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In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the first author (Breuß SIAM J. Numer. Anal. 43(3), 970–986 2005). Implicit notions are developed that are centered around a monotonicity criterion. We demonstrate a connection between a numerical scheme and a discrete entropy inequality, which is based on a classical approach by Crandall and Majda. Additionally, three implicit methods are investigated using the developed notions. Next, we conduct a convergence proof which is not based on a classical compactness argument. Finally, the theoretical results are confirmed by various numerical tests.
The inverse scattering problem for a conductive boundary condition and transmission eigenvalues
(2018)
In this paper, we consider the inverse scattering problem associated with an inhomogeneous media with a conductive boundary. In particular, we are interested in two problems that arise from this inverse problem: the inverse conductivity problem and the corresponding interior transmission eigenvalue problem. The inverse conductivity problem is to recover the conductive boundary parameter from the measured scattering data. We prove that the measured scatted data uniquely determine the conductivity parameter as well as describe a direct algorithm to recover the conductivity. The interior transmission eigenvalue problem is an eigenvalue problem associated with the inverse scattering of such materials. We investigate the convergence of the eigenvalues as the conductivity parameter tends to zero as well as prove existence and discreteness for the case of an absorbing media. Lastly, several numerical and analytical results support the theory and we show that the inside–outside duality method can be used to reconstruct the interior conductive eigenvalues.
In this work, we present a compact, bifunctional chip-based sensor setup that measures the temperature and electrical conductivity of water samples, including specimens from rivers and channels, aquaculture, and the Atlantic Ocean. For conductivity measurements, we utilize the impedance amplitude recorded via interdigitated electrode structures at a single triggering frequency. The results are well in line with data obtained using a calibrated reference instrument. The new setup holds for conductivity values spanning almost two orders of magnitude (river versus ocean water) without the need for equivalent circuit modelling. Temperature measurements were performed in four-point geometry with an on-chip platinum RTD (resistance temperature detector) in the temperature range between 2 °C and 40 °C, showing no hysteresis effects between warming and cooling cycles. Although the meander was not shielded against the liquid, the temperature calibration provided equivalent results to low conductive Milli-Q and highly conductive ocean water. The sensor is therefore suitable for inline and online monitoring purposes in recirculating aquaculture systems.
Electrolyte-insulator-semiconductor capacitors (EISCAP) belong to field-effect sensors having an attractive transducer architecture for constructing various biochemical sensors. In this study, a capacitive model of enzyme-modified EISCAPs has been developed and the impact of the surface coverage of immobilized enzymes on its capacitance-voltage and constant-capacitance characteristics was studied theoretically and experimentally. The used multicell arrangement enables a multiplexed electrochemical characterization of up to sixteen EISCAPs. Different enzyme coverages have been achieved by means of parallel electrical connection of bare and enzyme-covered single EISCAPs in diverse combinations. As predicted by the model, with increasing the enzyme coverage, both the shift of capacitance-voltage curves and the amplitude of the constant-capacitance signal increase, resulting in an enhancement of analyte sensitivity of the EISCAP biosensor. In addition, the capability of the multicell arrangement with multi-enzyme covered EISCAPs for sequentially detecting multianalytes (penicillin and urea) utilizing the enzymes penicillinase and urease has been experimentally demonstrated and discussed.
This paper investigates the interior transmission problem for homogeneous media via eigenvalue trajectories parameterized by the magnitude of the refractive index. In the case that the scatterer is the unit disk, we prove that there is a one-to-one correspondence between complex-valued interior transmission eigenvalue trajectories and Dirichlet eigenvalues of the Laplacian which turn out to be exactly the trajectorial limit points as the refractive index tends to infinity. For general simply-connected scatterers in two or three dimensions, a corresponding relation is still open, but further theoretical results and numerical studies indicate a similar connection.
