0021-972X/01/$03.00/0
The Journal of Clinical Endocrinology & Metabolism
Copyright © 2001 by The Endocrine Society
Vol. 86, No. 2
Printed in U.S.A.
The Development of Bone Strength at the Proximal
Radius during Childhood and Adolescence
E. SCHOENAU, C. M. NEU, F. RAUCH,
AND
F. MANZ
Children’s Hospital, University of Cologne (E.S., C.M.N., F.R.), D-50924 Cologne; and Research
Institute of Child Nutrition (C.M.N., F.M.), D-44225 Dortmund, Germany
ABSTRACT
Current investigations of bone development mostly focus on bone
mass, but bone strength may be functionally more important than
mass. Therefore, we compared the developmental changes in cortical
bone mass (BMCcort) and parameters of cortical bone strength [polar
moment of inertia, section modulus, and strength strain index (SSI)].
Analyses were performed at the 65% site of the proximal radius using
peripheral quantitative computed tomography. The study population
comprised 469 healthy subjects, 6 – 40 yr of age (273 females). Both in
prepubertal children (pubertal stage 1) and after puberty (pubertal
stage 5 and adults) all studied parameters were significantly higher
in males. During puberty (pubertal stages 2– 4) the gender-specific
differences were generally somewhat smaller. All of the measured
parameters increased significantly with age and pubertal stage. However, although the percent increase in BMCcort between the youngest
children and adults was similar between the genders, the increases
in polar moment of inertia, section modulus, and SSI were higher in
males. The ratio between section modulus and BMCcort was consistently higher in males after the age of 11 yr and after pubertal stage
2. Similar results were found for ratios between polar moment of
inertia or SSI and BMCcort. These results show that for a given bone
mass, males have stronger bones than females after pubertal stage 2.
This reflects the fact that in puberty males add bone mostly on the
periosteal surface, where the effect on bone strength is highest,
whereas females add bone on the endocortical surface, which has a
small effect on bone stability. The purpose of the mechanically inefficient endocortical apposition in female puberty might be to create a
reservoir of calcium for future pregnancy and lactation. (J Clin Endocrinol Metab 86: 613– 618, 2001)
I
N THE CURRENT literature bone development is commonly described as a process of bone mineral accretion,
which eventually leads to the accumulation of peak bone mass.
This focus on bone mass probably reflects the ease with which
this parameter can be measured using widely available densitometric techniques. However, describing bone development
simply in terms of bone mass changes veils the fact that the key
issue of bone development is to make bones stronger rather
than heavier (1). In fact, if maximizing bone mass in itself carried
an important functional advantage for the individual, the evolutionary process should have led to the formation of bones
with solid, not hollow, diaphyses. As it is, the anatomical features of bones suggest that bone development is set to attain
peak bone strength by using as little material as possible.
Obviously, for a bone of a given anatomical structure,
mass generally correlates with strength. However, a given
amount of material will influence the strength of a structure
differently depending on where it is located. Architectural
parameters have been devised that allow calculation of the
strength of a structure from the amount and distribution of
the raw material. Such size and shape parameters include the
polar moment of inertia and the section modulus (2, 3).
The polar moment of inertia is a measure of the distribution of material around the center of a specimen (Fig. 1). The
shear stress created in a bone by torque is inversely related
to the polar moment of inertia (2). Thus, in a bone with a
higher polar moment of inertia the same torque will result in
smaller shear stress than in a bone with a lower polar moment of inertia. The section modulus is a closely related
parameter (Fig. 1) that indicates the resistance of a bone to
stress. A higher section modulus, therefore, means that mechanical failure occurs at higher loads (4).
These architectural parameters have long been used in
bone biomechanical studies and have been found to be as
good indicators of the strength of bones as they are for
engineering purposes (1–3, 5). Algorithms have been developed to assess polar moment of inertia and section modulus
with techniques such as single or dual energy photon absorptiometry (5–7). However, some prior assumptions on
bone shape have to be made, which may introduce some
error. It is one of the advantages of peripheral quantitative
computed tomography (pQCT) that these architectural parameters can be easily and precisely determined (8).
In addition to the size and shape factors mentioned above,
the strength of a bone as an organ depends on the material
properties of bone as a tissue (4). A key material property is the
elastic modulus, or stiffness (2). It is difficult to measure stiffness
directly in vivo, as invasive testing is required. However, volumetric bone mineral density (BMD) of cortical bone in the narrow physiological range has an approximately linear relationship with elastic modulus (4) and can be determined by pQCT.
