Biomechanical stability of five fixation techniques for pediatric distal radius metaphyseal-diaphyseal junction fractures: a finite element analysis

Abstract

Pediatric distal radius metaphyseal-diaphyseal junction (DRMDJ) fractures represent a distinct and inherently unstable fracture pattern that frequently necessitates surgical intervention. The variability in current clinical management strategies, and there remains a paucity of biomechanical evidence to guide optimal fixation selection. A computed tomography (CT) image of the forearm were acquired from a 10-year-old male volunteer, and digital imaging and communications in medicine (DICOM) data were extracted for three-dimensional model reconstruction. A virtual fracture was simulated at the DRMDJ using computer-aided modeling technique. Five distinct fixation constructs were evaluated: locking plate, three crossed kirschner wires (K-wires), antegrade elastic stable intramedullary nailing (ESIN-A), retrograde elastic stable intramedullary nailing (ESIN-R), and external fixation. Finite element analysis (FEA) was performed to assess and compare the biomechanical performance of these fixation constructs under seven wrist loading conditions: flexion, extension, pronation, supination, ulnar deviation, radial deviation, and axial loading. Quantitative assessments were conducted using key biomechanical parameters, including peak displacement at the fracture site, peak Von Mises stress at the fracture site and peak Von Mises stress at the fixation constructs. The comparison was based on the locking plate as the reference. Regarding the peak overall displacement at fracture sites, the crossed K-wires demonstrated good stability across all loading conditions. Both ESIN-A and ESIN-R showed favorable performance only under radial deviation and axial loading, with significant displacement increase under rotational loads. The external fixation outperformed the locking plate in pronation loading condition, while remaining comparable to locking plate in other loading conditions, maintaining overall stability. Regarding peak Von Mises stress at the fracture site, the crossed K-wires demonstrated good performance under axial loading, pronation, and radial deviation conditions, while showing poor results under other conditions. Both ESIN-A and ESIN-R exhibited poor stability across all test conditions. The external fixation performed well under pronation, supination, ulnar deviation, axial loading, and radial deviation conditions, but showed inadequate performance during flexion and extension maneuvers. Regarding peak Von Mises stress at the fixation constructs, the crossed K-wires demonstrated good stress peak performance under pronation conditions but showed poor results under other postural conditions. Both ESIN-A and ESIN-R exhibited consistently poor stress peak performance across all test conditions. The external fixation demonstrated optimal stress peak performance under extension, pronation, supination, and axial loading conditions, outperforming steel plates in pronation and supination conditions while showing inferior performance in flexion, ulnar deviation, and radial deviation conditions. In the FEA model of pediatric DRMDJ fracture, the external fixation and locking plate constructs demonstrated comparable, relatively lower fracture-site displacement under the idealized loading conditions applied. The crossed K-wire construct—modeled in an optimal configuration that may be technically challenging to achieve clinically—showed intermediate biomechanical indices. ESIN-A and ESIN-R constructs exhibited greater displacement, which is consistent with the intentionally low structural stiffness inherent to elastic fixation and does not necessarily indicate clinical instability. These computational findings alone do not directly dictate clinical decision-making; while the results suggest that, from a purely structural perspective, constructs with lower inherent stiffness might theoretically require additional external support, such extrapolation remains speculative. Importantly, FEA cannot capture critical clinical factors, including pin-site infection, soft-tissue irritation, patient tolerance, and the dynamic elastic stabilization afforded by ESIN. Therefore, the present results should be regarded as comparative and hypothesis-generating, and their clinical translation requires validation through well-designed, multicenter prospective clinical studies.

