A BIOMECHANICS APPROACH TO THE INTERACTION OF HOST
IMPLANT SYSTEMS
By
GARY JOEL MILLER
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1977
ACKNOWLEDGEMENTS
I would like to thank Dr. George Piotrowski for suggesting
the area of intramedullary fixation for study, and for his guidance
and encouragement throughout this work. I am also indebted to
Dr. Larry L. Hench and Dr. Robert B. Gaither for their continual
support and valuable comments and criticisms.
My special thanks go to Dr. William C. Allen, now at the
University of Missouri Medical School, for his comments and
assistance with the many clinical aspects of this research endeavor;
and to my wife, Suzy, without whose encouragement and understanding
this work would have been impossible.
I would like to acknowledge the technical assistance of
Ms. Karla Smith, Mr. Thomas Carr, and Mr. Mike Hardee. I would
also like to thank Mrs. Loretta Thigpin, Ms. Susan deFalco,
Ms. Dee Schneider, and Ms. Pam Blalock for their assistance in
preparing this manuscript. Thanks are also due Mr. Robert Hagen
for his assistance in preparing the illustrations.
This research was aided by a grant from the Orthopaedic
Research and Education Foundation.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS . . . .. . ii
LIST OF TABLES . . . . . v
LIST OF FIGURES . . . . .. ... vi
ABSTRACT . . . . .. . . xii
Chapter
I. INTRODUCTION . . . . .... 1
Brief History of Intramedullary Fixation . 1
Previous Work . . . . . 4
The Present Research . . . . 7
II. PROPERTIES OF THE SYSTEM COMPONENTS: A REVIEW. . 8
The Intact Femur. . . . . 8
The Intramedullary Nail . . . ... 16
Summary . . . . . 21
III. DETERMINATION OF THE GEOMETRIC PROPERTIES
OF THE SYSTEM COMPONENTS. . . . ... 23
The Femur . . . . . 23
The Intramedullary Nail . . . .. 69
IV. MODELING OF THE OSTEOSYNTHESIS. . . ... 75
The Preliminary Idealized Model . . .. 75
Intramedullary Interfacial Behavior . .. 83
A General Intramedullary Osteosynthesis Model . 90
V. EXPERIMENTAL VERIFICATION OF THE MODELING
OF THE OSTEOSYNTHESIS . . . . 121
Well Characterized Systems. . . .. 121
In vitro Osteosynthesis . . . .. 134
Conclusions . . . . . 145
VI. BONAIL PREDICTION OF THE OSTEOSYNTHESIS
DEFLECTION. . . . .... .148
APPENDIX A. DEVELOPMENT OF THE DIFFERENTIAL
BEAM DEFLECTION EQUATIONS. . . ... 178
LIST OF REFERENCES ...................... .184
BIOGRAPHICAL SKETCH ................... 189
LIST OF TABLES
Table Page
3.1 Values for the mean sidetoside difference,
Tp, and standard deviations (in parentheses)
for the paired femurs . . .. . 34
3.2 Geometric properties of the 14 mm Fluted type
nail, with and without flutes . . .... .72
4.1 Finite difference computational molecules ..... 107
4.2 System properties for optimization evaluation ..... 119
LIST OF FIGURES
Figure
Page
2
15
17
1.1 Bones of the lower extremity . . .
2.1 The effect of strain rate on the material
properties of bone . . . ..
2.2 Crosssectional shapes of commonly used
intramedullary nails . . . .
2.3 Structural properties of commonly used
intramedullary nails . . . .
2.4 Elastic modulus for several implant materials. .
3.1 Schematic representation of femoral
length measurements. . . . .
3.2 Serial crosssections of a representative femur
with size reference marks in place . .
3.3 Definition of axes and distances for geometrical
property determination . . . .
3.4 Mohr's circle construction for locating principal
axes and directions of the crosssections. .
3.5 Gross cortical bone area as a function of
position for the left femurs . . .
3.6 Gross cortical bone area as a function of
position for the right femurs. . . .
3.7 Area moment of inertia, Ixx, as a function
of position for the left femurs. . . .
3.8 Area moment of inertia, Ixx, as a function
of position for the right femurs . . .
3.9 Area moment of inertia, lyy, as a function
of position for the left femurs. . . .
. 19
. 20
. 24
. 26
. 28
. 30
. 35
. 36
. 37
. 38
. 39
Figure
3.10 Area moment of inertia, I as a function
of position for the right lemurs . . .. 40
3.11 Principal moment of inertia, I as a function
of position for the left femurs. . . ... 41
3.12 Principal moment of inertia, I T, as a function
of position for the right femurs . . .. 42
3.13 Principal moment of inertia, I C, as a function
of position for the left femurs. . .... . 43
3.14 Principal moment of inertia, IC, as a function
of position for the right femurs . . .. 44
3.15 Polar moment of inertia, J, as a function of
position for the left femurs . . ... 45
3.16 Polar moment of inertia, J, as a function of
position for the right femurs. . . ... 46
3.17 Effective polar moment of inertia, Jeff, as a
function of position for the left femurs ...... 47
3.18 Effective polar moment of inertia, Jeff, as a
function of position for the right femurs. . ... 48
3.19 Principal angle orientation and relative
magnitude of the principal moments for
the femurs in group I. . . . ... 51
3.20 Principal angle orientation and relative
magnitude of the principal moments for
the femurs in group II . . . .... 53
3.21 Principal angle orientation and relative
magnitude of the principal moments for
the femurs in group III. . . . ... 55
3.22 Section modulus, Z, as a function of length
along the femur for two sample femurs compared
to data adapted from Koch (1917) . . .. 59
3.23 Graphical representation of overall femoral
length versus average cortical bone area ...... 66
3.24 Graphical representation of lesser trochanter
to femoral condyle length (Llesser) versus
average cortical bone area . . .... 67
Page
Figure
3.25 Graphical representation of the outer midshaft
diameter versus average cortical bone area . .. 68
3.26 Calculated geometric properties for several
intramedullary nail shapes . . .... 71
4.1 Schematic representation of preliminary idealized
osteosynthesis with applied fourpoint loading
and point contacts . . . . 76
4.2 Free body diagram of the outer tube with external
and point contact reaction loads . . .. 78
4.3 Free body diagram of the inner rod with point
contact reactions. . . . . .. 78
4.4 Idealized angular mismatch representation. . ... 80
4.5 Photograph showing the intramedullary nail in
place in the cast bone section for interfacial
stiffness determination. . . . ... 84
4.6 Schematic drawing of the selfaligning compression
fixture for interfacial stiffness determination. 86
4.7 Loaddeflection curves for interfacial behavior
of Kuntscher, Fluted and Schneider nails
in cancellus bone. . . . . ... 87
4.8 Loaddeflection curves for interfacial behavior
of Kuntscher, Fluted and Schneider nails
in cortical bone . . . . 88
4.9 Schematic diagram of a segment of the general
osteosynthesis model under distributed load q(x) 92
4.10 Free body diagram of an element of the bone
with external distributed load and interfacial
reaction load. .. . . . .. 92
4.11 Free body diagram of the nail with interfacial
reaction load. . . . .... 92
4.12 Schematic diagram of an osteosynthesis under
equally spaced fourpoint loading with a
midshaft transverse fracture . . .. 102
viii
Page
4.13 Schematic diagram of a healed osteosynthesis
under equally spaced fourpoint loading with
the nail remaining in situ . . . .. 105
4.14 Finite difference representation of the
osteosynthesis under fourpoint loading. . ... 110
4.15 Modified computational molecules for the
describing nondimensional differential
equations of the coupled system. . . ... 114
5.1 Schematic representation of the fourpoint
loading apparatus used for in vitro verification
studies. . . . . ... ... 122
5.2 Intact human femur with small dimples at 2 cm
intervals to aid in deflection measurement . .. .124
5.3 Intact human femur mounted in fourpoint loading
fixture for in vitro testing . . .... 125
5.4 Intact femur, with dial indicator in position,
in the fourpoint loading fixture. . . ... 126
5.5 Graphical comparative deflection results obtained
from the testing and modeling of a uniform steel
beam . . . . ... . . 129
5.6 Graphical comparative deflection results obtained
from the testing and modeling of a tapered
steel beam . . . . ... . 130
5.7 Measured deflections and BONAIL predictions for
an unnailed intact human femur under fourpoint
load . . . . ... ... .. 131
5.8 Comparative results obtained by measurement and
BONAIL prediction of a fourpoint loaded intact
femur with 12 mm Fluted nail in place. . ... 132
5.9 Closeup photograph of the fracture site of a
femur with Fluted nail in place. . . ... 136
5.10 Osteosynthesis in the test fixture with the
fracture surfaces distracted to show the
nail and fracture site location. . . ... 138
5.11 Osteosynthesis in the testing fixture for
in vitro verification of BONAIL predicted
deflection response. . . . ... 138
Figure
Page
Figure
5.12 Graphical presentation of actual deflection
measurement and BONAIL prediction for the
12 mm Fluted intramedullary osteosynthesis . .. .140
5.13 Presentation of results of deflection
measurement and BONAIL prediction for a 14 mm
Fluted intramedullary osteosynthesis . ... 141
6.1 Nondimensional midspan bone deflection for the
healed osteosynthesis with intramedullary
nail in situ . . . .... .. '. 151
6.2 Nondimensional interfacial loading profiles for a
healed osteosynthesis with interfacial stiffness
of 5 x 106 N/m/m at various rigidity ratios. ... .152
6.3 Nondimensional interfacial loading profiles for a
healed osteosynthesis with interfacial stiffness
of 5 x 107 N/m/m at various rigidity ratios. ... .153
6.4 Nondimensional interfacial loading profiles for a
healed osteosynthesis with interfacial stiffness
of 2 x 108 N/m/m at various rigidity ratios. ... .154
6.5 Nondimensional interfacial loading profiles for a
healed osteosynthesis at a modulus ratio of 13.0
for various interfacial stiffnesses. . ... 155
6.6 Nondimensional interfacial loading profiles
using different properties and stiffnesses
to produce equal midspan bone deflections. . ... 156
6.7 BONAIL predicted midspan deflections for a fractured
osteosynthesis as a function of modulus ratio for
various interfacial stiffnesses. . . ... 158
6.8 BONAIL predicted interfacial reaction profiles for
fractured osteosyntheses at a modulus ratio of
4.34 for several interfacial stiffnesses . ... 160
6.9 BONAIL predicted interfacial reaction profiles for
fractured osteosyntheses at a modulus ratio of
8.7 for several interfacial stiffnesses. . .. .161
6.10 BONAIL predicted interfacial reaction profiles for
fractured osteosyntheses at a modulus ratio of
13.0 for several interfacial stiffnesses 162
Page
Figure
6.11 Nondimensional fracture surface mismatch
as a function of modulus ratio for various
interfacial stiffness values ... . . .163
6.12 Fracture surface angulation as a function of
modulus ratio for various interfacial
stiffness values . . . . .. 164
A.1 A segment of a beam having been curved by
an applied moment Mb . . . .. .179
A.2 Stress distribution profiles developed in
the curved beam. . . . . .. 179
A.3 A segment of a beam under distributed
load, q(x) . . . . ... . 182
A.4 A differential element of the beam with
distributed load, q(x) and reaction
moments and shears . . . .... 182
Page
Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
A BIOMECHANICS APPROACH TO THE INTERACTION OF HOST
IMPLANT SYSTEMS
By
Gary Joel Miller
June 1977
Chairman: Robert B. Gaither
Cochairman: George Piotrowski
Major Department: Mechanical Engineering
A general model of an intramedullary osteosynthesis of the
femur is postulated. The model allows for variable geometric
properties along the length of the bone, and allows homogeneous
and isotropic material properties to be chosen. The model includes
an intramedullary nail of arbitrary material and geometric proper
ties running the full length of the bone and unvarying with position.
