasing the strength of the hip abductors resulted in a reduction of pain in NSLBP patients providing evidence for further research to identify specific musculature responsible for controlling pelvic motion.

Field-effect transistors fabricated from diluted magnetic semiconductor colloidal nanowires

Field-effect transistors (FETs) fabricated from undoped and Co2+-doped CdSe colloidal nanowires show typical n-channel transistor behaviour with gate effect. Exposed to microscope light, a 10 times current enhancement is observed in the doped nanowire-based devices due to the significant modification of the electronic structure of CdSe nanowires induced by Co2+-doping, which is revealed by theoretical calculations from spin-polarized plane-wave density functional theory.

Vibrational spectroscopy of the mineral meyerhofferite CaB3O3(OH)5·H2O – An assessment of the molecular structure

Meyerhofferite is a calcium hydrated borate mineral with ideal formula: CaB3O3(OH)5�H2O and occurs as white complex acicular to crude crystals with length up to �4 cm, in fibrous divergent, radiating aggregates or reticulated and is often found in sedimentary or lake-bed borate deposits. The Raman spectrum of meyerhofferite is dominated by intense sharp band at 880 cm�1 assigned to the symmetric stretching mode of trigonal boron. Broad Raman bands at 1046, 1110, 1135 and 1201 cm�1 are attributed to BOH in-plane bending modes. Raman bands in the 900–1000 cm�1 spectral region are assigned to the antisymmetric stretching of tetrahedral boron. Distinct OH stretching Raman bands are observed at 3400, 3483 and 3608 cm�1. The mineral meyerhofferite has a distinct Raman spectrum which is different from the spectrum of other borate minerals, making Raman spectroscopy a very useful tool for the detection of meyerhofferite in sedimentary and lake bed deposits.

First-principle studies of the formation and diffusion of hydrogen vacancies in magnesium hydride

Ab initio density functional theory (DFT) calculations are performed to study the formation and diffusion of hydrogen vacancies on MgH2(110) surface and in bulk. We find that the formation energies for a single H-vacancy increase slightly from the surface to deep layers. The energies for creating adjacent surface divancacies at two inplane sites and at an inplane and a bridge site are even smaller than that for the formation of a single H-vacancy, a fact that is attributed to the strong vacancy−vacancy interactions. The diffusion of an H-vacancy from an in-plane site to a bridge site on the surface has the smallest activation barrier calculated at 0.15 eV and should be fast at room temperature. The activation barriers computed for H-vacancy diffusion from the surface into sublayers are all less than 0.70 eV, which is much smaller than the activation energy for desorption of hydrogen on the MgH2(110) surface (1.78−2.80 eV/H2). This suggests that surface desorption is more likely than vacancy diffusion to be rate determining, such that finding effective catalyst on the MgH2 surface to facilitate desorption will be very important for improving overall dehydrogenation performance.

Ab initio studies of hydrogen desorption from low index magnesium hydride surface

The low index Magnesium hydride surfaces, MgH2(0 0 1) and MgH2(1 1 0), have been studied by ab intio Density Functional Theory (DFT) calculations. It was found that the MgH2(1 1 0) surface is more stable than MgH2(0 0 1) surface, which is in good agreement with the experimental observation. The H2 desorption barriers vary depending on the crystalline surfaces that are exposed and also the specific H atom sites involved – they are found to be generally high, due to the thermodynamic stability of the MgH2 system, and are larger for the MgH2(0 0 1) surface. The pathway for recombinative desorption of one in-plane and one bridging H atom from the MgH2(1 1 0) surface was found to be the lowest energy barrier amongst those computed (172 KJ/mol) and is in good agreement with the experimental estimates.

