An accurate and comprehensive measurement of forces and moments developed in a prosthetic limb is essential to the design and assessment of any constituent component of prostheses for transfemoral amputees. These may include a foot, knee, socket, shock absorber, and the implant used for direct skeletal fixation of the artificial leg (osseointegrated implant). 1
An understanding of the load bearing on the socket is of particular relevance to most transfemoral amputees because the main pain and discomfort they experience are related to the interaction between the socket and the residual limb. 2–4 As mentioned by Czerniecki and Gitter, 4 “the functional characteristics of the prosthetic limb may influence the effects of the applied forces on the residual limb and therefore influence the amputees perception of comfort.” Conversely, the degree of control of movement of a prosthetic limb is dependent on the ability of the amputee to transmit the appropriate forces through the socket.
For a sound understanding of these forces and moments applied on the residual limb, it is essential that the loads measured in experimental conditions reflect those produced during the daily life of transfemoral amputees. This article aims to describe a method that can be used to achieve the measurement of the true load experienced by the socket and the knee of transfemoral amputees during everyday situations.
CALCULATION OF LOAD BEARING WITH INVERSE DYNAMICS EQUATIONS
In principle, inverse dynamics equations enable the forces and moments at any point on a limb to be calculated from ground reaction forces and tridimensional kinematic data. These equations in particular could be used to calculate the reaction forces and moments along the three axes of the leg located at the ankle joint, knee joint, and hip joint and also at the bottom of the prosthetic socket. 1,5 However, the forces and moments obtained with these equations might present a number of limitations in terms of validation and calculation.
Although the theoretical principles of the inverse dynamics equations are well established, the forces and moments obtained this way were only estimated because of their dependence on the accuracy of measurement of the inertial characteristics of the artificial limb, including the residuum. This is also caused by the accumulation of the errors at each joint, because the forces and moments obtained for a given joint (e.g., the knee joint) are used as input to calculate the forces and moments at the following joint (e.g., the hip joint). For instance, the errors on the forces and moments applied on the socket of a transfemoral amputee result from the accumulation of the errors of the forces and moments calculated at the point of contact of the foot on the ground, the ankle joint, and the knee joint, as well as on the accuracy of measuring the inertial characteristics of each component below the socket (foot, knee, pylons, etc.). One way to validate the forces and moments obtained using the inverse dynamics is to measure them directly and to compare both results. Unfortunately, this validation remains to be presented because of a lack of means to directly measure these forces and moments.
Furthermore, the inverse dynamic method requires a conventional gait laboratory equipped with force-plates and a synchronized tridimensional motion analysis system. In most cases, the forces and moments are calculated for a single step of level walking in a straight line. Additionally, gait might not be natural, because there is a tendency for the amputee to “target” the force-plates. 6 Therefore, the load calculated under these controlled conditions reflects only partially the true loading experienced by the prosthetic leg of transfemoral amputees during their daily living activities. It is expected that other daily activities difficult to assess in gait settings could be more challenging than walking for some transfemoral amputees. Furthermore, these activities might possibly produce larger forces and moments than walking.
MEASUREMENT OF LOAD BEARING WITH CUSTOM-DESIGNED TRANSDUCERS
A few groups have developed custom-designed transducers that could bring the measurement of the load experienced by the socket of transfemoral prostheses one step further. 7,8 For example, Nietert et al. 7 have equipped a pylon with strain gauges to measure directly the loads generated in hip units of amputees with hip disarticulation prostheses. This homemade transducer was mounted between the ankle-foot device and knee unit or between knee and hip units. The main purpose of the research was “to determine the size of the moments and forces appearing at hip and knee joints, required for the determination of the appropriate test load level(s)” for setting international quality standards. Consequently, they reported only the relationship between the maximal values of forces and moments and the weight of amputees during several walking conditions (e.g., walking up and down stairs, on the grass, over a grassy hill, on gravel, and fast walking). Only patients with hip disarticulation having either no residuum or a very short one allow sufficient space between the prosthetic hip unit and the knee mechanism to accommodate the length of the pylon and transducer. Unfortunately, given the length of the residual limb, similar pylons cannot be used with transfemoral amputees.
