Effect of Calibration Method on Tekscan Sensor ...

Effect of Calibration Method on Tekscan Sensor Accuracy Jill M. Brimacombe Department of Mechanical Engineering, University of British Columbia, 6250 Applied Science Lane, Vancouver, BC, V6R 2L7, Canada

David R. Wilson Division of Orthopaedic Engineering Research, Department of Orthopaedics, and Vancouver Coastal Health Research Institute, University of British Columbia, 500-828 West 10th Avenue, Vancouver, BC, V6K 1L8, Canada

Antony J. Hodgson Department of Mechanical Engineering, University of British Columbia, 6250 Applied Science Lane, Vancouver, BC, V6R 2L7, Canada

Karen C. T. Ho Centre for Bioengineering Research and Education, and Department of Civil Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4, Canada

Carolyn Anglin1 Centre for Bioengineering Research and Education, and Department of Civil Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4, Canada e-mail: [email protected]

Tekscan pressure sensors are used in biomechanics research to measure joint contact loads. While the overall accuracy of these sensors has been reported previously, the effects of different calibration algorithms on sensor accuracy have not been compared. The objectives of this validation study were to determine the most appropriate calibration method supplied in the Tekscan program software and to compare its accuracy to the accuracy obtained with two user-defined calibration protocols. We evaluated the calibration accuracies for test loads within the low range, high range, and full range of the sensor. Our experimental setup used materials representing those found in standard prosthetic joints, i.e., metal against plastic. The Tekscan power calibration was the most accurate of the algorithms provided with the system software, with an overall rms error of 2.7% of the tested sensor range, whereas the linear calibrations resulted in an overall rms error of up to 24% of the tested range. The user-defined ten-point cubic calibration was almost five times more accurate, on average, than the 1 Corresponding author. Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received October 7, 2007; final manuscript received July 18, 2008; published online December 23, 2008. Review conducted by Richard E. Debski.

Journal of Biomechanical Engineering

power calibration over the full range, with an overall rms error of 0.6% of the tested range. The user-defined three-point quadratic calibration was almost twice as accurate as the Tekscan power calibration, but was sensitive to the calibration loads used. We recommend that investigators design their own calibration curves not only to improve accuracy but also to understand the range(s) of highest error and to choose the optimal points within the expected sensing range for calibration. Since output and sensor nonlinearity depend on the experimental protocol (sensor type, interface shape and materials, sensor range in use, loading method, etc.), sensor behavior should be investigated for each different application. 关DOI: 10.1115/1.3005165兴 Keywords: Tekscan, pressure sensor, calibration, accuracy, prosthetic joints

1

Introduction

Resistance-based force distribution sensors, such as those made by Tekscan Inc. 共South Boston, MA兲, are appealing for biomechanics research because they are thin and flexible and offer high resolution and straightforward data acquisition. They also provide realtime dynamic feedback, unlike static pressure films such as Fuji Prescale film. However, limitations in their accuracy have been identified by several authors in a range of biomechanical applications 关1–6兴. The choice of calibration protocol affects the accuracy of Tekscan sensors. The commercial Tekscan software offers two calibration options: a single-parameter linear calibration and a twoparameter power calibration. For the linear calibration, the user applies a single known force and the calibration consists of a straight line drawn on the applied force versus raw sensor output plot from 共0,0兲 through that measured point. This yields a linear calibration equation of the form y = mx 共Fig. 1兲. For the power calibration, the user applies two known forces, and the software finds a calibration curve of the form y = Axb plotted through 共0,0兲 and these two points 共Fig. 1兲. A recent study comparing the accuracy of the linear and power calculations for facet load testing in the spine 共using I-Scan 6900 QUAD sensors兲 concluded that the linear calibration was more accurate than the power calibration 关1兴; however, these findings apply only to the specific load range tested 共which was only up to 15% of the sensor range, where inaccuracies are greatest 关7兴兲, and a difference in accuracies was only seen during axial rotation motions of the spine, not in extension. Since the appropriateness of specific calibration routines may vary with interface materials, sensor type, sensor range, and experimental loading method 关8兴, these findings may not apply to all Tekscan sensors in all loading configurations. Custom calibration could provide an opportunity to improve the accuracy of measurements made with Tekscan sensors. Most investigators have not reported their calibration procedure, but it is reasonable to assume that they used one of the standard Tekscan calibrations. Researchers who have described using a custom nonlinear calibration 关9,10兴 did not describe the algorithm used, nor did they compare their results to the standard Tekscan calibrations. Depending on the experimental loading profile and the specified range of different sensor types, the applied loads may fall into the low range, high range, or full range of the sensor. Different calibration methods may favor one range over another. It is not clear whether custom calibration routines, which increase either the number of parameters in the fitted curve or the number of load levels included in the calibration protocol, could improve the accuracy of pressure measurements made with Tekscan sensors, nor, if they can improve accuracy, how much improvement could be expected. We therefore performed the current validation study to determine the most appropriate calibration method for Tekscan sensors

