Model and measurement studies on stages of prosthetic gait.


Future research

Although now it might seem possible that we can make predictions about certain phases of gait, which can eventually be used to improve the functional ability of prosthetic limb users, one more important step has to be made in this research process. If we want to improve the functional ability, we first have to see if we can improve the prosthetic limb design and the rehabilitation programs. Our models can contribute to this process, although the validity and usability of our models in both the conceptual and real world have to be verified further by experiments with TF amputees or with AB subjects using a prosthetic limb simulator device in various conditions, with various prosthetic components and properties in various environments (figure 1). Some of the predictions that have to be verified and confirmed, or some of the questions that arise from these models, are:

  • Is it possible to learn how to use the fast hip motion strategy, the GRF strategy and the leading limb strategy and does it have benefits in the real world to learn how to use these strategies?
  • How does trunk sway influences the four stages of gait?
  • How do our current models relate to the modern microprocessor controlled lower limb prosthetics?


Figure 1: An elementary depiction of the scientific method that shows how our conceptual models of the world are related to observations made within that real world 53 (original figure from Dym, 2004).
A: Phenomena and observations, described in the thesis of dr. A.H. Vrieling (2009).
B: Observations, models and predictions, described in the current thesis.
C: Predictions verified in the real world.


Is it possible to learn how to use the fast hip motion strategy, the GRF strategy and the leading limb strategy and does it have benefits to learn how to use these strategies? Based on the available relevant data and physical, mechanical and physiological principles, our models predicted that these strategies should be feasible. It is our expectation that, on the condition that a suitable rehabilitation program can be developed, TF amputees are able to make motions similar to the motions of the model.
A possible limiting factor that might interfere with adopting these strategies is the high demands that are placed on the already heavily used hip muscles. An increased absorption and energy generation by the muscles that control the hip joint of the amputated limb is necessary to compensate for the absence of the lower leg muscles during gait. This main compensatory strategy is seen in unilateral transtibial amputees during gait 16. It should be taken into account that these high demands might lead to overuse of these muscles.
A remark that has to be made here is that some parts of our models were verified and compared to the data of AB subjects using a knee walker prosthetic device. Hofstad et al. 17 reported bilaterally delayed and reduced responses in persons with a lower limb prosthesis. This finding reflects a basic reorganization within the central nervous system aimed at providing synchronized activity in both lower limbs, even though the peripheral deficit involves only one limb. In our AB subjects using the knee walker this reorganization probably did not occur, as their training was only limited to 100 steps on the device. This of course should be taking into account when verifying and validating the predictions of our models. On the other hand, these 100 steps were sufficient to teach the AB subjects how to use the prosthetic limb in a safe way, provided that they were paying attention to how they placed their device on the floor. Although literature is not conclusive on the effects of early weight bearing on stump healing, volume reduction and functional outcome 18, Kozáková et al. (2010) reported that faster prosthetic fitting and gait training decreases asymmetry from body weight distribution between both the limbs. Perhaps, faster prosthetic fitting influences the reorganization within the central nervous system. The subjects in the study by Hofstad (2009) were amputated more that 5 year before they were studied. Until recently immediate prosthetic fitting was not common, and perhaps these subjects were not trained with an immediate prosthesis fitting protocol. In that case, it would be interesting to repeat the study by Hofstad with TF amputees who were trained in an immediate prosthesis fitting program, and investigate how this influences the central nervous system.

Trunk sway

How does trunk sway influence the four stages of gait? Our models predicted that changes in all body segments influence the outcome of the models. For simplicity reasons, the motions of the trunk in our models were kept to a minimum. Observations revealed that TF amputees use a lot of trunk motion during gait, not only in the forward-backward direction, but also in the left-right direction. We also noticed that the TF amputee tended to hang over with their trunk toward their prosthetic side during the left-right trunk sway(figure 2). In common clinical practice this lateral trunk motion toward the transfemoral prosthetic limb (hang over strategy) is attributed to hip muscle weakness and deficient walking agility 20; 21. However, we saw the same motion in AB subjects when using a knee walker prosthetic device. Because these motion did not occurred during normal gait, we doubted whether the lateral trunk motion toward the transfemoral prosthetic limb can actually be attributed to hip muscle weakness and deficient walking agility. While exploring our models, we rationalized that three other possible reasons for this lateral trunk motion can be given. Our first explanation for this lateral trunk motion, which might be too simple and is probably incorrect, is that lateral trunk motion strategy is used to compensate asymmetrical contact times during gait. Two other explanations for the lateral trunk motion, that seem to be more valid, are the power strategy and balance strategy.


