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- ES-FEM (1)
- FS-FEM (1)
- S-FEM (1)
- Small Aral Sea (1)
- biomechanics (1)
- calorimetric gas sensor;hydrogen peroxide;wireless sensor system (1)
- cerebral small vessel disease (1)
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It has been shown that muscle fascicle curvature increases with increasing contraction level and decreasing muscle–tendon complex length. The analyses were done with limited examination windows concerning contraction level, muscle–tendon complex length, and/or intramuscular position of ultrasound imaging. With this study we aimed to investigate the correlation between fascicle arching and contraction, muscle–tendon complex length and their associated architectural parameters in gastrocnemius muscles to develop hypotheses concerning the fundamental mechanism of fascicle curving. Twelve participants were tested in five different positions (90°/105°*, 90°/90°*, 135°/90°*, 170°/90°*, and 170°/75°*; *knee/ankle angle). They performed isometric contractions at four different contraction levels (5%, 25%, 50%, and 75% of maximum voluntary contraction) in each position. Panoramic ultrasound images of gastrocnemius muscles were collected at rest and during constant contraction. Aponeuroses and fascicles were tracked in all ultrasound images and the parameters fascicle curvature, muscle–tendon complex strain, contraction level, pennation angle, fascicle length, fascicle strain, intramuscular position, sex and age group were analyzed by linear mixed effect models. Mean fascicle curvature of the medial gastrocnemius increased with contraction level (+5 m−1 from 0% to 100%; p = 0.006). Muscle–tendon complex length had no significant impact on mean fascicle curvature. Mean pennation angle (2.2 m−1 per 10°; p < 0.001), inverse mean fascicle length (20 m−1 per cm−1; p = 0.003), and mean fascicle strain (−0.07 m−1 per +10%; p = 0.004) correlated with mean fascicle curvature. Evidence has also been found for intermuscular, intramuscular, and sex-specific intramuscular differences of fascicle curving. Pennation angle and the inverse fascicle length show the highest predictive capacities for fascicle curving. Due to the strong correlations between pennation angle and fascicle curvature and the intramuscular pattern of curving we suggest for future studies to examine correlations between fascicle curvature and intramuscular fluid pressure.
Edge-based and face-based smoothed finite element methods (ES-FEM and FS-FEM, respectively) are modified versions of the finite element method allowing to achieve more accurate results and to reduce sensitivity to mesh distortion, at least for linear elements. These properties make the two methods very attractive. However, their implementation in a standard finite element code is nontrivial because it requires heavy and extensive modifications to the code architecture. In this article, we present an element-based formulation of ES-FEM and FS-FEM methods allowing to implement the two methods in a standard finite element code with no modifications to its architecture. Moreover, the element-based formulation permits to easily manage any type of element, especially in 3D models where, to the best of the authors' knowledge, only tetrahedral elements are used in FS-FEM applications found in the literature. Shape functions for non-simplex 3D elements are proposed in order to apply FS-FEM to any standard finite element.
Objective
Hemodialysis patients show an approximately threefold higher prevalence of cognitive impairment compared to the age-matched general population. Impaired microcirculatory function is one of the assumed causes. Dynamic retinal vessel analysis is a quantitative method for measuring neurovascular coupling and microvascular endothelial function. We hypothesize that cognitive impairment is associated with altered microcirculation of retinal vessels.
Methods
152 chronic hemodialysis patients underwent cognitive testing using the Montreal Cognitive Assessment. Retinal microcirculation was assessed by Dynamic Retinal Vessel Analysis, which carries out an examination recording retinal vessels' reaction to a flicker light stimulus under standardized conditions.
Results
In unadjusted as well as in adjusted linear regression analyses a significant association between the visuospatial executive function domain score of the Montreal Cognitive Assessment and the maximum arteriolar dilation as response of retinal arterioles to the flicker light stimulation was obtained.
