Inclusion of Muscle Forces Affects Finite Element Prediction of Compression Screw Pullout but Not Fatigue Failure in a Custom Pelvic Implant

Abstract

Custom implants used for pelvic reconstruction in pelvic sarcoma surgery face a high complication rate due to mechanical failures of fixation screws. Consequently, patient-specific finite element (FE) models have been employed to analyze custom pelvic implant durability. However, muscle forces have often been omitted from FE studies of the post-operative pelvis with a custom implant, despite the lack of evidence that this omission has minimal impact on predicted bone, implant, and fixation screw stress distributions. This study investigated the influence of muscle forces on FE predictions of fixation screw pullout and fatigue failure in a custom pelvic implant. Specifically, FE analyses were conducted using a patient-specific FE model loaded with seven sets of personalized muscle and hip joint contact force loading conditions estimated using a personalized neuromusculoskeletal (NMS) model. Predictions of fixation screw pullout and fatigue failure—quantified by simulated screw axial forces and von Mises stresses, respectively—were compared between analyses with and without personalized muscle forces. The study found that muscle forces had a considerable influence on predicted screw pullout but not fatigue failure. However, it remains unclear whether including or excluding muscle forces would yield more conservative predictions of screw failures. Furthermore, while the effect of muscle forces on predicted screw failures was location-dependent for cortical screws, no clear location dependency was observed for cancellous screws. These findings support the combined use of patient-specific FE and NMS models, including loading from muscle forces, when predicting screw pullout but not fatigue failure in custom pelvic implants.

1. Introduction

The surgical treatment of pelvic sarcoma, a malignant tumor in the pelvic region, typically involves partial pelvic resection, which has a high complication rate. When the lower limb can be preserved following tumor resection, the procedure is known as an internal hemipelvectomy. Following partial resection, the pelvis is left with a significant bony defect. Custom pelvic implants are an increasingly popular option for reconstruction of this defect. These implants are typically designed to recapitulate the patient’s original pelvic anatomy (as determined from medical imaging data) and are manufactured using 3D-printing technology. Compared to patients who do not receive custom implant reconstruction, those who receive reconstruction often achieve a relatively normal post-operative gait pattern without a limb length discrepancy [1,2]. However, custom implant reconstruction carries an increased risk of complications, such as infections [1,2,3] and mechanical failure of the fixation screws [2,4,5,6,7,8,9,10]. More specifically, screw pullout and fatigue failures, evidenced by screw loosening or breakage, may necessitate a revision surgery [9]. Currently, screw placement largely relies on the operating surgeon’s discretion, with the structural integrity and biomechanical behavior of the post-operative pelvic construct rarely being studied. Objective engineering assessments of screw placement could potentially reduce screw failures and improve the durability of custom pelvic implants.

Patient-specific finite element (FE) models have been employed to analyze the durability of custom pelvic implants within the post-operative pelvic construct [6,10,11,12,13,14,15,16,17,18,19,20,21]. In these studies, each patient-specific FE model is created by performing a virtual surgery on a patient-specific geometric model of the pre-operative pelvis. This virtual surgery involves “resecting” the pre-operative pelvis bone geometry according to the surgical plan and then “installing” the custom implant geometry, using simplified geometric models of the fixation screws. The resulting post-operative pelvic construct consists of geometric models of the post-operative pelvic bone, the metallic custom implant, and the metallic fixation screws. The construct is then converted into an FE model by meshing the geometry, adding material properties, and applying boundary and loading conditions.

While previous studies have made significant progress in constructing realistic post-operative pelvis + implant FE models capable of identifying potential screw failures, they have omitted realistic muscle forces from the loading conditions [6,10,11,12,13,14,15,16,17,18,19,20,21]. Most studies have assumed that the impact of post-operative muscle forces is negligible, arguing that numerous muscles are often disrupted or removed to achieve clear margins around the tumor during internal hemipelvectomy [13,21]. In a healthy hemipelvis, 21 different muscles are involved in mobilizing the hip joint, and several studies have demonstrated the importance of including muscle forces in FE analyses of the healthy pelvis [22,23]. However, to the authors’ knowledge, no study has investigated the effect of muscle forces on the predicted durability of the fixation screws used to secure a custom pelvic implant to the remaining pelvic bone, even though the assumption of negligible muscle influence has not been evaluated.

