Isometric Behavior Research Articles

The Anatomy and Isometry of Themedial Patellofemoral Ligament

Background Several techniques have been described for reconstruction of the medial patellofemoral ligament. However, the isometry of the medial patellofemoral ligament has not been studied. Purpose To define the anatomy and isometry of the medial patellofemoral ligament. Study Type Cadaveric study. Methods The authors dissected the medial patellofemoral ligament in 11 cadaveric knees and recorded its anatomic relationships. They evaluated the isometry of the medial patellofemoral ligament by obtaining measurements between various anatomic pairings at certain fixed angles of knee flexion. Results During knee flexion from 0° to 90°, the portion of the medial patellofemoral ligament from the inferior patellar attachment to the superior femoral attachment was nearly isometric, demonstrating an average change in length of only 1.1 mm. Statistical analysis showed the superior femoral attachment to be most significant in determining isometric behavior. Conclusions The most isometric portion of the medial patellofemoral ligament is the inferior portion of its patellar attachment extending to the superior portion of its femoral attachment, with the superior femoral attachment having the most notable influences on isometry. Clinical Relevance This study provides a detailed description of the anatomy of the medial patellofemoral ligament, as well as an evaluation of the isometric behavior of the ligament. Application of these data during reconstruction of the medial patellofemoral ligament may help to optimize patellofemoral stability.

Ligament fibre recruitment at the human ankle joint complex in passive flexion

Knowledge of ligament fibre recruitment at the human ankle joint complex is a fundamental prerequisite for analysing mobility and stability. Previous experimental and modelling studies have shown that ankle motion must be guided by fibres within the calcaneofibular and tibiocalcaneal ligaments, which remain approximately isometric during passive flexion. The purpose of this study was to identify these fibres. Three below-knee amputated specimens were analysed during passive flexion with combined radiostereometry for bone pose estimation and 3D digitisation for ligament attachment area identification. A procedure based on singular value decomposition enabled matching bone pose with digitised data and therefore reconstructing position in space of ligament attachment areas in each joint position. Eleven ordered fibres, connecting corresponding points on origin and insertion curves, were modelled for each of the following ligaments: posterior talofibular, calcaneofibular, anterior talofibular, posterior tibiotalar, tibiocalcaneal, and anterior tibiotalar. The measured changes in length for the ligament fibres revealed patterns of tightening and slackening. The most anterior fibre of the calcaneofibular and the medio-anterior fibre of the tibiocalcaneal ligament exhibited the most isometric behaviour, as well as the most posterior fibre of the anterior talofibular ligament. Fibres within the calcaneofibular ligament remain parallel in the transverse plane, while those within the tibiocalcaneal ligament become almost parallel in joint neutral position. For both these ligaments, fibres maintain their relative inclination in the sagittal plane throughout the passive flexion range. The observed significant change in both shape and orientation of the ankle ligaments suggest that this knowledge is fundamental for future mechanical analysis of their response to external forces.

Mathematical Modeling of In Vivo Isometric Force Response of Skeletal Muscle due to Duty Cycle

2353 Isometric force response of skeletal muscle is a well documented method of measuring performance. Over a sequence of isometric contractions, skeletal muscle will begin to fatigue from a failure in the excitation-contraction coupling (E-C coupling) process. It is unclear how isometric force changes with varying recovery time intervals (duty cycles) both between and during the contractions. PURPOSE: To model the in vivo isometric force response of skeletal muscle. METHODS: Testing was performed on the dorsiflexor muscles of Sprague-Dawley rats (n = 18) via needle electrodes placed across the peroneal nerve. Animals were randomly assigned to a short duty cycle group (10 sec), long duty cycle group (5 min), or medium duty cycle group (1 min). Each group performed a series of seven isometric contractions that were recorded in real-time. The force data for each contraction was discretized into ten points to model changes in real-time. Each group of ten points was designated as a set in the model. Each set was modeled with both a power law and decay curve to cover the most probable force response. To maintain a continuous equation, the power law and exponential curves were combined with an exponential weighting function, which preserved the best curve fitting properties from both the power law and exponential curves. To add set variability to the model, the coefficients which fit in the power law and exponential curve fitting methods for each contraction were fit to the sets using the polynomial curve fitting method. RESULTS: All three groups exhibited a similar pattern of isometric force drops between the contractions, but the degree and shape of these decrements was directly affected by duty cycle. The 5 min group showed moderate drops in force both between sets and within sets. The 1 min group showed similar results to the 5 min group with slightly more force decrements both between and within sets. The 10 sec group exhibited the most dramatic changes compared to the other groups. The weighting function remained constant between groups and within all contractions and was critical for maintaining an accurate model for the 10 sec group. CONCLUSION: Combinations of the power law and the exponential curve fits with the weighting function resulted in an accurate model of isometric behavior over seven isometric contractions using different duty cycles.