Thus, pQCT allows assessment of both architectural and
material components of bone strength. Combining both
types of indexes should allow close estimates of bone
strength (4). In fact, the product of volumetric cortical BMD
and cross-sectional moment of inertia is closely associated
with rat femur bending strength (9). A similar parameter,
the strength strain index (SSI), has been developed by
Schiessl et al. (Fig. 1) (10). This is calculated as the product of
Received July 21, 2000. Revision received October 24, 2000. Accepted
October 26, 2000.
Address all correspondence and requests for reprints to: Dr. Eckhard
Schoenau, Children’s Hospital, University of Cologne, Joseph Stelzmann Strasse 9, D-50924 Cologne, Germany.
613
614
SCHOENAU ET AL.
section modulus and volumetric cortical BMD normalized to
the maximal physiological cortical BMD of human bones
(11). The SSI has been shown to provide a good estimate of
the mechanical strength of human radii (12).
In this study we performed pQCT analyses at the proximal
radial diaphysis in children, adolescents, and young adults
to examine the developmental variations in polar moment of
inertia, section modulus, and SSI. This should allow evaluation of the development of bone strength at the proximal
radius. In addition, we investigated the relationship between
bone mass and architectural parameters of bone stability
during bone development.
Subjects and Methods
Subjects
The study population comprised 371 healthy children and adolescents as well as those parents who were below 40 yr of age (n ⫽ 107; 19
men and 88 women; aged 29 – 40 yr). Five children had to be excluded
from the present analysis because of motion artifacts during the mea-
JCE & M • 2001
Vol. 86 • No. 2
surement run. The results from 4 boys were excluded because a significant amount of trabeculized cortex interfered with the analysis of cortical bone. Thus, 362 children and adolescents (177 males and 185
females) were included in the following evaluation. The children were
participants in the DONALD (Dortmund Nutritional and Anthropometric Longitudinally Designed) study, an ongoing observational study
investigating the interrelations of nutrition, growth, and metabolism in
healthy children. This study is performed at the Research Institute for
Child Nutrition in Dortmund, Germany. The cohort was initially recruited through personal contacts of collaborators of the Research Institute and later through personal recommendation of parents whose
children were already participating. Overall, the study population
mostly comprised middle class families, and all participants were of
Caucasian origin. On an annual basis, all participants in this study
undergo a full medical history and examination starting in infancy.
Peripheral QCT analysis was performed once in each participant on the
occasion of a yearly check-up.
The stage of sexual development was determined by physical examination using the grading system defined by Tanner for pubic hair. Assessment of pubertal stage was refused by 26 boys and 27 girls. Forearm length
was measured at the nondominant forearm as the distance between the
ulnar styloid process and the olecranon using a caliper.
Informed consent was obtained from the children’s parents or from
subjects more than 18 yr old. In addition, written assent was also obtained from subjects between 14 –17 yr of age. The study protocol was
approved by the ethics committee of the University of Cologne and the
Bundesamt für Strahlenschutz (Federal Agency for Protection from Radiation, Salzgitter, Germany).
pQCT
FIG. 1. Definitions of polar moment of inertia, section modulus, and
SSI. A schematic view of a bone’s cross-section is shown. In the
formulae, A is the cross-sectional area of a voxel (in this study 0.4 ⫻
0.4 mm ⫽ 0.16 mm2), d is the distance of the voxel from the center of
gravity, vBMDvox is the volumetric bone mineral density in the voxel
(milligrams per cm3), dmax is the maximum distance of any of the
voxels of the cortical cross-section from the center of gravity, and
vBMDmax is the maximum mineral density of human bone under
physiological conditions. This corresponds to the mineral density of
cortical bone adjusted for porosity on the light microscopic level.
vBMDmax was set at 1200 mg/cm3 (11).
pQCT analysis was performed at the nondominant forearm using a
technology (XCT 2000, Stratec, Inc., Pforzheim, Germany) described
previously (13). The scanner was positioned at the site of the radius
whose distance to the distal radial articular cartilage corresponded to
65% of the ulnar length. A 2-mm-thick single tomographic slice was
taken at a voxel size of 0.4 mm. Image processing and calculation of
numerical values were performed using the manufacturer’s software
package (version 5.40, Stratec, Inc.).
