Existence and uniqueness of a fixed-point for local contractions

This paper proves the existence and uniqueness of a fixed-point for local contractions without assuming the family of contraction coefficients to be uniformly bounded away from 1. More importantly it shows how this fixed-point result can apply to study existence and uniqueness of solutions to some recursive equations that arise in economic dynamics.

Deeply divergent mitochondrial lineages reveal patterns of local endemism in chironomids of the Australian Wet Tropics

The Wet Tropics bioregion of north-eastern Australia has been subject to extensive fluctuations in climate throughout the late Pliocene and Pleistocene. Cycles of rainforest contraction and expansion of dry sclerophyll forest associated with such climatic fluctuations are postulated to have played a major role in driving geographical endemism in terrestrial rainforest taxa. Consequences for the distributions of aquatic organisms, however, are poorly understood.The Australian non-biting midge species Echinocladius martini Cranston (Diptera: Chironomidae), although restricted to cool, well-forested freshwater streams, has been considered to be able to disperse among populations located in isolated rainforest pockets during periods of sclerophyllous forest expansion, potentially limiting the effect of climatic fluctuations on patterns of endemism. In this study, mitochondrial COI and 16S data were analysed for E. martini collected from eight sites spanning theWet Tropics bioregion to assess the scale and extent of phylogeographic structure. Analyses of genetic structure showed several highly divergent cryptic lineages with restricted geographical distributions. Within one of the identified lineages, strong genetic structure implied that dispersal among proximate (<1 km apart) streams was extremely restricted. The results suggest that vicariant processes, most likely due to the systemic drying of the Australian continent during the Plio-Pleistocene, might have fragmented historical E. martini populations and, hence, promoted divergence in allopatry.

Toward multifactorial null models of range contraction in terrestrial vertebrates

The contraction of a species’ distribution range, which results from the extirpation of local populations, generally precedes its extinction. Therefore, understanding drivers of range contraction is important for conservation and management. Although there are many processes that can potentially lead to local extirpation and range contraction, three main null models have been proposed: demographic, contagion, and refuge. The first two models postulate that the probability of local extirpation for a given area depends on its relative position within the range; but these models generate distinct spatial predictions because they assume either a ubiquitous (demographic) or a clinal (contagion) distribution of threats. The third model (refuge) postulates that extirpations are determined by the intensity of human impacts, leading to heterogeneous spatial predictions potentially compatible with those made by the other two null models. A few previous studies have explored the generality of some of these null models, but we present here the first comprehensive evaluation of all three models. Using descriptive indices and regression analyses we contrast the predictions made by each of the null models using empirical spatial data describing range contraction in 386 terrestrial vertebrates (mammals, birds, amphibians, and reptiles) distributed across the World. Observed contraction patterns do not consistently conform to the predictions of any of the three models, suggesting that these may not be adequate null models to evaluate range contraction dynamics among terrestrial vertebrates. Instead, our results support alternative null models that account for both relative position and intensity of human impacts. These new models provide a better multifactorial baseline to describe range contraction patterns in vertebrates. This general baseline can be used to explore how additional factors influence contraction, and ultimately extinction for particular areas or species as well as to predict future changes in light of current and new threats.

Force patterns of hypoxic myocardium applied to oxygenated muscle preparations: Comparison with effects of regional ischemia on the contraction of non-ischemic myocardium

Objective: To examine the basis for local wall motion abnormalities commonly seen in patients with ischemic heart disease, computer-controlled isolated muscle studies were carried out. Methods: Force patterns of physiologically sequenced contractions (PSCs) from rat left ventricular muscle preparations under well-oxygenated conditions and during periods of hypoxia and reoxygenation were recorded and stored in a computer. Force patterns of hypoxic-reoxygenating and oxygenated myocardium were applied to oxygenated and hypoxic-reoxygenating myocardium, respectively. Results: Observed patterns of shortening and lengthening closely resemble those obtained from ischemic and non-ischemic myocardial segments using ultrasonic crystals in intact dog hearts during coronary occlusion and reperfusion, and are similar to findings reported in angiographic studies of humans with coronary artery disease. Conclusion: The current study, demonstrating motions of oxygenated isolated muscle preparations which are similar to those in perfused segments of intact hearts with regional ischemia, supports the concept that the multiple motions of both ischemic and non-ischemic segments seen in regional myocardial disease can be explained by interactions of strongly and weakly contracting muscle during the physiologic cardiac cycle.

