The residually stressed unloaded state of arteries: Membrane and thin cylinder approximations.

A solution is obtained for incompressible non-linearly elastic membranes that describes the bending of a cylindrical sector to form a perfect cylinder for a wide class of materials that includes isotropic materials and orthotropic materials reinforced by two families of mechanically equivalent fibres that are wound helically about the axial direction. Despite the relative simplicity of the physical problem, the solution of the corresponding boundary value problem for thick cylinders requires a numerical solution for even the simplest models. It is shown, however, that the thin shell solution provides an excellent approximation to the solution of the problem for cylindrical sectors whose thicknesses are an order of magnitude greater than that assumed for membranes. The approximate stress distribution in such thin shells is obtained. In these residually stressed cylinders, the radial stress is approximately zero but the hoop and axial stresses are finite. Estimates of the residual stresses in the unloaded state are obtained. A closed-form solution for the bending moment necessary to effect the deformation is also obtained.

Inflation of residually stressed Fung-type membrane models of arteries.

Elastic arteries are idealised as being incompressible orthotropic nonlinearly elastic cylinders. They are further idealised as being membranes in order to analyse the effect of the experimentally observed pre-stressing of arterial tissue on inflation. The pre-stress is modelled here using the opening-angle method. It is shown that there can be multiple unloaded states of arterial segments of Fung materials, suggesting the corresponding set of material parameters will not yield reliable predictions of arterial stress in three dimensions as there is no experimental evidence to support this non-uniqueness. It is also shown that the circumferential pre-strain has a simple magnifying scaling effect on the pressure-radial strain relation and on the axial force needed to maintain the membrane length during inflation; the effect of the axial pre-strain is more nuanced.

The effect of fiber-matrix interaction on the Poynting effect for torsion of fibrous soft biomaterials.

The response of fibrous soft tissues undergoing torsional deformations is a topic of considerable current interest. Such deformations are common in ligaments and tendons and are also of particular interest in cardiac mechanics. A well-known context where such issues arise is in understanding the mechanical response of papillary muscles of the heart. Thus the classical torsion problem for solid or hollow cylinders composed of rubber-like materials has received renewed recent attention in the context of anisotropic materials. Here we consider the torsion of a solid circular cylinder composed of a transversely isotropic incompressible fiber-reinforced hyperelastic material. The focus of the work is on examining the effect of fiber-matrix interaction on the axial stress response with emphasis on the Poynting effect. The classic Poynting effect for isotropic rubber-like materials where torsion induces elongation of the cylinder is shown to be significantly different for the transversely isotropic models considered here. For sufficiently small total angles of twist, well within the range of physiological response, a reverse-Poynting effect is shown to hold where the cylinder tends to shorten on twisting while for larger angles of twist, the usual positive Poynting effect occurs. It is shown that the influence of the fiber-matrix interaction is to enhance the reverse Poynting effect. The results are illustrated using experimental data of other authors for skeletal muscles and for brain white matter.

On the tension-compression switch hypothesis in arterial mechanics.

The tension-compression switch hypothesis for soft tissue proposes that when collagen fibres are compressed they do not contribute to the mechanical response which is then assumed to be the isotropic response of the extra-cellular matrix in which they are embedded. Such an assumption would seem reasonable. However, three difficulties with its use are discussed here. First it is shown that the admittedly scant experimental evidence available suggests that it does not have a completely sound physical basis. The possible paradoxical nature of the tension-compression switch has been previously identified by other authors. If the fibres are predicted to be in compression by an anisotropic model, then the resulting isotropic stretch of the fibres predicted by the tension-compression switch can be tensile. Thus the fibres can have a duality of being simultaneously tensile and compressive if the tension-compression switch is employed. This is illustrated here with a particular emphasis on the nature of the isotropic stretching of the fibres when compressed and the essential role of the linear theory when predicting the mechanical response for non-linear deformations of arterial tissue. Finally it is shown that use of the tension-compression switch can result in the failure of some models to predict the mechanical response in the material characterisation tests that were used to determine the values of their material constants. Thus some anisotropic models can have better predictive capability without the tension-compression switch.