Introduction

Forearm fractures are among the most common injuries in children, and the majority can be managed conservatively with closed reduction and cast immobilization. However, pediatric fractures occurring at the distal radius metaphyseal-diaphyseal junction (DRMDJ) represent a distinct and inherently unstable subtype, frequently requiring surgical intervention¹. The optimal fixation strategy for these fractures remains a subject of clinical debate. Open reduction and internal fixation with plate constructs can achieve anatomical reduction and stable fixation^2–4, enabling early wrist functional rehabilitation in pediatric patients. Open plating nonetheless requires a substantial volar incision, and the resulting prominent scar may raise aesthetic and psychological concerns in children. Furthermore, the need for a second surgery to remove the implant often diminishes acceptance among patients and their families. Percutaneous K-wire fixation is one of the commonly used surgical approaches for pediatric metaphyseal fractures, and reports have indicated satisfactory outcomes when applied to DRMDJ fractures^5–8. Elastic stable intramedullary nailing (ESIN) based on the “three-point fixation” principle, has become a widely used technique in pediatric orthopaedic practice. ESIN offers substantial advantages in the management of midshaft long bone fractures in children, and its indications continue to expand. The literature describes two ESIN protocols for pediatric DRMDJ fractures: the antegrade technique (ESIN-A)^9–11 and the retrograde technique (ESIN-R)^12–14. More recently, closed reduction combined with external fixation has yielded favorable clinical outcomes in the treatment of pediatric DRMDJ fractures^15,16. External fixation enables closed reduction through ligamentotaxis, with minimal soft-tissue trauma and stable fixation, allowing early rehabilitation and a prompt return to daily activities without the need for secondary implant removal, thereby satisfying minimally invasive and aesthetic requirements.

To date, the literature lacks biomechanical comparative analyses among these fixation modalities specifically for pediatric DRMDJ fractures. Finite element analysis (FEA) employs computer-based digital modeling to discretize physical structures into elements with defined material properties. By applying specific boundary and loading conditions, FEA generates stress and displacement contours, yielding quantitative biomechanical data^17–20. Owing to its high experimental reproducibility, FEA has been extensively applied in orthopaedic research. The aim of this study was to employ FEA to evaluate and compare the biomechanical behavior of five fixation constructs—locking plate, three crossed K-wires, ESIN-A, ESIN-R, and external fixation—in a pediatric DRMDJ fracture model under seven physiological loading directions: wrist flexion, extension, pronation, supination, ulnar deviation, radial deviation, and axial loading.

Patients and methods

Establishment of a pediatric DRMDJ fracture and fixation assembly model

This study recruited a healthy child volunteer (male, 10 years old, 132 cm height, 32 kg weight) with no prior history of congenital upper limb deformities or other traumatic injuries. Informed consent was obtained from the child’s guardian and the study was approved by the ethics committee of Ningbo No.6 hospital (Approval NO.2023-13K). According to the definition of DRMDJ by Lieber et al¹, the model requires fracture ends to be positioned within this region for subsequent internal fixation assembly and adaptation. The volunteers’ forearms were scanned using a Philips 64-slice spiral CT scanner to acquire DICOM-format raw data. The DICOM data were then processed using Mimics 21 (Materialise Company, Belgium) for extraction and parallel optimization of the ulna and radius. The optimized data was imported into Geomagic 2021 (Geomagic Company, USA) for surface processing and model feature optimization, followed by importation into SolidWorks 2023 (Dassault Systemes, France) for assembly. All fixation materials were commercially available products from Double Medical Technology Inc. (Xiamen, China). The constructs included: the locking plate combined with locking screws of 3.0 mm diameter, both ESIN-A and ESIN-R had a diameter of 2.5 mm, the crossed K-wires with a diameter of 1.8 mm(The configuration is two wires from distal to proximal and one wire from proximal to distal), the external fixation was assembled using four fixation wires (2.3 mm diameter), three carbon fiber connecting rods (3 mm diameter), and 6 connectors. A total of five fixation models were generated for subsequent FEA (Fig. 1).

Fig. 1.

Fracture model and model adaptation for various internal fixation constructs, where blue rings represent fracture lines. 1a locking plate fixation, 1b crossed K-wire fixation, 1c ESIN-A fixation, 1d ESIN-R fixation, and 1e external fixation.

Finite element analysis (FEA)

Creating a static analysis module in Ansys Workbench, assign material properties, and perform meshing using tetrahedral elements^21,22 (specific values see Table 1). Based on prior studies^22,23, standardize loading conditions as follows: 1. Torque: Apply 1 N·m torque to simulate six rotational motion conditions of the wrist joint: flexion, extension, pronation, supination, ulnar deviation, and radial deviation, 2. Axial loading: apply 100 N axial pressure to the distal radius. Finally, the mechanical data of different fixing schemes under seven operating conditions were obtained through FEA.

