The time course of in vivo recovery of transverse strain in high-stress tendons following exercise

Objective To evaluate the time course of the recovery of transverse strain in the Achilles and patellar tendon following a bout of resistance exercise. Methods Seventeen healthy adults underwent sonographic examination of the right patellar (n=9) and Achilles (n=8) tendons immediately prior to and following 90 repetitions of weight-bearing quadriceps and gastrocnemius-resistance exercise performed against an effective resistance of 175% and 250% body weight, respectively. Sagittal tendon thickness was determined 20 mm from the enthesis and transverse strain, as defined by the stretch ratio, was repeatedly monitored over a 24 h recovery period. Results Resistance exercise resulted in an immediate decrease in Achilles (t7=10.6, p<0.01) and patellar (t8=8.9, p<0.01) tendon thickness, resulting in an average transverse stretch ratio of 0.86±0.04 and 0.82±0.05, which was not significantly different between tendons. The magnitude of the immediate transverse strain response, however, was reduced with advancing age (r=0.63, p<0.01). Recovery in transverse strain was prolonged compared with the duration of loading and exponential in nature. The average primary recovery time was not significantly different between the Achilles (6.5±3.2 h) and patellar (7.1±3.2 h) tendons. Body weight accounted for 62% and 64% of the variation in recovery time, respectively. Conclusions Despite structural and biochemical differences between the Achilles and patellar tendon, the mechanisms underlying transverse creep recovery in vivo appear similar and are highly time dependent. These novel findings have important implications concerning the time required for the mechanical recovery of high-stress tendons following an acute bout of exercise.

The acute transverse strain response of the patellar tendon to quadriceps exercise

Introduction: The human patellar tendon is highly adaptive to changes in habitual loading but little is known about its acute mechanical response to exercise. This research evaluated the immediate transverse strain response of the patellar tendon to a bout of resistive quadriceps exercise. Methods: Twelve healthy adult males (mean age 34.0+/-12.1 years, height 1.75+/-0.09 m and weight 76.7+/-12.3 kg) free of knee pain participated in the research. A 10-5 MHz linear-array transducer was used to acquire standardised sagittal sonograms of the right patellar tendon immediately prior to and following 90 repetitions of a double-leg parallel-squat exercise performed against a resistance of 175% bodyweight. Tendon thickness was determined 20-mm distal to the pole of the patellar and transverse Hencky strain was calculated as the natural log of the ratio of post- to pre-exercise tendon thickness and expressed as a percentage. Measures of tendon echotexture (echogenicity and entropy) were also calculated from subsequent gray-scale profiles. Results: Quadriceps exercise resulted in an immediate decrease in patellar tendon thickness (P<.05), equating to a transverse strain of -22.5+/-3.4%, and was accompanied by increased tendon echogenicity (P<.05) and decreased entropy (P<.05). The transverse strain response of the patellar tendon was significantly correlated with both tendon echogenicity (r = -0.58, P<.05) and entropy following exercise (r=0.73, P<.05), while older age was associated with greater entropy of the patellar tendon prior to exercise (r=0.79, P<.05) and a reduced transverse strain response (r=0.61, P<.05) following exercise. Conclusions: This study is the first to show that quadriceps exercise invokes structural alignment and fluid movement within the matrix that are manifest by changes in echotexture and transverse strain in the patellar tendon., (C)2012The American College of Sports Medicine

Overweight and obesity alters the cumulative transverse strain in the Achilles tendon immediately following exercise

This research evaluated the effect of obesity on the acute cumulative transverse strain of the Achilles tendon in response to exercise. Twenty healthy adult males were categorized into ‘low normal-weight’ (BMI <23 kg m−2) and ‘overweight’ (BMI >27.5 kg m−2) groups based on intermediate cut-off points recommended by the World Health Organization. Longitudinal sonograms of the right Achilles tendon were acquired immediately prior and following weight-bearing ankle exercises. Achilles tendon thickness was measured 20-mm proximal to the calcaneal insertion and transverse tendon strain was calculated as the natural log of the ratio of post- to pre-exercise tendon thickness. The Achilles tendon was thicker in the overweight group both prior to (t18 = −2.91, P = 0.009) and following (t18 = −4.87, P < 0.001) exercise. The acute transverse strain response of the Achilles tendon in the overweight group (−10.7 ± 2.5%), however, was almost half that of the ‘low normal-weight’ (−19.5 ± 7.4%) group (t18 = −3.56, P = 0.004). These findings suggest that obesity is associated with structural changes in tendon that impairs intra-tendinous fluid movement in response to load and provides new insights into the link between tendon pathology and overweight and obesity.