Phantom Scatter and the A-SI EPID

Introduction: The use of amorphous-silicon electronic portal imaging devices (a-Si EPIDs) for dosimetry is complicated by the effects of scattered radiation. In photon radiotherapy, primary signal at the detector can be accompanied by photons scattered from linear accelerator components, detector materials, intervening air, treatment room surfaces (floor, walls, etc) and from the patient/phantom being irradiated. Consequently, EPID measurements which presume to take scatter into account are highly sensitive to the identification of these contributions. One example of this susceptibility is the process of calibrating an EPID for use as a gauge of (radiological) thickness, where specific allowance must be made for the effect of phantom-scatter on the intensity of radiation measured through different thicknesses of phantom. This is usually done via a theoretical calculation which assumes that phantom scatter is linearly related to thickness and field-size. We have, however, undertaken a more detailed study of the scattering effects of fields of different dimensions when applied to phantoms of various thicknesses in order to derive scattered-primary ratios (SPRs) directly from simulation results. This allows us to make a more-accurate calibration of the EPID, and to qualify the appositeness of the theoretical SPR calculations. Methods: This study uses a full MC model of the entire linac-phantom-detector system simulated using EGSnrc/BEAMnrc codes. The Elekta linac and EPID are modelled according to specifications from the manufacturer and the intervening phantoms are modelled as rectilinear blocks of water or plastic, with their densities set to a range of physically realistic and unrealistic values. Transmissions through these various phantoms are calculated using the dose detected in the model EPID and used in an evaluation of the field-size-dependence of SPR, in different media, applying a method suggested for experimental systems by Swindell and Evans [1]. These results are compared firstly with SPRs calculated using the theoretical, linear relationship between SPR and irradiated volume, and secondly with SPRs evaluated from our own experimental data. An alternate evaluation of the SPR in each simulated system is also made by modifying the BEAMnrc user code READPHSP, to identify and count those particles in a given plane of the system that have undergone a scattering event. In addition to these simulations, which are designed to closely replicate the experimental setup, we also used MC models to examine the effects of varying the setup in experimentally challenging ways (changing the size of the air gap between the phantom and the EPID, changing the longitudinal position of the EPID itself). Experimental measurements used in this study were made using an Elekta Precise linear accelerator, operating at 6MV, with an Elekta iView GT a-Si EPID. Results and Discussion: 1. Comparison with theory: With the Elekta iView EPID fixed at 160 cm from the photon source, the phantoms, when positioned isocentrically, are located 41 to 55 cm from the surface of the panel. At this geometry, a close but imperfect agreement (differing by up to 5%) can be identified between the results of the simulations and the theoretical calculations. However, this agreement can be totally disrupted by shifting the phantom out of the isocentric position. Evidently, the allowance made for source-phantom-detector geometry by the theoretical expression for SPR is inadequate to describe the effect that phantom proximity can have on measurements made using an (infamously low-energy sensitive) a-Si EPID. 2. Comparison with experiment: For various square field sizes and across the range of phantom thicknesses, there is good agreement between simulation data and experimental measurements of the transmissions and the derived values of the primary intensities. However, the values of SPR obtained through these simulations and measurements seem to be much more sensitive to slight differences between the simulated and real systems, leading to difficulties in producing a simulated system which adequately replicates the experimental data. (For instance, small changes to simulated phantom density make large differences to resulting SPR.) 3. Comparison with direct calculation: By developing a method for directly counting the number scattered particles reaching the detector after passing through the various isocentric phantom thicknesses, we show that the experimental method discussed above is providing a good measure of the actual degree of scattering produced by the phantom. This calculation also permits the analysis of the scattering sources/sinks within the linac and EPID, as well as the phantom and intervening air. Conclusions: This work challenges the assumption that scatter to and within an EPID can be accounted for using a simple, linear model. Simulations discussed here are intended to contribute to a fuller understanding of the contribution of scattered radiation to the EPID images that are used in dosimetry calculations. Acknowledgements: This work is funded by the NHMRC, through a project grant, and supported by the Queensland University of Technology (QUT) and the Royal Brisbane and Women's Hospital, Brisbane, Australia. The authors are also grateful to Elekta for the provision of manufacturing specifications which permitted the detailed simulation of their linear accelerators and amorphous-silicon electronic portal imaging devices. Computational resources and services used in this work were provided by the HPC and Research Support Group, QUT, Brisbane, Australia.

