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JPO Journal of Prosthetics & Orthotics:
doi: 10.1097/JPO.0b013e31826f66f0
Original Research Article

Use of a Load Cell and Force-Moment Analysis to Examine Transtibial Prosthesis Foot Rollover Kinetics for Anterior-Posterior Alignment Perturbations

Neumann, Edward S. PhD, CP, PE, FAAOP; Brink, Justin MSE, EI; Yalamanchili, Kartheek MSE, EI; Lee, Joon S. PhD

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Author Information

EDWARD S. NEUMANN, PHD, CP, PE, FAAOP, is affiliated with the Department of Civil and Environmental Engineering University of Nevada, Las Vegas.

JUSTIN BRINK, MSE, EI is affiliated with American Bio Engineers, Las Vegas, Nevada.

KARTHEEK YALAMANCHILI, MSE, EI is affiliated with Detroit Engineered Products, Troy, Michigan.

JOON S. LEE, PhD is affiliated with the Department of Mechanical Engineering, University of Nevada, Las Vegas.

Disclosure: The authors declare no conflict of interest.

Funding for this article was provided by the US Army Medical Research and Materiel Command (grant W81XWH-07-2-0084).

Correspondence to: Edward S. Neumann, PhD, CP, PE, FAAOP, Department of Civil and Environmental Engineering University of Nevada, Las Vegas, Box 4015, 4505 S Maryland Parkway, Las Vegas, NV 89154-4015; e-mail:

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ABSTRACT: Using four transtibial K4-level amputees as convenience subjects and six prosthetic feet, a load cell attached rigidly between the socket and pylon was used to measure loading effects on the residual limb that resulted when the prosthetic foot was perturbed 5 mm in an anterior-posterior direction from an initial alignment. By examining the relationship between normalized sagittal plane resultant forces and moments using force-moment analysis, the kinetic rollover characteristics of the feet and alignments were analyzed and compared. Additional variables examined included the angle of the line of action of the resultant force with respect to the pylon, and the distance from the load cell at which the line of action of the resultant force crossed the heel-to-toe axis of the load cell. Comparisons of the effects of the perturbations across subjects and feet revealed similar loading patterns within subjects for perturbations of the foot but noticeably different patterns across subjects and across different feet used by the same subject. For self-selected comfortable speed level walking, each subject exhibited differences in the magnitudes of the first and second peaks of the resultant forces and moments, but not all were statistically significant. Judgments of acceptable versus unacceptable alignments were not always matched by statistically significant differences.

The goal of this research was to develop and apply innovative concepts for using data obtained from a load cell to examine the effects of alignment perturbation on foot rollover for transtibial amputees. Load cells are now available for use in orthotics and prosthetics. Compared with conventional motion capture and force plate measurement, they are relatively inexpensive and easy to set up and use in clinical settings. A load cell attached rigidly between the pylon and socket will measure the forces and moments generated at the foot that impact the residual limb and can be used to examine the biomechanical response of individual amputees to feet of different designs in a variety of environments outside of the gait laboratory.1 Unlike conventional motion capture methods and the use of inverse dynamics to estimate kinetic parameters, the load cell requires no assumptions about the location of the ankle joint and no reflective markers need to be placed. The location of the center of rotation of the ankle joint on prosthetic feet is unknown and could move as the foot flexes.2 The load cell directly measures moments and forces at the level of the socket that methods of inverse dynamics can only estimate and does not require making assumptions about centers of joint rotation and the length of the respective moment arms. Because of this, there is less opportunity for error to creep into estimates of the forces and moments at the base of the socket, which may be an important location for modeling and understanding the impacts of loading on the residual limb.

A recent state-of-the-science review of research on transtibial alignment revealed that a comprehensive theory on the biomechanics of acceptable alignment has yet to emerge.3 Although many biomechanics variables have been examined in studies that perturbed specific foot alignment parameters, scientific understanding of what the amputee is seeking is still weak. The effects of perturbation on rollover kinetics have not been examined previously using force-moment plots that depict the interdependency of the variables. The research question was “can the data obtained from load cells and force-moment plots improve understanding of the effects of alignment on the kinetics of foot rollover?” In this study, anterior-posterior movement of the foot was selected as the alignment perturbation because it involves kinetics in the sagittal plane, which is the plane of most importance to forward progression, and perturbations can be measured and controlled easily in an experimental setting. In a departure from many earlier studies, this study includes 1) an examination of forces and moments produced by the foot that impact the residual limb during stance in a frame of reference attached to the prosthesis and residual limb; 2) the development of an innovative method for simultaneously examining the forces and moments by means of force-moment plots that allow rollover kinetics to be examined; 3) perturbations of small magnitude (±5 mm), which is less than that in many previous studies and close to the magnitude that a clinician might use in adjusting an alignment in to make it acceptable; and 4) the measurement of an amputee’s perception of alignment acceptability using a standard question format.

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A load cell attached rigidly between the pylon and socket of a transtibial prosthesis measures forces and moments with respect to three mutually orthogonal axes, X, Y, and Z, as shown in Figure 1. The axes are fixed with respect to the load cell and move with it as the prosthesis moves during gait. Thus, the load cell measures forces and moments as they would occur at the base of the socket and be perceived by the amputee on the residual limb rather than by a stationary observer with a fixed frame of orientation corresponding to the floor and walls of a gait laboratory. As will be demonstrated later, this can be advantageous for examining foot rollover and the biomechanical effects of alignment perturbation, although it is novel and departs from the conventions of a standard gait analysis.