Magic angles and fibre stretch in arterial tissue: Insights from the linear theory.

This work is motivated by the current widespread interest in modelling the mechanical response of arterial tissue. A widely used approach within the context of anisotropic nonlinear elasticity is to use an orthotropic incompressible hyperelasticity model which, in general, involves a strain-energy density that depends on seven independent invariants. The complexity of such an approach in its full generality is daunting and so a number of simplifications have been introduced in the literature to facilitate analytical tractability. An extremely popular model of this type is where the strain energy involves only three invariants. While such models and their generalisations have been remarkably successful in capturing the main features of the mechanical response of arterial tissue, it is generally acknowledged that such simplified models must also have some drawbacks. In particular, it is intuitively clear that the correlation of such models with experiment will suffer limitations due to the restricted number of invariants considered. Our purpose here is to use the linearised theory for infinitesimal deformations to provide some guidelines for the development of a more robust nonlinear theory. The linearised theory for incompressible orthotropic materials is developed and involves six independent elastic constants. The general stress-strain law is inverted to provide an expression for the fibre stretch in terms of the stress. We examine the linearised response for simple tension in two mutually perpendicular directions corresponding to the axial and circumferential directions in the artery, obtaining an explicit expression for the fibre stretch in terms of the applied tension, fibre angle and linear elastic constants. The focus is then on determining the range of fibre orientation angles that ensure that the fibres are in tension in these simple tension tests. It is shown that the fibre stretch is positive for both simple tension tests if and only if the fibre angle is restricted to lie between two special angles called generalised magic angles. For the special case where the strain-energy function for the nonlinear model depends only on the three invariants I1,I4,I6, it is shown that the corresponding linearised model, called the standard linear model (SLM), depends on three elastic constants and the fibre stretch is positive only in the small range of fibre angles between the classic magic angles 35.26° and 54.74°. However, when the two additional invariants I5,I7 are included in the nonlinear strain energy so that the corresponding linear model involves four elastic constants, it is shown that the domain of fibre angle for which the stretch is positive is much larger and that the fibre stretch is monotonic with respect to the fibre angle in this range.

Correction to 'An empirical measure of nonlinear strain for soft tissue indentation'.

[This corrects the article DOI: 10.1098/rsos.170894.].

Indentation of heterogeneous soft tissue: Local constitutive parameter mapping using an inverse method and an automated rig.

In the domain of soft tissue biomechanics, the development of numerical simulations has raised the experimental challenge of identifying local internal mechanical constitutive data of heterogeneous organs (e.g. brain tissue). In this context, this paper presents an ex-vivo alternative characterization method to full-field imaging techniques. It is based on automated, multiple indentations of an organ section using a custom-built rig, effectively allowing to map the viscoelastic and hyperelastic constitutive parameters of the tissue at the millimetre scale, under dynamic conditions. In this paper, this technique is described and used to map the constitutive data of three sections from porcine liver, kidney and brain tissues. The results of this mapping present strong evidence of correlation between the organ constituents (e.g. white/grey matter distribution) and the identified constitutive parameters. It was also found that brain and kidney tissues are highly heterogeneous in terms of identified properties, suggesting that such a technique is essential for fully characterizing their mechanical behaviour. This method opens the way to 3D mapping of constitutive parameters to feed finite element models of the organs with region-specific properties.

Poynting and reverse Poynting effects in soft materials.

