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Performance and Reliability of a Variable Rate, Force/Displacement Application System

      Abstract

      Objective

      Spinal manipulation therapy (SMT), an intervention used to treat low back pain, has been demonstrated to affect the stiffness of the spine. To adequately quantify the effects of SMT on stiffness, a device capable of applying specific parameters of manipulation in addition to measuring force-displacement values has been developed previously. Previously developed indentation techniques that quantify stiffness have been modified for novel use in evaluating SMT parameters. The reliability of stiffness measurements performed by the newly adapted device was assessed in this study.

      Methods

      Seven springs of varying stiffness were each indented 10 times by a variable rate force/displacement (VRFD) device. Indentations were performed at a rate of 0.5 mm/s to a maximal displacement of 4 mm. The stiffness coefficients for a middle portion of the resulting force-displacement graph and the terminal instantaneous stiffness (stiffness at end displacement) were calculated. The intraclass correlation and confidence interval were calculated for these stiffness measurements to assess device reliability.

      Results

      Repeated spring stiffness measures yielded an intraclass correlation coefficient value of 1.0. The mean stiffness values had narrow 95% confidence intervals ranging from 0.01 N/mm to 0.06 N/mm and small coefficients of variation.

      Conclusion

      This VRFD device provides highly reliable stiffness measurements in controlled conditions. Although in vivo reliability remains to be established, the results of this study support the use of the VRFD device in future trials investigating the impact of various SMT parameters on spinal stiffness.

      Key Indexing Terms

      Low back pain
      • Latimer J
      • Lee M
      • Adams R
      • Moran CM
      An investigation of the relationship between low back pain and lumbar posteroanterior stiffness.
      and spinal degeneration
      • Kawchuk GN
      • Kaigle AM
      • Holm SH
      • Rod Fauvel O
      • Ekstrom L
      • Hansson T
      The diagnostic performance of vertebral displacement measurements derived from ultrasonic indentation in an in vivo model of degenerative disc disease.
      are often associated with changes in spinal stiffness. To assess these changes, clinicians most often use a manual technique where postero-anterior forces are applied to the spine and the resulting tissue response is appreciated. Unfortunately, manual spinal stiffness assessment has been shown to have poor performance. Specifically, prior investigations have demonstrated that clinicians are unable to apply consistent forces,
      • Simmonds M
      • Kumar S
      • Lechelt E
      Use of a spinal model to quantify the forces and motion that occur during therapists' tests of spinal motion.
      perceive changes in the force displacement relationship,
      • Bjornsdottir SV
      • Kumar S
      Posteroanterior motion test of a lumbar vertebra: accuracy of perce ption.
      or judge spinal stiffness.
      • Maher C
      • Adams R
      Reliability of pain and stiffness assessments in clinical manual lumbar spine examination.
      As a result, many investigators have designed mechanical devices to increase measurement precision and accuracy when assessing spinal stiffness.
      • Latimer J
      • Goodsel MM
      • Lee M
      • Maher CG
      • Wilkinson BN
      • Moran CC
      Evaluation of a new device for measuring responses to posteroanterior forces in a patient population. Part 1: Reliability testing.
      • Kawchuk GN
      • Liddle TR
      • Fauvel OR
      • Johnston C
      The accuracy of ultrasonic indentation in detecting simulated bone displacement: a comparison of three techniques.
      • Tuttle N
      • Barrett R
      • Laakso L
      Postero-anterior movements of the cervical spine: repeatability of force displacement curves.
      • Owens EF
      • DeVocht JW
      • Wilder DG
      • Gudavalli MR
      • Meeker WC
      The reliability of a posterior-to-anterior spinal stiffness measuring system in a population of patients with low back pain.
      • Allison G
      • Edmonston S
      • Kiviniemi K
      • Lanigan H
      • Simonsen AV
      • Walcher S
      Influence of standardized mobilization on the posteroanterior stiffness of the lumbar spine in asymptomatic subjects.
      The mechanical device described in this study has been used previously by Pickar et al
      • Pickar JG
      An in vivo preparation for investigating neural responses to controlled loading of a lumbar vertebra in the anesthetized cat.
      • Pickar JG
      • Wheeler JD
      Response of muscle proprioceptors to spinal manipulative-like loads in the anesthetized cat.
      • Pickar JG
      • Kang YM
      Paraspinal muscle spindle responses to the duration of a spinal manipulation under force control.
      to apply rapid forces that simulate spinal manipulation therapy (SMT) in a feline model. Because this device can change the rate at which forces are applied, it may be possible to use the same device to apply lower force rates used in stiffness testing as well as the higher rates used in SMT application. Before using the variable rate, force/displacement (VRFD) device in an experimental setting to assess spinal stiffness, the device's reliability should be established with respect to stiffness assessment. Therefore, the objective of this study was to determine the reliability of the VRFD device in a benchtop setting. Given prior technology assessments,
      • Latimer J
      • Goodsel MM
      • Lee M
      • Maher CG
      • Wilkinson BN
      • Moran CC
      Evaluation of a new device for measuring responses to posteroanterior forces in a patient population. Part 1: Reliability testing.
      • Edmondston SJ
      • Allison GT
      • Gregg CD
      • Purden SM
      • Svansson GR
      • Watson AE
      Effect of position on the posteroanterior stiffness of the lumbar spine.
      device reliability could be considered to be excellent with intraclass correlation coefficient (ICC) values of 0.8 or higher
      during replicate tests to determine the stiffness of inanimate objects.

