The myofilament lattice: studies on isolated fibers. IV. Lattice equilibria in striated muscle.

Accounts of similarities between the thick filament lattice of striated muscle and smectic liquid-crystalline structures have focused upon an equilibrium between electrostatic (repulsive) and van der Waal's (attractive) forces. In living, intact muscle the fiber volume constitutes an additional important parameter which influences the amount of interaxial separation between the filaments. This is demonstrable by comparison of the lattice behavior of living fibers with that of fibers from which the sarcolemma has either been removed or made leaky by glycerination. These comparisons were made mainly by low-angle X-ray diffraction under conditions of changes in sarcomere length, ionic strength or osmolarity, and pH. Single fibers with the sarcolemma removed and glycerinated muscle have lattices which behave in accord with equilibrium liquid-crystalline systems in which the thick filament spacing is determined by the balance between electrostatic and van der Waal's forces. Conversely, osmotic and shortening studies demonstrate that the living, intact muscle has a lattice which behaves in accord with the so-called non-equilibrium (volume-constrained) liquid-crystalline condition in which the interaxial separation between the thick filaments is solely due to the amount of volume available as determined by the Donnan steady-state across the sarcolemma.     

Tension fluctuations in contracting myofibrils and their interpretation

Repulsive pressure has been measured as a function of lattice spacing in gels of tobacco mosaic virus (TMV) and in the filament lattice of vertebrate striated muscle. External pressures up to ten atm have been applied to these lattices by an osmotic stress method. Numerical solutions to the Poisson-Boltzmann equation in hexagonal lattices have been obtained and compared to the TMV and muscle data. The theoretical curves using values for k calculated from the ionic strength give a good fit to experimental data from TMV gels, and an approximate fit to that from the muscle lattice, provided that a charge radius for the muscle thick filaments of approximately 16 nm is assumed. Variations in ionic strength, sarcomere length and state of the muscle give results which agree qualitatively with the theory, though a good fit between experiment and theory in the muscle case will clearly require consideration of other types of forces. We conclude that Poisson-Boltzmann theory can provide a good first approximation to the long-range electrostatic forces operating in such biological gel systems.     

Coupled objective function to study the role of abdominal muscle forces in lifting using the kinematics-driven model

To circumvent the existing shortcoming of optimisation algorithms in trunk biomechanical models, both agonist and antagonist trunk muscle stresses to different powers are introduced in a novel objective function to evaluate the role of abdominal muscles in trunk stability and spine compression. This coupled objective function is introduced in our kinematics-driven finite element model to estimate muscle forces and to identify the role of abdominal muscles in upright standing while lifting symmetrically a weight at different heights. Predictive equations for the compression and buckling forces are developed. Results are also compared with the conventional objective function that neglects abdominal muscle forces. An overall optimal solution involving smaller spinal compression but higher trunk stability is automatically attained when choosing muscle stress powers at and around 3. Results highlight the internal oblique muscle as the most efficient abdominal muscle during the tasks investigated. The estimated relative forces in abdominal muscles are found to be in good agreement with the respective ratios of recorded electromyography activities.     

An electrostatic model with weak actin-myosin attachment resolves problems with the lattice stability of skeletal muscle

The stability of the filament lattice in relaxed striated muscle can be viewed as a balance of electrostatic and van der Waals forces. The simplest electrostatic model, where actin and myosin filaments are treated as charged cylinders, generates reasonable lattice spacings for skinned fibers. However, this model predicts excessive radial stiffness under osmotic pressure and cannot account for the initial pressure (∼1 kPa) required for significant compression. Good agreement with frog compression data is obtained with an extended model, in which S1 heads are weakly attached to actin when the lattice spacing is reduced below a critical value; further compression moves fixed negative charges on the heads closer to the myofilament backbone as they attach at a more acute angle to actin. The model predicts pH data in which the lattice shrinks as pH is lowered and protons bind to filaments. Electrostatic screening implies that the lattice shrinks with increasing ionic strength, but the observed expansion of the frog lattice at ionic strengths above 0.1 M with KCl might be explained if Cl⁻ binds to sites on the motor domain of S1. With myosin-myosin and actin-actin interactions, the predicted lattice spacing decreases slightly with sarcomere length, with a more rapid decrease when actin-myosin filament overlap is very small.     

