The Investigation of Cancerous Human Bone (Osteoclastoma) by Small-Angle X-Ray Scattering

A. PATEL,* B. CH. KHANDUALA, G. B. THAKUR,? AND H. LABISCHINSKI,$ Department of Physics, Berhampur University,

Berhampur- 760007, Orissa, India.

Synopsis

Small-angle X-ray scattering methods were applied to provide a pore analysis of cancerous human bone (osteoclastoma). For experimental measurements of the scattering intensities a small-angle Kratky camera, equipped with a counterattachment and a programmable step-scanning device, was used. By applying the theories of Kratky, Porod, Debye, and Bueche, applicable to a densely packed two-phase system belonging to a general micelle system, macromolecular parameters such as specific inner surface, length of coherence, range of inhomogeneity, void percentage, and transversal lengths 1, and iz were evaluated and found to be 4.69 X A-l, 21.39 A, 18.01 A, 0.21%, 18.01 A, and 8.53 X lo3 A, respectively. A comparison of these parameters with those of pure human bone revealed a macromolecular dissociation in osteoclastoma.

INTRODUCTION

Small-angle x-ray scattering is due to the heterogeneity of electron density occurring in matter at colloidal orders of magnitude. This idea has been es- tablished experimentally by Barton1 and Vineyard.2 Debye and Bueche,3y4 have reported on it in theory. Thus in particle scattering objects are reduced to a two-phase system, after Kahovec et al.5, in which objects contain regions ho- mogeneous in themselves but with two different electron densities that produce the scattering (Smoluechovski6). If the densities are uniform, no scattering will occur because interference is complete. When the substance is in a three-phase system, different theories are a ~ p l i e d . ~

In a densely packed, two-phase system belonging to a general micelle system one must resort to pore analysis of the substances. Therefore we restrict our- selves to macromolecular parameters derived from certain characteristic con- stants of the scattering curve. The theories of Kratkp were used to evaluate the macromolecular parameters such as specific inner surface, heterogeneity distance, coherence lengths, and percentage of void present in the specimen. Here we have taken bone tissue (osteoclastoma) which can be treated best as a two-phase system composed of a phase of hydroxyapatite microcrystals dispersed in a homogeneous matrix. The dispersing medium was a matrix of collagen fi- bers, ground substances, dissolved body salts, and water.g

* To whom correspondance should be addressed. Present address: Department of Chemistry

t Department of Orthopaedic, M.K.C.G. Medical College, Berhampur-760004, India; * Institute of Crystallography, Freie University, Berlin, West Germany.

& Chemical Engineering, Steven Institute of Technology, Hoboken, New Jersey 07030, U.S.A.

Journal of Polymer Science: Polymer Chemistry Edition, Vol. 21,2937-2944 (1983) 0 1983 John Wiley & Sons, Inc. CCC 0360-6376/83/102937-08$01.80

2938 PATEL ET AL.

The bones of younger animals are richer in the amorphous-to-x-ray phase than are those of older animals.1° In addition, experiments on bone resorption have shown that the x-ray amorphous content of bone mineral is more active meta- bolically than the crystalline. On the other hand, bone mineral consists of finely divided particles with a large specific surface and high specific reactivity. This surface provides an efficient interface for chemical interchange with body fluids and for bonding the organic phases of bone.ll Therefore we were tempted to evaluate macromolecular parameters like specific inner surface, transversal lengths, length of coherence, range of inhomogeneity, and percentage of void present in cancerous human bone (osteoclastoma) by small-angle x-ray scattering methods.

