Stress-specific differences in Distal Femoral Epiphysis of Leg Length Discrepancy and Pelvic Tilt. A Finite-Element Analysis

doi:10.21203/rs.3.rs-2334250/v1

Objective

This study aimed to compare the distal femoral epiphyseal stress of Leg Length Discrepancy and Pelvic Tilt, to explain the phenomenon of genu varum and genu valgum in children with unequal lower extremities or pelvic tilt.

Methods

The finite element models was established to analyze the distal femoral epiphyseal Equivalent Von Mises Stress, We reconstructed the right sacrum, pubis, ischium, and femur of a healthy child by finite element method, and generated the distal femoral epiphysis and other cartilage structures. The left femur was amputated (1, 2, 3, 4, 5, 6cm) to study the stress changes in the bilateral distal femoral epiphysis. In addition, we tilted the pelvis of four models and placed the distal femur at the same level to study the stress changes after the pelvis was tilted.

Results

The Equivalent Von Mises Stress distribution of the distal femoral epiphysis on both sides of the children with unequal lower limbs was uneven, and the stress stimulation on the lateral side was greater than that on the medial side. And when the pelvis is tilted, this stimulation is more obvious.

Conclusions

We reconstructed a healthy child's pelvis and femur by Finite-Element, including cartilage and epiphyseal structures. The left femur was amputated to simulate the Leg Length Discrepancy, the pelvis tilt was also studied. Both lead to the increased lateral stress, with pelvic tilt having a greater effect.

Epiphysis

Leg Length Discrepancy

Finite Element Analysis

Knee valgus or valgus is a common type of knee joint axis disorder in clinical. Children have great growth potential and are prone to genu varum and genu valgum during the growth period. The development of the distal femoral epiphysis makes an important contribution to the length of the lower extremity. However, when the growth of the medial and lateral epiphysis is not synchronized, the abnormality of the lower extremity axis will gradually be revealed. The main clinical manifestations of the knee joint axis disorder are genu varum and genu valgum.

The existing studies suggest that stress induces higher compressive and shear forces at the long bone-epiphyseal junction region, and that abnormal stress can affect the epiphysis(Vaca-Gonzalez et al. 2018). Studies have also demonstrated that chronic mechanical stress has a strong effect on the structure and tissue properties of bone(Carter et al. 1996). Endochondral ossification is a fundamental process in skeletal morphogenesis and chondroosseous biology, while mechanical stress is an important factor in bone development, altered joint load or movement can alter the pattern of ossification and growth at the developing bone end, while reduced joint force can delay the appearance of secondary ossification nuclei(Carter and Wong 1988). Children's immature bones are more sensitive to mechanical loads because their tissues are more elastic and remodeling processes are more active.

The Leg Length Discrepancy (LLD) will cause the body's center of gravity to shift, resulting in uneven distribution of stress. True LLD refers to the unequal length of the bones of the lower extremities on both sides, and is usually caused by abnormal development of the affected limb caused by a variety of pathological factors. Common associated conditions include developmental dislocation (dysplasia) of the hip (DDH), trauma, Perthes disease, and septic arthritis of the hip(Guo et al. 2019). The normal progression of the lower extremity from varum to valgum is well studied. The slight genu valgum of normal adult alignment is achieved by 7 years of age(Salenius and Vankka 1975). The misalignment of the knee joint axis is also manifested at this time. There are many causes of genu valgum (varum) in children. In addition to common cause of rickets, and cartilage developmental disorders, existing studies have confirmed that obesity has a clear relationship with genu valgum(Soheilipour et al. 2020)(Ciaccia et al. 2017). However, there is no research on the difference of stress distribution in the distal femoral epiphysis with LLD.

Our hypothesis was that the LLD would have an effect on the epiphysis of the distal femurs of both lower extremities, resulting in an abnormal knee joint axis. In this study, we used a finite element model to investigate the effect of unequal length and pelvic tilt on the epiphyseal stress of the distal femurs of both lower extremities. In addition, different combinations of bilateral lower extremity disparity(1, 2, 3, 4, 5, 6 cm) and pelvic tilt were evaluated.

This biomechanical study has been approved by our ethical review committee(No.202211002). A healthy child participated in this study (sex: female, age: 6 years, height: 135 cm, body weight: 35kg). Quantitative computed tomography (QCT) was scanned in combination with a calibration phantom. The resolution of each CT image was 512 by 512 pixels with a slice thickness of 1. 0 mm, and the pixel size was 0. 782 mm/pixel under 120 KV and 102. 50 mA conditions.

