Game-theoretical description of the go-or-grow dichotomy in tumor development for various settings and parameter constellations.

A medically important feature of several types of tumors is their ability to "decide" between staying at a primary site in the body or leaving it and forming metastases. The present theoretical study aims to provide a better understanding of the ultimate reasons for this so-called "go-or-grow" dichotomy. To that end, we use game theory, which has proven to be useful in analyzing the competition between tumors and healthy tissues or among different tumor cells. We begin by determining the game types in the Basanta-Hatzikirou-Deutsch model, depending on the parameter values. Thereafter, we suggest and analyze five modified variants of the model. For example, in the basic model, the deadlock game, Prisoner's Dilemma, and hawk-dove game can occur. The modified versions lead to several additional game types, such as battle of the sexes, route-choice, and stag-hunt games. For some game types, all cells are predicted to stay on their original site ("grow phenotype"), while for other types, only a certain fraction stay and the other cells migrate away ("go phenotype"). If the nutrient supply at a distant site is high, all the cells are predicted to go. We discuss our predictions in terms of the pros and cons of caloric restriction and limitations of the supply of vitamins or methionine. Our results may help devise treatments to prevent metastasis.

Evaluating a multimodal, clinical and work-directed intervention (RTW-PIA) to support sustainable return to work among employees with mental disorders: study protocol of a multicentre, randomised controlled trial.

BACKGROUND: Mental disorders (MDs) are one of the leading causes for workforce sickness absence and disability worldwide. The burden, costs and challenges are enormous for the individuals concerned, employers and society at large. Although most MDs are characterised by a high risk of relapse after treatment or by chronic courses, interventions that link medical-psychotherapeutic approaches with work-directed components to facilitate a sustainable return to work (RTW) are rare. This protocol describes the design of a study to evaluate the (cost-)effectiveness and implementation process of a multimodal, clinical and work-directed intervention, called RTW-PIA, aimed at employees with MDs to achieve sustainable RTW in Germany. METHODS: The study consists of an effectiveness, a health-economic and a process evaluation, designed as a two-armed, multicentre, randomised controlled trial, conducted in German psychiatric outpatient clinics. Sick-listed employees with MDs will receive either the 18-month RTW-PIA treatment in conjunction with care as usual, or care as usual only. RTW-PIA consists of a face-to-face individual RTW support, RTW aftercare group meetings, and web-based aftercare. Assessments will be conducted at baseline and 6, 12, 18 and 24 months after completion of baseline survey. The primary outcome is the employees´ achievement of sustainable RTW, defined as reporting less than six weeks of working days missed out due to sickness absence within 12 months after first RTW. Secondary outcomes include health-related quality of life, mental functioning, RTW self-efficacy, overall job satisfaction, severity of mental illness and work ability. The health-economic evaluation will be conducted from a societal and public health care perspective, as well as from the employer's perspective in a cost-benefit analysis. The design will be supplemented by a qualitative effect evaluation using pre- and post-interviews, and a multimethod process evaluation examining various predefined key process indicators from different stakeholder perspectives. DISCUSSION: By applying a comprehensive, multimethodological evaluation design, this study captures various facets of RTW-PIA. In case of promising results for sustainable RTW, RTW-PIA may be integrated into standard care within German psychiatric outpatient clinics. TRIAL REGISTRATION: The study was prospectively registered with the German Clinical Trials Register ( DRKS00026232 , 1 September 2021).

The morphology of the free-living females of Strepsiptera (Insecta).

The morphology of the adult free-living females of Mengenilla moldrzyki and Eoxenos laboulbenei (Strepsiptera, Mengenillidae) was documented with µCT-based 3D reconstructions and histological serial sections. External and internal features of both species are characterized by far-reaching specialization and structural simplification. The well-developed mandibles are moved by large muscles. Other mouthparts and their corresponding musculature are simplified or absent. The brain is partly shifted into the prothorax. It is followed by a single postcerebral ganglionic complex also containing the subesophageal ganglion and an unpaired abdominal nerve. Postcephalic sclerites are absent, except for the plate-like pronotum and small pleural sclerites. Wings and associated muscles are missing. The lumina of the large midgut and the anterior hindgut are disconnected. Seven bulb-shaped Malpighian tubules in M. moldrzyki is the highest number yet described for Strepsiptera. The 10-segmented abdomen lacks appendages. An unpaired birth organ opens ventrally on abdominal segment VII. The entire body cavity is filled with numerous freely floating eggs, 1386 in the specimen of M. moldrzyki and 721 in E. laboulbenei. Genital ducts, defined gonads, and genital glands are missing. The morphology of female Mengenillidae is discussed with respect to sexual dimorphism and structural features of the postembryonic stages. Phylogenetic implications are outlined.