Figure 2: Trunk rotation in TF subjects

Asymmetrical contact times

A 2D mathematical model 22 we created to investigate the lateral trunk motion showed relations between gait velocity, CoM position, CoP position and contact times in transfemoral amputees (figure 3). The model predicted that a hang over strategy leads to symmetrical contact times.


Figure 3: Relations between CoM, CoP, velocity and contact time in 7 TF subjects during gait. Notice the asymmetrical contact time between sound limb and prosthetic limb stance.

An inverted pendulum model demonstrated that the contact time during prosthetic gait is shorter on the prosthetic side, when the prosthetic limb is placed more outward, compared to the sound side. The higher acceleration ⃗a of the CoM toward the contralateral side is the result of the distance d between the CoP position under the stance foot and the projected CoM (CoM) position (figure 4).


Figure 4: Inverted pendulum CoM / CoP relation (front view). Note that the contact time is depending on gait width.

The 2D three elements Newton Euler constrained mixed dynamics model (figure 5) predicted that trunk sway toward the prosthetic side enlarges the contact time, resulting in more symmetrical contact times (figure 6). The predictions made by the model contribute to the theory that TF amputees have a tendency to walk with equal contact times.


Figure 5: Model compensating gait 1(front view). For the corresponding contact time see graphs in figure 5.


Figure 6: Contact time during gait of 2D 3 segment model presented in figure 5.

As stated in the introduction, this first explanation for this lateral trunk motion seems to be too simple and is probably incorrect. If the trunk motion is used to compensate the asymmetrical contact times, then why does the amputee not place his prosthetic limb more inward? The explanation, which is based on the predictions of a mathematical model, and the question which derives from this prediction, should be further investigated in both the real and the conceptual world.

Power and balance strategy

If the asymmetrical contact time explanation would be tested on TF amputees in the real world, by asking the amputees to place their foot more inward, we would probably hear from the amputee that placing the limb more inward, makes him feel less stable. This idea leads to two other explanations for the lateral trunk motion in TF amputees during walking. These explanations derive from a power hypothesis and a balance hypothesis. In these hypothesis, the lateral trunk motion is related to the absence of an active ankle function in the prosthetic limb. The lateral trunk motion is used to increase the GRF to compensate the loss of power in the ankle, or is used to control the position of the CoP under the prosthetic foot to compensate the loss of active balance control in the ankle.
These hypotheses are currently investigated by van Hal et al. in the SPRINT (smart mobility devices with improved patient prosthesis interaction) 23 project, an Innovative Medical Devices Initiative NL, from the Healthy Ageing Network Northern Netherlands (HANNN), which is commissioned by ZonMw, Den Haag. SPRINT contribues to the plans of the high-tech health farm by developing new rehabilitation techniques and devices that restore patient mobility and shift intramural rehabilitation to extramural care. SPRINT includes a unique multi-disciplinary combination of fundamental researchers, applied researchers, health care institutes and industries. This makes it possible to cover the entire chain of innovation, from fundamental research on mobility to market introduction of products. This part of the SPRINT project focuses on the idea that due to loss of active plantar and dorsal flexion of the ankle, TF amputees compensate for the lack of power during push off by actively counterrotating their trunk at the end of the stance phase from their prosthetic limb side towards the sound limb, which increases the GRF. The lack of active balance control at the prosthetic ankle can also be compensated with trunk motions, which are used to maintain the CoM within the base of support area. By placing the prosthetic limb more outward, resulting in a wider gait (figure 4), and keeping the CoM well within the base of this wide support area, a prosthetic limb user can create a safety margin, that will prevent falling over the prosthetic limb in the lateral direction, especially in challenging environments. The end goal of this project is to create a new prosthetic limb that mechanically supports the user optimizing his energy production while maintaining active balance on the prosthetic limb during gait.

