Medical Engineering & Physics 32 (2010) 623–629
Contents lists available at ScienceDirect
Medical Engineering & Physics journal homepage: www.elsevier.com/locate/medengphy
Ankle–foot simulator development for testing ankle–foot orthoses Hung-Jen Lai a , Chung-Huang Yu b , Hung-Chan Kao a,c , Wen-Chuan Chen a , Chi-Wei Chou a , Cheng-Kung Cheng a,c,∗ a
Institute of Biomedical Engineering, National Yang-Ming University, Taipei, Taiwan Department of Physical Therapy and Assistive Technology, National Yang-Ming University, Taipei, Taiwan c Orthopaedic Device Research Center, National Yang-Ming University, Taipei, Taiwan b
a r t i c l e
i n f o
Article history: Received 27 January 2010 Received in revised form 30 March 2010 Accepted 31 March 2010 Keywords: Ankle–foot simulator Ankle–foot orthoses Fatigue failure
a b s t r a c t The fatigue failure of thermoplastic ankle–foot orthoses (AFOs) was observed in clinics. However, there was no standard evaluation for the AFOs to enhance the understanding of how AFOs become more readily acceptable to patients. Therefore, this study aimed to develop an ankle–foot simulator (AFS) as a testing apparatus for AFOs, and performed a pilot test to investigate the failure mechanism of anterior ankle–foot orthosis (AAFO). The accuracy and repeatability of the AFS during cyclic walking, cyclic stepping and cyclic stepping with the AAFO in sagittal plane were measured. The root mean square errors (RMSEs) of cyclic walking of AFS compared to a target gait data were less than 80.52N and 2.55◦ in the vertical ground reaction force and in the kinematics, respectively. The RMSE of ankle plantarflexion and dorsiflexion of AFS in the cyclic stepping tests were less than 1.25◦ . The repeatability was assessed by standard deviation, which were less than 9.46N and 0.72◦ in all testing conditions. A typical failure progression of five AAFOs was observed and graded for four phases under cyclic stepping test. Failure always initiated at the junction of anterior tarsal bar and lateral (or medial) bar of the AAFOs, from which the rest failures were extended. It is suggested that this junction must be reinforced or prevented the stress concentration to elongate the endurance of AAFO. © 2010 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction Ankle–foot orthoses (AFOs) are applied to assist patients with abnormal muscle tone or muscle force of lower extremity. AFOs have benefits on force assistance for tibialis anterior-decelerating plantarflexion during heel-strike and assisting toe clearance during swing phase. In addition, non-hinged AFOs further resist ankle dorsiflexion during late stance of gait and raise the heel and play the role as the gastrocnemius-soleus muscle group [1]. AFOs may thus increase the patient’s walking cadence, walking speed [2] and reduce energy expenditure during ambulation [3]. In clinics, most of the functions of AFOs mentioned above are passively occurred by withstanding the flexing loading from users. Thus orthoses fatigue failure is inevitable. AFOs made of strong materials such as carbon fiber or metal could prolong their usage. However, low-temperature thermoplastic materials were widely used due to their lightweight and ease of
∗ Corresponding author at: Institute of Biomedical Engineering, National YangMing University, No. 155, Sec. 2, Li-Nong St., Taipei 112, Taiwan. Tel.: +886 228267355. E-mail address:
[email protected] (C.-K. Cheng).