The challenges involved in estimating post-operative muscle forces likely explain their exclusion from FE analyses of the post-operative pelvis. Although muscle forces have been estimated in the pelvic region for healthy subjects [22], such estimates have yet to be reported for pelvic sarcoma patients following reconstruction with a custom implant. Ideally, post-operative muscle forces could be reliably estimated based on pre-operative gait data, and two recent studies using data from the same pelvic sarcoma patient modeled in this study have made strides in this direction. Using experimental walking data collected prior to surgery, Li et al. developed a novel synergy-based computational method for estimating trunk muscle activations, where the lower extremity muscle activations were obtained from a personalized electromyography (EMG)-driven neuromusculoskeletal (NMS) model of the patient [24]. Although pre-operative muscle forces were also estimated, they were not reported. By applying similar internal hemipelvectomy surgical decisions and a similar custom pelvic implant design to a personalized neuromusculoskeletal model of a healthy subject, Vega et al. predicted whether post-operative walking function would be improved by retention and strengthening of the psoas muscle [25]. Although post-operative muscle forces were estimated to generate the predictive simulations of post-operative walking, they were not explicitly reported. With additional developments, related modeling methods could potentially be used to estimate post-operative muscle forces for application to a post-operative pelvis + implant FE model.

This study investigates the effect of muscle forces on predicted fixation screw durability for a custom pelvic implant implemented clinically in an actual pelvic sarcoma patient. Fixation screw durability was predicted using a patient-specific FE model of the post-operative pelvis + implant + screws, to which patient-specific estimates of post-operative muscle and hip joint contact forces were applied. Two screw failure modes were investigated: (1) pullout failure, based on simulated screw axial forces, and (2) fatigue failure, based on simulated screw von Mises stresses. The goal was to assess whether predictions of screw pullout and fatigue failure are altered by the addition of muscle forces to the FE analyses. The results provide valuable information that could potentially improve FE modeling processes used to predict fixation screw durability in custom pelvic implants.

2. Materials and Methods

2.1. Data Acquisition and Processing

Pre- and post-operative computed tomography (CT) scan, surgical plan, and custom pelvic implant geometry data were collected from a 46-year-old male subject (height: 1.73 m, weight: 85 kg). Post-operative walking, squatting, and stair climbing data were also collected. The subject was diagnosed with a pelvic sarcoma in the acetabular region of the right hemipelvis. Subsequently, the subject underwent an Enneking Type-II resection followed by endoprosthetic reconstruction using a commercial custom pelvic implant (Onkos Surgical, Parsippany, NJ, USA) with total hip replacement. Pelvic tumor resection and pelvic reconstruction were performed during a single surgical session at MD Anderson Cancer Center in Houston, TX. Institutional review board approvals were obtained from MD Anderson Cancer Center, the University of Texas Health Science Center, and Rice University for collection and retrospective analysis of medical and motion data. The subject provided written informed consent for all collected data.

Once the multi-planar pelvic bone resection was devised to remove the tumor with clear margins, the subject’s custom pelvic implant was designed to mimic the anatomical shape of his contralesional hemipelvis. The implant was made of 3D-printed biomedical-grade titanium alloy Ti-6Al-4V (Ti64) and secured to remaining bone through nine commercially available Ti64 compression screws (inner diameter: 3.0 mm, outer diameter: 6.5 mm, pitch: 2.75 mm, length: 15 to 80 mm; MicroPort Orthopedics, Arlington, TN, USA). The operating surgeon planned the location and trajectory of the screws and the orthopedic implant company incorporated corresponding screw holes into the subject’s custom pelvic implant design. Three cancellous bone screws were inserted through the implant’s acetabular cup—two into the ilium and one into the superior pubic ramus, while six bi-cortical screws were inserted through two extracortical flanges into the ilium—four through the anterior flange and two through the posterior flange (Figure 1a).

Post-operative walking data were collected from the subject eleven months after surgery following plateau in recovery. The experimental protocol, including the placement of static and dynamic retroreflective markers and surface and fine-wire electromyography (EMG) sensors, was as described in Li et al. [24]. The subject completed a static standing trial, a split-belt treadmill gait trial at a self-selected speed, squatting down and up trials, and stair ascent and descent trials during a single test session. Experimental data collected during all trials included video motion capture (Qualisys AB, Göteborg, Sweden), ground reaction (Bertec Corporation, Columbus, OH, USA), and wireless EMG (Cometa, Barberino Tavarnelle, Italy).

