Bone, 13, 327-330, (1992) Printed in the USA. All rights reserved
Copyright
8756-3282192 $5.00 + .OO 0 1992 Pergamon Press Ltd.
Trabecular Bone Pattern Factor-A New Parameter for Simple Quantification of Bone Microarchitecture M. HAHN,
M. VOGEL,
M. POMPESIUS-KEMPA
and G. DELLING
Department of Bone PathologylCenter for Biomechanic UKE, University of Hamburg, Martinistr. 52, D-2000 Hamburg 20, Germany Address for correspondence and reprints: Dipl. Ing. BMT Michael Hahn, Abteilung OsteopathologielZcntrum Biomechanik UKE, Martini&. 52,
D-2000 Hamburg, Germany. Abstract
understanding of osteopenias and other pathological conditions. Nevertheless, by using these parameters, a complete characterization of the trabecular lattice is not possible. Early changes in trabecular bone structure, such as small perforations, can not be detected. Only progressive disturbances in trabecular bone structure can be demonstrated. Among the first who tried to quantify the extent of intertrabecular connectivity were Compston et al. (1987) by counting the number of trabecular nodes and the number of free-ending trabeculae in two-dimensional sections. They could demonstrate age-related changes of trabecular bone structure, but no significant differences between male and female subjects. The degree of connectivity of spongy bone is determined mainly by the number of perforations. A perforation is the complete, osteoclastic penetration of plate- or rod-like trabeculae. In the beginning these fenestrations do not cause a drastic loss of trabecular bone volume (BVITV) , number (Tb. N) , and thickness (Tb.Th), but they lead to major changes of microarchitecture, and therefore diminish the stability of bone. For the quantification of early changes in trabecular bone structure in cases of bone loss syndromes we developed a new computerized procedure. This method allows the automatic estimation of Trabecular Bone Pattern factor (TBPf), which describes quantitatively the ratio of intertrabecular connectivity. In the following we report the functional principle and first results in normal subjects.
The stability of trabecular bone depends not only on the amount of bone tissue, but also on the three-dimensional orientation and connectedness of trabeculae, which is summarized as trabecular microarchitecture. In previous studies we could demonstrate that in three-dimensional bone tissue the relation of trabecular plates to rods is reflected in the ratio of concave to convex surfaces of the bone pattern in two-dimensional bone sections. For the quantification of the connectedness of these bone patterns we developed a new histomorphometric parameter called Trabecular Bone Pattern factor (TBPf). The basic idea is that the connectedness of structures can be described by the relation of convex to concave surfaces. A lot of concave surfaces represent a well connected spongy lattice, whereas a lot of convex surfaces indicate a badly connected trabecular lattice in twodimensional sections. By means of an automatic image analysis system we measure trabecular bone area (Al) and pe rhueter (Pl). A second measurement of these two parameters (now A2 and P2) is done after a simulated dilatation of trabeculae on the screen. This dilatation results in a characteristic change of bone area and perimeter depending on the relation of convex to concave surfaces. TBPf is defined as a quotient of the difference of the first and the second measurement: TBPf = (Pl - P2)/(Al - A2). First measurements of TBPf in 192 iliac crest bone biopsies of autopsy cases show that there is not only age-related loss of bone volume, but also a decrease of trabecular connectedness. By means of TBPf we can demonstrate a significant difference in the agerelated loss of trabecular connectivity between male and female individuals. Key Words: Trabecular microarchitecture-Automatic analysis-Bone histomorphometry.