      Methods

      Variable Rate Force/Displacement Device

      VRFD Overview

      The VRFD device is capable of performing vertebral postero-anterior indentations at high rates of loading to simulate SMT or at low rates to quantify stiffness. The VRFD device is composed of 5 major components (4 are shown in Fig 1): (1) a graphical computer interface; (2) a data acquisition board (USB-6212, National Instruments, Austin, Tex); (3) an electronic feedback, motor control system (Aurora Scientific, Dual Mode Lever System, Model 310C, Aurora, Ontario, Canada); (4) a custom-made indenter connected to the motor via a rotary to linear converter; and (5) a custom-made 3-dimensional positioning frame. In brief, the computer interface sends a voltage signal whose magnitude represents the desired output of the motor that in turn is controlled by the electronic feedback system. Transducer outputs from the control system provide both feedback control to the motor and output voltage to the computer. These signals represent the amount of displacement and force applied by the indenter, respectively. Paired values for applied displacement and force can then be plotted and stiffness derived from the resulting plot.
      Figure thumbnail gr1
      Fig 1Diagram representation of the VRFD device. The voltage control signal is sent through the device, and the force and displacement response signals are returned in a continuous loop.

      Components

      A custom graphical interface (LabView 8.6, National Instruments) enables the operator of the VRFD to program the input voltage signal that will control the magnitude and rate of indenter movement. The waveform constituting the signal is created using customized software (LabView 8.6) that generates an analog file containing an array of values corresponding to the desired input voltage. The rate at which the data acquisition board will ultimately send the voltage (the rate at which voltage should increase) and the maximum desired voltage are parameters that determine the number of voltage increments contained in the file and the value of each increment. Files containing unique displacement (voltage) rates and maximum displacement (voltage) magnitudes can be created in advance for conducting indentations of differing parameters. In the current study, a single rate of 0.5 mm/s was used to assess stiffness.
      The data acquisition board (Fig 1 [2]) is powered by, and connects to, a computer through a USB cable. The board sends the input signal for indentation to the electronic feedback control system at a rate of 1 kHz using 16-bit resolution.
      The electronic feedback motor control system (Fig 1 [3]) consists of an electronic feedback interface and a rotary moving coil motor (Fig 2, item A). The electronic feedback interface connects to the data acquisition board and receives the input voltage signal from the computer. This connection can be modified so that the input voltage controls either the displacement or force generated by the motor. In this study, the motor was used in displacement control exclusively. Motor movement is inherently rotational (Fig 2, item B).
      Figure thumbnail gr2
      Fig 2Schematic representation of the motor (A) and motor arm (B) connected to the rotary to linear converter, which is made of a fixed (Cf) and a movable (Cm) component applying displacements through the rod (D).
      Because the lever motion is rotary, a component was fabricated to convert rotational motion to linear motion. A portion of this converter (Fig 1 [4] and Fig 2, item Cf) was mounted onto a stationary, rigid positioning frame attached to the motor. The movable portion (Fig 2, item Cm) had an oblong horizontal opening into which a short shaft from the motor's 8-cm lever arm was inserted. The converter's moveable portion was guided by 2 rods traveling through linear bearings pressed into the converter's fixed portion. Actual indentation was performed by a 6-cm long titanium rod fixed in place at the bottom of Cf (Fig 2, item D). The rod was terminated with a 0.5-cm-thick plastic cap. Consequently, rotary motion of the lever arm created linear motion of the indenter's tip. Step changes in forces or displacement occur with response times of approximately 8 milliseconds.