2.2. Personalized Neuromusculoskeletal Model

A personalized full-body NMS model possessing lower extremity and abdominal muscles was developed in OpenSim [26,27] to estimate muscle and hip joint contact forces for each dynamic task. A pre-operative OpenSim model of the same patient previously developed by Li et al. [24] was used as a starting point. The parameter values of the model’s Hill-type muscle-tendon units (MTUs) (i.e., peak isometric strength, optimal muscle fiber length, tendon slack length) were personalized using an EMG-driven modeling method [24,28] applied to pre-operative walking data collected from the patient. Muscles with broad origins were represented using multiple lines of action and were modeled as multiple MTUs.

This initial NMS model was modified to estimate the patient’s post-operative muscle and hip joint contact forces during the dynamic motion trials. The pre-operative pelvis was replaced by the post-operative pelvis, which consisted of the remaining pelvis plus the custom implant. The hip center was adjusted slightly to match the hip center of the implant. The surgically removed muscles were also removed in the post-operative model. A total of 18 MTUs spanning the hip and abdomen were left in the post-operative model representing the muscles that were preserved during surgery. A list of the retained muscles can be found in Zhu et al. [10], which presented post-operative hip joint contact forces over the gait cycle calculated using the same NMS model. For muscles retained in the post-operative model, MTU attachment sites and parameter values were taken from the pre-operative model.

A sequence of four analyses were performed primarily in OpenSim 4.0 to estimate muscle and hip joint contact forces for each dynamic activity. First, the OpenSim Inverse Kinematics Tool was used to convert post-operative experimental marker motions into post-operative model joint motions. Second, the OpenSim Inverse Dynamics Tool was used to convert post-operative joint motions and experimental ground reaction data into post-operative net joint moments produced by lower body and abdominal muscles. Third, a custom Matlab 2021b (MathWorks, Natick, MA, USA) function was used to estimate leg and abdominal muscle forces via static optimization by minimizing the sum of squares of muscle activations for each time frame. Fourth, the OpenSim Analysis Tool was used to perform a Joint Reaction Analysis that estimated the hip joint contact forces produced by estimated hip muscle forces.

Seven critical external load cases were defined for subsequent FE analyses based on peak values of predicted hip joint contact forces during the dynamic motion trials (Figure 2). These critical load cases were labeled as GAIT 1, GAIT 2, SQDW, SQUP, STUP 1, STUP 2, and STDN, respectively. GAIT 1 and GAIT 2 corresponded to the first and third peaks of the hip joint contact force during a gait cycle, coinciding with the beginning and end of single-leg support. SQDW and SQUP corresponded to the peaks of hip joint contact force during the standing to squat down and squat down to standing motions, respectively. In this study, the squatting motion was associated with the motion to sit down and stand back up. STUP 1 and STUP 2 referred to the two peaks of hip joint contact forces that occur when walking up stairs, coinciding with the beginning and end of single-leg support. Lastly, STDN referred to the peak hip joint contact force that occurs when walking down stairs, coinciding with the beginning of single-leg support. It is worth noting that motion data during the second half of the stair-down motion was incomplete, and hence muscle and hip joint contact forces during the second half of the stair-down motion were unavailable. The muscle forces corresponding to these seven external load cases were identified and saved as well.

2.3. Patient-Specific Finite Element Model

An FE model of the post-operative ipsilesional hemipelvis assembly was constructed in Abaqus (Dassault Systèmes, Waltham, MA, USA, https://www.3ds.com/products/simulia/abaqus) to predict post-operative bone, implant, and screw stresses as previously described in Zhu et al. [10] (Figure 3). The foundation of the FE model was the patient-specific geometric model of the post-operative pelvis construct, which consisted of 16 parts: the implant, nine screws, the cortical and trabecular portions of remaining iliac and ischial bones, a sphere representing the femoral head of the subject’s hip joint replacement, and an intermediate liner between the acetabular cup and the femoral head (Figure 1b). After meshing of the geometry, the model consisted of 668,465 10-node quadratic tetrahedral elements (C3D10; average element size: 1.73 mm) with approximately 2.9 million degrees of freedom.