Table 1.

Material properties and element types for the finite element models.

Materia	Element type	Young’s modulus (MPa)	Poison’s ratio	Number of element	Number of nodes
Cortical bone	C4H10	16000	0.3	63936	124643
Cancellous bone	C4H10	150	0.3	50253	87574
K-wires	C4H10	200000	0.33	130980	245891
Plate-screws	C4H10	110000	0.33	138040	255558
ESIN-A	C4H10	110000	0.33	132900	246607
ESIN-R	C4H10	110000	0.33	133980	248622
External fixation	C4H10	200000	0.33	132871	250246

Assumptions in the finite element analysis process

To facilitate variable control and analysis, the following assumptions were established. Assumption 1: The pediatric DRMDJ fracture was modeled as a transverse fracture with anatomical reduction achieved prior to internal fixation assembly. Assumption 2: All fixation devices were assumed to secure the fracture ends in ideal positions. Bone tissue and all implant materials were assumed to be linearly elastic and isotropic. All implant–bone interfaces (screw–bone, K-wire–bone, and external fixation pin–bone) were idealized as fully bonded (tied contact), representing a state of complete osseointegration or rigid mechanical interlock, with no frictional or sliding behavior incorporated. Assumption 3: The proximal radius was maintained in a fully constrained fixation state, while control points were established at the distal fracture segment for load application. Assumption 4: Identical loading magnitudes were applied across all motion planes; muscle forces, the interosseous membrane, and ligamentous stabilizers were omitted, representing a substantial simplification of the physiological loading environment.

Data processing and statistical methods

This study used the locking plate fixation as the reference benchmark to calculate relative differences and conduct quantitative comparisons among the three indicators—displacement at the fracture site, Von Mises stress at the fracture site and Von Mises stress at the fixation constructs — under various operational conditions for the remaining four fixation constructs. A standardized formula was employed to calculate the relative difference percentage: Relative Difference Percentage (%) = [(Value of the comparison construct -Value of the locking plate fixation) ÷ Value of the locking plate fixation] × 100%. We explicitly define displacement at the fracture site as the primary endpoint, because it directly reflects the overall structural stability of the fixation construct. Von Mises stress at the fracture site and Von Mises stress at the fixation constructs are designated as secondary exploratory endpoints that provide complementary information.

Result

Variation of peak displacement at the fracture site under various operating conditions

Compared with the locking plate, the relative difference in overall displacement for the crossed K-wire construct ranged from 8.68% to 90.03% across the seven loading conditions. The smallest differences were observed under flexion, extension, ulnar deviation, radial deviation, and axial loading, whereas the largest differences were recorded under pronation and supination. For ESIN-A, the relative difference ranged from 21.77% to 2466.53%, with comparatively low values under radial deviation and axial loading, and substantially larger differences under the remaining conditions. ESIN-R exhibited a relative difference ranging from 40.17% to 1337.99%; the difference was relatively small under axial loading and moderate under radial deviation, while markedly larger differences were noted under all other loading directions. The external fixation construct showed a relative difference ranging from -17.85% to 62.35%. Notably, displacement was lower than that of the locking plate under pronation; differences were modest under flexion, and small relative differences were maintained under the remaining loading conditions. (Table 2, Fig. 2).

Table 2.

Peak displacement at the fracture site (mm).

	Locking plate	Crossed K-wires	ESIN-A	ESIN-R	External fixation
Flexion	2.8732	3.83	6.5018	11.181	4.6645
Extension	0.81356	1.0834	1.9217	1.8608	1.0131
Pronation	2.0267	3.8513	45.772	16.605	1.6649
Supination	1.7512	2.8556	44.945	25.182	1.7883
ulnar deviation	1.5827	2.0984	4.1655	6.6245	1.6968
radial deviation	1.7799	1.9426	2.5637	2.8978	1.9575
Axial loading	1.0878	1.1822	1.3246	1.5248	1.158

Fig. 2.