For all analyses except the determination of SSI, cortical bone was
identified at a threshold of 710 mg/cm3. To assess SSI, a threshold of
480 mg/cm3 was used according to the default settings of the manufacturer’s software. This choice of thresholds is based on technical
considerations regarding the partial volume effect, which is a source
of error in QCT (14). Partial volume effect refers to measurement
errors caused by voxels that are only partially filled with mineralized
bone. By choosing a threshold of 710 mg/cm3 (which is about midway
between the densities of fully mineralized bone and soft tissue), about
as many voxels that are only partially filled with cortical bone will
be included in the analysis as will be excluded. Thus, the error due
to the partial volume effect will be minimized. In the analysis of SSI,
the partial volume effect plays a smaller role, because the individual
density reading of each voxel is used for the calculation (Fig. 1).
FIG. 2. Age dependency of cortical bone mineral content in females (left) and males (right). Results in adults from 29 – 40 yr of age are indicated
as bars (mean ⫾ 2 SD).
BONE STRENGTH DEVELOPMENT
Therefore, a lower threshold can be used, which should allow a more
accurate analysis of the bone’s geometry. Cortical bone mineral content (BMCcort) represents the mass of mineral in a 1-mm-thick slice
of the cortical bone’s cross-section. Polar moment of inertia, section
modulus, and SSI were calculated as indicated in Fig. 1.
Statistical analyses
For comparisons between two groups, U tests were used. The significance of differences between more than two groups was calculated
by the Kruskal-Wallis test. For these calculations SAS 6.12 software
package (SAS Institute, Inc., Cary, NC) was used.
Results
Figures 2 and 3 display the variation with age in BMCcort
and in parameters of cortical architecture. The mean and sd of
these age-dependent results are shown in Tables 1 and 2; the
variations with pubertal stage are given in Tables 3 and 4. All
of the measured parameters increased significantly with age
and pubertal stage. BMCcort was higher in males in the young-
615
est age groups and after the age of 15 yr. Moment of inertia,
section modulus, and SSI tended to be higher in males in all age
groups, but the difference in females was significant only in the
8 –9 yr age group and after age 15 yr. Both in prepubertal
children (pubertal stage 1) and after puberty (pubertal stage 5)
all studied parameters were significantly higher in males. During puberty (pubertal stage 2– 4) the gender-specific differences
were generally somewhat smaller.
Between the age of 6 –7 yr and adulthood, the relative increase in BMCcort was similar between the genders (197% in
females, 200% in males). However, the relative increases in
polar moment of inertia, section modulus, and SSI were higher
in males. We therefore evaluated the developmental changes in
the ratio between these architectural parameters and BMCcort.
As shown in Fig. 4, the ratio between section modulus and
BMCcort was consistently higher in males after the age of 11 yr
and after pubertal stage 2. Similar results were found for polar
moment of inertia and SSI (data not shown).
FIG. 3. Age dependency of parameters of cortical architecture in females (left) and males (right). Results in adults from 29 – 40 yr of age are
indicated as bars (mean ⫾ 2 SD).
616
JCE & M • 2001
Vol. 86 • No. 2
SCHOENAU ET AL.
TABLE 1. Age dependency of cortical bone mass and architectural parameters in females
Age (yr)
6 –7
8 –9
10 –11
12–13
14 –15
16 –17
18 –23
Adults
n
BMCcort
(mg/mm)
Polar moment of
inertia (mm4)
Section modulus
(mm3)
SSI (mm3)
28
26
30
31
25
23
22
88
29 ⫾ 8a
43 ⫾ 10
52 ⫾ 12
64 ⫾ 19
76 ⫾ 11
81 ⫾ 11b
81 ⫾ 13a
86 ⫾ 11a
532 ⫾ 146
760 ⫾ 244b
1095 ⫾ 395
1408 ⫾ 555
1703 ⫾ 542
1848 ⫾ 449c
1755 ⫾ 466a
1926 ⫾ 545a
94 ⫾ 26
134 ⫾ 36b
179 ⫾ 48
215 ⫾ 64
254 ⫾ 55
268 ⫾ 51c
259 ⫾ 54a
279 ⫾ 55a
98 ⫾ 21
128 ⫾ 32b
169 ⫾ 46
201 ⫾ 62
245 ⫾ 51
258 ⫾ 47c
258 ⫾ 54a
280 ⫾ 55a
Values are the mean ⫾ SD. The variation with age group is significant at P ⬍ 0.0001 for each parameter (by Kruskal-Wallis test). The
significance for the difference between females and males of the same age group (by Mann-Whitney U test) is indicated in the footnotes.
a
P ⬍ 0.001.
b
P ⬍ 0.05.
c
P ⬍ 0.01.
