Estimation of tendon moment arms from three-dimensional magnetic resonance images

The validity and reliability of the Achilles tendon moment arm assessed with dual-energy X-ray absorptiometry, relative to MRI and ultrasound assessments

Dual-energy X-ray absorptiometry (DXA) in single energy mode has been shown to permit the visualisation of bone and soft tissue, such as the patellar tendon through two-dimensional sagittal imaging. However, there is no validated DXA-based measurement of the Achilles tendon moment arm (d_AT). The aims of this study were: 1) to compare in vivo DXA derived measurements of the d_AT at rest against two previously validated methods: tendon excursion (TE) and magnetic resonance imaging (MRI) at three ankle angles (-5°, 0° and +10°). 2) analyse the intra-day reliability of the DXA method at all ankle angles and compare between methods. Twelve healthy adults (mean ± SD: 31.4 ± 9.5 years; 174.0 ± 9.5 cm; 76.2 ± 16.6 kg) participated in this study, involving test-retest DXA scans, ultrasound scans and one MRI scan. The d_AT was defined as the distance from the centre of the calcaneal-tibial joint axis to the Achilles tendon (AT) muscle-tendon line of action. DXA derived d_AT measures were significantly greater than MRI measurements (19.7-24.9%) and were 45.2% significantly larger than the TE method. The test-retest reliability of the DXA technique at 0° was high [CV = 1.38%; ICC = 0.96] and despite the consistently larger d_AT lengths obtained using DXA, MRI and DEXA data were strongly correlated (r = 0.878, p < 0.001). In conclusion, the DXA technique allowed for highly reproducible in vivo d_AT measurement at rest, which has implications for the calculation of AT forces in vivo and the ability to predict the measurement from one tool to the other, thereby providing a novel basis to contrast existing and future studies.

Wrist tendon moment arms: Quantification by imaging and experimental techniques

Subject-specific musculoskeletal models require accurate values of muscle moment arms. The aim of this study was to compare moment arms of wrist tendons obtained from non-invasive magnetic resonance imaging (MRI) to those obtained from an in vitro experimental approach. MRI was performed on ten upper limb cadaveric specimens to obtain the centrelines for the flexor carpi radialis (FCR), flexor carpi ulnaris (FCU), extensor carpi radialis longus (ECRL), extensor carpi radialis brevis (ECRB), extensor carpi ulnaris (ECU), and abductor pollicis longus (APL) tendons. From these, the anatomical moment arms about each of the flexion-extension (FE) and radioulnar deviation (RUD) axes of the wrist were calculated. Specimens were mounted on a physiologic wrist simulator to obtain functional measurements of the moment arms using the tendon excursion method. No differences were observed between anatomical and functional values of the FE and RUD moment arms of FCR, ECRL and ECRB, and the RUD moment arm of ECU (p > .075). Scaling the anatomical moment arms relative to ECRB in FE and ECU in RUD reduced differences in the FE moment arm of FCU and the RUD moment arm of APL to less than 15% (p > .139). However, differences persisted in moment arms of FCU in RUD, and ECU and APL in FE (p < .008). This study shows that while measurements of moment arms of wrist tendons using imaging do not always conform to values obtained using in vitro experimental approaches, a stricter protocol could result in the acquisition of subject-specific moment arms to personalise musculoskeletal models.

Dependence of Muscle Moment Arms on In Vivo Three-Dimensional Kinematics of the Knee

Quantification of muscle moment arms is important for clinical evaluation of muscle pathology and treatment, and for estimating muscle and joint forces in musculoskeletal models. Moment arms estimated with musculoskeletal models often assume a default motion of the knee derived from measurements of passive cadaveric flexion. However, knee kinematics are unique to each person and activity. The objective of this study was to estimate moment arms of the knee muscles with in vivo subject- and activity-specific kinematics from seven healthy subjects performing seated knee extension and single-leg lunge to show changes between subjects and activities. 3D knee motion was measured with a high-speed stereo-radiography system. Moment arms of ten muscles were estimated in OpenSim by replacing the default knee motion with in vivo measurements. Estimated inter-subject moment arm variability was similar to previously reported in vitro measurements. RMS deviations up to 9.0 mm (35.2% of peak value) were observed between moment arms estimated with subject-specific knee extension and passive cadaveric motion. The degrees of freedom that most impacted inter-activity differences were superior/inferior and anterior/posterior translations. Musculoskeletal simulations used to estimate in vivo muscle forces and joint loads may provide significantly different results when subject- and activity-specific kinematics are implemented.

