Characterizing the effective stiffness of the pelvis during sideways falls on the hip

ARTICLE IN PRESS Journal of Biomechanics 43 (2010) 1898–1904

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Characterizing the effective stiffness of the pelvis during sideways falls on the hip Andrew C. Laing a,b,n, Stephen N. Robinovitch c,1 a

Injury Prevention and Mobility Laboratory, Department of Biomedical Physiology and Kinesiology, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada V5A 1S6 b Department of Kinesiology, University of Waterloo, 200 University Ave West, Waterloo, Ontario, Canada N2L 3G1 c Injury Prevention and Mobility Laboratory, Department of Biomedical Physiology and Kinesiology and School of Engineering Science, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada V5A 1S6

a r t i c l e in f o

a b s t r a c t

Article history: Accepted 16 March 2010

The force applied to the proximal femur during a fall, and thus hip fracture risk, is dependent on the effective stiffness of the body during impact. Accurate estimates of pelvis stiffness are required to predict fracture risk in a fall. However, the dynamic force–deflection properties of the human pelvis have never been measured in-vivo. Our objectives were to (1) measure the force–deflection properties of the pelvis during lateral impact to the hip, and (2) determine whether the accuracy of a mass-spring model of impact in predicting peak force depends on the characterization of non-linearities in stiffness. We used a sling and electromagnet to release the participant’s pelvis from heights up to 5 cm, simulating low-severity sideways falls. We measured applied loads with a force plate, and pelvis deformation with a motion capture system. In the 5 cm trials peak force averaged 1004 (SD 115) N and peak deflection averaged 26.3 (5.1) mm. We observed minimal non-linearities in pelvic force–deflection properties characterized by an 8% increase in the coefficient of determination for non-linear compared to linear regression equations fit to the data. Our model consistently overestimated peak force (by 49%) when using a non-linear stiffness equation, while a piece-wise non-linear fit (non-linear for low forces, linear for loads exceeding 300 N) predicted peak force to within 1% at our highest drop height. This study has important implications for mathematical and physical models of falls, including mechanical systems that assess the biomechanical effectiveness of protective devices aimed at reducing hip fracture risk. Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved.

Keywords: Hip fractures Sideways falls Pelvic stiffness Pelvic compliance Impact

1. Introduction Sideways falls with impact to the hip are the event most directly linked to hip fractures in older adults (Grisso et al., 1991; Nevitt and Cummings, 1993; Zuckerman, 1996). When such fractures occur, the force applied to the proximal femur exceeds its fracture threshold. A recent review of biomechanical studies of the fracture force of the cadaveric proximal femur, involving loading conditions that simulate sideways falls, indicates that the median fracture force is approximately 2830 N for older women and 4380 N for older men (Robinovitch et al., 2009a). However, to predict fracture risk during falls the magnitude of applied force must also be known (Hayes et al., 1991). As safety concerns preclude their in-vivo measurement during standing height falls,

n Corresponding author at: Department of Kinesiology, University of Waterloo, 200 University Ave West, Waterloo, Ontario, Canada N2L 3G1. Tel.: + 1 519 888 4567x38947; fax: + 1 519 746 6776. E-mail addresses: [email protected], [email protected] (A.C. Laing), [email protected] (S.N. Robinovitch). 1 Tel.: + 1 778 782 3556; fax: + 1 778 782 3040.

researchers must consider other means of characterizing the forces applied to the proximal femur during impact. An alternative to experimental measures is the use of mathematical models to predict impact dynamics. Robinovitch et al. (1997a) used a Voigt model (a mass supported by parallel spring and damper elements) to predict peak forces ranging from 1150 to 5288 N during sideways falls from standing height. For similar falls, van den Kroonenberg et al. (1995) used a simpler mass-spring model to predict peak forces of 2900, 3580, and 4260 N for 5, 50, and 95 percentile females, respectively. They concluded that such forces were sufficient to cause hip fracture in about 50% of older persons. Robinovitch et al. (1997b) demonstrated that impact dynamics during sideways falls are more dependent on elastic than viscous properties. Specifically, viscoelastic supports based on Voigt, Maxwell (in-series spring and damper elements) and standard linear solid (parallel spring and damper elements in series with a second spring) models were no more effective than a simple spring (elastic) support in predicting the peak force applied to the pelvis during a lateral impact. Consequently, the accuracy of mathematical models of impact depends primarily on how accurately the effective stiffness of the body is characterized.