molding. In Taiwan, more than 27,000 low-temperature thermoplastic AFOs were made a year (2007), and most of them were for stroke patients [4]. Another benefit for choosing low-temperature thermoplastic materials is that it is easier to be re-modified if the symptoms of patient were in progress, such as muscle tone or joint range of motion. Among various types of low-temperature thermoplastic AFOs, the anterior ankle–foot orthosis (AAFO) with non-hinged joint is widely used. While using the AAFO, the regions of tarsal and metatarsal are encased in the orthosis and the heel is able to contact on the ground [5,6]. As studies showed, AAFO do correct gait and provide ankle mediolateral [5] and postural stability [6,7] during walking or standing, and is suitable for indoor barefoot walking [8]. However, the drawback of this type of AFOs seems not able to sustain daily ambulation for a long time. Breakage of AAFO was commonly seen in clinics (Fig. 1). In addition, AFOs are usually made by therapists with their diverse experiences. Some of the AFOs experience failure within several months. Therefore, it is important to understand the failure mechanism of thermoplastic AFOs under specific loading condition. To date, the failure mechanism of thermoplastic AFOs is not clear, while it is an important reference indication to the health insurance policy. Although there were some studies estimating the properties of AFOs, such as stiffness, flexibility, viscoelastic-
1350-4533/$ – see front matter © 2010 IPEM. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.medengphy.2010.03.008
624
H.-J. Lai et al. / Medical Engineering & Physics 32 (2010) 623–629
sagittal plane. One linear actuator was applied to move foot of AFS upward and downward. A forceplate (4060NC, Bertec, USA) under the foot of AFS provides signals of the vertical ground reaction force (VGRF) for evaluating and controlling the kinetic performance of AFS (Fig. 3a). A computer with a motion controller (PCI-7344, NI, USA) ran a self-developed LabVIEW (version 8.2, NI, USA) program, which could control motors of AFS to the desired motions, including the gait data captured from a subject. The sagittal plane was defined on the AP axis of foot of AFS and perpendicular to the ground. 2.2. Ankle–foot simulator evaluation test
Fig. 1. A clinical low-temperature thermoplastic AAFO (using Orfit-NS material) fractured at the interface of tarsal bar and lateral bar of AAFO.
ity [9–14], and the stress distribution [16–18] of AFOs, we were unaware of study or simulator [15] focused on testing the fatigue failure of AFOs. Therefore, the purpose of this study was to develop an ankle–foot simulator (AFS) as a testing apparatus for AFOs, which included design, manufacture, and evaluate its performance. After that, this study performed a pilot study to investigate the failure mechanisms of AAFO by using the AFS. 2. Methods 2.1. Ankle–foot simulator design The AFS was designed to simulate a human’s leg comprising a foot, an ankle joint and shank. One emulated foot prosthesis (KFT0126R, Ken Dall, Taiwan) with two modified ankle joint axes was applied to the AFS (Fig. 2). One of the axes is the medial–lateral (M–L) axis, which provides ankle plantarflexion and dorsiflexion, and ensures lateral heel and toes (1st and 2nd) to be the ground-contacted region at heel-strike and toe-off of natural gait (Fig. 2, circles). The other axis is aligned to anterior–posterior (A–P) direction, which tilts up 15◦ to simulate longitudinal axis of the transverse tarsal joint, and allows ankle inversion and eversion. The effect of muscle tone was simulated by applying joint stiffness with springs mounted around the ankle joint of AFS. Ankle range of motion is adjustable manually. Two servo motors were applied to move shank of AFS forward/backward and flexion/extension in
Three test conditions were chosen to evaluate the performance of AFS, including cyclic walking [19], cyclic stepping and cyclic stepping with the AAFO. Cyclic walking of the AFS is to simulate the kinematics and kinetics of level walking in sagittal plane with continuous loading from heel-strike to toe-off. Cyclic stepping of the AFS is to simulate the simplified motions of stepping on the stairs, ramp, or transfer from sit-to-stand or stand-to-sit exercises with specified ankle plantarflexion and dorsiflexion. The third test was for further understanding the influence of wearing AAFO with an external constraint on the AFS. For these three tests, four parameters, VGRF, foot tilting angle (FT), angle of ankle joint (AJ), and shank tilting angle (ST) in sagittal plane were analyzed (Fig. 3b). For cyclic walking test, a healthy woman’s walking data gathered from motion analysis system (VICON 370, Oxford, UK) were chosen and inputted to the AFS as “target gait data”, in which the VGRF and the kinematic information of markers on the subject’s tibial wand, lateral malleolus, heel, and metatarsal head were calculated and simulated. The first 15 cycles of simulation were to fine-tune the trajectories of leg motion to minimize the error of VGRF. The error of VGRF was determined by subtracting the target VGRF from those of AFS performed in the last cycle. In order to reach the target VGRF, the linear actuator of AFS adjusted the up/down trajectories of foot to the forceplate proportional to the error of VGRF. The AFS therefore could perform VGRF close to the target VGRF gradually. After that, another 90 cycles of VGRF and the kinematic data of total six LED markers (Visualeyez 4000, PTI, Canada) on the AFS were recorded (Fig. 3c and d). Four of these six LED markers were mounted on the leg of AFS referring to the location of markers mounted on the subject’s leg; the other two were mounted on the forceplate for identifying the horizontal line (0◦ ) of the system. The accuracy of VRGF, FT, AJ and ST (AFS) was assessed by root mean square error (RMSE), and the repeatability
Fig. 2. One emulated foot prosthesis with modified M–L axis, A–P axis and springs for the AFS.