Limb, joint and pelvic kinematic control in the quail coping with steps upwards and downwards.

Small cursorial birds display remarkable walking skills and can negotiate complex and unstructured terrains with ease. The neuromechanical control strategies necessary to adapt to these challenging terrains are still not well understood. Here, we analyzed the 2D- and 3D pelvic and leg kinematic strategies employed by the common quail to negotiate visible steps (upwards and downwards) of about 10%, and 50% of their leg length. We used biplanar fluoroscopy to accurately describe joint positions in three dimensions and performed semi-automatic landmark localization using deep learning. Quails negotiated the vertical obstacles without major problems and rapidly regained steady-state locomotion. When coping with step upwards, the quail mostly adapted the trailing limb to permit the leading leg to step on the elevated substrate similarly as it did during level locomotion. When negotiated steps downwards, both legs showed significant adaptations. For those small and moderate step heights that did not induce aerial running, the quail kept the kinematic pattern of the distal joints largely unchanged during uneven locomotion, and most changes occurred in proximal joints. The hip regulated leg length, while the distal joints maintained the spring-damped limb patterns. However, to negotiate the largest visible steps, more dramatic kinematic alterations were observed. There all joints contributed to leg lengthening/shortening in the trailing leg, and both the trailing and leading legs stepped more vertically and less abducted. In addition, locomotion speed was decreased. We hypothesize a shift from a dynamic walking program to more goal-directed motions that might be focused on maximizing safety.

A Roadmap to Reconstructing Muscle Architecture from CT Data.

Skeletal muscle is responsible for voluntary force generation across animals, and muscle architecture largely determines the parameters of mechanical output. The ability to analyze muscle performance through muscle architecture is thus a key step towards better understanding the ecology and evolution of movements and morphologies. In pennate skeletal muscle, volume, fiber lengths, and attachment angles to force transmitting structures comprise the most relevant parameters of muscle architecture. Measuring these features through tomographic techniques offers an alternative to tedious and destructive dissections, particularly as the availability of tomographic data is rapidly increasing. However, there is a need for streamlined computational methods to access this information efficiently. Here, we establish and compare workflows using partially automated image analysis for fast and accurate estimation of animal muscle architecture. After isolating a target muscle through segmentation, we evaluate freely available and proprietary fiber tracing algorithms to reconstruct muscle fibers. We then present a script using the Blender Python API to estimate attachment angles, fiber lengths, muscle volume, and physiological cross-sectional area. We apply these methods to insect and vertebrate muscle and provide guided workflows. Results from fiber tracing are consistent compared to manual measurements but much less time-consuming. Lastly, we emphasize the capabilities of the open-source three-dimensional software Blender as both a tool for visualization and a scriptable analytic tool to process digitized anatomical data. Across organisms, it is feasible to extract, analyze, and visualize muscle architecture from tomography data by exploiting the spatial features of scans and the geometric properties of muscle fibers. As digital libraries of anatomies continue to grow, the workflows and approach presented here can be part of the open-source future of digital comparative analysis.

