574 Biochimica et Biop,~vsica Acta 883 (1986) 574-579 Elsevier

BBA 22451

X-ray determination of the crystallinity in bone mineral

N o r i o M a t s u s h i m a a, M a s a y u k i T o k i t a b a n d K u n i o H i k i c h i b

" Division of Liberal Arts and Science, School of Allied Health Professions, Sapporo Medical College, Minami-3, Nishi-17, Chuo-ku and b Department of Polymer Science, Faculty of Science, University of Hokkaido,

Kita-lO, Nishi-8, Kita-ku, Sapporo 060 (Japan)

(Received 24 March 1986)

Key words: Mineral content; X-ray diffraction; Ruland method; Crystallinity; (Bone)

The X-ray diffraction method of Ruland (Acta Crystallogr. 14 (1961) 1180-1185) used for the crystallinity determination of synthetic polymers was applied to the mineral present in mature rat cortical bone. The results obtained were compared with those obtained by other X-ray methods of Harper and Posner and Wakelin, Virgin and Crystal. It was concluded that the method of Ruland gives a more reliable determination of the crystallinity of hone mineral than other methods.

Introduction

X-ray diffraction analysis has been extensively employed for studying bone tissue since de Jong applied it for the first time [1-4]. X-ray diffraction and chemical analyses show that the mineral de- posited in mature bone is very similar to hydroxy- apatite (Cas(PO4)3(OH)). It is also known that the bone mineral is not entirely crystalline, as inferred from diffuse X-ray scattering. The non- crystalline phase is generally attributed to the very small size of crystallites a n d / o r the presence of an amorphous phase.

Up to date, the weight fraction of the crystal- line phase in bone mineral has been determined by using X-ray methods developed by Harper and Posner [5] and Wakelin et al. [6] and the infra-red method developed by Termine and Posner [7]. Recently, it was strongly suggested that use of the method of Harper and Posner should be discon- tinued [8]. The method of Wakelin et al., which at

first was developed for crystallinity determination in the field of organic polymer science, requires two calibration standards, one being 100% crystal- line and the other completely amorphous. How- ever, very recently Grynpas et al. [9] argued against the hypothesis that a completely amorphous phase is present in bone mineral. It thus seems desirable to establish a new method for the crystallinity determination of bone mineral.

Rulund [10] has devised another method for the crystallinity determination of polymers. This method, which makes use of neither crystalline nor amorphous calibration standards, has a good theoretical foundation.

The purpose of the present paper is to de- termine the crystallinity of the mineral in mature rat cortical bone using the method of Ruland and to compare the results obtained here with the results obtained by other X-ray methods.

Materials

Correspondence address: Division of Liberal Arts and Science, School of Allied Health Professions, Minami-3, Nishi-17, Chuo-ku, Sapporo 060, Japan.

Rat femoral cortical bone of one year of age was used. The bone was deproteinated by extrac- tion with hydrazine for 48 h at 55°C. It has been ascertained by Termine et al. [11] that the mor-

0304-4165/86/$03.50 © 1986 Elsevier Science Publishers B.V. (Biomedical Division)

phology of bone mineral is unchanged upon hy- drazine treatment.

Two reference standards were used also. We chose as a 100% crystalline standard commercial hydroxyapatite heated at 700°C for 2 h. Synthetic amorphous calcium phosphate was prepared by the method of Eanes et al. [12]: a 0.250 molar solution of (NH4)HPO 4 was rapidly added while stirring to a 0.750 molar solution of CaC12. The mixing of the reactants was completed within 15 min to avoid conversion into crystalline hydroxy- apatite, and then the precipitate was lyophilized. All samples were stored in a desiccator.

Harper and Posner method For the application of the method of Harper

and Posner [5] as well as that of Wakelin et al. [6] a Rigaku Denki diffractometer was used with a Phillips-line focus tube excitated at 35 kV and 20 mA. The monochromatization was achieved using Ni-filtered Cu-Ka radiation and a scintillation counter in combination with a pulse height analyzer. The symmetrical reflection mode was employed, and a 1 /2 ° divergence slit and a 0.3 mm receiving slit were used. The powdered sam- ples were step-scanned at 0.05 ° 2 ~ / s t ep , 80 s /s tep . The Harper and Posner method is based on a linear proportionality between the integrated intensity (Bragg peak area) in a crystalline phase in a mixture and its weight fraction, i.e. the crys- tallinity. The crystallinity of bone mineral, Xcr, is determined from a comparison of the integrated intensity of a crystalline phase in the bone mineral with the corresponding integrated intensity from a 100% crystalline hydroxyapatite standard. The fol- lowing equation, as definition of the crystallinity of the bone mineral, has been used [5]:

