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.     

Plantarflexor moment arms estimated from tendon excursion in vivo are not strongly correlated with geometric measurements

Geometric and tendon excursion methods have both been used extensively for estimating plantarflexor muscle moment arm in vivo. Geometric measures often utilize magnetic resonance imaging, which can be costly and impractical for many investigations. Estimating moment arm from tendon excursion measured with ultrasonography may provide a cost-effective alternative to geometric measures of moment arm, but how well such measures represent geometry-based moment arms remains in question. The purpose of this study was to determine whether moment arms from tendon excursion can serve as a surrogate for moment arms measured geometrically. Magnetic resonance and ultrasound imaging were performed on 19 young male subjects to quantify plantarflexor moment arm based on geometric and tendon excursion paradigms, respectively. These measurements were weakly correlated that approached statistical significance (R² = 0.21, p = 0.052), and moment arm from tendon excursion under-approximated geometric moment arm by nearly 40% (p < 0.001). This weak correlation between methods is at odds with a prior report (N = 9) of a strong correlation (R² = 0.94) in a similar study. Therefore, we performed 92,378 regression analyses (19 choose 9) to determine if such a strong correlation existed in our study population. We found that certain sub-populations of the current study generated similarly strong coefficients of determination (R² = 0.92), but 84% of all analyses revealed no correlation (p > 0.05). Our results suggest that the moment arms from musculoskeletal geometry cannot be otherwise obtained by simply scaling moment arms estimated from tendon excursion.     

Biarticular hip extensor and knee flexor muscle moment arms of the feline hindlimb

Moment arms are important for understanding muscular behavior and for calculating internal muscle forces in musculoskeletal simulations. Biarticular muscles cross two joints and have moment arms that depend on the angle of both joints the muscles cross. The tendon excursion method was used to measure the joint angle-dependence of hamstring (biceps femoris, semimembranosus and semitendinosus) moment arm magnitudes of the feline hindlimb at the knee and hip joints. Knee angle influenced hamstring moment arm magnitudes at the hip joint; compared to a flexed knee joint, the moment arm for semimembranosus posterior at the hip was at most 7.4 mm (25%) larger when the knee was extended. On average, hamstring moment arms at the hip increased by 4.9 mm when the knee was more extended. In contrast, moment arm magnitudes at the knee varied by less than 2.8 mm (mean=1.6 mm) for all hamstring muscles at the two hip joint angles tested. Thus, hamstring moment arms at the hip were dependent on knee position, while hamstring moment arms at the knee were not as strongly associated with relative hip position. Additionally, the feline hamstring muscle group had a larger mechanical advantage at the hip than at the knee joint.     

Tendon excursion and gliding: clinical impacts from humble concepts

As integral components of the musculoskeletal system, the primary function is transmission of muscle forces to the skeletal system. Proper excursion and gliding of the tendon determine the efficiency of this function. Studies of the tendon excursion and gliding based on two simple mechanical concepts have resulted in several significant clinical implications.     

A comprehensive and volumetric musculoskeletal model for the dynamic simulation of the shoulder function

We present a volumetric and extensive finite element model of the shoulder usable in the context of inverse control, in which the scapula is left unconstrained on the ribcage. Such a model allows for exploring various shoulder movements, which are essential for making patient-specific decisions. The proposed model consists of 23 volumetric muscles parts modelled using the finite element method. The glenohumeral, acromioclavicular and sternoclavicular joints are modelled with soft ball-socket constraints. The musculoskeletal model can be controlled by a tracking-based algorithm, finding the excitations values in the muscles needed to follow some target points. The moment arms obtained during abduction and rotation are compared with the literature, which includes results from cadaveric data and a fine FE model of the rotator cuff and the deltoid. We simulated the paralysis of serratus anterior, a main reason of scapular winging, and compared it with its physiological counterpart. A deficiency in the range of motion as well as a reduction in upward rotation were observed, which both corroborate clinical observations. This is one of the most comprehensive model of the shoulder, which can be used to study complex pathologies of the shoulder and their impact on functional outcome such as range-of-motion.     

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.     

