Investigation of Transfer Function Analysis as a Means to Predict Strain on Rat Tibiae from Ankle Torque Waveforms
Electrical Muscle Stimulation (EMS) is used as a countermeasure in animal disuse studies that seek to determine which forms of exercise are most effective in mitigating the effects of disuse atrophy on bone and muscle. Although EMS has been used for many years in our lab and others, few researchers have been able to quantify the levels of strain on rat tibiae during EMS and far fewer have investigated the causal relationship between torque produced at the ankle and strain on the tibia. This thesis sought to investigate the relationship between ankle torque and tibial strain by using a combination of techniques, namely: (1) the addition of rosette strain gages, (2) improved synchronization between ankle torque and tibial strain recordings, and (3) spectral analysis between torque and strain waveforms. In previous work, few methods existed to align torque and strain recordings temporally, as those data were recorded on separate computers and synchronizing events were not captured. Attempting to create a torque-strain crossplot with unsynchronized data does not always yield valid results, so a method of reliably synchronizing those data is required. This thesis developed methods to capture simultaneous (synchronizing) events in both torque and strain recordings and then used those captured events to synchronize data between two computers. Following that synchronization, stiffness calculations were run on torque-strain crossplots to determine linear-model relationships between torque and strain for each method of synchronization. The results from those regressions were then used to determine if one or more synchronization techniques are superior to others, in terms of repeatability or precision. The results of these analyses have shown that using portions of the curves can dramatically increase computing speed while providing high levels of repeatability in synchronization measures. After synchronization techniques had been investigated, 3-element rosette data were used to calculate the principal strains on the surface of the tibiae, and the percentage of principal strains that are accounted for in the axial direction. Since the strain environment changes along the axis of the bone, the principal strain data were plotted versus the distance from proximal epiphysis to rosette gage, and statistical analysis was presented. After rosette data were analyzed, the torque and strain data pairs were fed into a signal processing suite for the purpose of transfer function calculation. Using the synchronization methods outlined above, two means of synchronization were compared in the transfer function program. Results for these analyses demonstrated that transfer functions are slightly dependent on synchronization methods, but that calculated gains do not differ between synchronization techniques. The specific shapes of the transfer functions highlight the relative attenuation/amplification of frequencies in torque and strain signals. Specifically, a range of frequencies, commonly called a band, between 24 and 32Hz is attenuated by the soft tissues and mechanical linkages in the lower leg of rats. This finding gives researchers looking to increase or decrease modeling stimulus to bone a new piece of information about the relative efficiency of EMS exercise. For example, EMS performed at 24-25Hz might produce less strain in the tibia than EMS at 22-23Hz, despite the 22-23Hz stimulation producing marginally less torque.