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Determination of the structure of tissue samples using X-ray small angle scattering
PATHOLOGY RESEARCH AND PRACTICE © Urban &Fischer Verlag http://www.urbanfischer.defjournalsJprp
Determination of the Structure of Tissue Samples Using X-ray Small Angle Scattering Martin Bradaczek 1, Hans Guski2, Hans Bradaczek3 and Georgi G. Avtandilov4 'Department of Diagnostic and Interventional Radiology, Wolfsburg, Germany; ' Department of Pathology, University Hospital CharM, Humboldt Universitat, Berlin, Germany; 3Department of Cristallography, Freie Universitat Berlin, Germany; 41nstitute of Pathologic Anatomy, Russian Academy for Medical Sciences, Moscow, Russia
Summary X-ray small angle scattering has been used in material science for about 50 years. In diagnostic medicine, it has been applied for some years. The theoretical background is the diffraction of monochromatic X-rays by the electrons of small particles. The widening of the primary beam by those samples allows a conclusion regarding particle size, size distribution, and the form of the particles. The camera requires a well-defined and small X-ray beam which has to be entrapped exactly behind the sample. To date, the medical application has been carried out mainly by the comparison of the measured curve with that of standard samples. It can be suggested that in the near future its application in medicine will increase particularly with regard to in vivo measurements. For this purpose, new cameras will have to be developed. An exact evaluation of the result requires a thorough knowledge of the theoretical basis.
Introduction Since the discovery of X-ray diffraction in 1912 [9], several methods have been developed to determine the structure of crystals by X-ray diffraction. In the following years, the range of substances to be investigated has been expanded to polycrystalline and amorphous materials. The content of information, however, diminished with the decreasing order of samples. Around 1940, Kratky {7 J, Guinier and others [4J detected that a narrow X-ray beam-passing matter was Pat hal. Res. Pract. 196: 827-830 (2000)
spread out close to the primary beam. This scattering was called "small angle scattering", although it was at least a diffraction effect. In the fifties, this difference of determination triggered a discussion between Kratky [7] and Hosemann [6]. During the past fifty years, several cameras for X-ray small angle scattering have been developed, the most popular amongst them being the Kratk y- and the Kiesig-cameras, which have been in use for several purposes in material science. For any type of measurement, it can generally be postulated that the dimension of the tool has to be adapted approximately to that of the object. In the case of small angle scattering, the wave length of the used (Cu-) radiation is about 0.15 nm. Therefore, the method is sensitive only for objects in the range between 1 and (in ideal cases) 100 nm. If samples are larger (the dimension of blood cells is about 10,000 nm), only internal structures can be detected. In this context, a definition of the meaning of the term "object" seems to be necessary. Following the "Kinematical Theory of Xrays", it is evident that interferences are caused by the distribution of the electrons in the sample. It is necessary to have certain ranges of lower and higher electron densities of the dimension mentioned above_ Tissue samples cannot be expected to have ideal internal structures like spheres. Probably, it will be a mixture of more Address for correspondence: Martin Bradaczek, Klinik fUr Bildgebende Diagnostik und Interventionelle Radiologie. Sauerbruchstr. 7, D -38440 Wolfsburg. Gcnnany_ TeL: ++49 (0) 63 61-80 38 44: E-mail: [email protected] 0344-033812000/196/12-827 $15.00/0
828 . M. Bradaczek ct a!. or less defined density deviations. The small angle scattering measurement is normally not suited for measuring the exact structure of the electron density of more complex biological structures. The major goal of those measurements can only be to get a rough information on the size distribution of the density. Therefore, with the present knowledge, only comparison between standards and actual measurements is considered a suitable method to be used in diagnostic pathology. All the more, it is surprising to obtain clear differences in the measurement results between normal and tumor tissue. For routine examination in medicine, several applications have been described in the literature over the past few years /3, 5, IO}. The reason for this relatively late application might be explained by the fact that a connection between the theoretical background and the practical use could not be easily found . As shown in Material and Methods, X-ray small angle scattering is caused by the so-called particle size effect. The scattering depends on the size, size distribution , and the form of the particles in the sample. There would be significant progress ifit were possible to compare measurements of different samples (e.g., cancer tissue and normal tissue). It can be shown that there are possibilities of a unique diagnosis. Although the X-ray small angle scattering method in medicine is not yet fully developed, it has some advantages over conventional methods, allowing the examination of very small samples for in vivo measurements.
