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

121

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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