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applied
sciences
Article
Biomechanical Analysis of Two Types of
Osseointegrated Transfemoral Prosthesis
Agostino Igor Mirulla 1, Stefano Di Paolo 2, Francesco Di Simone 1, Tommaso Ingrassia 1 ,*,
Vincenzo Nigrelli 1, Stefano Zaffagnini 3and Laura Bragonzoni 2
1Department of Engineering, Universitàdegli Studi di Palermo, 90128 Palermo, Italy;
agostinoigor.mirulla@community.unipa.it (A.I.M.); francesco.disimone@community.unipa.it (F.D.S.);
vincenzo.nigrelli@unipa.it (V.N.)
2Department for Life Quality Studies, University of Bologna, Campus Rimini, 47921 Rimini, Italy;
stefanodipaolo92@gmail.com (S.D.P.); laura.bragonzoni4@unibo.it (L.B.)
3
Clinica Ortopedica e Traumatologica II, IRCCS Istituto Ortopedico Rizzoli, via Pupilli 1, 40136 Bologna, Italy;
stefano.zaffagnini@unibo.it
*Correspondence: tommaso.ingrassia@unipa.it
Received: 30 October 2020; Accepted: 19 November 2020; Published: 21 November 2020
Abstract:
In the last two decades, osseointegrated prostheses have been shown to be a good alternative
for lower limb amputees experiencing complications in using a traditional socket-type prosthesis;
however, restraining biomechanical issues, such as peri-prosthetic bone fractures or loosening, are
present. To better understand and overcome these limiting issues, and thus reduce the number
of implant failures, many studies have investigated the stress distribution on bone and implant
during normal daily activities. The aim of this study was a biomechanical analysis of two different
osseointegrated implants, a screw-type (OPRA) and a press fit system (OPL, Osseointegrated Prosthetic
Limb), to evaluate the stresses generated in bone and prosthesis during a fall. In particular, four
scenarios have been experimentally reproduced to determine the loads on the limb during different
kinds of fall. For this purpose, a motion capture system and a force plate have been used. Numerical
FEM (Finite Element Method) simulations have been performed to compare the behaviour of the
OPRA and OPL systems in different fall scenarios. The obtained results showed that a fall backwards
due to balance loss is the most stressful scenario among the ones analysed. As regards the comparison
between OPRA and OPL devices, it emerged they have similar behaviours in terms of peak values of
the stress, but the OPL implant generates larger high-stress areas in the distal femur as compared
with the OPRA system.
Keywords:
osseointegrated prosthesis; transfemoral amputee; finite element analysis; CAD;
OPRA; OPL
1. Introduction
Two main prosthetic systems are mainly used to treat transfemoral amputees: the socket-type
prosthesis and the OsseoIntegrated (OI) prosthesis. In the first case, a limb prosthesis is attached to the
stump of an amputee using a socket designed to fully contain the residual limb. This approach often
causes complications at the socket–stump interface mainly due to skin problems, poor fit, discomfort,
sweating and poor proprioception and controllability [
1
]. It has been observed that complications
associated with traditional socket-type prostheses can occur in more than 60% of patients [2,3].
Osseointegrated prostheses have been developed since the early 1990s [
4
] and thanks to their
design they make it possible to overcome many complications associated with socket-fitted implants.
OI prostheses, in fact, are based on osseointegration phenomena and do not require any socket. An
Appl. Sci. 2020,10, 8263; doi:10.3390/app10228263 www.mdpi.com/journal/applsci
Appl. Sci. 2020,10, 8263 2 of 16
osseointegrated prosthesis is directly attached to the skeletal system by percutaneous implant surgically
inserted in the medullary canal of the residual femur [
5
,
6
] and, as a result, the artificial limb can
be directly linked to the skeletal system. In particular, a stem, made of biocompatible material, is
inserted into the medullary canal of the residual bone and after the healing period, during which the
implant fully integrates with the bone tissue, the external prosthesis can be connected to the femur by
a percutaneous abutment.
To achieve an optimal osseointegration, the most important aspects are biocompatibility, shape
and surface treatment of stem, bone quality and surgical protocol, in addition to a gradual application
of load [
7
]. After the osseointegration has occurred, the patient develops a special condition, called
“osseoperception” [
8
]. It allows the patient to feel the weight of the prosthesis and thereby to activate
the residual muscles, improving the freedom of movement of patient and thus his quality of life [
9
–
15
].
Patients with OI prosthesis report greater improvement of quality of life and mobility, as well as pain
and infection reduction, compared to those with socket-type prosthesis [10,12,13,16,17].
Currently, two main designs are available for OI transfemoral prostheses: the screw-fixation
type and the press-fit one. Both systems are composed of an intramedullary stem (fixture) and a
coupling device (abutment) which passes through the soft tissues of the stump to link with the artificial
limb [
18
–
20
]. The two systems differ in structure and composition of the intramedullary stem. A
press-fit device is composed of a stem covered with a layer of highly porous metal [
4
,
21
] and achieves
skeletal integration as a result of bone penetration and ingrowth [
22
]. A screw-type device, instead, has
a threaded titanium stem that is screwed in the medullary cavity and has been developed by adapting
the technology used for osseointegrated dental implants. The press-fit device is usually used only
for transfemoral amputees [
23
]; the screw-type system, instead, is used both for transfemoral and
transhumeral implants [
24
]. The OPRA system (Integrum, Mölndal, Sweden) is the most representative
example of screw-type implants; OPL (Osseointegrated Prosthetic Limb, Permedica s.p.a., Milan, Italy)
and ISP Endo/Exo prostheses (ESKA Orthopaedic Handels, Lübeck, Germany) are the most common
press-fit devices. Nowadays, OPRA, ISP and OPL are the most commercially available systems for
direct skeletal attachment of external limb prostheses [1].