An algorithm for automated analysis of ultrasound images to measure tendon excursion in vivo

The accuracy of an algorithm for the automated tracking of tendon excursion from ultrasound images was tested in three experiments. Because the automated method could not be tested against direct measurements of tendon excursion in vivo, an indirect validation procedure was employed. In one experiment, a wire "phantom" was moved a known distance across the ultrasound probe and the automated tracking results were compared with the known distance. The excursion of the musculotendinous junction of the gastrocnemius during frontal and sagittal plane movement of the ankle was assessed in a single cadaver specimen both by manual tracking and with a cable extensometer sutured to the gastrocnemius muscle. A third experiment involved estimation of Achilles tendon excursion in vivo with both manual and automated tracking. Root mean squared (RMS) error was calculated between pairs of measurements after each test. Mean RMS errors of less than 1 mm were observed for the phantom experiments. For the in vitro experiment, mean RMS errors of 8-9% of the total tendon excursion were observed. Mean RMS errors of 6-8% of the total tendon excursion were found in vivo. The results indicate that the proposed algorithm accurately tracks Achilles tendon excursion, but further testing is necessary to determine its general applicability.     

A two-muscle,continuum-mechanical forward simulation of the upper limb

By following the common definition of forward-dynamics simulations, i.e. predicting movement based on (neural) muscle activity, this work describes, for the first time, a forward-dynamics simulation framework of a musculoskeletal system, in which all components are represented as continuous, three-dimensional, volumetric objects. Within this framework, the mechanical behaviour of the entire muscle–tendon complex is modelled as a nonlinear hyperelastic material undergoing finite deformations. The feasibility and the full potential of the proposed forward-dynamics simulation framework is demonstrated on a two-muscle, three-dimensional, continuum-mechanical model of the upper limb. The musculoskeletal model consists of three bones, i.e. humerus, ulna, and radius, an one-degree-of-freedom elbow joint, and an antagonistic muscle pair, i.e. the biceps and triceps brachii, and takes into consideration the contact between the skeletal muscles and the humerus. Numerical studies have shown that the proposed upper limb model is capable of predicting realistic moment arms and muscle forces for the entire range of activation and motion. Within the limitations of the model, the presented simulations provide, for the first time, insights into existing contact forces and their influence on the muscle fibre stretch. Based on the presented simulations, the overall change in fibre stretch is typically less than 3%, despite the fact that the contact forces reach up to 71% of the exerted muscle force. Movement-predicting simulations are achieved by minimising a nonlinear moment equilibrium equation. Based on the forward-dynamics simulation approach, an iterative solution procedures for position-driven (inverse dynamics) and force-driven scenarios have been proposed accordingly. Applying these methodologies to time-dependent scenarios demonstrates that the proposed methods can be linked to state-of-the-art control algorithms predicting time-dependent muscle activation levels based on principles of forward dynamics.     

Wrist and digital joint motion produce unique flexor tendon force and excursion in the canine forelimb

The force and excursion within the canine digital flexor tendons were measured during passive joint manipulations that simulate those used during rehabilitation after flexor tendon repair and during active muscle contraction, simulating the active rehabilitation protocol. Tendon force was measured using a small buckle placed upon the tendon while excursion was measured using a suture marker and video analysis method. Passive finger motion imposed with the wrist flexed resulted in dramatically lower tendon force (approximately 5 N) compared to passive motion imposed with the wrist extended (approximately 17 N). Lower excursions were seen at the level of the proximal interphalangeal joint with the wrist flexed (approximately 1.5 mm) while high excursion was observed when the wrist was extended or when synergistic finger and wrist motion were imposed (approximately 3.5 mm). Bivariate discriminant analysis of both force and excursion data revealed a natural clustering of the data into three general mechanical paradigms. With the wrist extended and with either one finger or four fingers manipulated, tendons experienced high loads of approximately 1500 g and high excursions of approximately 3.5 mm. In contrast, the same manipulations performed with the wrist flexed resulted in low tendon forces (4-8 N) and low tendon excursions of approximately 1.5 mm. Synergistic wrist and finger manipulation provided the third paradigm where tendon force was relatively low (approximately 4 N) but excursion was as high as those seen in the groups which were manipulated with the wrist extended. Active muscle contraction produced a modest tendon excursion (approximately 1 mm) and high or low tendon force with the wrist extended or flexed, respectively. These data provide the basis for experimentally testable hypotheses with regard to the factors that most significantly affect functional recovery after digital flexor tendon injury and define the normal mechanical operating characteristics of these tendons.     

