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Journal of Anatomy logoLink to Journal of Anatomy
. 2021 Feb 1;239(1):46–58. doi: 10.1111/joa.13399

Morphological divergence in the curvature of human femoral diaphyses: Tracing the central mass distributions of cross‐sections

Takeshi Imamura 1, Keiko Ogami‐Takamura 1,2,✉, Kazunobu Saiki 1, Ayami Hamamoto 1, Daisuke Endo 1, Kiyohito Murai 1, Keita Nishi 3, Junya Sakamoto 4, Keishi Okamoto 1, Joichi Oyamada 3, Yoshitaka Manabe 3, Toshiyuki Tsurumoto 1,2
PMCID: PMC8197953  PMID: 33527352

Abstract

The diaphysis of the human femoral bone has a physiological anterior curvature; additionally, there is a curvature to the medial side or lateral side. In addition to compression stress from gravity during standing, walking, and running, these bones are continuously exposed to complex stresses from the traction forces of the various strong muscles attached to them. The femoral diaphysis is subjected to these mechanical stresses, and the direction and size of its curvature are defined according to Wolff's law and the mechanostat theory of Frost. The purpose of this study was to quantitatively evaluate the curvature of the femoral diaphysis in Japanese skeletons by determining the curve connecting the central mass distributions (CMD) of cross‐sectional images. A total of 90 right femora (46 males and 44 females) were randomly selected from modern Japanese skeletal specimens. Full‐length images of these bones were acquired using a clinical computed tomography scanner. The range between the lower end of the lesser trochanter and the adductor tubercle of each femur was divided at regular intervals to obtain ten planes, and nine levels were analyzed. The CMD curve was determined by connecting the CMDs of each of the nine cross‐sections. First, the CMD of a cross‐section in each of the nine slices was calculated, and the nine trajectories were superimposed from above. Then, by converting the shape of the entire CMD curve to superimpose the coordinates of the endpoint on the starting point, a closed arc representing the curvature of the femur was determined. For both males and females, the patterns varied from mostly medial to largely lateral curvature. The size of the curvature also varied for individuals. By analyzing only the coordinates of the vertex of the CMD curve of each femoral bone, the outlines of the diaphyseal curvatures could be recognized. The femora were thereby divided into two groups: medial bending and lateral bending. Considering males and females together, the number in the lateral‐curvature group (n = 51) was larger than that in the medial‐curvature group (n = 39). Moreover, the average age of the lateral‐curvature group was significantly higher than that of the medial‐curvature group (p < 0.05). In males, with an increase in the cortical bone proportion of the cross‐sectional area, the anterior vertex of diaphyseal bending tended to be more prominent. This cortical proportion was significantly higher in the medial‐curvature groups than in the lateral‐curvature group (p < 0.01). The phenomena observed in this study may be related to pathophysiologies such as atypical fractures of the femur and osteoarthritis of the knee joints.

Keywords: bending, curvature, diaphysis, femur, shaft

Schematic diagrams of the central mass distribution (CMD) curves of all cases by gender. Each is superimposed with the start and endpoints at the origin of the coordinate axis. For each individual, since it is corrected by the length of the femur, the horizontal axis shows the x‐coordinate/femoral total length of each CMD, and the vertical axis shows the y‐coordinate/femoral total length of each CMD.

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1. INTRODUCTION

The femur is the longest and largest bone in the human body, and its shape has developed during the human evolution process for bipedality. In addition to compression stresses from gravity during standing, walking, and running, the femur is constantly exposed to complex stresses by traction forces from the various strong muscles attached to it. The diaphysis of the human femur has a physiological anterior curvature; moreover, there is also a curvature to the medial side or lateral side (Figure 1). According to Wolff's law (Wolff, 1986), because bone is continuously under mechanical stress, its shape changes gradually, that is, bone is formed in areas of increased strain and resorbed in areas of decreased strain. Alternatively, in the mechanostat theory proposed by Frost (2003), bone resorption and remodeling are caused by an increase/decrease in strain above a physiologically determined strain threshold or "set point", rather than continually changing with the strain (Frost, 1997; Frost, 2003). Indeed, at the microscopic level, such a biological response is observed in the cortices of the long bones that are compatible with the mechanical environment (Maeda et al., 2018; Matsuo et al., 2019; Skedros, 1995; Skedros et al., 2013).

FIGURE 1.

