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Effects of liner stiffness for trans-tibial prosthesis: a finite element contact model
Medical Engineering & Physics 26 (2004) 1–9 www.elsevier.com/locate/medengphy
Effects of liner stiffness for trans-tibial prosthesis: a finite element contact model Chih-Chieh Lin a, Chih-Han Chang a,∗, Chu-Lung Wu a, Kao-Chi Chung a, I-Chen Liao b a b
Institute of Biomedical Engineering, National Cheng Kung University, 1, University Road, Tainan 701, Taiwan School of Nursing, Hung Kuang Institute of Technology, 34, Chung-Chie Road, Sha Lu, Taichung 433, Taiwan Received 17 October 2002; received in revised form 7 April 2003; accepted 8 July 2003
Abstract The socket liner plays a crucial role in redistribution of the interface stresses between the stump and the socket, so that the peak interface stress could be reduced. However, how the peak stress is affected by various liner stiffnesses is still unknown, especially when the phenomenon of the stump slide within the socket is considered. This study employed nonlinear contact finite element analyses to study the biomechanical reaction of the stump sliding with particular attention to the liner stiffness effects of the transtibial prosthesis. To validate the finite element outcomes, experimental measurements of the interface stresses and sliding distance were further executed. The results showed that the biomechanical response of the stump sliding are highly nonlinear. With a less stiff liner, the slide distance of the stump would increase with a larger contact area. However, this increase in the contact area would not ensure a reduction in the peak interface stress and this is due to the combined effects of the non-uniform shape of the socket and the various sliding distances generated by the different liner stiffnesses. 2003 IPEM. Published by Elsevier Ltd. All rights reserved. Keywords: Trans-tibial socket; Liner stiffness; Interface stress; Finite element analysis
1. Introduction The socket is a fundamental component for prosthetic performance. Within the socket, the liner, which is in direct contact with the stump, plays an essential role in transmitting loads and distributing interface stresses to reduce the peak interface stress. The shape and material together determine the basic biomechanical function of the liner. In general, the liner shape is based on the socket shape, which is varied with different design concepts. The material governs the two most important mechanical factors of the liner: friction and stiffness. The effect of friction is, as a rule, an increase in shear stress and a reduction in contact pressure with larger friction coefficient [1]. However, the influence of liner stiffness is not so directly predictable, especially considering the sliding of the stump within the nonuniform-
Corresponding author. Tel.: +886-6-275-7575; fax: +886-6-2343270. E-mail address: [email protected] (C.-H. Chang). ∗
shaped prosthetic socket. This relative movement not only affects the interface stress distribution within the stump/liner, but also affects the gait pattern of the amputee. Due to complications regarding leg length discrepancy, the excessive downward displacement of the bone structure against the socket easily causes low-back pain in the amputee, joint deformation and scoliosis after long-term loading [2,3]. Both experimental and analytical approaches have been used to study the stump/socket system. Since the interface stresses between the stump and liner represent how the load is transferred from the stump to the socket, many studies have investigated the interface stresses by direct measurement using various sensors. Sanders [4] and Zhang et al. [5] recorded interface pressures and shear stresses with three-way sensors during walking. Covery and Buis [6] demonstrated that the interface pressure distribution of the patellar tendon bearing (PTB) and the hydrostatic sockets could be obtained with sensor arrays placed on the socket’s inner wall. These experimental approaches might be adequate to compare the biomechanical effects of different sockets, but it is
1350-4533/$30.00 2003 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/S1350-4533(03)00127-9
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difficult, if not impossible, to employ direct measurement approaches to investigate the biomechanical rationale of the stump/socket system, because of the difficult procedure employed in controlling and altering the design parameters during the experiments. On the other hand, simulation with finite element (FE) analysis might be more suitable to investigate the biomechanical mechanisms of stump/socket interactions. However, early FE models provided significant quantitative errors, compared with experimental measurement results, mostly due to the difficulty in setting up a realistic contact (sliding) interface between the stump and the liner. Recently, Zhang et al. [7] established a three-dimensional FE model with interface contact elements to investigate frictional effects in socket design. The simulated results correlated well with the stresses measured by three-way sensors. This suggests that current FE simulations are suitable for use as biomechanical evaluation tools for the prosthetic socket, provided that the FE model is sufficient to reflect the real-life conditions. This study presented a three-dimensional FE stump/liner model, which emphasizes geometric accuracy by use of computer tomography (CT) images of the stump and better simulation of the stump/liner interface by use of surface-to-surface contact elements. The objective of setting up this model was to investigate the biomechanical responses during the stump sliding process, with particular attention to the effect of the liner stiffness.
generated to represent the liner structure, as shown in Fig. 1a. The CT-derived planar contours of the bone and soft tissue structures were read into the CAD system (Pro/Engineering 2000, Parametric Technology Corporation, USA) and a solid model of the stump was constructed. From this solid model, tetrahedral elements were generated by the auto-mesh function of the CAD system, yielding the result described in Fig. 1b. To reduce computational complexity, the bone structure was assumed to be a single entity, i.e. the knee joint was not modeled within the stump. The interior nodes of the liner and exterior nodes of the stump were used as a pair of contacting surfaces (element types of contact 170 and target 174 in ANSYS 5.5, Swanson Analysis Inc., Huston, PA, USA) to simulate the stump/liner contact interface conditions (Fig. 1c). To simplify the model, socket structure was not included in the analysis. Instead the exterior nodes of the liner were fixed to simulate a hard socket boundary condition. In total, 8600 tetrahedron elements were generated to construct the stump; 988 brick elements were established to represent the liner, and 2200 contact elements were used to simulate the interface. The loading was applied as displacements of the stump, rather than forces on the stump. Three nodes on the superior surface of the bone structure were selected and assigned with the same vertical downward displacements in an incremental manner. Increment of the displacement loading was terminated when the total reaction force of the three loaded nodes reached 600 N (body weight of the subject) to simulate standing on a single leg.