MATERIALS AND METHODS

Osteoclastoma is a tumor arising at the end of long bones. The sample iden- tified as osteoclastoma was collected from the local medical college (M.K.C.G. Medical College, Berhampur, Orissa, India). It was powdered to destroy any orientation and packed tightly into a markcapillary tube. The x-ray unit which consisted of a Phillips PW 1140 diffraction tube fitted with a copper target was run at 50 KV and 50 mA during the time of exposure. The markcapillary tube which contained the sample was mounted in a Kratky camera12 which has a collimation system that can take measurements down to an angle corresponding to a Bragg value of 20,000 A. The scattering intensities were recorded with a proportional counter and a pulse-height discriminator as a detector for the Cu lines K , and Kg. Elimination of Kg was effected with a computer program suggested by Glatter.13 An electronically programmable step-scanning de- vice14J5 combined with a Phillips x-ray measuring instrument allowed automatic operation. The scattering curves were recorded several times and, as a rule, 20,000 pulses were registered for each measuring points. A statistical evaluation of the data16 and the influence of CuKg radiation were made by the Glatter13 method. Here we have represented I9 by a quantity X; that is, X = 2aI9, where 8’ is half of the scattering angle and a’ (20 cm) is the distance between the sample and the plane of registration. It was discovered that bone mineral shows a poorly resolved x-ray diffraction pattern which resembles that of the mineral hydrox- yapatite Ca10(P04)~ (0H)z. Chemical analysis of the bone mineral revealed calcium phosphate with a Ca:P ratio of hydroxyapatite and substantial amounts of COi- (5%), citrate (0.8%), Mg2+ (0.5%), and Na+ (0.7%) and trace amounts of C1-, F-, K+, Sr2+.

THEORY AND DISCUSSION

In a general two-phase system with close packing and random distribution of scattering particles, Guinierl7 plots do not show straight-line slopes. Ac- cording to the theory of Porodls it then becomes more advantageous to explore the tail end of the scattering curve to obtain physical information concerning the nature of the scattering particles. To test the bone tissues as a densely packed two-phase system a double logarithmic plot (Fig. I), which showed a slope of (-4), was plotted. Moreover, Eanes and Posnerg discuss the binary system of bone tissue in an x-ray study of bone minerals. Therefore, the Porodlg theory

INVESTIGATION OF CANCEROUS HUMAN BONE 2939

L 1

$2 - 0.8 - 0.4 - 0.1 L 9 X

Fig. 1. The double logarithmic curve.

can be used to evaluate the gross morphological structure of bone tissue (osteo- clastoma).

Evaluation of Macromolecular Parameters of Osteoclastoma

The invariant of the scattering curve introduced by Porod18 is given by

for desmeared intensity (Fig. 4), whereas Qth is given by

after Kratky,20 where w and w2 are the volume fractions of the void and air and matter, respectively, e’ is the electronic charge, m’ is the mass of electron, c’ is the velocity of light, x’ is the x-ray wavelength (A = 1.54 A), N’ is Avogadro’s number (6.025 X lO23), D’ is the effective sample thickness, PO’ is the intensity of the primary beam (3994.42 X lo4 countsh) a’ is the counter-sample distance (20 cm), and p’ is the electron density of the scattering particles. The intensity, which decreases proportionally to X-4, is based on the fact that homogeneous electron density distribution occurs in each phase. The I ( X ) X 4 us. X4 (Fig. 2) plot yields the background scattering constant K2 as the slope of the curve, suggested by Kratky.21

Percentage of w1

The effective sample thickness D’ is given by

2940 PATEL ET AL.

Fig. 2. A comparison of characteristic curves.

where the compact density 6, is the density of collagen (1.18 g/cm3, after Pomery and Milton22) and the apparent density 6, = 1.12 g/cm3. 4 is the inner diameter of the capillary tube (0.09 cm). The value of D calculated was 0.087 cm.

The electron density of the substance is given by Kratky et al.23 as

co CA

p = 6, - = 0.66,

where ZO is the sum of atomic numbers and ZA is the sum of atomic weights. We have specified ZOIZA as being equal to 0.56, as suggested by Posner and Betts.ll The primary beam intensity Po was calculated with a calibrated stan- dard (Lupolen) sample24 and the value was 3994.42 X lo4 countsh.

By equating Qenpt with Q t h we obtained

7.9 x 10-26 4T

530 = X3N2Paap 2w w 2

Substitution of the respective values in this equation yielded wlwz = 2.11 X because w2 N 1, the volume fraction of void contained in the sample, was 0.21%.

