1. Numerical Investigation of the Interdependence
Between Humeral Implant Position and Bone
Removal Amount for Total Elbow Arthroplasty
Alexander J. Heroux
August 23, 2013
1

2. The Elbow
• Hinge joint modifying the position of the hand
2
Extension
Flexion

3. Problems with the Elbow
• Fractures
• Elbow pain
• Arthritis
• Limited movement
3

4. Total Elbow Arthroplasty (TEA)
4
Humeral stem
Ulnar stem
Radial stem
• Common surgical procedure commonly used to
restore partial/total functionality of the elbow

5. Anatomical Definition of Humeral
Flexion Extension (FE ) Axis
5
Capitellum
Trochlea
sulcus
Trochlea
center
Capitellum
center
Flexion-
extension axis
Capitellum
Capitellum
center
Flexion-
extension Axis
Trochlea
sulcus
Trochlea
center
Native (bone) geometry
of the distal humerus
Prosthetic (implant) geometry
of the distal humerus

6. Bone/Implant Interference
6
Interference
zone
• During TEA, the implant is positioned to match
the native FE  prone to interference
distal humeral canal
enlargement
Broaching
Reaming
Rasping

7. Implantation Challenges
• Low TEA incidence  insufficient exposure to the
procedure  limited experience of the surgeons
• Canal reaming/broaching for enlargement/implant
alignment purposes  “blind” or “semi-blind” manner
– Experience-based, trial and error
– Error prone
• Excessive bone removal in an attempt to ensure proper
alignment might weaken the bone  implant failure
• Heat generation  thermal osteonecrosis
• Complication rate  28% (1993 – 2004)  rising
incidence and cost of revision surgery
7

8. Rationale/Motivation
• Minimized interference and malalignment
between implant and bone translates into:
– Minimal amount of cortical bone to be removed
– Better implant durability  lesser need for
revision surgery
– Better quality of life for TEA patients
8

9. Hypothesis
• An optimal implant posture (position and
orientation) can be determined to ensure:
– Minimization of the amount of interference
between implant and bone
– Minimization of the implant malalignment with
respect to native FE axis
9

10. Specific Aims
1. Determine accurate point-based
representations of the bone geometry
2. Minimize implant interference amount by
varying the implant posture
3. Simultaneously minimize implant
interference and malalignment
10

11. Specific Aim 1
Determine accurate point-based
representations of the bone geometry
11

12. Methodology
• Technique to automatically extract inner and
outer bone geometry out of planar CT data
12

13. Segmentation to Cloud Dataset
13
• CT data is easily convertible to polygonal mesh
format

14. Extraction of Outer Bone Contours
14
• Delaunay triangulation combined with nearest neighbor
technique used for outer contour
• Does not work for inner contours  “islands” not captured
correctly

15. Extraction of Inner Bone Contour
15
• “Binning” approach used

16. Samples of Bone
Contour Extraction Results
16

17. Completely Processed
Humeral Specimens
17

18. Specific Aim 2
Minimize implant interference amount
by varying the implant posture
18

19. Methodology
• Technique to minimize the interference by
ensuring that the posture is in the allowable
range
– Quantify implant posture (e.g. position and
orientation)
– Define the allowable range of the implant posture
– Determine the interference amount for a certain
implant posture
• Distance to inner bone
– Numerical solving approaches
• Brute force
• Global search
19

20. Defining Implant Posture
20
CC
P
I
XI
ˆi
FE
a
I
Y
I
ˆj
VV
a
I
Z
I
ˆk
IE
a
Capitellar
translation
Flexion-
extension
angle
Varus-valgus
angle
Internal-
external
angle

21. Allowable Implant Posture Ranges
21
• Very little information available in the clinical literature
– Kim et al. proposed a malalignment varus-valgus angle should remain
below 5 degrees to avoid complete implant wear
• Intervals on the non-conservative side
– Capitellar translation: 0 to 5 mm
– Flexion-extension angle: -5 to 5
– Varus-valgus angle: -5 to 5
– Internal-external angle: -5 to 5