The effects of the antagonist muscle force on intersegmental loading during isokinetic efforts of the knee extensors

Hamstrings activation when acting as antagonists is considered very important for knee joint stability. However, the effect of hamstring antagonist activity on knee joint loading in vivo is not clear. Therefore, the purpose of this study was to examine the differences in antagonistic muscle force and their effect on agonist muscle and intersegmental forces during isokinetic eccentric and concentric efforts of the knee extensors. Ten males performed maximum isokinetic eccentric and concentric efforts of the knee extensors at 30 degrees s(-1). The muscular and tibiofemoral joint forces were then estimated using a two-dimensional model with and without including the antagonist muscle forces. The antagonist moment was predicted using an IEMG-moment model. The predicted antagonist force reached a maximum of 2.55 times body weight (BW) and 1.16 BW under concentric and eccentric conditions respectively. Paired t-tests indicated that these were significantly different (p<0.05). A one-way analysis of variance indicated that when antagonist forces are included in the calculations the patella tendon, compressive and posterior shear joint forces are significantly higher compared to those calculated without including the antagonist forces. The anterior shear force was not affected by antagonist activity. The antagonists produce considerable force throughout the range of motion and affect the joint forces exerted at the knee joint. Further, it appears that the antagonist effect depends on the type of muscle action examined as it is higher during concentric compared to eccentric efforts of the knee extensors.     

Straightening Out the Elasticity of Myosin Cross-Bridges

In a contracting muscle, myosin cross-bridges extending from thick filaments pull the interdigitating thin (actin-containing) filaments during cyclical ATP-driven interactions toward the center of the sarcomere, the structural unit of striated muscle. Cross-bridge attachments in the sarcomere have been reported to exhibit a similar stiffness under both positive and negative forces. However, in vitro measurements on filaments with a sparse complement of heads detected a decrease of the cross-bridge stiffness at negative forces attributed to the buckling of the subfragment 2 tail portion. Here, we review some old and new data that confirm that cross-bridge stiffness is nearly linear in the muscle filament lattice. The implications of high myosin stiffness at positive and negative strains are considered in muscle fibers and in nonmuscle intracellular cargo transport.     

Constraining spine stability levels in an optimization model leads to the prediction of trunk muscle cocontraction and improved spine compression force estimates

A major limitation of optimization models of the spine has been the inability to accurately predict trunk muscle co-activity. Antagonist muscle activity is thought to be necessary to maintain adequate levels of spine stability but, in turn, creates increased loading on the spine. It is thus hypothesized that the CNS attempts to optimize the relationship between spine loading and spine stability in determining muscular activation patterns. This study presents an optimization model of the spine in which stability was constrained to target levels predicted from regression equations of independent loading variables. Objective functions were set to either minimize the sum of the cubed muscle forces or minimize the sum of the squared intervertebral forces at the L4-L5 disc level. Results demonstrate that the inclusion of stability constraints in optimization simulations produced realistic predictions of antagonist muscle activity and predictions of spine compression levels that agree more closely with EMG-based estimates, compared to simulations in which stability was unconstrained. It was concluded that spinal stability is a vital consideration for the CNS when dictating trunk muscle recruitment patterns.     

Spinal stiffness increases with axial load: another stabilizing consequence of muscle action.

