Orthopaedic Mechanics. Procedures and Devices

313 Pages·1981·26.853 MB·English

by  Dhanjoo N. Ghista, Robert Roaf

Orthopaedic Mechanics
Procedures and Devices
Volume II
EDITED BY
DHANJOO N. GHISTA ROBERT ROAF
Departments of Medicine Formerly Professor of
and Mechanical Engineering Orthopaedic and Accident Surgery
McMaster University University of Liverpool
Hamilton, Ontario, Canada England
1981
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Copy © 1981 by
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All Rights Reserved
No part of this book may be reproduced in any form by photostat, microfilm, or
any other means, without written permission from the publishers
British Library Cataloguing in Publication Data
Orthopaedic mechanics.
Vol. 2
1. Orthopedia
2. Biomedical engineering
I. Ghista, D. N. II. Roaf, R.
617'. 30028 RD732 77-93201
ISBN 0-12-281602-1
Printed in Great Britain by
Page Bros (Norwich) Ltd
Contributors
D. N. GHISTA Department of Mechanical Engineering Mechanics,
Michigan Technological University, Houghton, Michigan 49931, USA
(Present address: Departments of Medicine and Mechanical Engineer­
ing, McMaster University and Chedoke-McMaster Hospitals, Hamilton,
Ontario, Canada L8S 4L8)
G. GRANIK Department of Civil Engineering, New Jersey Institute of
Technology, Newark, New Jersey, USA
W. C. HAYES Department of Orthopaedic Surgery, Beth Israel Hospital,
330 Brookline Avenue, Boston, Massachusetts 02215, USA
J. L. NOWINSKI Department of Mechanical and Aerospace Engineering,
University of Delaware, Newark, Delaware 19711, USA
A. PEDOTTI Instituto di Electrotechnic ed Elettronica, Politechnico di
Milano, Piazza Leonardo da Vinci 32, Milano 20153, Italy
C. A. RODENBERGER Meiller Research Inc., P.O. Box CB, College
Station, Texas 77841, USA
I. D. STEIN Medical Service, Veterans Administration Hospital, East
Orange, New Jersey 07019, USA (Present address: Veterans Admin­
istration Medical Center, Erie, Pennsylvania 16501, USA)
L. W. SWENSON, Jr. Department of Mechanical Engineering, Design
Division, Stanford University, Stanford, California 94305, USA
D. F. WILLIAMS Biomaterials Division, Department of Dental Science,
University of Liverpool, Liverpool L69 3BX, England
V
Preface
This book (in conjunction with Volumes I and III) aims to provide a
state-of-the-art cum tutorial coverage of some pertinent topics on skeletal
mechanical properties, mechanics of stresses in skeletal structures under
functional loads as well as those due to fixation devices and implants,
mechanical design analyses of correction devices for skeletal deformities,
locomotion analysis and measurement based indices for assessment of
neuro-muscular disorders and rehabilitation, orthotic aids for paraplegics
and materials considerations for design of implants.
The first chapter logically starts with the design development of a device
for non-invasive evaluation of bone strength by determination of the in
vivo modulus of elasticity (and stiffness) of the tibia; this simplistic, but
biomechanically sound device, which invokes beam theory in a three-point
bending set-up, has direct clinical use in evaluating the treatment and
progress of bone disease.
The next chapter provides comprehensive finite-element stress analyses
of the proximal tibia, (i) for the intact human knee, with insight into high
shear stress-based implications for tibial condylar fractures and into the
modelling of the mechanical factors involved in the development of osteoar­
thritis, and (ii) due to the fixation of the tibial component of a total condylar
knee prosthesis, in order to develop criteria for optimal design of the tibial
component fixation.
The stresses and deformations resulting from forcing a prosthesis (such
as the Austin-Moore type prosthesis) into the medullary canal are analysed,
in Chapter 3, by means of a viscoelastic annular cylindrical tube model.
The viscoelastic analysis provides a basis for assessing the time-varying
osseous stress and deformation states (normalized in terms of the interface
pressure and bone geometry, respectively). It consequently warns the
orthopaedic surgeon against the use of excessive force while inserting the
stem, which is the most vulnerable phase of the procedure since the stresses
decay with time to about 50 per cent of their values developed at the time
of application of the load.
Although gait analysis constitutes one of the earliest endeavours of
biomechanics, Chapter 4 fulfils the need for a three-dimensional analysis
vii
viii PREFACE
to enable a more representative computation of muscle and joint forces.
