AN ABSTRACT OF THE THESIS OF
Sean T. Moran for the degree of Master of Science in Mechanical Engineering presented
on February 11, 2004.
Title: Elastic, Plastic and Total Strains in Human and Porcine Pedicle Trabecular Bone
and PU-foam After Pedicle Screw Insertion by Utilizing Functional Micro-CT Imaging.
Abstract approved:
Redacted for Privacy
Brian K. Bay
Pedicle screw breakage and loosening remain as clinical complications of short
segment instrumentation procedures for spinal stabilization. This study has directly
visualized and measured elastic, plastic and total vertebral pedicle trabecular bone fullfield strains in the regions immediately surrounding the pedicle screw during pedicle
screw insertion by utilizing functional microCT imaging and digital volume correlation.
Human, porcine and polyurethane foam samples were analyzed and compared. Analysis
showed that when osteoporotic human, normal human and porcine pedicle trabecular
bone samples were compared, osteoporotic samples showed higher peak plastic strains
and greater variability of these strains from their means. This suggests that osteoporotic
human samples are non-uniformly elastic and plastic, while normal human and porcine
samples are more uniformly elastic and plastic throughout the trabecular structure. PUfoams are not appropriate as models for pedicle trabecular bone in the in vivo
environment since strain results showed dissimilar plastic and elastic strain magnitudes
than human and porcine pedicle trabecular bone. This study may aid in the development
of performance criteria for new PU-foams and improved pedicle screw designs.
Elastic, Plastic and Total Strains in Human and Porcine Pedicle Trabecular Bone and PUfoam After Pedicle Screw Insertion by Utilizing Functional Micro-CT Imaging
by
Sean T. Moran
A THESIS
Submitted to
Oregon State University
In partial fulfillment of
the requirements for the
degree of
Master of Science
Presented February 11, 2004
Commencement June 2004
Master of Science thesis of Sean T. Moran
Presented on February 11, 2004.
APPROVED:
Redacted for Privacy
Major Prof, re
senting Mechanical Engineering
Redacted for Privacy
Head of the DepartmentrMechanica1 Engineering
Redacted for Privacy
Dean of
I understand that my thesis will become part of the permanent
collection of Oregon State University libraries. My signature below
authorizes release of my thesis to any reader upon request.
Redacted for Privacy
Sean T. Moran, Author
ACKNOWLEDGEMENTS
I would like to express my appreciation to all those who have offered support
during my education, be it financial, emotion or material. My wife, Jenny, who's
endlessly loving and supporting nature has given me inspiration to live life to its fullest.
My parents who have shown me that the only limits on life are the ones we set for
ourselves. My family, I thank for seeing the best in me always. The faculty of Oregon
State University who have presented to me the fundamentals of my education without
hopes of compensation. My fellow graduate students Scott Rutschman, Henri Saucy,
Matt Sutton and especially Dan Berry for their willingness to help and offer council and
training. Without their help this research would have been lost in 30GB of endless,
encrypted numbers. Lastly, but definitely not least I would like to thank Dr. Brian Bay.
His easy style of managing includes guidance, humor, intelligence and the desire to do
something extraordinary. I have learned and improved beyond my hopes as a graduate
student. May his good will come full-circle.
TABLE OF CONTENTS
Page
Introduction ..................................................................
2
Spinal Fixation & Stabilization ...................................
2
Pedicle Screws ......................................................
3
Previous Studies ....................................................
4
Motivation for Present Study .....................................
9
Present Study .......................................................
10
Digital Volume Correlation and Present Study ................
13
Materials and Methods ......................................................
18
Samples' Sources and Preparation ...............................
18
Equipment and Image Data Collection ..........................
20
Image Post Processing .............................................
23
Data Analysis .......................................................
23
Results ........................................................................
26
Error Analysis .......................................................
38
Discussion .....................................................................
40
Future Research ....................................................
42
Limitations of Study ................................................
43
Conclusion ...................................................................
43
Bibliography ..................................................................
47
Appendix A Additional Results ..........................................
50
LIST OF FIGURES
Page
Figure 1. Human Spine ....................................................
2
Figure 2. Pedicle screw insertion in typical posterior surgery. a)
Pedicle screw insertion location, b) Pedicle screw
insertion, and c) Multiple-level pedicle screws ...........
3
Figure 3. Pedicle screw system with precurved connection rods....
3
...........................
9
Figure 5. Cross-section of typical human, porcine and PU-foam
samples (left to right) ..........................................
10
Figure 6. Definition of screw thread geometry .........................
11
Figure 7. Example of a typical meshed region of interest shown
for sample: 4 1270-11-right. An outline of the region of
interest for a vertically resliced cross-section of the
sample (left) and modeled three-dimensional region of
interest (right) are shown .....................................
15
Figure 8. Flow-chart for Digital Volume Correlation .................
17
Figure 9. Pedicle Sample Prepared and Mounted .....................
19
Figure 10. Functional Imaging System including the x-ray source
and mechanical tester with rotational stages (right)
and image intensifier and CCD camera (left)............
21
Figure 11. Example of a typical region of interest shown for
sample: 4 1270-11-right. An outline of the region of
interest for a vertically resliced cross-section of the
sample (left) and modeled three-dimensional region
of interest (right) are shown ................................
24
Figure 12. Typical plot of plastic (a), elastic (b) and total (c)
minimum principle strains for a sample region of
interest. Sample 41270-11-right is shown ................
26
Figure 13. Typical plot of plastic (a), elastic (b) and total (c)
minimum principle strains for a sample region of
interest. Sample pig-14 is shown ...........................
27
Figure 4. Cellular rigid polyurethane foams
LIST OF FIGURES (Continued)
Page
Figure 14. Typical plot of plastic (top), elastic (middle) and total
(bottom) maximum shear strains for a sample region
of interest. Sample lOfoam is shown .....................
28
Figure 15. Typical histograms for plastic and elastic minimum
principle strain values. Histograms for 4 1258-11right, pig-14 and lOfoam are shown ........................
29
Figure 16. Typical nonparametric statistical comparison of each
sample for plastic and elastic minimum principle
strain values ..................................................
30
Figure 17. Typical nonparametric statistical comparison between
human, porcine and PU-foam samples (p<O.05) for
plastic and elastic minimum principle strain values....
31
Figure 18. 17th percentile plastic and elastic minimum principle
strain values versus bone volume fraction for each
sample........................................................
33
Figure 19. 17th 50th and 83rd percentile plastic (top) and elastic
(bottom) minimum principle strain values versus bone
volume fraction groups ......................................
36
Figure 20. Standard deviations from the 17th percentile plastic and
elastic minimum principle strain values for bone
volume fraction groups ....................................
37
LIST OF TABLES
Page
Table 1. Summary of Sample Labels and Source Type ...............
18
Table 2. Summary of Equipment and Manufacturers for
Functional Imaging System .....................................
21
Table 3. Summary of ANOVA p-test values upon comparison
between human and porcine samples ..........................
31
Table 4. Bone Volume Fraction Summary for Each Sample .........
32
Table 5. Summary of foams matching plastic and elastic minimum
principle strain performance criterion for BVF groups. %
variation of each foam from the mean for each group for
eachresult ........................................................
34
Table 6. Bone volume fraction bin range assignment and
definition for each sample ......................................
35
Table 7. Summary of ANOVA p-test values (p<O.O5) in
comparisons between groups for 17th 50th and 83'
percentile values of plastic elastic and total minimum
principle strain (MPS) ...........................................
38
Table 8. Summary of errors for minimum principle and maximum
shear strains for the average l7, 50th and 83rd percentile
values ..............................................................
39
LIST OF APPENDIX FIGURES & TABLES
Page
Figure 21. Minimum principal strains within the regions of
interest: Before insertion correlated with after
extraction. a) 41258-1 1-left-plastic-minprin,
b) 41258-11 -right-plastic-minprin ...........................
51
Figure 22. Maximum shear strains within the regions of interest:
Before insertion correlated with after extraction.
a) 41258-11 -left-plastic-maxshear,
b) 41258-11 -right-plastic-maxshear..........................
51
Figure 23. Minimum principal strains within the regions of
interest: Before insertion correlated with after
extraction. a) 41270-11-left-plastic-minprin,
b) 41270-11-right-plastic-minprin ...........................
52
Figure 24. Maximum shear strains within the regions of interest:
Before insertion correlated with after extraction.
a) 41270-11 -left-plastic-maxshear,
b) 41270-l1-right-plastic-maxshear ..........................
52
Figure 25. Minimum principal strains within the regions of
interest: Before insertion correlated with after
extraction. a) 38424-13-plastic-minprin,
b) 38424-14-plastic-minprin,
c) 38424-15-plastic-minpnn ...................................
53
Figure 26. Maximum shear strains within the regions of interest:
Before insertion correlated with after extraction. a)
38424-13-plastic-maxshear,
b) 38424-14-plastic-max shear,
c) 38424-l5-plastic-maxshear ..................................
53
Figure 27. Minimum principal strains within the regions of
interest: Before insertion correlated with after
extraction. a) pigl3-plastic-minprin,
b) pigl4-plastic-minpnn, c) pigl5-plastic-minpnn ..........
54
Figure 28. Maximum shear strains within the regions of interest:
Before insertion correlated with after extraction. a)
pigl3-13-plastic-maxshear,
b) pigl4-plastic-maxshear, c) pigl5-plastic-maxshear ......
54
LIST OF APPENDIX FIGURES & TABLES (Continued)
gç
Figure 29. Minimum principle strains within the regions of
interest: Before insertion correlated with after
extraction. a) lOfoam-plastic-minprin .......................
55
Figure 30. Minimum principle strains within the regions of
interest: Before insertion correlated with after
extraction. a) 1 2.Sfoam-plastic-minprin .....................
55
Figure 31. Histograms of plastic minimum principle strains for
each sample. 41258-11-left, 41258-11-right,
41270-11-left, 41270-11-right .................................
56
Figure 32. Histograms of plastic maximum shear strains for each
sample. 41258-11-left, 41258-11-right,
41270-li-left, 41270-li-right .................................
56
Figure 33. Histograms of plastic minimum principle strains for
each sample. 38424-13, 38424-14, 38424-15 ................
57
Figure 34. Histograms of plastic maximum shear strains for each
sample. 38424-13, 38424-14, 38424-15 .......................
57
Figure 35. Histograms of plastic minimum principle strains for
each sample. pigl3, pigl4, pigl5, lOfoam, 12.Sfoam .......
58
Figure 36. Histograms of plastic maximum shear strains for each
sample. pigl3, pigl4, pigl5, lOfoam, 12.5 foam ............
58
Figure 37. Minimum principal strains within the regions of
interest: Full insertion correlated with after extraction.
a) 41258-li -left-plastic-minprin,
b) 41258-11-right-plastic-minpnn ............................
59
Figure 38. Maximum shear strains within the regions of interest:
Full insertion correlated with after extraction.
a) 41258-11 -left-plastic-maxshear,
b) 41258-11 -right-plastic-maxshear ..........................
59
LIST OF APPENDIX FIGURES & TABLES (Continued)
Page
Figure 39. Minimum principal strains within the regions of
interest: Full insertion correlated with after
extraction. a) 41270-11 -left-plastic-minprin,
b) 41270-11 -right-plastic-minprin ..........................
60
Figure 40. Maximum shear strains within the regions of interest:
Full insertion correlated with after extraction.
a) 41270-11 -left-plastic-max shear,
b) 41270-11 -right-plastic-maxshear .......................
60
Figure 41. Minimum principal strains within the regions of
interest: Full insertion correlated with after
extraction. a) 38424-13-plastic-minprin,
b) 3 8424-14-plastic-minprin,
c) 38424-15-plastic-minprin ................................
61
Figure 42. Maximum shear strains within the regions of interest:
Full insertion correlated with after extraction.
a) 38424-13-plastic-maxshear,
b) 38424-14-plastic-maxshear,
c) 38424-l5-plastic-maxshear ...............................
