1 Introduction

The human foot can be divided into three parts: forefoot, midfoot, and hind foot. More specifically, the forefoot is composed of metatarsal bones and the proximal, middle, and distal toes; the midfoot is composed of three wedges, a navicular bone, and a cuboid bone; the hind foot is composed of the heel, talus, tibia, and the lower end of the fibula. Hallux valgus refers to a forefoot deformity in which the hallux deviates outwards beyond the normal physiological range at the first metatarsophalangeal joint. It is a complex and the most frequently-seen forefoot deformity involving multiple pathological changes, commonly known as the “big foot bone”.¹ Hallux valgus can be diagnosed by measuring the hallux valgus angle (HVA >20°) and/or the intermetatarsal angle (IMA >9°) on a foot radiograph.² It may also present extensive changes in soft tissue arch, sesamoid mechanism, and metatarsal wedge joint, and can cause pain and decreased mobility.^3,4 A hallux valgus deformity is usually formed by misaligned first metatarsal bone, hallux, and sesamoid bone. The degree of deformity can be determined by the values of HVA and IMA, and can be classified as mild, moderate, or severe.^5–7 With a general incidence ranged 23–35 %, hallux valgus can cause symptoms on the inner edge, sole, and little toe of the foot.⁸At present, the treatment of hallux valgus can be classified as surgical methods and conservative methods. Conservative treatment with orthotics usually has poor efficacy, and only surgery has the chance of complete cure.⁷ To date, over 100 surgical procedures for hallux valgus have been reported, among which Scarf osteotomy is one of the most commonly-used surgical procedures in clinical practice. It can effectively correct the deformity of patients with moderate to severe hallux valgus and restore their foot function. According to extensive experimental studies, Scarf osteotomy has shown a higher safety, faster postoperative healing, and a lower probability of non-healing compared to other surgical procedures, allowing patients to move down earlier and suffer less pain.^9–12 Moreover, considering that the presence of deformities in the coronal, horizontal, and sagittal planes of hallux valgus, Scarf osteotomy is the only surgery offering three-dimensional (3D) correction, and can therefore effectively correct moderate to severe hallux valgus deformities.^8,13

With the development of computer science and technology, digital orthopedics has emerged as a novel discipline, which promotes the use of Finite Element Analysis (FEA) in simulating real-world human physical systems (geometric and loading conditions). As a 3D, intuitive, and convenient digital approach, computer-aided simulation of Scarf osteotomy has provided new ideas and directions for non-invasive and visualized research of complex orthopedic surgeries including hallux valgus surgery. For the treatment of hallux valgus, osteotomy is the foundation, while the balance of soft tissue strength is the key to success. Therefore, comprehensive preoperative evaluation, surgical planning and simulation, and finite element analysis play a crucial role in optimizing surgical outcomes.^14,15 Due to low cost and high efficiency, finite element modeling for hallux valgus can help prevent the occurrence of postoperative complications and enable researchers to accurately understand the detailed morphology and mechanical changes of various structures involved.^16–18 Thus, this technique is able to serve clinical needs in a simple and efficient manner.

In this context, we aimed to construct a finite element model of hallux valgus in this study to simulate Scarf osteotomy by only changing the displacement of the distal end of the bone fragment while retaining other conditions unchanged. Based on comprehensive analysis of the relevant performance indicators, we hoped to provide reference for the surgical treatment of hallux valgus in clinical practice.

