3-1. Introduction
Sever's disease occurs frequently in boys aged 10-13 (Kvist and Heinonen 1991;
Micheli and Ireland 1987; Scharfbillig et al., 2009, 2011) who are, in general, undergoing a growth spurt and whose physical activity is higher than younger boys (Malina and Bouchard 1991). The higher body mass and physical activity for boys aged 10-13 than those under the age of 10, therefore, may partly account for the higher incidence of Sever's disease for boys aged 10-13.
Mechanically, the tensile stress at the attachment site of the Achilles tendon is not determined completely by the GRF alone. The CSA of the attachment site of the Achilles tendon and the mechanical advantage that is defined as the ratio of the Achilles tendon moment arm relative to the moment arm of the GRF (Biewener et al., 2004) are the additional structural parameters of foot and ankle for determining the tensile stress.
For example, if the onset of the growth spurt of body mass due to normal growth coincides with that in the CSA of the Achilles tendon insertion for a given mechanical advantage, the tensile stress at the attachment site of the Achilles tendon may be unchanged. Rauch et al (2004) found that the age of peak rate of increase in size due to normal growth varied considerably among different tissues in different body segments.
Therefore, the onset of growth spurt of foot and ankle and body dimensions should also vary due to normal growth. The tensile stress at the attachment site of the Achilles
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tendon for a given intensity of physical activity may be represented by an index determined from following parameters; body mass, the mechanical advantage and the CSA of the Achilles tendon insertion. This index should be the same among boys of various age groups, if the age-related difference in the physical activity, rather than the structural characteristics of the adolescent's foot and ankle, is the primary reason for the age-specificity in the incidence of Sever's disease. If not, the result may reveal additional biomechanical risk factors for explaining the age-specificity. The purpose of this study, therefore, was to examine the age-related differences in the structural parameters of foot and ankle that influence the tensile stress at the attachment site of the Achilles tendon.
3-2. Method Subjects
Forty boys and 19 young adult males voluntary participated in this study. Boys were divided into two groups (7-9 years old and 10-13 years old) (Table 3-1) on the basis of the epidemiological findings that the previous studies (Kvist and Heinonen 1991; Micheli and Ireland 1987; Scharfbillig et al., 2009; 2011) represented that Sever's disease occurs frequently for boys aged 10-13. The group of boys aged 7-9, therefore, represented as the low incidence group of Sever's disease and the group of boys aged 10-13 represented as the high incidence group. Informed consent was obtained from each young adult male subject before experiment. For boys, informed consent was also obtained from their parents. The experimental protocol of this study was approved by
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the Ethics Committee of Human Research at Waseda University (approval number;
2009-137).
Data collection
The result of Section 1 of Chapter 2 showed that a three-dimensional method can determine the Achilles tendon moment arm accurately as compared with two-dimensional center of rotation method. Then, it was found that the Achilles tendon moment arm determined in the rest condition corresponds well to that in the muscle contraction condition among individuals in Section 2 of Chapter 2. The method developed in Section 1 of Chapter 2 for the rest condition, therefore, can be used to determine the mechanical advantage. Each subject lay in a supine position on the bed of a magnetic resonance imaging (MRI) scanner (Signa HDxt, 1.5T, GE medical systems, USA). The right foot and the right lower leg of the subject were fixed on a custom-made apparatus constructed by the foot plate and the leg frame. For the fixation, the long-axis of the right foot was carefully aligned to the foot plate of the apparatus and the right foot was securely fastened to the foot plate by using three non-elastic bands. The long-axis of the right lower leg was also carefully aligned to the long axis of the leg frame, with the knees fully extended, and the lower extremity was securely fastened to the bed and the leg frame by using a Velcro tape. The foot position was described as the angle between the long-axis of the foot plate and the long-axis of the leg frame, and the neutral position of the foot was defined as the foot position of 90º. A series of right foot images were obtained at 10ºof dorsiflexion, neutral position and 10º of plantarflexion
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for the coronal plane and at neutral position for the transverse plane by using the MRI system with a head coil. The scan parameters for the coronal plane and the transverse plane scans are listed in Table 3-2.
Data reduction
The developed method in Section 1 of Chapter 2 was used to determine the Achilles tendon moment arm. The coronal MR imaging plane was aligned to the medio-lateral axis of the foot plate and the long-axis of the leg frame, so that the depth of the scanned images was aligned to the long-axis of the foot plate. The position of any given voxel in the series of coronal MR images was converted directly to the three-dimensional coordinates in a right handed orthogonal coordinate system. Selected bony landmarks of the tibia and the talus were visually identified from the obtained MR images and the three-dimensional coordinates of these points were recorded by using the computer-aided diagnosis system (PLUTO, Nagoya University, Japan). Four points for tibia (a1- a4) and three points for talus (b1- b3) were selected as the bony landmarks.