The nail and bone are assumed to be separated by a linearly elastic
layer which transmits the nailbone interfacial loading.
Nondimensional multicomponent beam equations which relate
external loading to deflection are presented. Boundary conditions
which describe fourpoint loaded osteosyntheses with transverse
midshaft fractures and osteosyntheses consisting of healed bones
with intramedullary nails remaining in situ are included. The
resulting equations are cast into finite difference form and are
solved with the aid of a digital computer program (BONAIL) using
numerical relaxation techniques.
Results of in vitro verification studies involving steel
beams, intact femurs, and femurs with intramedullary fixation are
presented and serve to substantiate the accuracy of the BONAIL
model. Both the effect of relative flexural rigidity of the com
ponents and the character of the interfacial layer are found to
play a major role in the solutions obtained.
Graphical results are presented for the nondimensional
midspan bone deflection, the transverse deflection mismatch and
angulation of the fracture surfaces, and the nailbone interfacial
loading profiles. These results are plotted as a function of the
relative nailbone elastic modulus ratios for various interfacial
layer stiffnesses.
These data indicate that the more flexurally rigid devices
reduce the overall midspan deflection, deflection mismatch, and
angulation. However, the use of different combinations of modulus
ratios and interfacial stiffnesses are found to result in comparable
deflections. This is caused by the different interfacial reaction
distributions and intensities which develop. Nonetheless, the
overall results appear to support using nails of high flexural
rigidity to effect lower deflections and therefore enhance primary
healing of the fracture. However, healed bones, with more rigid
nails remaining in situ, are subjected to significant load sharing
between the components, and the bone is partially protected from
stress. By being so protected, the functional remodeling at the
xiii
fracture may be hampered and result in a weakened bone which is
liable to refracture upon removal of the intramedullary nail.
The lack of information in the literature concerning the
geometric properties of the femur and the character of the nailbone
interface for use in modeling the system led to a parallel experi
mental study. Ten pairs of human femurs were processed to determine
the gross cortical area, area moments of inertia, principal moments
of inertia and principal angles, and polar moments of inertia at
serial points from the level of the lesser trochanter to the distal
metaphysis.
The results of this experimental study are presented graphi
cally as a function of position along the femoral length. While
considerable variation in properties is found from one pair to the
next ( 25% or more), no statistically significant rightleft bias
was observed.
In vitro experimental results of the interfacial stiffness
behavior of several nail types were also obtained in different bone
material. These results ranged over several orders of magnitude
and were dependent on both the nail crosssectional shape and the
nature of the medullary bone, i.e. cancellus or cortical.
CHAPTER I
INTRODUCTION
The femur is one of the major load carrying members in the
human body. It is the single bone which joins the knee to the hip
(Figure 1.1) and is therefore called upon to support essentially
the entire weight of the body during standing. During walking or
strenuous activity, this bone is subjected to loads several times
larger than the weight of the body. Fractures of the femur are
not uncommon, and present a management problem to the orthopaedic
surgeon. One common mode of treatment for transverse femoral
fractures involves the insertion of an intramedullary nail through
the marrow cavity of the bone, using this metal rod as a strut to
hold the two pieces of bone in alignment while they heal together.
Brief History of Intramedullary Fixation
Lambotte of Belgium (1913) has been credited with using the
first intramedullary nail in a clavicle in 1907. It was not until
1918, however, that Hey Groves of England used intramedullary nailing
for fixation of a fracture of the femur. Rush and Rush (1937, 1939)
presented the first cases of intramedullary fixation in the United
States using nails of round crosssection. Kuntscher's (1940)
classic treatise, "The Intramedullary Nailing of Fractures," served
to lend strong support to intramedullary nailing as a viable method
'~~~r~r ': *T .. I
Figure 1.1. Bones of the lower extremity
of fixation of fractured long bones. At that time, Kuntscher intro
duced his Vshaped crosssection nail which was said to be more
easily driven into the intramedullary canal than a solid nail because
its open crosssection allowed it to compress on insertion. This
shape was subsequently modified to a cloverleaf pattern which fol
lowed a guide pin more easily and provided greater nail strength.
Street et al. (1947) reported the use of the diamond
crosssection nail which had been developed by Dr. Hansen in
1945 to provide greater flexural and torsional rigidity. Schneider
designed a four flanged nail in 1950, which could be driven into
the intramedullary canal and engaged the endosteal surfaces with
its flanges to maintain torsional stability. Its crosssection was
also said to provide higher flexural rigidity than previous designs.
(Schneider, 1968). In 1967, the Fluted nail was used for the first
time (Allen, 1977). This nail was designed to provide increased
torsional and bending rigidity and better torsional gripping
of the intramedullary surfaces.
The reader gets the impression from a cursory review of these
clinical reports on the evolution of intramedullary devices that the
author's primary concern in redesign is to increase the torsional
and bending rigidity of the device in order to affect a better
osteosynthesis. There is, however, no experimental verification
that continued increases in rigidity will, in fact, produce this
desired result.
Previous Work
McKeever (1953) has summarized the general criteria for
design and application of an effective intramedullary device.
His conclusions, and those of the above investigators, can be
summarized as follows:
1. The nail should maintain alignment and apposition
of the fracture surfaces, i.e. close fit at the
fracture site.
2. It should permit compression of the apposing fracture
surfaces by allowing axial sliding of the bone seg
ments along the nail.
3. It should prevent torsion of the fractured bone
segments with respect to each other.
4. The nail must be constructed from materials which
meet biocompatibility requirements.
5. It should be able to withstand.the synamic bending
stresses applied by the bone segments and their
related muscle groups.
6. The nail must be rigid enough to provide suitable
bending stabilization so that new bone can form.
Many authors have directed their attention to meeting these
criteria which are generally accepted as necessary for the attainment
of good results using intramedullary nails in fracture fixation.
Lindahl (1962, 1967) stated that rigidity (6) and immobilization (1 and
3) are of the highest priority. Braden and Brinker (1973), Andersen
(1965), Andersen et al. (1962), and Hutzschenreuter et al. (1969) have
supported Lindahl and reiterate the need for "rigid fixation" to
affect proper healing using intramedullary nailing. Taylor (1963) has
also noted that the use of intramedullary nails which do not produce
complete rotational fixation (3) will lead to a higher incidence of
complications such as malunions and nonunions.
In clinical use, variable success has been reported in the
literature regarding intramedullary fixation. Wickstrom et al. (1968),
in a review of 324 total cases, cited many of the complications that
occur in the use of intramedullary fracture fixation. While many of
these complications were biological in nature (i.e. infections, etc.),
others were the result of improper implant choice or application.
These biological and biomechanical complications led to 3 1/2% of
the patients having delayed or nonunion of their fractures. These
data support the work of Nichols (1963), who also found a 3% delayed
union rate in intramedullary osteosyntheses.
Success or failure of this surgical procedure depends on the
mechanical interaction between the nail and the bone. Peters (1972)
has put the problem into perspective.
Studies of the most appropriate material for
immobilization of fractures must be correlated with
determination of the biomechanical factors which act
to increase and decrease fracture healing. The
material and method of application can then be de
signed to minimize the disruptive stress at the
fracture site and enhance those that increase
healing... If the healing process can be materially
speeded and nonunion prevented, months and years of
patient disability could be eliminated...(p.18)
Attempts to improve intramedullary fracture fixation have
focused on increasing bending rigidity, torsional rigidity, ultimate
strength, and biocompatibility of the nail, by experimenting with
variations in crosssectional geometry, length, and material com
position of the nails. Results reported to date are, however,
qualitative and have not been correlated with mechanical factors.
