A forward dynamics simulation of human lumbar spine flexion predicting the load sharing of intervertebral discs, ligaments, and muscles

Determining a musculoskeletal system's pre-stretched state using continuum-mechanical forward modelling and joint range optimization

The subject-specific range of motion (RoM) of a musculoskeletal joint system is balanced by pre-tension levels of individual muscles, which affects their contraction capability. Such an inherent pre-tension or pre-stretch of muscles is not measureable with in vivo experiments. Using a 3D continuum mechanical forward simulation approach for motion analysis of the musculoskeletal system of the forearm with 3 flexor and 2 extensor muscles, we developed an optimization process to determine the muscle fibre pre-stretches for an initial arm position, which is given human dataset. We used RoM values of a healthy person to balance the motion in extension and flexion. The performed sensitivity study shows that the fibre pre-stretches of the m. brachialis, m. biceps brachii and m. triceps brachii with 91 % dominate the objective flexion ratio, while m. brachiradialis and m. anconeus amount 7.8 % and 1.2 % . Within the multi-dimensional space of the surrogate model, 3D sub-spaces of primary variables, namely the dominant muscles and the global objective, flexion ratio, exhibit a path of optimal solutions. Within this optimal path, the muscle fibre pre-stretch of two flexors demonstrate a negative correlation, while, in contrast, the primary extensor, m. triceps brachii correlates positively to each of the flexors. Comparing the global optimum with four other designs along the optimal path, we saw large deviations, e.g., up to 15∘ in motion and up to 40% in muscle force. This underlines the importance of accurate determination of fibre pre-stretch in muscles, especially, their role in pathological muscular disorders and surgical applications such as free muscle or tendon transfer.

A new method to design energy-conserving surrogate models for the coupled, nonlinear responses of intervertebral discs

The aim of this study was to design physics-preserving and precise surrogate models of the nonlinear elastic behaviour of an intervertebral disc (IVD). Based on artificial force-displacement data sets from detailed finite element (FE) disc models, we used greedy kernel and polynomial approximations of second, third and fourth order to train surrogate models for the scalar force-torque -potential. Doing so, the resulting models of the elastic IVD responses ensured the conservation of mechanical energy through their structure. At the same time, they were capable of predicting disc forces in a physiological range of motion and for the coupling of all six degrees of freedom of an intervertebral joint. The performance of all surrogate models for a subject-specific L4 | 5 disc geometry was evaluated both on training and test data obtained from uncoupled (one-dimensional), weakly coupled (two-dimensional), and random movement trajectories in the entire six-dimensional (6d) physiological displacement range, as well as on synthetic kinematic data. We observed highest precisions for the kernel surrogate followed by the fourth-order polynomial model. Both clearly outperformed the second-order polynomial model which is equivalent to the commonly used stiffness matrix in neuro-musculoskeletal simulations. Hence, the proposed model architectures have the potential to improve the accuracy and, therewith, validity of load predictions in neuro-musculoskeletal spine models.

Invasiveness of decompression surgery affects modeled lumbar spine kinetics in patients with degenerative spondylolisthesis

Introduction: The surgical treatment of degenerative spondylolisthesis with accompanying spinal stenosis focuses mainly on decompression of the spinal canal with or without additional fusion by means of a dorsal spondylodesis. Currently, one main decision criterion for additional fusion is the presence of instability in flexion and extension X-rays. In cases of mild and stable spondylolisthesis, the optimal treatment remains a subject of ongoing debate. There exist different opinions on whether performing a fusion directly together with decompression has a potential benefit for patients or constitutes overtreatment. As X-ray images do not provide any information about internal biomechanical forces, computer simulation of individual patients might be a tool to gain a set of new decision criteria for those cases. Methods: To evaluate the biomechanical effects resulting from different decompression techniques, we developed a lumbar spine model using forward dynamic-based multibody simulation (FD_MBS). Preoperative CT data of 15 patients with degenerative spondylolisthesis at the level L4/L5 who underwent spinal decompression were identified retrospectively. Based on the segmented vertebrae, 15 individualized models were built. To establish a reference for comparison, we simulated a standardized flexion movement (intact) for each model. Subsequently, we performed virtual unilateral and bilateral interlaminar fenestration (uILF, bILF) and laminectomy (LAM) by removing the respective ligaments in each model. Afterward, the standardized flexion movement was simulated again for each case and decompression method, allowing us to compare the outcomes with the reference. This comprehensive approach enables us to assess the biomechanical implications of different surgical approaches and gain valuable insights into their effects on lumbar spine functionality. Results: Our findings reveal significant changes in the biomechanics of vertebrae and intervertebral discs (IVDs) as a result of different decompression techniques. As the invasiveness of decompression increases, the moment transmitted on the vertebrae significantly rises, following the sequence intact ➝ uILF ➝ bILF ➝ LAM. Conversely, we observed a reduction in anterior-posterior shear forces within the IVDs at the levels L3/L4 and L4/L5 following LAM. Conclusion: Our findings showed that it was feasible to forecast lumbar spine kinematics after three distinct decompression methods, which might be helpful in future clinical applications.

Muscle-driven forward dynamic active hybrid model of the lumbosacral spine: combined FEM and multibody simulation

Most spine models belong to either the musculoskeletal multibody (MB) or finite element (FE) method. Recently, coupling of MB and FE models has increasingly been used to combine advantages of both methods. Active hybrid FE-MB models, still rarely used in spine research, avoid the interface and convergence problems associated with model coupling. They provide the inherent ability to account for the full interplay of passive and active mechanisms for spinal stability. In this paper, we developed and validated a novel muscle-driven forward dynamic active hybrid FE-MB model of the lumbosacral spine (LSS) in ArtiSynth to simultaneously calculate muscle activation patterns, vertebral movements, and internal mechanical loads. The model consisted of the rigid vertebrae L1-S1 interconnected with hyperelastic fiber-reinforced FE intervertebral discs, ligaments, facet joints, and force actuators representing the muscles. Morphological muscle data were implemented via a semi-automated registration procedure. Four auxiliary bodies were utilized to describe non-linear muscle paths by wrapping and attaching the anterior abdominal muscles. This included an abdominal plate whose kinematics was optimized using motion capture data from upper body movements. Intra-abdominal pressure was calculated from the forces of the abdominal muscles compressing the abdominal cavity. For the muscle-driven approach, forward dynamics assisted data tracking was used to predict muscle activation patterns that generate spinal postures and balance the spine without prescribing accurate spinal kinematics. During calibration, the maximum specific muscle tension and spinal rhythms resulting from the model dynamics were evaluated. To validate the model, load cases were simulated from -10° extension to +30° flexion with weights up to 20 kg in both hands. The biomechanical model responses were compared with in vivo literature data of intradiscal pressures, intra-abdominal pressures, and muscle activities. The results demonstrated high agreement with this data and highlight the advantages of active hybrid modeling for the LSS. Overall, this new self-contained tool provides a robust and efficient estimation of LSS biomechanical responses under in vivo similar loads, for example, to improve pain treatment by spinal stabilization therapies.