Very sensitive fiber Bragg grating accelerometer using transverse forces with an easy over-range protection and low cross axial sensitivity

The first fiber Bragg grating (FBG) accelerometer using direct transverse forces is demonstrated by fixing the FBG by its two ends and placing a transversely moving inertial object at its middle. It is very sensitive because a lightly stretched FBG is more sensitive to transverse forces than axial forces. Its resonant frequency and static sensitivity are analyzed by the classic spring-mass theory, assuming the axial force changes little. The experiments show that the theory can be modified for cases where the assumption does not hold. The resonant frequency can be modified by a linear relationship experimentally achieved, and the static sensitivity by an alternative method proposed. The principles of the over-range protection and low cross axial sensitivity are achieved by limiting the movement of the FBG and were validated experimentally. The sensitivities 1.333 and 0.634 nm/g were experimentally achieved by 5.29 and 2.83 gram inertial objects at 10 Hz from 0.1 to 0.4 g (g = 9.8 m/s 2), respectively, and their resonant frequencies were around 25 Hz. Their theoretical static sensitivities and resonant frequencies found by the modifications are 1.188 nm/g and 26.81 Hz for the 5.29 gram one and 0.784 nm/g and 29.04 Hz for the 2.83 gram one, respectively.

Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes

Mathematical descriptions of birth–death–movement processes are often calibrated to measurements from cell biology experiments to quantify tissue growth rates. Here we describe and analyze a discrete model of a birth–death-movement process applied to a typical two–dimensional cell biology experiment. We present three different descriptions of the system: (i) a standard mean–field description which neglects correlation effects and clustering; (ii) a moment dynamics description which approximately incorporates correlation and clustering effects, and; (iii) averaged data from repeated discrete simulations which directly incorporates correlation and clustering effects. Comparing these three descriptions indicates that the mean–field and moment dynamics approaches are valid only for certain parameter regimes, and that both these descriptions fail to make accurate predictions of the system for sufficiently fast birth and death rates where the effects of spatial correlations and clustering are sufficiently strong. Without any method to distinguish between the parameter regimes where these three descriptions are valid, it is possible that either the mean–field or moment dynamics model could be calibrated to experimental data under inappropriate conditions, leading to errors in parameter estimation. In this work we demonstrate that a simple measurement of agent clustering and correlation, based on coordination number data, provides an indirect measure of agent correlation and clustering effects, and can therefore be used to make a distinction between the validity of the different descriptions of the birth–death–movement process.

Pull-through failures of crest-fixed steel claddings initiated by transverse splitting

Crest-fixed steel claddings made of thin, high strength steel often suffer from local pull-through failures at their screw connections during high wind events such as storms and hurricanes. Currently there aren't any adequate design provisions for these cladding systems except for the expensive testing provisions. Since the local pull-through failures in the less ductile steel claddings are initiated by transverse splitting at the fastener hole, analytical studies have not been able to determine the pull-through failure loads. Analytical studies could be used if a reliable splitting criterion is available. Therefore a series of two-span cladding tests was conducted on a range of crest-fixed steel cladding systems under simulated wind uplift loads. The strains in the sheeting around the critical fastener holes were measured until the pull-through failure. This paper presents the details of the experimental investigation and the results including a strain criterion for the local pull-through failure.

Recovery of transverse strain in high–stress tendons following exercise

Background. This study evaluated the time course of recovery of transverse strain in the Achilles and patellar tendons following a bout of resistance exercise. Methods. Seventeen healthy adults underwent sonographic examination of the right patellar (n = 9) or Achilles (n = 8) tendons immediately prior to and following 90 repetitions of weight–bearing exercise. Quadriceps and gastrocnemius exercise were performed against an effective resistance of 175% and 250% body weight, respectively. Sagittal tendon thickness was determined 20 mm from the tendon enthesis and transverse strain was repeatedly monitored over a 24 hour recovery period. Results. Resistance exercise resulted in an immediate decrease in Achilles (t7 = 10.6, P<.01) and patellar (t8 = 8.9, P<.01) tendon thickness, resulting in an average transverse strain of 0.14 ± 0.04 and 0.18 ± 0.05. While the average strain was not significantly different between tendons, older age was associated with a reduced transverse strain response (r=0.63, P<.01). Recovery of transverse strain, in contrast, was prolonged compared with the duration of loading and exponential in nature. The mean primary recovery time was not significantly different between Achilles (6.5 ± 3.2 hours) and patellar (7.1 ± 3.2 hours) tendons and body weight accounted for 62% and 64% of the variation in recovery time, respectively. Discussion. Despite structural and biochemical differences between the Achilles and patellar tendons [1], the mechanisms underlying transverse creep–recovery in vivo appear similar and are highly time dependent. Primary recovery required about 7 hours in healthy tendons, with full recovery requiring up to 24 hours. These in vivo recovery times are similar to those reported for axial creep recovery of the vertebral disc in vitro [2], and may be used clinically to guide physical activity to rest ratios in healthy adults. Optimal ratios for high–stress tendons in clinical populations, however, remain unknown and require further attention in light of the knowledge gained in this study.