Both good and bad results have been reported using similar surgical
techniques and intramedullary nails.
The above review of intramedullary fixation leads to two
major questions. Do the relative flexural rigidities of the nail
and bone have a significant effect on the displacements of the
fracture surfaces of the loaded osteosynthesis? Are there other
parameters which affect the performance of the system?
Allen et al. (1968) underscored the need for understanding
this interrelationship of the geometric, material, and structural
properties of the nail and bone in an intramedullary osteosynthesis.
However, quantification of the deflection at the fracture interface
of an osteosynthesis has not been published to date. Bourgois and
Burny (1972) took a first step in describing this complex problem.
In analyzing various loading configurations, they developed relation
ships between fracture callus rigidity and percentage healing. The
model used consisted of a cantilever beam (the intramedullary nail)
surrounded by bone, with a fracture callus present at the midsection.
Deflections were calculated for this type of system under a trans
verse end load. To carry out these calculations, an assumption of
complete bonding of the nail to the bone was implicitly made (i.e.
the interface between bone and nail transmitted shear stresses).
This transmission of shear stresses at the interface affects the
deflection results significantly and is not seen clinically with
intramedullary nails. However, first approximations on the effects
of variations in geometry, material, and fracture callus properties
on deflections were obtained. No other quantitative studies which
deal with intramedullary fixation have been found, and the following
investigation was therefore undertaken.
The Present Research
The present work is aimed at quantification of the nailbone
interactions and the relative displacements of the fracture surfaces
present during the bending of an osteosynthesis. Utilizing engine
ering techniques and analyses, supported by in vitro experimental
verification, the ability of different nail shapes and sizes to
maintain alignment and fracture surface apposition are presented.
A model of the femur is used which involves varying geometric
properties and constant material properties along its length. An
intramedullary nail of constant material and crosssectional
properties is within the bone. It is assumed that a fourpoint
bending load is applied; consequently, interfacial loading is
assumed to develop at the nailbone interface due to relative
differences in displacements of the nail and bone. Osteosyntheses
with and without fractures present are considered. Emphasis is
placed on the effects of the observed differences of structural
properties of currently used intramedullary nails on the inter
facial deflections at the fracture site and the expected contact
forces between the nail and the bone in the medullary canal.
CHAPTER II
PROPERTIES OF THE SYSTEM COMPONENTS: A REVIEW
The engineer is often faced with the need to analyze the
deflection behavior of load carrying machine elements. In order
to proceed, it is important that the engineer consider the elements
in a twofold manner. The first involves understanding of the
components as geometrical entities, i.e. their shape and/or dis
tribution of material. The second involves the appreciation of
the properties of the materials from which the elements or devices
are fabricated. By combining these two views, a quantitative
evaluation of the performance and interaction of the devices can
be performed. It is believed that understanding and modeling the
intramedullary osteosynthesis requires the same approach. There
fore, this thesis begins with an examination of the existing
information on the structural and material properties of the
components of the intramedullary osteosynthesis.
The Intact Femur
Geometrical Properties
Koch (1917) was one of the first to apply engineering
principles to the determination of the stress response of the
loaded femur. Using time consuming graphical methods, he analyzed
the shape and distribution of bone in a single human femur. He
showed that the external form of the bone, and its internal
structure, were proportioned in such a way as to resist axial,
bending and shear loads applied during normal activity with a
minimum use of material.
Photoelastic techniques (Pauwels, 1951) and stress lacquers
(Evans and Lissner, 1948, and Frankel, 1960) have also been used
to determine stress levels in bones under axial and bending loading.
More recently, Toridis (1969) and Rybicki et al. (1972) have pre
sented analyses using engineering beam theory to predict stress
levels throughout the femur. Their results indicate that engine
ering beam theory is applicable to analysis of the long bones in
the midshaft region. (The bone ends, with their flared structures,
are not adequately modeled using these methods.) Piziali et al.
(1976) analytically examined several assumptions inherent in the use
of classical engineering beam theory to long bones (specifically
tibias), and found that deflections due to shear deformations are
negligible, and that the effects of initial curvature are not
significant. The mismatch between the neutral axis of the
crosssection and the applied moment, however, introduces de
flection components perpendicular to applied loads. Their assumption
of linearly elastic properties led to predicted deflections which
were inversely proportional to the modulus of elasticity of the
bone with shear deformations causing negligible deviation in this
behavior. Yamada and Evans (1970) presented empirical loaddeflection
curves for long bones but did not relate these data to the actual
geometry of the bones involved.
Long bones have an irregular crosssectional geometry
which varies considerably along their length. The determination
of geometric properties, such as the area moments of inertia, is
necessary to apply the above cited strength results to other bones.
As Evans (1957) pointed out, much of the work on structural per
formance of long bones requires approximation of the geometric
properties of bones. Allen et al. (1968), realizing this problem,
predicted the structural rigidity of a femur in bending and torsion.
They used tedious numerical integration techniques which yielded
the moments of inertia necessary for calculation of the bending and
torsional rigidity of the femur. This work was, however, limited
to only three crosssections. Piotrowski and Wilcox (1971)
developed a computer program which performed the numerical
determination of the geometric properties and stresses in solid
(singly connected) crosssections and allowed the analysis of
over 200 crosssections of canine fibulae (Piotrowski, 1975).
The program was updated (Piotrowski and Kellman, 1973) to take
into account the presence of internal holes (the intramedullary
canal). Minns et al. (1975) used finite element techniques to
analyze four left tibias and reported variations in geometrical
properties as a function of length. They also found that geometrical
properties between bones can differ by 30% or more. Piziali et al.
(1976) determined the geometric properties of two femurs, two
fibulae and four tibiae. However, they presented only the tibial
information, which corresponded to that reported by Minns et al.
(1975).
It is important to note that adequate understanding of the
femur as a structure required the knowledge of the geometric
properties and response to load of the system under consideration.
Knowledge of only the load response is not sufficient to allow
for application of the results to the modeling of other loading
situations or bone configurations.
Material Properties
The material properties of bone have received more attention
than the geometric properties. Many hypotheses have been offered
to explain the microscopic behavior of bone. Currey (1964), Katz
(1970), and Kraus (1968) discuss the many theoretical lumped
parameter models used to describe the mechanical behavior of bone
substance on a microscopic scale. The present work, however, is
concerned with the macroscopic behavior of bone, and the interested
reader is referred to the above review articles for further dis
cussion of microscopic behavior and modeling.
As Kummer (1972) has pointed out in his review of the bio
mechanics of bone, bone is neither morphologically homogeneous nor
isotropic. In fact, Reilly and Burstein (1974) indicate that a
transversely isotropic model would be more accurate than the
homogeneous and isotropic representations which are often used in
bone modeling. Whether or not bone can be regarded as homogeneous
with respect to its macroscopic behavior, however, remains to be
seen.
Reilly (1974) and Reilly and Burstein (1974) have presented
a comprehensive, critical review of the literature on the mechanical
properties of human cortical bone. Their review gives a detailed
discussion of the many variations in mechanical properties of bone
presented throughout the literature. These include the effects
of specimen handling, and testing procedures for determination of
these elastic properties. Several articles referred to are dis
cussed below.
Reilly (1974) measured the following average properties for
freshly frozen human bone tested at high strain rates:
E' = 17.1 x 109 N/m2
E = 11.5 x 109 N/m2
v = 0.46
v' = 0.58
G' = 3.28 x 109 N/m2
where E is the modulus of elasticity, v is the Poisson's ratio, and
G is the shear modulus. The primed values refer to properties
found parallel to the long axis of the bone, and the unprimed values
refer to the radial and transverse properties. There are large dif
ferences in properties in these two orthogonal directions. The
values reported for E and E' are associated with standard deviations
of approximately 15%20% of the modulus if determined in tension,
and 7%10% if determined in compression. The Poisson's ratios had a
standard deviation which represented 30% of their mean values.
Standard deviations for the shear modulus were typically 10%.
These results for the variations to be expected in determin
ation of the material properties correlate well with the results
cited by Evans and Lebow (1951), who made additional observations
concerning the local variations in properties along the length of
a given bone. They found 2%8% variations in the modulus of
elasticity and similar variations in the ultimate strength and
hardness as well. These results indicate that, while there is
some variation to be expected in the properties measured at dif
ferent locations along a single bone, these variations are not
statistically significant when considering the overall scatter in
results obtained at several locations on several different femurs
as indicated by Reilly.
As Reilly (1974) noted, the average results he obtained in
measuring material properties were for freshly frozen, nonembalmed
bone. Many authors have dealt in considerable detail with the
effects of different treatment on the mechanical properties of
human cortical bone (Evans and Lebow, 1951; Evans, 1957; McElhaney
et al. 1964; Sedlin and Hirsch, 1966; Kraus, 1968; Kummer, 1972; and
Burstein et al. 1972). They made several salient observations:
1. There was no significant temperature effect on the
maximum failure stress (210 370). The modulus
of elasticity was found to increase slightly along
with maximum deflection at 370.
2. Air drying alters the physical properties in only
a few seconds, and a marked increase, as much as
25% or more, in the modulus of elasticity is observed.
A decrease in the observed plastic deformation occurs
as well.
3. While freezing increases the strength of the specimen
slightly, it does not alter any other properties.
4. Fixation in formalin does not appear to alter the
modulus of elasticity.
5. Significant differences were found in all the prop
erties of bone from individual to individual and
these are not correlated with age.
The results on the effects of embalming on the properties of
bone are equivocal. It has been suggested (Allen, 1977) that
embalming may have a highly variable effect on the mechanical
properties of the bone due to the differences in vascularity and,
therefore, disposition of the embalming medium.