      Positioning the motor with the attached lever arm, linear converter, and indentation rod (Fig 2) was performed by a custom built 3-dimensional frame railing system onto which the motor was mounted. This frame enabled the motor to be positioned along 3 orthogonal axes with a precision of 0.5 mm along each axis and 200 mm maximum travel.

      Calibration

      With the rotary to linear converter in place, the maximum force and displacement attainable by the motor was 50.0 N and 28.5 mm, respectively (as determined by the manufacturer). The manufacturer's calibration values (4.9 N/V and 2.85 mm/V) were confirmed experimentally by tracing the vertical position of the motor arm at 1-V increments then using a digital caliper to measure the distance between tracings. In addition, a linear variable differential transducer (0.1% error, MLT; Honeywell, Intertechnology, Don Mills, Ontario, Canada) was placed on Cm (Fig 2) to confirm that the manufacturer's conversion factors attained the desired displacement magnitude.

      Spring Piston System

      To assess the reliability of the VRFD device, 7 compression springs of varying stiffness were used as test media. Springs (A-G) were obtained from Century Spring, Los Angeles, Cal (manufacturer stiffness: 1.19-6.68 N/mm; free length: 10.2 cm; outer diameter: 2.5 cm; wire diameter: 0.3 cm). The range of spring stiffness was selected to cover the range of possible stiffness coefficients expected in future experiments.
      • Ianuzzi A
      • Pickar JG
      • Khalsa PS
      Determination of torque-limits for human and cat lumbar spine specimens during displacement-controlled physiological motions.
      Each spring was placed around a piston (Fig 3), and a 1-cm-thick rubber pad was placed between the indenter and the piston. The pad provided a compliant interface to prevent uncontrolled motor oscillations.

      Repeated Stiffness Testing

      The rod (Fig 2, item D) was positioned in line with the center of the spring piston system (Fig 3) and perpendicular to its compressive surface. The piston was initially preloaded by lowering the motor using the positioning frame. A 0.61-N preload was determined to be sufficiently high to compensate for the system's noise (±0.025 N of force output) and yet sufficiently low to prevent overloading the motor statically. The preload was also consistent with contact loads expected to be applied during future investigations.
      • Ianuzzi A
      • Pickar JG
      • Khalsa PS
      Determination of torque-limits for human and cat lumbar spine specimens during displacement-controlled physiological motions.
      • Pickar JG
      • Sung PS
      • Kang YM
      • Ge W
      Response of lumbar paraspinal muscles spindles is greater to spinal manipulative loading compared with slower loading under length control.
      After preload application, a 4-mm indentation was performed at 0.5 mm/s. In a previous study,
      • Kawchuk GN
      • Liddle TR
      • Fauvel OR
      • Johnston C
      The accuracy of ultrasonic indentation in detecting simulated bone displacement: a comparison of three techniques.
      a relatively fast indentation rate of 2.5 mm/s was shown to have diagnostic accuracy, but a slower rate of 0.5 mm/s was selected to differentiate indentation from the rate at which simulated SMT is to be performed in future experiments (1-3 mm/s). Each spring was compressed in this manner 10 times to provide repeated measures for reliability analysis.
      • Kawchuk G
      • Herzog W
      A new technique of tissue stiffness (compliance) assessment: its reliability, accuracy and comparison with an existing method.
      Between each of the 10 compressions, 5 to 10 seconds were allowed to pass to confirm or re-establish the preload magnitude using the 3-dimensional frame.

