Off-Axis Loading Fixture for Spine Biomechanics: Combined Compression and Bending

Abstract

The spine is a multi-tissue musculoskeletal system that supports large multi-axial loads and motions during physiological activities. The healthy and pathological biomechanical function of the spine and its subtissues are generally studied using cadaveric specimens that often require multi-axis biomechanical test systems to mimic the complex loading environment of the spine. Unfortunately, an off-the-shelf device can easily exceed 200,000 USD, while a custom device requires extensive time and experience in mechatronics. Our goal was to develop a cost-appropriate compression and bending (flexion–extension and lateral bending) spine testing system that requires little time and minimal technical knowledge. Our solution was an off-axis loading fixture (OLaF) that mounts to an existing uni-axial test frame and requires no additional actuators. OLaF requires little machining, with most components purchased off-the-shelf, and costs less than 10,000 USD. The only external transducer required is a six-axis load cell. Furthermore, OLaF is controlled using the existing uni-axial test frame's software, while the load data is collected using the software included with the six-axis load cell. Here we provide the design rationale for how OLaF develops primary motions and loads and minimizes off-axis secondary constraints, verify the primary kinematics using motion capture, and demonstrate that the system is capable of applying physiologically relevant, noninjurious, axial compression and bending. While OLaF is limited to compression and bending studies it produces repeatable physiologically relevant biomechanics, with high quality data, and minimal startup costs.

1 Introduction

The spine is a multi-tissue musculoskeletal system that supports large multi-axial loads and motions during physiological activities. Spine disorders, such as disc prolapse or herniation, spondylosis, and spinal stenosis, are associated with pain and loss of mobility for more than 20% of the population older than 50 years of age [1]. These disorders directly affect the structure and composition of the spine (e.g., extrusion of the nucleus pulposus). Ex vivo studies in cadaveric spines are often used to study how these structural and compositional changes impact function [2–5]. Prior work by our group [6,7] and others [4,5,8] has often focused on loading a single axis of interest (e.g., axial compression or pure moments). However, physiologically, the spine is rarely, if ever, loaded in a single axis. Therefore it is important to consider all six axes and coupled loading when evaluating spine function [2,9,10].

There are many methods for measuring multi-axial spine mechanics [11]. Most loading systems can be categorized into one of the following: (1) hexapod or stewart platform, (2) multi-axis robotic arm, (3) modified commercial test frame, or (4) custom build. Purchasing a commercial solution (options 1 and 2) offers advantages of turnkey operation, equipment validation, and preloaded programs. However, the cost of these systems can easily surpass 200,000 USD. Due to the substantial financial burden and sometimes limited programing interface, most biomechanics laboratories have resorted to the latter options. Custom builds are the most common approach and include the hexapods of Stokes [12] and Costi [13], and benchtop systems of Wilke [3,14], Bowden [15], Tushak [16], and Yamamoto [17]. These custom builds offer advantages of cost and customization (programing and actuators sized for the application of interest). However, these systems tend to require extensive development time and mechatronics expertise (design, machining, instrumentation, control theory, programing, validation) which eventually could be more costly to a laboratory than a turnkey device. A less utilized approach is to adapt a commercial test frame. Notable examples are the spine biomechanics test systems by Mannen [18] and Adams and Dolan [19]. Advantages of this approach include cost (use of existing actuators), complexity (use of existing software), and time. In addition, interfacing with common test frames (e.g., Instron, TA Electroforce, or MTS) may lead to widespread adoption. For this reason, we aimed to develop a multi-axial (axial compression + bending) spine testing system that mounted to an existing test frame.

Our solution was an off-axis loading fixture (OLaF) that attaches to an existing uni-axial test frame, something that many biomechanical laboratories and engineering and orthopedic departments have access to. Compared to other solutions, OLaF is constructed of off-the-shelf components (see Sec. S11.1 available in the Supplemental Materials on the ASME Digital Collection), requires little machining, can be attached to other test frames through a slight change in the interface bolt pattern, is lower cost (9250 USD), is controlled using existing software, and can be installed or removed in just a few minutes. The objectives of this paper are: (1) provide the design rationale for how OLaF develops primary motions and loads and minimizes secondary off-axis constraints, (2) demonstrate the primary kinematics using motion capture, and (3) evaluate OLaF across a range of testing scenarios. We propose that OLaF is a cost-appropriate technology for compression and bending biomechanical studies of functional spinal units (FSUs) or similar specimens.