Numerical solutions for thin film flow down the outside and inside of a vertical cylinder

We consider a model for thin film flow down the outside and inside of a vertical cylinder. Our focus is to study the effect that the curvature of the cylinder has on the gravity-driven instability of the advancing contact line and to simulate the resulting fingering patterns that form due to this instability. The governing partial differential equation is fourth order with a nonlinear degenerate diffusion term that represents the stabilising effect of surface tension. We present numerical solutions obtained by implementing an efficient alternating direction implicit scheme. When compared to the problem of flow down a vertical plane, we find that increasing substrate curvature tends to increase the fingering instability for flow down the outside of the cylinder, whereas flow down the inside of the cylinder substrate curvature has the opposite effect. Further, we demonstrate the existence of nontrivial travelling wave solutions which describe fingering patterns that propagate down the inside of a cylinder at constant speed without changing form. These solutions are perfectly analogous to those found previously for thin film flow down an inclined plane.

Vibrational spectroscopy of the phosphate mineral lazulite – (Mg, Fe)Al2(PO4)2·(OH)2 found in the Minas Gerais, Brazil

This research was done on lazulite samples from the Gentil mine, a lithium bearing pegmatite located in the municipality of Mendes Pimentel, Minas Gerais, Brazil. Chemical analysis was carried out by electron microprobe analysis and indicated a magnesium rich phase with partial substitution of iron. Traces of Ca and Mn, (which partially replaced Mg) were found. The calculated chemical formula of the studied sample is: (Mg0.88, Fe0.11)Al1.87(PO4)2.08(OH)2.02. The Raman spectrum of lazulite is dominated by an intense sharp band at 1060 cm-1 assigned to PO stretching vibrations of of tetrahedral [PO4] clusters presents into the HPO2/4- units. Two Raman bands at 1102 and 1137 cm-1 are attributed to both the HOP and PO antisymmetric stretching vibrations. The two infrared bands at 997 and 1007 cm-1 are attributed to the m1 PO3/4- symmetric stretching modes. The intense bands at 1035, 1054, 1081, 1118 and 1154 cm-1 are assigned to the v3PO3/4- antisymmetric stretching modes from both the HOP and tetrahedral [PO4] clusters. A set of Raman bands at 605, 613, 633 and 648 cm-1 are assigned to the m4 out of plane bending modes of the PO4, HPO4 and H2PO4 units. Raman bands observed at 414, 425, 460, and 479 cm-1 are attributed to the m2 tetrahedral PO4 clusters, HPO4 and H2PO4 bending modes. The intense Raman band at 3402 and the infrared band at 3403 cm-1 are assigned to the stretching vibration of the OH units. A combination of Raman and infrared spectroscopy enabled aspects of the molecular structure of the mineral lazulite to be understood.

Molecular dynamics simulation of fracture strength and morphology of defective graphene

Different types of defects can be introduced into graphene during material synthesis, and significantly influence the properties of graphene. In this work, we investigated the effects of structural defects, edge functionalisation and reconstruction on the fracture strength and morphology of graphene by molecular dynamics simulations. The minimum energy path analysis was conducted to investigate the formation of Stone-Wales defects. We also employed out-of-plane perturbation and energy minimization principle to study the possible morphology of graphene nanoribbons with edge-termination. Our numerical results show that the fracture strength of graphene is dependent on defects and environmental temperature. However, pre-existing defects may be healed, resulting in strength recovery. Edge functionalization can induce compressive stress and ripples in the edge areas of graphene nanoribbons. On the other hand, edge reconstruction contributed to the tensile stress and curved shape in the graphene nanoribbons.