2. Materials and methods 2.2. Determination of the material properties A unilateral trans-tibial amputee wearing a Kondylen Betrung Munster (KBM) suspension socket (a modification of the PTB socket) participated in this study. The subject had worn the socket for 9 years with no skin complications. The subject’s body weight was 60 kg. 2.1. Modeling of the FE mesh The initial relative position of the stump and socket, that is the socket being worn but prior to the application of body weight, was identified with the aid of the transverse CT scan. An in-house image processing system was employed to detect the contours of the stump (including both bone and soft tissue) as well as the socket. Since the liner could not be identified from the CT images, the outer contours of the liner were assumed to be identical to the inner contours of the socket, and the inner contours of the liner were constructed 6 mm inside the socket’s inner contours. Nodal points were placed on both the outer and inner liner contours. Stacking these liner contours and connecting the corresponding nodes between the contours, brick elements were
The material properties of the stump/liner system were assumed to be linear, regional-homogeneous and isotropic in this study. The properties of bone were adopted from the literature [8]. For improved simulation of the liner property, the compression test with the Instron system (Instron 1011, Germany) was performed on the liner. The load–displacement curve of the compression test was recorded and matched with a corresponding FE model to determine the elastic modulus of the liner via a trial and error approach (the Poisson’s ratio of the liner was set at 0.45), as shown in Fig. 2. Based on this procedure, the liner elastic modulus was selected to be 0.4 Mpa. To determine the soft tissue elastic modulus, a similar trial and error approach was used to match the finite element simulations with the corresponding compression test results in five regions of the stump. The compression test of the soft tissue was performed with a selfdeveloped indentor system (Fig. 3), while the soft tissue thickness of the corresponding finite element model was determined from the solid model of the stump. Elastic
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Fig. 1. Three-dimensional finite element mesh models of the stump/socket system: (a) liner mesh; (b) stump mesh; (c) contact pair interface mesh.
modulus and Poisson’s ratio for all materials of this stump/liner system are listed in Table 1. A simple tilting table device was used to detect the coefficient of friction (CoF) at the stump/liner interface. The CoF value was found to be 0.5 and was assigned on the stump/liner contact interface of the FE model. To investigate the effects of liner stiffness, five values for the elastic modulus, ranging from 0.4 to 0.8 Mpa, with an interval of 0.1 Mpa, were also employed in the liner structure of the FE model. 2.3. Measurement of the interface pressure and sliding distance
Fig. 2. Outcome of the liner compression material test. The upper figure shows the load–displacement curves. The lower figure is the vonMises stress distribution of the loaded liner.
To validate the outcomes of the FE simulations, the EMED-Pedar (Novel GmbH, Munich, Germany) pressure measurement system was used to quantify the stump/liner interface pressure. This sensor array system was originally adopted in a biomechanical study on the contact between the insole and the foot. The large sensor surface area was sufficient to remedy the sliding conTable 1 List of the values of elastic modulus and Poisson’s ratio used in the finite element models
Fig. 3. The self-developed manual indentor system used for the compression test of soft tissue.
Bone structures Soft tissues Patellar tendon Popliteal depression Anterolateral tibia Anteromedial tibia Others Liner Socket
Young’s modulus (Mpa)
Poisson’s ratio
15 500
0.28
2.49 0.7 0.35 0.3 0.06 0.4 to 0.8 Rigid surface
0.45 0.45 0.45 0.45 0.45 0.45
4
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dition of the stump against the socket. To compensate for the thickness of the EMED-Pedar, portions of the liner thickness were trimmed so that the sensor surface was flush with the stump/liner interface. To replicate the single leg stand loading during the FE simulation, an experienced prosthetist instructed the subject and adjusted the alignment of the prosthesis to avoid the rotation moment between the stump and the socket. Two lateral X-rays were taken to measure the sliding distance. In the first X-ray image, the intact leg was employed to support the whole body weight. This represented the unloaded state of the stump. The second image was taken when the full body weight was applied only on the stump. By superimposing the two X-ray images using the three landmarks placed on the socket, the bone downward displacement relative to the socket, could be measured by the distance between the socket landmarks and a marker placed at the bottom of the stump.
3. Results 3.1. Validation of the FE model The vertical downward displacement of the superior bone surface was 21.3 mm when the total of the reaction forces (at the three loaded nodes) reached 600 N for the 0.4 Mpa liner simulation. This displacement is comparable to the experimentally measured value, about 20 mm, on the selected subject with one-leg stand loading. The averaged peak interface pressures from experimental measurements were 590, 230, 660 and 190 Kpa on the anterior, lateral, posterior and medial surfaces of the stump, respectively. The simulated peak interface pressures of the 0.4 Mpa liner model under 600 N reaction force were 660, 397, 783 and 88 Kpa on the anterior, lateral, posterior and medial regions of the stump, respectively. Considering the many possible inaccuracies of the simulation model, particularly the material property and loading (see Section 4), differences between experimental measurements and simulated results could be regarded as insignificant. 3.2. Results of the FE simulation 3.2.1. General outcomes Although the whole bone structure slipped roughly 21 mm into the socket (0.4 Mpa model), the downward displacement on the soft tissue ranged from 12 to 21 cm, with the smallest displacement occurring at the posterior contact region of the stump as shown in Fig. 4.The contact pressure and friction (shear) stress distributions on the stump are shown in Fig. 5. The peak pressure was present at the posterior, while the peak friction stress occurred at the anterior (Table 2).
3.2.2. Sliding process In terms of the sliding process, the major supporting area was initially at the anterior and then gradually shifted to the posterior region, as observed from the contact pressure force (summation of the pressure multiplied by the area) (Fig. 6). The anterior contact region on the stump moved upward as it slid into the socket and the size of the anterior contact area on the stump remained roughly constant. The posterior contact region on the stump initially moved upward as it slid into the socket, then the posterior soft tissue reduced its downward displacement speed relative to the bone structure, i.e. the posterior soft tissue began to ‘pack’ within the liner, and the size of the posterior contact area on the stump increased. This packing effect would decrease the vertical downward displacement of soft tissue at the posterior contact area as mentioned in Section 3.2.1. 3.2.3. Effects of liner stiffness With the total of the three reaction forces reaching 600 N, the maximum vertical downward displacement of the superior bone surface with different liner stiffnesses are shown in the Fig. 7. As the value of the liner elastic modulus increased from 0.4 to 0.8 Mpa, the maximum downward displacement decreased from 21 to 17 mm, which is consistent with general mechanical concepts. However, the variations in peak interface stresses did not show a consistent trend as the liner stiffness changed. The values and regions of peak contact pressure and friction stresses of the five models are listed in Table 2. From the Table, it is obvious that the model with the 0.6 Mpa liner has the lowest values in both peak interface pressure and friction stress.
