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We present and evaluate a new approach to estimate calf muscle-tendon parameters and calculate calf muscle-tendon function during walking. We used motion analysis, ultrasound, and EMG data of the calf muscles collected in six young and six older adults during treadmill walking as inputs to a new optimal estimation algorithm. We used estimated parameters or scaled generic parameters in an existing approach to calculate muscle fiber lengths and activations. We calculated the fit with experimental data in terms of root mean squared differences (RMSD) and coefficients of determination (R2). We also calculated the calf muscle metabolic energy cost. RMSD between measured and calculated fiber lengths and activations decreased and R2 increased when estimating parameters compared to using scaled generic parameters. Moreover, R2 between measured and calculated gastrocnemius medialis fiber length and soleus activations increased by 19 % and 70 %, and calf muscle metabolic energy decreased by 25% when using estimated parameters compared to using scaled generic parameters at speeds not used for estimation. This new approach estimates calf muscle-tendon parameters in good accordance with values reported in literature. The approach improves calculations of calf muscle-tendon interaction during walking and highlights the importance of individualizing calf muscle-tendon parameters.

1.. Introduction: Gait analysis together with musculoskeletal modeling can be used to calculate muscle forces and assess pathological gait [1]. No generic, pediatric musculoskeletal models are available and, therefore, linear scaling methods are commonly used to personalize a generic, adult musculoskeletal model to the child’s anthropometry. 2. Research: How different are joint kinematics, joint kinetics and muscle force estimates of generic scaled models compared to medical-imaging based models in typically developing (TD) children? 3. Methods: 3D motion capture data and magnetic resonance images (MRI) of a TD boy (age: 8 years; height: 1.23 m; weight: 20.4 kg) were collected. Two musculoskeletal OpenSim models were created: (1) a scaled generic model (M_gen), and (2) a MRI-based model, which included subject-specific musculoskeletal geometry (M_mri) [2]. Joint kinematics, joint kinetics and muscle forces were calculated for each model using OpenSim 3.3 [3]. Joint kinematics, joint kinetics, muscle force waveforms, as well as femoral anteversion angle, neck-shaft angle and hip joint centre location were compared between both models. 4. Results: Joint kinematics and joint kinetics were surprisingly similar between the M_gen and M_mri with root-mean-square-differences below 2.8° and 0.05Nm/kg for joint angles and moments, respectively (Fig. 1, Fig. 2). Depending on the analyzed muscle, differences in muscle forces varied substantially (up to 230% difference) between the M_gen and M_mri (Fig. 3). Femoral anteversion and neck-shaft angles differed between M_gen and M_mri by 12 and 5 degrees, respectively. The hip joint centre position differed between both models by 5, 15 and 6 mm in the anterior/posterior, superior/inferior and medial/lateral direction, respectively.

Plantar pressure simulation driven by integrated 3D motion capture data, using both a finite element and a discrete element model, is compared for ten healthy and ten diabetic neuropathic subjects. The simulated peak pressure deviated on average between 16.7 and 34.2% from the measured peak pressure. The error in the position of the peak pressure was on average smaller than 4.2 cm. No method was more accurate than the other although statistical differences were found between them. Both techniques are thus complementary and useful tools to better understand the alteration of diabetic foot biomechanics during gait. ispartof: Computer Methods in Biomechanics and Biomedical Engineering vol:20 issue:13 pages:1442-1452 ispartof: location:England status: published

This paper compares geometry-based knee axes of rotation (transepicondylar axis and geometric center axis) and motion-based functional knee axes of rotation (fAoR). Two algorithms are evaluated to calculate fAoRs: Gamage and Lasenby's sphere fitting algorithm (GL) and Ehrig et al.'s axis transformation algorithm (SARA). Calculations are based on 3D motion data acquired during isokinetic dynamometry. AoRs are validated with the equivalent axis based on static MR-images. We quantified the difference in orientation between two knee axes of rotation as the angle between the projection of the axes in the transversal and frontal planes, and the difference in location as the distance between the intersection points of the axes with the sagittal plane. Maximum differences between fAoRs resulting from GL and SARA were 5.7° and 15.4mm, respectively. Maximum differences between fAoRs resulting from GL or SARA and the equivalent axis were 5.4°/11.5mm and 8.6°/12.8mm, respectively. Differences between geometry-based axes and EA are larger than differences between fAoR and EA both in orientation (maximum 10.6°).and location (maximum 20.8mm). Knee joint angle trajectories and the corresponding accelerations for the different knee axes of rotation were estimated using Kalman smoothing. For the joint angles, the maximum RMS difference with the MRI-based equivalent axis, which was used as a reference, was 3°. For the knee joint accelerations, the maximum RMS difference with the equivalent axis was 20°/s(2). Functional knee axes of rotation describe knee motion better than geometry-based axes. GL performs better than SARA for calculations based on experimental dynamometry.