Three-dimensional spinal shape changes during daily activities

MOTIVATION

Intuitive assessment of spinal motion poses a tremendous challenge to both physicians and computer modelers. On the one side, medically detailed analyses of spinal shapes, such as computer tomography or X-ray images, are usually subject to static boundary constraints, thereby omitting dynamic information. On the other side, complex computer simulations often lack proper calibration aside from few control points, particularly regarding the three-dimensional arrangement of the spinal column and its idiomotion.

PURPOSE

Here, we investigate whether the full three-dimensional changes in spinal shape over time can be concisely detected and depicted. Further, we assess which parts of the spine undergo significant changes during various daily activities.

METHODS

We utilize a set of previously published motion capture data from the spinous processes (sacrum up to vertebra C7) of 17 healthy individuals performing the daily tasks of standing, walking, stair climbing, sitting down, and lifting. These three-dimensional, time-dependent marker positions were approximated by a Bézier curve at each time instant. The curves' characteristics, i.e.curvature and torsion, were calculated and juxtaposed for each individual and each activity over time. A statistical parametric mapping revealed significant changes in spinal shape.

RESULTS

We found the individual spinal shape characteristics being recognizably preserved during all activities. The walking task did not significantly alter the spinal curvature, while sitting and forward bending significantly altered the lumber and whole spine curvature, respectively. Torsion did not show any significant alterations.

CONCLUSION

Based on these results, we suggest that individualized dynamic information on spinal shapes can improve (i) the evaluation of (healthy) motion characteristics, (ii) the detection of pathologies, and (iii) individualized computer simulation models.

Effect of neglecting passive spinal structures: a quantitative investigation using the forward-dynamics and inverse-dynamics musculoskeletal approach

Purpose: Inverse-dynamics (ID) analysis is an approach widely used for studying spine biomechanics and the estimation of muscle forces. Despite the increasing structural complexity of spine models, ID analysis results substantially rely on accurate kinematic data that most of the current technologies are not capable to provide. For this reason, the model complexity is drastically reduced by assuming three degrees of freedom spherical joints and generic kinematic coupling constraints. Moreover, the majority of current ID spine models neglect the contribution of passive structures. The aim of this ID analysis study was to determine the impact of modelled passive structures (i.e., ligaments and intervertebral discs) on remaining joint forces and torques that muscles must balance in the functional spinal unit. Methods: For this purpose, an existing generic spine model developed for the use in the demoa software environment was transferred into the musculoskeletal modelling platform OpenSim. The thoracolumbar spine model previously used in forward-dynamics (FD) simulations provided a full kinematic description of a flexion-extension movement. By using the obtained in silico kinematics, ID analysis was performed. The individual contribution of passive elements to the generalised net joint forces and torques was evaluated in a step-wise approach increasing the model complexity by adding individual biological structures of the spine. Results: The implementation of intervertebral discs and ligaments has significantly reduced compressive loading and anterior torque that is attributed to the acting net muscle forces by -200% and -75%, respectively. The ID model kinematics and kinetics were cross-validated against the FD simulation results. Conclusion: This study clearly shows the importance of incorporating passive spinal structures on the accurate computation of remaining joint loads. Furthermore, for the first time, a generic spine model was used and cross-validated in two different musculoskeletal modelling platforms, i.e., demoa and OpenSim, respectively. In future, a comparison of neuromuscular control strategies for spinal movement can be investigated using both approaches.

Active exoskeleton reduces erector spinae muscle activity during lifting

Musculoskeletal disorders (MSD) are a widespread problem, often regarding the lumbar region. Exoskeletons designed to support the lower back could be used in physically demanding professions with the intention of reducing the strain on the musculoskeletal system, e.g., by lowering task-related muscle activation. The present study aims to investigate the effect of an active exoskeleton on back muscle activity when lifting weights. Within the framework of the study, 14 subjects were asked to lift a 15 kg box with and without an active exoskeleton which allows the adjustment of different levels of support, while the activity of their M. erector spinae (MES) was measured using surface electromyography. Additionally, the subjects were asked about their overall rating of perceived exertion (RPE) during lifting under various conditions. Using the exoskeleton with the maximum level of support, the muscle activity was significantly lower than without exoskeleton. A significant correlation was found between the exoskeleton's support level and the reduction of MES activity. The higher the support level, the lower the observed muscle activity. Furthermore, when lifting with the maximum level of support, RPE was found to be significantly lower than without exoskeleton too. A reduction in the MES activity indicates actual support for the movement task and might indicate lower compression forces in the lumbar region. It is concluded that the active exoskeleton supports people noticeably when lifting heavy weights. Exoskeletons seem to be a powerful tool for reducing load during physically demanding jobs and thus, their use might be helpful in lowering the risk of MSD.

Emerging trends and research foci of deep learning in spine: bibliometric and visualization study

As the cognition of spine develops, deep learning (DL) emerges as a powerful tool with tremendous potential for advancing research in this field. To provide a comprehensive overview of DL-spine research, our study utilized bibliometric and visual methods to retrieve relevant articles from the Web of Science database. VOSviewer and CiteSpace were primarily used for literature measurement and knowledge graph analysis. A total of 273 studies focusing on deep learning in the spine, with a combined total of 2302 citations, were retrieved. Additionally, the overall number of articles published on this topic demonstrated a continuous upward trend. China was the country with the highest number of publications, whereas the USA had the most citations. The two most prominent journals were "European Spine Journal" and "Medical Image Analysis," and the most involved research area was Radiology Nuclear Medicine Medical Imaging. VOSviewer identified three visually distinct clusters: "segmentation," "area," and "neural network." Meanwhile, CiteSpace highlighted "magnetic resonance image" and "lumbar" as the keywords with the longest usage, and "agreement" and "automated detection" as the most commonly used keywords. Although the application of DL in spine is still in its infancy, its future is promising. Intercontinental cooperation, extensive application, and more interpretable algorithms will invigorate DL in the field of spine.

Recent Advances in Coupled MBS and FEM Models of the Spine—A Review

How back pain is related to intervertebral disc degeneration, spinal loading or sports-related overuse remains an unanswered question of biomechanics. Coupled MBS and FEM simulations can provide a holistic view of the spine by considering both the overall kinematics and kinetics of the spine and the inner stress distribution of flexible components. We reviewed studies that included MBS and FEM co-simulations of the spine. Thereby, we classified the studies into unidirectional and bidirectional co-simulation, according to their data exchange methods. Several studies have demonstrated that using unidirectional co-simulation models provides useful insights into spinal biomechanics, although synchronizing the two distinct models remains a key challenge, often requiring extensive manual intervention. The use of a bidirectional co-simulation features an iterative, automated process with a constant data exchange between integrated subsystems. It reduces manual corrections of vertebra positions or reaction forces and enables detailed modeling of dynamic load cases. Bidirectional co-simulations are thus a promising new research approach for improved spine modeling, as a main challenge in spinal biomechanics is the nonlinear deformation of the intervertebral discs. Future studies will likely include the automated implementation of patient-specific bidirectional co-simulation models using hyper- or poroelastic intervertebral disc FEM models and muscle forces examined by an optimization algorithm in MBS. Applications range from clinical diagnosis to biomechanical analysis of overload situations in sports and injury prediction.