Tibialis anterior moment arm: effects of measurement errors and assumptions

Accurate estimates of tibialis anterior (TA) muscle force are important in many contexts. Two approaches commonly used to estimate moment arms are the tendon excursion (TE) and geometric (GEO) methods. Previous studies report poor agreement between the two approaches.

PURPOSE

The purposes of this study were to 1) assess the effect of methodological variations in the two methods of moment arm estimation and 2) determine how these variations affect agreement between the methods.

METHODS

TA moment arms were determined using TE and GEO. Errors associated with tendon stretch/hysteresis, talus rotation relative to the foot, and the location of the line of action were investigated.

RESULTS

For TE, large errors in moment arm estimates across the range of motion were found when tendon length changes (P = 0.001) were not corrected for. For GEO, the estimated moment arm was reduced at an ankle angle of -15° when discrepancies between talus and foot rotations were accounted for or when an alternative tendon line of action was used either separately (effect size (ES), 0.46 and 0.58, respectively; P > 0.05) or together (ES, 0.89; P > 0.05). TE-derived moment arms were smaller than GEO-derived moment arms (ES, 0.68-4.86, varying by angle) before accounting for sources of error. However, these differences decreased after error correction (ES, 0.09-1.20, P > 0.05). Nonetheless, the shape of the moment arm-joint angle relation was curvilinear for TE but linear for GEO.

CONCLUSIONS

Of all methodological modifications, accounting for tendon length changes had the largest effect on TA moment arm estimates. We conclude that the TE method is viable to determine TA moment arms as long as changes in tendon length are accounted for.

Effects of the index finger position and force production on the flexor digitorum superficialis moment arms at the metacarpophalangeal joints - a magnetic resonance imaging study

BACKGROUND

The purpose of this study was to use magnetic resonance imaging to measure the moment arm of the flexor digitorum superficialis tendon about the metacarpophalangeal joint of the index, middle, ring, and little fingers when the position and force production level of the index finger was altered. A secondary goal was to create regression models using anthropometric data to predict moment arms of the flexor digitorum superficialis about the metacarpophalangeal joint of each finger.

METHODS

The hands of subjects were scanned using a 3.0 T magnetic resonance imaging scanner. The metacarpophalangeal joint of the index finger was placed in: flexion, neutral, and extension. For each joint configuration subjects produced no active force (passive condition) and exerted a flexion force to resist a load at the fingertip (active condition).

RESULTS

The following was found: (1) The moment arm of the flexor digitorum superficialis at the metacarpophalangeal joint of the index finger (a) increased with the joint flexion and stayed unchanged with finger extension; and (b) decreased with the increase of force at the neutral and extended finger postures and did not change at the flexed posture. (2) The moment arms of the flexor digitorum superficialis tendon of the middle, ring, and little fingers (a) did not change when the index metacarpophalangeal joint position changed (P>0.20); and (b) The moment arms of the middle and little fingers increased when the index finger actively produced force at the flexed metacarpophalangeal joint posture. (4) The moment arms showed a high correlation with anthropometric measurements.

INTERPRETATION

Moment arms of the flexor digitorum superficialis change due to both changes in joint angle and muscle activation; they scale with various anthropometric measures.

Sensitivity of model predictions of muscle function to changes in moment arms and muscle-tendon properties: a Monte-Carlo analysis

Hill-type muscle models are commonly used in musculoskeletal models to estimate muscle forces during human movement. However, the sensitivity of model predictions of muscle function to changes in muscle moment arms and muscle-tendon properties is not well understood. In the present study, a three-dimensional muscle-actuated model of the body was used to evaluate the sensitivity of the function of the major lower limb muscles in accelerating the whole-body center of mass during gait. Monte-Carlo analyses were used to quantify the effects of entire distributions of perturbations in the moment arms and architectural properties of muscles. In most cases, varying the moment arm and architectural properties of a muscle affected the torque generated by that muscle about the joint(s) it spanned as well as the torques generated by adjacent muscles. Muscle function was most sensitive to changes in tendon slack length and least sensitive to changes in muscle moment arm. However, the sensitivity of muscle function to changes in moment arms and architectural properties was highly muscle-specific; muscle function was most sensitive in the cases of gastrocnemius and rectus femoris and insensitive in the cases of hamstrings and the medial sub-region of gluteus maximus. The sensitivity of a muscle's function was influenced by the magnitude of the muscle's force as well as the operating region of the muscle on its force-length curve. These findings have implications for the development of subject-specific models of the human musculoskeletal system.