      Analysis and Statistics

      Continuous values for displacement and force during each indentation were recorded at 10 kHz and placed into separate files (Labview 8.6) resulting in 70 files (7 springs × 10 repetitions). For each indentation, the ascending portion of the force-time and displacement-time curves was cropped for the same time interval (Fig 4). Voltages were converted to engineering units using the motor's calibrated values. Force-displacement (FD) curves were created by plotting displacement on the x-axis and force on the y-axis. The beginning of each FD curve was established as zero spring displacement by subtracting the first value of the displacement signal from all displacement values. Each force and each displacement curve was smoothed by fitting the data to a fifth-order polynomial.
      • Kawchuk GN
      • Fauvel OR
      Sources of variation in spinal indentation testing: indentation site relocation, intraabdominal pressure, subject movement, muscular response, and stiffness estimation.
      Figure thumbnail gr4
      Fig 4A voltage-time graph demonstrating displacement and force signals collected by the VRFD device. The ascending portion of these plots was defined as the point in time where displacement increased from baseline to where displacement reached its first maximal value.
      From each smoothed FD curve, a midpoint experimental stiffness coefficient (Ke) was calculated for a 0.5-mm interval beginning at the midpoint (2-mm total displacement) from the maximum displacement of 4.0 mm.
      • Kawchuk GN
      • Fauvel OR
      Sources of variation in spinal indentation testing: indentation site relocation, intraabdominal pressure, subject movement, muscular response, and stiffness estimation.
      • Petty NJ
      • Maher C
      • Latimer J
      • Lee M
      Manual examination of accessory movements—seeking R1.
      The coefficient Ke was calculated by dividing the change in force by the change in displacement between 2 and 2.5 mm. In addition, a terminal instantaneous stiffness (TIS) coefficient was calculated based upon the force developed at 3.8-mm displacement (Fig 5). The maximal programmed displacement of 4 mm was not selected as the terminal displacement point to prevent calculation artifacts (±<0.01V) caused when the motor reversed direction and decompressed the spring (Table 1).
      Figure thumbnail gr5
      Fig 5FD curve analysis. A midpoint interval stiffness coefficient (K) was calculated by dividing the change in force by the change in displacement between 2 and 2.5 mm. The terminal instantaneous stiffness was also calculated in the same manner at 3.8 mm—a common displacement to all trials collected.
      Table 1Summary statistics: mean stiffness for Ke and TIS
      Midpoint interval (2.0-2.5 mm)TIS (3.8 mm)
      SpringMean stiffnessMean stiffness
      A1.08 (1.06-1.10)1.28 (1.25-1.31)
      0.01%0.02%
      B1.47 (1.44-1.50)1.65 (1.62-1.68)
      0.02%0.01%
      C1.61 (1.59-1.63)1.78 (1.77-1.79)
      0.01%0.00%
      D1.99 (1.96-2.02)2.13 (2.11-2.15)
      0.01%0.00%
      E2.47 (2.41-2.53)2.59 (2.57-2.61)
      0.04%0.00%
      F3.65 (3.62-3.68)3.60 (3.54-3.66)
      0.01%0.03%
      G4.03 (3.97-4.09)4.07 (4.01-4.13)
      0.02%0.02%
      Values are shown in newtons per milimeter (95% confidence interval). Coefficient of variation is given in % = (σ2/mean stiffness) × 100.
      The intraclass correlation coefficient (ICC, 3,1) was calculated for Ke and TIS values using a 2-way mixed model analysis of variance for the reliability of a single measurement (PASW Statistics 17.0, SPSS, IBM, Chicago, Ill). The 95% confidence interval and the coefficient of variation for spring stiffness were calculated for each spring to provide an estimate of precision.
      • Latimer J
      • Goodsel MM
      • Lee M
      • Maher CG
      • Wilkinson BN
      • Moran CC
      Evaluation of a new device for measuring responses to posteroanterior forces in a patient population. Part 1: Reliability testing.
      • Kawchuk GN
      • Fauvel OR
      • Dmowski J
      Ultrasonic indentation: a procedure for the noninvasive quantification of force-displacement properties of the lumbar spine.