2 Design Rationale of an Off-Axis Loading Fixture

Our primary specimens of interest are single level human thoracic and lumbar functional spinal units (FSUs). During testing we aim to achieve axial compressive forces up to 750 N (covers a range of daily tasks such as lying supine, sitting, standing, and walking [20]) and bending up to ±4 deg (encompasses flexion–extension and lateral bending) [10,17]. In addition, we aimed to minimize secondary forces and moments and set a target threshold of less than 5%. It should be noted that the target compressive load (750 N) is taken from reference literature in which excised cadaveric spine segments are axially loaded until the excised intradiscal pressure matches the in vivo intradiscal pressure [21–24].

2.1 Primary Motion and Load

2.1.1 Overview.

The off-axis loading fixture is designed to simultaneously provide bending (either flexion–extension or lateral bending) and axial compression. To achieve this, an upper assembly and lower assembly, see Figs. 1(a) and 1(b), are attached to an existing TA Electroforce 3510 test frame. The bolt patterns on the upper and lower assembly are the only two components that require modification to mount to another test frame (e.g., Instron or MTS).

Fig. 1.

(a) CAD model of OLaF and (b) image of OLaF with a spine mimic placed in flexion. The markers are optional and are later used to evaluate OLaF's kinematics through motion capture. Onthe upper assembly, (c) the spherical bearing provides rotational degrees-of-freedom in all three axes. A side and isometric view of the spherical bearing and housing are shown. One end of the cable is attached to the upper assembly and the other to the (d) machine head on the lower assembly. The machine head produces axial compression by pulling the cables into tension. Machine heads are often used as guitar tuners to adjust the string tension. Top, front, and isometric views of the machine head are shown. Note that CAD drawings are simplified to aid in visualization.

The upper assembly provides the offset loading that transforms linear motion from the actuator of the TA Electroforce 3510 to a rotation at the spherical bearing (Fig. 1(c)). This rotation is directly applied to the specimen (FSU), producing a bending moment. Additional detail is provided in Sec. 2.1.2. The specimen is placed between the upper assembly and lower assembly. A six-axis load cell (AMTI, MC3A-500) is placed below the specimen (hidden by the machine head) to quantify all forces and moments.

The lower assembly contains two machine heads (Figs. 1(b) and 1(d)) that apply a separate axial compressive force. This force is achieved with a cable that is attached to the upper assembly on one end and wrapped around the drum of the machine head at the other end. The drum is then rotated creating tension in the cable that applies axial compressive force to the FSU. Additional detail is provided in Sec. 2.1.3. The lower assembly also contains a custom X–Y stage with linear bearings to eliminate off-axis secondary constraints.

2.1.2 Bending Angle (R_X).

Bending is achieved by attaching the fixed end of a cantilevered beam to the specimen while the “free-end” of the beam is vertically displaced (Fig. 2). Under the assumption that the cantilevered beam is rigid and the fixed end is attached to an elastic foundation (specimen), the vertical displacement (T_Z ) required to achieve a given rotation is calculated using Eq. (1). In OLaF, the system applying the bending moment is more than 2 orders of magnitude stiffer (∼420 N·m/deg) than the disc (e.g., human lumbar spine ∼ 1 N·m/deg [2,25]); thus, we assume all deformations occur within the specimen

$$T_z=L_{\mathrm{Beam}}·\text{sin}\theta$$ (1)

Fig. 2.

(a) Machine coordinates are shown for three forces (F) and three moments (M). Translations (T) and rotations (R) use this same coordinate system. (B) Free body diagram of the upper assembly (top) and specimen (bottom). The total axial force (F_Z ) on the specimen is the sum of three separate forces (F _OLaF, F _Mass, F _Spring) that account for the load to induce bending, mass of the pivoting plate, and machine head compression, respectively. (c) All translations, rotations, forces, and moments are described using their common or symbolic name throughout the paper. In addition, we note whether they are a primary or secondary parameter.

The test frame's linear actuator is used to apply T_Z . The force (F _OLaF) required to displace the cantilevered beam multiplied by the distance between the instantaneous centers of rotation (L _Beam) is the applied moment (M_X ), see Fig. 2(b). Identification of the instantaneous center of rotation for the pinned joint (spherical bearing) is straight forward and does not change with bending. We assume that the instantaneous center of rotation for the FSU is the geometric center [15]; however, this is not necessarily true, especially in flexion–extension [26,27]. Furthermore, the instantaneous center of rotation changes with bending angle [26]. To approximate the angulation error, we assume a typical L _Beam = 159 mm and an uncertainty of ±5 mm. Given a target angulation of 4 deg, the real angle would lie between 3.88 and 4.13 deg, or a 3% error. We leave it to the user to decide if this is an acceptable error or if an external method of quantifying specimen kinematics is necessary for their application. In Sec. 3, we demonstrate a free method to externally track specimen angulation.