2 Research subject and methods

2.2

2.2 Methods

2.2.1

2.2.1 Finite element model

The patient's affected foot was scanned by a CT machine, and the captured data was imported into Mimics 21.0 software (Materialise, Belgium). After threshold segmentation, bone extraction, and skin extraction, a preliminary 3D model was constructed. The STL file generated by Mimics was further imported into the Geomagic Studio 2014 software (Geomagic, U.S.) for removing nail-shaped objects and excess features, surface smoothening, and accurate surface treatment. Subsequently, the surface of the entire model was shrunk inward by 1.5–3 mm to simulate the characteristics of cancellous bone. The obtained solid model file was imported into the Solidworks software (Dassault Systems, U.S.) for assembly of various bone blocks and simulation of joint cartilage. The hallux valgus model consists of 28 bone segments, including the tibia, fibula, talus, calcaneus, cuboid, navicular bone, 3 wedge-shaped bones, 5 metatarsal bones, and 14 phalanges. Then, a model of the foot standing on the ground was created, which was further assembled with the skin and ground to simulate the state of the affected foot standing still on the ground (see Fig. 1). Finally, the 3D model of hallux valgus was imported into the ANSYS software (ANSYS, U.S.) for finite element analysis.

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Fig. 1 Construction of the geometric model and finite element model of hallux valgus. (a) Preliminary 3D model of the foot; (b) Solidification of the 3D model; (c) Accurate surface (taking the first metatarsal bone as an example); (d) Cancellous bone; (e) Bone assembly; (f) Simulation of cartilage; (g) Simulation of the foot standing still on the ground.

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In order to better simulate the surface morphology of the bone structure to avoid stress concentration, the mesh shape was defined as a tetrahedral mesh with a mesh size of 3 mm. Moreover, the characterization of biomaterials is a key factor in finite element analysis. According to the relevant literature,^12,18–20 the materials used in this study were characterized by two parameters, elastic modulus (E) and Poisson's ratio (μ) (see Table 1).

Table 1 Biomaterial parameters.

Component	Elastic modulus (MPa)	Poisson's ratio (V)	Cross-sectional area (mm2)
Cortical bone	7300	0.3
Cancellous bone	300	0.3
Screw	11000	0.3
Cartilage	10	0.4
Skin soft tissue	1.15	0.49
Ground	17000	0.4

During finite element analysis, only the neutral state under the balanced standing condition was considered for static analysis. Specifically, the skin, tibia, fibula, and the upper surface of the talus were fixed. Then, a reaction force of half of the patient's weight (295N) was applied vertically upwards on the ground, and a force of half of the ground reaction force (147.5N) was applied vertically upwards at the Achilles tendon (see Fig. 2).

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Fig. 2 Boundary condition settings.

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To verify the validity of the model, the patient was asked to stand on the center area of the FreeStep plantar pressure testing system (Sensor Medical, Italy) in a stable and balanced state for static plantar pressure test, and the data was recorded after the system was stabilized. The measurement was repeated three times to take the average value for analysis. The results of static plantar pressure test were then compared with the results of finite element simulation.

2.2.2

2.2.2 Simulation of Scarf osteotomy

According to the relevant literature,^16,21,22 the Scarf osteotomy was simulated by dividing the whole structure into five equal parts. The osteotomy angle was set to 60°. The distances of the distal and proximal ends of the bone fragment were set to be equal. The center of the bone fragment was located at the center of the metatarsal bone. In Solidworks, a Z-shaped bone fragment of the first metatarsal bone was created and its distal end was pushed outwards by 2 mm, 4 mm, 6 mm, and 8 mm, respectively (other conditions retaining unchanged). Fig. 3 shows the Scarf osteotomy model when the distal end of the fragment was pushed outwards by 2 mm.

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Fig. 3 The Scarf osteotomy model when the distal end of the bone fragment was pushed outwards by 2 mm (with screw fixation).

