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.     

Neck muscle paths and moment arms are significantly affected by wrapping surface parameters

In this paper, we studied the effects of wrapping surfaces on muscle paths and moment arms of the neck muscle, semispinalis capitis. Sensitivities to wrapping surface size and the kinematic linkage to vertebral segments were evaluated. Kinematic linkage, but not radius, significantly affected the accuracy of model muscle paths compared to centroid paths from images. Both radius and linkage affected the moment arm significantly. Wrapping surfaces that provided the best match to centroid paths over a range of postures had consistent moment arms. For some wrapping surfaces with poor matches to the centroid path, a kinematic method (tendon excursion) predicted flexion moment arms in certain postures, whereas geometric method (distance to instant centre) predicted extension. This occurred because the muscle lengthened as it wrapped around the surface. This study highlights the sensitivity of moment arms to wrapping surface parameters and the importance of including multiple postures when evaluating muscle paths and moment arm.     

Neck muscle paths and moment arms are significantly affected by wrapping surface parameters

In this paper, we studied the effects of wrapping surfaces on muscle paths and moment arms of the neck muscle, semispinalis capitis. Sensitivities to wrapping surface size and the kinematic linkage to vertebral segments were evaluated. Kinematic linkage, but not radius, significantly affected the accuracy of model muscle paths compared to centroid paths from images. Both radius and linkage affected the moment arm significantly. Wrapping surfaces that provided the best match to centroid paths over a range of postures had consistent moment arms. For some wrapping surfaces with poor matches to the centroid path, a kinematic method (tendon excursion) predicted flexion moment arms in certain postures, whereas geometric method (distance to instant centre) predicted extension. This occurred because the muscle lengthened as it wrapped around the surface. This study highlights the sensitivity of moment arms to wrapping surface parameters and the importance of including multiple postures when evaluating muscle paths and moment arm.     

Genome segmentation using piecewise constant intensity models and reversible jump MCMC

The existence of whole genome sequences makes it possible to search for global structure in the genome. We consider modeling the occurrence frequencies of discrete patterns (such as starting points of ORFs or other interesting phenomena) along the genome. We use piecewise constant intensity models with varying number of pieces, and show how a reversible jump Markov Chain Monte Carlo (RJMCMC) method can be used to obtain a posteriori distribution on the intensity of the patterns along the genome. We apply the method to modeling the occurrence of ORFs in the human genome. The results show that the chromosomes consist of 5-35 clearly distinct segments, and that the posteriori number and length of the segments shows significant variation. On the other hand, for the yeast genome the intensity of ORFs is nearly constant.     

Variation of finger forces in maximal isometric grasp tests on a range of cylinder diameters

An investigation of maximal isometric cylindrical grasping actions of the hand is reported. A dynamometer is described which allows simultaneous measurement of both the normal forces and the tangential shear forces imposed by each of the three phalangeal segments of a finger during a test. Seventeen subjects were tested, grasping cylinders 31–116 mm in diameter. Normal grasp forces decreased significantly as cylinder size increased, while with large diameters, shear forces moved the skin towards the finger tip. In all cases the distal segments of the fingers imposed forces significantly larger than those of the middle and proximal segments. The mean contributions of fingers from index to little were: 30, 30, 22 and 18%, proportions that did not vary significantly for the range of grasp diameters. Forces acting during grasping activities are reported in greater detail, for a wider range of hand gripping postures, than previously available. These data are useful in the design of hand operated controls or in the prediction of tendon and joint forces in vivo for the design of implants.     

Nudged elastic band calculation of minimal energy paths for the conformational change of a GG non-canonical pair

The nudged elastic band (NEB) technique has been implemented in AMBER to calculate low-energy paths for conformational changes. A novel simulated annealing protocol that does not require an initial hypothesis for the path is used to sample low-energy paths. This was used to study the conformational change of an RNA cis Watson-Crick/Hoogsteen GG non-canonical pair, with one G syn around the glycosidic bond and the other anti. A previous solution structure, determined by NMR-constrained modeling, demonstrated that the GG pairs change from (syn)G-(anti)G to (anti)G-(syn)G in the context of duplex r(GCAGGCGUGC) on the millisecond timescale. The set of low-energy paths found by NEB show that each G flips independently around the glycosidic bond, with the anti G flipping to syn first. Guanine bases flip without opening adjacent base-pairs by protruding into the major groove, accommodated by a transient change by the ribose to C2'-exo sugar pucker. Hydrogen bonds between bases and the backbone, which lower the energetic barrier to flipping, are observed along the path. The results show the plasticity of RNA base-pairs in helices, which is important for biological processes, including mismatch repair, protein recognition, and translation. The modeling of the GG conformational change also demonstrates that NEB can be used to discover non-trivial paths for macromolecules and therefore NEB can be used as an exploratory method for predicting putative conformational change paths.     

