Determination of the dispersed amplitude in

mammograms, using The Bosso´s Filter.

Gastón Lefranc Miguel Bustamante, Alejandro Nuñez Dr. Marcelo Guardia

Universidad Católica Universidad de Las Américas Medical Doctor

de Valparaíso

Chile

217/11/01 ISC - IASTED - 2001

ABSTRACT

In this paper is presented some aspect that interferes in the formation of the mammography images.

On the base of these phenomena, using the filter of Bosso as a degradation model is considered the parameters proposing a new procedure of the calculation of the dispersed amplitude.

This approach should permit to do a better clinical of breast cancer.

317/11/01 ISC - IASTED - 2001

1. Introduction

One of the problems of public health related with the feminine gender is the mammary cancer.

This illness is one of the main causes of death, in the women between 15 and 54 years.

In the United States this type of cancer causes 12% of mortality among the sick patients.

This cancer demands an appropriate clinical diagnosis that allows to identify and to treat the illness on time. The most used method of diagnosis is the well-known technique as "mammography".

This technique consists on obtaining an x-ray of the mama under controlled conditions.

417/11/01 ISC - IASTED - 2001

1. Introduction….

In the mammography, the mamma is conditioned to be in a plane; traverse to this it crosses a beam of X rays whose incidence is on a radiographic plaque parallel to the mamma.

The specialist, to find possible tissue dysfunction, examines the radiographic image.

However, the interpretation in a diagnosis is difficult by the degradation effects and the limits of resolution of the plaque, since it has been observed that the presence of groupings of calcium inside the mamma it is an important signal in the possible formation of Cancer.

This grouping of calcium has a near size to the limit of resolution of the system, for that that it is important to obtain an image of better quality.

517/11/01 ISC - IASTED - 2001

1. Introduction….

This necessity to optimize the quality in the images for improving the diagnosis, is against the degradation taken place by the interaction of the radiation, but it also produces dispersed radiation (scattering) that in turn impacts on the radiographic plaque.

The dispersed radiation, besides the radiation of the main beam, is added to the total dose in a point of the plaque.

Near of this point of the incident ray, the dispersed radiation impacts on the vicinity, producing an image of the object degraded in their contours.

This, in definitive, changes the quality of the mammography.

617/11/01 ISC - IASTED - 2001

Others authors in this problem.

Several authors have stopped in this problem. In general, they have worked with operators of images, neural nets, wavelet transform to detect groupings of calcium related with presence of mammary cancer.

Berkman Shiner, Heang-Ping Chan [1], work with radiographic image, applying them a neural net, by means of regions of interest and comparison of textures.

Nico Karssemeijer and Guido M. You Brake [2], analyze the orientation of the radial pattern of specular lines, around a density knitted malicious.

717/11/01 ISC - IASTED - 2001

Others authors in this problem.

John Kook Kim, Jeong My Park et al. [3], develop an adaptive improvement of the image, using the first derivation and local statistic.

Antony Jalink, James McAdoo [4], investigate using a new mesh detector (CCD, charge coupled device), with which they study the dispersion of the radiation.

R.P. Highnam, J.M. Brady and B.J. Sheptone [5], develop a model that simulates degradation of the image for attenuation, dispersion and to a non-monochrome spectrum of the energy of the tube of cathodic rays.

Thomas S. Curry, James E. Dowdey, Robert C. Murry [7], discuss on geometric effects that affecting the image, in particular, the source of non punctual radiation.

817/11/01 ISC - IASTED - 2001

Mamographic images

The mamographic images are today a form for the clinical diagnosis of illnesses of mamma.

One of these illnesses is the mamma cancer whose detection urges for a good clinical diagnosis.

The formation of the mamographic image is a product of the interaction of the radiation with the matter and with the photographic plaque.

This interaction produces chemical changes in the emulsion that are revealed later on. In this process, the interaction with the organic matter (mamma), intermediate materials and the plaque produce degradation from the inherent image to the process.

