A model for steady isometric muscle activation

The present model of the motoneuronal (MN) pool – muscle complex (MNPMC) is deterministic and designed for steady isometric muscle activation. Time-dependent quantities are treated as time-averages. The character of the model is continuous in the sense that the motor unit (MU) population is described by a continuous density function. In contrast to most already published models, the wiring (synaptic weight) between the input fibers to the MNPMC and the MNs (about which no detailed data are known) is deduced, whereas the input–force relation is given. As suggested by experimental data, this relation is assumed to be linear during MU recruitment, but the model allows other, nonlinear relations. The input to the MN pool is defined as the number of action potentials per second in all input fibers, and the excitatory postsynaptic potential (EPSP) conductance in MNs evoked by the input is assumed to be proportional to the input. A single compartment model with a homogeneous membrane is used for a MN. The MNs start firing after passing a constant voltage threshold. The synaptic current–frequency relation is described by a linear function and the frequency–force transformation of a MU by an exponential function. The sum of the MU contraction forces is the muscle force, and the activation of the MUs obeys the size principle. The model parameters were determined a priori, i.e., the model was not used for their estimation. The analysis of the model reveals special features of the activation curve which we define as the relation between the input normalized by the threshold input of the MN pool and the force normalized by the maximal muscle force. This curve for any muscle turned out to be completely determined by the activation factor, the slope of the linear part of the activation curve (during MU recruitment). This factor determines quantitatively the relation between MU recruitment and rate modulation. This property of the model (the only known model with this property) allows a quantification of the recruitment gain (Kernell and Hultborn 1990). The interest of the activation factor is illustrated using two human muscles, namely the first dorsal interosseus muscle, a small muscle with a relatively small force at the end of recruitment, and the medial gastrocnemius muscle, a strong muscle with a relatively large force at the end of recruitment. It is concluded that the present model allows us to reproduce the main features of muscle activation in the steady state. Its analytical character facilitates a deeper understanding of these features. Received: 24 November 1997 / Accepted in revised form: 30 November 1998     

Application and validation of a three-dimensional mathematical model of the human masticatory system in vivo.

A previously described three-dimensional mathematical model of the human masticatory system, predicting maximum possible bite forces in all directions and the recruitment patterns of the masticatory muscles necessary to generate these forces, was validated in in vivo experiments. The morphological input parameters to the model for individual subjects were collected using MRI scanning of the jaw system. Experimental measurements included recording of maximum voluntary bite force (magnitude and direction) and surface EMG from the temporalis and masseter muscles. For bite forces with an angle of 0, 10 and 20 degrees relative to the normal to the occlusal plane the predicted maximum possible bite forces were between 0.9 and 1.2 times the measured ones and the average ratio of measured to predicted maximum bite force was close to unity. The average measured and predicted muscle recruitment patterns showed no striking differences. Nevertheless, some systematic differences, dependent on the bite force direction, were found between the predicted and the measured maximum possible bite forces. In a second series of simulations the influence of the direction of the joint reaction forces on these errors was studied. The results suggest that they were caused primarily by an improper determination of the joint force directions.     

Model sensitivity and use of the comparative finite element method in mammalian jaw mechanics: mandible performance in the gray wolf

Finite Element Analysis (FEA) is a powerful tool gaining use in studies of biological form and function. This method is particularly conducive to studies of extinct and fossilized organisms, as models can be assigned properties that approximate living tissues. In disciplines where model validation is difficult or impossible, the choice of model parameters and their effects on the results become increasingly important, especially in comparing outputs to infer function. To evaluate the extent to which performance measures are affected by initial model input, we tested the sensitivity of bite force, strain energy, and stress to changes in seven parameters that are required in testing craniodental function with FEA. Simulations were performed on FE models of a Gray Wolf (Canis lupus) mandible. Results showed that unilateral bite force outputs are least affected by the relative ratios of the balancing and working muscles, but only ratios above 0.5 provided balancing-working side joint reaction force relationships that are consistent with experimental data. The constraints modeled at the bite point had the greatest effect on bite force output, but the most appropriate constraint may depend on the study question. Strain energy is least affected by variation in bite point constraint, but larger variations in strain energy values are observed in models with different number of tetrahedral elements, masticatory muscle ratios and muscle subgroups present, and number of material properties. These findings indicate that performance measures are differentially affected by variation in initial model parameters. In the absence of validated input values, FE models can nevertheless provide robust comparisons if these parameters are standardized within a given study to minimize variation that arise during the model-building process. Sensitivity tests incorporated into the study design not only aid in the interpretation of simulation results, but can also provide additional insights on form and function.     