2.1.3 Axial Compression (F_Z).

Axial compression applied to the specimen is a summation of three force components (F_Z  = F _Spring + F _OLaF + F _Mass), see Fig. 2(b). The majority of the axial compression is F_Spring, which is achieved through a machine head mechanism (Fig. 1(d)). Machine heads are often used as guitar tuners to adjust string tension. In OLaF, the machine head (18:1 gear ratio) wraps a metal cable with an inline tension spring around a drum. With this system, we can apply up to 925 N of tension, by hand, to each side of the specimen for a combined maximum load of 1850 N. The FSU opposes the cable tension through compressive stress. It should be noted that, similar to a follower load [28], as the specimen bends the line of action for F _Spring also changes with the specimen.

While most of the compression is from F _Spring, it is important to account for the other forces. In particular, F _OLaF is an axial force required to produce the bending moment. Assuming a target angulation of ±4 deg, L _Beam = 159 mm, and bending stiffness of 1 N·m/deg, the estimated axial load variation will be ±50 N. Finally, the pivoting platform (lower-most component of the upper assembly) acts as a dead weight load (F _Mass) on the specimen even when the system is static, and no bending or spring tension is applied. F _Mass is 21 N and is again not a trivial mass depending on the experimental conditions. The linear combination of these terms gives the true axial force (F_Z  = F _Spring + F _OLaF + F _Mass).

2.1.4 Specimen Compliance-Induced Error in Bending Angle.

In addition to including F _OLaF in the total compression applied to the specimen, here we evaluate whether the compliance of the specimen during this loading could induce a meaningful measurement error in angulation. To make a conservative estimate of error, we use an estimated axial load variation due to F _OLaF (±50 N) and a lower estimate for human lumbar spine stiffness (∼600 N/mm) [2]. Given this, an axial force fluctuation of 50 N would yield a 0.083 mm axial deformation and an angulation error of 0.03 deg. This angulation error is less than 1% of the target angle. Note that angulation error is experimentally assessed in Sec. 6.1.

Applying this error to a functional spinal unit that has a known flexural stiffness of 1 N·m/deg leads to less than 5% error in the calculation of the flexural stiffness. It is up to the user to decide if this is an acceptable error or if an external method of quantifying specimen kinematics is necessary. In Sec. 3, we demonstrate a free method to externally track specimen angulation.

2.2 Secondary Off-Axis Motions and Loads.

In addition to the primary axes (Figs. 3(a) and 3(b)), OLaF also develops a secondary shear translation along the Y-axis (T_Y ). Under ideal conditions (specimen geometry, material properties, alignment, and high precision machining) all other secondary forces, moments, translations, and rotations would be zero. However, FSUs inherently develop coupled motions [2,9]. In this section, we discuss our design approach for minimizing secondary off-axis constraints, see Figs. 3(c)–3(f).

Fig. 3.

(a) and (b) OLaF's primary bending axis (R_X ) is driven by translations along T_Z . (c)–(d) OLaF provides passive control of all secondary axes.

2.2.1 Linear Bearing to Minimize Secondary Forces.

We have included an X–Y sliding stage (Fig. 1(a)) in the lower assembly to negate secondary shear forces. The mechanics used to produce bending in OLaF also produces a shear displacement along the Y-axis (T_Y ). As the free-end of the cantilevered beam is displaced vertically, the end attached to the specimen is forced to move through an arc with radius of L _Beam. Under small angles this shear is small but not insignificant, especially if the shear must be realized through shearing of the specimen.

The custom X–Y sliding stage sits on four linear rails (McMaster Carr, 9338T53) with a combined load capacity of 1960 N and travel range of ±25.4 mm (Figs. 3(c) and 3(d)). This range is large enough to permit the coupled shear translations that occur in FSU testing [2,9]. We experimentally investigate the shear forces and translations in Sec. 6.2.