McElhaney and Byars (1965), testing bovine bone in compression,
Panjabi et aZ. (1973), testing rabbit femora in torsion, and Burstein
and Frankel (1968), testing human bone in torsion, also point out
that the physical properties of bone may vary with changes in load
or strain application rates. Figure 2.1 indicates the large
variations in properties which may be expected.
Thus, as Reilly and Burstein (1974) have pointed out, data
can be extracted from the literature to support or contradict many
hypotheses. This is not due to any inherent ambiguities in the
data, but is rather due to the absence of standardization or unifi
cation of experimental approaches and goals. These large variations
in the reported data indicate the need for more work before the
intrinsic and extrinsic variations of bone properties are clearly
understood.
HUMAN
'max Suc
BOVINE
A Elastic Modulus
* Ultimate Strain
i I I I L L `
104 103 102 101 100
102 10j 10*
STRAIN RATE
Figure 2.1.
The effect of strain rate on the material
properties of bone (Bovine data from McElhaney
and Byars, 1965; Human data from Burstein
and Frankel, 1968)
Co
(0
0
C\J
CC
)
C
Cu X
E
t
The Intramedullary Nail
Geometrical Properties
Some of the more commonly used nail shapes are shown in
Figure 2.2. The American Society for Testing and Materials (1976)
has developed standard specifications for the geometry of Kuntscher,
or cloverleaf nails (F339), and for solid crosssection intramedullary
nails (F455) which include the Schneider and HansenStreet configura
tions. There has been no specification adopted to date for the
**
newly developed Fluted nail. It is important to note that these
are voluntary standards and that the manufacturers are not bound
by them in any way. In actuality, the dimensions obtained from
the implants themselves appear to vary considerably from nail to
nail and manufacturer to manufacturer for a given crosssectional
configuration. It is, therefore, important to consider these
devices on an individual basis for determining their geometric
properties. There has been little done in this area in the way of
characterizing the important geometric properties of intramedullary
devices.
Allen et aZ. (1968) examined the overall structural per
formance of various nail types in torsion and bending. These
included the Kuntscher, HansenStreet, and Schneider nails. They
neglected to note, however, the nail size being considered. The
F339, Specification for Cloverleaf Intramedullary Pins;
F455 Specification for Solid CrossSection Intramedullary Nails.
Sampson Corporation, Pittsburgh, PA.
Sampson Corporation, Pittsburgh, PA.
Figure 2.2. Crosssectional shapes of commonly
used intramedullary nails
Sampson Corporation (1976) used proposed ASTM standard test methods,
which appeared to be F383, to evaluate the bending rigidity, bending
strength, and torsional rigidity of these devices. Their comparative
results appear in Figure 2.3 ac. In this test method, however, the
geometrical properties were not explicitly considered. The data
needed to further model nail use in an osteosynthesis is, therefore,
only partially known.
Material Properties
The ASTM has also devised several recommended standard
specifications for the materials commonly used in implant manufacture
(F55, F56, F67, F75, F90, F136, F138, F139). These include the
chemical requirements, and the minimum acceptable mechanical
properties, including ultimate tensile strength, yield strength,
elongation, and reduction of area. Because of the effects of
machining, cold working, and processing techniques in fabrication
of implants from the annealed metals, these values for the unworked
*
F55, Specification for stainless steel bars and wire for
surgical implants; F56, Specification for stainless steel sheet
and strip for surgical implants; F67, Specification for unalloyed
titanium for surgical implants; F75, Specification for cast
cobaltchromiummolybdenum base alloy for surgical implants;
F90, Specification for wrought cobaltchromium alloy for surgical
implants; F136, Specification for titanium 6A14V ELI alloy for
use in clinical evaluation of surgical implant materials; F138,
Specification for stainless steel bars and wire for surgical
implants (Special quality); F139, Specification for stainless
steel sheet and strip for surgical implants (Special quality).
BONE 316SS INTRAMEDULLARY
{inside by outside DEVICES (diamelers in mm)
diameters in mm) 0 ( >
17X 29.,
16x28 (0I) BONE
S} SAMPSON
iSX27T. I KUNTSCHER
14X26 SCHNEIDER
13X25 *ANSESTREET
APPROPRIATE
12X24 \ROD SIZE
X2 \ due to FLUTES
II 23
OX 22
I16
14 7
13 .*1
:12 .11
11111\0 .8.9
<) ^"7y ^"~9
Figure 2.3.
Structural properties of commonly used intramedullary nails
(Data taken from Technical Memorandum 176, Sampson Corp.
Pittsburgh, Pa.)
600
soo
s
P 500
it
(3
Z 400
W
I
S300
I.
U)
200
z
a
a 100
0
BONE 316SS INTRAMEDULLARY
(inside by outside DEVICES diameters in mm
diameters in mm) 8 ( '
() BONE
a SAMPSON
400
o () KUNTSCHER
SCHNEIDER
S(0 UNSENSTR EET
APPROPRIATE
SIE \ ROD SIZE
S6 due to FLUTES
Q
. /
20 200
14X26
16X 25 2
S 4 X26 12
100 12X 24
11X23
tOX 22
1 2 10 .13
I1\ V2 12. I .^ 1*II
9 I7 5 o .O
0 4~ 1
a
0
C)
25
u 20
S15
10
"o
0
2
Cr Co Mo Alloy
cold
worked
annealed
Stainless n a
Steel
Ti6A14V
Bone
Figure 2.4. Elastic modulus for several implant materials
material have little use in evaluating the performance of the
devices themselves. Figure 2.4 gives the average values for the
moduli of elasticity of several alloys used in implants. These
values have been shown as ranges due to the effects of fabrication
techniques on the mechanical properties of the nails.
Summary
The review of the literature on the mechanical and geometric
properties of the components of an intramedullary osteosynthesis
of the femur, as presented above, has led to several observations.
1. While many investigations have been carried out in an
attempt to characterize the mechanical properties of
the femur, the large variations in results indicate
that careful consideration must be given to the use
of these results in the modeling of an osteosynthesis.
Indiscriminate use can lead to significant differences
in the results obtained.
2. Determination of the geometric properties of the femur
has received little attention. The information reviewed
above concerns itself with the rigidity and ultimate
properties of the nail and the bone. While the flexural
rigidity is related to the modulus of elasticity and
the area moment of inertia, the nonuniform geometry and
difficulty in specifying the modulus of elasticity of
the bone does not allow for the direct calculation of
the moment of inertia or other geometric properties.
3. The material properties of intramedullary nails have
been found to be adequate. Here again, however, care
must be exercised in the use of these properties so
that the effects of machining and other processing are
taken into account (Utah Biomedical Test Laboratory,
1975).
4. The loaddeflection behavior of several intramedullary
nails has been carriedout, and the geometric properties
necessary for modeling their use in an osteosynthesis
can be derived from this information.
22
Before a general modeling of the osteosynthesis can be carried
out, quantitative characterization of the geometric properties of the
femur must be performed. The first portion of the experimental work
presented here concerns itself with this characterization.
CHAPTER III
DETERMINATION OF THE GEOMETRIC PROPERTIES
OF THE SYSTEM COMPONENTS
The Femur
Materials and Methods
Ten pairs of embalmed human femurs were obtained and cleaned
of all soft tissue and periosteum. The femurs were then allowed
to air dry for one day. Information regarding age, sex, height,
and weight of the subjects was not available. Two reference
lengths were measured as shown in Figure 3.1. The first, L r
maj or'
was defined as the overall length of the femur as measured from
the most proximal portion of the femoral head to the most distal
portion of the femoral condyles. The second length, Llesser was
defined as the distance from the midpoint of the lesser trochanter
to the most distal portion of the femoral condyles. With the femur
resting on the posterior aspect of the femoral condyles and greater
trochanter, a small hole, approximately 3 mm diameter, running
approximately anterior to posterior, was drilled in the femur at
the level of the midpoint of the lesser trochanter. A 3 mm dowel
was inserted to act as a reference for position measurements along
the femur. The bone was placed in a plywood mold, with the dowel
marker in a vertical orientation, and plaster poured over it to
make a rectangular slab. After the plaster had set, 20 mm thick
Figure 3.1.
Schematic representation of the femoral
length measurements: Llesser, the lesser
trochanter to femoral condyle length, and
Major, the femoral head to condyle length
sections were marked off using the lesser trochanter marker as the
starting point. Approximately 16 serial sections were obtained
from each bone. These represented positions (measured proximal to
distal) from approximately 20% of the total femoral length, the
level of the lesser trochanter, to 80%, the level of the distal
metaphysis.
After sectioning and numbering, each section was carefully
cleaned of bone marrow and a size reference marked directly on the
surface of the plaster blocks (Figure 3.2). The size reference
marks were made so that the magnification and the location,
relative to a fixed axis, of each crosssectional image could
be maintained. Each block was projected on a large sheet of paper
using an opaque projector. A tracing of the cortical bone of each
crosssection and its reference line was produced. These tracings
were used to generate a set of coordinate points on computer punch
cards, representing the outside and inside boundaries of each
section, using a digitizing machine. The punched data deck of the
boundary coordinate points became the input information for the
SCADS computer program (Piotrowski and Kellman, 1973; Piotrowski
and Wilcox, 1971). The SCADS program was used to calculate the
geometrical properties of the crosssection as defined below.
