A method for performance comparison of polycentric knees and its application to the design of a knee for developing countries

Abstract

Background:

Polycentric knees for transfemoral prostheses have a variety of geometries, but a survey of literature shows that there are few ways of comparing their performance.

Objectives:

Our objective was to present a method for performance comparison of polycentric knee geometries and design a new geometry.

Study design:

In this work, we define parameters to compare various commercially available prosthetic knees in terms of their stability, toe clearance, maximum flexion, and so on and optimize the parameters to obtain a new knee design.

Methods:

We use the defined parameters and optimization to design a new knee geometry that provides the greater stability and toe clearance necessary to navigate uneven terrain which is typically encountered in developing countries.

Results:

Several commercial knees were compared based on the defined parameters to determine their suitability for uneven terrain. A new knee was designed based on optimization of these parameters. Preliminary user testing indicates that the new knee is very stable and easy to use.

Conclusion:

The methodology can be used for better knee selection and design of more customized knee geometries.

Clinical relevance

The method provides a tool to aid in the selection and design of polycentric knees for transfemoral prostheses.

Background

Transfemoral amputation occurs through the femur and is a common type of lower-limb amputation. A replacement limb (called TF or transfemoral prosthesis) must allow the user to control the knee joint by means of his or her residual limb to enable walking. The knee joint must be able to restore the functionality of the lost muscles—in particular, stability in the stance phase and control in the swing phase during walking.

Single-axis knees may be difficult to control or if locked, result in an unnatural gait.^1–6 Polycentric knee designs for prostheses can provide a more natural gait by allowing the knee to flex during walking while allowing the user to control the joint with less effort.^7,8 An appropriately designed polycentric knee, due to the changing position of the instantaneous center of rotation (ICR), can help a prosthesis user have better voluntary control—that is, the user may utilize the remaining thigh musculature more effectively to provide stable load bearing with lower effort than a hinge knee.^7,9 (The curve traced by the ICR as the knee flexes is referred to as the centrode.) Other advantages of a polycentric knee are high knee flexion angles and good toe clearance during swing due to limb length shortening.^10,11 A four-bar mechanism (4BM) is the simplest and most commonly used solution for a polycentric knee. A suitably designed polycentric knee can meet the needs of prosthesis users in developing countries, where stability and toe clearance are critical because of the extensive uneven terrain encountered. Approximately two out of three persons with a transfemoral amputation report falling at least once per year. ¹² Many prosthesis users develop gait abnormalities such as vaulting, hip hiking, or circumduction to compensate for inadequate toe clearance. ¹³ These gait deviations are undesirable because they reduce walking efficiency. ¹⁴

Four-bar knees can offer solutions for such problems. Empirical data and results from theoretical models have demonstrated that compared to single-axis knees, four-bar knees provide increased toe clearance (about 2.2 cm more on an empirical average, than single-axis knees) during the swing phase of gait for transfemoral prosthesis users. ¹¹

The LEGS M1^15,16 and the Stanford-Jaipur Knee^16–18 are both four-bar knees designed in the United States for developing countries, but with the primary focus of cost reduction. ¹⁷ We found only one polycentric knee developed with a focus on functionality for developing countries; the knee is a six-bar mechanism ¹⁸ whose primary purpose is to enable squatting. However, the size and complexity of this knee have made it unattractive for further development and use. This work is an attempt to develop a knee geometry that meets the functional demands of increased stability and toe clearance required to navigate the uneven terrain encountered in developing countries.

The geometries and centrodes of commercially available four-bar knees vary widely, which makes it difficult to compare their functionality. In this work, six parameters affecting the functionality of the four-bar knee, specifically to meet the needs of users walking on uneven terrain, were considered. These parameters based on linkage dimensions used to characterize the relative geometric performance of the knees and provide more information than a centrode alone to choose or design a knee based on requirements. The parameters were then optimized to design a four-bar knee geometry that would be better suited for uneven terrain than currently available knees. Optimization that takes into account hip flexion and extension moments the user can apply also enables finding a solution that provides good voluntary control, even for users with low residual limb capabilities.

Methods

To better understand the relative performance of various four-bar configurations, specific parameters are defined. The parameters are derived intuitively as well as from literature. While any number of parameters can be defined to apply the method, we focus on the increased stability and toe clearance needs of users walking on uneven terrain. The parameters provide quantitative means to characterize and compare the performance of different prosthetic knees based on knowledge of their link dimensions.

