Knee prostheses as medical products require careful application of quality and design tool to ensure the best performance. Therefore, quality function deployment (QFD) was proposed as a quality tool to systematically integrate consumer’s expectation to perceived needs by medical and design team and to explicitly address the translation of customer needs into engineering characteristics. In this study, full factorial design of experiment (DOE) method was accompanied by finite element analysis (FEA) to evaluate the effect of inner contours of femoral component on mechanical stability of the implant and biomechanical stresses within the implant components and adjacent bone areas with preservation of the outer contours for standard Co-Cr alloy and a promising functionally graded material (FGM). The ANOVA revealed that the inner shape of femoral component influenced the performance measures in which the angle between the distal and anterior cuts and the angle between the distal and posterior cuts were greatly influential. In the final ranking of alternatives, using multicriteria decision analysis (MCDA), the designs with FGM was ranked first over the Co-Cr femoral component, but the original design with Co-Cr material was not the best choice femoral component, among the top ranked design with the same material.
Poor estimation of the main product parameters may lead to high cost due to subsequent redesign or even to product failure. Development of regulatory and functional needs in a product is tremendously complex as it involves a number of compromises linking with the consumer. Furthermore, many compromises required during product design often lead to a suboptimal final design and to a reduction in the design process effectiveness. The process of selecting for best design parameters to fulfill the desired requirements deals with a lot of trade-offs. Functional specifications which can be related to the material and geometrical design need to be identified properly and to be mapped for the connections between them. Therefore, a systematic approach, which enables the designers to determine and map the correlation between the different functional specifications and design parameters, is highly demanded. It seems that there is no attempt for applying the combined quality function deployment-finite element analysis-multiattribute decision making-design of experiment (QFD-FEA–MADM–DOE) approach for design improvement.
One of the medical products that still lack sufficient design solutions is total knee replacements (TKRs), which suffer from aseptic loosening and eventual revision surgery [
Aseptic loosening problem, the related leading causes, and the engineering design solutions.
The methodology in this study contains four main steps: (1) determining the design variables and the design of computational experiments, (2) quality function deployment to translate the voice of customer to technical terms and performance outputs, and to determine their relative importance, (3) finite element analysis to predict the performance outputs for the design options generated using DOE, and (4) analysis of variance (ANOVA) to find significant factors and to evaluate the main and interaction effects of design variables, and then multiattribute decision making to rank the candidate design options. These steps are shown in Figure
Steps used in the methodology.
Various knee prosthesis designs are currently available in which the basic designs of femoral components are analogous; however the interface geometry of this component including the location pegs, the angles associated with the inner contour, and their respective lengths vary from a particular design to another [
Geometrical variables and their respective levels.
Run number | Factor 1 | Factor 2 | Factor 3 | Factor 4 |
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A: beta (deg) | B: gamma (deg) | C: delta (deg) | D: epsilon (deg) | |
1 | 125 | 98 | 140 | 88 |
2 | 125 | 98 | 125 | 88 |
3 | 140 | 90 | 140 | 94 |
4 | 125 | 98 | 140 | 94 |
5 | 125 | 90 | 125 | 94 |
6 | 140 | 98 | 140 | 94 |
7 | 140 | 98 | 140 | 88 |
8 | 125 | 90 | 140 | 88 |
9 | 125 | 98 | 125 | 94 |
10 | 140 | 90 | 125 | 94 |
11 | 140 | 90 | 140 | 88 |
12 | 140 | 98 | 125 | 94 |
13 | 125 | 90 | 125 | 88 |
14 | 125 | 90 | 140 | 94 |
15 | 140 | 90 | 125 | 88 |
16 | 140 | 98 | 125 | 88 |
Design variables of the inner contour.