Multibody Models of the Thoracolumbar Spine: A Review on Applications, Limitations, and Challenges

Numerical models of the musculoskeletal system as investigative tools are an integral part of biomechanical and clinical research. While finite element modeling is primarily suitable for the examination of deformation states and internal stresses in flexible bodies, multibody modeling is based on the assumption of rigid bodies, that are connected via joints and flexible elements. This simplification allows the consideration of biomechanical systems from a holistic perspective and thus takes into account multiple influencing factors of mechanical loads. Being the source of major health issues worldwide, the human spine is subject to a variety of studies using these models to investigate and understand healthy and pathological biomechanics of the upper body. In this review, we summarize the current state-of-the-art literature on multibody models of the thoracolumbar spine and identify limitations and challenges related to current modeling approaches.

Implications of range of motion requirements for the laxity of ligaments in a lumbar finite element model

Finite element models of the lumbar spine often adopt ligament properties from tensile tests without accounting for possible differences between testing and in situ initial ligament length. Such differences could result in laxities or preloads at the beginning of a simulation that would affect the ligament forces, tangent stiffness, and the posture at which they fail. In vivo and in vitro human experimental data reported laxities or preloads. However, laxities or preloads, which could also result from postural differences, are often neglected in simulation studies. This study proposes a numerical methodology to identify ranges of ligament laxities or preloads compatible with the selected tensile ligament properties, the model, and the range of motion (RoM) the model aims to simulate. The approach assumes that ligaments should remain in a safe elongation range for the complete RoM, and that each ligament should play a significant mechanical role in at least one load case. The methodology was applied to the functional spinal unit (FSU) models using the RoM from healthy subjects and ligament properties from the literature. Without laxity, some ligaments reached their elongation at failure within the RoM. Laxity ranges varied considerably (from -9.2 mm preload to 10.7 mm laxity) and flexion was the most critical load case to determine them. Their effect on the mobility response was also assessed. The effect on the mobility of a FSU was also assessed. While the proposed method cannot determine an exact laxity value, it is simple and it can be applied to any model to identify a plausible range of ligament initial length.

Effects of geometric individualisation of a human spine model on load sharing: neuro-musculoskeletal simulation reveals significant differences in ligament and muscle contribution

In spine research, two possibilities to generate models exist: generic (population-based) models representing the average human and subject-specific representations of individuals. Despite the increasing interest in subject specificity, individualisation of spine models remains challenging. Neuro-musculoskeletal (NMS) models enable the analysis and prediction of dynamic motions by incorporating active muscles attaching to bones that are connected using articulating joints under the assumption of rigid body dynamics. In this study, we used forward-dynamic simulations to compare a generic NMS multibody model of the thoracolumbar spine including fully articulated vertebrae, detailed musculature, passive ligaments and linear intervertebral disc (IVD) models with an individualised model to assess the contribution of individual biological structures. Individualisation was achieved by integrating skeletal geometry from computed tomography and custom-selected muscle and ligament paths. Both models underwent a gravitational settling process and a forward flexion-to-extension movement. The model-specific load distribution in an equilibrated upright position and local stiffness in the L4/5 functional spinal unit (FSU) is compared. Load sharing between occurring internal forces generated by individual biological structures and their contribution to the FSU stiffness was computed. The main finding of our simulations is an apparent shift in load sharing with individualisation from an equally distributed element contribution of IVD, ligaments and muscles in the generic spine model to a predominant muscle contribution in the individualised model depending on the analysed spine level.

Computational lumbar spine models: A literature review

BACKGROUND

Computational spine models of various types have been employed to understand spine function, assess the risk that different activities pose to the spine, and evaluate techniques to prevent injury. The areas in which these models are applied has expanded greatly, potentially beyond the appropriate scope of each, given their capabilities. A comprehensive understanding of the components of these models provides insight into their current capabilities and limitations.

METHODS

The objective of this review was to provide a critical assessment of the different characteristics of model elements employed across the spectrum of lumbar spine modeling and in newer combined methodologies to help better evaluate existing studies and delineate areas for future research and refinement.

FINDINGS

A total of 155 studies met selection criteria and were included in this review. Most current studies use either highly detailed Finite Element models or simpler Musculoskeletal models driven with in vivo data. Many models feature significant geometric or loading simplifications that limit their realism and validity. Frequently, studies only create a single model and thus can't account for the impact of subject variability. The lack of model representation for certain subject cohorts leaves significant gaps in spine knowledge. Combining features from both types of modeling could result in more accurate and predictive models.

INTERPRETATION

Development of integrated models combining elements from different model types in a framework that enables the evaluation of larger populations of subjects could address existing voids and enable more realistic representation of the biomechanics of the lumbar spine.

Augmenting the Cobb angle: Three-dimensional analysis of whole spine shapes using Bézier curves

BACKGROUND AND OBJECTIVE

The identification and classification of pathological spinal deformities poses a major challenge to any diagnostician. First, available medical images are usually two-dimensional projections, obscuring elaborated spatial information. Second, several measurement techniques with different thresholds for certain clinical syndromes make it difficult to classify measured results. Here, a method is presented to augment and standardize the analysis of spinal shapes in three dimensions.

METHODS

Regarding the first limitation, (semi-)automatic, three-dimensional segmentation techniques of medical images have already been developed. To overcome the second, we propose here a representation of the whole spine by a Bézier curve using the vertebral centers as control points. After normalization, a differential-geometric approach yields information on curvature and torsion at each spinal level as well as in between.

RESULTS

Based on literature data and multi-body simulations, we show how these quantities alter with individual posture and during motion. Robustness with respect to missing data is investigated. Approaches towards the identification of spinal disorders are motivated.

CONCLUSION

Our results emphasize the need for individualizable identification and classification of spinal deformities and give an outlook on how it might be achieved. The presented methodology constitutes the first fully three-dimensional analysis of spinal shapes, i.e. without the requirement of certain physiological planes (e.g. the sagittal plane) or landmarks (e.g. the apex vertebra).

