Optimization of active muscle force-length models using least squares curve fitting

The objective of this paper is to propose an asymmetric Gaussian function as an alternative to the existing active force-length models, and to optimize this model along with several other existing models by using the least squares curve fitting method. The minimal set of coefficients is identified for each of these models to facilitate the least squares curve fitting. Sarcomere simulated data and one set of rabbits extensor digitorum II experimental data are used to illustrate optimal curve fitting of the selected force–length functions. The results shows that all the curves fit reasonably well with the simulated and experimental data, while the Gordon–Huxley–Julian model and asymmetric Gaussian function are better than other functions in terms of statistical test scores root mean squared error and R-squared. However, the differences in RMSE scores are insignificant (0.3–6%) for simulated data and (0.2–5%) for experimental data. The proposed asymmetric Gaussian model and the method of parametrization of this and the other force–length models mentioned above can be used in the studies on active force–length relationships of skeletal muscles that generate forces to cause movements of human and animal bodies

Estimation of muscular forces from SSA smoothed sEMG signals calibrated by inverse dynamics-based physiological static optimization

The estimation of muscular forces is useful in several areas such as biomedical or rehabilitation engineering. As muscular forces cannot be measured in vivo non-invasively they must be estimated by using indirect measurements such as surface electromyography (sEMG) signals or by means of inverse dynamic (ID) analyses. This paper proposes an approach to estimate muscular forces based on both of them. The main idea is to tune a gain matrix so as to compute muscular forces from sEMG signals. To do so, a curve fitting process based on least-squares is carried out. The input is the sEMG signal filtered using singular spectrum analysis technique. The output corresponds to the muscular force estimated by the ID analysis of the recorded task, a dumbbell weightlifting. Once the model parameters are tuned, it is possible to obtain an estimation of muscular forces based on sEMG signal. This procedure might be used to predict muscular forces in vivo outside the space limitations of the gait analysis laboratory.Postprint (published version

Modelling, analysis and feedback control design for upright standing sways

Human body upright standing is inherently unstable, and as a bipedal creature, the body can implement several functions such as upright standing, walking and running, with the help of the central nervous system. Understanding the stability control of the human body during upright standing is important for prosthetic design and joint prostheses, walking restoration, diagnosis of nervous system diseases. Also, it is essential to anthropology, clinical research, aerospace science and kinesiology.Therefore, the objective of this work is to model the musculoskeletal system of human upright standing posture for analysis and control design of body sway. An asymmetric Gaussian function is proposed to model the force-length relationship and compared with other existing force-length models. By using least square curve fitting tools with a set of rabbit experimental data, and simulated data that represent sarcomere of the frog. Also, the implicit and explicit ordinary differential equations, are used to model muscle-tendon unit and compare the simulation results in term of singularity.In addition to, the equilibrium analysis is used to determine sway ranges during upright standing, and the equilibrium points can be used to linearize the model for feedback control design and stability analysis of the musculoskeletal system. Furthermore, a switching function is designed to model the intermittent activity of the MG muscle, where the parameters are optimised using the centre of gravity and electromyography data with Genetic Algorithm tool. The musculoskeletal system of the human body is modelled as a single inverted pendulum, which rotates around the ankle joint, in the sagittal plane only. The calf muscles especially the medial gastrocnemius activated intermittently, and soleus activated continuously are included in the model of the musculoskeletal system. The developed musculoskeletal system model is linearized in order to have clear stability analysis using Routh-Hurwitz stability criterion and eigenvalue analysis.The results show that the musculoskeletal system cannot be stabilised at the upright standing without feeding back angular velocity. The equilibrium analysis reveals how the sway range (sway points) depends on the used anatomical and anthropometry data. Finally, the stability analysis shows that during forwarding sway the calf muscles are shortening paradoxically and lengthening during backwards sway, which supports some existing experimental results. The model-based analysis which used in modelling the body upright standing, will help in analysis and understands the dynamics of the body during upright standing. Also, it assists in medical research, in clinical diagnostics and application

