Determining finger segmental centers of rotation in flexion-extension based on surface marker measurement

This paper describes the development of a novel algorithm for deriving finger segmental center of rotation (COR) locations during flexion-extension from measured surface marker motions in vivo. The algorithm employs an optimization routine minimizing the time-variance of the internal link lengths, and incorporates an empirically quantifiable relationship between the local movement of a surface marker around a joint (termed "surface marker excursion") and the joint flexion-extension. The latter relationship constrains and simplifies the optimization routine to make it computationally tractable. To empirically investigate this relationship and test the proposed algorithm, an experiment was conducted, in which hand cylinder-grasping movements were performed by 24 subjects (12 males and 12 females). Spherical retro-reflective markers were placed at various surface landmarks on the dorsal aspect of each subject's right (grasping) hand, and were measured during the movements by an opto-electronic system. Analysis of experimental data revealed a highly linear relationship between the "surface marker excursion" and the marker-defined flexion-extension angle: the average R(2) in linear regression ranged from 0.89 to 0.97. The algorithm successfully determined the CORs of the distal interphalangeal, proximal interphalangeal, and metacarpophalangeal joints of digits 2-5 during measured motions. The derived CORs appeared plausible as examined in terms of the physical locations relative to surface marker trajectories and the congruency across different joints and individuals.     

The accuracy of measuring glenohumeral motion with a surface humeral cuff

Conclusions about normal and pathologic shoulder motion are frequently made from studies using skin surface markers, yet accuracy of such sensors representing humeral motion is not well known. Nineteen subjects were investigated with flock of birds electromagnetic sensors attached to transcortical pins placed into the scapula and humerus, and a thermoplastic cuff secured on the arm. Subjects completed two repetitions of raising and lowering the arm in the sagittal, scapular and coronal planes, as well as shoulder internal and external rotation with the elbow at the side and abducted to 90°. Humeral motion was recorded simultaneously from surface and bone fixed sensors. The average magnitude of error was calculated for the surface and bone fixed measurements throughout the range of motion. ANOVA tested for differences across angles of elevation, raising and lowering, and differences in body mass index. For all five motions tested, the plane of elevation rotation average absolute error ranged from 0-2°, while the humeral elevation rotation average error ranged from 0-4°. The axial rotation average absolute error was much greater, ranging from 5° during elevation motions to approaching 30° at maximum excursion of internal/external rotation motions. Average absolute error was greater in subjects with body mass index greater than 25. Surface sensors are an accurate way of measuring humeral elevation rotations and plane of elevation rotations. Conversely, there is a large amount of average error for axial rotations when using a humeral cuff to measure glenohumeral internal/external rotation as the primary motion.     

Knee joint secondary motion accuracy improved by quaternion-based optimizer with bony landmark constraints

Skin marker-based motion analysis has been widely used in biomechanical studies and clinical applications. Unfortunately, the accuracy of knee joint secondary motions is largely limited by the nonrigidity nature of human body segments. Numerous studies have investigated the characteristics of soft tissue movement. Utilizing these characteristics, we may improve the accuracy of knee joint motion measurement. An optimizer was developed by incorporating the soft tissue movement patterns at special bony landmarks into constraint functions. Bony landmark constraints were assigned to the skin markers at femur epicondyles, tibial plateau edges, and tibial tuberosity in a motion analysis algorithm by limiting their allowed position space relative to the underlying bone. The rotation matrix was represented by quaternion, and the constrained optimization problem was solved by Fletcher's version of the Levenberg-Marquardt optimization technique. The algorithm was validated by using motion data from both skin-based markers and bone-mounted markers attached to fresh cadavers. By comparing the results with the ground truth bone motion generated from the bone-mounted markers, the new algorithm had a significantly higher accuracy (root-mean-square (RMS) error: 0.7 ± 0.1 deg in axial rotation and 0.4 ± 0.1 deg in varus-valgus) in estimating the knee joint secondary rotations than algorithms without bony landmark constraints (RMS error: 1.7 ± 0.4 deg in axial rotation and 0.7 ± 0.1 deg in varus-valgus). Also, it predicts a more accurate medial-lateral translation (RMS error: 0.4 ± 0.1 mm) than the conventional techniques (RMS error: 1.2 ± 0.2 mm). The new algorithm, using bony landmark constrains, estimates more accurate secondary rotations and medial-lateral translation of the underlying bone.     