917/11/01 ISC - IASTED - 2001

Degradation model of the image

This degradation type can be modeled by means of the action of a filter that supposedly acts on the non-degraded image, resulting an image, which is observed in the plaque.

Several models exist in the literature that gives the degradation effect. One of them is the Bosso´s Filter (Lefranc and Bustamante [7], [10]-[11]), has behavior as a pass high, pass band and pass low filter.

In this paper, on the base of these phenomena and the principles of physics involved in the problem, it is postulated the filter of Bosso as a degradation model of the image

1017/11/01 ISC - IASTED - 2001

THE BOSSO´S FILTER.

The analytical form of Bosso´s Filter is in the eq. 1:

Where: N: pixels number associated to filtering (matrix or

mask) r2 = (i2 + j2), Euclidean distance definition; where i,

j is the pixel position. The parameters are , a, and A(, a) is constant of

normalization.

22

λar

ar

e*Aa)λ,B(N,

22

Eq. 1

1117/11/01 ISC - IASTED - 2001

THE BOSSO´S FILTER.

The filter has a behavior that is strong depending of the , a values.

In previous works it has been shown that the filter acts as a pass high, pass band and pass low filter [7], [10]-[11].

The analytical form is similar to the degradation of the interaction of the radiation with the matter, in the dispersion of the radiation.

This reason permits to formulate a hypothesis that the Bosso´s Filter performs as a dispersion of the radiation in the matter.

22

λar

ar

e*Aa)λ,B(N,

22

1217/11/01 ISC - IASTED - 2001

3. THEORICAL ASPECTS

The attenuation of the intensity of a luminous beam that crosses certain transparent matter is given by the attenuation law:

I(x), intensity of the beam that crossed a body of thickness x;

I0 incident intensity and coefficient of linear attenuation. The radiation in the matter generates dispersion

radiation, that is the interaction of the incident radiation with the matter, basically electrons.

xeIxI 0)( Eq. 2

1317/11/01 ISC - IASTED - 2001

3. THEORICAL ASPECTS…

This interaction generates a luminous less energy radiation that the incident, but not worthless.

The hypothesis proposed is based that the interaction causes spherical waves that spread in a material media.

The intensity of the spherical waves can be described mathematically by the equation and it is related with ec. 2

Where Io´ is constant of proportionality between amplitude of the spherical waves and the inverse of the quadratic distance.

2

'0)(r

IrI ec

xeIxI 0)( Eq. 2 Eq. 3

1417/11/01 ISC - IASTED - 2001

The incident radiation and dispersion

inside a homogeneous mamma tissue

The radiation that receives radiographic plaque in a point (x,y) is the contribution of both phenomena.

Mamma

Beam incident

O (x,y)

d

r

Spherical waves Disperse radiation

d, thickness of the mamma r distance point O to point (x,y)

2

μr'0

μd0 r

eI)rδ(eIy)H(x,

The net intensity in the point (x,y) is:

Eq. 4

It is assumed that the mammary tissue, in the environment of the point O has a homogeneous behavior.

222 dρr Eq. 5

1517/11/01 ISC - IASTED - 2001

The degradation effect corresponds to the filter of Bosso.

The value of I’0 should not be similar to I0, because the interaction produces a smaller intensity to the incident.

Eq. 5 en Eq. 3:

The effect of the degradation, in the analytical form, corresponds to the filter of Bosso.

From previous works, it is known the behavior of the filter for different d y values. It is known that emulate the numerical conditions (d=0 and =0), agreeing with the hypotheses.

22

rρμ'0

μd0 dρ

eI)rδ(eIy)H(x,

22

Eq. 6

1617/11/01 ISC - IASTED - 2001

4. ESTIMATION OF d y PARAMETERS

The difficulty is in obtaining the values d and . In the work with digital images of the mamma, the

information is in terms of relative intensity H(x,y) eq. 4

If I0 is associated with the maximum intensity that can register the system, and taking an approximation of first order, to suppose that the first term described by the eq.3 prevails. This approximation is:

2

μr'0

μd0 r

eI)rδ(eIy)H(x,

2

'0)(r

IrI ec

)I

y)I(x,ln(

d

1y)μ(x,

0

Eq. 7

1717/11/01 ISC - IASTED - 2001

4. ESTIMATION OF d y PARAMETERS

d corresponds to the thickness of mamma under the conditions of obtaining of the image. This parameter is not fixed but gives a good reference value.

