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Finite element analysis (FEA) for the Point contact fixator screw drive, plate design, overcuts
S-B20
Finite Element Analysis (FEA) for the Point Contact Fixator Screw drive, plate design, overcuts
S. J. Biesina, D.Sc., S. Tepic, D.Sc. AO/ASIF
Research Institute,
Clavadelerstrasse,
7270 Davos Platz, Switzerland
Summary1 Finite Element (FE) analysis was performed to ensure that the newly designed plate for internal fixation, the Point Contact Fixator (PC-Fix), was at least as strong as existing implants used for the same clinical indications. The smaller holes of the PC-Fix allow for some reduction of the cross-sectional dimensions in comparison to a comparable Dynamic Compression Plate. The cross section of the PC-Fix changes along the length in order to provide for point contacts at the level of the screws and to reduce the strength between the holes. These major geometrical characteristics are produced by a longitudinal undercut and a set of transverse undercuts. They are supplemented by shallow cuts on the upper surface of the plate which reduce the effects of bending-induced stress concentration. All of these parameters have been optimized by iterative FE analysis. Equal strength requirement resulted in a modest, but important reduction of the implant size for the critical use in the forearm. In addition, the locking of the conical screw head into the PC-Fix has been analyzed and optimized in order to ensure proper locking of the screw. This has been achieved by a measured geometrical mismatch between the screw head and the hole in the fixator. The maximum compressive stress between the screw head and the fixator, which is considered a critical risk for galling, has been reduced by approximately 50 percent at the required insertion torque.
1 Abstracts in German, French, Italian, Spanish Japanese are printed at the end of this supplement.
and
Keywords:
Finite Element Analysis (FEA), bone plate
Introduction After several years of research, the biological improvements attainable with the Point Contact Fixator (PC-Fix) had been clearly demonstrated (1, 2). In preparation for clinical trials in humans, the design of the fixator was optimized using Finite Element (FE) analysis. The objective was to minimize the dimensions of the PC-Fix while maintaining the strength of conventional implants used for the same indications. For treatment of fractures in the forearm and tibia, the size of the implants is a major concern, but size reduction should not increase the risk of implant failure. Through years of successful clinical experience with implants ‘for internal fixation, the level of acceptable implant failure risk has been established. By at least matching the strength of the existing implants, the risk of failure will remain within the accepted range. Two major investigations were performed to analyze special features of the PC-Fix. The first dealt with locking of the conical shaped screw head into the fixator. Finite element methods were , used to determine geometric modifications of the screw head to ensure locking of the screw without the risk of jamming. The second investigation was performed to decrease the stress concentration at the edge of the screw hole on the top surface of the implant by removing material at strategic locations.
Bresina: Finite element analysis
S-B21
Method The I-DEAS (Integrated Design Engineering Analysis Software) computer aided design/computer aided engineering (CAD/CAE) software package from SDRC (Structural Dynamics Research Corporation, Milford, Ohio) running on a SGI (Silicon Graphics, Inc., Mountain View, California) Iris Indigo graphics workstation was used to define implant geometry, to generate the finite element model, and to calculate nodal displacements and stresses. Three-dimensional solid models were constructed within the CAD Solid Modeller. Once these solid models were built, the geometric information was used by the Finite Element Mesh Generation task to create mesh areas and mesh volumes. Nodes and elements are then generated from the mesh volume. The element distribution is controlled by setting global and local element sizes. In the regions of interest, i.e. the upper edge of the screw hole, the number of elements was increased to reduce the step between nodes and thus decrease errors associated with discretized models.
Conical screw head A one-quarter axisymmetric model of a conical hex screw head was constructed. To simulate the condition of the screw head locking into a hole with a perfectly matched angle of the cone, a uniform radial inward displacement was applied. The radial stress distribution generated from this displacement showed very high stresses around the bottom of the screw head. This corresponded to the surface wear observed on test screws that were inserted into holes of the same cone angle. The amount of torque used to lock the screws determines the push-out force. The push-out force is critical for transmitting bending loads from the bone to the implant and should be high enough for the fixator to fail in fatigue before the screw pushes out. Therefore, the necessary push-out force can be determined, which then provides the minimum insertion torque needed. With the required torque and the area of contact between the screw and the implant known, a uniform radial stress around the screw head could be calculated. For a 1000 N push-out force, a 2.50 MPa radial contact stress was required. This stress was then applied to the screw head and defined the resulting dimensional mismatch between the head and the hole that would provide a uniform radial contact stress. The resulting solution gives a complex surface geometry, which needed to be simplified to facilitate manufa$uring by conventional production techniques. The simplified solution was obtained by analyzing the effects of an angular mismatch between the cones of the screw head and the hole. The angular
mismatch was altered and the stress variation over the surface minimized whilst keeping the average stress at 250 MPa.