O músculo esquelético é responsável pela geração de força voluntária em animais, e a arquitetura muscular determina em grande parte os parâmetros de performance mecânica. A capacidade de analisar o desempenho muscular através da arquitetura muscular é, portanto, um passo fundamental para uma melhor compreensão da ecologia e evolução dos movimentos e morfologias. No músculo esquelético penado, o volume, o comprimento das fibras e os ângulos de fixação às estruturas de transmissão de força constituem os parâmetros mais relevantes da arquitetura muscular. A medição dessas propriedades por meio de técnicas tomográficas oferece uma alternativa às dissecções tediosas e destrutivas, especialmente pelo rápido aumento na disponibilidade de dados tomográficos. No entanto, há uma necessidade de métodos computacionais otimizados para acessar essas informações de forma eficiente. Aqui, estabelecemos e comparamos fluxos de trabalho usando análise parcialmente automatizada de imagem para estimativa rápida e precisa da arquitetura muscular em animais. Após isolar um músculo alvo por meio de segmentação, avaliamos os algoritmos disponíveis gratuitamente e pagos para o rastreamento de fibra (Fiber Tracing) para reconstruir as fibras musculares. Apresentamos um script que usa a API do Blender Python para estimar os ângulos de ligamento, o comprimento da fibra, o volume do músculo e a secção transversal fisiológica. Aplicamos esses métodos aos músculos de insetos e vertebrados e fornecemos instruções detalhadas de uso. Os resultados do rastreamento de fibra são consistentes em comparação com as medições manuais, mas requerem menos tempo. Finalmente, enfatizamos a capacidade do software de modelagem de código aberto Blender 3D tanto como uma ferramenta de visualização programável quanto uma ferramenta analítica para processar dados anatômicos digitalizados. Para muitos organismos, é possível extrair, analisar e visualizar a arquitetura muscular, explorando as características espaciais das tomografias e as propriedades geométricas das fibras musculares. À medida que as bibliotecas de anatomia digital continuam a crescer, os fluxos de trabalho e a abordagem apresentados aqui podem fazer parte do futuro da análise comparativa digital de código aberto.

El músculo esquelético es responsable de la generación de fuerza voluntaria en los animales y la arquitectura muscular determina en gran medida los parámetros de producción mecánica. La capacidad de analizar el rendimiento muscular a través de la arquitectura muscular es, por tanto, un paso clave hacia una mejor comprensión de la ecología y evolución de los movimientos y morfologías. En el músculo esquelético pennado, el volumen, la longitud de las fibras y los ángulos de fijación a las estructuras de transmisión de fuerza comprenden los parámetros más relevantes de la arquitectura muscular. La medición de estas características mediante técnicas tomográficas ofrece una alternativa a las disecciones tediosas y destructivas, sobre todo porque la disponibilidad de datos tomográficos está aumentando rápidamente. Sin embargo, existe la necesidad de métodos computacionales optimizados para acceder a esta información de manera eficiente. Aquí, establecemos y comparamos flujos de trabajo utilizando análisis de imágenes parcialmente automatizados para una estimación rápida y precisa de la arquitectura del músculo animal. Después de aislar un músculo objetivo a través de la segmentación, evaluamos algoritmos de trazado de fibras ("Fiber Tracing") patentados y gratuitos para reconstruir las fibras musculares. Presentamos un script que utiliza la API de Blender Python para estimar los ángulos de penación, la longitud de las fibras, el volumen muscular y el área de sección transversal fisiológica. Aplicamos estos métodos a los músculos de insectos y vertebrados y proporcionamos flujos de trabajo guiados. Los resultados del rastreo de fibras son consistentes en comparación con las mediciones manuales, pero requieren mucho menos tiempo. Por último, enfatizamos las capacidades del software 3D de código abierto Blender como herramienta de visualización y herramienta analítica programable para procesar datos anatómicos digitalizados. Por muchos organismos, es factible de extraer, analizar y visualizar la arquitectura muscular mediante la explotación de las características espaciales de las tomografías y las propiedades geométricas de las fibras musculares. A medida que las bibliotecas digitales de anatomías continúan creciendo, los flujos de trabajo y el enfoque presentados aquí pueden ser parte del futuro de código abierto del análisis comparativo digital.

A three-dimensional musculoskeletal model of the dog.

