A musculoskeletal model of the hand and wrist: model definition and evaluation

Abstract

To improve our understanding on the neuromechanics of finger movements, a comprehensive musculoskeletal model is needed. The aim of this study was to build a musculoskeletal model of the hand and wrist, based on one consistent data set of the relevant anatomical parameters. We built and tested a model including the hand and wrist segments, as well as the muscles of the forearm and hand in OpenSim. In total, the model comprises 19 segments (with the carpal bones modeled as one segment) with 23 degrees of freedom and 43 muscles. All required anatomical input data, including bone masses and inertias, joint axis positions and orientations as well as muscle morphological parameters (i.e. PCSA, mass, optimal fiber length and tendon length) were obtained from one cadaver of which the data set was recently published. Model validity was investigated by first comparing computed muscle moment arms at the index finger metacarpophalangeal (MCP) joint and wrist joint to published reference values. Secondly, the muscle forces during pinching were computed using static optimization and compared to previously measured intraoperative reference values. Computed and measured moment arms of muscles at both index MCP and wrist showed high correlation coefficients (r?=?0.88 averaged across all muscles) and modest root mean square deviation (RMSD?=?23% averaged across all muscles). Computed extrinsic flexor forces of the index finger during index pinch task were within one standard deviation of previously measured in-vivo tendon forces. These results provide an indication of model validity for use in estimating muscle forces during static tasks.     

Estimation of finger muscle tendon tensions and pulley forces during specific sport-climbing grip techniques

The present work displayed the first quantitative data of forces acting on tendons and pulleys during specific sport-climbing grip techniques. A three-dimensional static biomechanical model was used to estimate finger muscle tendon and pulley forces during the "slope" and the "crimp" grip. In the slope grip the finger joints are flexed, and in the crimp grip the distal interphalangeal (DIP) joint is hyperextended while the other joints are flexed. The tendons of the flexor digitorum profundus and superficialis (FDP and FDS), the extensor digitorum communis (EDC), the ulnar and radial interosseus (UI and RI), the lumbrical muscle (LU) and two annular pulleys (A2 and A4) were considered in the model. For the crimp grip in equilibrium conditions, a passive moment for the DIP joint was taken into account in the biomechanical model. This moment was quantified by relating the FDP intramuscular electromyogram (EMG) to the DIP joint external moment. Its intensity was estimated at a quarter of the external moment. The involvement of this parameter in the moment equilibrium equation for the DIP joint is thus essential. The FDP-to-FDS tendon-force ratio was 1.75:1 in the crimp grip and 0.88:1 in the slope grip. This result showed that the FDP was the prime finger flexor in the crimp grip, whereas the tendon tensions were equally distributed between the FDP and FDS tendons in the slope grip. The forces acting on the pulleys were 36 times lower for A2 in the slope grip than in the crimp grip, while the forces acting on A4 were 4 times lower. This current work provides both an experimental procedure and a biomechanical model that allows estimation of tendon tensions and pulley forces crucial for the knowledge about finger injuries in sport climbing.     

The effect of finger extensor mechanism on the flexor force during isometric tasks.

The role of the intrinsic finger flexor muscles was investigated during finger flexion tasks. A suspension system was used to measure isometric finger forces when the point of force application varied along fingers in a distal-proximal direction. Two biomechanical models, with consideration of extensor mechanism Extensor Mechanism Model (EMM) and without consideration of extensor mechanism Flexor Model (FM), were used to calculate forces of extrinsic and intrinsic finger flexors. When the point of force application was at the distal phalanx, the extrinsic flexor muscles flexor digitorum profundus, FDP, and flexor digitorum superficialis, FDS, accounted for over 80% of the summed force of all flexors, and therefore were the major contributors to the joint flexion at the distal interphalangeal (DIP), proximal interphalangeal (PIP), and metacarpophalangeal (MCP) joints. When the point of force application was at the DIP joint, the FDS accounted for more than 70% of the total force of all flexors, and was the major contributor to the PIP and MCP joint flexion. When the force of application was at the PIP joint, the intrinsic muscle group was the major contributor for MCP flexion, accounting for more than 70% of the combined force of all flexors. The results suggest that the effects of the extensor mechanism on the flexors are relatively small when the location of force application is distal to the PIP joint. When the external force is applied proximally to the PIP joint, the extensor mechanism has large influence on force production of all flexors. The current study provides an experimental protocol and biomechanical models that allow estimation of the effects of extensor mechanism on both the extrinsic and intrinsic flexors in various loading conditions, as well as differentiating the contribution of the intrinsic and extrinsic finger flexors during isometric flexion.     