FIGURE 1

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Examples of right femoral front view and lateral view images (three‐dimensional CT images). Focusing on the shape of the diaphysis, a 69‐year‐old male (left) is observed to have lateral curvature, while a 77‐year‐old male (right) shows medial curvature. (Medixant, RadiAnt DICOM Viewer ver.5.5.1. Dec 13, 2019. https://www.radiantviewer.com)

When observed macroscopically and three dimensionally, the femoral diaphysis has anterior, lateral, and medial curvatures. There are many reports that the curvature of the femoral diaphysis is involved in some pathological conditions, such as atypical femoral fracture (AFF), that is, stress fractures in the subtrochanteric or diaphyseal area, and osteoarthritis (OA) of the knee joint. Bisphosphonates (BPs), a treatment for osteoporosis, have recently been reported to increase the incidence of AFF, including stress fractures in the subtrochanteric region or proximal femur (Schilcher et al., 2015; Shane et al., 2010, 2014). Other reports suggest that the morphology of the proximal femur or the shape of the cortical bone is involved in the anatomical background of AFF (Hagen et al., 2014; Koeppen et al., 2012; Niimi et al., 2015; Szolomayer et al., 2017; Taormina et al., 2014). Meanwhile, many studies have examined the relationship between the alignment of the entire lower limb and the development and progression of OA of the knee joints. As a result, osteotomy surgeries to correct lower limb alignment have shown positive results. There are also reports on the relationship between knee OA and curvature of the femur. Yau et al. (2007) reported that the incidence of femoral or tibial bowing in the coronal plane was high in a Chinese population with end‐stage OA of the knee. The lateral curvature of the femoral diaphysis associated with aging may contribute to the initiation of varus‐type OA of the knee. These changes in the femoral bone may be followed by OA progression including varus femoral condylar orientation, medial joint space narrowing, and tibial plateau compression (Matsumoto et al., 2015). Higher femoral lateral bowing and slightly higher femoral internal torsion in the proximal diaphysis were observed in females with knee joint OA, compared with healthy subjects. These variations in females may be a structural adaptation to mechanical use (Mochizuki et al., 2017).

To evaluate these femoral curvatures, especially in clinical studies, anterior‐posterior X‐ray images of the femoral bones have been used, with assessments based on the angles made by lines drawn between reference points on the proximal and distal portions of the bone shafts (Hyodo et al., 2017; Kim et al., 2017; Mullaji et al., 2009; Nagamine et al., 2000; Oh et al., 2017, 2014a, 2014b; Park et al., 2019; Shin et al., 2017; Soh et al., 2015; Yau et al., 2007; Yoo et al., 2017). For these retrospective studies of patients, a simple method and limited radiation exposure are important considerations. However, if the X‐ray imaging method is not strictly defined and controlled, the reproducibility of measurement results is likely to be low. On the other hand, the femoral curvature has also been mentioned in anthropological studies from the viewpoint of changes in skeletal morphology (Bruns et al., 2002; De Groote et al., 2010; Dupej et al., 2017; Lacoste et al., 2018; Yamanaka et al., 2005). In these studies, the femoral diaphysis has been analyzed in detail in three dimensions. Abdelaal et al. (2016) adopted a method of regarding the curve connecting the center point of the medulla on femoral computed tomography (CT) cross‐sectional images. However, their method of determining the center point was to adopt the center point of the circle or ellipse that most closely fit within the medulla. Thus, although many studies have evaluated the femoral axis curvature, there is still no standardized method for its measurement. Hence, it is desirable to develop a more objective method for determining reference points. The purpose of this study was to quantitatively evaluate the curvature of the femoral diaphysis in Japanese skeletons by determining the curve connecting the central mass distributions (CMD) of cross‐sectional images, which are used as reproducible and stable reference points.

2. MATERIALS AND METHODS

2.1. Materials

The materials were the same skeletons used in our previous study (Imamura et al., 2019); from among the skeletal specimens of modern Japanese stored at Nagasaki University, 90 right femora, comprising 46 from males aged 20–89 years (mean age, 62.7 years) and 44 from females aged 31–87 years (mean age, 68.3 years), were examined (Table 1). Females were older on average than males, but there was no significant difference in age between the gender (p = 0.064). They were obtained from cadavers provided to the Nagasaki University School of Medicine for anatomical dissection by medical students between the 1950s and 1970s. Most of them were voluntarily donated, and most were from anonymous subjects. The sex and exact age at death of all the individuals were registered. After their dissection, their soft tissues were almost entirely removed to produce dry skeletal preparations. Those with obvious trauma or inflammatory joint diseases were excluded. All procedures performed in this study were in accordance with the standards of the Ethics Committee of Nagasaki University Graduate School of Biomedical Sciences (approval number: 15033076) and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards.

