Table of Contents:
This thesis describes the development of a new measurement system (the ZETOS-system) to determine the stiffness (expressed in term of a Youngs modulus) of bone cores, which are placed in long-term bioreactors. This system can also provide dynamic stimulation on the bone cores with standard signals (sinusoidal, square) as well as the generation of user-defined signals or physiological signals like Walking, Running and Jumping, which were gathered on force platforms (ground reaction forces). Signals can be filtered (highpass, lowpass).
Due to the one-dimensional arrangement of sensors and actuators it is impossible to measure the complete elastic tensor of bone cores.
In a long-term study we used trabecular bone of a Femur head and applied the physiological signal Jumping on the bone cores five minutes each day. An increase in stiffness of 2% per day was found whereas the bones of a control did not show any significant change. A third group of bones was also stimulated with Jumping, however this signal was highpass-filtered. The stiffness increase of this group was nearly at the same amount as the first group, which shows that higher frequency components are sufficient to produce bone remodeling.
The data of this measurement series were used to explain the non-linearities of strain/stress curves of the ZETOS-system by means of a force depending contact-area function. Non-linearities are caused by the roughness of the cutting surfaces. Mathematical models provide this:
- an estimation of the standard deviation of surface roughness
- the difference between external and internal strain in the bone cores
- the impossibility of the determination of the true Youngs modulus, because the compressive
load has to be restricted to the upper physiological limit in order to avoid overload.
Further data processing had been accomplished:
- The first deviation of displacement versus force to find a way to represent the contact area function mathematically. Obviously this function is not constant over the complete long-term period and could affect virtual stiffness increase. This effect however is rather low.
- Integration (potential energy), which led to an alternative way to calculate the value of the Youngs modulus. This method can be applied simultaneously during dynamic load under certain restrictions.
Relaxation measurements were also accomplished during the long-term experiment. Here I found two time constants at about 0.4 and 20 seconds. In order to achieve a good fit of the measured force-relaxation curves a continuous relaxation time spectrum is necessary around the smaller time constant. Data procession result in the representation of frequency-dependent storage- and loss-modulus as well as loss-factor and phase-shift between displacement and force in case of harmonic stimulation.
A comparison of the modulus spectra with the spectra of our physiological signals shows a selectivity of bone: There is some energy dissipation in case of walking and jumping. This effect is much lower in case of running, which might be necessary to support persistence in movements like attack, hunt and flight making movement more efficient and reducing the build up of heat.