The artificial olfactory image was proposed by Lundström et al. in 1991 as a new strategy for an electronic nose system which generated a two-dimensional mapping to be interpreted as a fingerprint of the detected gas species. The potential distribution generated by the catalytic metals integrated into a semiconductor field-effect structure was read as a photocurrent signal generated by scanning light pulses. The impact of the proposed technology spread beyond gas sensing, inspiring the development of various imaging modalities based on the light addressing of field-effect structures to obtain spatial maps of pH distribution, ions, molecules, and impedance, and these modalities have been applied in both biological and non-biological systems. These light-addressing technologies have been further developed to realize the position control of a faradaic current on the electrode surface for localized electrochemical reactions and amperometric measurements, as well as the actuation of liquids in microfluidic devices.
Many important properties of bacterial cellulose (BC), such as moisture absorption capacity, elasticity and tensile strength, largely depend on its structure. This paper presents a study on the effect of the drying method on BC films produced by Medusomyces gisevii using two different procedures: room temperature drying (RT, (24 ± 2 °C, humidity 65 ± 1%, dried until a constant weight was reached) and freeze-drying (FD, treated at − 75 °C for 48 h). BC was synthesized using one of two different carbon sources—either glucose or sucrose. Structural differences in the obtained BC films were evaluated using atomic force microscopy (AFM), scanning electron microscopy (SEM), and X-ray diffraction. Macroscopically, the RT samples appeared semi-transparent and smooth, whereas the FD group exhibited an opaque white color and sponge-like structure. SEM examination showed denser packing of fibrils in FD samples while RT-samples displayed smaller average fiber diameter, lower surface roughness and less porosity. AFM confirmed the SEM observations and showed that the FD material exhibited a more branched structure and a higher surface roughness. The samples cultivated in a glucose-containing nutrient medium, generally displayed a straight and ordered shape of fibrils compared to the sucrose-derived BC, characterized by a rougher and wavier structure. The BC films dried under different conditions showed distinctly different crystallinity degrees, whereas the carbon source in the culture medium was found to have a relatively small effect on the BC crystallinity.
To gain insight on chemical sterilization processes, the influence of temperature (up to 70 °C), intense green light, and hydrogen peroxide (H₂O₂) concentration (up to 30% in aqueous solution) on microbial spore inactivation is evaluated by in-situ Raman spectroscopy with an optical trap. Bacillus atrophaeus is utilized as a model organism. Individual spores are isolated and their chemical makeup is monitored under dynamically changing conditions (temperature, light, and H₂O₂ concentration) to mimic industrially relevant process parameters for sterilization in the field of aseptic food processing. While isolated spores in water are highly stable, even at elevated temperatures of 70 °C, exposure to H₂O₂ leads to a loss of spore integrity characterized by the release of the key spore biomarker dipicolinic acid (DPA) in a concentration-dependent manner, which indicates damage to the inner membrane of the spore. Intensive light or heat, both of which accelerate the decomposition of H₂O₂ into reactive oxygen species (ROS), drastically shorten the spore lifetime, suggesting the formation of ROS as a rate-limiting step during sterilization. It is concluded that Raman spectroscopy can deliver mechanistic insight into the mode of action of H₂O₂-based sterilization and reveal the individual contributions of different sterilization methods acting in tandem.
The deformation and damage laws of non-homogeneous irregular structural planes in rocks are the basis for studying the stability of rock engineering. To investigate the damage characteristics of rock containing non-parallel fissures, uniaxial compression tests and numerical simulations were conducted on sandstone specimens containing three non-parallel fissures inclined at 0°, 45° and 90° in this study. The characteristics of crack initiation and crack evolution of fissures with different inclinations were analyzed. A constitutive model for the discontinuous fractures of fissured sandstone was proposed. The results show that the fracture behaviors of fissured sandstone specimens are discontinuous. The stress–strain curves are non-smooth and can be divided into nonlinear crack closure stage, linear elastic stage, plastic stage and brittle failure stage, of which the plastic stage contains discontinuous stress drops. During the uniaxial compression test, the middle or ends of 0° fissures were the first to crack compared to 45° and 90° fissures. The end with small distance between 0° and 45° fissures cracked first, and the end with large distance cracked later. After the final failure, 0° fissures in all specimens were fractured, while 45° and 90° fissures were not necessarily fractured. Numerical simulation results show that the concentration of compressive stress at the tips of 0°, 45° and 90° fissures, as well as the concentration of tensile stress on both sides, decreased with the increase of the inclination angle. A constitutive model for the discontinuous fractures of fissured sandstone specimens was derived by combining the logistic model and damage mechanic theory. This model can well describe the discontinuous drops of stress and agrees well with the whole processes of the stress–strain curves of the fissured sandstone specimens.
