Funding from the American and International Societies of Biomechanics was provided for this study.

<ol>
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L., Dowling, J. J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Analysis+of+body+segment+parameter+differences+between+four+human+populations+and+the+estimation+errors+of+four+popular+mathematical+models.">Analysis of body segment parameter differences between four human populations and the estimation errors of four popular mathematical models.</a> J Biomech Eng. 125, 515-522 (2003).</li><li>Durkin, J. L., Dowling, J. J., Andrews, D. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+measurement+of+body+segment+inertial+parameters+using+dual+energy+X-ray+absorptiometry.">The measurement of body segment inertial parameters using dual energy X-ray absorptiometry.</a> J Biomech. 35, 1575-1580 (2002).</li><li>Jensen, R. 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H., Kerwin, D. G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Quantification+of+the+uncertainties+in+resultant+joint+moments+computed+in+a+dynamic+activity.">Quantification of the uncertainties in resultant joint moments computed in a dynamic activity.</a> J Sports Sci. 14, 219-231 (1996).</li><li>Hunter, J. P., Marshall, R. N., McNair, P. J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Segment-interaction+analysis+of+the+stance+limb+in+sprint+running.">Segment-interaction analysis of the stance limb in sprint running.</a> J Biomech. 37, 1439-1446 (2004).</li><li>Lin-Chan, S. J., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+effects+of+added+prosthetic+mass+on+physiologic+responses+and+stride+frequency+during+multiple+speeds+of+walking+in+persons+with+transtibial+amputation.">The effects of added prosthetic mass on physiologic responses and stride frequency during multiple speeds of walking in persons with transtibial amputation.</a> Arch Phys Med Rehabil. 84, 1865-1871 (2003).</li><li>Mattes, S. J., Martin, P. E., Royer, T. 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I. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Resultant+lower+extremity+joint+moments+in+below-knee+amputees+during+running+stance.">Resultant lower extremity joint moments in below-knee amputees during running stance.</a> J Biomech. 20, 529-541 (1987).</li><li>Vanicek, N., Strike, S., McNaughton, L., Polman, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Gait+patterns+in+transtibial+amputee+fallers+vs.+non-fallers:+Biomechanical+differences+during+level+walking.">Gait patterns in transtibial amputee fallers vs. non-fallers: Biomechanical differences during level walking.</a> Gait &amp; Posture. 29, 415-420 (2009).</li><li>Royer, T., Koenig, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Joint+loading+and+bone+mineral+density+in+persons+with+unilateral,+trans-tibial+amputation.">Joint loading and bone mineral density in persons with unilateral, trans-tibial amputation.</a> Clin Biomech. 20, 1119-1125 (2005).</li><li>Underwood, H. 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The authors declare that they have no competing financial interests.