Predicted pattern of human muscle activity during clenching derived from a computer assisted model: symmetric vertical bite forces

A computer assisted three-dimensional model of the jaw, based on linear programming, is presented. The upper and lower attachments of the muscles of mastication have been measured on a single human skull and divided into thirteen independent units on each side--a total of 26 muscle elements. The direction (in three dimensions) and maximum forces that could be developed by each muscle element, the bite reaction and two joint reactions are included in the model. It is shown for symmetrical biting that a model which minimizes the sum of the muscle forces used to produce a given bite force activates muscles in a way which corresponds well with previous observations on human subjects. A model which minimizes the joint reactions behaves differently and is rejected. An analysis of the way the chosen model operates suggests that there are two types of jaw muscles, power muscles and control muscles. Power muscles (superficial masseter, medial pterygoid and some of temporalis) produce the bite force but tend to displace the condyle up or down the articular eminence. This displacement is prevented by control muscles (oblique temporalis and lateral pterygoid) which have very poor moment arms for generating usual bite forces, but are efficient for preventing condylar slide. The model incorporates the concept that muscles consist of elements which can contract independently. It predicts that those muscle elements with longer moment arms relative to the joint are the first to be activated and, as the bite force increases, a ripple of activity spreads into elements with shorter moment arms. In general, the model can be used to study the three-dimensional activity in any system of joints and muscles.     

From single muscle fiber to whole muscle mechanics: a finite element model of a muscle bundle with fast and slow fibers

Muscles exhibit highly complex, multi-scale architecture with thousands of muscle fibers, each with different properties, interacting with each other and surrounding connective structures. Consequently, the results of single-fiber experiments are scarcely linked to the macroscopic or whole muscle behavior. This is especially true for human muscles where it would be important to understand of how skeletal muscles disorders affect patients’ life. In this work, we developed a mathematical model to study how fast and slow muscle fibers, well characterized in single-fiber experiments, work and generate together force and displacement in muscle bundles. We characterized the parameters of a Hill-type model, using experimental data on fast and slow single human muscle fibers, and comparing experimental data with numerical simulations obtained from finite element (FE) models of single fibers. Then, we developed a FE model of a bundle of 19 fibers, based on an immunohistochemically stained cross section of human diaphragm and including the corresponding properties of each slow or fast fiber. Simulations of isotonic contractions of the bundle model allowed the generation of its apparent force–velocity relationship. Although close to the average of the force–velocity curves of fast and slow fibers, the bundle curve deviates substantially toward the fast fibers at low loads. We believe that the present model and the characterization of the force–velocity curve of a fiber bundle represents the starting point to link the single-fiber properties to those of whole muscle with FE application in phenomenological models of human muscles.     

A new model for calculating muscle forces from electromyograms

A muscle model is described that uses electromyogram (EMG), muscle length and speed of contraction to predict muscle force. Physiological parameters are the Hill constants and the shape of the twitch response to a single stimulus. The model was incorporated in a jaw model of the rabbit and tested by predicting the bite force produced by the jaw muscles during mastication. The time course of the calculated force appeared to match the bite force, measured in vivo by a strain gauge, applied to the bone below the teeth. The variation in peak strain amplitude from cycle to cycle correlated with the variation predicted by the model. The peak amplitude of the integrated EMGs of individual jaw muscles showed an average correlation with peak strain of 0.41. Use of the sum of the available peak amplitudes, weighted according to their effect upon the bite force increased the correlation to 0.46; the model predicted bite forces showed a correlation of 0.57 with the strain. The increase in correlation was statistically significant. The muscle forces were calculated using a minimum number of easily obtainable constants.     