Conclusion
This is the first study determining retinal microvascular function as surrogate for cerebral microvascular function and cognition in hemodialysis patients. The relationship between impairment in executive function and reduced arteriolar reaction to flicker light stimulation supports the involvement of cerebral small vessel disease as contributing factor for the development of cognitive impairment in this patient population and might be a target for noninvasive disease monitoring and therapeutic intervention.
Thrombogenic complications are a main issue in mechanical circulatory support (MCS). There is no validated in vitro method available to quantitatively assess the thrombogenic performance of pulsatile MCS devices under realistic hemodynamic conditions. The aim of this study is to propose a method to evaluate the thrombogenic potential of new designs without the use of complex in-vivo trials. This study presents a novel in vitro method for reproducible thrombogenicity testing of pulsatile MCS systems using low molecular weight heparinized porcine blood. Blood parameters are continuously measured with full blood thromboelastometry (ROTEM; EXTEM, FIBTEM and a custom-made analysis HEPNATEM). Thrombus formation is optically observed after four hours of testing. The results of three experiments are presented each with two parallel loops. The area of thrombus formation inside the MCS device was reproducible. The implantation of a filter inside the loop catches embolizing thrombi without a measurable increase of platelet activation, allowing conclusions of the place of origin of thrombi inside the device. EXTEM and FIBTEM parameters such as clotting velocity (α) and maximum clot firmness (MCF) show a total decrease by around 6% with a characteristic kink after 180 minutes. HEPNATEM α and MCF rise within the first 180 minutes indicate a continuously increasing activation level of coagulation. After 180 minutes, the consumption of clotting factors prevails, resulting in a decrease of α and MCF. With the designed mock loop and the presented protocol we are able to identify thrombogenic hot spots inside a pulsatile pump and characterize their thrombogenic potential.
Microbial diversity studies regarding the aquatic communities that experienced or are experiencing environmental problems are essential for the comprehension of the remediation dynamics. In this pilot study, we present data on the phylogenetic and ecological structure of microorganisms from epipelagic water samples collected in the Small Aral Sea (SAS). The raw data were generated by massive parallel sequencing using the shotgun approach. As expected, most of the identified DNA sequences belonged to Terrabacteria and Actinobacteria (40% and 37% of the total reads, respectively). The occurrence of Deinococcus-Thermus, Armatimonadetes, Chloroflexi in the epipelagic SAS waters was less anticipated. Surprising was also the detection of sequences, which are characteristic for strict anaerobes—Ignavibacteria, hydrogen-oxidizing bacteria, and archaeal methanogenic species. We suppose that the observed very broad range of phylogenetic and ecological features displayed by the SAS reads demonstrates a more intensive mixing of water masses originating from diverse ecological niches of the Aral-Syr Darya River basin than presumed before.
Experience has shown that a priori created static resource allocation plans are vulnerable to runtime deviations and hence often become uneconomic or highly exceed a predefined soft deadline. The assumption of constant task execution times during allocation planning is even more unlikely in a cloud environment where virtualized resources vary in performance. Revising the initially created resource allocation plan at runtime allows the scheduler to react on deviations between planning and execution. Such an adaptive rescheduling of a many-task application workflow is only feasible, when the planning time can be handled efficiently at runtime. In this paper, we present the static low-complexity resource allocation planning algorithm (LCP) applicable to efficiently schedule many-task scientific application workflows on cloud resources of different capabilities. The benefits of the presented algorithm are benchmarked against alternative approaches. The benchmark results show that LCP is not only able to compete against higher complexity algorithms in terms of planned costs and planned makespan but also outperforms them significantly by magnitudes of 2 to 160 in terms of required planning time. Hence, LCP is superior in terms of practical usability where low planning time is essential such as in our targeted online rescheduling scenario.