Cortical bone area. The computer program determines the
area of cortical bone in each crosssection by integrating all
Department of Radiation Therapy, J. Hillis Miller Health
Center, Gainesville, Florida
2 6 10 14
3 7 11 15
99 '
4 12 16
I _
S5 9 13 17
Figure 3.2. Serial crosssections of a representative
femur with size reference marks in place
the differential area elements such that
AORT = dA = AA (3.1)
(CORT3
fA i
Area moments of inertia. The area moments of inertia, or
second moments of the area, are generally used in the calculation
of bending stresses and deflections and are a measure of the
distribution of the loadcarrying material about a set of orthogonal
axes. For this work the orthogonal reference axes were chosen to
be the mediolateral (xaxis), and the anteroposterior (yaxis)
planes. The moments of inertia are defined, referring to Figure
3.3, as
I = x2 dA = x dA. (3.2)
xx A i I
I = y2 dA = E y? dA. (3.3)
yy i 1 1
I = xy dA = xiy. dA. (3.4)
xy J 1 1
i
Principal angle and moments of inertia. Another set of
orthogonal axes, n and C, whose origin is at the centroid of the
crosssection can be determined such that
I = n dA = 0 (3.5)
JA
These axes are known as the principal axes, and correspond with
the axes of symmetry in crosssections which are symmetrical. For
nonsymmetrical crosssections these axes represent the least and
ANTERIOR
LATERAL
POSTERIOR
Figure 3.3.
Definition of axes and distances for
geometrical property determination
MEDIAL
most rigid directions of the crosssection. The principal moments
are then defined with reference to the principal axes or directions
as
n = n2 dA (3.6)
and
I = Cf 2 dA (3.7)
These quantities can be obtained from a Mohr's circle construction
(Beer and Johnston, 1962) as shown in Figure 3.4. The principal
angle, 0, between the xaxis and the naxis is calculated as
0 = arctan ( xy ) (3.8)
yy xx
The principal area moments of inertia are also readily computed
from I I and I as
xx yy xy
I +1 I I
I xx yy + 12 + xx yy (39)
nn 2 xy 2 J
and
I +1 / I I 2
I x yy 2 xx y (3.10)
2 2 xy 2
Polar moment of inertia. Used in determination of torsional
shear stresses and deflections of round crosssections, the polar
moment of inertia, or polar second moment of area, is defined as
J = fr2 dA (3.11)
/A
xx,Ixy
lIlnn l ii
Iyy,l
Figure 3.4.
Mohr's circle construction for locating
principal moment magnitudes and directions
of the crosssections
where r is.measured from the centroid of the crosssection. The
polar moment may be calculated using the previously determined
values of the moments of inertia, I and I Using trigonometry
xx yy
and referring to Figure 3.3
r2 = x2 + y2 (3.12)
Therefore, equation 3.11 can be rewritten as
J = f (x2 + y2)dA = x2 dA + f y2 dA (3.13)
and substituting equations 3.2 and 3.3 yields
J = I + I (3.14)
xx yy
The effective polar moment of inertia. The last property to
be considered is the "effective" polar moment of inertia, Jeff. As
eff
den Hartog (1952) has shown in his discussion of the torsion of
machine elements, a torsional stiffness, C, may be defined as the
torque, T, per unit twist, 0. That is
C T (3.15)
Further analysis of elements of circular crosssection leads to
the result that
C = G Jeff (3.16)
where G is the shear modulus of the material and Jeff is the
eff
effective polar moment of inertia. For circular crosssections
Jeff reduces to J. The noncircular crosssection requires a more
complex derivation to obtain the geometrical determination of the
torsional stiffness. Prandtl's "membrane analogy," as discussed
by den Hartog (1952) and Crandall (1956) allows for the determination
of an effective polar moment of inertia; thus the torsional stiffness
of noncircular crosssections may still be expressed as a product of
a material and geometric property. Thus, for noncircular sections,
T
S= C = G J (3.17)
0 eff
The effective polar moment of inertia is still a measure of the
area's distribution. However, in this case its value cannot be
obtained by the simple integration of differential area elements
as shown for the polar moment of inertia since it also depends on
the convolutions of the sections periphery. The development of the
equations for determination of Jeff are beyond the scope of this
work,however, and the interested reader is referred to the above
references for further discussion. The SCADS computer program
contains the algorithm for mathematically modeling the "membrane
analogy," and thus calculating Jeff and these results have been
included for comparison with the polar moment of inertia, J, as
defined in the previous section.
Results of the Geometric Properties of the Femur
Raw data for the gross cortical area (A), area moments of
inertia (Ixx and I ), principal moments of inertia (I and I ),
principal angle (0), polar moments of inertia (J), and effective
moment of inertia (Jeff), were extracted from the SCADS computer
runs for the ten femur pairs. The lefttoright variation of these
data, except for the principal angles to be discussed later, were
first evaluated at sequential points along the bone length (from
20% to 80% of the total bone length in 10% increments). As dis
cussed by Miller and Piotrowski (1974), the sidetoside difference,
d of any property is defined as
P P
d = (3.18)
p PL + PR
where PL and PR are the values of the property for the left and
right femurs respectively. The differences computed at each
incremental position were averaged to obtain the mean value of the
sidetoside difference, dp, and its standard deviation, S.D.,
for each pair of femurs. Table 3.1 summarizes these results. The
accumulated values, obtained by pooling the results from all ten
femur pairs, are also shown. The standard deviations have been
corrected for small sample sizes using the Bessel's Correction
(Moroney, 1951).
Figures 3.53.18 have been constructed to indicate the
overall values obtained for the geometrical properties of the right
femurs and the left femurs. The shaded band indicates the total
range over which the raw data falls. A line has been drawn to
indicate the calculated mean value of the property from 20% to
80% of the total bone length. Also included are vertical bars
which represent a range of plus and minus one standard deviation
from the mean.
Table 3.1. Values for the mean sidetoside difference, d ,
and standard deviations (in parentheses) for
the paired femurs
Bone dA d dl d d d
Bone # dA xx Vy Tn dJ Jeff
1 .005 .079 .006 .014 .005 .014 .003
(.022) (.058) (.033) (.034) (.034) (.032) (.041)
2 .018 .035 .059 .007 .034 .016 .0134
(.048) (.129) (.046) (.059) (.057) (.053) (.055)
3 .006 .036 .038 .004 .002 .018 .009
(.019) (.155) (.035) (.033) (.015) (.023) (.0191)
4' .005 .054 .004 .010 .061 .018 .032
(.020) (.037) (.036) (.030) (.026) (.021) (.021)
5 .003 .043 .024 .032 .010 .025 .026
(.030) (.042) (.043) (.037) (.060) (.032) (.041)
6 .001 .064 .030 .055 .045 .046 .032
(.037) (.032) (.034) (.031). (.036) (.026) (.049)
7 .056 .024 .041 .020 .024 .034 .058
(.024) (.081) (.067) (.052) (.099) (.048) (.034)
8 .002 .019 .020 .012 .024 .006 .002
(.016) (.043) (.055) (.040) (.057) (.032) (.043)
9 .007 .002 .025 .005 .018 .005 .006
(.020) (.080) (.049) (.074) (.063) (.064) (.052)
10 .022 .012 .006 .010 .011 .014 .011
(.037) (.054) (.028) (.043) (.028) (.045) (.053)
Pooled
mean .001 .001 .010 .001 .002 .004 .0035
Data
S.D. (.030) (.085) (.046) (.024) (.057) (.040) (.047)
t .11 .04 .69 .13 .11 .32 .24
P >.9 >.9 >.5 >.9 >.9 >.7 >.8
n = 10 for all cases
20 30 40 50 60 70 80
PERCENTAGE OF TOTAL LENGTH
Figure 3.5.
Gross cortical bone area as a function
of position for the left femurs
0
6 
o
PERCENTAGE OF TOTAL LENGTH
Figure 3.6.
Gross cortical bone area as a function
of position for the right femurs
t I I IL
oT
0
PERCENTAGE OF TOTAL LENGTH
Figure 3.7.
Area moment of inertia, Ixx, as a function
of position for the left femurs
I I r IL
51
oI
o0
PERCENTAGE OF TOTAL LENGTH
Figure 3.8.
Area moment of inertia, Ixx, as a function
of position for the right femurs
6r
5
. E
LU
U
U
LU

2
01O I I I i I ,
0 20 30 40 50 60 70 80
PERCENTAGE OF TOTAL LENGTH
Figure 3.9. Area moment of inertia, Iyy, as a function of
position for the left femurs
I I
40 50
PERCENTAGE OF TOTAL LENGTH
Figure 3.10.
Area moment of inertia, lyy, as a function of
position for the right femurs
Io
0
ir
.4
0
PERCENTAGE OF TOTAL LENGTH
Figure 3.11.
Principal moment of inertia, ln, as a function
of position for the left femurs
__ ^1 __ __
0 30 n
0 20 30 an n~ a
PERCENTAGE OF TOTAL LENGTH
Figure 3.12.
Principal moment of inertia, I as a function
of position for the right femurs
4
V) 3
LLu
Ur
J 2
1
0 II I
0 20 30 40 50 60 70 80
PERCENTAGE OF TOTAL LENGTH
Figure 3.13. Principal moment of inertia, IE as a function
of position for the left femurs
0 20 30 40 50 60 70
PERCENTAGE OF TOTAL LENGTH
Figure 3.14.
Principal moment of inertia, IEE, as a function
of position for the right femurs
.
CA
cr,
w
LJ
I
0
CU
wu
*JJ
E C I I I I T I
o 20 30 40 50 60 70 8
PERCENTAGE OF TOTAL LENGTH
Figure 3.15.
Polar moment of inertia, J, as a function
of position for the left femurs
111111
`K>
Ij
0 20 30 40 50 60 70 8
PERCENTAGE OF TOTAL LENGTH
Figure 3.16. Polar moment of inertia, J, as a function
of position for the right femurs
.1. 1111111 jIl
0 ,I I I 6 7
0 20 30 40 50 60 70
PERCENTAGE OF TOTAL LENGTH
Figure 3.17.