Femoral component as a key feature in current knee prostheses has been the focus of many studies related to materials. Scholars have been working on tailor and development of new biomaterials for this component to avoid mismatch of engineered materials properties with those of the biological ones and to provide acceptable performance without short-term and long-term failure. These include the generation of new metallic alloys and engineering ceramics [
To plan the computational experiments, a full factorial design was used. Full factorial design covers all possible combinations of a set of factors including both continuous and categorical ones. This design is the most conservative of all design types, as there is little ambiguity when all combinations of the factor settings are examined. The number of experiments (runs) in full factorial design depends on the number of factors levels; for example, designs with only two-level factors contain
Two-dimensional profiles of generated designs.
Extraction of all the relevant material/design selection criteria/indices needs a broad engineering knowledge and this sometimes makes it difficult for practitioners to take a decision related to design. In fact, even mistakenly missing a criterion, the results may be adversely affected [
The simplified house of quality.
The external walls of the house are the customer requirements. On the left side is a listing of the voice of the customer or what the customer expects in the product. The relative importance of the customers’ requirements can be judged based on priority scale developed as 1: not important, 2: important, 3: much more important, 4: very important, and 5: most important. The ceiling or second floor of the house contains the technical descriptors. Consistency of the product is provided through materials and design characteristics. The interior walls of the house are the relationships between customer requirements and technical descriptors. To quantify the relations between the customers’ needs and technical requirements (“Whats” and “Hows”), an appropriate scale is set for assigning the relative importance as 5: moderate, 7: strong, and 9: very strong. The technical characteristics may be beneficial (higher values are desired) or nonbeneficial (lower values are preferred) or target based [
Process of translating customer needs to material and design selection criteria.
House of quality (HoQ) can be used as an initial aid to deal with the trade-offs and can be coupled with multicriteria decision analysis to deal with the design selection process strategically.
The 3D models of femoral component, polyethylene insert (related to commercial implant), and femur, from the previous studies [
Materials properties used in FEA.
Materials |
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Co-Cr alloy | 240000 | 0.3 |
Alumina ceramic | 350000 | 0.21 |
Ti | 100000 | 0.3 |
Cortical bone | 17000 | 0.3 |
Cancellous bone | 400 | 0.3 |
Elastic-plastic behavior of ultra high molecular weight polyethylene.
Contact conditions were defined to apply finite sliding for pairs of surfaces including master and slave surfaces. The contact was applied both between the distal surface of the femoral component and proximal surface of tibial insert (articulating surfaces) and between the distal surface of the femur and proximal surface of femoral component (bone/implant interface surfaces). The friction coefficients between the femoral and tibial components were presumed to be 0.04 for Co-Cr alloy and 0.03 for alumina (last layer of FGM) [
Finite element mesh including CPS4R and CPS3.
The FEA of models with different inner contours for both materials were run under a load of 600 N (pressure) applied to the top surface of femur. For boundary conditions, the distal surface of the polyethylene insert was fully constrained from rotation and translation, and the femur was constrained from rotating in two directions whereas it was allowed to translate in the inferior-superior direction. To acquire the stress values in the femur, 10 regions of interest (ROI) were defined behind the interfaces (inner contours) as given in Figure
Regions of interest in the femoral bone.
TOPSIS has superior characteristics over other multiattribute decision making (MADM) methods and have been used widely for real world selection problems. Therefore in this paper, the extended version [
Ideal and anti-ideal solutions with two benefit criteria.
The steps of extended TOPSIS can be expressed as follows.
(1) Convert the raw measures
(2) Develop a set of importance weights (
(3) Multiply the columns of the normalized decision matrix by the associated weights:
(4) Identify the PIS:
(5) Identify the NIS:
(6) Develop a distance measure for each alternative to both ideal (
(7) Calculate the relative closeness to the ideal solution according to
(8) Rank alternatives by maximizing the ratio in Step (7). The larger the index value, the better the performance of the alternative.
The effects of the design variables on the responses were determined, after checking the normal probability plot of residuals using Design Expert software version 7.0.0. Prestatistical analysis demonstrated less contribution of material to the design objectives comparing to geometrical variables. For instance, the effect of material on the minimum of mean stresses at different region was less than all geometrical variables except for
ANOVA results for minimum of mean stresses in femur for Co-Cr alloy.