Frequency mixing magnetic detection (FMMD) is a sensitive and selective technique to detect magnetic nanoparticles (MNPs) serving as probes for binding biological targets. Its principle relies on the nonlinear magnetic relaxation dynamics of a particle ensemble interacting with a dual frequency external magnetic field. In order to increase its sensitivity, lower its limit of detection and overall improve its applicability in biosensing, matching combinations of external field parameters and internal particle properties are being sought to advance FMMD. In this study, we systematically probe the aforementioned interaction with coupled Néel–Brownian dynamic relaxation simulations to examine how key MNP properties as well as applied field parameters affect the frequency mixing signal generation. It is found that the core size of MNPs dominates their nonlinear magnetic response, with the strongest contributions from the largest particles. The drive field amplitude dominates the shape of the field-dependent response, whereas effective anisotropy and hydrodynamic size of the particles only weakly influence the signal generation in FMMD. For tailoring the MNP properties and parameters of the setup towards optimal FMMD signal generation, our findings suggest choosing large particles of core sizes dc > 25 nm nm with narrow size distributions (σ < 0.1) to minimize the required drive field amplitude. This allows potential improvements of FMMD as a stand-alone application, as well as advances in magnetic particle imaging, hyperthermia and magnetic immunoassays.
Muscle function is compromised by gravitational unloading in space affecting overall musculoskeletal health. Astronauts perform daily exercise programmes to mitigate these effects but knowing which muscles to target would optimise effectiveness. Accurate inflight assessment to inform exercise programmes is critical due to lack of technologies suitable for spaceflight. Changes in mechanical properties indicate muscle health status and can be measured rapidly and non-invasively using novel technology. A hand-held MyotonPRO device enabled monitoring of muscle health for the first time in spaceflight (> 180 days). Greater/maintained stiffness indicated countermeasures were effective. Tissue stiffness was preserved in the majority of muscles (neck, shoulder, back, thigh) but Tibialis Anterior (foot lever muscle) stiffness decreased inflight vs. preflight (p < 0.0001; mean difference 149 N/m) in all 12 crewmembers. The calf muscles showed opposing effects, Gastrocnemius increasing in stiffness Soleus decreasing. Selective stiffness decrements indicate lack of preservation despite daily inflight countermeasures. This calls for more targeted exercises for lower leg muscles with vital roles as ankle joint stabilizers and in gait. Muscle stiffness is a digital biomarker for risk monitoring during future planetary explorations (Moon, Mars), for healthcare management in challenging environments or clinical disorders in people on Earth, to enable effective tailored exercise programmes.
Advances in polymer science have significantly increased polymer applications in life sciences. We report the use of free-standing, ultra-thin polydimethylsiloxane (PDMS) membranes, called CellDrum, as cell culture substrates for an in vitro wound model. Dermal fibroblast monolayers from 28- and 88-year-old donors were cultured on CellDrums. By using stainless steel balls, circular cell-free areas were created in the cell layer (wounding). Sinusoidal strain of 1 Hz, 5% strain, was applied to membranes for 30 min in 4 sessions. The gap circumference and closure rate of un-stretched samples (controls) and stretched samples were monitored over 4 days to investigate the effects of donor age and mechanical strain on wound closure. A significant decrease in gap circumference and an increase in gap closure rate were observed in trained samples from younger donors and control samples from older donors. In contrast, a significant decrease in gap closure rate and an increase in wound circumference were observed in the trained samples from older donors. Through these results, we propose the model of a cell monolayer on stretchable CellDrums as a practical tool for wound healing research. The combination of biomechanical cell loading in conjunction with analyses such as gene/protein expression seems promising beyond the scope published here.
