A mechanical pivot-shift device for continuously applying defined loads to cadaveric knees

Abstract

Purpose

Current techniques to study the biomechanics of the pivot-shift utilize either static or poorly defined loading conditions. Here, a novel mechanical pivot-shift device that continuously applies well-defined loads to cadaveric knees is characterized and validated against the manual pivot-shift.

Methods

Six fresh-frozen human lower limb specimens were potted at the femur, mounted on a hinged testing base, and fitted with the mechanical device. Five mechanical and manual pivot-shift tests were performed on each knee by two examiners before and after transecting the ACL. Three-dimensional kinematics (anterior and internal-rotary displacements, and posterior and external-rotary velocities) and kinetics (forces and moments applied to the tibia by the device) were recorded using an optical navigation system and 6-axis load cell. Analysis of variance and Bland–Altman statistics were used to gauge repeatability within knees, reproducibility between knees, agreement between the mechanical and manual test methods, and agreement between examiners.

Results

The forces and moments applied by the device were continuous and repeatable/reproducible to within 4/10 % of maximum recorded values. Kinematic variables (excluding external-rotary velocity) were qualitatively and quantitatively similar to manual pivot-shift kinematics, and were more repeatable and reproducible.

Conclusion

The presented device induces pivot-shift-like kinematics by applying highly repeatable three-dimensional loads to cadaver knees. It is based on a simple mechanical principle and designed using easily obtainable components. Consequently, the device enables orthopaedic biomechanists to easily and reliably quantify the effect of ACL injury and reconstruction on pivot-shift kinematics.

Appendix

Design

The key features of the MPSD are a constant-tension spring that generates force and an external fixation (ex-fix) unit that holds the spring in a predetermined position relative to the tibia and femur. To generate the multi-planar loads required to induce a pivot-shift, the MPSD employs the principle of equivalent forces and moments [7], which states:

The resultant of a couple ${\mathbf {M}}$ and a force ${\mathbf {F}}$ in the plane of the couple is a single equal and parallel force in that plane at a distance $d = \Vert {\mathbf {F}}\Vert / \Vert {\mathbf {M}}\Vert$.

This principle implies that any combination of a torque and a perpendicular force can be produced by a single force, if its line of action is positioned appropriately. In the knee, components of valgus torque $M_{\mathrm{v}}$ and axial compression $F_{\mathrm{c}}$ can be produced by a line of action of force positioned laterally (Fig. 5b). Additional components of internal torque $M_{\mathrm{i}}$ and anterior shear $F_{\mathrm{a}}$ can be produced by orienting this line of action anteriorly (Fig. 5c).

Fig. 5

Working Principle of the mechanical pivot-shift device. a A spring attached between the points $P^{\mathrm{t}}$ and $P^{\mathrm{f}}$ produces a force ${\mathbf {F}}$ and moment ${\mathbf {M}}$. An ex-fix unit holds the position of $P^{\mathrm{t}}$ and $P^{\mathrm{f}}$ fixed relative to the tibia and femur, respectively. b In the frontal plane, ${\mathbf {F}}$ and ${\mathbf {M}}$ have compressive $F_{\mathrm{c}}$ and valgus $M_{\mathrm{v}}$ components. c In the sagittal plane, ${\mathbf {F}}$ and ${\mathbf {M}}$ have anterior $F_{\mathrm{a}}$ and flexion ($M_{\mathrm{f}}$, not shown) components. Additionally, in the transverse plane, ${\mathbf {M}}$ has an internal-rotary component $M_{\mathrm{i}}$. Near full extension, these forces and moments sublux an ACL-deficient knee. As the knee is flexed, $F_{\mathrm{a}}$ and $M_{\mathrm{i}}$ diminish in magnitude, allowing the knee to reduce (See also Fig. 2). The femoral and tibial coordinate systems are indicated by ${\mathbf {f}}_{\mathrm{i}}$ and ${\mathbf {t}}_{\mathrm{i}}$. The line of action of the force ${\mathbf {F}}$ is indicated by a dashed red line

To produce these forces and moments experimentally, an ex-fix unit (Synthes, Paoli, PA) was used to position a 48.0 N constant-tension spring (McMaster Carr, Santa Fe Springs, CA) ~15 cm lateral to the knee, oriented ~20° anteriorly with respect to the tibia. Based on this approximate position, it was estimated that the spring would produce ~7 N m of valgus torque and ~45 N of axial compression force throughout knee flexion, along with ~2.5 N m of internal torque and ~16 N of anterior force that would diminish as a function of knee flexion. Prior to the present study, the position of the spring was fine tuned so that it consistently induced a pivot-shift in an ACL-transected cadaver knee. In the selected position, the coordinates of the spring endpoints were $P_{f}^{f} = ( \pm 15.7,9.8,15.9)$ and $P_{f}^{f} = (\pm 15.7, 9.8, 15.9)$ (cm), measured in the tibia and femur coordinate frames, respectively ($\pm$: right/left legs).

