Application of a Neurofuzzy System to Identification of Some Classes of Soft Tissues Utilizing Experimental Data

Application of a Neurofuzzy System to Identification of Some Classes of Soft Tissues Utilizing Experimental Data M. A. Shirzi, A. A. Nikooyan*, M. R. Hairi Yazdi, A. A. Zadpoor, and C. Lucas

Abstract -In this paper, a combined neurofuzzy system is developed for identification of different classes of soft tissues and

for exploitation of their mechanical properties by using the experimental data. These data were resulted from forcedisplacement curves of soft tissues in uniaxial compression test. The developed system is able to identify a particular tissue among

the others. By utilization of fuzzy logic, similarity of experimental data to normal or average state can be identified. The similarity can be used as a criterion for assessment of health of tissues. A

code was developed to study performance and convergence of the

network. Results of the simulation showed that the network converges with a high velocity and is capable of identifying different types of soft tissues with a high degree of accuracy.

cancered soft tissues is normally increased due to increment of

density of the cells. The stress-strain and force-displacement curves of soft tissues differ in loading and unloading cycles owing to nonlinear . .

.

coelicity (eeae.g. [][ 1]) Duedto pene oflte complicated behaviors, one can hardly give a complete

description of mechanical behavior of the materials. Specifically, classic mathematical methods can hardly be successful. .

In the other hand

artificial

neural networks

(ANN)

are

used in nonlinear system identification (see e.g. [12]14.widely [14]). Due to nonlinear viscoelasticity of soft tissues, the idea

Keywords - Neurofuzzy, Soft Tissue, System Identification I. INTRODUCTION S OFT tissues show a nonlinear viscoelastic behavior. Exploiting nonlinear properties of soft tissues has always been a challenge of tissue engineering community. During past decades, different authors have presented a variety of constitutive equations to describe behavior of soft tissues (see e.g. [1]-[5]). However, there is no unique equation accounting for all aspects of nonlinearity of these materials. Prediction of nonlinear viscoelastic properties of soft tissues is crucial in development of models of them. The models are very important in robotic surgery and haptic processes. In pathological diagnosis, one tries to discover changes in properties of soft tissues when a special disease is happened. One of the most important parameters affected by diseases is the elasticity modulus. For example elasticity modulus of M. A. Shirzi is with Department of Mechanical Engineering, University of ). Tehran, Karegar Ave., Tehran, Iran (e-mail: [email protected] A. A. Nikooyan, is with Department of Biomedical Engineering, Amirkabir University of Technology, Hafez Ave., Tehran 15914, Iran (*corresponding

author to provide phone: +98-21-88258497; fax: +98-21-88072500; e-mail:

aasadi(0bme .aut.ac.i1r)[email protected]).

M. R. Hairi Yazdi is with Department of Mechanical Engineering, University of Tehran, Karegar Ave., Tehran, Iran (email: [email protected]) A. A. Zadpoor is with Department of Biomedical Engineering, Amirkabir University of Technology, Hafez Ave., Tehran 15914, Iran (e-mail: azadpour@ bme.aut.ac.ir).

C. Lucas is with Department of Computer and Electrical Engineering, University of Tehran, Karegar Ave., Tehran, Iran (e-mail: [email protected]).

I1-4244-0457-6/06/$20.OO ©2006 IEEE

n

of using ANNs for prediction of the highly nonlinear behavior of the materials come to mind. In addition, Fuzzy Logic is capable of describing nondeterministic phenomenon. Combination of ANN and fuzzy logic (neurofuzzy) is an efficient way for recognition and prediction nonlinear behavior of soft tissues. Indeed, neural networks, fuzzy systems, and combinations of these two have been widely used for cancer diagnosis of different organs of human body (see e.g. [15][19]). The cancer diagnosis techniques are usually haptic and too sensitive to sudden changes in properties of the soft tissues. Moreover, a progressive surgery method namely endoscopic surgery has been developed in the recent years (see e.g. [20][23]). Current trend of the field is to use smart surgery tools for prediction of the force that should be applied to a particular

tissue.

