Optimization Studies of Trans-tibial Prostheses: Numerical Models and Experimental Tests C. Colombo 1, E.G. Marchesin1, L. Vergani1 , E. Boccafogli 2 , G. Verni2 1) Dipartimento di Meccanica, Politecnico di Milano 2) Inail – Centro Protesi Budrio
already in the earliest design phase, taking into account from the beginning the individual factors above mentioned. In this way designers take possession of a powerful tool with a dual purpose: to maximize reliability and comfort. In particular, object of the present study is a multi purpose ankle-foot device designed by INAIL: two configurations are possible, for walking and swimming. This is possible by a relative inclination between the tibia axis and the foot, as shown in Fig. 1. The ankle is required to be water and seawater compatible, so the manufacturer’s decision was to produce it in titanium. In this study, in parallel with the experimental tests for the compliance to the standard, the attention is also focussed to the numerical model created starting from the design drawings. After its validation by a comparison between the FE simulation and the results of experimental tests on the device, other possible solutions in terms of materials and geometry are taken into consideration.
— Abstract —
This paper describes the work done at the Department of Mechanics in collaboration with INAIL, on a particular type of transtibial prosthesis. The discussed topics are different: firstly, an adaptable test bench was designed, in accordance with the standard, to run static strength and fatigue tests on the transtibial prostheses. By means this equipment, it is possible to perform tests on the prosthesis and on its individual components. After the description of some static tests, the prosthesis is also analysed by numerical FE simulations, performing structural analyses and simulating the experimental tests carried out using the bench. The numerical results of strains and displacements are compared with the corresponding experimental values measured on the prosthesis. The comparison allows validating the numerical models, which become a reliable and secure tool to perform optimizations varying the geometry and materials of the prosthesis.
I. I NTRODUCTION Limb loss is a traumatic event, both from physical as well as psychological point of view. During the postoperation and the rehabilitation phases, the medical team helps the patient to recover joint motion in order to restore the natural range of motion [1]. During this period, the patient is helped with a rehabilitative therapy therapy of the residual limb muscles, to allow a full and proper prosthesis use. In this stage of the rehabilitation, the prosthesis moves from a provisional model to a final one. By this time ti me the patient’s primary requirement becomes to lead a normal life by providing a mechanism that can replace the lost limb as close as possible to the original, both functionally and aesthetically. This goal is achieved by requiring higher performance to the prosthesis individual components and adapting the prosthesis to the person. In particular, the prosthesis must meet patients’ individual needs in terms of different requirements such as stability, durability and comfort. For this reason, when selecting components, the main parameters that must be taken into account are amputee weight, amputation type, stump conditions, habits and habitats [2]. Besides all these considerations, it is evident that the safety and the reliability of the prosthesis should be a primary goal. The aim of the experimental tests on such devices is, therefore, to achieve a tool to test the prosthesis safety, following the standards. Furthermore, developing a numerical model of a prosthesis means that the device optimization can be started
Fig. 1. INAIL prosthesis: walking (A) and swimming swimming configurations (B).
II. EXPERIMENTAL TEST EQUIPMENT ACCORDING TO ISO 10328 Object of this study is a modular prosthesis for transtibial amputees. In general, these kinds of prostheses are made of: − a liner: it is the direct interface with the stump. Its role is to create a soft gap, to avoid excessive forces transfer to the limb stump; − a socket: the rigid and custom-made element that covers the liner. Its function is to create a structural support for the whole prosthesis; − the attachments: they connect the various parts, acting as a coupling interface between the upper and lower prosthesis; − a pylon: equivalent to the tibia in a healthy subject, it is a tube of variable length linking the socket to the
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prosthetic foot; − an ankle: the component simulating the ankle joint to give a natural connotation to the walk; − a prosthetic foot: it guarantees the subject support and reflecting the behavior of a healthy foot in every stage of the walk. It is generally provided with an aesthetic coverage. For the compliance of this type of prostheses the reference standard is ISO 10328 [3], which sets out the procedures for carrying out experimental tests on all types of lower limb prostheses (transtibial and transfemoral). The standard identifies two load configurations at the maximum stress levels undergone by the limb during normal walk (shown in Fig. 2): − condition I: related to the instant of maximum loading occurring early in the stance phase of walking (heel contact); − condition II: related to the instant of maximum loading occurring late in the stance phase of walking (toe-off). For each load configuration there are three different load levels depending on physical parameters, locomotion characteristics and other factors related to the patient. In Table 1, the categories are given in detail. For the experimental tests according to these specifics, a test bench was designed and manufactured. It consists of two hydraulic actuators and a base for prosthesis constraining. The test bench is versatile to allow tests of all prostheses types in all configurations required by the standard. Depending on the required test, in fact, the load line has to be three-dimensional or two-dimensional according to the coordinate system f-o-u, which is integral with the prosthesis. A scheme of the prosthesis coordinate system is shown in Fig. 3.
a)
st
| 1 phase | 2
nd
phase |
rd
3 phase
u
o f Fig. 3. Reference coordinate system f-o-u, from ISO 10328.
