scholarly journals 3D Models Reveal the Influence of Achilles Subtendon Twist on Strain and Energy Storage

2021 ◽  
Vol 9 ◽  
Author(s):  
Katherine R. Knaus ◽  
Silvia S. Blemker
Keyword(s):  
Energy Storage ◽  
Cross Sections ◽  
Anatomical Variation ◽  
Complex Function ◽  
Transversely Isotropic ◽  
3D Models ◽  
Triceps Surae ◽  
Elliptical Cross ◽  
Longitudinal Stiffness ◽  
Triceps Surae Muscles

The Achilles tendon (AT) has complex function in walking, exchanging energy due to loading by the triceps surae muscles. AT structure comprises three subtendons which exhibit variable twist among themselves and between individuals. Our goal was to create 3D finite element (FE) models to explore AT structure-function relationships. By simulating subtendon loading in FE models with different twisted geometries, we investigated how anatomical variation in twisted tendon geometry impacts fascicle lengths, strains, and energy storage. Three tendon FE models, built with elliptical cross sections based on average cadaver measurements, were divided into subtendons with varied geometric twist (low, medium, and high) and equal proportions. Tendon was modeled as transversely isotropic with fascicle directions defined using Laplacian flow simulations, producing fascicle twist. Prescribed forces, representing AT loading during walking, were applied to proximal subtendon ends, with distal ends fixed, and tuned to produce equal tendon elongation in each case, consistent with ultrasound measurements. Subtendon fascicle lengths were greater than free tendon lengths in all models by 1–3.2 mm, and were longer with greater subtendon twist with differences of 1.2–1.9 mm from low to high twist. Subtendon along-fiber strains were lower with greater twist with differences of 1.4–2.6%, and all were less than free tendon longitudinal strain by 2–5.5%. Energy stored in the AT was also lower with greater twist with differences of 1.8–2.4 J. With greater subtendon twist, similar elongation of the AT results in lower tissue strains and forces, so that longitudinal stiffness of the AT is effectively decreased, demonstrating how tendon structure influences mechanical behavior.

Numerical Analysis of Branch Mechanical Response to Loading

2019 ◽  
Vol 45 (4) ◽  
Author(s):  
Barbora Vojáčková ◽  
Jan Tippner ◽  
Petr Horáček ◽  
Luděk Praus ◽  
Václav Sebera ◽  
...  
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Mechanical Response ◽  
Mechanical Analysis ◽  
Beam Deflection ◽  
Design System ◽  
Elliptical Cross ◽  
Static Mechanical ◽  
The Difference ◽  
Tree Uprooting

Failure of a tree can be caused by a stem breakage, tree uprooting, or branch failure. While the pulling test is used for assessing the first two cases, there is no device-supported method to assess branch failure. A combination of the optical technique, pulling test, and deflection curve analysis could provide a device-supported tool for this kind of assessment. The aim of the work was to perform a structural analysis of branch response to static mechanical loading. The analyses were carried out by finite element simulations in ANSYS using beam tapered elements of elliptical cross-sections. The numerical analyses were verified by the pulling test combined with a sophisticated optical assessment of deflection evaluation. The Probabilistic Design System was used to find the parameters that influence branch mechanical response to loading considering the use of cantilever beam deflection for stability analysis. The difference in the branch’s deflection between the simulation and the experiment is 0.5% to 26%. The high variability may be explained by the variable modulus of the elasticity of branches. The finite element (FE) sensitivity analysis showed a higher significance of geometry parameters (diameter, length, tapering, elliptical cross-section) than material properties (elastic moduli). The anchorage rotation was found to be significant, implying that this parameter may affect the outcome in mechanical analysis of branch behavior. The branch anchorage can influence the deflection of the whole branch, which should be considered in stability assessment.