For design, we use a heuristic search algorithm to find a suitable four-bar configuration with optimum values for the prescribed parameters that primarily define knee stability during stance and ground clearance during swing.

Standard dimensions for a prosthesis are defined as shown in Figure 1. This configuration is the same as that used by Radcliffe. ⁸ The cosmetic knee center is located at a height of 500 mm. The hip is located 450 mm above the knee center and vertically above the ankle. The heel is 50 mm behind the alignment reference line (ARL; the line joining the hip and ankle) and the toe lies 200 mm in front of the ARL.

Figure 1.

Calculation of x/y ratios for a typical four-bar knee.

The knee 4BM is located with respect to the ARL as follows:

1. The top front pivot of the 4BM is located at the cosmetic knee height.

2. The midpoint of the bottom link of the 4BM is located on the ARL.

In a four-bar knee, the ICR is determined by the intersection of the front and rear links extended. Load line (line of action of the ground reaction force (GRF)) is the line joining the hip joint and the center of pressure (CoP) on the foot. The CoP is the point at which the net GRF acts. The x/y ratio (Figure 1) is determined by the location of the ICR with reference to the load line. The location ahead or behind the load line is measured by x and the height of the knee center above the ground measured along the load line is y. For a polycentric knee, the x/y ratio depends on the geometry of the four-bar knee and varies with knee flexion.

Radcliffe ⁷ derived the equation for the hip moment required to control the knee as

$$M_h\mathrm{=}PL\left(x/y\right)$$

where M_h is the hip moment exerted by the prosthesis user, P is the load along the load line, L is the distance between the hip joint and the CoP along the load line, x is the normal distance of the ICR from the load line, and y is the elevation of ICR from CoP along the load line. The CoP is the point where the net GRF acts on the leg.

The following parameters are defined to characterize the stance and swing behavior of the knee and compare the various four-bar geometries.

Stance phase

Knee stability is the critical factor in the stance phase of walking. The prosthesis user must be able to prevent the knee from buckling with little or no effort.

Heel contact x/y ratio

Maintaining stability of the knee at heel contact is very important in the stance phase because the GRF at heel contact tends to be more than 120% of the body weight. This demands a large hip moment to maintain stability. Radcliffe^8,9 in his study showed that the hip moment required to maintain stability depends on a parameter called the heel contact x/y ratio which varies from knee to knee. Hence, this ratio is considered as a parameter. A negative heel contact x/y ratio implies that the knee is stable at heel contact without requiring any stabilizing hip moment, which is preferable.

Push-off x/y ratio

At push-off, the knee is always stabilized by a highly anterior load line (see Figure 1). But in order to initiate the swing, the knee has to flex at push-off. The prosthesis user achieves this by exerting a flexion moment at the hip, acting opposite to the stabilizing moment, to shift the load line behind the ICR. A smaller stabilizing moment would mean an easier push-off since the user can initiate flexion using a smaller hip moment. A smaller stabilizing moment is preferred at push-off, which means a push-off x/y ratio close to zero is desired at this stage of walking.

Flexion angle up to which the knee is stable without application of any hip moment

Apart from the heel contact stability and push-off hip moment, we need another desirable knee characteristic, which addresses the scenario where heel contact happens before the knee is fully extended. Landing on a flexed knee is very likely when walking on uneven terrain. Since the x/y ratio changes with knee flexion, ⁸ we need to know the range of knee flexion up to which the x/y ratio would remain negative or self-stabilizing at heel contact. Here, we assume that there is negligible change in the CoP between fully extended heel contact and partially knee flexed heel contact. This is a valid assumption since the heel functions as a pivot at initial stance. ¹⁹

The knee may not be fully extended at the instant of heel contact. It is important to ensure stability even when the heel contact occurs with a flexed knee. A measure of this stability would be the flexion angle at heel contact up to which the ICR lies in front of the load line. In other words, the flexion angle up to which the x/y ratio remains negative is of interest here. The larger the stable knee flexion range, the more stable the leg will be at heel contact even with the knee slightly flexed. This range defines the self-stabilizing region of the knee where no effort is required from the user.