The point a1 is the most proximal point of one reference marker attached to the tibia, the point a2 is the most distal point of the other reference marker attached to the tibia, the point a3 is the most distal tip of the medial malleolus, and the point a4 is the most distal point of the posterior bony projection forming the incisure fibularis. The point b1 is the most posterior tips of the lateral tubercle of the talus, the point b2 is the center of the posterior edge of the talus sulcus, and the point b3 is the most lateral tips of the lateral processus of talus. The right handed orthogonal coordinate systems embedded to the
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tibia and the talus were defined by using these bony landmarks. The ztibia was defined as the unit vector directed from a2 to a1. The ytibia was defined as the cross product of the ztibia and the temporal unit vector directed from a4 to a3. The xtibia was defined as the cross product of the ytibia and the ztibia. The ytalus was defined as the unit vector directed from b1 to b2. The ztalus was defined as the cross product of the temporal unit vector directed from b3 to b2 and the ytalus. The xtalus was defined as the cross product of the ytalus and the ztalus. The finite helical axis for the neutral position was calculated from the elements of the angular displacement of the tibia-embedded coordinate system relative to the talus-embedded coordinate system that occurred over the range from 10º of dorsiflexion and 10º of plantarflexion. The position of the point that the finite helical axis passes through was determined by using the algorithm proposed by Woltring et al (1985). The line of action of the Achilles tendon force at neutral position was determined as the straight line passing through the centers of cross-sectional areas of the Achilles tendon at the proximal insertion site to the soleus and the distal insertion site to the calcaneus. The shortest distance between the talocrural joint axis to the line of action of the Achilles tendon force projected to the orthogonal plane of the talocrural joint axis was determined as the Achilles tendon moment arm for neutral position.
The moment arm of the GRF was estimated with the assumptions that the GRF acted through the most anterior point of the first metatarsal bone and that the GRF was directed normal to the sole of foot. The shortest distance between the talocrural joint axis to the line of action of the GRF projected to the orthogonal plane of the talocrural joint axis was determined as the moment arm of the GRF for neutral position. The
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mechanical advantage was, then, calculated as the ratio of the Achilles tendon moment arm to the moment arm of the GRF (Biewener 1989).
The CSA of the Achilles tendon insertion representing the transverse attachment site of the Achilles tendon which the Achilles tendon force would act as tensile force was measured by using the transverse MR image of the foot. The most proximal image that the Achilles tendon inserts to the calcaneal epiphysis was chosen, and the CSA of the Achilles tendon insertion was measured (Figure 1). Finally, an index representing the tensile stress at the attachment site of the Achilles tendon (σ) was calculated as follows;
σ= [BW × (MA/MA)]/CSA
where BW, MAGRF and MAAT are body weight [N], the moment arm of the GRF [mm]
and the Achilles tendon moment arm [mm], respectively. The determined value indicates the magnitude of tensile stress that should be applied to the attachment site of the Achilles tendon is subject to when the GRF acting on the foot has the magnitude equal to body weight. The value, therefore, represents the tensile stress for a given individual who is standing still on one leg with the heel raised off the floor and also for the individual who is accelerating his center of body mass upwards at 1G on both legs with the heels raised off the floor. In case that the center of body mass is accelerating upwards at 2G on one leg, the tensile stress should be thrice as large as the index.
87 Statistical analysis
Descriptive data are presented as means ± standard deviations (SDs). One-way analysis of variance (ANOVA) with Bonfferonie’s post hoc test was conducted to assess the differences in each parameter among each age groups. The level of significance was set at 0.05.
3-3. Results
The means and SDs of the determined parameters were represented in Table 3.
The mean value of the Achilles tendon moment arm was significantly different among the age groups. The mean value of the moment arm of the GRF was significantly smaller in boys aged 7-9 (90 mm) than in boys aged 10-13 (107 mm) and young adult males (114 mm). No differences in the mean value of the mechanical advantage were observed among the groups. The mean value of the CSA of the Achilles tendon insertion was significantly greater in young adult males (117 mm2) than in boys aged 7-9 (69 mm2) and 10-13 (78 mm2), however no difference was observed in this between boys aged 7-9 and 10-13. The mean value of the index of the tensile stress was significantly greater in boys aged 10-13 (16.8 N/mm2) than in those aged 7-9 (12.2 N/mm2) and was not significantly different between boys aged 10-13 and young adult males (14.4 N/mm2).
3-4. Discussion
The present study examined the age-related differences in the structural
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parameters of foot and ankle and the index of the tensile stress at the attachment site of the Achilles tendon. The main finding of this study was that the index of the tensile stress was significantly greater in boys aged 10-13 than in those aged 7-9. This result suggests that a greater tensile stress should be developed at the attachment site of the Achilles tendon for boys aged 10-13 than those aged 7-9 even if the physical activity level is assumed to be the same.