Figure 1
Figure 1
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The forces can be described by vectors as Fxpos and Fxneg directed along the longitudinal axis of the foot, Fypos and Fyneg directed to the left of the foot, and Fzpoz and Fzneg directed parallel to the pylon. The notations x, y, and z denote the axis along which the X, Y, and Z components of the forces are measured with pos, indicating a force directed away from the origin of the axis system at the center of the load cell, and neg, indicating a force directed toward the origin. The resultants of the forces in each of the three anatomic planes can be computed by the Pythagorean Theorem as follows: sagittal plane FRS = (Fx2 + Fz2)1/2, frontal plane FRF = (Fy2 + Fz2)1/2, and transverse plane FRT = (Fy2 + Fx2)1/2. The moments, M, are the cross-product of the resultant forces in the sagittal, frontal, and transverse planes and their respective moment arms measured from the center of the load cell as follows: My = rS × FRS, Mx = rF × FRF, and Mz = rT × FRT. The moment arm r is perpendicular to the line of action of the resultant force. Moments are expressed as vectors measured along an axis perpendicular to the plane, defined by the resultant and moment arm, and can be represented by Mxpos and Mxneg for moments in the frontal plane, by Mypos and Myneg for moments in the sagittal plane, and by Mzpos and Mzneg for moments in the transverse plane. During stance, a moment is continuously created by the ground reaction force as it moves from an initial point of contact at the heel of the prosthetic foot during the beginning of loading response to a terminal point of contact at the toe after propulsion (Figure 2). Knowing the two coplanar forces and the moment they produce, the length of the respective moment arm at the load cell and the angle of the line of action of the resultant force can be calculated easily, which in turn makes it possible to examine four kinetic rollover variables as stance progresses: resultant force, moment, the length of the moment arm, and the angle of the line of action of the resultant force with respect to the pylon. These four variables are relatively easy to visualize, interpret, and relate to foot rollover. The transformations are described below and illustrated in Figure 2.

Figure 2
Figure 2
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For feet having no articulated ankle mechanism, the magnitude of the resultant force measured by the load cell will be very close in magnitude to the ground reaction force, and the line of action of the resultant force measured by the load cell will be very close to the line of action of the ground reaction force. Theory suggests that because of the linear and rotational acceleration and deceleration of the prosthesis during stance, the force and moment measured by the load cell will be slightly greater than the ground reaction force and the static moment it produces.4 However, nearly all of the force and moment occurring at the load cell and transmitted to the socket will comprise the ground reaction force and the moment it produces at the foot, which is transmitted through the foot to the pylon. As the ground reaction force moves from the heel toward the toe, it creates a moment at the base of the socket that changes from positive to negative. The forces and moments at the base of the socket are then distributed as pressures on the residual limb within the socket. At some point during stance, the resultant force will pass very close to or through the load cell, and at this time, the length of the moment arm will be at a minimum and produce either a very small or zero moment.

The equations for calculating the resultant force and the length of the moment arm from the load cell in a given plane using load cell measurements have been presented above. The equations for calculating the angle of the line of action of the resultant force with respect to the pylon in the sagittal and frontal planes from load cell data are θS = arctan (Fx/Fz) and θF = arctan (Fy/Fz), respectively. The equations for calculating the point at which the line of action of the resultant force passes through the X and Y axes of the load cell are X-ema = (My/FRS)/cos(θS) and Y-ema = (Mx/FRF)/cos(θF), respectively, where “ema” stands for “effective moment arm” to distinguish it from the true moment arm from the center of the load cell, which will be perpendicular to the line of action. In principle, given the angle of a line of action and the point at which it intersects the load cell axis, ema, the line of action can be projected to the prosthetic foot to give an indication of where on the foot the resultant is in contact with the ground and toward the knee to determine how close it passes to the center of the knee joint. The additional data needed to do this include the distances parallel to the pylon from the load cell axis to the bottom of the foot and to the knee joint. The relationships shown in Figure 2 imply that as the pylon becomes longer and the load cell further from the ground, which reflects a shorter residual limb and socket, the line of action will tend to pass closer to the load cell, which may result in a shorter moment arm and, thus, a moment of smaller magnitude, all other things held constant.

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A convenience sample of four unilateral transtibial amputee subjects was recruited (S1, S2, S3, and S4). Three subjects supplied spare sockets and the fourth subject used his/her everyday socket (Table 1). Inclusion criteria included functioning at a K3 or K4 level; ability to undertake walking without a loss of balance or an unsteady gait, which might imply a proneness to falling; and good socket fit. Using preparatory prostheses or having less than 1 year of experience, residual limb infections, open sores, and pain were grounds for exclusion. All subjects read and signed a letter of informed consent describing the protocol, which had been approved by the institutional review boards of the US Army Medical Research and Materiel Command and the University of Nevada, Las Vegas.