We assessed and compared sensitivities of dynamic simulations to musculotendon (MT) parameters for gait and dynamometer experiments. Our aim with this comparison was to investigate whether dynamometer experiments could provide information about MT-parameters that are important to reliably study MT-function during gait. This would mean that dynamometer experiments could be used to estimate these parameters. Muscle contribution to the joint torque (MT-torque) rather than relative MT-force primarily affects the resulting gait pattern and torque measured by the dynamometer. In contrast to recent studies, therefore, we assessed the sensitivity of the MT-torque, rather than the sensitivity of the relative MT-force. Based on sensitivity of the MT-torque to a parameter perturbation, MT-parameters of the knee flexors and extensors were classified in three categories: low, medium, and high. For gait, classification was based on the average sensitivity during a gait cycle. For isometric and isokinetic dynamometer experiments, classification was based on the highest sensitivity found in the experiments. The calculated muscle contributions to the knee torque during gait and dynamometer experiments had a high sensitivity to only a limited number of MT-parameters of the knee flexors and extensors, suggesting that not all MT-parameters need to be estimated. In general, the highest sensitivity was found for tendon slack length. However, for some muscles the sensitivity to the optimal fibre length or the maximal isometric muscle force was also high or medium. The classification of the individual MT-parameters for gait and dynamometer experiments was largely similar. We therefore conclude that dynamometer experiments provide information about MT-parameters important to reliably study MT-function during gait, so that subject-specific estimates of MT-parameters could be made based on dynamometer experiments.

s / Gait & Posture 42S (2015) S1–S90 S59 decreased IGFBP-3 concentrations compared to control in bothpreand post-training. http://dx.doi.org/10.1016/j.gaitpost.2015.03.103 Pattern recognition methods in clinical gait analysis – What do we gain? M. Bruderer-Hofstetter1,∗, F. Rast2, C. Bauer2, E. Graf2, A. Meichtry1 1 Institute of Physiotherapy, University of Applied Sciences Zurich, Winterthur, Switzerland 2 Laboratory for Motion Analysis, University of Applied Sciences Zurich, Winterthur, Switzerland Introduction and aim: Pattern recognition methods have been widely used in clinical gait analysis [1]. Although a combination of principal component analysis (PCA) and support vector machines (SVM) demonstrated a high sensitivity to visualize subtle differences inmovement patterns [2,3] the benefit of pattern recognition methods in clinical application remains uncertain. Therefore, the aim of our study was to compare the results of a discrete parameter analysis with a pattern recognition approach in order to detect differences in kinematics and kinetics between two different shod conditions. Patients/materials and methods: Five walking trials for each of the two conditions of 20 healthy subjects were captured using a 7-camera-motion-analysis-system (Vicon, 200Hz) and two forceplates (AMTI, 1000Hz). Discrete parameter analysis calculated a priori chosen kinematic and kinetic parameters. Pattern recognition approach (PCA) extracted gait features (PC) from an input matrix containing kinematic and kineticwaveforms. Subsequently, a SVM classifier with linear kernel function was applied to determine the optimal PC-subspace. Within the remaining PCs and all parameters paired sample t-testswere applied and Cohens’ d effect sizes were calculated. Results:Discrete parameter analysis revealed significant differences (p