TABLE 1.

Numbers of femoral bones analyzed in this study

Age Male Female
21–30 1 0
31–40 4 1
41–50 7 4
51–60 5 5
61–70 13 9
71–80 9 22
81–90 7 3
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2.2. CT imaging and extraction of the target images

Full‐length images of all the examined femora were obtained using clinical multislice CT (Activision 16; Toshiba Corp.) (X‐tube volume/current = 120 kV/100 mA, image matrix size; 512 × 512 pixels, slice thickness; 0.5 mm). These femora were scanned with their three points, the most posterior points of the medial and the lateral condyles and the most posterior point of the greater trochanter, placed in the same plane on the scanner table. The data were saved in Digital Imaging and Communication in Medicine (DICOM) format. The range between the lower end of the lesser trochanter and the adductor tubercle of each femur was divided into nine segments of equal length. The cross‐sections, including both ends, were labeled from top to bottom as “Level 1” to “Level 10”, creating nine levels (from Level 1 to Level 9) that were subsequently analyzed. Each of the DICOM data files was opened with ImageJ ver. 1.50 (NIH) and saved as a text image file. A 512 × 512 matrix consisting of text data of Hounsfield units (HU) was obtained, opened in Microsoft Excel (Office 2016, 64‐bit; Microsoft Corporation), and converted into an xls file. The values of the threshold for binarization were calculated as described in our previous study (Imamura et al., 2019), and were determined as follows: (i) all of the matrixes for these 10 sections were pasted into one Microsoft Excel sheet, and (ii) a histogram was created based a frequency table of HU to calculate the mean HU for the first peak (i.e., approximately −1000; mainly indicating the HU of the surrounding air) and the HU for the second peak (i.e., indicating the HU of the bone itself).

2.3. Calculating cortical index

In all the cross‐sections of each femur, the proportion of the femur cross‐sectional area occupied by cortical bone was calculated as the cortical index (CI). The CI values of the nine cross‐sections were averaged to get a mean value of CI (mCI).

2.4. Determination of the curve connecting the CMDs of nine cross‐sections in femoral diaphysis

2.4.1. Determination of the CMD for each cross‐section

First, the CMDs of the femoral cross‐section images were determined. In general, the intersection of two line segments dividing any two‐dimensional figure into two equal areas is the CMD. The CMD of the area including both cortical bone and the medulla in each cross‐sectional image was calculated by a macro in Microsoft Excel®. That is, when determining the line of the column direction and that in the row direction, their intersection was the CMD of the figure (Figure 2, red arrow).

FIGURE 2.

FIGURE 2

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Determining the central mass distribution (CMD) on cross‐sectional images. The CMD of the area containing the cortical bone and medulla of each cross‐sectional image were calculated using Microsoft Excel® macros. In the upper section, we set up serial perpendicular lines bisecting the cross‐sectional image to the left and right, and compared the areas of both. The perpendicular line with the smallest difference was taken as the line through the CMD. Further down, we set up parallel lines bisecting the top and bottom and compared the areas on both sides of the line; the parallel line with the smallest difference was taken as the passing through the CMD. The intersection of these two line segments is the CMD (red arrow). In the Excel sheet, the intersection cell of the column line and the row the line was determined, and was used as the CMD for this cross‐section

2.4.2. Determination of the CMD curve

The CMD curve was determined by connecting all CMDs of the nine cross‐sections of a femur. Figure 3 shows the procedure. First, the CMD of one cross‐section in each of the nine slices was calculated, all nine were superimposed from above, and the trajectory of these points, that is, the CMD curve, was drawn. By converting the shape of the entire CMD curve to superimpose the coordinates of the endpoint (red arrow) on the starting point (green arrow), a closed arc representing the curvature of the femur was determined.

FIGURE 3.

FIGURE 3

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Determination of the central mass distribution (CMD) curve. By connecting the CMDs of all nine cross‐sections for each femur and superimposing them from above, the trajectory of the points, that is, the CMD curve, was drawn. Then, by converting the shape of the entire CMD curve to superimpose the coordinates of the endpoint (red arrow) on the starting point (green arrow), a closed arc representing the curvature of the femur was determined. The CMDs of levels 1–9 are numbered from L1 (the starting point) to L9 (the endpoint) in the figures

Figure 4 shows representative examples in schematic form. Two femoral bones are viewed from above. In the upper example, the vertex of the curvature of the diaphysis is on the medial side, that is, it has a medial curvature. In the lower example, the vertex of the curvature is to the lateral side of the femoral shaft, that is, it has a lateral curvature.

