Finite element analysis of the pelvis after modular hemipelvic endoprosthesis reconstruction

Abstract

Purpose

The aim of this study was to investigate the biomechanics of the pelvis reconstructed with a modular hemipelvic prosthesis using finite element (FE) analysis.

Methods

A three-dimensional FE model of the postoperative pelvis was developed and input into the Abaqus FEA software version 6.7.1. Mesh refinement tests were then performed and a force of 500 N was applied at the lamina terminalis of the fifth lumbar vertebra along the longitudinal axis of the normal pelvis and the postoperative pelvis for three positions: sitting, standing on two feet, and standing on the foot of the affected side. Stress distribution analysis was performed between the normal pelvis and postoperative pelvis at these three static positions.

Results

In the normal pelvis, stress distribution was concentrated on the superior area of the acetabulum, arcuate line, sacroiliac joint, sacral midline and, in particular, the superior area of the greater sciatic notch. In the affected postoperative hemipelvis, stress distribution was concentrated on the proximal area of the pubic plate, the top of the acetabular cup, the connection between the CS-fixator and acetabular cup and the fixation between the prosthesis and sacroiliac joint.

Conclusions

Stress distribution of the postoperative pelvis was similar to the normal pelvis at three different static positions. Reconstruction with a modular hemipelvic prosthesis yielded good biomechanical characteristics.

Introduction

In recent decades, limb salvage surgery has become more common than hemipelvectomy in the treatment of primary pelvic sarcomas. However, hemipelvic reconstruction after sarcoma resection is critical and many methods for the approach exist, such as massive allograft [1–4], autoclaved autograft [5, 6], custom-made endoprosthesis combined with hip arthroplasty [7–9], modular saddle prosthesis [9–12], and modular hemipelvic endoprosthesis [13, 14]. The modular hemipelvic prosthesis is a new design that can be easily used in surgery and features flexible sizes. We performed this surgery with satisfactory functional outcomes, as previously reported [14].

Finite element (FE) analysis, which can accommodate large inter-subject variations in bone geometry and material properties, has been widely used to analyse pelvic biomechanics [15–19]. An empirically validated FE model can provide information on the static and dynamic responses of joint structures under a variety of loading and boundary conditions that would be difficult or impossible to obtain experimentally [20–22].

The objective of this study was to analyse the biomechanical characteristics of a modular hemipelvic endoprosthesis using FE analysis at different static positions.

Materials and methods

Between 2004 and 2008, twelve patients underwent periacetabular resections and reconstruction with a modular hemipelvic prosthetic system in West China Hospital, Sichuan University. Postoperatively, five patients were able to walk without support, three patients required braces to walk, and four patients were able to walk using a crutch. We chose one patient (male, 63 years old, 176 cm in height, 57 kg in weight) who had a similar hip joint rotation centre reconstruction on the uninjured side and could walk without any support postoperatively. This patient underwent an Enneking Type I/II/III pelvic resection, with resection of part of the gluteus maximus, gluteus medius and tensor fasciae latae. The pelvis was reconstructed using a modular hemipelvic endoprosthesis, and the muscles were reconstructed by suturing the remaining gluteus maximus, gluteus medius and tensor fasciae latae to the iliopsoas. The following steps were carried out, as outlined below.

Three-dimensional reconstruction model of pelvis

A three-dimensional reconstruction model of the pelvis was developed from the chosen patient, 17 months after surgery (Fig. 1). The patient had a long axis body CT scan (Philips Brilliance 64CT, Philips Healthcare, The Netherlands; slice thickness = 0.7 mm, 947slices) while both lower extremities were kept in a neutral position. Because of the titanium prosthesis, the three-dimensional reconstruction model was accompanied by artifacts. We eliminated image artifacts through the difference of the gray value between the prosthesis and artifacts in the CT image. The data were then input into Mimics software (version 8.1, Materialise, Leuven, Belgium) and the three-dimensional reconstruction model of the postoperative pelvis was acquired. Because the patient’s normal pelvis could not be reconstructed directly, we obtained the normal pelvis through copying the uninjured side onto the affected side (Fig. 2).

