A Dynamic Optimization Approach for Solving Spine Kinematics While Calibrating Subject-Specific Mechanical Properties

Inverse kinematics in cervical spine models: Effects of scaling and model degrees of freedom for extension and flexion movements

Intervertebral kinematics can affect model-predicted loads and strains in the spine; therefore knowledge of expected vertebral kinematics error is important for understanding the limitations of model predictions. This study addressed how different kinematic models of the neck affect the prediction of intervertebral kinematics from markers on the head and trunk. Eight subjects executed head and neck extension-flexion motion with simultaneous motion capture and biplanar dynamic stereo-radiography (DSX) of vertebrae C1-C7. A generic head and neck model in OpenSim was scaled by marker data, and three versions of the model were used with an inverse kinematics solver. The models differed according to the number of independent degrees of freedom (DOF) between the head and trunk: 3 rotational DOF with constraints defining intervertebral kinematics as a function of overall head-trunk motion; 24DOF with 3 independent rotational DOF at each level, skull-T1; 48DOF with 3 rotational and 3 translational DOF at each level. Marker tracking error was lower for scaled models compared to generic models and decreased as model DOF increased. The largest mean absolute error (MAE) was found in extension-flexion angle and anterior-posterior translation at C1-C2, and superior-inferior translation at C2-C3. Model scaling and complexity did not have a statistically significant effect on most error metrics when corrected for multiple comparisons, but ranges of motion were significantly different from DSX in some cases. This study evaluated model kinematics in comparison to gold standard radiographic data and provides important information about intervertebral kinematics error that are foundational to model validity.

Towards Wearable and Portable Spine Motion Analysis Through Dynamic Optimization of Smartphone Videos and IMU Data

BACKGROUND

Monitoring spine kinematics is crucial for applications like disease evaluation and ergonomics analysis. However, the small scale of vertebrae and the number of degrees of freedom present significant challenges for noninvasive and convenient spine kinematics estimation.

METHODS

This study developed a dynamic optimization framework for wearable spine motion tracking at the intervertebral joint level by integrating smartphone videos and Inertia Measurement Units (IMUs) with dynamic constraints from a thoracolumbar spine model. Validation involved motion data from 10 healthy males performing static standing, dynamic upright trunk rotations, and gait. This data included rotations of ten IMUs on vertebrae and virtual landmarks from three smartphone videos preprocessed by OpenCap, an application leveraging computer vision for pose estimation. The kinematic measures derived from the optimized solution were compared against simultaneously collected infrared optical marker-based measurements and in vivo literature data. Solutions only based on IMUs or videos were also compared for accuracy evaluation.

RESULTS

The proposed optimization approach closely matched the reference data in the intervertebral or segmental rotation range, demonstrating minimal angular differences across all motions and the highest correlation in 3D rotations (maximal Pearson and intraclass correlation coefficients of 0.92 and 0.94, respectively). Time-series changes of joint angles also aligned well with the optical-marker reference.

CONCLUSION

Dynamic optimization of the spine simulation that integrates IMUs and computer vision outperforms the single-modality method.

SIGNIFICANCE

This markerless 3D spine motion capture method holds potential for spinal health assessment in large cohorts in real-world settings without dedicated laboratories.

Identification of a lumped-parameter model of the intervertebral joint from experimental data