The procedure to implant these systems consists of the same main stages. Initially, the fixture is
surgically implanted into the medullary cavity. At a later stage, after a healing period during which the
fixture is maintained unloaded and the bone–implant integration occurs, the abutment is connected
to the fixture using a retaining bolt. The healing period varies depending on the type of implant:
about 6–8 weeks for the press-fit systems and up to 6 months for the OPRA implants [
25
,
26
]. In both
cases, after the fixture implantation, the bone–implant interface is irregular and consists of regions
with gaps between the bone and the stem and regions of direct contact between the bone and the
implant [
27
]. The gaps between the bone and the fixture will be later filled by compact bone thanks to
bone-remodelling processes [27].
The long term success of OI implants is highly related to the mechanical loading acting on the
bone and on the prosthesis during patients’ lifetime. Daily activities and unexpected critical events
may produce, obviously, loadings of different kinds and magnitude that could cause failures. Two of
the most common complications, in fact, are implant failures and peri-prosthetic bone fractures [
4
,
21
].
For these reasons, it is very interesting to fully understand the stress and strain distribution on the bone,
the prosthesis and at the bone/fixture interface. Due to the complexity of this kind of investigation,
numerical simulations are often used to assess the risks that patients can face. For several years, the
Finite Element Method (FEM) has been used largely to investigate medical problems, especially in the
field of orthopaedic implants [
28
–
30
]. Nowadays, the level of reliability and accuracy of FEM analyses
is very high and, in many cases, it is comparable with that of the experimental studies [31,32].
Several studies used FEM to investigate the stress distribution on bone and implants during
normal daily activities [
4
,
25
,
27
,
33
–
39
]. Nevertheless, no relevant studies in the literature have focused
on the effects of critical events, such as falls, on osseointegrated transfemoral implants.
Appl. Sci. 2020,10, 8263 3 of 16
The objective of this study was twofold. Firstly, different types of falls were investigated to
identify the most dangerous fall scenario, and secondly, how the stress distributions during a fall vary
depending on the specific prosthetic design was investigated. Two different implants, OPRA and OPL,
have been compared.
2. Materials and Methods
2.1. Experimental Evaluation of Loads
To experimentally evaluate the loads on the prosthetic limb during different fall scenarios, one
healthy subject (male, 90 kg, 1.80 m, 31 years old) has been recruited. The subject was equipped
with appropriate protections on knees, elbows and hands. The experimental tests were carried
out on a wooden walkway (Figure 1) containing one force plate (P-6000, BTS Bioengineering, BTS
Bioengineering, Garbagnate Milanese, Italy).
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 16
Several studies used FEM to investigate the stress distribution on bone and implants during
normal daily activities [4,25,27,33–39]. Nevertheless, no relevant studies in the literature have focused
on the effects of critical events, such as falls, on osseointegrated transfemoral implants.
The objective of this study was twofold. Firstly, different types of falls were investigated to
identify the most dangerous fall scenario, and secondly, how the stress distributions during a fall
vary depending on the specific prosthetic design was investigated. Two different implants, OPRA
and OPL, have been compared.
2. Materials and Methods
2.1. Experimental Evaluation of Loads
To experimentally evaluate the loads on the prosthetic limb during different fall scenarios, one
healthy subject (male, 90 kg, 1.80 m, 31 years old) has been recruited. The subject was equipped with
appropriate protections on knees, elbows and hands. The experimental tests were carried out on a
wooden walkway (Figure 1) containing one force plate (P-6000, BTS Bioengineering, BTS
Bioengineering, Garbagnate Milanese, Italy).
Figure 1. Experimental setup for load acquisition: wooden walkway and force plate.
Reflective markers were placed on the subject following a custom and simplified marker
protocol (Figure 2).
Figure 2. Marker-set protocol for motion capture data acquisition: side view (a) and front view (b).
The markers were placed on the external side of both lower limbs to track the positions of the
femurs, the tibias and the feet (Figure 3).
Figure 1. Experimental setup for load acquisition: wooden walkway and force plate.
Reflective markers were placed on the subject following a custom and simplified marker protocol
(Figure 2).
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 16
Several studies used FEM to investigate the stress distribution on bone and implants during
normal daily activities [4,25,27,33–39]. Nevertheless, no relevant studies in the literature have focused
on the effects of critical events, such as falls, on osseointegrated transfemoral implants.
The objective of this study was twofold. Firstly, different types of falls were investigated to
identify the most dangerous fall scenario, and secondly, how the stress distributions during a fall
vary depending on the specific prosthetic design was investigated. Two different implants, OPRA
and OPL, have been compared.
2. Materials and Methods
2.1. Experimental Evaluation of Loads
To experimentally evaluate the loads on the prosthetic limb during different fall scenarios, one
healthy subject (male, 90 kg, 1.80 m, 31 years old) has been recruited. The subject was equipped with
appropriate protections on knees, elbows and hands. The experimental tests were carried out on a
wooden walkway (Figure 1) containing one force plate (P-6000, BTS Bioengineering, BTS
Bioengineering, Garbagnate Milanese, Italy).
Figure 1. Experimental setup for load acquisition: wooden walkway and force plate.
Reflective markers were placed on the subject following a custom and simplified marker
protocol (Figure 2).
Figure 2. Marker-set protocol for motion capture data acquisition: side view (a) and front view (b).
The markers were placed on the external side of both lower limbs to track the positions of the
femurs, the tibias and the feet (Figure 3).
Figure 2. Marker-set protocol for motion capture data acquisition: side view (a) and front view (b).
The markers were placed on the external side of both lower limbs to track the positions of the
femurs, the tibias and the feet (Figure 3).
Appl. Sci. 2020,10, 8263 4 of 16
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 16
Figure 3. Subject equipped with protections and reflective markers for motion capture.