Screw hole stress reduction A model symmetric about the longitudinal mid-plane of the implant including a screw hole and the adjacent regions up to the next hole position was constructed. A uniform bending load was applied to the model and the von Mises stress at the upper edge of the screw hole was determined. Von Mises stress is used as a fatigue criterion, which is important since fatigue is the expected mode of failure. The stress at the edge of the hole caused by a bending load can be reduced by bringing the edge of the hole closer to the neutral axis of the implant cross section. As a first try, a longitudinal groove just wider than the width of the hole was created along the entire length of the implant. The depth of the groove was found to be optimal when the maximum stress at the edge of the hole within the groove was equal to the maximum stress at the top edge of the groove. If the groove was made deeper than this, the loss in strength due to the decrease of the cross-sectional area became more significant than the gain made by reducing the stress concentration at the hole edge. Additionally, the PCFix has transverse undercuts which already reduce the implant cross-section between the holes. Therefore, the groove on the upper surface was made discontinuous by creating short segmental grooves providing a smooth transition into and out of the holes and allowing the cross section between the holes to remain unchanged. The flat groove created a disadvantage by reducing the height of contact between the screw head and the fixator along the longitudinal centre-line. This could reduce the longitudinal stability of the screw to fixator interlock. Therefore, the flat profile of this short segmental groove or “overcut” was modified to permit material along the centre-line of the implant to remain. This undulating profile, low at the edges of the hole and high along the longitudinal centre-line, was then optimized to reduce the stress at the edge of the hole further.
S-B22 Results Conical screw head The normal stress distribution (x-axis in the cylindrical coordinate system refers to the radial direction) on the unmodified hex-head screw shows the high stresses on the bottom third of the screw head clearly (Fig. 1). The stress over the screw head varied by 580 MPa with a peak stress at the bottom of the screw head of 680 MPa. The normal stress distribution on the screw head with the final angular mismatch of 0.13 degrees between the cone of the screw head and the cone of the hole is shown in Figure 2. The stress variation over the surface was reduced to 200 MPa with an average stress of 250 MPa (orange region). However, there is still a band of higher stress near the bottom of the screw head, but it has a peak magnitude of only 340 MPa, half the peak stress in the original screw head. Screw hole stress reduction The von Mises stress distribution for the original implant is shown in Figure 3. The peak stress at the hole edge is 136 MPa. The von Mises stress for the implant with the optimized “overcut” is shown in Figure 4. The peak stress has been reduce to 105 MPa, which corresponds to a 30 percent increase in the strength of the implant.
Fig. 1: Normal stresses on a one-quarte 9 segment of a coni ical shaped scred head. The exact : match of the scre w head and the locking hole causes high compressive stresses on the lower portion of the screw head.
Conclusion FE analysis was used as a final step for fine-tuning the PC-Fix implant. The particular feature of screw locking was protected against mechanical complications. The efforts made were considered well justified in view of the seriousness of the consequences of an implant failure in clinical use and of the need to make new implants minimally invasive.
Fig. 2: Normal stresses over the same one-quarter segment of a conical screw head. The mismatch of the angle between the screw head and the locking hole has been optimized at 0.13 degrees to give a more even distribution.
S-B23
Bresina: Finite element analysis
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Fig. 3: Von Mises stress distribution on a plate/hole model loaded in pure bending. above clearly shows the stress concentration of 136 MPa at the hole edge.
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Fig. 4: Von Mises stress distribution on the plate with the special cutouts at the upper edge of the hole. The peak stress, located at the edge of the hole and the cutout, has been reduced to 105 MPa. Note that the peak stress in this figure is 2 colour bars lower than in figure 3.
References 1. Tepic S, Predieri M, Plavijanic M et al. Internal fixation with minimal plate-t&bone contact. Proc. 38th Annual Meeting ORS. 1992. 2. Remiger AR, Predieri M, Tepic S, Perren SM. Experimentelle Frakturbehandlung mit dem PointContact-Fixateur (PC-Fix) - eine in-vivo Studie an Schafen. In: Chirurg. Forum f. exp. u. klin. Forschung, Langenbecks Archiv Suppl. 1994:427-433.