Our results showed that the index of the tensile stress was greater in boys aged 10-13 than in those aged 7-9 and was not significantly different between boys aged 10-13 and young adult males. This result suggests that the attachment site of the Achilles tendon is subject to a greater tensile stress for the high incidence group of Sever's disease than the low incidence group even if the physical activity level is assumed to be the same. It also suggests that the increased tensile stress is attributable to unique characteristics of the structural and/or physical parameters for high incidence group. The index of the tensile stress was determined by three parameters; body mass, the mechanical advantage and the CSA of the Achilles tendon insertion. In the present study, body mass was found to be greater in older groups than in younger groups whereas the CSA of the Achilles tendon insertion in boys aged 10-13 was not different from boys aged 7-9 but was smaller than that in young adult males. These results suggest that the onset of growth spurt may vary among different structural and physical parameters. No difference in the mechanical advantage among the three groups suggests that the Achilles tendon moment arm and the moment arm of the GRF increase its length at a similar rate. The age-related difference in the index of the tensile stress,
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therefore, must be attributable to either the age-related differences in body mass or the CSA of the Achilles tendon insertion. The increase in the CSA of the Achilles tendon insertion between 7-9 and 10-13 years old groups was found to be 19% of the difference between 7-9 years old and young adult groups (Figure 3). This suggests that the CSA of the Achilles tendon insertion increases substantially after the age of 13. The corresponding increase in body mass between 7-9 and 10-13 years old groups was found to be 42%. The relative increase in the CSA of the Achilles tendon is notably smaller than that in body mass in the period between 7-9 and 10-13 years old. These results suggest that the onset of growth spurt for the CSA of the Achilles tendon insertion does not coincide with that for body mass, and this gap might result in the significantly large value in the index of the tensile stress for boys aged 10-13. The delayed onset of growth spurt for the CSA of the Achilles tendon insertion, therefore, may be an additional biomechanical factor that accounts for the age-specificity in the incidence of Sever's disease.
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The present study examined the age-related differences in the structural parameters of foot and ankle that influence the tensile stress at the attachment site of the Achilles tendon. The index representing the tensile stress at the attachment site of the Achilles tendon for a given intensity of physical activity was found to be significantly greater in boys aged 10-13 than in boys aged 7-9. The mechanical advantage was not different among the groups. Body mass was significantly greater in older groups than in younger groups. The CSA was not different between boy's groups and was greater in young adult males than in the boy's groups. These results suggest that the onset of growth spurt for the CSA does not coincide with that for body mass, and this gap might result in the significantly large value in the index for boys aged 10-13. The delayed onset of growth spurt for the CSA of the Achilles tendon insertion may be an additional biomechanical risk factor that account for the age-specificity in the incidence of Sever's disease.
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Figure 3-1 The typical transverse right foot image chosen for the measurement of CSA of the Achilles tendon insertion. The area surrounded by the white line indicates the CSA of the Achilles tendon insertion.
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The relative increase in the CSA of the Achilles tendon insertion (opened square) and body mass (opened circle) during the period from 7-9 years old to young adult. The mean values of each parameter for boys aged 7-9 and for young adult males were set as 0% and 100%, respectively.
7-9 years old
10-13 years old
young adult
80
60
40
20
body mass (kg)
140
120
100
80
CSA of the Achilles tendon 2 insertion (mm) 60
0 % 100 %
0 % 100 %
body ma ss CSA of the Achilles tendon insertion
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Table 3-1 The physical characteristics of the subjects (mean ± standard deviation).
boys aged 7-9 boys aged 10-13 young adult male
number of subjects 16 24 19
age (years) 7.9 s0.7 11.8 s1.1 26.2 s2.9
body height (m) 1.28 s0.08 1.52 s0.11 1.71 s0.05 body mass (kg) 28.1 s6.7 43.5 s10.9 64.6 s6.8
CChapter 3 94 Table 3-2 Scan parameters for the coronal and transverse planes. pulse sequencetime to echorepetition timeslice thicknessinterslice distancefield of viewmatrix coronal planeFast gradient echo2.7 ms7.5 ms2 mm0 mm300×300 mm256×256 pixcels transverse planeFast spin echo12.7 ms500 ms2 mm0 mm200×200 mm256×256 pixcels
CChapter 3 95 Table 3-3 The mean values and standard deviations of measured dimensions of the foot and ankle structure.
boys a g e d 7 -9 boys a g e d 10 -13 y o u n g ad u lt male A c h illes te ndon m o m e nt a rm (m m ) 31 s 6.1 37 s 6.6 44 s 6.4 m o m e nt a rm of th e G R F (m m ) 90 s 12.7 107 s 12.6 1 14 s 10.3 mech an ical ad v a n tag e 0.355 s 0.106 0.350 s 0.076 0.396 s 0.075 CS A of th e A c hi ll e s t e ndon in se rt ion (m m
2) 68.5 s 13.6 77.7 s 18.0 1 16.5 s 17.8 inde x of t h e s tre ss ( N /mm
2) 12.2 s 3.9 16.8 s 6.0 14.4 s 3.4
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