Materials and Methods
luted in a complex way. In vivo measurements may not be
possible with that type of camera. The Kiessing camera (Fig. 2) uses a point-like focus. It seems to be more flexible 10 use modern X-ray optical tools, such as collimators, which could be much smaller in size and better suited for in vivo measurements. The diffracted function should be evaluated in two dimensions. The major problem of all small angle cameras is the exact entrapping of the primary beam. Following the kinematical theory of X-ray diffraction, a monochromatic beam hitting the electrons of a sample emits a spherical wave. By overlapping all spherical waves of the different locations within thc sample in the detector, the information about the phases gets ol st, and the intensity corresponds to the square of the superposition of all waves. This iscallcd "phase problem of the crystallography", because this loss of phase information makes the recalculation of the structure of a sample much more complicated. With the structure of a sample being p (x,)\ zi, its diffraction diagram can be calculated by the Fouriertransform of pix, y, zi. F(It, k, Ii ;
f p ix. y, z)e-"""""" dxdydz**)
( I)
which might be written in a short form (2)
where x, y, z are coordinates in the physical space and h, k, I those in the Fourier space. This general formula is valid for all kinds of structures, except for perfect crystals where the dynamic theory has to be considered. In the case of small angle scattering, the form and thc size of particles within the sample are the determining factors.
In an imaginary sample consisting of spheres of constant The best known X-ray small angle instrument is the Kratky
(de termining) size and material (electron density), the assem-
tion. ]ts disadvantages are its relatively large size, a very broad primary beam . and the fact that it can measure only one
interference of rays between the spheres. Then the scattering
camera. (Fig. I). which has an excellent primary beam limitaside of the primary beam. Because of the overiapping of the broad reflected beam, the resulting curve has to be deconvo-
bly of the spheres should not be too dense, so that there is no
of this sample is just the scaUering of one sphere multiplied by the number n of spheres in the radiation range
FJ.: ; n . p0 .
f ('
')~1X,}:~J~
-?lfi{ir.tf"ky+I:)dxdydz
(3)
Linear Detector Primary beam limitator
where Sir. is the function of the sphere.
Sca tlered beam
I..., Fig. I. Conventional Kratky camcra.
Results and Discussion The Fourier transform of S, with the radius R can be expressed by [2}
Detec tor Sample Primary beam
.I, ;
FT(SJ ;
~
7r R] . 3(sin~ -
~cos~)/ ~
(4)
with ~; 27r Rlul and lu i; / h' + Ie' + I' G lass tube collimator
Primary beam hap
Fig. 2. Modified Kiessig earnem.
"dh, k, /) has approximately the form of cos Rlul. Roughly expressed, the width of the scattered profile is reciprocal to the size of the particles.
Small Angle Scattering in Tissue Samples . 829 Focu;
Polydisperse sample
Monodisperse sampl~ with nonspheric particles
Irtensity-ftrcticn of scattefirg
Fig. 3. Left: Principle of X-ray small angle scattering of monodisperse particles. Right: A sample with polydispersc and nonsphcric particles.
Relative Intensity 140
- - - - - --
-
- - - -- -- - - -- -
\ 120 -
i
Based on the width of the scattering curve, the size R (4) of the spheres can be roughly recalculated (Fig. 3). In reality, this can only be checked with such well-defined inorganic samples as explained above. If the sample contains spheres of various radii, their distribution can be described by a Maxwell function {lO}. Comparing the Fourier transform of the Maxwell function with the measurement, it is possible to obtain some information about the size distribution of spheres within the sample. If the form of the particles diverges significantly from the spheres, it can be determined by the form of the scaHering curve. In reality, the ideal shape of the particles (spheres) is reached only in very few cases. If, as in medicine, there is only a limited number of different samples to be measured, a comparison between a standard sample and the sample to be examined may lead to signi ficant results. Fig. 4 shows small angle scattering curves of three types of tissue samples: 1-3, breast canccr; 4-6, fibroadenoma; and 7-9, normal breast tissue II j. Small angle scattering can also be used to find out periodical elements in the sample. Fig. 5 shows the scattering image of Lipopolysaccharide membranes which arc stackcd periodically. The major goal of this paper was to show that small angle X-ray scattering opens several possibilities for powerful diagnostic methods. While this method has been used in material science and biology for several years, its development as a diagnostic tool in pathologic practice seems to be only at the beginning. The example of the scattering results of breast cancer (Fig. 4) may encourage other research groups to find new objects of investigation.