Measure of the stabilizing hip moment required after the stable knee flexion range

Now we will look at the ability of the knee to recover from a case of heel contact with the knee flexed beyond the self-stabilizing region. This would indicate the extent of voluntary control of the knee possible by the user. To quantify this, we look at the variation of heel contact x/y with respect to various angles of knee flexion at heel contact.

After the self-stabilizing knee flexion range, the heel contact x/y ratio has positive values, which is proportional to the hip moment the user has to apply to stabilize the knee. For the user to have sufficient control to maintain stability when contacting the ground with the knee flexed beyond the self-stabilizing range, the stabilizing hip moment to be applied must be small and consistent. Hence, the standard deviation of the positive segment of the x/y ratio about zero, up to 15° of knee flexion is considered as a parameter. A smaller standard deviation (across the data points) would mean a smaller and more consistent hip moment required for maintaining stability up to 15° of knee flexion.

Swing phase

In the swing phase, the primary performance index we are interested in is toe clearance.

Toe clearance

This is the clearance of the toe from the ground during swing. A four-bar knee has the inherent advantage of shank shortening during flexion.^10,11,14 The minimum toe clearance for normal walking happens at 23° hip flexion and 49° knee flexion. ²⁰ While the minimum toe clearance for a TF user may occur at other configurations of hip and knee flexion, for relative comparison among the knees, we use these values, similar to the approach of Gard et al. ¹⁰ The higher the minimum toe clearance, the lower the chances of stumbling during the swing phase. Figure 2 illustrates the calculation of minimum toe clearance for a typical four-bar knee.

Figure 2.

Illustration of minimum toe clearance calculation of a typical four-bar knee.

In addition to stability and toe clearance, another important lifestyle-influencing factor for prosthesis users in developing countries is the ability to kneel or sit cross-legged. Maximum knee flexion is therefore an important consideration, measured by the following parameter.

Maximum overall knee flexion

The maximum overall knee flexion possible is determined by the angle at which the shank or the rear link of the four-bar knee hits the rear side of the socket. Although commercial knees advertise maximum knee flexion angles based on the knee mechanism alone, that measure is inaccurate since it depends on the variation in the size and shape of the socket from user to user. Here, we set a reference socket size as the standard and calculate the maximum overall knee flexion. The justification for this choice is that for any given socket size the relative performance of the knees would be the same, namely, the knee which has the largest knee flexion for one user would still have the largest knee flexion for any other user.

The reference socket was modeled as a sphere of 120 mm diameter located 20 mm in front and 80 mm above the cosmetic knee center. Figure 3 shows the maximum knee flexion for a typical knee with the rear of the pylon stopped against the assumed nominal socket.

Figure 3.

Maximum knee flexion shown with socket held fixed.

Optimization

Having defined the parameters for characterizing four-bar knees, our target was a knee mechanism with the following features:

1. Stable and effortless heel contact and load bearing, which would mean a negative heel contact x/y ratio, a larger flexion angle up to which the ICR is behind the load line for stability, and a low stabilizing hip moment requirement for control with little effort.

2. Easy push-off, which corresponds to a push-off x/y ratio close to zero.

3. Maximized toe clearance during swing.

4. High knee flexion for kneeling and other activities.

Any planar four-bar linkage requires six generalized coordinates to define it completely. For instance, three vectors, each defined by magnitude and direction, completely describe a four-bar (fourth vector is obtained from the loop closure equation). Here, the coordinate system is chosen such that the y-axis coincides with the ARL and passes through the middle of the bottom link and the x-axis passes through the top front pivot. The generalized coordinates (Q1–Q6) to describe the four bars are ideally chosen as shown in Figure 4 so that certain geometric constraints can be easily incorporated in the synthesis.

Figure 4.

Generalized coordinates (Q1–Q6) chosen for the 4BM.

From coordinates Q1, Q2, and Q3, we can get the x and y coordinates of points C and D of the four-bar ABCD as shown in Figure 4. Now Q4 and Q5 give the location of the ICR, and the line joining point D and the ICR intersects the X axis to give the coordinates of point A. Point B lies on the line joining point C and the ICR. The y coordinate of point B is empirically set to lie between half of Q3 below the X axis and 30 mm above the X axis. Q6 is a ratio which locates point B in this range.

