The muscle line of action in current models of the human cervical spine: a comparison with in vivo MRI data

Cervical muscles are commonly represented by line-of-action models. This investigation evaluates the performance of three types of model implementations, based on their ability to mimic geometric in-vivo aspects of muscles. Five prominent pairs of neck muscles were reconstructed in three head positions using magnetic resonance imaging. Based on the reconstructions, muscle approximations were created that represent the muscles with piecewise straight lines. Measured and modelled muscle approximations were compared with respect to their pulling directions at the attachment sites and the overall distance between the muscle paths. Muscle lengths were evaluated in two ways. First, length discrepancies were determined between measured and modelled muscles depending on the head position. Second, the difference of muscle lengths in neutral and deflected head positions for measurement and models were calculated. The results indicate considerable differences between models and measurements. Pulling directions, for instance, differed by up to 40°, depending on the chosen muscle and the type of muscle implementation.     

Muscle and sarcomere lengths in the hind limb of the rabbit (Oryctolagus cuniculus) during a galloping stride

Rabbits were filmed galloping, and the length changes of the principal hind limb muscles were determined. Sarcomere lengths were measured in carcasses set by rigor mortis in four of the positions adopted during a stride. These sarcomere lengths were measured by means of a diffraction technique, devised for the purpose, using an ordinary microscope. Expected sarcomere lengths for three of the positions were predicted from that observed in the fourth, together with muscle length changes. A theoretical length-tension curve for rabbit muscle was constructed, using A and I filament lengths, it was shown that when the muscles were active, their sarcomere lengths corresponded to the plateau of the length-tension curve.     

Comparison between line and surface mesh models to represent the rotator cuff muscle geometry in musculoskeletal models

Accurate muscle geometry (muscle length and moment arm) is required to estimate muscle function when using musculoskeletal modelling. In shoulder, muscles are often modelled as a collection of independent line segments, leading to non-physiological muscles trajectory, especially for the rotator cuff muscles. To prevent this, a surface mesh model was developed and validated against 7 MRI positions in one participant. Mean moment arm errors was 11.4% for the line vs. 8.8% for the mesh model. While the model with independent lines led to some non-physiological trajectories, the mesh model gave lower misestimations of muscle lengths and moment arms.     

Active force-length relationship of human lower-leg muscles estimated from morphological data: a comparison of geometric muscle models

Muscle fibre lengths, pennation angles, and sarcomere lengths were measured (the latter by a diffraction technique) for each of the muscles of three embalmed lower-leg specimens. From these data and filament lengths from Walker & Schrodt (1973), the optimum fibre lengths were determined. Relationships between length and active force (at full activation) of the lower-leg muscles were calculated by use of (i) a unipennate muscle model, (ii) a bipennate model, and (iii) bipennate models in which the cosine of the pennation angle is approximated as length independent. It is concluded that the first two models are equally useful and that the use of the last models is discouraged in case of strongly pennated muscles. Non-uniformity of fibre parameters within one muscle appears to have little effect on the force-length relationship.     

Electromyography of superficial and deep neck muscles during isometric, voluntary, and reflex contractions

Increasingly complex models of the neck neuromusculature need detailed muscle and kinematic data for proper validation. The goal of this study was to measure the electromyographic activity of superficial and deep neck muscles during tasks involving isometric, voluntary, and reflexively evoked contractions of the neck muscles. Three male subjects (28-41 years) had electromyographic (EMG) fine wires inserted into the left sternocleidomastoid, levator scapulae, trapezius, splenius capitis, semispinalis capitis, semispinalis cervicis, and multifidus muscles. Surface electrodes were placed over the left sternohyoid muscle. Subjects then performed: (i) maximal voluntary contractions (MVCs) in the eight directions (45 deg intervals) from the neutral posture; (ii) 50 N isometric contractions with a slow sweep of the force direction through 720 deg; (iii) voluntary oscillatory head movements in flexion and extension; and (iv) initially relaxed reflex muscle activations to a forward acceleration while seated on a sled. Isometric contractions were performed against an overhead load cell and movement dynamics were measured using six-axis accelerometry on the head and torso. In all three subjects, the two anterior neck muscles had similar preferred activation directions and acted synergistically in both dynamic tasks. With the exception of splenius capitis, the posterior and posterolateral neck muscles also showed consistent activation directions and acted synergistically during the voluntary motions, but not during the sled perturbations. These findings suggest that the common numerical-modeling assumption that all anterior muscles act synergistically as flexors is reasonable, but that the related assumption that all posterior muscles act synergistically as extensors is not. Despite the small number of subjects, the data presented here can be used to inform and validate a neck model at three levels of increasing neuromuscular-kinematic complexity: muscles generating forces with no movement, muscles generating forces and causing movement, and muscles generating forces in response to induced movement. These increasingly complex data sets will allow researchers to incrementally tune their neck models' muscle geometry, physiology, and feedforward/feedback neuromechanics.     

