Tobias Siebert

Nonlinearities make a difference: comparison of two common Hill-type models with real muscle

Compared to complex structural Huxley-type models, Hill-type models phenomenologically describe muscle contraction using only few state variables. The Hill-type models dominate in the ever expanding field of musculoskeletal simulations for simplicity and low computational cost. Reasonable parameters are required to gain insight into mechanics of movement. The two most common Hill-type muscle models used contain three components. The series elastic component is connected in series to the contractile component. A parallel elastic component is either connected in parallel to both the contractile and the series elastic component (model [CC+SEC]), or is connected in parallel only with the contractile component (model [CC]). As soon as at least one of the components exhibits substantial nonlinearities, as, e.g., the contractile component by the ability to turn on and off, the two models are mechanically different. We tested which model ([CC+SEC] or [CC]) represents the cat soleus better. Ramp experiments consisting of an isometric and an isokinetic part were performed with an in situ cat soleus preparation using supramaximal nerve stimulation. Hill-type models containing force–length and force–velocity relationship, excitation–contraction coupling and series and parallel elastic force–elongation relations were fitted to the data. To test which model might represent the muscle better, the obtained parameters were compared with experimentally determined parameters. Determined in situations with negligible passive force, the force–velocity relation and the series elastic component relation are independent of the chosen model. In contrast to model [CC+SEC], these relations predicted by model [CC] were in accordance with experimental relations. In conclusion model [CC] seemed to better represent the cat soleus contraction dynamics and should be preferred in the nonlinear regression of muscle parameters and in musculoskeletal modeling.

All leg joints contribute to quiet human stance: A mechanical analysis

According to the state of the art model (single inverted pendulum) the regulation of quiet human stance seems to be dominated by ankle joint actions. Recent findings substantiated both in-phase and anti-phase fluctuations of ankle and hip joint kinematics can be identified in quiet human stance. Thus, we explored in an experimental study to what extent all three leg joints actually contribute to the balancing problem of quiet human stance. We also aimed at distinguishing kinematic from torque contributions. Thereto, we directly measured ankle, knee, and hip joint kinematics with high spatial resolution and ground reaction forces. Then, we calculated the six respective joint torques and, additionally, the centre of mass kinematics. We searched for high cross-correlations between all these mechanical variables. Beyond confirming correlated anti-phase kinematics of ankle and hip, the main results are: (i) ankle and knee joint fluctuate tightly (torque) coupled and (ii) the bi-articular muscles of the leg are well suited to fulfil the requirements of fluctuations around static equilibrium. Additionally, we (iii) identified high-frequency oscillations of the shank between about 4 and 8 Hz and (iv) discriminated potentially passive and active joint torque contributions. These results demonstrate that all leg joints contribute actively and concertedly to quiet human stance, even in the undisturbed case. Moreover, they substantiate the single inverted pendulum paradigm to be an invalid model for quiet human stance.

Characterization of isovelocity extension of activated muscle: a Hill-type model for eccentric contractions and a method for parameter determination.

Tension in eccentric contractions of skeletal muscles is expressed with a Hill-type model with a term containing a tension-velocity relation and a second term which is supposed to account for effects of contraction history. Based on experimental data (rat gastrocnemius medialis) a method is derived to uniquely characterize the tension-velocity relation in the first term. Also, a description of the second term is derived and its single additional parameter is determined. The model is tested in simulations. The experimental data used to characterize the model indicates that the slope of tension in the second phase of eccentric contractions is independent of muscle length.

Determination of three‐dimensional muscle architectures: validation of the DTI‐based fiber tractography method by manual digitization

In the last decade, diffusion tensor imaging (DTI) has been used increasingly to investigate three‐dimensional (3D) muscle architectures. So far there is no study that has proved the validity of this method to determine fascicle lengths and pennation angles within a whole muscle. To verify the DTI method, fascicle lengths of m. soleus as well as their pennation angles have been measured using two different methods. First, the 3D muscle architecture was analyzed in vivo applying the DTI method with subsequent deterministic fiber tractography. In a second step, the muscle architecture of the same muscle was analyzed using a standard manual digitization system (MicroScribe MLX). Comparing both methods, we found differences for the median pennation angles (P < 0.001) but not for the median fascicle lengths (P = 0.216). Despite the statistical results, we conclude that the DTI method is appropriate to determine the global fiber orientation. The difference in median pennation angles determined with both methods is only about 1.2° (median pennation angle of MicroScribe: 9.7°; DTI: 8.5°) and probably has no practical relevance for muscle simulation studies. Determining fascicle lengths requires additional restriction and further development of the DTI method.

Exercise Reveals the Interrelation of Physical Fitness, Inflammatory Response, Psychopathology, and Autonomic Function in Patients With Schizophrenia

Maintaining and improving fitness are associated with a lower risk of premature death from cardiovascular disease. Patients with schizophrenia are known to exercise less and have poorer health behaviors than average. Physical fitness and physiological regulation during exercise tasks have not been investigated to date among patients with schizophrenia. We studied autonomic modulation in a stepwise exhaustion protocol in 23 patients with schizophrenia and in matched controls, using spirometry and lactate diagnostics. Parameters of physical capacity were determined at the aerobic, anaerobic, and vagal thresholds (VT), as well as for peak output. VT was correlated with psychopathology, as assessed by the Positive and Negative Syndrome Scale, with the inflammatory markers IL-1β, IL-6, and TNF-α and with peak output. The MANOVA for heart and breathing rates, as well as for vagal modulation and complexity behavior of heart rate, indicated a profound lack of vagal modulation at all intensity levels, even after the covariate carbon monoxide concentration was introduced as a measure of smoking behavior. Significantly decreased physical capacity was demonstrated at the aerobic, anaerobic, and VT in patients. After the exercise task, reduced vagal modulation in patients correlated negatively with positive symptoms and with levels of IL-6 and TNF-α. This study shows decreased physical capacity in patients with schizophrenia. Upcoming intervention studies need to take into account the autonomic imbalance, which might predispose patients to arrhythmias during exercise. Results of inflammatory parameters are suggestive of a reduced activity of the anti-inflammatory cholinergic pathway in patients, leading to a pro-inflammatory state.