      Results

      Reliability

      The average ICC (3,1) for both Ke and TIS coefficients was 1.00. These ICC ratings can be considered to be “excellent.”
      Ke and TIS values from 10 repeated indentations for each of 7 springs are shown in Fig 6, Fig 7 respectively. Least squared regression lines were fitted to the repeated stiffness measurements for each spring. All regression line slopes ranged between 0.01 and −0.01 N/mm (Fig 6, Fig 7), suggesting there was no change in the stiffness of the springs over time.
      Figure thumbnail gr6
      Fig 6Midpoint interval (2.0-2.5 mm of displacement) stiffness coefficients taken from each FD curve in order of repeated trial (each letter designates a spring) and linear trend line.
      Figure thumbnail gr7
      Fig 7Terminal instantaneous stiffness (at 3.8 mm) stiffness coefficients taken from each FD curve in order of repeated trial (each letter designates a spring) and linear trend line.

      Discussion

      In this paper, stiffness data acquired by the VRFD device were assessed for their reliability. Our results show the VRFD device had high ICC values.

      Previous Posteroanterior Stiffness Testing

      Posteroanterior (PA) stiffness is most commonly assessed by clinicians using manual techniques. Maher and Adams
      • Maher C
      • Adams R
      Reliability of pain and stiffness assessments in clinical manual lumbar spine examination.
      reported that judgments of stiffness made in this way had poor reliability with ICC values for PA stiffness estimates of the lumbar spine ranging from 0.03 to 0.37. Simmonds et al
      • Simmonds M
      • Kumar S
      • Lechelt E
      Use of a spinal model to quantify the forces and motion that occur during therapists' tests of spinal motion.
      reported that clinicians are also unable to perceive applied force and resultant displacements accurately.
      As a response to the poor performance of manual stiffness testing, various mechanical PA stiffness testing devices have been developed. Their performance has been established by measuring the stiffness of beams, cadaveric spines, and live subjects (Table 2). Specifically, Lee and Svensson
      • Lee M
      • Svensson N
      Measurement of stiffness during simulated spinal physiotherapy.
      developed the spinal physiotherapy simulator (SPS) that they reported as having an ICC of 0.88 for stiffness coefficients calculated from the linear portion of the FD curve obtained in asymptomatic subjects. In addition, Lee and Evans
      • Lee R
      • Evans J
      Load-displacement-time characteristics of the spine under posteroanterior mobilisation.
      developed the spinal mobilizer to investigate the effect of tissue mobilization and relative intervertebral mobility. The spinal mobilizer applied loads to the surface of the skin overlying the selected lumbar vertebra and measured displacements of the indenter over the adjacent vertebra. This device was shown to have an ICC of 0.95 for maximal displacements.
      Table 2Previous devices: FD curve analysis, reliability, and accuracy
      StudyDeviceSubjectsFD curve analysisReliabilityAccuracy
      Lee and Svensson, 1990Spinal physiotherapy simulatorAluminum alloy beamsNot availableWithin 1% of true value
      L3 segment of symptomatic human subjectsICC, 0.88
      Lee and Evans, 1992Spinal mobilizerLumbar segments of asymptomatic human subjectsICC, 0.95Maximum error range ±0.8 mm
      Latimer et al, 1996Portable stiffness deviceBeamsNot availableMaximal error 2.5%
      ±1.8 N/mm 90% confidence interval
      Lumbar segments of symptomatic human subjectsStiffness coefficientICC, 0.96
      Edmontston, 1998Spinal posteroanterior mobilizerLumbar segments of asymptomatic human subjectsStiffness coefficient from 35 to 80 N intervalICC, 0.98±1.0 N/mm 95% confidence interval
      Owens, 2007Postero-to-anterior spinal stiffness systemLumbar segments of symptomatic human subjectsStiffness coefficient from 55 to 75 N intervalICC, 0.79Standard error of measurement 1.62 N/mm