Contributions of the individual muscles of the shoulder to glenohumeral joint stability during abduction

The aim of this study was to determine the relative contributions of the deltoid and rotator cuff muscles to glenohumeral joint stability during arm abduction. A three-dimensional model of the upper limb was used to calculate the muscle and joint-contact forces at the shoulder for abduction in the scapular plane. The joints of the shoulder girdle-sternoclavicular joint, acromioclavicular joint, and glenohumeral joint-were each represented as an ideal three degree-of-freedom ball-and-socket joint. The articulation between the scapula and thorax was modeled using two kinematic constraints. Eighteen muscle bundles were used to represent the lines of action of 11 muscle groups spanning the glenohumeral joint. The three-dimensional positions of the clavicle, scapula, and humerus during abduction were measured using intracortical bone pins implanted into one subject. The measured bone positions were inputted into the model, and an optimization problem was solved to calculate the forces developed by the shoulder muscles for abduction in the scapular plane. The model calculations showed that the rotator cuff muscles (specifically, supraspinatus, subscapularis, and infraspinatus) by virtue of their lines of action are perfectly positioned to apply compressive load across the glenohumeral joint, and that these muscles contribute most significantly to shoulder joint stability during abduction. The middle deltoid provides most of the compressive force acting between the humeral head and the glenoid, but this muscle also creates most of the shear, and so its contribution to joint stability is less than that of any of the rotator cuff muscles.     

Refined structure of bony fish muscle myosin filaments from low-angle X-ray diffraction data

Application of X-ray diffraction methods to the elucidation of the arrangement of the myosin heads on myosin filaments in resting muscles is made simpler when the muscles themselves are well ordered in 3D. Bony fish muscle for the vertebrates and insect flight muscle for the invertebrates are the muscles of choice for this analysis. The rich, well-sampled, low-angle X-ray diffraction pattern from bony fish muscle has previously been modelled with an R-factor of 3.4% between observed and calculated transforms on the assumption that the two heads in one myosin molecule have the same shape. However, recent evidence from other kinds of analysis of other muscles has shown that this assumption may not be valid. There is evidence that the motor domain of one head in each pair may interact with the neck region of the second head. This possibility has been tested directly in the present analysis which extends the X-ray modelling of fish muscle myosin filaments by permitting independent shape changes of the two heads in one molecule. The new model, with a computed R-factor of 1.19% against 56 independent reflections, shows that in fish muscle also there is a marked asymmetry in the organisation of each head pair.     

Fibre operating lengths of human lower limb muscles during walking

Muscles actuate movement by generating forces. The forces generated by muscles are highly dependent on their fibre lengths, yet it is difficult to measure the lengths over which muscle fibres operate during movement. We combined experimental measurements of joint angles and muscle activation patterns during walking with a musculoskeletal model that captures the relationships between muscle fibre lengths, joint angles and muscle activations for muscles of the lower limb. We used this musculoskeletal model to produce a simulation of muscle-tendon dynamics during walking and calculated fibre operating lengths (i.e. the length of muscle fibres relative to their optimal fibre length) for 17 lower limb muscles. Our results indicate that when musculotendon compliance is low, the muscle fibre operating length is determined predominantly by the joint angles and muscle moment arms. If musculotendon compliance is high, muscle fibre operating length is more dependent on activation level and force-length-velocity effects. We found that muscles operate on multiple limbs of the force-length curve (i.e. ascending, plateau and descending limbs) during the gait cycle, but are active within a smaller portion of their total operating range.     