In 1909, J. H. Poynting conducted a series of experiments on metal wires and found that loaded wires lengthen when twisted. Thus to maintain a constant length in such experiments, a compressive axial force would need to be applied at the ends of the specimen. This is the classical (positive) Poynting effect. Another example of such an effect arises when a soft material specimen is being axially sheared or rotated between two platens. The necessity to apply a normal force in order to maintain the relative distance between the platens is also often referred to as a Poynting-type effect. Both effects are inherently nonlinear phenomena. In recent papers, experimental data on the Poynting effect in soft solids have been reported. The seminal paper by Janmey et al. describes shearing experiments on hydrogels, impregnated with scleroproteins such as collagen and fibrin. It was shown that positive and negative (reverse) Poynting effects could occur. In this and subsequent papers by several authors, the microstructure of reinforced biogels involving semi-flexible filaments embedded in a soft matrix was exploited to examine the character of the normal stresses. The purpose of the present paper is to describe and review an alternative approach using the macroscopic phenomenological theory of hyperelasticity based on nonlinear continuum mechanics. Our aim is to demonstrate that such a theory can be used in a very transparent way to predict the occurrence of both positive and negative Poynting effects in anisotropic soft fibrous materials. It will be seen that material anisotropy plays a key role in the analysis.

Observational constraints on particle acidity using measurements and modelling of particles and gases.

In many parts of the world, the implementation of air quality regulations has led to significant decreases in SO2 emissions with minimal impact on NH3 emissions. In Canada and the United States, the molar ratio of NH3 : SO2 emissions has increased dramatically between 1990 and 2014. In many regions of North America, this will lead the molar ratio of NHx : SO4, where NHx is the sum of particle phase NH4+ and gas phase NH3, and SO4 is the sum of particle phase HSO4- and SO42-, to exceed 2. A thermodynamic model (E-AIM model II) is used to investigate the sensitivity of particle pH, and the gas-particle partitioning of NHx and inorganic nitrate, to the atmospheric NHx : SO4 ratio. Steep increases in pH and the gas fraction of NHx are found as NHx : SO4 varies from below 1 to above 2. The sensitivity of the gas fraction of nitrate also depends strongly on temperature. The results show that if NHx : SO4 exceeds 2, and the gas and particle phase NHx are in equilibrium, the particle pH will be above 2. Observations of the composition of particulate matter and gas phase NH3 from two field campaigns in southern Canada in 2007 and 2012 have median NHx : SO4 ratios of 3.8 and 25, respectively. These campaigns exhibited similar amounts of NH3, but very different particle phase loadings. Under these conditions, the pH values calculated using the observations as input to the E-AIM model were in the range of 1-4. The pH values were typically higher at night because the higher relative humidity increased the particle water content, diluting the acidity. The assumption of equilibration between the gas and particle phase NHx was evaluated by comparing the observed and modelled gas fraction of NHx. In general, E-AIM was able to reproduce the partitioning well, suggesting that the dominant constituents contributing to particle acidity were measured, and that the estimated pH values were realistic. These results suggest that regions of the world where the ratio of NH3 : SO2 emissions is beginning to exceed 2 on a molar basis may be experiencing rapid increases in aerosol pH of 1-3 pH units. This could have important consequences for the rates of condensed phase reactions that are acid-catalyzed.

A new formulation of slight compressibility for arterial tissue and its Finite Element implementation.

In order to avoid the numerical difficulties in locally enforcing the incompressibility constraint using the displacement formulation of the Finite Element Method, slight compressibility is typically assumed when simulating the mechanical response of arterial tissue. The current standard method of accounting for slight compressibility of hyperelastic soft tissue assumes an additive decomposition of the strain-energy function into a volumetric and a deviatoric part. This has been shown, however, to be inconsistent with the linear theory and results in cubes retaining their cuboid shape under hydrostatic tension and compression, which seems at variance with the reinforcement of arterial tissue with two families of collagen fibres. A remedy for these defects is proposed here, a solution which generalises the current standard model of slight compressibility to include two additional terms, one of which is quadratic in the [Formula: see text] invariants and the other quadratic in [Formula: see text]. Experimental data are used to motivate typical values for the associated material constants of these additional terms. Some simulations are performed to allow contrasts and comparisons to be made between the current standard model of slight compressibility and its generalisation proposed here.

An empirical measure of nonlinear strain for soft tissue indentation.