Biomechanical Analysis of the Human Finger Extensor Mechanism during Isometric Pressing

This study investigated the effects of the finger extensor mechanism on the bone-to-bone contact forces at the interphalangeal and metacarpal joints and also on the forces in the intrinsic and extrinsic muscles during finger pressing. This was done with finger postures ranging from very flexed to fully extended. The role of the finger extensor mechanism was investigated by using two alternative finger models, one which omitted the extensor mechanism and another which included it. A six-camera three-dimensional motion analysis system was used to capture the finger posture during maximum voluntary isometric pressing. The fingertip loads were recorded simultaneously using a force plate system. Two three-dimensional biomechanical finger models, a minimal model without extensor mechanism and a full model with extensor mechanism (tendon network), were used to calculate the joint bone-to-bone contact forces and the extrinsic and intrinsic muscle forces. If the full model is assumed to be realistic, then the results suggest some useful biomechanical advantages provided by the tendon network of the extensor mechanism. It was found that the forces in the intrinsic muscles (interosseus group and lumbrical) are significantly reduced by 22% to 61% due to the action of the extensor mechanism, with the greatest reductions in more flexed postures. The bone-to-bone contact force at the MCP joint is reduced by 10% to 41%. This suggests that the extensor mechanism may help to reduce the risk of injury at the finger joints and also to moderate the forces in intrinsic muscles. These apparent biomechanical advantages may be a result of the extensor mechanism''s distinctive interconnected fibrous structure, through which the contraction of the intrinsic muscles as flexors of the MCP joint can generate extensions at the DIP and PIP joints.     

An open-source model and solution method to predict co-contraction in the finger

A novel open-source biomechanical model of the index finger with an electromyography (EMG)-constrained static optimization solution method are developed with the goal of improving co-contraction estimates and providing means to assess tendon tension distribution through the finger. The Intrinsic model has four degrees of freedom and seven muscles (with a 14 component extensor mechanism). A novel plugin developed for the OpenSim modelling software applied the EMG-constrained static optimization solution method. Ten participants performed static pressing in three finger postures and five dynamic free motion tasks. Index finger 3D kinematics, force (5, 15, 30 N), and EMG (4 extrinsic muscles and first dorsal interosseous) were used in the analysis. The Intrinsic model predicted co-contraction increased by 29% during static pressing over the existing model. Further, tendon tension distribution patterns and forces, known to be essential to produce finger action, were determined by the model across all postures. The Intrinsic model and custom solution method improved co-contraction estimates to facilitate force propagation through the finger. These tools improve our interpretation of loads in the finger to develop better rehabilitation and workplace injury risk reduction strategies.     

Quantification of fingertip force reduction in the forefinger following simulated paralysis of extensor and intrinsic muscles