FIGURE 4.

FIGURE 4

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Schematic diagram showing two representative examples of determination of the central mass distribution (CMD) curve. In the upper example, the vertex of the curvature of the diaphysis is on the medial side, i.e., medial curvature. In the lower example, the vertex of the curvature is to the lateral side, indicating lateral curvature

2.5. Data analysis

In the analysis of the femoral diaphysis curvature, each measurement was divided by the total length of each femur in order to standardize the values.

2.5.1. Relationship between age and mCI

The mCI was calculated by averaging the CI values of nine cross‐sections of all femurs, and the relationship between those values and age was examined.

2.5.2. Overview of data for all CMD curves

After correcting the lengths of the curves with respect to each femoral length, they were compared by drawing the shapes of the curves connecting the CMDs of each slice, for all specimens.

2.5.3. Coordinates of the vertex of the curvature

For each curvature, the furthest point from the origin was taken as the vertex of the curvature to calculate the x‐ and y‐coordinates. These values were compared with the age of the individual and the value of mCI.

2.5.4. Comparison of the lateral‐curvature group and the medial‐curvature group

If the value of the x‐coordinate of the vertex calculated as described above was positive, the femoral diaphysis was evaluated as having a lateral curvature. Conversely, if the value was negative, it had a medial curvature. In this way, the specimens were divided into two subgroups. For both of the lateral‐curvature group and the medial‐curvature group, the average age and the value of mCI were compared. ANCOVA was used to compare the two groups to account for the effect of age.

2.5.5. Consideration of the level of a vertex in a curve

The vertex of each curve was examined at the level of the femoral trunk. This was tabulated by gender and by type of curvature.

2.5.6. Analysis of the average image of the curvature

The average values of x‐ and y‐coordinates of each CMD for all males and females were calculated, to draw an average image of the CMD curves by gender. The values of the coordinates of each point were compared between males and females. Males and females were further divided into two subgroups of large and small mCI to examine the characteristics of the shape of each CMD curve.

2.6. Statistical analysis

For the tests of correlation coefficients between mCI values and age, coordinates and age, and coordinates and mCI, we first tested the normality of the data distribution and then tested with Pearson's correlation coefficient if they were normally distributed or with Spearman's rank correlation coefficient if they were not. Populations of subgroups in males and females were compared for independence with the chi‐squared test. Differences in age and the values of mCI between the subgroups in males and females were tested with two‐factor factorial ANOVA. Differences in coordinates in the subgroups of males and females were assessed using the Tukey–Kramer multiple comparison test. For these statistical tests, we used the Excel analysis tool and commercial add‐in software with macros (Statcel, Useful Add‐in Forms on Excel 4th ed.; O.M.S. Publishing Co.). We analyzed the relationships between age and mCI in females separately, for the medial‐ and lateral‐curvature groups, using ANCOVA in JASP (Version 0.13.1) and JASP Team (2020) (https://jasp‐stats.org/).

3. RESULTS

3.1. Relationship between age and mCI

The relationship between age and the values of mCI of the nine cross‐sections in all femoral bones is shown in Figure 5. There was a significant negative correlation between these values for both males and females; the negative correlation was higher for females (r = −0.57, p < 0.01) than for males (r = −0.32, p < 0.05).

FIGURE 5.

FIGURE 5

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Relationship between age and the mean cortical index (mCI) values of nine cross‐sections in femoral bones. Significant negative correlations were found between these values for both males (r = −0.32, p = 0.032) and females (r = −0.57, p < 0.01); the negative correlation for females was greater than that for males