61
Figure 43. Minimum principal strains within the regions of
interest: Full insertion correlated with after
extraction. a) pigl3-plastic-minprin,
b) pigl4-plastic-minprin, c) pigl5-plastic-minpnn
62
Figure 44. Maximum shear strains within the regions of interest:
Full insertion correlated with after extraction.
a) pigl3-13-plastic-maxshear,
b) pigl4-plastic-maxshear, c) pigl5-plastic-maxshear...
62
Figure 45. Minimum principle strains within the regions of
interest: Full insertion correlated with after extraction
a) lOfoam-elastic-minprin .................................
63
Figure 46. Minimum principle strains within the regions of
interest: Full insertion correlated with after extraction
a) 12.5foam-elastic-minprin ...............................
63
LIST OF APPENDIX FIGURES & TABLES (Continued)
Page
Figure 47. Histograms of elastic minimum principle strains for
each sample. 41258-11-left, 41258-11 -right,
41270-11-left, 41270-11 -right .................................
64
Figure 48. Histograms of elastic maximum shear strains for each
sample. 41258-11-left, 41258-11-right,
41270-11-left, 41270-11-right .................................
64
Figure 49. Histograms of elastic minimum principle strains for
each sample. 38424-13, 38424-14, 38424-15 .................
65
Figure 50. Histograms of elastic maximum shear strains for each
sample. 38424-13, 3 8424-14, 3 8424-15 .......................
65
Figure 51. Histograms of elastic minimum principle strains for
each sample. pigl3, pigl4, pigl5, lOfoam, 12.Sfoam ......
66
Figure 52. Histograms of elastic maximum shear strains for each
sample. pigl3, pigl4, pigl5, lOfoam, 12.5foam ............
66
Figure 53. Minimum principal strains within the regions of
interest: Before insertion correlated with full insertion.
a) 41258-11 -left-total-minprin,
b) 41258-11-right-total -minprin
.............................
67
Figure 54. Maximum shear strains within the regions of interest:
Before insertion correlated with full insertion.
a) 41258-11-left-total-maxshear,
b) 41258-11 -right-total-maxshear .............................
67
Figure 55. Minimum principal strains within the regions of
interest: Before insertion correlated with full insertion.
a) 41270-11 -left-total-minprin,
b) 41270-11-right-total-minprin
..............................
68
Figure 56. Maximum shear strains within the regions of interest:
Before insertion correlated with full insertion.
a) 41270-11 -left-total-max shear,
b) 41270-l1-right-total-maxshear .............................
68
LIST OF APPENDIX FIGURES & TABLES (Continued)
Page
Figure 57. Minimum principal strains within the regions of
interest: Before insertion correlated with full
insertion, a) 38424-13-total-minpnn,
b) 38424-14-total-minprin,
c) 38424-15-total-minprin ...................................
69
Figure 58. Maximum shear strains within the regions of interest:
Before insertion correlated with full insertion.
a) 38424-13-total -maxshear,
b) 38424-l4-total-maxshear,
c) 38424-15-total-maxshear .................................
69
Figure 59. Minimum principal strains within the regions of
interest Before insertion correlated with full insertion.
a) pigl3-total-minprin,
b) pigl4-total-minprin, c) pigl5-total-minprin
70
Figure 60. Maximum shear strains within the regions of interest:
Before insertion correlated with full insertion.
a) pigl3-13-total-maxshear,
b) pigl4-total-maxshear, c) pigl5-total-maxshear
70
Figure 61. Minimum principle strains within the regions of
interest: Before insertion correlated with full
insertion a) lOfoam-total-minprin .........................
71
Figure 62. Minimum principle strains within the regions of
interest: Before insertion correlated with full
insertion a) 12.5foam-total-minprin .......................
71
Figure 63. Histograms of total minimum principle strains for each
sample. 41258-11-left, 41258-11-right,
41270-11-left, 41270-11-right .................................
72
Figure 64. Histograms of total maximum shear strains for each
sample. 41258-11-left, 41258-11-right,
41270-11-left, 41270-11-right .................................
72
LIST OF APPENDIX FIGURES & TABLES (Continued)
Figure 65. Histograms of total minimum principle strains for each
sample. 38424-13, 38424-14, 38424-15 ....................
73
Figure 66. Histograms of total maximum shear strains for each
sample. 38424-13, 38424-14, 38424-15 ....................
73
Figure 67. Histograms of total minimum principle strains for each
sample. pigl3, pigl4, pigl5, lOfoam, 12.5foam
74
Figure 68. Histograms of total maximum shear strains for each
sample. pigl3, pigl4, pigl5, lOfoam, 12.Sfoam
74
Figure 69. Non-parametric analysis of plastic, elastic and total
minimum principle strain results for each sample
75
Figure 70. Non-parametric analysis of plastic, elastic and total
maximum shear strain results for each sample
75
Figure 71. Comparison of bone volume fraction versus 17th
percentile plastic and elastic minimum principle
strains for each sample ......................................
76
Figure 72. Comparison of bone volume fraction versus 50th1
percentile plastic and elastic minimum principle
strains for each sample ......................................
77
Figure 73. Comparison of bone volume fraction versus 83td
percentile plastic and elastic minimum principle
strains for each sample .......................................
78
Figure 74. Nonparametric statistical comparison of minimum
principle strains for human vs pig samples using
ANOVA p-values (pczO.O5) .................................
79
Figure 75. Nonparametric statistical comparison of maximum
shear strains for human vs pig samples using
ANOVA p-values (p<O.O5) .................................
79
LIST OF APPENDIX FIGURES & TABLES (Continued)
Page
Figure 76. Comparison of grouped bone volume fractions versus
plastic, elastic or total minimum principle strains for
the 17th 50th and 83rd percentile values ...................
80
Figure 77. Comparison of grouped bone volume fractions versus
plastic, elastic or total maximum shear strains for the
17th, 50th
and 83'' percentile values .......................
81
Table 8. Summary of ANOVA p-test values (p<O.O5) in
comparisons between groups for 17th 50th and 83'
percentile values of plastic, elastic and total minimum
principle strain (MPS) .........................................
82
Elastic, Plastic and Total Strains in Human & Porcine Pedicle Trabecular Bone
After Pedicle Screw Insertion by Utilizing Functional Micro-CT Imaging
2
Introduction
Spinal Fixation & Stabilization
Patients with spinal injuries or disease which result in the instability or
dysfunction of a vertebral motion segment may require surgical
CI
Ical
intervention. These injuries may include damage to
intervertebral bodies or the disks that separate them (Figure 1).
Intervention techniques usually require arthrodesis.
C7
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LI
Arthrodesis is the surgical immobilization of ajoint. This
L5
SaGnini
procedure is commonly performed on the human spine in order
to bring spinal stability, which helps to eliminate pain and
Figure 1. Human
Spine. backpage.com
restore normal function.
Arthrodesis of the human spine creates a union, or fusion, between two vertebral
bodies after the removal of the intervertebral disk. Fusion may be accomplished by
utilizing bone grafts, internal fixation devices or by intervertebral fusion cages. Many
surgeons choose to use all three simultaneously.
The most common problems to occur in procedures for arthrodesis of the spine is
the lack of fusion due to instability of the fusion construct or low quality bone. Low bone
quality result from disease or age induced osteoporosis. Osteoporosis is a condition that
results in the deossification of bone. Relative motion between vertebral bodies during
healing may cause fibrous tissue growth near the healing zone instead of solid trabecular
bone. Pedicle screw fixation has become a popular method for creating a rigid construct
around the fusion site.
Pedicle Screws
Pedicle screws are used as a means to encourage fusion between vertebral bodies
by creating a rigid construct around the site of injury or disease with the purpose of
a)
D)
c)
Figure 2. Pedicle screw insertion in a typical posterior surgery. a) Pedicle screw insertion
location, b) Pedicle screw insertion, and c) Multiple-level pedicle screws.
(www.spine-surgery.com).
increased stability during healing (Figure 2).
Preformed rods are often used to bridge the gap
between pedicle screw heads. Multiple levels
may be treated. Figure 3 illustrates a multilevel
pedicle screw fixation system by SofamorDanek.
The connection rods are custom formed for each
patient during the procedure. Ligaments,
intervertebral disks and other material may be
removed after the connection rods are tensioned.
At this time, bone graft and/or intervertebral
Figure 3. Pedicle screw system
with precurved connection rods.
(www.sofamordanek.com).
cages may be installed in the newly empty space between the vertebral bodies.
Previous Studies
The success of pedicle screws in spinal stabilization procedures, screw purchase
in trabecular bone and human pedicle morphology have been well documented. Specific
pedicle screw insertion techniques (Kowaisky et al., 2000) have been compared and have
shown little difference in pullout performance. Many studies have been done by various
groups with the purpose of finding correlations between bone density, insertion
techniques, pedicle screw types and other variables to pullout strength. Isador et al.
(1998) found that when a pullout resistant nut was added to the Universal Spine System
anterior pedicle screw, that the pullout strength increased twofold. The nut also changed
the mode of failure to rely on the strength of the vertebral body rather than the
characteristics of the screw. Oktenoglu et al. (2001) used synthetic bone blocks to test
the pullout resistance for cancellous lateral mass screws, cortical lateral mass screws, and
pedicle screws. The group found that the optimum pilot hole preparation technique was
to drill a short pilot hole will a drill bit diameter less than the core diameter of the screw.
Chapman et al. (1996) tested 12 types of commercially available cannulated and
noncannulated cancellous bone screws in synthetic bone analogs. The group found that
tapping reduced the pullout strength by an average of 8% and that increasing the thread
shape factor increased screw purchase. Kowaisky et al. (2000) compared the pullout
resistance in human cervical pedicles after using the standard method and the Abumi
insertion method of cervical pedicle screw insertion. The group found no difference
between the two methods. Halvorson et al. (1994) found a correlation between bone
mineral density and axial pullout strength when using one of four lumbar pedicle screw
insertion techniques in frozen cadavenc lumbar spine segments. Pedicle screw pullout
5
strength was highly correlated with bone mineral density. Another group found that the
effectiveness of spinal implants in fixation is dependent upon the bone-implant interface,
and thus on vertebral bone density (Tan, 2003). The group found that pedicle screws did
not behave in a similar manner during axial compression and bending while inserted into
synthetic surrogates and lumbar vertebrae. Deformation magnitudes and toggle points for
the screws varied between the sample types. Kwok et al. (1996) studied insertion torque
and pullout strengths of conical and cylindrical pedicle screws that were inserted into
cadaveric spine segments. The group found that although conical profile pedicle screws
increased the required insertion torque, this did not allow the prediction of axial pullout
strengths. Meyers et al. (1996) found that by using density determined by quantitative
computed tomography used with insertion torque and in situ stiffness provides a strong
predictive ability of screw pullout as compared with other variables in the system such as
geometry and density as discovered by x-ray absorptiometry. Zdeblick et al. (1993)
found that insertion torque is a good indicator of bone-metal interface failure during a
cyclic failure mode. The group also found that smaller pedicle width correlated with
increased insertion torque and cycles to failure. The group discussed how this might
explain why patients with osteoporosis diagnosed through radiography may still obtain
stable fixation with pedicle screw systems.
The internal morphology of human pedicles has been studied (Manohar et al.,
2000) and correlated with the affects upon pedicle screw loading. McKinley et al. (1997)
investigated how pedicle morphology affected pedicle screw bending moments in
synthetic bone analogs by utilizing pedicle screws instrumented with internal strain
gages. The group discovered that in situ loads increased significantly as the pedicle
length increases and as pedicle height decreased. Weinstein et al. (1992) studied the
anatomical and technical consideration associated with pedicle screw instrumentation.
Moran et al. (1989) studied pedicle morphology, insertion techniques and other concerns
involved in transpedicular screw fixation. The group found that the use of a ganglion
knife resulted in higher pullout forces in 8 of 10 trials and gave greater control to screw
location and depth as compared to the use of a drilled hole.