Error propagation from kinematic data to modeled muscle-tendon lengths during walking

Kinematic data from 3D gait analysis together with musculoskeletal modeling techniques allow the derivation of muscle-tendon lengths during walking. However, kinematic data are subject to soft tissue artifacts (STA), referring to skin marker displacements during movement. STA are known to significantly affect the computation of joint kinematics, and would therefore also have an effect on muscle-tendon lengths which are derived from the segmental positions. The present study aimed to introduce an analytical approach to calculate the error propagation from STA to modeled muscle-tendon lengths. Skin marker coordinates were assigned uncorrelated, isotropic error functions with given standard deviations accounting for STA. Two different musculoskeletal models were specified; one with the joints moving freely in all directions, and one with the joints constrained to rotation but no translation. Using reference kinematic data from two healthy boys (mean age 9 y 5 m), the propagation of STA to muscle-tendon lengths was quantified for semimembranosus, gastrocnemius and soleus. The resulting average SD ranged from 6% to 50% of the normalized muscle-tendon lengths during gait depending on the muscle, the STA magnitudes and the musculoskeletal model. These results highlight the potential impact STA has on the biomechanical analysis of modeled muscle-tendon lengths during walking, and suggest the need for caution in the clinical interpretation of muscle-tendon lengths derived from joint kinematics.     

Influence of bicycle seat tube angle and hand position on lower extremity kinematics and neuromuscular control: implications for triathlon running performance

We investigated how varying seat tube angle (STA) and hand position affect muscle kinematics and activation patterns during cycling in order to better understand how triathlon-specific bike geometries might mitigate the biomechanical challenges associated with the bike-to-run transition. Whole body motion and lower extremity muscle activities were recorded from 14 triathletes during a series of cycling and treadmill running trials. A total of nine cycling trials were conducted in three hand positions (aero, drops, hoods) and at three STAs (73°, 76°, 79°). Participants also ran on a treadmill at 80, 90, and 100% of their 10-km triathlon race pace. Compared with cycling, running necessitated significantly longer peak musculotendon lengths from the uniarticular hip flexors, knee extensors, ankle plantar flexors and the biarticular hamstrings, rectus femoris, and gastrocnemius muscles. Running also involved significantly longer periods of active muscle lengthening from the quadriceps and ankle plantar flexors. During cycling, increasing the STA alone had no affect on muscle kinematics but did induce significantly greater rectus femoris activity during the upstroke of the crank cycle. Increasing hip extension by varying the hand position induced an increase in hamstring muscle activity, and moved the operating lengths of the uniarticular hip flexor and extensor muscles slightly closer to those seen during running. These combined changes in muscle kinematics and coordination could potentially contribute to the improved running performances that have been previously observed immediately after cycling on a triathlon-specific bicycle.     

Properties and function of extensible ligaments in the necks of turkeys (Meleagris gallopavo) and other birds

Highly extensible ligaments connect the neural spines of successive vertebrae in the proximal part of the neck in birds. Their elastic properties, and their lengths in different neck positions, have been investigated in experiments on turkeys. Their properties are very similar to those of the ligamentum nuchae of artiodactyls. They are stretched to large strains when the head is lowered but do not develop sufficient force to support the extended head and neck without the aid of muscles.     

In vivo measurements of moment arm lengths of three elbow flexors at rest and during isometric contractions

The purpose of this study was to determine in vivo moment arm lengths (MAs) of three elbow flexors at rest and during low- and relatively high-intensity contractions, and to examine the contraction intensity dependence of MAs at different joint positions. At 50°, 80° and 110° of elbow flexion, MAs of the biceps brachii, brachialis and brachioradialis were measured in 10 young men using sagittal images of the right arm obtained by magnetic resonance imaging, at rest and during 20% and 60% of isometric maximal voluntary elbow flexion. In most conditions, MAs increased with isometric contractions, which is presumably due to the contraction-induced thickening of the muscles. This phenomenon was especially evident in the flexed elbow positions. The influence of the contraction intensities on the increases in MAs varied across the muscles. These results suggest that in vivo measurements of each elbow flexor MA during contractions are essential to properly examine the effects on the interrelationships between elbow flexion torque and individual muscle forces.     

Dependence of jumping performance on muscle properties when humans use only calf muscles for propulsion

Using optimal control techniques, maximum height jumps were simulated for humans who held their body rigid except for the ankle. Three dynamic models of ankle torque generation based on known calf muscle properties were used. Force and kinematics obtained from the simulations using nominal and perturbed parameters were compared with data obtained from humans who had performed this type of jump. One torque model incorporated the series elastic, force-length and force-velocity properties of muscle. Our results suggest that higher jumps would be achieved by those who have the most compliant and fastest contracting muscles. It was also found that height attained depended much more on the ability of muscles to generate isometric force at long lengths than at short lengths. Studies of forward and strictly vertical jumps using similar computer methods suggest that for any maximal jump the optimal strategy is first to achieve a unique state (position, velocity and acceleration) with the feet flat on the ground, and then to maximally activate one's calf muscles until lift-off.     