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3 Test results

3.1

3.1 Validation of the finite element model of hallux valgus

Static plantar pressure test results: The gravity center of the patient was not evenly distributed between the two feet, but leant towards the right side. The right foot had a larger area, suggesting that it needed to bear more pressure from the body when standing. The position bearing with the highest pressure (M) was located at the right forefoot. Specifically, the right foot had an area of 133 cm², a load-bearing proportion of 55 %, an average pressure of 0.158 MPa, and a maximum pressure of 0.292 MPa (see Table 2 and Fig. 4). The maximum plantar stress in the finite element model was 0.25733 MPa, which is similar to that of plantar pressure test. In addition, the plantar pressure distribution cloud map of the finite element model is also similar to that derived from the test results. Specifically, the pressure was concentrated on the forefoot; the gravity center shifted backwards; the hind foot had a smaller stress area; there was stress concentration and the highest stress was detected at the heel. Based on the comparison between the finite element analysis results and test results, it can be concluded that the established finite element model of hallux valgus is valid and can be used for mechanical analysis (see Fig. 5).

Table 2 Static plantar pressure test results.

Indicator		Value
Forefoot	Area m2Load proportion %Body weight proportion %	843970
Hind foot	Area m2Load proportion %Body weight proportion %	501630
Combined	Area cm2Load proportion %Maximum pressure (MPa)Average pressure (MPa)	13355450244

Table 3 summarizes the stress values at various positions before and after Scarf osteotomy under four different settings.

(MPa)	Preoperative	2 mm	4 mm	6 mm	8 mm
1st metatarsal	1.0355	3.6024	7.1825	9.4711	8.5582
2nd metatarsal	0.40369	0.36867	0.34997	0.34062	0.42683
3rd metatarsal	1.8252	1.7213	1.6246	1.6225	1.6797
4th metatarsal	1.5225	1.2801	1.4569	1.4508	1.3592
5th metatarsal	1.8695	1.7363	1.6428	1.6066	1.5855
Heel	1.9236	1.5098	1.8018	1.7955	1.6414
Sole	0.25733	0.14645	0.14423	0.14375	0.15473

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Fig. 4 Static analysis.

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Fig. 5 Preoperative plantar pressure test.

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3.2

3.2 Stress values before and after Surgery(see Table 3 and Fig. 6)

3.2.1

3.2.1 Stress on metatarsal bones

As the distal end of the bone fragment was pushed outwards farther and farther, the stress on the first metatarsal bone was gradually increased (reaching the maximum value of 9.4711 MPa at 6 mm as shown in Fig. 6); on the contrary, the stresses on the second and third metatarsal bones were gradually decreased (declining to the minimum values of 0.34062 MPa and 1.6225 MPa, respectively, at 6 mm). The postoperative stresses on the fourth and fifth metatarsal bones were decreased under all settings compared to the preoperative condition.

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Fig. 6 The Von Mises stress cloud map of the Scarf osteotomy model when the bone fragment was pushed outwards by 6 mm. (a) First metatarsal bone; (b) Second metatarsal bone; (c) Third metatarsal bone; (d) Fourth metatarsal bone; (e) Fifth metatarsal bone; (f) Heel; (g) Sole.

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3.2.2

3.2.2 Stress on the heel and sole

The postoperative stress on the heel was decreased under all settings compared to the preoperative condition. As the distal end of the bone fragment was pushed outwards farther and farther, the stress on the sole showed a decreasing trend first and then began to increase (the minimum stress was 0.14375 MPa, observed at 6 mm), presenting a V-shaped distribution pattern.

3.2.3

3.2.3 Stress on the screws

The maximum Von Mises stress on the screws had the smallest value (40.995 MPa) when the distal end of the bone fragment was pushed outwards for 6 mm, and the stress distribution showed an N-shaped pattern (see Table 4 and Fig. 7).

Table 4 Von Mises stress on the screws.

Osteotomy displacement	2 mm	4 mm	6 mm	8 mm
Von Mises stress (MPa)	44.664	78.961	40.955	76.916

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Fig. 7 The Von Mises stress distribution cloud map of screws. (a) Osteotomy model with 2 mm displacement. (a) Osteotomy model with 2 mm displacement; (c) Osteotomy model with 4 mm displacement; (c) Osteotomy model with 6 mm displacement; (d) Osteotomy model with 8 mm displacement.