Objective estimates of fingertip force reduction following peripheral nerve injuries would assist clinicians in setting realistic expectations for rehabilitating strength of grasp. We quantified the reduction in fingertip force that can be biomechanically attributed to paralysis of the groups of muscles associated with low radial and ulnar palsies. We mounted 11 fresh cadaveric hands (5 right, 6 left) on a frame, placed their forefingers in a functional posture (neutral abduction, 45° of flexion at the metacarpophalangeal and proximal interphalangeal joints, and 10° at the distal interphalangeal joint) and pinned the distal phalanx to a six-axis dynamometer. We pulled on individual tendons with tensions up to 25% of maximal isometric force of their associated muscle and measured fingertip force and torque output. Based on these measurements, we predicted the optimal combination of tendon tensions that maximized palmar force (analogous to tip pinch force, directed perpendicularly from the midpoint of the distal phalanx, in the plane of finger flexion–extension) for three cases: non-paretic (all muscles of forefinger available), low radial palsy (extrinsic extensor muscles unavailable) and low ulnar palsy (intrinsic muscles unavailable). We then applied these combinations of tension to the cadaveric tendons and measured fingertip output. Measured palmar forces were within 2% and 5° of the predicted magnitude and direction, respectively, suggesting tendon tensions superimpose linearly in spite of the complexity of the extensor mechanism. Maximal palmar forces for ulnar and radial palsies were 43 and 85% of non-paretic magnitude, respectively (p<0.05). Thus, the reduction in tip pinch strength seen clinically in low radial palsy may be partly due to loss of the biomechanical contribution of forefinger extrinsic extensor muscles to palmar force. Fingertip forces in low ulnar palsy were 9° further from the desired palmar direction than the non-paretic or low radial palsy cases (p<0.05).     

Anatomical variations of the extensor tendons to the fingers over the dorsum of the hand: a study of 50 hands and a review of the literature

The extensor tendons to the fingers were studied in dissections of 50 fresh cadaveric hands, and the divisions of the tendons, as well as the communications (juncturae), were analyzed. The pattern of distribution most frequently observed was as follows. The extensor digitorum communis provided one tendon to the index finger, one to the middle finger, two to the ring finger, and none to the little finger. The extensor indicis exhibited one tendon, whereas the extensor digiti minimi exhibited two tendons. The extensor indicis tendon was always observed to lack a junctura tendinum. The extensor indicis was absent in both hands of one cadaver. A tendon slip from the extensor digiti minimi to the ring finger was observed in one hand. All surgeons must bear in mind the existence of these variations when performing common tendon transfers.     

Effects of rotator cuff tears on muscle moment arms: a computational study

Rotator cuff tears cause morphologic changes to cuff tendons and muscles, which can alter muscle architecture and moment arm. The effects of these alterations on shoulder mechanical performance in terms of muscle force and joint strength are not well understood. The purpose of this study was to develop a three-dimensional explicit finite element model for investigating morphological changes to rotator cuff tendons following cuff tear. The subsequent objectives were to validate the model by comparing model-predicted moment arms to empirical data, and to use the model to investigate the hypothesis that rotator cuff muscle moment arms are reduced when tendons are divided along the force-bearing direction of the tendon. The model was constructed by extracting tendon, cartilage, and bone geometry from the male Visible Human data set. Infraspinatus and teres minor muscle and tendon paths were identified relative to the humerus and scapula. Kinetic and kinematic boundary conditions in the model replicated experimental protocols, which rotated the humerus from 45 degrees internal to 45 degrees external rotation with constant loads on the tendons. External rotation moment arms were calculated for two conditions of the cuff tendons: intact normal and divided tendon. Predicted moment arms were within the 1-99% confidence intervals of experimental data for nearly all joint angles and tendon sub-regions. In agreement with the experimental findings, when compared to the intact condition, predicted moment arms were reduced for the divided tendon condition. The results of this study provide evidence that one potential mechanism for the reduction in strength observed with cuff tear is reduction of muscle moment arms. The model provides a platform for future studies addressing mechanisms responsible for reduced muscle force and joint strength including changes to muscle length-tension operating range due to altered muscle and tendon excursions, and the effects of cuff tear size and location on moment arms and muscle forces.     

Estimation of instantaneous moment arms of lower-leg muscles

Muscle moment arms at the human knee and ankle were estimated from muscle length changes measured as a function of joint flexion angle in cadaver specimens. Nearly all lower-leg muscles were studied: extensor digitorum longus, extensor hallucis longus, flexor digitorum longus, flexor hallucis longus, gastrocnemius lateralis, gastrocnemius medialis, peroneus brevis, peroneus longus, peroneus tertius, plantaris, soleus, tibialis anterior, and tibialis posterior. Noise in measured muscle length was filtered by means of quintic splines. Moment arms of the mm. gastrocnemii appear to be much more dependent on joint flexion angles than was generally assumed by other investigators. Some consequences for earlier analyses are mentioned.     