These groups clearly demonstrated that transducers could be particularly suitable to determining the true load bearing experienced by the socket and the knee of transfemoral amputees. The three components of force and moment could be measured directly without calculations, enabling a validation of results obtained with inverse dynamics equations. Also, the measurements could be conducted during many activities of daily living other than level walking in a straight line that could be more challenging for some transfemoral amputees (e.g., ascending and descending a slope and stairs). An unlimited number of steps of the prosthetic leg can be assessed providing a better assessment of the repeatability of transfemoral amputees’ locomotion. 9 In addition, the measure of the moment applied around the long axis of the socket is particularly relevant to the design of osseointegrated implants for transfemoral amputees, because this moment might be responsible for the problem of early loosening of the implant. 10,11,12
Unfortunately, custom-designed transducers could pose problems of calibration, reliability, and accuracy. In addition, discreet, reliable, and accurate commercial transducers are now widely available on the market at an affordable price.
USE OF COMMERCIAL TRANSDUCERS
Low-profile commercial transducers associated with wireless modems appeared particularly suitable to directly measure the loads applied on the socket of transfemoral amputees. 10,13 Reliable and accurate transducers are now widely available primarily for robotics and industrial applications. Suitable transducers must have a low profile to allow them to be mounted between the knee mechanism and the socket of transfemoral amputees. The force and the moment signals can be transmitted using a wireless modem and recorded remotely on a laptop, thus enabling the subject to perform activities freely without being tethered by a cable.
Previous studies have successfully used a commercial transducer to directly measure the forces and moments applied to the socket of transfemoral amputees during daily living activities. 10,13 To date, the method and the results of these studies have been reported only in abstract form. No published reports point to the use of such a transducer.
The objective of this study was to provide an extensive description of the direct measurement of the forces and moments applied to the socket of a transfemoral amputee during daily living activities. In particular, this article presents:
- The methods used to directly measure these forces and moments
- The means to measure the repeatability of the loading over a number of gait cycles
- Data representative of the range of activities that can be researched with this apparatus
- Examples of derived information that can be obtained from these data
One female transfemoral amputee participated in this study (age, 36 years; height, 1.60 m; mass, 62.65 kg; cause of amputation, osteosarcoma at age 19). The subject was selected because of her high functional level, because the distance to be walked and the length of time of initial testing might be significantly demanding. The length of her residuum of 22.5 cm corresponded to 48% of the length of her sound thigh. Sufficient space to mount the transducer below the socket and above the knee was obtained by dropping the prosthetic knee axis by 3 cm below the tibial plateau. The study received the Queensland University of Technology’s Human Research ethical approval to conduct this testing. The subject gave her informed consent before participating in this study.
The prosthesis used was composed of an ischial containment socket, the transducer, an Otto-Bock safety knee (Vienna, Austria), and a solid-ankle, cushion heel (SACH) foot (Figure 1). The socket used was specifically manufactured to replicate the internal geometry of the subject’s current socket and to incorporate an adapter to attach the transducer. This adaptor was custom-made in-house. No cosmetic foam cover was used. This prosthetic leg was set up and aligned by a qualified prosthetist (M.D.). The leg was worn for approximately 1 hour before the testing to ensure that the amputee was sufficiently accustomed to it and confident when walking on uneven surfaces.
The six-channel commercial transducer (Model 45E15A; JR3 Inc, Woodland, CA) was constructed from a solid billet of aluminum measuring 11.43 cm in diameter, 3.81 cm thick, and weighing less than 800 g. Its internal components consisted of strain gauges, amplifiers, and signal-conditioning circuitry. Data were processed using a calibration matrix to eliminate cross-talk. The three components of the forces and moments were measured with accuracy better than 1 N and 1 N/m, respectively. Each channel was sampled at 200 Hz.
The transducer was mounted to the socket using a custom-made spherical plate and to the knee using a pyramidal connector. The transducer was mounted in such a way that the vertical axis (z) of its coordinate system (T[O, x, y, z]) was aligned with the long axis of the socket and the residuum (Figure 1). The two other axes were mutually orthogonal. The anteroposterior (x) and mediolateral axes (y) of the transducer were aligned with those of the residuum thanks to a transform matrix applied afterward. Consequently, the coordinated system of the transducer was aligned with the local anatomical axes of the residuum.
The wireless modem (Ricochet Model 21062; Metricom Inc., Los Gatos, CA) used to transmit the data from the transducer to the nearby laptop was composed of a transmitter (11 × 5 × 2 cm) and a receiver (19 × 6 × 2 cm). The 200-g transmitter was connected to the transducer by a serial cable and was carried in a waist pack. The operating range outdoors was greater than 700 m.
