Hallux valgus is one of the most common foot disorders in civilized populations [1], with an estimated 33% of adults in shoe-wearing populations having some degree of this condition [2]. Hallux valgus can be treated conservatively or operatively, but the non-operative approach is considered as the first-line option [3].

More than 150 surgical procedures have been described for hallux valgus treatment [2]. Distal metatarsal Chevron osteotomy is indicated for correction of mild to moderate hallux valgus (if the hallux valgus angle is less than 300 and the intermetatarsal angle is less than 150 with a congruent metatarsophalangeal joint). The typical Chevron osteotomy (depicted as BCB’ in Fig. 1) has a simple 60⁰ angle and is very popular, because it provides stability, rapid healing and minimal shortening with a low complication rate [4-10]. Even though this is a successful technique for hallux valgus, more than a hundred versions of distal osteotomy have been described [1]; the large number of proposed techniques indicates that none of these techniques is entirely satisfactory, and there is certainly room for improvement.

Fig. (1). Two dimensional side views of two Chevron osteotomies applied at the metatarsal bone of the first ray in the human foot: Points BCB’ depict the classic 600 osteotomy, whereas points ACA’ depict the proposed 900 osteotomy. Point C indicates the center of the circle circumscribed to the bone head.

Finite element analysis (FEA) is a computational tool that is often used for structural analysis of mechanical systems [11]. In recent years, FEA is increasingly used in the biomedical sciences, with several applications of this methodology recently published, especially in dentistry [12] and in orthopaedic surgery [13, 14]. In the current work we present clinical data and FEA results for a 90⁰ Chevron osteotomy (depicted as ACA’ in Fig. 1). FEA results predict strong mechanical bonding for the 90^o osteotomy, with enhanced compressive stresses that keep the two bones together, and reduced shearing stresses that tend to slide the two bones apart, compared to the 60^o method. As our clinical data are very encouraging, and consistent with FEA results, we hope this new technique will contribute to improved patient comfort and quality of life.

Followup data from clinical application of this new method were collected an average 32.7 months after the operation (Table 2). Mean preoperative HVA was 34.1 degrees (range, 22 to 56 degrees) and mean preoperative IMA was 15.5 degrees (range, 10 to 29 degrees). At the last follow-up examination, mean postoperative HVA angle was 14.2 degrees (range, 0 to 28 degrees), mean postoperative IMA angle was 8.1 degrees (range, 6 to 22 degrees), and mean AOFAS score was 94.3 (range 67 to 100). Results were rated as excellent in fifty feet (80.64%), good in 8 feet (12.9%) and fair in 4 feet (6.45%). All osteotomies were fused and there were no cases of non-union, loosening, avascular metatarsal head necrosis or wound infection. Two patients with fair results experienced late recurrence of the deformity, but this was not clinically significant, and they refused any further treatment.

Both software packages (ANSYS and OOF) performed linear static structural FEA calculations and their outputs consist of sets of stress vector components along specific coordinate axes on each node of the model. Both data sets can be found as supplementary info at the web links listed in the Appendix [16, 17]. From these values, the average normal and average shear stress was calculated on the nodes of the 60⁰ and the 90⁰ osteotomies (Figs. 4, 5). In general, normal compressive (positive) stresses along an interface tend to keep the two parts together, while shear stresses tend to slide the two parts apart. Therefore better bonding is expected where the normal-to-shear stress ratio λ is positive and greater than 1. Table 3 shows the average λ produced by the two methods along the segments AC, CA’, BC and CB’ (Fig. 1) of the two osteotomies. For ease of comparison, all ratios are normalized in the 0 to 1 range. In general, FEA methods are complex and their results include some degree of uncertainty; however, in the present work we only attempted qualitative analysis, with no emphasis on detailed numerical data. In this qualitative fashion, results obtained with the ANSYS and OOF methods agree reasonably well. In particular, both methods predict that the largest λ occurs along the CA segment of the ACA’ (Fig. 1) osteotomy and it is 2 to 3 times larger than the second largest λ which occurs along the CB’ segment of the BCB’ osteotomy. Therefore a stronger bonding is expected for the 90⁰ ACA’ osteotomy compared to the classical 60⁰ Chevron osteotomy BCB’, and this finding may explain our excellent clinical results. However, the CA’ and the BC segments should also be taken into account, and both methods predict low normal stresses on these segments (Table 3). These interfaces will also influence healing time, but we believe that the strong bonding of the CA segment is the prevailing factor.