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Fig. 2 The configuration used to apply pressure to Tekscan sensors using an Instron materials testing machine Fig. 1 A schematic of the three calibration methods available with the Tekscan software that were used in the current study: 20% linear, 80% linear, and power. The raw output for the sensor is the sum of all individual sensel outputs, which range from 0 to 255. The Tekscan software uses the calibration equation to convert raw sensor output to calibrated loads during testing. The raw sensor output will lead to different calibrated forces depending on the equation used. In the case shown by the arrows, the 80% calibration results in much higher calibrated loads than the 20% and power calibrations. For higher loads, the 20% calibration results in much lower calibrated loads than the other two methods.

used in joint replacement research and analyzed the data for three different load ranges. Our two research questions were as follows. 共1兲 Of the Tekscan calibration methods, which one yields the most accurate pressure measurements? 共2兲 Can user-defined calibration protocols yield more accurate pressure measurements than the calibration routines provided in the system software?

2

Methods

2.1 Experimental Setup. To test the effects of different calibration algorithms on sensor output, three new and identical I-Scan pressure sensors 共model No. 5051– 2500 psi 共17.2 MPa兲兲 were conditioned, calibrated, and loaded using a materials testing machine 共Instron 8874, Canton, MA兲. Although we did not equilibrate the sensors 共i.e., digitally compensate for variations in individual sensels兲, this would have a negligible impact on our results since our loading cylinder, described below, covered close to 900 sensels and we were analyzing the resultant load rather than the load distribution. For biomechanical experiments, in which the contact areas are typically much smaller and load distribution may be the primary measure, we recommend equilibrating sensors prior to testing. We chose the given sensor range and shape to suit our intended application, which was cadaveric testing of the resurfaced patellofemoral joint. The range was chosen to accommodate the maximum expected pressures as estimated from previous studies of the resurfaced patellofemoral joint 关11–13兴. Our subsequent experimental testing 关14兴 confirmed that this was the correct sensor range to use. A test interface was created to mimic the material interface of a standard prosthetic joint, i.e., an articulation between plastic and metallic surfaces. Each sensor was compressed between a flat polyethylene disk 共diameter= 3.82 cm兲, which covered 45% of the sensor surface, and a larger metal plate 共Fig. 2兲. The relative stiffness between the metal and plastic was such that the deformation of the plate would have been negligible, making the exact choice of metal material 共in this case, aluminum兲 unimportant. The size of the disk was much larger than the typical contact area in replaced joints, but was chosen to cover a large portion of the sensor 034503-2 / Vol. 131, MARCH 2009

area for calibration, as recommended by the manufacturer 关8兴. Sensors were coated with surgical lubricant 共K-Y, Johnson & Johnson, Montreal, Canada兲 to reduce shear loads. For all conditioning, calibration, and loading cycles, we increased the force linearly over 10 s, held it constant for 5 s, and decreased it to zero linearly over 10 s. Sensors remained unloaded for 120 s between cycles. This loading sequence was designed to minimize transient effects such as drift and hysteresis and to produce quasi-steady-state responses, similar to the conditioning, calibrating, and loading sequence used in an earlier study of Tekscan sensors 关1兴. We conditioned all sensors four times at the maximum sensor range, corresponding to conditioning the sensor at a pressure that is 20% greater than the maximum expected pressure, as recommended by Tekscan 关8兴. 2.2 Calibration and Loading Sequence. Following conditioning, we performed the Tekscan-defined calibrations by loading the sensor at 20% and 80% of the maximum expected pressure. Tekscan’s calibration software was used to produce three calibrations: 20% linear, 80% linear, and power 共which uses both the 20% and 80% pressure values兲. Next, we subjected each sensor to two loading cycles, each consisting of ten evenly-spaced pressures from 10% to 100% of the maximum expected pressure applied in a random order. The first loading cycle was used to determine the calibration coefficients for our user-defined algorithms. The second loading cycle was used as the simulated experimental data to which all calibration algorithms were applied 共Fig. 3兲. This process mimics experimental practice in which the calibration is performed prior to experimental data acquisition. We investigated repeatability by loading one sensor through three sets of simulated experimental testing following calibration. 2.3 User-Defined Calibration Methods. We defined two types of calibration as follows. 共1兲 A ten-point cubic polynomial calibration 共a1x3 + b1x2 + c1x + d1兲, in which we loaded the sensors at ten evenly-spaced pressures between 1.46 MPa and 14.6 MPa 共i.e., between 10% and 100% of the maximum expected pressure兲 in a random order. We then performed a nonlinear least-squares fit of a cubic polynomial through the sensor output versus applied force data to minimize the cost function: C = ⌺共Fcalculated − FInstron兲2

