Analyse der Knochendeformation und Muskelkräfte der menschlichen Tibia

Für die Erforschung des Weltraums durch den Menschen, aber auch für die Gesundheit auf der Erde allgemein, ist ein grundlegendes Verständnis über die Adaption des Knochens essentiell. Die Regulierung des Auf- und Abbaus des Knochens wird über seine Deformation gesteuert, welche wiederum aus der mechanischen Belastung dessen resultiert. Diese Zusammenhänge zu verstehen, die Auswirkungen von verschiedenen Aktivitäten auf die Deformation des Knochens zu kennen und in Relation setzten zu können, ist der Schlüssel zu dem gesuchten, grundlegenden Verständnis. Im Zuge dieser Arbeit wurde hierfür eine Methode entwickelt, diese Zusammenhänge qualitativ und quantitativ herzuleiten. Basierend auf in vivo Messungen an der Tibia wurde ein Algorithmus zur in silico Analyse der vorliegenden Daten entwickelt. Dieser macht sich die Konsequenzen des Hookeschen Gesetzes in Form des Superpositionsprinzips zu Nutze, um quasi-invers aus der gemessenen Deformationsbewegung die dafür notwendigen Kräfte zu bestimmen. Diese können in einer Finite Elemente Analyse (FEA) mit den rekonstruierten Tibia-Knochen verwendet werden, um deren Spannungs-Dehnungs-Zustand zu bestimmen. Zur Validierung der Annahmen und Randbedingungen des Algorithmus wurde ein biomechanischer Messstand konstruiert. In diesem konnten in replica und ex vivo Untersuchungen durchgeführt werden. Zu diesem Zweck wurden Tibia-Replikate aus Komposite-Material bzw. Leichenbeine künstlich über Aktuatoren mit Kräften beaufschlagt und über eine spezielle Anwendung von Motion Capturing die Deformationsbewegung des Knochens gemessen. Die Auswertung der in vivo Daten mittels der in silico Analyse lieferte quantitative Ergebnisse zur Dehnung in der Tibia für diverse alltägliche Aktivitäten. Diese Ergebnisse sind, im Gegensatz zur bisherigen gängigen Methode, jedoch nicht auf einen singulären Messpunkt limitiert, sondern decken den kompletten rekonstruierten Bereich der Tibia ab. Dies führte zur Feststellung, dass die aktuell angenommenen Werte zu niedrig angesetzt sind. Hinzu kommt, dass die Analyse eine zeitliche und örtliche Varianz der Peak-Dehnungen im Knochen über den Ablauf einer Aktivität aufzeigt. Diese Ergebnisse verändern das bisherige Verständnis über die Knochenadaption und deren Regulierungsmechanismen

Muscle forces – Bone deformations Designing an inverse finite element algorithm

Bone remodeling and it’s capability to adapt to various environmental conditions is the topic of many present-day research. On Earth, many people suffer from bone atrophy and Osteoporosis with no real treatment available. Additionally, astronauts experience significant bone atrophy during their time in space. Therefore investigations are focusing on understanding the processes behind these effects, mainly in the long bones like the human femur and the tibia. The prime controlling mechanism for bone adaptation is the mechanical loading of the bone. Yet, contrary to common belief, it is not the body weight and its’ momentum that triggers bone adaption. Muscle forces are explicitly needed which, by contracting, exert a force on the bone and therefore a deformation. A descriptive example is shown in the figure on the right hand side: While balancing on the ball of the foot, the muscles exert a force three times larger than the body weight to keep the equilibrium. This force is induced into the tibia on top of the acting force due to the body weight. All of this points lead to the fact, that the muscles play an essential role in bone remodeling and adaption. However, since it is difficult to measure muscle forces in vivo, a novel approach is introduced here. It combines a classical forward Finite Element Analysis (FEA) with a linear optimization algorithm to create an inverse FEA, in order to solve the question: What forces do muscles exert on the bone

Muscle forces - bone deformations A novel approach to determine muscle forces corresponding to measured tibia deformations

Muscle-force induced strains in bone may be the key to bone-remodelling. But since it proofs to be very difficult to measure these forces directly in vivo, modelling has been the key to answers ever since. The abstract presents a novel approach to create a model that can calculate the forces generated by predefined muscle groups in respect to a given bone deformation. To achieve this, the model will make use of CT-data of the bone, measured bone deformation from an earlier on project and combine these to an inverse dynamics simulation of the lower limb. Thereby, the activated muscle-groups for certain activities can be determined, the occurring strain allotted to these and as a result a strain – activity – force – pattern is created. This data can then be used for further research in the field of bone-remodelling

Analyse der Knochendeformation und Muskelkräfte der menschlichen Tibia

A basic understanding of the adaptation of bone is essential for the exploration of space by humans, but also for human health on earth in general. The regulation of bone growth and decrease is controlled by its deformation, which in turn results from the mechanical loading of the bone. Understanding these connections, knowing the effects of different activities on the deformation of the bone, and being able to put them into relation, is the key to the fundamental understanding sought. In the course of this thesis, a method was developed to establish these relationships qualitatively and quantitatively. Based on in vivo measurements on the tibia, an algorithm was developed for the in silico analysis of the available data. The latter makes use of the implications of Hooke's law in the form of the superposition principle, in order to quasi-inverse determine the forces necessary to achieve the measured deformation. These can be used in a Finite Element Analysis (FEA) with the reconstructed tibia bones to determine their stress-strain state. For validation of the assumptions and boundary conditions of the algorithm a biomechanical test rig was constructed. With it, examinations were carried out in replica and ex vivo. For this purpose, tibia replicas of composite material or respectively cadaverous legs were artificially impacted by actuators, and the deformation movement of the bone was measured via a special application of motion capturing. The analysis of the in vivo data by means of the in silico analysis provided quantitative results on the average values and peak values of strain in the tibia, and this for various everyday activities. These results, however, are not limited to a single measuring point, as opposed to the current standard method, but cover the complete reconstructed area of the tibia. This led to the conclusion that the currently assumed peak values are listed too low. In addition, the analysis shows a temporal and local variance of the peak strain in the bone over the course of an activity. These results alter the previous understanding of bone adaptation and its regulatory mechanisms