The influence of body loading on implant loading has been studied by various
groups. Smith et al. (1996) used internally instrumented 7mm Cotrel-Dubousset pedicle
screws to measure flexion and extension moment at specific locations along the screw
axis. The method was validated and the technique may be used to measure in situ forces
within human pedicles for varying experiments. Rohlmann et al. (2000) studied the
affects of load carrying on the loads in internal spinal fixators by using instrumented
telemetenzed internal fixators. The group found that for reasonable load carrying, the
loads within the implants increased little. Yerby et al. (1997) substantiated previous
analytical models of pedicle screw bending moments in situ by utilizing instrumented
pedicle screws on cadaveric motion segments. McKinley et al. (1999) studied how
variations in surgical technique directly affect pedicle screw bending moments by using
instrumented pedicle screws.
Survivorship studies have been done in an attempt to quantify the efficacy of
pedicle screw systems and fixation procedures. Dickman et al. (1992) studied 104
patients that underwent transpedicular spinal instrumentation procedures. Various
conditions existed in patients yet severe back pain was consistent throughout the group.
At a 20 month follow-up period there was a 96% fusion rate. There were no operative
7
deaths, but major complications included a spinal epidural hematoma, three isolated
nerve root deficits, and three would infections. Instrumentation failure eventually
developed in 18 patients; nine were asymptomatic with a solid fusion. The other 9 were
symptomatic or had pseudarthrosis and required operative revision. Pseudarthrosis, or
false joint, is characterized by deossification of a bone followed by a bending fracture,
which affects the ability of the bone to form a normal callus. The author stated that
transpedicular instrumentation procedures using pedicle screws is an excellent method in
all respects.
McAfee et al. (1991) performed a case study of pedicle instrumentation cases
from 1985 to 1989. The total number of cases was 120 using two different types of
instrumentation. Out of 526 pedicle screws there were 22 problem screws. Those
problem pedicle screws involved 12 patients, seven of which had complete fusions and
the condition was only found incidentally during radiographic imaging. The remaining
patients had screw breakage in association with a pseudarthrosis. The survivorship was
predicted using life table calculation to be 80% at 10 years. The actual survivorship was
90% at 10 years, which is more closely related to other types of existing surgical implants
such as total hip arthroplasty.
Glaser et al. (2003) studied the long-term results of lumbar spine fusion
supplemented with pedicle screw fixation. Patients treated at the University of Iowa
Department of Orthopedic Surgery with lumbar pedicle screw fixation were reviewed.
Questionnaires were given before surgery and at follow-up evaluation time. Radiographs
were reviewed for evidence of hardware complications, fusion status, deformity, and
extent of degeneration around the fusion. Out of 234 patients, only 94 had complete
information. Radiographically, at the 10-year follow-up assessment, 242 of 244
instrumented segments showed no motion, with approximately 1/3 of these also showing
evidence of definite fusion.
Synthetic bone analogs have been shown to be excellent materials to simulate
trabecular bone for pullout strength testing. Chapman et al. (1996) showed that the
mechanical properties of porous polyurethane (PU) foams might be matched to the
mechanical properties of various trabecular bone qualities. The group showed similar
shear properties and suggested that PU foams are an excellent choice to simulate the
pullout strength of pedicle screws. Gibson and Ashby et al. (1997) studied cellular PU
foams and found that they may be used as models for cellular solid (Gibson, 1985) and
when formulated properly, correspond well to those of cancellous bone. Szivek et al.
(1995) studied three different formulations of porous PU foams prepared from Daro foam
components with a range of mechanical properties to simulate trabecular bone. Fenech et
al. (1999) studied cellular solid criterion for the prediction of axial, shear and failure
properties of bovine trabecular bone. The purpose was to use cellular solid criterion in
application to multiaxial loading in order to understand the failure behavior of trabecular
bone.
Thompson et al. (2003) studied four different commercially available PU foams,
by Sawbones, Inc., two of which were investigated during this present study. The group
found that Young's moduli for the PU foams were at the lower end for trabecular bone
(Currey, 1998), while the three lowest density foams has shear moduli comparable with
trabecular bone (Knauss, 1981). The foam samples had unexpected behavior in shear
failure suggesting that these foams should not be used to model failure or yield properties
of trabecular bone.
Motivation for Present Study
Pedicle screw breakage and loosening remain as clinical complications of short
segment instrumentation procedures for spinal stabilization. The mechanical behavior of
various screw designs has largely been
investigated through pullout testing, often in
synthetic bone analogs (Figure 4) (see previous
section). Although a useful approach, these tests
do not provide information on the bone/screw
micromechanical interaction, which is an
Figure 4. Cellular rigid
important factor in both short and long-term
polyurethane foams.
(www.sawbones.com).
stability of the construct. In addition, pedicle screw pullout failure rarely occurs alone in
vivo. Typical pedicle screw failure is often complex and involves multiple failure modes
simultaneously.
Animal models are often used to design and validate new spinal instrumentation
technology. Although there are physical similarities between human and animal bone
they are not the same and loading is not the same in vivo. PU-foams are often used to
model screw pullout strength in trabecular bone. Figure 5 illustrates typical crosssectioned examples of human, porcine and PU-foam samples. It is clearly seen that these
samples are different in trabecular density, geometry and uniformity. Comparison of
human, porcine and PU-foam samples is necessary to gain insight into whether porcine
10
and foam samples are adequate to model human trabecular bone during pedicle screw
insertion.
Figure 5. Cross-section of typical human, porcine and PU-foam samples (left to right).
Present Study
It is hypothesized that plastic and elastic strains within the vertebral pedicle
trabecular bone contribute to pedicle screw purchase in different ways. Plastic strain or
crushing of trabecular bone around the screw provides mechanical interlocking as the
screw is fully inserted. Elastic strain in the trabecular bone surrounding the pedicle screw
provides forces normal to screw geometry. These elastic forces not only help to hold the
screw in place, but also help absorb energy during in vivo loading. By characterization
of elastic and plastic strains it may be better understood how mechanical interlocking of
crushed trabecular bone around the screw and elastic deformation of the surrounding
trabecular bone are responsible for screw purchase.
Bone volume fraction (BVF), or apparent density (AD) may be used as a
measurement of trabecular bone quality. Thompson et al. (2003) suggested that when
11
AD is compared to material properties for PU foams with different densities, similar
relationships to theoretical cellular solid criterion and mechanical properties (Gibson and
Ashby, 1997) exist. If cellular solid criteria are established for trabecular bone, and foam
properties may be matched based upon AD, then validation for foam as models for
trabecular bone may result. This may also lead to validation for the use of animal models
for pedicle screw instrumentation research. Cellular solid criteria for trabecular bone
may be the focus of future research, however this study will discuss whether PU foams
are appropriate models for the simulation of pedicle screw insertion into pedicle
trabecular bone. This will be investigated by comparing the elastic and plastic strains
that develop within human and porcine pedicle trabecular bone and PU-foam samples.
Critical sectional areas give threaded fasteners their strength and fracture
characteristics (Blake, 1986). Figure 6 illustrates the geometry of screw threads.
Hr
PTH O
E.flOOT
\
I
/1
I-PtTcH
I
c
in iiiiiiiii
II IIII1IJ1
1)AO
H
fl
A. XtEN*t 1)AC$
Figure 6. Definition of screw thread geometry.
These areas are important to the failure of the threaded fastener or the material that it is
fastening. The cross-sectional area of the fastener, through the thread, is important to
12
resist tensile and shear failure. The shear area of the external thread resists shearing of
the screw thread, resulting in pullout. These types of failures of instrumentation do occur
in vivo and are directly associated with the material quality and the in vivo environment
discussion. The shear area of the internal thread resists the pullout of the threaded
fastener by shearing of the fastened material. This area is very important to pedicle screw
instrumentation failure in vivo. The lines along the minor diameter in Figure 6 define
the shear area for the external threads, while the lines along the major diameter define the
shear area for the internal threads. During a pullout failure of a pedicle screw, the
trabecular bone surrounding the screw shears on a macroscopic level. Yet on a scale of
similar magnitude to trabecular struts, local crushing of those struts begins and the
trabecular structure fails as the screw shears the bulk material. Bulk material shear
properties of trabecular bone govern this mode of failure. Trabecular bone is not a
continuous material. It is made up of interconnected strut-type element that maintain an
open-cell cellular solid (Gibson and Ashby, 1997). Although direct pullout of pedicle
screws in vivo is rare, pullout is often a consequence of screw loosening due to cyclic in
vivo loading.
This study has utilized a microCT based technique to directly measure bony
deformation within the samples during pedicle screw insertion. This technique allows the
direct calculation of strains from displacement data without any underlying assumptions
for the internal material properties of the samples. This is valuable for this study due to
the highly nonlinear nature of trabecular bone. Elastic, plastic and total strains within the
vertebral pedicle trabecular bone directly surrounding the screw were calculated.
13
The assessment of plastic strains is based on the notion that the insertion process
will produce both plastic and elastic strains, and that the elastic strains will disappear
after screw removal. Comparison of digital volumes in the before insertion images with
fully inserted images would give the total strain field, whereas comparison of before
insertion with after extraction will isolate the plastic strain field. Finally, comparing fully
inserted images with images after extraction would measure the elastic strain fields.
Quantification and spatial distribution of plastic and elastic pedicle trabecular
bone strains may provide insight into the micro-interaction between pedicle trabecular
bone and pedicle screws. Further investigation may prove useful in the design of pedicle
screws for patients with varying levels of bone density or disease, such as osteoporosis.
Digital Volume Correlation and Present Study
Digital Volume Correlation (Bay et al., 1999; Smith et al., 2001, 2002) is the
three-dimensional extension of two-dimensional digital image correlation (Bruck et al.,
1989; Sutton et al., 1983). Two-dimensional image correlation uses distinct patterns that
are inherent or added to the surface of the material to measure sample displacements
during experimental procedures. Speckling the sample surface with an airbrush or spray
paint often creates adequate surface patterns. A region of interest (ROl) is defined within
the sample as a means to view the region of direct interest with respect to the experiment.
The region of interest is created and meshed using the meshing tool of an FEA package.
The mesh defines discrete points, which are used for direct experimental measure of
displacements. Digital images are then taken of the sample before and after loading. A
computer algorithm defines a subregion of speckle around each point for the unloaded
14
image. The algorithm then directly measures sample displacements by identifying the
location of the subregion for each point in the unloaded and loaded images. Using this
displacement data, strains may be directly calculated for the region of interest.
Digital Volume Correlation was utilized in this study to evaluate the plastic,
elastic and total strains within the vertebral pedicle trabecular bone during pedicle screw
insertion. High-resolution computed tomography was used to create digital image
volumes of the samples. Varying grayscale value regions in the digital image volume
represent the natural bone density variation within the trabecular bone in the samples.
These grayscale regions allow the Digital Volume Correlation technique to track the bony
deformations within the sample during pedicle screw insertion by matching patterns
between the unloaded and loaded image volumes.
A pattern-matching algorithm is applied to each point in the region of interest that
is defined within the original, unloaded digital image volume. This region of interest is
meshed, which defines points that represent the location of distinct voxels, or three-
dimensional pixels. Figure 7 illustrates a meshed region of interest for a typical sample.
A starting
15
-' I
I
'la
Figure 7. Example of a typical meshed region of interest shown for sample: 41270-11right. An outline of the region of interest for a vertically resliced cross-section of the
sample (left) and modeled three-dimensional region of interest (right) are shown.
point is selected and a subvolume around that point is used to match patterns between the
unloaded and loaded image volumes by the minimization of a sum-of-squares objective
function. This objective function minimization finds the location within the loaded
image volume that is a best match for each point in the unloaded image volume. The
objective function is defined as,
ge
1
H'
C(g)=(B(p+g+m)_A(p+m)}2
93
mm
2
where the parameters are as listed below:
p is the displacement measurement location,
g is a trial displacement vector,
m1
is an offset to a location within a subvolume,
w is the number of points within a subvolme,
16
A are the values from the unloaded image data,
B are the values from the loaded image data.
Determination of a starting point that is relatively close to the global minimum,
and avoids local minima, is fundamental in the nonlinear minimization. To ensure this
occurs a search range of voxel coordinates from p is defined and a coarse estimate for the
minimum is calculated. This procedure directly minimizes the first location to within one
voxel and sets the stage for the above outlined subvoxel minimization routine.