Retinal endothelial function in cardiovascular risk patients: A randomized controlled exercise trial
(2020)
The aim of this study was to investigate, for the first time, the effects of high-intensity interval training (HIIT) on retinal microvascular endothelial function in cardiovascular (CV) risk patients. In the randomized controlled trial, middle-aged and previously sedentary patients with increased CV risk (aged 58 ± 6 years) with ≥ two CV risk factors were randomized into a 12-week HIIT (n = 33) or control group (CG, n = 36) with standard physical activity recommendations. A blinded examiner measured retinal endothelial function by flicker light-induced maximal arteriolar (ADmax) and venular (VDmax) dilatation as well as the area under the arteriolar (AFarea) and venular (VFarea) flicker curve using a retinal vessel analyzer. Standardized assessments of CV risk factors, cardiorespiratory fitness, and retinal endothelial function were performed before and after HIIT. HIIT reduced body mass index, fat mass, and low-density lipoprotein and increased muscle mass and peak oxygen uptake (VO2peak). Both ADmax (pre: 2.7 ± 2.1%, post: 3.0 ± 2.2%, P = .018) and AFarea (pre: 32.6 ± 28.4%*s, post: 37.7 ± 30.6%*s, P = .016) increased after HIIT compared with CG (ADmax, pre: 3.2 ± 1.8%, post: 2.9 ± 1.8%, P = .254; AFarea, pre: 41.6 ± 28.5%*s, post: 37.8 ± 27.0%*s, P = .186). Venular function remained unchanged after HIIT. There was a significant association between ∆-change VO2peak and ∆-changes ADmax and AFarea (P = .026, R² = 0.073; P = .019, R² = 0.081, respectively). 12-weeks of HIIT improved retinal endothelial function in middle-aged patients with increased CV risk independent of the reduction in classical CV risk factors. Exercise has the potential to reverse or at least postpone progression of small vessel disease in older adults with increased CV risk under standard medication. Dynamic retinal vessel analysis seems to be a sensitive tool to detect treatment effects of exercise interventions on retinal microvascular endothelial function in middle-aged individuals with increased CV risk.
A light-addressable potentiometric sensor (LAPS) is a field-effect-based (bio-) chemical sensor, in which a desired sensing area on the sensor surface can be defined by illumination. Light addressability can be used to visualize the concentration and spatial distribution of the target molecules, e.g., H+ ions. This unique feature has great potential for the label-free imaging of the metabolic activity of living organisms. The cultivation of those organisms needs specially tailored surface properties of the sensor. O2 plasma treatment is an attractive and promising tool for rapid surface engineering. However, the potential impacts of the technique are carefully investigated for the sensors that suffer from plasma-induced damage. Herein, a LAPS with a Ta2O5 pH-sensitive surface is successfully patterned by plasma treatment, and its effects are investigated by contact angle and scanning LAPS measurements. The plasma duration of 30 s (30 W) is found to be the threshold value, where excessive wettability begins. Furthermore, this treatment approach causes moderate plasma-induced damage, which can be reduced by thermal annealing (10 min at 300 °C). These findings provide a useful guideline to support future studies, where the LAPS surface is desired to be more hydrophilic by O2 plasma treatment.
Suspension depletion approach for exemption of infected Solanum jasminoides cells from pospiviroids
(2018)
Despite numerous studies, viroid elimination from infected plants remains a very challenging task. This study introduces for the first time a novel ‘suspension depletion’ approach for exemption of Solanum jasminoides plants from viroids. The proposed method implies initial establishment of suspension cultures of the infected plant cells. The suspended cells were then physically treated (mild thermotherapy, 33 °C), which presumably delayed the replication of the viroid. The viroid concentration in the treated biomass was monitored weekly using pospiviroid-specific PCR. After 10–12 weeks of continuous treatment, a sufficient decrease in viroid concentration was observed such that the infection became undetectable by PCR. The treated single cells then gave rise to microcolonies on a solid culture medium and the obtained viroid-negative clones were further promoted to regenerate into viroid-free plants. Three years of accumulated experimental data suggests feasibility, broad applicability, and good efficacy of the proposed approach.