Experimental verification of the modified spring-mass theory of fiber Bragg grating accelerometers using transverse forces

A fiber Bragg grating (FBG) accelerometer using transverse forces is more sensitive than one using axial forces with the same mass of the inertial object, because a barely stretched FBG fixed at its two ends is much more sensitive to transverse forces than axial ones. The spring-mass theory, with the assumption that the axial force changes little during the vibration, cannot accurately predict its sensitivity and resonant frequency in the gravitational direction because the assumption does not hold due to the fact that the FBG is barely prestretched. It was modified but still required experimental verification due to the limitations in the original experiments, such as the (1) friction between the inertial object and shell; (2) errors involved in estimating the time-domain records; (3) limited data; and (4) large interval ∼5 Hz between the tested frequencies in the frequency-response experiments. The experiments presented here have verified the modified theory by overcoming those limitations. On the frequency responses, it is observed that the optimal condition for simultaneously achieving high sensitivity and resonant frequency is at the infinitesimal prestretch. On the sensitivity at the same frequency, the experimental sensitivities of the FBG accelerometer with a 5.71 gram inertial object at 6 Hz (1.29, 1.19, 0.88, 0.64, and 0.31 nm/g at the 0.03, 0.69, 1.41, 1.93, and 3.16 nm prestretches, respectively) agree with the static sensitivities predicted (1.25, 1.14, 0.83, 0.61, and 0.29 nm/g, correspondingly). On the resonant frequency, (1) its assumption that the resonant frequencies in the forced and free vibrations are similar is experimentally verified; (2) its dependence on the distance between the FBG’s fixed ends is examined, showing it to be independent; (3) the predictions of the spring-mass theory and modified theory are compared with the experimental results, showing that the modified theory predicts more accurately. The modified theory can be used more confidently in guiding its design by predicting its static sensitivity and resonant frequency, and may have applications in other fields for the scenario where the spring-mass theory fails.

Non-linear refined finite element elastic analysis of steel frames with generalized transverse member loads

In the finite element modelling of steel frames, external loads usually act along the members rather than at the nodes only. Conventionally, when a member is subjected to these transverse loads, they are converted to nodal forces which act at the ends of the elements into which the member is discretised by either lumping or consistent nodal load approaches. For a contemporary geometrically non-linear analysis in which the axial force in the member is large, accurate solutions are achieved by discretising the member into many elements, which can produce unfavourable consequences on the efficacy of the method for analysing large steel frames. Herein, a numerical technique to include the transverse loading in the non-linear stiffness formulation for a single element is proposed, and which is able to predict the structural responses of steel frames involving the effects of first-order member loads as well as the second-order coupling effect between the transverse load and the axial force in the member. This allows for a minimal discretisation of a frame for second-order analysis. For those conventional analyses which do include transverse member loading, prescribed stiffness matrices must be used for the plethora of specific loading patterns encountered. This paper shows, however, that the principle of superposition can be applied to the equilibrium condition, so that the form of the stiffness matrix remains unchanged with only the magnitude of the loading being needed to be changed in the stiffness formulation. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. The results are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple structural frames.

A nonlinear observer for estimating transverse stability parameters of marine surface vessels

This paper presents a nonlinear observer for estimating parameters associated with the restoring term of a roll motion model of a marine vessel in longitudinal waves. Changes in restoring, also referred to as transverse stability, can be the result of changes in the vessel's centre of gravity due to, for example, water on deck and also in changes in the buoyancy triggered by variations in the water-plane area produced by longitudinal waves -- propagating along the fore-aft direction along the hull. These variations in the restoring can change dramatically the dynamics of the roll motion leading to dangerous resonance. Therefore, it is of interest to estimate and detect such changes.