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.

MRI of weight bearing and movement

Conventional, static magnetic resonance imaging (MRI) is able to provide a vast amount of information regarding the anatomy and pathology of the musculoskeletal system. However, patients, especially those whose pain is position dependent or elucidated by movement, may benefit from more advanced imaging techniques that allow for the acquisition of functional information. This manuscript reviews a variety of advancements in MRI techniques that are used to image the musculoskeletal system dynamically, while in motion or under load. The methodologies, advantages and drawbacks of stress MRI, cine-phase contrast MRI and real-time MRI are discussed as each has helped to advance the field by providing a scientific basis for understanding normal and pathological musculoskeletal anatomy and function. Advancements in dynamic MR imaging will certainly lead to improvements in the understanding, prevention, diagnosis and treatment of musculoskeletal disorders. It is difficult to anticipate that dynamic MRI will replace conventional MRI, however, dynamic MRI may provide additional valuable information to findings of conventional MRI.

Probabilistic Modeling of Knee Muscle Moment Arms: Effects of Methods, Origin–Insertion, and Kinematic Variability

In musculoskeletal modeling, reliable estimates of muscle moment arms are an important step in accurately predicting muscle forces and joint moments. The degree of agreement between the two common methods of calculating moment arms-tendon excursion (TE) and geometric origin-insertion, is currently unknown for the muscles crossing the knee joint. Further, measured moment arm data are subject to variability in estimation of attachment sites as points from irregular surfaces on the bones, and due to differences in joint kinematics observed in vivo. Thus, the objectives of the present study were to compare moment arms of major muscles crossing the knee joint obtained from TE and geometric methods using a finite element-based lower extremity model, and to quantify the effects of potential muscle origin-insertion and tibiofemoral kinematic variability on the predicted moment arms using probabilistic methods. A semiconstrained, fixed bearing, posterior cruciate-retaining total knee arthroplasty was included due to available in vivo kinematic data. In this study, muscle origin and insertion locations and kinematic variables were represented as normal distributions with standard deviations of 5 mm for origin-insertion locations and up to 1.6 mm and 3.0 degrees for the kinematic parameters. Agreement between the deterministic moment arm calculations from the two methods was excellent for the flexors, while differences in trends and magnitudes were observed for the extensor muscles. Model-predicted deterministic moment arms from both methods agreed reasonably with the experimental values from available literature. The uncertainty in input parameters resulted in substantial variability in predicted moment arms, with the size of 1-99% confidence interval being up to 41.3 and 35.8 mm for the TE and geometric methods, respectively. The sizeable range of moment arm predictions and associated excursions has the potential to affect a muscle's operating range on the force-length curve, thus affecting joint moments. In this study, moment arm predictions were more dependent on muscle origin-insertion locations than the kinematic variables. The important parameters from the TE method were the origin and insertion locations in the sagittal plane, while the insertion location in the sagittal plane was the dominant parameter using the geometric method.

Image-based musculoskeletal modeling: Applications, advances, and future opportunities

Computer models of the musculoskeletal system are broadly used to study the mechanisms of musculoskeletal disorders and to simulate surgical treatments. Musculoskeletal models have historically been created based on data derived in anatomical and biomechanical studies of cadaveric specimens. MRI offers an abundance of novel methods for acquisition of data from living subjects and is revolutionizing the field of musculoskeletal modeling. The need to create accurate, individualized models of the musculoskeletal system is driving advances in MRI techniques including static imaging, dynamic imaging, diffusion imaging, body imaging, pulse-sequence design, and coil design. These techniques apply to imaging musculoskeletal anatomy, muscle architecture, joint motions, muscle moment arms, and muscle tissue deformations. Further advancements in image-based musculoskeletal modeling will expand the accuracy and utility of models used to study musculoskeletal and neuromuscular impairments.