Y~Jb Xcr = E l c ( ! )

where ~ I b is the summed integrated intensity of the (310) and (002) reflections of the bone mineral sample, and E I c is the summed integrated inten- sity of the (310) and (002) reflections of the 100% crystalline hydroxyapatite standard, determined under experimentally identical conditions.

Fig. 1 shows X-ray diffraction patterns from the powdered samples of bone mineral studied

575

i I, !'

2e

Fig. 1. X-ray diffraction patterns between 24.0 and 29.0 and 37.0 and 42.0 degrees 2v ~. A, the mineral in mature rate cortical bone; B, highly crystalline synthetic hydroxyapatite.

and the crystalline hydroxyapatite used as a stan- dard. The integrated intensities of the (002) and (310) reflections from the bone mineral sample were measured by summing the counts over the ranges of 2~ = 24.50-27.0 ° and 38.0°-41.4 °, re- spectively, and subtracting the background ob- tained by linear interpolation between minima oia either side of each peak. The integrated intensity of the (002) reflection contains a very small contri- bution from the unsolved (201) reflection, while the (310) peak includes the unsolved (212) and (221) reflections in addition to the (310) reflection. Because we used a bone mineral sample from which the non-mineral constituents (water, col- lagen, etc.) were removed, the X-ray absorption for the non-mineral constituents were not taken account. The Harper and Posner method yielded a value of 0.53 for Xcr.

Wakelin, Virgin and Crystal method The principle of the Wakelin et al. method [6] is

based on the measurements of intensity dif- ferences over an angular range of sufficient size to include most of the crystalline peaks. Their method represents numerically the degree of order in a given specimen relative to the minimum and maxi- mum values that are observed in a sampling of specimens of the same species. For that reason it is necessary to compare the scattering intensity of a specimen in question point by point with the corresponding intensity from the reference stan- dards of minimum and maximum crystallinity. The crystallinity, Xcr , termed 'crystallinity index'

576

is defined as follows [6]:

20m

E lb -- la 20o

x . 2o~ (2)

where Ic, I a and I b a r e the numerical values of the scattering intensity of crystalline hydroxy- apatite standard, the amorphous calcium phos- phate standard and the samples of unknown crys- tallinity, respectively, at all incremental points be- tween angular limits 2~ 0 and 20 m. Eqn. 2 is seen to be a measure of the area between the curves of I b and I a divided by the area between the curves of I c and I a.

The scattering intensities of the bone mineral sample were measured over the angular range 2 0 = 20.00-50.0 ° under identical conditions to those used with the Harper and Posner method, as shown in Fig. 2. The scattering intensity was cor- rected for the X-ray absorption, because the ab- sorption coefficient of amorphous calcium phos- phate differed from those of the bone mineral and crystalline hydroxyapati te used. The resulting value for Xcr was 0.48.

Ruland Method The method of Ruland [10] is an absolute one

that does not require reference standards. X-ray measurements on the powdered sample were made on a Rigaku Denki diffractometer with a scintilla- tion counter. The monochromatization of C u - K a radiation generated at 35 kV and 22 mA was achieved by a Ross balanced filter. The symmetri- cal reflection mode was employed, and the detec- tor was scanned in steps of 2t~ = 0.1 ° and 0.4 ° over angular ranges 20 = 10.0°-135.0 ° and 135.0°-162.2 ° , respectively. Divergence slits of 1 / 6 °, 1 / 2 °, 1 °, 2 ° and 4 ° were used, depending on the range scanned, and a 0.3 m m receiving slit was used. The angular range scanned was over- lapped to allow for internal scaling. The scattering intensity was measured for a fixed counting time period giving a minimum of 10000 counts at each step. Angular dependence of the X-ray absorption correction was neglected by using thick samples. Because the Ca : P ratio of mature rat bone mineral