2.2.2 Spherical Bearing to Minimize Secondary Moments.

A spherical bearing (Fig. 1(c)) is used to provide three rotational degrees-of-freedom. The spherical bearing (McMaster Carr, 63195K16) allows for rotations up to ±19 deg in R_Y and R_Z (Figs. 3(e) and 3(f)). These secondary rotational degrees-of-freedom are large enough to allow for coupled rotations that occur in FSU testing [2,9]. The spherical bearing is self-lubricated and has a rated load capacity of 88.3 kN.

3 Motion Capture

In Sec. 2.1.2, we suggested using the measured axial translation (T_Z ) of the upper assembly to calculate specimen bending, assuming a small error in bending angle was acceptable. Here we develop an alternative method for kinematic analysis, using a smartphone video recorder and kinovea, a free and open-source motion analysis software. The smartphone used in this work was an iPhone 13. The smartphone was mounted to a tripod and recorded high definition (1080p) video at 30 frames per second. Nine red markers were placed on OLaF and captured within the video frame (Fig. 4(a)). In addition to the markers on OLaF, we use an index card aligned with the image plane to calibrate the image perspective. This calibration is a built-in function for kinovea.

Fig. 4.

(a) OLaF in the reference (neutral) position for a L1 to L2 FSU mimic (for visualization purposes) and (b) the FSU is placed in flexion. Fiducials on OLaF are used for tracking

The video data were imported into kinovea, and each of the points of interest was identified and automatically tracked through the experiment. Position data were exported and analyzed using a custom matlab ^® script to calculate displacements (T_Y , T_Z ) and rotation (R_X ) as a function of time. We compare the motion capture results to the angle calculated based on the measured axial translation of the linear actuator. It should be noted that this motion analysis is limited to the plane of interest and only provides two-dimensional information.

4 Performance Analysis

To quantify the performance of OLaF, we calculate system noise and error. The calculations for each of these outcome measures are provided below. In addition, we define the operating limits of OLaF in Table 1.

Table 1.

Transducer range, motion and load limits, accuracy, and noise for the test frame (TA Electroforce 3510), six-axis load cell (AMTI MC3A-500), and OLaF

Parameter translation (T), rotation (R), force (F), and moment (M)	Test frame	Six-axis load cell	OLaF
Transducer range	TZ  = 25 mm		TZ  = 25 mm
		FX and FY  = 1112 N	FX and FY  = 1112 N
		FZ  = 2224 N	FZ  = 2224 N
		MX and MY  = 56 N·m	MX and MY  = 56 N·m
		MZ  = 28 N·m	MZ  = 28 N·m
Motion limits (T and R)	TZ  = 25 mm	No Moving Elements	& TX and TY  = 25.4 mm
			TZ  = 25 mm
			& RX  = 30 deg
			& RY and RZ  = 19 deg
Load limits (F and M)	FX and FY  = 330 N		FX and FY  = 330 N
	MX and MY  = 80 N·m	See transducer range	& FZ  = 1850 N
	MZ  = 100 N·m		& MX and MY  = 31.8 N·m
			MZ  = 28 N·m
Calibrated accuracy	TZ  = 0.065 mm		TZ  = 0.065 mm
		FX and FY  = 2.5 N	FX and FY  = 2.5 N
		FZ  = 6.6 N	FZ  = 6.6 N
		MX and MY  = 0.20 N·m	MX and MY  = 0.20 N·m
		MZ  = 0.12 N·m	MZ  = 0.12 N·m
RMS noise	Not tested in isolation	Not tested in isolation	*TZ  = 0.005 mm
			*FX and FY  = 0.08 N
			*FZ  = 0.4 N
			*MX and MY  = 0.003 N·m
			*MZ  = 0.002 N·m

All values are given as ±value (i.e., test frame T_Z  = ±25 mm). Bold values indicate operational limits defined by the test frame or load cell. Operational limits not defined by the test frame or load cell are based on the kinematics or manufactured components of OLaF (e.g., range of motion of X–Y stage and safe working load for cables) and are indicated by an ampersand (&). The calibrated accuracy is taken from the calibration report from the manufacturer or supplier of each component. Values experimentally determined by the authors are indicated by an asterisk (*). In principle, alternative test frames and load cells can be swapped into this table to define new operational limits.

4.1 System Noise and Error.

System noise and error are calculated using the root-mean-square (RMS) method, see Eq. (2),

$$\mathrm{RMS}=\sqrt{\frac{\sum _i^n{\left(x_i-\overline{x}\right)}^2}{n}}$$ (2)

where (x_i ) are individual measures, ( $\overline{x}$ ) is the mean signal, and (n) is the number of measures.