3.2. Schematic diagrams of the CMD curves of all cases

Figure 6 shows schematic diagrams of the CMD curves of all cases by sex. Each is superimposed with the start and endpoints at the origin of the coordinate axis. For each individual, since it is corrected by the length of the femur, the horizontal axis shows the x‐coordinate/femoral total length of each CMD, and the vertical axis shows the y‐coordinate/femoral total length of each CMD. In these figures, when the vertex of the CMD curve is on the left side of the central y‐axis, the femur has a medial curvature, and when on the right, a lateral curvature. For both males and females in Figure 6, there were various patterns from large medial to large lateral curvature. The size of the curvature also varied for individuals. In almost half of both males and females, the curve spread across the y‐axis. This indicated that few individuals were extremely curved either medially or laterally. However, for some femora, the entire curve was to the right side of the y‐axis in both males and females, that is, their entire diaphyses were completely lateral. In contrast, the entire curve was spread to the left side of the axis, that is, the femur's entire diaphysis was completely medial, in three males, and slightly so in one female. Furthermore, when observing each of the CMD curves carefully, in most cases of both males and females, the closed curve indicating the CMD curve was found to be continuous in the counterclockwise direction from the proximal portion of the right femoral diaphysis to the distal portion. In all femurs, the proximal part of the femur first curved laterally and then gradually curved anteriorly, and finally curved relatively medially in the distal part.

FIGURE 6.

FIGURE 6

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Schematic diagrams of the central mass distribution (CMD) curves of all cases by gender. Each is superimposed with the start and endpoints at the origin of the coordinate axis. For each individual, since it is corrected by the length of the femur, the horizontal axis shows the x‐coordinate/femoral total length of each CMD, and the vertical axis shows the y‐coordinate/femoral total length of each CMD. If the vertex of the CMD curve is on the left side of the central y‐axis, the femur has a medial curvature, and if on the right side, a lateral curvature

3.3. Vertex coordinates of the CMD curves

Figure 7 is a scatterplot showing only the coordinates of the vertex of the CMD curve of each femoral bone. Males and females are color coded to show each distribution more clearly. The extent of the curvature of all femur curvatures shown in Figure 6 can be shown and compared for each gender. The analysis of each coordinate is described below.

FIGURE 7.

FIGURE 7

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Scatterplot of only the coordinates of the vertex of the central mass distribution curve of each femoral bone. Male and female points are color coded to show each distribution more clearly. The horizontal axis shows x‐coordinates/femoral total length of vertex point, and the vertical axis the y‐coordinate/femoral total length of each vertex

3.4. Examination of the femoral shaft levels where the vertices of the curve exist

In many cases, the vertices of each curve were located at level 5 of the femoral diaphysis, that is, almost at the middle portion of the diaphysis (Table 2). However, in some cases the vertices were at level 4.

TABLE 2.

Diaphyseal levels at which the vertex of the femoral curve was present. The vertex of the femoral diaphysis was tabulated by gender and type of curvature. In many cases, curve vertices were located at Level 5 of the femoral diaphysis, that is, almost at the middle of the diaphysis. However, in some cases the vertices were at Level 4

Male Female
Medial Lateral Medial Lateral
Slice 4 2 2 4 5
Slice 5 15 25 18 19
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3.5. Comparison between the lateral‐ and medial‐curvature groups

Using the Y‐axis as a border, the femoral bones were divided into two groups; the medial‐curvature group had a vertex on the left side of the Y‐axis, while the lateral‐curvature group had a vertex on the right side. We compared the populations of the two groups by gender (Figure 8, left). For males, the medial‐ and lateral‐curvature groups were similar, numbering 22 and 24 bones, respectively. For females, the medial‐curvature group comprised 17 femora, and the lateral‐curvature group 27; the difference between males and females was not significant (p = 0.38). Next, we compared the ages of the groups (Figure 8, middle). For males, the average age of the medial‐curvature group was 58.4 (SD = 17.0) years, and that of the lateral‐curvature group was 66.6 (SD = 15.0) years. For females, the average of the medial‐curvature group was 64.4 (SD = 13.2) years, and that of the lateral‐curvature group was 70.7 (SD = 8.4) years. Considering males and females together, the average age of the lateral‐curvature group was significantly higher than that of the medial‐curvature group (p = 0.01); however, the differences were not independently significant for males or females (p = 0.75). We also compared the mCI values of the groups (Figure 8, right). For males, mCI of the medial‐curvature group was 0.61 (SD = 0.07), and mCI of the lateral‐curvature group was 0.59 (SD = 0.05), with no significant difference. In contrast, for females, the value of mCI in the medial‐curvature group was 0.55 (SD = 0.08), and that of the lateral‐curvature group, 0.49 (SD = 0.08), was significantly lower (p < 0.05). Moreover, considering these groups of males and females together, the mCI value was significantly higher in the medial‐curvature groups than in the lateral‐curvature groups (p < 0.01). Furthermore, since age also significantly affected the value of femoral diaphysis mCI, a comparison between the lateral and medial‐curvature groups was made using ANCOVA in females (Figure 9). Although the mCI values tended to be higher in the lateral‐curvature group, the difference in age between the two groups had a certain influence on the mCI value in females; the p‐value approached significance (0.06).

