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Author: Yeh-Liang Hsu, Yung-Chieh Hung, Ju-Zhong Yin (2006-10-28); recommended: Yeh-Liang Hsu (2007-08-02).
Note: This paper is published in Journal of Medical and Biological Engineering, Vol. 26, No. 4, December 2006, p. 177-185.

Design of a Novel Total Knee Prosthesis Using TRIZ

Abstract

The ultra-high molecular weight polyethylene (UHMWPE) type of knee implant usually has high contact stress, often higher than the yield point of UHMWPE tibial platform, which results in wear. As wear progresses, the polyethylene meniscus component becomes successively thinner, and the wear debris or particles will accumulate on the dished surface of the meniscus.

In this study, a novel design concept of using a convex meniscus shape is generated using “theory of inventive problem-solving (TRIZ)”, so that the wear debris or particles will not accumulate on the surface of the meniscus. In the meantime, the geometry of the sliding surface of the meniscus remains concave in the A-P direction to conform to the shape of the femoral component. The contact surface between the femoral component and the meniscus are designed as “double enveloping surfaces” to provide a smooth sliding interface with a large contact area.

After the novel design concept is generated, the detailed dimensions and the interface surfaces between the components are then carefully designed. The motion of the new knee prosthesis is simulated using a kinematics computer simulation software and compared with that of a four-bar linkage system replicating the polycentric motion of the true knee joint.

Keyword: total knee prosthesis, TRIZ

1.     Introduction

Disease and trauma affecting the articular surfaces of the knee joint are commonly treated by replacing surgically the articulating ends of the femur and tibia with prosthetic femoral and tibial implants, referred to as “total knee replacement (TKR)”. These knee implants are made of materials that exhibit a low coefficient of friction as they articulate against one another so as to restore normal pain-free knee function.

A TKP (total knee prosthesis) generally comprises a femoral component having a pair of condylar surfaces, a tibial component having a tibial platform fixed to the resected tibia, and a bearing component usually of low friction plastic material interposed between the condylar surfaces and the tibial platform. The bearing component generally has dished surfaces for receiving the condylar surfaces of the femoral component. The bearing component can be made to be fixed onto the tibial platform or be rotatable and/or slidable in the anterior/posterior direction.

During the motion of TKP, the tibia-femoral interface bears loading several times larger than its body weight. In normal functions, the applied forces are uniformly distributed on the polyethylene (PE) cushion at the tibiofemoral cavity. Owing to long-term compression on the polyethylene part, wear at the polyethylene-bearing surface is one of the critical factors limiting the long-term success of the prosthesis [Blunn et al., 1992; Landy and Walker, 1988; Jordan et al., 2002]. Today, TKP failures are caused by wear and consequences of wear such as osteolysis [Cadami et al., 1994; Ingram et al., 2004].

Polyethylene wear of the articular surface is a well-known complication of total knee prosthesis [Feng et al., 1994; Huang et al., 1999; Kennedy et al., 2003]. Factors that play a role in the accelerated wear of the tibial polyethylene component, include tibiofemoral articular geometry, polyethylene thickness, extremity and implant alignment, and the quality of the polyethylene [Feng et al., 1994].

The so-called “third particle problem” is often discussed among surgeons as a typical reason for the accelerated wear of the tibial polyethylene component. Figure 1 shows a TKP that is widely used, which consists of a shiny Co-Cr femoral component, a white ultra-high molecular weight polyethylene (UHMWPE) bearing, and a metal tibial tray. UHMWPE wear particles are generated around the joint region due to the articulation motion between the metal parts and UHMWPE components. It is observed that various wear particles are embedded among the peri-prosthetic tissues or synovial fluid around the failed artificial joints. Several studies have isolated UHMWPE particles from the tissues retrieved from the revision surgery [Campbell et al., 1995; Hirakawa et al., 1996; Minoda et al., 2003].

Figure 1. Total knee prosthesis

Wear removes polyethylene material from the UHMWPE components. As wear progresses, not only does the function of the bearing deteriorate with plastic loss, the debris generated in the wear process can also evoke inflammatory reactions within the joint [Schmalzried et al., 1992; Kadoya et al., 1997; DeHeer et al., 2001].

