Mechanical Properties of Long Leaves: Experiment and Theory.

The static properties of leaves with parallel venation from terrestrial orchids of the genus Epipactis were modelled as coupled elastic rods using the geometrically exact Cosserat theory and the resulting boundary-value problem was solved numerically using a method from Shampine, Muir and Xu. The response of the leaf structure to the applied force was obtained from preliminary measurements. These measurements allowed the Young's modulus of the Epipactis leaves to be determined. The appearance of wrinkles and undulation characteristics for some leaves has been attributed to the small torsional stiffness of the leaf edges.

Erratum: Capturing the wide variety of impaired fracture healing phenotypes in Neurofibromatosis Type 1 with eight key factors: a computational study.

This corrects the article DOI: 10.1038/srep20010.

Mathematical modelling of the degradation behaviour of biodegradable metals.

A mathematical model for the biodegradation of magnesium is developed in this study to inspect the corrosion behaviour of biodegradable implants. The aim of this study was to provide a suitable framework for the assessment of the corrosion rate of magnesium which includes the process of formation/dissolution of the protective film. The model is intended to aid the design of implants with suitable geometries. The level-set method is used to follow the changing geometry of the implants during the corrosion process. A system of partial differential equations is formulated based on the physical and chemical processes that occur at the implant-medium boundary in order to simulate the effect of the formation of a protective film on the degradation rate. The experimental data from the literature on the corrosion of a high-purity magnesium sample immersed in simulated body fluid is used to calibrate the model. The model is then used to predict the degradation behaviour of a porous orthopaedic implant. The model successfully reproduces the precipitation of the corrosion products on the magnesium surface and the effect on the degradation rate. It can be used to simulate the implant degradation and the formation of the corrosion products on the surface of biodegradable magnesium implants with complex geometries.

Capturing the wide variety of impaired fracture healing phenotypes in Neurofibromatosis Type 1 with eight key factors: a computational study.

Congenital pseudarthrosis of the tibia (CPT) is a rare disease which normally presents itself during early childhood by anterolateral bowing of the tibia and spontaneous tibial fractures. Although the exact etiology of CPT is highly debated, 40-80% of CPT patients are carriers of a mutation in the Neurofibromatosis Type 1 (NF1) gene, which can potentially result in an altered phenotype of the skeletal cells and impaired bone healing. In this study we use a computational model of bone regeneration to examine the effect of the Nf1 mutation on bone fracture healing by altering the parameter values of eight key factors which describe the aberrant cellular behaviour of Nf1 haploinsufficient and Nf1 bi-allelically inactivated cells. We show that the computational model is able to predict the formation of a hamartoma as well as a wide variety of CPT phenotypes through different combinations of altered parameter values. A sensitivity analysis by "Design of Experiments" identified the impaired endochondral ossification process and increased infiltration of fibroblastic cells as key contributors to the degree of severity of CPT. Hence, the computational model results have added credibility to the experimental hypothesis of a genetic cause (i.e. Nf1 mutation) for CPT.

Mechanisms of cell migration in the adult brain: modelling subventricular neurogenesis.

Neurogenesis has been the subject of active research in recent years. Although the majority of neurons form during the embryonic period, neurogenesis continues in restricted regions of the mammalian brain well into adulthood. In rodent brains, neuronal migration is present in the rostral migratory stream (RMS), connecting the subventricular zone to the olfactory bulb (OB). The migration in the RMS is characterised by a lack of dispersion of neuroblasts into the surrounding tissues and a highly directed motion towards the OB. This study uses a simple mathematical model to investigate several theories of migration of neuroblasts through the RMS proposed in the literature, including chemo-attraction, chemorepulsion, general inhibition and the presence of a migration-inducing protein. Apart from the general inhibition model, all the models were able to provide results in good qualitative correspondence with the experimental observations.

A mathematical model of adult subventricular neurogenesis.

Neurogenesis has been the subject of active research in recent years and many authors have explored the phenomenology of the process, its regulation and its purported purpose. Recent developments in bioluminescent imaging (BLI) allow direct in vivo imaging of neurogenesis, and in order to interpret the experimental results, mathematical models are necessary. This study proposes such a mathematical model that describes adult mammalian neurogenesis occurring in the subventricular zone and the subsequent migration of cells through the rostral migratory stream to the olfactory bulb (OB). This model assumes that a single chemoattractant is responsible for cell migration, secreted both by the OB and in an endocrine fashion by the cells involved in neurogenesis. The solutions to the system of partial differential equations are compared with the physiological rodent process, as previously documented in the literature and quantified through the use of BLI, and a parameter space is described, the corresponding solution to which matches that of the rodent model. A sensitivity analysis shows that this parameter space is stable to perturbation and furthermore that the system as a whole is sloppy. A large number of parameter sets are stochastically generated, and it is found that parameter spaces corresponding to physiologically plausible solutions generally obey constraints similar to the conditions reported in vivo. This further corroborates the model and its underlying assumptions based on the current understanding of the investigated phenomenon. Concomitantly, this leaves room for further quantitative predictions pertinent to the design of future proposed experiments.

Variation in Lyman-alpha fine structure components for Cl XVII during a tokamak plasma shot.

In this Brief Report we study the measured and modeled Lyman-alpha intensity ratios for hydrogenlike Cl XVII in a deuterium base plasma in the Joint European Torus tokamak and examine the agreement between experiment and theory for a particular plasma shot. A collisional-radiative model is used to calculate the values of the intensity ratios using measured plasma parameters for comparison with line-of-sight values. When variations in the electron parameters during the discharge are taken into account, the variations in the modeled values are seen to follow the experimental data. The difference between the values of observed and modeled intensity ratios is discussed.

Time evolution of Lyman-alpha fine-structure components for Al XIII.

We present a comparison of measured and theoretically modeled Lyman-alpha intensity ratios of hydrogenlike Al XIII impurity ions in a deuterium base plasma in the COMPASS-D tokamak. The time evolution of the intensity ratios is computed from a collisional-radiative model using measured plasma parameters and compared with line-of-sight integral values measured using a high-resolution crystal spectrometer. The variations in the modeled values follow the experimental data in the case of the L-mode plasma, taking into account variations in the electron parameters during the discharges. Apparent discrepancies between the observed and calculated ratios in the case of the H-mode plasma are attributed to line blending due to satellites of nearby Fe emission.