Functional links between canine height and jaw gape in catarrhines with special reference to early hominins

This study tests the hypothesis that decreased canine crown height in catarrhines is linked to (and arguably caused by) decreased jaw gape. Associations are characterized within and between variables such as upper and lower canine height beyond the occlusal plane (canine overlap), maximum jaw gape, and jaw length for 27 adult catarrhine species, including 539 living subjects and 316 museum specimens. The data demonstrate that most adult male catarrhines have relatively larger canine overlap dimensions and gapes than do conspecific females. For example, whereas male baboons open their jaws maximally more than 110% of jaw length, females open about 90%. Humans and hylobatids are the exceptions in that canine overlap is nearly the same in both the sexes and so is relative gape (ca. 65% for humans and 110% for hylobatids). A correlation analysis demonstrates that a large portion of relative gape (maximum gape/projected jaw length) is predicted by relative canine overlap (canine overlap/jaw length). Relative gape is mainly a function of jaw muscle position and/or jaw muscle‐fiber length. All things equal, more rostrally positioned jaw muscles and/or shorter muscle fibers decrease gape and increase bite force during the power stroke of mastication, and the net benefit is to increase the mechanical efficiency during chewing. Similarly, more caudally positioned muscles and/or longer muscle fibers increase the amount of gape and decrease bite force. Overall, the data support the hypothesis that canine reduction in early hominins is functionally linked to decreased gape and increased mechanical efficiency of the jaws. Am J Phys Anthropol, 2013. © 2012 Wiley Periodicals, Inc.     

Force generation performance and motor unit recruitment strategy in muscles of contralateral limbs.

The purpose of the present study was to determine whether the motor unit (MU) recruitment strategy of the agonist and antagonist muscles in the dominant arm differs from that in the non-dominant arm. The median frequency (MF) of the power density spectrum (PDS) of the electromyogram (EMG) was used as a tracking parameter to describe the MU recruitment. In 8 subjects the EMG was recorded from the biceps brachii and triceps brachii of each limb during isometric elbow flexion performed in a ramp fashion. Force was increased from 0 to 100% of the maximum voluntary contraction (MVC) in 3 s following a track displayed on an oscilloscope. When comparing the dominant versus non-dominant arm we found no statistical difference in the MU recruitment pattern of the biceps brachii and the triceps. Because the dominant arm was not always the better performing arm, we grouped the data according to the ability of the subjects to track the ramp signal. In this case we found a statistically significant difference between the better and worse performing arm in the full MU recruitment of the biceps. A more precise and accurate control of the increase in force was obtained when the central nervous system selected a slower and prolonged recruitment of MUs in the agonist muscle.     

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.     

Coactivation of jaw muscles: recruitment order and level as a function of bite force direction and magnitude

The aim of this study was to obtain insight into the coactivation behaviour of the jaw muscles under various a priori defined static loading conditions of the mandible. As the masticatory system is mechanically redundant, an infinite number of recruitment patterns is theoretically possible to produce a certain bite force. Using a three-component force transducer and a feedback method, subjects could be instructed to produce a bite force of specific direction and magnitude under simultaneous registration of the EMG activity of anterior and posterior temporal, masseter and digastric muscles on each side. Forces were measured at the second premolars. Vertical, anterior, posterior, lateral and medial force directions were examined; in each direction force levels between 50 N and maximal voluntary force were produced. The results show that for all muscles the bite force-EMG relationship obeys a straight-line fit for forces exceeding 50 N. The relationship varies with bite force direction, except in the case of the digastric muscles. Variation is small for the anterior temporal and large for the posterior temporal and masseter muscles. The relative activation of muscles for a particular force in a particular direction in unique, despite the redundancy.     

The image of motor units architecture in the mechanomyographic signal during the single motor unit contraction: in vivo and simulation study