The biomechanical model of the long finger extensor mechanism and its parametric identification

The extensor mechanism of the finger is a structure transmitting the forces from several muscles to the finger joints. Force transmission in the extensor mechanism is usually modeled by equations with constant coefficients which are determined experimentally only for finger extension posture. However, the coefficient values change with finger flexion because of the extensor mechanism deformation. This induces inaccurate results for any other finger postures. We proposed a biomechanical model of the extensor mechanism represented as elastic strings. The model includes the main tendons and ligaments. The parametric identification of the model in extension posture was performed to match the distribution of the forces among the tendons to experimental data. The parametrized model was used to simulate three degrees of flexion. Furthermore, the ability of the model to reproduce how the force distribution in simulated extensor mechanism changes according to the muscle forces was also demonstrated. The proposed model could be used to simulate the extensor mechanism for any physiological finger posture for which the coefficients involved in the equations are unknown.     

Finger joint coordination during tapping

We investigated finger joint coordination during tapping by characterizing joint kinematics and torques in terms of muscle activation patterns and energy profiles. Six subjects tapped with their index finger on a computer keyswitch as if they were typing on the middle row of a keyboard. Fingertip force, keyswitch position, kinematics of the metacarpophalangeal (MCP) and the proximal and distal interphalangeal (IP) joints, and intramuscular electromyography of intrinsic and extrinsic finger muscles were measured simultaneously. Finger joint torques were calculated based on a closed-form Newton–Euler inverse dynamic model of the finger. During the keystroke, the MCP joint flexed and the IP joints extended before and throughout the loading phase of the contact period, creating a closing reciprocal motion of the finger joints. As the finger lifted, the MCP joint extended and the interphalangeal (IP) joints flexed, creating an opening reciprocal motion. Intrinsic finger muscle and extrinsic flexor activities both began after the initiation of the downward finger movement. The intrinsic finger muscle activity preceded both the IP joint extension and the onset of extrinsic muscle activity. Only extrinsic extensor activity was present as the finger was lifted. While both potential energy and kinetic energy are present and large enough to overcome the work necessary to press the keyswitch, the motor control strategies utilize the muscle forces and joint torques to ensure a successful keystroke.     

Knee muscle moment arms from MRI and from tendon travel.

We tested magnetic resonance imaging (MRI) as a means to collect geometric data for moment arm estimation. A knee specimen in five successive flexion postures was scanned by MRI, while simultaneously tendon positions of loaded muscles were measured (long head of biceps femoris, lateral and medial gastrocnemius, gracilis, rectus femoris, sartorius, semimembranosus, semitendinosus, and tensor fasciae latae). Discrete rotation centres were derived from MRI pictures. Moment arms were estimated as the distances from these centres to the tendons. The ratio of tendon travel over the increment of joint angulation was the alternative, more reliable estimate of the moment arm. An important principal shortcoming of MRI is the impossibility of accounting for force distribution in taut tissue. As a consequence, for some muscles, considerable inaccuracies in moment arm estimation are found in a relatively small range of joint angulation (up to about 30% for the rectus femoris and semimembranosus). For the tensor fasciae latae, the moment arm cannot be estimated by MRI, while the estimate by tendon travel is unreliable owing to the deformability and attachments of the fascia lata.     