Effective polar moment of inertia, Jeff, as a
function of position for the left femurs
8
LJ 6
4
2
0 I I
0 20 30 40 50 60 70 80
PERCENTAGE OF TOTAL LENGTH
Figure 3.18. Effective polar moment of inertia, Jeff, as a co
function of position for the right femurs
10r
The values of the principal angles are more difficult to
present. These values appear to have fallen into three main
groupings. Representatives of these three groups are shown
graphically in Figures 3.193.21. Here, the values of principal
moments along the length of a pair of femurs are shown as scaled
orthogonal lengths in their actual principal angle orientation.
In the first two cases, there is a gradual angular displacement
to the principal axes, going proximal to distal. The principal
axes were not well defined in case III.
Discussion of the Geometric Properties
Rightleft variability. Using the pooled means which were
calculated from the data presented in Table 3.1, the Student's
t Test (Moroney, 1951) was applied to compare the resulting dis
tributions with the hypothesis that there is no rightleft bias
in the geometric properties, i.e. d = 0. In this particular case,
p
the value of t is indicative of the ratio of the mean to the
standard deviation. The nonzero mean values seen in Table 3.1
are quite likely to occur by chance since they are smaller than
the data's inherent scatter, represented by the standard deviations.
The actual statistical results have been included in the table and
indicate that P, the probability of t being this large or larger
by chance, is greater than 0.5 in all cases. One can thus conclude,
with considerable certainty, that there was no rightleft bias in
the geometric properties of the femurs investigated.
Figure 3.19.
Principal angle orientation and relative magnitude
of the principal moments as a function of position
for a representative pair of femurs from group I
(the darker line indicates the larger moment
of inertia, I )
DISTAL
Left Right
7LF9
PROXIMAL
Figure 3.20. Principal angle orientation and relative magnitude
of the principal moments as a function of position
for a representative pair of femurs from group II
(the darker line indicates the larger moment of
inertia, I )
DISTAL
Left
Right
3LF9
PROXIMAL
Figure 3.21. Principal angle orientation and relative magnitude
of the principal moments as a function of position
for a representative pair of femurs from group III
(the darker line indicates the larger moment of
inertia, I )
rnn
DISTAL
+e
Left
Right
PROXIMAL
8LF9
Miller and Piotrowski (1974) showed that one can expect the
standard deviation of the sidetoside difference in the torsional
strength of paired animal bones to be about 9%. The results obtained
above for the standard deviation of the sidetoside difference in
the polar moment of inertia was of the order of 4%. This indicates
that, while the geometric variability has some effect on the observed
strength variations of whole bones, it does not account for all of
it. The strength of whole bones, however, depends on both geometric
and material properties. Reilly (1974) reported that one can expect
variability in ultimate torsional strength of bony material to be
approximately 4%. Thus, it would appear that the combination of
geometric and material variability adequately describes the scatter
found in the strength of whole bones.
Gross Cortical Area. The flared outward shape of the femur
might imply a similar cortical bone area distribution. This is not
the case, however, due to the thinning of the cortex which occurs
in the flared metaphysial regions. The crosssectional area of
bone as shown graphically in Figures 3.5 and 3.6, tends to increase
only slightly from the level of the lesser trochanter to approxi
mately 40% of the bone length. This is where the isthmus, or
narrowest section of the intramedullary canal, is found. The cortical
area then decreases monotonically to the knee. At the most distal
data point taken, 80% from proximal, the area is approximately
2.5 cm2. This resulting area, just proximal to the knee, is slightly
larger than the proximal tibia area, just distal to the knee, pre
sented by Minns et al. (1975) and Piziali et al. (1976). Thus,
ignoring the discontinuity at the knee, the lower limb appears to
be a tapered column of bone mass. This shape reduces the amount
of bone appearing distally, and results in a minimization of the
bones' contribution to the mass moment of inertia of the limb about
the hip. Thus, compared to a limb with bone mass evenly distributed
along its length, the torques necessary to accelerate the extremity
during locomotion are reduced, with the result that the energy
necessary to accelerate the limb is also decreased and higher
efficiency can be maintained.
The slight increase in area seen in the proximal portion of
the femur is due to the presence of the gluteal tuberosity and the
beginning of the linea aspera. These areas allow for the attachment
of the muscle groups which, while providing for rotations about the
hip, also apply significant axial loading in the region due to their
poor mechanical advantage. These axial loads tend to reduce the
tensile stresses set up by bending of the femur due to the loading
of the femoral head, but also requires the need for additional bone
area to maintain suitable compressive stress levels.
Area moments of inertia. It is important to note at the
outset of this discussion of the area moments of inertia (Figures
3.73.10) and polar moment of inertia (Figures 3.15 and 3.16) that
there is a relationship between the two, as shown in equation (3.14).
These properties influence the stress levels caused by different
forms of loading, namely bending and torsion. These properties
also influence the rigidity of the system under these different
loading configurations.
The bending stresses, o, developed in the outer surface of
a beam with an applied bending moment, M, may be represented by
Mc
a = M (3.19)
where c is the distance from the centroid of the section to the
outer surface, and I is the area moment of inertia. The quantity
I/c is often referred to as the section modulus, Z, of the beam.
Figure 3.22 shows the results obtained from the calculation of the
section modulus for two representative femurs. Also included is
the result obtained by Koch (1917) in his detailed analysis of a
single femur. While the magnitudes are quite similar, the results
obtained here indicate that the section modulus decreases slightly
from proximal to distal. Koch (1917) and Rybicki et al. (1972)
also note that when a downward load is applied to the femoral head,
the bending moment in the xplane increases rapidly from the femoral
head to the level of the lesser trochanter and then decreases
monotonically to the knee. Thus, the bending stresses, equal to
M/Z, decrease from the lesser trochanter to the knee, but more
gradually than the bending moment itself. This corresponds well
with the bending stress distribution reported by Rybicki in his
analytical modeling of the femur.
The increase in the area moment of inertia I in the
xx'
proximal femur, also results in an increase in the flexural rigidity
of the bone in this region. This is due to the direct proportionality
between the rigidity and the moment of inertia. The femoral condyles,
which are the bearing surfaces of the knee joint, allow muscular
2 *
**.. data from Koch (1917)
1 Femur 3L
 Femur 3R
Ia
SPROXIMAL
DISTAL
Figure 3.22. Section modulus, Z, as a function of length
along the femur for two sample femurs compared
to data derived from Koch (1917)
E
I I
NI
insertions, and provide areas for attachment of the ligaments which
stabilize the knee joint, are responsible for the increase in I
xx
in the last 15%20% of length. This results in an increase in the
flexural rigidity of the femur in this region as well.
The anteroposterior moment of inertia, I (Figures 3.9
and 3.10) is smaller in magnitude than I in the proximal femur.
xx
It also decreases in magnitude over the proximal 40% of'length,
and then remains almost constant until the femoral condyles are
reached. One reason for the initially larger relative values of
I is the large bending loads which appear in this plane due to
Yy
the femoral head loading, as well as forces generated by the large
gluteus maximus muscle used in extending the hip.
Principal moments and directions. The principal moments of
inertia, In and I were calculated and their principal angle,
relative to the mediolateral direction, was determined. The
magnitudes of these principal moments show a curved profile
(Figures 3.113.14) similar to that for the values of I
xx
However, the orientation of the principal axes was quite remarkable.
Study of the principal axes of the ten femur pairs led to the obser
vation that the femoral crosssectional shape at the midshaft
appears to fall into three basic categories. A midshaft section
from the left femur of representatives of each of these groups has
been included in Figures 3.193.21 along with scaled orthogonal
lines representing the relative magnitudes of the principal moments.
(The heavier of the two lines indicates the larger value, I .)
Of the ten femur pairs examined, four pairs were found to be
in the first group, four pairs in the second group and two pairs
in the third group.
The first group, shown in Figure 3.19,has an elliptical
crosssectional shape whose major axis, I runs anteroposterior
at the midshaft. There is definite rightleft symmetry as seen in
this figure. At the proximal end of the femur, the major axis is
inclined at an angle which provides greatest rigidity in the
approximate direction of the femoral neck and head. As the midshaft
is approached, the linea aspera dominates the crosssection, result
ing in a principal angle of approximately 90 (the anteroposterior
direction). In the distal portion, the major axis rotates and
comes to an almost mediolateral orientation corresponding well
with the femoral condyles.
The second group, Figure 3.20, has an elliptical crosssection
at the midshaft as well, but is perhaps less pronounced than in the
previous group. However, the I axis begins in a more mediolateral
position and remains as such throughout the length of the femur.
Thus the more rigid direction, corresponding to the I direction,
is now 90 from that of the first group. Here again, the rightleft
symmetry is maintained.
The third group, Figure 3.21, has a profile in'the proximal
segment which is similar in magnitude and direction to the second
type described above. However, as the midshaft is approached, the
magnitudes of I and I are almost equal, in contrast to groups
I and II, and determination of the principal direction is uncertain
due to the relatively small size of the Mohr's circle in comparison
to the magnitudes of I and I Thus, the bone has no preferen
xx yy
tially rigid direction until the femoral condyles are reached. The
only generalization which can be made here is that in all groups
the principal direction is mediolateral at the femoral condyles.
An attempt to explain the above observations led to the
consultation of the anthropological literature. Comas (1960) makes
several observations relative to the point of femoral shape. The
linea aspera, in the femur of people of the more modern civilizations,
is more pronounced in males than females. The more robust skeleton
of the male has broad areas for muscular attachment and the linea
aspera may develop in such a way as to produce a large, rough, crest
shaped protrusion not unlike that seen in group I (Figure 3.19).