H.-J. Lai et al. / Medical Engineering & Physics 32 (2010) 623–629
625
Fig. 3. (a) The AFS apparatus with a camera system. (b) The parameters (FT, AJ, and ST) of AFS were evaluated by (c) the motion analysis system with six LED markers (arrows) and a forceplate for the tests of cyclic walking, cyclic stepping without AAFO, and (d) cyclic stepping with AAFO.
of VRGF, FT, AJ and ST was assessed by mean standard deviations (SD) as follows:
100
Repeatabilitywalk
⎛ ⎞2 100 90 1 1 ⎝ AFSi − Targetj ⎠ Accuracywalk = 100
j=1
90
i=1
j
⎛
1 ⎝ = 100 j=1
90
(AFSij − AFSj ) i=1 90 − 1
2
⎞ ⎠
where i is AFS trials, total 90 cycles were analyzed. j is % of stance phase, integral, total 100% was analyzed. For cyclic stepping test without or with AAFO, the processes were as follows (Fig. 4): shank of AFS tilted 105◦ , along this shank
Fig. 4. (a)–(f) The cyclic stepping test with ankle plantarflexion and then dorsiflexion, (g) and (h) foot lifted and returned for next cycle.
626
H.-J. Lai et al. / Medical Engineering & Physics 32 (2010) 623–629
Table 1 The accuracy and repeatability of AFS in three testing conditions were evaluated. Test items
Walking (n = 90)
Stepping without AAFO (n = 20)
Accuracy (RMSE)
VGRF (N) FT (◦ ) AJ (◦ ) ST (◦ )
Repeat.* (SD)
80.52 1.94 2.14 2.55
9.46 0.53 0.33 0.48
Accuracy (RMSE)
Stepping with AAFO (n = 20) Repeat.* (SD)
Plantar.†
Dorsi.‡
NA 0.67§ 0.06 0.63
NA 0.05§ 0.37 0.43
4.90 0.60 0.72 0.38
Accuracy (RMSE)
Repeat.* (SD)
Plantar.†
Dorsi.‡
NA 2.09§ 1.25 0.85
NA 0.61§ 1.00 0.40
5.36 0.39 0.46 0.25
NA: no reference for accuracy assessment; Repeat.*: repeatability; Plantar.†: plantarflexion 15◦ ; Dorsi.‡: dorsiflexion 20◦ . § Data here were compared to 0◦ while foot of AFS stepped on the forceplate.