During rapid deceleration of the body, tendons buffer part of the elongation of the muscle-tendon unit (MTU), enabling safe energy dissipation via eccentric muscle contraction. Yet, the influence of changes in tendon stiffness within the physiological range upon these lengthening contractions is unknown. This study aimed to examine the effect of training-induced stiffening of the Achilles tendon on triceps surae muscle-tendon behavior during a landing task. Twenty-one male subjects were assigned to either a 10-week resistance-training program consisting of single-leg isometric plantarflexion (n = 11) or to a non-training control group (n = 10). Before and after the training period, plantarflexion force, peak Achilles tendon strain and stiffness were measured during isometric contractions, using a combination of dynamometry, ultrasound and kinematics data. Additionally, testing included a step-landing task, during which joint mechanics and lengths of gastrocnemius and soleus fascicles, Achilles tendon, and MTU were determined using synchronized ultrasound, kinematics and kinetics data collection. After training, plantarflexion strength and Achilles tendon stiffness increased (15 and 18%, respectively), and tendon strain during landing remained similar. Likewise, lengthening and negative work produced by the gastrocnemius MTU did not change detectably. However, in the training group, gastrocnemius fascicle length was offset (8%) to a longer length at touch down and, surprisingly, fascicle lengthening and velocity were reduced by 27 and 21%, respectively. These changes were not observed for soleus fascicles when accounting for variation in task execution between tests. These results indicate that a training-induced increase in tendon stiffness does not noticeably affect the buffering action of the tendon when the MTU is rapidly stretched. Reductions in gastrocnemius fascicle lengthening and lengthening velocity during landing occurred independently from tendon strain. Future studies are required to provide insight into the mechanisms underpinning these observations and their influence on energy dissipation.
Comparison of different training algorithms for the leg extension training with an industrial robot
(2018)
In the past, different training scenarios have been developed and implemented on robotic research platforms, but no systematic analysis and comparison have been done so far. This paper deals with the comparison of an isokinematic (motion with constant velocity) and an isotonic (motion against constant weight) training algorithm. Both algorithms are designed for a robotic research platform consisting of a 3D force plate and a high payload industrial robot, which allows leg extension training with arbitrary six-dimensional motion trajectories. In the isokinematic as well as the isotonic training algorithm, individual paths are defined i n C artesian s pace by sufficient s upport p oses. I n t he i sotonic t raining s cenario, the trajectory is adapted to the measured force as the robot should only move along the trajectory as long as the force applied by the user exceeds a minimum threshold. In the isotonic training scenario however, the robot’s acceleration is a function of the force applied by the user. To validate these findings, a simulative experiment with a simple linear trajectory is performed. For this purpose, the same force path is applied in both training scenarios. The results illustrate that the algorithms differ in the force dependent trajectory adaption.
Training-induced increase in Achilles tendon stiffness affects tendon strain pattern during running
(2019)
Background
During the stance phase of running, the elasticity of the Achilles tendon enables the utilisation of elastic energy and allows beneficial contractile conditions for the triceps surae muscles. However, the effect of changes in tendon mechanical properties induced by chronic loading is still poorly understood. We tested the hypothesis that a training-induced increase in Achilles tendon stiffness would result in reduced tendon strain during the stance phase of running, which would reduce fascicle strains in the triceps surae muscles, particularly in the mono-articular soleus.
Methods
Eleven subjects were assigned to a training group performing isometric singleleg plantarflexion contractions three times per week for ten weeks, and another ten subjects formed a control group. Before and after the training period, Achilles tendon stiffness was estimated, and muscle-tendon mechanics were assessed during running at preferred speed using ultrasonography, kinematics and kinetics.
Results
Achilles tendon stiffness increased by 18% (P <0:01) in the training group, but the associated reduction in strain seen during isometric contractions was not statistically significant. Tendon elongation during the stance phase of running was similar after training, but tendon recoil was reduced by 30% (P <0:01), while estimated tendon force remained unchanged. Neither gastrocnemius medialis nor soleus fascicle shortening during stance was affected by training.
Discussion
These results show that a training-induced increase in Achilles tendon
stiffness altered tendon behaviour during running. Despite training-induced changes in tendon mechanical properties and recoil behaviour, the data suggest that fascicle shortening patterns were preserved for the running speed that we examined. The asymmetrical changes in tendon strain patterns supports the notion that simple inseries models do not fully explain the mechanical output of the muscle-tendon unit during a complex task like running.