The minimization routine uses the Levenberg-Marquardt variation of the GaussNewton technique for subvoxel precision (Gill et al,
1981).
This technique efficiently
minimizes sum-of-square-differences objective functions. This method requires
interpolation since voxel locations are integer valued and objective function and Jacobian
values used in the procedure are real valued. Tricubic interpolation (Lancaster and
Saldauskas,
1986)
is used to determine the real intermediate values between voxels.
The result upon minimization for each point in the region of interest is a
displacement vector for that point. This procedure is repeated for every point in the
region of interest (Figure 7), which defines the displacement vector field. Displacement
data is smoothed by fitting a second-order approximation of the strain tensor to a cloud of
displacement values local to each point (Geers et al.,
1996).
This operation acts to reduce
the noise associated with the measurement for each point in the region of interest. Figure
8 illustrates the flowchart for Digital Volume Correlation.
17
In 111 alizati on
Ou4ut
Read in Spatial
locatiofts of points
Write displacement estimate g)
for each location (p)
Low! SuLw olume
Loop
Repeat tbr next location(pt
I
Read subvolume from
unloaded image volume
centered at pOint (ii)
Start Point Determination
Define search range and
select least C(g) for integer
alued g within range
Error Minimization
Flag displacement values
when range or coiwergence
fiulures occur.
Mini,nization to SuinoxelL eve!
Mininuze C(g) with
Levenberg-Marquardt method.
hetk coin ergenge and range
t.
Figure 8. Flow-chart for Digital Volume Correlation.
The error minimization for the DVC procedure ensures that data for particular
points with local minima and poorly defined objective functions are excluded during the
minimization of the objective function. Many local minima may exist which minimize
the objective function. The global minimum is the desired result of the minimization
routine. The objective function may also be poorly defined for a particular point, which
will never converge to a minimum. This convergence failure criterion ensures that
objective functions that are poorly defined for particular points are neglected during data
collection.
LI
Materials and Methods
Samples' Sources and Preparation
This study included seven (7) human
cadaveric and three (3) porcine pedicle samples as
Table 1. Summary of Sample
Labels and Source Type
Sample Name
well as two (2) polyurethane (PU) foam samples.
41258-li-left
41258-li-right
Table 1 summarizes the label designation and
41270-11-left
41270-11 -right
source type for each sample. Tissue samples were
prepared at the Department of Orthopaedic Surgery
3 8424-13
3 8424-14
3 8424-15
Pig-13
at the Cleveland Clinic Foundation in Cleveland,
Pig-14
Ohio. Each tissue sample was removed from the
Pig-l5
lOfoam
12.Sfoam
patient or animal and trimmed along the axis of the
Source Type
Human
Human
Human
Human
Human
Human
Human
Porcine
Porcine
Porcine
PU foam
PU foam
pedicle with approximate dimensions of 30 x 30 x 80 (width x depth x length) mm. The
samples were drilled, tapped, instrumented with conical 5.5 x 45mm pedicle screws to a
minimal depth and frozen until the time of image data collection. PU samples were
prepared by cutting through the thickness into a rectangular prism to approximate
dimensions of 35 x 35 x 65 (width x depth x length) mm. A hole was drilled into each
PU sample with a 3mm bit to depth equal to the pedicle screw insertion length. These
samples were composed with densities of 0.16g/cc (l0pcf) and 0.20g/cc (12.Spcf). These
PU foam densities have been shown to be similar in apparent density and shear strengths
of human trabecular bone (Chapman, 1996, and Thompson, 2003).
Before image data acquisition the samples were thawed, trimmed flat at the
mounted end, wrapped in gauze and the thumb portion of large latex gloves were
stretched over them. This was done to decrease any risk of contamination to surrounding
19
areas during handling and to retain sample moisture
content during testing. Although each tissue
sample was tested for blood-borne pathogens, the
utmost care was taken by assuming that each
sample was contaminated. Finally, each sample
was mounted in a mm deep platen using
polymethylmethacrylate (PMMA) (Figure 9).
Pedicle screws were manufactured of either
polyetheretherkeytone (PEEK) or carbon fiber (one
sample). A preliminary study was done in order to
Figure 9. Pedicle Sample
Prepared and Mounted
assess the viability of each of the two materials for
this study. Both materials performed in a similar manner with respect to the goals of the
study. These materials were selected for the preliminary study for their radiolucent
properties since a Computer Assisted Tomographic (CAT or CT) technique is utilized in
this study. This minimized the microCT artifacts often associated with metallic implants
during data acquisition utilizing CT imaging. X-ray artifacts occur in metallic samples
due to their relatively high atomic numbers and density. As x-ray photons enter the
boundaries of a metallic material, they are much more likely to collide with electrons and
be either absorbed or scattered. When scattering occurs, x-ray photos are more likely to
be deflected from their original paths and at varying degrees. This acts to blur the x-ray
images and is called x-ray artifact.
It was assumed that the interaction between the PEEK and carbon fiber pedicle
screws and the trabecular bone or PU foam of the samples would not differ from that of
,j]
metallic screws. Since PEEK, carbon fiber and titanium screws are stiffer and denser
than trabecular bone and the study is focusing on how trabecular bone deforms around
the pedicle screw, this is a reasonable assumption. However, there is a mechanical
loading scenario during which this would not be a good assumption. If the trabecular
bone is dense enough in certain regions, or if the screw interacts with cortical bone, then
the screw will be put into bending during insertion. In this loading scenario each screw
type behaves differently from one another due to the differences in elastic tensile moduli
and ductility. The elastic tensile moduli for PEEK, carbon fiber and titanium are
approximately 3.4GPa, 124-I37GPa and 105-I2OGPa, respectively. Although carbon
fiber is stiff as compared to titanium, it is brittle and can break into shards, which was the
case for one of the early test samples. This sample was not used for data acquisition for
this study. Titanium and carbon fiber pedicle screws will deform little under applied
bending moments. These screws will stay relatively straight during the screw insertion
path. PEEK screws under similar applied bending moments will deform to a greater
degree. This translates to different screw paths and bone crushing profiles for the
different screw types under bending. This type of loading was minimized for this study
by ensuring straight tapped paths through the center of the samples.
Equipment and Image Data Collection
This study utilizes a custom functional microCT imaging system to collect
experimental image data. This equipment includes an Instron mechanical tester, a
Newport rotational stage, a Thomson image intensifier, a Retiga CCD Camera and a Fein
21
Focus x-ray source. Table 2 summarizes the equipment included in the custom
functional microCT imaging system.
Table 2. Summary of Equipment and Manufacturers for Functional Imaging System
Instron Co.
Newport, Inc.
Thomson Tubes Electroniques
Qimaging, Burnaby
Fein Focus, Inc.
Instron 4444
RVI2OPP
TH9438HX
Retiga
FXE
Mechanical Testing Apparatus
Rotational Stages
Image Intensifier
1024 x 1280, 10-bit CCD Camera
160.20 .tCT x-ray source
Figure 10 shows the functional imaging system as it lies within a lead chamber. The
CCD camera resides behind the image intensifier as may be seen in the left image. The
x-ray source and the mechanical tester with rotational stages are shown in the right image
in Figure 10.
Figure 10. Functional CT imaging System including the x-ray source and mechanical
tester with rotational stages (right) and image intensifier and CCD camera (left).
22
The functional imaging system allows the user to control the position of samples
and the power of the x-ray source in order to produce high-resolution images of the
sample. The rotational stages in the mechanical tester may be precisely controlled
through 360 degrees of rotation. Samples in the system are subjected to x-rays, which
produce an x-ray shadow that is intensified, converted to visible light and captured by the
CCD camera as a high-resolution digital radiographic image. This is done for many
angles and custom software is then used to correct the images for distortions caused by
the image intensifier and to reconstruct these images (Feldkamp et al., 1984) into a digital
image volume. Digital image volumes that coincide with unloaded and loaded states may
be compared by utilizing additional custom software. The result is the direct
measurement of deformations and the direct calculation of strains that occurred between
the two states without any underlying assumptions of material properties.
Once mounted, image data sets were taken for each sample in an unloaded state.
This image data is required for a baseline data set. A second image set was taken under
identical conditions. These two image data sets are referred to as the repeat-unload
image data sets. These image data sets are important in order to minimize and
characterize the error associated with the process for each sample. Pedicle screws were
then rotated until full screw insertion has occurred and an image data set was acquired.
Then the pedicle screw was extracted to the initial position and a final image data set was
acquired. These load steps were chosen in order to extract plastic, elastic and total fullfield strain data as described in the Data Analysis section of this study.
Each image data set consisted of 500 radiographic images with a resolution of 504
x 636 that were collected through a full 360-degree rotation. This resulted in a total of
23
four (4) image data sets of 156.5 MB each for a total of 626 MB for each sample. There
were twelve (12) samples for a total of 7.5 GB of raw data. The power level for the x-ray
source was set to 50 KVp with a total exposure time of 200 ms per projection image. The
power level for the PU foam samples was 41 KVp with an exposure time of 260 ms.
Bright and dark field images were taken for each sample at the identical system settings.
Bright and dark field images are used to set upper and lower grayscale values for each
pixel location. These values are then used to scale the individual pixel grayscale values
for each pixel in each digital image before image reconstruction.
Image Post Processing
The natural distortions caused by the x-ray source and the image intensifier, as
discussed the Equipment and Image Data Collection section corrected using images of a
metallic plate with a precisely machined grid of known geometry and the bright field and
dark field images collected during data acquisition. After image correction, image
volumes were reconstructed to 8-bit, 500 x 500 x 624 digital image volume composed of
cubic voxels with a resolution of approximately 50 microns (Feldkamp et al., 1984).
Data Analysis
Reconstructed digital image volumes were reoriented for each sample by utilizing
the similarities between human and porcine samples at the necked region of the trimmed
pedicles. This reorientation was done for the sake consistency between samples.
Software for the manipulation and visualization of digital image volumes included Scion
Image (Scion Corporation, Frederick, MD) and Image J (Wayne Rasband, National
Institutes of Health, USA).
Three digital image volume states were used for image comparison with the goal
of isolating plastic, elastic and total strains within the pedicles during pedicle screw
insertion. These states were 1) before screw insertion (BI), at 2) full screw insertion (F!),
and 3) after screw extraction (AE).
Digital Volume Correlation (DVC) was used to directly measure the elastic
plastic and total strains for a distinct, three-dimensional region of interest within each
sample. This region of interest was chosen for its proximity to the pedicle screw upon
insertion and for its bone quality for each sample. Upon insertion and extraction, the
pedicle screw entered and fully exited the selected regions of interest, respectively.
Approximately 2000 points distributed within the regions were analyzed for
displacements and strains by correlation of imaging volumes from the previously defined
screw insertion and extraction states. Figure 11 illustrates an example of a typical region
Figure 11. Example of a typical region of interest shown for sample: 41270-liright. An outline of the region of interest for a vertically resliced cross-section of the
sample (left) and modeled three-dimensional region of interest (right) are shown.
25
of interest. Image modeling and post processing of digital volume correlations were done
using MSC Patran 2001 version r2a (MSC Software Corporation, Santa Ana, CA).
The region of interest for each sample was modeled and meshed with Patran with
approximately 2000 nodes. These nodes are used as a basis for the measurement of
displacements between digital image volumes. A nodal position file was exported from
Patran for use in the Digital Volume Correlation procedure, which is discussed in the
Digital Volume Correlation and Present Study section of this study. This procedure
results in files containing the nodal displacements and nodal strains between selected
digital image volumes for each region of interest.
Digital Volume Correlation was executed to isolate plastic, elastic and total
strains during pedicle screw insertion and removal and Patran was used to post-process
the data. Minimum principle and maximum shear strains were viewed and images were
collected. Minimum principle strains were chosen to report since the insertion of pedicle
screws into bone is compressive in nature. Maximum shear strains were chosen since an
accepted mode of failure testing for pedicle screws is pullout testing. Pullout of pedicle
screws occurs when a PU foam or trabecular bone fails in shear (Dawson, 2003; Blake,
1986). Report files containing data for plastic, elastic and total minimum principle and
maximum shear strains were exported from Patran and were further processes using
Microsoft Excel (Microsoft Corporation). Excel was used to produce various figures,
which are shown in the results section.