Determination of 3D spinal kinematics without defining a local vertebral coordinate system

In this paper a method is presented to calculate Euler's angles of rotation of a body segment during locomotion without a priori defining the location of the center of rotation, and without defining a local vertebral coordinate system. The method was applied to in vivo spinal kinematics. In this method, the orientation of each segment is identified by a set of three markers. The orientation of the axes of rotation is calculated based on the average position of the markers during one stride cycle. Some restrictions and assumptions should be made. The approach is viable only when the average orientation of the anatomical axes of rotation of each spinal segment during a stride cycle coincides with the three axes of the laboratory coordinate system. Furthermore, the rotations should be symmetrical with respect to both sides of the plane of symmetry of the spinal segment, and the subject should move parallel to one axis of the laboratory coordinate system. Since in experimental conditions these assumptions will only be met approximately, errors will be introduced in the calculated angles of rotation. The magnitude of the introduced errors was investigated in a computer simulation experiment. Since the maximal errors did not exceed 0.7° in a range of misalignments up to 10° between the two coordinate systems, the approach proved to be a valid method for the estimation of spinal kinematics.     

Segmental motion of forefoot and hindfoot as a diagnostic tool

Segmental motions derived from non-invasive motion analysis are being used to investigate the intrinsic functional behavior of the foot and ankle in health and disease. The goal of this research was to examine the ability of a generic segmented model of the foot to capture and differentiate changes in internal skeletal kinematics due to neuromuscular disease and/or trauma. A robotic apparatus that reproduces the kinematics and kinetics of gait in cadaver lower extremities was employed to produce motion under normal and aberrant neuromuscular activation patterns of tibialis posterior and/or tibialis anterior. Stance phase simulations were conducted on 10 donor limbs while recording three-dimensional kinematic trajectories of (1) skin-mounted markers used clinically to construct segmented foot models, and (2) bone-mounted marker clusters to capture actual internal bone motion as the gold standard for comparison. The models constructed from external marker data were able to differentiate the kinematic behaviors elicited by different neuromuscular conditions in a manner similar to that using the bone-derived data. Measurable differences between internal and externally measured kinematics were small, variable and random across the three axes of rotation and neuromuscular conditions, with a tendency toward more differences noted during early and late stance. Albeit slightly different, three-dimensional motion profiles of the hindfoot and forefoot segments correlated well with internal skeletal motion under all neuromuscular conditions, thereby confirming the utility of measuring segmental motions as a valid means of clinical assessment.     

A new non-orthogonal decomposition method to determine effective torques for three-dimensional joint rotation

This paper describes a new non-orthogonal decomposition method to determine effective torques for three-dimensional (3D) joint rotation. A rotation about a joint coordinate axis (e.g. shoulder internal/external rotation) cannot be explained only by the torque about the joint coordinate axis because the joint coordinate axes usually deviate from the principal axes of inertia of the entire kinematic chain distal to the joint. Instead of decomposing torques into three orthogonal joint coordinate axes, our new method decomposes torques into three "non-orthogonal effective axes" that are determined in such a way that a torque about each effective axis produces a joint rotation only about one of the joint coordinate axes. To demonstrate the validity of this new method, a simple internal/external rotation of the upper arm with the elbow flexed at 90 degrees was analyzed by both orthogonal and non-orthogonal decomposition methods. The results showed that only the non-orthogonal decomposition method could explain the cause-effect mechanism whereby three angular accelerations at the shoulder joint are produced by the gravity torque, resultant joint torque, and interaction torque. The proposed method would be helpful for biomechanics and motor control researchers to investigate the manner in which the central nervous system coordinates the gravity torque, resultant joint torque, and interaction torque to control 3D joint rotations.     

The effects of knee joint kinematics on anterior cruciate ligament injury and articular cartilage damage

This study determined which knee joint motions lead to anterior cruciate ligament (ACL) rupture with the knee at 25° of flexion. The knee was subjected to internal and external rotations, as well as varus and valgus motions. A failure locus representing the relationship between these motions and ACL rupture was established using finite element simulations. This study also considered possible concomitant injuries to the tibial articular cartilage prior to ACL injury. The posterolateral bundle of the ACL demonstrated higher rupture susceptibility than the anteromedial bundle. The average varus angular displacement required for ACL failure was 46.6% lower compared to the average valgus angular displacement. Femoral external rotation decreased the frontal plane angle required for ACL failure by 27.5% compared to internal rotation. Tibial articular cartilage damage initiated prior to ACL failure in all valgus simulations. The results from this investigation agreed well with other experimental and analytical investigations. This study provides a greater understanding of the various knee joint motion combinations leading to ACL injury and articular cartilage damage.     