Neuromuscular strength training of the leg extensor muscles plays an important role in the rehabilitation and prevention of age and wealth related diseases. In this paper, we focus on the design and implementation of a Cartesian admittance control scheme for isotonic training, i.e. leg extension and flexion against a predefined weight. For preliminary testing and validation of the designed algorithm an experimental research and development platform consisting of an
industrial robot and a force plate mounted at its end-effector has been used. Linear, diagonal and arbitrary two-dimensional motion trajectories with different weights for the leg extension and flexion part are applied. The proposed algorithm is easily adaptable to trajectories consisting of arbitrary six-dimensional poses and allows the implementation of individualized trajectories.
To prevent the reduction of muscle mass and loss of strength coming along with the human aging process, regular training with e.g. a leg press is suitable. However, the risk of training-induced injuries requires the continuous monitoring and controlling of the forces applied to the musculoskeletal system as well as the velocity along the motion trajectory and the range of motion. In this paper, an adaptive norm-optimal iterative learning control algorithm to minimize the knee joint loadings during the leg extension training with an industrial robot is proposed. The response of the algorithm is tested in simulation for patients with varus, normal and valgus alignment of the knee and compared to the results of a higher-order iterative learning control algorithm, a robust iterative learning control and a recently proposed conventional norm-optimal iterative learning control algorithm. Although significant improvements in performance are made compared to the conventional norm-optimal iterative learning control algorithm with a small learning factor, for the developed approach as well as the robust iterative learning control algorithm small steady state errors occur.
Achilles tendon rupture (ATR) patients have persistent functional deficits in the triceps surae muscle–tendon unit (MTU). The complex remodeling of the MTU accompanying these deficits remains poorly understood. The purpose of the present study was to associate in vivo and in silico data to investigate the relations between changes inMTU properties and strength deficits inATR patients. Methods: Elevenmale subjects who had undergone surgical repair of complete unilateral ATR were examined 4.6 ± 2.0 (mean ± SD) yr after rupture. Gastrocnemius medialis (GM) tendon stiffness, morphology, and muscle architecture were determined using ultrasonography. The force–length relation of the plantar flexor muscles was assessed at five ankle joint angles. In addition, simulations (OpenSim) of the GM MTU force–length properties were performed with various iterations of MTU properties found between the unaffected and the affected side. Results: The affected side of the patients displayed a longer, larger, and stiffer GM tendon (13% ± 10%, 105% ± 28%, and 54% ± 24%, respectively) compared with the unaffected side. The GM muscle fascicles of the affected side were shorter (32% ± 12%) and with greater pennation angles (31% ± 26%). A mean deficit in plantarflexion moment of 31% ± 10% was measured. Simulations indicate that pairing an intact muscle with a longer tendon shifts the optimal angular range of peak force outside physiological angular ranges, whereas the shorter muscle fascicles and tendon stiffening seen in the affected side decrease this shift, albeit incompletely. Conclusions: These results suggest that the substantial changes in MTU properties found in ATR patients may partly result from compensatory remodeling, although this process appears insufficient to fully restore muscle function.
Performing tasks, such as running and jumping, requires activation of the agonist and antagonist muscles before (motor unit pre-activation) and during movement performance (Santello and Mcdonagh, 1998). A well-timed and regulated muscle activation elicits a stretch-shortening cycle (SSC) response, naturally occurring in bouncing movements (Ishikawa and Komi, 2004; Taube et al., 2012). By definition, the SSC describes the stretching of a pre-activated muscle-tendon complex immediately followed by a muscle shortening in the concentric push-off phase (Komi, 1984).
Given the importance of SSC actions for human movement, it is not surprising that many studies investigated the biomechanics of this phenomenon; in particular, drop jumps (DJs) represent a good paradigm to study muscle fascicle and tendon behavior in ballistic movements involving the SSC.
Within a DJ, three main phases [pre-activation, braking, and push-off (PO; Komi, 2000)] have been recognized and extensively studied in common and challenging conditions, such as changes in load, falling height, or simulated hypo-gravity (Avela et al., 1994; Arampatzis et al., 2001; Fukashiro et al., 2005; Ishikawa et al., 2005; Sousa et al., 2007; Ritzmann et al., 2016; Helm et al., 2020).