The material properties of the patient’s cortical bone, trabecular bone, custom implant, and fixation screws were defined in the post-operative FE model as described in Zhu et al. [10]. In brief, cortical bone, the metallic custom implant, and the metallic fixation screws were assigned homogeneous material properties based on values reported in the literature [29,30,31]. In contrast, trabecular bone was assigned heterogeneous material properties derived from the patient’s pre-operative CT scan data. The image intensity of each pixel within the trabecular bone regions was extracted, calibrated [32,33], and converted to Young’s modulus value using published empirical relationships [34]. The voxel-specific Young’s modulus values were then mapped to each node associated with trabecular bone in the FE model. A comprehensive summary of the material properties for all FE model components may be found in Zhu et al. [10].

Physiological boundary conditions were applied to the post-operative FE model to account for the interactions between the hemipelvis and its surrounding anatomical structures. The model was constrained by three sets of springs representing the joints and ligaments that remained connected to the operated hemipelvis. Two sets of linear springs were defined at the sacroiliac and pubic joint surfaces to simulate the stiffness of the ligaments and cartilage at these joints. The total spring stiffness in the normal direction was 103.09 kN/mm at the sacroiliac joint and 4.24 kN/mm at the pubic joint [14,23,35,36,37], while the spring stiffness in the tangential direction was set to 10% of that in the normal direction. A third set of linear springs was defined at the medial margin of the ischial tuberosity to represent the sacrotuberous ligament. These springs were restricted to compressing only in the direction of the ligament with a total spring stiffness of 1.5 kN/mm [14,23,36].

Two types of modeling methods were used to describe the interactions between different FE model components. The first type of modeling method was a unilateral contact that was assumed to be “hard” in the normal direction and frictionless in the tangential direction. The contact model was implemented between the implant and resected bone, allowing them to come into contact with or separate from each other. The second type of modeling method was a tied constraint, where the constrained surfaces were bonded together without separation. The tied constraint was implemented between the femoral head and liner of the total hip replacement and between the liner and the custom implant acetabular cup.

Each compression screw included in the post-operative pelvis construct was modeled using Abaqus’ built-in “bolt load with constant length” screw modeling method (Figure 4a), which was recently shown to match the results of physics-based screw modeling methods closely [10]. Tied constraints were used between each screw and its surrounding bone, and a contact model was defined between each screw head and its corresponding screw hole in the implant. A pretension step was used to generate a desired pretension force ($F_P$) applied directly to the core of each screw via a Bolt Load in Abaqus. This force was applied within the free zone of each screw along the axial direction before any external loads were applied (Figure 4b). The magnitude of the desired pretension force to be induced within the free zone of each screw was calculated following the methods described in Zhu et al. [10] and ranged from 149.7 N to 717.5 N. For comparison, the magnitude of the calculated pullout failure threshold ranged from 221.4 N to 1060.9 N. Following the pretension step, a simulation step was performed during which external loads were applied to the FE model and the stress distribution within each screw and its surrounding structures was calculated.

During the FE analyses, each of the seven external load cases was simulated with and without corresponding muscle forces. The seven selected peaks of the post-operative hip joint contact force were applied as a concentrated force at the center of the representative femoral head. When included, the associated muscle forces were applied as surface tractions to selected node sets on the surface of the remaining bone mesh, representing the attachment areas of the 18 retained MTUs (Figure 1c). The muscle attachment node sets were selected by referencing a human anatomy atlas available through Complete Anatomy software (3D4Medical, Dublin, Ireland, https://3d4medical.com/). All simulations were performed on a 16-processor 3.70-GHz Windows workstation.

The results of the FE analyses were post-processed to evaluate the likelihood of two screw failure modes—pullout failure and high-cycle fatigue failure. The predicted axial force and peak von Mises stress for each of the nine screws were computed for the seven external load cases with and without the muscle forces. The computed pullout failure threshold was compared to the predicted axial force experienced by each screw to determine the likelihood of screw pullout failure. Similarly, the estimated endurance limit of a Ti64 screw was compared to the predicted peak von Mises stress experienced by the screw core to determine the likelihood of high-cycle fatigue failure. The von Mises stress distribution within the first 1 mm of the screw core was neglected to avoid stress concentrations. The endurance limit of the screws used in this study was estimated to be 542.2 MPa [10]. Finally, for each screw, the predicted axial forces and peak von Mises stresses from the seven external load cases were converted into a weighted axial force and a weighted peak von Mises stress, where the weights were taken from estimates for the annual number of motion cycles for different activities as reported in Bergmann et al. [38] (

Table 1. Annual load cycles for each load case according to the work of Bergmann et al. [38]. Motions to squat downward and return to a standing position in the present study were associated with sitting down and standing up.