A 4-camera motion capture system (BTS Smart-DX, BTS Bioengineering, Garbagnate Milanese,
Italy) was used to acquire marker trajectories during all tests. Marker trajectories and force data were
collected at 400 Hz. Volume and static calibrations were performed according to the BTS Smart-DX
guidelines before the experimental tests. Kinematic data of hip, knee and ankle along the sagittal
plane were elaborated in the dedicated motion capture software (BTS Smart Tracker and BTS Smart
Analyzer, BTS Bioengineering, Garbagnate Milanese, Italy) for all the falling scenarios. The position
of the knee center during falls was interpolated through the BTS Smart Analyzer software, since it
was not possible to place the markers on anatomical landmarks, such as epicondyles, due to knee
protections. The following common fall scenarios have been investigated:
Fall Forward (FF): during walking, the subject falls forward and impacts both knees on the
ground;
Fall Forward with Balance Loss (FF BL): during walking, the subject loses balance and falls
forward with his hands on the ground and leans on the prosthetic limb by bending the hip and
the knee;
Fall Backwards with Balance Loss (FB BL): from an orthostatic position, the subject goes back,
impacts his healthy foot against an obstacle and loses balance. To restore it, the subject extends
the hip and leans on his prosthetic limb;
Fall Backwards “By Push” (FB BP): from an orthostatic position, the subject experiences a sudden
push along the sagittal plane. The subject loses balance, and steps back with the contralateral
limb lifted and the prosthetic limb on the ground.
The analysed fall scenarios were previously identified as typical and frequently occurring in
individuals with transfemoral amputation [40]. Each type of fall was repeated 10 times to verify the
repeatability of the test and the accuracy of the data collected. The measured kinematic data
(positions of femur, tibia, knee and foot) were correlated with the forces measured by the force-plate
during falls. In this way, after synchronizing kinematic data and measured loads, the forces and
Figure 3. Subject equipped with protections and reflective markers for motion capture.
A 4-camera motion capture system (BTS Smart-DX, BTS Bioengineering, Garbagnate Milanese,
Italy) was used to acquire marker trajectories during all tests. Marker trajectories and force data were
collected at 400 Hz. Volume and static calibrations were performed according to the BTS Smart-DX
guidelines before the experimental tests. Kinematic data of hip, knee and ankle along the sagittal
plane were elaborated in the dedicated motion capture software (BTS Smart Tracker and BTS Smart
Analyzer, BTS Bioengineering, Garbagnate Milanese, Italy) for all the falling scenarios. The position
of the knee center during falls was interpolated through the BTS Smart Analyzer software, since it
was not possible to place the markers on anatomical landmarks, such as epicondyles, due to knee
protections. The following common fall scenarios have been investigated:
•
Fall Forward (FF): during walking, the subject falls forward and impacts both knees on the ground;
•
Fall Forward with Balance Loss (FF BL): during walking, the subject loses balance and falls forward
with his hands on the ground and leans on the prosthetic limb by bending the hip and the knee;
•
Fall Backwards with Balance Loss (FB BL): from an orthostatic position, the subject goes back,
impacts his healthy foot against an obstacle and loses balance. To restore it, the subject extends
the hip and leans on his prosthetic limb;
•
Fall Backwards “By Push” (FB BP): from an orthostatic position, the subject experiences a sudden
push along the sagittal plane. The subject loses balance, and steps back with the contralateral limb
lifted and the prosthetic limb on the ground.
The analysed fall scenarios were previously identified as typical and frequently occurring in
individuals with transfemoral amputation [
40
]. Each type of fall was repeated 10 times to verify the
repeatability of the test and the accuracy of the data collected. The measured kinematic data (positions
of femur, tibia, knee and foot) were correlated with the forces measured by the force-plate during falls.
Appl. Sci. 2020,10, 8263 5 of 16
In this way, after synchronizing kinematic data and measured loads, the forces and moments at the
distal part of the residual femur have been evaluated through force-transfer calculations.
The schemes and reference systems used for force-transfer calculations are shown in
Figure 4, where:
•
The lower limb is schematically represented with three uniaxial and infinitely rigid elements (red
in Figure 4);
•X-Y-Z is the reference system of the force plate;
•xB-yB-zBis the reference system of the bone (femur);
•tis the length of tibia;
•fis the distance between the knee and the implant position along the femur;
•
cand grepresent, respectively, the angle between foot and tibia and the angle between tibia
and femur.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 16
moments at the distal part of the residual femur have been evaluated through force-transfer
calculations.
The schemes and reference systems used for force-transfer calculations are shown in Figure 4,
where:
The lower limb is schematically represented with three uniaxial and infinitely rigid elements
(red in Figure 4);
X-Y-Z is the reference system of the force plate;
xB-yB-zB is the reference system of the bone (femur);
t is the length of tibia;
f is the distance between the knee and the implant position along the femur;
c and g represent, respectively, the angle between foot and tibia and the angle between tibia and
femur.
Figure 4. Schemes and reference systems used to calculate loads at the bone/implant interface.
Calculated forces and moments have been used as boundary conditions for subsequent FEM
analyses.
2.2. 3D CAD Modelling and FEM Model
Two different prostheses, a press-fit (OPL) and a screw type (OPRA), have been analysed. The
CAD models of the prostheses (Figure 5) were created using a 3D parametric modelling software
(SolidWorks, Dassault Systèmes, Vélizy-Villacoublay, France). Both models of the prostheses are
composed of two main parts: an intramedullary stem (fixture) and a transcutaneous part (abutment).
Figure 5. CAD models of the prosthetic implants analysed: OPL (on the left) and OPRA (on the right).
The CAD model of the bone was created using DICOM images from a CT-scan of a human
femur. Subsequently, the main steps of the surgical implantation of the prosthesis have been virtually
reproduced by means of SolidWorks. Final CAD models of the implant/bone assemblies of both
prostheses are shown in Figure 6.
Figure 4. Schemes and reference systems used to calculate loads at the bone/implant interface.
Calculated forces and moments have been used as boundary conditions for subsequent
FEM analyses.
2.2. 3D CAD Modelling and FEM Model
Two different prostheses, a press-fit (OPL) and a screw type (OPRA), have been analysed. The
CAD models of the prostheses (Figure 5) were created using a 3D parametric modelling software
(SolidWorks, Dassault Syst
è
mes, V
é
lizy-Villacoublay, France). Both models of the prostheses are
composed of two main parts: an intramedullary stem (fixture) and a transcutaneous part (abutment).
Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 16
moments at the distal part of the residual femur have been evaluated through force-transfer
calculations.
The schemes and reference systems used for force-transfer calculations are shown in Figure 4,
where:
The lower limb is schematically represented with three uniaxial and infinitely rigid elements
(red in Figure 4);
X-Y-Z is the reference system of the force plate;
xB-yB-zB is the reference system of the bone (femur);
t is the length of tibia;
f is the distance between the knee and the implant position along the femur;
c and g represent, respectively, the angle between foot and tibia and the angle between tibia and
femur.
Figure 4. Schemes and reference systems used to calculate loads at the bone/implant interface.
Calculated forces and moments have been used as boundary conditions for subsequent FEM
analyses.
2.2. 3D CAD Modelling and FEM Model
Two different prostheses, a press-fit (OPL) and a screw type (OPRA), have been analysed. The
CAD models of the prostheses (Figure 5) were created using a 3D parametric modelling software
(SolidWorks, Dassault Systèmes, Vélizy-Villacoublay, France). Both models of the prostheses are
composed of two main parts: an intramedullary stem (fixture) and a transcutaneous part (abutment).
Figure 5. CAD models of the prosthetic implants analysed: OPL (on the left) and OPRA (on the right).
The CAD model of the bone was created using DICOM images from a CT-scan of a human
femur. Subsequently, the main steps of the surgical implantation of the prosthesis have been virtually
reproduced by means of SolidWorks. Final CAD models of the implant/bone assemblies of both
prostheses are shown in Figure 6.
Figure 5.
CAD models of the prosthetic implants analysed: OPL (on the
left
) and OPRA (on the
right
).
The CAD model of the bone was created using DICOM images from a CT-scan of a human
femur. Subsequently, the main steps of the surgical implantation of the prosthesis have been virtually
reproduced by means of SolidWorks. Final CAD models of the implant/bone assemblies of both
prostheses are shown in Figure 6.
Appl. Sci. 2020,10, 8263 6 of 16
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 16
Figure 6. CAD models of the implant/bone assemblies: OPL (on the left) and OPRA (on the right).
Considering that, nowadays, numerical methods ensure very accurate and reliable results and
are commonly used to evaluate the behaviour of orthopaedic implants [41–45], numerical simulations
have been performed on both models to investigate how stress distributions vary during a fall. In
particular, a FEM-based approach has been used and virtual simulations [24,46] have been performed
using the commercial software Ansys Workbench (Ansys Inc., Canonsburg, PA, USA). To obtain
highly reliable numerical models, the FEM models have been set up following a largely validated
protocol [30,47,48]. Ten-node tetrahedral elements (SOLID187) were used to mesh the femur and the
implant, and eight-node surface-to-surface (CONTA174 and TARGE170) contact elements [30] were
used to mesh the bone/prosthesis interfaces (Figure 7).
Figure 7. Meshed model (screw type prosthesis).
A preliminary convergence analysis (convergence threshold value: 5%) [28,30] was performed
to set the most suitable element dimension. The mesh has been refined at the interface between the
intramedullary stem and the bone to improve the accuracy of the solution. The final meshes consisted
of about 1,597,175 elements and 2,289,288 nodes for screw type implant, and 1,172,140 elements and
1,680,070 nodes for press-fit prothesis. Regarding the mechanical properties of the materials, the bone
was considered as an orthotropic material, with the principal direction aligned along the long axis of
the bone [49], while the prostheses (Ti6Al4V alloy) were considered as isotropic. The bone and the
titanium alloy were considered as elastic linear hardening materials.
Tables 1 and 2 report, respectively, the mechanical properties of the bone and of the titanium
alloy Ti6Al4V. In Table 1, E1, E2, E3, G12, G13, G23, n12, n13 and n23, respectively, represent the Young’s
moduli (Ei), the shear moduli (Gij) and the Poisson ratios (nij) along the radial (1), transverse (2) and
longitudinal (3) directions of the cortical bone [48,50]. In Table 2, E, n and σy represent, respectively,
the Young’s modulus, the Poisson’s ratio and the yield tensile stress of the titanium alloy.
Table 1. Main mechanical properties of the cortical bone [51].
E1 (GPa)
E2 (GPa)
E3 (GPa)
G12 (GPa)
G13 (GPa)
G23 (GPa)
n12
n13
n23
6.91
8.51
18.4
2.41
3.56
4.91
0.49
0.12
0.14
Figure 6. CAD models of the implant/bone assemblies: OPL (on the left) and OPRA (on the right).
Considering that, nowadays, numerical methods ensure very accurate and reliable results and are
commonly used to evaluate the behaviour of orthopaedic implants [
41
–
45
], numerical simulations
have been performed on both models to investigate how stress distributions vary during a fall. In
particular, a FEM-based approach has been used and virtual simulations [
24
,
46
] have been performed
using the commercial software Ansys Workbench (Ansys Inc., Canonsburg, PA, USA). To obtain
highly reliable numerical models, the FEM models have been set up following a largely validated
protocol [
30
,
47
,
48
]. Ten-node tetrahedral elements (SOLID187) were used to mesh the femur and the
implant, and eight-node surface-to-surface (CONTA174 and TARGE170) contact elements [
30
] were
used to mesh the bone/prosthesis interfaces (Figure 7).
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 16
Figure 6. CAD models of the implant/bone assemblies: OPL (on the left) and OPRA (on the right).
Considering that, nowadays, numerical methods ensure very accurate and reliable results and
are commonly used to evaluate the behaviour of orthopaedic implants [41–45], numerical simulations
have been performed on both models to investigate how stress distributions vary during a fall. In
particular, a FEM-based approach has been used and virtual simulations [24,46] have been performed
using the commercial software Ansys Workbench (Ansys Inc., Canonsburg, PA, USA). To obtain
highly reliable numerical models, the FEM models have been set up following a largely validated
protocol [30,47,48]. Ten-node tetrahedral elements (SOLID187) were used to mesh the femur and the
implant, and eight-node surface-to-surface (CONTA174 and TARGE170) contact elements [30] were
used to mesh the bone/prosthesis interfaces (Figure 7).