This paper addresses the role of lumbar spinal motion segment stiffness in spinal stability. The stability of the lumbar spine was modelled with loadings of 30 Nm or 60 Nm efforts about each of the three principal axes, together with the partial body weight above the lumbar spine. Two assumptions about motion segment stiffness were made: first the stiffness was represented by an 'equivalent beam' with constant stiffness properties; second the stiffness was updated based on the motion segment axial loading using a relationship determined experimentally from human lumbar spinal specimens tested with 0, 250 and 500 N of axial compressive preload. Two physiologically plausible muscle activation strategies were used in turn for calculating the muscle forces required for equilibrium. Stability analyses provided estimates of the minimum muscle stiffness required for stability. These critical muscle stiffness values decreased when preload effects were used in estimating spinal stiffness in all cases of loadings and muscle activation strategies, indicating that stability increased. These analytical findings emphasize that the spinal stiffness (as well as muscular stiffness) is important in maintaining spinal stability, and that the stiffness-increasing effect of 'preloading' should be taken into account in stability analyses.     

Computation of trunk equilibrium and stability in free flexion-extension movements at different velocities

Velocity of movement has been suggested as a risk factor for low-back disorders. The effect of changes in velocity during unconstrained flexion-extension movements on muscle activations, spinal loads, base reaction forces and system stability was computed. In vivo measurements of kinematics and ground reaction forces were initially carried out on young asymptomatic subjects. The collected kinematics of three subjects representing maximum, mean and minimum lumbar rotations were subsequently used in the kinematics-driven model to compute results during the entire movements at three different velocities. Estimated spinal loads and muscle forces were significantly larger in fastest pace as compared to slower ones indicating the effect of inertial forces. Spinal stability was improved in larger trunk flexion angles and fastest movement. Partial or full flexion relaxation of global extensor muscles occurred only in slower movements. Some local lumbar muscles, especially in subjects with larger lumbar flexion and at slower paces, also demonstrated flexion relaxation. Results confirmed the crucial role of movement velocity on spinal biomechanics. Predictions also demonstrated the important role on response of the magnitude of peak lumbar rotation and its temporal variation.     

Compliant realignment of binding sites in muscle: transient behavior and mechanical tuning.

The presence of compliance in the lattice of filaments in muscle raises a number of concerns about how one accounts for force generation in the context of the cross-bridge cycle--binding site motions and coupling between cross-bridges confound more traditional analyses. To explore these issues, we developed a spatially explicit, mechanochemical model of skeletal muscle contraction. With a simple three-state model of the cross-bridge cycle, we used a Monte Carlo simulation to compute the instantaneous balance of forces throughout the filament lattice, accounting for both thin and thick filament distortions in response to cross-bridge forces. This approach is compared to more traditional mass action kinetic models (in the form of coupled partial differential equations) that assume filament inextensibility. We also monitored instantaneous force generation, ATP utilization, and the dynamics of the cross-bridge cycle in simulations of step changes in length and variations in shortening velocity. Three critical results emerge from our analyses: 1) there is a significant realignment of actin-binding sites in response to cross-bridge forces, 2) this realignment recruits additional cross-bridge binding, and 3) we predict mechanical behaviors that are consistent with experimental results for velocity and length transients. Binding site realignment depends on the relative compliance of the filament lattice and cross-bridges, and within the measured range of these parameters, gives rise to a sharply tuned peak for force generation. Such mechanical tuning at the molecular level is the result of mechanical coupling between individual cross-bridges, mediated by thick filament deformations, and the resultant realignment of binding sites on the thin filament.     