Fig. (4). A plane x-y view of the bone model shown in Fig. (3), with Finite Element Analysis nodes (tiny dots) created by the ANSYS software while evaluating normal and shear stresses with the 60o and 90o osteotomies. Due to the discrete nature of the analysis, the two osteotomies cannot be represented by exact straight segments. Filled triangles indicate the nodes chosen to represent the 900 osteotomy, whereas filled circles indicate the nodes chosen to represent the 600 osteotomy. Point C (arrow) is the center of the circle shown in Fig. (1).

Fig. (5). A plane x-y view of the bone model shown in Fig. (3), with Finite Element Analysis nodes (tiny dots) created by the OOF software while evaluating normal and shear stresses with the 60o and 90o osteotomies. Due to the discrete nature of the analysis, the two osteotomies cannot be represented by exact straight segments. Filled triangles indicate the nodes chosen to represent the 900 osteotomy, whereas filled circles indicate the nodes chosen to represent the 600osteotomy. Point C (arrow) is the center of the circle shown in Fig. (1).

Our results indicate that the 90⁰ angle may be a good choice for Chevron osteotomy. Good clinical results have been reported in 80-90% of patients having the typical 60⁰ osteotomy [4, 6, 9] with recurrences or under-corrections occurring in 10-14% of cases [5, 7, 8]. However, a recent study by Torkki et al. [10] reported inferior results, probably due to the number of different surgeons (including trainees) who performed these operations and the unselected study population.

Data obtained from applying FEA analysis to a bone model seem to explain the good clinical results observed in our patient cohort. These results are easier to explain physically if the bone is approximated by a straight long beam under longitudinal compression. This is a well known example in the theory of elasticity, with maximum and zero normal stress along the directions of 0⁰ and ± 90⁰ with respect to the beam axis, and maximum shear stress at ± 45⁰. In the case of the metatarsal bone, all forces in Fig. (3) (except F₂) are almost parallel to the long axis of the bone. Because the metatarsal bone has an elongated shape, this bone can be approximated by a beam, and this crude approximation can help us understand the distribution of stresses along the bone. As the ± 30⁰ BCB’ osteotomy (Fig. 1) is close to the ± 45⁰ case, a large shear stress is to be expected. In contrast, as the AC and CA segments resemble the 90⁰ and 0⁰ cases, normal stresses are expected to be maximum and zero respectively.

In this manuscript we present our experience with the 90-degree Chevron osteotomy on a patient cohort of 51 women who had surgery for 62 Hallux Valgus deformities, and we also present results of Finite Element Analysis (FEA) of the 90^o Chevron osteotomy. Compared to the 60^o method, FEA predicts enhanced mechanical bonding, with stronger compressive stresses and weaker shearing stresses with the 90⁰ Chevron osteotomy. Our good long-term clinical results, together with results of Finite Element Analysis, suggest that the 90⁰ angle Chevron osteotomy is a good alternative to the classic 60^o method in patients with mild to moderate Hallux Valgus who need surgery.

Charalambos Matzaroglou, performed many operations, collected data and drafted manuscript.

Panagiotis Bougas, assisted with most operations and collected data.

Elias Panagiotopoulos, supervised most operations, directed patient care and revised manuscript.

Alkis Saridis performed many operations, collected data and revised manuscript.

Menelaos Karanikolas provided anesthesia for many procedures, organized, revised and submitted manuscript.

Dimitris Kouzoudis provided data, conducted Finite Element Analysis, and revised manuscript.

This work was supported solely by Department Funds. All authors declare that they have no conflict of interest to report.