We developed a Kalman smoothing algorithm to improve estimates of joint kinematics from measured marker trajectories during motion analysis. Kalman smoothing estimates are based on complete marker trajectories. This is an improvement over other techniques, such as the global optimisation method (GOM), Kalman filtering, and local marker estimation (LME), where the estimate at each time instant is only based on part of the marker trajectories. We applied GOM, Kalman filtering, LME, and Kalman smoothing to marker trajectories from both simulated and experimental gait motion, to estimate the joint kinematics of a ten segment biomechanical model, with 21 degrees of freedom. Three simulated marker trajectories were studied: without errors, with instrumental errors, and with soft tissue artefacts (STA). Two modelling errors were studied: increased thigh length and hip centre dislocation. We calculated estimation errors from the known joint kinematics in the simulation study. Compared with other techniques, Kalman smoothing reduced the estimation errors for the joint positions, by more than 50% for the simulated marker trajectories without errors and with instrumental errors. Compared with GOM, Kalman smoothing reduced the estimation errors for the joint moments by more than 35%. Compared with Kalman filtering and LME, Kalman smoothing reduced the estimation errors for the joint accelerations by at least 50%. Our simulation results show that the use of Kalman smoothing substantially improves the estimates of joint kinematics and kinetics compared with previously proposed techniques (GOM, Kalman filtering, and LME) for both simulated, with and without modelling errors, and experimentally measured gait motion.

The purpose of this paper is to show that every finite dimensional division algebra of minimal rank, i.e., of minimal complexity with respect to the noncommutative model of computation, is a finite simple field extension. Moreover, we investigate the structure of the variety of optimal algorithms for the computation of the multiplication in such fields modulo the isotropy group of the problem.

This paper contains the general frame of a theory of varieties of algorithms for the computation of bilinear mappings. In particular, we shall study linear mappings which operate on algo0rithm varieties. It will be shown that every bilinear mapping Φ defines in a natural way a group of automorphisms operating on the variety of optimal algorithms for Φ. This group is called the isotropy group of Φ. For some important classes of bilinear mappings these groups will be determined. Applications of these results will appear in parts II and III of this work.

A supersymmetric integral theorem that extends results of Parisi, Sourlas, Efetov, Wegner, and others is rigorously proved. In particular, arbitrary generators are allowed in the integrand (instead of canonical ones) and the invariance condition is very much relaxed. The connection with Cauchy’s integral formula is made transparent. In passing, the unitary Lie supergroup is studied by using elementary methods. Applications in the theory of disordered systems are discussed.

In this paper we will show that Strassen's algorithm for the computation of the product of 2 × 2-matrices is essentially unique. As an application of this result we will answer the question to what extent elements of the trivial algorithm for 2 × 2-matrix multiplication can be used in an optimal one.

The aim of this paper is to prove several theorems of Radon-Nikodym-type, which hold both in real and non-archimedean integration theory. As an application of these theorems and of the classical Radon-Nikodym theorem, we give a description of the second dual\(\mathbb{D}\)(X,ℂ) of the space of all continuous complex valued functions on the locally compact space X, which vanish at infinity.

In this paper we consider optimal algorithms for the computation of Φ :( x , y )↦ ( xy , yx ), where x , y are 2×2-matrices over a field K . It is shown that, if the characteristic of K is different from two, then optimal algorithms for the computation of Φ have length nine. Moreover, there are several different equivalence classes of optimal algorithms for Φ. If K = GF(2), then optimal algorithms for the computation of Φ have length ten.

If A is a finite-dimensional associative k-algebra with unit, then its rank R( A ), i.e. its bilinear complexity, is never less than 2dim A −# M ( A ) . A is said to be of minimal rank if R( A )=2dim A −# M ( A ) . In this paper we determine for infinite perfect fields k all commutative k-algebras of minimal rank. Roughly speaking, these algebras are built up from simply generated structures which annihilate each other. Furthermore, we indicate how this result can be used to obtain new lower bounds for the rank of specific commutative algebras.

Let U,V,W be finite dimensional vector spaces over a field k and let : U x V ~ W be a bilinear mapping. The (multiplicative) complexity L(@) of # is defined as the least rE I~ such that there are linear forms u 1,...,u r,v 1,...,v r 6 (UxV)* and elements w 1,...,wr6 W satisfying r #(x,y) = Z up(x,y) vp(x,y) wp for all (x,y)E U xV. p=1 The r-tuple ((up,vp,wp)6(UxV)*x(UxV)*x W , I