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.     

Combining animal movements and behavioural data to detect behavioural states

Animal movement paths show variation in space caused by qualitative shifts in behaviours. I present a method that (1) uses both movement path data and ancillary sensor data to detect natural breakpoints in animal behaviour and (2) groups these segments into different behavioural states. The method can also combine analyses of different path segments or paths from different individuals. It does not assume any underlying movement mechanism. I give an example with simulated data. I also show the effects of random variation, # of states and # of segments on this method. I present a case study of a fisher movement path spanning 8 days, which shows four distinct behavioural states divided into 28 path segments when only turning angles and speed were considered. When accelerometer data were added, the analysis shows seven distinct behavioural states divided into 41 path segments.     

Determination of biomechanical characteristics of restrictive adhesions and of functional impairment after flexor tendon surgery: a methodological study of rabbits.

Formation of restrictive adhesions is one of the main obstacles in rehabilitation following hand surgery. Most experimental work, however, involves only a macroscopic and/or histologic evaluation of the amount of adhesions, and their functional characteristics are poorly described. The aim of this study was to develop an experimental technique for characterization of the biomechanical properties of the finger-tendon unit. An instrument was developed for continuous and simultaneous recording of tensile load, tendon excursion and angular rotation in the distal interphalangeal joint of rabbit digits. Utilizing this instrument, it was revealed that the first 50 degrees of flexion required virtually no tensile load either in unoperated digits or immediately after tenorrhaphy. Thereafter, the load required to obtain further flexion was progressively increased. The strength of adhesions, determined 2 weeks after tenorrhaphy, was best expressed as the maximum tensile load recorded before 50 degrees of flexion was reached. This measurement could also be used to register the strength of the tendon repair and to detect partial tendon rupture during the measurement. The technique allows both adequate measurements of the strength of the adhesions and of the tendon gliding ability after flexor tendon surgery.     

Morphometry of Macaca mulatta forelimb. I. Shoulder and elbow muscles and segment inertial parameters

The present study examined the morphometric properties of the forelimb, including the inertial properties of the body segments and the morphometric parameters of 21 muscles spanning the shoulder and/or elbow joints of six Macaca mulatta and three M. fascicularis. Five muscle parameters are presented: optimal fascicle length (L(0)(M)), tendon slack length (L(S)(T)), physiological cross-sectional area (PCSA), pennation angle (alpha(0)), and muscle mass (m). Linear regressions indicate that muscle mass, and to a lesser extent PCSA, correlated with total body weight. Segment mass, center-of-mass, and the moment of inertia of the upper arm, forearm, and hand are also presented. Our data indicate that for some segments, radius of gyration (rho) predicts segment moment of inertia better than linear regressions based on total body weight. Key differences between the monkey and human forelimb are highlighted.     

The role of tenascin-C in adaptation of tendons to compressive loading

Although most tendon regions are subjected primarily to high tensile loads, selected regions, primarily those that directly contact bones that change the direction of the tendon, must withstand high compressive loads as well. Compressed tendon regions differ from regions subjected to primarily tensile loads: they have a fibrocartilaginous structure with spherical cells surrounded by a matrix containing aggrecan and collagen types I and II, in contrast regions not exposed to compression have a fibrous structure with spindle shaped fibroblasts surrounded by a matrix of dense, longitudinally oriented type I collagen fibrils. The spherical shape of cells in fibrocartilagenous regions indicates these cells are more loosely attached to the matrix than their spindle-shaped counterparts in fibrous regions, a feature that may help to minimize cell deformation during tendon compression. We hypothesized that expression of tenascin-C, an anti-adhesive protein, is part of the adaptation of tendon cells to compression that helps establish and maintain fibrocartilaginous regions. To test this hypothesis we compared tenascin-C content and expression in compressed (distal) versus uncompressed (proximal) segments of bovine flexor tendons. Immunohistochemistry and immunoblot analyses showed that tenascin-C content was increased in the distal tendon where it co-distributed with type II collagen and aggrecan. Tendon cells from the distal segments expressed more tenascin-C than did cells from the proximal segments for up to four days in cell culture, indicating that increased tenascin-C expression is a relatively stable feature of the distal cells. These observations support the hypothesis that tenascin-C expression is a cellular adaptation to compression that helps establish and maintain fibrocartilagenous regions of tendons.     

