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Research Papers

# Injury Tolerance and Moment Response of the Knee Joint to Combined Valgus Bending and Shear Loading

[+] Author and Article Information
Dipan Bose, Kavi S. Bhalla, Costin D. Untaroiu, B. Johan Ivarsson, Jeff R. Crandall

Department of Mechanical and Aerospace Engineering, University of Virginia, 1101 Linden Avenue, Charlottesville, VA 22902

Shepard Hurwitz

Department of Orthopeadic Surgery, University of Virginia, 1101 Linden Avenue, Charlottesville, VA 22902

J Biomech Eng 130(3), 031008 (Apr 28, 2008) (8 pages) doi:10.1115/1.2907767 History: Received March 02, 2007; Revised September 06, 2007; Published April 28, 2008

## Abstract

Valgus bending and shearing of the knee have been identified as primary mechanisms of injuries in a lateral loading environment applicable to pedestrian-car collisions. Previous studies have reported on the structural response of the knee joint to pure valgus bending and lateral shearing, as well as the estimated injury thresholds for the knee bending angle and shear displacement based on experimental tests. However, epidemiological studies indicate that most knee injuries are due to the combined effects of bending and shear loading. Therefore, characterization of knee stiffness for combined loading and the associated injury tolerances is necessary for developing vehicle countermeasures to mitigate pedestrian injuries. Isolated knee joint specimens $(n=40)$ from postmortem human subjects were tested in valgus bending at a loading rate representative of a pedestrian-car impact. The effect of lateral shear force combined with the bending moment on the stiffness response and the injury tolerances of the knee was concurrently evaluated. In addition to the knee moment-angle response, the bending angle and shear displacement corresponding to the first instance of primary ligament failure were determined in each test. The failure displacements were subsequently used to estimate an injury threshold function based on a simplified analytical model of the knee. The validity of the determined injury threshold function was subsequently verified using a finite element model. Post-test necropsy of the knees indicated medial collateral ligament injury consistent with the clinical injuries observed in pedestrian victims. The moment-angle response in valgus bending was determined at quasistatic and dynamic loading rates and compared to previously published test data. The peak bending moment values scaled to an average adult male showed no significant change with variation in the superimposed shear load. An injury threshold function for the knee in terms of bending angle and shear displacement was determined by performing regression analysis on the experimental data. The threshold values of the bending angle $(16.2deg)$ and shear displacement $(25.2mm)$ estimated from the injury threshold function were in agreement with previously published knee injury threshold data. The continuous knee injury function expressed in terms of bending angle and shear displacement enabled injury prediction for combined loading conditions such as those observed in pedestrian-car collisions.

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## Figures

Figure 8

Injury threshold function for valgus bending of the knee based on the simple analytical model of the knee. The dark circles (●) represent the failure bending angle (αvalgus) and the corresponding shear displacement (dshear) for all dynamic tests. The dark solid line shows the injury threshold function (d=1189.3−6850.8sin2(0.28+0.0087α)) determined by regression analysis of the experimental failure data. The light dashed line represents the injury threshold function (d=1152−6400sin2(0.26+0.0087α)) based on anatomical parameters estimated from a knee numerical model.

Figure 9

Injury threshold of the knee as predicted by the numerical model. The numerical model with appropriate boundary conditions is shown on the left.

Figure 7

Frequency of each ligament injury for all 40 knee bending tests. The number in parenthesis indicates the percentage of cases in which a particular combination of ligaments was injured.

Figure 6

Sensitivity of shear displacement (dsheaṟfail) to the M:V in the 3PT bending set-up. A regression line (R2=0.0756) of the data is superposed on the plot.

Figure 5

Plot of measured bending moment (Mvalgus) as a function of bending angle (αvalgus) for (a) 4PT bending and (b) 3PT bending tests (b). While the dark curves represent the inertially compensated load cell response scaled to a 50th percentile adult male, the light curves represent the scaled load cell response. The dotted elliptical boundary in (a) shows the inertial effects observed in the uncompensated moment response data.

Figure 3

Comparison of quasistatic knee moment (Mvalgus) bending angle (αvalgus) histories from previous studies (11-12), with the results from the present study. The solid dark lines show the results from the present study compared to the quasistatic response corridor reported by Ramet (12) (study: R1). The grey ◇, ○, and ◻ denote the mean of all ligament failure values reported by Ramet (12) (R1), Kajzer , (11) at 20km∕h (K1), and Kajzer (11) at 16km∕h (K2), respectively. The bars on the mean values represent one standard deviation. The dark ◇ denotes the mean of ligament failure observed in the present study.

Figure 2

Analytical model representing the relationship between the kinematic parameters (αvalgus and dshear) at the strain failure threshold. In the figure, θ and h represent the geometrical parameters of the knee, L is the unstrained length of the MCL, L′ is the elongated length due to bending, and L″ is the final elongated length due to bending and shear.

Figure 1

Schematic of the experimental setup for knee bending test with an enlarged view of the knee specimen to describe the equations used in the inertial compensation procedure Eqs. 1,2. The twin prong impactor was used for 4PT pure bending loading, whereas the single prong impactor (in transparent dashed lines) was used for 3PT combined loading. The geometrical dimension LM:V refers to the magnitude of the M:V for the test setup (refer to Bose (13)). MF, VF and MK, Vk denote the bending moment and shear force, recorded at the load cell and estimated at the knee joint center, respectively. XF and Xk are the distances between the midsection of the six-axis load cell and the center of gravity (CG) of the proximal knee segment, and between the CG of the proximal knee segment and the distal end of the femoral condyles. ϴ and u denote the angular and linear displacements of the proximal knee segment.

Figure 4

Comparison of dynamic and static bending moment-angle (Mvalgus−αvalgus) history between matched pair specimens

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