Fig. 1.

a MRI scan shows the tumour before surgery. b Radiographic image of the pelvis 12 months after surgery. A CS-fixator; B acetabular cup; C pubic plate

Fig. 2.

The three-dimensional reconstruction model of the pelvis before surgery (a) and after surgery (b)

Finite element (FE) model of pelvis

The model of three-dimensional reconstruction was input into the Abaqus software (version 6.7.1, Dassault Systemes, Vélizy-Villacoublay, France) and mesh refinement tests were performed. The final FE model consisted of 622,833 tetrahedral elements for the reconstructed pelvis, 728,432 tetrahedral elements for the normal pelvis and 106,103 shell elements for the prosthesis. We applied a force of 500 N to the lamina terminalis of the fifth lumbar vertebra along the longitudinal axis of the normal pelvis and the postoperative pelvis for three positions: sitting, standing on two feet, and standing on the foot of the affected side. The strength of the periacetabular muscles was not considered because it was greatly affected by the widespread resection and could not be calculated accurately.

All implant components were made of continuous isotropy elastomeric materials. Material property values of the implant components were provided by Chunli Zhengda Co. (Beijing, China) (Fig. 3). The CS-fixator and the connection between the CS-fixator and acetabular cup were made of TC4 titanium. The pubis plate was made of TA2 titanium. Values of cortical bone are reported in Table 1 [15, 20, 22–25].

Fig. 3.

a Acetabular cup. b CS-fixator. c Assembly of the acetabular cup and CS-fixator. d Pubic plate

Table 1.

Values of cortical bone and modular hemipelvic endoprosthesis components

Material	Elasticity (GPa)	Poisson’s ratio	Fatigue resistance (MPa)
Cortical bone	17	0.3	Acetabulum 120
TA2 Titanium	105	0.33	Tensile strength (σb) 500, Yield strength (σ0.2) 405
TC4 Titanium	115	0.33	Tensile strength (σb) 965, Yield strength (σ0.2) 905

Results

Three-dimensional reconstruction model of the normal pelvis

Stress distribution was concentrated on the superior area of the acetabulum, arcuate line, sacroiliac joint, sacral midline and, in particular, the superior area of the greater sciatic notch (Table 2; Fig. 4).

Table 2.

Maximum stress in different places of the normal pelvis (MPa)

Location	Two-legged stance	Single-legged stance	Sitting
Superior sacral midline	0.8	1.2	1.0
Sacroiliac joint	0.9	2.5	1.1
Superior area of greater sciatic notch	1.7	4.0	1.6

Fig. 4.

Stress distribution of the normal pelvis during two-legged stance position (a), single-legged stance position (b), and sitting (c)

The three-dimensional reconstruction model of postoperative pelvis

Stress distribution of the affected hemipelvis was concentrated on the proximal area of the pubic plate, the top of the acetabular cup, the connection between the CS-fixator and acetabular cup and the fixation between the prosthesis and sacroiliac joint (Table 3; Fig. 5).

Table 3.

Maximum stress in different places of postoperative pelvis (MPa)

Location	Two-legged stance	One-legged stance on affected leg	Sitting
Connection between CS-fixator and acetabular cup	4.3	12.8	5.0
Fixation between prosthesis and sacroiliac joint	2.8	3.0	3.2
Superior region of the arcuate line	0.5	1.3	0.8
Sacroiliac joint of the uninjured side	1.5	1.1	1.4
Superior area of greater sciatic notch of the uninjured side	1.6	0.8	1.7

Fig. 5.

Stress distribution of the postoperative pelvis during two-legged stance position (a), one-legged stance position on the affected leg (b) and sitting (c)

Discussion

There are many methods to reconstruct the hemipelvis after sarcoma resection, but each method has its own limitations, such as high complication rate or poor functional outcome [26]. The modular hemipelvic endoprosthesis has been applied recently with good results [13, 14]. It is difficult to assess the stress and strain distributions throughout the entire pelvis using simplified mathematical models, implanted prostheses, or via experiments with cadaveric tissue [20]. However, FE analysis, which can accommodate large inter-subject variations in bone geometry and material properties, provides an attractive approach to analysing pelvic mechanics.