Finite Element Analysis (FEA) for the Point Contact Fixator Screw drive, plate design, overcuts
S. J. Biesina, D.Sc., S. Tepic, D.Sc. AO/ASIF
Research Institute,
Clavadelerstrasse,
7270 Davos Platz, Switzerland
Summary1 Finite Element (FE) analysis was performed to ensure that the newly designed plate for internal fixation, the Point Contact Fixator (PC-Fix), was at least as strong as existing implants used for the same clinical indications. The smaller holes of the PC-Fix allow for some reduction of the cross-sectional dimensions in comparison to a comparable Dynamic Compression Plate. The cross section of the PC-Fix changes along the length in order to provide for point contacts at the level of the screws and to reduce the strength between the holes. These major geometrical characteristics are produced by a longitudinal undercut and a set of transverse undercuts. They are supplemented by shallow cuts on the upper surface of the plate which reduce the effects of bending-induced stress concentration. All of these parameters have been optimized by iterative FE analysis. Equal strength requirement resulted in a modest, but important reduction of the implant size for the critical use in the forearm. In addition, the locking of the conical screw head into the PC-Fix has been analyzed and optimized in order to ensure proper locking of the screw. This has been achieved by a measured geometrical mismatch between the screw head and the hole in the fixator. The maximum compressive stress between the screw head and the fixator, which is considered a critical risk for galling, has been reduced by approximately 50 percent at the required insertion torque.
1 Abstracts in German, French, Italian, Spanish Japanese are printed at the end of this supplement.
and
Keywords:
Finite Element Analysis (FEA), bone plate
Introduction After several years of research, the biological improvements attainable with the Point Contact Fixator (PC-Fix) had been clearly demonstrated (1, 2). In preparation for clinical trials in humans, the design of the fixator was optimized using Finite Element (FE) analysis. The objective was to minimize the dimensions of the PC-Fix while maintaining the strength of conventional implants used for the same indications. For treatment of fractures in the forearm and tibia, the size of the implants is a major concern, but size reduction should not increase the risk of implant failure. Through years of successful clinical experience with implants ‘for internal fixation, the level of acceptable implant failure risk has been established. By at least matching the strength of the existing implants, the risk of failure will remain within the accepted range. Two major investigations were performed to analyze special features of the PC-Fix. The first dealt with locking of the conical shaped screw head into the fixator. Finite element methods were , used to determine geometric modifications of the screw head to ensure locking of the screw without the risk of jamming. The second investigation was performed to decrease the stress concentration at the edge of the screw hole on the top surface of the implant by removing material at strategic locations.
Bresina: Finite element analysis
S-B21
Method The I-DEAS (Integrated Design Engineering Analysis Software) computer aided design/computer aided engineering (CAD/CAE) software package from SDRC (Structural Dynamics Research Corporation, Milford, Ohio) running on a SGI (Silicon Graphics, Inc., Mountain View, California) Iris Indigo graphics workstation was used to define implant geometry, to generate the finite element model, and to calculate nodal displacements and stresses. Three-dimensional solid models were constructed within the CAD Solid Modeller. Once these solid models were built, the geometric information was used by the Finite Element Mesh Generation task to create mesh areas and mesh volumes. Nodes and elements are then generated from the mesh volume. The element distribution is controlled by setting global and local element sizes. In the regions of interest, i.e. the upper edge of the screw hole, the number of elements was increased to reduce the step between nodes and thus decrease errors associated with discretized models.
Conical screw head A one-quarter axisymmetric model of a conical hex screw head was constructed. To simulate the condition of the screw head locking into a hole with a perfectly matched angle of the cone, a uniform radial inward displacement was applied. The radial stress distribution generated from this displacement showed very high stresses around the bottom of the screw head. This corresponded to the surface wear observed on test screws that were inserted into holes of the same cone angle. The amount of torque used to lock the screws determines the push-out force. The push-out force is critical for transmitting bending loads from the bone to the implant and should be high enough for the fixator to fail in fatigue before the screw pushes out. Therefore, the necessary push-out force can be determined, which then provides the minimum insertion torque needed. With the required torque and the area of contact between the screw and the implant known, a uniform radial stress around the screw head could be calculated. For a 1000 N push-out force, a 2.50 MPa radial contact stress was required. This stress was then applied to the screw head and defined the resulting dimensional mismatch between the head and the hole that would provide a uniform radial contact stress. The resulting solution gives a complex surface geometry, which needed to be simplified to facilitate manufa$uring by conventional production techniques. The simplified solution was obtained by analyzing the effects of an angular mismatch between the cones of the screw head and the hole. The angular
mismatch was altered and the stress variation over the surface minimized whilst keeping the average stress at 250 MPa.