Sarcomere length organization as a design for cooperative function amongst all lumbar spine muscles

The functional design of spine muscles in part dictates their role in moving, loading, and stabilizing the lumbar spine. There have been numerous studies that have examined the isolated properties of these individual muscles. Understanding how these muscles interact and work together, necessary for the prediction of muscle function, spine loading, and stability, is lacking. The objective of this study was to measure sarcomere lengths of lumbar muscles in a neutral cadaveric position and predict the sarcomere operating ranges of these muscles throughout full ranges of spine movements. Sarcomere lengths of seven lumbar muscles in each of seven cadaveric donors were measured using laser diffraction. Using published anatomical coordinate data, superior muscle attachment sites were rotated about each intervertebral joint and the total change in muscle length was used to predict sarcomere length operating ranges. The extensor muscles had short sarcomere lengths in a neutral spine posture and there were no statistically significant differences between extensor muscles. The quadratus lumborum was the only muscle with sarcomere lengths that were optimal for force production in a neutral spine position, and the psoas muscles had the longest lengths in this position. During modeled flexion the extensor, quadratus lumborum, and intertransversarii muscles lengthened so that all muscles operated in the approximate same location on the descending limb of the force-length relationship. The intrinsic properties of lumbar muscles are designed to complement each other. The extensor muscles are all designed to produce maximum force in a mid-flexed posture, and all muscles are designed to operate at similar locations of the force-length relationship at full spine flexion.     

Three-dimensional temporomandibular joint muscle attachment morphometry and its impacts on musculoskeletal modeling

In musculoskeletal models of the human temporomandibular joint (TMJ), muscles are typically represented by force vectors that connect approximate muscle origin and insertion centroids (centroid-to-centroid force vectors). This simplification assumes equivalent moment arms and muscle lengths for all fibers within a muscle even with complex geometry and may result in inaccurate estimations of muscle force and joint loading. The objectives of this study were to quantify the three-dimensional (3D) human TMJ muscle attachment morphometry and examine its impact on TMJ mechanics. 3D muscle attachment surfaces of temporalis, masseter, lateral pterygoid, and medial pterygoid muscles of human cadaveric heads were generated by co-registering measured attachment boundaries with underlying skull models created from cone-beam computerized tomography (CBCT) images. A bounding box technique was used to quantify 3D muscle attachment size, shape, location, and orientation. Musculoskeletal models of the mandible were then developed and validated to assess the impact of 3D muscle attachment morphometry on joint loading during jaw maximal open-close. The 3D morphometry revealed that muscle lengths and moment arms of temporalis and masseter muscles varied substantially among muscle fibers. The values calculated from the centroid-to-centroid model were significantly different from those calculated using the ‘Distributed model’, which considered crucial 3D muscle attachment morphometry. Consequently, joint loading was underestimated by more than 50% in the centroid-to-centroid model. Therefore, it is necessary to consider 3D muscle attachment morphometry, especially for muscles with broad attachments, in TMJ musculoskeletal models to precisely quantify the joint mechanical environment critical for understanding TMJ function and mechanobiology.     

Measuring muscle and joint geometry parameters of a shoulder for modeling purposes.

An extensive set of muscle and joint geometry parameters was measured of the right shoulder of an embalmed male. For all muscles the optimal muscle fiber length was determined by laser diffraction measurements of sarcomere length. In addition, tendon length and physiological cross-sectional area were determined. The parameter set was needed to enhance the reliability of a computer model of the shoulder (Van der Helm, 1994a,b Journal of Biomechanics 27, 527-550, 551-569). With the model, an abduction of the arm was simulated in seven positions, at 30 degrees intervals. In each of the simulated arm positions, actual sarcomere lengths were calculated from the lengths of 104 muscle elements, distributed over 16 shoulder muscles. For most muscle elements, the simulated abduction appeared to take place within the sarcomere length range in which the muscle elements can exert force. The muscle elements can then act on the ascending limb as well as on the plateau and on the descending limb of the relative force-length curves of sarcomeres. The produced data set is not only important for the refinement of shoulder modeling, but also for functional analyses of shoulder movements in general.     