Stresses and Deformations of Toroidal Shells of Elliptical Cross Section: With Applications to the Problems of Bending of Curved Tubes and of the Bourdon Gage

1952 ◽  
Vol 19 (1) ◽  
pp. 37-48
Author(s):  
R. A. Clark ◽  
T. I. Gilroy ◽  
E. Reissner
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Practical Interest ◽  
Closed Shell ◽  
Open Shell ◽  
Elliptical Cross Section ◽  
Axially Symmetric ◽  
Elliptical Cross ◽  
Two Parameters ◽  
Toroidal Shells

Abstract This paper is concerned with the application of the theory of thin shells to several problems for toroidal shells with elliptical cross section. These problems are as follows: (a) Closed shell subjected to uniform normal wall pressure. (b) Open shell subjected to end bending moments. (c) Combination of the results for the first and second problems in such a way as to obtain results for the stresses and deformations in Bourdon tubes. In all three problems the distribution of stresses is axially symmetric but only in the first problem are the displacements axially symmetric. The magnitude of stresses and deformations for given loads depends in all three problems on the magnitude of the two parameters bc/ah and b/c where b and c are the semiaxes of the elliptical section, a is the distance of the center of the section from the axis of revolution, and h is the thickness of the wall of the shell. For sufficiently small values of bc/ah trigonometric series solutions are obtained. For sufficiently large values of bc/ah asymptotic solutions are obtained. Numerical results are given for various quantities of practical interest as a function of bc/ah for the values 2, 1, 1/2, 1/4 of the semiaxes ratio b/c. It is suggested that the analysis be extended to still smaller values of b/c and to cross sections other than elliptical.

Glaciological Problems Set by the Control of Dangerous Lakes in Cordillera Blanca, Peru. II. Movement of a Covered Glacier Embedded within a Rock Glacier

1977 ◽  
Vol 18 (79) ◽  
pp. 255-274 ◽  
Author(s):  
Louis Lliboutry
Keyword(s):  
Cross Sections ◽  
Rock Glacier ◽  
Measured Velocity ◽  
Elliptical Cross ◽  
Cordillera Blanca ◽  
The Holocene ◽  
Glacier Tongue ◽  
Proglacial Lake

AbstractIn front of Laguna Parón there is a huge moraine which turns through 90° in the middle of the valley and with a narrow covered glacier on the top. It has been studied by electrical exploration, and using the displacements of 43 marked boulders on the glacier. Assuming a uniform balance on the glacier tongue and semi-elliptical cross-sections, it has been possible to estimate this balance and the glacier thickness. A great amount of the measured velocity comes from the creep of the moraine itself, which seems 10 be a kind of rock glacier, probably without interstitial ire. It must have taken all the Holocene to be formed. During its complex history a proglacial lake must have formed at some time, the rupture of which explains the crooked form.

Dynamic Force Responses in Electrically Stimulated Triceps Surae Muscles: Effects of Fatigue and Temperature

1999 ◽  
Vol 23 (5) ◽  
pp. 436-439 ◽  
Author(s):  
Dietmar Rafolt ◽  
Eugen Gallasch ◽  
Winfried Mayr ◽  
Hermann Lanmuller
Keyword(s):  
Triceps Surae ◽  
Dynamic Force ◽  
Triceps Surae Muscles

Study on non-local effects in dimers of circular and elliptical cross-sections

2021 ◽  
Author(s):  
Xi Zhang ◽  
Wenyuan Wu ◽  
Yanchun Gong ◽  
Suhong He ◽  
Fangping Wu ◽  
...  
Keyword(s):  
Absorption Spectrum ◽  
Electric Field ◽  
Cross Section ◽  
Cross Sections ◽  
Field Enhancement ◽  
Radius Of Curvature ◽  
Electric Field Enhancement ◽  
Nonlocal Effects ◽  
Elliptical Cross ◽  
Non Local

Abstract The nonlocal effects of dimers consisted of two cylinders are studied, whose cross section is elliptical. Importantly, the results with dimers whose cross section is circular are compared. For comparison, the curvature of the ellipse is set the same with the circle, and four different geometries are considered. The electric field enhancement at the gap center and the absorption spectrum of the dimers are calculated. For the second geometry, either the electric field enhancement at the gap center or the absorption spectrum is approximately calculated using the first geometry, the frequencies corresponding to the peaks are totally different. Similarly, for the fourth geometry, either the electric field enhancement at the gap center or the absorption spectrum is approximately calculated using the third geometry, the disciplines of the peak values change as radius of curvature increases are totally different.

