Post on 13-Feb-2020
A nonparametric modeling approach
of soft tissue deformation by ANFIS
Ivan Figueroa-Garcıa, Gisela Sanchez-Sosa, Ricardo Dıaz-Domınguez, Francisco Rodrıguez-Villagomez,
Joel C. Huegel Member, IEEE and Alejandro Garcıa-Gonzalez Member, IEEE
Abstract— This paper presents a nonparametric modelingapproach to soft tissue deformation utilizing an Adaptive NeuralFuzzy Inference System (ANFIS). The model is tested with realdata. In order to obtain a consistent set of experimental data,a variable-velocity electro-mechanical platform applies single-point force to deform a soft tissue sample. A Motion Capturesystem obtains the position of twenty markers on the surfaceof the sample tissue. With applied force and position data ofthe central marker as inputs and the position of the remainingmarkers as outputs, an ANFIS system was designed and trained.The trained estimator is tested with experimental data underartificial noise conditions. The estimation of the position for aparticular marker compared with the Motion Capture positiondata shows that the algorithm performs with less than 1% error.
I. INTRODUCTION
Given the importance of surgical and other medical proce-
dures, the development of training systems that simulate such
procedures is a dynamic research area. Realistic simulations
intend to enable surgeons and internists to increase practice
hours on programmable systems, thereby reducing trauma to
patients, easing the task of surgeons, and providing better
treatment at a lower cost. In order to achieve these goals,
computational simulators require tissue interaction modeling.
Artificial intelligence algorithms have been applied as
universal approximators of functions over a compact domain.
Particularly, well known artificial neural networks success-
fully carry out this task. In this sense, many approaches have
been followed to implement this type of algorithm as non-
parametric models of processes, especially when only partial
or uncertain information is available. This section presents a
brief introduction to the problem of tissue modeling and its
importance in the medical area, followed by a brief review
of the Artificial Neural Fuzzy Inference System (ANFIS)
algorithm, implemented to estimate the position of tissue
segments.
A. Tissue modeling approaches
Since mechanically correct models must be integrated
with the computer simulation to provide realistic simulations,
research efforts have been directed to representing and testing
this type of tissue characterizations.
I. Figueroa-Garcıa and Joel C. Huegel are with theBiomechatronics Chair, Tecnologico de Monterrey, Mexicoivan.figueroa@itesm.mx
G. Sanchez-Sosa and A. Garcıa-Gonzalez are with theBiomedical Eng. Department, Tecnologico de Monterrey, Mexicoalexgargo@itesm.mx
In 2000 Gorman et al. proposed a six tissue layered model
for lumbar puncture simulation with force feedback. Each
layer was modeled as a thin box and the resistance force
calculations varied depending upon the material in the layer
model, the depth of insertion, and the insertion angle of the
needle [1].
Instead of boxes representing different types of human
tissue, Kwon et al. used voxels calculated off line from a
CT scan. The model did not consider damping forces, hence
biomechanical accuracy was limited [2].
DiMaio et al. presented a puncture experiment with a
vision system and visual landmarks on a deformable phantom
tissue. They calculated a transformation matrix that described
3D deformations via a 2D video capture of visual landmarks
placed over the phantom and instrumented probes [3].
Okamura et al. presented an experimental procedure for
acquiring data from ex-vivo tissue to populate a force model.
In this approach, data were collected from bovine livers
using a 1 DOF robot equipped with a load cell and needle
attachment. CT imaging was used to identifying different
relative velocities between the needle and tissue. Needle
diameter and tip type effects were modeled using a silicone
rubber phantom [4].
Also in ex-vivo, Saraf et al. studied the phenomena of
soft human tissues in hydrostatic compression and simple
shear using a modified Kolsky bar technique. The dynamic
response of human tissues from stomach, heart, liver, and
lung was obtained and analyzed to provide measures of
dynamic bulk modulus and shear response for each tissue
type [5].