Ecological and phylogenetic variability in the spinalis muscle of snakes

Understanding the origin and maintenance of functionally important subordinate traits is a major goal of evolutionary physiologists and ecomorphologists. Within the confines of a limbless body plan, snakes are diverse in terms of body size and ecology, but we know little about the functional traits that underlie this diversity. We used a phylogenetically diverse group of 131 snake species to examine associations between habitat use, sidewinding locomotion and constriction behaviour with the number of body vertebrae spanned by a single segment of the spinalis muscle, with total numbers of body vertebrae used as a covariate in statistical analyses. We compared models with combinations of these predictors to determine which best fit the data among all species and for the advanced snakes only (N = 114). We used both ordinary least‐squares models and phylogenetic models in which the residuals were modelled as evolving by the Ornstein–Uhlenbeck process. Snakes with greater numbers of vertebrae tended to have spinalis muscles that spanned more vertebrae. Habitat effects dominated models for analyses of all species and advanced snakes only, with the spinalis length spanning more vertebrae in arboreal species and fewer vertebrae in aquatic and burrowing species. Sidewinding specialists had shorter muscle lengths than nonspecialists. The relationship between prey constriction and spinalis length was less clear. Differences among clades were also strong when considering all species, but not for advanced snakes alone. Overall, these results suggest that muscle morphology may have played a key role in the adaptive radiation of snakes.     

Architecture of the human gastrocnemius muscle and some functional consequences

Measurements were performed on the m. gastrocnemius of eight human cadavers in order to describe, in some detail, the architecture of the muscle and its heads. The fibres of the lateral head contain more sarcomeres than those of the medial head. The effect of this difference on the length-force curve of the muscle, calculated with a planimetric muscle model, is diminished by the effect of the difference of fibre angle with respect to the line of pull of the muscle. Within the heads some variation of the number of sarcomeres of the proximal and distal fibres occurs in all muscles. In the lateral head the distal fibres contain fewer sarcomeres than the proximal fibres. In the medial head this is also found in some heads, while others show the reverse. In the lateral head the longer fibres have smaller angles of attachment to the tendon plate and vice versa, while in the medial heads this relationship is only found occasionally. Some variation in the number of sarcomeres is found in the fibres of one bundle. The effects of variations in the number of sarcomeres on the length-force curve are probably insignificant at greater muscle lengths, but may have some importance for the individual with relatively small muscle lengths.     

Musculo-skeletal modelling of NMES-evoked knee extension in spinal cord injury

The objective of this study was to explore relationships among constants used in musculo-skeletal models predicting torque generated about the knee by the quadriceps muscles. A model was developed and matched to data collected from individuals with spinal cord injury performing quadriceps contractions evoked using neuromuscular electrical stimulation. After fitting tendon slack lengths to the quadriceps muscles, the model was able to accurately match experimentally measured knee extension torques using previously reported values for the moment arm-knee angle and force-velocity relationships. Fitting new constants to these relationships did not improve the match between measured and modelled knee extension torques. There was significant interaction between variables used within the model. Using a narrower active force-length relationship for the muscles required the model to have smaller moment arms about the knee to accurately match measured torque across the full range of motion. Reduced moment arms, however, lowered the model's linear velocity of muscle shortening for each angular velocity of the knee, requiring different constants within the force-velocity relationship to predict the appropriate amount of torque decline. The present study demonstrates that, when a model does not fit the observed data, it is difficult to determine exactly which components are responsible because of the interdependent nature of parameters.     

Maximum isometric arm forces in the horizontal plane

In this paper, we measured the maximum isometric force at the hand in eight directions in the horizontal plane and at five positions in the workplace. These endpoint forces were the result of shoulder horizontal adduction/abduction and elbow flexion/extension torques. We found that the normalized maximum forces of all the six subjects deviated less than 15%, despite intra-subject differences in muscle strength of more than a factor of two. The maximum forces were found to systematically depend on the force direction and on the hand position in the workspace. The largest forces were found in a direction approximately along the line connecting shoulder joint and hand, and the smallest forces perpendicular to that line, thereby forming an elliptically shaped pattern. The elongation of the pattern was the largest for those hand positions having the more extended elbow joint. By using a lumped six-muscle model, with two mono-articular muscle pairs and one bi-articular pair, we were able to predict the observed force patterns. Here, we assumed that one of the muscles generates its maximum force and the others adjust their output to point the endpoint force in the required direction. We used a principal component analysis of the surface EMGs of simultaneously measured representatives of four of the six muscles. With the same model, we were then able to determine the principal directions of all the six muscle groups.