      Tuttle, 2008Passive movement assessment deviceCervical segments of asymptomatic human subjectsCurve shapesCoefficients of multiple determination, 0.96N/A
      Although both the SPS and the spinal mobilizer provided highly reliable measurements of PA stiffness, others have commented that the technology is bulky
      • Latimer J
      • Goodsel MM
      • Lee M
      • Maher CG
      • Wilkinson BN
      • Moran CC
      Evaluation of a new device for measuring responses to posteroanterior forces in a patient population. Part 1: Reliability testing.
      and may be difficult to operate.
      • Kawchuk GN
      • Liddle TR
      • Fauvel OR
      • Johnston C
      The accuracy of ultrasonic indentation in detecting simulated bone displacement: a comparison of three techniques.
      In addition, these devices are not able to perform higher rate indentations
      • Lee M
      • Svensson N
      Measurement of stiffness during simulated spinal physiotherapy.
      • Lee R
      • Evans J
      Load-displacement-time characteristics of the spine under posteroanterior mobilisation.
      • Lee M
      • Steven GP
      • Crosbie J
      • Higgs RJ
      Variations in posteroanterior stiffness in the thoracolumbar spine: preliminary observations and proposed mechanisms.
      for dual use in SMT application.
      Latimer et al
      • Latimer J
      • Goodsel MM
      • Lee M
      • Maher CG
      • Wilkinson BN
      • Moran CC
      Evaluation of a new device for measuring responses to posteroanterior forces in a patient population. Part 1: Reliability testing.
      improved upon these initial devices by developing a smaller, portable device that could be used in clinics to assess symptomatic subjects with low back pain. This device provided highly reliable measurements (ICC of 0.96) with a 90% confidence interval of 1.8 N/mm for the slope of the linear region of the FD curve between 30 and 90 N. Similarly, the group of Edmondston and Allison
      • Edmondston SJ
      • Allison GT
      • Gregg CD
      • Purden SM
      • Svansson GR
      • Watson AE
      Effect of position on the posteroanterior stiffness of the lumbar spine.
      used the spinal posteroanterior mobilizer to determine the effect of patient position, load orientation,
      • Allison GT
      • Edmondston SJ
      • Roe CP
      • Reid SE
      • Toy DA
      • Lundgren HE
      Influence of load orientation on the posteroanterior stiffness of the lumbar spine.
      and mobilizations
      • Allison G
      • Edmonston S
      • Kiviniemi K
      • Lanigan H
      • Simonsen AV
      • Walcher S
      Influence of standardized mobilization on the posteroanterior stiffness of the lumbar spine in asymptomatic subjects.
      on lumbar PA stiffness. The spinal posteroanterior mobilizer provided an ICC of 0.98 and a 95% confidence interval of 1.0 N/mm for the stiffness coefficients calculated from the 35 to 80 N section of the slope of the FD curve. These 2 devices improved on the SPS and the spinal mobilizer with their size and portability but still lacked the ability to perform higher rate indentations.
      • Latimer J
      • Goodsel MM
      • Lee M
      • Maher CG
      • Wilkinson BN
      • Moran CC
      Evaluation of a new device for measuring responses to posteroanterior forces in a patient population. Part 1: Reliability testing.
      • Edmondston SJ
      • Allison GT
      • Gregg CD
      • Purden SM
      • Svansson GR
      • Watson AE
      Effect of position on the posteroanterior stiffness of the lumbar spine.
      Each of these devices offers highly reliable measurements, which is a significant improvement over manual assessment techniques. Unfortunately, these devices have been tested on different types of subjects and spinal locations, which make the reliability coefficients difficult to compare.