In this paper, we have developed a combined neurofuzzy system which can learn the empirical data resulted from forcedisplacement curves of soft tissues and is capable of recognizing new curves and describing their properties. In of health of soft tissues. addition, the system systemcanis predict designe abedt level identif alparticular tissue The designed system iS able to identify a particular tissue among the others. This is of great degree of importance in invasive robotic surgery. Furthermore, similarity of test data of

~~~~~anew tissue to the normal or average state can be identified by using fuzzy logic. Therefore,

one can

evaluate healthiness of

tissues provided that sufficiently accurate and reliable data of normal state is in hand.

II. METHODOLGY

The experimental data from force-displacement curves of both loading and unloading cycles have been used in the study. The data are resulted from uniaxial compression tests carried out on five different tissues. The tests are performed either by the authors or other investigators. The data come from forcedisplacement curves in both loading and unloading cycles of test of the human breast fibrograndular tissue [6], canine kidney tissue [7], human heel pad tissue [8], pig liver tissue [9] and [10], and human brain tissue [11] selected to train the networks. However, it should be noted that the designed networks are potentially capable of identifying ten different types of soft tissues. However, according to the design specifications, the number of tissue types which can be identified by the system may be readily increased by using more neurons in the output layer. The complete system used in this study was constructed from two independent sections. The first section contains two subsections, namely a neural network and a fuzzy section. The second part is a database that contains some empirical formulas which describe mechanical properties of the desired soft tissue. Schematic of the complete system is given in Fig.

--1

1

P

-------------

lvq U i~K

V X

vq

In the neural network section, two subsections are trained independently using the experimental data from forcedisplacement curves as network inputs. One of these

subsections is more sensitive to the force-displacement curves

in loading and another one is more sensitive to unloading. As previously stated, the force-displacement curves of soft tissues are not essentially the same in loading and unloading cycles. Normally, force in the unloading phase is smaller than loading phase. It is primarily because of the energy dissipation during loading caused by the hysterisis phenomenon. At the beginning, a single neural network was used to identify type of the tissue and it was seen that the learning rate is too low and in some conditions the system diverges. It seemed to us that it would possibly be a good idea to use two independent subsections for the neural network. Normally, this improvement can increase rate of learning and convergence of the system. In spite of complexity of the system, a simple multi layer perceptron (MLP) was used to design the neural networks. Limited effect of unknown faults, increased rate of learning, and higher level of convergence are advantages of simple systems. Both of the subsections used back propagation (BP) algorithm to adjust the weights in their synapses. The sigmoid functions were used as activation functions of both networks. Training was performed in parallel but simultaneously in both subsections of the network. As a result, the first subsection, after training, was more accurate in identification of the loading curves whereas the second was more accurate in the case of the unloading curves. Subsection specialized in the loading curves had two main neuron layers. The hidden layer contained 30 and the output layer had 10 neurons. The subsection specialized in the unloading curves had three main neuron layers.

|v

u

JV

Fig. 1. A schematic of the complete neurofuzzy

The first hidden layer had 20; the second had 10, and the output had 4neurons. For both subsections of the network, number of inputs was 40 from which 20 were force inputs and

20 were displacement inputs. Number of the layers and the neurons for each layer was determined on a trial and error basis. After training process, each subsection of the network was able to independently identify type of the tissue. Each subsection had an error in identification of the soft tissue. Considering sensitivity and independency of subsections, the errors of two subsections are not necessarily the same. For example, the error of loading phase for breast tissue may be equal to 0.3 while one's of the unloading phase may be around 0.1.

Application of a dual network calls for two results in the output. These results have uncertainty and utilization of the fuzzy logic can be helpful for getting more accurate results. Thus, the fuzzy section is used for more precise identification of the system and for accurate prediction of the tissue's health level.

A mathematically defined factor was introduced to process the error of each subsection of the network. It was called veracity factor (VF). The VF accounts for veracity of the output of the network result and can be used in the fuzzy section as input. The VF is defined as follows T

1 | n

l9j

(I (Di, ) -

j=l tmax 0 | 1ij

(")

2 < 0.8

lt

> 0.8

TABLE I

VF of Loading

Part High High High Medium Medium

Where ,th gj:is the veracity factor of the j"' neuron in the output layer, number n:is of the neurons in the output layer, i = 1, 2: 1 is for loading and 2 is for unloading phase of the

Part High

Medium

Low

Low

Medium

Low

Medium low

Medium low

Low

Low

Low

VF of Loading Part

Low

Too low TABLE2 FUZZY RULES FOR UNLOADING PHASE. VF of Unloading Membrane Probability

Part

Medium Low High Medium Low High

High

Too high Medium high Medium low High Medium Low Medium high

Medium

Medium low Too low

Low

Loading- 0.5

Membrane Probability

Too high High Medium high Medium Medium

High