Receptor Mechanisms Underlying Heterogenic Reflexes Among the Triceps Surae Muscles of the Cat

1999 ◽  
Vol 81 (2) ◽  
pp. 467-478 ◽  
Author(s):  
T. Richard Nichols
Keyword(s):  
Triceps Surae ◽  
Spinal Reflex ◽  
Medial Gastrocnemius ◽  
Entire Group ◽  
Passive Components ◽  
Mechanical Coupling ◽  
Golgi Tendon Organs ◽  
Reflex Pathways ◽  
Tendon Organs ◽  
Triceps Surae Muscles

Receptor mechanisms underlying heterogenic reflexes among the triceps surae muscles of the cat. The soleus (S), medial gastrocnemius (MG), and lateral gastrocnemius (LG) muscles of the cat are interlinked by rapid spinal reflex pathways. In the decerebrate state, these heterogenic reflexes are either excitatory and length dependent or inhibitory and force dependent. Mechanographic analysis was used to obtain additional evidence that the muscle spindle primary ending and the Golgi tendon organ provide the major contributions to these reflexes, respectively. The tendons of the triceps surae muscles were separated and connected to independent force transducers and servo-controlled torque motors in unanesthetized, decerebrate cats. The muscles were activated as a group using crossed-extension reflexes. Electrical stimulation of the caudal cutaneous sural nerve was used to provide a particularly strong activation of MG and decouple the forces of the triceps surae muscles. During either form of activation, the muscles were stretched either individually or in various combinations to determine the strength and characteristics of autogenic and heterogenic feedback. The corresponding force responses, including both active and passive components, were measured during the changing background tension. During activation of the entire group, the excitatory, heterogenic feedback linking the three muscles was found to be strongest onto LG and weakest onto MG, in agreement with previous results concerning the strengths of heteronymous Ia excitatory postsynaptic potentials among the triceps surae muscles. The inhibition, which is known to affect only the soleus muscle, was dependent on active contractile force and was detected essentially as rapidly as length dependent excitation. The inhibition outlasted the excitation and was blocked by intravenous strychnine. These results indicate that the excitatory and inhibitory effects are dominated by feedback from primary spindle receptors and Golgi tendon organs. The interactions between these two feedback pathways potentially can influence both the mechanical coupling between ankle and knee.

Estrogen attenuates the cardiovascular and ventilatory responses to central command in cats

2002 ◽  
Vol 92 (4) ◽  
pp. 1635-1641 ◽  
Author(s):  
Shawn G. Hayes ◽  
Nicolas B. Moya Del Pino ◽  
Marc P. Kaufman
Keyword(s):  
Triceps Surae ◽  
Central Command ◽  
Neuronal Function ◽  
Ventilatory Responses ◽  
Exercise Pressor Reflex ◽  
Arterial Blood ◽  
Static Contraction ◽  
17Β Estradiol ◽  
Pressor Reflex ◽  
Triceps Surae Muscles

Static exercise is well known to increase heart rate, arterial blood pressure, and ventilation. These increases appear to be less in women than in men, a difference that has been attributed to an effect of estrogen on neuronal function. In decerebrate male cats, we examined the effect of estrogen (17β-estradiol; 0.001, 0.01, 0.1, and 1.0 μg/kg iv) on the cardiovascular and ventilatory responses to central command and the exercise pressor reflex, the two neural mechanisms responsible for evoking the autonomic and ventilatory responses to exercise. We found that 17β-estradiol, in each of the three doses tested, attenuated the pressor, cardioaccelerator, and phrenic nerve responses to electrical stimulation of the mesencephalic locomotor region (i.e., central command). In contrast, none of the doses of 17β-estradiol had any effect on the pressor, cardioaccelerator, and ventilatory responses to static contraction or stretch of the triceps surae muscles. We conclude that, in decerebrate male cats, estrogen injected intravenously attenuates cardiovascular and ventilatory responses to central command but has no effect on responses to the exercise pressor reflex.