0021-9290/$ - see front matter Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2010.03.025

ARTICLE IN PRESS A.C. Laing, S.N. Robinovitch / Journal of Biomechanics 43 (2010) 1898–1904

er a

turnbuckle

ca m

a er

2. Methods

electromagnet

m ca

Robinovitch et al. (1991, 1997a) used low energy ‘pelvis release experiments’ to characterize the effective stiffness of the pelvis from the natural frequency of oscillation in the force record. For forces below 300 N, they observed effective stiffness to increase with increasing force (presumably due to increasing contact area and tissue compression as the impact progressed). However, for loads beyond 300 N stiffness remained constant. Consequently, they ignored non-linearities when reporting effective pelvic stiffness for females landing with their trunks horizontal (mean (SD)¼30.4 (3.6) kN/m) or laterally flexed (49.6 (19.8) kN/m) (Robinovitch et al., 1997a). However, the validity of these linear estimates of pelvic stiffness can be questioned from several perspectives. First, the end loads employed by Robinovitch et al. (1991) were less than 500 N, perhaps an insufficient range to evaluate potential nonlinearities. Second, no effort was made to validate model predictions based on these stiffness estimates using data from higher fall heights. Finally, the lack of direct measures of pelvis stiffness during impact (and an under-appreciation of how this influences force generation) has caused some groups to ignore this parameter in developing rigid systems to evaluate hip protectors (Derler et al., 2005; Nabhani and Bamford, 2002; van Schoor et al., 2006) and compliant flooring (Maki and Fernie, 1990; Nabhani and Bamford, 2004). Our objectives for this study were two-fold. First, we aimed to determine whether there are significant non-linearities in the invivo force–deflection properties of the pelvis during sideways falls. Our second aim was to examine whether the accuracy of mathematical model predictions of peak force are influenced by the method used to characterize potential non-linearities in pelvic stiffness.

1899

nylon sling reflective markers

h positioning mat

force plate

positioning mat

Fig. 1. Experimental schematic. A sling and electromagnet were used to raise and suddenly release the participant’s pelvis from heights (h) of 0 (sling just barely touching the ground), 1.25, and 5 cm above the landing surface, simulating the impact stage of a sideways fall on the hip. The time-varying force applied to the hip region during impact was measured with a force plate, while pelvic compression was assessed by using a high-speed motion capture system (representative cameras illustrated) to measure the position of reflective markers on the force plate and the participant’s right greater trochanter. We used surgical positioning mats placed under the shin and shoulder to ensure consistent postures across trials. These mats are filled with polystyrene beads which form an impression of the body, and compress together upon application of a vacuum to form a relatively rigid support, which should have minimal influence on the measured stiffness.

2.1. Experimental protocol Study participants consisted of 14 women with mean (SD) age of 23.1 (2.4) years, body mass of 56.4 (5.0) kg, height of 1.64 (0.05) m, body mass index (BMI) of 20.9 (1.6) kg/m2, and pelvic width of 34.2 (1.4) cm. We chose to evaluate women as they have a three-fold greater lifetime risk for hip fracture than men (Cummings and Melton, 2002). All participants provided written informed consent and the study was approved by the Committee on Research Ethics at Simon Fraser University. The experimental protocol involved using a sling and electromagnet to raise and suddenly release the participant’s pelvis, simulating the impact stage of a sideways fall on the hip (Fig. 1). To conduct a trial, we first positioned the participant lying on her left side, with her left shoulder flexed overhead, hips flexed at 45 degrees, and knees flexed at 75 degrees. This position simulates a sideways fall where the shin and upper extremity contact the ground just before the pelvis (Laing and Robinovitch, 2008a; Laing et al., 2006), as observed in video recordings of real-life falls experienced by older adults in long-term care facilities (Robinovitch et al., 2009b). The participant wore tight-fitting cycling shorts during the trials. We positioned the participant’s pelvis in a nylon sling with the inferior and superior borders contacting the upper thigh and iliac crest. A steel cable connected the sling to an electromagnet. We used an in-series turnbuckle to raise the pelvis so a gap of 0 (barely contacting), 1.25, or 5 cm existed between the ground and the skin overlying the greater trochanter. The latter heights were selected based on free-fall predictions that impact velocities would be approximately 0.5 and 1.0 m/s, respectively, and our experience that drop heights greater than 5 cm can create bruising and tenderness. Just prior to sling release, we instructed the participant to relax her core and extremity muscles. At random times after confirming her readiness, we released the electromagnet causing the participant’s pelvis to fall onto the landing surface. During each trial the force applied to the hip region was measured with a force plate (model 6090-15; Bertec Corp., Columbus, USA) sampled at 960 Hz. We used a 240 Hz, eight-camera motion measurement system (Motion Analysis Corporation, Santa Rosa, USA) to record the position of reflective markers fixed to the skin overlying the participant’s right greater trochanter and to the top of the force plate. Our camera placement ensured that the 3-dimensional coordinates of all markers were measured throughout the impact event. The participant completed four consecutive trials at each randomly assigned drop height. Trials were repeated if we observed pelvic rotation about the anteroposterior axis during impact.