Cloud map of displacement changes at the fracture site under various operating conditions. From left to right are locking plate, crossed K-wires, ESIN-A, ESIN-R, and external fixation, from top to bottom are motion scenarios of the wrist joint: flexion, extension, pronation, supination, ulnar deviation, and radial deviation,and Axial loading.

Variation of peak Von Mises stress at the fracture site under various operating conditions

Relative to the locking plate, the peak fracture-site von Mises stress for the crossed K-wire construct differed by 32.40% to 391.93% across loading conditions. The smallest relative difference occurred under axial loading, followed by moderate differences under pronation and radial deviation, whereas larger differences were observed under the remaining conditions. ESIN-A showed relative differences ranging from 117.65% to 826.63%, and ESIN-R from 184.43% to 1111.09%; both constructs exhibited considerably higher fracture-site stress values than the locking plate under all loading conditions tested. For external fixation, the relative difference ranged from 15.85% to 254.77%, with the smallest differences under pronation, supination, ulnar deviation, and axial loading, a moderate difference under radial deviation, and larger differences under flexion and extension. (Table 3, Fig. 3).

Table 3.

Peak Von Mises stress at the fracture site (MPa).

	Locking plate	Crossed K-wires	ESIN-A	ESIN-R	External fixation
Flexion	30.766	71.199	180.6	220.88	109.15
Extension	6.9101	33.993	64.031	58.181	21.604
Pronation	29.557	47.531	84.613	130.81	34.242
Supination	21.223	61.177	144.54	257.03	25.154
ulnar deviation	34.339	69.962	208.17	258.78	45.962
radial deviation	21.38	32.547	76.702	90.03	35.212
Axial loading	17.125	22.674	37.273	48.709	21.957

Fig. 3.

Stress variation cloud map of fracture site under various operating conditions. From left to right are locking plate, crossed K-wires, ESIN-A, ESIN-R, and external fixation, from top to bottom are motion scenarios of the wrist joint: flexion, extension, pronation, supination, ulnar deviation, and radial deviation,and Axial loading.

Variation of peak Von Mises stress at fixation constructs under various operating conditions

Compared with the locking plate, the relative difference in peak implant stress for crossed K-wires ranged from 72.30% to 2517.38%; the lowest relative difference was observed under pronation, whereas substantially higher values were obtained under all other loading directions. ESIN-A and ESIN-R demonstrated relative differences ranging from 345.64% to 1675.56% and from 235.35% to 1675.73%, respectively, with both constructs yielding notably higher implant stress values under every loading condition tested. For external fixation, the relative difference ranged from −26.15% to 304.53%; implant stress was lower than that of the locking plate under extension, pronation, and supination, moderately higher under axial loading, and higher under flexion, ulnar deviation, and radial deviation. (Table 4, Fig. 4).

Table 4.

Peak von mises stress at fixation constructs (MPa).

	Locking plate	Crossed K-wires	ESIN-A	ESIN-R	External fixation
Flexion	86.274	746.23	707.91	1532	349
Extension	61.566	704.23	490.99	206.46	79.563
Pronation	415.74	716.33	1852.7	2801	307.01
Supination	376.75	801.89	1862.4	2309.2	352.98
ulnar deviation	83.301	726.34	537.58	1051.7	191.02
radial deviation	35.606	720.83	492.69	229.18	118.95
Axial loading	27.361	716.14	485.81	116.33	47.668

Fig. 4.

Stress variation cloud map of fixation constructs under various operating conditions. From left to right are locking plate, crossed K-wires, ESIN-A, ESIN-R, and external fixation, from top to bottom are motion scenarios of the wrist joint: flexion, extension, pronation, supination, ulnar deviation, and radial deviation,and Axial loading.