For the calculation of I0’ it has to assume the following hypothesis: The total intensity deposited in the plaque is equal to I0. This implies that the integral of H(x,y) on the surface it should be equaled at I0. I0’ is

Where z(,d) is la integral of eq. 9.

),(

)1(),( 0

'0 dz

eIyxI

d

Eq. 8

dd

edz

d

022

22

),( Eq. 9

1817/11/01 ISC - IASTED - 2001

4. ESTIMATION OF d y PARAMETERS

The calculation of this parameters is based on the works of Lefranc and Bustamante [7], -[10]-[11], the infinite is replaced by a value of 100 d.

This is because of the function decays very quick in the range of the value of m positive.

This new image is the contribution of the radiation dispersed in the central pixel.

When subtracting Io(x,y) to the image Io´(x,y) an image is obtained without the contribution of the dispersion. An image is achieved with more detail.

1917/11/01 ISC - IASTED - 2001

5. EXPERIMENTAL PROCEDURE

To obtain a result it is used a computer of 64 MB of RAM, with a hard disk of 10 Gigabytes and a processor Pentium III. An IDL program for the development is utilized, with routines that were described and the integration was achieved on the base of the Simpson integral

A mammography of medium size is digitized in a scanner to 256 tones of gray, bmp format.

2017/11/01 ISC - IASTED - 2001

Digital Image of original mammography

A mammography of medium size is digitized in a scanner to 256 tones of gray, bmp format.

A technique that uses a tube to examine the ducts of milk helps to detect mammary cancer when finding the illness at a cellular level, before the mammogram.

This technique allows the doctors to look through the direct nipple in the ducts of milk, where this type of cancer usually develops.

tube

2117/11/01 ISC - IASTED - 2001

Obtained image of the subtraction of I0 (x,y)– I’0(x,y).

Applying, to the original image, the procedure of the calculation of I0’ with the value of d=5 and a value of given by the expression (7), an IDL program with a macro of the IDL (TVcl), displays the following image.

Notes the internal structures of the mamma. Bigger contrast and internal structures of

mamma. The micro calcifications visibility in the image

filtered with regard to the original images. The resulting images is insufficient to

appreciate the effect taken place on micro calcifications, difficult to see in the original image.

2217/11/01 ISC - IASTED - 2001

An image with I0’ with the value of d=15.

When applying the procedure of the calculation of I0’ with the value of d=15, the contrast is very good and it can be the micro calcification, but the piece of metallic of reference (tube), doesn't give trust in the image, because of the noise that appears around the tube.

2317/11/01 ISC - IASTED - 2001

Mammogram d=5Mammogram d=20

With d =5, the image is poor in contrast and the Micro calcifications are not seen.

If it is used to d=20 the image is bad

2417/11/01 ISC - IASTED - 2001

Mammogram with d=10.

Using of I0’ with the value of d=10, the image has less contrast, being possible recognizes the micro calcifications in the image, that means a probability of cancer.

2517/11/01 ISC - IASTED - 2001

CONCLUSIONS

In this paper has been presented some aspect that interferes in the formation of the mammography images.

On the base of a degradation model based on the filter of Bosso, it has been able to obtain the parameters starting from the information characteristic of the phenomenon.

With this information permits to reconstruct an image of the mamma that observes, in more contrast, that the original one.

With the degradation model, the parameters proposed a new procedure of the calculation of the dispersed amplitude.

Using the parameter d=10, it is obtained a new image without noise around the tube and another distortions.

This is a starting point to new research with this type of images.

The results obtain is a good approach to do a better clinical diagnosis of breast cancer.