The mechanomyographic (MMG) signal analysis has been performed during single motor unit (MU) contractions of the rat medial gastrocnemius muscle. The MMG has been recorded as a muscle surface displacement by using a laser distance sensor. The profiles of the MMG signal let to categorize these signals for particular MUs into three classes. Class MMG-P (positive) comprises MUs with the MMG signal similar to the force signal profile, where the distance between the muscle surface and the laser sensor increases with the force increase. The class MMG-N (negative) has also the MMG profile similar to the force profile, however the MMG is inverted in comparison to the force signal and the distance measured by using laser sensor decreases with the force increase. The third class MMG-M (mixed) characterize the MMG which initially increases with the force increases and when the force exceeds some level it starts to decrease towards the negative values. The semi-pennate muscle model has been proposed, enabling estimation of the MMG generated by a single MU depending on its localization. The analysis have shown that in the semi-pennate muscle the localization of the MU and the relative position of the laser distance sensor determine the MMG profile and amplitude. Thus, proposed classification of the MMG recordings is not related to the physiological types of MUs, but only to the MU localization and mentioned sensor position. When the distance sensor is located over the middle of the muscle belly, a part of the muscle fibers have endings near the location of the sensor beam. For the MU MMG of class MMG-N the deflection of the muscle surface proximal to the sensor mainly influences the MMG recording, whereas for the MU MMG class MMG-P, it is mainly the distal muscle surface deformation. For the MU MMG of MMG-M type the effects of deformation within the proximal and distal muscle surfaces overlap. The model has been verified with experimental recordings, and its responses are consistent and adequate in comparison to the experimental data.     

Biomechanics of a muscular hydrostat: a model of lapping by a reptilian tongue

We have developed a quantitative model of an example of a muscular hydrostat, a reptilian tongue, and have used this model to study a functional movement, protrusion and retrusion, a form of lapping. The model tongue consists of a longitudinal muscle that shortens the tongue when it contracts, and a circumferential muscle wrapped around the longitudinal muscle that lengthens the tongue when it contracts. The anatomy of the model tongue and the pattern of activation of its muscles are based on studies of the tongue of the lizard Tupinambis nigropunctatus (Smith 1984). The mechanics of pressure vessels were used to derive a relationship between the forces in the two muscles. Muscle force production was modelled as the product of length/tension properties, force/velocity properties, and activation due to neural inputs (incorporating both recruitment and firing period). Passive forces were modeled as a force in parallel with the longitudinal muscle. Muscle activation dynamics were modeled as a first order low pass filter. When the model tongue is short, the two muscles can lengthen or shorten it with comparable forces, but as it lengthens, the force that the circumferential muscle can exert drops precipitously. When the tongue is long, it can neither be very stiff, nor can it generate much force. The model also reproduces the kinematics of lapping movements actually observed in Tupinambis.     

Finite element simulations of a hip joint with femoroacetabular impingement

In this study, a three-dimensional finite element (FE) model based on the specific anatomy of a patient presenting a femoroacetabular impingement of the ‘cam’-type is developed. The FE meshes of the structures of interest are obtained from arthrographic magnetic resonance images. All soft tissues are considered linear elastic and isotropic, and the bones were assumed rigid. A compression of the femur on the acetabular cavity as well as flexural movements and internal rotations are applied. Stresses and contact pressures are evaluated in this patient-specific model in order to better interpret the mechanism of aggression of the femoral and acetabular cartilages. The corresponding results are presented and discussed. The values obtained for the contact pressures are similar to those reported by other models based on idealised geometries. An FE analysis of a non-cam hip is also performed for comparison with the pathological case.     

A functional analysis of carnassial biting

The jaw mechanism of carnivores is studied using an idealized model (Greaves, 1978). The model assumes: (i) muscle activity on both sides of the head, and (ii) that the jaw joints and the carnassial teeth are single points of contact between the skull and the lower jaw during carnassial biting. The model makes the following predictions: (i) in carnivores with carnassial teeth the resultant force of the jaw muscles will be positioned approximately 60% of the way from the jaw joint to the tooth—this arrangement delivers the maximum bite force possible together with a reasonably wide gape (remembering that bite force and gape cannot both be maximized); (ii) in an evolutionary sense, if greater bite force is required at the carnassial tooth, either the animal will get larger so as to deliver an absolutely larger bite force or the architecture of the muscles may change, becoming more pinnate, for example, but jaw geometry (i.e. the relative positions of the jaw joints, the carnassial tooth, and the muscle resultant force) will not change; (iii) if greater gape is required, the animal will get larger so as to have longer jaws and therefore an absolutely wider gape or change its muscle architecture allowing for greater stretch while the geometry remains unchanged; and (iv) in animals with a longer shearing region (e.g. the extinct hyaenodonts) the shearing region will be approximately 20% of jaw length and the muscle resultant force will be positioned approximately 60% of the way from the jaw joint to the most anterior shearing tooth.     