axis, foot was approached to the forceplate until foot flat, after that, holding for 150 ms, then foot lifted and shank moved forward for foot approached to the forceplate again with shank tilted 70◦ , after foot flat, holding for 150 ms, and then foot lifted and shank returned for next cycle. The angles of 105◦ and 70◦ were determined as “target angles”. The period including holding and return time was 1.8 s/cycle. Both target angles (105◦ as plantarflexion 15◦ , 70◦ as dorsiflexion 20◦ ) and test period (0.56 Hz) met the requirement of the cyclic test in ISO22675. The stiffness of ankle joint was set to simulate a flaccid leg (no spring) of stroke patients. The passive ankle inversion and eversion of AFS were allowed within ±3◦ . The LED markers were mounted as same as the markers in cyclic walking test for motion analysis. In order to decrease the interference from the strength change of an AAFO, only 20 cycles were run and analyzed. Theoretically, AJ is equal to ST while foot of AFS is flat on the ground. The angles of AJ and ST in plantarflexion and dorsiflexion were determined by averaging those samples in the holding time (150 ms). The accuracy of AJ and ST was assessed by RMSE compared to the target angles. The repeatability of VGRF, AJ and ST was assessed by SD as follows:
20 1 Accuracystep(plantar,dorsiflexion) = (AFSi − Target)2 20
Repeatabilitystep =
20 i=1
i=1
(AFSi − AFSi )
2
20 − 1
where i is AFS trials, total 20 cycles were analyzed. There was no accuracy test of VGRF in cyclic stepping test due to the ankle joint of AFS was set to flaccid type, and therefore VGRF will highly depend on the strength of AFO while foot of AFS approached on the ground. The frame rate of motion analysis system was set to 60 Hz, and the sampling rate of forceplate was 100 Hz. Both equipments were calibrated before the test.
continue testing or not. In addition, one USB camera was set for capturing the images of the AAFO while the orthosis every stepped on the forceplate at the holding time (Fig. 3a). These images were recorded for investigating the failure progression of AAFO retrospectively. The lifespan of AAFO was the tested cycles before AAFO fatigue failure. 3. Results The ankle–foot simulator is a novel apparatus and has been developed for testing AFOs (Fig. 3a). The accuracy and repeatability of AFS in cyclic walking, cyclic stepping, and cyclic stepping with AAFO were evaluated (Table 1). The AFS could simulate a subject’s walking VGRF with 80.52N RMSE, in which the double peak forces (607N and 676N) were achieved (Fig. 5a). At the same time, the AFS achieved the motion pattern approximated to the subject’s gait data with the RMSE less than 2.55◦ (Fig. 5b–d). For cyclic stepping without or with AAFO, the AJ of AFS reached the target angles with the RMSEs less than 0.37◦ and 1.25◦ , respectively (Fig. 6a and c). Stepping with AAFO induced higher VGRF for about 100N than that of without AAFO (Fig. 6b and d). For the pilot AAFO fatigue failure test, the averaged lifespan of five AAFOs was 38,498 ± 8386 cycles. Three of the five AAFOs experienced fatigue failure at medial side of ankle and the other two at lateral side. The typical failure progression was found in the following four phases: phase 0: the medial and lateral bars of AAFO were deformed (expanded) while ankle plantarflexion and dorsiflexion without observable breakages (Fig. 7a); phase 1: a separation occurred at the junction of anterior tarsal bar and medial (or lateral) bar of the AAFO (Fig. 7b). This separation began at anterior side and then was gradually extended to the posterior side (Fig. 7c). Phase 2: a crack occurred at the junction of tarsal bar and posterior-medial (or -lateral) bar of AAFO (Fig. 7d). Phase 3: a completed crack occurred at the interface of tarsal bar and medial (or lateral) bar of AAFO (Fig. 7e and f). In this AAFO test, the phases 1 and 2 started at the 2.25% and 92.09% of lifespan, respectively. 4. Discussion