The domestic dog is interesting to investigate because of the wide range of body size, body mass, and physique in the many breeds. In the last several years, the number of clinical and biomechanical studies on dog locomotion has increased. However, the relationship between body structure and joint load during locomotion, as well as between joint load and degenerative diseases of the locomotor system (e.g. dysplasia), are not sufficiently understood. Collecting this data through in vivo measurements/records of joint forces and loads on deep/small muscles is complex, invasive, and sometimes unethical. The use of detailed musculoskeletal models may help fill the knowledge gap. We describe here the methods we used to create a detailed musculoskeletal model with 84 degrees of freedom and 134 muscles. Our model has three key-features: three-dimensionality, scalability, and modularity. We tested the validity of the model by identifying forelimb muscle synergies of a walking Beagle. We used inverse dynamics and static optimization to estimate muscle activations based on experimental data. We identified three muscle synergy groups by using hierarchical clustering. The activation patterns predicted from the model exhibit good agreement with experimental data for most of the forelimb muscles. We expect that our model will speed up the analysis of how body size, physique, agility, and disease influence neuronal control and joint loading in dog locomotion.

Influence of spatial structure on protein damage susceptibility: a bioinformatics approach.

Aging research is a very popular field of research in which the deterioration or decline of various physiological features is studied. Here we consider the molecular level, which can also have effects on the macroscopic level. The proteinogenic amino acids differ in their susceptibilities to non-enzymatic modification. Some of these modifications can lead to protein damage and thus can affect the form and function of proteins. For this, it is important to know the distribution of amino acids between the protein shell/surface and the core. This was investigated in this study for all known structures of peptides and proteins available in the PDB. As a result, it is shown that the shell contains less susceptible amino acids than the core with the exception of thermophilic organisms. Furthermore, proteins could be classified according to their susceptibility. This can then be used in applications such as phylogeny, aging research, molecular medicine, and synthetic biology.

Calculating the optimal hematocrit under the constraint of constant cardiac power.

In humans and higher animals, a trade-off between sufficiently high erythrocyte concentrations to bind oxygen and sufficiently low blood viscosity to allow rapid blood flow has been achieved during evolution. Optimal hematocrit theory has been successful in predicting hematocrit (HCT) values of about 0.3-0.5, in very good agreement with the normal values observed for humans and many animal species. However, according to those calculations, the optimal value should be independent of the mechanical load of the body. This is in contradiction to the exertional increase in HCT observed in some animals called natural blood dopers and to the illegal practice of blood boosting in high-performance sports. Here, we present a novel calculation to predict the optimal HCT value under the constraint of constant cardiac power and compare it to the optimal value obtained for constant driving pressure. We show that the optimal HCT under constant power ranges from 0.5 to 0.7, in agreement with observed values in natural blood dopers at exertion. We use this result to explain the tendency to better exertional performance at an increased HCT.

Tracking tendon fibers to their insertion - a 3D analysis of the Achilles tendon enthesis in mice.

Tendon insertions to bone are heavily loaded transitions between soft and hard tissues. The fiber courses in the tendon have profound effects on the distribution of stress along and across the insertion. We tracked fibers of the Achilles tendon in mice in micro-computed tomographies and extracted virtual transversal sections. The fiber tracks and shapes were analyzed from a position in the free tendon to the insertion. Mechanically relevant parameters were extracted. The fiber number was found to stay about constant along the tendon. But the fiber cross-sectional areas decrease towards the insertion. The fibers mainly interact due to tendon twist, while branching only creates small branching clusters with low levels of divergence along the tendon. The highest fiber curvatures were found within the unmineralized entheseal fibrocartilage. The fibers inserting at a protrusion of the insertion area form a distinct portion within the tendon. Tendon twist is expected to contribute to a homogeneous distribution of stress among the fibers. According to the low cross-sectional areas and the high fiber curvatures, tensile and compressive stress are expected to peak at the insertion. These findings raise the question whether the insertion is reinforced in terms of fiber strength or by other load-bearing components besides the fibers. STATEMENT OF SIGNIFICANCE: The presented study is the first analysis of the 3D fiber tracks in macroscopic tendon samples as determined by a combination of cell-maceration, phase-contrast µCT and template-based tracking. The structural findings change the understanding of the tendon-bone insertion and its biomechanics: (1) The insertion is not reinforced in terms of fiber numbers or sizes. Its robustness remains unexplained. (2) The orientation of fibers in the tendon center is higher than in the margins. This arrangement could inspire material development. (3) Fibers inserting at a protrusion of the insertion area stem from a distinct portion within the tendon. The results show that fibrous structure analysis can link macro- to micromechanics and that it is ready for the application to complete muscle-tendon units.