22. Simplified Implant Geometry
22
• Implant stem is idealized to 16 line segments (fillet
edges) that are intersected with planar slices of the
bone

23. Determination of the
Interference Amount
23
Maximum
interference
Interfering region
Inner contour
points
Outer contour
points
Implant stem
cross section
Non-interfering region
• Interference/posture = summation of the maximum
interference/slice for the entire bone

24. Initial Point = Optimization Baseline
24
Sam ple
No.
Im plant Position Im plant Orientation
min
D
[m m ]
CC
X
[m m ]
CC
Y
[m m ]
CC
Z
[m m ]
FE
a
[]
VV
a
[]
IE
a
[]
1 0 0 0 0.2380 0 0 110
2 0 0 0 -5.6105 0 0 450
3 0 0 0 -6.1328 0 0 275

25. Brute Force Approach
25
• Discretize the 6D space of the implant posture
and calculate interference amount for all
possible combinations
• 207,636 combinations of input parameters 
computationally expensive!
Input
Param eter
Im plant Position Im plant Orientation
r [m m ] q [] j [] FE
a [] VV
a [] IE
a []
Lower bound 0 0 -180 -5 -5 -5
Upper Bound 5 180 180 5 5 5
Increm ent 1 45 45 1 1 1
Total values 6 5 8 11 11 11

26. Global Search Approach
• Gradient-based search
• Computationally efficient
26
Generate initial
population
Run local optimization
on initial population
Compare local
optimized solutions
Determine global
minimum

27. Optimization Results for Maximum
Distance to Inner Bone
27
0
10
20
30
40
50
60
1 2 3
InterferenceAmount[mm]
Humeral Specimen
Brute Force
Global Search

28. Solving Time
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1 2 3
Time[days]
Humeral Specimen
Brute Force
Global Search
28

29. Discussion
29
• High variability between bone samples
• Non-interfering conditions can be achieved in a
variety of ways:
1. Primarily upward translational motion (specimen 1)
2. Primarily anterior/posterior translational motion with
maximized angular variations (specimen 2)
3. Minimal translational motion combined with maximized
angular malalignment (specimen 3)
• Interval bounds reached in most cases
• Rotational constraints more restrictive than
translational ones

30. Clinically-Relevant Results
30
Posterior
Medial
Anterior
Lateral
• Developed technique can be used to predict where most
cortical bone has to be intraoperatively removed to allow
implant insertion  valuable preoperative planning tool

31. Specific Aim 3
Simultaneous minimization of implant
interference and malalignment
31

32. Methodology
• Technique to minimize both implant interference
and malalignment
– Determine the interference and malalignment amount
for a certain implant posture
• Distance to outer bone
• Area of interference
– Numerical solving approaches
• Brute Force
• Global Search
• Genetic Algorithm
• Double Objective
32

33. Distance to the Outer Bone
• Sufficient amount of bone stock in each CT
slice
33
Minimum Distance to Outer
Bone
Inner contour points
Stem cross section
Non-interfering region
Interfering
region

34. Distance to Outer Bone
Results
34
Distance to Inner Bone [mm]
DistancetoOuterBone[mm]
• Linear relationship between the distance to the outer bone and
the distance to the inner bone
R2 = 0.816 R2 = 0.986 R2 = 0.985

35. Determination of the
Interference Amount
35
Interfering Area
Interfering region
Inner contour
points
Outer contour
points
Implant stem
cross section
Non-interfering region
• Interference/posture = summation of the interfering areas/slice
for the entire bone

36. Genetic Algorithm
36
Generate initial
population of
chromosomes
Evaluate the
fitness of the
population
Stopping
criteria
met?
Generate new
children
population
through mutation
or crossovers
Solution
Generated
Yes
No
• No proof of
convergence
• Quick to arrive at a
solution