TABLE 2. Age dependency of cortical bone mass and architectural parameters in males
Age
(yr)
n
BMCcort
(mg/mm)
Polar moment of
inertia (mm4)
Section modulus
(mm3)
SSI (mm3)
6 –7
8 –9
10 –11
12–13
14 –15
16 –17
18 –23
Adults
27
22
31
27
27
21
22
19
36 ⫾ 8
47 ⫾ 6
53 ⫾ 9
58 ⫾ 9
75 ⫾ 18
90 ⫾ 15
105 ⫾ 16
108 ⫾ 14
632 ⫾ 217
937 ⫾ 279
1227 ⫾ 357
1465 ⫾ 379
2066 ⫾ 717
2353 ⫾ 689
3205 ⫾ 810
3464 ⫾ 1035
114 ⫾ 31
161 ⫾ 36
192 ⫾ 41
224 ⫾ 44
286 ⫾ 78
328 ⫾ 75
403 ⫾ 77
430 ⫾ 85
110 ⫾ 29
150 ⫾ 35
181 ⫾ 40
209 ⫾ 42
266 ⫾ 67
308 ⫾ 67
388 ⫾ 70
419 ⫾ 84
Values are the mean ⫾
SD.
The variation with age group is significant at P ⬍ 0.0001 for each parameter (by Kruskal-Wallis test).
TABLE 3. Dependency of cortical bone mass and architectural parameters on pubertal stage in females
Pubertal
stage
n
Age (yr)
BMCcort
(mg/mm)
Polar moment of
inertia (mm4)
Section
modulus
(mm3)
SSI (mm3)
1
2
3
4
5
64
13
14
9
58
8.5 ⫾ 1.7
11.1 ⫾ 1.0
11.7 ⫾ 1.0
13.2 ⫾ 1.4
16.1 ⫾ 2.4
40 ⫾ 12a
50 ⫾ 15b
55 ⫾ 8
70 ⫾ 8
82 ⫾ 12c
747 ⫾ 298a
1064 ⫾ 400b
1090 ⫾ 292a
1502 ⫾ 399
1840 ⫾ 509c
129 ⫾ 44a
175 ⫾ 53a
182 ⫾ 36a
230 ⫾ 46
267 ⫾ 57c
126 ⫾ 38a
165 ⫾ 49b
169 ⫾ 35c
217 ⫾ 43
259 ⫾ 53c
The adult group was not included in pubertal stage 5. Values are the mean ⫾ SD. The variation with age group is significant at P ⬍ 0.0001
for each parameter (by Kruskal-Wallis test). The significance for the difference between females and males of the same age group (Mann-Whitney
U test) is indicated in the footnotes.
a
P ⬍ 0.01.
b
P ⬍ 0.05.
c
P ⬍ 0.001.
TABLE 4. Dependency of cortical bone mass and architectural parameters on pubertal stage in males
Pubertal
stage
n
Age (yr)
BMCcort
(mg/mm)
Polar moment of
inertia (mm4)
Section modulus
(mm3)
SSI (mm3)
1
2
3
4
5
70
14
10
14
43
8.8 ⫾ 1.9
11.5 ⫾ 1.3
12.5 ⫾ 1.0
14.0 ⫾ 1.2
17.8 ⫾ 2.7
46 ⫾ 12
59 ⫾ 9
60 ⫾ 10
71 ⫾ 14
94 ⫾ 20
942 ⫾ 403
1456 ⫾ 396
1595 ⫾ 239
1909 ⫾ 612
2753 ⫾ 849
157 ⫾ 52
223 ⫾ 45
238 ⫾ 32
269 ⫾ 64
360 ⫾ 85
149 ⫾ 49
209 ⫾ 41
225 ⫾ 25
248 ⫾ 57
343 ⫾ 79
The adult group was not included in pubertal stage 5. Values are the mean ⫾ SD. The variation with age group is significant at P ⬍ 0.0001
for each parameter (by Kruskal-Wallis test).
