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sevans80
05-30-1997, 02:25 AM
I posted a question a few weeks ago regarding the use of fracture
mechanics concepts in the analysis and prediction of fractures of
bones. Here are the replies I received, plus a few opinions of my
own.

I asked why there seemed to be so little in the literature regarding
the use of fracture mechanics concepts, although a number of people
have measured (or attempted to measure) the fracture properties of
bones. Here is what I think:

(1) Fracture mechanics comes in two main flavours: the work of
fracture/ critical strain energy release rate/ Gc approach, and the
critical stress intensity/ Kc approach. Of these, the former uses a
real material property which is easy to measure and has a proper
physical meaning, but is very difficult to use to predict fracture
since it is necessary to account for all of the stored strain energy
and other energy coming in or out of the system. The latter approach
is excellent for predicting fracture, from straightforward stress
analysis, but depends on a variable (the stress intensity) that is an
artefact of complicated mathematics and has little physical meaning.
Since the maths that produces this variable assumes that the
material is homogenous, isotropic and linearly elastic, it is dubious and
difficult to apply this approach to biological materials such as
bone.

(2). Bones do not generally fail by a single large crack, but
instead by a gradual accumulation of microcracking. In this respect,
bone is similar to many composites, or to concrete. As a result, a
continuum damage approach may be more fruitful.

(3). The additional confounding factor is that bone is constantly
repairing itself, and arguably exists in a state of permanent damage
in equilibrium with constant repair processes. This makes the
argument of Taylor et al. that fatigue processes are a controlling
influence on bone remodelling seem quite persuasive. I was glad to
see that this is being followed further.

My conclusion:
There are a lot of complications in applying fracture mechanics to
bones- and fracture mechanics is complicated enough at the best of
times. In many applications, moreover, it does not provide much
information of any great value that cannot be obtained by other
means. However, I suspect that there is still some scope for using
computational fracture mechanics techniques to understand the
mechanisms of some fractures, especially where fracture occurs very
rapidly, for example as a result of an impact.

Here are the replies I received:

>From Peter Zioupos:

Dear Dr Evans
I saw your request for an exchange of ideas on Fracture mechanics bone
data and how to use it. As you very well noted there are no studies or
other work yet where the FM produced parameters have been usefully put
into practice. This has been pointed out by Melvin in his review
article of this field in the TRANS ASME 1994 paper. The problem is I
think very fundamental and has three major directions: what kind of
material bone really is; what do we expect from FM in the predictive
sense? and what happens in nature (in-vivo) in fracture problems. 1)
our perception of bone has changed considerably lately since more and
more emphasis is given on the 'yielding' properties of bone (as by
microcracking) in general and around stress concentrators. Bone is now
safely called semi-brittle and LEFM is inappropriate to use. EPFM
though may still derive more meaningful parameters in the future. 2)
predicting critical conditions from the original LEFM results as by
using the principle of a critical crack length and a critical stress
intensity factor has also had its day. This approach did not offer
something new even where it mattered most (in comparing dry.v.wet or
gresh.v.embalmed bone). 3) the real in-vivo situation is more
confusing though. Fractures in life are either sudden and catastrophic
events (where impact properties may have been more relevant to study)
or slow progressive 'stress fracture' phenomena. In the latter case
the generation of a great number of microcracks over a length of time
softens the tissue which is riddled with these tiny non-connecting
cracks as oppossed to a single major crack driven through the
structure. The tissue stays intact till the major crack is initiated
(the critical conditions for which may have more to do with the local
maximum sustainable density of microcracks than the stress/energy
conditions at its tip) and invariably once the major crack is started
the tissue is finished as this macrocrack drives through the tissue in
very high speed. Therefore, finding the conditions that are needed to
drive a single major crack through the bone structure (by fatigue
cycling on CT specimens) is not a desperatelly important task. Even
for the remodelling studies that you mentioned (Prof Taylor from
Dublin is having a go at it) the relevant behaviour that matters is
that of short (physically or even microscopically small) cracks. And
we know nothing about it! I myself have been very critical of
applications of FM of the past although I reckon that more holistic
approaches (as by combining FM and Continuum Damage Mechanics) have a
lot to offer. I expressed some of these views in
J.Mat.Sci.29:978-986:1994; Med.Eng.Phys.16:203-212:1994;
Phil.TransR.Soc.347:383-396:1995; J.Biomech.29:989-1002:1996; and
Clin.Biomech.11:365-375:1996.