In the specific case of the prosthesis object of this study, principal static proof tests are required. Due to the particular nature of this device, only static tests were planned, since it is not designed for common walking. The load level chosen for the tests is related to the P5 category, that is the most critical one. For the same reason, the foot size used for the test is the biggest available, generating the highest bending at the ankle. At first, the origin of the coordinate system is placed at the intersection between the longitudinal axis of the foot and the effective ankle-joint centerline. In this way the reference planes of the ankle (uA) and knee (uK ) are also identified, since their offsets are specified in the standard. The standard also includes the reference points on the planes where the load line has to pass at. Once the load line is fixed in a three-dimensional configuration, it is possible to find its inclination angles compared to the three principal axis, as shown in Tab. 2.
|
Table 2. Summary of the characteristic measurements for the correct placing of the prosthesis for the experimental tests.
b)
Condition I
Plane
Condition II
o-u
Fig. 2. Schematization of the stance and of the normal walk (a) and relative interpretation of the ISO 10328 standard with the two loading conditions (b).
f-u f-o o-u f-u
Table 1. Categories of patients according to ISO 10328 standard.
Category P3 P4 P5
f-o
Patient’s weight Max 60 kg Max 80 kg Max 90 kg
Loading condition I I I II II II
Load line equation u =
- 5.243 ⋅o + 236.7 u = 5⋅f + 240 o = - 0.953 ⋅f - 0.626 u = - 31.34 ⋅o - 601.3 u = - 8.77 ⋅f + 1132 o = 0.279 ⋅f - 55.30
Angle [°] 11 11 46 2 7 16
On the test bench these calculations are reflected by tilting the prosthesis axis with respect to the hydraulic actuator piston one. In this case only one actuator is used
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because the two load configurations can be implemented separately. Fig. 3 shows the experimental configuration and used equipment for the principal static proof test. During the experimental tests, in load control, piston displacements and ankle strains are recorded, in the different test configurations, for the prosthesis in walking arrangement. The arrangement for swimming, indeed, is not taken into consideration in the experimental tests, since the prosthesis results less loaded in this condition [4]. Loading condition I
ankle prosthesis mechanical behaviour. Therefore, the prosthetic foot is considered in the numerical simulations as a “black box”, whose characteristics, in terms of stiffness, are obtained from experimental tests carried out in similar conditions as the ones shown in Fig. 3 for the single foot unit. Experimental measured stiffness varies in function of the considered loading conditions (I or II) as well as of the applied load. The inner part of the prosthetic foot is indeed made of different materials: wood, for the structural part near to the ankle joint, composite and rubber, for the intermediate and external parts. The mechanical answer to different load levels is therefore different since the behaviour is globally non linear. To avoid such simulations, not object of interest for the ankle manufacturer, but with the aim of providing a valid tool by the numerical model, a linear behaviour is used to describe the foot equivalent stiffness. The foot equivalent stiffness is obtained by comparing the experimental displacements of the piston to the numerical values, as shown in Fig. 4. The geometry of the prosthetic foot is obtained by means of a triangulation 3D laser scanner and the reverse engineering technique.
Loading condition II
Fig. 4. An example of the comparison between experimental and numerical displacements, for the foot component and toe-off loading condition (II).
Fig. 3. Experimental principal static proof test: three-dimensional configuration.
III. NUMERICAL SIMULATIONS
Further numerical simulations are run afterwards considering the foot and the ankle units, joined together by rigid coupling. The ankle is made of different subcomponents, all in titanium and the behaviour of these parts is modelled as linear. In this second type of simulations, comparisons for the models’ validation are provided by means of comparisons not only with experimentally measured displacements, but also with strains placed on the ankle. Strain gauges are applied on the ankle, in easily accessible regions, where a sufficient strain is generated to provide a valid signal. In this way, the validated numerical models by means of the comparison with experimental results becomes a valid tool for further considerations on the prosthesis design. In Tab. 3 the comparison between the numerical (εnum) and experimental (εecp) strains is shown. The values of the numerical strains are calculated in correspondence of the strain gages applied to the ankle.