Validation of a Patient-Specific Musculoskeletal Model for Lumbar Load Estimation Generated by an Automated Pipeline From Whole Body CT

Background: Chronic back pain is a major health problem worldwide. Although its causes can be diverse, biomechanical factors leading to spinal degeneration are considered a central issue. Numerical biomechanical models can identify critical factors and, thus, help predict impending spinal degeneration. However, spinal biomechanics are subject to significant interindividual variations. Therefore, in order to achieve meaningful findings on potential pathologies, predictive models have to take into account individual characteristics. To make these highly individualized models suitable for systematic studies on spinal biomechanics and clinical practice, the automation of data processing and modeling itself is inevitable. The purpose of this study was to validate an automatically generated patient-specific musculoskeletal model of the spine simulating static loading tasks.

Methods: CT imaging data from two patients with non-degenerative spines were processed using an automated deep learning-based segmentation pipeline. In a semi-automated process with minimal user interaction, we generated patient-specific musculoskeletal models and simulated various static loading tasks. To validate the model, calculated vertebral loadings of the lumbar spine and muscle forces were compared with in vivo data from the literature. Finally, results from both models were compared to assess the potential of our process for interindividual analysis.

Results: Calculated vertebral loads and muscle activation overall stood in close correlation with data from the literature. Compression forces normalized to upright standing deviated by a maximum of 16% for flexion and 33% for lifting tasks. Interindividual comparison of compression, as well as lateral and anterior–posterior shear forces, could be linked plausibly to individual spinal alignment and bodyweight.

Conclusion: We developed a method to generate patient-specific musculoskeletal models of the lumbar spine. The models were able to calculate loads of the lumbar spine for static activities with respect to individual biomechanical properties, such as spinal alignment, bodyweight distribution, and ligament and muscle insertion points. The process is automated to a large extent, which makes it suitable for systematic investigation of spinal biomechanics in large datasets.

Current development and prospects of deep learning in spine image analysis: a literature review

BACKGROUND AND OBJECTIVE

As the spine is pivotal in the support and protection of human bodies, much attention is given to the understanding of spinal diseases. Quick, accurate, and automatic analysis of a spine image greatly enhances the efficiency with which spine conditions can be diagnosed. Deep learning (DL) is a representative artificial intelligence technology that has made encouraging progress in the last 6 years. However, it is still difficult for clinicians and technicians to fully understand this rapidly evolving field due to the diversity of applications, network structures, and evaluation criteria. This study aimed to provide clinicians and technicians with a comprehensive understanding of the development and prospects of DL spine image analysis by reviewing published literature.

METHODS

A systematic literature search was conducted in the PubMed and Web of Science databases using the keywords "deep learning" and "spine". Date ranges used to conduct the search were from 1 January, 2015 to 20 March, 2021. A total of 79 English articles were reviewed.

KEY CONTENT AND FINDINGS

The DL technology has been applied extensively to the segmentation, detection, diagnosis, and quantitative evaluation of spine images. It uses static or dynamic image information, as well as local or non-local information. The high accuracy of analysis is comparable to that achieved manually by doctors. However, further exploration is needed in terms of data sharing, functional information, and network interpretability.

CONCLUSIONS

The DL technique is a powerful method for spine image analysis. We believe that, with the joint efforts of researchers and clinicians, intelligent, interpretable, and reliable DL spine analysis methods will be widely applied in clinical practice in the future.

‘Falling heads’: investigating reflexive responses to head–neck perturbations

Background

Reflexive responses to head–neck perturbations affect the injury risk in many different situations ranging from sports-related impact to car accident scenarios. Although several experiments have been conducted to investigate these head–neck responses to various perturbations, it is still unclear why and how individuals react differently and what the implications of these different responses across subjects on the potential injuries might be. Therefore, we see a need for both experimental data and biophysically valid computational Human Body Models with bio-inspired muscle control strategies to understand individual reflex responses better.

Methods

To address this issue, we conducted perturbation experiments of the head–neck complex and used this data to examine control strategies in a simulation model. In the experiments, which we call ’falling heads’ experiments, volunteers were placed in a supine and a prone position on a table with an additional trapdoor supporting the head. This trapdoor was suddenly released, leading to a free-fall movement of the head until reflexive responses of muscles stopped the downwards movement.

Results

We analysed the kinematic, neuronal and dynamic responses for all individuals and show their differences for separate age and sex groups. We show that these results can be used to validate two simple reflex controllers which are able to predict human biophysical movement and modulate the response necessary to represent a large variability of participants.

Conclusions

We present characteristic parameters such as joint stiffness, peak accelerations and latency times. Based on this data, we show that there is a large difference in the individual reflexive responses between participants. Furthermore, we show that the perturbation direction (supine vs. prone) significantly influences the measured kinematic quantities. Finally, ’falling heads’ experiments data are provided open-source to be used as a benchmark test to compare different muscle control strategies and to validate existing active Human Body Models directly.

Effect of different seat heights on lumbar spine flexion during stand-to-sit motion

[Purpose] This study aimed to investigate the movement of the thorax, lumbar spine, and pelvis when healthy participants sit on a chair, and to identify the kinematic characteristics due to changes in the height of the seat. [Participants and Methods] Twenty healthy participants (14 males, 6 females; mean age, 29 ± 5 years) were recruited for this study. They performed stand-to-sit motion using one seat with a height of 100% that of the lower leg length (standard) and another with a height of 60% that of the lower leg length (lower). A three-dimensional motion analysis system and four force plates were used to analyze each joint angle. [Results] The mean lumbar spine flexion angle was significantly increased in the lower versus the standard seat. As a kinematic characteristic, the pelvis tilted posteriorly while the thorax tilted anteriorly, which increased the lumbar spine flexion angle. The pelvis was tilted posteriorly when the hip joint flexed about 60° regardless of the seat height. [Conclusion] The lumbar spine flexion angle increased in the lower seat stand-to-sit motion, which suggested an increase in the load on the lumbar spine. The lumbar spine flexion angle was influenced by the characteristic movements of the thorax and pelvis.

Load Distribution in the Lumbar Spine During Modeled Compression Depends on Lordosis

Excessive or incorrect loading of lumbar spinal structures is commonly assumed as one of the factors to accelerate degenerative processes, which may lead to lower back pain. Accordingly, the mechanics of the spine under medical conditions, such as scoliosis or spondylolisthesis, is well-investigated. Treatments via both conventional therapy and surgical methods alike aim at restoring a "healthy" (or at least pain-free) load distribution. Yet, surprisingly little is known about the inter-subject variability of load bearings within a "healthy" lumbar spine. Hence, we utilized computer tomography data from 28 trauma-room patients, whose lumbar spines showed no visible sign of degeneration, to construct simplified multi-body simulation models. The subject-specific geometries, measured by the corresponding lumbar lordosis (LL) between the endplates of vertebra L1 and the sacrum, served as ceteris paribus condition in a standardized forward dynamic compression procedure. Further, the influence of stimulating muscles from the M. multifidus group was assessed. For the range of available LL from 28 to 66°, changes in compressive and shear forces, bending moments, as well as facet joint forces between adjacent vertebrae were calculated. While compressive forces tended to decrease with increasing LL, facet forces were tendentiously increasing. Shear forces decreased between more cranial vertebrae and increased between more caudal ones, while bending moments remained constant. Our results suggest that there exist significant, LL-dependent variations in the loading of "healthy" spinal structures, which should be considered when striving for individually appropriate therapeutic measures.

