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Challenges for computational
biomechanics for medicine
Karol Miller
Visiting Professor. University of Luxembourg
Intelligent Systems for Medicine Lab.
The University of Western Australia
35 Stirling Highway
Crawley WA 6009, AUSTRALIA
Email: karol.miller@uwa.edu.au
http://www.mech.uwa.edu.au/~kmiller
http://school.mech.uwa.edu.au/ISML/
Institute of Mechanics and
Advanced Materials
Karol Miller
Perth
The University of Western Australia
Karol Miller
Russell Taylor’s prophecy:
The market for scientific computations in medicine
would be as large as in engineering by 2020
Computer-Integrated Surgery (CIS) systems will
improve clinical outcomes and the efficiency of
health care delivery. CIS systems will have a similar
impact on surgery to that long since realised in
Computer-Aided Design (CAD) and ComputerIntegrated Manufacturing (CIM).
Karol Miller
Oden, Belytschko, Babuska, Hughes:
One of the greatest challenges for mechanists is
to extend the success of computational
mechanics to fields outside traditional
engineering, in particular to biology, biomedical
sciences, and medicine
Karol Miller
GENG4405
Karol Miller
5
Our main motivation - image-guided
Image of brain tumour (green)
neurosurgery
is superimposed on patient as
an aid to surgical planning and
navigation
Courtesy of SPL, Harvard
Karol Miller
The brain is
complicated…
But we only
wish to
compute
displacements
Courtesy
Prof. Wies Nowinski,
A-Star, Singapore
Karol Miller
Gargantuan challenges:
1. For biomechanical computations to be practical in a clinical
environment, computational grids must be obtained
from standard diagnostic medical images automatically
and rapidly.
2. Real-time computations on commodity hardware
3. Real-time simulation of cutting, damage and
propagation of discontinuities
4. Mathematical formulations that are weakly sensitive to
uncertainties in mechanical properties of tissues are
necessary.
Karol Miller
Gargantuan challenges:
1. For biomechanical computations to be practical in a clinical
environment, computational grids must be obtained
from standard diagnostic medical images
automatically and rapidly.
The current practice of patient-specific model generation
involves image segmentation and finite element meshing.
Both present themselves as formidable problems that are very
difficult to automate. Entirely novel approaches are needed.
Karol Miller
Challenge 1: efficient generation of
patient-specific computational grids from medical
images
Many days of tedious work
Joldes et al. (2009), MICCAI 2009, Part II, LNCS 5762, pp. 300-307
Karol Miller
Patient-Specific Finite
Element Meshes
Joldes et al. (2009), MICCAI 2009,
Part II, LNCS 5762, pp. 300-307
c)
d)
e)
Karol Miller
Neuroimage as a computational model?
[Pa]
6000
Tumour
Brain
Ventricle
3000
0
2D MRI slice
“Hard” segmentation
Assignment of
mechanical
properties based
on statistical
tissue classification
Karol Miller
Comparison between FE model and fuzzy mesh-free model constructed respectively from
segmentation and fuzzy tissue classification.
(a) T2 MRI of the brain with the tumour and ventricles present, notice that no clear boundaries can be easily defined,
especially for the tumour, (b) finite element model of ventricles generated from segmentation, (c) finite element model of the
tumour generated from segmentation, (d) fuzzy tissue classification of ventricle, (e) fuzzy tissue classification of tumour,
(f) fuzzy mesh-free
model of ventricle and
(g) fuzzy mesh-free
model of tumour, green
dots represent nodes
while grey grids
represent uniform
background integration
grids. Notice that no
specific tissue class is
defined in the domain.
Material properties are
assigned directly to the
integration points based
on fuzzy classification
results.
Zhang et al. (2013), IJNMBE 29(2), pp. 293–308
Karol Miller
3D patient-specific meshless computational
grid of the brain
Green – parenchyma
Red – ventricles
Blue - tumour
Miller et al. (2012), J. Biomech. 45(15), pp. 2698-2701
Karol Miller
Evaluation of accuracy for
three cases
Left column: Finite Element
Models, with parenchyma, tumour
(red) and ventricle (blue) modelled
separately.
Middle column: Fuzzy Mesh-free
Model without explicitly separating
the tumour and ventricles, fuzzy
tissue classifications of tumour
(red), and ventricle (blue) are
shown as cloud superimposed on
the image; Nodes are shown as
green dots.