In vivo moment arm determination using B-mode ultrasonography

The tendon excursion of the tibialis anterior (TA) muscle was measured in vivo using B-mode ultrasonography in seven subjects under three force levels (0, 30 and 60% maximal voluntary contraction, MVC). For each force level, the TA moment arm (m) was determined by calculating the derivative of the tendon excursion relative to the ankle angle (a). A dynamometer controlled the ankle angle while force levels were monitored. The parametric model proposed by Miller and Dennis (1996), m = R sin(a + delta), where R is the largest moment arm and delta represents the offset angle of R from 90 degrees, was used in a least-squares fit of the relationship between moment arm and ankle angle. The R values at 0% MVC were significantly smaller than those at 30 and 60% MVC. The values of calculated moment arm at 0% MVC were not considered adequate estimates of the TA moment arm because of the possible confounding effect of the slackness of the relaxed muscle-tendon unit in more dorsiflexed positions. The moment arm values at 30 and 60% MVC were believed to provide reliable estimates of those of TA since the application of tension probably reduced the effects of the slackness of the muscle-tendon unit and tendon elongation on tendon excursion measurement at these force levels. Since the ultrasonographic technique is an in vivo application of the tendon excursion technique and therefore takes the functional meaning into consideration, it can yield more significant moment arms than other in vivo or cadaver techniques.     

Anatomy of raccoon (Procyon lotor) and coati (Nasua narica and N. nasua) forearm and leg muscles: relations between fiber length, moment-arm length, and joint-angle excursion

Muscle architecture, moment arms, and locomotor movements in the distal limb segments of the procyonids Nasua (coati) and Procyon (raccoon) are analyzed with reference to patterns of muscle fiber length. This study addresses the hypothesis that relative fiber lengths among muscles in a muscle group can be predicted on the basis of correlates of muscle tension. The results include the following: consistent patterns of fiber length of muscles in a muscle group exist within and between the two genera. Differences in fiber length between muscles can be accounted for by two principal correlates of muscle excursion--length of a muscle's moment arm about a joint and joint-angle excursion. Muscle fiber pinnation permits increased tendon excursion, but this effect is relatively small in comparison to the effects of moment-arm length and joint-angle excursion. Corollary action between two or more joints (or lack thereof) is an important factor in determination of fiber lengths.     

Patellar tendon and hamstring moment-arms and cross-sectional area in patients with anterior cruciate ligament reconstruction and controls

The purpose of this study was to examine the moment-arm and cross-sectional area (CSA) of the patellar tendon (PT) and the hamstrings after anterior cruciate ligament (ACL) reconstruction. The right knee of five males who underwent ACL reconstruction with a PT graft and five age-matched controls was scanned using magnetic resonance image scans. Based on three-dimensional (3D) solids of the PT, CSAs and moment-arms of semitendinous (ST), biceps femoris (BF) long head and semimembranosus (SM) were estimated. Analysis of variance indicated no significant group differences in muscle moment-arms (p>0.05). 3D moment-arms of PT, ST and BF were significantly lower than the corresponding 2D values (p < 0.05). The ACL group displayed a significantly higher maximum BF CSA, a lower ST CSA (p < 0.05) but similar PT and SM CSAs compared with controls. It is concluded that any alterations in PT properties 1 year after harvesting do not affect knee muscle moment-arms compared with age-matched controls. Moment-arm estimation differed between 3D and 2D data, although it did not affect comparisons between ACL reconstruction group and controls. Design of rehabilitation programmes should take into consideration a potential alteration in hamstring morphology following surgery with a PT graft.     

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.     

Sensitivity of an equine distal limb model to perturbations in tendon paths, origins and insertions

As equine musculoskeletal models become common, it is important to determine their sensitivity to the simplifications used. A subject-specific distal forelimb model was created using bones extracted from CT scans to examine movement from in-vivo invasive-marker motion capture. The movements of the sesamoid bones were simulated using the constraints of maintaining an isometric virtual ligament and maintaining contact between the appropriate articular surfaces, creating a variable moment arm for the tendons. The simulation of the proximal sesamoid bones was compared to movement recorded in-vitro. The paths and origins used for the deep digital flexor tendon (DDFT), superficial digital flexor tendon (SDFT) and suspensory ligament (SL) were altered and the effects on their calculated strains during trot stance were examined. The most influential alteration tested was the dorsopalmar changes to the tendon paths at the level of the proximal sesamoid bones, which led to a maximum length reduction of 4 and 2 mm for the SDFT and DDFT, respectively. Alterations to the virtual origins of the SDFT and DDFT were not influential leading to up to a 0.01% effect on strains for a 1cm dorsopalmar shift. In the SL, the choice of the proximal or distal edge of the proximal attachment site varied the strains calculated by up to 1% (3 mm). These results show that within the anatomically realistic spectrum, changes to tendon paths can have an appreciable effect on calculated strains; however the origin sites chosen are not as influential as changes to paths at the metacarpo-phalangeal joint.     