2.2. Data analysis Briefly, our approach involved characterizing effective pelvic stiffness from the data in the zero drop height trials. We used two characterization techniques based on either the measured frequency of vibration in ground reaction force or the pelvic force–deflection data. The final step involved inputting the stiffness estimates into a mass-spring model to predict the time-varying forces at all drop heights as a means for model validation and evaluation. The measured variation in impact force was dominated by a single natural frequency (Fig. 2). This allowed for easy detection of the time and magnitude (through a customized MATLAB routine) of impact initiation (Timp, Fimp), peak force (Tmax, Fmax), minimum force (Tmin, Fmin), and final resting force (Fm). We used these outcomes from the zero drop height trials to estimate parameter values for a massspring model. Effective mass (m) and period of oscillation (T) were calculated as: m¼ Fm/g and T¼ 2n(Tmin  Tmax) and averaged across the four trials. Within-subject variability was low as indicated by coefficient of variability values averaged across participants of 3.3% for m, and 8.3% for T. We then calculated effective stiffness (kvibe) as kvibe ¼ o2n m, where the natural frequency (on) was calculated as: on ¼ 2p/T. We also measured the force–deflection properties of the pelvis during the zero drop height trials. As the sling would have occluded reflective markers on the left (impacting) side of the pelvis, pelvic width was defined as the vertical distance between the markers on the right greater trochanter and the force plate at the instant of impact initiation (Timp). Pelvic deflection (x) was calculated as the decrease in pelvic width from Timp to Tmax. For each participant we combined the data from all four trials to create scatterplots of applied force (F) versus pelvis deflection (x) and used a least squares regression approach to generate first and second order polynomial fits to the data (Fig. 3A, B, D, E). Both functions were forced through an intercept of zero, and coefficients were constrained to positive values to prevent negative force predictions. The functions were differentiated to determine effective stiffness (k1st and k2nd) as follows: 1st order : F ¼ A x,  2

k1st ¼ dF=dx ¼ A

2nd order : F ¼ B x þ A x,

k2nd ¼ dF=dx ¼ 2 B x þ A

Based on Robinovitch et al. ’s (1991) observation that effective stiffness plateaued at forces greater than 300 N, we also defined a stiffness parameter using

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A.C. Laing, S.N. Robinovitch / Journal of Biomechanics 43 (2010) 1898–1904 a piece-wise non-linear fit (kcombo) equal to the force-varying value of k2nd for the low force range (0 to 300 N) and to the instantaneous value of k2nd at 300 N for forces above this transition point (Fig. 3C, F). To assess potential non-linearities in pelvic force–deflection properties at higher impact energies, we also used the regression approach described above to generate polynomial fits to the data from the 1.25 and 5 cm drop heights. Parameter identification was performed only at the zero drop height condition for several reasons. First, it allowed for a direct comparison of our stiffness estimates to those of Robinovitch et al. (1991, 1997a). Second, from experience we knew it was easiest – and perhaps feasible for older adults in future studies – to perform trials at the zero drop height due to decreased impact force and greater participant comfort. Consequently we were interested in testing whether the parameters identified from this ‘convenient’ condition would accurately predict impact forces at higher drop heights. Similarly, for mathematical model validation (see Section 2.3) we desired different datasets for parameter identification and force prediction. Finally, the impact event was longest in the zero drop height condition, which was important for ensuring an appropriately large force– deflection dataset for the regression analyses used to estimate k1st, k2nd, and kcombo.