Kinematics

Four kinematic variables were selected to characterize the pivot-shift. Anterior displacement, AD (mm), and internal-rotary displacement, IRD (°), quantified the magnitude of tibial subluxation. Posterior velocity, PV (mm/s), and external-rotary velocity, ERV (°/s), quantified the speed of tibial reduction. AD and IRD were extracted from the relative joint displacement matrix ${\mathbf D}$, while PV and ERV were extracted from the absolute joint velocity matrix $\hat{\mathbf{V }}$ [29]:

$$\begin{aligned} \begin{aligned} \qquad {\mathbf D}&= {\mathbf T} _{\mathrm{ref}}^{-1}(\theta ) ~ {\mathbf T} _{\mathrm{trial}}(\theta ) \\&= \begin{bmatrix} {\mathbf Q}&{\mathbf {d}} \\ {\mathbf {0}}^\intercal&1 \end{bmatrix} \\ \hbox {AD}&:= \begin{bmatrix} 0&1&0 \end{bmatrix} {\mathbf {d}} \\ \hbox {IRD}&:= \pm \tan ^{-1}_2(Q_{12},Q_{11}) \end{aligned} \quad \begin{aligned} \hat{\mathbf{V }}&= {\mathbf T} _{\mathrm{trial}}^{-1} ~ \dot{\mathbf{T }}_{\mathrm{trial}} \\&= \begin{bmatrix} \hat{{\varvec{\omega }}}&{\mathbf {v}} \\ {\mathbf {0}}^\intercal&0 \end{bmatrix} \\ \hbox {PV}&:= \begin{bmatrix} 0&-1&0 \end{bmatrix} {\mathbf {v}} \\ \hbox {ERV}&:= \begin{bmatrix} 0&0&\mp 1 \end{bmatrix} {\varvec{\omega }} \end{aligned} \end{aligned}$$

where ${\mathbf T} = \left[ \begin{array}{ll} {\mathbf R} &{} {\mathbf {p}} \\ {\mathbf {0}}^\intercal &{} 1 \end{array}\right]$ is the homogeneous transformation matrix representing the motion of the tibia relative to the femur, and $\dot{\mathbf{T }}$ is the time derivative of ${\mathbf T}$. Motions during experimental trials ${\mathbf T} _{\mathrm{trial}}$ and during intact passive flexion ${\mathbf T} _{\mathrm{ref}}$ were expressed as a function of the same knee flexion angle $\theta$. The Euler angles corresponding to knee flexion–extension ($\theta$), varus–valgus, and internal–external rotation were extracted from the rotation matrix ${\mathbf R}$ following the convention of Grood and Suntay [15].

Kinetics

The loads acting on the tibia were both predicted based on the spring configuration and measured directly with a load cell. The force ${\mathbf {F}}$ and moment ${\mathbf {M}}^{O^{\mathrm{t}}}$ applied to the tibia by the 48.0 N spring were predicted using the equations:

$$\begin{aligned} {\mathbf {F}}&= 48 ~ \hat{\mathbf {u}}&{\mathbf {M}}^{O^{\mathrm{t}}}&= {\mathbf {r}} \times {\mathbf {F}} \\ \hat{\mathbf {u}}&= \frac{P^{\mathrm{f}} - P^{\mathrm{t}}}{\Vert P^{\mathrm{f}} - P^{\mathrm{t}}\Vert }&{\mathbf {r}}&= P^{\mathrm{t}} - O^{\mathrm{t}} \end{aligned}$$

where $\hat{\mathbf {u}}$ is the unit vector directed along the line of action of spring force, and ${\mathbf {r}}$ is the moment arm from the origin $O^{\mathrm{t}}$ of the tibia.

These predicted forces and moments were compared to measured ones by expressing both sets in the tibial coordinate frame. First the force ${\mathbf {F}}$ and moment ${\mathbf {M}}^{O^{\mathrm{c}}}$ applied to the load cell by the spring were measured directly. These loads were then transformed to the tibial coordinate frame using the equation:

$$\begin{aligned} \begin{bmatrix} {\mathbf {F}}_{\mathrm{t}} \\ {\mathbf {M}}_{\mathrm{t}}^{O^{\mathrm{t}}} \end{bmatrix} = {\mathbf A}_{({\mathbf T} _{\mathrm{trial}})} ~ \begin{bmatrix} {\mathbf {F}}_{\mathrm{c}} \\ {\mathbf {M}}_{\mathrm{c}}^{O^{\mathrm{c}}} \end{bmatrix} \end{aligned}$$

where ${\mathbf A} _{({\mathbf T} _{\mathrm{trial}})}$ is the 6-by-6 adjoint matrix [29] that varies as the tibia moves relative to the femur and load cell, and the subscripts $_{\mathrm{t}}$ and $_{\mathrm{c}}$ indicate that force and moment vectors are expressed in the coordinate frames of the tibia and the load cell, respectively.