)
'J ~ 100
.\ ',\
·..l11\
~J
80·
[) 60 ·
.1 '
..\ \
'.\ ~
[Breast ~
40 ,
20
........ , ".
- -"
,.,. --~~., ~
..
Fig. 4. Comparison of samples from normal tissue and different tumors of the breast.
Fig. 5. Small angle scattering of lipopolysaccharidcs of Salmonella bacteria using a Kiessig camera.
830 . M. Bradaczek et a!.
References I. Avtandilov G, Barsanova T, Dembo A, Lazarev P, Paukshto M, Shkolnik L, Zayratiyants 0 (1999) Histostereometry and ultra low angle X-ray scaltering: New non-invasive morphological diagnostic method of breast cancer. VirchowsArch435: 183 2. Bradaczek H (1981) Potential energy calculations of molecular and crystal structures in Fourier space. J Phys C: Solid State Phys 14: 1-7 3. Grant JA, Morgan MJ, Davis JR, Davies DR, Wells P (1993) X-ray diffraction microtomography. Meas Sci Technol4: 83-87 4. Guinier A ( 1952) Zeitschrift fUr Metallkunde 43: 217 5. Harding G, Kosanetzky J, Neitzel U (1985) Elastic scatter computer tomography. Phys Med BioI 30: 183- 186 6. Hosemann R, Bagchi SN (1962) Direct Analysis of Diffraction by Malter, North-Holland Publ ishing Company, Amsterdam
7. Kratky 0 (1940) Rontgenographische Untersuchung des hochdispersen Verteilungszustandes in einem Faserstoff. Z Elektrochcm 46: 535-555 8. Labischinski H, Barnickel G, Bradaczek H, Naumann D, Rietschel ET, Giesbrecht P (1985) High state of order of isolated bacterial lipopolysaccharide and its possible contribution to the permeation barrier property of the outer membrane. J Bacteriol 162: 9-20 9. v. Laue M (1960) RontgenSlrahlinterferenzen. 3rd ed. Akadem Verlagsges, FrankfurtlMain 10. Westmore MS, Fenster A, Cunningham IA (1996) Angular-depended coherent scalter measured with a diagnostic X-ray image intensifier-based imaging system. Med Phys 23:723-733
Received: January 31,2000 Accepted in revised version: July 18,2000
Determination of the Structure of Tissue Samples Using X-ray Small Angle Scattering Martin Bradaczek 1, Hans Guski2, Hans Bradaczek3 and Georgi G. Avtandilov4 'Department of Diagnostic and Interventional Radiology, Wolfsburg, Germany; ' Department of Pathology, University Hospital CharM, Humboldt Universitat, Berlin, Germany; 3Department of Cristallography, Freie Universitat Berlin, Germany; 41nstitute of Pathologic Anatomy, Russian Academy for Medical Sciences, Moscow, Russia
Summary X-ray small angle scattering has been used in material science for about 50 years. In diagnostic medicine, it has been applied for some years. The theoretical background is the diffraction of monochromatic X-rays by the electrons of small particles. The widening of the primary beam by those samples allows a conclusion regarding particle size, size distribution, and the form of the particles. The camera requires a well-defined and small X-ray beam which has to be entrapped exactly behind the sample. To date, the medical application has been carried out mainly by the comparison of the measured curve with that of standard samples. It can be suggested that in the near future its application in medicine will increase particularly with regard to in vivo measurements. For this purpose, new cameras will have to be developed. An exact evaluation of the result requires a thorough knowledge of the theoretical basis.