Attempts made to solve this problem include elaborate and often costly locking systems to minimize relative motion at the interface between the bearing insert and the metal tibial tray. For example, the mobile meniscal bearing allows more physiological movement and replaces the A-P translation of the femoral component on the tibial polyethylene surface with the A-P gliding of the femoral metal component in articulation with the congruent surfaces of the platform on the tibial tray. This concept therefore alleviates the wear rate of the polyethylene, improves the kinematics and helps the fixation to the bone by reducing the stress at the interface [Goodfellow et al., 1978; Psychoyios et al., 1998]. One of the problems encountered when using mobile meniscal bearing systems is the constant wear that occurs between the meniscus (UHMWPE) and the femoral component (Co-Cr materials) due to articulation. The typical femoral component has two lower convex surfaces, which are compatible with the concave surfaces of the meniscus component. The meniscus is not constrained, so that it can move in the anterior-posterior direction and/or the medial-lateral direction, which often creates small wear particles or debris and accumulates on the upper surfaces of the meniscus component. In vivo the generation of submicron-sized polyethylene wear debris (PWD) can cause adverse cellular reactions in the surrounding tissues, resulting in macrophage activity and necrosis of the bone-prosthesis interface [Schmalzried et al., 1994; Morawski et al., 1995; Horowitz et al., 1998].

To deal with the problems discussed above, TRIZ is used as the concept generator for proposing a novel knee prosthesis design in this study. TRIZ (Theory of Inventive Problem Solving) was put forward by a former Soviet Union scientist Altshuller, who after studying almost 400,000 patents, deemed that it is possible to turn this theory into a systematic method [Terninko et al., 1998; Shulyak et al., 1997]. TRIZ is an available tool for design engineers to handle conflict conditions during the innovation design problem solving process [Savransky, 2000].

In this study, a novel design concept of using a convex meniscus shape is generated using TRIZ, as shown in Figure 2, so that the wear debris or particles will not accumulate on the surface of the meniscus. In the meantime, the geometry of the sliding surface of the meniscus remains concave in the A-P direction to conform to the shape of the femoral component. The contact surface between the femoral component and the meniscus are designed as “double enveloping surfaces” to provide a smooth sliding interface with a large contact area. The guide surface on the tibial platform is also carefully designed to provide proper guidance during flexion-extension by the interaction of femoral cam and tibial guide curve. The interface between the meniscus and tibial platform is designed to allow certain amount of A-P translation and internal-external rotation between the two components.

 

Figure 2. A novel design concept of total knee prosthesis

The rest of this paper is organized as follows. Section 2 presents how the novel design concept of the new total knee prosthesis was generated using TRIZ. Section 3 describes the interface surface design of each component of the new total knee prosthesis. The motion of the knee prosthesis model is also simulated by a kinematics simulation software. Then the motion of the new knee prosthesis is compared with that of a four-bar linkage system replicating the polycentric motion of the true knee joint in Section 4. At last, Section 5 concludes this paper.

2.     Generating a novel design concept of the new total knee prosthesis using TRIZ

As shown in Figure 3, the conceptual framework in this study comprises of five main stages which basically follows the classical TRIZ problem solving process [Domb, 1998]. The initial input to the entire process is a list of identified problems from existing product or design. At stage one and two, these original problems are defined with the language of TRIZ in order to provide insightful information for the further problem solving. After problem definition, the problems are structured into typical TRIZ contradictions by using contradiction analysis. At stage four, some TRIZ problem resolution tools are employed to eliminate the formulated contradictions. At stage five, the feasibilities of the solutions are then evaluated. If solutions are still not found after contradiction elimination, or some other new problems occur after solution evaluation, the problem solving process must be iterated back to the first stage to redefine the original situation. These five stages will be described in details below.

Figure 3. The design process using TRIZ

(1)   Preliminary problem analysis

The objective of this stage is to identify and collect existing problems in existing products or designs. As mentioned earlier, a typical knee prosthesis comprises a femoral component, a tibial, and a bearing component. The bearing component generally has dished surfaces for receiving the condylar surfaces of the femoral component. Some problems occur after long-term usage:

(a)    The polyethylene meniscus bearing surfaces of the total knee suffer wear damages. Wear removes the polyethylene material from the polyethylene meniscus component. As wear progresses, the polyethylene meniscus component becomes successively thinner, and the wear debris or particles will accumulate on the dished surface of the meniscus.

(b)   TKP usually has high contact stress, often higher than the yield point of UHMWPE tibial platform, resulting in wear.

