# Blood Cells Images- Based on Chaos Theory

**ABSTRACT** The fractal functions are considered a good choice to represent natural tissue surfaces. W hich werechosen because of the importance of short period characteristics of classifying images since the fractaldimension of a surface has an approximation of complete relation with surface toughness. Therefore, the ideaof using a new group of fractal characteristics is utilized to differentiate medical images. This workdemonstrates the technique of using chaos theory and principles of fractal engineering in the processes ofdescribing and differentiating medical images of red blood cells and while blood cells. A group consisted oftwo fractal characteristics, which are the fractal dimension, and the Lacunarity are developed to describe anddifferentiate medical images. An alternative method of box counting and mass radius is implemented tocalculate those two fractal characteristics of images surface Furthermore, an instructional program designedby using PowerPoint and includes three instructional modules depending on system? approach knowledge basedof using chaos theory and fractal engineering m the medical applications.

**0**Bookmarks

**·**

**95**Views

- Citations (4)
- Cited In (0)

- [Show abstract] [Hide abstract]

**ABSTRACT:**Many biological objects appear to have self-similar structures which can be characterized by their fractal dimension D. However, applications of the concept of fractal geometry are rather scarce in cell and tissue biology. Here we adapt and analyse critically 3 methods of digital image analysis to measure D of cellular profiles. As prototype examples we investigate in detail 2 samples of cells: (i) human T-lymphocytes from normal donors, and (ii) hairy leukemic cells. It is shown that D correlates to the structural complexity of the individual cell contour. The calculated D values for cells out of the same cell line scatter around a mean value D = 1.15 for T-lymphocytes (S.D. = 0.03) and D = 1.34 for hairy leukemic cells (S.D. = 0.04). Consequently, we interprete D as a statistical measure for the sample's fractal dimension.International Journal of Bio-Medical Computing 11/1994; 37(2):131-8. -
**Self – Affinity and lacunarity of Chromatin Texture in Being and Malignant Breast Epathelial Cell Nuclci**. J E Andwer . 397-400. -
**Improving the performance of spatial and Frequency Filters to Enhance Monochromatic Digital Images**. R K Gabber . 5.

Page 1

Research Journal of Applied Sciences, Engineering and Technology 1(3): 121-124, 2009

ISSN: 2040-7467

© Maxwell Scientific Organization, 2009

Submitted Date: June 14, 2009Accepted Date: August 05, 2009Published Date: October 20, 2009

Corresponding Author: Saad Al-Shaban, Communication and Electronics Department/ college of engineering, University of

Jerash, Jerash, Jordan

121

Blood Cells Images- Based on Chaos Theory

Saad Al-Shaban, Inaam A.M. Al -Sadik and Maha A. Amir

Communication and Electronics Department/ college of engineering,

University of Jerash, Jerash, Jordan

Abstract: The fractal functions are considered a good choice to represent natural tissue surfaces. Which were

chosen because of the importance of short period characteristics of classifying images since the fractal

dimension of a surface has an approximation of complete relation with surface toughness. Therefore, the idea

of using a new group of fractal characteristics is utilized to differentiate medical images. This work

demonstrates the technique of using chaos theory and principles of fractal engineering in the processes of

describing and differentiating medical images of red blood cells and while blood cells. A group consisted of

two fractal characteristics, which are the fractal dimension, and the Lacunarity are developed to describe and

differentiate medical images. An alternative method of box counting and mass radius is implemented to

calculate those two fractal characteristics of images surface Furthermore, an instructional program designed

by using PowerPoint and includes three instructional modules depending on system? approach knowledge based

of using chaos theory and fractal engineering m the medical applications.

Key words: Cells images, fractal geometry, van koch curve, elay and gerlach model

INTRODUCTION

Fractal geometry and Chaos theory provide us with

a new perspective lo view the world. For centuries we

have used the line as a basic building block lo understand

the objects around us. Chaos science uses a different

geometry called Fractal geometry. Fractal geometry is a

new language used to describe, model and analyze

complex forms found in nature. Fractal provide a different

way of observing and modeling complex phenomena than

Euclidean Geometry or the calculus developed by Leibniz

and Newton also the biologists diagnose dynamical

diseases and others (Andwer, 1998). Fractal and Chaos

modeling is applied in different Held, Target recognition,

Remote sensing (Chang, et al , 1992). Used for describing

the data in biology and physical science, medical image

through out fractal dimension of bones. Retina vessels

Diseases of lungs and concur. It is found that the

Recognition by the fractal dimension is effective over

other methods (Gabber, 2001), The exactly self-similar

objects such as Mandelbrot set or Van Koch curve differ

from the statistical self-similar objects like The coastline

in one significant aspect. Upon magnification, segment of

the coastline look like, but never exactly like segments at

different scales. The concept of fractal dimension,

however, can also be applied to such statistically self-

similar objects- Each small section of a coastline looks

like (but not exactly like) a larger portion. When using a

ruler of size r to measure a coastline's length, the total

length equals the ruler size (r) times the number {N (r)}

of steps of size r taken in tracing the coast (Jonescu,

2003).