To what extent is joint and muscle mechanics predicted by musculoskeletal models sensitive to soft tissue artefacts?

Musculoskeletal models are widely used to estimate joint kinematics, intersegmental loads, and muscle and joint contact forces during movement. These estimates can be heavily affected by the soft tissue artefact (STA) when input positional data are obtained using stereophotogrammetry, but this aspect has not yet been fully characterised for muscle and joint forces. This study aims to assess the sensitivity to the STA of three open-source musculoskeletal models, implemented in OpenSim.A baseline dataset of marker trajectories was created for each model from experimental data of one healthy volunteer. Five hundred STA realizations were then statistically generated using a marker-dependent model of the pelvis and lower limb artefact and added to the baseline data. The STA׳s impact on the musculoskeletal model estimates was finally quantified using a Monte Carlo analysis.The modelled STA distributions were in line with the literature. Observed output variations were comparable across the three models, and sensitivity to the STA was evident for most investigated quantities. Shape, magnitude and timing of the joint angle and moment time histories were not significantly affected throughout the entire gait cycle, whereas magnitude variations were observed for muscle and joint forces. Ranges of contact force variations differed between joints, with hip variations up to 1.8 times body weight observed. Variations of more than 30% were observed for some of the muscle forces.In conclusion, musculoskeletal simulations using stereophotogrammetry may be safely run when only interested in overall output patterns. Caution should be paid when more accurate estimated values are needed.     

A kinematic model of the flexor tendons of the hand

The multi-joint model is a kinematic simulation of the long flexor tendons of the fingers. The tendons modeled are the flexor pollicis longus, the flexor digitorum profundus, and the flexor digitorum superficialis. The simulated tendons are displayed on an Evans and Sutherland PS330 color graphics terminal attached to a display of articulated bones of the hand. As a user changes the position of the joints of the simulated hand, the simulation displays the new tendon path and the excursion of the tendon for the new position of the hand. The multi-joint model is one component of a comprehensive model for use in a hand biomechanics computer workstation.     

Known data on applied regenerative medicine in tendon healing

Tendons and ligaments are important structures in the musculoskeletal system. Ligaments connect various bones and provide stability in complex movements of joints in the knee. Tendon is made of dense connective tissue and transmits the force of contraction from muscle to bone. They are injured due to direct trauma in sports or roadside accidents. Tendon healing after repair is often poor due to the formation of fibro vascular scar tissues with low mechanical property. Regenerative techniques such as PRP (platelet-rich plasma), stem cells, scaffolds, gene therapy, cell sheets, and scaffolds help augment repair and regenerate tissue in this context. Therefore, it is of interest to document known data (repair process, tissue regeneration, mechanical strength, and clinical outcome) on applied regenerative medicine in tendon healing.     

Predictions of co-contraction depend critically on degrees-of-freedom in the musculoskeletal model

In biomechanics, the calculation of individual muscle forces during movements is based on a model of the musculoskeletal system and a method for extracting a unique set of muscle forces. To obtain a unique set of muscle forces, non-linear, static optimisation is commonly used. However, the optimal solution is dependent on the musculoskeletal geometry, and single joints may be represented using one, two or three degrees-of-freedom. Frequently, a system with multiple degrees-of-freedom is replaced with a system that contains a subset of all the possible degrees-of-freedom. For example, the cat ankle joint is typically modelled as a planar joint with its primary degree-of-freedom (plantar-dorsiflexion), whereas, the actual joint has three rotational degrees-of-freedom. Typically, such simplifications are justified by the idea that the reduced case is contained as a specific solution of the more general case. However, here we demonstrate that the force-sharing solution space of a general, three degrees-of-freedom musculoskeletal system does not necessarily contain the solutions from the corresponding one or two degrees-of-freedom systems. Therefore, solutions of a reduced system, in general, are not sub-set solutions of the actual three degrees-of-freedom system, but are independent solutions that are often incompatible with solutions of the actual system. This result shows that representing a three degrees-of-freedom system as a one or two degrees-of-freedom system gives force-sharing solutions that cannot be extrapolated to the actual system, and vice-versa. These results imply that general solutions cannot be extracted from models with fewer degrees-of-freedom than the actual system. They further emphasise the need for precise geometric representation of the musculoskeletal system, if general force-sharing rules are to be derived.     