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4 Discussions

Hallux valgus is the most common foot deformity in foot and ankle surgery, which can seriously affect the patients’ shoe wearing and even walking.²³ As a surgical treatment of hallux valgus, Scarf osteotomy is the first Z-shaped osteotomy of the longitudinal axis of the first metatarsal bone reported by Meyer in 1926. In 1991, Weil described this Z-shaped osteotomy using the word “Scarf” for the first time, and in 2000, Weil et al. popularized this procedure in clinical practice.²⁴ At present, Scarf osteotomy has become one of the commonly used surgical methods for treating hallux valgus. Simple Scarf osteotomy, i.e., Z-shaped osteotomy, has significant advantages in the treatment of hallux valgus, characterized by strong corrective ability, good stability, high clinical application value and high safety.^9,11,25 Postoperative deformity recurrence is the most common complication after surgical treatment. Scarf osteotomy can not only effectively correct deformities, but also preserve the range of motion of the first metatarsophalangeal joint, leaving space for fusion surgery to deal with recurrence.²⁶ Compared with other types of osteotomies, Scarf osteotomy can achieve comprehensive correction, so it can offer strong corrective ability and good corrective effect, effectively restoring the normal structure and function of the foot. Meanwhile, it can reduce the risk of postoperative joint stiffness and cause less surgical trauma, allowing patients to recover faster and suffer less postoperative pain. Moreover, Scarf osteotomy can also improve the appearance of the foot by adjusting the foot structure, providing better stability and reducing the risk of recurrence.^27,28 It is also noteworthy that Scarf osteotomy has greatly reduced the incidence of postoperative complications, such as metastatic plantar pain, bone non-healing, and metatarsal necrosis. To date, a number of modified and combined Scarf osteotomies for the treatment of hallux valgus have been reported. For example, Zheng Wenyuan et al.²² reported that the first metatarsal joint Swanson prosthesis joint replacement combined with the first metatarsal osteotomy and bone grafting could effectively correct hallux valgus. However, there is still limited research on the conventional double-screw translational Scarf osteotomy. Therefore, in this study, we aimed to conduct finite element analysis to explore the stress changes in various parts of the foot and the screws after Scarf osteotomy under different translational displacements, in order to develop more accurate diagnosis and treatment plans and provide guidance and theoretical basis for clinical practice.

In this study, we compared the preoperative results obtained from the FreeStep plantar pressure testing system with the data obtained from finite element analysis. It was found that the plantar stress distribution of the finite element model was similar to that derived from the test data (i.e., similar stress distribution positions and numerical values). The stress on the forefoot accounted for 75 % of the overall stress in the finite element model, and accounted for 71 % of the overall stress in the static analysis cloud map. In both systems, the pressure was mainly distributed in the forefoot. In the finite element model, the maximum stress was found at the heel, which is similar in position to point M (the maximum pressure point) on the static analysis cloud map, and their values are also similar. This fully confirms the validity of the established finite element model of hallux valgus.

In the simulation of the Scarf osteotomy with four different translational displacements, it was found that, under the same loading and boundary conditions, the Von mises stress on the first metatarsal bone was the highest when the bone fragment was pushed outwards for 6 mm. Under this setting, the Von mises stress on the first metatarsal bone achieved the most significant increase, accounting for 65 % of the total stress of all metatarsal bones, and was 9 times of the preoperative value. Scarf osteotomy with 6 mm displacement can restore the stress on the first metatarsal bone, relieve the stress on lateral metatarsal bones, and improve the stress distribution of the forefoot, therefore effectively correcting the hallux valgus deformity and improving the symptoms of metastatic plantar pain. At the same time, the maximum von Mises stresses on the second and third metatarsal bones under the 6 mm setting were reduced by 16 % and 11 % respectively compared to the preoperative values, and were the lowest among the four settings. This suggests that the 6 mm setting can effectively reduce the stress on the second and third metatarsal bones, which is the key to reducing metastatic pain and preventing the occurrence of metastatic pain at the second and third metatarsal bones after surgery. In addition, the stress on the fifth metatarsal bone was decreased by 14 %. Before surgery, the total stress on the first and fifth metatarsal bones accounted for 44 % of the total stress of all metatarsals, while in the 6 mm Scarf osteotomy model, the total stress on the first and fifth metatarsal bones accounted for 76 % of the total stress of all metatarsal bones, indicating an increase of 32 %. This is compliant with the normal physiological condition that the first and fifth metatarsal bones should be the main load-bearing positions of the foot. Overall, Scarf osteotomy can increase the stress on the first metatarsal bone, relieve the stress on lateral metatarsal bones, change the force-bearing position and level on the forefoot, and reduce the probability of postoperative metastatic plantar pain. After the surgery, the patient's plantar pressure distribution tends to return normal. Precise and customized Scarf osteotomy is conducive to enhancing osteotomy accuracy, making the plantar pressure distribution more reasonably, and shortening the surgical and postoperative recovery time.