The subject was asked to walk in straight line on a smooth level surface, to ascend and descend a slope and a set of stairs, and to walk around a circle. 10,13 The details of each activity are provided in Table 1. The choice of these activities was not guided by the limitation of the apparatus used, allowing assessment of an unlimited number and type of activities. The straight level walking was included as the baseline activity; other activities were chosen because they were considered more challenging yet frequently performed by amputees in their home or working environments.
The subject was instructed to perform each activity at her natural pace and as she would usually perform it during daily life. The subject occasionally used the handrail when ascending and descending the slope and the stairs. She also chose to take two stairs at a time when ascending (with her sound leg) and descending (with her prosthetic leg).
Although the apparatus used allowed recording of an unlimited number of trials and gait cycles, the subject was asked to repeat each activity six times. The subject was free to take a sufficient resting period between each trial and activity, if necessary, to avoid a fatigue effect.
The raw force and moment data generated by the transducer were preprocessed and analyzed as follows:
Step 1: Selection of Relevant Segment of Data to Analyze
As described in Figure 2, the first and the last strides recorded for each trial were discarded to avoid the initiation and termination of walking. This was done to ensure that the analysis included only the data obtained when the subject walked at a uniform pace. 6
Step 2: Determination of Gait Events
The curve of the vertical force was used to detect manually the heel contact and toe-off with a demonstrated accuracy of ± 0.01 seconds. This accuracy was determined in a preliminary study in which the detection of gait events using the method above was compared with force-plate data collected simultaneously.
Step 3: Averaging and Normalization
The forces and moments obtained for the six trials of an activity were collated in one group. Then, the forces and moments produced during each support phase and complete gait cycle of the prosthetic leg were subdivided into 100 equal increments to be time-normalized from 0 to 100%. This eliminated time variations among gait cycle (Figure 3) or support phases (Figures 4 and 5). The force and moment curves could then be plotted with the same time scale, as well as the averaging of these curves for each activity (Figure 4). The total number of support phases or gait cycles of the prosthetic leg averaged for each activity is provided in Table 1.
RESULTS AND DISCUSSION
An example of the three components of forces and moments obtained during level walking in a straight line has been presented in Figure 3.
Incidentally, it can be noticed that unexpected spikes occurred around the toe-off on the curve of the force applied on the anteroposterior axis. It is more likely that these spikes were actually caused by the unlocking mechanism of the safety knee, allowing the swing phase of the prosthetic leg. Similar spikes also occurred at the end of the swing phases for the three components of the forces and moments, particularly for the moment around the anteroposterior axis. These spikes were caused by the terminal impact of the knee when the shin section ended the swing phase and reached the full extension. These spikes, which, by occurring in the final part of the swing phase, proved the presence of impact, were not eliminated despite the efforts of the prosthetist. Furthermore, these results demonstrated the ability of the method proposed in the article to measure what a trained prosthetist cannot pickup during dynamic alignment. It can also be observed that the force applied on the long axis of the socket is actually slightly negative during the swing phase because of the traction created by the gravity acting on the mass of the prosthesis, located below the transducer when the prosthetic foot is off the floor.
ASSESSMENT OF REPEATABILITY
One aim of this article was to present the means to measure the repeatability of the forces and moments over a number of gait cycles. As an example, Figure 3 represents the superimposition of each component of force and moment over 62 gait cycles of the prosthetic leg during level walking in a straight line. The number of strides of the prosthetic leg that were measured for each activity is presented in Table 1.
The number of gait cycles provided for each activity reflected the functional outcome of the subject tested in the framework of the protocol measurement. These numbers were not impeded by the apparatus used because it could measure an unlimited number of steps.
RANGE OF ACTIVITIES
This article also aimed to present data relating to a range of activities that could be measured using this technique. Figures 4 and 5 represent the mean of each component of force and moment, respectively, for each activity during the support phase. For the sake of clarity, the standard deviations are not displayed, given the repeatability of the data illustrated in Figure 3.
The data indicate that for several activities, the magnitude of the forces and moments is greater for level walking either at a given time or over the duration of the support phase. For example, ascending a slope produced a larger moment around the y-axis than walking over the entire support phase. Also, walking around a circle produced a higher moment about the long axis of the socket than walking during the push-off phase of the support.
EXAMPLES OF DERIVATIVE INFORMATION
Various pieces of information can be derived from raw forces and moments presented above, focusing on comparison of patterns, specific values of forces and moments at a given time (minimum, maximum, and points of interest), impulse of the forces 14 and temporal variables (stride frequency, duration of the gait cycle, swing, support phases of the prosthetic leg). Only two pieces of this derived information will be presented here: the stride frequency and the impulse.
