Estimation of the effective static moment arms of the tendons in the index finger extensor mechanism

A novel technique to estimate the contribution of finger extensor tendons to joint moment generation was proposed. Effective static moment arms (ESMAs), which represent the net effects of the tendon force on joint moments in static finger postures, were estimated for the 4 degrees of freedom (DOFs) in the index finger. Specifically, the ESMAs for the five tendons contributing to the finger extensor apparatus were estimated by directly correlating the applied tendon force to the measured resultant joint moments in cadaveric hand specimens. Repeated measures analysis of variance revealed that the finger posture, specifically interphalangeal joint angles, had significant effects on the measured ESMA values in 7 out of 20 conditions (four DOFs for each of the five muscles). Extensor digitorum communis and extensor indicis proprius tendons were found to have greater MCP ESMA values when IP joints are flexed, whereas abduction ESMAs of all muscles except extensor digitorum profundus were mainly affected by MCP flexion. The ESMAs were generally smaller than the moment arms estimated in previous studies that employed kinematic measurement techniques. Tendon force distribution within the extensor hood and dissipation into adjacent structures are believed to contribute to the joint moment reductions, which result in smaller ESMA values.     

Estimating in vivo passive forces of the index finger muscles: Exploring model parameters

We compared predicted passive finger joint torques from a biomechanical model that includes the exponential passive muscle force–length relationship documented in the literature with finger joint torques estimated from measures in ten adult volunteers. The estimated finger joint torques were calculated from measured right index fingertip force, joint postures, and anthropometry across 18 finger and wrist postures with the forearm muscles relaxed. The biomechanical model predicting passive finger joint torques included three extrinsic and three intrinsic finger muscles. The values for the predicted passive joint torques were much larger than the values calculated from the fingertip force and posture measures with an average RMS error of 7.6 N cm. Sensitivity analysis indicated that the predicted joint torques were most sensitive to passive force–length model parameters compared to anthropometric and postural parameters. Using Monte Carlo simulation, we determined a new set of values for the passive force–length model parameters that reduced the differences between the joint torques calculated from the two methods to an average RMS value of 0.5 N cm, a 94% average improvement of error from the torques predicted using the existing data. These new parameter values did vary across individuals; however, using an average set for the parameter values across subjects still reduced the average RMS difference to 0.8 N cm. These new parameters may improve dynamic modeling of the finger during sub-maximal force activities and are based on in vivo data rather than traditional in vitro data.     

A musculoskeletal model of the human lower extremity: the effect of muscle, tendon, and moment arm on the moment-angle relationship of musculotendon actuators at the hip, knee, and ankle

We have developed a musculoskeletal model of the human lower extremity for computer simulation studies of musculotendon function and muscle coordination during movement. This model incorporates the salient features of muscle and tendon, specifies the musculoskeletal geometry and musculotendon parameters of 18 musculotendon actuators, and defines the active isometric moment of these actuators about the hip, knee, and ankle joints in the sagittal plane. We found that tendon slack length, optimal muscle-fiber length, and moment arm are different for each actuator, thus each actuator develops peak isometric moment at a different joint angle. The joint angle where an actuator produces peak moment does not necessarily coincide with the joint angle where: (1) muscle force peaks, (2) moment arm peaks, or (3) the in vivo moment developed by maximum voluntary contractions peaks. We conclude that when tendon is neglected in analyses of musculotendon force or moment about joints, erroneous predictions of human musculotendon function may be stated, not only in static situations as studied here, but during movement as well.     

Development of a dynamic index finger and thumb model to study impairment

Modeling of the human hand provides insight for explaining deficits and planning treatment following injury. Creation of a dynamic model, however, is complicated by the actions of multi-articular tendons and their complex interactions with other soft tissues in the hand. This study explores the creation of a musculoskeletal model, including the thumb and index finger, to explore the effects of muscle activation deficits. The OpenSim model utilizes physiological axes of rotation at all joints, passive joint torques, and appropriate moment arms. The model was validated through comparison with kinematic and kinetic experimental data. Simulated fingertip forces resulting from modeled musculotendon loading largely fell within one standard deviation of experimental ranges for most index finger and thumb muscles, although agreement in the sagittal plane was generally better than for the coronal plane. Input of experimentally obtained electromyography data produced the expected simulated finger and thumb motion. Use of the model to predict the effects of activation deficits on pinch force production revealed that the intrinsic muscles, especially first dorsal interosseous (FDI) and adductor pollicis (ADP), had a substantial impact on the resulting fingertip force. Reducing FDI activation, such as might occur following stroke, altered fingertip force direction by up to 83° for production of a dorsal fingertip force; reducing ADP activation reduced force production in the thumb by up to 62%. This validated model can provide a means for evaluating clinical interventions.     