2.3. Pilot test on AAFO fatigue failure A low-temperature thermoplastic material (Orfit-NS, 3.2 mm thickness, non-perforated, Orfit Industries, Belgium) was used to make the AAFO for the AFS. Five AAFOs were molded by one clinical therapist to minimize the variation of manual techniques. The pre-cut thermoplastic material was softened by heating to 70 ◦ C for 5 min in water bath, and shaped on the AFS with 90◦ of AJ within 15 min. Then the AAFO was cooled at room temperature for 30 min before the cyclic test. The setting for AAFO fatigue failure test is the same as cyclic stepping test, except the test was run until the maximal crack or tear length on the orthosis is greater than the half of mediolateral width of AAFO; or medial bar or lateral bar of AAFO cracked or tore completely (fatigue failure). For the test of every 4000 cycles (2 h), the AFS stopped for 5 min for investigators to evaluate the status of the AAFO and to determine whether to
To date, several studies used simulators to test the failure of total ankle implant or ankle prosthesis [20] but not AFOs. Most of the AFO tests focused on the stiffness, flexibility, viscoelasticity [9–14], and stress distribution [16–18] of AFOs under loading except the study by Lunsford et al. reporting the by-product of microfracture on the AFO after their viscoelastic test [13]. However, Lunsford et al. fixed the bottom of AFO on a horizontal plane and moved the dummy shank forwards and backwards to simulate ankle dorsiflexion and plantarflexion [13]. This kind of setting was suitable for viscoelastic test but different from our clinical observation, such as the fixed AFO bottom and the rotation center (RC) of ankle–foot. In this study, several features of the AFS were improved for testing AFO. Firstly, the change of RC of ankle–foot of AFS during stepping or walking that affect AFO deformation could be simulated. Fig. 4b and c shows the ‘heel rocker’ that the forefoot of AFS approached to the ground
H.-J. Lai et al. / Medical Engineering & Physics 32 (2010) 623–629
627
Fig. 5. Cyclic walking test. Comparing target gait data (n = 1, bold line) and the AFS gait data (n = 90, thin lines) in (a) VGRF, (b) FT, (c) AJ, and (d) ST parameters.
with the RC close to the heel. In this phase, the AFO sustains ankle plantarflexion. Fig. 4e and f shows the ‘ankle rocker’ that the RC was at the M–L axis of ankle joint. The AFO now sustains ankle dorsiflexion. Secondly, the AFO was bound on the AFS with two Velcro straps the same as a patient wearing an AFO. These could provide realistic deformation and motion pattern of AFO while ankle flex. Thirdly, the AFS can be programmed to simulate a subject’s gait with the feedback control of VGRF in sagittal plane. The impact of the AFO to the ground thus could be better simulated (Fig. 5a). Furthermore, the mechanism of adjustable ankle joint stiffness (using springs) was designed for further simulating subject’s muscle tone since abnormal muscle tone may result in preloads on the AFO. Finally, the fatigue failure progression of AFOs along with ground reaction
force (GRF) can be recorded through a forceplate. The changes in the GRF under the same kinematic loading condition could reflect the structural strength of AFO. The AFS could simulate a normal subject’s gait, including the kinetics and kinematics in sagittal plane with certain errors. The RMSE (80.5N) in VGRF was mainly resulted from the rising delay (about 0.06 s) at heel-strike (Fig. 5a), which was caused by insufficient torque of motors against the inertia of AFS and should be replaced with higher torque motors in the future study. However, the RMSE were not divergent during repeated cyclic tests. And the pattern of double peak forces of VGRF was simulated after heelstrike; the impact energy (integrated from time-VGRF diagram) was approximated to 97.10% compared with the subject’s data;
Fig. 6. Cyclic stepping test. The AJ and ST in (a) and (c) charts were the averaged data for 20 cycles, and (b) and (d) were the corresponding VGRF.
628
H.-J. Lai et al. / Medical Engineering & Physics 32 (2010) 623–629
Fig. 7. (a)–(e) and (f) The typical failure progression (phases 0–3) of the AAFO under cyclic stepping test. Solid arrows indicate failure locations.