Table 1
Table 1
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A commercially produced load cell featuring digital output was used to measure forces and moments at the base of the socket (Model 45E15A4 1000N125; JR3, Woodlands, CA, USA).5–14 The calibration and decoupling matrix were incorporated by JR3 into the electronics, and offset and scaling factors were incorporated into the data processing software. Reported error was +0.25% of the measured range, and laboratory testing found the resultant force to be within 2% of the values reported by a forceplate (Kistler 9281C) using a simulated gait. Placed in a backpack worn by the subjects were a JR3 sensor interface board, a PC104/Plus single board computer (WindSystems model PPM-GX-ST) onto which Windows-embedded XP (Microsoft) was installed, battery packs, a power module (14.8 V, 4400 mAh), and a wireless network adaptor (range, 46 m indoors and 92 m outdoors). The masses of the load cell and backpack were 0.794 and 2.27 kg, respectively. The data from the load cell were transmitted to a laptop using the wireless components and were recorded. Data were processed to have an orientation that directed forces and moments toward the residual limb rather than toward the interior walls of the socket. The load cell was machined by the manufacturer with four threaded bolt holes in the standard pattern so that prosthetic adaptors could be attached directly to it. Data capture was at 100 Hz, the greatest stable rate for the load cell.

A Spectrum Alignment System (Hosmer, Campbell, CA, USA), which produced 1 mm of anterior-posterior movement of the foot with each revolution of an adjusting screw, was bolted to the distal face of the load cell. The pylon, which was inserted into a sleeve on the alignment system, was perpendicular to the X and Y axes of the load cell and parallel to the Z axis. A standard female adaptor was bolted to the anterior face of the load cell and the socket attached to it (Figure 1).

Subject 1 provided a TruStep foot (College Park Industries, Fraser, MI, USA) that the subject had used previously but was now keeping as a spare foot. Three new SACH feet of identical design (Ohio Willow Wood, Mt Sterling, OH, USA) were obtained for S2, S3, and S4. Subject 3 reported having no previous experience with a SACH foot, and S2 reported very limited experience. Subject 4 provided, in addition, two energy storage and return feet supplied by the manufacturer, the PerfectStride and BioStride (BioQuest, Bakersfield, CA, USA), which allowed comparisons among three feet worn by the same subject. Subject 4 had previous adaptation experience with the SACH and PerfectStride feet, but the BioStride was a new design and experience with it was less. Subject 4 requested a firm heel plug in his SACH foot; the other two subjects were provided medium firmness heel plugs. The variety of foot designs and levels of experience intentionally added a potential source of variation in the data and facilitated examination of load cell data under a variety of conditions similar to what might be encountered in clinical practice.

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The protocol called for a certified prosthetist to replace each subject’s original pylon with a pylon shortened to allow the load cell and the Spectrum Alignment System to be attached and to produce an alignment that matched the original alignment as closely as possible. After the prosthesis was donned, subjects were queried to determine if the alignment was acceptable, and adjustments were made, if necessary. Subjects were allowed to walk on the prosthesis for approximately 5 minutes to adapt to the foot and initial alignment. Each subject was then asked to balance on the prosthetic limb and lift the sound limb from the floor so that the weight of the subject supported by the load cell during single limb support on the prosthetic side could be obtained; this recorded force was used to normalize the data for each subject. Each subject was instructed to take approximately 15 steps on the prosthetic side at a self-selected comfortable walking speed down a long level hallway, which would allow several steps at the beginning and end of the trial that were not representative of walking at a steady velocity to be discarded from analysis. After the initial walking trial (0 mm of perturbation) and without doffing the prosthesis, the foot was moved anterior 5 mm (+5) and the walking trial was repeated, and then the foot was moved posterior 5 mm (−5) and the walking trial was repeated. Subjects were blinded to the initial alignment as well as to direction of movement for each perturbation. Perturbations were carried out with subjects seated so that they could not see the direction of the adjustment, and several false perturbations were made before each experimental perturbation was set for a walking trial. For the initial alignment and after each perturbation, subjects were handed a card that asked “Does this alignment feel like it would be acceptable for you to use?” and were given the response choices of “yes,” “no,” or “I don’t know.”

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To help meet the goal of the research, a graphic user interface (GUI) was developed to break down the stream of digital data from the load cell into 50 consecutive intervals of equal duration during stance for each step on the prosthetic side. Each interval thus represented 2% of stance duration for a step. The GUI was based on MATLAB and processed the three forces and three moments for export in an Excel-compatible format. The first 10 consecutive steps that were similar with respect to the appearance of the Fzpos data were selected for processing and analysis, and load cell data were exported from the GUI as six 50 × 10 matrices (fifty 2% intervals × 10 steps), with each cell of the matrix reporting the mean of the load cell data for the 2% interval and step. Excel was then used to analyze the data and prepare the graphs depicting the relationships among the variables of interest.

Because the perturbation involved an anterior-posterior translation of the prosthetic foot, analysis was limited to sagittal plane Fz and Fx forces and My moment about the Y axis. To normalize the data, forces recorded by the load cell were divided by the weight of the subject proximal to the load cell in N to represent force as a percentage of body weight and moments were divided by the mass of the subject in kilograms to represent moment as Nm/kg of body mass. The normalized sagittal plane resultant force FRS and moment My = (My2)1/2 were computed for successive 2% intervals of each step’s stance phase. Taking the resultant of My changed negative load cell values from mid through late stance to positive values and facilitated the interpretation of rollover characteristics on the plots. Means were computed for the 10 steps that were selected for analysis for each alignment and plots were prepared of the mean normalized resultant force versus mean normalized resultant moment as stance progressed from heel contact to toe-off. These plots permitted good visual depictions of rollover kinetics with respect to force and moment relationships and facilitated visual examination of changes in moment arm lengths because the slope of a line connecting the origin of a plot to a point on the normalized force-moment curve (normalized My/normalized FRS) was proportional to the length of the moment arm at the load cell.