Source | Sum of squares | df | Mean square |
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A-beta | 0.426201 | 1 | 0.426201 | 11.01392 | 0.021 |
B-gamma | 4.833423 | 1 | 4.833423 | 124.9056 | 0.0001 |
C-delta | 0.055955 | 1 | 0.055955 | 1.445983 | 0.283 |
D-epsilon | 8.626668 | 1 | 8.626668 | 222.9309 | <0.0001 |
AB | 0.209491 | 1 | 0.209491 | 5.413679 | 0.0675 |
AC | 0.018615 | 1 | 0.018615 | 0.481052 | 0.5188 |
AD | 0.284554 | 1 | 0.284554 | 7.353474 | 0.0422 |
BC | 0.029604 | 1 | 0.029604 | 0.765017 | 0.4218 |
BD | 1.676965 | 1 | 1.676965 | 43.33623 | 0.0012 |
CD | 0.018299 | 1 | 0.018299 | 0.472881 | 0.5223 |
Residual | 0.193483 | 5 | 0.038697 | ||
Total | 16.37326 | 15 |
The interactions of
Interaction effects of design variables on minimum of mean stresses of ROI: (a) interaction effect of
The ANOVA table of the model for the maximum standard deviation of ROI stresses (Table
ANOVA results for maximum STDV of stresses in femur for Co-Cr alloy.
Source | Sum of squares | df | Mean square |
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A-beta | 0.092434 | 1 | 0.092434 | 1.486293 | 0.2772 |
B-gamma | 3.893795 | 1 | 3.893795 | 62.6102 | 0.0005 |
C-delta | 0.787533 | 1 | 0.787533 | 12.66312 | 0.0162 |
D-epsilon | 1.484719 | 1 | 1.484719 | 23.87351 | 0.0045 |
AB | 0.349913 | 1 | 0.349913 | 5.626419 | 0.0638 |
AC | 0.106938 | 1 | 0.106938 | 1.71951 | 0.2467 |
AD | 0.008447 | 1 | 0.008447 | 0.135817 | 0.7276 |
BC | 0.01 | 1 | 0.01 | 0.160796 | 0.705 |
BD | 0.003122 | 1 | 0.003122 | 0.050203 | 0.8316 |
CD | 0.971295 | 1 | 0.971295 | 15.61791 | 0.0108 |
Residual | 0.310955 | 5 | 0.062191 | ||
Total | 8.019152 | 15 |
Effects of design variables on maximum STDV of stresses in ROIs: (a) main effect of
The ANOVA table of the model for the maximum micromotion at bone-implant interface is presented in Table
ANOVA results for maximum micromotion at femur-implant interface for Co-Cr alloy.
Source | Sum of squares | df | Mean square |
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A-beta | 90.0601 | 1 | 90.0601 | 144.2624 | <0.0001 |
B-gamma | 2613.254 | 1 | 2613.254 | 4186.029 | <0.0001 |
C-delta | 2.0449 | 1 | 2.0449 | 3.275614 | 0.1301 |
D-epsilon | 9015.503 | 1 | 9015.503 | 14441.44 | <0.0001 |
AB | 89.6809 | 1 | 89.6809 | 143.6549 | <0.0001 |
AC | 1.1025 | 1 | 1.1025 | 1.766034 | 0.2413 |
AD | 2.9929 | 1 | 2.9929 | 4.794163 | 0.0801 |
BC | 2.5281 | 1 | 2.5281 | 4.049625 | 0.1003 |
BD | 158.5081 | 1 | 158.5081 | 253.9055 | <0.0001 |
CD | 0.1849 | 1 | 0.1849 | 0.296181 | 0.6097 |
Residual | 3.1214 | 5 | 0.62428 | ||
Total | 11978.98 | 15 |
Effects of design variables on maximum micromotion at femur-implant interface: (a) interaction effect of
The influential parameters for FGM femoral component were also identified. Same factors are significant for minimum of mean stresses and maximum of STDV of stresses (see Table
Comparison of significant design factors for Co-Cr and FGM in all responses.