Purpose
In vivo, a loss of mesh porosity triggers scar tissue formation and restricts functionality. The purpose of this study was to evaluate the properties and configuration changes as mesh deformation and mesh shrinkage of a soft mesh implant compared with a conventional stiff mesh implant in vitro and in a porcine model.
Material and Methods
Tensile tests and digital image correlation were used to determine the textile porosity for both mesh types in vitro. A group of three pigs each were treated with magnetic resonance imaging (MRI) visible conventional stiff polyvinylidene fluoride meshes (PVDF) or with soft thermoplastic polyurethane meshes (TPU) (FEG Textiltechnik mbH, Aachen, Germany), respectively. MRI was performed with a pneumoperitoneum at a pressure of 0 and 15 mmHg, which resulted in bulging of the abdomen. The mesh-induced signal voids were semiautomatically segmented and the mesh areas were determined. With the deformations assessed in both mesh types at both pressure conditions, the porosity change of the meshes after 8 weeks of ingrowth was calculated as an indicator of preserved elastic properties. The explanted specimens were examined histologically for the maturity of the scar (collagen I/III ratio).
Results
In TPU, the in vitro porosity increased constantly, in PVDF, a loss of porosity was observed under mild stresses. In vivo, the mean mesh areas of TPU were 206.8 cm2 (± 5.7 cm2) at 0 mmHg pneumoperitoneum and 274.6 cm2 (± 5.2 cm2) at 15 mmHg; for PVDF the mean areas were 205.5 cm2 (± 8.8 cm2) and 221.5 cm2 (± 11.8 cm2), respectively. The pneumoperitoneum-induced pressure increase resulted in a calculated porosity increase of 8.4% for TPU and of 1.2% for PVDF. The mean collagen I/III ratio was 8.7 (± 0.5) for TPU and 4.7 (± 0.7) for PVDF.
Conclusion
The elastic properties of TPU mesh implants result in improved tissue integration compared to conventional PVDF meshes, and they adapt more efficiently to the abdominal wall. © 2017 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 106B: 827–833, 2018.
The integration of biomolecular logic principles with electronic transducers allows designing novel digital biosensors with direct electrical output, logically triggered drug-release, and closed-loop sense/act/treat systems. This opens new opportunities for advanced personalized medicine in the context of theranostics. In the present work, we will discuss selected examples of recent developments in the field of interfacing enzyme logic gates with electrodes and semiconductor field-effect devices. Special attention is given to an enzyme OR/Reset logic gate based on a capacitive field-effect electrolyte-insulator-semiconductor sensor modified with a multi-enzyme membrane. Further examples are a digital adrenaline biosensor based on an AND logic gate with binary YES/NO output and an integrated closed-loop sense/act/treat system comprising an amperometric glucose sensor, a hydrogel actuator, and an insulin (drug) sensor.
Sterilisation processes are compulsory in medicine, pharmacy, and food industries to prevent infections of consumers and microbiological contaminations of products. Monitoring the sterilisation by conventional microbiological methods is time- and lab-consuming. To overcome this problem, in this work a novel biosensor has been proposed. The sensor enables a fast method to evaluate sterilisation processes. By means of thin-film technology the sensor's transducer structures in form of IDEs (interdigitated electrodes) have been fabricated on a silicon substrate. Physical characterisation of the developed sensor was done by AFM, SEM, and profilometry. Impedance analyses were conducted for the electrical characterisation. As microbiological layer spores of B. atrophaeus have been immobilised on the sensing structure; spores of this type are a well-known sterilisation test organism. Impedance measurements at a fixed frequency over time were performed to monitor the immobilisation process. A sterilisation process according to aseptic filling machines was applied to demonstrate the sensor functionality. After both, immobilisation and sterilisation, a change in impedance could successfully be detected.