The angle θS and effective moment arm X-ema also were computed for each 2% interval. Values of X-ema were normalized to the length of the foot to indicate proportions of foot length anterior and posterior to the load cell. Plots were prepared to examine the relationship between the mean resultant force and the mean of the angle of the line of action. The force-moment plots and force-angle plots provided a way of visualizing the relationships among the resultant force, moment, moment arm, and line of action during stance progression. Results were compared between the initial alignment and adjacent +5 mm and −5 mm perturbations within subjects during the first and second peaks of the resultant force using paired two-tailed t-tests with unequal variances for n = 10 steps and p < 0.05.

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Figure 3 plots the resultant normalized force versus normalized resultant moment during stance. Key portions of the curve for examining rollover include the region in the vicinity of the first force peak and leading up to it, the region between the first and second force peaks, and the region in the vicinity of the second force peak and leading away from it. These indicate the response of the foot during heel contact and rollover to foot-flat, during foot-flat, and during forefoot rollover and toe-off, respectively. The distance between each pair of the small dots represents 2% of stance, and the curves indicate how the resultant forces and moments change together during stance. The timing of any event can be determined from the processed matrices computed by the GUI. Because there are 50 intervals, the percentage of stance associated with any interval can be computed as twice the index of the GUI interval minus 1. For example, an event that occurs during the 12th of the 50 GUI intervals occurs during 2 × 12 − 1 = 23% of stance.

Figure 3
Figure 3
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The three curves for each subject indicate the relationships between resultant force and moment for the initial alignment and each perturbation. Table 2 reports the values of the first and second peaks of the resultant force and the corresponding moments along with the percentage of stance during which the peaks occurred. Table 2 also reports the interval during stance when the minimum moment occurred after heel loading. Figure 4 plots the angle of the line of action, θS, versus the resultant force FRS. Table 3 presents the values of θS, and X-ema at the first and second peaks of the resultant force along with the span of the angles and moment arms between the peaks and indicates statistically significant differences due to perturbation.

Table 2
Table 2
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Figure 4
Figure 4
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Table 3
Table 3
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In the Figure 3 plots, heel contact occurs on the far left end of the bottom leg of each triangle. Stance progresses to the right toward the first peak of the resultant force, in the vicinity of which the moment begins to change rapidly. Moment then increases toward the second peak of the resultant force as the line of action of FRS progresses toward the toe. This is represented by the vertical portion of the curve. Between the first and second force peaks, the resultant force decreases and a trough forms in the curve; a similar trough occurs in a ground reaction force curve. After the second peak of the resultant force, stance progresses toward the left along the top leg of the triangle and both force and moment decrease as toe-off occurs. The magnitude of the true moment arm at any point on the curve can be approximated by constructing and inspecting a straight line that connects the origin of the graph with the point. The slope of the line represents normalized moment divided by normalized force. If two points are being compared, a general principle that can be used is that the steeper the slope of the line, the greater the length of the true moment arm at the load cell. These lines can be visualized easily on the plots without actually having to construct them; a straightedge can be used to make comparisons. Based on the relative angles of constructed lines within the force-moment plots, it can be discerned that the length of the heel moment arm will be greatest near the beginning of the curve at heel contact and the length of the toe moment arm will be greatest near the end of the curve at toe-off.

If data used for the plots were not normalized and the plots were expressed in Newtons versus Newton-meters, then the slope of the constructed line would provide the true moment arm. The slopes of the lines constructed on the normalized curves differ from those of the nonnormalized curves by a constant proportion. By using the trigonometric relationships presented earlier, the effective moment arm can be calculated if the true moment arm and the slope of the line of action are known. Both can be computed from load cell data for each interval during stance.

The appearance of the curve near the first force peak indicates the rollover behavior of the foot with respect to heel loading and the transition to foot-flat. The sagittal plane force-moment curve always approaches or touches the force axis when the line of action of the force passes through the center of the load cell and the moment approaches or becomes zero. At this instant, the true moment arm is zero. This occurs near the first peak after heel contact. The appearance of the curve near this point can be examined to determine whether the first peak of the resultant force occurs before, during, or subsequent to the moment arm of zero length. When the shape of the curve near the first force peak forms a closed loop, it indicates that the resultant force begins to decrease from its first peak before the line of action reaches the center of the load cell as it moves anterior from the heel. The resultant force continues to decrease slightly as the line of action passes through the center of the load cell and moves toward the toe. If the loop is open, it indicates that the moment becomes zero before the first peak occurs, and the moment arm associated with the first peak will be anterior to the load cell.

When the line of action passes through the center of the load cell with a negative slope, which was found to be the case for most feet and subjects, it means that the line of action is directed toward the posterior of the pylon at the level of the load cell. This implies that if the line were extended to the bottom of the foot, it would contact the ground on the anterior side of the pylon midpoint and toward the toe rather than on the posterior side of the pylon and toward the heel.