4. Discussion 4.1. Model set-up Three factors govern the reliability of FE analysis: geometry, material and boundary conditions. In this study, the realistic of the geometry was assured, within a tolerable level, by the CT images. This was further confirmed by the almost identical locations (which differed by less than 1 cm) of the peak interface pressure between the simulated and measured results on the four regions (anterior, posterior, medial and lateral). This demonstrated that the major support sites of the stump against the socket were similar between the experimental and FE models. (The exact sites of peak pressure in the four regions are not presented in the results, because of the difficulty in describing their locations and as their exact positions are relatively insignificant.) However, the effect of neglecting the socket structure needs further investigation. The assumption of the linear material property of the
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Fig. 4. The downward displacement distributions on the stump exterior surface: (a) anterior view; (b) lateral view; (c) posterior view; (d) medial view.
Fig. 5. The interface stress distributions between the stump and the socket for Liner 0.4 model: (a) pressure distribution; (b) friction (shear) stress distribution.
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Table 2 List of the values and locations of peak contact pressure and peak friction (shear) stress for different liner models
Liner Liner Liner Liner Liner
0.4 0.5 0.6 0.7 0.8
Peak pressure
Peak friction stress
783 780 607 634 645
314 373 287 298 307
kPa kPa kPa kPa kPa
(post. region) (ant. region) (ant. region) (ant. region) (ant. region)
kPa kPa kPa kPa kPa
(ant. (ant. (ant. (ant. (ant.
region) region) region) region) region)
Fig. 6. Pressure force (summation of the element contact pressure multiplied by the element contact area) at the anterior, posterior, medial and lateral regions of the stump for Liner 0.4. The horizontal axis is the downward displacement of the bone structure.
Fig. 7. Maximum downward displacement of bone structure for Liner 0.4, Liner 0.5, Liner 0.6, Liner 0.7 and Liner 0.8 models under 600 N of reaction force.
liner used in this study was reasonable, as demonstrated in the compression test results (Fig. 2). However, the load–displacement curve from the indentor test on the soft tissue did not show a near-linear line and variations existed from test to test. These are due to the more noticeable nonlinear property of the soft tissue and the deviation in manually controlled loading. However, to simplify the FE computation, for each region a single value of elastic modulus was used in the trial and error
phase. This simplification of the soft tissue material property should demonstrate dissimilarities between the FE and experimental results especially on the stress value. Nevertheless, the difference between the outcomes of these two approaches are within an acceptable range for the FE model to be employed to inspect both the sliding process and the liner stiffness effects. With the surface-to-surface contact elements representing the stump/liner interface, the sliding phenomenon could be simulated by the FE model. These simulated bone displacements (17 to 21mm for the five-liner models) were within the range of other experimental measurements (11 to 23 mm) on various PTB sockets [9,10]. More importantly, these considerable slip distances induced a nonlinear effect on the biomechanical response of the interface, which is difficult to predict with previous linear FE models [11,12]. These nonlinear effects could easily be identified form the force–displacement curves in Fig. 6. This indicated that to properly reflect the biomechanical behavior of the stump/liner interface, the sliding of the stump within the socket should be considered within the FE model, especially for the socket with potentially large slip, such as the PTB design. Apart from the contact interface, loading is another issue that needed to be considered in the FE analysis. Three features were included for assigning the loading: magnitude, location and distribution. In this study, the loading was given as a uniform displacement on the superior bone surface, instead of force. This tactic would cause the (reaction) forces on the three loaded nodes to auto-redistribute themselves, so that the rotation (moment) effects on the stump could be minimized. In addition, the location of the three loaded nodes must be considered. From our experience, the selected locations could influence the FE results (see Section 4.2.2). Improper selection of the loaded nodes could prevent the convergence of the nonlinear FE simulations. However, based on our tests, as long as the three loaded nodes are far enough apart to cover most of the superior bone surface, the effect of the locations of the three nodes was minimal. With this uniform displacement approach, loading could provide a suitable condition for other parameters, e.g. liner stiffness, to be studied. 4.2. Sliding process 4.2.1. Stiffness effects In the sliding process of the 0.4 Mpa model, due to the large elastic modulus assigned at the anterior softtissue (patellar–tendon region), the compression deformation was mostly on the liner (compare the anterior contact regions of Fig. 8a and b). This resulted in the anterior contact location on the liner remaining at almost the same site, while the soft tissue contact location moved upward as the stump slides into the socket and
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Fig. 8. (a) Sagittal section view of the mesh model at initial position. (b) Sagittal section view for Liner 0.4 model at maximum displacement.