Specific Inner Surface

The specific inner surface, which is defined as phase boundary area per unit volume of the dispersed phase, is given by

for desmeared intensity. Substitution of respective values yielded

0 V - = 4.69 x 10-4 A-1

INVESTIGATION OF CANCEROUS HUMAN BONE 2941

Transversal Lengths

If we shot arrows through the system in all directions, measured the average intersectional lengths of the arrows with the two phases, and called them transversal lengths 11 and t2, we would obtain

and

for this substance.

The Range of Inhomogeneity

The range of inhomogeneity 1, is given by

1, = 4 (F) w1w2 = 4 (j w1

because w2 = 1 or 1, = 11; thus the range of inhomogeneity corresponds to the reduced mass in mechanics.

The Length of Coherence

The coherence length I , is given by

where E = J;I (X)X dX is the integrated scattered energy equal to 736.20 cm2. By substituting the respective values we obtained 1, = 21.39 A.

Comparison of Results

With the help of the methods discussed we also evaluated the macromolecular parameters of pure bone under identical experimental conditions. The results of desmeared and smeared scattering intensities are listed in Table I.

TABLE I Comparison of Results

Void O N 11 12 1, 6 , Sample x 10-4A-1 (A) x 103A (A) (g/cm3)

Osteoclastoma 0.21 4.69 18.01 8.53 21.39 1.12 0.10 1.75 24.22 22.85 13.61 -

Pure bone 0.17 4.19 16.23 9.53 24.82 1.30 a 0.085 2.66 12.78 15.03 15.79 -

a

a Results calculated from smeared intensities.

2942 PATEL ET AL.

The scattering curves, the plots for the constants K1 and Ka, and the invariant curves of pure and cancerous bone have also been compared (Figs. 2,3 , and 4) in a study of macromolecular deformations in cancerous bone (osteoclas- toma).

CONCLUSIONS

The results obtained by the small-angle x-ray method are more precise and accurate when applied to a monodispersed colloidal system in which interparticle interference is completely absent. With a concentration that is too high inter- ference of the waves scattered by the single ptirticle, which flattens out the in- nermost portion of the scattering curve, takes place. With a strongly polydis- persed solution for which the distribution of particle sizes or voids ranges from colloidal to smaller dimensions the scattering intensity often rises to high values at small angles. It has been shown that interparticle interference is predomi- nant,25 particularly in the inner portion of the curve.

In a densely packed two-phase system, which belongs to a general micelle system like ours the tail portion of the scattering curve26 is used to determine the characteristic or run constant of the scattering curve which is proportional to the total surface area of the scattering particles. Therefore, we should be contented with the pore analysis of a substance that is made with the invariant Q and run constant K1. Some complications, however, are met in measuring the tail end of the curve at large angles and errors occur in the evaluation of the invariant Q and run constant K1. First, the value of scattering intensity is small in this range and multiplication of the high value of X increases the value of I ( X ) X 2 ; thus the invariant curve is elongated at large angles. This elongation

x (cm)

Fig. 3. A comparison of scattering curves. (0) Pure bone, (0) osteoclastoma.

INVESTIGATION OF CANCEROUS HUMAN BONE 2943

NCm)

Fig. 4. A comparison of invariant curves. (0) Pure bone, (0) osteoclastoma.

is eliminated by the application of a broad primary beam which counteracts the decrease in inten~ity.~7 Second, the scattering curve of a system often consists of particles and voids or dissolved particles which prevent it from approximating the final value of zero. This is the effect caused by the “liquid structure” of the particles. Luzzati et a1.28 concluded that fluctuation of electron density in small angles leads to an additional constant term K2 which must be subtracted from the scattering curve.