共1兲

where Fcalculated was a cubic function of the raw sensor output and FInstron was the applied force measured by the Instron load cell. 共2兲 A three-point quadratic polynomial calibration 共a2x2 + b2x + c2兲, which can be determined using matrix algebra to solve the three equations in three unknowns. We evaluated six different load sets to investigate which produced the lowest value of C in Eq. 共1兲 over the full range: 10–50– Transactions of the ASME

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Fig. 3 Timeline of calibrations and loading. This sequence was performed for three identical sensors. For one of the sensors, three sets of experimental data were taken to test for repeatability of the results for the same calibration algorithm.

100%, 0–20–80%, 0–50–100%, 0–40–100%, 0–60–100%, and 10–60–100% of the maximum expected pressure. The lsqrnonlin optimization function within MATLAB® 共Mathworks, Natick, MA兲 was used to calculate the coefficients of the cubic and quadratic polynomial fits. Note that the point 共0,0兲 was not explicitly included in either user calibration. We saved all force data as raw 共uncalibrated兲 values so that each of the five calibration algorithms 共three Tekscan and two user-defined兲 could be applied to the same raw output. Measurement accuracy was defined as the root mean square 共rms兲 error between the calibrated Tekscan output and the Instron load cell measurements.

3

Results

The raw output was nonlinearly related to the applied loading, which produced visibly curved relations between applied load and measured output when using linear calibrations 共Fig. 4兲; in turn, there were clear differences in accuracy amongst the calibration

Fig. 4 Output for one sensor calibrated using the five different calibration algorithms showing overestimation of the loads when using the 80% linear calibration at lower loads and underestimation of the loads when using the 20% linear calibration at higher loads

Journal of Biomechanical Engineering

Fig. 5 Average rms errors of Tekscan and user-defined calibration algorithms for three different testing ranges. The calibration points used for the three-point polynomial „10%, 50%, and 100%… were chosen to minimize rms errors over the full range; other selections could reduce errors in the high or low range. Error bars show the standard deviation for the three sensors tested.

algorithms 共Fig. 5兲. Of the three Tekscan calibrations tested, the power calibration was the most accurate, providing almost ten times the accuracy of the 20% linear calibration across the range of the sensor. The rms errors of the measured pressures for the 20% linear, 80% linear, and power calibrations over the full sensor range were 3.55⫾ 0.19 MPa, 1.53⫾ 0.08 MPa, and 0.39⫾ 0.14 MPa, respectively, corresponding to 24%, 11%, and 2.7% of the tested sensor range 共Fig. 5兲. The 80% calibration dramatically overestimated values in the low range 共by up to 72%兲, while the 20% calibration dramatically underestimated values in the high range. The Tekscan power calibration performed well over the low range of the sensor 共from 0% to 30% of the maximum expected pressure, the rms error was 0.5%兲, but produced a rms error of 2.2% of the tested range at the high range of the sensor 共from 70% to 100% of the maximum expected pressure兲 共Fig. 5兲. Both user-defined polynomial calibrations were more accurate in this study than the Tekscan calibrations over the full range 共Fig. 5兲. The three-point quadratic calibration results presented are for the best selection of calibration points 共10–50–100兲 for the full range. The quadratic and cubic calibrations had rms errors of 0.18⫾ 0.02 MPa 共1.2% of the full tested range兲 and 0.08⫾ 0.03 MPa 共0.6% of the full tested range兲, respectively. Over the full range, the ten-point cubic calibration was almost five times more accurate on average than the power calibration. The three-point quadratic calibration, which required only one extra calibration point compared to the Tekscan power calibration, produced results that were more than twice as accurate as the Tekscan power calibration over the full range. However, its accuracy in the lower range was reduced compared to both the power and the 20% linear calibrations. Of the five other combinations evaluated, calibration points at 0%, 20%, and 80% of the maximum pressure yielded the best accuracy for the low range 共rms error of 1.5% compared to 1.9% for the 10–50–100 combination at the sacrifice of a higher full-range rms error of 2.6% compared to 1.2%兲, while 0%, 60%, and 100% yielded the best accuracy for the high range 共rms error of 0.5% compared to 0.7% for the 10–50–100 combination, but a full-range error of 3.9%兲. The repeatability of the ten-point calibration algorithm, for the three repeated sets of experimental data, was excellent, giving a standard deviation over the tested range of only 0.2%. MARCH 2009, Vol. 131 / 034503-3