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.     

Finger joint force minimization in pianists using optimization techniques

A numerical optimization procedure was used to determine finger positions that minimize and maximize finger tendon and joint force objective functions during piano play. A biomechanical finger model for sagittal plane motion, based on finger anatomy, was used to investigate finger tendon tensions and joint reaction forces for finger positions used in playing the piano. For commonly used piano key strike positions, flexor and intrinsic muscle tendon tensions ranged from 0.7 to 3.2 times the fingertip key strike force, while resultant inter-joint compressive forces ranged from 2 to 7 times the magnitude of the fingertip force. In general, use of a curved finger position, with a large metacarpophalangeal joint flexion angle and a small proximal interphalangeal joint flexion angle, reduces flexor tendon tension and resultant finger joint force.     

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.     

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).     

Method of determination of three dimensional index finger moment arms and tendon lines of action using high resolution MRI scans

High-resolution MRI scans, in conjunction with CAD software, were used to determine the three-dimensional moment arms and force vector direction cosines for 11 structures passing the interphalangeal and metacarpophalangeal joints of the index finger. The results are presented for five different angles of joint flexion for a single subject. The moment arm data obtained differ from previous studies, where results have been derived from tendon excursion techniques or geometrical models. These dissimilarities have been accounted for by the differences in experimental techniques.     

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.     

The sensitivity of endpoint forces produced by the extrinsic muscles of the thumb to posture

This study utilizes a biomechanical model of the thumb to estimate the force produced at the thumb-tip by each of the four extrinsic muscles. We used the principle of virtual work to relate joint torques produced by a given muscle force to the resulting endpoint force and compared the results to two separate cadaveric studies. When we calculated thumb-tip forces using the muscle forces and thumb postures described in the experimental studies, we observed large errors. When relatively small deviations from experimentally reported thumb joint angles were allowed, errors in force direction decreased substantially. For example, when thumb posture was constrained to fall within ±15° of reported joint angles, simulated force directions fell within experimental variability in the proximal–palmar plane for all four muscles. Increasing the solution space from ±1° to an unbounded space produced a sigmoidal decrease in error in force direction. Changes in thumb posture remained consistent with a lateral pinch posture, and were generally consistent with each muscle’s function. Altering thumb posture alters both the components of the Jacobian and muscle moment arms in a nonlinear fashion, yielding a nonlinear change in thumb-tip force relative to muscle force. These results explain experimental data that suggest endpoint force is a nonlinear function of muscle force for the thumb, support the continued use of methods that implement linear transformations between muscle force and thumb-tip force for a specific posture, and suggest the feasibility of accurate prediction of lateral pinch force in situations where joint angles can be measured accurately.     

Biomechanical properties of the crimp grip position in rock climbers

Rock climbers are often using the unique crimp grip position to hold small ledges. Thereby the proximal interphalangeal (PIP) joints are flexed about 90 degrees and the distal interphalangeal joints are hyperextended maximally. During this position of the finger joints bowstringing of the flexor tendon is applying very high load to the flexor tendon pulleys and can cause injuries and overuse syndromes. The objective of this study was to investigate bowstringing and forces during crimp grip position. Two devices were built to measure the force and the distance of bowstringing and one device to measure forces at the fingertip. All measurements of 16 fingers of four subjects were made in vivo. The largest amount of bowstringing was caused by the flexor digitorum profundus tendon in the crimp grip position being less using slope grip position (PIP joint extended). During a warm-up, the distance of bowstringing over the distal edge of the A2 pulley increased by 0.6mm (30%) and was loaded about 3 times the force applied at the fingertip during crimp grip position. Load up to 116N was measured over the A2 pulley. Increase of force in one finger holds by the quadriga effect was shown using crimp and slope grip position.     

Effect of object width on muscle and joint forces during thumb-index finger grasping

The objective of this study was to identify the impact of modifying the object width on muscle and joint forces while gripping objects. The experimental protocol consisted to maintain horizontally five objects of different widths (3.5, 4.5, 5.5, 6.5, and 7.5 cm) with a thumb-index finger grip. Subjects were required to grasp spontaneously the object without any instruction regarding the grip force (GF) to apply. A biomechanical model of thumb-index finger pinch was developed to estimate muscle and joint forces. This model included electromyography, fingertip force, and kinematics data as inputs. The finger joint postures and the GF varied across the object widths. The estimated muscle forces also varied significantly according to the object width. Interestingly, we observed that the muscle force/GF ratios of major flexor muscles remain particularly stable with respect to the width whereas other muscle ratios differed largely. This may argue for a control strategy in which the actions of flexors were preserved in spite of change in joint postures. The estimated joint forces tended to increase with object width and increased in the distal-proximal sense. Overall, these results are of importance for the ergonomic design of handheld objects and for clinical applications.     