Model geometry and 3D Measurement

Based on the CT data, we obtained a realistic model A in QCT (Mimics 21. 0. Belgium). Since the obtained bone model was rough, we used Geomagic software for surface treatment. (Geomagic 2013. America). To simplify the model, the same morphology was maintained during later stages of development. In order to avoid differences caused by bilateral limb asymmetry, we cut the right femur, ischium, pubic and half of sacrum, and the whole 3D model B are mirrored through the midsagittal plane. That is, the left and right consistent model B was obtained by mirroring (Solidwork 2019. America). By reversely extracting the area of epiphysis that is not captured by QCT in Mimics software, the distal femoral epiphysis and part of the cartilage are modeled, the rest of cartilage generated by Solidwork software(Fig. 1). The cartilaginous areas of the femoral head and the acetabulum were artificially developed by offsetting the cortical part of the femoral head by 2 mm outward in Geomagic software, we obtained the femoral head cartilage, and the rest of the cartilage was obtained by filling the gap between the cortical bones in Solidwork. The model B included three regions: diaphysis, growth plate and cartilage .

Group C and D models are obtained by modifying the model B. Cut off the left mid-femur of model B with 1, 2, 3, 4, 5, 6 cm respectively, generated our model C1-6(Fig. 2). The pelvis of the model in group C is horizontal, and in the next operation, we tilted the pelvis, aligned the femoral head with the acetabulum, and the distal end of femur was in the same level to obtain four models (1, 2, 3, 4 cm) of D1 to D4. Because the distance between the left and right acetabular centers was 86mm after the pelvis of the D5 model was tilted, and the minimum distance between the left and right femoral heads was 107 mm, the D5 model could not be reconstructed in the D group.

In our study, the length of the femur was defined as the distance from the femoral head to the distal end of the femur. Finally, the left femur length of Model B was 295. 8 mm. The anteversion angle of the femur was 35. 8°, and the neck-shaft angle was 138. 7°. It is worth noting that the normal pelvis has some anteversion, and in our model this value is specified in terms of the angle of sacral inclination, the angle between the sacral surface and the horizontal in the sagittal plane is 39. 2°. Since the human body does not stand upright on the ground when receiving CT scans, the femur will present a certain angle with the surface of the horizontal sacrum on the coronal plane. In model B, this angle is 86. 5°. The D1 to D4 models is 83. 3°, 75. 7°, 69. 9°and 63. 0°respectively.

Loading and Sensitivity studies

All bony areas were assumed to be cortical bone throughout(Grosland and Brown 2002; Kaku et al. 2004). The material properties of cortical bone (Young's modulus 17 GPa; Poisson's ratio 0. 30) and cartilage (Young's modulus 15 MPa; Poisson's ratio 0. 45) were defined based on values derived from the literature(Fishkin et al. 2006). The model of the growth plate adopts a constant Young's modulus of 6 MPa and a Poisson's ratio of 0. 49 to account for the almost incompressible material(Beaupre et al. 2000; Tanck et al. 2004). Due to the irregular geometry, the bone and cartilage meshes are formed with linear four-noded tetrahedra. Cortical bone and cartilage are assumed to have linear elastic properties. Here a nonlinear elastic model is used, furthermore, the load applied was static and constant. All models were solved by ANASYS finite element solver (ANSYS 19. 0 America).

By dividing the irregular bones with tetrahedral elements, and refining the mesh in the local area, the mesh size in the cartilage area is set to 1 mm, and the mesh size of the growth plate area is set to 0. 5 mm. After our model has completed the 95% convergence verification of the grid, the final number of cells in Model B generated 853, 583 nodes and 4, 208, 933 elements.

In the ANSYS software, we simulated the loads in the standing condition of the human body. An axial load of 350 N parallel to the direction of the femur was applied to the upper surface of the sacrum(Fig. 3). And limit the displacement of the distal femur in three dimensions. To avoid the effect of asymmetric bones on the results, we did not model muscles and ligaments, Considering that we are simulating the conditions of static standing, a previous study analyzed the contributions of these muscles and confirmed negligible effects relative to the muscles included in the model(Ardila et al. 2013; Zwawi et al. 2017). The rest of the model C and D are obtained by similar methods. Figure 4 shows the distribution of the displacement in the model B. The highest displacement in the iliac bone was 2. 06214 mm, a value similar to those in previous studies(Lei et al. 2017), and no point of maximum stress was found. Loads are then applied and submitted for solving.