Glenohumeral stability in simulated rotator cuff tears

Rotator cuff tears disrupt the force balance in the shoulder and the glenohumeral joint in particular, resulting in compromised arm elevation torques. The trade-off between glenohumeral torque and glenohumeral stability is not yet understood. We hypothesize that compensation of lost abduction torque will lead to a superior redirection of the reaction force vector onto the glenoid surface, which will require additional muscle forces to maintain glenohumeral stability. Muscle forces in a single arm position for five combinations of simulated cuff tears were estimated by inverse dynamic simulation (Delft Shoulder and Elbow Model) and compared with muscle forces in the non-injured condition. Each cuff tear condition was simulated both without and with an active modeling constraint for glenohumeral stability, which was defined as the condition in which the glenohumeral reaction force intersects the glenoid surface. For the simulated position an isolated tear of the supraspinatus only increased the effort of the other muscles with 8%, and did not introduce instability. For massive cuff tears beyond the supraspinatus, instability became a prominent factor: the deltoids were not able to fully compensate lost net abduction torque without introducing destabilizing forces; unfavorable abductor muscles (i.e. in the simulated position the subscapularis and the biceps longum) remain to compensate the necessary abduction torque; the teres minor appeared to be of vital importance to maintain glenohumeral stability. Adverse adductor muscle co-contraction is essential to preserve glenohumeral stability.     

Seated whole body vibrations with high-magnitude accelerations--relative roles of inertia and muscle forces

Reliable computation of spinal loads and trunk stability under whole body vibrations with high acceleration contents requires accurate estimation of trunk muscle activities that are often overlooked in existing biodynamic models. A finite element model of the spine that accounts for nonlinear load- and direction-dependent properties of lumbar segments, complex geometry and musculature of the spine, and dynamic characteristics of the trunk was used in our iterative kinematics-driven approach to predict trunk biodynamics in measured vehicle's seat vibrations with shock contents of about 4g (g: gravity acceleration of 9.8m/s(2)) at frequencies of about 4 and 20Hz. Muscle forces, spinal loads and trunk stability were evaluated for two lumbar postures (erect and flexed) with and without coactivity in abdominal muscles. Estimated peak spinal loads were substantially larger under 4Hz excitation frequency as compared to 20Hz with the contribution of muscle forces exceeding that of inertial forces. Flattening of the lumbar lordosis from an erect to a flexed posture and antagonistic coactivity in abdominal muscles, both noticeably increased forces on the spine while substantially improving trunk stability. Our predictions clearly demonstrated the significant role of muscles in trunk biodynamics and associated risk of back injuries. High-magnitude accelerations in seat vibration, especially at near-resonant frequency, expose the vertebral column to large forces and high risk of injury by significantly increasing muscle activities in response to equilibrium and stability demands.     

Computational stability of human knee joint at early stance in Gait: Effects of muscle coactivity and anterior cruciate ligament deficiency

As one of the most complex and vulnerable structures of body, the human knee joint should maintain dynamic equilibrium and stability in occupational and recreational activities. The evaluation of its stability and factors affecting it is vital in performance evaluation/enhancement, injury prevention and treatment managements. Knee stability often manifests itself by pain, hypermobility and giving-way sensations and is usually assessed by the passive joint laxity tests. Mechanical stability of both the human knee joint and the lower extremity at early stance periods of gait (0% and 5%) were quantified here for the first time using a hybrid musculoskeletal model of the lower extremity. The roles of muscle coactivity, simulated by setting minimum muscle activation at 0–10% levels and ACL deficiency, simulated by reducing ACL resistance by up to 85%, on the stability margin as well as joint biomechanics (contact/muscle/ligament forces) were investigated. Dynamic stability was analyzed using both linear buckling and perturbation approaches at the final deformed configurations in gait. The knee joint was much more stable at 0% stance than at 5% due to smaller ground reaction and contact forces. Muscle coactivity, when at lower intensities (<3% of its maximum active force), increased dynamic stability margin. Greater minimum activation levels, however, acted as an ineffective strategy to enhance stability. Coactivation also substantially increased muscle forces, joint loads and ACL force and hence the risk of further injury and degeneration. A deficiency in ACL decreases total ACL force (by 31% at 85% reduced stiffness) and the stability margin of the knee joint at the heel strike. It also markedly diminishes forces in lateral hamstrings (by up to 39%) and contact forces on the lateral plateau (by up to 17%). Current work emphasizes the need for quantification of the lower extremity stability margin in gait.     