Introduction Since the discovery of X-ray diffraction in 1912 [9], several methods have been developed to determine the structure of crystals by X-ray diffraction. In the following years, the range of substances to be investigated has been expanded to polycrystalline and amorphous materials. The content of information, however, diminished with the decreasing order of samples. Around 1940, Kratky {7 J, Guinier and others [4J detected that a narrow X-ray beam-passing matter was Pat hal. Res. Pract. 196: 827-830 (2000)
spread out close to the primary beam. This scattering was called "small angle scattering", although it was at least a diffraction effect. In the fifties, this difference of determination triggered a discussion between Kratky [7] and Hosemann [6]. During the past fifty years, several cameras for X-ray small angle scattering have been developed, the most popular amongst them being the Kratk y- and the Kiesig-cameras, which have been in use for several purposes in material science. For any type of measurement, it can generally be postulated that the dimension of the tool has to be adapted approximately to that of the object. In the case of small angle scattering, the wave length of the used (Cu-) radiation is about 0.15 nm. Therefore, the method is sensitive only for objects in the range between 1 and (in ideal cases) 100 nm. If samples are larger (the dimension of blood cells is about 10,000 nm), only internal structures can be detected. In this context, a definition of the meaning of the term "object" seems to be necessary. Following the "Kinematical Theory of Xrays", it is evident that interferences are caused by the distribution of the electrons in the sample. It is necessary to have certain ranges of lower and higher electron densities of the dimension mentioned above_ Tissue samples cannot be expected to have ideal internal structures like spheres. Probably, it will be a mixture of more Address for correspondence: Martin Bradaczek, Klinik fUr Bildgebende Diagnostik und Interventionelle Radiologie. Sauerbruchstr. 7, D -38440 Wolfsburg. Gcnnany_ TeL: ++49 (0) 63 61-80 38 44: E-mail: [email protected] 0344-033812000/196/12-827 $15.00/0
828 . M. Bradaczek ct a!. or less defined density deviations. The small angle scattering measurement is normally not suited for measuring the exact structure of the electron density of more complex biological structures. The major goal of those measurements can only be to get a rough information on the size distribution of the density. Therefore, with the present knowledge, only comparison between standards and actual measurements is considered a suitable method to be used in diagnostic pathology. All the more, it is surprising to obtain clear differences in the measurement results between normal and tumor tissue. For routine examination in medicine, several applications have been described in the literature over the past few years /3, 5, IO}. The reason for this relatively late application might be explained by the fact that a connection between the theoretical background and the practical use could not be easily found . As shown in Material and Methods, X-ray small angle scattering is caused by the so-called particle size effect. The scattering depends on the size, size distribution , and the form of the particles in the sample. There would be significant progress ifit were possible to compare measurements of different samples (e.g., cancer tissue and normal tissue). It can be shown that there are possibilities of a unique diagnosis. Although the X-ray small angle scattering method in medicine is not yet fully developed, it has some advantages over conventional methods, allowing the examination of very small samples for in vivo measurements.
Materials and Methods
luted in a complex way. In vivo measurements may not be
possible with that type of camera. The Kiessing camera (Fig. 2) uses a point-like focus. It seems to be more flexible 10 use modern X-ray optical tools, such as collimators, which could be much smaller in size and better suited for in vivo measurements. The diffracted function should be evaluated in two dimensions. The major problem of all small angle cameras is the exact entrapping of the primary beam. Following the kinematical theory of X-ray diffraction, a monochromatic beam hitting the electrons of a sample emits a spherical wave. By overlapping all spherical waves of the different locations within thc sample in the detector, the information about the phases gets ol st, and the intensity corresponds to the square of the superposition of all waves. This iscallcd "phase problem of the crystallography", because this loss of phase information makes the recalculation of the structure of a sample much more complicated. With the structure of a sample being p (x,)\ zi, its diffraction diagram can be calculated by the Fouriertransform of pix, y, zi. F(It, k, Ii ;
f p ix. y, z)e-"""""" dxdydz**)
( I)
which might be written in a short form (2)
where x, y, z are coordinates in the physical space and h, k, I those in the Fourier space. This general formula is valid for all kinds of structures, except for perfect crystals where the dynamic theory has to be considered. In the case of small angle scattering, the form and thc size of particles within the sample are the determining factors.
In an imaginary sample consisting of spheres of constant The best known X-ray small angle instrument is the Kratky
(de termining) size and material (electron density), the assem-
tion. ]ts disadvantages are its relatively large size, a very broad primary beam . and the fact that it can measure only one
interference of rays between the spheres. Then the scattering
camera. (Fig. I). which has an excellent primary beam limitaside of the primary beam. Because of the overiapping of the broad reflected beam, the resulting curve has to be deconvo-
bly of the spheres should not be too dense, so that there is no
of this sample is just the scaUering of one sphere multiplied by the number n of spheres in the radiation range
FJ.: ; n . p0 .
f ('
')~1X,}:~J~
-?lfi{ir.tf"ky+I:)dxdydz
(3)
Linear Detector Primary beam limitator
where Sir. is the function of the sphere.
Sca tlered beam
I..., Fig. I. Conventional Kratky camcra.