Simulating the electromagnetic‐thermal treatment of thin aluminium layers for adhesion improvement
(2015)
A composite layer material used in packaging industry is made from joining layers of different materials using an adhesive. An important processing step in the production of aluminium-containing composites is the surface treatment and consequent coating of adhesive material on the aluminium surface. To increase adhesion strength between aluminium layer and the adhesive material, the foil is heat treated. For efficient heating, induction heating was considered as state-of-the-art treatment process. Due to the complexity of the heating process and the unpredictable nature of the heating source, the control of the process is not yet optimised. In this work, a finite element analysis of the process was established and various process parameters were studied. The process was simplified and modelled in 3D. The numerical model contains an air domain, an aluminium layer and a copper coil fitted with a magnetic field concentrating material. The effect of changing the speed of the aluminium foil (or rolling speed) was studied with the change of the coil current. Statistical analysis was used for generating a general control equation of coil current with changing rolling speed.
An enzyme-based multi-parameter biosensor is developed for monitoring the concentration of formate, d-lactate, and l-lactate in biological samples. The sensor is based on the specific dehydrogenation by an oxidized β-nicotinamide adenine dinucleotide (NAD+)-dependent dehydrogenase (formate dehydrogenase, d-lactic dehydrogenase, and l-lactic dehydrogenase, respectively) in combination with a diaphorase from Clostridium kluyveri (EC 1.8.1.4). The enzymes are immobilized on a platinum working electrode by cross-linking with glutaraldehyde (GA). The principle of the determination scheme in case of l-lactate is as follows: l-lactic dehydrogenase (l-LDH) converts l-lactate into pyruvate by reaction with NAD+. In the presence of hexacyanoferrate(III), the resulting reduced β-nicotinamide adenine dinucleotide (NADH) is then regenerated enzymatically by diaphorase. The electrochemical detection is based on the current generated by oxidation of hexacyanoferrate(II) at an applied potential of +0.3 V vs. an Ag/AgCl reference electrode. The biosensor will be electrochemically characterized in terms of linear working range and sensitivity. Additionally, the successful practical application of the sensor is demonstrated in an extract from maize silage.
Poly(N-isopropylacrylamide) (PNIPAAm) hydrogel films with incorporated graphene oxide (GO) were developed and tested as light-stimulated actuators. GO dispersions were synthesized via Hummers method and characterized toward their optical properties and photothermal energy conversion. The hydrogels were prepared by means of photopolymerization. In addition, the influence of GO within the hydrogel network on the lower critical solution temperature (LCST) was investigated by differential scanning calorimetry (DSC). The optical absorbance and the response to illumination were determined as a function of GO concentration for thin hydrogel films. A proof of principle for the stimulation with light was performed.
A new microfluidic assembly method for semiconductor-based biosensors using 3D-printing technologies was proposed for a rapid and cost-efficient design of new sensor systems. The microfluidic unit is designed and printed by a 3D-printer in just a few hours and assembled on a light-addressable potentiometric sensor (LAPS) chip using a photo resin. The cell growth curves obtained from culturing cells within microfluidics-based LAPS systems were compared with cell growth curves in cell culture flasks to examine biocompatibility of the 3D-printed chips. Furthermore, an optimal cell culturing within microfluidics-based LAPS chips was achieved by adjusting the fetal calf serum concentrations of the cell culture medium, an important factor for the cell proliferation.
A concept for a new generation of an integrated multi-functional biosensor/actuator system is developed, which is based on biomolecular logic principles. Such a system is expected to be able to detect multiple biochemical input signals simultaneously and in real-time and convert them into electrical output signals with logical operations such as OR, AND, etc. The system can be designed as a closed-loop drug release device triggered by an enzyme logic gate, while the release of the drug induced by the actuator at the required dosage and timing will be controlled by an additional drug sensor. Thus, the system could help to make an accurate and specific diagnosis. The presented concept is exemplarily demonstrated by using an enzyme logic gate based on a glucose/glucose oxidase system, a temperature-responsive hydrogel mimicking the actuator function and an insulin (drug) sensor. In this work, the results of functional testing of individual amperometric glucose and insulin sensors as well as an impedimetric sensor for the detection of the hydrogel swelling/shrinking are presented.