Figure 7. Meshed model (screw type prosthesis).
A preliminary convergence analysis (convergence threshold value: 5%) [28,30] was performed
to set the most suitable element dimension. The mesh has been refined at the interface between the
intramedullary stem and the bone to improve the accuracy of the solution. The final meshes consisted
of about 1,597,175 elements and 2,289,288 nodes for screw type implant, and 1,172,140 elements and
1,680,070 nodes for press-fit prothesis. Regarding the mechanical properties of the materials, the bone
was considered as an orthotropic material, with the principal direction aligned along the long axis of
the bone [49], while the prostheses (Ti6Al4V alloy) were considered as isotropic. The bone and the
titanium alloy were considered as elastic linear hardening materials.
Tables 1 and 2 report, respectively, the mechanical properties of the bone and of the titanium
alloy Ti6Al4V. In Table 1, E1, E2, E3, G12, G13, G23, n12, n13 and n23, respectively, represent the Young’s
moduli (Ei), the shear moduli (Gij) and the Poisson ratios (nij) along the radial (1), transverse (2) and
longitudinal (3) directions of the cortical bone [48,50]. In Table 2, E, n and σy represent, respectively,
the Young’s modulus, the Poisson’s ratio and the yield tensile stress of the titanium alloy.
Table 1. Main mechanical properties of the cortical bone [51].
E1 (GPa)
E2 (GPa)
E3 (GPa)
G12 (GPa)
G13 (GPa)
G23 (GPa)
n12
n13
n23
6.91
8.51
18.4
2.41
3.56
4.91
0.49
0.12
0.14
Figure 7. Meshed model (screw type prosthesis).
A preliminary convergence analysis (convergence threshold value: 5%) [
28
,
30
] was performed
to set the most suitable element dimension. The mesh has been refined at the interface between the
intramedullary stem and the bone to improve the accuracy of the solution. The final meshes consisted
of about 1,597,175 elements and 2,289,288 nodes for screw type implant, and 1,172,140 elements and
1,680,070 nodes for press-fit prothesis. Regarding the mechanical properties of the materials, the bone
was considered as an orthotropic material, with the principal direction aligned along the long axis of
the bone [
49
], while the prostheses (Ti6Al4V alloy) were considered as isotropic. The bone and the
titanium alloy were considered as elastic linear hardening materials.
Tables 1and 2report, respectively, the mechanical properties of the bone and of the titanium
alloy Ti6Al4V. In Table 1, E
1
, E
2
, E
3
, G
12
, G
13
, G
23
, n
12
, n
13
and n
23
, respectively, represent the Young’s
moduli (E
i
), the shear moduli (G
ij
) and the Poisson ratios (n
ij
) along the radial (1), transverse (2) and
longitudinal (3) directions of the cortical bone [
48
,
50
]. In Table 2, E, n and
σy
represent, respectively,
the Young’s modulus, the Poisson’s ratio and the yield tensile stress of the titanium alloy.
Appl. Sci. 2020,10, 8263 7 of 16
Table 1. Main mechanical properties of the cortical bone [51].
E1(GPa) E2(GPa) E3(GPa) G12 (GPa) G13 (GPa) G23 (GPa) n11 n13 n23
6.91 8.51 18.4 2.41 3.56 4.91
0.49 0.12 0.14
Table 2. Main mechanical properties of the titanium alloy Ti6Al4V [30].
Material E (GPa) n σy(MPa)
Ti6Al4V 115 0.33 890
According to previous studies [
52
,
53
], a bonded contact was imposed at the intramedullary
stem/bone interface to simulate a total osseointegration. As for the contact algorithm, the augmented
Lagrangian method was used [
54
]. As regards the boundary conditions, a fixed support constraint
was applied to the proximal femur; the forces and the moments, calculated as described in previous
Section 2.1, were applied on the end of the abutment.
2.3. Data Post Processing: Failure Analysis
To evaluate possible mechanical failures of the bone or the prosthesis, the equivalent stress values
have been calculated and verified for all fall scenarios. Peak stresses,
σmax
, have been compared with
the corresponding material strengths (S). According to [
51
], the strength of the bone (S
bone
) has been
calculated as S
bone
=114 x
ρash1.72
, where the ash density has been assumed to be
ρash
=1.22 g/cm
3
,
thereby obtaining S
bone
=160.5 MPa. Considering that plastic deformations could invalidate the
prosthesis functionality, the yield tensile stress of the titanium alloy (
σy
) has been used to calculate the
strength of the prosthesis (S
prosthesis
=
σy
=890 MPa). Bone or prosthesis failure risk was identified
when σmax_bone
Sbone
>1 or σmax_prosthesis
Sprosthesis
>1.
To evaluate also possible failures at the bone/implant interface, the Hoffman criterion [
55
] has
been used. This criterion transforms the local interface stress state to a value, termed Hoffman number
or H, representing the probability of interface disruption [
56
]. A failure is expected to occur when
H>1; for H <1 no interface failure is expected. The Hoffman number (H) over the bone/implant
interface has been calculated as [25]:
H=1
ScStσ2
n+1
St
−1
Scσn+σ2
s
S2
s
Sc=32.4 ×ρ1.85
app
St=14.5 ×ρ1.71
app
Ss=21.6 ×ρ1.65
app
ρapp =1.79 ×ρash +0.0119
(1)
σnand σsare the normal (tensile) and shear stress respectively.
3. Results
3.1. Loads during Falls
Forces and moments on the abutment have been calculated as described previously in Section 2.1.
A limited time of 400 ms after the impact has been considered. The peak values of forces and
moments, in fact, always occurred in this time for all analysed fall scenarios. Figure 8shows the plots
of forces/moments vs. time. The calculated loads have been used as boundary conditions for the
FEM analyses.