Repeat unload digital image volumes were collected for the purposes of error
minimization and quantification of system noise. This analysis is summarized in the
results section.
26
Results
Plastic, elastic and total minimum
5 14-
principle strain results were generated and
images taken for each region of interest. A
1-os-
typical example of these images is illustrated
in Figure 12 for sample 41270-11-right with
fixed scaling. It may be observed that the
-712---
peak plastic strains (top) occur in a different
region that the peak elastic strains (middle).
-1.12-
This may be indicative of some local material
-1 53-
properties within the sample such as low bone
density or bone integrity in the plastic
-1.94-
(crushing) zone. Regions of peak elastic
strains (middle) are not well defined (dark) in
the total strain plot (bottom). Remaining
-2.75-
plastic, elastic and total minimum principle
strain plots reside in Appendix A.
-. 16-
-
-39- 02
Figure 12. Typical plot of plastic (top),
elastic (middle) and total (bottom)
minimum principle strains for a
sample region of interest.
Sample 41270-11-right is shown.
27
Plastic, elastic and total minimum
principle strain results were generated and
images taken for each region of interest. A
typical example of these images is illustrated in
Figure 13 for sample pig-l4. It may be
observed that the peak plastic strains (top) occur
in a different region that the peak elastic strains
(middle). This may be indicative of some local
material properties within the sample. Peak
plastic strain values do not dominate peak
elastic strain values. This may be deduced by
observing the total minimum principle strain
plot and by understanding that the total
minimum principle strains are a summation of
plastic and elastic strains. Regions of peak
elastic strains (middle) are well defined (dark)
in the total strain plot (bottom). Remaining
plastic, elastic and total minimum principle
strain plots reside in Appendix A.
Figure 13. Typical plot of plastic (top),
elastic (middle) and total (bottom) minimum
principle strains for a sample region of interest.
Sample pig-14 is shown.
28
Plastic, elastic and total minimum principle
strain results were generated and images taken for
each region of interest. A typical example of these
images is illustrated in Figure 14 for sample lOfoam.
It may be observed that the peak elastic strains
(middle) have greater magnitudes the peak plastic
strains (top). Remaining plastic, elastic and total
maximum shear strain plots reside in Appendix A.
Histograms of binned plastic, elastic and total
strain values with fixed scaling were generated for
minimum principle and maximum shear strains for
each sample. Figure 15 shows typical histograms for
plastic, elastic and total minimum principle strain
values for samples 41270-li-right, pig-l4 and lOfoam.
It may be observed that sample pig-14 has more
uniformly distributed elastic and total strain values
throughout the trabecular structure. Histograms were
also plotted for maximum shear strains for each
sample, which reside in Appendix A.
Figure 14. Typical plot of plastic (top),
elastic (middle) and total (bottom) maximum
shear strains for a sample region of interest.
Sample lOfoam is shown.
29
4I2$4I'dØI.pItic p.*rn,m Prindple rIn
4l2ft4t.dØ.d.*c InuT PdI,dple Strn
xo
Io
10
10
1UQ
Ilo
i/i/i//i//il ill/i
f//i////qIf//i/I
Bin
PIpI.
2O
pIWd.Bffn Mb.ln.in. P.IneIçI. St.in
2O
10
10
.1z,o
10
1ulo
1o.n.1,k
p.mc,l. U*
lQn.1tk I.InlBiom Prindpk Strn
lo
l2OO
lcoo
Bl,
Figure 15. Typical histograms for plastic and elastic minimum principle strain values.
Histograms for 41258-11-right, pig-l4 and lOfoam are shown.
30
Nonparametric statistical analyses were required to characterize the individual
strain distributions since the data is not normally distributed. In this approach the 17th,
50th
and 83 percentile values, which correspond to one standard deviation from the
mean on either side of normally distributed data, are extracted from the data for each
result type. The assumption is then made that data is normally distributed across the
sample set. Figure 16 illustrates a typical nonparametric statistical comparison of each
sample for plastic and elastic minimum principle strain values. The remaining
nonparametric comparison results reside in Appendix A.
Iln8n.m P44olpI. Sfra84 ro, P1581k R..114.
Minklom PrinolpI. SirsIns Is, E1584k R.SWIS
.158-02
.3 54-02
-1 3E-02
41255.114.8
.fl3
41258-l14l8
-138-02
-114-02
41270-114.0
41270.-Il4Igllt
25424-IS
-0E-03
38424-44
C
41 270-II-n;I
38424-IS
-704-03
34424-IS
38424-14
8
-7.04-03
38424-IS
PIg-L3
.558.45
Rg-L4
-504-43
.304.03
101b.Sn
-300-83
-1.04-03
S 1270-11.145
-904-43
1 Ofusni
-, 00-03
37%
50%
85%
17%
50%
83%
Figure 16. Typical nonparametric statistical comparison of each sample for
plastic and elastic minimum principle strain values.
Plastic, elastic and total strain values were compared for minimum principle and
maximum shear strains. ANOVA p-tests were used to determine whether the difference
between human and porcine samples were significantly different with a criterion of
p<0.05. Figure 17 represents a comparison between human and porcine samples for
plastic and elastic minimum principle strains using nonparametric statistical analysis and
ANOVA p-test criterion. The strain values are also shown for PU-foam, but are not
compared using the ANOVA p-test criterion. Only one of each type of PU foam was
31
tested since other studies have shown PU foams to be highly uniform and consistent
properties (Chapman, 1996, Thompson, 2003) with little variability when compared to
tissue samples (see previous studies section). It may be observed that the strain
magnitudes and variations between percentile values are much lower than for human and
porcine samples. The remaining results figures reside in Appendix A. Table 3
summarizes the ANOVA p-value results for each of the results types and samples.
Figure 17. Typical nonparametric statistical comparison between human, porcine and
PU-foam samples (p<O.O5) for plastic and elastic minimum principle strain values.
Table 3. Summary of ANOVA p-test values upon comparison
between human and porcine samples.
It may be observed in Table 3 and Figure 17 that plastic strains are not different between
samples, while elastic strains are different with the exception of the peak (17th percentile
minimum principle and 83' percentile maximum shear) values. The trend is for porcine
samples to have similar plastic strains to human samples, while having larger elastic
32
strains. The trend for peak strains is for human samples to have higher plastic strains,
while porcine samples have higher elastic strains.
Bone volume fraction within each region of interest for each sample was
measured using Scion Image and a
custom macro. The custom macro used
Table 4. Bone Volume Fraction Summary
for Each Sample
grayscale thresholding to define BVF
Sample
Bone Source
BVF (%)
4 1258-li-left
Human
Human
Human
Human
Human
Human
Human
Pig
Pig
Pig
PU-foam
PU-foam
26.2
24.3
29.9
24.5
for each slice of the reconstructed image
volume and averaged them to attain the
total BVF for each region of interest.
Table 4 summarizes the bone volume
41258-li-right
41270-li-left
41270-11-right
38424-13
38424-14
38424-15
Pig-l3
fraction measurement for each sample
Pig-14
Pig-15
lOfoam
and sample source type. This data was
12.Sfoam
15.3
19.7
15.1
46.6
48.7
43.2
21.4
31.4
collected for the purpose of finding a correlation between bone volume fraction and
plastic, elastic and total pedicle trabecular bone performance during pedicle screw
insertion. Plastic, elastic and total strain values for the 17th, 50th and 83rd percentile were
plotted against bone volume fraction values for minimum principle strains. A typical
example of these figures for the 17th percentile plastic and elastic minimum principle
strains is illustrated in Figure 18. It may be observed that for 17th percentile values of
plastic and elastic minimum principle strain, the foam samples are not good models for
pedicle trabecular bone strains for either human or porcine samples. The criteria for this
observation is that for a foam sample to be a good model for this study, the density, and
therefore the modulus, as well as the strain performance should be similar. Remaining
figures for the 50th and 83rd percentile values exist in Appendix A.
33
11th P-centile Plaic Mninui Principle Sham vs Bone Vokune Fraction
Bor* Vdtje Frction(%J
-0.016
A
-0.014
A
-0.012
£39424-B
£3942414
A
-001
A412-l1-lft
A
A
£412%-l1- nght
£41270-Il-kit
A
£41270-Il-right
U
pig-B
pI4
U
pigt5
A
lOfoam
12.Sloacn
-0L04
-0.W2
0
10
15
35
25
35
35
43
45
53
11th Percentile EIa1c Mninun Principle Sbainvs Bone Volume Fraction
Bone Vdume Fraotion(%)
-0.016
A
-0.014
-0.012
A38424-13
£3942414
j
£384245
-001
£41253-Il- kit
£41253-Il- right
£41270-Il- kit
£41210-Il-right
U
2
.
pigr3
A
.2
-0.U6
pil4
A
-0.1334
l0foam
12.6fam
A
-0.032
0
10
15
23
25
33
35
43
45
53
Figure 18. 17th percentile plastic and elastic minimum principle strain
values versus bone volume fraction for each sample.
34
A performance criterion for whether a PU foam is an appropriate model for the
study of pedicle screw purchase has been defined. For a PU foam to be an appropriate
model for pedicle screw purchase in pedicle trabecular bone, the elastic and plastic strain
results (minimum principle strains results for
17th 50th
or 83rd percentile values) must
vary from the mean of the BVF group results by no more than the variability between
BFV group samples from their mean. This statement is a requirement for the
performance of PU foam to not be significantly different from bone performance. Table
5 summarizes which foams are appropriate for modeling pedicle screw insertion for this
study. It may be noted that only one result for 83Id percentile plastic minimum principle
strain value met the criterion, however this was very close, meaning that it would be an
outlier in the data set if it were to be considered valid. The trends in the data support the
..
lack of testing more PU foam samples.
Table 5. Summary of foams matching plastic and elastic minimum principle strain
performance criterion for BVF groups. % variation of each foam from the mean for each
group for each result.*
!
Type
PS
. .
Group
lOfoam
L
..foarn
2
75.6(51.6)
50.7(20.3)
28.1(13.0)
83.2(22.4)
69.8(12.6)
50.9(18.0)
66.5(29.4)
42.7(32.4)
29.9(28.9)
76.1(26.3)
41.8(24.5)
16.1(17.7)
3
76.0(6.0)
72.3(30.2)
69.1(31.7)
72.4(11.4)
69.2(15.9)
57.9(20.9)
1
78.5(51.6)
53.7(20.3)
26.0(13.0)
88.3(22.4)
82.7(12.6)
80.1(18.0)
2
70.4(29.4)
46.1(32.4)
29.7(28.9)
83.3(26.3)
66.8(24.5)
66.0(17.7)
3
78.9(6.0)
73.9(30.2)
68.3(31.7)
80.8(11.4)
82.4(15.9)
83.0(20.9)
* ( ) indicates required % value of ± 1 STDEV from the mean for performance criteria
In order to explore the possibility of a correlation between bone volume fraction
and strain performance during pedicle screw insertion, natural bone volume fraction
groups were defined. The bone volume fraction group for each sample is summarized in
Table 6.
35
Table 6. Bone volume fraction bin range assignment and definition for each sample.
Sample
Bone Volume Fraction (%)
Bone Volume Fraction Group
41258-11-left
26.2
24.3
29.9
24.5
2
15.3
19.7
15.1
1
46.6
48.7
43.2
3
41258-lI-right
41270-11-left
41270-11-right
38424-13
38424-14
38424-15
Pig-13
Pig-14
Pig-l5
2
2
2
1
1
3
3
The bone volume fraction bin designations in Table 5 were used to plot 17th, 50th
and 83" percentile values of plastic, elastic and total strain for minimum principle and
maximum shear strains versus bone volume fraction bins. Figure 19 shows
and
83k'
17th, 501h
percentile plastic and elastic minimum principle strain values versus bone
volume fraction groups. The remaining figures reside in Appendix A.