the vertical displacement at the anterior region of the soft tissue is almost the same as the bone structure (Fig. 4a). This indicated that when a senor is fixed to the socket to measure the anterior interface stress during experiments, the measured values are not located at the same position on the soft tissue, but distributed over a range roughly equal to the bone displacement. For the posterior region, the soft tissue elastic modulus was of the same order as the liner. Accordingly, the compression deformation was distributed on both the soft tissue and the liner (compare the posterior contact regions of Fig. 8a and b). The posterior soft tissue is packed into the socket’s bell shape when the stump slides a certain amount into the socket. This results in a smaller posterior soft tissue displacement, compared with the bone structure, and an increase in the posterior contact area as the stump slides into the socket. Therefore, the posterior contact force was initially less than the anterior contact force, due to the smaller elastic modulus of the posterior soft tissue, and which increased more rapidly than the anterior force due to the packing effect (Fig. 6). 4.2.2. Loading effects With regard to the reaction forces of the nodes, the most anterior node initially had the largest downward reaction force, while the most posterior node had an ‘upward’ reaction force. This was due to the same downward displacement being applied on the three loaded nodes. Since the posterior region of the socket offered less resistance than the anterior region in the initial slip process (as stated in Section 4.2.1), to maintain the same
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downward displacements for these two nodes, the posterior loaded node must have an upward reaction force to reduce its slip distance. Thus, the distribution of the three reaction forces could induce a loading center (averaged loading position of the three reaction forces with zero moment on the superior bone surface) located at the anterior of the geometric center of the superior bone surface, in order to decrease the posterior downward displacement. As the stump slides further into the socket, the increasing posterior socket resistance caused the posterior reaction force to flip downwards and increase in magnitude, while the anterior reaction force decreased. In other words, the loading center moved posteriorly in order to maintain the same downward displacement for the three loaded nodes. From this observation of the reaction forces, it can be concluded that if uniform pressure were applied on the superior surface of the bone structure, the stump would slip more on the posterior region and have a different resting position, as demonstrated in this simulation. The interface stress could then differ tremendously from the results of this analysis. This indicates that the loading distribution (not just the loading magnitude) plays a very sensitive role in determining the interface stress. This might explain the variations of interface stresses from experimental measurement on the same subject at different trial sections, because a small differences in the standing posture could cause variations in loading center, and thus variations in the interface stresses. 4.3. Liner stiffness effects The effects of liner stiffness on trans-tibial socket have been studied by Zhang et al. [7] and Silver-Thorn and Childress [1] using FE analyses. In Zhang’s study the averaged interface stress was not sensitive to the liner stiffness, which was different from the results of this study. Although the slip/friction interface was included in Zhang’s model, the exterior of the stump surface was modeled identically with the interior surface of the liner, which induced a total contact condition between the stump and socket. This total contact interface would minimize the sliding in the simulations, which could be observed from the less than 10 mm of vertical displacement in Zhang’s model, even with zero friction and 800 N of loading. In the FE model used by Silver-Thorn and Childress [1], the interface stress demonstrated a moderately sensitive response to the liner material. This outcome is consistent with our simulations. However, the interface stress variations were different between our two studies. In their results, the interface stress either decreased or increased (depending on the locations) in relation to the liner stiffness. However, in our study, the minimal peak interface stresses occurred in the liner 0.6 Mpa model, which was neither highest nor lowest liner stiffness
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Table 3 List of the sizes of total contact area for the five different liner models at the maximum downward displacement Total contact area Liner Liner Liner Liner Liner
0.4 0.5 0.6 0.7 0.8
13918 12314 11984 11791 11730
mm2 mm2 mm2 mm2 mm2
(Table 2). The main reason could be that Silver-Thorn and Childress [1] ignored the sliding behavior. Two parameters were examined to clarify the variations of interface stress against liner stiffness. Firstly the total contact areas of the five liner stiffness models were listed in Table 3. From the Table, it can be seen that the contact areas increased with reduction of the liner stiffness, which is consistent with general mechanical concept. However, this increase of contact area did not always induce a reduction in peak interface stress. The compression depths (horizontal displacement at the peak stress sites) on the stump anterior, lateral, posterior, and medial regions of the five models were list in Table 4. From Table, the compression depth does not show a clear relationship with the changes in the liner stiffness. This demonstrated that the combined effects of the various stump sliding distances and the non-uniform shape of the socket could be the major reason for the variations of interface stresses. Finally, it is noted that the convergence of the nonlinear FE simulation could not be achieved, with our modeling approach, on the liner with elastic modulus less than 0.4 Mpa. Further improvements on the modeling technique are under analysis with the latest version of the FE package.
5. Conclusion This study established a three-dimensional stump/socket FE model with accurate tomography-based stump geometry and improved surface-to-surface contact Table 4 List of the horizontal contact depths at the peak pressure locations of the anterior, lateral, posterior, and medial regions of the stump for the five different liner models
Liner Liner Liner Liner Liner
0.4 0.5 0.6 0.7 0.8
A
L
P
M
2.60 2.37 2.33 2.24 2.49
5.71 5.65 4.01 4.70 5.87
9.19 11.76 9.30 11.08 14.91
5.06 3.26 2.80 4.63 2.59
interface conditions to investigate the biomechanical responses during stump sliding. Three conclusions could be drawn from this study. First, the stump sliding behavior is a vital factor in the socket evaluation for it could induce highly non-linear reactions in other mechanical indices. Second, the peak interface stresses are moderately sensitive to the liner stiffness. But the effect of liner stiffness is not straightforward and could not be examined alone. Other design factors, such as socket shape, should be considered together to actually reflect the liner stiffness influence. Last, but not least, the FE analysis could be a suitable and affordable approach to study the rationale of the complicated stump/socket system. More realistic finite element models, e.g. with socket structure, are continuously required to investigate the stump/socket system. Only with sufficient biomechanical knowledge of this system could the socket design process be improved effectively.
Acknowledgements The authors would like to thank the National Science Council, Republic of China, for its financial support of this work under contract No. NSC89-2614-E006-010.
References [1] Silver-Thorn MB, Childress DS. Parametric analysis using the finite element method to investigate prosthetic interface stress for person with trans-tibial amputation. Journal of Rehabilitation Research and Development 1996;33:227–38. [2] Giles LG, Taylor JR. Low-back pain associated with leg length inequality. Spine 1981;6:510–21. [3] Papaioannou T, Stokes I, Kenwright J. Scoliosis associated with limb-length inequality. Journal of Bone and Joint Surgery-American 1982;64:59–62. [4] Sanders JE. Effects of alignment changes on stance phase pressures and shear stresses on transtibial amputees: Measurements from 13 transducer sites. IEEE Transactions on Rehabilitation Engineering 1998;6:21–31. [5] Zhang M, Turner-Smith AR, Tranner A, Roberts VC. Clinical investigation of the pressure and shear stress on the trans-tibial stump with a prosthesis. Medical Engineering and Physics 1998;20:188–98. [6] Buis AWP, Convery P. Socket/stump interface dynamic pressure distributions recorded during the prosthetic stance phase of gait of a trans-tibial amputee wearing a hydrocast socket. Prosthetics and Orthotics International 1999;23:107–12. [7] Zhang M, Turner-Smith AR, Roberts VC, Tanner A. Friction action at lower limb/prosthetic socket interface. Medical Engineering and Physics 1996;18:207–14. [8] Steege JW, Childress DS. Finite element estimation of pressure at the below-knee socket interface. In: Report of ISPO Workshop on CAD/CAM in prosthetics and Orthotics, Seattle. 1988. p. 71–82. [9] Eriksson U, Lempberg R. Roentgenological study of movements of the amputation amputation stump within the prosthesis socket in below knee amputees fitted with a PTB prosthesis. Acta Orthopaedica Scandinavica 1969;40:520–9.