In-vivo measurement of dynamic joint motion using high speed biplane radiography and CT: application to canine ACL deficiency

Dynamic assessment of three-dimensional (3D) skeletal kinematics is essential for understanding normal joint function as well as the effects of injury or disease. This paper presents a novel technique for measuring in-vivo skeletal kinematics that combines data collected from high-speed biplane radiography and static computed tomography (CT). The goals of the present study were to demonstrate that highly precise measurements can be obtained during dynamic movement studies employing high frame-rate biplane video-radiography, to develop a method for expressing joint kinematics in an anatomically relevant coordinate system and to demonstrate the application of this technique by calculating canine tibio-femoral kinematics during dynamic motion. The method consists of four components: the generation and acquisition of high frame rate biplane radiographs, identification and 3D tracking of implanted bone markers, CT-based coordinate system determination, and kinematic analysis routines for determining joint motion in anatomically based coordinates. Results from dynamic tracking of markers inserted in a phantom object showed the system bias was insignificant (-0.02 mm). The average precision in tracking implanted markers in-vivo was 0.064 mm for the distance between markers and 0.31 degree for the angles between markers. Across-trial standard deviations for tibio-femoral translations were similar for all three motion directions, averaging 0.14 mm (range 0.08 to 0.20 mm). Variability in tibio-femoral rotations was more dependent on rotation axis, with across-trial standard deviations averaging 1.71 degrees for flexion/extension, 0.90 degree for internal/external rotation, and 0.40 degree for varus/valgus rotation. Advantages of this technique over traditional motion analysis methods include the elimination of skin motion artifacts, improved tracking precision and the ability to present results in a consistent anatomical reference frame.     

Non-invasive assessment of soft-tissue artifact and its effect on knee joint kinematics during functional activity

The soft-tissue interface between skin-mounted markers and the underlying bones poses a major limitation to accurate, non-invasive measurement of joint kinematics. The aim of this study was twofold: first, to quantify lower limb soft-tissue artifact in young healthy subjects during functional activity; and second, to determine the effect of soft-tissue artifact on the calculation of knee joint kinematics. Subject-specific bone models generated from magnetic resonance imaging (MRI) were used in conjunction with X-ray images obtained from single-plane fluoroscopy to determine three-dimensional knee joint kinematics for four separate tasks: open-chain knee flexion, hip axial rotation, level walking, and a step-up. Knee joint kinematics was derived using the anatomical frames from the MRI-based, 3D bone models together with the data from video motion capture and X-ray fluoroscopy. Soft-tissue artifact was defined as the degree of movement of each marker in the anteroposterior, proximodistal and mediolateral directions of the corresponding anatomical frame. A number of different skin-marker clusters (total of 180) were used to calculate knee joint rotations, and the results were compared against those obtained from fluoroscopy. Although a consistent pattern of soft-tissue artifact was found for each task across all subjects, the magnitudes of soft-tissue artifact were subject-, task- and location-dependent. Soft-tissue artifact for the thigh markers was substantially greater than that for the shank markers. Markers positioned in the vicinity of the knee joint showed considerable movement, with root mean square errors as high as 29.3 mm. The maximum root mean square errors for calculating knee joint rotations occurred for the open-chain knee flexion task and were 24.3°, 17.8° and 14.5° for flexion, internal–external rotation and abduction–adduction, respectively. The present results on soft-tissue artifact, based on fluoroscopic measurements in healthy adult subjects, may be helpful in developing location- and direction-specific weighting factors for use in global optimization algorithms aimed at minimizing the effects of soft-tissue artifact on calculations of knee joint rotations.     

Optimal Superpositioning of Flexible Molecule Ensembles

Analysis of the internal dynamics of a biological molecule requires the successful removal of overall translation and rotation. Particularly for flexible or intrinsically disordered peptides, this is a challenging task due to the absence of a well-defined reference structure that could be used for superpositioning. In this work, we started the analysis with a widely known formulation of an objective for the problem of superimposing a set of multiple molecules as variance minimization over an ensemble. A negative effect of this superpositioning method is the introduction of ambiguous rotations, where different rotation matrices may be applied to structurally similar molecules. We developed two algorithms to resolve the suboptimal rotations. The first approach minimizes the variance together with the distance of a structure to a preceding molecule in the ensemble. The second algorithm seeks for minimal variance together with the distance to the nearest neighbors of each structure. The newly developed methods were applied to molecular-dynamics trajectories and normal-mode ensembles of the Aβ peptide, RS peptide, and lysozyme. These new (to our knowledge) superpositioning methods combine the benefits of variance and distance between nearest-neighbor(s) minimization, providing a solution for the analysis of intrinsic motions of flexible molecules and resolving ambiguous rotations.     