After the first peak force, the moment then increases as the line of action moves toward the toe and the second peak force occurs. Along with this, the length of the moment arm at the load cell increases, as shown by the slopes of the lines connecting the origin to the points; they increase in magnitude. However, the resultant force usually continues to decease until it reaches a minimum between the first and second peaks. The shape of the curve between the two force peaks reveals the rollover kinetics of midstance and forefoot loading. If points of the curve in this region appear to lie on a single straight line that has been constructed to the origin, then it suggests little or no change in the length of the moment arm, which could be interpreted as a dead spot in the foot. Alternatively, if the curve moves between the two force peaks with little decrease in the magnitude of the resultant force, or if the curve has an unusual shape, it suggests that the kinetic rollover behavior around the midpoint of the foot may be atypical. After the second peak force, the curves exhibit a nearly linear shape and slope toward the origin of the plot as the resultant force decreases until toe-off occurs. The relative lengths of the moment arms change by only a small amount.

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Subjects 1 and 2 judged only one of the three alignments to be acceptable, S3 judged two alignments to be acceptable, and S4 judged all alignments acceptable for all feet, with the exception of the +5 mm perturbation for the PerfectStride, which was reported as uncertain.

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As shown in Table 2, for all subjects except S3, the line of action of the resultant force passed through the load cell (moment approached zero) after the first peak of resultant force, indicating that first peak force loading occurred when the moment arm was over the heel and was short in length. The intervals when the moment reached a minimum value are shown in Table 3. For S2, the curves suggest that the first peak may have occurred nearly simultaneous with the minimum moment, when the line of action of the resultant passed through the load cell. In contrast, the first peak force for S3 occurred after the line of action of the resultant force had passed through the load cell and the moment arm was toward the forefoot. Judging from the slopes of the lines connecting the origin to successive points on the portion of the curve before the force minimum between the two peaks, the magnitude of the resultant force did not change greatly as the length of the moment arm progressed rapidly further out toward the force minimum, suggesting that the peaking was experienced over a relatively long portion of the forefoot lever while the length of the lever arm increased rapidly. The trough between the peaks then occurred, after which there was not much further progression of the moment arm toward the toe, although both force and moment increased nearly linearly. The points all appeared to fall on or very close to a line connecting the curve with the origin. This suggested a possible dead spot in the foot. The timing of the first resultant force peak for S3 also was delayed and occurred between 31% and 33% of stance compared with the other subjects, whose first peaks occurred between 21% and 27% of stance (Table 2). The plots for S3 indicate a rollover pattern very dissimilar to the plots for the other subjects and feet. The angle versus force curves in Figure 4 provide further evidence of the atypical rollover behavior of S3’s SACH foot and will be discussed below.

These characteristics of the curves for S3 may indicate premature foot-flat and a dead spot during rollover, a common complaint for feet having soft heels and short forefoot lever arms such as the SACH, and may be the reason why S4 requested a firm heel plug-in his SACH foot. The firm plug may have been the reason why the first peak for S4 occurred with a moment arm toward the heel and the first peak force occurred earlier at 25% to 27% of stance before the resultant force passed through the load cell. S4’s response to the SACH foot also did not exhibit a dead spot on the forefoot; the length of the moment arm could be seen to increase as both the force and moment approached the second peak force. The minimum moment for S4 occurred relatively late, at 35% to 39% of stance. For S2, it can be noted from the curves and tabled values for this subject that the first peak force occurred close to the interval of zero moment, giving the curves a more flattened, pointed appearance near the first peak of force. The portion of the curves between the two force peaks also appeared more typical of S1 and S4. Subject 2 may have attempted to control the location of the first peak through compensatory gait because after the experiment, the subject commented that he would not want to walk very far on the foot—it took too much effort.

For S1’s TruStep and S4’s BioStride feet, the curves exhibited a smooth rollover, with the first peak force occurring before the minimum moment; a concave and relatively symmetric appearance between the first and second peaks; and the length of the moment arms increasing throughout stance with no apparent dead spots. For S4’s BioStride foot, the magnitudes of the first and second peak forces were lower than for the PerfectStride, and the transition between the two peaks did not exhibit a concave appearance, suggesting that the variation in loading of the residual limb due to variation in the resultant force may have been less and fairly constant.

For all subjects and all perturbations, the peak resultant moment was never greater than it was at the second peak force. Once the second peak force had been achieved, both force and moment decreased together nearly linearly, and the plots suggest that the moment arms did not continue to move outward much toward the toe. This may be a hallmark of a passive foot, which is incapable of generating ankle force on its own during normal gait—propulsive force cannot be increased as the moment arm length is held constant, nor can the moment arm length be increased while peak propulsive force is developed and held.

The plots indicated that the force-moment relationships appeared highly similar within subjects for a given foot when the anterior-posterior position of the foot was shifted. Small changes in peak forces and moments could be seen, and some differences were statistically significant, but the curves had similar shapes. With respect to comparison of curve shapes between acceptable and unacceptable alignments across subjects, there was not a sufficiently large range of alignment perturbations to undertake a group statistical analysis. Larger numbers of acceptable and unacceptable alignments would be needed for each subject to establish the range of acceptable alignments. However, a visual comparison of the three curves within the subjects who found at least one alignment unacceptable or questionable suggests that differences in force-moment relationships may exist. Statistically significant differences are presented in Tables 2 and 3.