>From John Hipp :

Although we have not used classical fracture mechanics to understand
actual clinical fractures of bones, we have tried many other methods
that may help to understand the potential role of classical fracture
mechanics. We have worked for many years to develop good clinical
guidelines for predicting pathologic fractures in the spine and long
bones that have metastatic defects. We have completed several
investigations where simulated defects were created in whole bones and
the failure load was measured. In most investigations, we also
measured the failure load of intact bones for comparison. We have
tried numerous techniques to predict the failure load of the bones,
including finite element models (with various failure criteria),
geometric properties from computed tomography and MRI, composite beam
theory based analysis of CT and MRI data, and bone mineral content.
For simple loading conditions, axial rigidity measured from CT does an
excellent job at predicting failure load of intact vertebrae and
vertebrae with simulated or actual defects (in press right now).
Composite beam theory does an excellent job of predicting bending,
axial and torsional failure loads of trabecular bone cores with
simulated defects (manuscripts in preparation). In both these cases,
excellent means that the relatively simple measurements that account
for both the geometry of the bone and defect as well as the bone
density predict over 90 percent of the variation in measured failure
loads. Similar results have been reported by several investigators
using a variety of test methods. These measurements do not account for
nominal stress concentrations or stresses at crack tips. For the
proximal femur, the bone mineral content alone predicts between 50 and
95 percent of the variation in measured failure load, depending on
whether there is a simulated defect in the bone and how the bone was
tested. For an engineer, it is surprising that simple measurements
that do not account for stress concentrations, complex multi-axial
failure criteria, etc work as well as they do. Perhaps fracture
mechanics can be used to improve our ability to predict failure loads,
but there may be even bigger challenges to overcome before clinical
fractures can be reliably predicted. As was nicely pointed out by in
1957 by Backman and later strongly emphasized by Hayes and Myers and
others, predicting failure load is only part of the problem. We also
need to know the applied loads, and it is not easy to predict all of
the loads that a bone will see. Finally, after you think you have the
greatest way to predict failure loads and applied loads, you need to
prove that your methods are sensitive and specific in clinical
practice so that clinicains will be believers and insurance will pay.
This generally requires finding true positive cases of people that
have fractured and have pre-fracture measurements. Sophisticated
engineering is only part of the solution.

You should also read the excellent work of Lakes et al on
couple-stress effects. There is also alot more literature available on
fracture mechanics of bone then is suggested by your email as well as
a growing body of literature on failure criteria for bone. I can send
some references if requested.

Good luck

John A. Hipp, PhD
Baylor College of Medicine

>From Edward Draper :

Sam, Hi

I've been involved in bone fracture healing mechanics for
years.

It's my experience that the biological variability and the
complexity of bone as a material/structure that trying to
predict fracture configurations is difficult, except in the
broadest terms eg spiral fracture is a a sign of a
torsional load during injury.

Every day we get in patients who have undergone what appear
to be very similar modes of injuries with quite dissimilar
fracture patterns.

Edward Draper PhD BSc CEng MIMechE MIPEMB
Principal Research Fellow in Bioengineering
Royal Postgraduate Medical School


>From Mark Taylor :

Dear Dr Evans,

I am a member of Prof Bonfields group at the IRC in Biomedical
materials and though I cannot answer your question myself, I suggest
that you contact Deepak Vashishth (email-D.Vashishth@qmw.ac.uk). He is
nearing completion of his Ph.D. thesis on the fracture mechanics of
bone and will probably be able to tell you why this technique has not
been applied to whole bones.

(....)

Kind regards,

Mark


>From Craig Nevin :

Hi Sam.

I have just submitted a paper on the dynamic functions of the
metatarsals. I am preparing another on a case study of a second
metatarsal fracture in a runner, and have looked at primate feet. I
am toying with various notions concerning bone fractures. My initial
results look exceptionally good, but I have not yet delved into the
literature.

I think a lot of the problem is to do with the fact that most
biomechanical models use either classical engineering principles which
do not apply to bone. Also, most biomechanic work is based on muscle
models. When these are combined to explain bone fractures, they just
don't add up. Their predictive capacity is less than 50%, which means
that you can never quite be sure whether the model is right or wrong.

I am interested in your thoughts on the subject.

Regards
Craig Nevin
Anatomical Engineer

> Dear Craig,

> My feeling is that the stress intensity factor approach, being based
> on all sorts of mathematical assumptions, is unlikely to ever work
> very well in a non- homogenous, anisotropic composite material such
> as bone. However, the alternative approach of looking at the strain
> energy release rate and the work of fracture seems to me to have
> some potential, being based on fundamental material properties and
> conservation of energy.

Sounds promising.