36
P1.1k Mnkniu,n Principle Sueli. vi Bon. Volun,. Erector.
tar. fla flmeta, c.aw. r.fr
-1
flS2
.1
-l.flt42
.9_43
i
-5t-O3
-3.O3
161 .197
243.299
43.2.48.1
lOt.r (314)
61.1k Minin.n rPnrndpl. 58dm vi Son. V,Ion..
l2.511 (31.4)
ctoe
Son. flsntft.ctinfl 18e 1%)
-, A48.62
-in
IU1Th.PmcelIe 981..
.8Th ParSale VS.,
-8
nd PewS. vase
01
L i
-2..O3
is, .19.7
24.3.291
432-48.7
¶08.0(31.4)
15,14)
Figure 19. 17th, 50th and 83rd percentile plastic (top) and elastic (bottom) minimum
principle strain values versus bone volume fraction groups.
It is clear that the lowest bone volume fraction group had greater mean 17th
percentile plastic minimum principle strains than the denser groups. There is no
significant difference between the mean
171h
percentile values of elastic minimum
principle strain; however, their deviations from the means are different. As the bones
become more dense the plastic and elastic deviation from the mean become much less
(Figure 20). This suggests that low bone volume fraction (osteoporotic) samples are non-
37
uniformly elastic and not stiff, while greater bone volume fraction samples are uniformly
elastic and stiff throughout the trabecular structure. Table 7 summarized the ANOVA ptest values for significant difference (p<O.O5) between bone volume fraction groups. A
Complete table including maximum shear results resides in Appendix A.
Stndd DMI.n. *em EluI ITib P..dfl. M.
fVF Gp.
511-03
411-03
411.03
311.03
311.03
211.03
211-03
1.11.03
111.03
S.Z.04
511403
Grow'
011.2
OrowO
Figure 20. Standard deviations from the 17th percentile plastic and elastic minimum
principle strain values for bone volume fraction groups.
Table
7. Summary of ANOVA p-test values (p<O.O5) in comparisons between groups
50th
and 83rd percentile values of plastic elastic and total minimum principle
for l7,
Group 1: 15.1
* Bone Volume Fraction Groups (%):
19.7; Group 2: 24.3 - 29.9; Group 3: 43.2 -48.7.
Error Analysis
The validity of experimental data requires some knowledge of error inherent to
the data acquisition system. Error analysis for the system used in this study was
accomplished by the comparison on two distinct unloaded or repeat-unloaded image
volumes. Theoretically, the comparison of the unloaded and repeat-unloaded image
volumes should result in null strain tensors. Therefore, by comparison of these two
image volumes total system error may be assessed. Sources of error within the system
may be mechanical or analytical in nature.
Repeat unloaded images were taken for each sample and post-processed in Patran.
The results were used to refine the parameters used for the Digital Volume Correlation
until the error was minimized for each sample. Error results were then analyzed for three
typical sample types. One error analysis was completed for a typical sample from each of
the bone volume fraction subgroups. This not only allowed errors to be compared
39
between human and porcine samples, but between the three bone volume fraction
subgroups as well.
Total system error results were generated for minimum principle and maximum
shear strains for each of the three samples. These errors ranged from between a
minimum and maximum of 0.03% to 0.9%, respectively, for minimum principle strain.
These errors ranged from between a minimum and maximum of 0.0 1% to 0.99%,
respectively, for maximum principle strain. Extreme values are not necessarily good
indicators of sample behavior. Nonparametric analysis similar to that done for other
results for this study was applied to the error analysis as well. The minimum and
maximum minimum principle and maximum shear strain values of the
17th 50th
and 83Id
percentile values are summarized in Table 8. These strains are deemed acceptable when
considering that maximum measured strains are on the order of 7%. This equates to
approximately 3% error at maximum strain reading.
Table 8. Summary of errors for minimum principle and maximum shear strains for the
average 17th, 50th and 83rd percentile values.
Error(%)
0.22
Error(%)
5Uth
83
l7t
0.11
0.06
0.08
J
5O
0.13
3:j
021
II
Discussion
Plastic, elastic and total pedicle trabecular bone full-field strains have been
characterized for regions immediately surrounding pedicle screws during insertion into
human, porcine and PU-foam samples. A functional microCT 3-D imaging technique has
been utilized to accomplish this. Pedicle trabecular bone strains were measured by
comparisons between varying loading states for each sample. Digital image volumes
were created for before insertion (BI), full insertion (PT), and after extraction (AE) states
of pedicle screw insertion. Total strains, which include both plastic and elastic strains,
are introduced into the samples during pedicle screw insertion. Total strain results were
generated upon comparison of BI and Fl image volume states. Plastic strains were
isolated by the notion that no new plastic strains were introduced during pedicle screw
extraction. Comparison between BI and AE loading states produced solely plastic
strains. Elastic strains were revealed during the extraction of the pedicle screw. As the
screw is extracted all elastic energy is restored to its equilibrium state. Elastic strains
results were generated with comparisons between FT and AE loading states. Plastic,
elastic and total strain behavior of human, porcine and polyurethane (PU) foam samples
were compared. Bone volume fraction (BVF) groups were defined and used as a means
of comparison as well.
We hypothesized that these different types of trabecular bone strains contribute to
pedicle screw purchase in different ways. Plastic strains, or crushing of trabecular bone,
contribute to screw purchase by mechanical interlocking between screw thread geometry.
Elastic strains contribute to screw purchase by exerting normal forces to the screw
geometry. Normal patient motion causes implant loading, which is distributed along
41
implant-bone interfaces. Elastic strains also act as a sort of shock absorber for the forces
involved in normal in vivo loading. Characterization of elastic and plastic strains in
human, porcine and synthetic trabecular bone analogs may create a greater understanding
of how these strain components contribute to pedicle screw purchase and give insight into
the validity of using PU foams as models for trabecular bone tissue.
The experimental technique utilized for this study directly measures sample
strains without any underlying assumptions of pedicle trabecular bone material
properties. The variability between samples, uncertainty about material properties and
the highly nonlinear material behavior of trabecular bone during plastic deformation
make the use of analytical models unreliable for this type of study.
Characterization of bony deformations in pedicles during pedicle screw insertion
required various comparisons. Plastic, elastic and total minimum principle and maximum
shear strain results were generated for each sample. Minimum principle strains results
were chosen to present since the loading and crushing of bone during pedicle screw
insertion is compressive in nature. Maximum shear strain results were generated since
previous research has shown that trabecular bone fails in shear during pedicle screw
pullout (Chapman, 1996, and Thompson, 2003).
Pullout testing in tissue and PU foam has been established as a means of
comparing different pedicle screw instrumentation designs. Dawson et al. (2003)
discussed the clinical relevance of such testing and how the in vivo environment rarely
causes pedicle screws to fail in the pullout mode. The group concluded that pullout
testing should not be used as an indicator of clinical performance. We hypothesized that
plastic and elastic strains in any synthetic bone analog should behave in a similar manner
42
to that of trabecular bone in order to be considered as valid in vivo models. We have
shown that synthetic bone analogs have dissimilar strain performance and therefore
should not be considered as accurate models for trabecular bone. Others have also
suggested that PU foams should not be used to model yield and ultimate properties of
trabecular bone without further testing (Thompson, 2003).
Plastic, elastic and total strain measurements during pedicle screw insertion were
much lower in magnitude for PU-foams as is illustrated in Figure 17. This may be
explained on a mechanistic basis. Trabecular bone tissue is much different that PU-foam.
Trabecular bone tissue is highly variable in its strut-like structures creating an open
cellular solid network. PU-foams are a closed cellular solid with material stiffness much
greater than that of trabecular bone (see previous studies section). The differences in
strain behavior may be attributed to the micro-interaction between these very dissimilar
structures.
Future Research
Continued research may focus on the differences in pedicle trabecular bone
performance while using varying pedicle screws designs. These screw designs may
include tapered and cylindrical geometries. Since bovine and porcine bone specimens as
animal models are often utilized in the assessment of new spinal instrumentation,
understanding the differences in bone performance between human and animal bones
may improve instrumentation designs. Future research may focus on the differences
between human and animal models with the purpose of ascertaining the most efficient
way to use animal models for research into better human spinal instrumentation. More
43
realistic loading with instrumented spine segments and cyclic loading could help in
understanding how pedicle screws fail in vivo. Synthetic bone analogs have real benefits
is orthopedic research, but researchers must not be too hasty in using them. PU foams
may be studied for performance criteria in contrast to nonrealistic loading scenarios such
as pullout testing. The experimental technique used for this study could be used to
develop new PU-foams that more closely exhibit the behavior of trabecular bone.
Limitations of Study
The experimental technique utilized for this study is unique and valuable, yet its
limitations must be fully disclosed. The sample sizes that may be processed in the system
are limited to approximately 80 x 80 x 200 (width x depth x height) mm. This limits
many application of the technique. The technique only works for samples with distinct
internal patterns or geometry of varying density. X-ray artifact must also be considered
when utilizing this technique and minimized for maximum resolution and useful image
data. This study was limited in scope to loads occurring during pedicle screw insertion.
Conclusion
MicroCT imaging and Digital Volume Correlation have been utilized to
characterize the plastic, elastic and total pedicle trabecular bone strains during pedicle
screw insertion. Human, porcine and PU-foam samples have been compared with the
intent of finding tends or similarities in material behavior. Bone volume fraction groups
were also created and compared. The validity of using PU foams as synthetic analogs for
trabecular bone with pedicle screw research has been investigated.
44
Comparison between human and porcine samples showed that there are
differences between many of their strain magnitudes and strain distributions as
summarized in Table 3. The main points are summarized below:
Peak values of plastic and elastic strains were not different between human and
porcine samples.
Mean and lower magnitudes of plastic strains were not different between human
and porcine samples
Mean and lower magnitudes of elastic strains were different between human and
porcine samples, with porcine elastic strains being greater.
Peak plastic strains were considerably lower for porcine samples than for the least
dense (osteoporotic) human samples
Elastic and plastic strain behavior is similar between human and porcine samples
during the application of relatively high strains. Elastic behavior of porcine trabecular
bone is greater than human trabecular bone for relatively lower loading. This suggests
that during normal loading conditions such as daily activities, that porcine trabecular
bone may not be a good model for human trabecular bone. This is important since the
elastic properties are what give trabecular bone the ability to adjust to in vivo loading
during healing before trabecular bone damage occurs. This may be important to fusion
studies done on live animals under restricted activity schedules as models for human
bone tissue. Osteoporotic trabecular bone crushes much more easily that porcine bone,
which is to be expected.
Bone volume fraction (BVF) groups were defined and data was compared
between groups. It was shown that:
Peak plastic strains are greatest in samples with the least B\F.
Elastic strains are not different between human and porcine samples, however the
magnitudes of the standard deviations from their means are greater as BVF
decreases.
45
This suggests that low bone volume fraction (osteoporotic) samples are nonuniformly elastic and plastic and not stiff, while samples with greater bone volume
fraction are uniformly elastic and plastic and stiff throughout the trabecular structure.
Comparisons between trabecular bone tissue and PU foam samples show that
their behavior is different. It has been shown that the PU foams are valid models for
pedicle screw pullout when comparing pedicle screw holding strengths (Chapman, 1996).
Dawson et al. (2003) discussed the clinical relevance pullout testing of pedicle screws in
PU foams and suggested that they should not be used as such. Thompson et al. (2003)
suggested that PU foams should not be used to model the yield and ultimate properties of
trabecular bone without further testing. We have found that PU foams are not relevant as
models for pedicle screws in trabecular bone, since their plastic and elastic strain
behaviors are not within any reasonable measure close to that of human or porcine
trabecular bone.
