International audienceNon-rigid registration is often used for 3D representations during surgical procedures. It needs to provide good precision in order to guide the surgeon properly. We propose here a method that allows the computation of a local upper bound of the registration confidence over the whole organ volume. Using a bio-mechanical model, we apply tearing forces over the whole organ to compute the upper bound of the degrees of freedom left by the registrations constraints. Confrontation of our method with experimental data shows promising results to estimate the registration confidence. Indeed, the computed maximum error appears to be a real upper bound

Baksic, Paul

Bayle, Bernard

Chabanas, Matthieu

Courtecuisse, Hadrien

English

Archive Ouverte en Sciences de l'Information et de la Communication

HAL Id: hal-02238974
https://hal.archives-ouvertes.fr/hal-02238974
Submitted on 1 Aug 2019
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FEM-based confidence assessment of non-rigid
registration
Paul Baksic, Hadrien Courtecuisse, Matthieu Chabanas, Bernard Bayle
To cite this version:
Paul Baksic, Hadrien Courtecuisse, Matthieu Chabanas, Bernard Bayle. FEM-based confidence as-
sessment of non-rigid registration. Surgetica 2019, 2019, Rennes, France. ￿hal-02238974￿
P. BAKSIC et al. Surgetica 2019 Rennes, France – 17 - 18 June
FEM-based confidence
assessment of non-rigid
registration
Paul BAKSIC1,2, Hadrien COURTECUISSE1, Matthieu CHABANAS2 and Bernard
BAYLE1
1 University of Strasbourg, CNRS, AVR-ICube, F67000 Strasbourg France
2 Univ. Grenoble Alpes, CNRS, Grenoble INP, TIMC-IMAG, F38000 Grenoble France
Contact: p.baksic@unistra.fr
N
on-rigid registration is often used for
3D representations during surgical proce-
dures. It needs to provide good precision
in order to guide the surgeon properly. We pro-
pose here a method that allows the computation
of a local upper bound of the registration confi-
dence over the whole organ volume. Using a bio-
mechanical model, we apply tearing forces over
the whole organ to compute the upper bound
of the degrees of freedom left by the registra-
tions constraints. Confrontation of our method
with experimental data shows promising results
to estimate the registration confidence. Indeed,
the computed maximum error appears to be a
real upper bound.
1 Introduction
While performing a surgery, the surgeon’s goal is to
minimize the risk for the patient. For this purpose,
minimally invasive surgery has been favored over tra-
ditional open surgery, especially in abdominal surgery.
Such procedures can be very challenging for the prac-
titioner to perform. It is mainly due to the fact that
they don’t see what they are doing through their own
eyes. Views are often showed through a screen and
captured either with an endoscope, Ultrasound probe
or other devices. This is challenging because it forces
the surgeon to mentally map what he sees to what he
is doing. A way to help surgeons during the surgery is
to add virtual information on the screen, for instance
the 3D volume of a tumor into a liver. This should
provide information allowing him to resect a minimum
of healthy tissues.
To reach this objective, one first needs to make a
registration of the organ that the surgeon is seeing
through the measurement device. Combining a bio-
mechanical model to data extracted from intraoperative
images have yielded good results. This can be done
either by using some points extracted from the surface
[1, 2], the whole surface [3] or information on the organ
volume extracted from ultrasounds [4]. Yet all the
above methods are subject to errors. Through this
method, we propose a tool providing an estimation of
the confidence of a model-based registration method.
Figure 1: High confidence (low mobility) areas are colored
with shorter wavelength (blue). If the degree of
confidence is lower than a threshold, the elements
become transparent.
2 Method
Our method takes as input the Finite Element mesh
of the organ in the registered state. The registration
can be performed by one of the method cited above
or any method combining a biomechanical model with
measured data. The method consists on evaluating the
maximum mobility of the model at each point of its
mesh, the confidence being high when the mobility of
the point is low. The main assumption of the paper
Page 1 of 3
P. BAKSIC et al. Surgetica 2019 Rennes, France – 17 - 18 June
is that the deformation generated by the surgeon dur-
ing the procedure does not damage tissues. Therefore,
the maximum mobility is computed by applying an
upper bound stress taken from the literature, known
to cause irreversible deformations to the organ while
satisfying the registration constraints into the simula-
tion. This stress is successively applied along multiple
directions on the model, in order to test each degree
of freedom of the organ. Those directions are given
by D = (x,−x,y,−y, z,−z). The computation of the
mobility c at each point i is formalized in the following
equation :
ci = max
f
(||qi − C(d× f × k)||) with d ∈ D (1)
Where C is a non linear function providing the positions
of the model at static equilibrium after the application
the volume force f multiplied by the surrounding vol-
ume k. The rest positions of the model are considered
to be the positions provided by the registration method.
This may lead to more mobility of the model because of
the lack of internal stress which usually rigidify the tis-
sue. This way, the computed displacement remains an
upper bound. The confidence map can be represented
as shown on the figure 1.
Figure 2: Volume of a lamb liver with the outer markers
in red and the inner ones in green.
3 Confrontation to real data
Our method was tested on a data set of an ex-vivo liver
of a lamb. External markers were put on the surface,
which were then used to perform the registration along
with internal markers that were used to evaluate the
accuracy of the registration method. Then the volumes
of the liver and the markers were segmented from CT-
Scans in five different positions of the lamb liver.
Cross-registrations were performed between the dif-
ferent positions of the liver using external markers. We
used a linear elastic model of the deformation along
with a corotational finite element formulation [5] of the
problem on tetrahedron elements. This formulation
shows good results and gives good approximations of
the non-linearity of the deformation while keeping low
time complexity. The liver finite element model pa-
rameters are given by a Young modulus of 6kPa and
a Poisson ration of 0.499 as found in the literature for
healthy livers [8]. After the registrations, the distance
between internal markers segmented from the CT im-
ages and the one provided by the model were considered
as ground truth values of the registrations’ accuracy.
Our method was then applied on each configuration
of the liver, in order to compute the theoretical upper
bound of mobility. Given the material properties of
the model described above, the force f used in the
equation 1 is parameterized to reach 30% of strain. In-
deed, despite the stress leading to tissue tearing vary
amongst patients, this value is, according to the litera-
ture [6, 7], identified as an upper-bound value leading
to irreversible deformations of the tissue.
4 Results
The mechanical study performed by our method takes
into account the complex coupling between constraints
provided by image data. Indeed, as shown in figure 1,
the resulting confidence map provided by our method is
not directly related to the distance with external mark-
ers. Instead, it provides complex shapes that cannot be
generated with simple geometric primitives. Figure 3
shows that our method predicted 96.6% of the time a
real upper bound of the registration accuracy.
0 5 10 15 20 25 30
0
10
20
30
Predicted error (mm)
M
ea
su
re
d
er
ro
r
(m
m
)
Deformation 1
Deformation 2
Deformation 3
Deformation 4
Deformation 5
Figure 3: Predicted error given by our method with respect
to the measured error (given by the cross registra-
tions) at each inner marker. Each label stands
for a different target configuration.
5 Conclusion
We proposed a method allowing to evaluate the regis-
tration accuracy of internal structures. The method
provides an upper bound uncertainty of positions of
a biomechanical model, that can be used to discrimi-
nate and display only the reliable parts of the model
in the augmented view. Future works concern addi-
tional validation study with more data and registration
methods.
Page 2 of 3
P. BAKSIC et al. Surgetica 2019 Rennes, France – 17 - 18 June
References
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Page 3 of 3


FEM-based confidence assessment of non-rigid registration

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FEM-based confidence assessment of non-rigid registration

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