FIGURE 8.

FIGURE 8

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Comparison between the medial‐curvature group and lateral‐curvature group. Left: In males, the two groups were approximately equal in number, but lateral curvature tended to be more common in females. Center: Comparison of the two groups by age. Considering males and females together, the mean age of the lateral‐curvature group was significantly higher than that of the medial‐curvature group (p < 0.05), but the difference was not independently significant for either gender in isolation. Right: Comparison of the mean cortical index (mCI) values of both groups. When the medial‐ and lateral‐curvature groups were combined, the males had significantly higher values than the females (p < 0.01). When considering males and females in these groups combined, the mCI values were significantly higher in the medial‐curvature group than in the lateral‐curvature group (**p < 0.01). Furthermore, among females, the mCI values in the medial flexion group were significantly lower than those in the lateral flexion group (p < 0.05)

FIGURE 9.

FIGURE 9

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Relationship between age and mean cortical index (mCI) values in females. ANCOVA was used to compare the medial‐ and lateral‐curvature groups. Although there was no significant difference between these groups (p = 0.060), the former's mCI tended to be higher than that of the latter

3.6. Relationship between the vertex coordinates and age

The x and y coordinates of the vertices and age are shown as a scatter plot in Figure 10. The correlation coefficient between the x‐coordinate and age for females was 0.24 (p = 0.11). That is, in females, there was a slight tendency for the vertex of the CMD curve to be located laterally with increasing age. This suggested that, although there was no significant correlation, the curvatures for females tended to move laterally with age, changing the curvature of the femoral diaphysis. In contrast, in males, both x‐ and y‐coordinates of vertices were not affected by age (p = 0.29 and 0.27, respectively).

FIGURE 10.

FIGURE 10

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Scatterplot of the relationship between the x‐coordinate of the vertex and age (left), and between the y‐coordinate and age (right). In females, the correlation coefficient between the x‐coordinate and age was 0.24 (p = 0.11), indicating a weak correlation tendency. In contrast, the correlation coefficient between the y‐coordinate and age was 0.013 (p = 0.93). In males, the x‐ and y‐coordinates of vertices were not affected by age (p = 0.29 and 0.27, respectively)

3.7. Relationship between vertex coordinates and mCI

The coordinates of the vertices and the values of mCI are shown as a scatter plot in Figure 11. In this study, the value of the y‐coordinate of the vertex indicated the degree of anterior convexity of the femoral shaft. A weak positive correlation of 0.27 (p = 0.07) was observed between the y‐coordinate value of the vertex and the cortex thickness in males. This indicates that, in males, the anterior curvature of the femoral diaphysis increases with the proportion of cortical bone. In contrast, in females, a moderate negative correlation −0.25 (p = 0.10) was found between the x‐coordinate and mCI, indicating that the lateral curvature of the femoral diaphysis increases inversely with the proportion of cortical bone in females.

FIGURE 11.

FIGURE 11

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Scatterplot of the relationship between the x‐coordinate of the vertex and the mean cortical index (mCI) (left), and between the y‐coordinate and mCI (right). A weak negative correlation coefficient of −0.25 (p = 0.10) was seen between the female x‐coordinate and mCI. Moreover, a weak positive correlation (correlation coefficient 0.27, p = 0.07) was observed between the y‐coordinate value of the vertex and mCI in males

3.8. Average position of the coordinates of CMD curves

Figure 12 left shows the calculation of average positions of the coordinates of the CMD for each cross‐section, by sex. The curve in females tended to be slightly more lateral than that in males, but the difference was not significant. In Figure 12, middle and right, males and females are each divided into a large‐mCI group and a small‐mCI group, and the average positions of CMD curves for each subgroup are shown. The large‐mCI and small‐mCI groups for each sex contained equal numbers; 23 each for males (small‐mCI; 0.45–0.60, large‐mCI; 0.61–0.70) and 22 each for females (small‐mCI; 0.35–0.511, large‐mCI; 0.515–0.68). For males, the y‐coordinates of the large‐mCI group were significantly larger than those of the small‐mCI group (p < 0.05 in Level 3 and Level 6, p < 0.01 in Level 4 and Level 5); that is, the midshafts of femoral bones of males in the large‐mCI group tended to bend anteriorly. In contrast, for females, the average values of the x‐coordinates of the small‐mCI group were relatively larger than those of the large‐mCI group; however, the difference was not significant in all levels.