Right column: Difference of the
simulation results (computed
deformation field) from the two
models over the whole problem
domain [mm].
Karol Miller
The 'double doughnut' General Electric 1.5T open magnet at
the Brigham and Women's Hospital, Boston seen end-on
(left) and from the side (right), recently replaced by AMIGO
Karol Miller
Whole-body meshless model for CT registration
Displacements of the order of 10 cm
source image
target image
Whole-body meshless model.
Tissue properties are assigned
automatically to integration points,
based on fuzzy classification
Li et. al (2014) Medical Image Analysis
Karol Miller
Evaluation of registration accuracy
The dotted line and dashed line (they are nearly overlapping) represent lung contours extracted from
images registered using deformations predicted by means of the meshless model used in this study
and previously validated finite element model. The solid line is the lung contour extracted from the
target image.
Li et. al (2014) Medical Image Analysis
Karol Miller
Gargantuan challenges:
2. In surgical simulation interactive (haptic) rates (i.e. at least
500 Hz) are necessary for force and tactile feedback delivery.
In intra-operative image registration one needs to provide a
surgeon with updated images in less than 40 seconds.
To achieve these, real-time computational speeds for
highly non-linear models with at least 100,000 degrees of
freedom must be achieved on commodity computing
hardware.
Joldes et al. (2010) Computer methods in applied mechanics and engineering
199 (49), 3305-3314
Karol Miller
Graphics Processing Unit
http://www.gpucomputing.net/
Computational Biomechanics Community http://gpucomputing.net/?q=node/218
1536 cores
Karol Miller
What does GPU like?
• Problems that can be expressed as data-parallel computations –
the same program is executed on many data elements in parallel
What does GPU not like?
•Communications (between cores and especially with CPU and
external devices)
Explicit algorithms are therefore preferable
Karol Miller
Amazing performance!
Comparison of computational times when using GPU and CPU
Deformation
No. of
Computation time (s)
elements Abaqus CPU
GPU
static
Compression
GPU Speed up (x)
Abaqus
static
CPU
3732
57.7
1.76
2120
32.7
1087
69.1
2.37
458.6
29.1
48000
Extension
Karol Miller
Table 1: Structure of the brain meshes used
Mesh
Number
of
nodes
Number of elements
Hexa
Linear
ANP
tetras
tetras
Skull
Total
Number
elements of nodes
Original 12693
10596
4831
1398
16825
1993
3960
Refined
84768
32439
8085
125292
7945
15840
95669
Number
of
triangles
Table 2: Computation times for brain shift simulation
Mesh
No. of steps required for
convergence (δ = 10E-4)
Run time for 3000
steps (s)
CPU
GPU
CPU
GPU
Original
1887
2103
79.7
Refined
3120
3091
543.4
3.54
19.95
Speed up
(x)
22.5
27.2
Wittek et al. (2010) Progress in Biophysics and Molecular Biology, 103, 292-303
In comparison Courtecuisse et al. (2014) Medical Image Analysis 18 394–410
has a brain model with 1734 nodes…
Karol Miller
Head impact simulation (time-accurate)
Computations conducted on a PC with a Tesla C1060
GPU having 4 GB of RAM and 240 cores.
Karol Miller
• nodes: 1101559
• elements: 1061799 - hexas
• Computation time: 40000 steps in 15 minutes
Karol Miller
Broader impact on the practice
of engineering computations

Using our algorithms on GPU’s can potentially allow computing
large, non-linear problems between 500 and 5000 times faster
than using commercial software on standard computers.

Close-to-real-time interactive use of FEM computations for design
seems to be within reach. And this can be achieved on computing
hardware costing ca. $10000!

General large nonlinear engineering computations that are
currently most often subcontracted to specialized consultancies will
be possible on desktop computers (such as Tesla
Supercomputer).

Design engineers will be able to run simulations of their design
concepts interactively, greatly increasing the number of cases they
are able to consider.
Karol Miller
Gargantuan challenges:
3. Surgical manipulation involves not only large deformations
of soft tissues but also cutting and (often unintentional)
damage.
Modelling and real-time simulation of cutting, damage and
propagation of discontinuities remains an unsolved and
very challenging problem of computational biomechanics.