Apart from all the parameters discussed earlier, there are some geometric constraints that are necessary to constrain the overall size of the linkage and the ICR location. These constraints make the problem less intensive computationally and the resultant four bars more practical from aesthetic and manufacturing standpoints. These are listed below:

1. The front to back width of the linkage (Q1). This is judiciously constrained to lie between 20 and 50 mm considering the aesthetics of the knee. A size smaller than 20 mm may impose manufacturing constraints.

2. Overall length of the linkage below knee center height (Q3). This is constrained to lie between 20 and 80 mm, again for aesthetics.

3. Instantaneous center height range (Q5). The maximum height is limited to 400 mm to avoid a hyper-stabilized knee and minimum height is set at 100 mm as it has been observed that a higher IC height results in higher toe clearance. ²¹

4. Horizontal location of the instantaneous center (Q4). The location was constrained to a range of 5–60 mm behind the ARL to avoid hyper-stability.

Then, the optimization problem for the four-bar knee is defined as:

• Minimize heel contact x/y;

• Maximize push-off x/y;

• Maximize stable knee flexion;

• Maximize toe clearance;

• Minimize measure of stabilizing hip moment;

• Maximize overall knee flexion.

Subject to the constraints (all in mm)

• 20 < Q1 < 50;

• −40 < Q2 < 40;

• 20 < Q3 < 80;

• −60 < Q4 < −5;

• 100 < Q5 < 400;

• 0 < Q6 < 1.

This is a multi-objective optimization problem. The domain was found to be highly irregular because completely different sets of values were able to give similar results, that is, two completely different 4BMs were able to generate similar centrodes. Hence, a multi-objective genetic algorithm was used to search the parameter domain for optimum four bars. The algorithm begins by choosing a random population of four bars, ranks them and the best of them undergo crossover to form a new generation of improved four bars. This is repeated until there is no further improvement in the overall health of the population and thus we get a pareto optimal set. This set contains different knee configurations which have different combinations of optimum values for each of the six selected parameters. Weights for the various parameters can be chosen depending on the requirement. For instance, a 4BM (Proto1) was synthesized with zero weight for maximum knee flexion. The final 4BM (IITM knee) was then handpicked from those with good stability, toe clearance, and also based on design (manufacturing) suitability.

Informed consent was obtained from two active male users to try the IITM knee. Ethics committee approval for the user trials was obtained at the SMS Hospital in Jaipur, India, where the trials were conducted.

Results

Table 1 lists the parameters of the IITM knee along with those for four commercial 4BM and Proto1. The parameters for each knee were computed by measuring its link lengths.

Table 1.

Comparison of IITM knee with commercial four-bar configurations and Proto1.

Parameters (direction of improvement)	Four-bar knee configurations
	Proteval	Ottobock 3R36	Ottobock 3R55	Ottobock 3R70	Proto1	IITM knee
Heel contact x/y (min.)	−0.061	0.003	0.029	−0.015	−0.042	−0.057
Push-off x/y (max.)	−0.079	−0.135	−0.108	−0.133	−0.166	−0.136
Stable knee flexion in degrees (max.)	0	0	0	0	3	2
Measure of stabilizing hip moment required after the stable knee flexion range (min.)	0.124	0.112	0.126	0.112	0.106	0.117
Toe clearance measure in mm (max.)	2.2	−2.4	19.4	−2.8	11.5	11
Maximum overall flexion in degrees (max.)	159	157	117	160	95	145

Figure 5 is a radar diagram that presents a visual comparison of the various knees with respect to the chosen parameters. The scale chosen for the diagram is arbitrary since the objective is only a relative comparison. Figure 5 also shows the sum (in parentheses) of the values on all the axes for each of the knees, assuming equal weights and indicates that the IITM knee has the best score among the compared knees. The subjective feedback from the user trials indicated the IITM knee to be very stable and easy to control even while negotiating stairs and ramps.

Figure 5.

Radar diagram for a visual performance comparison of several four-bar knees. The number in parentheses next to the knee name indicates the overall score for each knee.

IITM knee has a negative x/y value making it self-stabilizing during heel contact. It has the second-best stable flexion angle, reasonably low hip moment requirement in the group and has toe clearance as good as Ottobock 3R55 and better than all other knees. It also has a commercially competitive maximum overall flexion.

The final design for the IITM knee is shown in Figure 6.

Figure 6.

Final IITM knee design.