For most subjects, with the foot shifted posterior, moment tended to increase during heel loading and decrease as toe-off approached for a given level of resultant force. Among the acceptable alignments for S1 and S2 and all feet for S4, the heel moment arm length as measured at the load cell was shifted more posterior with a posterior shifting of the foot, as might be expected. With the foot shifted anterior, the opposite tended to occur. The appearance of the curves was noticeably different across subjects, implying that each subject exhibited a unique loading pattern. In particular, the appearance of the curves for the SACH feet varied considerably among S2, S3, and S4. The patterns also appeared different across feet for S4, implying potentially different loading patterns when feet of different design are used by the same individual.

Three subjects (S1, S2, and S3) judged as unacceptable the alignment that produced the highest first resultant force peak (Table 2). The same three subjects judged as acceptable the alignment producing the maximum second resultant force peak. In contrast, S4, who requested a firm heel plug in his SACH foot, judged the alignment producing the highest first resultant force peak acceptable for all three feet, and the magnitude of the first peak was higher than that of the second peak. Thus, S1, S2, and S3 exhibited consistency, but the firm heel plug requested by S4 and the lack of an unacceptable alignment in the range of experimental perturbations for S4 make it difficult to generalize.

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A consistency in the relationship between resultant force and line of action was found within subjects as feet were perturbed, but a large variation across subjects was observed, and there was variation across feet for S4 (Figure 4). As stance progressed, the angle θS always increased toward the posterior of the pylon, and simultaneous with this, X-ema moved anterior toward the toe, indicating that the point of contact of the foot with the ground also was moving toward the toe during rollover. The exact position of the point of contact and the respective point at which the keel of the foot was being loaded could be determined by projecting the line of action to the foot. This was outside the scope of the study.

It was observed that the angles of the line of action were low for the SACH feet worn by S2 and S3 compared with the TruStep worn by S1, the SACH foot with the firm heel plug worn by S4, and the PerfectStride and BioStride feet worn by S4. The lower the value of the angle is, the more closely the line of action paralleled the pylon, which could influence joint moments at the knee as well as the loading pattern transmitted to the socket. The span between the angles of the first and second force peaks of the initial alignment, ΔθS°, was largest for S1 and S4, smaller for S2, and smallest for S3. A small angle for the line of action angle together with a low ΔθS° would be consistent with a small range of variation in the length of the moment arm during rollover, which is supported by the ΔX-ema values for the SACH feet used by S2 and S3, as shown in Table 3.

Statistically significant changes in θS occurred for 67% of the perturbations at the first peak of resultant force and for 42% of the perturbations at the second peak. However, the difference in the span of the angle of the line of action between the first and second peaks, span ΔθS°, was significantly different for only 25% of the perturbations, suggesting that the subjects tended to compensate for anterior-posterior foot perturbation in a manner that maintained a fairly constant difference in line of action angle between force peaks. This may have implications for joint range of motion during stance and the magnitude of the moment generated at the knee and hip. The point at which the line of action crossed the X axis during the force peaks, X-ema, also varied widely between subjects for the initial alignment (Table 3). Statistically significant differences in X-ema were found for 17% of the perturbations at the first peak and 58% at the second peak; significant changes in the span ΔX-ema were found for 42% of the perturbations. Comparing 42% to the lower percentage of significant differences for span ΔθS, 25%, suggests that subjects may have tended to compensate for perturbation in a way that produced changes in the proportion of the keel length used rather than the angle of the line of action with respect to the pylon, which also may have implications for joint range of motion and moment at the knee and hip during stance.

As mentioned previously, S2 and S3 had the smallest span of angles between the first and second force peaks (Table 3), but this may have been caused by the small amount of time given them to adapt to the SACH foot. Having previous experience using their prosthetic feet, S1 and S4 exhibited a larger span of angles. Subject 3 also exhibited the lowest ΔX-ema, which was only 16% to 21% of the length of the SACH foot used. In contrast, S1 and S4 exhibited spans that were 40% to 44% and 28% to 32% of foot length, respectively, using energy-storage-and-release feet that the subjects had experience with before data collection.

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The data from the experiment and the methods developed demonstrate that the load cell can provide measurement of time-wise changes in rollover kinetics during stance. The forces and moments measured by the load cell at the distal end of the socket will impact the residual limb and may have consequences at the knee and hip. Variables that can be examined with load cell measurements include the magnitude of the resultant force, the magnitude of the moment, the length of the moment arm that produces the moment, and the angle of the line of action of the resultant force with respect to the pylon. The timing associated with loading events also can be determined. With these measurements, subjects, feet, and alignments can be described quantitatively, contrasted, and compared in novel ways.

A number of studies have examined the effects for anterior-posterior perturbation of the foot on transtibial amputees, but the scientific and clinical value of many of the studies has been limited by sample sizes of only one or two subjects, failure to ask subjects standard questions about the acceptability of an alignment, or use of large linear perturbations atypical of the smaller magnitude perturbations that most clinicians make to achieve an acceptable alignment.15–26 Some studies lacked tests of statistical significance and made no mention of blinding. The variability among loading patterns for the four subjects and six feet in the current study indicates that scientific generalizations cannot be made from studies that use only one or two subjects and a single type of foot. Data from the load cell and GUI used 10 consecutive steps per walking trial, and more steps could be processed to produce multiple matrices, which could then be concatenated before the use of statistical tests. The use of standard questions and blinding can be implemented easily.

