Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334-368] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths and is close to a convection CFL condition for large mean free paths. Our analysis is based on very simple energy estimates. © 2010 Society for Industrial and Applied Mathematics.

Single-cell functional analysis of parathyroid adenomas reveals distinct classes of calcium sensing behaviour in primary hyperparathyroidism.

Primary hyperparathyroidism (PHPT) is a common endocrine neoplastic disorder caused by a failure of calcium sensing secondary to tumour development in one or more of the parathyroid glands. Parathyroid adenomas are comprised of distinct cellular subpopulations of variable clonal status that exhibit differing degrees of calcium responsiveness. To gain a clearer understanding of the relationship among cellular identity, tumour composition and clinical biochemistry in PHPT, we developed a novel single cell platform for quantitative evaluation of calcium sensing behaviour in freshly resected human parathyroid tumour cells. Live-cell intracellular calcium flux was visualized through Fluo-4-AM epifluorescence, followed by in situ immunofluorescence detection of the calcium sensing receptor (CASR), a central component in the extracellular calcium signalling pathway. The reactivity of individual parathyroid tumour cells to extracellular calcium stimulus was highly variable, with discrete kinetic response patterns observed both between and among parathyroid tumour samples. CASR abundance was not an obligate determinant of calcium responsiveness. Calcium EC50 values from a series of parathyroid adenomas revealed that the tumours segregated into two distinct categories. One group manifested a mean EC50 of 2.40 mM (95% CI: 2.37-2.41), closely aligned to the established normal range. The second group was less responsive to calcium stimulus, with a mean EC50 of 3.61 mM (95% CI: 3.45-3.95). This binary distribution indicates the existence of a previously unappreciated biochemical sub-classification of PHPT tumours, possibly reflecting distinct etiological mechanisms. Recognition of quantitative differences in calcium sensing could have important implications for the clinical management of PHPT.

A Mechanical Analysis of Suspensory Locomotion in Primates and Other Mammals

For primates, and other arboreal mammals, adopting suspensory locomotion represents one of the strategies an animal can use to prevent toppling off a thin support during arboreal movement and foraging. While numerous studies have reported the incidence of suspensory locomotion in a broad phylogenetic sample of mammals, little research has explored what mechanical transitions must occur in order for an animal to successfully adopt suspensory locomotion. Additionally, many primate species are capable of adopting a highly specialized form of suspensory locomotion referred to as arm-swinging, but few scenarios have been posited to explain how arm-swinging initially evolved. This study takes a comparative experimental approach to explore the mechanics of below branch quadrupedal locomotion in primates and other mammals to determine whether above and below branch quadrupedal locomotion represent neuromuscular mirrors of each other, and whether the patterns below branch quadrupedal locomotion are similar across taxa. Also, this study explores whether the nature of the flexible coupling between the forelimb and hindlimb observed in primates is a uniquely primate feature, and investigates the possibility that this mechanism could be responsible for the evolution of arm-swinging.

To address these research goals, kinetic, kinematic, and spatiotemporal gait variables were collected from five species of primate (Cebus capucinus, Daubentonia madagascariensis, Lemur catta, Propithecus coquereli, and Varecia variegata) walking quadrupedally above and below branches. Data from these primate species were compared to data collected from three species of non-primate mammals (Choloepus didactylus, Pteropus vampyrus, and Desmodus rotundus) and to three species of arm-swinging primate (Hylobates moloch, Ateles fusciceps, and Pygathrix nemaeus) to determine how varying forms of suspensory locomotion relate to each other and across taxa.

From the data collected in this study it is evident the specialized gait characteristics present during above branch quadrupedal locomotion in primates are not observed when walking below branches. Instead, gait mechanics closely replicate the characteristic walking patterns of non-primate mammals, with the exception that primates demonstrate an altered limb loading pattern during below branch quadrupedal locomotion, in which the forelimb becomes the primary propulsive and weight-bearing limb; a pattern similar to what is observed during arm-swinging. It is likely that below branch quadrupedal locomotion represents a “mechanical release” from the challenges of moving on top of thin arboreal supports. Additionally, it is possible, that arm-swinging could have evolved from an anatomically-generalized arboreal primate that began to forage and locomote below branches. During these suspensory bouts, weight would have been shifted away from the hindlimbs towards forelimbs, and as the frequency of these boats increased the reliance of the forelimb as the sole form of weight support would have also increased. This form of functional decoupling may have released the hindlimbs from their weight-bearing role during suspensory locomotion, and eventually arm-swinging would have replaced below branch quadrupedal locomotion as the primary mode of suspensory locomotion observed in some primate species. This study provides the first experimental evidence supporting the hypothetical link between below branch quadrupedal locomotion and arm-swinging in primates.