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[10] Grevsten S, Erikson U. A roentgenological study of the stumpsocket contact and skeletal displacement in the PTB-suction prosthesis. Uppsala Journal of Medical Science 1975;80:49–57. [11] Brennan JM, Childress DS. Finite element and experimental investigation of above-knee amputee limb/prosthesis aystem: a
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comparative study. ASME Advances in Bioengineering 1991;20:547–50. [12] Reynolds DP, Lord M. Interface load analysis for computer-aided design of below-knee prosthetic socket. Medical and Biological Engineering and Computing 1992;30:419–26.
Effects of liner stiffness for trans-tibial prosthesis: a finite element contact model Chih-Chieh Lin a, Chih-Han Chang a,∗, Chu-Lung Wu a, Kao-Chi Chung a, I-Chen Liao b a b
Institute of Biomedical Engineering, National Cheng Kung University, 1, University Road, Tainan 701, Taiwan School of Nursing, Hung Kuang Institute of Technology, 34, Chung-Chie Road, Sha Lu, Taichung 433, Taiwan Received 17 October 2002; received in revised form 7 April 2003; accepted 8 July 2003
Abstract The socket liner plays a crucial role in redistribution of the interface stresses between the stump and the socket, so that the peak interface stress could be reduced. However, how the peak stress is affected by various liner stiffnesses is still unknown, especially when the phenomenon of the stump slide within the socket is considered. This study employed nonlinear contact finite element analyses to study the biomechanical reaction of the stump sliding with particular attention to the liner stiffness effects of the transtibial prosthesis. To validate the finite element outcomes, experimental measurements of the interface stresses and sliding distance were further executed. The results showed that the biomechanical response of the stump sliding are highly nonlinear. With a less stiff liner, the slide distance of the stump would increase with a larger contact area. However, this increase in the contact area would not ensure a reduction in the peak interface stress and this is due to the combined effects of the non-uniform shape of the socket and the various sliding distances generated by the different liner stiffnesses. 2003 IPEM. Published by Elsevier Ltd. All rights reserved. Keywords: Trans-tibial socket; Liner stiffness; Interface stress; Finite element analysis
1. Introduction The socket is a fundamental component for prosthetic performance. Within the socket, the liner, which is in direct contact with the stump, plays an essential role in transmitting loads and distributing interface stresses to reduce the peak interface stress. The shape and material together determine the basic biomechanical function of the liner. In general, the liner shape is based on the socket shape, which is varied with different design concepts. The material governs the two most important mechanical factors of the liner: friction and stiffness. The effect of friction is, as a rule, an increase in shear stress and a reduction in contact pressure with larger friction coefficient [1]. However, the influence of liner stiffness is not so directly predictable, especially considering the sliding of the stump within the nonuniform-
Corresponding author. Tel.: +886-6-275-7575; fax: +886-6-2343270. E-mail address: [email protected] (C.-H. Chang). ∗
shaped prosthetic socket. This relative movement not only affects the interface stress distribution within the stump/liner, but also affects the gait pattern of the amputee. Due to complications regarding leg length discrepancy, the excessive downward displacement of the bone structure against the socket easily causes low-back pain in the amputee, joint deformation and scoliosis after long-term loading [2,3]. Both experimental and analytical approaches have been used to study the stump/socket system. Since the interface stresses between the stump and liner represent how the load is transferred from the stump to the socket, many studies have investigated the interface stresses by direct measurement using various sensors. Sanders [4] and Zhang et al. [5] recorded interface pressures and shear stresses with three-way sensors during walking. Covery and Buis [6] demonstrated that the interface pressure distribution of the patellar tendon bearing (PTB) and the hydrostatic sockets could be obtained with sensor arrays placed on the socket’s inner wall. These experimental approaches might be adequate to compare the biomechanical effects of different sockets, but it is
1350-4533/$30.00 2003 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/S1350-4533(03)00127-9
2
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difficult, if not impossible, to employ direct measurement approaches to investigate the biomechanical rationale of the stump/socket system, because of the difficult procedure employed in controlling and altering the design parameters during the experiments. On the other hand, simulation with finite element (FE) analysis might be more suitable to investigate the biomechanical mechanisms of stump/socket interactions. However, early FE models provided significant quantitative errors, compared with experimental measurement results, mostly due to the difficulty in setting up a realistic contact (sliding) interface between the stump and the liner. Recently, Zhang et al. [7] established a three-dimensional FE model with interface contact elements to investigate frictional effects in socket design. The simulated results correlated well with the stresses measured by three-way sensors. This suggests that current FE simulations are suitable for use as biomechanical evaluation tools for the prosthetic socket, provided that the FE model is sufficient to reflect the real-life conditions. This study presented a three-dimensional FE stump/liner model, which emphasizes geometric accuracy by use of computer tomography (CT) images of the stump and better simulation of the stump/liner interface by use of surface-to-surface contact elements. The objective of setting up this model was to investigate the biomechanical responses during the stump sliding process, with particular attention to the effect of the liner stiffness.