It can be noticed that the greatest values of the forces always occur along the longitudinal axis
of the femur (F
xB
). Two peaks of about 2500 N were calculated for the FF and FF BL fall scenarios.
Appl. Sci. 2020,10, 8263 8 of 16
Regarding the moments, the highest values have been found for the anteroposterior flexion moment
(MzB). A peak value of about 407 N·m has been calculated for the FB BL fall scenario.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 16
Figure 8. Plots of forces and moments vs. time calculated for different fall scenarios: Fall Forward
(FF), Fall Forward with Balance Loss (FF BL), Fall Backwards with Balance Loss (FB BL), Fall
Backwards “By Push” (FB BP).
It can be noticed that the greatest values of the forces always occur along the longitudinal axis
of the femur (FxB). Two peaks of about 2500 N were calculated for the FF and FF BL fall scenarios.
Regarding the moments, the highest values have been found for the anteroposterior flexion moment
(MzB). A peak value of about 407 N·m has been calculated for the FB BL fall scenario.
3.2. FEM Analyses
The FEM analyses of all different fall scenarios converged at an average time of 93 ± 10 min.
Table 3 reports the peak values of the equivalent von Mises stress on the external part of the
femur and on the implant.
Table 3. Peak values of the equivalent stress (MPa) calculated for different fall scenarios: Fall Forward
(FF), Fall Forward with Balance Loss (FF BL), Fall Backwards with Balance Loss (FB BL), Fall
Backwards “By Push” (FB BP).
Femur Implant
Screw-Type Press Fit Screw-Type Press Fit
FF 93 91 607 723
FF BL 59 49 913 855
FB BL 161 152 1286 1546
FB BP 63 59 602 557
It can be pointed out that the highest values were found for the FB BL scenario. This result agrees
with the trends of the forces/moments over the time plotted in Figure 8. It is probable that very high
values of the anteroposterior flexion moment (MzB) measured during the FB BL scenario (Figure 8)
overstress the implant/bone assembly. Figure 9 shows the plots of the maximum values of the von
Mises stress on the bone during the falls. Only the values related to the OPL system have been
reported because very similar trends have been observed using the two kinds of prostheses (OPRA
and OPL). From these plots it is possible to detect at what time the peak values occur and also to
correlate the variations of the maximum stress values on the bone and the imposed boundary conditions
(Figure 8).
Figure 8.
Plots of forces and moments vs. time calculated for different fall scenarios: Fall Forward (FF),
Fall Forward with Balance Loss (FF BL), Fall Backwards with Balance Loss (FB BL), Fall Backwards “By
Push” (FB BP).
3.2. FEM Analyses
The FEM analyses of all different fall scenarios converged at an average time of 93 ±10 min.
Table 3reports the peak values of the equivalent von Mises stress on the external part of the femur
and on the implant.
Table 3.
Peak values of the equivalent stress (MPa) calculated for different fall scenarios: Fall Forward
(FF), Fall Forward with Balance Loss (FF BL), Fall Backwards with Balance Loss (FB BL), Fall Backwards
“By Push” (FB BP).
Femur Implant
Screw-Type Press Fit Screw-Type Press Fit
FF 93 91 607 723
FF BL 59 49 913 855
FB BL 161 152 1286 1546
FB BP 63 59 602 557
It can be pointed out that the highest values were found for the FB BL scenario. This result agrees
with the trends of the forces/moments over the time plotted in Figure 8. It is probable that very high
values of the anteroposterior flexion moment (M
zB
) measured during the FB BL scenario (Figure 8)
overstress the implant/bone assembly. Figure 9shows the plots of the maximum values of the von
Mises stress on the bone during the falls. Only the values related to the OPL system have been reported
because very similar trends have been observed using the two kinds of prostheses (OPRA and OPL).
From these plots it is possible to detect at what time the peak values occur and also to correlate the
variations of the maximum stress values on the bone and the imposed boundary conditions (Figure 8).
In all analysed fall scenarios, both for the OPL and the OPRA system, the maximum values of the
von Mises stress has been found on the abutment (Figure 10), which is always the most stressed part of
the prosthesis. In the FB BL scenario, the maximum value of the von Mises stress on the prosthetic
implant, both using the OPRA and the OPL implant, exceeded the ultimate tensile stress of the titanium
alloy. In this condition, a failure of the abutment of the prosthesis is expected (Figure 10).
Appl. Sci. 2020,10, 8263 9 of 16
Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 16
FB BP
63
59
602
557
It can be pointed out that the highest values were found for the FB BL scenario. This result agrees
with the trends of the forces/moments over the time plotted in Figure 8. It is probable that very high
values of the anteroposterior flexion moment (MzB) measured during the FB BL scenario (Figure 8)
overstress the implant/bone assembly. Figure 9 shows the plots of the maximum values of the von
Mises stress on the bone during the falls. Only the values related to the OPL system have been
reported because very similar trends have been observed using the two kinds of prostheses (OPRA
and OPL). From these plots it is possible to detect at what time the peak values occur and also to
correlate the variations of the maximum stress values on the bone and the imposed boundary conditions
(Figure 8).
Figure 9. OPL prosthesis: Plots of the maximum values of the equivalent stress on the bone during
different fall scenarios: Fall Forward (FF), Fall Forward with Balance Loss (FF BL), Fall Backwards
with Balance Loss (FB BL), Fall Backwards “By Push” (FB BP).
In all analysed fall scenarios, both for the OPL and the OPRA system, the maximum values of
the von Mises stress has been found on the abutment (Figure 10), which is always the most stressed
part of the prosthesis. In the FB BL scenario, the maximum value of the von Mises stress on the
prosthetic implant, both using the OPRA and the OPL implant, exceeded the ultimate tensile stress
of the titanium alloy. In this condition, a failure of the abutment of the prosthesis is expected (Figure
10).
Figure 9.
OPL prosthesis: Plots of the maximum values of the equivalent stress on the bone during
different fall scenarios: Fall Forward (FF), Fall Forward with Balance Loss (FF BL), Fall Backwards with
Balance Loss (FB BL), Fall Backwards “By Push” (FB BP).
Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 16
Figure 10. Fall Backwards with Balance Loss (FB BL) scenario: von Mises stress distribution on the
OPRA (top) and the OPL (bottom) prosthesis
Figure 11 shows the equivalent stress distributions on femur using the OPRA and the OPL
implant. It can be noticed that in both cases the maximum value of the von Mises stress is very high
but, probably, no failure of the bone occurs. This is because, due to very high stresses on the
prosthesis, a failure of the abutment occurs before the bone could be damaged.
Figure 10.
Fall Backwards with Balance Loss (FB BL) scenario: von Mises stress distribution on the
OPRA (top) and the OPL (bottom) prosthesis.
Appl. Sci. 2020,10, 8263 10 of 16
Figure 11 shows the equivalent stress distributions on femur using the OPRA and the OPL implant.
It can be noticed that in both cases the maximum value of the von Mises stress is very high but,
probably, no failure of the bone occurs. This is because, due to very high stresses on the prosthesis,
a failure of the abutment occurs before the bone could be damaged.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 16
Figure 10. Fall Backwards with Balance Loss (FB BL) scenario: von Mises stress distribution on the
OPRA (top) and the OPL (bottom) prosthesis
Figure 11 shows the equivalent stress distributions on femur using the OPRA and the OPL
implant. It can be noticed that in both cases the maximum value of the von Mises stress is very high
but, probably, no failure of the bone occurs. This is because, due to very high stresses on the
prosthesis, a failure of the abutment occurs before the bone could be damaged.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 16
Figure 11. Fall Backwards with Balance Loss (FB BL) scenario: von Mises stress distribution on femur
using the OPRA (top) and the OPL (bottom) device.
Regarding the bone/implant interface, the H number, calculated through the Hoffman formula,
was always lower than 1, thereby ensuring that no failure at the bone/implant interface occurs. The
highest values, calculated for OPRA and OPL implants during FB BL fall scenario, are 0.58 and 0.27,
respectively.
4. Discussion
Today, lower limb amputations can be treated by socket prostheses, which represent the
standard of care for amputees but often are associated with significant socket–interface problems, or
by osseointegrated prostheses, which involves direct attachment of the artificial limb to the skeletal
residuum. Because osseointegrated limb prostheses are a fairly recent method, numerous studies
have been carried out in recent years, mainly to investigate which parameters could reduce implant
failures. Many studies have investigated osseointegrated implants during normal daily activities
such as walking. Currently, in fact, most of the research activities have investigated the stresses’
distribution in the bone during static loading, but no relevant studies have investigated how the
safety of the implantation is affected by the stresses generated during a fall.
In the present study, different fall scenarios have been investigated to experimentally determine
the loads on a limb in a critical event like a fall. Subsequently, the calculated loads have been used to
compare, by FEM analyses, the behaviour of two different transfemoral osseointegrated prostheses
during falls, to verify if failures of bone or implant could occur. A typical screw-type implant (OPRA)
and a press fit one (OPL) have been analysed.
As regards the measured loads on the limb in different fall scenarios, it was found that the most
stressful configurations are the falls forward (both FF and FF BL) and the fall backwards with balance
loss (FB BL), while the fall backwards “by push” has shown, on average, the lowest values of forces
and moments. In particular, it was observed that:
Peak values of the longitudinal force occur during falls forward;
Very high values of the anteroposterior flexion moment on the limb occur in the FB BL fall
scenario.
This last result could be justified by analysing the dynamics of this kind of fall scenario. In fact,
a fall caused by loss of balance, especially if backwards, could be more unpredictable and unexpected
than other types of fall (e.g., falls caused by push), during which the subject could forecast the impact.
For this reason, the high bending moment calculated in the FB BL fall could be due to the unexpected
loss of balance and the following extreme attempt to restore it. Moreover, this result agrees with those
obtained by Schwarze et al. [57] and Welke et al. [11]. In both studies, different fall scenarios (both
forward and backward) were analysed through a musculoskeletal model to determine the influence
of transfemoral amputation length on the loads of OI prosthetic implants. Both studies found that fall
backward scenarios are the most dangerous and, above all, the ones with highest anteroposterior
Figure 11.
Fall Backwards with Balance Loss (FB BL) scenario: von Mises stress distribution on femur
using the OPRA (top) and the OPL (bottom) device.
Regarding the bone/implant interface, the H number, calculated through the Hoffman formula,
was always lower than 1, thereby ensuring that no failure at the bone/implant interface occurs. The
highest values, calculated for OPRA and OPL implants during FB BL fall scenario, are 0.58 and
0.27, respectively.
4. Discussion
Today, lower limb amputations can be treated by socket prostheses, which represent the standard
of care for amputees but often are associated with significant socket–interface problems, or by
osseointegrated prostheses, which involves direct attachment of the artificial limb to the skeletal
residuum. Because osseointegrated limb prostheses are a fairly recent method, numerous studies
have been carried out in recent years, mainly to investigate which parameters could reduce implant
failures. Many studies have investigated osseointegrated implants during normal daily activities such
as walking. Currently, in fact, most of the research activities have investigated the stresses’ distribution
Appl. Sci. 2020,10, 8263 11 of 16
in the bone during static loading, but no relevant studies have investigated how the safety of the
implantation is affected by the stresses generated during a fall.
In the present study, different fall scenarios have been investigated to experimentally determine
the loads on a limb in a critical event like a fall. Subsequently, the calculated loads have been used to
compare, by FEM analyses, the behaviour of two different transfemoral osseointegrated prostheses
during falls, to verify if failures of bone or implant could occur. A typical screw-type implant (OPRA)
and a press fit one (OPL) have been analysed.
As regards the measured loads on the limb in different fall scenarios, it was found that the most
stressful configurations are the falls forward (both FF and FF BL) and the fall backwards with balance
loss (FB BL), while the fall backwards “by push” has shown, on average, the lowest values of forces
and moments. In particular, it was observed that:
•Peak values of the longitudinal force occur during falls forward;
•
Very high values of the anteroposterior flexion moment on the limb occur in the FB BL fall scenario.