Previous attempts to verify the validity of PU foams as trabecular bone models
have focused on measurements of continuous material properties such as the modulus of
elasticity, density, compressive maximum stress, shear modulus and the maximum shear
stress. These properties are useful, but focus mainly on the failure properties of the
implant in trabecular bone. We suggest that these become secondary to the specification
of PU foams as models for trabecular bone by elastic and plastic strain performance
below failure level loading. If the plastic and elastic strain behavior of PU foams are
matched to that of trabecular bone, then inexpensive testing may be done to better
understand the affects of implants on trabecular bone surrounding spinal instrumentation
46
during in vivo loading. Pedicle screws rarely fail in the in vivo environment by pullout,
but as a consequence of screw loosening during normal in vivo loading.
Pedicle screw designs that maximize screw purchase by utilizing the elastic or
plastic interaction with trabecular bone may improve the performance of pedicle screw
instrumentation. Understanding the bony deformations around the screws is critical to
this process. Due to the highly nonlinear nature of the trabecular bone deformations and
the uncertainty of local material properties, it is unlikely that analytical approaches would
yield relevant information.
47
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Appendix A
Additional Results
51
PLASTIC STRAINS
2.5Q-
2.27
a) 41258-Il -left-plastic-minprin
a) 41258-I 1-Ieft-plastic-maxshear
1.3:/-
9,17
b) 41258-11 -right-plastic-minprin
b) 41258-Il -right-plastic-maxshear
Figure 21. Minimum principal strains
within the regions of interest: Before
insertion correlated with after extraction.
Figure 22. Maximum shear strains
within the regions of interest: Before
insertion correlated with after extraction.
2 '1
22-
2C
16O-
2. 37_
a) 4 1270-1 1-left-plastic-minprin
a) 41270-11 -left-plastic-maxshear
1 -1- c2
-171-
-
917-fl2
rn-
5_g1
-235-
-2 68-
b) 41270-1 1-right-plastic-minprin
b) 4 1270-11-right-plastic-maxshear
Figure 23. Maximum shear strains
within the regions of interest: Before
insertion correlated with after extraction.
Figure 24. Maximum shear strains
within the regions of interest: Before
insertion correlated with after extraction.
53
N
a) 38424-13-plastic-minprin
a) 38424-13-plastic-maxshear
1.29-
b) 38424-14-plastic-minprin
b) 38424-14-plastic-maxshear
c) 38424-15-plastic-minprin
c) 38424-15-plastic-maxshear
Figure 25. Minimum principle strains
within the regions of interest: Before
insertion correlated with after extraction.
Figure 26. Maximum shear strains
within the regions of interest: Before
insertion correlated with after extraction.
54
a) pigl3-plastic-minprin
b) pigl4-plastic-minprin
b) pigl4-plastic-maxshear
I
'
c) pigl5-plastic-minprin
c) pigl5-plastic-maxshear
Figure 27. Minimum principle strains
within the regions of interest: Before
insertion correlated with after extraction.
Figure 28. Maximum shear strains
within the regions of interest: Before
insertion correlated with after extraction.
55
a) 1 Ofoam-plastic-minprin
Figure 29. Minimum principle strains
within the regions of interest: Before
insertion correlated with after extraction.
a) 1 2.5foam-plastic-minprin
Figure 30. Minimum principle strains
within the regions of interest: Before
insertion correlated with after extraction.
4I2S-I1-I.ft.pb Mohrn.o Pdntple SU
4i25l.I14p00.tC M.0I,rnm, ShIarIttin
I2
vrw
//iiI,iiy//i/,//
a-
412I1td4$l0IIk
4125*-I1.dtj,1dr Me,Om Pflo.I. Sirin
tSiI
Stit
soss.
I600-
IS,'
loo
12eo
ioo
4CC
21,'
ceo--
41270 tJSt.pIatIc Ilnimaim PTIflcIpIe Sirs.
41 270114117, pint c Maximuan liMit Sits.
700
___________
______________
ceo
20
/ / / ,'/3 / /1//i//i//
/71;?/
7,
17
,
,-
,
.
7j
S.
41270I1qI*.pI0tdc Maximlol, She., SITSn
4I27041.flgtwj,10Ie MnImuI.1 POncipIt Its.
7c
1
21
7
21'
SI,
Figure3l. Histograms of plastic
minimum principle strains for each
sample.
Figure 32. Histograms of plastic
maximum shear strains for each sample.
3$4I.I3çI00tR Mnlnmrt, Prkxdpl, Srrin
1200
//i/iiIi///i///
.:-&.
yY
,.
Sen
38424-t4-plaslic Maximum Shear Strain
3I424l4.pIx& MnIn,un, P,lflotpl. Sfrstn
f/f f/I/fiji/f/i//I
'IiiiiE
----.
n
'I.
1V
00
'1
'V
Bk,
3S42845-pIaOttc Wn00nr Sh
3M2-I-pISk Mrdtm.n Prindple S1rn
000-----
700
800
802
Strait,
700
800
t
II.
000
200
¶00
0 -'
0'
70''
Bk,
Figure 33. Histograms of plastic
minimum principle strains for each
sample.
/
t
i//i//I//i//i//i
Sr
'r
'V
'V
00
00
"1
'7
'V
Sin
Figure 34. Histograms of plastic
maximum shear strains for each sample.
58
-
__._c
U.w ,*
r___c
..a
IIiiJ
SC
flflt
TLSSW$SI& Mt*fl. PI*Xt4C S*t
lOtIC ,amn w
1Mall-pa,*c MflIfltCI Prrnc,l. SW
Figure 35. Histograms of plastic
minimum principle strains for each
sample.
Figure 36. Histograms of plastic
maximum shear strains for each sample.
ELASTIC STRAINS
-
380-
5.00
3.46-
:
'-rw
/
64-
-
2.77-
L.
2A2-
a) 41258-11-left-elastic-minprin
a) 41258-11-Ieft-elastic-maxsh.
I
2.08-
L63-
173-
139-
734-
105-
-2.69-
702-
-3.05--
3.57-
4.4o-a
I
--
1.30-04
b) 41258-11 -right-elastic-minprin
b) 41258-lI-right-elastic-maxshear
Figure 37. Minimum principle strains
within the regions of interest: Full
insertion correlated with after extraction.
Figure 38. Maximum shear strains
within the regions of interest: Full
insertion correlated with after extraction.
3 80-
lAo-
209-
3.11-
-5.64-
a) 41270-1 1-left-elastic-minprin
a) 41270-1 1-left-elastic-maxsh.
-163-
3-57
b) 41270-li -right-elastic-minprin
b) 41270-11 -right-elastic-maxshear
Figure 39. Minimum principle strains
within the regions of interest: Full
insertion correlated with after extraction.
Figure 40. Maximum shear strains
within the regions of interest: Full
insertion correlated with after extraction.
61
11.-
a) 38424-13-elastic-minprin
a) 38424-13-elastic-maxshear
4.47-
3
4 -
32C-
1 93-
'C
a) 38424-14-elastic-rninprin
b) 3 8424-14-elastic-maxshear
153-
T
a
a) 3 8424-15-elastic-minprin
c) 38424-15-elastic-maxshear
Figure 41. Minimum principle strains
within the regions of interest: Full
insertion correlated with after extraction.
Figure 42. Maximum shear strains
within the regions of interest: Full
insertion correlated with after extraction.
62
r_
-C'?.
/
.7
2.09-
a) pigl3-elastic-maxshear
16-
L64-
141-
b) pigl4-elastic-minprin
b) pigl4-elastic-maxshear
-217-
722-
-3.11-
4 _94-
-3.46-
2.65-
3.70-04LJ
c) pigl5-elasticminprin
c) pigl5-elastic-maxshear
Figure 43. Minimum principle strains
within the regions of interest: Full
insertion correlated with after extraction.
Figure 44. Maximum shear strains
within the regions of interest: Full
insertion correlated with after extraction.
1.53-
5.76-s
-3.77-D
I
E
-I 3.1-10
-021-10
-419 (0
-1.10-I
10
-1.21--I
- 1.37-I
10
-1.52-I
-9.01-10
63-I
-8%-Ill
Figure 45. Minimum principle strains
within the regions of interest: Full
insertion correlated with after extraction.
Figure 46. Minimum principle strains
within the regions of interest: Full
insertion correlated with after extraction.
64
4125l.1.Ift.I.00k Mifli.fl000 P,lndpl. Strkl
415I.11.4yS.hlyti,, W.tlynytp Shet, SfrtIfl
000.
400
.
41201.fl40*.10010
808 Pl1n4.
à
412
t#Ot.I.tyi, M.lirnl,, Sh..y Stylis
000
000
V
400
2003
41270.l14dl.tI.Ic RS*lttul PlincEk Styli,
41flt41.10038.4001C 5,1*1811 ShIV TSn
400
350
300
050
-
ISO
100
50
f//f If bill//fl
4127041.0014i,ttIc 1*num Prhlciple Styli,
Figure 47. Histograms of elastic
minimum principle strains for each
sample.
4127041.dgtl..tatylc Rbximffi, ShIM Styli.
Figure 48. Histograms of elastic
maximum shear strains for each sample.
3342443..laStc Minimum Pnincipi. Strain
450
35424.13.Iaae Makimum 511W Strait,
600
460
606 -
360
500
250
200
ISO
ISO
50
fl.
0
4
.1
60
60
'In
3842444-.I.,tK Minimum Pflndpêe Stain
30424-14.15.1k M5oiioan, Sh.a, Strain
710
610
510
410
200
600
60
Sb,
.-
60
60
4
60
60
'.
4
0
3$42445ltl0 IS,lmum P.lnIdpIe Strain
1060
200
-11,/i'
Figure 49. Histograms of elastic
minimum principle strains for each
sample.
Figure 50. Histograms of elastic
maximum shear strains for each sample.
-
p103.Inbc RtlffiI.Jft1 pfl,cIpl.
_._* ..mm,
al
N
wJ
C l!0
I
let
i/rn-,,"
- 1W,a etlWtl
J
-:___
ii
p¼..l.k Irn
l$.PTthCEttt*
CM*
CM
IS*dflIC Im
lUOC.Iak S*mSl PrWWt9ll TSn
'4-
t
101
L/''hW1
nt - - -
T
1t54*tC
ranS01.
a.
if
Figure 51. Histograms of elastic
minimum principle strains for each
sample.
Figure 52. Histograms of elastic
maximum shear strains for each sample.
7
TOTAL STRAINS
76-
a) 41258-11-left-total-minprin
a) 41258-I 1-left-total-maxshear
122-
269-
215-
1.62-
1.o-.
L
5-45-
1
b) 41258-li-right-total-minprin
Figure 53. Minimum principle strains
within the regions of interest: Before
insertion correlated with full insertion.
b) 4 1258-1 1-right-total-maxshear
Figure 54. Maximum shear strains
within the regions of interest: Before
insertion correlated with full insertion.
5.9t
C
536-C
/
4.33-C
429-C
376- C
3 22-
a) 41270-11 -left-total-minprin
a) 41270-11 -Ieft-total-maxshear
2.6
2.15-
t62-
45-.
I
100-
b) 41270-11-right-total-minprin
Figure 55. Minimum principle strains
within the regions of interest: Before
insertion correlated with full insertion,
b) 4 1270-1 1-right-total-maxshear
Figure 56. Maximum shear strains
within the regions of interest: Before
insertion correlated with full insertion.
-7
328-
a) 3 8424-13-total-minprin
a) 38424-13-total-maxshear
-291-
-
b) 38424-14-total-minprin
c) 38424-15-total-minprin
Figure 57. Minimum principle strains
within the regions of interest: Before
insertion correlated with full insertion,
b) 38424-14-total-maxshear
c) 38424-15-total-maxshear
Figure 58. Maximum shear strains
within the regions of interest: Before
insertion correlated with full insertion.
70
a) pigl3-total-rninprin
a) pigl3-total-maxshear
b) pigl4-total-minprin
b) pigl4-total-maxshear
c) pigl54otal-minprin
c) pigl5-total-rnaxshear
Figure 59. Minimum principle strains
within the regions of interest: Before
insertion correlated with full insertion.
Figure 60. Maximum shear strains
within the regions of interest: Before
insertion correlated with full insertion.