Anteroposterior flattening, as represented by the second group
presented above, is observed in the female skeleton.
This observation was reiterated by Maples (1977) who indicated
that the anthropological and forensic medicine literature suggests
that a pronounced linea aspera is indicative of the male and a
flattened diaphyseal shape of the femur may be indicative of the
female. Maples cautioned, however, that generalization is very
tenuous in this regard.
From a biomechanics point of view, the large linea aspera of
the male increases the rigidity of the system in the plane needed
to resist the large bending loads of the flexors and extensors
of the thigh and knee so that moderate stress levels are maintained.
One might also conjecture that the wider pelvis of the female
results in larger bending loads in the mediolateral plane and a
principal axis oriented in that plane. Unfortunately, the sex of
the femoral samples studied here was unknown, and substantiation of
this hypothesis must remain for further study.
Polar moment of inertia. The polar moment of inertia, J, is
distributed in a manner similar to I (Figures 3.15 and 3.16), due
XX
to its dependence on I and I as discussed in the previous
xx yy
section. In the proximal femur, the relative increase in this
property appears to be due to the several internal and external
rotators of the hip which attach in this area and apply torsional
loading to the bone.
In the midshaft region, the values for J do not vary con
siderably due to the uniform torsional loading which is distributed
along the length of the bone. As was discussed in the previous
section on area moments of inertia, the distal femur must also
maintain a fairly large area for support of the cartilagenous
bearing surface of the knee. It accomplishes this by using a
preponderance of cancellus bone which aids in distribution of the
joint loading force. In order to maintain the torsional strength
of the system, however, a thin layer of cortical bone is distributed
at the periphery of this area and the polar moment of inertia is
maintained with efficient use of material. This larger polar
moment of inertia also aids in reducing the loads in the collateral
ligaments necessary to maintain joint stability.
Effective polar moment of inertia. The effective polar
moment of inertia calculated for the noncircular bone crosssections,
using the SCADS computer program, are shown in Figures 3.17 and 3.18.
While the profile of the distribution is similar to that found for
the polar moment of inertia given in the previous section, the
magnitudes of Jeff are approximately 10%15% less. The greatest
differences appear in the distal portion of the bone. Thus, the
nonsymmetry of the bone crosssections result in a decrease in the
actual torsional rigidity of the bone.
Discussion of the Observed Scatter in Properties
The magnitude of the observed scatter in the geometric cal
culations, characterized by the standard deviations, ranged up to
20%25% of the mean values. The somewhat larger standard deviations
present at the ends of the bones are due to the difficulty in
discerning the corticocancellus bone interface of the intra
medullary canal. In light of the discussion of the inherent
differences in individuals presented above, this large range does
not seem unreasonable. The maximum error of the SCADS computer
program, for calculations on well defined geometries, has been
shown to be 5% or less (Piotrowski and Kellman, 1973).
In an attempt to quantify the remaining 20% of variation,
nondimensionalization of the observed properties using other
dimensions of the bones was carried out. It was hoped that a
general characteristic shape of each of the property distributions
along the bone length could be generated in this way. Using the
overall length, Lmajor, and the lesser trochanter to femoral condyle
length, Llesser, (Figure 3.1) as nondimensionalization parameters,
did not, however, reduce the magnitudes of the scatter. In fact,
as can be seen in Figures 3.23 and 3.24, there is no correlation
between these lengths and the average calculated bone area. There
is also no correlation between the average area and the midshaft
outer.diameter (Figure 3.25). One must conclude, therefore, that
there are significant differences in the bone properties of dif
ferent individuals and that these differences are dependent on many
variables. This is consistent with the thought (Comas, 1960) that
it is build and/or body weight, sex, age and general physical con
dition and not height alone, which determines the size and shape of
an individuals bones. Unfortunately, this information was not
available for consideration in this study.
Conclusion
Even with the substantial scatter present in the geometric
properties discussed in this chapter, the general property dis
tribution profiles are valid. Several conclusions can be made
from the results presented.
1. No statistically significant rightleft bias is evident
in the geometric properties presented.
2. The geometric properties calculated using the SCADS
computer program adjoins the tibial information pre
sented by Minns et al. (1975) and Piziali et al. (1976).
3. The area distribution profiles do not mirror the out
ward appearance of the femur. In fact, the entire
lower limb has a "tapered column" distribution of
bone area, with the greater area appearing in the
proximal femur. This distribution of bone aids in
efficient ambulation.
4. The flared shape of the femur is more pronounced in the
mediolateral plane than in the anteroposterior plane,
and I and I the respective area moments of inertia,
mirroxthis ard appearance.
mirror this onward appearance.
0 AR vs. Lmajor r=0.21
* AL vs. Lmajor r=0.41
0 0
52.0
50.0
48.0
46.0
44.0
42.0
40.0
0
* 0
0o
L^ I  1  I 
2.5 3.0 3.5 4.0 4.5 5.
AVERAGE AREAS (cm2)
Figure 3.23.
Graphical representation of the overall femoral length versus
average cortical bone area with the respective correlation
coefficients, r, for the right and left femurs
0
0
o AR vs. Lesser r=0.31
* AL vs. Llesser r=0.50
0 O
44.0
42.0
40.0
38.0
36.0
AVERAGE
AREAS (cm2)
Figure 3.24.
Graphical representation of the lesser trochanter to femoral
condyle length, Llesser, versus average cortical bone area
with respective correlation coefficients, r, for the right
and left femurs
00
0
*
34
I I 1
r
Ot
0 AR vs. dR r=0.38
* AL vs. dL r=0.42
S00
0
0
S0
AVERAGE AREAS (cm2)
Figure 3.25.
Graphical representation of the outer midshaft diameter
versus average cortical bone area with the respective
correlation coefficients, r, for the right and left femurs
3.2
3.0
2.8
2.6
I I 1
4
5. The principal directions were found to fall into three
major groups. There are those femurs which are most
rigid in the anteroposterior plane; those which are
most rigid in the mediolateral plane; and those which
appear to have no preferential orientation. Anthro
pological information available suggests that these
differences are sexlinked.
6. The calculated effective polar moment of inertia
using the "membrane analogy" indicates that the
noncircularity of the bone crosssection results
in torsional rigidities which are 10%15% less than
is predicted by the symmetrical polar moment 'of
inertia calculations.
7. The geometric property profiles are distributed along
the bone length in a highly efficient use of the material
so that "strength to weight" optimization appears to be
maintained under complex loading configurations.
The results which have been obtained in this geometric study
of the femur are consistent with the small amount of information
available in the literature and the data presented in Figures
3.53.22 can be used in the subsequent structural modeling of this
bone.
The Intramedullary Nail
Materials and Methods
Determination of the geometric properties of five intra
medullary nails was carried out. These included four nails, of
differing types (Figure 2.2), intended for implantation in a 13 mm
reamed intramedullary canal (13 mm Schneider, 13 mm Kuntscher,
13 mm x 11 mm HansenStreet, and 12 mm Fluted). A 14 mm Fluted
nail, intended for subsequent use in an in vitro osteosynthesis
model, was also processed.
A transverse section, approximately 2 mm thick, was cut
from the midportion of commercially supplied intramedullary nails
of the above nominal sizes. The sections were then ground and
carefully deburred. In a manner similar to that described in the
previous section for femoral geometry determinations, these sections
were projected and an enlarged tracing of their crosssectional
outline made. Coordinate points of the boundaries were produced
using the digitizing unit and were input to the SCADS computer
program for geometric property determination. The 14 mm Fluted
nail was processed with and without its flutelike protrusions to
appraise the significance of these gripping points on the overall
geometric properties of the device.
Results
Figure 3.26 shows the results obtained for the geometric
property determination of the four nail types considered. These
results include the gross area, area moments of inertia, polar
moment of inertia, and principal moments of inertia as defined at
the beginning of this chapter. Also included in the figure are the
axes orientations used for geometric property determination. The
principal angles were.zero in all cases due to the orientations
used, i.e. the nails were oriented in their principal directions
during processing. Table 3.2 shows the results obtained from
the geometric processing of the 14 mm Fluted intramedullary nail.
xx lyy Ill 122
L e e
0.251
0.20)
0.15
0.10
4e
0.031
LEGEND
 FLUTED (12mm)
 HANSENSTREET (13mm)
 SCHNEIDER
9 KUNTSCHER
ORIENTATION
y
S ,X Fluted
4
0.051
5~~x
(13mm)
(13 mm)
HansenStreet
Schneider
Kuntscher
Figure 3.26. Calculated geometrical properties for several intramedullary nail shapes
(all nails are intended for use in a nominal 13 mm reamed medullary canal)
1.11
0.09F
0.95
0.7F
0.071
0.5
0.05
0.3
I
 .. _
Table 3.2. Geometric properties of
with and without flutes
the 14 mm Fluted type nail,
14 mm Nail
With Without
Flutes Flutes
Area (.cm2) 1.12 1.00
Ix (cm4) 0.19 0.16
xx
I (cm4) 0.19 0.16
yy
J (cm4) 0.38 0.32
Ill (cm4) 0.19 0.16
122 (cm4) 0.19 0.16
0 0.0 0.0
Discussion
The results obtained using the SCADS computer program are
approximate due to the difficulties inherent in processing the
intricate geometry of these crosssections. Independent cal
culations indicate that the results obtained are within 5% of the
exact values. The Fluted nail has the largest values for all the
geometric properties determined. This has a pronounced effect on
its relative bending and torsional rigidity. Its very high
crosssectional symmetry also makes it insensitive to the orienta
tion of the applied loading. The Schneider nail also has a high
degree of symmetry, while the HansenStreet and Kuntscher nails
are sensitive to orientation due to large differences observed in
their orthogonal geometric properties.