and the SD in the VGRF, FT, AJ and ST were less than 1.30%, 0.83%, 1.90% and 0.80% of performed full-scales of AFS, respectively. Further evaluation tests about simulating patients’ gait with an AFO are required if the fatigue failure mechanism of a custom-made AFO in their typical gait is concerned. The AFS could also perform stepping on the ground with ankle plantarflexion and dorsiflexion. For cyclic stepping tests, we observed that the distal part of AAFO deformed and tended to slide anteriorly and posteriorly (about 5 mm) relative to the foot of AFS while ankle flexed. The deformed and slid AAFOs were also observed in clinics due to the RC is posterior to the nonhinged AAFO while ankle flex. The AFS was set to move with the same motion trajectories in both cyclic stepping tests without and with AAFO; however, the deformed AAFO actually increased the thickness under foot, which increased the FT about 1.42◦ in plantarflexion and 0.56◦ in dorsiflexion, as compared to those of without AAFO. In addition, the AAFO constrained the ankle joint and resisted the driving force of AFS. The angles of ankle plantarflexion and dorsiflexion of AFS were thus decreased about 1.19◦ and 0.63◦ , and the VGRF was increased about 100N, as compared to those of without AAFO. These evaluation tests provided the information about the actual kinematic and kinetics conditions applied by the AFS, and gave us chance to correct the errors by modifying the settings of AFS. The settings of AFS could be achieved automatically by further integrating the gyroscope or tilting sensors in the AFS, which feedback the signals of angular velocity or tilting angles performed by the AFS rather than using other motion analysis system. The results of pilot test on AAFO fatigue failure were based on some conditions or limitations of AFS: firstly, only sagittal plane motions of AFS were concerned in this study. The motions of shank in frontal and transverse planes were constrained and could be improved by modifying the design of AFS in future. However, the passive ankle inversion and eversion in frontal plane were allowed within ±3◦ in this study. This was to simulate a flaccid foot in an AAFO. Secondly, as there is no standard for AFOs fatigue failure test yet, the test angles and period of this AAFO fatigue failure test were referred to the most related standard: the cyclic test in ISO22675 (Prosthetics-Testing of ankle–foot devices and foot units—Requirements and test methods). The maximal plantarflexion and dorsiflexion suggested by the ISO standard were 15◦ and 20◦ respectively. However, with the AJ errors shown in Table 1, the actual tested angles in our study were about 13.75◦ in plantarflexion and 19◦ in dorsiflexion. The actual tested angles were still larger than those of stroke patients ambulating with AFOs [1], but usually occurred while patients take the exercises, such as up and down
the stairs. This AAFO fatigue failure test showed the results of using harsh loading conditions and would thus decrease the testing cycles while fatigue failure of AAFO was reached. On the other hand, the application of the test loading conditions of ISO 22675 is guided by ISO 22676. The ISO22676 suggests a crank-rocker mechanism for cyclic bending the ankle–foot prostheses in sagittal plane, but its mechanism is too simple to adjust the testing angles, VGRF, and the effect of muscle tone that are required for testing AFOs, instead, these parameters in AFS are programmable or adjustable. Thirdly, the materials of foot and shank of AFS are rubber and ABS. No emulated soft tissues were applied on the AFS and might cause higher contact force on the AAFO with non-ductile Velcro straps during tests. Finally, although five AAFOs were made by one clinical therapist to decrease the variation of manual techniques, the manual force and temperature on the AAFO were difficult to quantify during molding and could affect the bonding strength of thermoplastic material. The bond of anterior tarsal bar and medial (or lateral) bar of AAFO was always separated first during the test, where was close to the location of peak von Mises stress analyzed by our previous finite element analysis [18]. The type of final AAFO fatigue failure (Fig. 7f) also showed high consistency to our clinical findings (Fig. 1). Therefore, the AAFO fatigue failure test by the AFS is applicable. The junction of anterior tarsal bar and medial (or lateral) bar of AAFO (Fig. 7f, bold arrow) is the key breaking point, which should be reinforced to prevent the following failure of AAFO. 5. Conclusions With several limitations, the ankle–foot simulator with cyclic walking and cyclic stepping conditions have been developed and evaluated and can be an applicable apparatus for testing AFOs (AAFO). The typical failure progression of low-temperature thermoplastic AAFO was observed under cyclic stepping test with the simulation of flaccid foot. And the junction of anterior tarsal bar and lateral (or medial) bar of AAFO is believed as the key location which should be reinforced or prevented the stress concentration to improve the endurance of AAFO. Acknowledgments The authors acknowledge the financial support from the National Science Council (NSC) of Taiwan (NSC 97-2221-E-010004-MY3), and thanks to Mr. Wan-Meng Lee for the assistance in data collection.