Computer investigation of ACL orientation during passive range of motion

No quantitative data are reported in the literature regarding the orientation of anterior cruciate ligament (ACL) fibers during passive range of motion. In this study we performed an original qualitative and quantitative analysis in eight cadaver knees, examining ACL elongation and 3D orientation. Computer elaboration of anatomical and kinematic data obtained by a six degrees-of-freedom electrogoniometer enabled a mathematical and statistical evaluation of the 3D behavior of the ACL. Our data confirmed the isometric behavior of ACL. The inclination of ACL with respect to the tibial plateau decreases with flexion from 56° to 33°. Orientation of ACL with respect to the femoral notch increases with flexion from 4° to 58°. The ACL orientation in a medio-lateral direction changes from 24° to 52°. The postero-lateral and the antero-medial bundle have different angular variations, mainly with respect to the tibial plateau and medio-lateral direction. This quantitative and qualitative information not only increases the anatomical knowledge of the ACL, but could also be important in developing or improving the surgical strategy for ACL reconstruction.

Hindlimb muscle function in relation to speed and gait: in vivo patterns of strain and activation in a hip and knee extensor of the rat (Rattus norvegicus).

Understanding how animals actually use their muscles during locomotion is an important goal in the fields of locomotor physiology and biomechanics. Active muscles in vivo can shorten, lengthen or remain isometric, and their mechanical performance depends on the relative magnitude and timing of these patterns of fascicle strain and activation. It has recently been suggested that terrestrial animals may conserve metabolic energy during locomotion by minimizing limb extensor muscle strain during stance, when the muscle is active, facilitating more economical force generation and elastic energy recovery from limb muscle-tendon units. However, whereas the ankle extensors of running turkeys and hopping wallabies have been shown to generate force with little length change (<6% strain), similar muscles in cats appear to change length more substantially while active. Because previous work has tended to focus on the mechanical behavior of ankle extensors during animal movements, the actions of more proximal limb muscles are less well understood. To explore further the hypothesis of force economy and isometric behavior of limb muscles during terrestrial locomotion, we measured patterns of electromyographic (EMG) activity and fascicle strain (using sonomicrometry) in two of the largest muscles of the rat hindlimb, the biceps femoris (a hip extensor) and vastus lateralis (a knee extensor) during walking, trotting and galloping. Our results show that the biceps and vastus exhibit largely overlapping bursts of electrical activity during the stance phase of each step cycle in all gaits. During walking and trotting, this activity typically commences shortly before the hindlimb touches the ground, but during galloping the onset of activity depends on whether the limb is trailing (first limb down) or leading (second limb down), particularly in the vastus. In the trailing limb, the timing of the onset of vastus activity is slightly earlier than that observed during walking and trotting, but in the leading limb, this activity begins much later, well after the foot makes ground contact (mean 7% of the step cycle). In both muscles, EMG activity typically ceases approximately two-thirds of the way through the stance phase. While electrically active during stance, biceps fascicles shorten, although the extent of shortening differs significantly among gaits (P<0.01). Total average fascicle shortening strain in the biceps is greater during walking (23+/-3%) and trotting (27+/-5%) than during galloping (12+/-5% and 19+/-6% in the trailing and leading limbs, respectively). In contrast, vastus fascicles typically lengthen (by 8-16%, depending on gait) over the first half of stance, when the muscle is electrically active, before shortening slightly or remaining nearly isometric over much of the second half of stance. Interestingly, in the leading limb during galloping, vastus fascicles lengthen prior to muscle activation and exhibit substantial shortening (10+/-2%) during the period when EMG activity is recorded. Thus, patterns of muscle activation and/or muscle strain differ among gaits, between muscles and even within the same muscle of contralateral hindlimbs (as during galloping). In contrast to the minimal strain predicted by the force economy hypothesis, our results suggest that proximal limb muscles in rats operate over substantial length ranges during stance over various speeds and gaits and exhibit complex and changing activation and strain regimes, exemplifying the variable mechanical roles that muscles can play, even during level, steady-speed locomotion.

In vivo muscle force-length behavior during steady-speed hopping in tammar wallabies.