generated to represent the liner structure, as shown in Fig. 1a. The CT-derived planar contours of the bone and soft tissue structures were read into the CAD system (Pro/Engineering 2000, Parametric Technology Corporation, USA) and a solid model of the stump was constructed. From this solid model, tetrahedral elements were generated by the auto-mesh function of the CAD system, yielding the result described in Fig. 1b. To reduce computational complexity, the bone structure was assumed to be a single entity, i.e. the knee joint was not modeled within the stump. The interior nodes of the liner and exterior nodes of the stump were used as a pair of contacting surfaces (element types of contact 170 and target 174 in ANSYS 5.5, Swanson Analysis Inc., Huston, PA, USA) to simulate the stump/liner contact interface conditions (Fig. 1c). To simplify the model, socket structure was not included in the analysis. Instead the exterior nodes of the liner were fixed to simulate a hard socket boundary condition. In total, 8600 tetrahedron elements were generated to construct the stump; 988 brick elements were established to represent the liner, and 2200 contact elements were used to simulate the interface. The loading was applied as displacements of the stump, rather than forces on the stump. Three nodes on the superior surface of the bone structure were selected and assigned with the same vertical downward displacements in an incremental manner. Increment of the displacement loading was terminated when the total reaction force of the three loaded nodes reached 600 N (body weight of the subject) to simulate standing on a single leg.
2. Materials and methods 2.2. Determination of the material properties A unilateral trans-tibial amputee wearing a Kondylen Betrung Munster (KBM) suspension socket (a modification of the PTB socket) participated in this study. The subject had worn the socket for 9 years with no skin complications. The subject’s body weight was 60 kg. 2.1. Modeling of the FE mesh The initial relative position of the stump and socket, that is the socket being worn but prior to the application of body weight, was identified with the aid of the transverse CT scan. An in-house image processing system was employed to detect the contours of the stump (including both bone and soft tissue) as well as the socket. Since the liner could not be identified from the CT images, the outer contours of the liner were assumed to be identical to the inner contours of the socket, and the inner contours of the liner were constructed 6 mm inside the socket’s inner contours. Nodal points were placed on both the outer and inner liner contours. Stacking these liner contours and connecting the corresponding nodes between the contours, brick elements were
The material properties of the stump/liner system were assumed to be linear, regional-homogeneous and isotropic in this study. The properties of bone were adopted from the literature [8]. For improved simulation of the liner property, the compression test with the Instron system (Instron 1011, Germany) was performed on the liner. The load–displacement curve of the compression test was recorded and matched with a corresponding FE model to determine the elastic modulus of the liner via a trial and error approach (the Poisson’s ratio of the liner was set at 0.45), as shown in Fig. 2. Based on this procedure, the liner elastic modulus was selected to be 0.4 Mpa. To determine the soft tissue elastic modulus, a similar trial and error approach was used to match the finite element simulations with the corresponding compression test results in five regions of the stump. The compression test of the soft tissue was performed with a selfdeveloped indentor system (Fig. 3), while the soft tissue thickness of the corresponding finite element model was determined from the solid model of the stump. Elastic
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Fig. 1. Three-dimensional finite element mesh models of the stump/socket system: (a) liner mesh; (b) stump mesh; (c) contact pair interface mesh.
modulus and Poisson’s ratio for all materials of this stump/liner system are listed in Table 1. A simple tilting table device was used to detect the coefficient of friction (CoF) at the stump/liner interface. The CoF value was found to be 0.5 and was assigned on the stump/liner contact interface of the FE model. To investigate the effects of liner stiffness, five values for the elastic modulus, ranging from 0.4 to 0.8 Mpa, with an interval of 0.1 Mpa, were also employed in the liner structure of the FE model. 2.3. Measurement of the interface pressure and sliding distance
Fig. 2. Outcome of the liner compression material test. The upper figure shows the load–displacement curves. The lower figure is the vonMises stress distribution of the loaded liner.
To validate the outcomes of the FE simulations, the EMED-Pedar (Novel GmbH, Munich, Germany) pressure measurement system was used to quantify the stump/liner interface pressure. This sensor array system was originally adopted in a biomechanical study on the contact between the insole and the foot. The large sensor surface area was sufficient to remedy the sliding conTable 1 List of the values of elastic modulus and Poisson’s ratio used in the finite element models
Fig. 3. The self-developed manual indentor system used for the compression test of soft tissue.
Bone structures Soft tissues Patellar tendon Popliteal depression Anterolateral tibia Anteromedial tibia Others Liner Socket
Young’s modulus (Mpa)
Poisson’s ratio
15 500
0.28
2.49 0.7 0.35 0.3 0.06 0.4 to 0.8 Rigid surface
0.45 0.45 0.45 0.45 0.45 0.45
4
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dition of the stump against the socket. To compensate for the thickness of the EMED-Pedar, portions of the liner thickness were trimmed so that the sensor surface was flush with the stump/liner interface. To replicate the single leg stand loading during the FE simulation, an experienced prosthetist instructed the subject and adjusted the alignment of the prosthesis to avoid the rotation moment between the stump and the socket. Two lateral X-rays were taken to measure the sliding distance. In the first X-ray image, the intact leg was employed to support the whole body weight. This represented the unloaded state of the stump. The second image was taken when the full body weight was applied only on the stump. By superimposing the two X-ray images using the three landmarks placed on the socket, the bone downward displacement relative to the socket, could be measured by the distance between the socket landmarks and a marker placed at the bottom of the stump.
3. Results 3.1. Validation of the FE model The vertical downward displacement of the superior bone surface was 21.3 mm when the total of the reaction forces (at the three loaded nodes) reached 600 N for the 0.4 Mpa liner simulation. This displacement is comparable to the experimentally measured value, about 20 mm, on the selected subject with one-leg stand loading. The averaged peak interface pressures from experimental measurements were 590, 230, 660 and 190 Kpa on the anterior, lateral, posterior and medial surfaces of the stump, respectively. The simulated peak interface pressures of the 0.4 Mpa liner model under 600 N reaction force were 660, 397, 783 and 88 Kpa on the anterior, lateral, posterior and medial regions of the stump, respectively. Considering the many possible inaccuracies of the simulation model, particularly the material property and loading (see Section 4), differences between experimental measurements and simulated results could be regarded as insignificant. 3.2. Results of the FE simulation 3.2.1. General outcomes Although the whole bone structure slipped roughly 21 mm into the socket (0.4 Mpa model), the downward displacement on the soft tissue ranged from 12 to 21 cm, with the smallest displacement occurring at the posterior contact region of the stump as shown in Fig. 4.The contact pressure and friction (shear) stress distributions on the stump are shown in Fig. 5. The peak pressure was present at the posterior, while the peak friction stress occurred at the anterior (Table 2).