These studies show that the timing and amount of triceps-surae muscle-tendon unit pre-activation in DJs are differentially regulated based on the load applied to the muscle, being optimal in normal “Earth” gravity conditions (Avela et al., 1994), but decreased in simulated hypo-gravity, hyper-gravity (Avela et al., 1994; Ritzmann et al., 2016), or unknown conditions (i.e., unknown falling heights; Helm et al., 2020). Some authors indicated that, when falling from heights different from the optimal one [defined as the drop height giving a maximum DJ performance indicated as peak ground reaction force (GRF) or jump high], electromyographic (EMG) activity of the plantar flexors increases from lower than optimal to higher than optimal heights (Ishikawa and Komi, 2004; Sousa et al., 2007).
These findings highlight the ability of the central nervous system to regulate the timing and amount of pre-activation according to different jumping conditions, thus regulating muscle fascicle length, tendon and joint stiffness as well as position, in order to safely land on the ground and quickly re-bounce.
Similarly, to pre-activation, also in the braking phase, the plantar flexors are differentially regulated. In optimal height (i.e., load) jumping conditions, gastrocnemius medialis (GM) fascicles shorten at early ground contact (possibly due to the intervention of the stretch reflex; Gollhofer et al., 1992) and behave quasi-isometrically in the late braking phase, enabling tendon elongation, and storage of elastic energy (Gollhofer et al., 1992; Fukashiro et al., 2005; Sousa et al., 2007). When increasing the falling height (augmenting the impact GRF), the quasi-isometric behavior of fascicles disappears, and fast fascicle lengthening occurs (Ishikawa et al., 2005; Sousa et al., 2007).
In the third and last PO phase, fascicles shorten and the tendon releases the elastic energy previously stored. Bobbert et al. (1987) reported no influence of jumping height on the work done and on the net vertical impulse assessed during PO; this observation suggests that, despite an optimal DJ performance might be achieved only in specific conditions (falling heights, loads), the central nervous system seems to be able to regulate muscle behavior in order to effectively perform the required task also in challenging situations.
Although the regulation of triceps-surae muscle-tendon unit in DJs has been extensively investigated, very few studies focused on sarcomeres behavior during the performance of this SSC movement (Kurokawa et al., 2003; Fukashiro et al., 2005, 2006). Sarcomeres represent muscle contractile units and are known to express different amounts of force depending on their length (Gordon et al., 1966; Walker and Schrodt, 1974); thus, understanding the time course of their responses during DJs is fundamental to gain further insights into muscle force-generating capacity. In vivo measurement of sarcomere length in humans has been so far been performed only in static positions and under highly controlled experimental conditions (Llewellyn et al., 2008; Sanchez et al., 2015). Instead, human sarcomere length estimation (achieved by dividing GM measured fascicle length for a fixed sarcomere number) in dynamic contractions provided an indirect measure of sarcomere operating range during squat jump, countermovement jump, and DJ (Fukashiro et al., 2005, 2006; Kurokawa et al., 2003). The results of these studies showed that sarcomeres operate in the ascending limb of their length-tension (L-T) relationship in all types of jumps, and particularly so in DJ.
However, most of the available observations on sarcomere and muscle fascicle behavior were made in condition of constant gravity. Thus, in order to understand how sarcomere and muscle fascicle length are regulated in variable gravity conditions, we performed experiments in a parabolic flight, involving variable gravity levels, ranging from about zero-g to about double the Earth’s gravity (1 g; Waldvogel et al., 2021).
Specifically, the aims of the present study were as follows:
1. To investigate the ability of the neuromuscular system in regulating fascicle length in response to conditions of variable gravity.
2. To estimate sarcomere operative length in the different DJ phases, in order to calculate its theoretical force production and its possible modulation in conditions of variable gravity.
We hypothesized that muscle fascicles would be differentially regulated in different gravity conditions compared to 1 g, particularly in anticipation of landing and re-bouncing in unknown gravity levels. In addition, we hypothesized that sarcomeres would operate in the upper part of the ascending limb of their L-T relationship, possibly lengthening during the braking phase (especially in hyper-gravity) while operating quasi-isometrically in 1 g.