Robustness during Aging-Molecular Biological and Physiological Aspects.

Understanding the process of aging is still an important challenge to enable healthy aging and to prevent age-related diseases. Most studies in age research investigate the decline in organ functionality and gene activity with age. The focus on decline can even be considered a paradigm in that field. However, there are certain aspects that remain surprisingly stable and keep the organism robust. Here, we present and discuss various properties of robust behavior during human and animal aging, including physiological and molecular biological features, such as the hematocrit, body temperature, immunity against infectious diseases and others. We examine, in the context of robustness, the different theories of how aging occurs. We regard the role of aging in the light of evolution.

Determination of scoring functions for protein damage susceptibility.

Protein damage (partly followed by protein aggregation) plays a significant role in ageing, cancer and in neurodegenerative and other diseases. It is known that the proteinogenic amino acids differ in their susceptibility to non-enzymatic modification, such as hydroxylation, peroxidation, chlorination etc. In a novel bioinformatics approach, we introduce measures to quantify the susceptibility of the 20 standard proteinogenic amino acids to such modification. Based on these amino acid scores, we calculated different susceptibilities for 116,387 proteins, testing various scoring approaches. These approaches are based on review articles, text mining and a combination of both. We also show an application by combining the score information with a tool for visualization.

Non-Destructive Determination of Muscle Architectural Variables Through the Use of DiceCT.

The fascicular architecture of skeletal muscle dictates functional parameters such as force production and contractile velocity. Muscle microarchitecture is typically determined by means of manual dissection, a technique that is inherently destructive to specimens. Furthermore, fascicle lengths and pennation angles are commonly assessed at only a limited number of sampling sites per muscle. We present the results of a digital technique to non-destructively assess muscle architectural variables for three jaw-adductor muscles within a specimen of the cercopithecine primate Macaca fascicularis (crab-eating macaque). The specimen is first subjected to a contrast-enhanced staining protocol to increase the density of internal soft tissues. High-resolution µCT scans are then collected and segmented to isolate individual muscles. A textural orientation algorithm is then applied to each muscle volume to reconstruct constituent muscle fascicles in three dimensions. Using this technique, we report muscle volume, fascicle length, angle of pennation, and physiological cross-sectional area (PCSA) for each muscle. These data are compared to results collected using traditional dissection of the contralateral muscles. Reconstructions of muscle volume and pennation angle closely correspond to the dissection results. The degree of similarity between measurements of fascicle length and PCSA varies between muscles, with temporalis demonstrating the greatest disparity between techniques; likely reflecting the complex geometry and fascicular arrangement of this muscle. The described technique samples a much larger number of fascicles than had previously been possible and non-destructively investigates the internal architecture of preserved specimens. We conclude that this approach demonstrates great potential for quantifying muscle internal architecture. Anat Rec, 301:363-377, 2018. © 2018 Wiley Periodicals, Inc.

Mathematical models for explaining the Warburg effect: a review focussed on ATP and biomass production.

For producing ATP, tumour cells rely on glycolysis leading to lactate to about the same extent as on respiration. Thus, the ATP synthesis flux from glycolysis is considerably higher than in the corresponding healthy cells. This is known as the Warburg effect (named after German biochemist Otto H. Warburg) and also applies to striated muscle cells, activated lymphocytes, microglia, endothelial cells and several other cell types. For similar phenomena in several yeasts and many bacteria, the terms Crabtree effect and overflow metabolism respectively, are used. The Warburg effect is paradoxical at first sight because the molar ATP yield of glycolysis is much lower than that of respiration. Although a straightforward explanation is that glycolysis allows a higher ATP production rate, the question arises why cells do not re-allocate protein to the high-yield pathway of respiration. Mathematical modelling can help explain this phenomenon. Here, we review several models at various scales proposed in the literature for explaining the Warburg effect. These models support the hypothesis that glycolysis allows for a higher proliferation rate due to increased ATP production and precursor supply rates.

Causes of upregulation of glycolysis in lymphocytes upon stimulation. A comparison with other cell types.