Modelling tendon excursions and moment arms of the finger flexors: anatomic fidelity versus function

A detailed musculoskeletal model of the human hand is needed to investigate the pathomechanics of tendon disorders and carpal tunnel syndrome. The purpose of this study was to develop a biomechanical model with realistic flexor tendon excursions and moment arms. An existing upper extremity model served as a starting point, which included programmed movement of the index finger. Movement capabilities were added for the other fingers. Metacarpophalangeal articulations were modelled as universal joints to simulate flexion/extension and abduction/adduction while interphalangeal articulations used hinges to represent flexion. Flexor tendon paths were modelled using two approaches. The first method constrained tendons with control points, representing annular pulleys. The second technique used wrap objects at the joints as tendon constraints. Both control point and joint wrap models were iteratively adjusted to coincide with tendon excursions and moment arms from a anthropometric regression model using inputs for a 50th percentile male. Tendon excursions from the joint wrap method best matched the regression model even though anatomic features of the tendon paths were not preserved (absolute differences: mean<0.33 mm, peak<0.74 mm). The joint wrap model also produced similar moment arms to the regression (absolute differences: mean<0.63 mm, peak<1.58 mm). When a scaling algorithm was used to test anthropometrics, the scaled joint wrap models better matched the regression than the scaled control point models. Detailed patient-specific anatomical data will improve model outcomes for clinical use; however, population studies may benefit from simplified geometry, especially with anthropometric scaling.     

Moment arms and musculotendon lengths estimation for a three-dimensional lower-limb model

This paper presents a set of polynomial expressions that can be used as regression equations to estimate length and three-dimensional moment arms of 43 lower-limb musculotendon actuators. These equations allow one to find, at a low computational cost, the musculotendon geometric parameters required for numerical simulation of large musculoskeletal models. Nominal values for these biomechanical parameters were established using a public-domain musculoskeletal model of the lower limb (IEEE Trans. Biomed. Eng. 37 (1990) 757). To fit these nominal values, regression equations with different levels of complexity were generated, based on the number of generalized coordinates of the joints spanned by each musculotendon actuator. Least squares fitting was used to identify regression equation coefficients. The goodness of the fit and confidence intervals were assessed, and the best fitting equations selected.     

Motor control theories improve biomechanical model of the hand for finger pressing tasks

BackgroundBiomechanical models are a useful tool to estimate tendon tensions. Unfortunately, in previous fingers' models, each finger acts independently from the others. This is contradictory with hand motor control theories which show that fingers are functionally linked in order to balance the wrist/forearm joint with minimal tendon tensions. (i.e. principle of minimization of the secondary moments). We propose to adapt a hand biomechanical model according to this principle by including the wrist joint. We will determine whether the finger tendon tensions changed with the wrist joint added to the model.MethodsTwo models have been tested: one considering fingers independently (model A) and one with the fingers mechanically linked by the inclusion of the wrist balance (model B). A single set of data, additional results from the literature and in-vivo values have been used to compare the results.ResultsModel A corroborates previous results in the literature. Contrast results were obtained with model B, especially for the Ring and Little fingers. Different tendon tensions were obtained, particularly, in finger extensor muscles critical to balance the wrist.DiscussionWe discuss the biomechanical results in accordance with the hand/finger motor control theories. It appears that the wrist joint balance is critical for finger tendon tension estimation. When including the wrist joint into finger models, the tendon tension estimations agree well with the minimization of secondary moments and the force deficit.     

An improved multi-joint EMG-assisted optimization approach to estimate joint and muscle forces in a musculoskeletal model of the lumbar spine