Influential factors | ||||||||||||||||||
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Min of mean stress | Max of STDV stress | Max of micromotion | ||||||||||||||||
Co-Cr |
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FGM |
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Positive (+) or negative (−) effect of the main and interactions effects (coefficient of regression models).
The conceptual design begins with gathering of the voices of the customer as functional requirements. Expectations of customers (patients), medical, and design teams from implant (femoral component) in a knee replacement surgery are shown in Figure
Customers performance needs in design of femoral component and complementary requirements detected by the medical and design team.
Figure
House of quality including requirements, engineering characteristics, and obtained weights.
Degree of importance | Engineering characteristics (How) | ||||||||
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Stress level in femur (A) | Nonuniformity of stress distribution in femur (B) | Displacement at bone-implant interface (C) | Stress level at femoral corner points (F) | Stress level in peg (D) | Mass (E) | Biocompatibility (G) | Hardness (H) | ||
Prioritized customer |
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Req1 | 2 | ● | |||||||
Req2 | 3 | ⊙ | ● | ||||||
Req3 | 5 | ◯ | ● | ||||||
Req4 | 4 | ● | |||||||
Req5 | 4 | ● | ⊙ | ||||||
Req6 | 4 | ● | |||||||
Absolute weight | 36 | 28 | 36 | 21 | 27 | 43 | 45 | 36 | |
Relative weight for design selection criteria (input for Tables |
0.19 | 0.15 | 0.19 | 0.11 | 0.14 | 0.23 | — | — | |
Relative weight for material and design selection criteria (input for Table |
0.13 | 0.10 | 0.13 | 0.08 | 0.10 | 0.16 | 0.17 | 0.13 | |
Prioritized technical descriptors |
+9 ● strong.
+7 ⊙ moderate.
+5 ◯
Performance of Co-Cr alloy designs in different criteria and ranking orders scenarios by TOPSIS method.
Objectives | Max | Min | Min | Min | Min | Min | Relative closeness to the ideal solution | Ranking |
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Relative weights of design criteria | 0.19 | 0.15 | 0.19 | 0.11 | 0.14 | 0.23 | ||
A | B | C | D | E | F | |||
Design 1 | 2.919 | 3.116 | 34.70 | 24.67 | 900.79 | 115.4 | 0.4080 | 12 |
Design 2 | 3.605 | 3.428 | 44.60 | 24.74 | 918.17 | 114.7 | 0.4075 | 13 |
Design 3 | 1.570 | 2.189 | 20.13 | 26.22 | 804.59 | 72.9 | 0.6180 | 1 |
Design 4 | 1.771 | 2.221 | 21.35 | 26.26 | 925.80 | 108.2 | 0.4315 | 10 |
Design 5 | 2.962 | 2.682 | 35.46 | 27.05 | 901.99 | 73.9 | 0.5865 | 4 |
Design 6 | 4.244 | 1.884 | 45.55 | 27.35 | 874.13 | 109.8 | 0.5212 | 6 |
Design 7 | 1.600 | 1.306 | 20.27 | 27.79 | 849.11 | 122.3 | 0.4487 | 9 |
Design 8 | 1.804 | 1.336 | 21.50 | 27.86 | 867.89 | 86.9 | 0.5750 | 5 |
Design 9 | 1.213 | 2.464 | 87.99 | 17.00 | 934.89 | 101.5 | 0.2863 | 16 |
Design 10 | 1.352 | 1.815 | 97.54 | 25.52 | 813.68 | 79.0 | 0.4637 | 8 |
Design 11 | 0.845 | 0.958 | 61.94 | 10.05 | 779.58 | 69.0 | 0.6107 | 2 |
Design 12 | 0.851 | 1.309 | 62.35 | 10.12 | 883.21 | 109.8 | 0.4086 | 11 |
Design 13 | 1.293 | 2.470 | 90.74 | 17.13 | 885.27 | 85.9 | 0.3960 | 15 |
Design 14 | 1.408 | 1.813 | 99.12 | 25.55 | 892.91 | 68.3 | 0.4690 | 7 |
Design 15 | 0.892 | 1.148 | 63.25 | 10.11 | 796.96 | 68.3 | 0.6033 | 3 |
Design 16 | 0.871 | 1.311 | 60.43 | 10.10 | 866.49 | 116.5 | 0.4000 | 14 |
A: minimum of stress mean in different regions explained in Figure
B: maximum of stress STDV in different regions (MPa).