The knee has been designed to meet the ISO 10328:2006 ²² standards for load-bearing. Additional salient features of the knee are as follows:

• Pyramid adapter front to back adjustment of ±8 mm to enable customization of the stability;

• Adjustable Bump Stop to compensate for wear;

• Friction adjustment for setting the walking speed;

• Adjustable extension assist;

• Maximum flexion of 145°.

Discussion

Previous comparisons among polycentric knees have been made on the following aspects: stability at heel strike and push-off,^6,8,14,23 swing phase kinematics,^6,14,23 and cosmetics.^14,23 Comparisons have been limited to stability at full extension based on the knee center location behind the alignment line above the anatomical center. Radcliffe ⁹ presents a comparison for stability and ease of push-off in terms of geometric ratios of the 4BM at heel contact and push-off, again with a fully extended knee, but does not address other issues like toe clearance, which has been studied separately.^10,11 This work combines and builds on previously reported work to compare existing knees based on their suitability for use specifically in developing countries and then presents a practical method that uses six quantifiable parameters to design a more suitable knee.

Synthesis methods for four-bar knees are typically based on predefined centrodes. Centrode-based methods are used to optimize for stability at heel contact,^7,9 locate the ICR in the zone of voluntary control, ²⁴ or follow an arbitrarily considered centrode for the knee motion. ²⁵ Hobson ²⁶ used optimization methods to synthesize a 4BM that has a centrode passing through centrode points corresponding to arbitrarily chosen reference knee flexion angles. In this method too, a hypothetical reference centrode must be chosen. The main drawback of such methods is that there is no reported ideal centrode, nor is one possible because of variations in users’ capabilities. Our work considers the diversity in residual capabilities of the amputees and hence uses minimization of the hip moment for voluntary control as one of the optimization criteria.

Our work focused on stability and toe clearance as the principal criteria for the design since the goal was suitability to navigate uneven terrain. Therefore, ability to control stability whether the user makes initial contact with the ground with the knee fully extended or slightly flexed is important. This stability has to be counterbalanced with the effort required at push-off since a hyper-stable knee is difficult to flex for initiation of swing. However, the effort required for push-off has lower weight in the overall design since the loading from the ground on the limb at push-off is considerably lower than at heel contact. The only characteristic considered for the swing phase is toe clearance to prevent stumbling on uneven terrain. Other characteristics of the knees during swing such as the nonlinearity of the swing movement with a 4BM ¹⁴ or swing time were not taken into account for comparison or design. Cosmesis for walking and sitting were also not considered since the functionality for uneven terrain was our primary goal. However, maximum flexion allowed by the knee was considered to allow the user to kneel, sit cross-legged, and so on to meet lifestyle needs. Factors like a spring assist and friction damping that influence the swing phase dynamics are auxiliary systems and not directly related to the 4BM or its synthesis and were also not considered.

Greene ¹⁴ proposed that the stability at heel contact and toe-off can be used to evaluate relative energy loss and also related limb shortening to energy efficiency since that would make gait compensations such as hip hiking, vaulting, and circumduction unnecessary for ground clearance. While the same arguments can be applied to our knee design, we have not quantified energy consumption directly and the influence of weight distribution of the prosthesis has also not been considered. However, the method itself is not subject to these limitations and can be easily extended to design or select knees based on a chosen set of parameters and corresponding weights.

The IITM knee represents the best compromise that meets the competing requirements as defined. Many other solutions are also possible depending on the constraints posed and weights applied. An example was Proto1, which had excellent stability but poor overall knee flexion.

In this study, the primary purpose was to present the method for knee design and selection. Future work includes gait studies with prosthesis users to evaluate kinematics, kinetics, and energy consumption, along with other gait parameters.

Conclusion

Commercially available prosthetic knees advertise their centrodes, but the centrode alone provides little information on the actual functionality of the knee or its suitability for a particular user. This work presents six quantifiable measures for comparing the geometries of polycentric knees with a focus on stability and toe clearance requirements for navigating uneven terrain. The influence of the four-bar geometry on relevant aspects of the knee performance is compared across several commercially available knees. Based on this study, we have shown that there is scope for improvement in currently existing knees in terms of their functionality for developing countries and have designed a knee that provides greater stability and toe clearance to better navigate uneven terrain.

Gait studies are required to validate the results of the method. The methodology presented can be used to design more customized knee geometries depending on specific needs and can make custom prosthetic knee design cost-effective when combined with modern three-dimensional (3D) printing technologies.