However, the more direct and clinically useful benefit (for implementation
in a gait laboratory), provided by this chapter is a newly developed system
for on-line monitoring of spatio-temporal representation of the ground
reaction during the stance phase of the gait step. Not only are the resulting
"butterfly diagrams" characteristics of specific motor disorders but they
can also be employed as on-line patient feedback for assisting rehabilitation.
It is not often that a simplistic, yet biologically rational and mechanically
sound, device for correction of a deformity is available. The Torqheel
device is one such device for correcting a lower extremity rotational deform­
ity causing foot misalignment. It is a dynamic device which activates the
corrective forces by a collapse of the rubber ribs when ground contact is
made, thereby creating a rotational displacement of the heel about its
centre. The design analysis as well as the clinical evaluation of this now
commercially produced device is presented in Chapter 5.
For the successful long-term function of an implant, the biomechanical
design should also incorporate the biomaterials influence on the mechanics
of in situ fixation and stabilization as well as on the tribological character­
istics of the implant. The last chapter, while comprehensively elucidating
these phenomena, (on the basis of materials science factors for biomaterials
degradation and tissue response), illustrates implementation of these con­
siderations in the case of some popular orthopaedic implants.
With the above delineated scope, the book is intended to elucidate the
biomechanical considerations for designing orthopaedic procedures and
devices. It is not meant to be a guide for the clinical orthopaedic surgeon.
Rather it is one step removed from that. By emphasizing mechanics of
skeletal responses and rehabilitation devices, the book is geared to furnish
the orthopaedic mechanics researcher with the basis and considerations
that need to be invoked in devising optimal procedures and devices. Of
course, for the mechanics students who would be taking a course in
biomechanics prior to embarking on their dissertations, the book shows
how appropriate theoretical and experimental mechanics techniques can
be employed to reveal orthopaedic mechanisms and provide more accurate
guides to correction and fixation of deformities and fractures by application
of corrective and stabilizing forces by means of surgery and/or
prosthetic-orthotic devices.
We would like to take this opportunity to thank all the contributors for
their patient efforts in enabling us to prepare this book.
Dhanjoo N. Ghista and Robert Roaf
December, 1980
1
Tibiometry
A non-invasive in vivo method for testing
the strength of the tibia
I. D. STEIN* and G. GRANIK
Veterans Administration Hospital, East Orange and Department of Civil
Engineering, New Jersey Institute of Technology
I. Introduction 1
II. Theory 2
A. Model set-up 5
B. Model set-up 7
C. The determination of the moment of inertia . . .. 8
III. Design 15
IV. Procedure 21
A. Clinical testing 21
B. Results 22
C. Unresolved technical problems 23
D. Future evolution of the device 27
References 28
I. Introduction
Testing bone strength in the living subject should be very useful in evalu­
ating the treatment and progress of metabolic bone disease. The results
could be used as a basis of comparison amongst study groups as well as for
* Research project No. 8123-02.
1
2 I. D. STEIN and G. GRANIK
long-term evaluation of individual patients and could be used to assess the
effects of disease, the effectiveness of treatment, the adverse side effects
in treatment of non-osseous disease (e.g. anticonvulsants) and the conse­
quences of physiological stress such as diving and space flight.
Investigators and clinicians rely on indirect and often semiquantitative
methods such as radiography, gamma absorption, biopsy, neutron acti­
vation and mineral balance studies (Frame et al., 1973), but to date there
is no reliable, non-invasive, in vivo method of testing bone strength. This
dearth is understandable, as tests on human subjects must generally be
safe, non-invasive and nearly painless, while bones are mostly deeply
buried in soft tissue and not accessible for mechanical testing. We have,
however, been develeping a method for in vivo human bone testing which
meets the above criteria. Most technical obstacles have been cleared, and
we feel the technique is fast approaching the threshold of clinical
applicability.
II, Theory
The most logical test mode is three-point bending, and the best parameter
is the modulus of elasticity, as this can be measured at small loads and
deformations without any danger of damage to the bone. The extremities
can all be suitably positioned on a support frame, however, with the
exception of the tibia and ulna, none present an entire face at the skin
surface. The ulna is unsuitable because the wrist supinates during loading.