Materials and Methods In principle, TBPf can be estimated in undecalcified histological sections, ultra-thin grindings, or surface stained block grindings (Hahn et al. 1991). By means of a video camera the microscopic image of the histological specimen is transferred to an automatic image analyzing system (IBAS 2000). The grey level image is transformed to a binary image, thus allowing a clear separation between trabecular bone and bone marrow. Artefacts are eliminated using appropriate program steps or interactive operations if necessary. Trabecular bone surfaces are smoothed moderately to exclude small influences on the results due to fractal surface phenomenons (Olah 1976). This smoothing does not result in a change of the bone structure or trabecular thickness. It leads only to a closing of small resorption lacunae and preparation artefacts. Bone area (Al) and bone perimeter (Pl) are measured automatically. A second measurement of these two parameters (now A2 and P2) is done after a simulated dilatation of trabeculae on the screen (Fig, 1). The computer-based dilatation results in a thickening of the trabeculae. This dilatation is performed by a
image
Introduction Structures are described in general by their porosity, density, and the configuration of several structure elements. Especially in bone histomorphometry, many parameters for the estimation of bone structure have been established. The most important parameters are Bone Volume (BVITV), Trabecular Number (Tb.N), Trabecular Thickness (Tb.Th), and Trabecular Separation (Tb.Sp) (Partitt et al. 1987). Measurement and calculation of these values is relatively easy, and they are essential for the 321
M. Hahn et al.: TBPF quantification
328 BONE AREA ,
-
1
A BONE AREA
?MET;RPl
0
cl
PERIMETER
P2
DILATATION
)
OF A CONVEX STRUCTURE
of trabecular
microarchitecture
sured automatically to allow a comparison between these two parameters. We measured one slice of each biopsy completely with a minimum field size of 25 mm’. The mean age of the male subjects (n = 95) was 48 2 20 years; females (n = 97) were 50 + 2 I years. All specimens were embedded undecalcified and cut to a thickness of 6 p.m. The specimens were stained by v. Kossa. All cases were measured twice by two different observers without knowledge of age or sex. Inter-observer variation (determined according to Delling et al. 1980) was small (max. 5%) because nearly all measuring steps are performed automatically. Statistical evaluation was done using single regression analysis. Comparison of mean values in different groups and age decades was performed by using two-tailed Student’s r-test. Significance was accepted at a level of p < 0.05. Results
PERIMETER BONE AREA
~5BONE AREA
~2
0
Fig. I. The model demonstrates the influence of artificial dilatation on Bone Area and Bone Perimeter. There is an increase of bone area without regard to curvature, but an increase of bone perimeter with convex surfaces only. Because of a decrease of bone perimeter with concave sur-
faces, there are negative as well as positive values for TBPf. rank order operator (median filter), and leads to a thickening of the trabeculae of one pixel, corresponding to about 5 pm. The intention to use the smallest possible dilatation was to avoid the confluence of narrow structures. TBPf is defined to be the quotient of the differences of the first and the second measurement. TBPf = (PI - P2)/(Al
- A2)
The concept of TBPf is to get a value for the relation of convex to concave structural elements. Measurement of the curvature of trabecular bone perimeter directly is not practical because of the difficult estimation of convex and concave surfaces. The dilatation of the structure avoids these problems. The step of dilatation results always in an increase of bone area. P2 can be higher, lower, or equal to Pl. This depends on the relation of convex to concave surfaces. Instead of using Pl - P2 alone, for the calculation of TBPf we divided (Pl - P2) by (Al - A2) for the following reasons: to get independency of the &ea of the measuring field; to get an unequivocal description of the structure (in contrast to (PI - P2)ITissue Area); By using (Pl - P2)/(Al - A2), the extent of convex structures is overestimated (in contrast to (PI - P2)iTissue Area). This is useful for the analysis of osteoporosis which is characterized by mainly convex structures; Up to now, we analyzed more than 300 bone biopsies and model structures, and we found that using APIAA (compared to AP or AA