High-k perovskite oxide of barium strontium titanate (BST) represents a very attractive multi-functional transducer material for the development of (bio-)chemical sensors. In this work, a Si-based sensor chip containing Pt interdigitated electrodes covered with a thin BST layer (485 nm) has been developed for multi-parameter chemical sensing. The chip has been applied for the contactless measurement of the electrolyte conductivity, the detection of adsorbed charged macromolecules (positively charged polyelectrolytes of polyethylenimine) and the concentration of hydrogen peroxide (H2O2) vapor. The experimental results of functional testing of individual sensors are presented. The mechanism of the BST sensitivity to charged polyelectrolytes and H2O2 vapor has been proposed and discussed.
We present a sensor concept based on copper(II)oxide (CuO) nanofibres for the detection of hydrogen peroxide (H2O2) vapour in the percent per volume (% v/v) range. The fibres were produced by using the electrospinning technique. To avoid water condensation in the pores, the fibres were initially modified by an exposure to H2S to get an enclosed surface. By a thermal treatment at 350 °C the fibres were oxidised back to CuO. Thereby, the visible pores disappear which was verified by SEM analysis. The fibres show a decrease of resistance with increasing H2O2 concentration which is due to the fact that hydrogen peroxide is an oxidising gas and CuO a p-type semiconductor. The sensor shows a change of resistance within the minute range to the exposure until the maximum concentration of 6.9% v/v H2O2. At operating temperatures below 450 °C the corresponding sensor response to a concentration of 4.1% v/v increases. The sensor shows a good reproducibility of the signal at different measurements. CuO seems to be a suitable candidate for the detection of H2O2 vapour at high concentrations.
Resistance behaviour of the sensor under exposure to H2O2 vapours between 2.3 and 6.9% v/v at an operating temperature of 450 °C.
In this work, a multi-sensor chip for the investigation of the sensing properties of different types of metal oxides towards hydrogen peroxide in the ppm range is presented. The fabrication process and physical characterization of the multi-sensor chip are described. Pure SnO2 and WO3 as well as Pd- and Pt-doped SnO2 films are characterized in terms of their sensitivity to H2O2. The sensing films have been prepared by drop-coating of water-dispensed nano-powders. A physical characterization, including scanning electron microscopy and X-ray diffraction analysis of the deposited metal-oxide films, was done. From the measurements in hydrogen peroxide atmosphere, it could be shown, that all of the tested metal oxide films are suitable for the detection of H2O2 in the ppm range. The highest sensitivity and reproducibility was achieved using Pt-doped SnO2.
Calibration plot of a SnO2, WO3, Pt-, and Pd-doped SnO2 gas sensor for H2O2 concentrations in the ppm range.
A wireless sensor system based on the industrial ZigBee standard for low-rate wireless networking was developed that enables real-time monitoring of gaseous H2O2 during the package sterilization in aseptic food processes. The sensor system consists of a remote unit connected to a calorimetric gas sensor, which was already established in former works, and an external base unit connected to a laptop computer. The remote unit was built up by an XBee radio frequency (RF) module for data communication and a programmable system-on-chip controller to read out the sensor signal and process the sensor data, whereas the base unit is a second XBee RF module. For the rapid H2O2 detection on various locations inside the package that has to be sterilized, a novel read-out strategy of the calorimetric gas sensor was established, wherein the sensor response is measured within the short sterilization time and correlated with the present H2O2 concentration. In an exemplary measurement application in an aseptic filling machinery, the suitability of the new, wireless sensor system was demonstrated, wherein the influence of the gas velocity on the H2O2 distribution inside a package was determined and verified with microbiological tests.