A comparison of the scattering curves of pure and cancerous human bone (osteoclastoma) (Fig. 3) led us to the conclusion that the polydispersity in pure bones is greater than that in osteoclastoma because the scattering curves of pure bone rise sharply as the scattering angles decrease. In Figure 2 the K1 and K2 values of pure bone and osteoclastoma indicate that the macromolecular struc- ture is liquified when the pure bone is invaded by cancer. Because the run constant K1 is proportional to the total surface area of the scattering particles, the comparison of K1 values in Figure 2 also indicates that a dissociation of scattering particles occurs in osteoclastoma. The high percentage of void, the transversal length 11 in void, and the low value of the length of coherence 1, and 6, in Table I are in agreement with the fact that dissociation of the scattering particles occurs in osteoclastoma. Because the invariant of the scattering curve Q depends on the total volume of the dispersed phase and is independent on the shape and size of the particle responsible for scattering, it is seen in Figure 4 that the volume of the dispersed phase is greater in osteoclastoma. The low value of I , and high value of 1, in cancerous human bone are indicative of retarded metabolism in osteoclastoma. These findings may throw light on the tertiary structural deformation of human bone invaded by cancer.

The authors wish to thank the Council of Scientific and Industrial Research (New Delhi) for awarding a research fellowship to B. Ch. Khanduala to carry out this work. They are also grateful to Professor H. Bradaczek who made the experimental facilities a t his laboratories a t Freie University, Berlin (West) available to them.

2944 PATEL ET AL.

References

1. H. M. Barton, Phys. Reu., 79,211 (1950). 2. G. H. Vineyard, Phys. Reu., 74,1076 (1948). 3. P. Debye and A. M. Bueche, J. Appl. Phys., 20,518 (1949). 4. P. Debye and A. M. Bueche, Theoretical and Applied Colloid Chemistry, Vol. 7, Reinhold,

5. L. Kahovec, G. Porod, and H. Ruck, Kolloid Z., 133,16 (1950). 6. M. V. Smoluechovski, Ann. Phys., 21,756 (1906). 7. 0. Kratky and I. Pilz, Q. Rev. Biophys., 5,481 (1972). 8. 0. Kratky, Progr. Biophys., 13,107 (1963). 9. E. D. Eanes and A. S. Posner, Proceedings of the Conference Held at Syracuse University,

June 1965, on Small-Angle X-Ray Scattering, H . M . Brumberger, Ed., Gorden and Breach, New York, 1967.

New York, 1950.

10. J. D. Termine and A. S. Posner, Science, 153,1523 (1966). 11. A. S. Posner and F. Betts, Acc. Chem. Res., 8,273 (1975). 12. 0. Kratky and Z. Skala, Z. Elektrochern., 62,73 (1958). 13. 0. Glatter, J. Appl. Crystallogr., 10,415 (1977). 14. 0. Kratky and C. Kratky, Z. Znstrumentenkd., 72.302 (1964). 15. H. Leopold, Elektronik, 14,359 (1965). 16. P. Zipper, Acta Phys. Austriaca, 30,143 (1969). 17. A. Guinier, J . Chem. Phys., 40,133 (1943). 18. G. Porod, Kolloid Z., 124;83 (1951). 19. G. Porod, Kolloid Z., 125,51 (1952). 20. 0. Kratky, G. Porod, A. Sekora, and B. Paletta, J . Polym. Sci., 16,163 (1955). 21. 0. Kratky, Naturforscher, 18,180 (1963). 22. C. D. Pomery and R. G. Milton, J. SOC. Leather Trades Chem., 35,360 (1951). 23. 0. Kratky and G. Miholic, J. Polym. Sci., A2,449 (1963). 24. I. Pilz and C. Kratky, J . Colloid Interface Sci., 24,211 (1967). 25. An. N. J. Heyn, Appl. Phys., 26,519 (1955). 26. S. Guinier and G. Fournet, Small-Angle Scattering of X-Rays, Wiley, New York, 1955, pp.

27. 0. Kratky, Pure Appl. Chem., 12,483 (1966). 28. V. Luzzati, K. Witz, and A. Micolaiett, J. Mol. B i d , 3,367 (1961).

158.

Received October 8,1982 Accepted March 22,1983