Design and analysis of a novel mechanical loading machine for dynamic in vivo axial loading

Abstract

This paper describes the construction of a loading machine for performing in vivo, dynamic mechanical loading of the rodent forearm. The loading machine utilizes a unique type of electromagnetic actuator with no mechanically resistive components (servotube), allowing highly accurate loads to be created. A regression analysis of the force created by the actuator with respect to the input voltage demonstrates high linear correlation (R(2) = 1). When the linear correlation is used to create dynamic loading waveforms in the frequency (0.5-10 Hz) and load (1-50 N) range used for in vivo loading, less than 1% normalized root mean square error (NRMSE) is computed. Larger NRMSE is found at increased frequencies, with 5%-8% occurring at 40 Hz, and reasons are discussed. Amplifiers (strain gauge, linear voltage displacement transducer (LVDT), and load cell) are constructed, calibrated, and integrated, to allow well-resolved dynamic measurements to be recorded at each program cycle. Each of the amplifiers uses an active filter with cutoff frequency at the maximum in vivo loading frequencies (50 Hz) so that electronic noise generated by the servo drive and actuator are reduced. The LVDT and load cell amplifiers allow evaluation of stress-strain relationships to determine if in vivo bone damage is occurring. The strain gauge amplifier allows dynamic force to strain calibrations to occur for animals of different sex, age, and strain. Unique features are integrated into the loading system, including a weightless mode, which allows the limbs of anesthetized animals to be quickly positioned and removed. Although the device is constructed for in vivo axial bone loading, it can be used within constraints, as a general measurement instrument in a laboratory setting.

Figure 1

Linear regression (n = 3) is performed to access the linearity of the FELA. Since the system is highly linear, the equation can be utilized to create computer controlled dynamic force waveforms.

Figure 2

The mechanical arrangement of the bone loading device has all components in series. In this vertical arrangement, the forcing unit will have to offset the effects of gravity on the thrust rod, but this is a compromise as it is easier to position specimens.

Figure 3

An amplifier for the dc LVDT was created so that high displacement resolution could be obtained. The use of DIP switches (only two shown, SW = 8, SW = 6) allows a trade off in amplifier gain and working range to be made with different size animal models.

Figure 4

A differential amplifier (INA121) is used to take the difference from each side of the Wheatstone bridge so that the signal from the load cell and strain gauge can be amplified. A series of switches (only two SW shown) allow the gain of the op-amp (LM741) to be adjusted, giving a trade off in load resolution to the maximum load which can be measured (saturation). A trimpot is used to adjust the dc level out of the instrumentation amplifier.

Figure 5

The NRMSE is computed between the measured value from the load cell and the loading waveform (Sin), as demonstrated in a 1 Hz, 10 N dataset. The Sin only diverges enough from the measured values so that it is visible in the very top and bottom of the waveform. In those areas where the two diverge, the NRMSE increases the most.

Figure 6

Cyclic loading to failure of a one-month old mouse forelimb at 2.5 N demonstrates the ability of the LVDT amplifier and load cell to detect damage (change in elastic modulus and creep damage). Only the last ten loading cycles are shown.

Figure 7

A calibration of strain in response to applied force. This type of calibration will be used for future work with the loading device. It allows different in vivo strains to be applied that are within a range known to induce biological effects. This calibration is the average of three different mouse forearms (three-month old female TOPGAL mice) which are each loaded at four different frequencies (0.5, 1, 2, and 4 Hz) and averaged at six load points.

Figure 8

In order to bond with a small mouse bone, the strain gauge (left) is trimmed into its bonding area (right), which reduces its area from 18 mm² to ∼1.5 mm². A hemocytometer with 1 mm grid spacing (0.25 mm minor tick marks), is used as the background on both images.