H.-J. Lai et al. / Medical Engineering & Physics 32 (2010) 623–629
Conflict of interest None declared. References [1] Lehmann JF, Esselman PC, Ko MJ, Smith JC, deLateur BJ, Dralle AJ. Plastic ankle–foot orthoses: evaluation of function. Arch Phys Med Rehabil 1983;64:402–7. [2] Gök H, Küc¸ükdeveci A, Altinkaynak H, Yavuzer G, Ergin S. Effects of ankle–foot orthoses on hemiparetic gait. Clin Rehabil 2003;17:137–9. [3] Franceschini M, Massucci M, Ferrari L, Agosti M, Paroli C. Effects of an ankle–foot orthosis on spatiotemporal parameters and energy cost of hemiparetic gait. Clin Rehabil 2003;17:368–72. [4] National Health Insurance Research Database. Taipei, Taiwan: NHRI Publication; 2007. [5] Wu SH. An anterior direct molding ankle–foot orthosis. J Occup Ther Assoc Roc 1992;10:75–81. [6] Chen CL, Yeung KT, Wang CH, Chu HT, Yeh CY. Anterior ankle–foot orthosis effects on postural stability in hemiplegic patients. Arch Phys Med Rehabil 1999;80:1587–92. [7] Chen CK, Hong WH, Chu NK, Lau YC, Lew HL, Tang SFT. Effects of an anterior ankle-foot orthosis on postural stability in stroke patients with hemiplegia. Am J Phys Med Rehabil 2008;87:815–20. [8] Wong AMK, Tang FT, Wu SH, Chen CM. Clinical trial of a low-temperature plastic anterior ankle foot orthosis. Am J Phys Med Rehabil 1992;71:41–3. [9] Cappa P, Patane F, Pierro MM. A novel device to evaluate the stiffness of anklefoot-orthosis devices. J Biomech Eng 2003;125:913–7.
629
[10] Cappa P, Patane F, Rosa GD. A continuous loading apparatus for measuring three-dimensional stiffness of ankle-foot orthoses. J Biomech Eng 2005;127:1025–9. [11] Nagaya M. Shoehorn-type ankle-foot orthoses: prediction of flexibility. Arch Phys Med Rehabil 1997;78:82–4. [12] Klasson B, Convery P, Raschke S. Test apparatus for the measurement of the flexibility of ankle-foot orthoses in planes other than the loaded plane. Prosthet Orthot Int 1998;22:45–53. [13] Lunsford TR, Ramm T, Miller JA. Viscoelastic properties of plastic pediatric AFOs. J Prosthet Orthot 1994;6:3–9. [14] Chu TM. Determination of peak stress on polypropylene ankle-foot orthoses due to weight change using strain gage technology. Exp Tech 2000;24:28– 30. [15] Aubin PM, Cowley MS, Ledoux WR. Gait simulation via a 6-DOF parallel robot with iterative learning control. IEEE Trans Biomed Eng 2008;55:1237– 40. [16] Chu TM, Reddy NP. Stress distribution in the ankle-foot orthosis used to correct pathological gait. J Rehabil Res Dev 1995;32:349–60. [17] Chu TM, Reddy NP, Padovan J. Three-dimensional finite element stress analysis of the polypropylene, ankle-foot orthosis: static analysis. Med Eng Phys 1995;17:372–9. [18] Cheng KH, Lai HJ, Cheng HC, Chen WC, Chou CW, Cheng CK. Investigating the failure factors of low temperature thermoplastic anterior ankle-foot-orthosis by finite element analysis. In: 4th World Congress on Bioengineering WACBE. 2009. [19] Lai HJ, Yu CH, Chen WC, Chang TW, Lin KJ, Cheng CK. Development of a walking robot for testing ankle foot orthosis—Robot validation test. In: 13th International Conference on Biomedical Engineering. 2009. p. 1061–4. [20] Affatato S, Leardini A, Leardini W, O’Connor JJ, Viceconti M. Wear results of a new design of ankle prosthesis. J Biomech 2006;39(Suppl. 1):S143.