alone) is best suited to show the age-dependent changes of bone structure. TBPf leads to low values in cases of well connected trabecular bone, whereas a lot of isolated trabeculae result in high values of TBPf. All steps of the computer program are part of the standard software of the IBAS 2000. The applied standard magnification of our measurement procedure is 12.5X. In the present study, 192 iliac crest bone cylinders of normal subjects were analyzed. All these specimens were taken in a vertical direction (according to the procedure of Burkhardt 1966) from autopsy cases. In all cases death was sudden due to accidents. In addition to TBPf, Bone Volume (BVITV) was mea-
As expected, bone volume (BVITV) decreases in male (regression equation between BVITV and age: y = 23.29 - 0.0864x, r* = 0.113; slope of regression: p < 0.05) and female (regression equation between BVITV and age: y = 23.69 - 0.108x, r* = 0.225; slope of regression: p < 0.05) subjects during the course of aging in nearly the same way. In Fig. 2 the individual values are combined to age-decades. A significant difference between male and female subjects cannot be demonstrated in any decade. TBPf increases in female subjects with age (regression equation between TBPf and age: y = 0.439 + 0.0145x, ra = 0.146; slope of regression: p < O.OOl), whereas in male subjects an age-related increase of TBPf could not be demonstrated (regression equation between TBPf and age: y = 0.733 + 0.003x, r2 = 0.006; slope of regression: p = 0.48). So, in postmenopausal females (>50 yrs.) there is an increase in TBPf in relation to females 50 years old or younger (comparison of the mean value of the two groups: 2 p < 0.001). Consequently, in older women trabecular bone structure is characterized by an increased proportion of convex elements relative to concave elements, indicating more isolated trabecular profiles in the two-dimensional section and increased conversion of plates to struts in the real three-dimensional bone. In Fig. 3 the mean values of TBPf of each decade are shown for male and female subjects. There is a significant difference in TBPf (2~ < 0.05) between mean values of males and females for each decade over 50 years.
Trabecular bone pattern factor (TBPf) is an index that describes the connectedness of individual trabeculae in a two-dimensional BV TV (%]
20
Ed female q male
2
3
4
5
6
7
8
decades
9
of age
Fig. 2. Age-dependent loss of Bone Volume (BV/TV). There is no significant difference in the decrease in BViTV in any decade between male and female subjects.
M. Hahn et al.: TBPF quantification of trabecular microarchitecture
329
TBPf (mm-‘)
64
4l female male
zp < 0.05
Fig. 3. Trabecular Bone Pattern factor (TBPf) in relation to age. In contrast to Bone Volume, TBPf shows a significant difference between the mean values for male and female subjects from the sixth decade on.
section. The connectedness of the three-dimensional trabecular network is mainly determined by the relation of trabecular plates to struts. This can be demonstrated in studies involving surface stained block grindings of trabecular bone. This kind of preparation allows the combined two- and three-dimensional analysis of bone structure (Delling et al. 1990; Vogel et al. 1989). A large number of plate-like structures leads to a well connected, threedimensional spongy lattice. In the two-dimensional section or at the stained surface of the block grindings, this structure is represented by a continuous bone pattern. In contrast, usually, a small number of plates and a large number of struts results in a less well connected pattern or a lot of free-ending trabeculae in the two-dimensional plane (Fig. 4). The basic idea in the creation of TBPf was the fact that all patterns or structures can be described by their relation between concave and convex surfaces. Simplified, that means a lot of convex structures indicate a badly connected pattern. A lot of concave structures is the result of a well connected bone pattern. It is possible to estimate the relation between concave and convex elements of a structure by the measurement of bone perimeter and bone area before and after a dilatation of the bone structure. If there are mainly convex parts, the bone perimeter will be larger (AP positive) after the thickening of the structure, proportional to the number of convex elements. If there are more concave parts, the bone perimeter will be smaller (AP negative) at the second measurement. So the change of the bone