Fig 5 shows the growth plate stress distribution for Model B, where the stress is focused in the edge region of the anterior and posterior sides, the anterior side is larger than the posterior side, and there is no noticeable difference between the medial and lateral sides. Fig 6 shows the stress distribution of models C1-6 and D1-4. In panel C, the results display that the stress distribution of the left and right leg growth plates is very different, and the area of high stress on the left is always larger than the right side. Moreover, with the shortening of the length of the left femur in panel D, the area of high stress gradually increased, gradually extending from the lateral to the medial side. But the right-side stress region gradually extends to a slightly lateral region.

The stress area of central growth plate on the left side is more concentrated on panel D, which is not consistent with model C, and the stress area on the right leg is more concentrated in the medial area.

Table 1 shows the maximum stress and average stress on both sides of the 11 groups of models. In group C, with the shortening of the limb length on the affected side, the maximum and average stress on both sides did not shift significantly, while in group D, with the shortening of the limb length with the increase of the pelvic inclination angle, the maximum stress and the average stress both increased.

	Max stress on the left（MPa）	Mean stress on the left（MPa）	Max stress on the right（MPa）	Mean stress on the right（MPa）
Model B	0. 72345	0. 13272	0. 86522	0. 14284
Model C1	0. 85079	0. 11120	1. 03180	0. 12008
Model C2	0. 78941	0. 11053	0. 93375	0. 11726
Model C3	0. 78957	0. 11792	0. 85355	0. 12126
Model C4	0. 84401	0. 11251	0. 92662	0. 11723
Model C5	0. 78742	0. 11381	0. 90052	0. 11371
Model C6	0. 86407	0. 12340	0. 88867	0. 11829
Model D1	0. 67025	0. 10442	0. 68303	0. 10453
Model D2	0. 87163	0. 12868	0. 78159	0. 11949
Model D3	1. 08809	0. 14460	0. 91234	0. 12343
Model D4	1. 13895	0. 16211	0. 91826	0. 12602
Table 1. The maximum stress and average stress of models B, C, and D are shown. The value of group C does not show a linear change, but the maximum stress and average stress of group D both increase gradually.

The model obtained using computer inverse modeling is comparable to the morphological characteristics of the real bone morphology. In fact, the model roughly predicts the morphology of the growth plate, highlighting its main features, such as irregular disc-like structures, rather than simple two planes that are parallel to each other. Using computer models, the upper body weight load can be approximated, and ideal results can be approximated using a load close to the body weight.

There are many factors that cause the LLD. Zhang et al. divided the etiology into the following three types: upper pelvic, intra pelvic and lower pelvic(Zhang et al. 2015). In our models, intrapelvic and lower pelvic are considered. However, we did not study the reason for the LLD. Through computer simulation of the two cases, we found stress distributions in these two cases is different. The lateral stress of the epiphysis of the shorter femur is shifted laterally, and considering the pelvic tilt, the epiphyseal stress of the longer femur is shifted lateral. The reason for the stress on the intrapelvic is greater than the reason under the pelvic cavity, but our results rely on the results of computer simulation, and there is still a lack of the corresponding relationship between the computer simulation value and the real stress value. Our study only had a change in trend and did not account for the effect of specific value of growth plate stress.

The shape obtained by the bone is highly dependent on the location of the load. In the present study, the distal femoral epiphysis was mechanically loaded, but this behavior was an approximate simulation of the standing situation, since gait, stance, and weight bearing can all affect changes in loading as the bone grows in children. Therefore, future work will improve the model to enable it to apply mechanical loads in more poses .(Vaca-Gonzalez et al. 2018)

Treatment of lower extremity angular deformities is an active area of research, and patients with deformities are challenging due to the physically complex growth potential of the distal femur. Multiple successful techniques have been proposed to address associated deformities with varying technical complexity, patient morbidity. However, in skeletally immature patients, their growth can be adjusted to correct the deformity, such as the 8 plate. In skeletally mature patients, lower extremity angle deformities are usually managed with a femoral osteotomy. Resection combined with guided growth as an alternative to traditional corrective osteotomy in patients(Masquijo et al. 2020). Distal medial hemi-epiphyseal screw fixation and non-absorbable fibrous nails are an effective and safe method for correcting children with idiopathic genu valgum, and postoperative outcomes were not different from those of the standard 8-plate technique(Martinez et al. 2019). Considering the stress difference caused by the unequal length of the lower limbs, we suggest that the early level of pelvic realization in such children is beneficial to compensate for this asymmetric difference.