Load Case	Annual Cycles [×1000]	Normalized [%]
GAIT 1, GAIT 2	1369.3	47.2
SQDN, SQUP	20.1	0.7
STUP 1, STUP 2, STDN	41.4	1.4
Total	2903.0	100.0

). Weighted axial force and peak von Mises stress values facilitated assessment of how inclusion or exclusion of muscle forces affected the likelihood of pullout or fatigue failure for each screw.

3. Results

3.1. Estimated Post-Operative Hip Muscle and Joint Contact Forces

The personalized NMS model provided continuous estimates of hip muscle and joint contact forces for 18 MTUs derived from the 12 preserved muscle groups. Hip joint contact force magnitudes for the seven external load cases ranged from 989.4 N in GAIT 1 to 1484.1 N in STUP 1 (

Table 2. Estimated hip muscle and joint contact forces for each of the seven external load cases.

		GAIT 1			GAIT 2			SQDN			SQUP
		FX [N]	FY [N]	FZ [N]	FX [N]	FY [N]	FZ [N]	FX [N]	FY [N]	FZ [N]	FX [N]	FY [N]	FZ [N]
Hip Joint Contact Force		40.2	977.6	−146.9	257.9	1141.7	−106.5	−1129.7	561.3	−601.1	−1009.5	578.6	−636.8
Preserved Muscle	MTU
Biceps Femoris Longhead	BFFLH	0.5	−15.1	1.6	0.0	0.0	0.0	307.0	−66.3	156.9	261.3	−73.4	142.4
External Obliques	EO10	0.0	0.0	0.0	−0.1	7.4	1.5	3.8	23.9	0.4	3.5	24.6	0.1
	EO12	0.0	0.0	0.0	−11.3	25.2	0.2	−12.7	92.4	−18.0	−13.3	82.3	−16.8
Gluteus Maximus	GLMAX1	2.3	−54.4	27.3	0.1	−2.0	1.0	5.6	−134.2	67.3	1.6	−38.3	19.2
	GLMAX2	0.3	−44.9	25.9	0.0	0.0	0.0	1.7	−231.1	133.3	1.1	−150.8	86.9
Gluteus Medius	GLMED1	−45.5	−110.5	7.0	−88.6	−206.8	9.4	−0.4	−2.1	0.4	−0.3	−1.6	0.3
	GLMED2	−6.7	−82.7	30.9	−7.5	−83.2	30.6	0.2	−2.0	0.9	0.1	−1.4	0.6
	GLMED3	2.2	−60.1	40.7	1.0	−37.7	25.7	4.7	−16.0	11.2	29.4	−104.1	75.8
Internal Obliques	IO2	27.7	11.5	−17.6	0.4	0.2	−0.3	0.6	0.2	−0.4	0.7	0.3	−0.5
	IO4	0.2	0.1	0.0	18.3	11.9	4.0	85.8	49.5	4.3	73.5	45.3	2.8
	IO5	20.9	5.2	10.3	20.0	7.2	9.4	98.5	39.0	26.6	74.6	32.0	19.5
Pectineus	PECT	−0.4	−0.5	0.4	−0.4	−0.4	0.3	29.0	−33.9	122.0	17.9	−26.3	86.4
Rectus Femoris	RECFEM	0.0	−0.1	0.0	−13.5	−145.3	−16.4	375.0	−107.2	148.4	378.7	−139.5	157.5
Rectus Abdominis	RECT_ABD	0.3	0.4	0.1	0.3	0.5	0.2	0.3	0.4	0.2	0.4	0.5	0.2
Sartorius	SART	−0.1	−3.5	−0.5	−3.1	−18.1	−5.5	23.9	−12.5	4.9	32.9	−20.4	7.5
Semimembranosus	SEMIMEM	7.7	−87.4	−4.4	0.0	0.0	0.0	0.2	0.0	0.1	36.3	−11.1	13.0
Semitendinosus	SEMITEN	9.1	−95.2	−3.3	0.0	0.0	0.0	30.5	−6.9	10.8	69.3	−20.5	26.5
Tensor Fasciae Latae	TFL	−0.5	−4.6	0.7	−33.3	−179.3	10.6	0.0	0.0	0.0	0.0	0.0	0.0
		STUP 1			STUP 2			STDN
		FX [N]	FY [N]	FZ [N]	FX [N]	FY [N]	FZ [N]	FX [N]	FY [N]	FZ [N]
Hip Joint Contact Force		−381.1	1417.8	−217.5	−47.6	1307.0	−301.2	58.6	1261.2	−228.3
Preserved Muscle	MTU
Biceps Femoris Longhead	BFFLH	0.0	0.0	0.0	0.1	0.0	0.0	0.0	0.0	0.0
External Obliques	EO10	5.0	45.6	−0.2	0.1	21.3	4.3	−0.6	7.0	1.1
	EO12	−21.3	84.7	−15.2	−17.8	51.5	−2.1	−3.2	6.4	−0.5
Gluteus Maximus	GLMAX1	0.9	−20.8	10.5	0.0	−0.5	0.2	0.0	0.0	0.0
	GLMAX2	0.0	−5.0	2.9	0.0	−0.4	0.2	0.0	0.0	0.0
Gluteus Medius	GLMED1	−0.3	−1.2	0.2	−46.1	−353.2	44.0	−0.7	−2.4	0.3
	GLMED2	2.5	−43.1	21.0	0.5	−4.6	1.7	0.0	−0.6	0.3
	GLMED3	14.9	−64.3	56.0	2.8	−10.0	6.0	16.5	−88.5	71.0
Internal Obliques	IO2	10.7	5.1	−8.0	0.2	0.1	−0.1	0.3	0.2	−0.2
	IO4	97.2	69.8	0.4	35.8	20.5	9.0	1.5	1.2	0.4
	IO5	79.4	39.4	19.2	11.9	3.8	5.9	0.4	0.2	0.2
Pectineus	PECT	−0.4	−0.6	0.5	34.5	−88.4	133.0	−0.4	−0.5	0.3
Rectus Femoris	RECFEM	−1.1	−64.6	−3.0	159.0	−99.8	23.5	−2.4	−20.1	−3.7
Rectus Abdominis	RECT_ABD	0.4	0.5	0.2	0.2	0.3	0.1	66.1	97.3	38.7
Sartorius	SART	−6.8	−44.0	−8.6	0.2	−0.2	0.0	−13.5	−56.2	−19.0
Semimembranosus	SEMIMEM	0.0	0.0	0.0	206.0	−105.7	16.7	0.0	0.0	0.0
Semitendinosus	SEMITEN	0.0	0.0	0.0	133.9	−66.7	13.8	0.0	0.0	0.0
Tensor Fasciae Latae	TFL	−1.6	−63.3	6.6	0.0	−0.1	0.0	−7.3	−81.6	2.3