C: maximum contact slip at femoral component/bone interface (
D: maximum peg stress (MPa).
E: area of cross section (mm2).
F: maximum stress at corner points of inner contour (MPa).
Performance of FGM designs in different criteria and ranking orders scenarios by TOPSIS method.
Objectives | Max | Min | Min | Min | Min | Min | Relative closeness to the ideal solution | Ranking |
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Relative weights of design criteria | 0.19 | 0.15 | 0.19 | 0.11 | 0.14 | 0.23 | ||
A | B | C | D | E | F | |||
Design 1 | 3.100 | 2.655 | 30.61 | 20.16 | 900.79 | 14.4 | 0.6029 | 4 |
Design 2 | 3.818 | 3.449 | 39.58 | 23.54 | 918.17 | 14.3 | 0.5540 | 8 |
Design 3 | 1.707 | 2.208 | 17.93 | 14.09 | 804.59 | 13.1 | 0.6566 | 3 |
Design 4 | 1.925 | 2.245 | 19.16 | 14.34 | 925.8 | 12.2 | 0.6011 | 5 |
Design 5 | 3.150 | 2.668 | 31.24 | 21.26 | 901.99 | 29.0 | 0.4385 | 14 |
Design 6 | 4.466 | 1.866 | 40.36 | 24.17 | 874.13 | 13.8 | 0.6730 | 1 |
Design 7 | 1.741 | 1.249 | 18.03 | 14.71 | 849.11 | 14.7 | 0.6581 | 2 |
Design 8 | 1.961 | 1.349 | 19.25 | 14.97 | 867.89 | 33 | 0.4678 | 11 |
Design 9 | 1.327 | 2.456 | 79.44 | 12.76 | 934.89 | 12.8 | 0.4582 | 12 |
Design 10 | 1.480 | 1.814 | 87.88 | 15.83 | 813.68 | 18.6 | 0.4582 | 13 |
Design 11 | 0.932 | 1.017 | 57.53 | 7.55 | 779.58 | 22.2 | 0.5300 | 9 |
Design 12 | 0.941 | 1.326 | 57.93 | 7.86 | 883.21 | 12.0 | 0.5603 | 6 |
Design 13 | 1.353 | 2.460 | 83.24 | 12.88 | 885.27 | 17.5 | 0.4180 | 15 |
Design 14 | 1.462 | 1.835 | 90.14 | 15.81 | 892.91 | 18.4 | 0.4120 | 16 |
Design 15 | 0.940 | 1.206 | 58.59 | 7.59 | 796.96 | 22.6 | 0.5103 | 10 |
Design 16 | 0.934 | 1.328 | 58.56 | 7.88 | 866.49 | 13.6 | 0.5552 | 7 |
A: minimum of stress mean in different regions explained in Figure
B: maximum of stress STDV in different regions (MPa).
C: maximum contact slip at femoral component/bone interface (
D: maximum peg stress (MPa).
E: area of cross section (mm2).
F: maximum stress at corner points of inner contour (MPa).
Ranking of top materials and designs scenarios with regard to all technical criteria obtained from QFD.