      Analysis techniques

      In addition to difficulties in comparing ICCs derived from different devices and experimental conditions, a standard measure of stiffness has not been adopted to enable comparisons across studies although most have calculated stiffness coefficients from a preselected force interval.
      • Latimer J
      • Goodsel MM
      • Lee M
      • Maher CG
      • Wilkinson BN
      • Moran CC
      Evaluation of a new device for measuring responses to posteroanterior forces in a patient population. Part 1: Reliability testing.
      • Owens EF
      • DeVocht JW
      • Wilder DG
      • Gudavalli MR
      • Meeker WC
      The reliability of a posterior-to-anterior spinal stiffness measuring system in a population of patients with low back pain.
      • Allison G
      • Edmonston S
      • Kiviniemi K
      • Lanigan H
      • Simonsen AV
      • Walcher S
      Influence of standardized mobilization on the posteroanterior stiffness of the lumbar spine in asymptomatic subjects.
      • Shirley D
      • Lee M
      • Ellis E
      The relationship between submaximal activity of the lumbar extensor muscles and lumbar posteroanterior stiffness.
      To address this issue, Latimer et al
      • Latimer J
      • Lee M
      • Adams RD
      The effects of high and low loading forces on measured values of lumbar stiffness.
      compared different force interval widths and sections of the FD curve and found that wider sections provided more reliable stiffness coefficients but that higher force intervals provided poor reliability in asymptomatic subjects. In the present study, a displacement interval was deemed preferable because a standard force interval would not have covered the same region of the FD curve due to the range of stiffness coefficients of our springs.
      • Shirley D
      • Lee M
      • Ellis E
      The relationship between submaximal activity of the lumbar extensor muscles and lumbar posteroanterior stiffness.
      The testing in this study was performed in displacement-control mode, which further supports the selection of a displacement interval. Disparities in the confidence interval widths occurred between the stiffness coefficient Ke and TIS for each spring; however, there was no trend indicating which of these 2 stiffness measures was over all more reliable. It should be noted that the plotted FD data from each spring is in most instances linear. Although these data can be modeled with a single stiffness coefficient, complementary techniques to calculate stiffness from plotted data were used as these techniques (Ke and TIS) have been used previously to evaluate force displacement data in clinical trials.
      • Stanton T
      • Kawchuk G
      The effect of abdominal stabilization contractions on posteroanterior spinal stiffness.

      Limitations

      This study design did not rule out the possibility of a systematic measurement error present in our collected data. Our use of stiffness measures used previously in clinical studies (Ke and TIS) ruled out the possibility of comparing our spring stiffness values with the manufacturer's values (Km), which were derived and calculated with unknown methods. Therefore, comparisons between Ke, TIS, and Km were not considered valid.
      Importantly, the VRFD device is small and has limited force (50 N) and displacement (28 mm) capabilities compared to the devices reviewed above. As a result, the VRFD would not be capable of generating sufficient load or displacement to test humans with parameters used previously (>100 N).
      • Latimer J
      • Goodsel MM
      • Lee M
      • Maher CG
      • Wilkinson BN
      • Moran CC
      Evaluation of a new device for measuring responses to posteroanterior forces in a patient population. Part 1: Reliability testing.
      • Lee R
      • Evans J
      Load-displacement-time characteristics of the spine under posteroanterior mobilisation.
      In its present form, the VRFD device would be inadequate for human experimentation unless the motor was replaced with a more powerful model and the ability to provide a greater linear displacement during the indentation possible.
      Even with the mechanical reliability of the VRFD device, it is important to consider that the reliability of stiffness measurements obtained may change when used in an in vivo setting. In vivo tissues are known to be more difficult to measure given their rate-dependent properties and may therefore produce less reliable measurements due to their complex and dynamic nature.
      • Lee R
      • Evans J
      Load-displacement-time characteristics of the spine under posteroanterior mobilisation.
      ,
      • Nicholson L
      • Maher C
      • Adams R
      • Phan-Thien N
      Stiffness properties of the human lumbar spine: a lumped parameter model.
      • Nordin M
      • Frankel V
      Biomechanics of tendons and ligaments.
      • Little J
      • Khalsa P
      Human lumbar spine creep during cyclic and static flexion: creep rate, biomechanics, and facet joint capsule strain.
      Furthermore, Kawchuk and Fauvel
      • Kawchuk GN
      • Fauvel OR
      Sources of variation in spinal indentation testing: indentation site relocation, intraabdominal pressure, subject movement, muscular response, and stiffness estimation.
      identified factors that may reduce device reliability during in vivo PA stiffness testing including intraabdominal pressure changes due to breathing, and indenter repositioning error between trials.