Microprocessor controlled lower limb prosthetics

How do our current models relate to the modern microprocessor controlled lower limb prosthetics? Although we did not simulate microprocessor controlled lower limbs (MCLL), which consist of adaptive microprocessor controlled knees (MPKs) and/or ankles, the current developments in this relatively new area are too important to ignore in this part of the thesis. Since our models showed that the position and motion of the CoP and the orientation of the GRF are very important for both gait and balance with a conventional prosthetic limb, the advantages of the MCLL over the conventional prosthetic limbs indicate that these limbs are of significance in that perspective. Powered MCLL can offer the possibility to steer the motion and position of the CoP and the orientation of the GRF, provided that adequate algoritms algorithms are used. The use of these limbs should be further investigated, amongst others with mathematical models, to improve their functionality which depends on the right choice of hardware and appropriate software algorithms.
Being able to detect events and cycles is essential for mathematical models that are used to control adaptive prosthetic limbs. The algorithms we developed in MATLAB (MathWorks○R) were able to detect robustly single events during post processing. The detection algorithms were based on several assumptions and contained many conditions and criteria that had to be met. We were able to detect these events, because we knew, for example, that the force plate data contained a single step in a certain direction. Unfortunately, the current algorithms are not useful in situations in which the gait direction is uncertain, or in which the direction of gait would change during the step. To detect an event in these situations, the algorithms have to be modified by adding more conditions, making them more robust.
To detect single events in real time in a large variety of possible motions, not only modifications of our algorithms are necessary. The relatively slow MATLAB programming environment is not suitable for real time single event detection. Therefore, developments are made, and parts of the algorithms are now used in other software environments in which real time evaluation of events is possible. As stated before, the current developments in the modern microprocessor controlled lower limb prosthetics are too important to ignore. Therefore, some of our thoughts about adaptability, necessities and prosthetic limb control are described below.


Nederhand et al 24 reported that a higher stiffness of a conventional mechanical prosthetic ankle results in better dynamic balance control. In contrast to this finding, Fey et al 25 found that decreasing foot stiffness can increase prosthesis range of motion, mid-stance energy storage and late-stance energy return. However, they also reported that the net contributions to forward propulsion and swing initiation may be limited as additional muscle activity to provide body support becomes necessary. Soares et al 16 stated that rigid feet lead to a fast step from foot strike to toe off, which causes not only changes in the behavior of the prosthetic limb during the stance phase, but also in the sound limb during the swing phase. According to their review, dynamic feet produce different behavior, with increased symmetry between the prosthetic limb and sound limb during the stance and swing phases. This relates to the elasticity of these feet, which gives rise to a more harmonic transition between foot strike and toe-off during the stance phase, since they provide greater range of motion for the prosthetic ankle. Based on these studies and the contradictions found, it appears that it would be preferable to have prosthetic limbs that are adaptive to the environments in which they are used and are able to change their properties on the fly based on the requirements the users impose.
It seems that MCLL enable the patients to stand and walk symmetrically and improve the functional ability of the TF amputee 26; 27; 28; 29; 30; 31, which is in line with the wishes of the TF amputee. Ulger et al 32 showed that when TF amputee used a hydraulic knee joint energy consumption decreased, subjects’ satisfaction increased and gait was near normal compared to when using their old mechanical knee joint. Fradet et al 33 reported that their findings suggest that the adapted mode of a microprocessor-controlled prosthetic ankle leads to more physiologic kinematics and kinetics in the lower limbs and reported that patients felt safer. Studies investigating powered MCLL reported that using these devices influenced the motions of the prosthetic limb 31, resulting in a more symmetrical motion 28, significantly improving function and balance 27; 30 and producing several kinematical characteristics comparable to healthy walking 26 compared to when using the conventional mechanical devices.