perimeter-made by the dilatation-depends on the relation of concave to convex structural elements. -In contrast to bone perimeter, bone area always increases after the dilatation. The consideration of AA in addition to AP in the calculation of TBPf leads to a moderate overaccentuation of convex parts in the structure. Therefore, trabecular perforations (leading to an increase in convex surfaces) result in a very fast change of TBPf. Furthermore, an independence of the mea&ing fieldsize is given in this way. By means of a computer-assisted image analyzing system, it is simple to estimate TBPf. After the definition of the measuring area, the procedure can be performed automatically. Analyses of models have shown that TBPf is a very sensitive parameter for the detection of changes in trabecular bone structure. This is very useful for the discovery of minimal modifications to the spongy lattice. Small changes resulting, for instance, from perforations may cause a loss of bone stability without a striking loss in bone volume (Kleerekoper et al. 1985) (Fig. 5). TBPf depends both on the width of the dilatation and the selected magnification. To get reliable values, which allow the comparison of TBPf in different biopsies, it is necessary always to use the same degree of dilatation and magnification. We use
(b)
(c>
Fig. 4. Surface stained block grinding. (a) An impression of the three-
dimensional bone structure and the relation between struts and plate-like trabeculae (dark field illumination). (b) Set of the corresponding stained surface with the two-dimensional bone pattern. (BV/TV = 12.42%; TBPf = 0.36 mm-‘). (c) A second bone pattern with nearly the same Bone Volume (12.34%). but a lower value of TBPf (0.11 mm- ‘). a very small degree of dilatation (ie, one pixel, corresponding to about 5 p,m at the applied magnification of 12.5X) to avoid the trabeculae becoming confluent after their simulated dilatation. It seems to be quite appropriate to use a low magnification for the measurement. This leads to a large measuring area and thus to a fast analysis of the whole biopsy. Furthermore, the surface of trabecular bone is structured in a fractal manner and, therefore, it is quite obvious that the measured perimeter of bone depends on the applied magnification. This is the same for the conventional measurement of bone perimeter by means of a test grid system (Olah 1976). This first application of TBPf was performed in 192 normal subjects. The analysis of the trabecular bone structure reveals
Hahn et al.: TBPF quantification
M.
WITH NO PERFORATION TBPF
= - 1,35 (mm-‘)
BV/TV =
29,2 (%)
PERFORATION
of trabecular
microarchitecture
even more. the three-dimensional configuration of trabeculae and their extent of connectivity are important for the stability of bone. The contribution of other factors of bone quality, such as brittleness and orientation of collagen fibers to bone stability, are not clear up to now. TBPf seems to be able to detect early stages of bone loss syndromes and other bone disorders accompanied by structural changes that may present with an increased or reduced number of perforations. but still no dramatic changes of bone volume (e.g., primary hyperparathyroidism (Vogel et al. submitted for publication). acromegaly, renal osteodystrophies, and osteoporosis (Pompesius-Kempa et al. 1989).
WITH 3 PERFORATIONS TBPF
= - 0,91 (mm-‘)
BV/TV =
28,8 (%)
AcXnow/rdgment:
This study was supported by Deutsche ForschungsgeDe 19819-I.
meinschaft
References
PERFORATION
Burkhardt.
R. Praparatwe
Voraussetrugen
then Knwhenmarks. Birkrnhager-Frenkel.
WITH 12 PERFORATIONS TBPF
= - 0,20 (mm-‘)
BV/TV =
B/u D. H.;
M. F.: Schmttr.
cancellou
hone structure.
J. E.: Mellish,
iliac cwt
27,9 (%)
trabecular
G
427:
0
Fig. 5. The scheme elucidates the principle changes of the bone strucwe due to perforations. There is just a small change. in Bone Volume, but a dramatic loss of connected bone structure with an increase of convex surfaces.
Clrrmont\.
Age-related
E
changes in
1988.
N. .I X
Age-related
change m
bone structure in man. Bow
Luehmann.
H.. Baron, R.. Matheaa. reproducibility.
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Olah,
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Wicland.
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hone qructure
ot the
Bow Morphornern. Pm redrn,qs c)f the 5th International Conp-rss on Bone Morphomrtry. July 24-29. 1988. Niigata. Japan. Nishimura Smith-Gordon; 256 \pm--Rewlts
259. Hahn.
of a new simultaneous
Vogel.