3.2.2. Sliding process In terms of the sliding process, the major supporting area was initially at the anterior and then gradually shifted to the posterior region, as observed from the contact pressure force (summation of the pressure multiplied by the area) (Fig. 6). The anterior contact region on the stump moved upward as it slid into the socket and the size of the anterior contact area on the stump remained roughly constant. The posterior contact region on the stump initially moved upward as it slid into the socket, then the posterior soft tissue reduced its downward displacement speed relative to the bone structure, i.e. the posterior soft tissue began to ‘pack’ within the liner, and the size of the posterior contact area on the stump increased. This packing effect would decrease the vertical downward displacement of soft tissue at the posterior contact area as mentioned in Section 3.2.1. 3.2.3. Effects of liner stiffness With the total of the three reaction forces reaching 600 N, the maximum vertical downward displacement of the superior bone surface with different liner stiffnesses are shown in the Fig. 7. As the value of the liner elastic modulus increased from 0.4 to 0.8 Mpa, the maximum downward displacement decreased from 21 to 17 mm, which is consistent with general mechanical concepts. However, the variations in peak interface stresses did not show a consistent trend as the liner stiffness changed. The values and regions of peak contact pressure and friction stresses of the five models are listed in Table 2. From the Table, it is obvious that the model with the 0.6 Mpa liner has the lowest values in both peak interface pressure and friction stress.
4. Discussion 4.1. Model set-up Three factors govern the reliability of FE analysis: geometry, material and boundary conditions. In this study, the realistic of the geometry was assured, within a tolerable level, by the CT images. This was further confirmed by the almost identical locations (which differed by less than 1 cm) of the peak interface pressure between the simulated and measured results on the four regions (anterior, posterior, medial and lateral). This demonstrated that the major support sites of the stump against the socket were similar between the experimental and FE models. (The exact sites of peak pressure in the four regions are not presented in the results, because of the difficulty in describing their locations and as their exact positions are relatively insignificant.) However, the effect of neglecting the socket structure needs further investigation. The assumption of the linear material property of the
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Fig. 4. The downward displacement distributions on the stump exterior surface: (a) anterior view; (b) lateral view; (c) posterior view; (d) medial view.
Fig. 5. The interface stress distributions between the stump and the socket for Liner 0.4 model: (a) pressure distribution; (b) friction (shear) stress distribution.
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Table 2 List of the values and locations of peak contact pressure and peak friction (shear) stress for different liner models
Liner Liner Liner Liner Liner
0.4 0.5 0.6 0.7 0.8
Peak pressure
Peak friction stress
783 780 607 634 645
314 373 287 298 307
kPa kPa kPa kPa kPa
(post. region) (ant. region) (ant. region) (ant. region) (ant. region)
kPa kPa kPa kPa kPa
(ant. (ant. (ant. (ant. (ant.
region) region) region) region) region)
Fig. 6. Pressure force (summation of the element contact pressure multiplied by the element contact area) at the anterior, posterior, medial and lateral regions of the stump for Liner 0.4. The horizontal axis is the downward displacement of the bone structure.
Fig. 7. Maximum downward displacement of bone structure for Liner 0.4, Liner 0.5, Liner 0.6, Liner 0.7 and Liner 0.8 models under 600 N of reaction force.
liner used in this study was reasonable, as demonstrated in the compression test results (Fig. 2). However, the load–displacement curve from the indentor test on the soft tissue did not show a near-linear line and variations existed from test to test. These are due to the more noticeable nonlinear property of the soft tissue and the deviation in manually controlled loading. However, to simplify the FE computation, for each region a single value of elastic modulus was used in the trial and error
phase. This simplification of the soft tissue material property should demonstrate dissimilarities between the FE and experimental results especially on the stress value. Nevertheless, the difference between the outcomes of these two approaches are within an acceptable range for the FE model to be employed to inspect both the sliding process and the liner stiffness effects. With the surface-to-surface contact elements representing the stump/liner interface, the sliding phenomenon could be simulated by the FE model. These simulated bone displacements (17 to 21mm for the five-liner models) were within the range of other experimental measurements (11 to 23 mm) on various PTB sockets [9,10]. More importantly, these considerable slip distances induced a nonlinear effect on the biomechanical response of the interface, which is difficult to predict with previous linear FE models [11,12]. These nonlinear effects could easily be identified form the force–displacement curves in Fig. 6. This indicated that to properly reflect the biomechanical behavior of the stump/liner interface, the sliding of the stump within the socket should be considered within the FE model, especially for the socket with potentially large slip, such as the PTB design. Apart from the contact interface, loading is another issue that needed to be considered in the FE analysis. Three features were included for assigning the loading: magnitude, location and distribution. In this study, the loading was given as a uniform displacement on the superior bone surface, instead of force. This tactic would cause the (reaction) forces on the three loaded nodes to auto-redistribute themselves, so that the rotation (moment) effects on the stump could be minimized. In addition, the location of the three loaded nodes must be considered. From our experience, the selected locations could influence the FE results (see Section 4.2.2). Improper selection of the loaded nodes could prevent the convergence of the nonlinear FE simulations. However, based on our tests, as long as the three loaded nodes are far enough apart to cover most of the superior bone surface, the effect of the locations of the three nodes was minimal. With this uniform displacement approach, loading could provide a suitable condition for other parameters, e.g. liner stiffness, to be studied. 4.2. Sliding process 4.2.1. Stiffness effects In the sliding process of the 0.4 Mpa model, due to the large elastic modulus assigned at the anterior softtissue (patellar–tendon region), the compression deformation was mostly on the liner (compare the anterior contact regions of Fig. 8a and b). This resulted in the anterior contact location on the liner remaining at almost the same site, while the soft tissue contact location moved upward as the stump slides into the socket and
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Fig. 8. (a) Sagittal section view of the mesh model at initial position. (b) Sagittal section view for Liner 0.4 model at maximum displacement.