Muscle compensation strategies to maintain glenohumeral joint stability with increased rotator cuff tear severity: A simulation study

Rotator cuff tear (RCT) in older adults may cause decreased muscle forces and disrupt the force balance at the glenohumeral joint, compromising joint stability. Our objective was to identify how increased RCT severity affects glenohumeral joint loading and muscle activation patterns using a computational model. Muscle volume measurements were used to scale a nominal upper limb model’s peak isometric muscle forces to represent force-generating characteristics of an average older adult male. Increased RCT severity was represented by systematically decreasing peak isometric muscle forces of supraspinatus, infraspinatus, and subscapularis. Five static postures in both scapular and frontal planes were evaluated. Results revealed that in both scapular and frontal planes, the peak glenohumeral joint contact force magnitude remained relatively consistent across increased RCT severity (average 1.5% and −4.2% change, respectively), and a relative balance of the transverse force couple is maintained even in massive RCT models. Predicted muscle activations of intact muscles, like teres minor, increased (average 5–30% and 4–17% in scapular and frontal planes, respectively) with greater RCT severity. This suggests that the system is prioritizing glenohumeral joint stability, even with severe RCT, and that unaffected muscles play a compensatory role to help stabilize the joint.     

Stair climbing is more critical than walking in pre-clinical assessment of primary stability in cementless THA in vitro

Pre-clinical testing of hip endoprostheses is a mandatory requirement before clinical release. Inadequate loading conditions may lead to lower elastic and plastic interface movements than those occurring post-operatively in vivo. This study investigated the influence of patient activity on the primary stability of cementless prostheses with a special emphasis on active simulation of muscle forces. A loading setup, based on validated musculo-skeletal analyses, was used to generate the hip contact force during walking and stair climbing by transmitting muscle forces through the femur. In addition, a loading configuration which only generated the hip contact force occurring during stair climbing at the prosthesis head was simulated. CLS prostheses were implanted in 18 composite femora and subjected to cyclical loading. The relative micro-movements at the bone-prosthesis interface were determined and appeared to be extremely sensitive to the specific patient activity. Compared to walking, stair climbing generated higher micro-movements, with pronounced axial and rotational components. Stair climbing with the femur loaded by the resultant hip contact force only exhibited a characteristic valgus tilt of the stem with significantly lower interface micro-movements than under active simulation of muscle forces. The analyses suggest that stair climbing induced the highest mechanical instability at the bone-prosthesis interface, a level which may compromise the necessary osseointegration process. Active simulation of muscle forces considerably affects the primary stability of cementless hip endoprostheses. Pre-clinical in vitro tests should therefore simulate stair climbing and include muscle activity in the assessment of initial implant stability, otherwise micro-movements may be underestimated and the primary stability overestimated.     

Lumbar spinal muscle activation synergies predicted by multi-criteria cost function

The hypothesis that control of lumbar spinal muscle synergies is biomechanically optimized was studied by comparing EMG data with an analytical model with a multi-component cost function that could include (1) trunk displacements, (2) intervertebral displacements, (3) intervertebral forces; (4) sum of cubed muscle stresses, and (5) eigenvalues for the first two spinal buckling modes. The model's independent variables were 180 muscle forces. The 36 displacements of 6 vertebrae were calculated from muscle forces and the spinal stiffness. Calculated muscle activation was compared with EMG data from 14 healthy human subjects who performed isometric voluntary ramped maximum efforts at angles of 0 degrees, 45 degrees, 90 degrees, 135 degrees and 180 degrees to the right from the anterior direction. Muscle activation at each angle was quantified as the linear regression slope of the RMS EMG versus external force relationship, normalized by the maximum observed EMG.There was good agreement between the analytical model and EMG data for the dorsal muscles when the model included either minimization of intervertebral displacements or minimization of intervertebral forces in its cost function, but the model did not predict a realistic level of abdominal muscles activation. Agreement with EMG data was improved with the sum of the cubed muscle stresses added to the cost function. Addition of a cost function component to maximize the trunk stability produced higher levels of antagonistic muscle activation at low efforts than at greater efforts. It was concluded that the muscle activation strategy efficiently limits intervertebral forces and displacements, and that costs of higher muscle stresses are taken into account, but stability does not appear to be maximized. Trunk muscles are apparently not controlled solely to optimize any one of the biomechanical costs considered here.     