Internal motional amplitudes and correlated bond rotations in an alpha-helical peptide derived from 13C and 15N NMR relaxation

Peptide GFSKAELAKARAAKRGGY folds in an alpha-helical conformation that is stabilized by formation of a hydrophobic staple motif and an N-terminal capping box (Munoz V. Blanco FJ, Serrano L, 1995, Struct Biol 2:380-385). To investigate backbone and side-chain internal motions within the helix and hydrophobic staple, residues F2, A5, L7, A8, and A10 were selectively 13C- and 15N-enriched and NMR relaxation experiments were performed in water and in water/trifluoroethanol (TFE) solution at four Larmor frequencies (62.5, 125, 150, and 200 MHz for 13C). Relaxation data were analyzed using the model free approach and an anisotropic diffusion model. In water, angular variances of motional vectors range from 10 to 20 degrees and backbone phi,psi bond rotations for helix residues A5, L7, A8, and A10 are correlated indicating the presence of Calpha-H, Calpha-Cbeta, and N-H rocking-type motions along the helix dipole axis. L7 side-chain CbetaH2 and CgammaH motions are also correlated and as motionally restricted as backbone CalphaH, suggesting considerable steric hindrance with neighboring groups. In TFE which stabilizes the fold, internal motional amplitudes are attenuated and rotational correlations are increased. For the side chain of hydrophobic staple residue F2, wobbling-in-a-cone type motions dominate in water, whereas in TFE, the Cbeta-Cgamma bond and phenyl ring fluctuate more simply about the Calpha-Cbeta bond. These data support the Daragan-Mayo model of correlated bond rotations (Daragan VA, Mayo KH, 1996, J Phys Chem 100:8378-8388) and contribute to a general understanding of internal motions in peptides and proteins.     

Comparison of different calculations of three-dimensional joint kinematics from video-based system data

When skin-fixed marker trajectories are used to calculate 3D joint kinematics, the measurement errors (i.e. the difference between the trajectories of the external markers and those of the skeleton) influence to some extent the accuracy of the results, depending both on the calculation method and on the axes about which the rotations are expressed. The purpose of this paper is to compare several expressions of joint angular variations. Two kinematic concepts are used to calculate the changes in the orientation of the distal segment versus the proximal one: the first method consists of computing the components of the spatial attitude vector, the second one deals with the determination of elementary rotations about successive axes. For each of these methods, two sets of three axes are tested to express the results: the axes forming the reference frame affixed to the body segment adjacent to the joint (named fixed axes), and a set consisting of a first axis belonging to the proximal segment, a third axis belonging to the distal segment and a second (floating) axis defined as the cross-product between the two other ones (named mobile axes). To compare these four distinct expressions on the knee joint, numerical simulations of perturbed skin marker trajectories are performed, based on experimental data recorded by a Motion Analysis system during a normal gait cycle. A significant difference is pointed out only for the internal–external rotation angle, for which the best expression — from the viewpoint of sensitivity to experimental errors — is obtained using the components of the attitude vector in a segment-embedded reference frame.     

Are coupled rotations in the lumbar spine largely due to the osseo-ligamentous anatomy?--a modeling study

Prior studies have found that primary rotations in the lumbar spine are accompanied by coupled out-of-plane rotations. However, it is not clear whether these accompanying rotations are primarily due to passive (discs, ligaments and facet joints) or active (muscles) spinal anatomy. The aim of this study was to use a finite element (FE) model of the lumbar spine to predict three-dimensional coupled rotations between the lumbar vertebrae, due to passive spinal structures alone. The FE model was subjected to physiologically observed whole lumbar spine rotations about in vivo centres of rotation. Model predictions were validated by comparison of intra-discal pressures and primary rotations with in vivo measurements and these showed close agreement. Predicted coupled rotations matched in vivo measurements for all primary motions except lateral bending. We suggest that coupled rotations accompanying primary motions in the sagittal (flexion/extension) and transverse (axial rotation) planes are primarily due to passive spinal structures. For lateral bending the muscles most likely play a key role in the coupled rotation of the spine.     

