Published on *Podiatry Today* (http://www.podiatrytoday.com)

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*When performing bunion surgery, one must keep in mind various biomechanical considerations. These authors discuss factors such as the intermetatarsal angle and metatarsal declination as well as the importance of pronation and first ray hypermobility.*

Bunions occur in 0.89 percent of the population and the incidence increases with age.^{1} About 6.5 percent of people 18 to 44 years old have bunions and this increases to 16.2 percent in the 45- to 64-year age group. For those over 65, the bunions can occur in over 22 percent of the population. Females have the condition at a ratio of approximately 3:1 over men, which most likely is due to footwear.^{1}

The etiology of bunions is multi-factorial. Root and colleagues describe four types of conditions (biomechanical, arthritic, neuromuscular and traumatic) that may lead to hallux valgus deformity.^{2} Factors such as shoe gear and genetics play indirect roles.

Bunions were originally thought to be a swelling of the soft tissue or an enlargement of the first metatarsal head, or possibly both. The early bunion surgeries aimed at removing the underlying bursa alone or in combination with an exostectomy of the first metatarsal head. This type of surgery was beneath many of the surgeons of the times so the understanding of the pathology and development of new surgical techniques were slow in occurring. In 1881, Reverdin presented the first real surgery to attack hallux abducto valgus.^{3} The Reverdin procedure is considered to be the forerunner of all the newer procedures we know today.

Geometry is critical in podiatric surgery. Many of the procedures that we use currently for different pathologies are determined by biomechanical angles. In particular, bunion surgeries are determined by the angle of the first metatarsal relative to the second metatarsal and the hallux itself. After determining what procedure to perform, there are many geometric concerns that we need to be aware of when performing bunion surgery.

The intermetatarsal angle is an important consideration when determining what type of bunion surgery to perform. For example, when performing a closing base wedge osteotomy of a transverse orientation, it is important to figure out the size of the wedge one should remove to bring the first ray into better alignment. The goal of this osteotomy is to make the first and second metatarsal approximately parallel.

One can determine the amount of wedge to resect before surgery by assessing the intermetatarsal angle. After measuring the intermetatarsal angle, utilize the law of similar triangles to figure out the size of the wedge that you should remove. The law of similar triangles states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.^{4} Therefore, using this particular geometric proof, the wedge removed should be “similar” to the predetermined intermetatarsal angle.

An osteotomy can be an integral part of a bunion procedure to realign the first metatarsal. Every time the surgeon performs an osteotomy, it shortens the bone by at least the width of the blade. The first metatarsal has a declination angle that is not parallel to the weightbearing surface. Any bone cut action will shorten the first metatarsal longitudinally and thereby elevate it by the amount of the blade width.

Therefore, one can determine elevation of the first metatarsal not only by the width of the blade but also by the declination of the first metatarsal in relationship to the ground. The greater the declination, the greater the elevation as the metatarsal shortens along its longitudinal axis. Elevation can lead to many complications in bunion surgery. These complications include: second ray overload resulting in painful callus; capsulitis; plantar plate tears leading to predisloaction syndrome; neuromas; and stress fractures.

Another way elevation can occur is by wedge resection of the bone. Consider again the proximal closing base wedge osteotomy. Determine the amount of elevation by the angle of the hinge of the apex or axis. In performing this osteotomy with the axis perpendicular to the bone, the bone will elevate along the arc of a circle. The higher the pitch of the bone, the more significant this elevation becomes. If the osteotomy has an axis that is 90 degrees to the ground, the bone will move along the transverse plane and not elevate. Of course, one must be conscious of the orientation of the axis in the frontal plane as well. If the axis has any valgus angulation, there can be elevation and shorting in this plane.

There is a directly proportional relationship between a high intermetatarsal angle and high hallux abductus angle. As the hallux deviates laterally and the metatarsal deviates medially, the extensor hallucis longus tendon deviates laterally and becomes more bowstrung. The higher the intermetatarsal angle, the shorter the effective length of the extensor hallucis longus tendon becomes. This lateral deviation of the extensor hallucis longus tendon accelerates bunion formation and valgus rotation of the hallux.