37. Optimization Results for Implant Area
37
0
0.5
1
1.5
2
2.5
3
3.5
4
1 2 3
InterferenceAmount[mm3]
Humeral Specimen
Brute Force
Global Search
Genetic Algorithm

38. Double Objective Approach
38
f2(x) (min)
f1(x)
(min)
Test
Space
Candidate
Solutions

39. Optimization Results
Equal Weights
39
fmal(x)
(min)
fmal(x)
(min)
fmal(x)
(min)
fint(x)
(min)
(0.02162, 0.06936) (0.3544, 0.04397) (0.1885, 0.03035)

40. Optimization Results Comparing
Malalignment/Interference Amount
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 2 3
NormalizedMalalignment
Humeral Specimen
40
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
1 2 3
NormalizedInterference
Humeral Specimen
Double Objective
Global Search
Brute Force
Genetic Algorithm

41. Clinically-Relevant Results
41
Inner Bone
Boundary
Implant
Interference
Implant
Interference

42. Contributions
• First attempt to propose means to determine
position and amount of bone to be removed
to ensure reduced implant malalignments
– Preoperative/offline qualitative (quantitative)
guidance for canal reaming/broaching
• A number of novel and computationally-
efficient tools were developed to accomplish
the main goal of the study
42

43. Study Limitations
• Segmentation errors
• Binning resolution reduction errors
• Surgeons repeatability and accuracy to place
the implant in targeted position
43

44. Future Directions
• Experimental validation of the numerical results
• Extrapolation through analogy to other relevant
arthroplastic procedures involving stem
prosthetics (hip, knee, shoulder)
• Integration with navigatedimplantation systems
to ensure accurate implant positioning =
according to numerical predictions
44

45. Acknowledgements
• Biomedical Engineering
Research Laboratory, HULC
– Dr. James Johnson
– Dr. Graham King
• Computer-Assisted Medical
Intervention Training (CAMI)
Program
45
• Supervisors
– Dr. Remus Tutunea-Fatan
– Dr. Shaun Salisbury
– Dr. Ahmad Barari
• Advisory Committee
– Dr. Louis Ferreira
– Dr. Ilia Polushin

46. 46
Sample No.
Optimization
Algorithm
Implant Position Implant Orientation
Δmin[mm] Δmin[% Volume]
XCC[mm] YCC[mm] ZCC[mm] αFE[] αVV[] αIE[]
1
“Brute force” point 0.00 0.00 5.00 -1.00 2.00 -4.00 50.96 3.84
Global point search -1.68 -0.36 4.69 -1.43 0.33 -5.00 39.62 2.60
"Brute force" volume -2.12 0 2.12 -1 0 -3 - 3.09
Global volume search -0.68 -1.85 4.60 1.50 0.19 0.61 - 2.57
Genetic algorithm -0.87 0.75 -1.28 -0.35 0.915 -1.02 - 3.57
2
“Brute force” point -4.00 0.00 0.00 -5.00 2.00 -5.00 3.58 0.38
Global point search -3.99 0.00 -0.33 -5.00 1.82 -5.00 3.40 0.31
"Brute Force" volume -3.54 0 -3.54 -5 3 -5 - 0.25
Global volume search -4.04 0.049 -1.38 -4.99 2.24 -5.00 - 0.25
Genetic algorithm -2.34 -0.70 -2.59 -1.58 4.16 -2.42 - 0.86
3
“Brute force” 1.50 -1.50 -2.12 -3.00 -5.00 -5.00 0.00 0.0345
Global point search 0.52 -0.59 -0.66 -0.77 -5.00 -5.00 0.00 0.0252
"Brute Force" volume 2 -2 -2.83 -5 -5 -5 - 0.037
Global volume search 0.12 -0.08 -0.21 -4.40 -4.83 2.30 - 0.037
Genetic algorithm 0.062 0.000 0.67 -3.87 -4.84 3.65 - 0.0669