the vertical displacement at the anterior region of the soft tissue is almost the same as the bone structure (Fig. 4a). This indicated that when a senor is fixed to the socket to measure the anterior interface stress during experiments, the measured values are not located at the same position on the soft tissue, but distributed over a range roughly equal to the bone displacement. For the posterior region, the soft tissue elastic modulus was of the same order as the liner. Accordingly, the compression deformation was distributed on both the soft tissue and the liner (compare the posterior contact regions of Fig. 8a and b). The posterior soft tissue is packed into the socket’s bell shape when the stump slides a certain amount into the socket. This results in a smaller posterior soft tissue displacement, compared with the bone structure, and an increase in the posterior contact area as the stump slides into the socket. Therefore, the posterior contact force was initially less than the anterior contact force, due to the smaller elastic modulus of the posterior soft tissue, and which increased more rapidly than the anterior force due to the packing effect (Fig. 6). 4.2.2. Loading effects With regard to the reaction forces of the nodes, the most anterior node initially had the largest downward reaction force, while the most posterior node had an ‘upward’ reaction force. This was due to the same downward displacement being applied on the three loaded nodes. Since the posterior region of the socket offered less resistance than the anterior region in the initial slip process (as stated in Section 4.2.1), to maintain the same
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downward displacements for these two nodes, the posterior loaded node must have an upward reaction force to reduce its slip distance. Thus, the distribution of the three reaction forces could induce a loading center (averaged loading position of the three reaction forces with zero moment on the superior bone surface) located at the anterior of the geometric center of the superior bone surface, in order to decrease the posterior downward displacement. As the stump slides further into the socket, the increasing posterior socket resistance caused the posterior reaction force to flip downwards and increase in magnitude, while the anterior reaction force decreased. In other words, the loading center moved posteriorly in order to maintain the same downward displacement for the three loaded nodes. From this observation of the reaction forces, it can be concluded that if uniform pressure were applied on the superior surface of the bone structure, the stump would slip more on the posterior region and have a different resting position, as demonstrated in this simulation. The interface stress could then differ tremendously from the results of this analysis. This indicates that the loading distribution (not just the loading magnitude) plays a very sensitive role in determining the interface stress. This might explain the variations of interface stresses from experimental measurement on the same subject at different trial sections, because a small differences in the standing posture could cause variations in loading center, and thus variations in the interface stresses. 4.3. Liner stiffness effects The effects of liner stiffness on trans-tibial socket have been studied by Zhang et al. [7] and Silver-Thorn and Childress [1] using FE analyses. In Zhang’s study the averaged interface stress was not sensitive to the liner stiffness, which was different from the results of this study. Although the slip/friction interface was included in Zhang’s model, the exterior of the stump surface was modeled identically with the interior surface of the liner, which induced a total contact condition between the stump and socket. This total contact interface would minimize the sliding in the simulations, which could be observed from the less than 10 mm of vertical displacement in Zhang’s model, even with zero friction and 800 N of loading. In the FE model used by Silver-Thorn and Childress [1], the interface stress demonstrated a moderately sensitive response to the liner material. This outcome is consistent with our simulations. However, the interface stress variations were different between our two studies. In their results, the interface stress either decreased or increased (depending on the locations) in relation to the liner stiffness. However, in our study, the minimal peak interface stresses occurred in the liner 0.6 Mpa model, which was neither highest nor lowest liner stiffness
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Table 3 List of the sizes of total contact area for the five different liner models at the maximum downward displacement Total contact area Liner Liner Liner Liner Liner
0.4 0.5 0.6 0.7 0.8
13918 12314 11984 11791 11730
mm2 mm2 mm2 mm2 mm2
(Table 2). The main reason could be that Silver-Thorn and Childress [1] ignored the sliding behavior. Two parameters were examined to clarify the variations of interface stress against liner stiffness. Firstly the total contact areas of the five liner stiffness models were listed in Table 3. From the Table, it can be seen that the contact areas increased with reduction of the liner stiffness, which is consistent with general mechanical concept. However, this increase of contact area did not always induce a reduction in peak interface stress. The compression depths (horizontal displacement at the peak stress sites) on the stump anterior, lateral, posterior, and medial regions of the five models were list in Table 4. From Table, the compression depth does not show a clear relationship with the changes in the liner stiffness. This demonstrated that the combined effects of the various stump sliding distances and the non-uniform shape of the socket could be the major reason for the variations of interface stresses. Finally, it is noted that the convergence of the nonlinear FE simulation could not be achieved, with our modeling approach, on the liner with elastic modulus less than 0.4 Mpa. Further improvements on the modeling technique are under analysis with the latest version of the FE package.
5. Conclusion This study established a three-dimensional stump/socket FE model with accurate tomography-based stump geometry and improved surface-to-surface contact Table 4 List of the horizontal contact depths at the peak pressure locations of the anterior, lateral, posterior, and medial regions of the stump for the five different liner models
Liner Liner Liner Liner Liner
0.4 0.5 0.6 0.7 0.8
A
L
P
M
2.60 2.37 2.33 2.24 2.49
5.71 5.65 4.01 4.70 5.87
9.19 11.76 9.30 11.08 14.91
5.06 3.26 2.80 4.63 2.59
interface conditions to investigate the biomechanical responses during stump sliding. Three conclusions could be drawn from this study. First, the stump sliding behavior is a vital factor in the socket evaluation for it could induce highly non-linear reactions in other mechanical indices. Second, the peak interface stresses are moderately sensitive to the liner stiffness. But the effect of liner stiffness is not straightforward and could not be examined alone. Other design factors, such as socket shape, should be considered together to actually reflect the liner stiffness influence. Last, but not least, the FE analysis could be a suitable and affordable approach to study the rationale of the complicated stump/socket system. More realistic finite element models, e.g. with socket structure, are continuously required to investigate the stump/socket system. Only with sufficient biomechanical knowledge of this system could the socket design process be improved effectively.
Acknowledgements The authors would like to thank the National Science Council, Republic of China, for its financial support of this work under contract No. NSC89-2614-E006-010.
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