When one performs bunion surgery to realign the first ray, one may need to lengthen the shortened extensor hallucis longus tendon or hallux extensus could occur. Using the Pythagorean theorem can prove this.^{4} The theorem can be written as an equation relating to lengths of the sides of a right triangle: A^{2} + B^{2} = C^{2}.

The hypotenuse or C, which represents the extensor hallucis longus tendon, is actually shorter when the intermetatarsal angle is higher. As one places the first ray into its proper alignment, the extensor hallucis longus tendon may not have enough length to balance the hallux in its neutral position between flexion and extension.

Structural hallux abductus occurs when the proximal articular set angle and the distal articular set angle are above normal. Even a mild hallux abductus can become more significant by moving the metatarsal head laterally and not addressing the articular set angles (i.e. iatrogenic hallux abductus).^{5} When the first metatarsal head moves laterally, the hallux abductus angle may become more relevant as the hallux may now abut the second digit. One may need to address this new iatrogenic hallux abductus surgically in order to realign the hallux parallel to the second digit. In this case, the surgeon can again apply the theory of similar triangles.

There are many different geometric considerations when performing bunion surgery. Often, the intermetatarsal angle is a major consideration when determining the best procedure. With a closing base wedge osteotomy, one can see how the size of the wedge correlates to the intermetatarsal angle and how the orientation of the axis can influence shortening and elevation of the first metatarsal.

Also of importance with any osteotomy is how the width of the blade and declination of the first metatarsal can cause shortening and subsequent elevation. While realigning the bony architecture of the first ray is critical, one must consider the surrounding soft tissues, particularly the extensor hallucis longus. The bowstring effect of the extensor hallucis longus on longstanding bunion deformities can be powerful and restoring its effective length can help limit digital deformities.

Lastly, do not forget the hallux abductus angle and associated articular set angles. Realigning the hallux for functional and aesthetic purposes often means paralleling the second toe/ray. As with the proximal closing base wedge, one can use the theory of similar triangles to determine the degree of wedge for a distal procedure.

We have discussed the geometric importance of intermetatarsal angle, metatarsal declination, the importance of the axis of an osteotomy and the hallux abductus angle. Additional biomechanical and geometric concerns include how much pronation has occurred in the foot, hypermobility of the first ray, the length of the first metatarsal and possible contractures of the soft tissue. The best outcomes result from combining the art of bunion surgery and the above geometric principles.

*Dr. Mozena is in private practice at the Town Center Foot Clinic in Portland, Ore. He is a Fellow of the American College of Foot and Ankle Surgeons and is board certified in foot and ankle surgery. He is an associate of Western Health Sciences University Podiatric and Surgery Department.*

*Dr. Arndt is in private practice at the Town Center Foot Clinic in Portland, Ore.*

**References**

1. Adams PF, Hendershot GE, Marano MA. Current estimates from the National Health Interview Survey, 1996. National Center for Health Statistics. *Vital Health Stat 10.* 1999; 200(1):1-203.

2. Root ML, Orien WP, Weed JH. Forefoot deformity caused by abnormal subtalar joint pronation. In: *Normal and Abnormal Function of the Foot and Ankle: Clinical Biomechanics, Vol 2.* Clinical Biomechanics, Los Angeles, 1977, pp. 349-462.

3. Reverdin J. De la deviation en dehors du gros orteil (hallux valgus, vulg. “oignon,” “bunions,” “Ballen”) et de son traitement chirurgical. *Trans Int Med Congr* 1881; 2:406-412.

4. Jurgensen R, Brown R, Jurgensen J. *Geometry*. McDougal Littell Inc., Evanston, IL, 2000.

5. Mozena JD, Beede G, Jones PC. Iatrogenic hallux abductus secondary to first ray surgery. *Podiatry Today*. 1999; 12(4):39-42.

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