But some progress reported in
Courtecuisse et al. (2014) Medical Image Analysis 18 394–410
Jin et al. (2014) Computer Methods in Biomechanics and Biomedical Engineering.
17(7) 800-811
Karol Miller
Gargantuan challenges:
4. Human soft tissues are highly variable, and despite recent
progress in magnetic resonance (MR) and ultrasound
elastography, their in-vivo properties are difficult to obtain.
Therefore mathematical formulations that are weakly
sensitive to uncertainties in mechanical properties of
tissues are necessary.
Some progress reported in
Miller and Lu (2013) Journal of the Mechanical Behavior of Biomedical Materials.
27, 154-166
Karol Miller
From
http://euromech534.emse.fr/
To this end,ttp://euromech534.emse.fr/
it becomes a common practice to combine video based full-field
measurements of the displacements experienced by tissue samples in vitro with a
custom inverse method to infer, using nonlinear regression, the best-fit material
parameters. Similar approaches also exists for characterizing tissues in vivo where
advanced medical imaging can provide precise measurements of tissue deformation
under different modes of action and inverse methodologies are used to derive material
properties from those data.
But perhaps we can obtain useful, patient-specific
results WITHOUT the knowledge of patient-specific
mechanical properties of tissues?
Karol Miller
Simplistic, homogeneous linear-elastic case
If our loading is through the enforced motion of boundary conditions (dimension
[mm]) and our result is a displacement field (in [mm]), this result cannot depend on a
stress parameter (dimension [Pa]).
The result may still depend on Poisson’s ratio, but not for almost incompressible
materials.
This suggests that if we are able to formulate our biomechanical investigations as
Dirichlet problems (i.e. problems driven by enforced motion of boundaries) we
can expect to obtain meaningful patient-specific results without knowledge of
patient-specific properties of tissues.
Karol Miller
Extension of cylindrical samples (Miller, J. Biomech.
2001) – deformed shape does not depend on mechanical
properties
Z/H
f(Z)
Analogical result for
compression (Miller, J.
Biomech. 2005)
Sides of deformed samples for Neo-Hookean and Extreme Mooney material models
for extensions h/H=1.1, 1.2, 1.3
Karol Miller
Image registration: results
Center of Gravity Displacements (mm)
Ventricles
Tumor
Material Model/
Analysis Type
∆X
∆Y
∆Z
∆X
∆Y
∆Z
MRI Determined
3.4
0.2
1.7
5.5
-0.2
1.7
Hyperviscoelastic material/
Geometrically non-linear
analysis
2.6
-0.1
2.1
5.2
-0.4
2.7
Hyperelastic material/
Geometrically non-linear
analysis
2.6
-0.1
2.1
5.2
-0.4
2.7
Linear elastic material/
Geometrically non-linear
analysis
2.6
-0.1
2.1
5.0
-0.5
2.7
Linear elastic material/
Linear analysis
0.7
0.2
1.9
3.7
-0.3
2.6
32
Karol Miller
CONCLUSIONS - the challenges awaiting us:
1. For biomechanical computations to be practical in a clinical
environment, computational grids must be obtained from standard
diagnostic medical images automatically and rapidly -> possible
solution: meshless solution methods with fuzzy tissue
classification (but perhaps something like cutFEM can be better but as
yet no demonstration for realistic nonlinear problems exists…)
2. Real-time computations on commodity hardware -> possible solution:
use GPUs
3. Real-time simulation of cutting, damage and propagation of
discontinuities -> ???
4. Mathematical formulations that are weakly sensitive to uncertainties in
mechanical properties of tissues are necessary -> reformulate as
Dirichlet problems?
Karol Miller
Acknowledgements:
FNR, University of
Luxembourg and
Stephane!
Prof. Ron Kikinis (Harvard)
Prof. Simon Warfield (Harvard)
Prof. Kiyoyuki Chinzei (AIST)
Dr Toshikatsu Washio (AIST)
Prof. Adam Wittek
(ISML, UWA)
A/Prof. Grand Joldes
(ISML, UWA)
and many very talented
research students
Funding: ARC, NHMRC,
THANK YOU
NIH, NVIDIA,
Leverhulme Trust
Karol Miller
Look for it in the
bookstore near you…
Karol Miller
And these as well…
Karol Miller