The state-of-the-science review of published studies concluded that amputees find a range of alignments acceptable, but the range varies across individuals.3 The studies most directly comparable with the current study were those that included more than three subjects and attempted to determine the range of anterior-posterior positions of the foot that amputees found acceptable.17,19,20 The ranges found in these studies were, respectively, −5 to + 30 mm for 7 subjects, −15 to + 35 mm for 6 subjects, and −6.5 to +6.5 mm for 10 subjects. In the current study, the break point between an acceptable and unacceptable alignment was found for three of the four subjects, with the fourth subject finding one of the alignments questionable for one of the feet used. For S2 only, the range of alignments reported as acceptable was spanned in the experiment and appeared to be less than 5 mm on either side of the initial alignment. However, determining the range of acceptable alignments was not a goal of the study. The finding that, after perturbations, the angles associated with the lines of action, θS, tended to change significantly was not in agreement with previous research based on three subjects, which found that the differences in the angles of the lines of action were not significantly different after perturbation.27

An interesting question for future research is whether amputee reporting of alignment acceptability could be probabilistic, with amputees judging some of the same alignments as acceptable, some as unacceptable, and some as questionable, depending on random factors that occur during gait as alignment is perceived subjectively by the amputee. For S3, each of the three alignments was repeated five times in random order with the subject blinded. The −5 mm perturbation was judged acceptable by S3 60% of the time and unacceptable 40% of the time; the initial alignment was judged acceptable 60% of the time and unacceptable 40% of the time; and the +5 mm perturbation was judged acceptable 20% of the time, unacceptable 60% of the time, and uncertain 20% of the time. Load cell measurements were not taken, making it impossible to compare the rollover kinetics of the same alignments. It also became apparent that the repetitive nature of the judgment task was producing mental fatigue, which could invalidate subjective measurement. However, given the step-to-step variability of gait combined with the very strong likelihood that the judgment task involves a stochastic process described by the Theory of Signal Detection, the hypothesis that acceptability judgments may be probabilistic in nature does not seem unreasonable.28

The kinematic theory of rollover shape provides additional insight into the results. Rollover shape theory uses geometrical relationships to hypothesize that an acceptable alignment results as long as a perturbation keeps the rollover shape of the foot similar to that of the anatomic foot and the perturbation moves the foot along the path of its rollover shape.15 Perturbation of the foot in an anterior and posterior direction, as done in this study, could move the foot out of the anatomic rollover shape envelope unless the subject is able to develop an appropriate compensatory gait or the flexion angle of the socket is changed. It can be speculated that S2 may have developed a compensatory gait strategy that overcame many of the rollover deficiencies of the SACH foot.

The current study produced kinetic data on rollover as well as geometric data, and results suggest that the kinetic variables obtained from the load cell could be linked to the kinematic variables of rollover shape to produce a comprehensive theory of alignment. As the effective moment arm and angle of the line of action changed with alignment perturbation, the moment also changed, and it is likely that both force and moment are related to the rollover shape of the foot and its alignment. A larger sample of subjects and careful experimental design would be needed to study any hypothesized relationships and draw strong scientific conclusions.

Paradigms that are used to teach alignment and the biomechanics of prosthetic gait to clinicians are not based on measurements of kinetic variables but make assumptions about the forces and moments that exist and their lines of action.29,30 Often, these assumptions are implicit in alignment paradigms. One reason for the absence of quantitative relationships is a lack of a verified theory to explain the link between gait kinetics and kinematics and the acceptability of an alignment.31

The results of this study tentatively suggest that future studies might examine the relationship between acceptability and the magnitudes of the first and second peaks of the resultant force and the associated moment. As the foot was moved anterior and posterior, tradeoffs between the magnitudes of the first and second peaks of the resultant force appeared. Anterior movement of the foot often decreased the first peak of the resultant force and modified the associated moment and increased the second peak of the resultant force and modified the associated moment. Posterior movement of the foot tended to have the opposite effect. This was not observed to occur universally across all subjects and feet, however. The only relationship that appeared most consistently across subjects and feet was between the magnitude of the first and second peaks of the resultant force and acceptability of the alignment.

Except for S4, who requested a firm heel plug, the alignment producing the greatest first peak was always judged unacceptable. For all subjects, the alignment producing the greatest second peak was always judged acceptable. Because the first peak is associated with weight transfer to the prosthetic side and the impact of heel loading along with the retarding of forward motion, it seems reasonable for amputees to seek an alignment that keeps the first peak low. Because the second peak is associated with propulsion and forward movement, it seems reasonable for amputees to seek an alignment that has a high second peak. Factors that could influence this generalization include the response characteristics of prosthetic feet, socket fit-residual limb pressure relationships, or joint physiology constraints. These may work alone or in combination to constrain the ability of the amputee to generate force using anatomic hip and knee joints on the amputated limb.