Testosterone-induced development of the rat levator ani muscle

The perinatal development of the levator ani (LA) muscle in male and female rats was investigated by measuring the total number of muscle units (MU) (i.e., mononucleate cells, clustered or independent myotubes, and muscle fibers) in transverse semithin sections of the entire muscle and the MU cross-sectional area in 22-day-old fetuses (F22), 1-day-old (D1 = day of birth), 3-day-old (D3), and 6-day-old (D6) newborns. Male muscle contained 350 +/- 64 MU on F22, twice that of the female. The number of MU increased markedly in males from F22, but changed little in females; the number of MU in males was 760% that of females on D6. The MU cross-sectional area was greater in males on F22 (120.8 micron(s)2 +/- 7.5) and D1 (155.2 micron(s)2 +/- 64.8) than in females (F22: 89.2 micron(s) +/- 14.2, D1: 64.1 micron(s)2 +/- 19.7) and dropped to about 30 X micron(s)2 in both sexes on D6. Female rats given a single injection of testosterone propionate (TP) before D7 showed a significant increase in the number of fibers, but no increase in cross-sectional area. TP given after D7 had no effect on the fiber number, but increased the average cross-sectional area. The increase in fiber number induced by postnatal TP treatment was a permanent effect, still quantifiable in 15-month-old females. We conclude that the sexual dimorphism of the rat LA muscle is principally due to a dramatic increase in the MU number in male muscles during the perinatal period, rather than to involution of the fibers in female muscles as it is widely accepted. This increase seems to be, at least partly, under the control of testosterone.     

Influence of the method of TM joint total replacement implantation on the loading of the joint on the opposite side

The temporomandibular (TM) joint is one of the most used joints in the human body, and any defect in this joint has a significant influence on quality of life. The objective of this study was to create a parametric numerical finite element (FE) analysis to compare the effect of surgical techniques used for total TM joint replacement implantation on loading the TM joint on the other side. Our hypothesis is that for the optimal function of all total TM joint replacements used in clinical practice it is crucial to devise a minimally invasive surgical technique, whereby there is minimum resection of masticatory muscles. This factor is more important than the design of the usually used total TM joint replacements. The extent of muscle resection influences the mechanical loading of the whole system. In the parametric FE analyses, the magnitude of the TM joint loading was compared for four different ranges of muscle resections during bite, using an anatomical model. The results obtained from all FE analyses support our hypothesis that an increasing extent of the muscle resection increased the magnitude of the TM joint overloading on the opposite side. The magnitude of the TM joint overloading increased depending on the muscle resection to 235% for bite on an incisor and up to 491% for bite on molars. Our study leads to a recommendation that muscle resection be minimised during replacement implantation and to a proposal that the attachment of the condylar part of the TM joint replacement be modified.     

Influence of the method of TM joint total replacement implantation on the loading of the joint on the opposite side

The temporomandibular (TM) joint is one of the most used joints in the human body, and any defect in this joint has a significant influence on quality of life. The objective of this study was to create a parametric numerical finite element (FE) analysis to compare the effect of surgical techniques used for total TM joint replacement implantation on loading the TM joint on the other side. Our hypothesis is that for the optimal function of all total TM joint replacements used in clinical practice it is crucial to devise a minimally invasive surgical technique, whereby there is minimum resection of masticatory muscles. This factor is more important than the design of the usually used total TM joint replacements. The extent of muscle resection influences the mechanical loading of the whole system. In the parametric FE analyses, the magnitude of the TM joint loading was compared for four different ranges of muscle resections during bite, using an anatomical model. The results obtained from all FE analyses support our hypothesis that an increasing extent of the muscle resection increased the magnitude of the TM joint overloading on the opposite side. The magnitude of the TM joint overloading increased depending on the muscle resection to 235% for bite on an incisor and up to 491% for bite on molars. Our study leads to a recommendation that muscle resection be minimised during replacement implantation and to a proposal that the attachment of the condylar part of the TM joint replacement be modified.     