We quantified the transducer noise by attaching OLaF to the test frame and commanded the linear actuator to hold a static position (T_Z ). The data from the transducers (position sensor and load cell) are collected and used to calculate the RMS noise. We found the noise to be less than the calibrated accuracy of each component (see Table 1). This test demonstrates that OLaF does not compromise component accuracy. Furthermore, OLaF was cycled five times between ±4 deg against a near frictionless pivot. The load cell registered 0.6 N of noise in F_Z and 0.01 N·m of noise in M_X . Again, this is less than the calibrated accuracy of the transducers and demonstrates that the dynamics of OLaF do not compromise the accuracy of the system.

4.2 Operating Limits.

The operating limits (Table 1) define the capabilities of OLaF. The factors used to define operating limits are the range of the transducers, motion of the moving elements, and safe working load of individual components. These parameters are used to ensure high quality data and prevent damage to OLaF and the existing test frame. The modular nature of OLaF allows the user to select alternative system components (e.g., test frame) and update Table 1 based on the new specifications.

5 Performance Tests

In the sections Design Rationale of an Off-Axis Loading Fixture and Performance Analysis, we described the design rationale and operating limits of OLaF. In this section, we outline the testing procedures and a host of performance checks to demonstrate the practical capabilities and limitations of OLaF.

5.1 Testing Procedure.

To assess the performance of OLaF, we use a standard testing protocol that is outlined below. The specific values used for testing are shown in Table 2.

Table 2.

Test parameters for all performance tests. Note that a nominal load of 0 is ∼ 21 N due to F _Mass (see Sec. 2.1.3)

Test number	Test identity	Material	Angle (deg)	Frequency (Hz)	Cycles (#)	Nominal load (N)
1	Motion capture	Spring	±4	0.5	5	0
2	Axial load			0.5	5	0 versus 200
3	X–Y stage constraints			0.5	5	0
4	Cycling frequency			0.01 to 1.0	5	0
5	Test duration			0.5	3600	200
6	Flexion-extension	FSU	±3	0.5	5	200
7	Lateral bending		±4
8	Directionality testing		±4

1. Attach OLaF to the test frame (upper and lower assembly) (Fig. 1)

2. If using a motion capture system—set up and calibrate (Sec. 3)

3. Define bending amplitude (R_X ), frequency, and number of cycles (Table 2)

4. Calculate the axial translation (T_Z ) (Eq. (1)), speed, and duration necessary to achieve the desired bending dynamics

5. Input the desired waveform into the test frame's software (wintest 7 for TA Electroforce)

6. Zero the six-axis load cell

7. Attach the specimen to OLaF in a neutral position [28]

8. Apply the desired compressive load (F_Z ) using the machine heads (Table 2) while maintaining a neutral FSU position [28]

9. If using a motion capture system—start recording

10. Start the experiment

Following testing, the bending stiffness is calculated using a least squares linear regression to the last three cycles of the moment (M_X ) versus angle (R_X ) data. The reported bending stiffness values for the FSU should be taken with caution as the FSU displayed the expected nonlinear behavior. We have chosen to use a linear regression to detect relative changes rather than absolute values.

5.2 Performance Tests.

We evaluate OLaF's performance using eight different tests that are outlined in Table 2. Note that test number and identity are referenced in subsequent sections.

Test parameters were set based on typical FSU biomechanical testing [4,5,9,10,29,30]. A range of frequencies and cycle numbers can be used to simulate various aspects of daily life. We have chosen 0.5 Hz, Fig. 5(a), to demonstrate the capability of OLaF to perform bending tests at a moderate physiological speed [20]. Furthermore, the disc achieves a steady-state like performance by the third cycle [4,31]; thus we perform five cycles and use the last three for analysis, Fig. 5(b). A 200 N axial load was chosen to produce a physiologically relevant load in the human lumbar spine. A 200 N axial load on the human lumbar spine approximates a 0.23 MPa NP pressure, which represents physiological conditions such as lying supine [5,21].

Fig. 5.