Results and Discussion The Fourier transform of S, with the radius R can be expressed by [2}
Detec tor Sample Primary beam
.I, ;
FT(SJ ;
~
7r R] . 3(sin~ -
~cos~)/ ~
(4)
with ~; 27r Rlul and lu i; / h' + Ie' + I' G lass tube collimator
Primary beam hap
Fig. 2. Modified Kiessig earnem.
"dh, k, /) has approximately the form of cos Rlul. Roughly expressed, the width of the scattered profile is reciprocal to the size of the particles.
Small Angle Scattering in Tissue Samples . 829 Focu;
Polydisperse sample
Monodisperse sampl~ with nonspheric particles
Irtensity-ftrcticn of scattefirg
Fig. 3. Left: Principle of X-ray small angle scattering of monodisperse particles. Right: A sample with polydispersc and nonsphcric particles.
Relative Intensity 140
- - - - - --
-
- - - -- -- - - -- -
\ 120 -
i
Based on the width of the scattering curve, the size R (4) of the spheres can be roughly recalculated (Fig. 3). In reality, this can only be checked with such well-defined inorganic samples as explained above. If the sample contains spheres of various radii, their distribution can be described by a Maxwell function {lO}. Comparing the Fourier transform of the Maxwell function with the measurement, it is possible to obtain some information about the size distribution of spheres within the sample. If the form of the particles diverges significantly from the spheres, it can be determined by the form of the scaHering curve. In reality, the ideal shape of the particles (spheres) is reached only in very few cases. If, as in medicine, there is only a limited number of different samples to be measured, a comparison between a standard sample and the sample to be examined may lead to signi ficant results. Fig. 4 shows small angle scattering curves of three types of tissue samples: 1-3, breast canccr; 4-6, fibroadenoma; and 7-9, normal breast tissue II j. Small angle scattering can also be used to find out periodical elements in the sample. Fig. 5 shows the scattering image of Lipopolysaccharide membranes which arc stackcd periodically. The major goal of this paper was to show that small angle X-ray scattering opens several possibilities for powerful diagnostic methods. While this method has been used in material science and biology for several years, its development as a diagnostic tool in pathologic practice seems to be only at the beginning. The example of the scattering results of breast cancer (Fig. 4) may encourage other research groups to find new objects of investigation.
)
'J ~ 100
.\ ',\
·..l11\
~J
80·
[) 60 ·
.1 '
..\ \
'.\ ~
[Breast ~
40 ,
20
........ , ".
- -"
,.,. --~~., ~
..
Fig. 4. Comparison of samples from normal tissue and different tumors of the breast.
Fig. 5. Small angle scattering of lipopolysaccharidcs of Salmonella bacteria using a Kiessig camera.
830 . M. Bradaczek et a!.
References I. Avtandilov G, Barsanova T, Dembo A, Lazarev P, Paukshto M, Shkolnik L, Zayratiyants 0 (1999) Histostereometry and ultra low angle X-ray scaltering: New non-invasive morphological diagnostic method of breast cancer. VirchowsArch435: 183 2. Bradaczek H (1981) Potential energy calculations of molecular and crystal structures in Fourier space. J Phys C: Solid State Phys 14: 1-7 3. Grant JA, Morgan MJ, Davis JR, Davies DR, Wells P (1993) X-ray diffraction microtomography. Meas Sci Technol4: 83-87 4. Guinier A ( 1952) Zeitschrift fUr Metallkunde 43: 217 5. Harding G, Kosanetzky J, Neitzel U (1985) Elastic scatter computer tomography. Phys Med BioI 30: 183- 186 6. Hosemann R, Bagchi SN (1962) Direct Analysis of Diffraction by Malter, North-Holland Publ ishing Company, Amsterdam
7. Kratky 0 (1940) Rontgenographische Untersuchung des hochdispersen Verteilungszustandes in einem Faserstoff. Z Elektrochcm 46: 535-555 8. Labischinski H, Barnickel G, Bradaczek H, Naumann D, Rietschel ET, Giesbrecht P (1985) High state of order of isolated bacterial lipopolysaccharide and its possible contribution to the permeation barrier property of the outer membrane. J Bacteriol 162: 9-20 9. v. Laue M (1960) RontgenSlrahlinterferenzen. 3rd ed. Akadem Verlagsges, FrankfurtlMain 10. Westmore MS, Fenster A, Cunningham IA (1996) Angular-depended coherent scalter measured with a diagnostic X-ray image intensifier-based imaging system. Med Phys 23:723-733
Received: January 31,2000 Accepted in revised version: July 18,2000