Intuitive assessment of modeled lumbar spinal motion by clustering and visualization of finite helical axes

A variety of medical imaging procedures, cadaver experiments, and computer models have been utilized to capture, depict, and understand the motion of the human lumbar spine. Particular interest lies in assessing the relative movement between two adjacent vertebrae, which can be represented by a temporal evolution of finite helical axes (FHA). Mathematically, this FHA evolution constitutes a seven-dimensional quantity: one dimension for the time, two for the (normalized) direction vector, another two for the (unique) position vector, as well as one for each the angle of rotation around and the amount of translation along the axis. Predominantly in the literature, however, movements are assumed to take place in certain physiological planes on which FHA are projected. The resulting three-dimensional quantity - the so-called centrode - is easily presentable but leaves out substantial pieces of available data. Here, we investigate and assess several possibilities to visualize subsets of FHA data of increasing dimensionality. Finally, we utilize an agglomerative hierarchical clustering algorithm and propose a novel visualization technique, namely the quiver principal axis plot (QPAP), to depict the entirety of information inherent to hundreds or thousands of FHA. The QPAP method is applied to flexion-extension, lateral bending, and axial rotation movements of a lumbar spine within both a reduced model as well as a complex upper body system.

Embodiment of intra-abdominal pressure in a flexible multibody model of the trunk and the spinal unloading effects during static lifting tasks

The role of intra-abdominal pressure (IAP) in spinal load reduction has remained controversial, partly because previous musculoskeletal models did not introduce the pressure generating mechanism. In this study, an integrated computational methodology is proposed to combine the IAP change with core muscle activations. An ideal gas relationship was introduced to calculate pressure distribution within the abdominal cavity. Additionally, based on flexible multibody dynamics, a muscle membrane element was developed by incorporating the muscular fiber deformation, inter-fiber stiffness, and volume constancy. This element was then utilized in discretizing the diaphragm and transversus abdominis, forming an IAP-muscle coupling system of the abdominal cavity. Based on this methodology, a forward dynamic simulation of spinal flexion was presented to examine the unloading effect of abdominal breathing. The results confirm that core muscle contraction during the abdominal breathing cycle can substantially reduce the forces of spinal compression together with trunk extensor muscles, and this effect is more pronounced when the IAP increase is produced by contraction of the transversus abdominis. This unloading effect still holds even with the co-activation of other abdominal muscles, providing a potential choice when designing trunk movements during weight-lifting tasks.

Rules of nature's Formula Run: Muscle mechanics during late stance is the key to explaining maximum running speed

The maximum running speed of legged animals is one evident factor for evolutionary selection-for predators and prey. Therefore, it has been studied across the entire size range of animals, from the smallest mites to the largest elephants, and even beyond to extinct dinosaurs. A recent analysis of the relation between animal mass (size) and maximum running speed showed that there seems to be an optimal range of body masses in which the highest terrestrial running speeds occur. However, the conclusion drawn from that analysis-namely, that maximum speed is limited by the fatigue of white muscle fibres in the acceleration of the body mass to some theoretically possible maximum speed-was based on coarse reasoning on metabolic grounds, which neglected important biomechanical factors and basic muscle-metabolic parameters. Here, we propose a generic biomechanical model to investigate the allometry of the maximum speed of legged running. The model incorporates biomechanically important concepts: the ground reaction force being counteracted by air drag, the leg with its gearing of both a muscle into a leg length change and the muscle into the ground reaction force, as well as the maximum muscle contraction velocity, which includes muscle-tendon dynamics, and the muscle inertia-with all of them scaling with body mass. Put together, these concepts' characteristics and their interactions provide a mechanistic explanation for the allometry of maximum legged running speed. This accompanies the offering of an explanation for the empirically found, overall maximum in speed: In animals bigger than a cheetah or pronghorn, the time that any leg-extending muscle needs to settle, starting from being isometric at about midstance, at the concentric contraction speed required for running at highest speeds becomes too long to be attainable within the time period of a leg moving from midstance to lift-off. Based on our biomechanical model, we, thus, suggest considering the overall speed maximum to indicate muscle inertia being functionally significant in animal locomotion. Furthermore, the model renders possible insights into biological design principles such as differences in the leg concept between cats and spiders, and the relevance of multi-leg (mammals: four, insects: six, spiders: eight) body designs and emerging gaits. Moreover, we expose a completely new consideration regarding the muscles' metabolic energy consumption, both during acceleration to maximum speed and in steady-state locomotion.

A geometry- and muscle-based control architecture for synthesising biological movement

A key problem for biological motor control is to establish a link between an idea of a movement and the generation of a set of muscle-stimulating signals that lead to the movement execution. The number of signals to generate is thereby larger than the body's mechanical degrees of freedom in which the idea of the movement may be easily expressed, as the movement is actually executed in this space. A mathematical formulation that provides a solving link is presented in this paper in the form of a layered, hierarchical control architecture. It is meant to synthesise a wide range of complex three-dimensional muscle-driven movements. The control architecture consists of a 'conceptional layer', where the movement is planned, a 'structural layer', where the muscles are stimulated, and between both an additional 'transformational layer', where the muscle-joint redundancy is resolved. We demonstrate the operativeness by simulating human stance and squatting in a three-dimensional digital human model (DHM). The DHM considers 20 angular DoFs and 36 Hill-type muscle-tendon units (MTUs) and is exposed to gravity, while its feet contact the ground via reversible stick-slip interactions. The control architecture continuously stimulates all MTUs ('structural layer') based on a high-level, torque-based task formulation within its 'conceptional layer'. Desired states of joint angles (postural plan) are fed to two mid-level joint controllers in the 'transformational layer'. The 'transformational layer' communicates with the biophysical structures in the 'structural layer' by providing direct MTU stimulation contributions and further input signals for low-level MTU controllers. Thereby, the redundancy of the MTU stimulations with respect to the joint angles is resolved, i.e. a link between plan and execution is established, by exploiting some properties of the biophysical structures modelled. The resulting joint torques generated by the MTUs via their moment arms are fed back to the conceptional layer, closing the high-level control loop. Within our mathematical formulations of the Jacobian matrix-based layer transformations, we identify the crucial information for the redundancy solution to be the muscle moment arms, the stiffness relations of muscle and tendon tissue within the muscle model, and the length-stimulation relation of the muscle activation dynamics. The present control architecture allows the straightforward feeding of conceptional movement task formulations to MTUs. With this approach, the problem of movement planning is eased, as solely the mechanical system has to be considered in the conceptional plan.