The role of reactive oxygen species in the modulation of the contraction induced by angiotensin II in carotid artery from diabetic rat

The modulation played by reactive oxygen species on the angiotensin II-induced contraction in type I-diabetic rat carotid was investigated. Concentration-response curves for angiotensin II were obtained in endothelium-intact or endothelium-denuded carotid from control or streptozotocin-induced diabetic rats, pre-treated with tiron (superoxide scavenger), PEG-catalase (hydrogen peroxide scavenger), dimethylthiourea (hydroxyl scavenger), apocynin [NAD(P) H oxidase inhibitor], SC560 (cyclooxygenase-1 inhibitor), SC236 (cyclooxygenase-2 inhibitor) or Y-27632 (Rho-kinase inhibitor). Reactive oxygen species were measured by flow cytometry in dihydroethidium (DHE)-loaded endothelial cells. Cyclooxygenase and AT1-receptor expression was assessed by immunohistochemistry. Diabetes increased the angiotensin II-induced contraction but reduced the agonist potency in rat carotid. Endothelium removal, tiron or apocynin restored the angiotensin II-induced contraction in diabetic rat carotid to control levels. PEG-catalase, DMTU or SC560 reduced the angiotensin II-induced contraction in diabetic rat carotid at the same extent. SC236 restored the angiotensin II potency in diabetic rat carotid. Y-27632 reduced the angiotensin II-induced contraction in endothelium-intact or -denuded diabetic rat carotid. Diabetes increased the DHE-fluorescence of carotid endothelial cells. Apocynin reduced the DHE-fluorescence of endothelial cells from diabetic rat carotid to control levels. Diabetes increased the muscular cyclooxygenase-2 expression but reduced the muscular AT1-receptor expression in rat carotid. In summary, hydroxyl radical, hydrogen peroxide and superoxide anion-derived from endothelial NAD(P) H oxidase mediate the hyperreactivity to angiotensin II in type I-diabetic rat carotid, involving the participation of cyclooxygenase-1 and Rho-kinase. Moreover, increased muscular cyclooxygenase-2 expression in type I-diabetic rat carotid seems to be related to the local reduced AT1-receptor expression and the reduced angiotensin II potency. (C) 2011 Elsevier B. V. All rights reserved.

The immediate effects of local and adjacent acupuncture on the tibialis anterior muscle: a human study

Abstract Background This study compares the immediate effects of local and adjacent acupuncture on the tibialis anterior muscle and the amount of force generated or strength in Kilogram Force (KGF) evaluated by a surface electromyography. Methods The study consisted of a single blinded trial of 30 subjects assigned to two groups: local acupoint (ST36) and adjacent acupoint (SP9). Bipolar surface electrodes were placed on the tibialis anterior muscle, while a force transducer was attached to the foot of the subject and to the floor. An electromyograph (EMG) connected to a computer registered the KGF and root mean square (RMS) before and after acupuncture at maximum isometric contraction. The RMS values and surface electrodes were analyzed with Student's t-test. Results Thirty subjects were selected from a total of 56 volunteers according to specific inclusion and exclusion criteria and were assigned to one of the two groups for acupuncture. A significant decrease in the RMS values was observed in both ST36 (t = -3.80, P = 0,001) and SP9 (t = 6.24, P = 0.001) groups after acupuncture. There was a decrease in force in the ST36 group after acupuncture (t = -2.98, P = 0.006). The RMS values did not have a significant difference (t = 0.36, P = 0.71); however, there was a significant decrease in strength after acupuncture in the ST36 group compared to the SP9 group (t = 2.51, P = 0.01). No adverse events were found. Conclusion Acupuncture at the local acupoint ST36 or adjacent acupoints SP9 reduced the tibialis anterior electromyography muscle activity. However, acupuncture at SP9 did not decrease muscle strength while acupuncture at ST36 did.