The present study has inherent limitations. First, the FE model was based on the anatomy of a single patient. Second, the role of muscles or ligaments was not examined because of difficulty assessing the soft tissue changes after excision and reconstruction of the pelvis. Of course, anatomical variations of the pelvis and the extent of the excision may affect the results. We hope to address these limitations in a future study.

When comparing the contralateral side of the postoperative pelvis with the normal pelvis, we found that the stress distribution profiles were similar. Stresses were mostly concentrated along the inside and top of the acetabular cup, similar to the distribution of stresses along the acetabular contact surface of the normal pelvis. This implies the affected side of the postoperative pelvis had little change in stress distribution and approached the physiological condition.

We compared the stress distributions of the affected side of the postoperative pelvis with the contralateral side and the normal pelvis at different positions: standing on two feet, standing on the foot of the affected side, and sitting. While standing on two feet and standing on the affected foot, stress concentration of the normal pelvis was on the superior area of the acetabulum, arcuate line, the greater sciatic notch, sacroiliac joint and the sacral midline. The maximum stress appeared on the inside and top of the acetabulum and the superior area of the greater sciatic notch. Stress concentration of the postoperative pelvis was on the proximal end of the pubic plate, the top of the acetabular cup, the connection between the CS-fixator and acetabular cup and the fixation between the prosthesis and sacroiliac joint. The maximum stress appeared on the top of the acetabular cup and the connection between the CS-fixator and acetabular cup. During sitting, stress concentration of the normal pelvis was on the ischial tuberosity, superior area of the greater sciatic notch, sacroiliac joint and the sacral midline. The maximum stress appeared on the ischial tuberosity. Stress concentration of the postoperative pelvis was on the proximal end of the pubic plate, the top of the acetabular cup, the connection between CS-fixator and acetabular cup and the fixation between the prosthesis and sacroiliac joint. The maximum stress appeared on the sacroiliac joint. All of the above demonstrates that stress distribution on the affected side of the postoperative pelvis was similar to the contralateral side and the normal pelvis. Although the distribution of stresses on the affected side of the postoperative pelvis varied at different positions, the magnitude of stresses was obviously greater than for the contralateral side and the normal pelvis, which may be because of the smaller volume of the modular hemipelvic endoprosthesis.

For all three static positions, the modular hemipelvic endoprosthesis was safe and fatigue was unlikely to occur because the maximum stress was much lower than the implant’s tensile strength and yield strength. However, the stresses incurred during static positions are not the biggest stresses borne by the pelvis [27]. Stress borne by the pelvis is only 81 % of body weight when standing on one foot. However, stress on the pelvis increases to four to seven times body weight when walking steadily, and even ten times body weight when running and jumping [28, 29]. In order to analyse the biomechanics of the modular hemipelvic endoprosthesis more accurately, stresses on the pelvis while walking steadily should be investigated. That is the next study to be addressed.

The proximal end of the pubic plate endured a high stress distribution in all three positions, especially while standing on the affected foot and during sitting (Fig. 6). However, the pubic plate (TA2 titanium) only had a tensile strength of 500 MPa and a yield strength of 405 MPa, much lower than that of TC4 titanium (965 MPa tensile strength, 905 MPa yield strength). That may be a reason for the breakage of the proximal pubic plate reported in two cases by Guo et al. [13]. The pubic fixation may require some improvements.

Fig. 6.

The stress distribution of the implant components during two-legged stance (a), one-legged stance on the affected leg (b), and sitting (c). The red arrows indicate the proximal pubic plate bears high stresses

We conclude that the FE model well analysed the stress distribution of the pelvis reconstructed with modular hemipelvic endoprosthesis in three static positions. The concentration of stress in the pelvis reconstructed with the modular hemipelvic endoprosthesis resembles that of the normal pelvis during static positions.