In this review, we revisit the metabolic shift from respiration to glycolysis in lymphocytes upon activation, which is known as the Warburg effect in tumour cells. We compare the situation in lymphocytes with those in several other cell types, such as muscle cells, Kupffer cells, microglia cells, astrocytes, stem cells, tumour cells and various unicellular organisms (e.g. yeasts). We critically discuss and compare several explanations put forward in the literature for the observation that proliferating cells adopt this apparently less efficient pathway: hypoxia, poisoning of competitors by end products, higher ATP production rate, higher precursor supply, regulatory effects, and avoiding harmful effects (e.g. by reactive oxygen species). We conclude that in the case of lymphocytes, increased ATP production rate and precursor supply are the main advantages of upregulating glycolysis.

Reconstruction of muscle fascicle architecture from iodine-enhanced microCT images: A combined texture mapping and streamline approach.

Skeletal muscle models are used to investigate motion and force generation in both biological and bioengineering research. Yet, they often lack a realistic representation of the muscle's internal architecture which is primarily composed of muscle fibre bundles, known as fascicles. Recently, it has been shown that fascicles can be resolved with micro-computed tomography (µCT) following staining of the muscle tissue with iodine potassium iodide (I2KI). Here, we present the reconstruction of the fascicular spatial arrangement and geometry of the superficial masseter muscle of a dog based on a combination of pattern recognition and streamline computation. A cadaveric head of a dog was incubated in I2KI and µCT-scanned. Following segmentation of the masseter muscle a statistical pattern recognition algorithm was applied to create a vector field of fascicle directions. Streamlines were then used to transform the vector field into a realistic muscle fascicle representation. The lengths of the reconstructed fascicles and the pennation angles in two planes (frontal and sagittal) were extracted and compared against a tracked fascicle field obtained through cadaver dissection. Both fascicle lengths and angles were found to vary substantially within the muscle confirming the complex and heterogeneous nature of skeletal muscle described by previous studies. While there were significant differences in the pennation angle between the experimentally derived and µCT-reconstructed data, there was congruence in the fascicle lengths. We conclude that the presented approach allows for embedding realistic fascicle information into finite element models of skeletal muscles to better understand the functioning of the musculoskeletal system.

What can we learn from Einstein and Arrhenius about the optimal flow of our blood?

BACKGROUND: The oxygen flow in humans and other higher animals depends on the erythrocyte-to-blood volume ratio, the hematocrit. Since it is physiologically favourable when the flow of oxygen transport is maximum it can be assumed that this situation has been achieved during evolution. If the hematocrit was too low, too few erythrocytes could transport oxygen. If it was too high, the blood would be very viscous, so that oxygen supply would again be reduced. METHODS: The theoretical optimal hematocrit can be calculated by considering the dependence of blood viscosity on the hematocrit. Different approaches to expressing this dependence have been proposed in the literature. Here, we discuss early approaches in hydrodynamics proposed by Einstein and Arrhenius and show that especially the Arrhenius equation is very appropriate for this purpose. RESULTS & CONCLUSIONS: We show that despite considerable simplifications such as neglecting the deformation, orientation and aggregation of erythrocytes, realistic hematocrit values of about 40% can be derived based on optimality considerations. Also the prediction that the ratio between the viscosities of the blood and blood plasma at high shear rates nearly equals Euler's constant (2.718) is in good agreement with observed values. Finally, we discuss possible extensions of the theory. For example, we derive the theoretical optimal hematocrit for persevering divers among marine mammals to be 65%, in excellent agreement with the values observed in several species. GENERAL SIGNIFICANCE: These considerations are very important for human and animal physiology since oxygen transport is an important factor for medicine and physical performance.

Intramuscular architecture of the autochthonous back muscles in humans.