A

J

fl / ,

ill ; I I . ~ ',

2JO • . . . . • i_ J I 2

25 3 0 3 5 4 0 4 5 5 0

2 0

7 j ~ ~ - ~ - . . _ J

J__

2 0 25 3 0 3 5 4 0 4 5 5 0

20

~ _ _ i J. 1 L . . . . . . . . . . J. 2 0 25 3 0 3 5 4 0 4 5 5 0

2 0

Fig. 2. X-ray diffraction patterns between 20.0 and 50.0 de- grees 20. A, the mineral in mature rat cortical bone; B, synthetic amorphous calcium phosphate; C, highly crystalline synthetic hydroxyapatite.

is very close to that of hydroxyapatite, we rea- sonably assume in the Ruland analysis that the non-crystalline phase of bone mineral studied has the same chemical composition as the crystalline one, namely, that both the crystalline and non- crystalline phases consist of hydroxyapatite.

After correction for the polarization factor, the corrected intensity Icor(S ) was normalized to an

absolute unit using the following equation:

l(s) =t~Icor(S)-Iinc(S) (3)

where l(s) is the intensity of total coherent scattering (Bragg peaks plus diffuse scattering) of bone mineral in electron units, normalized to the average per atom of the magnitude of the scatter- ing vector (s = 2 sin O/)~). /3 is the normalization factor, and Ii.~(s) is the intensity of Compton scattering. The normalization constant was de- termined by the method of Norman [13].

The crystallinity of the bone mineral sample, X¢~, is defined using this coherent scattering as follows:

2 £ s GO)as X.=C. fo~s~l(s)ds

(4)

where Icr(S ) is the intensity of coherent scattering under Bragg peaks. The correction factor, C, is given by

c = £oo q : ( , ) e_ , , ,~ (5)

where

~=ENifi2/ENi (6)

is the weighted mean square of the atomic form factor of hydroxyapatite, f~ is the form factor of an atom of type i, and N i is the number of such atoms. The imperfection factor, k, arises since thermal motion and lattice imperfection cause part of the X-ray intensity scattered from the crystal- line region to appear in the diffuse scattering.

Eqns. 4 and 5 give

fo~S21cr(s)ds ~ 2 fos (s)as (7)

The two parameters crystallinity, Xcr, and imper- fection factor, k, have to be determined simulta- neously. Moreover, the finite range of 20 of the experimental data (and of s) necessarily limits the

577

integration range from 2#0 = 10.0 ° (So = 0.1) to 20m = 162.2 ° (Sin = 1.2).

When a number of integration intervals (limits s o and Sm) over larger regions of s are chosen, the next equation should be satisfied:

fs sZl(s)ds = s"s2~ s ds Sm fs O f ( ) (8)

The crystallinity thus can be estimated with rea- sonable accuracy by the limited-range intervals of Eqn. 7.

f, lms2G( s )ds

X~r=C(k ) fsi,,s2i(s)d s (9)

For fixed s 0, if s m is large enough, the inferred crystallinity is independent of sm. Therefore, the best value of Xcr is determined by varying the disorder parameter (k), computing Xcr as a func- tion of the upper limit (sin), and finding the value of k that yields a constant Xcr, i.e., independent of sm.

Fig. 3 shows the curves plotted as s21(s) vs. s of the powdered sample of bone mineral studied. The total intensity was resolved (using the Spline function) into the diffuse scattering contribution and the crystalline diffraction contribution, S2Icr(S). When s o = 0.1, we can choose s m = 0.6 for a minimum value of s m using Eqn. 8. Table I shows the numerical results which were obtained

3O

Z

2o

%

o .o o.2

r i i i i

0 . 4 0 . 6 0 .8 1 .0 1 ,2

s (A - 1 )

Fig. 3. X-ray diffraction curves s2l(s) versus s for the mineral in mature rat cortical bone.

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TABLE I

CRYSTALLINE FRACTION, X~r , OF THE MINERAL IN MATURE RAT CORTICAL BONE AS A FUNCTION OF k AND INTEGRATION INTERVAL

Interval k = 0.0 k = 1.2 k = 2.0

(So --Sin) 0.1-0.6 0.456 0.570 0.657 0.1-0.8 0.387 0.555 0.690 0.1-1.0 0.332 0.563 0.757 0.1-1.2 0.281 0.571 0.821

Mean Xcr 0.57

TABLE II

COMPARISON BETWEEN THE CRYSTALLINE FRAC- TION OF THE BONE MINERAL, Xcr, OBTAINED BY THREE X-RAY METHODS

Method Mature rat Human cortical femoral bone cortical

bone a

Harper and Posner 0.53 0.43 Wakelin et al. 0.48 0.53 Ruland 0.57

a According to Grynpas, M.D. [14].

using four angular ranges terminating at s m = 0.6, 0.8, 1.0, 1.2. As shown in Table I, the most reliable value of Xc~ was estimated to be 0.57 by setting k equal to 1.2.