FIGURE 12.

FIGURE 12

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Calculations of the average position of the coordinates of the central mass distribution (CMD) for each cross‐section, by gender. Left: male and female; females tended to be slightly more lateral than males, but no significant sex differences were observed. Middle: the large mean cortical index (mCI) group and the small‐mCI group in males; the y‐coordinates of the large‐mCI group were significantly larger than those of the small‐mCI group (p < 0.05 in Level 3 and Level 6, p < 0.01 in Level 4 and Level 5); namely, the midshafts of femoral bones of males in the large‐mCI group bent anteriorly. Right: the large‐mCI group and the small‐mCI group in females. The small‐mCI group tended to have more lateral curvature of the femoral diaphysis than the large‐MCI group. None of these differences were significant

4. DISCUSSION

4.1. Measurement method of femoral diaphysis curvature

Several attempts have been made to determine the curvature of the femur from 3D images (Abdelaal et al., 2016; Akamatsu et al., 2016; Karakaş & Harma, 2008; Lu et al., 2012; Mochizuki et al., 2017; Schmitt et al., 2019). In these, the "center point" of the femoral cross‐section was the basis for determining the curvature. However, the methods for determining the center point were not always explicitly described, and some were determined by hand, so reproducibility remains an issue. Some studies considered the curve connecting the entirety or part of the centerline of the femur as part of the circumference and an indicator of its radius (Karakaş & Harma, 2008; Lu et al., 2012; Schmitt et al., 2019). However, since the results of the present study have shown that the curvature of the femoral shaft is not simple, it is not appropriate to consider the femoral curvature as part of a single circumference in this way. In the present study, we evaluated the curvature of the entire region, including the medullary cavity. This method has been employed in many published studies on femoral curvature. It should be noted that we have used the term "Central Mass Distributions (CMD)" in this study, not in a mechanical sense, but rather to describe the center point of a particular irregularly shaped figure. Using the measurement method adopted in this study, it is possible to determine the CMD of each cross‐section strictly by calculation, and we expect that more reproducible results can be obtained. Furthermore, to think about femoral morphology from a biomechanical perspective, a morphological analysis of the cortical bone in isolation would be necessary (Macintosh et al., 2013). This method can also be applied to a displacement analysis of the CMDs in the cortical bone region. We used Microsoft Excel ® for data analysis in this study, but the same image processing could be achieved using image processing software such as ImageJ, BoneJ, or MATLAB.

4.2. Considerations of the results of this study

This study showed that the curvatures of femoral shafts are highly diverse; the number of the lateral‐curvature group was larger than that of the medial‐curvature group, and this tendency was more notable among females, even if there was no significant difference between males and females. It was reported that the degree of femoral shaft anterior bending with age increased in females (Karakaş & Harma, 2008). In our study, when males and females were considered together, the average age of the lateral‐curvature group was significantly higher than that of the medial‐curvature group. Notably, in females, the vertex of the CMD curve tended to be located more laterally with increasing age. In contrast, for males and females together, the proportion of the cortex in the cross‐sectional area was significantly higher in the medial‐curvature group than in the lateral‐curvature group. Additionally, in males, with increasing proportion of cortical bone, the anterior vertex of diaphyseal bending tended to be more prominent. Nevertheless, although there was no significant difference between the medial‐ and lateral‐curvature groups in females, the mCI of the former tended to be greater than that of the latter. It is not possible to determine whether there is a direct link between the two phenomena, due to the combination of cortical thinning of the femoral diaphysis and its tendency to become more pronounced with age. It is conceivable that the shape of the femoral diaphysis changes according to Wolff's law and mechanostat theory of Frost, affected by the biomechanical environment. In future studies, it will be necessary to verify the presence or absence of a link between the two phenomena by planning further investigations such as biomechanical experiments.

4.3. Femoral diaphyseal curvature and atypical femoral fractures

Several studies have suggested an association between AFF and BPs. However, Oh et al. (2014b) reported 12 cases of low‐energy femoral shaft fractures associated with bowing deformity; six of them were not treated with BPs at all, and he proposed the concept of stress fractures of the bowed femoral shaft (SBFs) as a subtype of AFFs. Stress fractures associated with femoral diaphyseal bowing deformity do exist, and should be recognized as another cause of AFFs. Both anterolateral femoral bowing and loss of thigh muscle are highly associated with the occurrence of AFFs (Shin et al., 2017). Moreover, Morin et al. (2016) reported that patients with AFF exhibited femoral geometry parameters that resulted in a higher tensile mechanical load on the lateral side. This could play a critical role in the pathogenesis of AFFs; the lateral femoral bowing angle was associated with the location of the fractures (Yoo et al., 2017). The present study revealed a wide variety of lateral to medial curvature of the femoral diaphysis. Individuals with higher degrees of lateral curvature would morphologically be predicted to have a concentration of mechanical stress around the sub‐trochanteric portion; AFF may perhaps tend to occur in individuals with these morphological characteristics.