Interaction of transverse electromagnetic waves with counterpropagating surface waves at a plasma-dielectric interface

The nonlinear interaction of high-frequency transverse electromagnetic waves normally incident from a plasma region on to a dielectric with two surface waves (SWs) propagating in the opposite directions along the interface is studied. This interaction is found to be stable causing a slight modulation to the SWs in contrast to the decay instability for longitudinal plasma waves. The corresponding nonlinear frequency shift of the SWs is obtained and analyzed.

Biaxial fiber Bragg grating accelerometer using axial and transverse forces

We demonstrate the first biaxial fiber Bragg grating (FBG) accelerometer using axial and transverse forces. An inertial object is fixed at the middle of two FBGs inscribed in one fiber. The difference between the resonant wavelengths of the two FBGs can distinguish the acceleration in the axial direction, while being insensitive in the transverse direction. The average of the resonant wavelengths of the two FBGs can distinguish the acceleration in the transverse direction, while being insensitive in the axial direction. In the experiments, when the transverse direction was vertical, the crest-to-trough sensitivity at 5 Hz and resonant frequency of the average were 0.545 nm/g and 34.42 Hz, respectively. When the axial direction was vertical, those of the difference were 0.0454 nm/g and 900 Hz, respectively. For each FBG, the crest-to-trough sensitivity at 5 Hz and resonant frequency in the transverse/vertical direction were 24 and 1/26 times those in the axial/vertical direction, respectively.

Intervertebral staple grading system with micro-CT

Introduction Intervertebral stapling is a leading method of fusionless scoliosis treatment which attempts to control growth by applying pressure to the convex side of a scoliotic curve in accordance with the Hueter-Volkmann principle. In addition to that, staples have the potential to damage surrounding bone during insertion and subsequent loading. The aim of this study was to assess the extent of bony structural damage including epiphyseal injury as a result of intervertebral stapling using an in vitro bovine model. Materials and Methods Thoracic spines from 6-8 week old calves were dissected and divided into motion segments including levels T4-T11 (n=14). Each segment was potted in polymethylemethacrylate. An Instron Biaxial materials testing machine with a custom made jig was used for testing. The segments were tested in flexion/extension, lateral bending and axial rotation at 37⁰C and 100% humidity, using moment control to a maximum 1.75 Nm with a loading rate of 0.3 Nm per second for 10 cycles. The segments were initially tested uninstrumented with data collected from the tenth load cycle. Next an anterolateral 4-prong Shape Memory Alloy (SMA) staple (Medtronic Sofamor Danek, USA) was inserted into each segment. Biomechanical testing was repeated as before. The staples were cut in half with a diamond saw and carefully removed. Micro-CT scans were performed and sagittal, transverse and coronal reformatted images were produced using ImageJ (NIH, USA).The specimens were divided into 3 grades (0, 1 and 2) according to the number of epiphyses damaged by the staple prongs. Results: There were 9 (65%) segments with grade 1 staple insertions and 5 (35%) segments with grade 2 insertions. There were no grade 0 staples. Grade 2 spines had a higher stiffness level than grade 1 spines, in all axes of movement, by 28% (p=0.004). This was most noted in flexion/extension with an increase of 49% (p=0.042), followed by non-significant change in lateral bending 19% (p=0.129) and axial rotation 8% (p=0.456) stiffness. The cross sectional area of bone destruction from the prongs was only 0.4% larger in the grade 2 group compared to the grade 1 group (p=0.961). Conclusion Intervertebral staples cause epiphyseal damage. There is a difference in stiffness between grade 1 and grade 2 staple insertion segments in flexion/extension only. There is no difference in the cross section of bone destruction as a result of prong insertion and segment motion.

Lower partial moment and information entropy-based dynamic electricity purchasing strategy

In the electricity market environment, load-serving entities (LSEs) will inevitably face risks in purchasing electricity because there are a plethora of uncertainties involved. To maximize profits and minimize risks, LSEs need to develop an optimal strategy to reasonably allocate the purchased electricity amount in different electricity markets such as the spot market, bilateral contract market, and options market. Because risks originate from uncertainties, an approach is presented to address the risk evaluation problem by the combined use of the lower partial moment and information entropy (LPME). The lower partial moment is used to measure the amount and probability of the loss, whereas the information entropy is used to represent the uncertainty of the loss. Electricity purchasing is a repeated procedure; therefore, the model presented represents a dynamic strategy. Under the chance-constrained programming framework, the developed optimization model minimizes the risk of the electricity purchasing portfolio in different markets because the actual profit of the LSE concerned is not less than the specified target under a required confidence level. Then, the particle swarm optimization (PSO) algorithm is employed to solve the optimization model. Finally, a sample example is used to illustrate the basic features of the developed model and method.