(2)   Problem modelling and formulation

Based on the analysis of the problem situation above, further problem modeling and formulation can be done by using the TRIZ technique of Problem Formulator (PF)[Zlotin et al., 2001]. The purpose of problem modeling is to build a function model by using function analysis, while problem formulation is to formulate an exhaustive set of problem statements on the basis of the function diagram.

In this research, commercial software TechOptimizer 4.0 from Invention Machine Corporation is used in the following TRIZ process. It is used to model product functions and provide assistance in understanding what aspects of a product need improvement, and which of the inventive principles are most applicable.

Figure 4 shows the “function model” of the knee prosthesis design problem, built in TechOptimizer 4.0. In Figure 4, a rectangle represents a “system component”, the solid line represents a “useful function”, the dotted line represents a “harmful function”, and the cross-solid line represents an “excessive useful function”. All components of the knee prosthesis are built into the function model showing useful, harmful and excessive actions linking the various components.

Figure 4. Function model for typical knee prosthesis

In Figure 4, there are two major harmful functions to be solved by TRIZ:

l          The femoral condylar abrades the meniscus.

l          The meniscus bears a large contact stress from the femoral condylar.

(3)   Contradiction analysis

From the TRIZ viewpoint, these two problems are translated into the following “contradictions” expressed by the 39 design parameters of TRIZ. The two problems can be reorganized and stated as,

“I want to prevent wear debris or particles accumulated on the surface of the meniscus by changing the structure of the meniscuc, which leads to a problem of shortage of stability in knee prosthesis.”

“I want to reduce contact stress between the femoral component and the tibial platform by changing the combination of the femoral and the tibial platform, which leads to a problem of increasing component numbers.”

(4)   Contradiction elimination

To eliminate formulated contradictions effectively, TRIZ provides a set of powerful tools and principles, such as ARIZ, substance-field analysis, 40 inventive principles and contradiction table, etc. Among them, the 40 inventive principles and contradiction table are considered one of the most accessible and useful TRIZ problem resolution techniques.

The contradiction table in the TRIZ theory contains 39 design parameters and 40 generic principles for solving the contradictions. As shown in Table 1, to solve the first problem described above, the parameter to be improved is No. 15 “duration of a moved object”, and the major parameter not to deteriorate is No. 13 “stability of the object’s composition”. The three generic principles in the corresponding brackets is Principle 13 (the other way around), Principle 3 (local quality), and Principle 35 (parameter changes).

Table 1. The contradiction table for the first problem

Characteristics

Characteristic that is getting worse

1

2

13

39

Weight of a moving object

Weight of stationary object

Stability of the object’s

composition

Productivity

Characteristic to be improved

1

Weight of a moving object

 

 

 

1, 35, 19, 39

 

35, 3, 24, 37

2

Weight of stationary object

 

 

 

26, 39, 1, 40

 

1, 28, 15, 35

 

 

 

 

 

 

15

Durability of a moved object

19, 5, 34, 31

 

 

13, 3, 35

 

35, 17, 14, 19

 

 

 

 

 

 

39

Productivity

35, 26, 24, 37

28, 27, 15, 3

 

35, 3, 22, 39

 

 

In TRIZ, Principle 13 has three explanations: (1) invert the action(s) used to solve the problem (e.g. instead of cooling an object, heat it), (2) make movable parts (or the external environment) fixed, and fixed parts movable, and (3) turn the object (or process) “upside down”.

As shown in Table 2, to solve the second problem described above, the parameter to be improved is No. 11 “stress or pressure”, and the major parameter not to deteriorate is No. 26 “quantity of substance”. The three generic principles in the corresponding brackets is Principle 10 (preliminary action), Principle 14 (curvature increase), and Principle 36 (phase transitions).

Table 2. The contradiction table for the second problem

Characteristics

Characteristic that is getting worse

1

2

26

39

Weight of a moving object

Weight of stationary object

Quantity of substance

Productivity

Characteristic to be improved

1

Weight of a moving object

 

 

 

3, 26, 18, 31

 

35, 3, 24, 37

2

Weight of stationary object

 

 

 

19, 6, 18, 26

 

1, 28, 15, 35

 

 

 

 

 

 

11

Stress or pressure

10, 36, 37, 40

13, 29, 10, 18

 

10, 14, 36

 

10, 14, 35, 37

 

 

 

 

 

 

39

Productivity

35, 26, 24, 37

28, 27, 15, 3

 

35, 38

 

 

In TRIZ, Principle 14 has three explanations: (1) instead of using rectilinear parts, surfaces, or forms, use curvilinear ones, move from flat surfaces to spherical ones, from cubical (parallelepiped) parts to ball-shaped structures, (2) use rollers, balls, spirals, and domes, and (3) go from linear to rotary motion, use centrifugal forces.