The stride frequency was chosen because it is one of the primary gait parameters clinicians assess. 15Table 1 provides the mean and standard deviations of the stride frequency of the prosthetic leg for each activity. The mean stride frequency during descending a slope was higher than straight level walking. All the other activities presented a slower mean stride frequency than straight level walking.
The impulse represented by the force-time integral corresponds to the quantity of forces applied on the socket. 14 This mechanical parameter was chosen because it informs the prosthetist of the actual overall usage of the prosthesis over the support phases, because the impulse takes into account not only the magnitude but also the duration of the load applied. Furthermore, the impulse provides crucial information to engineers concerned with the fatigue of the prosthetic component. Figure 6 provides the mean and standard deviation of the impulse of the forces along the three axes of the prosthetic leg during the support phases for each activity. The impulse on the three axes was similar or smaller than walking in a straight line for all of the activities except for walking around a circle on the mediolateral axis, as well as ascending a slope and stairs and walking around a circle on the long axis. Consequently, it could be concluded, for this subject, that descending a slope and stairs put an overall load on the residuum smaller than walking in straight line.
A new apparatus based on a commercial transducer and a wireless modem allowing the measurement of the forces and moments transmitted through the socket has been presented. An example of the raw results of these forces and moments as well as some of the information derived were provided for one transfemoral amputee to illustrate the capacities of this new apparatus.
This article demonstrated that the proposed apparatus was an improvement on the current method of using a gait laboratory 1,5 to assess the load applied on the residuum and the knee of transfemoral amputees. The superiority of this technique rested on the combination of the direct measurement of the loading, the discreet size of the transducer, and the absence of cables to transmit the data. These three major assets enabled the measurement of the true loading on the residuum during real, every-day situations.
This method was particularly efficient to quantify the load applied on the residuum, but it might not provide relevant information to explain and understand the load obtained. This limitation could be alleviated by collecting simultaneous kinematic data, which would determine the causes of the forces and moments measured by the transducer. However, we anticipate that the method presented here would be used largely by multidisciplinary teams facing the challenge of safely restoring the locomotion of transfemoral amputees fitted with a conventional socket or osseointegrated implant. 11,12
The apparatus presented here can already be used at this stage of development by engineers and biomechanists. Engineers could refine the design of conventional prosthetic components (foot, knee, socket) and components for direct skeletal fixation (implant, abutment, torque and shock absorbers) by using this apparatus during each of the eight typical phases of the design process (load bearing requirement, functions, alternatives, refinement and selection of alternative design, prototypes, implementation, and evaluation). This apparatus is particularly relevant to determine the load-bearing requirement on knee, socket, or implant. Furthermore, engineers could use the data as input for numerical representation of the components, particularly for finite element models. In addition, this apparatus could be used by biomechanists aiming to validate the results obtained with inverse dynamics equations. Typically, these equations are applied to calculate the forces and moments on the axes of the ankle joint, knee joint, and hip joint. In principle, however, the load applied on the residuum can be calculated using inverse dynamics equations, assuming that the distance between the knee joint and the transducer is known. Consequently, this method could be validated by comparing the forces and moments measured directly by the transducer with the ones calculated using the inverse dynamics equations.
Furthermore, the apparatus presented here is a stepping-stone in on-board and user-friendly sensors to be used by clinical teams including prosthetists, orthopedic surgeons, physiotherapists, etc. This proposed method could be potentially used particularly by prosthetists and physiotherapists during clinical practice because it could aid the decision-making process by providing quantitative feedback about the rehabilitation program and fitting of lower limb amputees. For instance, it could be used by prosthetists to refine the alignment of the prosthetic leg and the design of a quadrilateral or ischial containment socket. Finally, the use of the apparatus presented here is particularly crucial for the clinical teams concerned with transfemoral amputees fitted with an osseointegrated implant for a direct skeletal fixation of the artificial leg. 11,12 The measurement of the true load applied on the fixation is particularly essential, not only to design specific components such as implant, abutment, torque and shock absorbers, and knee, but also to establish a relevant rehabilitation program after the insertion of the fixation, including gradual load-bearing exercises.
We acknowledge Prof. Mark Pearcy, Dr. Tim Barker, and Dr. James Smeathers for their valuable contribution and feedback during the writing of this manuscript.
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