The study by Zhang et al. confirmed that unilateral DDH can lead to LLD, but did not show the relationship between LLD and the axis of the knee joint(Zhang et al. 2018). The increased valgum angle may be associated with increased medial femoral condyle height, decreased lateral femoral condyle height, and decreased lateral distal femoral angle(Li et al. 2014). The novelty of our study is that we reported the possible effect of mechanical stress on the posterior femoral distal femur on genu valgum, and we found that the epiphyseal stress on the affected side was mostly concentrated on the lateral side, which confirmed the uneven stress distribution. The medial and lateral distal femoral epiphysis will receive different stress stimulation, resulting in the disorder of the knee joint axis. Therefore, when treating children with genu varum or genu valgum, the length matching of the two femurs should be considered, or combined with pelvic tilt. Guo et al(Guo et al. 2012)reported that the severity of genu valgum deformity was strongly positively correlated with lateral displacement of the femoral head, but not with superior displacement. Li et al research show knee radiographic changes in patients with unilateral DDH were not associated with LLD(Li et al. 2014). In our research, through 3D reconstruction, the pelvis, femur, cartilage structures are completely simulated, and the measurement is performed directly on the model without measuring the image.

Guo et al (Guo et al. 2019) studied the LLD after total hip arthroplasty in adults with DDH and suggested that changes in lower extremity length may not only lead to LLD but also change the angle of the pelvis. In 1983, Friberg et al(Friberg 1983) demonstrated that LLD can cause changes in coronal and cross-sectional angles of the pelvis and spine. Zhang Z et al. (Zhang et al. 2018) found the distance from the inferior border of the sacroiliac joint to the ankle joint, which they named relative limb length (RLL), and they measured it differently from ours. They found that the length of the affected limb could be shorter or longer, but it was more likely to be longer. Similarly, it is still unclear where the critical value of mechanical stimulation to stimulate the growth of the epiphysis is. Appropriate mechanical stimulation promotes the growth of the epiphysis, while excessive stimulation may damage the epiphysis and cause growth arrest. As Wolff rules, a healthy human or animal's bones adapt to the loads they are subjected to(Julius 1893).

The information obtained from this mechanobiochemical model may be useful for exploring the impact of loading conditions on normal and abnormal joint development in future biomedical research. In addition, this model facilitates understanding of factors involved in morphogenesis during early stages of development for preventive treatment of congenital skeletal abnormalities. Nonetheless, further work is required to account for factors such as different mechanical stimuli, ossification of the epiphysis, and the different shapes that the epiphyseal plate acquires during bone development.

The disadvantage of this study is that although we obtained a growth plate structure close to the normal model, the real structure is a gradual change in the bone-epiphyseal junction area rather than a direct change in the 3D model. In addition, we did not study the effects of different postures, femoral-sacral angle, pelvic inclination, etc. on the growth plate, and our study was limited to the stress distribution under this model, which is not applicable to all the unequal lengths of the lower extremities. Also, due to the limitations of the finite element technique, we abandoned the modeling of cancellous bone in the simulation process, which would not account for the cortical division of the growth plate region. Similarly, our model simply considers the static structure, without considering the bones and muscles, and the following research needs more attention.

Acknowledgments:

Ethical Approval:

This research work was supported by the ethic committee of Honghui Hospital, Xi'an Jiaotong University.(No.202211002)

Competing interests:

The authors declare to have no competing interests.

Acknowledgements Funding:

No funding or grant support.

Authors' contributions:

Huanan Bai and Qingda Lu wrote the main manuscript text, Xiaoming Wang、Xiaoju Liang、Haoruo Jia and Huan Wang participated in the interpretation of the results, Qiang Jie designed and participated in computer operation.

Availability of data and materials :

There are no restrictions to the availability of any materials and data.

All authors agree with the publication and with the availability of data and materials.

Author Huanan Bai can be contacted ([email protected]) regarding the availability of data and materials.

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No competing interests reported.

Stress-specific differences in Distal Femoral Epiphysis of Leg Length Discrepancy and Pelvic Tilt. A Finite-Element Analysis

Status:

Version 1

Abstract

Objective

Methods

Results

Conclusions

Figures

Introduction

Materials And Methods

Model geometry and 3D Measurement

Loading and Sensitivity studies

Results

Discussion

Declarations

References

Additional Declarations

Status:

Version 1