MCLL, that not all operate in the same manner, ultimately seek to mimic the human anatomical control system (true-to-life system), by incorporating sensor input, processing, output actuation, and feedback input features 34 and accommodate for environmental factors. The prosthetic devices have to combine sufficient dynamic balance control, with adequate energy storage and return capacities and still contribute to propulsion. Devices differ in the ability to accommodate for the various environmental factors and in the extent to which accommodation can be achieved. The resultant output of the device incorporates resistive and/or powered actuation strategies into each move. These conditions require some necessities, which can only be fulfilled by microprocessor controlled combinations of complex mechanical components, hydraulic components and powered components.
One of the necessities is that powered MCLL must have sufficient energy at their disposal to move the limbs. Up until now, the technology is limited by the size and the weight required for a motor and batteries in the prosthesis to provide sufficient net energy. In a recent study, Sup et al. 26 reported that they developed a powered transferoral prosthetic knee and ankle that can provide a range of 12.2 km of level walking and 9.2 km of 5 degrees upslope walking. In terms of steps, these numbers translate to a range of 11.000 to 13.800 steps on a single charge of the 115 Wh battery (weight: 700 g). Healthy individuals who take more than 10.000 steps per day are classified as ’active’, are ’highly active’ if they make more than 12.500 steps per day 35. Sup et al. reported that the average power consumption for level walking at self-selected speed of their prosthetic limb was 50 W, with an average net energy delivery by the ankle of 12 J per stride. By comparison, the ankle joint of a similar healthy subject would provide approximately 16 J net energy per stride 36; 37. Sup et al. state that an increased energy delivery with increasing slope correlates with the increased energy requirements of upslope walking, which in turn correspond to increasing the potential energy of the body center of mass as the user walks up the slope. With the information about the subject’s mass, the battery energy, the walking distance and the corresponding slope angles provided in the article, and assuming an electrical motor efficiency of 75%, we calculated that the powered prosthetic limb produced less than 15% of the energy that was needed to increase the potential energy. Of course, this is more than what can be produced with a passive prosthesis, which has no ability to deliver net energy, but not as much as what a sound limb would produce. Since the subject was able to walk upslope, we assume that the other 85% is provided by the sound limb and the hip on the prosthetic limb side. Therefore, we conclude that even with a powered prosthetic limb, there is sound limb dependency.
Another necessity is that a robust real time control loop with multiple controllers should be established. MCLL use several strategies to control the limbs. Computational intrinsic control uses sensor information on ambulation, cadence and environment. This form of control has to be combined with interactive extrinsic control, that uses EMG sensors, pattern recognition systems and cortical or peripheral nerve sensors. These two have to be connected to human subjects, who have their own control mechanisms, that use not only mechanical cues but also visual and auditorial cues that are picked up before the information by the MCLL is picked up. Based on our experiences, it seems difficult to establish a robust real time control loop with multiple controllers. Our subjects showed behaviour that we interpret as ’want to be in control’. This feeling of being in control is only possible if the amputees gain extended physiological proprioception 38, similar to a baseball player who has a sense of where the sweet-spot 39 of a ’static’ bat is. With ’adaptable’ prosthetics where the position and stiffness of the joint changes, there may be limited association of joint position of the prosthesis as it adapts to the environment. To increase confidence in spatial orientation of the prosthesis correlated with the ambulated environments, it seems that very intelligent control, combined with proper biomechanical movement of the prosthesis, is essential.


We agree with Martin et al. 34 that control strategies of the computational intrinsic control or interactive extrinsic control input methods are arguably the most difficult technical barrier for the next generation of prostheses. The movement of the limbs requires precise accommodation for a wide variance of factors, and the ability of the prosthesis to ’think, respond, and react’ to environmental changes based on the limited number of sensory and neural inputs is challenging. What makes prosthetics increasingly difficult, when compared with purely robotic systems, is the coupling of man and machine. Although robotic devices have been able to achieve relatively natural bipedal gait, the human factor adds great complexity to the developmental process.
As long as the motions are cyclic, and the deviations from this cyclic motion are limited, the sufficiently fast algorithms, which are the core of the control methods, are able to adjust the properties of the prosthetic limb, to counteract the consequences of these deviations. To counteract deviation, not only real time sensory information is used by the algorithms, but also information from several cycles before the current state. This combination of information is necessary to prevent undesired oscillation between the control of the prosthetic limb and the control of the TF amputee 40. The consequence is that sudden changes in the current environment are not immediately counteracted. For example, it takes at least one step walking upslope before a computer controlled prosthetic ankle is adjusted to a more dorsal flexion position 26, which eases the upslope walking. Fortunately, although the prosthetic ankle is not adjusted at the first step on the slope, the algorithms seem to be adequate during daily life. Also, for known, not suddenly changing, single events, for example sitting down and standing up 28, appropriate algoritms appear to be available by recognizing patterns in prosthesis sensor data in real time, without the need for instrumentation of the sound-side leg 41. The ÖssurR○ Power KneeTM assists in hese motions by accelerating and decelerating the body’s mass, mimicking concentric quadriceps function in a body weighted condition. Data are initially used to train models, which classify the patterns as standing, sitting, or walking 41. Trained models are subsequently used to infer the user’s intent in real time. For cyclic motions and the known, not suddenly changing, single events appropriate algorithms seem to be available. To our opinion, the biggest challenge now is to develop algorithms that assist TF amputee during unexpected single events, for example stumbling, being pushed or a quick turn at the end of the walkway, in real time. Detection of these events and responding with adequate reactions is very difficult, and seems only possible if multi sensor information is used to reduce false alarm rates 42. Compensatory stepping strategies should be further investigated, as the control of control of volitional and compensatory limb movements differs in some fundamental ways. Also, visual attention studies should be performed to investigate gaze behaviour in during unfamiliar and complex situations. Information about sudden changes in movements and suddenly redirected gaze will probably have to be part of the algorithms needed, as balance-recovery reaction is typically modulated on the basis of visuospatial environmental information 43.
There is still much work to be done in this area. To our opinion the current state of knowledge in this area is best expressed by the title of the paper by Zhang et al. (2011), mostly because of the first word: ’Towards design of a stumble detection system for artificial legs’


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