Discussion

The DRMDJ constitutes a distinct anatomical segment of the distal radius. Studies^24–26 indicate that DRMDJ fractures exhibit higher rates of complete displacement and greater angular reduction loss compared to metaphyseal or diaphyseal fractures, along with inferior stability. Consequently, surgical intervention is recommended for pediatric DRMDJ fractures presenting with complete displacement resulting in “back-to-back” deformity and challenging manual reduction, particularly in adolescent patients with limited bone remodeling capacity. Beyond the inherent difficulties in managing these injuries, there exists no unified consensus regarding the optimal fixation method, and substantial variability in clinical practice persists. Carsten Krohn et al.¹⁴ reported that properly positioned K-wires represent an effective and minimally invasive technique, although precise K-wire placement can be technically challenging. Those authors utilized retrograde precision-molded ESIN-R for fixation and considered this approach a truly minimally invasive and sufficiently stable alternative. However, they emphasized that if adequate fracture reduction cannot be achieved, plate fixation—which is not minimally invasive—should be considered. Another clinical study including 113 patients compared the therapeutic efficacy of ESIN-A, K-wires and ESIN-R⁹. The results demonstrated that ESIN-R offers advantages such as shorter operative time, reduced intraoperative blood loss, lower radiation dose, higher alignment accuracy, and lower complication rates. The authors stressed that precise dual pre-bending of the nail is essential for optimal fixation outcomes. Li et al.¹⁵ reported that in the treatment of adolescent DRMDJ fractures, external fixation frames are associated with shorter operative time, less tendon irritation, and superior imaging outcomes compared with K-wires. The authors candidly acknowledged as a limitation that other fixation techniques, including ESIN and plate fixation, were not included in their comparison. Our research team previously conducted a retrospective study on the use of external fixation frames for pediatric DRMDJ fractures, which yielded satisfactory clinical outcomes ¹⁶. However, this finding may be subject to confirmation bias, independent validation by other centers is encouraged. Overall, the current literature describes five primary fixation constructs in common clinical use: locking plate, percutaneous crossed K-wires, ESIN-A, ESIN-R, and external fixation^4–16.

In the present FEA model, the locking plate construct was employed as a rigid internal fixator benchmark for comparative purposes, However, it should be noted that in simple pediatric fracture patterns, compression plating that permits controlled micromotion is typically preferred to promote direct bone healing, and the use of locking plates is not routine. A critical question remains: how does the biomechanical behavior of alternative fixation strategies—specifically crossed K-wires, ESIN, and external fixation—compare to that of a maximally rigid plating construct under idealized loading conditions? The rapid advancement of finite element analysis (FEA) in orthopedics has established it as a widely utilized comparative biomechanical research tool, although its inherent simplifications must be acknowledged^8–12,20,21. A key feature of the present study is the construction of a standardized pediatric DRMDJ fracture model, onto which the five fixation techniques were applied, enabling systematic comparison. The primary biomechanical endpoint was defined as peak displacement at the fracture site, reflecting overall construct stability. Von Mises stress at the fracture site and Von Mises stress at the fixation constructs served as secondary exploratory endpoints.

The crossed K-wires construct—modeled in an optimal configuration that may be technically difficult to achieve in clinical practice—demonstrated favorable fracture displacement control and acceptable stress distribution under most loading conditions. However, implant stress was relatively concentrated, particularly under rotational loading, where the computed von Mises stress approached magnitudes that may warrant caution. Because yield strength and fatigue limits were not explicitly incorporated, these stress values cannot be directly translated into a failure probability. Nonetheless, the pattern suggests that, from a purely structural standpoint, activities generating forearm rotation might expose the crossed K-wires construct to elevated implant loads, combined with the acknowledged technical challenges of achieving the idealized wire trajectories in the DRMDJ region, while the findings do not dictate clinical protocols.

Regarding the ESIN-A and ESIN-R constructs, the greater displacements and higher implant stresses observed under rotational loading must be interpreted within the biomechanical concept of ESIN. It is important to emphasize that the locking plate was selected as a rigid reference construct for comparative purposes, the analysis inherently quantifies structural stiffness and does not assess the biological suitability of different fixation stiffness levels. Unlike rigid fixation, ESIN is designed to provide elastic stability, allowing controlled deformation with subsequent recoil that dynamically re-centers the fracture fragments. Therefore, the larger displacement values obtained in this linear static FEA reflect the intentionally low structural stiffness of the construct and do not equate to clinical instability. The “three-point support” principle could not be fully reproduced in a simplified computational model lacking periosteum, muscular forces, and the interosseous membrane, which contribute to load sharing in vivo. Consequently, the stress patterns observed in ESIN models should be regarded as indicative of the loading experienced by the implant under the specific boundary conditions tested, but cannot be used to infer a high risk of fixation failure or to mandate supplementary plaster immobilization. Indeed, multiple clinical studies^9–14 have reported satisfactory outcomes with ESIN for pediatric distal forearm fractures. The present FEA findings, therefore, emphasize the limitations of a static linear analysis in capturing the dynamic function of elastic fixation, rather than demonstrating poor mechanical performance of ESIN.