Form follows function: A computational simulation exercise on bone shape forming and conservation

Two transformation laws of different complexity have been applied in a computer simulation study in order to investigate adaptation processes of bone-like structures under load pattern comparable to those acting on the diaphysis of long bones. It has been found that torsion along the long axis is important to the evolvement and maintenance of tube like structure, and that favoured such tube-like structures will emerge from a variety of starting geometries, provided that torsion along the long axis is present and certain parameters of the transformation algorithms are set appropriately. When outside this regime, mechano-adaption generated truss like structures are favoured. The mechanostat-like algorithms are able to explain flexure neutralization, the auto-correction of a long bone’s shape after poorly healed fractions in children. Asymmetric distribution of bending forces does not impact on the symmetry of favoured geometries. In conclusion, the present results demonstrate that the mechanical environment per se is able, at least in theory, to generate shaft-like structures

Torsion - an underestimated form shaping entity in bone adaptation?

Objectives: There is ample agreement that the specific shape of a bone is related to the loads it has to carry. It is also believed that bones mechano-adapt in order to 'find' this shape. The open question is which signals constitute the determinants of this adapation. Recent in vivo experiments show that torsion is a significant load component in human tibia, and a computational study of the mechanostat has indicated that torsion could play a role in the shaping of tubular long bones. Methods: An earlier computational approach is further progressed to systematically study the relative importance of axial compression, lateral bending and axial torsion. Results: Results demonstrate that shape-driving potential towards tubular shapes is greatest for torsion, followed by bending and least for axial compression. Multiple linear regression analysis confirmed the dominant role of torsion, in particular for the 2nd moment of intertia. The obtained results were largely unaffected by starting conditions. e.g. either from a grid or through reshaping under disuse. Conclusions: Strong support has been found for the hypothesis torsion could be more important than suggested in previous studies as a component of the mechanical environment of bones. This will apply to the shafts of long bones, and also to the femoral neck

Torsion – an underestimated form shaping entity in bone adaptation?

Objectives: There is ample agreement that the specific shape of a bone is related to the loads it has to carry. It is also believed that bones mechano-adapt in order to ‘find’ this shape. The open question is which signals constitute the determinants of this adapation. Recent in vivo experiments show that torsion is a significant load component in human tibia, and a computational study of the mechanostat has indicated that torsion could play a role in the shaping of tubular long bones. Methods: An earlier computational approach is further progressed to systematically study the relative importance of axial compression, lateral bending and axial torsion. Results: Results demonstrate that shapedriving potential towards tubular shapes is greatest for torsion, followed by bending and least for axial compression. Multiple linear regression analysis confirmed the dominant role of torsion, in particular for the 2nd moment of intertia. The obtained results were largely unaffected by starting conditions, e.g. either from a grid or through reshaping under disuse. Conclusions: Strong support has been found for the hypothesis torsion could be more important than suggested in previous studies as a component of the mechanical environment of bones. This will apply to the shafts of long bones, and also to the femoral nec

A refined Mechanostat Model of Bone Transformation

Bone is a living tissue that shows adaptation in shape and structure, if the prevailing load conditions are significantly changing. One example is the loss of bone mass of astronauts under microgravity, which can already be measured after missions of medium duration. Transformation laws derived from experimental data have been able to explain morphologic adaptation of the microstructure of trabecular bone to external loads. In the present work the focus is on the hypothesis, that the same transformation law is able to govern shape adaptation and adaptation of microstructure depending only on the different load pattern. This work is an effort to concile the famous phenomenologic mechanostat model of Frost [Frost 2000] with a mechanistic approach of Huiskes and his co-workers [Huiskes, 2000]. The present in-silico study has shown that the mechanostat scheme based on basic mechanistic principles can engender diverse load bearing structure depending on the different needs: the epiphysis collecting loads from different directions prefers trussy structure, the torsion and axial load bearing shaft prefers tubular structure. That is similar to the findings in bone with the difference, that the “trussy” structure in epiphysis is much finer, namely spongy. That seems to be a scaling problem to be analysed in the future

Form follows function: a computational simulation exercise on bone shape forming and conservation

The present paper explores whether the shape of long bone shafts can be explained as a mere result of mechano-adapation. A computer simulation study was conducted in order to investigate adaptation processes of bone-like structures under load patterns comparable to those acting on the diaphysis of long bones. The aim of the study was to have a deeper look into the relationship between typical loading patterns and resulting bone shape and structure. The simulations are based on a mechanistic model approach for mechano-transduction and bone transformation. Results of the simulations are that axial torsion around the long axis is important for the evolvement and maintenance of tube-like structures. Of note such structures can form from a variety of starting geometries, provided that axial torsion is present. The selection of the set-point parameter for the regulation of load adapted bone transformation has an impact on the final structure as well. In conclusion, the present study confirms the mechanical environment's potential to generate shaft-like structures and demonstrates the respective boundary condition