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2.3. Model simulations We performed subject-specific simulations with a mass-spring model to predict the compressive force generated at the hip for all three drop heights. A preliminary analysis demonstrated little influence of damping during the initial compressive phase as evidenced by temporal coupling of peak force and peak deflection (Fig. 4). These findings concurred with Robinovitch et al. ’s (1997b) observations that peak force during sideways falls is dominated by elastic (rather than velocity-dependent) mechanisms, and together provided the justification for not considering damping in our simulations. Model inputs comprised subject-specific values of effective mass and stiffness averaged across the zero drop height trials. We differentiated the greater trochanter position data to determine the subject-specific impact velocity for

0 0.1

0

0.2 time (s)

0.3

0.4

Fig. 2. Example force vs. time trace observed in the zero drop height condition. The points indicated were used in the free vibration response approach of characterizing parameter values for a mass-spring model (inset). T¼ 0 corresponds to the time of impact initiation (Timp, Fimp).

r2

y = 1.0x2+0.8x+0

y = 23.3x+0

= 0.911

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Fig. 3. Example force vs. deflection datasets from the four repeated trials with a single participant in the zero drop height (A, B, C) and 5 cm drop height (D, E, F) conditions. Illustrated are: (A and D) 1st order polynomial fits; (B and E) 2nd order polynomial fits; (C and F) piece-wise non-linear fit approach which used the 2nd order polynomial for forces up to 300 N, and the tangent value at 300 N for all forces above this transition point. The regression equations for each approach are noted, along with the coefficient of variability values (r2) for the 1st and 2nd order polynomial fits.

ARTICLE IN PRESS A.C. Laing, S.N. Robinovitch / Journal of Biomechanics 43 (2010) 1898–1904

Table 1 A cross-participant average (SD) of the parameter values used in our mass-spring model simulations. With the exception of impact velocity, all parameters were determined from data in the zero drop height condition.

1000

40 force deflection

1901

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Average (SD)

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force (N)

deflection (mm)

30

10

m (kg) kvibe (N/m) k1st (N/m) k2nd A constant k2nd B constant kcombo linear phase (N/m) impact velocity 0 cm (m/s) impact velocity 1.25 cm (m/s) impact velocity 5 cm (m/s)

24.1 23696 20922 800478 9306 31784 0.087 0.456 0.917

(3.3) (7165) (3482) (730112) (8099) (10266) (0.039) (0.04) (0.061)

200

0 0

0.05

0.1

0.15

each drop height (Table 1). We used MATLAB to solve the equation of motion mx€ þ kx ¼ mg for x(t), and compressive force was given by F¼ kx. We repeated model simulations using the four estimates of effective pelvic stiffness (kvibe, k1st, k2nd, and kcombo). For each stiffness estimate we calculated the average difference (%) between the experimental values and model predictions of peak force (Fdif) at all drop heights.

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40 force

2.4. Statistics

deflection

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3. Results

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20 400

force (N)

deflection (mm)

30 600

10 200

0 0

0.05

0.1

0.15

We used paired t-tests to test for differences between the linear stiffness estimates kvibe and k1st. The match between the force–deflection data and regression equations was evaluated via coefficient of determination (r2). We a priori chose an r2 increase in 0.1 to signify a substantially improved fit. We used two-factor repeated measures analysis of variance (ANOVA) to test the effect of stiffness calculation method (kvibe, k1st, k2nd, kcombo) and drop height (0, 1.25, 5 cm) on Fdif. All statistical analyses were performed with a software package using an a of 0.05 (SPSS Version 16.0, SPSS Inc., Chicago, USA).

0 0.2

time (s) Fig. 4. Example force and deflection vs. time traces observed for trials in the 0, 1.25, and 5 cm drop height conditions. Peak force and peak deflection occurred at approximately the same time, suggesting the dominant effect of elastic vs. viscous elements in force generation. Note: the data presented here are from a different participant than the data shown in Fig. 2.