The problems related to this particular prosthesis are different and depend on its specific use. During the amputee walking, it is important to take into consideration the mechanical loading conditions, while when he/she is swimming the environmental factors become important. Mechanical and chemical conditions are therefore to be taken into account in the design and compliance of the ankle prosthesis. Since the foot prosthesis is made of different components, numerical simulations dealing with its structural analysis have to take into account the stiffness of each part. Three types of FE analyses are run [4]: − on the foot unit, as a standing alone component; − on the foot and ankle device, joined together; − on single components of the ankle device (sub-models). In particular, in this work the attention is focussed on the
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Table 3. Comparison between experimental and numerical results in terms of strains.
Loading condition I I II II
Applied force [N] 1024 2240 920 2013
εexp
εnum
[με] -96 -120 129 257
[με] -106 -121 141 258
the use of different cheaper materials, instead of titanium. For instance, three other materials, resistant to the corrosion, are considered: an inox austenitic steel (AISI310), an Aluminium alloy (Al7075) and an inox duplex steel (1.4462 or X2CrNiMoN22-5-3). As indicated by the safety factor in Tab. 3 for each analysed material, the choice of Al alloy resulted too strict, while it is possible the use of the two inox steels.
Diff. [%] -10.4 -0.8 -9.3 -0.4
The comparison is proposed at two different force levels, for both the loading conditions I/II. These two forces correspond to the settling and to the proof test force to be applied for static tests according to [3]. In Tab. 3 it is evident that the percentage differences between the experimental and numerical strain values are vey reduced in correspondence of the maximum applied load during the tests. Numerical simulations are therefore also run on single components of the ankle device, as sub-models. Object of this part of the study are in particular two pins placed inside the titanium ankle, where the stress condition resulted the highest during the previous simulation. These sub-models are loaded considering displacement fields. Results in terms of Von Mises stresses are shown in Fig. 5. After the validation of the numerical models, these become a reliable and secure tool to perform optimizations on the designed device. In particular, considerations can be proposed by varying the geometry and materials of the ankle prosthesis designed by INAIL, called model 1.
Table 4. Comparisons of the maximum Von Mises stress in the ankle from numerical simulations – loading condition II. Model 1: as designed by INAIL, model 2: optimized geometry.
Numerical model 1_Ti6Al4V 2_Ti6Al4V 2_AISI310 2_Al7075 2_Duplex
Max VM stress [MPa] 535.1 301.9 223.4 312.3 315.4
Diff. [%] -43.6 -58.3 -41.6 -41.1
UTS [MPa] 920 920 500 370 450
Safety factor 1.72 3.09 2.24 1.18 1.43
IV. CONCLUSIONS In the present paper, after a general introduction on transtibial lower limb prostheses and related standard, two main points were discussed. From the experimental point of view a description was presented on: − the preparation of the test equipment, which need to be versatile and applicable to different tests, such as principal (3D) and separate (2D arrangement) static tests, as well as fatigue (2D). This resulted in the use of a bench consisting of two hydraulic actuators, a control system and a fixed support boundary condition. − the experimental test on an ankle foot prosthesis, with a static tests in three dimensional configuration. During these tests, piston displacements and prosthesis strains are recorded. Considering the numerical FE simulation, a model of the prosthesis was developed and validated by a comparison with the experimental results. Once validated, the model was used as a powerful tool for the opti mization of: − the prosthetic ankle geometry, varying in particular a fillet where stresses concentrated; − the used material and alternative solutions. These proposed solutions resulted in an improvement of the stress condition on the ankle device, and in a cheaper and more reasoned use of the commercially available materials.
Fig. 5. Stress field in two sub-models of the ankle device: Von Mises stress component.
An optimized geometry is studied (model 2), paying attention to the region of maximum Von Mises stress. In particular, a modification of a fillet radius deeply changes the stress value, as indicated in Tab. 4. In this table, the maximum Von Mises stress is compared to the ultimate tensile stress (UTS), and the safety factor is calculated as their ratio. In model 2 the maximum stress is almost an half with respect to model 1. This consideration gives space to
R EFERENCES [1]Whittle MW, Gait analysis: an introduction, Elsevier, 2003. [2]October 2010: http://www.dmti.unifi.it/bioingegneria/ita/didattica_ita /Protesi%20ed%20ortesi/09%20-%20protesi%20arto%20inferiori.pdf [3]ISO 10328:2006, Prosthetics – Structural testing of lower-limb prostheses – Requirements and test methods. [4]De Giorgi A, Studio sperimentale e numerico di protesi transtibiale per cammino e nuoto, Master thesis, Politecnico di Milano, A.A. 2009-10.
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