With respect to the stress on the screws, it was found that the maximum Von mises stress was ranged 44.664–78.961 MPa under four different settings, all within the yield strength of titanium alloy, therefore able to ensure effective and stable fixation.²⁹ Under the 6 mm setting, the maximum von Mises stress on the screws was the lowest (40.995 MPa). By observing the screw stress cloud map, it can be found that there was stress concentration at the screw head in the other three settings rather than the 6 mm setting, which means that the 6 mm setting can yield more uniform and reasonable stress distribution, and probably better stability. This is very important for maintaining the postoperative stability of the body. Monitoring and analyzing the stress and stress distribution on the screws can effectively prevent problems like screw loosening and deformation, providing more reliable support for clinical practice.

Some limitations of this study should be pointed out. First, we only performed static analysis but not dynamic analysis. Although our finite element model has been validated through plantar pressure test, it cannot completely replace in vivo research for the reason that the accuracy of biomaterial parameters and connections between anatomical structures cannot be guaranteed.

5 Conclusions

Based on precise and customized preoperative design and finite element analysis, it was found that the Scarf osteotomy with the distal end of the bone fragment pushed outwards for 6 mm could yield the best treatment effect for hallux valgus. Under this setting, the stress on the first metatarsal bone was the highest, while the stresses on the second and third metatarsal bones were the lowest, suggesting that it can relieve the stress on lateral metatarsal bones and improve the stress distribution of the forefoot. Overall, Scarf osteotomy under 6 mm setting can effectively correct hallux valgus deformities, reduce the incidence of metastatic plantar pain and prevent the recurrence of metastatic plantar pain after surgery. By improving the patient's plantar stress distribution, this surgical setting is expected to provide better clinical outcomes.

CRediT authorship contribution statement

Min Zhang: Conceptualization, Resources, Investigation, Writing – original draft, Writing – review & editing. Ling Zhang: Conceptualization, Supervision. Shitao Fang: Investigation, Resources. Yun Wang: Investigation, Resources. Jinkun Guo: Investigation, Resources. Lei Mi: Project administration, Funding acquisition.

Guardian/patient's consent

Informed consent was obtained from the patient whose computed tomography data were used in this study.

Data availability

The datasets used and analysed during the current study are available from the corresponding author on reasonable request.

Ethics approval and consent participate

The Ethics Committee of Hunan Brain Hospital approved the study. Informed consent was obtained from the patient whose computed tomography data were used in this study. All methods were carried out in accordance with relevant guidelines and regulations.The whole research process follows the Declaration of Helsinki.

Ethics approval and consent participate

The Ethics Committee of Hunan Brain Hospital approved the study and the use of computed tomography data for this study. Informed consent was obtained from the patient whose computed tomography data were used in this study. All methods were carried out in accordance with relevant guidelines and regulations.

Funding

This study was sponsored by the Hunan Provincial Science and Technology Innovation Project (No.2021SK50806).