Tendon displacements during voluntary and involuntary finger movements

In the human hand, independent movement control of individual fingers is limited. One potential cause for this is mechanical connections between the tendons and muscle bellies corresponding to the different fingers. The aim of this study was to determine the tendon displacement of the flexor digitorum superficialis (FDS) of both the instructed and the neighboring, non-instructed fingers during single finger flexion movements. In nine healthy subjects (age 22–29 years), instructed and non-instructed FDS finger tendon displacement of the index, middle and ring finger was measured using 2D ultrasound analyzed with speckle tracking software in two conditions: active flexion of all finger joints with all fingers free to move and active flexion while the non-instructed fingers were restricted. Our results of the free movement protocol showed an average tendon displacement of 27 mm for index finger flexion, 21 mm for middle finger flexion and 17 mm for ring finger flexion. Displacements of the non-instructed finger tendons (≈12 mm) were higher than expected based of the amount of non-instructed finger movement. In the restricted protocol, we found that, despite minimal joint movements, substantial non-instructed finger tendon displacement (≈9 mm) was still observed, which was interpreted as a result of tendon strain. When this strain component was subtracted from the tendon displacement of the non-instructed fingers during the free movement condition, the relationship between finger movement and tendon displacement of the instructed and non-instructed finger became comparable. Thus, when studying non-instructed finger tendon displacement it is important to take tendon strain into consideration.     

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.     

Static and dynamic human flexor tendon–pulley interaction

The aim of the study was to investigate the influence of a preceding flexion or extension movement on the static interaction of human finger flexor tendons and pulleys concerning flexion torque being generated. Six human fresh frozen cadaver long fingers were mounted in an isokinetic movement device for the proximal interphalangeal (PIP) joint. During flexion and extension movement both flexor tendons were equally loaded with 40 N while the generated moment was depicted simultaneously at the fingertip. The movement was stopped at various positions of the proximal interphalangeal joint to record dynamic and static torque. The static torque was always greater after a preceding extension movement compared to a preceding flexion movement in the corresponding same position of the joint. This applied for the whole arc of movement of 0–105°. The difference between static extension and flexion torque was maximal 11% in average at about 83° of flexion. Static torque was always smaller than dynamic torque during extension movement and always greater than dynamic torque during flexion movement. The kind of preceding movement therefore showed an influence to the torque being generated in the proximal interphalangeal joint. The effect could be simulated on a mechanical finger device.     

Studies on the tendinous compartments of the extensor muscles on the back of the human hand and their tendon sheaths. I

In 47 dissected right and left hands of adults of both sexes, kept in a moist condition, significant practical-clinical investigations of the transitional zone between forearm and hand were undertaken. In particular it was sought to determine the characteristic sizes of the extensor retinaculum, the osteofibrous tunnels, the insertion tendons of the hand and finger extensor muscles, and their tendon sheaths. Together with the palmar carpal ligament, the 2 to 3 cm wide extensor retinaculum annularly surrounds the whole circumference of the carpus. It extends obliquely from radial-proximal to ulnar-distal and conducts the extensor tendons over the carpal articulations. According to recent studies, it is divided into a superficial and a deep fibrous layer. From the undermost surface, vertical and oblique septa run to the plane of the forearm and carpal bones. They separate the fibrous portion of the 6 tendinous compartments of the dorsum manus. In 8.5% of cases, an accessory and completely independent tunnel of the extensor pollicis brevis muscle exists in the material investigated, and in 2.2% of cases, there is an additional tunnel for the extensor carpi radialis muscle. Hence, one occasionally finds 8 separate osteofibrous gliding compartments for the extensor muscles in the dorsal hand region. The longest tunnel belongs, as a rule, to the extensor digiti minimi muscle, whilst the widest pertains to the extensor digitorum muscle. Within the tunnel and also proximal and distal to it, the extensor tendons are surrounded by synovial sheaths. Because of its wide encroachment on the dorsum of the hand, the insertion tendon of the extensor digiti minimi muscle possesses the longest tendon sheath, measuring 68.8 mm. The next longest sheath, that of the extensor pollicis longus muscle, which measures 56.2 mm, begins further proximal to the gap of the radiocarpal articulation. In 12.8% of cases, there are divided sheaths of the abductor pollicis longus and of the extensor pollicis brevis muscle. The tendon sheath of both extensor carpi radiales muscles is frequently divided into 2 compartments which, in 2/3 of cases, communicate. The compartment of the extensor carpi radialis brevis muscle, in 91.5% of cases, shares a window-like opening with the roof of the synovial vagina of the extensor pollicis longus muscle. The tendon sheath of the long extensor muscles of the fingers originates 5 mm proximal to the forearm border of the extensor retinaculum and has a communal recess. The IVth tendon sheath opens distally and splays out in a glove-like manner to some distal recesses.(ABSTRACT TRUNCATED AT 400 WORDS)     