Muscle-driven and torque-driven centrodes during modeled flexion of individual lumbar spines are disparate

Lumbar spine biomechanics during the forward-bending of the upper body (flexion) are well investigated by both in vivo and in vitro experiments. In both cases, the experimentally observed relative motion of vertebral bodies can be used to calculate the instantaneous center of rotation (ICR). The timely evolution of the ICR, the centrode, is widely utilized for validating computer models and is thought to serve as a criterion for distinguishing healthy and degenerative motion patterns. While in vivo motion can be induced by physiological active structures (muscles), in vitro spinal segments have to be driven by external torque-applying equipment such as spine testers. It is implicitly assumed that muscle-driven and torque-driven centrodes are similar. Here, however, we show that centrodes qualitatively depend on the impetus. Distinction is achieved by introducing confidence regions (ellipses) that comprise centrodes of seven individual multi-body simulation models, performing flexion with and without preload. Muscle-driven centrodes were generally directed superior–anterior and tail-shaped, while torque-driven centrodes were located in a comparably narrow region close to the center of mass of the caudal vertebrae. We thus argue that centrodes resulting from different experimental conditions ought to be compared with caution. Finally, the applicability of our method regarding the analysis of clinical syndromes and the assessment of surgical methods is discussed.

Estimation of Trunk Muscle Forces Using a Bio-Inspired Control Strategy Implemented in a Neuro-Osteo-Ligamentous Finite Element Model of the Lumbar Spine

Low back pain (LBP), the leading cause of disability worldwide, remains one of the most common and challenging problems in occupational musculoskeletal disorders. The effective assessment of LBP injury risk, and the design of appropriate treatment modalities and rehabilitation protocols, require accurate estimation of the mechanical spinal loads during different activities. This study aimed to: (1) develop a novel 2D beam-column finite element control-based model of the lumbar spine and compare its predictions for muscle forces and spinal loads to those resulting from a geometrically matched equilibrium-based model; (2) test, using the foregoing control-based finite element model, the validity of the follower load (FL) concept suggested in the geometrically matched model; and (3) investigate the effect of change in the magnitude of the external load on trunk muscle activation patterns. A simple 2D continuous beam-column model of the human lumbar spine, incorporating five pairs of Hill's muscle models, was developed in the frontal plane. Bio-inspired fuzzy neuro-controllers were used to maintain a laterally bent posture under five different external loading conditions. Muscle forces were assigned based on minimizing the kinematic error between target and actual postures, while imposing a penalty on muscular activation levels. As compared to the geometrically matched model, our control-based model predicted similar patterns for muscle forces, but at considerably lower values. Moreover, irrespective of the external loading conditions, a near (<3°) optimal FL on the spine was generated by the control-based predicted muscle forces. The variation of the muscle forces with the magnitude of the external load within the simulated range at the L1 level was found linear. This work presents a novel methodology, based on a bio-inspired control strategy, that can be used to estimate trunk muscle forces for various clinical and occupational applications toward shedding light on the ever-elusive LBP etiology.

Moment-rotation behavior of intervertebral joints in flexion-extension, lateral bending, and axial rotation at all levels of the human spine: A structured review and meta-regression analysis

Spinal intervertebral joints are complex structures allowing motion in multiple directions, and many experimental studies have reported moment-rotation response. However, experimental methods, reporting of results, and levels of the spine tested vary widely, and a comprehensive assessment of moment-rotation response across all levels of the spine is lacking. This review aims to characterize moment-rotation response in a consistent manner for all levels of the human spine. A literature search was conducted in PubMed for moment versus rotation data from mechanical testing of intact human cadaveric intervertebral joint specimens in flexion-extension, lateral bending, and axial rotation. A total of 45 studies were included, providing data from testing of an estimated 1,648 intervertebral joints from 518 human cadavers. We used mixed-effects regression analysis to create 75 regression models of moment-rotation response (25 intervertebral joints × 3 directions). We found that a cubic polynomial model provides a good representation of the moment-rotation behavior of most intervertebral joints, and that compressive loading increases rotational stiffness throughout the spine in all directions. The results allow for the direct evaluation of intervertebral ranges of motion across the whole of the spine for given loading conditions. The random-effects outcomes, representing standard deviations of the model coefficients across the dataset, can aid understanding of normal variations in moment-rotation responses. Overall these results fill a large gap, providing the first realistic and comprehensive representations of moment-rotation behavior at all levels of the spine, with broad implications for surgical planning, medical device design, computational modeling, and understanding of spine biomechanics.

Lumbar spinal ligament characteristics extracted from stepwise reduction experiments allow for preciser modeling than literature data

Lumbar ligaments play a key role in stabilizing the spine, particularly assisting muscles at wide-range movements. Hence, valid ligament force–strain data are required to generate physiological model predictions. These data have been obtained by experiments on single ligaments or functional units throughout the literature. However, contrary to detailed spine geometries, gained, for instance, from CT data, ligament characteristics are often inattentively transferred to multi-body system (MBS) or finite element models. In this paper, we use an elaborated MBS model of the lumbar spine to demonstrate how individualized ligament characteristics can be obtained by reversely reenacting stepwise reduction experiments, where the range of motion (ROM) was measured. We additionally validated the extracted characteristics with physiological experiments on intradiscal pressure (IDP). Our results on a total of in each case 160 ROM and 49 IDP simulations indicated superiority of our procedure (seven and eight outliers) toward the incorporation of classical literature data (on average 71 and 31 outliers).

A systems-theoretic analysis of low-level human motor control: application to a single-joint arm model

Continuous control using internal models appears to be quite straightforward explaining human motor control. However, it demands both, a high computational effort and a high model preciseness as the whole trajectory needs to be converted. Intermittent control shows great promise for avoiding these drawbacks of continuous control, at least to a certain extent. In this contribution, we study intermittency at the motoneuron level. We ask: how many different, but constant muscle stimulation sets are necessary to generate a stable movement for a specific motor task? Intermittent control, in our perspective, can be assumed only if the number of transitions is relatively small. As application case, a single-joint arm movement is considered. The muscle contraction dynamics is described by a Hill-type muscle model, for the muscle activation dynamics both Hatze's and Zajac's approach are considered. To actuate the lower arm, up to four muscle groups are implemented. A systems-theoretic approach is used to find the smallest number of transitions between constant stimulation sets. A method for a stability analysis of human motion is presented. A Lyapunov function candidate is specified. Thanks to sum-of-squares methods, the presented procedure is generally applicable and computationally feasible. The region-of-attraction of a transition point, and the number of transitions necessary to perform stable arm movements are estimated. The results support the intermittent control theory on this level of motor control, because only very few transitions are necessary.