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4

Discussion

In this study, we determined which Tekscan-defined calibration method provided the most accurate pressure measurements, and whether user-defined calibration methods increased accuracy. Of the Tekscan calibrations, the power calibration yielded the most accurate pressure measurements for this testing configuration— under 3% rms error across the full sensing range. Both userdefined calibration methods yielded more accurate results than the Tekscan methods over the full range, with the ten-point cubic calibration yielding the most accurate pressure measurements. The differences in accuracy for different selections of calibration points in the three-point quadratic calibration highlight the importance of selecting optimal calibration points to yield the most accurate results within the desired testing range. Alternative selections, such as 10–20–30% or 70–80–90% or the maximum range, could be chosen to maximize the accuracy within the given range. Our results reinforce and enhance the understanding that the most appropriate calibration to use with Tekscan sensors depends on where the anticipated pressures lie within the pressure range of the sensors used. Since the sensors are resistive, the response is not linear, although over a small range it appears approximately linear. The Tekscan literature states that linear calibrations are suitable for tests over a limited loading range, and the power calibration is preferable for tests in which loads vary considerably 关8兴. A limitation of this study is that we did not quantify other factors known to affect Tekscan accuracy, although these factors were controlled. For example, only one type of Tekscan sensor was studied. We also did not test what effect curved contact surfaces might have on the sensor’s output because these effects were not directly relevant to our primary goal of assessing differences between calibration algorithms. We expect that general differences in calibration algorithms will also apply to curved configurations, although the details of the calibration process would likely be different. To calibrate using curved surfaces, the location of each sensel of the sensor must be known with respect to the implant surfaces in order to determine the directions of the force vectors acting on the sensor and shear loads must be negligible. The accuracy of the system may be lower than reported when used in dynamic loading situations due to the effects of shear loads, loading between curved surfaces, or small contact areas. Readings may also be subject to drift 关4兴, although we tried to minimize this effect by taking our measurements at a consistent time after the load was applied. The results we obtained are only applicable to overall measurements of applied pressure; errors in individual sensels could be much larger than errors for the overall sensor 关2,8兴. Finally, sensor output and output variability depend on the stiffness of the contact materials 关8,15,16兴 and we only tested one combination of materials; however, the results can be applied to prosthetic joints that involve the articulation of plastic and metallic surfaces with relative stiffnesses comparable to the experimental setup used in this study. While the repeatability in our relatively ideal conditions was high, users should be aware that repeatability is often an issue during experimental testing 关3,4,6,14兴. In addition to the problem of drift 关4,6兴, Tekscan sensors can experience signal degradation, i.e., a loss of sensitivity, over time 关6,14兴. Users should be aware of this and take measures to address it by 共a兲 repeating measurements under identical conditions multiple times during testing to test for signal changes, 共b兲 randomizing the order of experimental testing to avoid a consistent bias with time, 共c兲 minimizing shear loads by lubricating the surfaces, 共d兲 protecting the sensor from

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any other unusual loading such as twisting of the electrical leads, and 共e兲 repeating the calibration at the end of testing. Since it is straightforward to export sensor outputs and to calibrate the data externally, we recommend using user-defined calibration protocols to improve measurement accuracy. Performing an initial ten-point calibration allows the user to characterize the complete load curve, determine at what load the greatest errors occur, and select the most appropriate number and spacing of calibration points to use. We also recommend calibrating each sensor individually to achieve the greatest accuracy because the raw values and calibration equations differ for each sensor; nevertheless, if the variations in accuracy are acceptable to the user following initial testing, and the number of sensors used is large, the user may choose to apply a single calibration algorithm to all sensors used. The calibration method used is one of many variables that must be planned, monitored, controlled, and reported to optimize results when using Tekscan sensors.

Acknowledgment This work was supported by the Michael Smith Foundation for Health Research, the Natural Sciences and Engineering Research Council of Canada 共NSERC兲, and the Canadian Arthritis Network.

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