Development of a continuum mechanics model of passive skeletal muscle

Skeletal muscle force evaluation is difficult to implement in a clinical setting. Muscle force is typically assessed through either manual muscle testing, isokinetic/isometric dynamometry, or electromyography (EMG). Manual muscle testing is a subjective evaluation of a patient’s ability to move voluntarily against gravity and to resist force applied by an examiner. Muscle testing using dynamometers adds accuracy by quantifying functional mechanical output of a limb. However, like manual muscle testing, dynamometry only provides estimates of the joint moment. EMG quantifies neuromuscular activation signals of individual muscles, and is used to infer muscle function. Despite the abundance of work performed to determine the degree to which EMG signals and muscle forces are related, the basic problem remains that EMG cannot provide a quantitative measurement of muscle force. Intramuscular pressure (IMP), the pressure applied by muscle fibers on interstitial fluid, has been considered as a correlate for muscle force. Numerous studies have shown that an approximately linear relationship exists between IMP and muscle force. A microsensor has recently been developed that is accurate, biocompatible, and appropriately sized for clinical use. While muscle force and pressure have been shown to be correlates, IMP has been shown to be non-uniform within the muscle. As it would not be practicable to experimentally evaluate how IMP is distributed, computational modeling may provide the means to fully evaluate IMP generation in muscles of various shapes and operating conditions. The work presented in this dissertation focuses on the development and validation of computational models of passive skeletal muscle and the evaluation of their performance for prediction of IMP. A transversly isotropic, hyperelastic, and nearly incompressible model will be evaluated along with a poroelastic model

The Viscoelastic Properties of Passive Eye Muscle in Primates. I: Static Forces and Step Responses

The viscoelastic properties of passive eye muscles are prime determinants of the deficits observed following eye muscle paralysis, the root cause of several types of strabismus. Our limited knowledge about such properties is hindering the ability of eye plant models to assist in formulating a patient's diagnosis and prognosis. To investigate these properties we conducted an extensive in vivo study of the mechanics of passive eye muscles in deeply anesthetized and paralyzed monkeys. We describe here the static length-tension relationship and the transient forces elicited by small step-like elongations. We found that the static force increases nonlinearly with length, as previously shown. As expected, an elongation step induces a fast rise in force, followed by a prolonged decay. The time course of the decay is however considerably more complex than previously thought, indicating the presence of several relaxation processes, with time constants ranging from 1 ms to at least 40 s. The mechanical properties of passive eye muscles are thus similar to those of many other biological passive tissues. Eye plant models, which for lack of data had to rely on (erroneous) assumptions, will have to be updated to incorporate these properties

Estimating individual muscle forces in human movement

If individual muscle forces could be routinely calculated in vivo, non-invasively, considerable insight could be obtained into the etiology of injuries and the training of muscle for rehabilitation and sport. As there are generally more muscles crossing a joint than there are degrees of freedom at the joint, determining the individual forces in the muscles crossing a joint is a non-trivial problem. This study focused on the development of the procedures necessary to estimate the individual muscle forces during a dumbell curl, and the measurement procedures required for the determination of the necessary input parameters. The procedures developed could easily be applied to other body movements. [Continues.

Hip Mechanics of Unilateral Drop Landings

Increased hip forces are a proposed factor for osteoarthritis and femoroacetabular impingement. These forces can be estimated through musculoskeletal modeling using measured kinematics and kinetics. An understanding of hip joint loading during landing in a asymptomatic population will begin to elucidate what, if any, sex differences exist and how changes in landing condition alter hip mechanics. The overall purpose of this dissertation was to explore how sex and landing condition effect landing mechanics. Landing mechanics were quantified using ground reaction forces (GRF), hip joint forces (HJF), and lower extremity kinematics during unilateral drop landings from 30-cm, 40-cm, and 50-cm, as well as, a 40-cm land-and-cut task. The relationships between sex and limb side, sex and landing task, and sex and landing height on landing mechanics were assessed using three sub-studies. Eighty-three, recreationally active, adult volunteers completed landing tasks (40 participants completed the land-and-cut task). For sex-limb side, bilateral differences (right versus left) were examined at 40-cm. No bilateral differences were identified. For sex-landing task, 40-cm drop landings were compared to land-and-cuts. Higher peak GRF (pGRF) and pGRF loading rates were identified for landing-only. Landing-only tasks were performed with less ankle dorsiflexion range of motion for landing (ROML) and impact (ROMI) phases. Landing-only tasks demonstrated more hip adduction ROML and more hip flexion ROMI. For sex-landing height, landings were compared between 30-cm and 50-cm. Increasing landing height resulted in increased pGRF, pHJF, pGRF loading rate, and pHJF loading rate. With increased height, larger 3-D hip and knee flexion ROMI and ROML were identified, as well as increased ankle dorsiflexion ROML. There were no interaction effects between sex and landing condition. Sex differences across sub-studies demonstrated consistent trends. In all studies, females incurred larger pGRF compared to males, yet only the landing height analysis demonstrated increased pHJF. Females exhibited larger hip adduction and reduced hip rotation ROML. Females exhibited larger hip flexion, hip adduction, and knee flexion ROMI. The landing task analysis identified increased female ankle dorsiflexion ROMI. Sex differences were identified between landing conditions, yet the lack of sex-landing condition interaction indicates both sexes may utilize similar modifications in response to changing landing conditions