Modeling investigation of learning a fast elbow flexion in the horizontal plane—prediction of muscle forces and motor units action

Experimental investigation of practicing a dynamic, goal-directed movement reveals significant changes in kinematics. Modeling can provide insight into the alterations in muscle activity, associated with the kinematic adaptations, and reveal the potential motor unit (MU) firing patterns that underlie those changes. In this paper, a previously developed muscle model and software (Raikova and Aladjov, Journal of Biomechanics, 35, 2002) have been used to investigate changes in MU control, while practicing fast elbow flexion to a target in the horizontal plane. The first trial (before practice) and the last trial (after extensive practice) of two subjects have been simulated. The inputs for the simulation were the calculated external moments at the elbow joint. The external moments were countered by the action of three flexor muscles and two extensor ones. The muscles have been modeled as a mixture of MUs of different types. The software has chosen the MU firing times necessary to accomplish the movement. The muscle forces and MUs firing statistics were then calculated. Three hypotheses were tested and confirmed: (1) peak muscle forces and antagonist co-contraction increase during training; (2) there is an increase in the firing frequency and the synchronization between MUs; and (3) the recruitment of fast-twitch MUs dominates the action.     

An Approach to the Biomechanics of the Masticatory Apparatus of Early Miocene (Santacrucian Age) South American Ungulates (Astrapotheria, Litopterna, and Notoungulata): Moment Arm Estimation Based on 3D Landmarks

Notoungulates, litopterns, and astrapotheres are among the most representative mammals of the early Miocene Santacrucian Age. They comprise a diversity of biological types and sizes, from small forms, comparable to rodents, to giants with no analogues in modern faunas. Traditionally, all of them have been considered herbivores; this diversity is reflected in different morphologies of the masticatory apparatus, suggesting a variety of feeding habits. The application of biomechanics to the study of fossil mammals is a good approach to test functional hypotheses. Jaws act as a lever system, with the pivot at the temporomandibular joint, with masticatory muscles providing the input force, whereas the output force is produced by the teeth on food. The moment arms of the lines of action of the muscles can be estimated to analyze relationships between bite force and bite velocity. A morphogeometric approach inspired by Vizcaíno et al. (1998) is applied to estimate muscle moment arms in a static 3D bite model based on three-dimensional landmarks and semilandmarks on crania with mandibles in occlusion. This new 3D geometric method to evaluate jaw mechanics demonstrated its reliability when applied to a control sample of extant mammals that included carnivores, herbivores, and omnivores. Our results indicate that, except for Pachyrukhos, in no Santacrucian ungulate does the masseter muscle have greater mechanical advantage than the temporalis. Among them, notoungulates have a better configuration to develop force on the molar tooth row than litopterns. This indicates a diet richer in tough plant materials for Santacrucian notoungulates (e.g., grass or even bark) than for litopterns (e.g., dicots). This is consistent with recent ecomorphological approaches applied to this fauna. Finally, the approach proposed here proves to be useful for comparing masticatory performance and it is a powerful tool to validate ecomorphological dietary hypotheses in fossil taxa.     

Residual force enhancement exceeds the isometric force at optimal sarcomere length for optimized stretch conditions.

Residual force enhancement (FE) following stretch of an activated muscle is a well accepted property of skeletal muscle contraction. However, the mechanism underlying FE remains unknown. A crucial assumption on which some proposed mechanisms are based is the idea that forces in the enhanced state cannot exceed the steady-state isometric force at a sarcomere length associated with optimal myofilament overlap. Although there are a number of studies in which forces in the enhanced state were compared with the corresponding isometric forces on the plateau of the force-length relationship, these studies either did not show enhanced forces above the plateau or, if they did, they lacked measurements of sarcomere lengths confirming the plateau region. Here, we revisited this question by optimizing stretch conditions and measuring the average sarcomere lengths in isolated fibers, and we found that FE exceeded the maximal isometric reference force obtained at the plateau of the force-length relationship consistently (mean+/-SD: 4.8+/-2.1%) and by up to 10%. When subtracting the passive component of FE from the total FE, the enhanced forces remained greater than the isometric plateau force (mean+/-SD: 4.3+/-2.0%). Calcium-induced increases in passive forces, known to be present in single fibers and myofibrils, are too small to account for the FE observed here. We conclude that FE cannot be explained exclusively with a stretch-induced development of sarcomere length nonuniformities, that FE in single fibers may be associated with the recruitment of additional contractile force, and that isometric steady-state forces in the enhanced state are not uniquely determined by sarcomere lengths.