The external fixation construct exhibited displacement control comparable to that of the locking plate, with relatively uniform implant stress distribution and lower peak fracture-surface stresses under several loading conditions. These biomechanical observations suggest that, in this idealized model, external fixation may provide a mechanically protective environment. However, it is essential to recognize that FEA cannot evaluate pin-site infection, soft-tissue irritation, patient tolerance, or the postoperative care burden, all of which are particularly relevant in the pediatric population. Thus, while the external fixation appears biomechanically promising in this comparative analysis, its clinical utility must be weighed against these well-documented drawbacks.

Several limitations of this study should be carefully considered: (1) To control variables, the fracture model assumed a simplified transverse gap and did not account for irregular fracture morphologies, the periosteum, ligaments, or muscle forces, which contribute substantially to in vivo stability. (2) A single CT-derived geometry from a healthy 10-year-old male was used; thus, inter-individual variability in bone size, cortical thickness, and skeletal maturity is not represented, limiting generalizability. (3) Identical load magnitudes were applied across all movement directions based on published estimates, whereas actual wrist loading is direction-dependent and influenced by body weight and dynamic muscle activity. (4) The materials were modeled as isotropic, homogeneous, and linearly elastic, which does not capture the anisotropic and viscoelastic nature of pediatric bone, nor the behavior of the physis. Implant–bone interfaces were assumed fully bonded, representing an idealized condition. For the interpretation of the implant stress differences reported in Table 4, it should be noted that the yield strengths and fatigue limits of the constituent materials were not explicitly incorporated into the model. Consequently, the observed stress values should be regarded strictly as comparative indicators and do not permit inferences regarding the risk of mechanical failure. (5) A mesh convergence analysis was performed, but nonlinear, fatigue, or failure analyses were not conducted, and the absence of experimental validation against cadaveric or synthetic bone models means the model should be regarded as exploratory and comparative rather than predictive. These simplifications necessitate cautious interpretation, and future studies incorporating subject-specific models, more physiological loading, and experimental validation are warranted.

In conclusion, under the idealized conditions of this FEA model, the external fixation and locking plate constructs exhibited comparable, relatively low fracture-site displacement. The crossed K-wired construct showed good biomechanical indices, but achieving the ideal configuration of two distal and one proximal wires remains clinically challenging. both the ESIN-A and ESIN-R constructs demonstrated larger displacements, which is consistent with the elastic fixation concept and does not imply clinical failure. These computational findings are hypothesis-generating and do not directly dictate clinical recommendations. Corroboration through experimental biomechanical testing and well-designed, multicenter prospective clinical studies is required to establish the clinical relevance and reliability of these observations.

Author contributions

HYZ and JC collected the data. MYW and HYZ wrote the first draft of the manuscript. SNL and CG contributed to data interpretation, HYZ and JC edited the manuscript, and approved the final version. All authors read and approved the final manuscript.

Funding

Funded by Ningbo Clinical Research Center for Orthopedics, Sports Medicine & Rehabilitation (2024L004)

Data availability

The data presented in this study are available in article All data supporting the findings of this study are available within the paper.

Declarations

Competing interests

The authors declare no competing interests.

Ethics approval and consent to participate

This work was conducted in accordance with the Declaration of Helsinki (2000) of the World Medical Association. Written informed consent was obtained from the participating minor’ legal guardians prior to their inclusion in the study. Ethical approval for this research protocol was granted by the ethics committee of Ningbo No.6 hospital (Approval NO.2023-13K).