To quantify the resultant joint forces and moments during movement, an inverse dynamics model of the system of interest is needed when working with empirical data. For lower extremity biomechanics, inverse dynamics models typically represent the foot, shank, and thigh as rigid bodies. Input for these models come from three primary sources: a) motion kinematics, b) ground reaction forces, and c) segment anthropometrics and inertial properties. Motion data are collected with a variety of motion analysis systems, but all systems essentially provide the basic kinematics of the movement (position, velocity, and acceleration). Ground reaction forces are collected with a force plate and provide the contact forces acting on the feet. Anthropometrics are measurements taken directly from the body using rulers, flexible tapes, and/or calipers.&#160;These anthropometric measurements are used to estimate the inertial properties of the body segments used in the inverse dynamics analyses. Inertial properties include the mass, center of mass (COM) location and moment of inertia (MOI) of the segment relative to an axis through the segment COM or the proximal or distal joint. Methodologies and equipment used for collecting motion and ground reaction force data are similar among research groups, but inertial estimations of body segments can vary widely among researchers depending on which method the researcher chooses for estimating these inertial properties.
Various techniques available for estimating the inertial properties of a fully intact human body segment include: 1) regression equations based on cadaver data1-5, 2) mathematical models (i.e., geometric models)6,7, and 3) scanning &#38; imaging techniques8-15. Many of these techniques require direct measurements from the body, but it has previously been shown that regardless of the estimation method being used, the precision of body segment inertial estimates based on these methods is high16. It has also been shown that errors in the estimates of the inertial properties of intact body segments have minimal impact on the magnitudes of resultant joint moments during walking17,18. Joint moments are influenced to a greater extent by ground reaction forces, center of pressure locations, moment arm lengths, and segment kinematics17-19. Therefore, it is not surprising that methods for estimating inertial properties of body segments vary widely across the literature when using able-bodied individuals as research participants given that small errors in these estimates are likely to have little impact on outcomes of the study.
Many of these inertial estimations for a fully intact body segment are often used for estimating the inertial properties of prostheses for lower extremity amputees. Modern lower limb prostheses are fabricated using lightweight materials resulting in prosthetic limbs that are much lighter than the limbs they replace. This results in an inertial asymmetry between the prosthetic limb and intact limb. Compared with a typical intact shank and foot, the mass of a below-knee prosthesis and residual limb is approximately 35% less and has a center of mass located approximately 35% closer to the knee joint20-23. The lower mass and more proximal mass distribution of the prosthetic limb also produces a much lower (~60%) moment of inertia relative to the knee joint for the prosthetic limb compared to that of the intact shank and foot. Although researchers24,25 have previously suggested that using intact inertial estimates for the prosthetic limb have little effect on joint kinetic estimates, these comparisons focused on resultant joint moments during the stance phase of walking, where the ground reaction force dominates the moment produced at the joint. During swing, where ground reaction forces are not present, the reduced inertial properties of the prosthesis are more likely to influence estimates of resultant joint moments. Given that some researchers e.g., 26-32 utilize intact segment inertia properties to represent prosthesis inertial properties and otherse.g. 21-23 estimate prosthesis inertial properties directly, it is important to understand the impact of the methods chosen for estimating the inertial properties of the prosthesis. Minimizing the time required for measuring inertial properties of the prosthesis was an important consideration in the development of our technique. In the technique presented here the prosthesis remains fully intact for all measurements to reduce measurement times and avoid any additional times associated with realigning the prosthesis after measurement.
Thus, the purpose of this study was two-fold: 1) demonstrate a technique that can be used directly to estimate the inertial properties of a below-knee prosthesis, and 2) contrast the effects of the proposed technique and that of using intact limb inertial properties on joint kinetic estimates during walking in unilateral, transtibial amputees. It was hypothesized that joint kinetic magnitudes are larger when inertial properties of the intact shank and foot are used as the inertial estimates for the prosthesis compared to direct measurements of the prosthesis inertial properties.

<table border="0" cellpadding="0" cellspacing="0">
	<tbody>
		<tr height="105">
			<td height="105" style="height:105px;width:216px;">Oscillation Rack &#38; Reaction Board</td>
			<td style="width:144px;">Custom Built</td>
			<td style="width:119px;"></td>
			<td style="width:167px;">Outer cage made from 80/20 aluminum, inner cage from various thicknesses of solid of aluminum.</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:216px;">Laboratory scale</td>
			<td style="width:144px;"></td>
			<td style="width:119px;"></td>
			<td style="width:167px;"></td>
		</tr>
		<tr height="63">
			<td height="63" style="height:63px;width:216px;">NI LabView</td>
			<td style="width:144px;">National Instruments</td>
			<td style="width:119px;"></td>
			<td style="width:167px;">Software for recording TTL pulses from infrared photocell.</td>
		</tr>
		<tr height="84">
			<td height="84" style="height:84px;width:216px;">BNC-1050</td>
			<td style="width:144px;">National Instruments</td>
			<td style="width:119px;"></td>
			<td style="width:167px;">BNC Breakout box with direct pin connections to the data acquisition card</td>
		</tr>
		<tr height="105">
			<td height="105" style="height:105px;width:216px;">MATLAB</td>
			<td style="width:144px;">Mathworks Inc.</td>
			<td style="width:119px;"></td>
			<td style="width:167px;">Software for processing oscillation and reaction board data to predict inertial properties of prosthesis.</td>
		</tr>
	</tbody>
</table>

oscillation and reaction board techniques for estimating inertial properties of a below-knee prosthesis