We observed no significant difference between the linear effective stiffnesses estimated via the free vibration response and the force–deflection data (t(13)¼ 1.217, p ¼0.245; Table 1). Specifically, kvibe averaged 23696 (SD 7165) N/m and k1st averaged 20922 (3482) N/m. In contrast, the linear portion of kcombo at forces above 300 N (31784 (10266) N/m) was significantly higher than kvibe (t(13) ¼2.219, p¼0.045) and k1st (t(13) ¼4.577, p¼0.001). The force–deflection properties of the pelvis demonstrated only slight non-linearity characterized by increasing stiffness as deflection increased. The r2 for the 2nd order regression equation compared to the 1st order fit increased by 0.036 (from 0.899 to 0.935) for the zero drop height condition, by 0.091 (from 0.830 to 0.922) for the 1.25 cm drop height, and by 0.083 (from 0.783 to 0.866) for the 5 cm drop height. ANOVA demonstrated that the method used to characterize stiffness had a significant influence on the accuracy of Fmax predictions (F3,13 ¼43.6, p o0.001; Table 2, Figs. 5 and 6). Fdif averaged across drop heights was best for the mass-spring model using k1st (mean (SD)¼4.7 (13.9)%) and kvibe (6.7 (13.7)%) followed by kcombo (13.2 (15.8)%) and k2nd (49.2 (27.7)%). The accuracy of model predictions of Fmax was also influenced by drop height (F2,13 ¼ 11.3, p ¼0.001; Table 2, Fig. 6). Overall, the model had higher accuracy at the 5 cm drop height (mean (SD) Fdif ¼8.1 (28.6)%) compared to the zero (Fdif ¼22.9 (21.5)%) and 1.25 cm (Fdif ¼ 24.3 (24.3)%) drop heights. We also observed a significant interaction indicating that the effect of stiffness calculation method on Fdif differed across drop heights (F3,39 ¼19.4, p o0.001; Table 2, Fig. 6). Fdif using k2nd (which always over-predicted Fmax) remained relatively constant across drop heights. In contrast, Fmax predictions using kvibe, k1st,

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Table 2 Average (SD) experimental values and model predictions of Fmax across stiffness estimates and drop heights. Fdif indicated as % difference from experimental. Fmax in Newtons (SD) Drop height (cm) Experimental Model with

0

kvibe k1st k2nd kcombo

433 482 481 621 517

% difference from experimental (SD)

1.25 (76) (66) (65) (92) (58)

576 647 631 883 679

5 (83) (91) (75) (128) (62)

1004 951 918 1456 995

1500 actual kvibe k1st kcombo 1000 force (N)

k2nd

500

0 0

0.05

0.1 time (s)

0.15

0.2

Fig. 5. Comparison of actual (experimental) data with model predictions of force vs. time for a single trial by a typical participant in the 5 cm drop height condition. As was common, peak force was overestimated by a model incorporating the nonlinear stiffness element k2nd, and more accurately matched by models incorporating kvibe, k1st, and kcombo.

and kcombo tended to improve as drop height increased. At our highest condition, kcombo provided the most accurate prediction with Fdif averaging  0.3 (SD 11.6)%. In our highest energy condition we observed maximum experimental values of Fmax of 1156 N (mean¼1004 (SD 115) N) and peak deflection of 37.4 mm (mean¼ 26.3 (5.1) mm).

4. Discussion This study provides the first records of the dynamic force– deflection properties of the human pelvis in-vivo during sideways falls, and the first direct comparisons of experimental and model predictions of applied force. Related to our first aim, we found the non-linearities in pelvic stiffness during lateral impact to be relatively subtle, based on an improvement of only 8% in the r2 when fitting a 2nd order polynomial equation to the force– deflection data compared to a 1st order linear equation. Regarding our second aim, we found that a mass-spring model incorporating our non-linear estimate of pelvic stiffness k2nd (which increases continually in magnitude with increasing force) consistently overestimated Fmax (by 49% on average). In contrast, a model incorporating our piece-wise stiffness parameter kcombo (which transitions at 300 N from a non-linear to linear stiffness) was accurate to within 0.3% on average in predicting Fmax. Collectively,

0 (115) (157) (121) (299) (113)

NA 12.5 12.1 46.1 21.1

1.25

(10.7) (10.6) (30.8) (14.9)

NA 12.7 10.2 55.3 19.0

5

(9.7) (10.4) (27.0) (11.7)