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PompesiwKempa, Mikroarchitektur \chlecht
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P. J.. (ed.): Paris. Annour
; Kleerekoper.
M.:
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Vogel.
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bone mtcroarchitecture
(pHPT).
M.:
Knochens H.-G..
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: Hahn,
Virchuw M.:
& Heuck,
Arthrv. Submitted
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T. H. W..
der Ge-
Neuerr
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1989;4/(20~210). volume and improved hyperparathyreoid-
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& Heuck,
dw O.strologir. Berlin: Springer-Verlag; ular spacing contribute
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in patients with primary
chttecture of the human spine. Willert
Weinstem
01
of structural
J. Clrrl. Imrsr. 72:139&-1409:
bone architecture
und Diagnose.
trabecular
M
M.
1985
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ErgrhnhwrnderOsreolqie.Berlin: Spnnger-Verlag: Vogel. M : Hahn. M.: Delling. G. Increased trabecular bone Vogel.
A
Am. J Med. 82 (Suppl. lB):68-72; 1987.
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: Parfttt.
histomorphometr-v. Second International
between surface. volume.
bone III agmg and I” osteoporosis. A. 41. Trabecular
Virrhow-s
in the pathogenesls
T~ssur Int. 37:594-597:
July 1976. Meunier,
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J.: Sudhaker Rao, D mtcrobtmcture
Cal
Copyright
8756-3282192 $5.00 + .OO 0 1992 Pergamon Press Ltd.
Trabecular Bone Pattern Factor-A New Parameter for Simple Quantification of Bone Microarchitecture M. HAHN,
M. VOGEL,
M. POMPESIUS-KEMPA
and G. DELLING
Department of Bone PathologylCenter for Biomechanic UKE, University of Hamburg, Martinistr. 52, D-2000 Hamburg 20, Germany Address for correspondence and reprints: Dipl. Ing. BMT Michael Hahn, Abteilung OsteopathologielZcntrum Biomechanik UKE, Martini&. 52,
D-2000 Hamburg, Germany. Abstract
understanding of osteopenias and other pathological conditions. Nevertheless, by using these parameters, a complete characterization of the trabecular lattice is not possible. Early changes in trabecular bone structure, such as small perforations, can not be detected. Only progressive disturbances in trabecular bone structure can be demonstrated. Among the first who tried to quantify the extent of intertrabecular connectivity were Compston et al. (1987) by counting the number of trabecular nodes and the number of free-ending trabeculae in two-dimensional sections. They could demonstrate age-related changes of trabecular bone structure, but no significant differences between male and female subjects. The degree of connectivity of spongy bone is determined mainly by the number of perforations. A perforation is the complete, osteoclastic penetration of plate- or rod-like trabeculae. In the beginning these fenestrations do not cause a drastic loss of trabecular bone volume (BVITV) , number (Tb. N) , and thickness (Tb.Th), but they lead to major changes of microarchitecture, and therefore diminish the stability of bone. For the quantification of early changes in trabecular bone structure in cases of bone loss syndromes we developed a new computerized procedure. This method allows the automatic estimation of Trabecular Bone Pattern factor (TBPf), which describes quantitatively the ratio of intertrabecular connectivity. In the following we report the functional principle and first results in normal subjects.
The stability of trabecular bone depends not only on the amount of bone tissue, but also on the three-dimensional orientation and connectedness of trabeculae, which is summarized as trabecular microarchitecture. In previous studies we could demonstrate that in three-dimensional bone tissue the relation of trabecular plates to rods is reflected in the ratio of concave to convex surfaces of the bone pattern in two-dimensional bone sections. For the quantification of the connectedness of these bone patterns we developed a new histomorphometric parameter called Trabecular Bone Pattern factor (TBPf). The basic idea is that the connectedness of structures can be described by the relation of convex to concave surfaces. A lot of concave surfaces represent a well connected spongy lattice, whereas a lot of convex surfaces indicate a badly connected trabecular lattice in twodimensional sections. By means of an automatic image analysis system we measure trabecular bone area (Al) and pe rhueter (Pl). A second measurement of these two parameters (now A2 and P2) is done after a simulated dilatation of trabeculae on the screen. This dilatation results in a characteristic change of bone area and perimeter depending on the relation of convex to concave surfaces. TBPf is defined as a quotient of the difference of the first and the second measurement: TBPf = (Pl - P2)/(Al - A2). First measurements of TBPf in 192 iliac crest bone biopsies of autopsy cases show that there is not only age-related loss of bone volume, but also a decrease of trabecular connectedness. By means of TBPf we can demonstrate a significant difference in the agerelated loss of trabecular connectivity between male and female individuals. Key Words: Trabecular microarchitecture-Automatic analysis-Bone histomorphometry.