The purpose of this study was two-fold: 1) demonstrate a technique that can be used to directly estimate the inertial properties of a below-knee prosthesis, and 2) contrast the effects of the proposed technique and that of using intact limb inertial properties on joint kinetic estimates during walking in unilateral, transtibial amputees. An oscillation and reaction board system was validated and shown to be reliable when measuring inertial properties of known geometrical solids. When direct measurements of inertial properties of the prosthesis were used in inverse dynamics modeling of the lower extremity compared with inertial estimates based on an intact shank and foot, joint kinetics at the hip and knee were significantly lower during the swing phase of walking. Differences in joint kinetics during stance, however, were smaller than those observed during swing. Therefore, researchers focusing on the swing phase of walking should consider the impact of prosthesis inertia property estimates on study outcomes. For stance, either one of the two inertial models investigated in our study would likely lead to similar outcomes with an inverse dynamics assessment.

Inertial properties of the prosthetic leg distal to the knee were lower than those of the intact leg (Table 1). Averaged across participants, prosthetic side mass was 39% less, moment of inertia about a transverse axis through the knee was 52% less, and the center of mass location was 24% closer to the knee compared with values for the intact leg.
<table border="1" cellpadding="0" cellspacing="0" fo:keep-together.within-page="always" width="553">
	<tbody>
		<tr>
			<td>Subject</td>
			<td>Intact* Mass (kg)</td>
			<td>Pros&#8224; Mass (kg)</td>
			<td>Est. Mass difference (kg)</td>
			<td>&#8225;Ikneeintact (kg&#183;m2)</td>
			<td>Ikneepros (kg&#183;m2)</td>
			<td>Intact CM below the knee joint (m)</td>
			<td>Pros CM below the knee joint (m)</td>
		</tr>
		<tr>
			<td>A</td>
			<td>6.03</td>
			<td>4.27</td>
			<td>1.76</td>
			<td>0.604</td>
			<td>0.325</td>
			<td>0.268</td>
			<td>0.215</td>
		</tr>
		<tr>
			<td>B</td>
			<td>6.07</td>
			<td>3.39</td>
			<td>2.68</td>
			<td>0.400</td>
			<td>0.196</td>
			<td>0.215</td>
			<td>0.177</td>
		</tr>
		<tr>
			<td>C</td>
			<td>5.80</td>
			<td>3.12</td>
			<td>2.68</td>
			<td>0.575</td>
			<td>0.194</td>
			<td>0.264</td>
			<td>0.198</td>
		</tr>
		<tr>
			<td>D</td>
			<td>5.72</td>
			<td>3.17</td>
			<td>2.55</td>
			<td>0.559</td>
			<td>0.317</td>
			<td>0.265</td>
			<td>0.191</td>
		</tr>
		<tr>
			<td>E</td>
			<td>7.14</td>
			<td>4.65</td>
			<td>2.49</td>
			<td>0.742</td>
			<td>0.325</td>
			<td>0.276</td>
			<td>0.200</td>
		</tr>
		<tr>
			<td>F</td>
			<td>6.23</td>
			<td>4.22</td>
			<td>2.01</td>
			<td>0.585</td>
			<td>0.287</td>
			<td>0.260</td>
			<td>0.192</td>
		</tr>
		<tr>
			<td>Mean &#177; STD</td>
			<td>6.17 &#177; 0.51</td>
			<td>3.80 &#177; 0.66</td>
			<td>2.36 &#177; 0.38</td>
			<td>0.578 &#177; 0.109</td>
			<td>0.274 &#177; 0.063</td>
			<td>0.258 &#177; 0.022</td>
			<td>0.196 &#177; 0.013</td>
		</tr>
	</tbody>
</table>
*Intact refers to values for the combined intact shank and foot. 
&#8224;Pros refers to values for the combined prosthesis and residual limb. 
&#8225;Moment of inertia about a transverse axis through the knee.
Table 1. Comparison of inertial properties between the prosthetic and intact limbs from the knee down.
Resultant joint forces (Figure 3) and moments (Figure 4) at the ankle, knee, and hip were affected by the inertial parameters used in the inverse dynamics model. Specifically, joint kinetics were reduced during swing initiation (~65% of the gait cycle) and swing termination (~95% of the gait cycle) when direct measures of prosthesis inertia were used in inverse dynamics assessments compared with regressions based on intact anatomy (Table 2). Effect sizes suggest these differences during swing were not trivial (&#8805;1.0). In addition, joint kinetic values increased on average by 80% during swing initiation and