Development of a Prototype Over-Actuated Biomimetic Prosthetic Hand

The loss of a hand can greatly affect quality of life. A prosthetic device that can mimic normal hand function is very important to physical and mental recuperation after hand amputation, but the currently available prosthetics do not fully meet the needs of the amputee community. Most prosthetic hands are not dexterous enough to grasp a variety of shaped objects, and those that are tend to be heavy, leading to discomfort while wearing the device. In order to attempt to better simulate human hand function, a dexterous hand was developed that uses an over-actuated mechanism to form grasp shape using intrinsic joint mounted motors in addition to a finger tendon to produce large flexion force for a tight grip. This novel actuation method allows the hand to use small actuators for grip shape formation, and the tendon to produce high grip strength. The hand was capable of producing fingertip flexion force suitable for most activities of daily living. In addition, it was able to produce a range of grasp shapes with natural, independent finger motion, and appearance similar to that of a human hand. The hand also had a mass distribution more similar to a natural forearm and hand compared to contemporary prosthetics due to the more proximal location of the heavier components of the system. This paper describes the design of the hand and controller, as well as the test results.     

A technique for normalizing centre of pressure paths

Centre of pressure paths may be expected to provide useful information in the analysis of gait. In this paper, a technique for normalizing and averaging centre of pressure paths is presented. It utilizes force data obtained from force platform measurements together with information about the placement of the foot on the force platform. This placement is described by specifying the location of the 'centre' and 'midline' of the foot which are defined for a footprint. The coordinate system associated with a footprint is defined and centre of pressure locations are determined in relation to this system. A comparison of the centre of pressure paths obtained using this method and the method proposed by Cavanagh [J. Biomechanics 11, 487-491 (1978)] shows significant differences. It is concluded that the selection of an appropriate technique to obtain centre of pressure paths is important.     

A Compact Representation of Drawing Movements with Sequences of Parabolic Primitives

Some studies suggest that complex arm movements in humans and monkeys may optimize several objective functions, while others claim that arm movements satisfy geometric constraints and are composed of elementary components. However, the ability to unify different constraints has remained an open question. The criterion for a maximally smooth (minimizing jerk) motion is satisfied for parabolic trajectories having constant equi-affine speed, which thus comply with the geometric constraint known as the two-thirds power law. Here we empirically test the hypothesis that parabolic segments provide a compact representation of spontaneous drawing movements. Monkey scribblings performed during a period of practice were recorded. Practiced hand paths could be approximated well by relatively long parabolic segments. Following practice, the orientations and spatial locations of the fitted parabolic segments could be drawn from only 2–4 clusters, and there was less discrepancy between the fitted parabolic segments and the executed paths. This enabled us to show that well-practiced spontaneous scribbling movements can be represented as sequences (“words”) of a small number of elementary parabolic primitives (“letters”). A movement primitive can be defined as a movement entity that cannot be intentionally stopped before its completion. We found that in a well-trained monkey a movement was usually decelerated after receiving a reward, but it stopped only after the completion of a sequence composed of several parabolic segments. Piece-wise parabolic segments can be generated by applying affine geometric transformations to a single parabolic template. Thus, complex movements might be constructed by applying sequences of suitable geometric transformations to a few templates. Our findings therefore suggest that the motor system aims at achieving more parsimonious internal representations through practice, that parabolas serve as geometric primitives and that non-Euclidean variables are employed in internal movement representations (due to the special role of parabolas in equi-affine geometry).     

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.     

