Kay Leichsenring

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.

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.

On the anisotropy of skeletal muscle tissue under compression.

This paper deals with the role of the muscle fibres and extracellular matrix (ECM) components when muscle tissue is subjected to compressive loads. To this end, dissected tissue samples were tested in compression modes which induced states of fibres in compression (I), in tension (II) or at constant length (III), respectively. A comparison of the stress responses indicated that the tissue behaviour is significantly different for these modes, including differences between the modes (I) and (III). This contradicts the paradigm of many constitutive models that the stress response can be decomposed into an isotropic part relating to the ECM and an anisotropic fibre part the contribution of which can be neglected under compression. Conversely, the results provide experimental evidence that there is an anisotropic contribution of the fibre direction to the compressive stress. Interpreting these results in terms of recent microscopical studies, potential connections between the observed behaviour and the structure of muscle ECM are established.

Compressive properties of passive skeletal muscle-the impact of precise sample geometry on parameter identification in inverse finite element analysis.

Due to the increasing developments in modelling of biological material, adequate parameter identification techniques are urgently needed. The majority of recent contributions on passive muscle tissue identify material parameters solely by comparing characteristic, compressive stress-stretch curves from experiments and simulation. In doing so, different assumptions concerning e.g. the sample geometry or the degree of friction between the sample and the platens are required. In most cases these assumptions are grossly simplified leading to incorrect material parameters. In order to overcome such oversimplifications, in this paper a more reliable parameter identification technique is presented: we use the inverse finite element method (iFEM) to identify the optimal parameter set by comparison of the compressive stress-stretch response including the realistic geometries of the samples and the presence of friction at the compressed sample faces. Moreover, we judge the quality of the parameter identification by comparing the simulated and experimental deformed shapes of the samples. Besides this, the study includes a comprehensive set of compressive stress-stretch data on rabbit soleus muscle and the determination of static friction coefficients between muscle and PTFE.

Intermuscular pressure between synergistic muscles correlates with muscle force

ABSTRACT 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). Summary: The intermuscular pressure between synergistic muscles correlates with muscle force.

Tissue-scale anisotropy and compressibility of tendon in semi-confined compression tests

In this study, porcine tendon tissue was tested with a dedicated semi-confined compression set-up that enables us to induce states of either fibrils in compression (mode I), tension (mode II) or at constant length (mode III), respectively. The results suggest that tendon tissue is compressible and demonstrates a significantly stiffer response in mode I than in mode III. This implies that the fibril direction remains the axis of transverse isotropy in compression and that it provides an anisotropic contribution to the tissue stress. These results, which are important for the development of constitutive models for tendon tissue, are discussed with respect to the hierarchical structure of the extracellular matrix.

Changes in three-dimensional muscle structure of rabbit gastrocnemius, flexor digitorum longus, and tibialis anterior during growth

Muscular contraction dynamics depends on active and passive muscle properties (e.g., the force-velocity relation) as well as on the three-dimensional (3D) muscle structure (e.g., the muscle fascicle architecture and aponeurosis dimensions). Much is known about active muscle force generation and the muscle architecture at a particular age (mostly for adult specimens), but less is known about changes in muscle structure during growth. The present study analyzed growth-related changes in the muscle structure of rabbit gastrocnemius lateralis (GL), gastrocnemius medialis (GM), flexor digitorum longus (FDL), and tibialis anterior (TA). Changes in tendon length, muscle belly dimensions (length, width, thickness), as well as aponeurosis length, width, and area were determined using 55 rabbits between 18 and 108 days old. Additionally, the 3D muscle fascicle architecture of five rabbits of different ages (21, 37, 50, 70, 100 days) was determined using a manual digitizer. We found an almost linear increase over time in most of the geometrical parameters observed. GL and GM showed very similar growth characteristics. In contrast to the pronounced increase in muscle belly length of GL and GM, FDL and TA exhibited more uniform muscle belly growth in length, width, and thickness. In general, the aponeuroses of the muscles exhibited lower growth rates in width than in length, and aponeurosis areas were larger than physiological cross-sectional areas. There were almost no changes in fascicle lengths with increasing age for GL, GM, and FDL. In contrast, there was a clear increase in TA fascicle length from about 20 to over 40mm. Pennation angles of TA (11.0 ± 2.1°) and FDL (16.7 ± 3.2°) remained almost unchanged but increased for GL from 13.4 ± 3.3° to 24.3 ± 6.5° from the youngest to the oldest animal. For all muscles observed, the tendon-muscle fascicle length ratio (rTFL) changed during growth. GL and GM exhibited similar increases in rTFL from about 4-8. FDL showed the highest ratio, which increased from about 8-13, whereas TA had the lowest ratio, which decreased slightly from 2 to 1.5. The outcomes demonstrate new findings regarding changes in 3D muscle architecture and aponeurosis shape during growth, and they provide information for muscle force generation, functional relevance, and adaptation with respect to animal age. Therefore, the results help to improve understanding of muscle growth processes and can be used as input data for muscle growth modeling.

Long-term mechanical behaviour of skeletal muscle tissue in semi-confined compression experiments

In this study, porcine skeletal muscle tissue was tested until 112 hours post mortem using a semi-confined compression device that induces fascicles to enter one of the states of compression (mode I), tension (mode II), or constant length (mode III). Based on the authors׳ previous studies (Böl et al., 2014, 2015a), the anisotropic mechanical behaviour of the tissue was analysed, with a special focus on the testing time post mortem. The results suggest that the tissue exhibits significant anisotropic behaviour during the first hours of post mortem but that this anisotropy becomes insignificant at later time points. Interestingly, the compressibility of the tissue is more or less unaffected by the testing time. These results are discussed especially with respect to tissue microstructure.

Effects of growth on muscle, tendon and aponeurosis tissues in rabbit shank musculature.

There exist several studies using morphological analyses of skeletal muscles to obtain a better understanding of muscle structure. The structural information obtained are primarily determined from single muscle components using individual animals of discrete ages. Further, little is known about changing dimensions of the aponeurosis, which is an important load‐transferring interface in muscle mechanics. Thus, the aim of the present study was to determine how the muscle, tendon, and particularly the aponeurosis geometry of the rabbit shank musculature (M. soleus, M. extensor digitorum longus, and M. plantaris) change during growth. In doing so, morphological studies on muscles of eighty‐nine female rabbits aged between 18 and 108 days were conducted. We found an almost linear increase over time in all of the geometrical parameters observed. The aponeurosis of the muscles exhibited lower growth rates in width than in length. The distal and proximal aponeurosis areas were nearly identical. The ratio of aponeurosis area to the physiological cross‐sectional area was 2.54, 2.54, and 1.88 for M. soleus, M. extensor digitorum longus, and M. plantaris, respectively. M. extensor digitorum longus and M. soleus exhibited a nearly similar tendon‐muscle fascicle length ratio during growth, increasing from 2.86 to 5.30 and 3.48 to 6.16, respectively. Interestingly, the tendon‐muscle fascicle length ratio of the M. plantaris started initially with a much higher value (∼8) and increased to ∼18. Taken together, these results provide insight into the structure of the muscle‐tendon complex and thus, a general understanding of muscle growth. Anat Rec, 300:1123–1136, 2017.