Table II shows the crystallinity value of the mineral in mature rat bone used for a comparison between three X-ray methods. The erystallinity value obtained by the Ruland method is higher than those obtained by the Harper and Posner and Wakelin et al. methods.

Discussion

It is clear from the above explanation that both the Harper and Posner and Wakelin et al. meth- ods are simpler, less time-consuming and give only relative values of crystallinity. On the other hand, the Ruland method involves rather laborious calculations and gives an absolute value of crystal- linity.

Harper and Posner [5] employed crystalline standard hydroxyapatite having the same crystal- linity size a n d / o r crystal perfection as the bone mineral samples used for the crystaltinity de- termination of bone mineral. However, even if such a crystalline standard is selected for use in Eqn. 1, it has been reported by Miller and Burnell [8] that this results in an overestimation of the amount of non-crystalline material present in bone mineral. They attributed this to the effects of crystal-size distributions, which may vary for dif- ferent crystallographic directions in bone mineral.

Table II includes the crystallinity values of mineral in human femoral cortical bone obtained by Grynpas [14], who used a powdered fluoro- apatite (Cas(PO4)3F) as a pure crystalline material. He reported that the Wakelin et al. method was more reliable than the Harper and Posner method, because it takes into account the large angular range of X-ray diffraction patterns. The fluoroapatite does not clearly represent the crystalline mineral present in bone. X-ray radial distribution function analysis of hydroxyapatite and amorphous calcium phosphate [9] and com- puter simulation of X-ray diffraction patterns of microcrystalline hydroxyapatite [15] showed that amorphous calcium phosphate is distinct from hydroxyapatite. Phosphorus NMR study of solid amorphous calcium phosphate [16] also showed that it is not a poorly crystalline hydroxyapatite. Synthetic amorphous calcium phosphate thus does not represent the true non-crystalline mineral in bone. Therefore, the Wakelin et al. method cannot be used to determine the crystallinity of bone mineral.

As described above, not only the non-crystal- line mineral but also the disorder of the crystalline part contribute to the diffuse scattering. Only the Ruland method takes into account the effects of the diffuse scattering due to the disorder, which probably lowers the crystallinity value obtained by the other two methods. The results shown in Table II may indicate such a lowering behavior, though the Harper and Posner method seems to give a value comparable with that of the Ruland method.

The imperfection factor, k, obtained together with the crystallinity is described by the sum of three terms due to thermal motions (k x) and

lattice imperfections of the first (k~) and second (kll) kind [17]:

k = k T + k t + kll (10)

Crystal-structure studies [19] led to a mean iso- tropic thermal vibration coefficient of B = 0.47, which gives k T = B / 2 = 0.24 A 2. Thus k - kT has a value of 1.0, which is about 4-times as large as the value of kT. This indicates that the contribu- tion from the lattice imperfections to the disorder of the crystalline region of bone mineral is more predominant than that from the thermal motion. However, how these imperfections are appor- tioned between types I and II cannot be de- termined from the Ruland method of analysis. Wheeler and Lewis [18] argued that the crystalline hydroxyapatite of untreated mature cortical bovine bone is characterized by lattice imperfection of type II; it has a paracrystalline structure. It seems to be the subject of further research whether lattice imperfections of both the first and second kinds are present in the crystalline mineral of bone.

In conclusion, we showed that the Ruland method for the crystallinity determination of bone mineral gives a more reliable value.

Acknowledgement

We gratefully acknowledge Dr. C.G. Vonk of DSM Central Laboratory for useful suggestions for the correction of the Compton scattering and Dr. K. Kumazaki of Hokkaido Institute of Tech- nology for the preparation of crystalline hydroxy-

579

apatite. The dedicated technical assistance of Mr. T. Kinami and Mr. K. Takahashi is also greatly appreciated.

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