In vivo forces generated by finger flexor muscles do not depend on the rate of fingertip loading during an isometric task

Risk factors for activity-related tendon disorders of the hand include applied force, duration, and rate of loading. Understanding the relationship between external loading conditions and internal tendon forces can elucidate their role in injury and rehabilitation. The goal of this investigation is to determine whether the rate of force applied at the fingertip affects in vivo forces in the flexor digitorum profundus (FDP) tendon and the flexor digitorum superficialis (FDS) tendon during an isometric task. Tendon forces, recorded with buckle force transducers, and fingertip forces were simultaneously measured during open carpal tunnel surgery as subjects (N=15) increased their fingertip force from 0 to 15N in 1, 3, and 10s. The rates of 1.5, 5, and 15N/s did not significantly affect FDP or FDS tendon to fingertip force ratios. For the same applied fingertip force, the FDP tendon generated more force than the FDS. The mean FDP to fingertip ratio was 2.4+/-0.7 while the FDS to tip ratio averaged 1.5+/-1.0 (p<0.01). The fine motor control needed to generate isometric force ramps at these specific loading rates probably required similar high activation levels of multiple finger muscles in order to stabilize the finger and control joint torques at the force rates studied. Therefore, for this task, no additional increase in muscle force was observed at higher rates. These findings suggest that for high precision, isometric pinch maneuvers under static finger conditions, tendon forces are independent of loading rate.     

Moment arms of the human digital flexors

For the extrinsic hand flexors (flexor digitorum profundus, FDP; flexor digitorum superficialis, FDS; flexor pollicis longus, FPL), moment arm corresponds to the tendon's distance from the center of the metacarpalphalangeal (MP), proximal interphalangeal (PIP), or distal interphalangeal (DIP) joint. The clinical value of establishing accurate moment arms has been highlighted for biomechanical modeling, the development of robotic hands, designing rehabilitation protocols, and repairing flexor tendon pulleys (Brand et al., 1975; An et al., 1983; Thompson and Giurintano, 1989; Deshpande et al., 2010; Wu et al., 2010). In this study, we define the moment arms for all of the extrinsic flexor tendons of the hand across all digital joints for all digits in cadaveric hands.     

Using EMG data to constrain optimization procedure improves finger tendon tension estimations during static fingertip force production

Determining tendon tensions of the finger muscles is crucial for the understanding and the rehabilitation of hand pathologies. Since no direct measurement is possible for a large number of finger muscle tendons, biomechanical modelling presents an alternative solution to indirectly evaluate these forces. However, the main problem is that the number of muscles spanning a joint exceeds the number of degrees of freedom of the joint resulting in mathematical under-determinate problems. In the current study, a method using both numerical optimization and the intra-muscular electromyography (EMG) data was developed to estimate the middle finger tendon tensions during static fingertip force production. The method used a numerical optimization procedure with the muscle stress squared criterion to determine a solution while the EMG data of three extrinsic hand muscles serve to enforce additional inequality constraints. The results were compared with those obtained with a classical numerical optimization and a method based on EMG only. The proposed method provides satisfactory results since the tendon tension estimations respected the mechanical equilibrium of the musculoskeletal system and were concordant with the EMG distribution pattern of the subjects. These results were not observed neither with the classical numerical optimization nor with the EMG-based method. This study demonstrates that including the EMG data of the three extrinsic muscles of the middle finger as inequality constraints in an optimization process can yield relevant tendon tensions with regard to individual muscle activation patterns, particularly concerning the antagonist muscles.