Variations of local heat transfer coefficient in piped flow of viscous liquids

Measurements were carried out to determine local coefficients of heat transfer in short lengths of horizontal pipe, and in the region of an discontinuity in pipe diameter. Laminar, transitional and turbulent flow regimes were investigated, and mixtures of propylene glycol and water were used in the experiments to give a range of viscous fluids. Theoretical and empirical analyses were implemented to find how the fundamental mechanism of forced convection was modified by the secondary effects of free convection, temperature dependent viscosity, and viscous dissipation. From experiments with the short tube it was possible to determine simple empirical relationships describing the axial distribution of the local 1usselt number and its dependence on the Reynolds and Prandtl numbers. Small corrections were made to account for the secondary effects mentioned above. Two different entrance configurations were investigated to demonstrate how conditions upstream could influence the heat transfer coefficients measured downstream In experiments with a sudden contraction in pipe diameter the distribution of local 1u3se1t number depended on the Prandtl number of the fluid in a complicated way. Graphical data is presented describing this dependence for a range of fluids indicating how the local Nusselt number varied with the diameter-ratio. Ratios up to 3.34:1 were considered. With a sudden divergence in pipe diameter, it was possible to derive the axial distribution of the local Nusse1t number for a range of Reynolds and Prandtl numbers in a similar way to the convergence experiments. Difficulty was encountered in explaining some of the measurements obtained at low Reynolds numbers, and flow visualization techniques wore used to determine the complex flow patterns which could lead to the anomalous results mentioned. Tests were carried out with divergences up to 1:3.34 to find the way in which the local Nusselt number varied with the diameter ratio, and a few experiments were carried out with very large ratios up .to 14.4. A limited amount of theoretical analysis of the 'divergence' system was carried out to substantiate certain explanations of the heat transfer mechanisms postulated.

Bioengineered Approaches to Prevent Hypertrophic Scar Contraction

Burn injuries in the United States account for over one million hospital admissions per year, with treatment estimated at four billion dollars. Of severe burn patients, 30-90% will develop hypertrophic scars (HSc). Current burn therapies rely upon the use of bioengineered skin equivalents (BSEs), which assist in wound healing but do not prevent HSc. HSc contraction occurs of 6-18 months and results in the formation of a fixed, inelastic skin deformity, with 60% of cases occurring across a joint. HSc contraction is characterized by abnormally high presence of contractile myofibroblasts which normally apoptose at the completion of the proliferative phase of wound healing. Additionally, clinical observation suggests that the likelihood of HSc is increased in injuries with a prolonged immune response. Given the pathogenesis of HSc, we hypothesize that BSEs should be designed with two key anti-scarring characterizes: (1) 3D architecture and surface chemistry to mitigate the inflammatory microenvironment and decrease myofibroblast transition; and (2) using materials which persist in the wound bed throughout the remodeling phase of repair. We employed electrospinning and 3D printing to generate scaffolds with well-controlled degradation rate, surface coatings, and 3D architecture to explore our hypothesis through four aims.

In the first aim, we evaluate the impact of elastomeric, randomly-oriented biostable polyurethane (PU) scaffold on HSc-related outcomes. In unwounded skin, native collagen is arranged randomly, elastin fibers are abundant, and myofibroblasts are absent. Conversely, in scar contractures, collagen is arranged in linear arrays and elastin fibers are few, while myofibroblast density is high. Randomly oriented collagen fibers native to the uninjured dermis encourage random cell alignment through contact guidance and do not transmit as much force as aligned collagen fibers. However, the linear ECM serves as a system for mechanotransduction between cells in a feed-forward mechanism, which perpetuates ECM remodeling and myofibroblast contraction. The electrospinning process allowed us to create scaffolds with randomly-oriented fibers that promote random collagen deposition and decrease myofibroblast formation. Compared to an in vitro HSc contraction model, fibroblast-seeded PU scaffolds significantly decreased matrix and myofibroblast formation. In a murine HSc model, collagen coated PU (ccPU) scaffolds significantly reduced HSc contraction as compared to untreated control wounds and wounds treated with the clinical standard of care. The data from this study suggest that electrospun ccPU scaffolds meet the requirements to mitigate HSc contraction including: reduction of in vitro HSc related outcomes, diminished scar stiffness, and reduced scar contraction. While clinical dogma suggests treating severe burn patients with rapidly biodegrading skin equivalents, these data suggest that a more long-term scaffold may possess merit in reducing HSc.