My ideas on stress fractures are that the bone remodels and resorbs
at an equal rate. Increased stress merely induces bone healing in the
microfractures, therefore standard ultimate fatigue strength is a none
starter. My interest in the matter stems from an unlikely scource. I
was measuring the kinematics of the metatarsals. To do this I clamped
the shafts to a table. But as I moved the toe, the bones splintered.
Now kinematic theory is defined as the study of motion without regard
to the forces causing that motion. That, I discovered was fine in
theory but try as I might I could not contrive the circumstances where
the bones would not fracture. I then relised that the bones are only
as strong as they need be to cope with the pysiological stress levels.


Engineers design structures wastefully, huge factors of safety etc.
But my approach is to learn from the bones, afterall they know EXACTLY
what the stresses are that they are being subject to.

It seems to me that you have a similar problem. The rib, for
example, is stabbed. It breaks because it is not strong enough. My
metatarsals fractured when I used invasive methods. If I had take the
simple expedient of amputating the foot before testing the metatarsal,
it would not have broken. But amputation, I seems to me, is hardly
the best cure for bone fractures!

I am therefore interested in (1) the process of bone remodelling as a
measure of physiological function (2) attempting to understand
physiological (mechanical) bone structure in terms of bone
remodelling.

Based on my kinematic work, I made certain predictions about the
relative sizes of the metatarsals. The theoretical prediction was
that the first metatarsal should be four times stronger than the
second metatarsal in torsion; or twice the diameter. I measured the
perimeters of the shafts in the main primates. Then I did the stats.
I predicted a ratio of 2.0; the answer I got was 1.99!

This prediction was based on equal torsional stress levels in
all bone, wherever it may be.

Recently I got a referral from a runner with a stress fracture. We
recontructed MRI images of the metatarsals. I am now looking at
relating the thickness of the cortex, to the biomechanical function.
I have fiddled a bit, looking for patterns, as I believe that the data
will enable me to make certain predictions on the precise mechanisms
of bone remodelling. If I can recognize a pattern the theory must
follow. Early stages and its digressing from my thesis.

But, I am going to rigorously pull the data apart and see what I can
make of it. But I first have to seen what has been done in the
literature, and would like to know what curveballs to throw at my
predictions.

You comments

Craig

Dear Craig,

There is a huge amount of literature about bone remodelling,
associated especially with Rik Huiskes et al. at the University of
Nijmegen. In particular Harry Weinans and subsequently Margarite (?)
Mullender have developed a model that produces a realistic trabecular
architecture from a simple remodelling theory by a chaotic process.
You might be able to apply some of this work to your problems- I don't
see why you shouldn't be able to work backwards from the structure of
the bone to deduce its function. Also Patrick Prendergast has
apparently done more work on the fatigue/ bone remodelling theory that
I mentioned in my original query.

Best wishes,

Sam.


>From Tom Persing :

Dr. Evans,

I am interested in hearing your responses. If it is convenient, you
may simply forward relevant responses to me. If you were planning on
summarizing the responses and posting the summary to the list, that
would also work for me.

I work the forensic side of the business, mainly car accidents. I've
seen some literature a while back, but don't remember where it was.
I'll do some digging and see if I can come up with it. Tom Persing
lab@airmail.net


>From viceconti@tecno.ior.it (Marco Viceconti):

I'll tell you my opinion soon on your question; meanwhile look at

Viceconti, M. and Seireg, A. A generalized procedure for predicting
bone mass regulation by mechanical strain. Calcif Tissue Int
47:196-301, 1990

and to works from Patrick Prendergast on J biomechanics; both works
assume the bone microfractures as the stimuli for the bone
remodelling. David Taylor was at that time the advisor of Patrick.


Marco


Thanks once again to all that replied for you intelligent and helpful
comments.

Here is my original query again:

>Does anyone know of any studies that have used fracture mechanics
>concepts to predict and/ or analyse fractures of bones?
>
>My initial study of the literature has confirmed my impression that
>while there have been a number of studies of the fracture properties
>of bone (notably by Bonfield et al., Melvin and Evans and Norman et
>al.), there have been few serious attempts to use the measured
>properties to predict actual fractures. In fact, apart from an
>intriguing paper by Taylor, presented at Fatigue '94 (?), which
>argued that fatigue processes could provide a controlling mechanism
>for bone remodelling, I don't know of any successful attempts to use
>fracture mechanics to predict or understand actual clinical fractures
>of bones.
>
>Why have fracture mechanics concepts not been more widely used in
>this context? I can think of plenty of possible reasons myself- what
>is your opinion?
>
>Thank you very much for your help,
>
>Best wishes,
>
>Sam.
Dr. Sam Evans,
Medical Systems Engineering Research Unit,
UWC School of Engineering,
PO Box 688, The Parade,
Cardiff CF2 3TE, UK.
Tel. (01222) 874533 or (01222) 874000 x5926
Fax. (01222) 874533