NA  5.0  8.2 46.1  0.3

(12.7) (10.8) (30.8) (11.6)

these results indicate that non-linearities in pelvic stiffness during lateral impact are limited predominantly to forces below 300 N. This study adds to the literature that reports on the compliance of the pelvis during lateral impact. Our kvibe estimate (mean (SD)¼ 23696 (7165)) was similar to that reported by Robinovitch et al. (1997a) for women with muscles relaxed (k¼ 28231 (8307) N/m). Although our linear estimate obtained from force–deflection data was slightly lower (k1st ¼20922 (3482) N/m), the linear portion of kcombo (31784 (10266) N/m) was similar to Robinovitch et al.’s value. A complementary line of evidence supporting our stiffness values comes from impact studies with cadaveric specimens. Specifically, high-energy lateral impact tests with cadavers (using impact velocities up to 9.4 m/s) have yielded pelvic fracture tolerances of 20–33% for pelvic compression (Cavanaugh et al., 1990; Etheridge et al., 2005; Viano et al., 1989). For a 36 cm wide pelvis (Laing and Robinovitch, 2008b), 30% compression would equate to a deflection of approximately 11 cm, similar to the deformation that a mass-spring model would predict using our stiffness estimates during falls from standing height (in comparison, peak pelvic compression values in our 0, 1.25, and 5 cm drop height trials averaged 5%, 6%, and 8%, respectively). Thus, our results correspond with the existing literature which demonstrates that the pelvis has substantial compliance during lateral impact. It is instructive to compare our impact force estimates to the fracture force of the older proximal femur, since the ratio of impact force divided by fracture force reflects the ’’factor of risk’’ for hip fracture during a fall (Hayes et al., 1991). As mentioned previously, the force required to fracture the proximal femur harvested from cadavers of older women, when tested in a sideways fall loading configuration, averages 2830 N, with a standard deviation of about 1100 N (Robinovitch et al., 2009a). In comparison, our model simulations, based on the kcombo stiffness parameter, predict that the peak force applied to the hip is 1846 N for a sideways fall involving an impact velocity of 2 m/s, 2649 N for a 3 m/s impact velocity, and 3434 N for a 4 m/s impact velocity. Feldman and Robinovitch (2007) found that pelvis impact velocities during sideways falls average 3.0 m/s, with a standard deviation of 1.0 m/s. Collectively, these results suggest that typical sideways falls in older adults produce factors of risk ranging between approximately 0.65 and 1.2. This indicates that, even under severe falling conditions, the factor of risk for hip fracture is only slightly above 1. Thus, even modest reductions in impact force (as achieved through wearable hip protectors or compliant flooring), or increases in fracture strength (as achieved through pharmaceuticals or exercise) should provide substantial protective benefits against hip fracture. Our results have important implications for the design of mechanical systems that test the force attenuation provided by protective devices including hip protectors and compliant floors. A mass-spring model in series with a compliant protective element (Laing et al., 2006) suggests that unrealistically stiff

ARTICLE IN PRESS A.C. Laing, S.N. Robinovitch / Journal of Biomechanics 43 (2010) 1898–1904

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Fig. 6. Scatterplots of mass-spring model predictions of Fmax vs. actual Fmax for all participants at the 0, 1.25, and 5 cm drop heights using: (A) kvibe; (B) k1st; (C) k2nd; and (D) kcombo.

systems will overestimate the force attenuation provided by such devices. For example, the model predicts that a protective element (of stiffness kf ¼13 kN/m) in-series with a pelvis (of stiffness kp ¼25 kN/m) will reduce peak force by 35% compared to an unpadded impact. However, if kp is increased to 75 kN/m the predicted force attenuation increases to an unrealistically high value of almost 60%. Such contradictory evidence is mirrored in the mechanical test literature, with reports of the force attenuation provided by one popular hip protector (Safehip Classic) ranging from 18.2% (Robinovitch et al., 1995a) to 83.7% (Nabhani and Bamford, 2002). Thus, the current results will inform ongoing efforts towards the development of international standards for mechanical systems used to test such devices (Robinovitch et al., 2009a). This study had several limitations. First, our falls were of relatively low severity with maximum impact velocity averaging 0.917 (SD 0.061). However, we have observed values as low as 1.0 m/s during unexpected falls from standing when participants break the fall with an outstretched hand (Feldman and Robinovitch, 2007). Furthermore, during 5 cm drop heights Laing et al. (2006) observed applied forces within the range of fracture strengths for femurs from older women (Robinovitch et al., 2009a), and pilot trials at higher drop heights resulted in bruising and tenderness in some participants. Consequently, we regard the pelvis release paradigm as an effective means of simulating low severity, but clinically relevant falls that are sufficient to characterize the non-linearities in pelvic stiffness. Second, while we instructed participants to relax their muscles before each trial, we did not confirm this with electromyography. Although Robinovitch et al. (1991) initially