Structural and Material Optimization for Automatic Synthesis of Spine-Segment Mechanisms for Humanoid Robots with Custom Stiffness Profiles

Typical artificial joints for humanoid robots use actual human body joints only as an inspiration. The load responses of these structures rarely match those of the corresponding joints, which is important when applying the robots in environments tailored to humans. In this study, we proposed a novel, automated method for designing substitutes for a human intervertebral joint. The substitutes were considered as two platforms, connected by a set of flexible links. Their structural and material parameters were obtained through optimization with a structured Genetic Algorithm, based on the reference angular stiffnesses. The proposed approach was tested in three numerical scenarios. In the first test, a mechanism with angular stiffnesses corresponded to the actual L4–L5 intervertebral joint. Scenarios 2 and 3 featured mechanisms with geometry and structure comparable to the joint, but with custom stiffness profiles. The obtained results proved the effectiveness of the proposed method. It could be employed in the design of artificial joints for humanoid robots and orthotic structures for the human spine. As the approach is general, it could also be extended to different body joints.

On Laterally Perturbed Human Stance: Experiment, Model, and Control

Understanding human balance is a key issue in many research areas. One goal is to suggest analytical models for the human balance. Specifically, we are interested in the stability of a subject when a lateral perturbation is being applied. Therefore, we conducted an experiment, laterally perturbing five subjects on a mobile platform. We observed that the recorded motion is divided into two parts. The legs act together as a first, the head-arms-trunk segment as a second rigid body with pelvis, and the ankle as hinge joints. Hence, we suggest using a planar double-inverted pendulum model for the analysis. We try to reproduce the human reaction utilizing torque control, applied at the ankle and pelvis. The fitting was realized by least square and nonlinear unconstrained optimization on training sets. Our model is not only able to fit to the human reaction, but also to predict it on test sets. We were able to extract and review key features of balance, like torque coupling and delays as outcomes of the aforementioned optimization process. Furthermore, the delays are well within the ranges typically for such compensatory motions, composed of reflex and higher level motor control.

Gradient-based optimization with B-splines on sparse grids for solving forward-dynamics simulations of three-dimensional, continuum-mechanical musculoskeletal system models

Investigating the interplay between muscular activity and motion is the basis to improve our understanding of healthy or diseased musculoskeletal systems. To be able to analyze the musculoskeletal systems, computational models are used. Albeit some severe modeling assumptions, almost all existing musculoskeletal system simulations appeal to multibody simulation frameworks. Although continuum-mechanical musculoskeletal system models can compensate for some of these limitations, they are essentially not considered because of their computational complexity and cost. The proposed framework is the first activation-driven musculoskeletal system model, in which the exerted skeletal muscle forces are computed using 3-dimensional, continuum-mechanical skeletal muscle models and in which muscle activations are determined based on a constraint optimization problem. Numerical feasibility is achieved by computing sparse grid surrogates with hierarchical B-splines, and adaptive sparse grid refinement further reduces the computational effort. The choice of B-splines allows the use of all existing gradient-based optimization techniques without further numerical approximation. This paper demonstrates that the resulting surrogates have low relative errors (less than 0.76%) and can be used within forward simulations that are subject to constraint optimization. To demonstrate this, we set up several different test scenarios in which an upper limb model consisting of the elbow joint, the biceps and triceps brachii, and an external load is subjected to different optimization criteria. Even though this novel method has only been demonstrated for a 2-muscle system, it can easily be extended to musculoskeletal systems with 3 or more muscles.

A hill-type muscle model expansion accounting for effects of varying transverse muscle load

Recent studies demonstrated that uniaxial transverse loading (F_G) of a rat gastrocnemius medialis muscle resulted in a considerable reduction of maximum isometric muscle force (ΔF_im). A hill-type muscle model assuming an identical gearing G between both ΔF_im and F_G as well as lifting height of the load (Δh) and longitudinal muscle shortening (Δl_CC) reproduced experimental data for a single load. Here we tested if this model is able to reproduce experimental changes in ΔF_im and Δh for increasing transverse loads (0.64 N, 1.13 N, 1.62 N, 2.11 N, 2.60 N). Three different gearing ratios were tested: (I) constant G_c representing the idea of a muscle specific gearing parameter (e.g. predefined by the muscle geometry), (II) G_exp determined in experiments with varying transverse load, and (III) G_f that reproduced experimental ΔF_im for each transverse load. Simulations using G_c overestimated ΔF_im (up to 59%) and Δh (up to 136%) for increasing load. Although the model assumption (equal G for forces and length changes) held for the three lower loads using G_exp and G_f, simulations resulted in underestimation of ΔF_im by 38% and overestimation of Δh by 58% for the largest load, respectively. To simultaneously reproduce experimental ΔF_im and Δh for the two larger loads, it was necessary to reduce F_im by 1.9% and 4.6%, respectively. The model seems applicable to account for effects of muscle deformation within a range of transverse loading when using a linear load-dependent function for G.

Human body modeling method to simulate the biodynamic characteristics of spine in vivo with different sitting postures

The aim of this study is to model the computational model of seated whole human body including skeleton, muscle, viscera, ligament, intervertebral disc, and skin to predict effect of the factors (sitting postures, muscle and skin, buttocks, viscera, arms, gravity, and boundary conditions) on the biodynamic characteristics of spine. Two finite element models of seated whole body and a large number of finite element models of different ligamentous motion segments were developed and validated. Static, modal, and transient dynamic analyses were performed. The predicted vertical resonant frequency of seated body model was in the range of vertical natural frequency of 4 to 7 Hz. Muscle, buttocks, viscera, and the boundary conditions of buttocks have influence on the vertical resonant frequency of spine. Muscle played a very important role in biodynamic response of spine. Compared with the vertical posture, the posture of lean forward or backward led to an increase in stress on anterior or lateral posterior of lumbar intervertebral discs. This indicated that keeping correct posture could reduce the injury of vibration on lumbar intervertebral disc under whole-body vibration. The driving posture not only reduced the load of spine but also increased the resonant frequency of spine.

RIGID MUSCULOSKELETAL MODELS OF THE HUMAN BODY SYSTEMS: A REVIEW

Advancing the knowledge of the biomechanics of the human body is essential to improve the clinical decision-makings of musculoskeletal disorders in the framework of in silico medicine. An impressive number of research projects focused on the development of rigid-body musculoskeletal models have been conducted over the world thanks to the new research directives. However, the application of these models in clinical practices remains a challenging issue. The objective of this review paper was to present the most current rigid-body musculoskeletal models of the human body systems and to analyze their trends and weaknesses for clinical applications. Then, recommendations were proposed for future researches toward fully clinical decision support. A systematic review process was performed. Well-selected studies related to the most current rigid-body 3D musculoskeletal models for each body system component (jaw, cervical spine, upper limbs, lumbar spine, and lower limbs) were summarized and explored. Trends in rigid musculoskeletal modeling are highlighted as personalization, new imaging techniques for specific joint kinematics, and computational efficiency. Weaknesses are highlighted as modeling assumptions, use of generic model, lack of modeling consensus, model validation, and parameter and model uncertainties. Future directions related to joint and muscle modeling, neuro-musculoskeletal modeling, model validation, data and model uncertainty quantification are recommended.