Conversely, to acquire in-vivo data from human tissue, Su
et al. aimed toward the characterization of the mechanical
behavior of human forearm soft tissue. They presented a
combined traditional indentation test with MRI techniques
to the quantification of the tissue material properties using
a finite element (FE) model of the skin-fat-muscle-bone
tissues. The simulation results did not actually reflect the
properties of real soft tissue due to the material model they
assigned [6].
Another approach to develop realistic tissue model for
interaction involves hybrid neuro-fuzzy systems. This type of
system can be used to simulate stiffness, viscosity and inertia.
Using a neural network structure, Radetzky et al. presented
local changes to the system like cuts or ruptures due the
interaction with a specific tool tip [7].
Abolhassani et al. , however, stated that current models
include only mass-spring and finite element solutions. Thus,
The Fourth IEEE RAS/EMBS International Conferenceon Biomedical Robotics and BiomechatronicsRoma, Italy. June 24-27, 2012
978-1-4577-1198-5/12/$26.00 ©2012 IEEE 118
by using multiprocessor systems and highly parallel infor-
mation structures such as artificial neural networks, they
achieved suitable modeling of complex tissue in real-time
simulations. Elastography and target displacement combined
with tool position measurements offer a validation technique
for complex models [8].
B. ANFIS structure as function approximation
The ANFIS (Artificial Neural Fuzzy Inference System) is
a hybrid system because it is the result of a combination of
two or more computational intelligence techniques. The aim
of combing the techniques is to complement their unique
characteristics for a more robust system. A neural network
provides learning adaptation and generalization, while fuzzy
logic can reason with imprecise information yet can not
extract the rules used to make decisions [9].
Fuzzy inference systems and multilayer neural networks
are universal function approximators. Therefore, a multilayer
neural network can be approximated using a fuzzy inference
system. For a system to be considered as a universal appro-
ximator it must satisfy the Stone-Weierstrass theorem [10].
The use of intelligent hybrid systems grows rapidly with
successful application in many areas including process con-
trol, engineering design, financial trading, credit evaluation,
medical diagnosis, and cognitive simulation.
The computational process for fuzzy neural systems starts
with the development of a fuzzy neuron, which is a com-
puter structure based on biological neuronal morphologies.
Then, learning mechanisms are implemented by modeling
the synaptic connectors which incorporates fuzziness into
neural networks. Finally, a leading algorithm is developed
for adjusting the synaptic weights. Possible models of fuzzy
neural systems are reported by Fuller et al. [11].
In ANFIS, neural network structures tune membership
functions of fuzzy systems to be employed as decision-
making systems. Although fuzzy logic can encode expert
knowledge directly using rules with linguistic labels, it usu-
ally requires considerable time to design and tune the mem-
bership function which quantitatively defines these linguistic
labels. Neural network learning techniques can automate this
process and substantially reduce development time and cost
while improving performance [11].
This work proposes the use of a hybrid neural fuzzy
system for estimating the displacement of an arbitrary tissue
point. The remainder of the paper is organized as follows:
Section II presents the development of the experimental plat-
form, the Motion Capture set up, and the ANFIS general de-
sign. Section III includes the characterization of the electro-
mechanical platform force sensor, the acquired data of the
Motion Capture system and the result of the ANFIS training
and testing processes for one arbitrary marker estimation.
II. METHODOLOGY
A. Practical Platform Design
In order to have repeatable data generation from tissue
deformation, a test platform was designed and created. This
platform consists of a crank-slider mechanism mounted on a
18 mm thick acrylic base. The mechanism design is shown in
Fig. 1. The mechanism construction restricts the movement
of p2 to the vertical direction as shown in eq 2.
Fig. 1. Crank-slider mechanism for moving the tool tip vertically.