In vivo human tendinous tissue stretch upon maximum muscle force generation

In the present study, we examined the hypothesis that stretch of tendinous tissue in the human tibialis anterior (TA) muscle-tendon unit upon isometric dorsiflexion maximum voluntary contraction (MVC) varies along the entire tendinous component length. Ultrasound-based measurements of the excursions of the TA tendon origin and proximal end of the TA central aponeurosis were taken in the transition from rest to MVC in six men. Subtracting the TA tendon origin excursion from the excursion of the aponeurosis proximal end, the aponeurosis excursion was estimated. Estimation of the aponeurosis proximal region excursion was obtained subtracting the excursion of the insertion point of a central region fascicle on the aponeurosis from the whole aponeurosis excursion. Subtracting tendon excursion from the excursion of the central fascicle insertion point, the aponeurosis distal region excursion was estimated. Strain values were calculated dividing the excursions obtained by the original resting lengths. All excursions and lengths were measured in the mid-longitudinal axis of the TA muscle-tendon unit at the neutral anatomical ankle position. Tendon excursion and strain were 0.5+/-0. 08 cm (mean+/-SE) and 3.1+/-0.2%, respectively. Aponeurosis excursion and strain were 1.1+/-0.15 cm and 6.5+/-0.6%, respectively. Aponeurosis distal region excursion and strain were 0.3+/-0.05 cm and 3.5+/-0.3%, respectively. Aponeurosis proximal region excursion and strain were 0.8+/-0.12 cm and 9.2+/-1%, respectively. Aponeurosis excursion and strain were larger by 110-120% (P<0.05) compared with tendon. Aponeurosis proximal region excursion and strain were larger by 165-170% (P<0.05) compared with aponeurosis distal region. These findings are in line with results from in vitro animal material testing and have important implications for theoretical models of muscle function.     

Studies in flexor tendon wound healing: neutralizing antibody to TGF-beta1 increases postoperative range of motion

The postoperative outcome of hand flexor tendon repair remains limited by tendon adhesions that prevent normal range of motion. Recent studies using in situ hybridization techniques have implicated transforming growth factor beta-1 (TGF-beta1) in both intrinsic and extrinsic mechanisms of repair. TGF-beta1 is a growth factor that plays multiple roles in wound healing and has also been implicated in the pathogenesis of excessive scar formation. The purpose of this study was to examine the effect of neutralizing antibody to TGF-beta1 in a rabbit zone II flexor tendon wound-healing model. Twenty-two adult New Zealand White rabbits underwent complete transection of the middle digit flexor digitorum profundus tendon in zone II. The tendons were immediately repaired and received intraoperative infiltration of one of the following substances: (1) control phosphate-buffered saline; (2) 50 microg neutralizing antibody to TGF-beta1; (3) 50 microg each of neutralizing antibody to TGF-beta1 and to TGF-beta2. Eight rabbits that had not been operated on underwent analysis for determination of normal flexion range of motion at their proximal and distal interphalangeal joints, using a 1.2-N axial load applied to the flexor digitorum profundus tendon. All rabbits that had been operated on were placed in casts for 8 weeks to allow maximal tendon adhesion and were then killed to determine their flexion range of motion. Statistical analysis was performed using the Student's unpaired t test. When a 1.2-N load was used on rabbit forepaws that had not been operated on, normal combined flexion range of motion at the proximal and distal interphalangeal joints was 93+/-6 degrees. Previous immobilization in casts did not reduce the range of motion in these forepaws (93+/-4 degrees). In the experimental groups, complete transection and repair of the flexor digitorum profundus tendon with infiltration of control phosphate-buffered saline solution resulted in significantly decreased range of motion between the proximal and distal phalanges [15+/-6 degrees (n = 8)]. However, in the tendon repairs infiltrated with neutralizing antibody to TGF-beta1, flexion range of motion increased to 32+/-9 degrees (n = 7; p = 0.002). Interestingly, a combination of neutralizing antibody to TGF-beta1 and that to TGF-beta2 did not improve postoperative range of motion [18+/-4 degrees (n = 7; p = 0.234)]. These data demonstrate that (1) the rabbit flexor tendon repair model is useful for quantifying tendon scar formation on the basis of degrees of flexion between proximal and distal phalanges; (2) intraoperative infiltration of neutralizing antibody to TGF-beta1 improves flexor tendon excursion; and (3) simultaneous infiltration of neutralizing antibody to TGF-beta2 nullifies this effect. Because TGF-beta1 is thought to contribute to the pathogenesis of excessive scar formation, the findings presented here suggest that intraoperative biochemical modulation of TGF-beta1 levels limits flexor tendon adhesion formation.