In patients with Legg–Calvé–Perthes disease (LCPD), the head of the femoral bone dies temporarily, disconnecting its blood supply¹⁾. The etiology of this disease is not certain, although factors including vascular, traumatic, constitutional, endocrine, racial, and socioeconomic factors have been suggested^1-3).

Several mechanical factors have been suggested in the deformation of the femoral head in patients with LCPD^2,4,5). One study suggested that the deformation may be a result of excessive force applied to the femoral head^6-8), and changes in bone mineral density (BMD) of the femur and containment are also considered important factors⁸⁾.

A study by Karimi et al.⁹⁾ examined the difference between the loads applied to the femoral head in patients with LCPD compared with normal subjects. According to the results, fewer joint contact forces and moments were applied to the femoral head in patients with LCPD compared with normal subjects⁹⁾. Of particular interest, the use of assistive devices such as the Scottish Rite Orthosis not only decreased the loads but also increased joint contact force while walking⁹⁾.

Other studies have also examined changes in BMD of the femoral head. Some studies have reported lower BMD of the femoral bone in LCPD subjects compared with normal subjects^8,10). However, no difference in BMD was observed between the affected and unaffected sides¹⁰⁾.

According to the theory of containment, introduced in 1,954 based on observations conducted on pigs^2,11), the contact area of the hip joint is maximized in the position of internal rotation, flexion, and abduction^2-4,7,12). If this theory is correct, the outcomes of treatment using assistive devices that position the hip joint in the previously described manner should be preferable to no treatment. However, the results of studies on this topic did not support the effectiveness of the containment approach^2,11).

Closure of blood vessels in this group of subjects is another theory that has recently emerged regarding the etiology of LCPD¹³⁾. According to this theory, death of the femoral head may be caused by a decrease in the blood supply, which occurs due to obstruction of blood vessels, meaning that the diameter of blood vessels decreases due to compression of bone resulting from applied loads. The supply of blood to the femoral head decreases as the diameter of blood vessels decreases¹³⁾. With decreasing BMD, greater than usual deformation of the femoral head was observed in this group of subjects^8,10). Therefore, exertion of a force on blood vessels will cause them to close. In this case, death of the bone is caused by a change in the blood supply resulting from changes in BMD. A summary of theories on the etiology of Perthes disease explaining the objective of the current study is shown in Fig. 1.

Figure 1. A summary of the potential reasons for the etiology of Legg–Calvé–Perthes disease (LCPD) describing the objective of the current study. BMD: bone mineral density.

The objective of this study was to examine the effects of changes in BMD on the supply of blood to the femoral head. The main hypothesis associated with this study was that a change (decrease) in BMD can decrease the supply of blood to the femoral head.

An ethical approval was obtained from the Ethical Committee of Shiraz University of Medical Sciences. This study was based on simulation and computed tomography (CT) scan was obtained from our data bases; therefore, no consent form was obtained.

A male aged 11 years, with a body weight of 360 N and body height of 1.54 m was recruited for inclusion in this study. The subject had Perthes disease on his right side. Scoring of the severity of LCPD was based on the Stolberg classification, based on the latest follow-up X-ray. The severity of Perthes disease was classified as grade III (aspherical congruency, loss of head shape greater than 2 mm)¹⁴⁾. According to the Catterall classification, the patient had Perthes disease on the right side with a severity of II (anterior involvement less than 50%)¹⁴⁾. Fig. 2 shows the anteroposterior view of both the unaffected and Perthes-affected sides. CT scan images of the Perthes patient, taken from both the healthy and Perthes-affected sides, were used in this study. The images were selected from the available CT scan image databases of Shiraz University of Medical Sciences. Three-dimensional (3D) models of the pelvis and hip joints were created from these CT scan images using Mimics software (Materialize Interactive Medical Image Control system, ver. 19) for research, produced by Materialize Company in Belgium. The images were exported to this software as Dicom files, and the femur, pelvis, and articular cartilage were modeled separately in this software.