), with retained muscles exerting forces on the pelvis in various directions depending on the activity. Interestingly, while the estimated hip joint contact forces for the two external load cases related to squatting (i.e., SQDN and SQUP) were similar, the corresponding estimated muscle forces were notably different for many muscles in terms of both magnitude and direction. Estimated muscle forces for each dynamic trial can be found in Appendix A.

3.2. Screw Failure Analyses

Predicted screw axial forces differed substantially between loading conditions without and with muscle forces (Figure 5). Cortical screws 1–4 generally experienced higher, and Cortical screws 5–6 lower, axial forces for all load cases when muscle forces were included in the FE analyses. The one exception was Cortical screw 1 for the STUP 1 load case. Furthermore, while Cortical screws 1–4 were generally below the pullout failure limit without muscle forces, they all reached or exceeded the pullout failure limit for multiple load cases with muscle forces. The notable exception was again Cortical screw 1 for the STUP 1 load case, which dropped from above to below the pullout failure limit when muscle forces were included. In contrast, cancellous screws demonstrated no clear trends in axial forces related to the inclusion or exclusion of muscle forces in the FE analyses. Nonetheless, for all three cancellous screws, between one and three load cases produced an axial force that was at or above the pullout failure limit without muscle forces and that dropped to below the pullout failure limit with muscle forces. On average, cortical screws experienced a larger absolute percent change in axial force than did cancellous screws when muscle forces were added.