Production of hydroxyl radicals in contracting skeletal muscle of cats

1996 ◽  
Vol 81 (3) ◽  
pp. 1197-1206 ◽  
Author(s):  
C. A. O'Neill ◽  
C. L. Stebbins ◽  
S. Bonigut ◽  
B. Halliwell ◽  
J. C. Longhurst
Keyword(s):  
Skeletal Muscle ◽  
Triceps Surae ◽  
Oxygen Species ◽  
Static Contraction ◽  
Maximal Tension ◽  
Cumulative Production ◽  
Triceps Surae Muscles ◽  
Specific Species

Reactive oxygen species increase during exhaustive contraction of skeletal muscle, but characterization of the specific species involved and their rates of production during nonexhaustive muscle contraction have not been investigated. We hypothesized that the production rate of hydroxyl radical (.OH) increases in contracting muscle and that this rate is attenuated by pretreatment with deferoxamine (Def) or dimethylthiourea (DMTU). We measured the rate of production of .OH before, during, and after 5 min of intermittent static contraction of the triceps surae muscles in cats (n = 6) using the formation of p-, m-, and o-tyrosines by hydroxylation of phenylalanine. L-Phenylalanine (30 mg/kg i.v.) was administered to each animal 3 min before contraction. Blood samples were collected from the popliteal vein 1 min before contraction; 1, 3, and 4.5 min during contraction; and 1 min after contraction. During and after contraction, the cumulative production rates of p-, m-, and o-tyrosines were elevated by 42.84 +/- 5.41, 0.25 +/- 0.04, and 0.21 +/- 0.03 nmol.min-1.g-1, respectively, compared with noncontracting triceps surae muscles. Pretreatment with Def (10 mg/kg i.v.; n = 5) or DMTU (10 mg/kg i.v.; n = 4) decreased the cumulative rates of production of p-, m-, and o-tyrosines during and after contraction. Additionally, the rate of tyrosine production increased in proportion to the percentage of maximal tension developed by the triceps surae muscles. These results directly demonstrate that .OH is produced in vivo in the skeletal muscle of cats during intermittent static contraction and that production can occur before the onset of fatigue.

Gadolinium attenuates exercise pressor reflex in cats

2001 ◽  
Vol 280 (5) ◽  
pp. H2153-H2161 ◽  
Author(s):  
Shawn G. Hayes ◽  
Marc P. Kaufman
Keyword(s):  
Pressor Response ◽  
Oxygen Demand ◽  
Muscle Afferents ◽  
Triceps Surae ◽  
Mechanical Stimuli ◽  
Group Iii ◽  
Exercise Pressor Reflex ◽  
Static Contraction ◽  
Pressor Reflex ◽  
Triceps Surae Muscles

The exercise pressor reflex, which arises from the contraction-induced stimulation of group III and IV muscle afferents, is widely believed to be evoked by metabolic stimuli signaling a mismatch between blood/oxygen demand and supply in the working muscles. Nevertheless, mechanical stimuli may also play a role in evoking the exercise pressor reflex. To determine this role, we examined the effect of gadolinium, which blocks mechanosensitive channels, on the exercise pressor reflex in both decerebrate and α-chloralose-anesthetized cats. We found that gadolinium (10 mM; 1 ml) injected into the femoral artery significantly attenuated the reflex pressor responses to static contraction of the triceps surae muscles and to stretch of the calcaneal (Achilles) tendon. In contrast, gadolinium had no effect on the reflex pressor response to femoral arterial injection of capsaicin (5 μg). In addition, gadolinium significantly attenuated the responses of group III muscle afferents, many of which are mechanically sensitive, to both static contraction and to tendon stretch. Gadolinium, however, had no effect on the responses of group IV muscle afferents, many of which are metabolically sensitive, to either static contraction or to capsaicin injection. We conclude that mechanical stimuli arising in contracting skeletal muscles contribute to the elicitation of the exercise pressor reflex.

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