Figure 2. Hip joint on the perthes (A) and sound side (B).

In the next step, the 3D models of the components were exported to 3Mat software, also produced by Materialize Company for smoothing and remeshing. Modeling of the femoral vessels, including the foveolar and retinacular arteries, was performed to match their anatomical structure. Free CAD software was then used to convert the components from standard triangle language to part format¹³⁾. Fig. 3 shows the model used in this study, showcasing the final model consisting of the pelvis, hip, articular cartilage, and blood vessels.

Figure 3. Model of a hip joint with Perthes disease.

The mechanical properties of bone and cartilage were determined based on available data from the literature, Table 1^10,13,15), and outputs for the Mimics software. The volume mesh produced was imported from 3Mat to Mimics to assign the materials. This software defines a number of sampling points within each element and interpolates the gray level relating to their coordinates from the original CT¹⁰⁾. The gray level is proportional to apparent bone density. Calculation of Young’s modulus (E) was performed automatically by the Mimics software based on equations developed by Karimi and Nodoshan¹⁰⁾ and Morgan et al.¹⁶⁾, where E represents Young’s modulus and ρ represents apparent bone density.

Table 1 . The Mechanical Properties of Hip Joint Parts Used in This Study^10,13,15).

Parameter	Young’s modulus of elasticity (MPa)		Poisson’s ratio
	Normal	Perthe	Normal	Perthes
Femur	11,880	4,470	0.3	0.3
Acetabulum	11,880	4,470	0.3	0.3
Cartilage	2	2	0.49	0.49
Blood vessel	0.11	0.11	0.495	0.495
Labrum	5	5	0.45	0.45

E=6850ρ^1.49

In particular, assessment of BMD, based on the approach described above, was performed for all parts of the acetabulum and head of the femur, based on CT scan images. Abaqus software was used to determine the stress and strain of bones and blood vessels while walking. The 3D models of pelvis, femur, cartilage, and blood vessels were aligned with each other in Abaqus software. The supportive ligaments of the hip joint including the iliofemoral, pubofemoral, and ischiofemoral ligaments, were modeled as spring elements.

The force of the muscles of the hip joint during walking was applied to the model. The forces of the gluteus medius (anterior, middle, and posterior parts), sartorius, gluteus maximus (anterior, middle, and posterior parts), iliacus, and rectus femoris were also applied to the model. These forces were obtained from data on Perthes patients at level walking from previous studies published by the authors⁶⁾.

It is important to note that the main blood vessels of the femoral head, including retinacular arteries (superior, anterior, posterior, and inferior) and the foveolar artery, were modeled in this study. The force of the muscles of the hip joint was applied to the model along the line connecting the origin and insertion of the muscles. The pelvic bone was selected as a boundary condition in this study.

The BMD of the femur was applied to both normal and pathological models. The average value of BMD of the femur on both the normal and Perthes sides was determined from studies previously published by the author and in the literature¹⁰⁾. Analysis of parameters including stress developed in the femoral head and blood vessels, the strain of blood vessels, and changes in the diameter of blood vessels under four different conditions was performed:

(1) Condition 1: Normal femoral head (with normal BMD) and articular cartilage with a thickness of 1.5 mm

(2) Condition 2: Normal femoral head (with normal BMD) and articular cartilage with a thickness of 3.3 mm

(3) Condition 3: Pathological femoral head (with Perthes BMD) and articular cartilage with a thickness of 1.5 mm

(4) Condition 4: Pathological femoral head (with Perthes BMD) and articular cartilage with a thickness of 3.3 mm

It should be noted that the selection of conditions was based on pathology (normal and Perthes) as well as the thickness of articular cartilage. Selection of conditions was based on information obtained from literature⁷⁾, which indicated that increased thickness of articular cartilage can occur in patients with Perthes disease. The effects of the disease under conditions 1 and 2 were examined, while the effects of articular cartilage thickness on the supply of blood to the femoral head under conditions 3 and 4 was examined.