Predicted screw peak von Mises stresses also differed substantially between loading conditions without and with muscle forces (Figure 6). Cortical screws 1–4 generally experienced slightly higher, and Cortical screws 5–6 slightly lower, peak von Mises stresses for all load cases when muscle forces were included in the FE analyses. However, the corresponding absolute percent changes were much smaller than for axial forces. Similarly, cancellous screws generally demonstrated slightly lower peak von Mises stresses across load cases when muscle forces were included. The primary exception was Cancellous screw 3 for the GAIT 1 load case. However, the corresponding absolute percent changes were again small. Only for Cancellous screw 3 would inclusion of muscle forces alter the prediction of whether the peak von Mises stress would substantially exceed the screw’s endurance limit. For this screw with and without muscle forces, the peak von Mises stress occurred at approximately the same location in the screw, where the screw became embedded in the bone (Figure 7). In addition to the changes in the maximum stress magnitude, the stress distribution patterns changed slightly between simulations without and with muscle forces, implying that the inclusion of muscle forces changed the load transfer direction within the post-operative pelvis. On average, cancellous screws showed a larger absolute percent increase in peak von Mises stress compared to cortical screws when muscle forces were added.

When the FE results from different activities were weighted by annual load cycles, muscle forces were found to exert a considerable influence on predicted axial forces for most screws (Figure 8). The most vulnerable screw for pullout failure changed from Cancellous 3 without muscle forces to Cortical 3 with muscle forces. In contrast, muscle forces were found to exert a relatively small influence on predicted von Mises stresses. Both without and with muscle forces, the screw most vulnerable to fatigue failure was Cancellous 3.

4. Discussion

This study investigated the influence of muscle forces on FE predictions of fixation screw durability in a custom pelvic implant. Predicted screw axial forces and von Mises stresses were compared to failure limits with and without estimated muscle forces applied. The post-operative muscle forces estimates were obtained from a personalized NMS model of the same patient for whom the FE model of the post-operative pelvis was developed. Muscle forces were found to have a considerable influence on the predicted durability analysis of the fixation screws. They generally had a greater influence on predicted screw axial force than on predicted screw von Mises stress. This finding suggests that assessment of the likelihood of pullout failure would be more sensitive to the inclusion of muscle forces than would assessment of the likelihood of fatigue failure. However, whether exclusion or inclusion of muscle forces would yield more conservative screw failure predictions was inconclusive, as some screws were predicted to be more susceptible to failure with muscle forces while others were predicted to be less susceptible with muscle forces.

Several studies have developed FE models to assess the structural integrity of the pelvis reconstructed with a custom implant [6,10,11,12,13,14,15,16,17,18,19,20,21]; however, muscle forces were often omitted, likely due to challenges in predicting post-operative muscle forces following significant anatomical changes. Because the accuracy of an FE analysis depends heavily on the imposed boundary and loading conditions, it is crucial to evaluate how exclusion of muscle forces impacts the accuracy of the FE results.

The findings of the study suggest that inclusion of muscle forces redirects the load transfer between the hip joint and the reconstructed pelvis. The predicted axial forces and von Mises stresses of the screws inserted through the posterior flange (i.e., Cortical screws 5–6) were generally decreased by the inclusion of the muscle forces. In contrast, the predicted axial forces and von Mises stresses of the screws inserted through the anterior flange (i.e., Cortical screws 1–4) were generally increased. This second observation agrees with the findings of a previous study by Dalstra and Huiskes [22], where FE models of a healthy pelvis with muscle forces included were found to exhibit elevated stresses near the posterior part of the ilium. The influence of muscle forces on the predicted axial force and von Mises stress in the cancellous screws was less consistent. This difference may be associated with the longer length and closer proximity to the hip joint of the cancellous screws compared to the cortical screws.

While our study demonstrated that predicted screw axial forces and von Mises stresses were sensitive to the inclusion of muscle forces, the findings were limited by how post-operative muscles were modeled in the NMS and the FE models. These muscles were assumed to remain attached to bone at their original origins in both the NMS and FE models, and the estimated muscle forces were applied as surface tractions directly on the surface of the remaining bone in their respective muscle attachment areas. However, during the surgery, each of the 12 retained muscles was detached temporarily at its origin to gain access to the tumor and later reattached to a polypropylene mesh sutured to the remaining pelvic bone. The detachment and reattachment of muscles may have moved the muscle origins and also caused the muscles to pull on a flexible surface rather than on rigid bone. Furthermore, the effect of muscle detachment and subsequent reattachment on muscle strength was not considered. The retained muscles in the post-operative NMS model were defined to have similar strength, optimal muscle fiber length, and tendon slack length properties to those in the pre-operative model. However, the assumption that the retained muscles were not impacted substantially by the surgery requires more thorough investigation.