Intrinsic muscle contribution to the metacarpophalangeal joint flexion moment of the middle, ring, and small fingers

PURPOSE

To analyze the relative contribution of the intrinsic muscles to the flexion moment potential of the metacarpophalangeal (MCP) joints of the middle, ring, and small fingers and to calculate the moment potential loss occurring with deep motor branch, low, or high ulnar nerve palsy or low median nerve palsy.

METHODS

Eleven fresh cadaver hands were used. A small wire sutured to each tendon was connected to an excursion transducer containing a constant-tension spring. The tendon excursion and the MCP joint rotation were measured simultaneously during 10 to 16 cycles of passive flexion/extension cyclic motion. The moment arm was calculated from the tendon excursion-joint rotation curve as the derivative of the curve. The flexion moment potential was calculated by multiplying the moment arm with the known tension fractions of the muscles.

RESULTS

When the MCP joint was at 0 degrees of flexion the relative moment potential contributions of the intrinsic muscles to MCP joint flexion were 8%, 13%, and 28% in the middle, ring, and small fingers, respectively. Moment potential losses were 7%, 13%, and 6% in the middle, ring, and small fingers, respectively, in deep motor branch ulnar nerve palsy. In low ulnar nerve palsy the losses were 7%, 13%, and 28%, respectively. In high ulnar nerve palsy they were 7%, 64%, and 82%, respectively. Low median nerve palsy, however, resulted in a moment potential loss at the middle finger MCP joint of less than 2%.

CONCLUSIONS

The relative contribution of the intrinsic muscles to the total flexion moment at the MCP joint was different for each finger. The small finger had a large intrinsic contribution, primarily because of the larger moment arms of the hypothenar muscles.

Human patellar tendon moment arm length: measurement considerations and clinical implications for joint loading assessment

Detailed understanding of the knee joint loading requires the calculation of muscle and joint forces in different conditions. In these applications the patellar tendon moment arm length is essential for the accurate estimation of the tibiofemoral joint loading. In this article, different methods that have been used to determine the patellar tendon moment arm length under in vivo and in vitro conditions are reviewed. The limitations and advantages associated with each of the methods are evaluated together with their applications in the different loading conditions that the musculoskeletal system is subjected to. The three main measurement methods that this review considers are the geometric method, the tendon excursion method and the direct load method. A comparison of relevant quantitative results is presented to asses the impact of the errors of each method on the quantification of the patellar tendon moment arm and the implications for joint loading assessment in clinical applications.

Relevance of mandibular helical axis analysis in functional and dysfunctional TMJs

The helical axis (HA), or motion screw, yields a comprehensive description of joint motion. The perspective representation of this axis clearly visualizes the regularity of mandibular functional movements (Yatabe et al. 1997. Journal of Dentist Research 76, 714-719 and Gallo et al. 2000. Journal of Dental Research 79, 1566-1572). In this study, the sensitivity of the HA representation was investigated relative to (a) irregularities in pathologic motion of clicking temporomandibular joints (TMJs) for jaw opening/closing and (b) differences in food bolus size and consistency for unilateral mastication in subjects with normal TMJs. Mandibular motion relative to the head was acquired using a jaw tracker with six degrees-of-freedom with a sampling frequency of 70 Hz. The HA was calculated according to an eigenvalue method (Spoor and Veldpaus 1980. Journal of Biomechanics 13, 391-393) and parameters were defined describing its position and orientation relative to the anatomy. We analyzed 39 subjects with unilateral or bilateral reciprocal TMJ clicking during jaw opening/closing and seven asymptomatic subjects during unilateral mastication of five different types of soft and hard food in two different bolus sizes. The results showed a greater variability of the HA parameters in the group of clicking joints than in the asymptomatic group: in particular, the area in which the HA moved was wider in clicking joints than in normal ones and the HA in clicking TMJs had a much greater fluctuation than in normal ones. During unilateral mastication, for more consistent food or a bigger bolus the HA showed a significantly greater excursion of the orientation parameters. Furthermore a significantly greater excursion of the dorsoventral and of the craniocaudal component of the distance vector from the HA to the condyle were found. The helical axis analysis of mandibular movements was sensitive to kinematic irregularities of the mandible due to an internal joint derangement as well as to differences in food bolus size and consistency.