reported that muscle activity strongly influences the effective stiffness of the body, they later retracted these statements after conducting experiments using more refined techniques (Robinovitch et al., 1997a). Consequently, we believe that the effective stiffness values measured in the current study should be accurate for the range of muscle activities that might exist during a fall event. Third, for safety reasons we were unable to enroll older women as study participants. Although frail older adults may have greater effective stiffness, this influence on fracture risk may be partially offset by likely decreases in effective mass. Additional research is warranted to assess the potential influence of advanced aged on both of these parameters. Fourth, we did not measure the thickness of the soft tissues overlying the greater trochanter, which can influence applied loads during lateral pelvic impacts (Etheridge et al., 2005; Majumder et al., 2008; Robinovitch et al., 1995b). However, trochanteric soft tissue thickness correlates with BMI (Maitland et al., 1993), and the relatively low BMIs among our participants suggest they represent the lower range of soft tissue thickness, similar to older women at highest risk for hip fracture. Finally, we only considered a mass-spring model in our simulations. However, we are confident of its appropriateness as we simulated only the first half-period of oscillation during which damping appeared to have little influence (as indicated by the similarity in times to peak force and peak deflection (Fig. 4)). Furthermore, Robinovitch et al. (1997b) demonstrated that for lateral pelvic impacts, a massspring model predicts impact dynamics with accuracies equal or superior to that provided by other common support models (e.g. Voigt, standard linear solid or Maxwell). This suggests that although viscous elements play an important role in

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A.C. Laing, S.N. Robinovitch / Journal of Biomechanics 43 (2010) 1898–1904

damping subsequent oscillations, they likely have minimal influence on peak force applied to the pelvis during lateral impact. This is the first study to measure the force–deflection properties of the pelvis in-vivo during sideways falls, and the results validate previous estimates of pelvic stiffness based on the natural frequency of oscillation in ground reaction force. In addition, this study provides the first direct comparisons of experimental and model predictions of impact force during sideways falls on the pelvis. An important application of these results is in the design of mathematical and physical models of sideways falls that provide valid, and consistent, estimates of the biomechanical effectiveness of external hip fracture interventions.

Conflict of interest At the time this study was conducted SNR had secured GrantIn-Aid funding from the Tytex Group to support studies related to the biomechanics of wearable hip protectors. ACL has previously received funding for conference travel from the Tytex Group. These relationships had no bearing on any aspect of the study reported herein. No person other than ACL and SNR had input into any aspect of the study and subsequent reporting of data.

Acknowledgements This research was funded in part by an operating grant from the Natural Sciences and Engineering Research Council of Canada (NSERC; grant # RGPIN239735). ACL was supported by fellowships from the Michael Smith Foundation for Health Research and NSERC, and SNR was supported by the Canada Research Chairs program. References Cavanaugh, J.M. Walilko, J.T. Malhotra, A. Zhu, Y. King, A.I., 1990. Biomechanical response and injury tolerance of the pelvis in twelve sled side impacts. In: Proceedings of the 34th Stapp Car Crash Conference. Warrendale, PA. Cummings, S.R., Melton, L.J., 2002. Epidemiology and outcomes of osteoporotic fractures. Lancet 359, 1761–1767. Derler, S., Spierings, A.B., Schmitt, K.U., 2005. Anatomical hip model for the mechanical testing of hip protectors. Medical Engineering & Physics 27, 475–485. Etheridge, B.S., Beason, D.P., Lopez, R.R., Alonso, J.E., McGwin, G., Eberhardt, A.W., 2005. Effects of trochanteric soft tissues and bone density on fracture of the female pelvis in experimental side impacts. Ann Biomed Eng 33, 248–254.

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