(5)   Solution evaluation

Principles 13 and 14 are utilized to generate the new concept in our novel knee prosthesis design. Principle 13 proposes to “invert the actions,” and to “turn the object upside down”. The analogical thinking on these two principles generates the new concept of using a convex meniscus shape, as opposed to the typical dished shape, so that the wear debris or particles will not accumulate on the surface of the meniscus.

However, the shape of the femoral condylar is also convex. Using a convex meniscus shape will further increase the contact stress between the femoral condylar and the meniscus. Figure 5 shows a solution example of Principle 14 provided by TechOptimizer 4.0: the worm and worm gear wheel are made in the form of globoids (in the form of the inner surface of an open torus). This design increases contact area and reduces contact zone stresses. This concept can be employed to solve the problem of high contact stress.

Figure 5. A solution example provided by TechOptimizer

(6)   New concept of the knee prosthesis design

Finally, a novel design concept of using a convex meniscus shape and a “double enveloping” contact surface for the femoral condylar is shown in Figure 6. The upper surface of the meniscus is designed as a plurality of convex surfaces for engagement with concave surfaces on the inferior side of the femoral component, so that the wear debris or particles will not accumulate on the surface of the meniscus. In the meantime, the geometry of the sliding surface of the meniscus remains concave in the A-P direction to conform to the shape of the femoral component, as shown in Figure 7. The double enveloping contact surface of the femoral condylar provides a smooth sliding interface with a large contact area.

       

Figure 6. A convex meniscus shape and a “double enveloping” contact surface for femoral condylar

Figure 7. The flexion-extension contact surfaces

3.     Interface surface design and simulation

After the design concept is generated, the detailed designs of the interface surfaces are carried out with the aid of kinematics simulation software Working Model. There are three major interface surfaces: the flexion-extension contact surface between the meniscus and the femoral component, the flexion-extension guide surface, and the meniscal-sliding surface.

(1)   Flexion-extension contact surface

In the new design concept, the contact surface between the femoral and meniscus are designed into “double enveloping surfaces” to provide a smooth sliding interface with a large contact area. As shown in Figure 8, the sagittal condylar profile was constructed from curves of radii 15, 40, and 32 mm for the posterior, distal and anterior sections, respectively. The anterior-posterior length of meniscus was 42 mm. The minimum thickness of the femoral condylar is 8.64 mm.

The bearing surface of the meniscus includes an anterior radius 40 mm to conform to the femoral condylar surface when the femoral condylar is sitting on the meniscus. When the femoral condylar flexes, the posterior radius (15 mm) comes into contact with the meniscus, as shown in Figure 8. This conformed curvature design, as well as the “double enveloping” contact surface design described in the previous section, should be able to distribute the pressure and reduce contact stress when standing or in the flexion-extension.

Figure 8. The 3-D model of the novel knee prosthesisFlexion-extension guide surface

As shown in Figure 9, a guide surface is designed as an integral part of the tibial platform to guide the A-P displacement of the femoral condylar during flexion. The guidepost is located at the extreme posterior end of the femoral condylar sections. The tibial guide surface interacts with the post to imitate natural posterior femoral rollback by limiting and defining the pivot between the femoral component posterior post and the tibial component.

 

Figure 9. Flexion-extension guide surface

To design the profile of the guide surface, the trajectory of the guidepost in Working Model simulation when the femoral condylar flexes from 0° to 150° is plotted, as shown in Figure 10. The outer edge of the trajectory is used as the profile of the guide surface, so that the guide post will always be in contact with the guide surface in flexion.

Figure 10. Outer edge of the trajectory

(2)   Meniscal-sliding surface

As shown in Figure 11, a meniscal post component is designed to be implanted in the upper portion of the tibia. The post may serve to guide the meniscal component in the A-P direction and allows rotation with respect to the tibial plateau component as the femur and tibia move from a position of full extension to a position of flexion.