      Significance

      Changes in spinal stiffness have been associated with low back pain,
      • Latimer J
      • Lee M
      • Adams R
      • Moran CM
      An investigation of the relationship between low back pain and lumbar posteroanterior stiffness.
      spinal degeneration,
      • Kawchuk GN
      • Kaigle AM
      • Holm SH
      • Rod Fauvel O
      • Ekstrom L
      • Hansson T
      The diagnostic performance of vertebral displacement measurements derived from ultrasonic indentation in an in vivo model of degenerative disc disease.
      and range of motion.
      • Sran MM
      • Khan KM
      • Zhu Q
      • Oxland TR
      Posteroanterior stiffness predicts sagittal plane midthoracic range of motion and three-dimensional flexibility in cadaveric spine segments.
      Therefore, stiffness assessments may provide insight into relevant changes in spinal properties attributed to disease or therapy. Latimer et al
      • Latimer J
      • Lee M
      • Adams R
      • Moran CM
      An investigation of the relationship between low back pain and lumbar posteroanterior stiffness.
      found an 8% decrease in stiffness coefficients as low back pain decreased in patients; however, investigations into the effect of manual therapies aimed at normalizing spinal stiffness have been unable to detect significant changes.
      • Allison G
      • Edmonston S
      • Kiviniemi K
      • Lanigan H
      • Simonsen AV
      • Walcher S
      Influence of standardized mobilization on the posteroanterior stiffness of the lumbar spine in asymptomatic subjects.
      • Tuttle N
      • Barrett R
      • Laakso L
      Posteroanterior movements in tender and less tender locations of the cervical spine.
      The reliability of the VRFD device is equivalent if not superior to that of previously reported devices. The high reliability
      of this device suggests that the detection of small changes in stiffness after SMT intervention may be possible.

      Conclusion

      In a benchtop setting, the VRFD device provides highly reliable stiffness measurements over a range of stiffness coefficients related to future experiments. The results of this study support the future use of the VRFD device in trials investigating the impact of SMT and other interventions that may influence spinal stiffness. Protocols to establish the reliability of in vivo measurements using the VRFD device are still necessary; the full characterization of the accuracy of stiffness measurements using this device is unknown.

      Funding Sources and Potential Conflicts of Interest

      Support for this project was provided by the National Institutes of Health (U19 AT004137). Support for Greg Kawchuk was provided by the Canada Research Chairs program. No conflicts of interests were reported by the authors.

      Practical Applications

      • The variable rate force/displacement application system provides highly reliable stiffness measurements in inanimate objects.
      • Direct comparisons to previous devices are limited by the various mediums tested and analysis techniques used.
      • This device can perform high loading rates to simulate spinal manipulation therapy.

      Acknowledgment

      The authors thank Dean Macken and Steven Struckman at the University of Iowa Design and Prototyping Center for the design and construction of the rotary to linear converter and 3-dimensional positioning frame.

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