Through predictive simulations, multibody models can aid the treatment of spinal pathologies by identifying optimal surgical procedures. Critical to achieving accurate predictions is the definition of the intervertebral joint. The joint pose is often defined by virtual palpation. Intervertebral joint stiffnesses are either derived from literature, or specimen-specific stiffnesses are calculated with optimisation methods. This study tested the feasibility of an optimisation method for determining the specimen-specific stiffnesses and investigated the influence of the assigned joint pose on the subject-specific estimated stiffness. Furthermore, the influence of the joint pose and the stiffness on the accuracy of the predicted motion was investigated. A computed tomography based model of a lumbar spine segment was created. Joints were defined from virtually palpated landmarks sampled with a Latin Hypercube technique from a possible Cartesian space. An optimisation method was used to determine specimen-specific stiffnesses for 500 models. A two-factor analysis was performed by running forward dynamic simulations for ten different stiffnesses for each successfully optimised model. The optimisations calculated a large range of stiffnesses, indicating the optimised specimen-specific stiffnesses were highly sensitive to the assigned joint pose and related uncertainties. A limited number of combinations of optimised joint stiffnesses and joint poses could accurately predict the kinematics. The two-factor analysis indicated that, for the ranges explored, the joint pose definition was more important than the stiffness. To obtain kinematic prediction errors below 1 mm and 1° and suitable specimen-specific stiffnesses the precision of virtually palpated landmarks for joint definition should be better than 2.9 mm.

Bridging the sim2real gap. Investigating deviations between experimental motion measurements and musculoskeletal simulation results-a systematic review

Musculoskeletal simulations can be used to estimate biomechanical variables like muscle forces and joint torques from non-invasive experimental data using inverse and forward methods. Inverse kinematics followed by inverse dynamics (ID) uses body motion and external force measurements to compute joint movements and the corresponding joint loads, respectively. ID leads to residual forces and torques (residuals) that are not physically realistic, because of measurement noise and modeling assumptions. Forward dynamic simulations (FD) are found by tracking experimental data. They do not generate residuals but will move away from experimental data to achieve this. Therefore, there is a gap between reality (the experimental measurements) and simulations in both approaches, the sim2real gap. To answer (patho-) physiological research questions, simulation results have to be accurate and reliable; the sim2real gap needs to be handled. Therefore, we reviewed methods to handle the sim2real gap in such musculoskeletal simulations. The review identifies, classifies and analyses existing methods that bridge the sim2real gap, including their strengths and limitations. Using a systematic approach, we conducted an electronic search in the databases Scopus, PubMed and Web of Science. We selected and included 85 relevant papers that were sorted into eight different solution clusters based on three aspects: how the sim2real gap is handled, the mathematical method used, and the parameters/variables of the simulations which were adjusted. Each cluster has a distinctive way of handling the sim2real gap with accompanying strengths and limitations. Ultimately, the method choice largely depends on various factors: available model, input parameters/variables, investigated movement and of course the underlying research aim. Researchers should be aware that the sim2real gap remains for both ID and FD approaches. However, we conclude that multimodal approaches tracking kinematic and dynamic measurements may be one possible solution to handle the sim2real gap as methods tracking multimodal measurements (some combination of sensor position/orientation or EMG measurements), consistently lead to better tracking performances. Initial analyses show that motion analysis performance can be enhanced by using multimodal measurements as different sensor technologies can compensate each other's weaknesses.

Variability of intervertebral joint stiffness between specimens and spine levels

Introduction: Musculoskeletal multibody models of the spine can be used to investigate the biomechanical behaviour of the spine. In this context, a correct characterisation of the passive mechanical properties of the intervertebral joint is crucial. The intervertebral joint stiffness, in particular, is typically derived from the literature, and the differences between individuals and spine levels are often disregarded. Methods: This study tested if an optimisation method of personalising the intervertebral joint stiffnesses was able to capture expected stiffness variation between specimens and between spine levels and if the variation between spine levels could be accurately captured using a generic scaling ratio. Multibody models of six T12 to sacrum spine specimens were created from computed tomography data. For each specimen, two models were created: one with uniform stiffnesses across spine levels, and one accounting for level dependency. Three loading conditions were simulated. The initial stiffness values were optimised to minimize the kinematic error. Results: There was a range of optimised stiffnesses across the specimens and the models with level dependent stiffnesses were less accurate than the models without. Using an optimised stiffness substantially reduced prediction errors. Discussion: The optimisation captured the expected variation between specimens, and the prediction errors demonstrated the importance of accounting for level dependency. The inaccuracy of the predicted kinematics for the level-dependent models indicated that a generic scaling ratio is not a suitable method to account for the level dependency. The variation in the optimised stiffnesses for the different loading conditions indicates personalised stiffnesses should also be considered load-specific.