Objectives | Max | Min | Min | Max | Min | Max | Max | Max | Relative closeness to the ideal solution | Ranking | |
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Relative weights | 0.13 | 0.10 | 0.13 | 0.08 | 0.10 | 0.16 | 0.17 | 0.13 | |||
Design options | A | B | C | D | E | F | G | H | |||
Co-Cr alloy | Original | 1.86 | 1.69 | 21.93 | 421.4 | 7.04 | 339.5 | 1 | 1 | 0.4531 | 6 |
Design 3 | 1.570 | 2.189 | 20.13 | 423.78 | 6.68 | 377.1 | 1 | 1 | 0.4554 | 5 | |
Design 11 | 0.845 | 0.958 | 61.94 | 439.95 | 6.47 | 381 | 1 | 1 | 0.4142 | 8 | |
Design 15 | 0.892 | 1.148 | 63.25 | 439.89 | 6.61 | 381.7 | 1 | 1 | 0.4064 | 9 | |
Design 5 | 2.962 | 2.682 | 35.46 | 422.95 | 7.49 | 376.1 | 1 | 1 | 0.4367 | 7 | |
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FGM | Design 6 | 4.466 | 1.866 | 40.36 | 24.83 | 3.03 | 18.2 | 3 | 3 | 0.5868 | 1 |
Design 7 | 1.741 | 1.249 | 18.03 | 34.29 | 2.95 | 17.3 | 3 | 3 | 0.5809 | 2 | |
Design 3 | 1.707 | 2.208 | 17.93 | 34.91 | 2.79 | 18.9 | 3 | 3 | 0.5584 | 3 | |
Design 1 | 3.100 | 2.655 | 30.61 | 28.84 | 3.13 | 17.6 | 3 | 3 | 0.5537 | 4 |
A: minimum of stress mean in different regions explained in Figure
B: maximum of stress STDV in different regions (MPa).
C: maximum contact slip at femoral component/bone interface (
D: safety index of peg (difference between yield of material and maximum peg stress which is 450 and 49 MPa for Co-Cr alloy and FGM resp.).
E: weight index (area of cross section
F: safety index of main body (difference between yield of material and maximum stress at corner points of inner contour in which yields of 450 and 32 MPa for Co-Cr alloy and FGM were considered, resp.).
G: biocompatibility of material.
H: hardness of interface material with PE insert.
One by one matching of technical requirements with selection criteria.
Tables
It can be seen from Tables
The present study was designed to determine the effect of inner shape geometries and material on performance of femoral component using FEA, DOE, QFD, and MADM techniques. The findings complement earlier studies on advantages of FGM over Co-Cr alloy, which is the most prevalent material for this component. The results also showed that the angle between the distal and anterior cuts and the angle between the distal and posterior cuts are the most influential factors in all responses; however the interactions were also observed. An important outcome of the present study is the fact that the geometry of femoral component using standard Co-Cr alloy is not the optimum one; the performance of component can be improved either by geometry modification for Co-Cr alloy or optimized geometry for FGM. The present study confirms previous findings that the current design of femoral component still is not the optimum and contributes additional evidence that suggests more broadly research on dimension of interface geometry in addition to angles. However, it would be more fruitful to focus on improving geometry of component with functionally graded material. Since the study was conducted using 2D FEA, the generalizability of these results may subject to some limitations. Nevertheless, these findings enhance our understanding on the most important factors and will serve as a base for future 3D studies. It was shown that how applying quality and design tools in the product-planning phase can help in translating the customer’s requirements. MADM methods in combination of DOE can improve design process in which DOE determines important design factors and MADM helps in ranking of design scenario with diverse qualitative and quantitative data. Design decision making problems need different information in which it is not possible to find the best design only based on design of experiments methods and the related optimization software. Together these results provide important insights into designer on how to improve performance of current knee implants.
The authors declare no conflict of interests.
This research project was supported by Islamic Azad University, Semnan Branch, with Grant no. 18744, and the authors would like to show their grateful thanks for the close cooperation.