Materials and Methods In principle, TBPf can be estimated in undecalcified histological sections, ultra-thin grindings, or surface stained block grindings (Hahn et al. 1991). By means of a video camera the microscopic image of the histological specimen is transferred to an automatic image analyzing system (IBAS 2000). The grey level image is transformed to a binary image, thus allowing a clear separation between trabecular bone and bone marrow. Artefacts are eliminated using appropriate program steps or interactive operations if necessary. Trabecular bone surfaces are smoothed moderately to exclude small influences on the results due to fractal surface phenomenons (Olah 1976). This smoothing does not result in a change of the bone structure or trabecular thickness. It leads only to a closing of small resorption lacunae and preparation artefacts. Bone area (Al) and bone perimeter (Pl) are measured automatically. A second measurement of these two parameters (now A2 and P2) is done after a simulated dilatation of trabeculae on the screen (Fig, 1). The computer-based dilatation results in a thickening of the trabeculae. This dilatation is performed by a
image
Introduction Structures are described in general by their porosity, density, and the configuration of several structure elements. Especially in bone histomorphometry, many parameters for the estimation of bone structure have been established. The most important parameters are Bone Volume (BVITV), Trabecular Number (Tb.N), Trabecular Thickness (Tb.Th), and Trabecular Separation (Tb.Sp) (Partitt et al. 1987). Measurement and calculation of these values is relatively easy, and they are essential for the 321
M. Hahn et al.: TBPF quantification
328 BONE AREA ,
-
1
A BONE AREA
?MET;RPl
0
cl
PERIMETER
P2
DILATATION
)
OF A CONVEX STRUCTURE
of trabecular
microarchitecture
sured automatically to allow a comparison between these two parameters. We measured one slice of each biopsy completely with a minimum field size of 25 mm’. The mean age of the male subjects (n = 95) was 48 2 20 years; females (n = 97) were 50 + 2 I years. All specimens were embedded undecalcified and cut to a thickness of 6 p.m. The specimens were stained by v. Kossa. All cases were measured twice by two different observers without knowledge of age or sex. Inter-observer variation (determined according to Delling et al. 1980) was small (max. 5%) because nearly all measuring steps are performed automatically. Statistical evaluation was done using single regression analysis. Comparison of mean values in different groups and age decades was performed by using two-tailed Student’s r-test. Significance was accepted at a level of p < 0.05. Results
PERIMETER BONE AREA
~5BONE AREA
~2
0
Fig. I. The model demonstrates the influence of artificial dilatation on Bone Area and Bone Perimeter. There is an increase of bone area without regard to curvature, but an increase of bone perimeter with convex surfaces only. Because of a decrease of bone perimeter with concave sur-
faces, there are negative as well as positive values for TBPf. rank order operator (median filter), and leads to a thickening of the trabeculae of one pixel, corresponding to about 5 pm. The intention to use the smallest possible dilatation was to avoid the confluence of narrow structures. TBPf is defined to be the quotient of the differences of the first and the second measurement. TBPf = (PI - P2)/(Al
- A2)