Dynamic segmental kinematics of the lumbar spine during diagnostic movements

Background: In vivo measurements of segmental-level kinematics are a promising avenue for better understanding the relationship between pain and its underlying, multi-factorial basis. To date, the bulk of the reported segmental-level motion has been restricted to single plane motions. Methods: The present work implemented a novel marker set used with an optical motion capture system to non-invasively measure dynamic, 3D in vivo segmental kinematics of the lower spine in a laboratory setting. Lumbar spinal kinematics were measured for 28 subjects during 17 diagnostic movements. Results: Overall regional range of motion data and lumbar angular velocity measurement were consistent with previously published studies. Key findings from the work included measurement of differences in ascending versus descending segmental velocities during functional movements and observations of motion coupling paradigms in the lumbar spinal segments. Conclusion: The work contributes to the task of establishing a baseline of segmental lumbar movement patterns in an asymptomatic cohort, which serves as a necessary pre-requisite for identifying pathological and symptomatic deviations from the baseline.

Towards improving the accuracy of musculoskeletal simulation of dynamic three-dimensional spine rotations with optimizing model and algorithm

BACKGROUND

The accuracy of musculoskeletal simulations greatly relies on model structures and optimization algorithms. This study investigated the unclarified influence of accounting for several commonly-simplified different model components and optimization criteria on spinal musculoskeletal simulations.

METHODS

The study constructed a full-body musculoskeletal model with passive components of functional spinal units and spinal muscles subject-specifically refined. A muscle redundancy solver was built with 15 optimization criteria. Three-dimensional spine rotations and spinal muscle activities were measured using optical motion capture and electromyogram techniques when eight healthy volunteers performed standing, flexion/extension, lateral bending, and axial rotation. The effect of the model with four different conditions of the passive components and the sensitivity of the 15 optimization criteria on simulations were investigated.

RESULTS

Accounting for the refined passive components significantly improved the simulation accuracy. Different optimization criteria behaved distinctly for different motions. Generally minimizing the sum of squared muscle activations outperformed the others, with the highest averaged correlation coefficient (0.82) between the estimated erector spinae muscle activations and measured electromyography and with the estimated joint compression forces comparable to in vivo reference data.

CONCLUSION

This study highlights the importance of passive model components and proposes a suitable optimization framework for realistic spinal musculoskeletal simulations.

Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications

Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.

Synergy Analysis of Back Muscle Activities in Patients with Adolescent Idiopathic Scoliosis Based on High-Density Electromyogram

Adolescent idiopathic scoliosis (AIS) is a common structural spinal deformity and is typically associated with altered muscle properties. However, it is still unclear how muscle activities and the underlying neuromuscular control are changed in the entire scoliotic zone, restricting the corresponding pathology investigation and treatment enhancements. In this study, high-density electromyogram (HD-EMG) was utilized to explore the neuromuscular synergy of back muscle activities. For each of ten AIS patients and ten healthy subjects for comparison, a high-density electrode array was placed on their back from T8 to L4 to record EMG signals when performing five spinal motions (flexion/extension, lateral bending, axial rotation, siting, and standing). From the HD-EMG recordings, muscle synergies were extracted using the non-negative matrix factorization method and the topographical maps of EMG root-mean-square were constructed. For both the AIS and healthy subjects, the experimental results indicated that two muscle synergy groups could explain over 90% of recorded muscle activities for all five motions. During flexion/extension, the patients presented statistically significant higher activations on the convex side in the entire root-mean-square maps and synergy vector maps (p <0.05). During lateral bending and axial rotation, the patients exhibited less activated muscles on the dominant actuating side relative to the contralateral side and their synergy vector maps showed a less homogenous and more diffuse distribution of muscle contraction with statistically different centers of gravity. The findings suggest that a scoliotic spine might adopt an altered modular muscular coordination strategy to actuate different dominant muscles as adapted compensations for the deformation.