Moderate to large macropodids can increase their speed while hopping with little or no increase in energy expenditure. This has been interpreted by some workers as resulting from elastic energy savings in their hindlimb tendons. For this to occur, the muscle fibers must transmit force to their tendons with little or no length change. To test whether this is the case, we made in vivo measurements of muscle fiber length change and tendon force in the lateral gastrocnemius (LG) and plantaris (PL) muscles of tammar wallabies Macropus eugenii as they hopped at different speeds on a treadmill. Muscle fiber length changes were less than +/-0.5 mm in the plantaris and +/-2.2 mm in the lateral gastrocnemius, representing less than 2 % of total fiber length in the plantaris and less than 6 % in the lateral gastrocnemius, with respect to resting length. The length changes of the plantaris fibers suggest that this occurred by means of elastic extension of attached cross-bridges. Much of the length change in the lateral gastrocnemius fibers occurred at low force early in the stance phase, with generally isometric behavior at higher forces. Fiber length changes did not vary significantly with increased hopping speed in either muscle (P>0.05), despite a 1. 6-fold increase in muscle-tendon force between speeds of 2.5 and 6.0 m s-1. Length changes of the PL fibers were only 7+/-4 % and of the LG fibers 34+/-12 % (mean +/- S.D., N=170) of the stretch calculated for their tendons, resulting in little net work by either muscle (plantaris 0.01+/-0.03 J; gastrocnemius -0.04+/-0.30 J; mean +/- s.d. ). In contrast, elastic strain energy stored in the tendons increased with increasing speed and averaged 20-fold greater than the shortening work performed by the two muscles. These results show that an increasing amount of strain energy stored within the hindlimb tendons is usefully recovered at faster steady hopping speeds, without being dissipated by increased stretch of the muscles' fibers. This finding supports the view that tendon elastic saving of energy is an important mechanism by which this species is able to hop at faster speeds with little or no increase in metabolic energy expenditure.

Almost Isometric Maps of the Hyperbolic Plane

of D, then d(Tp,Tq) = d(p,q) for all TeJi thus maps in Ji are hyperbolic isometrics. The Schwarz-Pick theorem asserts that if/:Z)->Z) is analytic then / decreases distances, . fl .t . „ d{Ap\M)^d{p,q), (1.1) or lnnnitesimally, i-W/OI 0. Following C. McMullen, we write M(c) for the set of analytic / : / ) -> / ) such that whenever B is a hyperbolic ball in D, diam (/(£)) ^ diam(5)-c, where diam denotes diameter in the hyperbolic metric. For example, n M(C) = jt, c>0 while f(z) = z eM(c) provided c is large. This paper gives three characterizations of the set M(c). The first characterization concerns nearly isometric behavior along certain geodesies, and the second is in terms of angular derivatives at boundary points. Each/eM(c) is a Blaschke product, and the third characterization is by the distribution of the zeros. We thank Curt McMullen for bringing M(c) to our attention and for the results of the next section.

Testing for isometry during reconstruction of the anterior cruciate ligament. Anatomical and biomechanical considerations.

Instrumented tibiofemoral (bone-to-bone) excursion wires were implanted in the mid-substance of the anteromedial, central, and posterior fiber-regions of the anterior cruciate ligament through limited anterior and posterior arthrotomies in eight fresh knees from cadavera. The change in the distance of linear separation between each pair of osseous fiber-insertion sites was measured and was plotted against the angle of flexion of the knee as the knee was cycled through a 120-degree range of motion. Testing conditions likely to be present during intraoperative testing for isometry were used (anterior cruciate fibers transected, quadriceps relaxed, femur stabilized with the patient in the supine position and the leg freely dependent, and motion of the knee induced in neutral rotation by force applied at the level of the foot). In no instance did the insertion-site centers of any fiber-region exhibit isometric behavior (change in the distance of linear separation of 1.0 millimeter or less). The least deviations from isometry (range, 1.4 to 3.1 millimeters) were observed for the anteromedial sites, under conditions when the gravitational dependency of the lower leg was constrained. When the leg hung in a dependent manner during passive motion, the deviation from isometry of the anteromedial sites of insertion increased significantly (range, 2.8 to 5.6 millimeters). The central sites of insertion were generally less isometric than the anteromedial sites, and the posterior sites were the least isometric, regardless of testing conditions.

Calculation of Parameters for the Age of Tendon Fibres and a Rheological Model for Their Visco-Elastic Behaviour

Tendon fibres of different-aged rats were submitted to denaturation and their isometric and isotonic behaviour was recorded. The fit of the curves led to analytical expressions depending on the parameters which characterize the age of the subject. A rheological model is given which satisfies the experimental data and which is interpretable in a molecular way.