Automated muscle wrapping using finite element contact detection

Realistic muscle path representation is essential to musculoskeletal modeling of joint function. Algorithms predicting these muscle paths typically rely on a labor intensive predefinition of via points or underlying geometries to guide wrapping for given joint positions. While muscle wrapping using anatomically precise three-dimensional (3D) finite element (FE) models of bone and muscle has been achieved, computational expense and pre-processing associated with this approach exclude its use in applications such as subject-specific modeling. With the intention of combining advantageous features of both approaches, an intermediate technique relying on contact detection capabilities of commercial FE packages is presented. We applied the approach to the glenohumeral joint, and validated the method by comparison against existing experimental data. Individual muscles were modeled as a straight series of deformable beam elements and bones as anatomically precise 3D rigid bodies. Only the attachment locations and a default orientation of the undeformed muscle segment were pre-defined. The joint was then oriented in a static position of interest. The muscle segment free end was then moved along the shortest Euclidean path to its origin on the scapula, wrapping the muscle along bone surfaces by relying on software contact detection. After wrapping for a given position, the resulting moment arm was computed as the perpendicular distance from the line of action vector to the humeral head center of rotation.This approach reasonably predicted muscle length and moment arm for 27 muscle segments when compared to experimental measurements over a wide range of shoulder motion. Artificial via points or underlying contact geometries were avoided, contact detection and multiobject wrapping on the bone surfaces were automatic, and low computational cost permitted wrapping of individual muscles within seconds on a standard desktop PC. These advantages may be valuable for both general and subject-specific musculoskeletal modeling.     

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.     

Structural study of anhydrous tendon chitosan obtained via chitosan/acetic acid complex

The molecular structure and packing arrangement of anhydrous tendon chitosan was determined by the X-ray fibre diffraction method together with the linked-atom least-squares refinement technique. The specimen was prepared from chitosan/acetic acid complex which was obtained by exposing tendon chitosan to acetic acid vapour at room temperature for several days. There is high degree of orientation and crystallinity compared with the specimen obtained by the annealing method. Two chitosan chains are present in an orthorhombic unit cell of dimensions a = 8.26(2), b = 8.50(1), c (fibre axis) = 10.43(2) A and space group P2(1)2(1)2(1). The 2-fold helical chain is stabilised by O3 triple bond O5 hydrogen bond with the gt orientation of O6. There are direct hydrogen bonds (N2 triple bond O6) between adjacent chains along the a-axis, which makes a sheet structure parallel to the ac-plane. On the other hand, no hydrogen bond is found between the sheets.     

Evaluation of affine fiber kinematics in human supraspinatus tendon using quantitative projection plot analysis

Structural constitutive modeling approaches are often based on the assumption of affine fiber kinematics, even though this assumption has rarely been evaluated experimentally. We are interested in applying mathematical models to understand the mechanisms responsible for the inhomogeneous, anisotropic, and non-linear properties of human supraspinatus tendon (SST); however, the relationship between macroscopic and fiber-level deformation in this tendon remains unknown and current methods for making this assessment are inadequate. Therefore, the purpose of this study was to develop an improved method for quantitatively assessing agreement between two distributions and to examine the affine assumption in SST by comparing experimental fiber alignment to affine model predictions using this analysis approach. Measured fiber angle values of SST samples in uniaxial tensile tests were compared with predictions of affine fiber deformation using modified projection plots, which provide a method for qualitative and quantitative comparisons of two distributions. The projection plot metrics of offset and range, which were developed in this study, are of particular benefit by providing a quantitative representation of agreement that can be subjected to statistical comparisons. For SST, offset and range values varied by tendon location and test orientation, with more affine deformation evidenced for tendon regions of higher alignment. Results suggest that non-affine fiber behavior is dependent on specific tissue, orientation of the applied stretch relative to the fiber organization, and length scale of the observation. In addition, this study has established a method for evaluating the affine assumption in other tissues.     

A dynamic simulator to evaluate distal radio-ulnar joint kinematics

In order to perform cadaveric biomechanical studies of the human forearm and distal radio-ulnar joint, a dynamic simulator has been constructed. The device is based upon a Plexiglas frame, to which the ulna is secured in a vertical orientation and the humerus in a horizontal orientation. The hand is secured in a sliding bar linkage to a stepper-motor that is used to rotate the forearm. The tendons to be loaded are connected to pneumatic actuators that provide agonist and antagonist muscle loading resulting in torque along the forearm axis. The muscle loading profiles and magnitudes are programmable as a function of the pronation-supination position and direction. A magnetic tracking system is used to collect three-dimensional kinematics data of up to four segments, in conjunction with the muscle tendon loads, forearm torque and other prescribed experimental measures. All functions are under PC control using custom software written with LabVIEW (National Instruments, Austin, TX). For the DRUJ testing, the validity of the tendon loading protocol to produce physiologic torque/rotation patterns was verified using in vivo data. The relationship of individual muscle forces to forearm torque was determined by a cadaveric study.