Effect of uphill and downhill walking on walking performance in geriatric patients using a wheeled walker

BACKGROUND

Wheeled walkers are recommended to improve walking performance in older persons and to encourage and assist participation in daily life. Nevertheless, using a wheeled walker can cause serious problems in the natural environment. This study aimed to compare uphill and downhill walking with walking level in geriatric patients using a wheeled walker. Furthermore, we investigated the effect of using a wheeled walker with respect to dual tasking when walking level.

METHODS

A total of 20 geriatric patients (median age 84.5 years) walked 10 m at their habitual pace along a level surface, uphill and downhill, with and without a standard wheeled walker. Gait speed, stride length and cadence were assessed by wearable sensors and the walk ratio was calculated.

RESULTS

When using a wheeled walker while walking level the walk ratio improved (0.58 m/[steps/min] versus 0.57 m/[steps/min], p = 0.023) but gait speed decreased (1.07 m/s versus 1.12 m/s, p = 0.020) when compared to not using a wheeled walker. With respect to the walk ratio, uphill and downhill walking with a wheeled walker decreased walking performance when compared to level walking (0.54 m/[steps/min] versus 0.58 m/[steps/min], p = 0.023 and 0.55 m/[steps/min] versus 0.58 m/[steps/min], p = 0.001, respectively). At the same time, gait speed decreased (0.079 m/s versus 1.07 m/s, p < 0.0001) or was unaffected.

CONCLUSION

The use of a wheeled walker improved the quality of level walking but the performance of uphill and downhill walking was worse compared to walking level when using a wheeled walker.

Intermuscular pressure between synergistic muscles correlates with muscle force

The purpose of the study was to examine the relationship between muscle force generated during isometric contractions (i.e. at a constant muscle–tendon unit length) and the intermuscular (between adjacent muscles) pressure in synergistic muscles. Therefore, the pressure at the contact area of the gastrocnemius and plantaris muscle was measured synchronously to the force of the whole calf musculature in the rabbit species Oryctolagus cuniculus. Similar results were obtained when using a conductive pressure sensor, or a fibre-optic pressure transducer connected to a water-filled balloon. Both methods revealed a strong linear relationship between force and pressure in the ascending limb of the force-length relationship. The shape of the measured force–time and pressure–time traces was almost identical for each contraction (r=0.97). Intermuscular pressure ranged between 100 and 700 mbar (70,000 Pa) for forces up to 287 N. These pressures are similar to previous (intramuscular) recordings within skeletal muscles of different vertebrate species. Furthermore, our results suggest that the rise in intermuscular pressure during contraction may reduce the force production in muscle packages (compartments).

Force reduction induced by unidirectional transversal muscle loading is independent of local pressure

Transversal unidirectional compression applied to muscles via external loading affects muscle contraction dynamics in the longitudinal direction. A recent study reported decreasing longitudinal muscle forces with increasing transversal load applied with a constant contact area (i.e., leading to a simultaneous increase in local pressure). To shed light on these results, we examine whether the decrease in longitudinal force depends on the load, the local pressure, or both. To this end, we perform isometric experiments on rat M. gastrocnemius medialis without and with transversal loading (i) changing the local pressure from 1.1-3.2Ncm(-2) (n=9) at a constant transversal load (1.62N) and (ii) increasing the transversal load (1.15-3.45N) at a constant local pressure of 2.3Ncm(-2) (n=7). While we did not note changes in the decrease in longitudinal muscle force in the first experiment, the second experiment resulted in an almost-linear reduction of longitudinal force between 7.5±0.6% and 14.1±1.7%. We conclude that the observed longitudinal force reduction is not induced by local effects such as malfunction of single muscle compartments, but that similar internal stress conditions and myofilament configurations occur when the local pressure changes given a constant load. The decreased longitudinal force may be explained by increased internal pressure and a deformed myofilament lattice that is likely associated with the decomposition of cross-bridge forces on the one hand and the inhibition of cross-bridges on the other hand.

The effect of parameters of equilibrium-based 3-D biomechanical models on extracted muscle synergies during isometric lumbar exertion

A hallmark of more advanced models is their higher details of trunk muscles represented by a larger number of muscles. The question is if in reality we control these muscles individually as independent agents or we control groups of them called "synergy". To address this, we employed a 3-D biomechanical model of the spine with 18 trunk muscles that satisfied equilibrium conditions at L4/5, with different cost functions. The solutions of several 2-D and 3-D tasks were arranged in a data matrix and the synergies were computed by using non-negative matrix factorization (NMF) algorithms. Variance accounted for (VAF) was used to evaluate the number of synergies that emerged by the analysis, which were used to reconstruct the original muscle activations. It was showed that four and six muscle synergies were adequate to reconstruct the input data of 2-D and 3-D torque space analysis. The synergies were different by choosing alternative cost functions as expected. The constraints affected the extracted muscle synergies, particularly muscles that participated in more than one functional tasks were influenced substantially. The compositions of extracted muscle synergies were in agreement with experimental studies on healthy participants. The following computational methods show that the synergies can reduce the complexity of load distributions and allow reduced dimensional space to be used in clinical settings.

Three-Dimensional Muscle Architecture and Comprehensive Dynamic Properties of Rabbit Gastrocnemius, Plantaris and Soleus: Input for Simulation Studies

The vastly increasing number of neuro-muscular simulation studies (with increasing numbers of muscles used per simulation) is in sharp contrast to a narrow database of necessary muscle parameters. Simulation results depend heavily on rough parameter estimates often obtained by scaling of one muscle parameter set. However, in vivo muscles differ in their individual properties and architecture. Here we provide a comprehensive dataset of dynamic (n = 6 per muscle) and geometric (three-dimensional architecture, n = 3 per muscle) muscle properties of the rabbit calf muscles gastrocnemius, plantaris, and soleus. For completeness we provide the dynamic muscle properties for further important shank muscles (flexor digitorum longus, extensor digitorum longus, and tibialis anterior; n = 1 per muscle). Maximum shortening velocity (normalized to optimal fiber length) of the gastrocnemius is about twice that of soleus, while plantaris showed an intermediate value. The force-velocity relation is similar for gastrocnemius and plantaris but is much more bent for the soleus. Although the muscles vary greatly in their three-dimensional architecture their mean pennation angle and normalized force-length relationships are almost similar. Forces of the muscles were enhanced in the isometric phase following stretching and were depressed following shortening compared to the corresponding isometric forces. While the enhancement was independent of the ramp velocity, the depression was inversely related to the ramp velocity. The lowest effect strength for soleus supports the idea that these effects adapt to muscle function. The careful acquisition of typical dynamical parameters (e.g. force-length and force-velocity relations, force elongation relations of passive components), enhancement and depression effects, and 3D muscle architecture of calf muscles provides valuable comprehensive datasets for e.g. simulations with neuro-muscular models, development of more realistic muscle models, or simulation of muscle packages.