Muscle force partitioning methods and musculoskeletal system simplifications are key modeling issues that can alter outcomes, and thus change conclusions and recommendations addressed to health and safety professionals. A critical modeling concern is the use of single-joint equilibrium to estimate muscle forces and joint loads in a multi-joint system, an unjustified simplification made by most lumbar spine biomechanical models. In the context of common occupational tasks, an EMG-assisted optimization method (EMGAO) is modified in this study to simultaneously account for the equilibrium at all lumbar joints (M-EMGAO). The results of this improved approach were compared to those of its conventional single-joint equivalent (S-EMGAO) counterpart, the latter method being applied to the same lumbar joints but one at a time. Despite identical geometrical configurations and passive contributions used in both models, computed outcomes clearly differed between single- and multi-joint methods, especially at larger trunk flexed postures and during asymmetric lifting. Moreover, muscle forces predicted by L5-S1 single-joint analyses do not maintain mechanical equilibrium at other spine joints crossed by the same muscles. Assuming that the central nervous system does not attempt to balance the external moments one joint at a time and that a given muscle cannot exert different forces at different joints, the proposed multi-joint method represents a substantial improvement over its single-joint counterpart. This improved approach, hence, resolves trunk muscle forces with biological integrity but without compromising mechanical equilibrium at the lumbar joints.     

The contribution of the wrist, elbow and shoulder joints to single-finger tapping

We aimed to determine the role of the wrist, elbow and shoulder joints to single-finger tapping. Six human subjects tapped with their index finger at a rate of 3 taps/s on a keyswitch across five conditions, one freestyle (FS) and four instructed tapping strategies. The four instructed conditions were to tap on a keyswitch using the finger joint only (FO), the wrist joint only (WO), the elbow joint only (EO), and the shoulder joint only (SO). A single-axis force plate measured the fingertip force. An infra-red active-marker three-dimensional motion analysis system measured the movement of the fingertip, hand, forearm, upper arm and trunk. Inverse dynamics estimated joint torques for the metacarpal-phalangeal (MCP), wrist, elbow, and shoulder joints. For FS tapping 27%, 56%, and 18% of the vertical fingertip movement were a result of flexion of the MCP joint and wrist joint and extension of the elbow joint, respectively. During the FS movements the net joint powers between the MCP, wrist and elbow were positively correlated (correlation coefficients between 0.46 and 0.76) suggesting synergistic efforts. For the instructed tapping strategies (FO, WO, EO, and SO), correlations decreased to values below 0.35 suggesting relatively independent control of the different joints. For FS tapping, the kinematic and kinetic data indicate that the wrist and elbow contribute significantly, working in synergy with the finger joints to create the fingertip tapping task.     

Normal force distribution and posture of a hand pressing on a flat surface

Hand strength data are needed to understand and predict hand postures and finger loads while placing the hand on an object or surface. This study aims to analyze the effect of hand posture and surface orientation on hand force while pressing a flat surface. Twelve participants, 6 females and 6 males ages 19–25, performed three exertions (100%, 30% and 10% MVC- Maximum Voluntary Contraction) perpendicular to a plate in 4 angles (−45°, 0°, 45° and 90° with respect to the horizontal plane) at elbow height. Exertions involved pushing in two postures: (1) whole hand and (2) constrained to only using the fingertips. Inter-digit joint angles were recorded to map hand and finger motions and estimate joint moments for each condition. Participants exerted twice the force when pushing with whole hand vs. fingertips. 72–75% of the total force was exerted over the base of the palm, while only 11–13% with the thumb for exertions at 90°, 45° or 0° plate angles. Males maximum force for pushing at 0°, 45° and 90° plates averaged 49% higher than females for the whole hand and 62% for the fingertips (p < 0.01). There was no significant sex difference (p > 0.05) for the −45° plate. Thumb joint loads were generally higher than the other individual fingers (p < 0.05) in all % MVC and accounted for 12% of total force during whole hand exertions. On average, joint moments were 30% higher during fingertip conditions vs. whole hand. Thumb and finger joint moment magnitudes when pushing the plate at 100% MVC indicated that Metacarpophalangeal (MCP) joint moments were higher (p < 0.05) than Distal Interphalangeal joints (DIP) and Proximal Interphalangeal joints (PIP) under whole hand and fingertips conditions.     

Balancing a force on the fingertip of a two-dimensional finger model without intrinsic muscles

A slightly flexed human middle finger can balance an external force on the fingertip. Internal stabilization is also possible, which means that the externally unloaded finger can be kept stiff. We want to analyse whether in these situations the intrinsic hand muscles are needed. Distances from tendons to flexion axes are taken from the literature and are substituted in the moment equilibrium equations of a two-dimensional finger model. Diagrams illustrate the statically indeterminate problem of solving tendon forces. The possibilities for equilibrium without intrinsics appear to depend mainly on four tendon-to-joint distances. These distances determine to which of two groups a finger belongs: (1) one in which intrinsics are not necessary for internal stabilization nor for balancing a force on the fingertip in any direction in the sagittal plane; (2) one in which, without intrinsics, internal stabilization is impossible and only dorso-distally directed forces on the fingertip can be balanced.