In a study by Rush et al.⁷⁾, the thickness of cartilage in the femoral and acetabular regions of patients with Perthes disease was determined using magnetic resonance imaging. The study included 20 subjects with Perthes disease. According to the results of their study, the average increase in cartilage thickness compared to normal ranged from 1.8 to 3.9 mm, depending on the specific location within the joint⁷⁾.

Parameters including the stress applied to hip joint structures on both the normal and Perthes-affected sides, as well as the deformation of these structures, were used in the final analysis. Because this is a case study, no statistical analysis was performed for the final assessment.

The stresses that developed in the femoral head, acetabulum, articular cartilage, foveolar, and retinacular arteries are shown in Table 2. As shown in the table, stress in the femoral head increased under condition 2 compared to condition 1. Stress in the articular cartilage also increased under condition 2 compared to condition 1. Under condition 3 (Perthes with normal thickness of articular cartilage), the stress in all components, particularly the femur, showed a significant increase compared to normal conditions (conditions 1 and 2). Stress in the foveolar and retinacular arteries ranged between 2.9-4.41 MPa and 1.47-2.94 MPa, respectively. These values represent the force divided by area developed in the arteries in MPa. An increase in the level of stress that developed on the articular surfaces represents greater deformation of bone and greater collapse of the articular arteries.

Table 2 . Stress Developed in Various Parts of the Hip Joint and Foveolar and Retinacular Arteries (MPa).

Condition	Femoral head	Labrum	Cartilage	Foveolar artery	Retinacular artery
1	0.00-1.45	0.00-1.45	5.80-7.30	0.00-1.45	0.00-1.45
2	0.00-3.80	0.00-3.80	26.00-30.00	0.00-3.80	0.00-3.80
3	1.90-2.10	1.74-3.48	0.00-1.74	2.90-4.41	1.47-2.94
4	0.00-1.40	0.00-1.40	7.00-8.40	0.00-1.40	0.00-1.40

The deformations of the femoral head, acetabulum, and articular cartilage are shown in Table 3. As shown in the table, the deformation of the femoral head was greater under conditions 2 and 3 compared to the other conditions. Conversely, less deformation of the acetabulum was observed compared with the other components of the hip joint and remained relatively consistent across conditions.

Table 3 . The Maximum Deformation (mm) of Femoral Head, Acetabulum, and Cartilage under Conditions 1-4.

Condition	Femoral head	Acetabulum	Cartilage
1	0.64-0.97	0.00-0.32	2.26-2.59
2	3.17-3.60	0.00-0.45	3.17-3.60
3	2.20-2.54	0.00-0.31	2.20-2.54
4	0.16-0.17	0.00-0.01	0.10-0.11

The maximum deformation of blood vessels is shown in Table 4. As shown in the table, deformations of foveolar and retinacular arteries showed a significant increase under condition 2 compared to condition 1. On the Perthes side with normal thickness of articular cartilage, deformation of both foveolar and retinacular arteries was greater than under condition 1.

Table 4 . The Maximum Deformation (mm) of Blood Vessels in Conditions 1-4.

Condition	Foveolar artery			Retinacular artery
	End 1	Middle	End 2	End 1	Middle	End 2
1	0.21-0.368	0.21-0.368	0.21-0.368	0.12-0.138	0.034-0.052	0.19-0.21
2	3.17-3.6	1.36-1.8	3.17-3.6	4.9-5.44	4.9-5.44	3.4-4.5
3	0.95-1.2	0-0.317	0.95-1.27	0-0.317	0-0.317	0-0.317
4	0-0.0005	0-0.0005	8.5×10–4 to 1.28×10–3	1.7×10–3 to 2.14×10–3	0-0.0005	0.0047-0.005

Although its introduction dates back more than 100 years, knowledge regarding ,the cause of Perthes disease as well as the most suitable treatment approaches is limited²⁾. Despite various theories regarding the cause of this disease, the treatment outcomes based on these theories have not been successful. It appears that this disease and the deformation of the femoral head may be caused by obstruction of blood vessels due to changes in BMD. Therefore, the objective of this study was to examine the effect of changes in BMD and thickness of articular cartilage (seen mainly in Perthes disease) on blood vessels of the femoral bone under this condition.