Rotational flexibility of the human knee due to varus/valgus and axial moments in vivo

Knee ligamentous injuries persist in the sport of Alpine skiing. To better understand the load mechanisms which lead to injury, pure varus/valgus and pure axial moments were applied both singly and in combination to the right knees of six human test subjects. The corresponding relative knee rotations in three degrees of freedom were measured. Knee flexion angles for each test subject were 15 and 60 degrees for the individual moments and 60 degrees for the combination moments. For both knee flexion angles the hip flexion angle was 0 degrees. Leg muscles were quiescent and axial force was minimal during all tests. Tables of data include sample statistics for each of four flexibility parameters in each loading direction. Data were analyzed statistically to test for significant differences in flexibility parameters between the test conditions. In flexing the knee from 15 to 60 degrees, the resulting knee rotations under single moments depended upon flexion angle with varus, valgus, and internal rotations increasing significantly. Also, rotations were different depending on load direction; varus rotation was significantly different and greater than valgus rotation at both flexion angles. Also external rotation was significantly different and greater than internal at 15 degrees flexion, but not at 60 degrees flexion. Coupled rotations under single moments were also observed. Applying pure varus/valgus moments resulted in coupled external/internal rotations which were inconsistent and hence not significant. Applying pure axial moments resulted in consistent and hence significant varus/valgus rotations; an external axial moment induced varus rotation and an internal axial moment induced valgus rotation. For combination moments, varus/valgus rotations decreased significantly from those rotations at similar load levels in the single moment studies. Also, a varus moment significantly increased external rotation and a valgus moment significantly decreased internal rotation. These differences indicate significant interaction between corresponding load combinations. These results suggest that load interaction is a potentially important phenomenon in knee injury mechanics.     

Comparing non-invasive scapular tracking methods across elevation angles,planes of elevation and humeral axial rotations

Altered scapular motions premeditate shoulder impingement and other musculoskeletal disorders. Divergent experimental conditions in previous research precludes rigorous comparisons of non-invasive scapular tracking techniques. This study evaluated scapular orientation measurement methods across an expanded range of humeral postures. Scapular medial/lateral rotation, anterior/posterior tilt and protraction/retraction was measured using an acromion marker cluster (AMC), a scapular locator, and a reference stylus. Motion was captured using reflective markers on the upper body, as well as on the AMC, locator and stylus. A combination of 5 arm elevation angles, 3 arm elevation planes and 3 arm axial rotations was examined. Measurement method interacted with elevation angle and plane of elevation for all three scapular orientation directions (p < 0.01). Method of measurement interacted with axial rotation in anterior/posterior tilt and protraction/retraction (p < 0.01). The AMC had strong agreement with the reference stylus than the locator for the majority of humeral elevations, planes and axial rotations. The AMC underestimated lateral rotation, with the largest difference of ∼2° at 0° elevation. Both the locator and AMC overestimated posterior tilt at high arm elevation by up to 7.4°. Misestimations from using the locator could be enough to potentially obscure meaningful differences in scapular rotations.     

Use of dual Euler angles to quantify the three-dimensional joint motion and its application to the ankle joint complex

This paper presents a modified Euler angles method, dual Euler angles approach, to describe general spatial human joint motions. In dual Euler angles approach, the three-dimensional joint motion is considered as three successive screw motions with respect to the axes of the moving segment coordinate system; accordingly, the screw motion displacements are represented by dual Euler angles. The algorithm for calculating dual Euler angles from coordinates of markers on the moving segment is also provided in this study. As an example, the proposed method is applied to describe motions of ankle joint complex during dorsiflexion–plantarflexion. A Flock of Birds electromagnetic tracking device (FOB) was used to measure joint motion in vivo. Preliminary accuracy tests on a gimbal structure demonstrate that the mean errors of dual Euler angles evaluated by using source data from FOB are less than 1° for rotations and 1 mm for translations, respectively. Based on the pilot study, FOB is feasible for quantifying human joint motions using dual Euler angles approach.     