Indentation is a primary tool in the investigation of the mechanical properties of very soft tissue such as the brain. However, the usual material characterization protocols are not applicable because the resulting deformation is inhomogeneous, with even the identification of the amount of strain ambiguous and uncertain. Focusing on spherical indentation only, a standard is needed to quantify the amount of strain in terms of the probe radius and displacement so that different indentation experiments can be compared and contrasted. It is shown here that the minimum axial value of the Eulerian logarithmic strain tensor has many desirable properties of such a standard, such as invariance under the choice of material model, and experimental conditions for a given probe displacement. The disadvantage of this measure is that sophisticated finite element techniques need to be used in its determination. An empirical relation is obtained between this strain and the probe radius and displacement to circumvent this problem, and it is shown that this relationship is an excellent predictor of the strain measure. Two essential features of this empirical measure for nonlinear strains are that the exact strain measure for the linear theory is recovered on restriction to infinitesimal deformations and that the simulations use models based on reliable and accurate indentation data obtained from freshly harvested murine brains using a bespoke micro-indentation device.

Contribution of Arctic seabird-colony ammonia to atmospheric particles and cloud-albedo radiative effect.

The Arctic region is vulnerable to climate change and able to affect global climate. The summertime Arctic atmosphere is pristine and strongly influenced by natural regional emissions, which have poorly understood climate impacts related to atmospheric particles and clouds. Here we show that ammonia from seabird-colony guano is a key factor contributing to bursts of newly formed particles, which are observed every summer in the near-surface atmosphere at Alert, Nunavut, Canada. Our chemical-transport model simulations indicate that the pan-Arctic seabird-influenced particles can grow by sulfuric acid and organic vapour condensation to diameters sufficiently large to promote pan-Arctic cloud-droplet formation in the clean Arctic summertime. We calculate that the resultant cooling tendencies could be large (about -0.5 W m-2 pan-Arctic-mean cooling), exceeding -1 W m-2 near the largest seabird colonies due to the effects of seabird-influenced particles on cloud albedo. These coupled ecological-chemical processes may be susceptible to Arctic warming and industrialization.

Finite element implementation of a new model of slight compressibility for transversely isotropic materials.

Modelling transversely isotropic materials in finite strain problems is a complex task in biomechanics, and is usually addressed by using finite element (FE) simulations. The standard method developed to account for the quasi-incompressible nature of soft tissues is to decompose the strain energy function (SEF) into volumetric and deviatoric parts. However, this decomposition is only valid for fully incompressible materials, and its use for slightly compressible materials yields an unphysical response during the simulation of hydrostatic tension/compression of a transversely isotropic material. This paper presents the FE implementation as subroutines of a new volumetric model solving this deficiency in two FE codes: Abaqus and FEBio. This model also has the specificity of restoring the compatibility with small strain theory. The stress and elasticity tensors are first derived for a general SEF. This is followed by a successful convergence check using a particular SEF and a suite of single-element tests showing that this new model does not only correct the hydrostatic deficiency but may also affect stresses during shear tests (Poynting effect) and lateral stretches during uniaxial tests (Poisson's effect). These FE subroutines have numerous applications including the modelling of tendons, ligaments, heart tissue, etc. The biomechanics community should be aware of specificities of the standard model, and the new model should be used when accurate FE results are desired in the case of compressible materials.

Dynamic mechanical properties of murine brain tissue using micro-indentation.

In the past 50 years significant advances have been made in determining the macro-scale properties of brain tissue in compression, tension, shear and indentation. There has also been significant work done at the nanoscale using the AFM method to characterise the properties of individual neurons. However, there has been little published work on the micro-scale properties of brain tissue using an appropriate indentation methodology to characterise the regional differences at dynamic strain rates. This paper presents the development and use of a novel micro-indentation device to measure the dynamic mechanical properties of brain tissue. The device is capable of applying up to 30/s strain rates with a maximum indentation area of 2500 µm(2). Indentation tests were carried out to determine the shear modulus of the cerebellum (2.11 ± 1.26 kPa, 3.15 ± 1.66 kPa, 3.71 ± 1.23 kPa) and cortex (4.06 ± 1.69 kPa, 6.14 ± 3.03 kPa, 7.05 ± 3.92 kPa) of murine brain tissue at 5, 15, and 30/s up to 14% strain. Numerical simulations were carried out to verify the experimentally measured force-displacement results.