There have also been some reports in which the site of AFF was affected by the degree of curvature of the femur. Park et al. (2019) indicated that the presence of anterolateral bowing and the level of the vertex of the bowed femur were important factors related to the fracture height of AFFs. Furthermore, it was reported that the location of AFFs could be determined by individual stress distributions influenced by femoral bowing and the neck‐shaft angle (Oh et al., 2017). The present study results showed that the majority of the curvature vertices were located in Slice 5, that is, the middle of the femoral shaft, which is slightly more distal than the previously reported site of AFF preference. However, in AFFs associated with bisphosphonate use, more distal diaphyseal fractures occurred with a higher degree of anterior and lateral femoral bow (Soh et al., 2015).

Increases in the degree of the lateral bending of the femur increase the stress in the tension direction applied to the femoral cortex on the lateral side. This may cause stress fractures coupled with cortical bone thinning of this site. We previously showed that the cortical bone thickness and cortical bone cross‐sectional area of the bone shaft decrease significantly with age, especially in females (Imamura et al., 2019). This study revealed that in female femoral bones with a thin cortex, the shaft tended to be laterally displaced; this might be a biological adaptation against the thinning cortical bone to obtain maximum mechanical efficiency, in accordance with Wolff's law (Wolff, 1986) and the mechanostat theory of Frost (2003).

4.4. Femoral diaphyseal curvature and osteoarthritis of the knee joint

Further experiments and verification, including biomechanical analysis and finite‐element method analysis, are required in order to verify how much the femoral diaphyseal curvature affects the stress applied to the knee joint. However, in order to discuss the effect on the knee joint, it will be necessary to consider the influence of the alignment of not only the femur but also the entire lower limb, so it is not easy to comprehensively address this problem. Nevertheless, as curvature to the lateral side of the femoral diaphysis affects the stress distribution to the knee joint, the likelihood of promoting the occurrence and progression of cartilage degeneration of the knee joint would be high. The present study revealed a progressive tendency for lateral curvature of the skeleton in older Japanese women, coupled with thinning of the cortical bone. This may increase weight bearing on the medial component of the knee joint and contribute to the progression of medial OA. However, with respect to the effect of the degree of anterior curvature on the knee joint, it is necessary to consider such changes in a dynamic stress distribution due to walking and motion, so the situation becomes more complex.

4.5. Limitations

This study had some limitations: (i) This was a cross‐sectional study of right femurs from 90 individuals. Thus, it was not possible to track morphological changes over time. (ii) Records of health status, medication, and activities before death for each individual were not available. (iii) Due to the nature of the anatomical skeletal collection comprising a donor population, the sample was skewed toward an older age range. Moreover, the ages of the females were higher than those of the males, even if there was no significant difference between them. (iv) This study only analyzed image data taken with the femora placed horizontally on a CT scanner table, and not actual standing or walking conditions. Therefore, it was not possible to accurately reproduce the conditions of the femur that reflect human activity.

5. CONCLUSIONS

DICOM data were extracted from CT images of the femoral bones, and the morphology of the diaphysis was analyzed. The curvatures of the femoral shafts were highly diverse, and tended to be affected by aging. A decrease in the proportion of cortical bone in the femoral cross‐sectional area might be related to the femoral shaft bending. The phenomena observed in this study may be related to pathophysiologies such as osteoarthritis of the knee joints and atypical fractures of the femur.

CONFLICT OF INTEREST

The authors have no conflicts of interest to declare.

AUTHOR CONTRIBUTIONS

T.I., K.T., J.S., J.O., Y.M., K.O., and T.T. conceived and designed the study. K.S., A.H., and K.N. carried out the acquisition of CT data. T.I., K.T., A.H., and T.T. analyzed and interpreted the data. T.I., K.T., and T.T. carried out statistical analyses. T.I., K.T., K.S., J.S., K.O., and T.T. contributed to the drafting of the manuscript. K.N., J.O., D.E., and K.M. contributed to the critical revision of the manuscript and approval of the article.

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