Based on normalized weighted axial force, our FE models without and with muscle forces predicted that Cancellous screw 3 would be susceptible to pullout failure, which proved to be an accurate prediction. Following the completion of this study, the authors learned that the patient experienced a pullout failure of Cancellous screw 3 and eventually underwent revision surgery to fill in the resulting osseous defect 16 months after the initial surgery. While the FE model without muscle forces ranked Cancellous screw 3 as the most susceptible to pullout failure, the FE model with muscle forces ranked Cortical screw 3 as the most susceptible, with Cortical screws 1 and 2 also being susceptible. However, to date, none of those screws has pulled out. Our FE analyses predicted potential screw pullout (and fatigue) failures at a single snapshot in time and thus could not predict a possible sequence of failures. It was also possible that cortical screw failures would be more difficult to observe in X-ray images than are cancellous screw failures. Given that eight screws were used in the ilium region, failure of any of these screws might not be visible in imaging data as the remaining screws might maintain fixation visually despite the failure.

Due to the lack of a better understanding of the post-operative status of retained muscles, we would suggest that FE analysis of screw fixation durability be performed using FE models with and without muscle forces. However, this limitation does not change the premise of our study, which was that predicted axial forces and von Mises stresses within each fixation screw may be sensitive to the inclusion of muscle forces in the FE model. Further investigation should focus on (1) estimating muscle forces using post-operative muscle-tendon model parameters in the NMS model and/or (2) exploring methods to apply muscle forces in a more realistic manner in the FE model.

Because the hip joint contact forces used in our study were also estimated using the personalized NMS model, these forces were subject to the same potential issues as discussed above for muscle forces. In addition, at least for other joints, the prediction muscle forces from net joint moments using static optimization has been shown to underestimate joint contact forces [39]. Despite these factors, our hip joint contact forces estimated post-operatively remained comparable to reported hip joint contact forces measured in vivo [40]. To our knowledge, this is the first study to use personalized hip joint contact forces for pelvis FE analyses, as prior studies typically used hip joint contact forces derived from Bergmann et al. [40]. In addition, no study has reported estimated post-operative muscle forces for a specific pelvic sarcoma patient. The primary reason is likely that previous studies have not combined a patient-specific NMS model with a patient-specific FE model for assessing the reconstructed pelvis of a pelvic sarcoma patient.

In past similar studies, due to the lack of patient-specific experimental data, estimation of various FE model parameters had to rely on previously published data. However, we collected patient-specific pre- and post-operative experimental data to build the patient-specific FE model in a manner consistent with practices reported in similar studies. For example, the heterogeneous material properties of trabecular bone were estimated using the patient’s pre-operative CT scan images along with established image processing techniques and strongly correlated empirical relations. Nonetheless, the actual material properties of the post-operative pelvic construct may differ significantly from our estimates. Due to the retrospective nature of this study and the use of a human subject, the material properties and other parameters in the patient-specific FE model could not be validated experimentally, nor could they be evaluated using a different implant design due to the patient specific nature of the implant.

We made several necessary assumptions when applying the boundary conditions to our FE model. First, three sets of linear springs were used to represent the sacroiliac joint, pubic joint, and the sacrotuberous ligaments, respectively, where the stiffness of these various sets of springs was obtained from values reported in the literature. Second, a “hard” contact model was implemented between the implant and resected bone, and a tied constraint was applied between the femoral head and liner of the total hip replacement and between the liner and the custom implant acetabular cup. Third, a screw model using Abaqus’ built-in functions was used to model the interaction between the fixation screws and implant. Indeed, these assumptions may have affected the FE results presented in this study. However, since it is currently impossible to conduct in vivo experiments on a human subject to measure bone screw stresses and strains, it is not currently possible to validate our simulation results experimentally. Nevertheless, our study demonstrated that the influence of post-operative muscle forces should not be assumed to be negligible.

In conclusion, this study evaluated the influence of muscle forces on the predicted likelihood of screw failures using a patient-specific post-operative FE model of a pelvis reconstructed with a custom implant. We found that estimated fixation screw axial forces but not von Mises stresses were sensitive to the inclusion of estimated muscle forces in the FE analyses. Though it remains unclear whether including or excluding muscle forces would yield more conservative predictions of screw failures, our findings suggest that FE analyses of screw durability in custom pelvic implants should be performed both without and with muscle forces included. By including patient-specific muscle and hip joint contact forces estimated by a patient-specific NMS model, this study marks an important step toward building a comprehensive patient-specific FE framework for evaluating the structural integrity of the reconstructed pelvis following pelvic sarcoma surgery.