Analysis of human mandibular mechanics based on screw theory and in vivo data

In this paper the mechanics of human mandibular function is described in terms of the associated screws. The two distinct, yet related features of jaw mechanics, involving the motion itself as well as the forces, are both functions of the anatomical constraints, namely the contact areas that exist within the temporomandibular joint, and the forces of the muscles and tendons that allow motion to occur. The relationships that exist between these two aspects of jaw-motion are identified in this paper showing that muscle forces can be uniquely represented in terms of the action screw. This new approach to analyzing the mechanics of jaw-motion also incorporates the previously studied motion screw or helical axis. A consistent dynamic model is formulated where the action screw is used to represent the action of the closing muscle forces while the moment arms of the muscle forces are determined about the motion screw representing mandibular kinematics. The action screw formulation is verified using in vivo motion data and MR image information for a single asymptomatic subject. The results confirm the feasibility of the method and its application in dental research. A general increase in the mechanical advantage of most muscles, in the distance between action and motion screws as well as in the expended energy towards the end of the jaw-closing phase was observed. Asymmetries in the distribution of muscle force magnitudes appeared to influence the resultant force and moment of the action screw but had little effect on its spatial location. The method presented is intended to facilitate understanding of mandibular function and dysfunction.

Imaging-based estimates of moment arm length in intact human muscle-tendons

The muscle-tendon moment arm length, i.e. the perpendicular distance from the muscle-tendon action line to the rotation centre of the joint that the muscle-tendon spans, is responsible for transforming muscle force and linear displacement to joint moment and rotation. In this paper, previous work on in vivo measurements of human muscle-tendon moment arms at rest and during isometric maximal voluntary contraction (MVC) is reviewed. The results obtained by actual measurements on 2-D magnetic resonance images indicate that the moment arm lengths of the Achilles and tibialis anterior tendons increase during MVC compared with rest by between 22% and 44%, due to (1) joint displacement, (2) muscle thickening and (3) stretching of collagenous structures mediating the action of tendon. However, moment arm length calculations based on the virtual work principle fail to show the above effect. Potentially severe mechanical limitations of the latter method as adapted under in vivo conditions raise questions about its validity during muscle contraction.

Three-dimensional CT imaging of flexor tendon ruptures in the hand and wrist

OBJECTIVE

The purpose of this study is to determine the applicability of 3D CT imaging in the evaluation of flexor tendon rupture in the hand and wrist.

DESIGN

Twenty-four digits in 22 patients (18 adults, 4 children) with a spectrum of finger flexion disturbances were investigated by a multidetector-row CT scanner, and diagnosed by 3D CT image with the volume rendering technique. The accuracy of the image diagnosis was confirmed operatively in 20 digits.

RESULTS

3D CT imaging gave a precise analysis in all adult cases. It clearly depicted the location of rupture and tendon stump. All of the 12 digits diagnosed from the images as tendon rupture were operated on, and the operational finding correlated well with the diagnosis based on the image. In the children, the image analysis was equivocal.

CONCLUSIONS

3D CT imaging can be useful when the diagnosis of flexor tendon rupture cannot be made based on trauma history and clinical examinations, and can be helpful in surgical planning.

Mandibular helical axis pathways during mastication

Condylar and incisor trajectories are often used for the study of mandibular movements. Condylar trajectories, however, depend on the location of the reference point and can be interpreted erroneously. In contrast, the helical axis analysis yields an unequivocal description of rigid body kinematics. The aim of this study was to analyze the mandibular helical axis during mastication. Seven subjects without signs and symptoms of craniomandibular disorders and with class I occlusion were recorded by means of the opto-electronic system Jaws-3D during unilateral mastication of bread cubes (2-cm side). The helical axis was computed every 14 ms with a rotation threshold of 1 . Parameters describing its spatial orientation and position relative to the condyles were calculated. The helical axis changed orientation and position more pronouncedly during the closing than during the opening phases of mastication. The orientation varied significantly from beginning to end of closing but not of opening, indicating less fluctuation of the helical axis on opening than on closing. Also, the distance dCP between helical axis and reference condylar point varied more significantly (p < 0.05) on the working than on the balancing side: On the working side, dCP decreased during both opening and closing, whereas on the balancing side, dCP increased only for closing. Furthermore, the helical axis pathway often showed a bowing ventrally to the balancing condyle, indicating that, during closing, the balancing condyle still translated backward while essentially only rotation occurred around the working condyle. Thus, the helical axis changed its position and orientation continuously during mastication.