Deficiencies in numerical models of anisotropic nonlinearly elastic materials.

Incompressible nonlinearly hyperelastic materials are rarely simulated in finite element numerical experiments as being perfectly incompressible because of the numerical difficulties associated with globally satisfying this constraint. Most commercial finite element packages therefore assume that the material is slightly compressible. It is then further assumed that the corresponding strain-energy function can be decomposed additively into volumetric and deviatoric parts. We show that this decomposition is not physically realistic, especially for anisotropic materials, which are of particular interest for simulating the mechanical response of biological soft tissue. The most striking illustration of the shortcoming is that with this decomposition, an anisotropic cube under hydrostatic tension deforms into another cube instead of a hexahedron with non-parallel faces. Furthermore, commercial numerical codes require the specification of a 'compressibility parameter' (or 'penalty factor'), which arises naturally from the flawed additive decomposition of the strain-energy function. This parameter is often linked to a 'bulk modulus', although this notion makes no sense for anisotropic solids; we show that it is essentially an arbitrary parameter and that infinitesimal changes to it result in significant changes in the predicted stress response. This is illustrated with numerical simulations for biaxial tension experiments of arteries, where the magnitude of the stress response is found to change by several orders of magnitude when infinitesimal changes in 'Poisson's ratio' close to the perfect incompressibility limit of 1/2 are made.

Ion chromatographic separation and quantitation of alkyl methylamines and ethylamines in atmospheric gas and particulate matter using preconcentration and suppressed conductivity detection.

Two methods based on ion chromatography (IC) were developed for the detection of methyl and ethyl alkyl amines (methylamine (MA), ethylamine (EA), dimethylamine (DMA), diethylamine (DEA), trimethylamine (TMA) and triethylamine (TEA)) and NH(3)/NH(4)(+) in online atmospheric gas-particle and size-resolved particulate samples. The two IC methods were developed to analyze samples collected with an ambient ion monitor (AIM), an online gas-particle collection system, or with a Micro Orifice Uniform Deposit Impactor (MOUDI) for size-resolved particle samples. These methods enable selective and (semi-) quantitative detection of alkyl amines at ambient atmospheric concentrations (pptv and pgm(-3)) in samples where significant interferences can be expected from Na(+) and NH(4)(+), for example marine and rural air masses. Sample pre-concentration using a trace cation column enabled instrumental detection limits on the order of pmol (sub-ng) levels per sample, an improvement of up to 10(2) over current IC methods. Separation was achieved using a methanesulfonic acid gradient elution on Dionex CS12A and CS17 columns. The relative standard deviations in retention times during 3 weeks continuous (hourly) sampling campaigns ranged from 0.1 to 0.5% and 0.2 to 5% for the CS12A and CS17 across a wide dynamic range of atmospheric concentrations. Resolution of inorganic and organic cations is limited to 25min for online samples. Mass-dependent coelution of NH(4)(+)/MA/EA occurred on the CS12A column and DEA/TMA coeluted on both columns. Calibrations of ammonium show a non-linear response across the entire calibration range while all other analytes exhibit high linearity (R(2)=0.984-0.999), except for EA and TEA on the CS12A (R(2)=0.960 and 0.941, respectively). Both methods have high analytical accuracy for the nitrogenous bases ranging from 9.5 to 20% for NH(3) and <5-15% for the amines. Hourly observations of amines at Egbert, ON in October 2010 showed gaseous DMA and TMA+DEA at 1-10pptv in air, while particulate DMA and TMA+DEA were present at 0.5-4ng m(-3). A size-resolved particulate sample collected over 23h was found to contain DMA, TMA+DEA and MEA at 1.78, 8.15 and 0.03ngm(-3) mass loadings, with the amine mass enhanced in particle sizes between 100 and 1000nm. These results highlight a need for very sensitive and selective detection of methyl and ethyl amines in addition to NH(3) in continuous online monitoring strategies.