Many training concepts take muscle properties such as contraction speed or muscle topography into account to achieve an optimal training outcome. Thus far, the internal architecture of muscles has largely been neglected, although it is well known that parameters such as pennation angles or the lengths of fascicles but also the proportions of fleshy and tendinous fascicle parts have a major impact on the contraction behaviour of a muscle. Here, we present the most detailed description of the intramuscular fascicle architecture of the human perivertebral muscles available so far. For this, one adult male cadaver was studied. Our general approach was to digitize the geometry of each fascicle of the muscles of back proper (Erector spinae) - the Spinalis thoracis, Iliocostalis lumborum, Longissimus thoracis and the Multifidus thoracis et lumborum - and of the deep muscles of the abdomen - Psoas minor, Psoas major and Quadratus lumborum - during a layerwise dissection. Architectural parameters such as fascicle angles to the sagittal and the frontal planes as well as fascicle lengths were determined for each fascicle, and are discussed regarding their consequences for the function of the muscle. For example, compared with the other dorsovertebral muscles, the Longissimus thoracis can produce greater shortening distances because of its relatively long fleshy portions, and it can store more elastic energy due to both its relatively long fleshy and tendinous fascicle portions. The Quadratus lumborum was outstanding because of its many architectural subunits defined by distinct attachment sites and fascicle lengths. The presented database will improve biomechanical models of the human trunk by allowing the incorporation of anisotropic muscle properties such as the fascicle direction into finite element models. This information will help to increase our understanding of the functionality of the human back musculature, and may thereby improve future training concepts.

Comparison of various approaches to calculating the optimal hematocrit in vertebrates.

An interesting problem in hemorheology is to calculate that volume fraction of erythrocytes (hematocrit) that is optimal for transporting a maximum amount of oxygen. If the hematocrit is too low, too few erythrocytes are present to transport oxygen. If it is too high, the blood is very viscous and cannot flow quickly, so that oxygen supply to the tissues is again reduced. These considerations are very important, since oxygen transport is an important factor for physical performance. Here, we derive theoretical optimal values of hematocrit in vertebrates and collect, from the literature, experimentally observed values for 57 animal species. It is an interesting question whether optimal hematocrit theory allows one to calculate hematocrit values that are in agreement with the observed values in various vertebrate species. For this, we first briefly review previous approaches in that theory. Then we check which empirical or theoretically derived formulas describing the dependence of viscosity on concentration in a suspension lead to the best agreement between the theoretical and observed values. We consider both spatially homogeneous and heterogeneous distributions of erythrocytes in the blood and also possible extensions, like the influence of defective erythrocytes and cases where some substances are transported in the plasma. By discussing the results, we critically assess the power and limitations of optimal hematocrit theory. One of our goals is to provide a systematic overview of different approaches in optimal hematocrit theory.

On a phenomenological model for fatigue effects in skeletal muscles.

This work deals with the development and implementation of a new fatigue model for simulating fatigue effects in skeletal muscles. Basic idea of this modelling strategy is an approach that divides the fibres of a muscle into three groups: fibres in the active state, those that are already fatigued and fibres in the resting state. All fibres are able to switch between the different groups by defining adequate rates. In this way a continuous transfer of fibres between those three states has been described. Rooted on an incompressible, hyperelastic constitutive law with transversely isotropic characteristics the fatigue model has been implemented in the framework of the finite element method. Numerical examples are given in order to illustrate the ability of this model. Further, we validate the model by fatigue experiments of the rat soleus muscle. In doing so, it proves that the model is able to predict physiological observations and mechanical test results.

A novel method of studying fascicle architecture in relaxed and contracted muscles.

A muscle's architecture, described by geometric variables such as fascicle pennation angles or lengths, plays a crucial role in its functionality. Usually, single parameters are used to estimate force vectors or lengthening rates, thereby assuming that they represent the architecture properly and are constant during contraction. To describe muscle architecture in more detail and compare relaxed and contracted states, we developed and validated a new approach. The m. soleus of the laboratory rat was shock-frozen while relaxed and under isometric contraction, reconstructed three-dimensionally from histological sections, and fascicle lengths, curvatures and pennation angles, as well as the shape of the aponeuroses were analysed. Remarkable differences in volume distribution and the shapes of the aponeuroses as well as locally varying changes in the fascicle architecture were observed. While the mean pennation angle increased by only 2° due to contraction, local changes of up to 4° were observed. Fascicle curvature increased in the distal but remained unchanged in the proximal parts. Our approach may help to identify functional subunits within the muscle, i.e., regions with homogeneous architectural properties. Our results are discussed regarding the input parameters essential for realistic muscle modelling and challenge maximum isometric force estimations that are based on the physiological cross-sectional area or the Hill-model.