Three-dimensional surface geometries of the rabbit soleus muscle during contraction: input for biomechanical modelling and its validation

There exists several numerical approaches to describe the active contractile behaviour of skeletal muscles. These models range from simple one-dimensional to more advanced three-dimensional ones; especially, three-dimensional models take up the cause of describing complex contraction modes in a realistic way. However, the validation of such concepts is challenging, as the combination of geometry, material and force characteristics is so far not available from the same muscle. To this end, we present in this study a comprehensive data set of the rabbit soleus muscle consisting of the muscles’ characteristic force responses (active and passive), its three-dimensional shape during isometric, isotonic and isokinetic contraction experiments including the spatial arrangement of muscle tissue and aponeurosis–tendon complex, and the fascicle orientation throughout the whole muscle at its optimal length. In this way, an extensive data set is available giving insight into the three-dimensional geometry of the rabbit soleus muscle and, further, allowing to validate three-dimensional numerical models.

The effects of parallel and series elastic components on the active cat soleus force-length relationship

Typically, active muscle force is calculated by subtracting measured passive force from measured total force for corresponding whole muscle lengths (standard method). From a mechanical point of view, this requires a parallel elastic component (PEC) that is arranged in parallel to both the series elastic component (SEC) and the contractile component (CC). From a morphological point of view, however, the PEC should be rather in parallel to the CC, and both in series to the SEC (model [CC]). In this study, we investigated the differences in active muscle force estimated with these two different approaches and their impact on the interpretation of experiments. We measured passive forces without stimulation and total forces during supramaximal stimulation of six cat soleus muscles in end-held isometric contractions from lengths near active insufficiency to lengths close to inducing stretch damage. The active forces estimated with model [CC] reach about 10% higher maximum isometric forces and reveal about 10% longer optimal lengths of the CC compared to the standard method. Model choice affects the interpretation of the physiological working range and residual force enhancement. The active force-length relationships of the contractile component determined with model [CC] agree better with the theoretical sarcomere force-length relationship.

Work partitioning of transversally loaded muscle: experimentation and simulation

Skeletal muscles are surrounded by other muscles, connective tissue and bones, which may transfer transversal forces to the muscle belly. Simple Hill-type muscle models do not consider transversal forces. Thus, the aim of this study was to examine and model the influence of transversal muscle loading on contraction dynamics, e.g. on the rate of force development and on the maximum isometric muscle force (Fim). Isometric experiments with and without transversal muscle loading were conducted on rat muscles. The muscles were loaded (1.3 N cm− 2) by a custom-made plunger which was able to move in transversal direction. Then the muscle was fully stimulated, the isometric force was measured at the distal tendon and the movement of the plunger was captured with a high-speed camera. The interaction between the muscle and the transversal load was modelled based on energy balance between the (1) work done by the contractile component (CC) and (2) the work done to lift the load, to stretch the series elastic structures and to deform the muscle. Compared with the unloaded contraction, the force rate was reduced by about 25% and Fim was reduced by 5% both in the experiment and in the simulation. The reduction in Fim resulted from using part of the work done by the CC to lift the load and deform the muscle. The response of the muscle to transversal loading opens a window into the interdependence of contractile and deformation work, which can be used to specify and validate 3D muscle models.

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.

Muscle force depends on the amount of transversal muscle loading

Skeletal muscles are embedded in an environment of other muscles, connective tissue, and bones, which may transfer transversal forces to the muscle tissue, thereby compressing it. In a recent study we demonstrated that transversal loading of a muscle with 1.3Ncm(-2) reduces maximum isometric force (Fim) and rate of force development by approximately 5% and 25%, respectively. The aim of the present study was to examine the influence of increasing transversal muscle loading on contraction dynamics. Therefore, we performed isometric experiments on rat M. gastrocnemius medialis (n=9) without and with five different transversal loads corresponding to increasing pressures of 1.3Ncm(-2) to 5.3Ncm(-2) at the contact area between muscle and load. Muscle loading was induced by a custom-made plunger which was able to move in transversal direction. Increasing transversal muscle loading resulted in an almost linear decrease in muscle force from 4.8±1.8% to 12.8±2% Fim. Compared to an unloaded isometric contraction, rate of force development decreased from 20.2±4.0% at 1.3Ncm(-2) muscle loading to 34.6±5.7% at 5.3Ncm(-2). Experimental observation of the impact of transversal muscle loading on contraction dynamics may help to better understand muscle tissue properties. Moreover, applying transversal loads to muscles opens a window to analyze three-dimensional muscle force generation. Data presented in this study may be important to develop and validate muscle models which enable simulation of muscle contractions under compression and enlighten the mechanisms behind.