Rigid‐body motions of interacting proteins dominate multispecific binding of ubiquitin in a shape‐dependent manner

To understand the dynamic aspects of multispecificity of ubiquitin, we studied nine ubiquitin–ligand (partner protein) complexes by normal mode analysis based on an elastic network model. The coupling between ubiquitin and ligand motions was analyzed by decomposing it into rigid‐body (external) and vibrational (internal) motions of each subunit. We observed that in total the external motions in one of the subunits largely dominated the coupling. The combination of external motions of ubiquitin and the ligands showed general trends of rotations and translations. Moreover, we observed that the rotational motions of ubiquitin were correlated to the ligand orientations. We also identified ubiquitin atomic vibrations that differentiated the orientation of the ligand molecule. We observed that the extents of coupling were correlated to the shapes of the ligands, and this trend was more pronounced when the coupling involved vibrational motions of the ligand. In conclusion, an intricate interplay between internal and external motions of ubiquitin and the ligands help understand the dynamics of multispecificity, which is mostly guided by the shapes of the ligands and the complex. Proteins 2014; 82:77–89. © 2013 Wiley Periodicals, Inc.     

Measurement of the screw-home motion of the knee is sensitive to errors in axis alignment

Measurements of joint angles during motion analysis are subject to error caused by kinematic crosstalk, that is, one joint rotation (e. g., flexion) being interpreted as another (e.g., abduction). Kinematic crosstalk results from the chosen joint coordinate system being misaligned with the axes about which rotations are assumed to occur. The aim of this paper is to demonstrate that measurement of the so-called "screw-home" motion of the human knee, in which axial rotation and extension are coupled, is especially prone to errors due to crosstalk. The motions of two different two-segment mechanical linkages were examined to study the effects of crosstalk. The segments of the first linkage (NSH) were connected by a revolute joint, but the second linkage (SH) incorporated gearing that caused 15 degrees of screw-home rotation to occur with 90 degrees knee flexion. It was found that rotating the flexion axis (inducing crosstalk) could make linkage NSH appear to exhibit a screw-home motion and that a different rotation of the flexion axis could make linkage SH apparently exhibit pure flexion. These findings suggest that the measurement of screw-home rotation may be strongly influenced by errors in the location of the flexion axis. The magnitudes of these displacements of the flexion axis were consistent with the inter-observer variability seen when five experienced observers defined the flexion axis by palpating the medial and lateral femoral epicondyles. Care should be taken when interpreting small internal-external rotations and abduction-adduction angles to ensure that they are not the products of kinematic crosstalk.     

3D finite element models of shoulder muscles for computing lines of actions and moment arms

Accurate representation of musculoskeletal geometry is needed to characterise the function of shoulder muscles. Previous models of shoulder muscles have represented muscle geometry as a collection of line segments, making it difficult to account for the large attachment areas, muscle–muscle interactions and complex muscle fibre trajectories typical of shoulder muscles. To better represent shoulder muscle geometry, we developed 3D finite element models of the deltoid and rotator cuff muscles and used the models to examine muscle function. Muscle fibre paths within the muscles were approximated, and moment arms were calculated for two motions: thoracohumeral abduction and internal/external rotation. We found that muscle fibre moment arms varied substantially across each muscle. For example, supraspinatus is considered a weak external rotator, but the 3D model of supraspinatus showed that the anterior fibres provide substantial internal rotation while the posterior fibres act as external rotators. Including the effects of large attachment regions and 3D mechanical interactions of muscle fibres constrains muscle motion, generates more realistic muscle paths and allows deeper analysis of shoulder muscle function.     

Analysis of conformational motions and related key residue interactions responsible for a specific function of proteins with elastic network model

Protein collective motions play a critical role in many biochemical processes. How to predict the functional motions and the related key residue interactions in proteins is important for our understanding in the mechanism of the biochemical processes. Normal mode analysis (NMA) of the elastic network model (ENM) is one of the effective approaches to investigate the structure-encoded motions in proteins. However, the motion modes revealed by the conventional NMA approach do not necessarily correspond to a specific function of protein. In the present work, a new analysis method was proposed to identify the motion modes responsible for a specific function of proteins and then predict the key residue interactions involved in the functional motions by using a perturbation approach. In our method, an internal coordinate that accounts for the specific function was introduced, and the Cartesian coordinate space was transformed into the internal/Cartesian space by using linear approximation, where the introduced internal coordinate serves as one of the axes of the coordinate space. NMA of ENM in this internal/Cartesian space was performed and the function-relevant motion modes were identified according to their contributions to the specific function of proteins. Then the key residue interactions important for the functional motions of the protein were predicted as the interactions whose perturbation largely influences the fluctuation along the internal coordinate. Using our proposed methods, the maltose transporter (MalFGK₂) from E. Coli was studied. The functional motions and the key residue interactions that are related to the channel-gating function of this protein were successfully identified.