A novel miniature in-line load-cell to measure in-situ tensile forces in the tibialis anterior tendon of rats

Abstract

Direct measurements of muscular forces usually require a substantial rearrangement of the biomechanical system. To circumvent this problem, various indirect techniques have been used in the past. We introduce a novel direct method, using a lightweight (~0.5 g) miniature (3 x 3 x 7 mm) in-line load-cell to measure tension in the tibialis anterior tendon of rats. A linear motor was used to produce force-profiles to assess linearity, step-response, hysteresis and frequency behavior under controlled conditions. Sensor responses to a series of rectangular force-pulses correlated linearly (R2 = 0.999) within the range of 0-20 N. The maximal relative error at full scale (20 N) was 0.07% of the average measured signal. The standard deviation of the mean response to repeated 20 N force pulses was ± 0.04% of the mean response. The step-response of the load-cell showed the behavior of a PD2T2-element in control-engineering terminology. The maximal hysteretic error was 5.4% of the full-scale signal. Sinusoidal signals were attenuated maximally (-4 dB) at 200 Hz, within a measured range of 0.01-200 Hz. When measuring muscular forces this should be of minor concern as the fusion-frequency of muscles is generally much lower. The newly developed load-cell measured tensile forces of up to 20 N, without inelastic deformation of the sensor. It qualifies for various applications in which it is of interest directly to measure forces within a particular tendon causing only minimal disturbance to the biomechanical system.

Fig 1. Working principle of the load-cell.

A: Schematic representation of the clamping mechanism of the load cell. The illustration shows the dimensions of the load-cell as well as the position and orientation of the strain-gauges (SG) of the front side. The SGs on the back-side are positioned and orientated analogously. The circuit in the lower left corner shows the connection of the SG´s as temperature compensated half-bridge B: Manufactured load-cell in comparison to a 5 Euro-cent coin without clamping screws.

Fig 2. Measurement setup.

A Bose linear motor applied preprogrammed patterns of force to the newly developed load-cell. The force measured with the reference sensor was used to correlate the output voltage of the load-cell with the load applied. The load-cell was tested using a dried tibialis anterior tendon of a rat which connected the device to the measurement set up.

Fig 3. Testing protocol.

Applied patterns of force to evaluate the behavior of the load-cell. A) Rectangular force-pulses of different amplitude–used to obtain calibration data. B) Rectangular force-step for evaluation of rapid changes. C) Triangular force-pattern to investigate hysteresis of the load-cell. D) Sinusoidal force-patterns of various frequencies to characterize the frequency behavior of the load-cell.

Fig 4. Tendon shrinkage.

Measurement of the relative shortening during drying of the tibialis anterior tendon of a rat.

Fig 5. Calibration curve.

Change in output-voltage (V_diff) normalized to the bridge voltage (0.562 V) of the load-cell in relation to changes of force (F_diff), measured with rectangular force pulses of different amplitudes. Crosses depict the results of the individual measurements for each force-level (amplitude). The individual measurements appear as single cross in the diagram due to the low variation. The solid grey line shows a linear regression performed on this data.

Fig 6. Step response.

A) Illustration of the normalized signals measured with the reference sensor (dark grey trace) and the load-cell (light grey trace). The black trace represents a fitting (R² = 0.977) to the normalized load-cell signal, considering the normalized reference-signal as input. The model of the load-cell is represented schematically as block-diagram of an additive combination of a P and two PT1 elements with the overall behavior of a PD2T2 element. B) The inverse transfer function of the PD2T2 model was used to correct the force response of a single twitch and a short burst (stimulation frequency 60 Hz). The exemplary data reveals an underestimation of the measured peak-forces by 14.3% for single twitches and 6.8% for short bursts.

Fig 7. Hysteresis.

Hysteresis was obtained by superimposing four consecutive responses, to a triangular force-pattern, measured with the load-cell. The hysteresis shows its highest width at 9.84 N which amounted to 30 μV / V.

Fig 8. Frequency response.

Frequency attenuation of the signals measured with the reference-sensor (dark grey trace) and the load-cell (black trace), in combination with the attenuation predicted by the calculated model of the load-cell (light grey trace). The model fits the measured load-cell data well at lower frequencies. For frequencies higher than 10 Hz a further decrease is observed in the measured data, revealing a maximal attenuation of -4.2 dB at a frequency of 200 Hz.