In the second aim, we further investigate the impact of scaffold longevity on HSc contraction by studying a degradable, elastomeric, randomly oriented, electrospun micro-fibrous scaffold fabricated from the copolymer poly(l-lactide-co-ε-caprolactone) (PLCL). PLCL scaffolds displayed appropriate elastomeric and tensile characteristics for implantation beneath a human skin graft. In vitro analysis using normal human dermal fibroblasts (NHDF) demonstrated that PLCL scaffolds decreased myofibroblast formation as compared to an in vitro HSc contraction model. Using our murine HSc contraction model, we found that HSc contraction was significantly greater in animals treated with standard of care, Integra, as compared to those treated with collagen coated-PLCL (ccPLCL) scaffolds at d 56 following implantation. Finally, wounds treated with ccPLCL were significantly less stiff than control wounds at d 56 in vivo. Together, these data further solidify our hypothesis that scaffolds which persist throughout the remodeling phase of repair represent a clinically translatable method to prevent HSc contraction.

In the third aim, we attempt to optimize cell-scaffold interactions by employing an anti-inflammatory coating on electrospun PLCL scaffolds. The anti-inflammatory sub-epidermal glycosaminoglycan, hyaluronic acid (HA) was used as a coating material for PLCL scaffolds to encourage a regenerative healing phenotype. To minimize local inflammation, an anti-TNFα monoclonal antibody (mAB) was conjugated to the HA backbone prior to PLCL coating. ELISA analysis confirmed mAB activity following conjugation to HA (HA+mAB), and following adsorption of HA+mAB to the PLCL backbone [(HA+mAB)PLCL]. Alican blue staining demonstrated thorough HA coating of PLCL scaffolds using pressure-driven adsorption. In vitro studies demonstrated that treatment with (HA+mAB)PLCL prevented downstream inflammatory events in mouse macrophages treated with soluble TNFα. In vivo studies using our murine HSc contraction model suggested positive impact of HA coating, which was partiall impeded by the inclusion of the TNFα mAB. Further characterization of the inflammatory microenvironment of our murine model is required prior to conclusions regarding the potential for anti-TNFα therapeutics for HSc. Together, our data demonstrate the development of a complex anti-inflammatory coating for PLCL scaffolds, and the potential impact of altering the ECM coating material on HSc contraction.

In the fourth aim, we investigate how scaffold design, specifically pore dimensions, can influence myofibroblast interactions and subsequent formation of OB-cadherin positive adherens junctions in vitro. We collaborated with Wake Forest University to produce 3D printed (3DP) scaffolds with well-controlled pore sizes we hypothesized that decreasing pore size would mitigate intra-cellular communication via OB-cadherin-positive adherens junctions. PU was 3D printed via pressure extrusion in basket-weave design with feature diameter of ~70 µm and pore sizes of 50, 100, or 150 µm. Tensile elastic moduli of 3DP scaffolds were similar to Integra; however, flexural moduli of 3DP were significantly greater than Integra. 3DP scaffolds demonstrated ~50% porosity. 24 h and 5 d western blot data demonstrated significant increases in OB-cadherin expression in 100 µm pores relative to 50 µm pores, suggesting that pore size may play a role in regulating cell-cell communication. To analyze the impact of pore size in these scaffolds on scarring in vivo, scaffolds were implanted beneath skin graft in a murine HSc model. While flexural stiffness resulted in graft necrosis by d 14, cellular and blood vessel integration into scaffolds was evident, suggesting potential for this design if employed in a less stiff material. In this study, we demonstrate for the first time that pore size alone impacts OB-cadherin protein expression in vitro, suggesting that pore size may play a role on adherens junction formation affiliated with the fibroblast-to-myofibroblast transition. Overall, this work introduces a new bioengineered scaffold design to both study the mechanism behind HSc and prevent the clinical burden of this contractile disease.

Together, these studies inform the field of critical design parameters in scaffold design for the prevention of HSc contraction. We propose that scaffold 3D architectural design, surface chemistry, and longevity can be employed as key design parameters during the development of next generation, low-cost scaffolds to mitigate post-burn hypertrophic scar contraction. The lessening of post-burn scarring and scar contraction would improve clinical practice by reducing medical expenditures, increasing patient survival, and dramatically improving quality of life for millions of patients worldwide.