In our simulation using Working Model, there is a 4.05 mm sliding distance in the A-P direction when the femoral condylar flexes from 0° to 150°. Therefore, the radius of the meniscal post is set to be 9 mm and that of the tibial plate hole is set to be 12 mm to allow this sliding.

Figure 11. Meniscal-sliding surface

4.     Comparison between knee prosthesis and true knee joint

After the novel design concept and the detailed dimensions are generated, the motion of the new knee prosthesis is simulated using a kinematics computer simulation software. Then the motion of the new knee prosthesis is compared with that of a four-bar linkage system replicating the polycentric motion of the true knee joint.

A three-dimensional tibiofemoral joint model of the new knee prosthesis was constructed as shown in Figure 12. The orthogonal coordinate system XYZ was attached to the centroid of femoral condylar. The Y-axis coincided with the long axis of the tibia, the X-axis was in the anterior direction, and the Z-axis was in the medial direction.

Figure 12. 3-D model of tibiofemoral joint

Figure 13 to Figure 16 show the simulation results of the new TKP. In the simulation, the new TKP flexes from 0° to 150°. When the new TKP flexes close to 150°, the posterior direction displacement of femur center is 8.98mm (Figure 13), the amount of axial rotation is 15.16° (Figure 14), the A-P displacement is 4.05mm (Figure 15), and the M-L displacement is 4mm (Figure 16).

Figure 13. Movement of A-P contact position of the centroid of femoral condylar

Figure 14. Axial rotation

Figure 15. Anterior-Posterior displacement

Figure 16. Medial-Lateral displacement

A four-bar linkage system was proposed to replicate the polycentric motion of the knee that occurs during passive knee flexion-extension [Goodfellow and O’Connor, 1994]. As shown in Figure 17, it is assumed that the ligaments are straight inextensible line elements attached to the bones, each one at a single point and having no strength in bending. Since the movements allowed to the bones at the human knee occur mainly in the sagittal plane, it is adequate to identify the knee as a two-dimensional single degree of freedom linkage.

The cruciate ligaments are represented as two inextensible fibers, which, together with the femur and the tibia, are analyzed as a crossed four-bar linkage. The ligaments together with the two bones from the “cruciate” linkage ABCD. AD is called the tibial link, the line joining the attachment points of the two ligaments to the tibia, and it is regarded as the fixed bar of the knee mechanism. BC is the femoral link.

Figure 17. Elements of the knee model

The motion of the knee prosthesis developed in this research and simulated by Working Model is compared with the motion generated by the four-bar linkage model. Figure 18 shows the trajectories of points B and C when the femoral condylar flexes from 0° to 150°. The motion of the new knee prosthesis developed in this research exhibits similar trends as the motion replicated by the four-bar linkage system.

Figure 18. Movement of Point B and C during flexion from 0° to 150°

Finally Figure 19 shows the prototype of the new knee prosthesis fabricated by CNC (computer numerical control) machining. Note that the interfaces between the new TKP and femoral condylar and tibial condylar are the same as traditional TKP.

Figure 19. The prototype of our new knee prosthesis

5.     Conclusion

In this paper, TRIZ is applied to the design of a novel total knee prosthesis to solve the problems of high contact stress and the wear debris accumulation. This new design concept uses a convex meniscus shape so that the wear debris or particles will not accumulate on the surface of the meniscus. In the meantime, the geometry of the sliding surface of the meniscus remains concave in the A-P direction to conform to the shape of the femoral component. The contact surface between the femoral component and the meniscus are designed as “double enveloping surfaces” to provide a smooth sliding interface with a large contact area. The motion of the new knee prosthesis is simulated by kinematics computer simulation software, and a prototype is produced using CNC machining.

This paper demonstrates how the conceptual design method TRIZ is applied to the biomedical engineering field. The new TKP design generated in this research also received two patents, ROC 547070 and ROC 547069. To further develop the design concept into real a commercial product, intensive physical tests considering various factors, such as the real lubrication occurs in the implant, are needed in the future.

Acknowledgement

The authors wish to thank Professor H.C. Liu and Professor T.W. Lu of Institute of Biomedical Engineering, National Taiwan University, for their valuable input during the process of this research. This research is sponsor by the National Science Council, Taiwan, grants No. NSC89-2614-E-155-002. This support is gratefully acknowledged.

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