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RE: Vertebrate long bone strength (implications for dinosaurs)

  Eventually we'll get to the point where we can accurately model bone 
infrastructure and material composition (with cortical, lamellar, cancellous 
and trabecular bone and arrangement of trabecular pillars/plates and 
intercamarate/camellate bone walls) as a regular feature for longbone and 
cranialbone analyses. We're not quite there yet, but I think a methodology that 
takes total bone shape into account over modelling as a variation of a cylinder 
is at least one step in the right direction. (The authors *do* seem to have an 
FEA bias, though, a hard bias to overcome!) Plugging into the analytical tool 
the struc6ture of different types of bones may require multiple overlain 
models, as it may not be possible to perform such an analysis with current 
tools due to the need to compose the different layers with different 
assumptions (don't most models just assume cancellous bone, without any value 
to cortex?).


  Jaime A. Headden
  The Bite Stuff (site v2)

"Innocent, unbiased observation is a myth." --- P.B. Medawar (1969)

"Ever since man first left his cave and met a stranger with a
different language and a new way of looking at things, the human race
has had a dream: to kill him, so we don't have to learn his language or
his new way of looking at things." --- Zapp Brannigan (Beast With a Billion 

> Date: Wed, 21 Nov 2012 12:56:42 -0500
> From: biologyinmotion@gmail.com
> To: bcreisler@gmail.com
> CC: dinosaur@usc.edu
> Subject: Re: Vertebrate long bone strength (implications for dinosaurs)
> Thanks to Ben for posting this heads up. I just grabbed the full paper (it's 
> free!) and am giving it a read through. I am quite enjoying the manuscript 
> and the topic is of great importance. My one critique would be that while the 
> MS certainly shows that FEA and beam theory get very different answers for 
> compressive strength estimation, it isn't clear from the paper how the 
> authors know that FEA is getting closer to the right answer. They presume 
> this is the case (so far as I can tell so far) based on violations of 
> assumptions in beam theory, but FEA makes assumptions, as well, and it isn't 
> clear how the authors are dealing with that side of things. In the 
> conclusions, they do seem to take note of this issue:
> "Future studies applying FEA to long bone stress estimation
> should proceed with caution, however, particularly when variables
> such as applied forces and material properties remain
> uncertain. This is necessarily the case in palaeontological
> studies, and, therefore, sensitivity analyses should be carried
> out in order to quantify the effect of the error introduced by
> these unknowns. It must be emphasized that applying an
> overly simplified FEA model to a complex biomechanical problem
> may result in incorporating just as many assumptions
> into the analysis as the application of classic beam theory."
> Cheers,
> --Mike H.
> On Nov 21, 2012, at 12:36 PM, Ben Creisler wrote:
> > From: Ben Creisler
> > bcreisler@gmail.com
> >
> > A new paper. The pdf is free:
> >
> >
> > Charlotte A. Brassey Lee Margetts, Andrew C. Kitchener, Philip J.
> > Withers, Phillip L. Manning and William I. Sellers (2013)
> > Finite element modelling versus classic beam theory: comparing methods
> > for stress estimation in a morphologically diverse sample of
> > vertebrate long bones.
> > Journal of the Royal Society Interface10 (79): 20120823
> > doi: 10.1098/rsif.2012.0823
> > http://rsif.royalsocietypublishing.org/content/10/79/20120823.abstract
> >
> >
> >
> > Classic beam theory is frequently used in biomechanics to model the
> > stress behaviour of vertebrate long bones, particularly when creating
> > intraspecific scaling models. Although methodologically
> > straightforward, classic beam theory requires complex irregular bones
> > to be approximated as slender beams, and the errors associated with
> > simplifying complex organic structures to such an extent are unknown.
> > Alternative approaches, such as finite element analysis (FEA), while
> > much more time-consuming to perform, require no such assumptions. This
> > study compares the results obtained using classic beam theory with
> > those from FEA to quantify the beam theory errors and to provide
> > recommendations about when a full FEA is essential for reasonable
> > biomechanical predictions. High-resolution computed tomographic scans
> > of eight vertebrate long bones were used to calculate diaphyseal
> > stress owing to various loading regimes. Under compression, FEA values
> > of minimum principal stress (σmin) were on average 142 per cent (±28%
> > s.e.) larger than those predicted by beam theory, with deviation
> > between the two models correlated to shaft curvature (two-tailed p =
> > 0.03, r2 = 0.56). Under bending, FEA values of maximum principal
> > stress (σmax) and beam theory values differed on average by 12 per
> > cent (±4% s.e.), with deviation between the models significantly
> > correlated to cross-sectional asymmetry at midshaft (two-tailed p =
> > 0.02, r2 = 0.62). In torsion, assuming maximum stress values occurred
> > at the location of minimum cortical thickness brought beam theory and
> > FEA values closest in line, and in this case FEA values of τtorsion
> > were on average 14 per cent (±5% s.e.) higher than beam theory.
> > Therefore, FEA is the preferred modelling solution when estimates of
> > absolute diaphyseal stress are required, although values calculated by
> > beam theory for bending may be acceptable in some situations.
> >
> > ===
> >
> >
> > Science magazine Science Shots online news mentions how this study may
> > apply to dinosaurs:
> >
> > http://news.sciencemag.org/sciencenow/2012/11/scienceshot-curves-are-tough-on-.html
> >
> > "The strategy might be especially useful in reconstructing animals
> > that are extinct, such as dinosaurs. Overestimating the strength of a
> > dinosaur's leg bones by ignoring the effects of bone curvature may, in
> > turn, mean overestimating how much weight those bones could have
> > supported. Turns out, large dinos like Tyrannosaurus rex and the
> > lumbering sauropods might have been somewhat slimmer than previously
> > believed."