Mechanical Control of Root Growth: A Computer Simulation.

The root system is very important for the stability of a tree. External wind forces must be transferred by the roots into the soil. Therefore, the tree root system must be large and strong enough to prevent breakage and uprooting. The shape of the root system is also important for the tree's stability. This paper investigates the shape of the root system with regard to the external loading forces and soil properties. The material properties of the soil are very important for the failure of the root-soil plate. The strength of soil depends on its resistance to shear stresses. Resistance to shear is provided by the friction between the soil particles and is proportional to the normal force between them (Mohr-Coulomb failure criterion). Root-reinforced soil can be compared with a composite material in which fibres (roots) of relatively high tensile strength are embedded in a matrix of lower tensile strength (soil). Plant root scan increase the shear resistance of the soil. At Forschungszentrum Karlsruhe the so-called SKO method was modified to predict root morphologies of trees for different loading and soil conditions.The predictions are based on the assumption that the optimum root design (in the purely mechanical sense!) is a design that guarantees an even distribution of the shear loading along the roots. This approach gives good qualitative agreement with the root formation observed in nature for cases considered here. It is clear that this mechanical optimum can be disturbed drastically by biological growth regulators.

Effects of mechanical loading on the profile of human femoral diaphyseal geometry.

In vivo bone behaviour predictions with respect to altered loading conditions, implants, and endoprostheses are highly desirable to avoid untoward effects such as implant loosening and breakage. This knowledge does not relate only to the result but also to the mechanisms of bone adaptation and bone growth. Since bone growth is assumed to be determined essentially by the loading history, the morphology of the human femoral midshaft region was analysed to extract those loading cases responsible for the actual cross-sectional geometry. This was achieved by the application of computer-aided optimization (CAO), a procedure supplementing a finite element analysis which allows for simulation of adaptive bone growth. A simulated load was applied to a cylinder, and the resulting changes in geometry were compared with the geometry of three ex vivo samples. Apparently, standard loading cases alone (axial loading, bending, torsion), or at consecutive or simultaneous application, did not yield the characteristic morphology of the femoral shaft region. Only the introduction of the adductor muscle force in various combinations with other standard loadings resulted in femoral mid-shaft geometries comparable with the ex vivo specimens.

[A new guide and 2 new cruciate ligament anchors for securing prosthetic cruciate ligaments to the femur]. / Ein neues Zielgerät und zwei neue Kreuzbandanker zur Befestigung von prosthetischem Kreuzbandersatz am Femur.

A new drilling device for the correct localization of drilling holes has been developed for the fixation of cruciate ligament prostheses. We describe how the device is employed under surgical operating conditions. Its accuracy in application is demonstrated in a cadaver knee. The device has also been used clinically with success. Two new anchors for the fixation of the ligaments are proposed.

[Effects of hollow shaft endoprosthesis on stress distribution in cortical bone]. / Die Auswirkungen der Hohlschaftendoprothese auf die Spannungsverteilung in der Kortikalis.

Generally, conduction of the forces from the distal end of the prosthesis stem into the surrounding cortical bone effects a local load increase in the bone. Where bone and stem are in close contact "stress protection" is hardly avoidable, and this, together with the load increase, results in the formation of a "plug of bone" beneath the tip of the prosthesis. Since the prosthesis stem rests on this bone "plug", additional "stress protection" of the femur results, which may possibly lead to total failure of the femur and/or the prosthesis. A 3-dimensional FEM-analysis shows that the hollow-stem prosthesis helps to decrease the stress peak beneath the tip of the prosthesis, while at the same time the stress in the proximal cortical bone increases. The increase in the loading of the bone inevitably causes a reduction in bone breakdown through "stress shielding" in this region.

Some effects of global joint morphology on local stress aberrations near imprecisely reduced intra-articular fractures.

Cadaver models of contact pressure aberration near displaced intra-articular fractures complement clinical experience, but inter-specimen variability often complicates interpretation of in vitro data. A contact finite element formulation is here used to study juxta-articular stress distributions in a plane strain model of tibial plateau step-off incongruity. Attention is focused on the influence of global morphologic parameters: intact joint surface curvatures, cartilage thickness, and cartilage stiffness. The computed stress distributions agreed well with experimental recordings for a typical 3 mm incongruity in an otherwise normal joint. Both decreased cartilage thickness and increased cartilage modulus led to elevations in the peak local contact stress, and to concentration of contact stress near the edge of the step-off incongruity. Similar effects were seen when reduction of global joint congruency was modelled by decreasing the concavity of the tibial plateau. While the observed degree of coupling between global morphology and local stress aberration was by no means negligible, the sensitivity of the stresses to variations in individual parameters was relatively mild. This suggests that the finite element results will be useful for experimental data interpretation.

[The cruciate ligaments as the major mechanism of control of the movement of the knee joint]. / Die Kreuzbänder als wesentlicher Steuermechanismus der Kinematik des Kniegelenks.

The kinematics of the knee joint is considered with the special regard to the cruciate ligaments. An optimum place for the fixation of ligament substitute is calculated. Anatomic preparations of cadaver knee joints proved this predictions to be correct. Placing the ligament substitute at this place the ligaments behave isometrically.