71
T'
a) lOfoam-total-minprin
2
121
I 3'-
a) 12.5foam-total-minprin
'05
I 21-
_1611-32
Figure 61. Minimum principle strains
within the regions of interest: Before
insertion correlated with full insertion.
lot-
Figure 62. Minimum principle strains
within the regions of interest: Before
insertion correlated with full insertion.
72
412SI.414.4ot9 inmnP8nUp. 00r.i,
1000
4t2SH1.l.ft40ta M4IiflIOn, $b.t Sttstfl
1800
8400
82%
800
I//I/I//I//I//I/i
412$t41.d9IS4SII IirnS. Shoot SflS.n
1400
*1l7041.I,f840I
Mt*UthO pItlC$314
r
41270.tt4dI.tOIIl &ITItfl SIIStSfl
1,1/fiff, I/f If/i
4127044.dgI*IOIM Itlimlu pmcLI. Itra,
41210-t1-rtSht.totS M.xInrn... Stint SITS.,
IIff/ff/1f I//f/I
Figure 63. Histograms of total
minimum principle strains for each
sample.
Figure 64. Histograms of total
maximum shear strains for each sample.
73
3U14-l34tI MInrn.m Prh.ipI. SI1,,
iI//iff//,(////i/i
8424-l4-4ol
t.,-
,
,
Pnirnm Pñ,,oipI Sfrá.
,#,#,
Y, V'
SM
3B424.I541I rni,rn
3S424-44-4ol
Pindpk Strain
w
ximrn Sh
... ..
..
St,,
-
,,
Bin
38424-l5-o& Mxinnini Shn, SIrin
I/i f/I/f/f/f 1/11/
Figure 65. Histograms of total
minimum principle strains for each
sample.
Figure 66. Histograms of total
maximum shear strains for each sample.
74
Pd3tld MS*fltfl P*dpI. SirEn
fll4_ fl*ulUll SW. STSl
coo
,000
--.
-
Jo.
_.
750
"xc
7oc
lx,
5°
-I
,llii*o.MiSnMIl p'xlcI.Se
p100444* 5-4*Wm Sb.. 11TM
OcO
'4,
0
1000
go,
I
L
I
///iSIiIi/I/iI/
.,
5-
ISIW.4.
100*11101115511*44 Sx,
IIfl - 005wa
,i,iIi/iii/Iji,ii/ii
S.
l2.MoN.l.lo
1011*1104.114*4,114 .InI.
ThWThWW/Th'flf
Figure 67. Histograms of total
minimum principle strains for each
sample.
Figure 68. Histograms of total
maximum shear strains for each sample.
75
Mimimon. IrIntIpl, 011Sn rot Plastic Rotull.
-1.50-02
MUI.nail Cheer 84-ole for 815011184*0103
--
--
1.00-02
.0.38.02
U47258-Il-IIlI
841258-ll-4950
.0.18-02
84 1288-I I-In
41258-I1.It418
l.2E.02
84127011-118
41270-l1-I40
4l270.II.4911
a
008.02
41Z70-I0-d548
0 -9.00-03
t
025424-13
-
050-03
-7.08-03
835424-IS
-5.00-03
PIg-L3
P19L4
509.
835424-IS
::::
I-i!IL-lIIIIItif1lk:
17%
31424-14
O
[
-
:::
83%
17%
50%
03%
M.xMtn Sk. SlotS, for 0504-c 8.51St
Ptttul.n P,InclpI. 800S,n for 8035110 Snot
.158-02
E.O2
--- _______________
2.08.02
1-41-
541253-81-114
41150-l1-18
U4l258.Il-o9lt
-1.IE-02
841275-Il-IoS
541275.1 ,.ogrl
-
84 0270-1 5-01503
038124-13
83842444
838424.15
.708-03
38424.05
1.08.02
P543
-305.03
41275-lI-1IgN
1.08-02
D35524-13
RO-li
P0g-L4
L
-_______________________
000-03
SlOtoens
012 Often
-1
0,0(0100
17%
50%
03%
07%
o 12.010501
52%
UoSnwn $8450 Stan is. Total #501001.
8.5115,
-218.02
008-02
1.08-02
41108.11-1.8
-108-02
50%
E
05PI0-L!
Bisons
___________________________ 41258-Il-d9N
a
::
-l.1E-02
4120$-I1-1010
14125011-01503
841270-11-140
841275-11-01503
0.48.02
5,28-02
038424-03
334201-14
1,08-02
:
17%
50%
03%
Figure 69. Non-parametric analysis of
plastic, elastic and total minimum
principle strain results for each sample.
17%
50%
53%
Figure 70. Non-parametric analysis of
plastic, elastic and total maximum shear
strain results for each sample.
76
koiinPuincipleSin
17th Peeentile PIac
none Volume Fraction
Boo. Vdurn. F,otion(54)
A
0.014
2.012
£3942l-r3
A
£38421- 14
.001
£41211-
A
A
0.w8
£412I1- ,I8ht
£412?-I1-I5
A
£41270.11. ri bt
.pig-)4
Upg.5
A
12,0ee
2(04
1(02
n
15
25
3D
3D
8)
35
Ijib Percontile (larSic lVbnirnrn-. Pliliciple Sham us Bone Vokunie Fraction
Bore Vthrne Friorr(1j
-ao1
A
-0.014
.0.012
£38424.8
£38424
-001
£4-It- kit
U
&412%-I1-rithl
A
£41270-Il- riF
Ipl3
plI4
A
A
125ioe
.0(04.
A
.
0
1]
3D
25
3D
35
0)
Figure 71. Comparison of bone volume fraction versus 17th percentile plastic and elastic
minimum principle strains for each sample.
77
50th Pe,cen(ile PIk InkmanPflne,Ie 5inv Bone VknneFraction
kr,e FAi,n f%)
A
A
.0004
00335
£38424-C
£3842440
U
£30424.6
.0003
£412-I1.It
£4I2-I1igM
A
£41210-I1-I*
0,0335
£412Th-I1-dl
pG
£
A
-0002
.p8Iq
p-I5
A
0.0015
-0031
0.0303
0
10
35
15
3)
35
50th Poonte EIak MninunPflnciple Sbin
4)
fln.Voki
4)
6)
Fraction
Ftion
Bor. Vd.
.0.006
U
.0035
U
£38431.0
£3842414
£394346
£412414ft
£412. II. ,i9ht
£41270- 1146
A
A
A41V011-riht
Up1g43
A
-0.032
LA
A
U pi
14
pjgd5
1o,n
12.5lo,,,
S
A
'0.031-
0'
10
15
3)
35
3)
35
4)
4)
Figure 72. Comparison of bone volume fraction versus 50th percentile plastic and elastic
minimum principle strains for each sample.
*3rd Pce.1*Ie Ptai*ic minin-a,n PinipIe Strain s Bone Vekrn. Fradion
Bne Volume
Fnction(%)
U
A
£39424-n
£3942414
£39424-B
-0502
A
A41211-Iaft
.
:
A
.0.0715
£41210-I1-kft
£4127011-
rit
A
plA
A
-0001
A
-
0.0705
.
U
25
10
3)
*3rd Perr.liIe Elaetk
nin
35
47
47
inciple Strain y,Bone Volun Fracilon
Bna Vokar,.
F,otion (%)
-lD
U
.a0725.
U
£294240
.0502.
£3942414
a3e424.B
£412-I1- left
£412-I1-riaht
£41v0.u1- left
.
£4127O-I1-M
P9
:
A
A
-0501
A
pi9.14
A
.p
4.
A
1Z51o.,
U
A
o.c005
0
15
15
25
33
35
47
47
Figure 73. Comparison of bone volume fraction versus 83rd percentile plastic and elastic
minimum principle strains for each sample.
79
Human vs Pig Sani.s Inc
Plastic lanivum Principle Strain
Human vs Pig Sanpin tar
Plastic MaiSimin Sinai Strain
-_________
-1.5052
I 15.02
I 81002
I:75582
p-till
I
p-mi
I
__
7%
51%
I58iin.viianvn nP,Saotn
82%
0127.05
sl25lo1m
FIN-n S.n*. opus_n.. lDlauu aI2.tigagaI
Human vs Pig SanWl.s to,
Hunosu vs Ply Saaj.ln (or
Elastic Maxhvolm SEnt St,ain
Elastic Minimum PIlilcIpI, Shun
.15052
060001
I
P.482
__________
1
p.0*
4
.5002
___________________________________
-- --
iitOO
I
-stile-as
-- _____________________
I.5042
J0.516.03
"0-si
550-03
S
p-roil
1-0818
,
- uSsr,
_
i-ti
_.I
1.
.
77%
51%
ICIIIv...SnnS.
82*
7%
51%
ePui 5p5 Ulleic, niaslosni
82%
SirIus. up. IrIS. tlOO.n Ii 01 Slaunol
IImafl vs Pig SanI (or
Total Mthànoffi Plincipi. lila.
Human vs Pig S.uTpin log
TOtal Maxutmim Shea. Than
I Ct-CO
-1
lEO?
I2O0O2
p-ta'
-I 505?
I
.1.5052
r-a
B 15.03
SleEt]
p-lila
-0505]
p-i--v
17%
5175
gas
lulivon ImpS. 071.8.150. InS... 01250051
::&..
7%
i-:
00%
13%
110mm Saopsu 0P 501.5. 1101011 erO.SImamI
Figure 74. Nonparametnc statistical
comparison of minimum principle
strains for human vs porcine and PUfoam samples using ANOVA p-values
Figure 75. Nonparametric statistical
comparison of maximum shear strains
for human vs porcine and PU-foam
samples using ANOVA p-values
(p<o.05).
(p<o.05).
Plinhir Minhn;imP,k,dpl. Sham a. Son. Vail,... F,,,dIon
Bale 448Ma00.CIMI hI ape 'o1
.1 K502
-I XE 02
-I
-9 (SE £3
E
L1
I...
15.1 -087
243-a,
432-48.7
bEau Q14J
125
(314)
Figure 76. Comparison of grouped bone volume fractions versus plastic, elastic or total
minimum principle strains for the l7, 50th and 83t percentile values.
81
tttk Maflne.,. Shear Shah.. 'so Bt.,.Veiuru. Fraction
2..O2
atw
I
8
liz-rn
a
0
11lh P&lie V1
I
l02
.Vaflpr.v.de,,,.jet
0830
iz
a.
PrVttlS WiNS
4
-.
101 -lOS
243.290
100l2,a
432481
12.5t*n4J1 4)
In VhasFIat.ri Gsa.. Fri
Total Maxipairu Slr.ar SliSno Vt Boo. Valor,. Fraction
I
rrf
I 45802
115802
I .iz-o2
l7Ol P58,104. VeiN,
liar
end
PIta-u.
lees
Lii
I
::
159.107
243-299
432.487
80.. OOi001r P040*.,
13(214)
125148T1(314)
Crow. Fri
Figure 77. Comparison of grouped bone volume fractions versus plastic, elastic or total
maximum shear strains for the 17th, 50th and 83 percentile values.
82
Table 9. Summary of ANOVA p-test values (p<O.O5) in comparisons between groups
for 17th 50th and 83rd percentile values of plastic, elastic and total minimum principle
strain (MPS).
V1Pérceiitile;j.
Elastic Plastic
Value
j
Group
*
Compared
17%
50%
83%
17%
1
2
2
3
50%
83%
1 -3
50%
83%
17
Group 1: 15.1
MPS
MPS
I
.
0.374
0.498
0.894
0.076
Total
MPS
Elastic
MSS
.
0.110 0.209 0.844
0.004 0.047 0.963
0.011 0.064 0.406
0.451 0.369 0.013
0.03 1
0.007 0.005 0.119
0.022
0.007 0.005 0.875
0.957
0.045 0.409 0.019
0.079
0.887 0.024 0.111
0.037
0.393 0.054 0.490
* Bone Volume Fraction Groups (%):
I
I
Plastic
.
SS
0.175
0.093
0.035
0.0002
0.0004
0.777
0.9330
0.8230
0.050
I
I
I
Total
MSS
0.247
0.078
0.181
0.003
0.003
0.038
0.021
0.025
0.815
19.7; Group 2: 24.3 -29.9; Group 3: 43.2-48.7.