Isoprene emissions in Africa inferred from OMI observations of formaldehyde columns.

We use 2005-2009 satellite observations of formaldehyde (HCHO) columns from the OMI instrument to infer biogenic isoprene emissions at monthly 1 × 1° resolution over the African continent. Our work includes new approaches to remove biomass burning influences using OMI absorbing aerosol optical depth data (to account for transport of fire plumes) and anthropogenic influences using AATSR satellite data for persistent small-flame fires (gas flaring). The resulting biogenic HCHO columns (ΩHCHO) from OMI follow closely the distribution of vegetation patterns in Africa. We infer isoprene emission (E ISOP) from the local sensitivity S = ΔΩHCHO / ΔE ISOP derived with the GEOS-Chem chemical transport model using two alternate isoprene oxidation mechanisms, and verify the validity of this approach using AMMA aircraft observations over West Africa and a longitudinal transect across central Africa. Displacement error (smearing) is diagnosed by anomalously high values of S and the corresponding data are removed. We find significant sensitivity of S to NOx under low-NOx conditions that we fit to a linear function of tropospheric column NO2. We estimate a 40% error in our inferred isoprene emissions under high-NOx conditions and 40-90% under low-NOx conditions. Our results suggest that isoprene emission from the central African rainforest is much lower than estimated by the state-of-the-science MEGAN inventory.

A randomized trial of a brief intervention for obesity in college students.

WHAT IS ALREADY KNOWN ABOUT THIS SUBJECT: • Brief motivational interventions have been found to be efficacious for obesity in older adult populations. • Brief motivational interventions including delivery of personalized feedback have been found to be efficacious for reducing college student drinking. WHAT THIS STUDY ADDS: • First study to test the efficacy of a one-session, brief motivational intervention for obesity among college students. • One session brief motivational interventions may have an impact on the reduction of calorie-dense foods and beverages. • A brief, one-session motivational interview with personalized feedback may not be an intensive enough intervention for obesity treatment among college students. SUMMARY: Young adults are at an increased risk for weight gain as they begin college and this has implications for the onset of future health consequences. Brief motivational interventions (BMIs) have been found to be effective with college students for reducing risky health behaviours such as alcohol consumption, but have not been developed and tested with a primary goal of reducing obesity. BMIs have been developed and tested for the treatment of obesity and weight-related health behaviours (WRHB) in other populations, such as adults and adolescents, with promising results. The purpose of the following study was to develop and test the efficacy of a BMI for weight loss among overweight and obese college students. Seventy undergraduate students (85.7% female, 57.1% African-American) completed an assessment about WRHBs and then were randomized to either receive a single 60-min BMI plus a booster phone call or to assessment only. At 3 months post-intervention, effect sizes within the intervention group were twice as large as within the assessment-only group on reductions in high-calorie foods and beverages. However, there were no statistically significant differences between groups on body mass index or WRHBs. The one-session nature of the session might not have been enough to produce significant change in weight.

Is simulation based medicine training the future of clinical medicine?

The training of physician in the art and science of clinical medicine presents several challenges that are well suited to simulation based medical education (SBME). Modern patient centered medical education seeks to provide comprehensive "hands-on" clinical exposure for physicians in training, while simultaneously providing maximum individual patient comfort and safety. The ethical conundrum is obvious: direct patient contact is needed in order to educate the best clinical physicians and surgeons, but patients have an expectation to be treated and have surgery performed only by highly trained healthcare personnel. This is the kernel of the "medical educators dilemma". Simulation based medical education can partially solve "the medical educators dilemma" by providing realistic medical education in a safe, error tolerant environment with convenience and advantages over conventional "bedside" training but is it real medicine or make believe!