termination when intact inertial estimates were used compared with direct measures of the prosthesis inertial properties. Thus, when inertial properties of an intact limb were used to model the prosthetic side, joint kinetic profiles of the prosthetic side during swing more closely resembled those of an intact limb (see Figures 3 and 4). During stance, a number of statistical differences were observed. The largest effect size for any difference during stance was observed for the hip anterioposterior resultant joint force (ES = 0.86). Although this effect size is large and still considered as part of stance, the peak value for this measure occurred during terminal stance (~52%), or as the limb was transitioning into swing. Effect sizes for all other significant differences observed during stance ranged from 0.01 to 0.41, which would be considered small effects with the larger of these values being observed in the hip resultant joint reaction forces. Although significant differences were found during stance, these differences when considered in terms of the size of the difference (i.e., effect sizes) might lead one to question the meaningfulness of these differences.
<img alt="Figure 3" fo:content-width="5in" src="/files/ftp_upload/50977/50977fig3highres.jpg" width="500" /> 
Figure 3. Resultant joint reaction forces of the ankle, knee, and hip in the anterioposterior (left panels) and vertical directions (right panels). Data were averaged across subjects for presentation. The stance phase begins at 0% of the gait cycle with foot contact and ends at approximately 60% of the gait cycle with toe-off. Swing continues until the next foot contact of the same leg at 100% of the gait cycle. <a href="https://www.jove.com/files/ftp_upload/50977/50977fig3highres.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" fo:content-width="5in" src="/files/ftp_upload/50977/50977fig4highres.jpg" width="500" /> 
Figure 4. Resultant joint moments about a transverse axis (a.k.a, mediolateral axis) through the ankle, knee, and hip. Data were averaged across subjects for presentation. The stance phase begins at 0% of the gait cycle with foot contact and ends at approximately 60% of the gait cycle with toe-off. Swing continues until the next foot contact of the same leg at 100% of the gait cycle.
<img alt="Table 2" fo:content-width="6in" src="/files/ftp_upload/50977/50977table2.jpg" width="600" /> 
Table 2. Peak resultant joint reaction forces and moments averaged across subjects and statistical comparisons between the two inertial models for the prosthetic side's joint kinetics. Notes: Mean data are presented as mean(SD). % Gait Cycle column represents the average percentage across subjects where the peak value occurred for that variable. p&#60;.05 considered significant.

Watch this Scientific Journal Video about Oscillation and Reaction Board Techniques for Estimating Inertial Properties of a Below-knee Prosthesis at JoVE.com

Oscillation and Reaction Board Techniques for Estimating Inertial Properties of a Below-knee Prosthesis

Body segmental inertial properties are required for inverse dynamics modeling. Using an oscillation and reaction board technique, inertial properties of below-knee prostheses were measured. Using direct measures of prosthesis inertia in the inverse dynamics model of the prosthetic leg resulted in lower magnitudes of resultant joint forces and moments.

The purpose of this study was two-fold: 1) demonstrate a technique that can be used to directly estimate the inertial properties of a below-knee ...

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16.6K vistas.  University of Northern Colorado.  Se requieren segmentarias del cuerpo inercial para el modelado de la dinámica inversa. Usando una técnica de oscilación y tablero de reacción, propiedades inerciales de prótesis debajo de la rodilla se midieron. El uso de medidas directas de inercia prótesis en el modelo de la dinámica inversa de la pierna protésica resultó en magnitudes más bajas de las fuerzas y momentos conjuntas resultantes. 