The motor that moves the mechanism is a Pittman DC
Servo Gearmotor GM9236S025 with a 500 pulse per revo-
lution optical-incremental encoder. The mechanism forward
kinematics are given by:
P1 = l1cos(α)x+ l1sin(α)y (1)
P2 = 0x+[l2sin(β )+ l1sin(α)] y (2)
β = cos−1
[
l1cos(α)
l2
]
(3)
where l1 = 0.07m, l2 = 0.2m, and α is the motor encoder
measurement.
The instrumented tool has on the back of the tip holder
a force sensor, the FlexiForceT M model 1-617. This sensor
has the following features: Sensor diameter: 9.53mm, sensor
force range: from 0 to 110 N, and a 200 KHz bandwidth.
The sensor consists of piezo-resistive ink between two plastic
layers. When force is applied by the rigid material of the tool
tip to the whole sensor area, a force measurement becomes
available.
Since the sensor varies in resistance when force is ap-
plied, a variable-gain inverting amplifier circuit is used, as
recommended by the supplier with a feedback resistance
RF = 10MΩ to convert the force on the sensor area to a
voltage signal.
On the top of the acrylic base a medium thickness (
0.1524 mm) rubber dental dam is placed with an area of
[152.4 x 152.4] mm. This membrane serving, as a phantom
tissue, permits measurements for platform validation. The
dental dam is secured by twin aluminum plates on opposite
sides. The plates are fastened by screws to the test platform
acrylic base. The mechanism deforms the dam from beneath;
therefore, position of the tool tip and force measurements can
be made. Furthermore, the top of the dam remains clear to
measure the deformation through optical means and, in this
particular work, with Motion Capture equipment.
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B. Motion Capture
The electro-mechanical test platform is taken to the Mo-
tion Capture (MoCap) laboratory equipped with ViconT M
cameras and BladeT M software in order to make displace-
ment measurements through optical markers. Small reflective
markers (5 mm diameter) normally used for facial expression
capture are adhered with double-sided tape on the top side of
the dam. Fig 2 shows a diagram of the marker placement over
the dam. A set of eight infrared stroboscopic video cameras
are placed surrounding the test platform. The first step is to
properly calibrate the cameras to ensure all cameras view all
markers. This process is done with five markers as depicted
in Fig. 3.
The cameras have an infrared light emitter source that
markers reflect. The camera captures this reflection and the
center of the marker is calculated via software. Once the
calibration process is done, each camera can recognize the
markers separately and a reference coordinate system is set.
The test platform is removed from the center of the cameras
and a special triangular tool is then placed at the center of
the recording area. When the camera software defines the
coordinate system and reference frame through the triangular
tool, the tool is removed and replaced by the test platform.
Fig. 2. Placement diagram of the reflective motion capture markers overthe dental dam used as phantom tissue.
Fig. 3. Calibration of 8 cameras before recording the test platform.
In the MoCap room, the platform is covered with non-
reflective materials to avoid false measurements as shown
in Fig. 4. The camera arrangement described in this section
can be seen in Fig. 5. With this experiment environment,
data was collected through the MoCap software.
Fig. 4. This figure shows the platform covered by MoCap actor clothingused for human movement and marker positioning on deformable dentaldam for movement capturing.
Fig. 5. Experiment setup at MoCap Lab with 8 cameras surrounding thetest platform.
C. ANFIS Design
There exist many published papers presenting the ANFIS
general structure [12], [13]. Based on the assumption that
a minimal set of inputs in an ANFIS structure is two, the
governing rule set with two IF-THEN rule is as follows:
RULE 1 : I f x is A1 and y is B1 then f1 = p1x+q1y+r1 (4)
RULE 2 : I f x is A2 and y is B2 then f2 = p2x+q2y+r2 (5)
where x and y are inputs partitioned in Ai and Bi subsets (i
= 1, 2). This is a Sugeno type fuzzy system, which means
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Fig. 6. This figure shows the ANFIS model structure with two inputs, oneoutput and five layers.
the outputs for each one of the rules is a linear combination
of the input values. The structure is shown in Fig. 6.