Length=r*N®(1)

The properly that objects can lake statistically self-

similarity while at some time different in details at

different length scales is the central feature of fractals in

nature . Under an affine transform, on the other hand,

each of (he E-coordinates of X may be sealed by a

different ratio (r1,r2, r3,.........., rE). Similarly, S is

transformed to r (S) with points at (r1x1, r2x2,......., rExE)

Abounded set S is self -affine when S is the union of

N distinct subset each of which is similar in distribution

to r(s) . The fractal dimension D, however is not easily

defined as with self-similarity, now we can summarize

some of the main features of fractals:

?They have a fine structure; which mean? that, they

contain details at arbitrarily small scales. The more

we enlarge, for example, the picture of the

Mandelbrot set, the more details became apparent to

the eyes.

?They are too irregular to be described in traditional

geometrical language, both locally and globally.

?Often, they have form of self-similarity, perhaps

approximate or statistical.

?Usually, their fractal dimensions are greater than

their topological dimensions.

?In most cases of interest, they are defined in a very

simple way, perhaps recursively . For example one

construction of Mandelbrot set consisted of

repeatedly adding the square of the complex number.

Successive steps give increasingly good

approximations to the final Mandelbrot set.

?Although they are in some ways quite large set (they

are uncountable infinite ), their size are not quantified

Page 2

Res. J. Appl. Sci. Eng. Technol., 1(3): 121-124, 2009

122

by the usual measures such as length or area or

volume as in the traditional Euclidean shape,

? Although they have an intricate detailed structure, the

actual definitions of them are very straightforward.

?Method of classical geometry and calculus are not

suited for Studying fractals and thus we need

alternative techniques, the main tool of fractal

geometry is the fractal dimension.

MATERIALS AND METHODS

Testing Models: there are several models are used for

medical images, blood testing as follows :

?Box counting model ( Kadham , 2002),

?Mass-radius method (Macculary, Candpaki, c, 1990).

? Petrosian's Algorithm Model (Mana, 2004),

? Lacunarity and Texture Measures Models

(Nonnenmacher, et al., 1994; Penn, 2004; Saban,

2004 and Snenber, et al., 2000).

? Ely and Gerlach model (Xia and Gaow , 1996).

Instructional Design: Instructional Design is the

systematic development of instructional specifications

using learning and instructional theory to ensure the

quality of instruction. It is the entire process of analysis of

learning needs and goals development of instructional

materials and activities; and tryout and evaluation and the

development of a delivery system to meet those needs. R

Fig. 1: shows component of instructional design process.

includes of all Instruction and learner activities (Wielgus,

et al., 2000) (Fig. 1).

Ely and Gerlach model: The Ely and Gerlach model is

an attempt to portray graphically a method of

systematically planning instruction. Incorporated in this

model are two items; the necessity of carefully defined

goals and the tactics on how to reach each goal. Both

parts are absolutely essential for effective teaching ( Xia

and Gaow, 1996), Fig. 2. this method at present work has

been adapted for blood cells testing.

Research Procedures: The researchers have determined

the information specified of the used images (RBC\

Fig. 2: Shows Ely £& Gerlach model

Page 3

Res. J. Appl. Sci. Eng. Technol., 1(3): 121-124, 2009

123

Fig. 3: shown the flowchart of research procedures

Table 1: Mean value? of fractal dimension using box counling method.mass radius method of used RBC\ WBC for (L^^O) and ®^^).

NumberRBC infected imageRBC uninfected imageWBC infected image WBC uninfected image

of ImageFractal dimension (D) Fractal dimension (D)Fractal dimension (D)Fractal dimension (D)

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

BC MRBC MRBC MRBCMR

12.8732.9014.0194.3013.283.6231.4761.511

2 2.8852.9044.0684.3513.276 3.6241.4471.481

32.887 2.9084.1364.353 3.2783.626 1.428 1.471

42.8892.908 4.203 4.1913.279 3.6251.471.451

52.892.944.2254.1513.277 3.6231.4721.445

Mean:2.882.944.134.2583.273.62 1.45 1.44

?:0.0060.0040.0080.008 0.001 0.0010.02 0.002

WBC) represented by image dimension (64*64) and their

gray level is about 0 to 255 within (bmp) file, then

designing and implementing a program in (Visual basic

V.6) language lo calculate the fractal dimension and

lacunarily by using box counting method and mass radius

techniques to application the chaos theory in this images

also designing tihe instructional program according to a

system approach (Ely and Gerlach) model as a developed

technique in the learning process to provide learner with

the key principles of chaos theory and fractal engineering.