The data input to the test frame is (a) a linear translation along the Z-axis (T_Z ). The RMS error between the input and measured waveform is 0.22 mm. The linear translation is converted to a (b) angular rotation (calculated angle) by the spherical bearing. The target waveform is 0.5 Hz, ±4 deg, for five cycles. We analyze the last three complete cycles (blue region). (c) Motion capture (MoCap) data are postprocessed using Kinovea. The MoCap angle is compared to the calculated angle. The RMS error between the measured waveform and MoCap is 0.35 deg. (d) A magnified view from the peak of the 3rd cycle. The data demonstrate two shortcomings of the MoCap system: (1) slower frame rate that produces fewer data points and (2) lower resolution that produces step like behavior).

6 Performance Testing: Spring

For performance tests 1 to 5 a compression die spring was chosen to minimize viscoelastic effects. The spring was purchased from McMaster-Carr (9595K39) with a nominal spring rate of 280 N/mm. The spring was then potted in Ortho-Jet acrylic resin to facilitate mounting in OLaF. The potting reduced the effective spring length and increased the axial spring stiffness to 430 N/mm, see Fig. S.11.1 available in the Supplemental Materials on the ASME Digital Collection. Testing demonstrated a linear response up to 950 N of axial compression.

6.1 Performance Test 1: Motion Capture.

In Performance Test 1 we aimed to demonstrate a near zero-cost system for motion capture and compare the bending angle between the calculated (Eq. (1)) and measured (motion capture). First, we establish the accuracy of the input waveform to the output response. Using Eq. (1), the desired bending (R_X ) amplitude is transformed into an axial translation (T_Z ). An example input waveform to achieve ±4 deg of bending is shown in Fig. 5(a). It should be noted that the measured position (test frame displacement sensor) of the system differs slightly from the input waveform. The RMS error is ∼0.22 mm. Converting this translational error to a rotational error gives 0.08 deg.

With the accuracy of the input waveform to output response confirmed we next aimed to demonstrate the zero-cost motion capture system. To do this, we used a personal smartphone camera with a free motion analysis software (kinovea) to quantify the dynamics of OLaF. The results of the motion capture are shown in Figs. 5(c) and 5(d) and appear to be very well correlated. The RMS error between motion capture and the calculated bending angle was 0.35 deg (<4% error). The cause of this error likely stems from the slow frame rate and resolution in the motion capture system used. Other potential sources of error include nonplanar motion (R_Y and R_Z ), component tolerances (bearings), an incorrectly measured or changing center of rotation, and system compliance (beams and bolted connections). Despite this, we propose that a 4% error for a near zero-cost motion capture system is acceptable. Applications requiring more accuracy may use a higher fidelity motion capture system with fully automated point tracking.

6.2 Performance Tests 2 and 3: Load and X–Y Stage.

Performance Tests 2 and 3 evaluate the effect of axial compression variability (due to F _OLaF and applied F _Spring) and effect of the X–Y stage to eliminate secondary off-axis constraints. Recall that F_Z is a summation of three contributing forces (F _OLaF, F _Mass, F _Spring), see Sec. 2.1.3. In the reference experiment, we tension the machine heads to yield a nominal F _Z = 200 N and the X–Y stage is unconstrained in T_X and T_Y (Figs. 6(a) and 6(d)). The calculated bending stiffness was 0.76 N·m/deg. The peak secondary shear and moment were 2.1 N and 0.1 N·m, which are <4% of the applied axial load (200 N) and bending moment amplitude (3.2 N·m).

Fig. 6.

Resulting (a)–(c) forces and (d)–(f) moments when testing with and without applying an additional compressive load through the machine head (F _Spring), and with and without the X–Y stage to minimize the secondary constraints. (a) and (d) OLaF is loaded to F _Mean ∼ 200 N in F_Z . The X–Y stage is unconstrained. The bending stiffness is 0.76 N·m/deg. (b) and (e) The load imposed by the machine heads is removed, producing F _Mean = 21 N and a force variation (ΔF) ±17 N. Under a stress-free reference configuration F _Mean = F _Mass. Furthermore, ΔF = F _OLaF and is the offset force required to bend the specimen. See Sec. 2.1.3 for additional information. The bending stiffness is 0.67 N·m/deg. (c) and (f) The X–Y stage is constrained by shaft collars and forces all shear displacements to occur within the specimen. The response of the specimen is greatly affected by this constraint and violates our goal of minimizing secondary constraints.

Next, the axial load from F _Spring is removed (Fig. 6(b)) and the experiment is repeated. Figures 6(b) and 6(e) demonstrate a similar moment-angle response with secondary forces and moments remaining negligible. The mean compression force, F _Mean = 21 N, corresponds to the mass of the upper assembly (F _Mass). The change in force during loading, ΔF = 17 N, corresponds to the F_OLaF required to achieve the desired rotation.