This leaves the tibia, a large bone in the leg of approximately triangular
cross-section, whose entire anteromedial surface is subcutaneous. Although
its smaller companion bone, the fibula, participates in the formation of the
ankle mortice, there is no detectable rotation of the leg during application
of the load. The presence of this bone does, however, create theoretical
problems which will be considered later.
Strictly speaking, the modulus of elasticity is a measure of stiffness, not
strength, and some very brittle materials such as chalk have a high elastic
modulus but fail at low stresses. Therefore it was necessary to determine
whether or not stiffness and strength correlated well in bone. This was
done in postmortem rib segments, using modulus of rupture, a reasonable
approximation of strength in bending, with the results shown in Fig. 1.
Similar results were obtained in compression testing of vertebral bodies.
High correlation is evident, indicating that it is valid to make inferences
as to strength from the modulus of elasticity.
1. TIBIOMETRY 3
S
B
I
R
s -
l
a
e
s
a
p
a
g
e
M
,
E
d.Mega pa seals —RIBS
Fig. 1 The correlation of the moduli of elasticity and rupture in fresh postmortem rib
2
segments. The numbers in parentheses represent pounds/inch
The tibiometer set-up is shown in Figs 2 and 3. For a simply supported,
3
centrally loaded beam, the modulus of elasticity (E) is E = (AP)L /(A<5)
48/ where the load increment (AP) and testing span (L) are known while
the corresponding deflection increment (A6) and geometric moment of
inertia of cross-section at the load (I) must be determined. In this for­
mulation, however, Ad is that which occurs under the load. It cannot be
Rack and pinion adjuster
Fig. 2 Tibiometer, first generation prototype. Diagram of side view, cut away, of leg, loading
and support elements and strain gauges with their rack-and-pinion adjusters
4 i. D. STEIN and G. GRANIK
View along axis of leg
Fig. 3 Tibiometer: diagram of cross-section with leg in testing position at point of load
application. The four sets of load frame guide bearings are shown. The tibia (above) and
fibula (below) are shaded
measured because the skin between the tibia and the applied load, though
thin, is compressed during the test. In fact, more displacement results from
the compressibility of the skin than from bending of the tibia, so whether
deflection is measured under or over the load, it will represent mainly skin
compression. Naturally, deflection could only be measured on the upper­
most subcutaneous surface (Fig. 2) to which the load is applied, as all other
surfaces are totally inaccessible owing to soft tissue. However, at distances
of 1 in. or more from the point of load application, the skin is unaffected,
and deflections of applied strain gauges represent the sums of bending and
total downward movement of the tibia from compression of soft tissues
over the supports (Fig. 4). It is possible, using a minimum of three strain
wwmJmsm
.*.* * * * i *
i
i
Fig. 4 Diagram showing the components of displacement at strain gauges in various positions.
Each arrow has a heavy portion denoting the component of displacement resulting from
downward movement of the entire leg and a lighter portion for the component due to tibial
bending. All motions, especially the latter, are exaggerated for purposes of illustration.
Downward movement is generally somewhat greater at the proximal than at the distal end
5
1. TIBIOMETRY
1
I*< - fl M-
r
I >• 2
> 1 f
1 • • • X
k _ J
«2
vv
*3 33
Pb Po
L L
Fig. 5 Lateral diagram of a supported beam with three strain gauges, for reference in eqns
(1) to (11). The lengths of the arrows for the y or displacement values were selected for
graphical clarity and are unrelated to the magnitude of displacement. See Fig. 4 for illustration
of relative displacement magnitudes
gauges to develop a set of equations that will yield E and true deflection
under the load. In the following derivation, refer to Fig. 5 for the description
of all symbols used.
A. Model Set-up
A simply supported beam, location of load known, but not necessarily
central, location of supports known, supports yielding, and deflections
known at three points between supports. The basic differential equation
2 2
of the elastic curve is EId yldx = M, where M = M(x) and E and / are
constant. On substituting the expressions for M(x), we get:
2 2
EI dy/dx = (Pb/L)x, for 0 ^ x ^ a (1)
The right-hand term being the bending moment.
2 2
EI dy/dx = - (Pa/L)x + Pa, for a ^ x ^ L (2)
To define the slope of the elastic curve of the beam within the specified
limits, we integrate eqns (1) and (2), giving, respectively:
2
EI dy/dx = (Pb/2L)x + c (3)
x
2
EI dyldx = -(Pa/2L)x + Pax + c (4)
3
Then, to find the deflection of each point from the pre-load base-line,