Tentatively, it could be speculated that an acceptable alignment may be one that allows the amputee to attain a desired walking speed using a preferred kinetic and geometric rollover pattern for a specific percentage of steps with an expenditure of energy and amount of perceived socket pressure that is below acceptability threshold levels for the amputee. The energy and pressure acceptability thresholds and specific percentage of steps will vary among amputees. An unacceptable alignment could be one that does not meet these objectives. Energy cost is a function of the compensatory joint movements and muscle strengths that are necessary to attain the desired speed and rollover pattern. Perceived socket pressure is a function of the magnitude of the rollover forces and moments, socket design, the specific region of the socket—such as the patella tendon or distal tibia—and residual limb characteristics related to pressure sensitivity. The force-moment plots and first and second peak resultant forces may be indicators of how well the alignment allows walking speed goals and the kinetics of the preferred rollover pattern to be achieved; higher second peaks of propulsive force and lower first peaks of braking force may be desirable as long as the timing of the peaks and other rollover characteristics of the foot satisfy the preferences of the amputee. There are two possible extensions of this speculative hypothesis. First, it is possible that in contrast to an unacceptable alignment, at an acceptable alignment, there may be lower pressures in some regions of the socket during early stance because of lower first peak forces and moments and higher pressures in other regions during late stance because of higher second peak forces and moments. This hypothesis is consistent with previous research that reported findings based on two or three subjects for whom intrasocket pressures exhibited either maximum or minimum values at acceptable alignments.24,32 Second, amputee preferences for the design characteristics of feet may be based on relationships similar to the ones hypothesized for the acceptability of alignment.

When comparing acceptable with unacceptable alignments, tests of significance of the load cell measurements sometimes indicated no significant differences, although trends were evident (Table 3). The Theory of Signal Detection may offer a theoretical basis for explaining why statistically significant differences might not appear even though amputees make judgments that imply that they can detect differences.28 When amputees accept an alignment that has the potential for producing any discomfort or tissue trauma or prevents them from achieving an efficient gait, the cost to them can be very high. Because of the high personal cost, the levels of confidence that amputees associate with acceptance or rejection of an alignment may be much less conservative than the probabilities used in science to test scientific hypotheses. It is possible that probabilities >0.05 better reflect an amputee’s judgment of alignment acceptability. Another possibility is that the effects of the forces and moments are amplified as they produce pressure on the residual limb. Very small changes in the forces and moments at the base of the socket could produce differences in pressure that are noticeable to the amputee.

An additional observation from study results is that when feet undergo mechanical testing to determine energy storage and release characteristics, if the results are going to be used to prescribe feet or assist with clinical decision making, then the mechanical loading patterns should match those of amputees. With amputees, the first peak resultant force does not occur at the posterior end of the heel, but close to the pylon or slightly anterior to it. The line of action may be sloped. The second peak resultant force may not be located at the most anterior end of the keel, but where the amputee is able to place it using a compensatory gait, and its line of action will be sloped toward the pylon. It should not be assumed that the amputee will fully use the length of heel or forefoot keel moment arms and produce the maximum energy storage and release of which the foot is capable for a given body mass. Because rollover patterns vary among amputees, a range of loading patterns may need to be examined when undertaking mechanical tests of feet to determine the effectiveness of designs that provide energy storage and release.

A literature review was conducted to determine the possible influence that the mass of the JR3 45E15A4 load cell could have on gait.33–42 The available evidence suggested that heavier masses or masses located more distally on the prosthesis could have an effect. Subjects did not report any perceived affects on their gait from the load cell. Load cells might be designed to weigh less and be smaller.

To produce load cell data having maximum use for scientific research, bench alignment would need to be carried out in a manner that ensures that the X, Y, and Z coordinates of the center of the load cell, patella tendon bar, and longitudinal axis of the foot are represented by a coordinate system having a horizontal surface parallel to the ground. This would require that, during bench alignment, the pylon remains vertical and parallel to the Z axis of the load cell when the heel of the foot is elevated by its heel height. The flexion angle and location of the tibia should be measured, rather than the angle of the geometric center of the socket, because the tibia is the relevant biomechanical axis for transmitting the forces and moments produced at the knee joint and resisting the forces and moments that are produced by the foot and transmitted to the socket during stance. During dynamic alignment, all angular socket adjustments should be carried out proximal to the load cell, and all anterior-posterior, medial-lateral, and rotational adjustments of the foot should be carried out distal to the load cell. Doing this would make it possible to project the line of action of the resultant force to both the knee and foot, which would facilitate evaluating consequences at the joints of the leg and the rollover response of the foot. The modular design of endoskeletal prosthesis components makes it tempting to avoid these principles during dynamic alignment, but if they are not followed, there will be a loss of the geometric controls that are necessary to project the line of action to the bottom of the foot or knee.

Earlier experimental research that was limited by the instrumentation available at the time showed a high correlation between the forces and moments occurring at the base of the socket and the pressures on the patellar tendon and gastrocnemius regions of the residual limb (R2 = 0.877 and 0.960, respectively).43 This raises a research question as to whether it may be possible to estimate pressures on the residual limb using the forces and moments measured by a load cell attached to the base of a socket.

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The load cell offers a relatively simple and inexpensive way for clinicians and scientists to conduct research on both clinical problems and research hypotheses concerning the rollover characteristics of feet and amputee preferences for alignments. Plotting two load cell variables simultaneously, such as normalized resultant force versus normalized resultant moment or normalized resultant force versus angle of the line of action, permits the examination of loading relationships that otherwise might not be detected. These methods could be used to examine questions related to foot design, prescriptions for feet, or alignment or to quantify the gait of an amputee and monitor changes in gait during rehabilitation. Load cells also might be used to conduct research on the relationships between the forces and moments occurring at the base of the socket and the intrasocket pressures experienced by the residual limb. Further research would be necessary to explore these questions, and research should be expanded to include amputees functioning at the K2 and K3 levels.

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KEY INDEXING TERMS: transtibial amputees; prosthetic foot rollover; alignment perturbation; load cell; force-moment analysis

© 2012 American Academy of Orthotists & Prosthetists


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