The concept of TBPf is to get a value for the relation of convex to concave structural elements. Measurement of the curvature of trabecular bone perimeter directly is not practical because of the difficult estimation of convex and concave surfaces. The dilatation of the structure avoids these problems. The step of dilatation results always in an increase of bone area. P2 can be higher, lower, or equal to Pl. This depends on the relation of convex to concave surfaces. Instead of using Pl - P2 alone, for the calculation of TBPf we divided (Pl - P2) by (Al - A2) for the following reasons: to get independency of the &ea of the measuring field; to get an unequivocal description of the structure (in contrast to (PI - P2)ITissue Area); By using (Pl - P2)/(Al - A2), the extent of convex structures is overestimated (in contrast to (PI - P2)iTissue Area). This is useful for the analysis of osteoporosis which is characterized by mainly convex structures; Up to now, we analyzed more than 300 bone biopsies and model structures, and we found that using APIAA (compared to AP or AA alone) is best suited to show the age-dependent changes of bone structure. TBPf leads to low values in cases of well connected trabecular bone, whereas a lot of isolated trabeculae result in high values of TBPf. All steps of the computer program are part of the standard software of the IBAS 2000. The applied standard magnification of our measurement procedure is 12.5X. In the present study, 192 iliac crest bone cylinders of normal subjects were analyzed. All these specimens were taken in a vertical direction (according to the procedure of Burkhardt 1966) from autopsy cases. In all cases death was sudden due to accidents. In addition to TBPf, Bone Volume (BVITV) was mea-
As expected, bone volume (BVITV) decreases in male (regression equation between BVITV and age: y = 23.29 - 0.0864x, r* = 0.113; slope of regression: p < 0.05) and female (regression equation between BVITV and age: y = 23.69 - 0.108x, r* = 0.225; slope of regression: p < 0.05) subjects during the course of aging in nearly the same way. In Fig. 2 the individual values are combined to age-decades. A significant difference between male and female subjects cannot be demonstrated in any decade. TBPf increases in female subjects with age (regression equation between TBPf and age: y = 0.439 + 0.0145x, ra = 0.146; slope of regression: p < O.OOl), whereas in male subjects an age-related increase of TBPf could not be demonstrated (regression equation between TBPf and age: y = 0.733 + 0.003x, r2 = 0.006; slope of regression: p = 0.48). So, in postmenopausal females (>50 yrs.) there is an increase in TBPf in relation to females 50 years old or younger (comparison of the mean value of the two groups: 2 p < 0.001). Consequently, in older women trabecular bone structure is characterized by an increased proportion of convex elements relative to concave elements, indicating more isolated trabecular profiles in the two-dimensional section and increased conversion of plates to struts in the real three-dimensional bone. In Fig. 3 the mean values of TBPf of each decade are shown for male and female subjects. There is a significant difference in TBPf (2~ < 0.05) between mean values of males and females for each decade over 50 years.
Trabecular bone pattern factor (TBPf) is an index that describes the connectedness of individual trabeculae in a two-dimensional BV TV (%]
20
Ed female q male
2
3
4
5
6
7
8
decades
9
of age
Fig. 2. Age-dependent loss of Bone Volume (BV/TV). There is no significant difference in the decrease in BViTV in any decade between male and female subjects.
M. Hahn et al.: TBPF quantification of trabecular microarchitecture
329
TBPf (mm-‘)
64
4l female male
zp < 0.05
Fig. 3. Trabecular Bone Pattern factor (TBPf) in relation to age. In contrast to Bone Volume, TBPf shows a significant difference between the mean values for male and female subjects from the sixth decade on.