[Structural analysis of the Y nail and a design with reduced impact stress]. / Strukturanalyse des Y-Nagels und eine Formgebung mit reduzierter Kerbspannung.

The Y-nail used for osteosynthesis of pertrochanteric fractures is studied with respect to its failure, stress analysis and some proposals are made to get a more fatigue resistant design.

[Plate fracture--a finite element for the calculation of notch tension around differently shaped plates]. / Der Plattenbruch--eine Finite-Elemente-Analyse zur Berechnung der Kerbspannungen an verschieden geformten Plattenlöchern.

A hole in a plate loaded by bending induces notch stresses in it's surrounding. This stress amplification depends on the shape of the hole. In the present paper this effect is studied by use of the Finite Element Method systematically. It was found that longer holes induce lower notch stresses than circular holes. Some tendency to find the optimate hole shape with lowest stresses is shown. Following this way the danger of plate failure by cracking may be reduced. The shape of the cross-section of the plate was fixed during this considerations.

[Effect of the slot on the failure of medullary nails by buckling and bending loads]. / Der Einfluss des Schlitzes auf das Versagen von Marknägeln durch Knicken und bei Biegebelastung.

The influence of the localisation of the slot in intramedullary femoral nails is considered experimentally with respect to a possible new accident. It was found, that a ventral slot gives best behaviour of plastic deformation as well as in the load-displacement-curve. If the region of the slot is loaded by compression, great plastic torsion and buckling effects can be seen.

[Defective shaft positioning in medullary nailing as a result of play of the nail--a biomechanical analysis]. / Die Achsenfehlstellung bei der Marknagelung als Folge des Nagelspiels--eine biomechanische Analyse.

The influence of the nail wall thickness on the stress distribution is shown for the AO-nail as well as the Küntscher-nail. The quality of the analytical solution is proved by demonstrating that the presence of the slot in the nail does not shift the bending stresses merely. The gap between nail and bone is shown to be responsible for misalignments in the fracture.

[Theoretical studies on stress protection in fractures treated by osteosynthesis]. / Theoretische Untersuchungen zum Verständnis der "Stressprotektion" bei osteosynthetisch versorgten Frakturen.

Using a simple model geometry the effect of stress protection in a bone caused by combination with a metal plate is studied. It is found that no global stress protection exists in any case. The stresses in the bone can be higher than in the homogeneous bone without any reinforcement. Therefore, a consideration of any special type of implantation should be done.

[Biomechanical studies of bone treated with intramedullary nailing, with special reference to possible axis deviations]. / Biomechanische Untersuchungen des mit Marknagel versorgten Knochens unter spezieller Beachtung möglicher Achsenfehlstellungen.

The effect of a misalignement of a nailed bone on the stress distribution in the cross section is shown theoretically. Also for pure axial loading of the bone a superposed bending due to the misalignement produces large tension stresses as well in the nail as in the bone, when the fracture is not healed. After healing the stresses in the nail and in the bone are reduced striking. The removing of the nail does not increase the stresses in the bone significantly.

Mathematical, clinical, and laboratory study of hemodynamic changes in the placental circulation.

Various rheological properties of blood were investigated in pregnant and non-pregnant women of similar age. The results from 27 women with abnormal pregnancies were compared to those obtained from 17 non-pregnant women. In abnormal pregnancies we found a reduction of the erythrocyte filtration and a pathological use in red cell aggregation and in the shear resistance of the aggregates. Fractional light transmission (T7/T0) was higher than 1.0, suggesting that pressure gradients in the capillary circulation are not sufficient to disperse red cell aggregates. Thus, rheological factors may be partly responsible for the clinical consequences of pre-eclampsia. Pathological red blood cell aggregation and stagnation are consequences of the changed flow properties in the microcirculation. Even a small decrease of the local pressure gradients in the microcirculation of patients with pre-eclampsia would impair the dispersal of red blood cells and lead to their increased aggregation. Complete occlusion of the placental circulation by these aggregates would impair oxygen transfer at a speed that has been calculated from a diffusion equation based on the concept of the placenta as a hollow cylinder.

[Changes in the blood rheology and their influence on the oxygen diffusion in normal and pathological pregnancies (author's transl)]. / Rheologische Veränderungen des Blutes in der normalen und pathologischen Schwangerschaft und deren Einfluss auf die Sauerstoffdiffusion.

Blood viscosity studies were carried out at regular intervals in 51 patients with normal pregnancy and in 27 patients with high risk pregnancy, i.e. with EPH-gestosis and placental insufficiency. During gestation the relative blood viscosity is significantly increased compared to 15 normal non-pregnant women. At a corrected hematocrit of 45% we found a direct correlation to plasma fibrinogen and to the blood sedimentation rate. Although the whole blood viscosity does not indicate any change in normal pregnant women, there is, however, a viscosity increase in the last trimester of high risk pregnancies. Additionally a mathematical model of the oxygen diffusion in the placental cotyledo demonstrates rapid decrease of the oxygen partial pressure in the maternal intervillous channel if the microcirculation of the "Placenton" is impaired.