Impedance spectroscopy: A tool for real-time in situ monitoring of the degradation of biopolymers
(2013)
Investigation of the degradation kinetics of biodegradable polymers is essential for the development of implantable biomedical devices with predicted biodegradability. In this work, an impedimetric sensor has been applied for real-time and in situ monitoring of degradation processes of biopolymers. The sensor consists of two platinum thin-film electrodes covered by a polymer film to be studied. The benchmark biomedical polymer poly(D,L-lactic acid) (PDLLA) was used as a model system. PDLLA films were deposited on the sensor structure from a polymer solution by using the spin-coating method. The degradation kinetics of PDLLA films have been studied in alkaline solutions of pH 9 and 12 by means of an impedance spectroscopy (IS) method. Any changes in a polymer capacitance/resistance induced by water uptake and/or polymer degradation will modulate the global impedance of the polymer-covered sensor that can be used as an indicator of the polymer degradation. The degradation rate can be evaluated from the time-dependent impedance spectra. As expected, a faster degradation has been observed for PDLLA films exposed to pH 12 solution.
Suburethral slings as well as different meshes are widely used treating stress urinary incontinence and prolaps in women. With the development of MiniSlings and special meshes using less alloplastic material anchorage systems become more important to keep devices in place and to put some tension especially on the MiniSlings. To date, there are many different systems of MiniSlings of different companies on the market which differ in the structure of the used meshes and anchors. A new objective measurement method to compare different properties of MiniSling systems (mesh and anchor) is presented in this article. Ballistic gelatine acts as soft tissue surrogate. Significant differences in parameters like pull-out strength of anchors or shrinkage of meshes under loading conditions have been determined. The form and size of the anchors as well as the structural stability of the meshes are decisive for a proper integration. The tested anchorings sytems showed markedly different mechanical function at their respective load bearing capacity. As the stable fixation of the device in tissue is a prerequisite for a permanet reinforcement, the proposed test system permits further optimisation of anchor and mesh devices to improve the success of the surgical treatment
This paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node-based smoothed FEM in combination with a primal–dual algorithm. An associated primal–dual form based on the von Mises yield criterion is adopted. The primal-dual algorithm together with a Newton-like iteration are then used to solve this associated primal–dual form to determine simultaneously both approximate upper and quasi-lower bounds of the plastic collapse limit and the shakedown limit. The present formulation uses only linear approximations and its implementation into finite element programs is quite simple. Several numerical examples are given to show the reliability, accuracy, and generality of the present formulation compared with other available methods.
Unravelling the factors determining the allocation of carbon to various plant organs is one of the great challenges of modern plant biology. Studying allocation under close to natural conditions requires non-invasive methods, which are now becoming available for measuring plants on a par with those developed for humans. By combining magnetic resonance imaging (MRI) and positron emission tomography (PET), we investigated three contrasting root/shoot systems growing in sand or soil, with respect to their structures, transport routes and the translocation dynamics of recently fixed photoassimilates labelled with the short-lived radioactive carbon isotope 11C. Storage organs of sugar beet (Beta vulgaris) and radish plants (Raphanus sativus) were assessed using MRI, providing images of the internal structures of the organs with high spatial resolution, and while species-specific transport sectoralities, properties of assimilate allocation and unloading characteristics were measured using PET. Growth and carbon allocation within complex root systems were monitored in maize plants (Zea mays), and the results may be used to identify factors affecting root growth in natural substrates or in competition with roots of other plants. MRI–PET co-registration opens the door for non-invasive analysis of plant structures and transport processes that may change in response to genomic, developmental or environmental challenges. It is our aim to make the methods applicable for quantitative analyses of plant traits in phenotyping as well as in understanding the dynamics of key processes that are essential to plant performance.