(Fig. 3)

RESULTS

Five samples of each kind of red blood cells (RBC)

and infected while blood (WBC) cells are chosen, in

addition lo five samples of uninfected cells and for a

different ages, The result attainted in Table 1 indicate

mean values of fractal dimension using box counting

method, mass radius method of used RBC, WBC for

(Lmax =30) and (r =32). The relation between maximum

side length box (Lmax ) used to calculate the fractal

dimension and its values and values of Lacunarity shows

that uninfected cells have shapes and relation different

from those of infected cells . (Fig. 4a,b).

illustrates the relation between the Lmax and values

of fractal feature (fractal dimension and Lacunarity) for

the infected cells RBC Fig. 4b illustrates the relation

between the radius r and values of fractal Feature (fractal

dimension and Lacunarity) for the infected cells RJ3C(5)

illustrates the relation between the Lmax and values of

fractal feature (fractal dimension and Lacunarity )for the

infected cells WBC. ( Maha, 2005).

CONCLUSION

A novel approach has been presented to detect and

classify the electronic microscope image for RBC and

WBC infected and uninfected by using the concept of

chaos theory (Table 1)]. The properties and characteristics

of a fractal set are not completely determined by its fractal

dimension. Indeed fractals that have the same fractal

Page 4

Res. J. Appl. Sci. Eng. Technol., 1(3): 121-124, 2009

124

(a)

(b)

Fig. 4: Show the calculated fractal features versus the

maximum length of box.

dimension may look very different, they have different

"texture", more specifically, different Lacunarity. It is a

counterpart to the fractal dimension that describes the

texture of a fractal- The surface irregularity has shown as

increase in neoplaststic cells of leukemia cells was

connected with their fractal dimension increases for

normal cells, fractal dimension =1.44. whereas for

neoplastic ones >1.44. Values of fractal dimension in box

counting method are round to be Lmax>64 (larger than

the size of the images) .This unsuitability. Fractal

dimension allows to perform the mathematical estimation

of chaos theory. Mass radius method is applied in

measurements of images when radius (r=32). Dimension

analysis is a tool to quantify structure information of

artificial and natural objects. It is also designing an

instructional program according to the methodology of

system approach Ely and Gerlach model and in the form

of instructional modules helped to overcome the

individual differences among learners.

REFERENCES

Andwer, J.E., 1998. Self – Affinity and lacunarity of

Chromatin Texture in Being and Malignant Breast

Epathelial Cell Nuclci . Physical Review letters, Am.

Physical., 80(2): 397-400.

Chang, J., et al., 1992. Image Segmentation and local

Ftractal Analysis of MR Image. IEEE, New

York, 2(1).

Gabber, R.K., 2001. Improving the performance of spatial

and Frequency Filters to Enhance Monochromatic

Digital Images, M.Sc. Thesis, University of

Technlogy, Baghdad, pp: 5.

Jonescu, B., 2003. Fractal and Second – Order Statistics

For the Calcaneum Trabecular structure Analysis.

http:/www.Omdrive.Memphis.Edu/hazhar/public

/chaos.html, pp: 33.

Kadhum, M., 2002. Discrimination the Medical Images

using Fractal Geometry Technique, M.Sc. Thesis,

University of technology, Baghdad,

Macaulary, C. and Palcic, 1990. Fractal Texture Features

Based on Optical Density Surface Area, Anal. Quant.

Cyt and Hist, 12(6): 394-398.

Maha, A.A., 2005. Blood cells images – Based on Chaos

theory, Ph.D thesis submitted to the University of

Technology/ Baghdad/Iraq.

Mana, G., 2004, Chaos and Fractal Real World :

Nonlinear Analysis of Cardiovscular Variability

Series, http:/www.p.zzal.da.html, biomedical Eng.

Milano, Italy, pp: 1-13.

Matazaki, T., 1993. Analysis of Tissue Information on

Medical Images Using Fractal Dimensions. SPIE-The

Information society for optical Eng., 1898: 526-531.

Nonnenmacher, T.F., et al., 1994. Digital Images

Analysis of Self – Similar Cell Profiles , Int. J.

Biomed. Comput., 37(2): 131-138.

Penn, E., 2004." Training and Instructional Design ",

University of Michigan, http:/www.Umich.edu/ed26/

define.html,

Saban, N., 2004. A Micro Computer – Based Study on

Vehicle Effects on Biochemical Signals in low

Frequency, Ph.D, Thesis, University of Technology,

Baghdad,

Snenber, P.M., et al., 2000. Ultrasound and light

Seattering From a Suspension of Reversible Fractal

in Clusters in Shear Flow, http://www.Springer

verlage, Eur.PHs, pp: 41-53.

Wielgus, E., et al., 2000. Fractal analysis of placenta

Mature Villi in Healthy, Smoking and non-Smoking

Women, Laboratory investigation, Med. Sci. Mont,

6(2): 271-277.

Xia, D. and W. Gao, 1996. Fractal Geometry Based

Classification Approach for the Recognition of Lung

cancer cells, Issue: 2167.