The results obtained from the processing of the 14 mm
Fluted nail were quite interesting. The flutelike projections
of this nail, primarily intended to maintain torsional stability
of the bone fragments, have a significant effect on the area and
polar moment of inertia. These properties increase almost 20%
with the addition of the flutes to the crosssection while
increasing the area of the section by only 12%.
It is important to note that only one sample of each nail
type was processed. Measurement of the outer dimensions of a few
other samples of similar nails from different manufacturers indicate
that there is considerable difference in the crosssections of nails
made by different companies. Changes in the wall thickness of a
74.
Kuntscher nail, for example, without altering the outside dimensions,
causes significant changes in the flexural rigidity of the device.
The preliminary results reported here are sufficient to allow for
verification of the osteosynthesis modeling to be carried out at
this time. However, a more detailed study is indicated so that
the effect of implant variability on geometric properties of the
devices can be accurately determined.
CHAPTER IV
MODELING OF THE OSTEOSYNTHESIS
The Preliminary Idealized Model
To gain insight into the parameters affecting the deflections
occurring in an osteosynthesis under bending loading, an elementary
model was analyzed using engineering beam theory. This model, as
shown in Figure 4.1, consisted of an outer tube with a transverse
cut, representing the fractured bone, and a central rod, representing
the intramedullary nail, passing the full length of the system.
Fourpoint bending loading was assumed to be applied to the outer
tube with equal spacing between the loading points. Clearances
were assumed to be such that the rod and tube interacted only at
idealized point contacts, as shown in Figure 4.1, and that no
deformations occurred at these points. The space between the
fracture surfaces was assumed to be just wide enough so that these
surfaces did not contact during deflection. The moduli of elasticity
of the outer tube and inner rod, Eb and En, were assumed to be con
stant throughout, and the components were restricted to linearly
elastic behavior. The crosssectional geometry of these components
was also assumed to be constant along the system length. Thus, the
moments of inertia of the tube and rod, Ib and In, were unvarying
along the length of the model.
Figure 4.1. Schematic representation of the preliminary idealized
osteosynthesis model with equally spaced fourpoint
external loading and point contact reactions between
the nail and bone fragments
Free Body Diagram of the Outer Tube
Due to the symmetry of this system, a free body diagram for
half of the outer tube is constructed as shown in Figure 4.2. With
an applied load P at each of the external loading points, and rod
reactions R1 and R2 as shown, vertical force equilibrium yields
P + R1 + R2 = 0 (4.1)
and
R1 = R2 = R (4.2)
Static moment equilibrium about the left end of the tube yields
PL RL
3 = 0 (4.3)
3 2
so that
2
R = R =R P (4.4)
Free Body Diagram of the Inner Rod
As shown in Figure 4.3, a free body diagram of the inner
rod can be constructed with reaction loads as shown. Note the
idealized point contacts of the nailbone interaction.
Deflection Equations
The flexural rigidities of the inner rod (N) and the outer
tube (B) are defined as
N = E I (4.5)
n n
B = Eb Ib
(4.6)
P
L/3 L/6
R1 R
P
Figure 4.2.
Figure 4.3.
Free body diagram of half of the
outer tube with external and point
contact reaction loads
Free body diagram of the inner rod
with idealized point contact reactions
IT6P
'12 % PIIY '12
/3
where En and Eb are the modulus of elasticity of the inner rod and
outer tube respectively, and In and Ib are the area moments of
inertia for the inner rod and outer tube respectively.
The reaction loads on the rod are applied to each end and the
midspan of the component (Figure 4.3). The midspan deflection, z,
for the three point loaded span in this configuration can be written
(Roark, 1954) as
pL3
z= (4.7)
36N
where P is the load applied to the outer tube, of length L, at its
four loading points.
Similarly, from the outer tube free body diagram (Figure 4.2),
an angular deflection of the fracture surface, relative to its
original centerline, can be defined as
PL2
0 PL2 (4.8)
b 64.8B
The outer tube has been constrained to contact the inner rod
only at its idealized contact points, and the centerline of the
inner rod is now inclined at an angle 0 which may be approximated,
for small deflections, as
S z (4.9)
n (L/2)
The fracture interfacial deflection angle, Ot, relative to the
vertical axis, can be obtained, as shown in Figure 4.4, by super
imposing equations (4.8) and (4.9) as defined above. Due to the
symmetry of the system, the total angular mismatch of the system,
Figure 4.4. Idealized angular mismatch representation
with the overall angulation, Ot, equal to
the difference in nail angulation, 0 ,
and bone angulation, 0b
T0 is twice 0t and if
pL2 pL2
t n b 18N 64.8B10)
then
PL2 B
T 2 x 2 (3.6 1) (4.11)
TP@L/3 64.8B N
The values obtained for the angular deflection of the fracture
interface are dependent on the applied load configuration. For
example, if the downward applied loads are assumed to be located
at positions L/4 in from each end of the system, instead of at L/3
as discussed above, the resulting angular deflection becomes
PL2 B
2 x 128B (2.66 1) (4.12)
P@L/4
While the form of the equations remain the same, their
coefficients take on new values. Nonetheless, several observations
can be made. The application of bending loads to an idealized
system such as the one shown indicates that an optimum flexural
rigidity ratio exists (N/B = 3.6 or 2.66 depending on the configura
tion) which results in no angular mismatch of the fracture surfaces.
This implies that in an actual osteosynthesis, where the outer tube
represents the bone, and the rod represents the intramedullary nail,
some optimum property ratio could result in a minimum fracture
surface angulation.
While the many assumptions used to derive the results obtained
above were necessary to allow for the application of elementary
engineering beam equations, these assumptions are not necessarily
consistent with the configuration of an actual intramedullary
osteosynthesis as discussed in Chapter I. The geometry of the
bone, as discussed in Chapter III, is not uniform along its length.
The intimate contact between the nail and the bone, needed to
maintain torsional rigidity of the fragments, does not allow for
large enough clearances to assure only point contacts. 'Large
clearances would also allow for unacceptable relative transverse
motion at the fracture site under shearing loads. Also, as loads
are applied to the system, the reactions cause simultaneous, but
unequal, deflections to take place in the components. Interactions
at other than the original contact points will take place once the
mismatch exceeds the clearance, and, as the loads increase, local
deformations at the contact points will occur. These deformations
result in redistribution of the reaction forces along the nailbone
interface, changing the loading configurations and the relative
deflections.
While the simplified model indicates that an optimum relation
ship between the component properties may minimize deflections at
the fracture site, a more general model, which more closely
duplicates the actual osteosynthesis, is necessary before a
quantitative evaluation of this hypothesis can be obtained.
In light of the previous discussions, the material properties
of the nail and the bone, and the geometric properties of the nail,
may be considered to be arbitrary constants whose values depend on
the nail and bone under consideration. The model should, however,
account for the nonuniformity of the bone's geometric properties so
that the bone's flexural rigidity is properly represented as it
varies along its length. It should also provide intimate contact
between the nail and the bone, but should allow for longitudinal
sliding of the components. The nailbone interface should be
assumed to develop an arbitrary interfacial loading profile which
is dependent on the relative deflections occurring between the nail
and the bone. Contact between the fracture surfaces will be assumed
to be nonexistent.
The previous work cited in proceeding chapters allows for
quantification of all the parameters discussed in the previous
paragraph except for the nailbone interfacial reactions. In order
to obtain quantitative information on this interaction, an experi
mental investigation was performed.
Intramedullary Interfacial Behavior
Methods and Materials
A matched pair of embalmed femurs was cleaned of soft tissue
and periosteum. At all times the bones were kept moist using a
saline solution drip. The bones were cast in plaster, and as soon
as the plaster had set, several 20 mm thick sections were cut from
the diaphysial and metaphysial regions of the bone. These sections
were then placed in saline solution until testing.
A Kuntschner nail (13 mm), Schneider nail (13 mm), or Fluted
nail (12 mm) was placed in the intramedullary canal of these
sections as shown in Figure 4.5. Each of these samples was placed
.4
Figure 4.5.
Photograph showing the intramedullary nail in
place in the cast bone section for interfacial
stiffness determination
on a selfaligning compression fixture (Figure 4.6) for loading
of the nailbone interface. Using an Instron universal testing
machine at a crosshead speed of 0.02 mm/min, the nails were pressed
against the endosteal surface, which contained either cancellus or
cortical bone. Loaddeflection curves were obtained, along with a
measurement of the section thickness, for further calculations.
The results obtained from the loaddeflection curves were
used to obtain the interfaciall stiffness" of the cancellus and
cortical bone of the femur in contact with different nail shapes.
This stiffness was defined as the slope of the loaddeflection
curve divided by the specimen thickness. Thus, a parameter relating
force per deflection per unit length could be obtained for subsequent
use in the general modeling of the osteosynthesis.
Results
Representative curves for the loaddeflection response of the
different nail types tested in cancellus and cortical bone are shown
in Figures 4.7 and 4.8 along with the testing configurations used.
Even with the small number of samples tested, the similarity
in the loaddeflection response of the different nail types during
testing in cancellus bone led to the definition of three overall
interfacial stiffness regimes. The first interfacial stiffness range
was low in magnitude and appeared to be due to the initial crushing
of the cancellus bone. A transition region was observed as the
deflection increased. This was followed by a higher stiffness
level after significant deflection and packing had taken place.
These different regimes are shown as different line types in the
INTRAMEDULLARY
NAIL
BONE
IN
SECTION
PLASTER
SELFALIGNING
SUPPORT
Figure 4.6.
Schematic drawing of the selfaligning
compression fixture for interfacial
stiffness determination