Table 5 shows the interrelationship between bone mass
and architectural parameters. For both genders, indexes of
architecture were highly interrelated, with correlation coefficients of 0.98 and 0.99. The association between these parameters and BMCcort was slightly less close.
Discussion
In this study we describe the normal development of cortical bone mass and architectural indexes of bone strength at
the proximal radius. The study population comprised children and adolescents as well as their parents, and thus these
BONE STRENGTH DEVELOPMENT
FIG. 4. Dependency of the ratio between section modulus and cortical
bone mineral content on age and pubertal stage. The significance of
the difference between genders is indicated for each age group: *, P ⬍
0.05; **, P ⬍ 0.01; ***, P ⬍ 0.001.
TABLE 5. Pearson’s correlation coefficients between cortical bone
mass and architectural parameters
Section
Modulus
Polar Moment
of Inertia
0.92
0.98
0.99
0.92
0.98
0.87
0.94
0.99
0.99
0.95
0.99
0.92
SSI
Female
BMCcort
Polar moment of inertia
Section modulus
Male
BMCcort
Polar moment of inertia
Section modulus
617
(15). We have previously shown that this general pattern can
also be observed at the 65% site of the proximal radius (13).
In subjects without bone disease, volumetric bone mineral
density in the cortex changes very little (a few percentage
points) between the age of 6 yr and adulthood (18, 19). Therefore, SSI is mostly determined by the section modulus, which
increased by about 300 – 400% in the current study. As shown
by the close interrelationship between SSI and the parameters
of bone architecture, these indexes basically provided redundant information in the present study. However, this may be
different in disorders with abnormal intracortical porosity or
mineralization, such as osteoporosis or osteomalacia.
The absolute values for parameters of bone stability were
higher in males than in females. This is not a surprising finding,
as it is well known that men have stronger bones than women,
which is commonly attributed to higher bone mass in men. This
gender difference in bone mass was also obvious in the present
study. However, we found higher ratios between architectural
parameters and BMCcort in postpubertal males compared with
females. This means that for a given cortical bone mass, males
have stronger bones than females due to differences in bone
mass distribution (Fig. 5). The reason for this difference is that
in puberty males add bone to the periosteal surface, where the
effect on bone strength is highest. In contrast, females add bone
to the endocortical surface, where it has a relatively small effect
on bone stability. Thus, pubertal bone development in males
appears to be more efficient with regard to attaining maximal
bone strength by using as little material as possible.
What, then, might be the purpose of the mechanically
inefficient endocortical apposition of bone during female
puberty? As puberty is the time of sexual maturation, it
appears appropriate to interpret the corresponding changes
as a preparation for reproductive functions. During pregnancy and lactation women have to transfer a large amount
of calcium to their fetus/newborn (20). To achieve this calcium transfer, women lose a substantial amount of bone,
notably during the period of lactation (20). In that perspective it makes sense that female puberty is associated with the
accumulation of bone that is of little mechanical value. A
reservoir of calcium is created that can be tapped during later
periods of lactation without compromising bone stability.
All correlations are statistically significant (P ⬍⬍ 0.0001).
two groups are not independent. This may introduce some
bias when the children and adolescents group is compared
with the adult cohort, but should not influence the analysis
of age- and gender-related changes in the children and adolescents group, which was the main focus of this study.
According to the classical work of Garn et al., the development of cortical bone takes a gender-specific course (15).
Before puberty the cortexes of girls and boys undergo periosteal expansion and endocortical resorption. However, during puberty endocortical apposition occurs in girls, but not
in boys. Endocortical apposition during female puberty is a
well documented phenomenon, which was also found in
studies on the midradius (16) and the femoral shaft (17).
Periosteal expansion proceeds longer in boys than in girls,
leading to a larger external bone size in men than in women
FIG. 5. Schematic representation of the effect of bone cross-sectional
geometry on parameters of bone stability. The right and the left bone
cross-sections have the same cortical area, and thus cortical bone
mass is identical. However, the external diameter is greater in the
right bone. For this reason, polar moment of inertia and section
modulus are considerably higher.
618
SCHOENAU ET AL.
Acknowledgments
The technical support of Stratec, Inc., is gratefully acknowledged. We
are indebted to the entire staff of the Research Institute for Child Nutrition for continuing support.
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