Discussion on the state of water in the myofilament lattice and other biological systems, based on the fact that the usual concepts of colloid stability can not explain the stability of the myofilament lattice

Application of the usual concepts of colloid stability shows that the in vivo spacings between the myofilaments, making up the contractile part of the muscle myofibrils, correspond to energies of 10(-4) to 10(-1) kT. Refinements in the calculations of the electrostatic and Van der Waals-London energies do not significantly modify these values. Therefore, theory does not predict the observed stability of the myofilament lattice. It is shown that the interfilament water very likely plays an active role in the myofilament lattice. More generally, the structure of water in living cells is probably different from that of bulk water.     

Extension of a state-of-the-art optimization criterion to predict co-contraction

Most studies concerned with the prediction of muscle forces have tried to predict a physiologically reasonable, synergistic muscle behavior. In addition to the load sharing of synergistic muscles, co-contraction of antagonistic muscles also occurs. An extension to a standard quadratic criterion for the calculation of muscle forces is presented in this study. This extension however is not limited to quadratic optimization. The extension is applied to a planar, one degree of freedom model of the human knee. For this model an analytical solution is presented. With the extended criterion it was possible to predict and control the amount of co-contraction for the knee model. The enforced antagonistic muscle activity led to higher agonistic muscle activity. In the absence of an external load flexor and extensor muscles were activated. As a consequence the knee joint was preloaded. This might indicate that antagonistic muscle activity is generated to maintain or improve joint stability. In conclusion, this study presents a novel approach to predict co-contraction when using optimization techniques to determine muscle forces by introducing a shift parameter for the optimization criterion.     

Effect of load position on muscle forces, internal loads and stability of the human spine in upright postures

A novel kinematics-based approach coupled with a non-linear finite element model was used to investigate the effect of changes in the load position and posture on muscle activity, internal loads and stability margin of the human spine in upright standing postures. In addition to 397 N gravity, external loads of 195 and 380 N were considered at different lever arms and heights. Muscle forces, internal loads and stability margin substantially increased as loads displaced anteriorly away from the body. Under same load magnitude and location, adopting a kyphotic posture as compared with a lordotic one increased muscle forces, internal loads and stability margin. An increase in the height of a load held at a fixed lever arm substantially diminished system stability thus requiring additional muscle activations to maintain the same margin of stability. Results suggest the importance of the load position and lumbar posture in spinal biomechanics during various manual material handling operations.     

Subject-specific thumb muscle activity during functional tasks of daily life

BackgroundThe trapeziometacarpal joint is subjected to high compressive forces during powerful pinch and grasp tasks due to muscle loading. In addition, muscle contraction is important for stability of the joint. The aim of the present study is to explore if different muscle activation patterns can be found between three functional tasks.MethodsIsometric forces and fine-wire electromyographic (fEMG) activity produced by three intrinsic and four extrinsic thumb muscles were measured in 10 healthy female volunteers. The participants performed isometric contractions in a lateral key pinch, a power grasp and a jar twist task. The tasks were executed with and without EMG recording to verify if electrode placement influenced force production.ResultsA subject-specific muscle recruitment was found which remained largely unchanged across tasks. Extrinsic thumb muscles were significantly more active than intrinsic muscles in all tasks. Insertion of the fEMG electrodes decreased force production significantly in all tasks.ConclusionThe thumb muscles display a high variability in muscle activity during functional tasks of daily life. The results of this study suggest that to produce a substantial amount of force, a well-integrated, but subject-specific, co-contraction between the intrinsic and extrinsic thumb muscles is necessary.