section. The connectedness of the three-dimensional trabecular network is mainly determined by the relation of trabecular plates to struts. This can be demonstrated in studies involving surface stained block grindings of trabecular bone. This kind of preparation allows the combined two- and three-dimensional analysis of bone structure (Delling et al. 1990; Vogel et al. 1989). A large number of plate-like structures leads to a well connected, threedimensional spongy lattice. In the two-dimensional section or at the stained surface of the block grindings, this structure is represented by a continuous bone pattern. In contrast, usually, a small number of plates and a large number of struts results in a less well connected pattern or a lot of free-ending trabeculae in the two-dimensional plane (Fig. 4). The basic idea in the creation of TBPf was the fact that all patterns or structures can be described by their relation between concave and convex surfaces. Simplified, that means a lot of convex structures indicate a badly connected pattern. A lot of concave structures is the result of a well connected bone pattern. It is possible to estimate the relation between concave and convex elements of a structure by the measurement of bone perimeter and bone area before and after a dilatation of the bone structure. If there are mainly convex parts, the bone perimeter will be larger (AP positive) after the thickening of the structure, proportional to the number of convex elements. If there are more concave parts, the bone perimeter will be smaller (AP negative) at the second measurement. So the change of the bone perimeter-made by the dilatation-depends on the relation of concave to convex structural elements. -In contrast to bone perimeter, bone area always increases after the dilatation. The consideration of AA in addition to AP in the calculation of TBPf leads to a moderate overaccentuation of convex parts in the structure. Therefore, trabecular perforations (leading to an increase in convex surfaces) result in a very fast change of TBPf. Furthermore, an independence of the mea&ing fieldsize is given in this way. By means of a computer-assisted image analyzing system, it is simple to estimate TBPf. After the definition of the measuring area, the procedure can be performed automatically. Analyses of models have shown that TBPf is a very sensitive parameter for the detection of changes in trabecular bone structure. This is very useful for the discovery of minimal modifications to the spongy lattice. Small changes resulting, for instance, from perforations may cause a loss of bone stability without a striking loss in bone volume (Kleerekoper et al. 1985) (Fig. 5). TBPf depends both on the width of the dilatation and the selected magnification. To get reliable values, which allow the comparison of TBPf in different biopsies, it is necessary always to use the same degree of dilatation and magnification. We use
(b)
(c>
Fig. 4. Surface stained block grinding. (a) An impression of the three-
dimensional bone structure and the relation between struts and plate-like trabeculae (dark field illumination). (b) Set of the corresponding stained surface with the two-dimensional bone pattern. (BV/TV = 12.42%; TBPf = 0.36 mm-‘). (c) A second bone pattern with nearly the same Bone Volume (12.34%). but a lower value of TBPf (0.11 mm- ‘). a very small degree of dilatation (ie, one pixel, corresponding to about 5 p,m at the applied magnification of 12.5X) to avoid the trabeculae becoming confluent after their simulated dilatation. It seems to be quite appropriate to use a low magnification for the measurement. This leads to a large measuring area and thus to a fast analysis of the whole biopsy. Furthermore, the surface of trabecular bone is structured in a fractal manner and, therefore, it is quite obvious that the measured perimeter of bone depends on the applied magnification. This is the same for the conventional measurement of bone perimeter by means of a test grid system (Olah 1976). This first application of TBPf was performed in 192 normal subjects. The analysis of the trabecular bone structure reveals
Hahn et al.: TBPF quantification
M.
WITH NO PERFORATION TBPF
= - 1,35 (mm-‘)
BV/TV =
29,2 (%)
PERFORATION
of trabecular
microarchitecture
even more. the three-dimensional configuration of trabeculae and their extent of connectivity are important for the stability of bone. The contribution of other factors of bone quality, such as brittleness and orientation of collagen fibers to bone stability, are not clear up to now. TBPf seems to be able to detect early stages of bone loss syndromes and other bone disorders accompanied by structural changes that may present with an increased or reduced number of perforations. but still no dramatic changes of bone volume (e.g., primary hyperparathyroidism (Vogel et al. submitted for publication). acromegaly, renal osteodystrophies, and osteoporosis (Pompesius-Kempa et al. 1989).
WITH 3 PERFORATIONS TBPF
= - 0,91 (mm-‘)
BV/TV =
28,8 (%)
AcXnow/rdgment:
This study was supported by Deutsche ForschungsgeDe 19819-I.
meinschaft
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