Finally, we disabled the linear bearings using shaft collars to lock the X–Y stage, forcing all off-axis coupled shear motions to be carried by the specimen. This constrained system produces a greatly different response (Figs. 6(c) and 6(f)) with large F_Z and F_Y amplitudes >100 N and a bending moment that is ∼ 5X greater and in the opposite direction compared to the unconstrained conditions. These results demonstrate that the use of an unconstrained X–Y stage (Figs. 3(c) and 3(d)) is a necessary design requirement for OLaF and we employ the use of the unconstrained X–Y stage to eliminate secondary off-axis constraints from here on.

6.3 Performance Test 4: Frequency.

Performance Test 4 aims to evaluate the effect of cycling frequency on the measured response. Specifically, we are interested in determining when inertial effects from the moving mass begin to influence the response. For this reason, we use the spring to isolate OLaF's inertia by excluding the potential role of the rate-dependent behavior of the specimen. We varied the test frequency over 2 orders of magnitude (0.01, 0.05, 0.1, 0.5, and 1.0 Hz). Between the slowest and the fastest frequency, the bending stiffness changed less than 2% (0.73 versus 0.74 N·m/deg), see Fig. 7. The secondary shears and moments were similarly insensitive to the cycling frequency (Figs. S11.2 and S11.3 available in the Supplemental Materials). The data demonstrate that under this range of loading frequencies and amplitude there is a negligible inertial effect.

Fig. 7.

The resulting (a) axial force and (b) bending moment are shown for a range of cycling frequencies (0.01 to 1.0 Hz). At 1 Hz there is a small shift in the measured responses. The linear bending stiffness was 0.73 and 0.74 N·m/deg at 0.01 and 1.0 Hz, respectively. Note that the relative axial force is shown by centering the mean force about 0 N.

6.4 Performance Test 5: Test Duration.

OLaF was run for 2 h (3600 cycles) to determine the stability of the system and the potential for long-term or fatigue testing. We performed this test on the compression spring to again remove any viscoelastic effects. The response of cycles 3-5 and 3598 to 3600 are shown in Fig. 8(a). The moment versus angle traces (Fig. 8(b)) are nearly identical despite being measured nearly 2 h apart. The stability of the system is well suited for longer duration testing up to at least 2 h.

Fig. 8.

(a) The compression spring was cycled 3600 times at 0.5 Hz at ±4 deg. (b) The bending stiffnesses (0.76, 0.76, and 0.77 N·m/deg) are calculated using linear regressions for cycles 3 to 5, 3598 to 3600, and 0 to 3600. The nearly constant bending stiffness demonstrates the stability of OLaF.

7 Performance Testing: Functional Spinal Units

The off-axis loading fixture was designed for spine biomechanics testing; therefore, a human donor FSU (male, 60 years of age, L1–L2) was used as a representative specimen. The whole spine was stored at −20 °C. On the day of dissection, the specimen was defrosted in a vacuum sealed bag and submerged in a 27 °C water bath for 2 h. The surrounding soft tissue and posterior elements were resected. The specimen was aligned (Fig. 9(a)) and potted in Ortho-Jet acrylic resin under fluoroscopic guidance. Saline-soaked gauze was wrapped around the disc during potting to maintain hydration. The potted FSU was then submerged in PBS at 4 °C with a 55.6 N static load for 19 h to reach a steady-state level of hydration and avoid supraphysiologic hydration [4,9,20,32].

Fig. 9.

(a) Anatomical coordinate system showing Translations (T) and Rotations (R). Anatomical Forces (F) and Moments (M) also follow this same coordinate system. (b)Flexion-extension and (c) lateral bending of a human L1-L2 FSU, see Table 2 for experimental conditions. (d) Lateral bending of the same FSU after removing the specimen and rotating it 180 deg about the Z-axis. We observed a similar moment-angle response.

7.1 Performance Tests 6 and 7.

Performance Tests 6 and 7 evaluated the FSU in flexion–extension and lateral bending (Figs. 9(b) and 9(c)). The moment-angle response has the expected shape and peak values based on existing literature [8,9,12,15,33–35]. Furthermore, the nonlinearity and hysteresis observed in Fig. 9 is also expected. In agreement with prior work, cycles 3 to 5 produce a consistent overlapping response demonstrating a steady-state performance for short duration testing. The secondary forces and moments (not shown) remained below the 5% threshold.