This last result could be justified by analysing the dynamics of this kind of fall scenario. In fact, a
fall caused by loss of balance, especially if backwards, could be more unpredictable and unexpected
than other types of fall (e.g., falls caused by push), during which the subject could forecast the impact.
For this reason, the high bending moment calculated in the FB BL fall could be due to the unexpected
loss of balance and the following extreme attempt to restore it. Moreover, this result agrees with
those obtained by Schwarze et al. [
57
] and Welke et al. [
11
]. In both studies, different fall scenarios
(both forward and backward) were analysed through a musculoskeletal model to determine the
influence of transfemoral amputation length on the loads of OI prosthetic implants. Both studies
found that fall backward scenarios are the most dangerous and, above all, the ones with highest
anteroposterior moment at the level of amputation. These findings are consistent with the loads
obtained experimentally in our study by motion capture. However, in [
5
,
28
] no FEM analyses were
performed, so no comparison can be made in terms of stresses on bone, implant and their interface.
Regarding the comparison between OPRA and OPL implants, for all analysed falls, it emerged
that peak values of the equivalent stress on the femur are always quite similar. On the other hand,
sometimes very different stress distributions over the bone have been found. In particular, it was found
the distal part of the residual bone is, on average, more stressed using the OPL device. This is clear
when observing plots of the von Mises stress on the bone, for example in Figures 11 and 12 that show
the equivalent stress distributions for FB BL and FF BL scenarios.
It can be noticed that the internal areas of the distal femur are much more stressed (larger red
coloured zones) when using the OPL prosthesis than the OPRA one. Moreover, it was observed that
for the FB BL scenario, representing the most stressful configuration for the bone, the percentage
of highly stressed volume strongly varies when comparing the two implants. In particular, it was
calculated that the percentages of the volume of the bone where stress values are higher than 95%
of the maximum stress are 7.2% and 2.4% for OPL and OPRA implant, respectively. All this data is
interesting and should be studied in-depth for long-term successful outcomes. Stress distribution, in
fact, could strongly affect the bone resorption phenomenon that often occurs using OI implants [
20
,
58
].
In terms of bone/implant interfaces, no risk of fracture exists using the Hoffman criteria.
Regarding the risk of failure, the results in Table 3demonstrate that, during some fall scenarios,
mechanical failures could occur, particularly in the prosthetic implant. However, most prosthetic
implants are equipped with security/locked systems that should reduce the risk of failure on bone
and prosthesis. Nevertheless, periprosthetic fractures and loosening due to very high stress values
are widely reported in the literature [
59
,
60
], so the obtained results should be considered for future
improvements of the design of OI prostheses.
Appl. Sci. 2020,10, 8263 12 of 16
Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 16
moment at the level of amputation. These findings are consistent with the loads obtained
experimentally in our study by motion capture. However, in [5,28] no FEM analyses were performed,
so no comparison can be made in terms of stresses on bone, implant and their interface.
Regarding the comparison between OPRA and OPL implants, for all analysed falls, it emerged
that peak values of the equivalent stress on the femur are always quite similar. On the other hand,
sometimes very different stress distributions over the bone have been found. In particular, it was
found the distal part of the residual bone is, on average, more stressed using the OPL device. This is
clear when observing plots of the von Mises stress on the bone, for example in Figures 11 and 12 that
show the equivalent stress distributions for FB BL and FF BL scenarios.
Figure 12. Fall Forward with Balance Loss (FF BL) scenario: von Mises stress distribution on femur
using the OPRA (top) and the OPL (bottom) device
It can be noticed that the internal areas of the distal femur are much more stressed (larger red
coloured zones) when using the OPL prosthesis than the OPRA one. Moreover, it was observed that
for the FB BL scenario, representing the most stressful configuration for the bone, the percentage of
highly stressed volume strongly varies when comparing the two implants. In particular, it was
calculated that the percentages of the volume of the bone where stress values are higher than 95% of
the maximum stress are 7.2% and 2.4% for OPL and OPRA implant, respectively. All this data is
interesting and should be studied in-depth for long-term successful outcomes. Stress distribution, in
fact, could strongly affect the bone resorption phenomenon that often occurs using OI implants
[20,58].
In terms of bone/implant interfaces, no risk of fracture exists using the Hoffman criteria.
Regarding the risk of failure, the results in Table 3 demonstrate that, during some fall scenarios,
mechanical failures could occur, particularly in the prosthetic implant. However, most prosthetic
Figure 12.
Fall Forward with Balance Loss (FF BL) scenario: von Mises stress distribution on femur
using the OPRA (top) and the OPL (bottom) device.
5. Conclusions
Loads during different fall scenarios have been experimentally evaluated by a motion capture
system and a force plate. Calculated loads could be effectively used for numerical analyses of different
kinds of prostheses. On the basis of the obtained results, it can be stated the fall backwards with
balance loss, among the scenarios analysed, is the most stressful. OPRA and OPL devices have similar
behaviours during falls in terms of peak values of the equivalent stress on bone and prostheses,
but OPL implant stresses the distal part of the femur more than the OPRA device. This should be
considered if this kind of implant is used in poor-quality bone. Further studies should investigate
design optimization of the prosthesis to further limit the risk of bone fracture and implant failure
during critical events like falls, thereby improving long-term successful outcomes.
Author Contributions:
Conceptualization, A.I.M., F.D.S., T.I. and L.B.; Data curation, A.I.M., F.D.S. and S.D.P.;
Methodology, A.I.M., F.D.S., T.I. and L.B.; Software, A.I.M., F.D.S. and T.I.; Validation, F.D.S., T.I., L.B. and S.Z.;
Supervision, T.I., V.N., L.B. and S.Z.; Writing—original draft, A.I.M., S.D.P. and T.I.; Writing—review and editing,
T.I. and L.B. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Appl. Sci. 2020,10, 8263 13 of 16
Conflicts of Interest: The authors declare no conflict of interest.
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