~~~~~~Low

network, t11 : is the error value of the jth neuron in the output layer, tix: is the maximum positive error value in the output layer, 91: is the weighting factor accounting for scales of the errors in loading and unloading phases

VF of Unloading

Low High Medium

High Medium Medium Medium Low

.t .0.j

Fuzzy RULES FOR LOADING PHASE

Medium

High High

j

t

(DB). This section contains some formulas such as constitutive equations and any other empirical equation that describes properties and behaviors of the soft tissues. After identifying type of the tissue, the neurofuzzy system is able to predict mechanical properties of soft tissues by using the DB. Some empirical relations between one-dimensional stiffness and displacement offered by Ahmadian and Nikooyan [24] were used in our study.

UnIoading 01.5

Resuft for Loading -=s 9

3

5

=

I_____

The greater the veracity factor, the greater the tissue _=___ 0 identification precision. The veracity factor will be introduced _I_ 0 1 to the fuzzy section as its input. In that section, type of the Fig. 2. Fuzzy rules for loading part tissue is determined in accordance with veracity factors. for Uhlbading = 05 Furthermore, if type of the tissue is known, the tissue's health Loddg = 05 Uhlbdihg = 0 Re§Uft _______rl will be predicted accordingly. The fuzzy section makes its _________ decisions by applying the fuzzy rules. The rules are defined as conditional linguistic sentences. A fuzzy rule for the veracity 3 4 factor may be expressed as follows "If the veracity factor of the loading phase is high and that's L_ .>e =__ 6 of the unloading phase is high too, the tissue will probably 7 ,. _ belong to the desired class". All possible situations of veracity factors and the probability 8 are shown in Tables 1land2 for loading and unloading phases, iI II ______ respectively. Moreover, Fig. 2 and 3 show schematics of these 1 0 1 01 a rules for loading and unloading phases, respectively. The second section of the designed system was the database Fig. 3. Fuzzy rules for unloading part

These equations are derived from experimental data and can be expressed as

2(3

K abe'(2 2~~~~~~~~~ (2) ~ KI('S) = E aibie ~~i 2

In addition to living tissues, synthetic tissues can be identified by employing this method. The point is of a great importance in manufacturing processes of synthetic tissues.

b

KH(8p~!2aKb28~C

K

0.3

~0.25 Where K1 and K H are one-dimensional stiffness of the groups 1 and 2, a is the displacement, and ai, bi, and c are0 0.1 tissue constants. These constants have been determined for some soft tissues in reference [24]. According to Ahmadian 0.05 and Nikooyan [24], soft tissues can be divided into two Brain TissDue distinct groups, namely 1 and 2, based on their behavior in the Liver Tissue toe-region.

Heelpad

III. SIMULATION RESULTS We developed a simulation code for implementation of the idea. C++ and MATLAB were the programming languages of the code. Experimental data of uniaxial compression tests were used for training of the neurofuzzy system. These experimental data were in the form of force-displacement curves of loading and unloading phases. The system was trained to become capable of identifying five different classes of soft tissues including breast, kidney, liver, heel pad, and brain tissues. Both networks of loading and unloading phases were rapidly converged. As previously discussed, we divided the neural network section into two different subsections. One of these subsections is more expert in loading phase and the other is more expert in unloading phase. If a new set of data is introduced to the system, the system will identify the soft tissue from which these data are gathered. Potentially, the system can identify up to 10 classes of soft tissues. To improve the idea of using a fuzzy section after neural network, we examined a system with no fuzzy section by a 10 test samples. The squared identification error of the system is shown in the Fig. 4. This error can be improved by application factr and an inclusion inlso Of of a fuzzy fuz section. setin Fig. Fig.55 Ofofvract veracity factor depicts identification error of the improved neurofuzzy system. We observed that the identification error was reduced by 56%.

10 Tssue 8

Kidney Tissue

Number of the Test

Breast Tissue

Fig. 4. Normalized error ofthe neural network's output before using fuzzy section

0.3 025

=

02

00

Brain Tissue

0

LiverTssue Heelpad Tssue

Kidney ssue Breast Tissue 0

1

8

~

4

theNumber of Test ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2

network's output after using fuzzy Fig. 5. Normalized error of the neural section

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