The results of this study showed that a decrease in BMD of the femoral bone not only increased the stress that developed in the hip joint components but also increased the deformation (comparison of conditions 1 and 3). In particular a high degree of deformation was observed in the blood vessels of the femoral head under condition 3 (Perthes with normal thickness of articular cartilage). It was interesting to observe that an increase in the thickness of the articular cartilage under the normal BMD condition not only increased the stress applied on joint components but also increased the deformation. However, under the Perthes condition, an increase in thickness of articular cartilage caused a decrease in stress and deformations of the blood vessels (Table 3, 4).

The results of this study demonstrated that a decrease in BMD in Perthes patients can increase the stress applied on the hip joint structures and also deformation of the components. More specifically, in Perthes patients, deformation of blood vessels is greater than under the normal condition, as shown in Table 4, meaning that in this group of subjects, blood vessel obstruction occurs under weight-bearing conditions. However, this occurs during the initial stage of this disease. The stress and final deformations of the articular cartilage structures shows an eventual decline due to an increase in thickness of articular cartilage. This may be a mechanism used by the body for protecting the femoral head.

In the results of this study, an interesting finding was that an increase in thickness of articular cartilage with normal BMD caused an increase in both the stress and deformation of articular structures. If the increase in thickness of articular cartilage occurred before any change in BMD, this may be a factor influencing the supply of blood to the femoral head. This means that an increase in thickness of articular cartilage in patients with Perthes led to a decrease in the blood supply which finally influences BMD and dead of the bone.

Evidence in the literature supports changes in thickness of articular cartilage in patients with Perthes disease^6,7). In a study by Joseph⁶⁾, osteoporosis of the acetabular roof, irregularities of the counter, premature fusion of triradiate cartilage, and hypertrophy of articular cartilage, all associated with changes in dimensions were observed in 155 Indian children with Perthes disease. However, these changes were mainly observed in older subjects. Another study by Rush et al.⁷⁾ also reported an increase in thickness of articular cartilage ranging from 1.8 to 3.9 mm in patients with Perthes disease.

Based on these studies and the findings of the current study, it can be concluded that a noticeable increase in thickness of articular cartilage was observed in Perthes patients compared to normal subjects. This increase may serve as a mechanism for protecting the femoral head from further damage. The results of a study by Pinheiro et al.¹⁷⁾ also support this theory, suggesting that vascular obstruction to the epiphysis may occur when there is delayed ossification and when articular cartilage shows reduced stiffness under compression.

There are some limitations associated with this study. The main limitation is that it is a case study, thus the findings should be interpreted with caution. Another limitation is that while the change in thickness of articular cartilage was examined, changes in the mechanical properties of the cartilage were not considered. It appears that changes in the mechanical properties of the cartilage may also affect the stress applied to the hip joint structure. Therefore, conduct of a future study including a larger number of subjects using the same methodology is recommended.

Based on the findings of this study, changes in BMD of the femoral head can affect the stress and deformation of the femoral head. Greater deformation occurs in the blood vessels of the femoral head in this group of patients compared to normal subjects. While an increase in articular cartilage in normal subjects can increase stress and deformation of the articular structures, it decreases stress and deformation in Perthes patients (possibly as a protective mechanism used by the body to reduce stress in patients with Perthes). It is important to note that this study was based on a single case simulation and therefore, a definitive conclusion cannot be made. Conduct of a study using the same approach but including a larger number of subjects is recommended.

No funding to declare.

No potential conflict of interest relevant to this article was reported.