7.2 Performance Test 8: Directionality.

The load that drives bending (F _OLaF) produces an unbalanced load with a greater F_Z in one direction of bending than the other (Fig. 6(a)). Performance Test 8 aims to evaluate the impact of this load variation since axial load has been shown to influence the stiffness of human FSUs [8,12,15,35]. After testing the FSU in the reference position for lateral bending (Fig. 9(c)), we removed the specimen and rotated it 180 deg. The results are shown in Fig. 9(d) and demonstrate minor differences between the two configurations (Reference = 1.36 versus Rotate = 1.32 N·m/deg, a minimal 3% change).

8 Summary

In this work we developed an off-axis loading fixture (OLaF) that mounts to an existing uni-axial test frame and provides combined bending (demonstrated up to 6 deg (Fig. S.11.4 available in the Supplemental Materials on the ASME Digital Collection) and 1 Hz (Fig. 7)) and compression (demonstrated up to 950 N (Fig. S.11.1 available in the Supplemental Materials), capable of 1850 N (Table 1)) to physiological levels [21,24].

Through a series of performance tests, we demonstrated OLaF provides compression and bending while minimizing secondary off-axis loads to less than 5%, has minimal inertial effects up to 1 Hz, and can be used for long duration testing (2 h of runtime, Fig. 8). In addition to testing with a linear compression spring we also demonstrate OLaF for use with a human FSU. The specimen was tested in flexion–extension and lateral bending. The functional response of the FSU was conserved when the specimen orientation was rotated 180 deg.

By designing OLaF for a single purpose (compression + bending) we achieved a cost-effective solution (9,250 USD) that can be easily mounted to and removed from common uni-axial test frames. Furthermore, OLaF is controlled using the same program as the test frame and the six-axis load cell data is collected using the manufacturer's software; this minimizes technical challenges associated with developing custom software. Finally, a near zero-cost motion capture system, while not required, was implemented using a smartphone camera and kinovea (a free motion analysis software).

8.1 Limitations.

While OLaF offers several advantages, we acknowledge the following limitations. First, and most importantly, the axial load F_Z is not constant. F_Z varies primarily through F _OLaF, which is required to induce bending and is proportional to the flexural stiffness of that axis. A typical flexural stiffness of 1 N·m/deg, undergoing 4 deg of bending, with a L _Beam of 0.159 m, will produce a force variation of 25 N. To reduce this variation a longer L _Beam could be used (L _Beam = 0.5 m produces an 8 N variation). However, this requires greater axial travel to achieve the same degree of bending and will depend on the capabilities of each instrument. While imposing a 25 N variation on a 100 N axial load yields a 25% variation in F_Z , this is only a 3.3% variation on a 750 N axial load. Therefore, OLaF maybe better suited to higher axial loads which are more representative of sitting, standing, and walking, rather than lying supine [21,24]. Further, it should be noted that axial load is not constant during physiological activities, such as walking, which has a 0.12 MPa (∼106 N) variation [24].

Second, bending in OLaF is controlled and calculated from the displacement of the linear actuator. This calculation does not account for specimen compliance, creep, misalignment with the instantaneous center of rotation, changing instantaneous center of rotation [26,27], or slip at the mounting or potting interface. Despite these assumptions, we found good agreement using the near zero-cost two-dimensional motion capture system (4% error), which also contains sources of error. Implementing a higher fidelity motion capture system would cost an additional 10,000 USD for a low-end system.

Finally, OLaF is limited to evaluating one axis of bending and compression at a time. Additional axes are not supported by OlaF's design, and the specimen must be rotated for sequential testing of flexion–extension and then lateral bending. Torsion is another desirable loading modality for spine biomechanics research; however, many uni-axial test frames such as the one used in this study have attachments that enable compression + torsion testing.

8.2 Conclusion.

The primary purpose of this study was to develop a cost-appropriate solution for flexion–extension or lateral bending of FSUs under physiological, noninjurious, compressive loads and rotations. We designed OLaF to mount to an existing test frame as it offered a reliable actuator and transducer, reduced design and technical complexity, lowered equipment costs, and maintained a small footprint. OLaF can perform compression + bending tests of functional spinal units over a range of physiological loads, frequencies, and angles.

Supplementary Material

Supplementary Material

Supplementary PDF

Funding Data

• National Institute of General Medical Sciences (Grant No. P20GM139760; Funder ID: 10.13039/100000057).