The node functions in the same layer belong to the same
function family as described:
Layer 1: every node in this layer is a square node
(see Fig. 6) with a node function:
O1i = ‖µAi
(x)‖ (6)
where x is the input to node i, O is the membership grade of
a fuzzy set Ai and it specifies the degree to which the given
input x satisfies the quantifier A, and µ is the triangular
membership function given by:
µAi(x) = exp
[
−
(
x− ci
ai
)2]
(7)
where both ai and ci is the parameter set. Parameters in this
layer are referred to as premise parameters.
Layer 2: every node in this layer is a circle node,
labeled M in Fig. 6, whose output is the product of all
incoming inputs:
Wi = µAi(x)∗µBi(x), i = 1,2 (8)
Each node output represents the firing strength of a rule.
Layer 3:every node labeled as encircled N in Fig. 6.
The i− th node calculates the ratio of the i-th rule’s firing
strength to the sum of all rules firing strengths:
Wi =Wi
W1 +W2, i = 1,2 (9)
Outputs of this layer will be called normalized firing
strengths.
Layer 4: including adaptive nodes and is given as:
O41 =Wi fi =Wi(pix+qiy+ ri) (10)
where Wi is the output of layer 3 and pi, qi, ri is the
parameter set. Parameters in this layer will be referred to as
the consequent parameters.
Layer 5: includes a single labeled encircled E node
(see Fig. 6) with the function of summation.
Overall out put = O51 = ∑
i
Wi fi =
∑i
Wi fi
∑i
Wi
(11)
Eq. 11 represents the nonlinear mapping between inputs
and output, it means this is the nonparametric model. The
merit of the ANFIS is that it practices a hybrid learning
process for the estimation of the premise and consequent
parameters [13].
For this work, input x is the force registered in marker 1
(m1) and the input y is the position in vertical axis. We have
selected an input partitioned into two subsets and represented
by triangular membership functions for each input. The
conclusion part of eq. 4 is the estimated position of the
neighboring markers of the central marker m1. It means the
goal is to estimate the position of the i-th marker mi from
available information of m1.
The learning algorithm is selected as a hybrid method
that uses back propagation for parameter associated with an
input membership function and a least square estimation for
parameters associated with output membership. All data were
processed in Matlab’s Simulink and ANFIS toolboxes.
III. RESULTS
The results are presented in three subsections where sub-
section III-A presents the electro-mechanical test platform
built, subsection III-B presents the acquired data through the
MoCap system and subsection III-C presents the results of
trained inference system performance.
A. Test Platform
The built platform is shown in Fig. 7. Both the
FlexiForceT M sensor and motor encoder are connected to a
Quanser Q8-USB data acquisition card that enables Matlab
Simulink to save the measured data into workspace variables.
Fig. 7. Testing platform: mechanical system is at the left side slightlydeforming the rubber dam.
The characterization of the FlexiForceT M sensor was
made by placing known weights on the sensor area and
measuring the sensor’s output voltage signal given by the
drive circuit ranging from 0 to 12V. Twenty weights were
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measured and each weight was measured three times. A
force/voltage linear relationship was found in the force range
of 0 to 10N. This linear relationship, shown in eq. 12, has a
coefficient of determination R2 = 0.99.
Force = 0.2382∗ (Voltage)+0.0544 (12)
The response of force sensor is depicted in Fig. 8 and
exhibits high sensibility to changes, being the maximum
registered force in this experiment 2.9N.
Fig. 8. Force measured by tool tip and force sensor.
B. Motion Capture data
Minumum variations achieved are on the order of
1x10−4mm.