Estimation of musculotendon parameters for scaled and subject specific musculoskeletal models using an optimization technique.

A challenging aspect of subject specific musculoskeletal modeling is the estimation of muscle parameters, especially optimal fiber length and tendon slack length. In this study, the method for scaling musculotendon parameters published by Winby et al. (2008), J. Biomech. 41, 1682-1688, has been reformulated, generalized and applied to two cases of practical interest: 1) the adjustment of muscle parameters in the entire lower limb following linear scaling of a generic model and 2) their estimation "from scratch" in a subject specific model of the hip joint created from medical images. In the first case, the procedure maintained the muscles׳ operating range between models with mean errors below 2.3% of the reference model normalized fiber length value. In the second case, a subject specific model of the hip joint was created using segmented bone geometries and muscle volumes publicly available for a cadaveric specimen from the Living Human Digital Library (LHDL). Estimated optimal fiber lengths were found to be consistent with those of a previously published dataset for all 27 considered muscle bundles except gracilis. However, computed tendon slack lengths differed from tendon lengths measured in the LHDL cadaver, suggesting that tendon slack length should be determined via optimization in subject-specific applications. Overall, the presented methodology could adjust the parameters of a scaled model and enabled the estimation of muscle parameters in newly created subject specific models. All data used in the analyses are of public domain and a tool implementing the algorithm is available at https://simtk.org/home/opt_muscle_par

A comparative study of surrogate musculoskeletal models using various neural network configurations

Title from PDF of title page, viewed on August 13, 2013Thesis advisor: Reza R. DerakhshaniVitaIncludes bibliographic references (pages 85-88)Thesis (M.S.)--School of Computing and Engineering. University of Missouri--Kansas City, 2013The central idea in musculoskeletal modeling is to be able to predict body-level (e.g. muscle forces) as well as tissue-level information (tissue-level stress, strain, etc.). To develop computationally efficient techniques to analyze such models, surrogate models have been introduced which concurrently predict both body-level and tissue-level information using multi-body and finite-element analysis, respectively. However, this kind of surrogate model is not an optimum solution as it involves the usage of finite element models which are computation intensive and involve complex meshing methods especially during real-time movement simulations. An alternative surrogate modeling method is the use of artificial neural networks in place of finite-element models. The ultimate objective of this research is to predict tissue-level stresses experienced by the cartilage and ligaments during movement and achieve concurrent simulation of muscle force and tissue stress using various surrogate neural network models, where stresses obtained from finite-element models provide the frame of reference. Over the last decade, neural networks have been successfully implemented in several biomechanical modeling applications. Their adaptive ability to learn from examples, simple implementation techniques, and fast simulation times make neural networks versatile and robust when compared to other techniques. The neural network models are trained with reaction forces from multi-body models and stresses from finite element models obtained at the interested elements. Several configurations of static and dynamic neural networks are modeled, and accuracies close to 93% were achieved, where the correlation coefficient is the chosen measure of goodness. Using neural networks, the simulation time was reduced nearly 40,000 times when compared to the finite-element models. This study also confirms theoretical concepts that special network configurations--including average committee, stacked generalization, and negative correlation learning--provide considerably better results when compared to individual networks themselves.Introduction -- Methods -- Results -- Conclusion -- Future work -- Appendix A. Various linear and non-linear modeling techniques -- Appendix B. Error analysi