Because any arbitrary movement of any part of the body is the result of skeletal muscle activity, proper muscle functioning is of major importance for the quality of life. Numerical and experimental research shows the importance of spatial effects to skeletal muscle mechanical functioning, which means that local effects inside a muscle can affect its behavior elsewhere. Yet, for the sake of simplicity, this is often neglected in experiments or numerical models. This thesis addresses spatial effects of skeletal muscle mechanics in two field of research. The first general aim regards the interaction between contraction and perfusion, the second objective relates to muscle deformation during isometric contraction. Both are studied using a combination of animal experiments and numerical simulations, using a finite element model of perfused contracting skeletal muscle.
The commonly most accepted hypothesis regarding the interaction between contraction and muscle perfusion is the vascular waterfall theory. This theory ascribes the amount of perfusion during contraction to the difference between arterial and tissue pressure, rather than to the arterial-venous pressure gradient. This phenomenon is inevitably present during highly controlled pressure box experiments. To determine the interaction between perfusion and contractions, total arterial inflow and venous outflow during contractions of various strengths are measured. These variables closely relate to each other. Total arterial inflow decreases 90% during forceful contractions, whereas vascular volume only decreases 0.21% of total muscle volume. The numerical model is used to interpret these experimental findings. Total flow signals, calculated by the model, are compared to experiments for validation. Simulations qualitatively agree with experiments; similar characteristics, particularly in the venous flow signal, are obvious. However, the model output quantitatively differs from experiments. From the combination of experiments and simulations it is concluded that the vascular volume change during contraction comes largely to the account of venous blood volume. This localized effect in the hierarchical dimension of the vascular tree, the large impact of contraction on perfusion and the minimal volume change are in agreement with the vascular waterfall theory.
This vascular waterfall theory is mainly studied using pressure boxes. These are used to apply an external pressure to a muscle, which results in a homogeneous tissue pressure. However, during contractions, intramuscular pressure is distributed. The interaction between distributed pressure during contraction and the behavior of the vascular waterfall is further explored using the finite element model. Simulations show that the spatial distribution of pressure and flow in separate blood compartments depends on the number of arteries and veins that is modeled. This difference is caused by spatial interaction between the heterogeneous intramuscular pressure and venous pressure during contraction. Therefore, extrapolation of the generally accepted vascular waterfall principles to local intramuscular phenomena is disallowed in situations in which geometrical effects may be important.
To study the importance of geometrical effects for muscle mechanics, muscle deformation is considered. Muscle deformation relates to muscle function, because sarcomere length directly depends on deformation. In an experimental study, longitudinal and transverse strains at the muscle surface during isometric contraction are determined from three-dimensional displacement measurements of fluorescent markers that are attached to the muscle surface. With decreasing total muscle length, longitudinal and transverse strain in aponeurosis and superficial muscle fibers increase. Aponeurosis transverse strain increases twice as much as transverse strain in superficial muscle fibers with decreasing muscle length. Further, it was shown that transverse strain in superficial muscle fibers compensates for differences in longitudinal strain during contractions at different muscle lengths. Although surface area change of the aponeurosis during contraction depends on muscle length, the surface area change of superficial muscle fibers equals -11%, independent of initial muscle length. Assuming incompressible muscle tissue, strain in the direction perpendicular to the muscle surface equals 11%. Because transverse strain maximally reaches 9%, it is concluded that superficial muscle fibers change aspect ratio during isometric contraction, whereas the degree of this change depends on initial muscle length. For the difference between the behavior of muscle and aponeurosis transverse strain and for the changing aspect ratio with changing muscle length, it is concluded that three-dimensional deformation depends on muscle length and should be accounted for when studying muscle mechanics at different lengths.
To allow comparison of deformation measurements with numerical simulations, anatomically realistic geometrical information must be included in the model. Validation of model deformation with experimental data benefits from comparison of contractions under various conditions. One applicable variation regards the initial muscle length changes, studied in chapter 4. This study shows that for such purpose, an actual three-dimensional muscle geometry should be used. Therefore, a detailed reconstruction of the rat triceps surae muscle based on histological slides has been generated, from which a three-dimensional mesh of the medial gastrocnemius muscle is derived. This mesh can be used in finite element simulations of skeletal muscle contraction. However, because the mesh lacks accurate fiber direction data, proper comparison between simulated and experimentally determined deformation is not possible. For practical considerations, simulations in other parts of the thesis use a two-dimensional mesh that represents the midsagittal longitudinal section through the medial gastrocnemius muscle.
Searching for suitable ways to include three-dimensional muscle fiber directions in a reconstruction, MRI techniques are given attention. Diffusion tensor imaging is validated as to measure fiber directions within 5° accuracy. In combination with high-resolution MRI, a mesh of the anterior tibialis muscle, including realistic muscle fiber directions, an internal and an external aponeurosis, is generated. As an example of the use of this method in mechanical studies, internal deformation of this particular muscle during contraction is calculated, which is hard to determine experimentally.
In general, the present thesis studies spatial effects of skeletal muscle functioning regarding perfusion and deformation. It is shown how muscle perfusion can be influenced by geometrical effects, whereas deformation is essentially a three-dimensional phenomenon. Finite element simulations and experiments are used in close harmony in this thesis. Both experiments and simulations benefit from this interaction. The model was used to interpret experiments (chapter 2) and to calculate phenomena that cannot be measured experimentally (chapter 3) or with great efforts, using advanced and expensive techniques like tagging MRI. On the other hand, experiments were invoked to validate the model (chapter 2) and to draw general conclusions regarding the use of comparable models (chapter 4). Further, experiments support the model by providing accurate geometrical input (chapters 5 and 6)
|Hill AV. The heat of shortening and the dynamic constants of muscle. Proc R Soc Lond B Biol Sci. October 10, 1938;126(843):136-195.
|Zajac FE. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit Rev Biomed Eng. 1989;17(4):359-411.