Screw hole stress reduction A model symmetric about the longitudinal mid-plane of the implant including a screw hole and the adjacent regions up to the next hole position was constructed. A uniform bending load was applied to the model and the von Mises stress at the upper edge of the screw hole was determined. Von Mises stress is used as a fatigue criterion, which is important since fatigue is the expected mode of failure. The stress at the edge of the hole caused by a bending load can be reduced by bringing the edge of the hole closer to the neutral axis of the implant cross section. As a first try, a longitudinal groove just wider than the width of the hole was created along the entire length of the implant. The depth of the groove was found to be optimal when the maximum stress at the edge of the hole within the groove was equal to the maximum stress at the top edge of the groove. If the groove was made deeper than this, the loss in strength due to the decrease of the cross-sectional area became more significant than the gain made by reducing the stress concentration at the hole edge. Additionally, the PCFix has transverse undercuts which already reduce the implant cross-section between the holes. Therefore, the groove on the upper surface was made discontinuous by creating short segmental grooves providing a smooth transition into and out of the holes and allowing the cross section between the holes to remain unchanged. The flat groove created a disadvantage by reducing the height of contact between the screw head and the fixator along the longitudinal centre-line. This could reduce the longitudinal stability of the screw to fixator interlock. Therefore, the flat profile of this short segmental groove or “overcut” was modified to permit material along the centre-line of the implant to remain. This undulating profile, low at the edges of the hole and high along the longitudinal centre-line, was then optimized to reduce the stress at the edge of the hole further.
S-B22 Results Conical screw head The normal stress distribution (x-axis in the cylindrical coordinate system refers to the radial direction) on the unmodified hex-head screw shows the high stresses on the bottom third of the screw head clearly (Fig. 1). The stress over the screw head varied by 580 MPa with a peak stress at the bottom of the screw head of 680 MPa. The normal stress distribution on the screw head with the final angular mismatch of 0.13 degrees between the cone of the screw head and the cone of the hole is shown in Figure 2. The stress variation over the surface was reduced to 200 MPa with an average stress of 250 MPa (orange region). However, there is still a band of higher stress near the bottom of the screw head, but it has a peak magnitude of only 340 MPa, half the peak stress in the original screw head. Screw hole stress reduction The von Mises stress distribution for the original implant is shown in Figure 3. The peak stress at the hole edge is 136 MPa. The von Mises stress for the implant with the optimized “overcut” is shown in Figure 4. The peak stress has been reduce to 105 MPa, which corresponds to a 30 percent increase in the strength of the implant.
Fig. 1: Normal stresses on a one-quarte 9 segment of a coni ical shaped scred head. The exact : match of the scre w head and the locking hole causes high compressive stresses on the lower portion of the screw head.
Conclusion FE analysis was used as a final step for fine-tuning the PC-Fix implant. The particular feature of screw locking was protected against mechanical complications. The efforts made were considered well justified in view of the seriousness of the consequences of an implant failure in clinical use and of the need to make new implants minimally invasive.
Fig. 2: Normal stresses over the same one-quarter segment of a conical screw head. The mismatch of the angle between the screw head and the locking hole has been optimized at 0.13 degrees to give a more even distribution.
S-B23
Bresina: Finite element analysis
,,(
o.
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1
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,
,01.0.
~.,0~.0.
I
00s.0.
I
10n.0.
I
IPB.05
Fig. 3: Von Mises stress distribution on a plate/hole model loaded in pure bending. above clearly shows the stress concentration of 136 MPa at the hole edge.
1
2II:,OL
L LP.
lSl.05
This view into the hole from
Fig. 4: Von Mises stress distribution on the plate with the special cutouts at the upper edge of the hole. The peak stress, located at the edge of the hole and the cutout, has been reduced to 105 MPa. Note that the peak stress in this figure is 2 colour bars lower than in figure 3.
References 1. Tepic S, Predieri M, Plavijanic M et al. Internal fixation with minimal plate-t&bone contact. Proc. 38th Annual Meeting ORS. 1992. 2. Remiger AR, Predieri M, Tepic S, Perren SM. Experimentelle Frakturbehandlung mit dem PointContact-Fixateur (PC-Fix) - eine in-vivo Studie an Schafen. In: Chirurg. Forum f. exp. u. klin. Forschung, Langenbecks Archiv Suppl. 1994:427-433.