Fig. 9 shows the followed trajectories along vertical axis
for some of the twenty markers, MoCap provides the infor-
mation of markers position at any of three axes. Still the
force is applied to the phantom tissue only in the vertical
axis, thus having information mainly in this axis. We have
limited data analysis of the marker movement in only the
vertical direction because it the electro-mechanical platform
deforms the dam in only this axis. Marker m1 presents the
higher amplitude with a maximum peak of 41.5 mm. The
MoCap system and the electro-mechanical platform are not
synchronized. Nevertheless, the video capture starts before
the platform starts moving and the marker motion is an easily
detected event in the data as it occurs after motor encoder
pulses start.
This data was introduced to the ANFIS identifier structure.
C. Trajectories estimation by ANFIS
As previously explained, raw data of the markers position
was used for training of the ANFIS. This work’s goal is
to reconstruct the trajectory of each marker on the surface
considering available information (position and force) of the
central marker m1 (marker distribution can be seen in Fig.
2). This means, reconstructing the trajectory for the closest
markers m2, m3, m4, m5, m6. For the second layer of
markers m7, m8, m9, m10, the information of the central
markers and the information obtained for the first estimators
m2 to m6 is added.
The selected data for presenting the algorithm’s function
is taken from marker m4. Data for the training stage is shown
Fig. 9. Veritical axis position variation in markers. It is visible that centralmarker m1 is higher than the others with a maximum peak of 0.0415m
in Fig. 10. Considering this dataset and samples at the same
time of position of m4, we obtained the surface decision of
our ANFIS estimator (Fig. 13). As can be appreciated this
is a nonlinear mapping between force and position of m1
and position of m4. Complete training was obtained after
30 epochs with and error of 0.001, by a hybrid learning
algorithm.
Fig. 10. Training data set. Force and position of m1.
In order to test our trained ANFIS, experimental data
of force and position for marker 1 was used, signals were
corrupted with cuasi-white additive noise, with a magnitude
of 3% of the original signal. Fig. 11 shows the input signals
after manipulation. The comparison between estimated posi-
tion for m4 and real position registered by MoCap system,
is presented in Fig. 12, where a 1% error was calculated
due to noise. This error percentage does not mean that the
ANFIS fails 1 out of a hundred times to estimate the mi
position. It means that the trained system converges with
a 1% difference despite the noise presence. Similar results
were obtained for markers at the first layer. Once the training
process has concluded, ANFIS can be used as a mathematical
nonparametric model of markers, specifically for the position
variable. A possible extension in the number of degrees of
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freedom can be done by a similar approach, obtaining some
structure called Multi-ANFIS or MANFIS.
Fig. 11. Set data to test the trained ANFIS: Force sensed by the tool tipand position of m1 are corrupted with white noise.
Fig. 12. The real position registered by the MoCap system and overlaidon the estimated position data calculated by the ANFIS under artificiallynoisy conditions for m4.
IV. CONCLUSIONS AND FUTURE WORK
The constructed platform allows varied velocity conditions
in order to estimate different viscoelastic materials. This is
the main behavior model in human and animal tissues. Mo-
tion Capture systems provides excellent precision and reso-
lution for small variations in the membrane. Furthermore, the
experimental set up is fast and provides reliable information.
Due to the satisfactory performance of the trained ANFIS for
estimating trajectories of markers based on a central position
and force measurement, soft tissue deformation estimation is
possible with this procedure. Since all the markers are placed
in the same phantom tissue, the general assumption is that
there is a mechanical relation between marker measurements.
The nonparametric modeling of the ANFIS allows that local
properties of single point measurements can be used to model
other points, constructing more complex models without
losing the influence of any of the points.
Fig. 13. Mapping between position and force inputs in m1 to estimatedposition of m4 after the ANFIS trained process. The surface shows a non-linear relation.
In further work, complete trajectories (x, y and z) should
be considered in a Hierarchichal Multi ANFIS structure. Ve-
locity variation should be done in order to study behavior of
real human tissue. Different geometry tool tips for measuring
irregular deformations should be implemented.
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