Geometric Analysis of the Weil Osteotomy

INTRODUCTION

Metatarsalgia and intractable plantar keratosis (IPK) are common problems seen in forefoot disorders. Synovitis and injury of the stabilizing structures of the lesser metatarsophalangeal (MTP) joints often accompany metatarsalgia. Chronic synovitis may eventually cause deterioration of the collateral ligaments and joint capsule with subsequent destabilization of the MTP joint ² . The commonly observed deformities range from pain without deformity to deviation, subluxation, or dislocation of lesser toes ³ .

Morton ⁸ first reported the association of a long second metatarsal with metatarsalgia. The observation that abnormal metatarsal protrusion frequently is associated with metatarsalgia led to the use of shortening osteotomies, such as the Weil, to treat metatarsalgia ¹⁷ . This osteotomy was first performed by LS Weil and was popularized in Europe by Barouk ⁹ . Several clinical papers have described the effectiveness of this procedure ^4,9,13,15,17 . Debate continues regarding the biomechanics and the optimal technique of this osteotomy.

This study evaluated the osseous anatomy of the lesser metatarsals and the geometry of the Weil osteotomy. Saw blades specially designed to reduce the vertical displacement of the capital fragment of the lesser metatarsal after the Weil osteotomy were evaluated as well.

MATERIALS AND METHODS

Five fresh or fresh-frozen cadaver trans-tibial amputation specimens were used for the anatomic study. The soft tissues on the dorsum of the foot were removed, exposing the dorsal surfaces of the metatarsals. The dorsal diaphyseal surface of each metatarsal was outlined using a thin stainless steel wire. A metal marker was used along the plantar surface of the foot to provide a baseline for angular measurements. The hindfoot was held in neutral varus and valgus position, with the tibia perpendicular to the plantar surface of the foot. Fifteen pounds of force were applied through the tibia. A lateral radiograph was obtained with the foot rotated so the wire was perpendicular to the radiographic beam. The angle between the metal marker on the plantar surface of the foot and the wire outlining the dorsal diaphyseal surface of the metatarsal defined the inclination of the metatarsal.

Next, the phalanges and the soft tissues about the metatarsal heads were removed. A caliper (Digital caliper, Catalog #721 A-6/150, L.S., Starrett Co, Athol, MA; measuring error of 0.3 mm) was used to measure the vertical height of the metatarsal head in the region of the Weil osteotomy. Three measurements were taken at what was judged to be the widest portion of the metatarsal head both perpendicular to the plantar surface of the foot and perpendicular to the longitudinal axis of the metatarsal. The largest measurement was recorded as the height of the head in each plane for each series of measurements.

A series of sawblades were tested to determine the effective size of each blade's kerf. The kerf is the thickness of material removed by a saw blade during a cut. First, each of the blades tested was measured with the digital caliper to determine the actual thickness of the blade. The effective kerfs of the blades were initially evaluated in Sawbones® models (Pacific Research Laboratories, WA). Two different hand-held surgical saws (model 4100 and TPS, Stryker, Kalamazoo, MI) were compared to determine the effect of the power head on saw blade performance. The model 4100 saw was used for all cadaver testing.

The blades were then tested on the cadaver metatarsals. A standard thickness blade (2296-33-115 Stryker, Kalamazoo, MI) and three specially designed thick blades (Figure 1) (Saw blades 5400-33-115CPT, 5400-33-116CPT, and 5400-33-117CPT; Stryker, Kalamazoo, MI) were used for this test. In addition, two standard saw blades, double loaded (“stacked”), and a standard blade double loaded with the thickest blade also were tested. Multiple parallel cuts were made perpendicular to the articular surface of the distal metatarsal. The cuts made were approximately half the normal depth of a Weil osteotomy to provide rigidity to the walls of the cut during measurement. The digital caliper was used to measure the kerf or the thickness of the cut. Care was taken to ensure that the micrometer was perpendicular to the direction of the bone cut. This was repeated for all five metatarsals in the five specimens using the standard blades, test blades, and combinations of blades.

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Fig. 1:

Standard thin blade with the three thick saw blades. From the top, the blade thickness is 1.61 mm, 1.45 mm, 1.29 mm, and 0.42 mm.

The data obtained in the cadaver study were then used to create a geometric model of the Weil osteotomy. The relationship between the shortening of the metatarsal and the plantar displacement of the metatarsal head was described by a geometric equation. The metatarsal head height data were then used to suggest appropriate length of fixation used for the Weil osteotomy.

RESULTS

The results of the radiographic examination of the metatarsal inclination showed a large variation in the five specimens (Table 1). The inclination varied by up to 14 degrees for the first metarsal. The lesser metatarsals showed less variation and a decrease in the mean value as the measurements moved lateral from the second to the fifth metatarsals.

The mean height of the metatarsal head perpendicular to the longitudinal axis of the metatarsal was 18.8 mm for the second metatarsal, 17.5 for the third and fourth, and 15.9 for the fifth (Table 2). The height of the metarsal head was reduced when measured perpendicular to the plantar surface of the foot. The height of the metatarsal heads showed a wide variation. This variation was largely related to the presence of large plantar condyles on some digits. When present, these ridges significantly increased the height of the head in our measurements.

The thickness of the actual saw blades was consistent between blades as measured by the digital calipers (Table 3). The cuts in the Sawbones® models demonstrated that the effective cuts were larger than the actual size of the saw blade. When the cuts on Sawbones® models were performed with the two power heads, the largest difference in average cut size was 0.06 mm between the mean values for each saw. This difference was considered minimal and all cadaver studies were done with the model 4100.

It was noted during the testing that loading two saw blades (“stacking”) increased the variation in the effective kerf of the saw. This was not a surprise, because on several of the cuts the doubled blades diverged, resulting in a thin wafer of bone remaining in the cut. We attempted to minimize this effect by inspecting the blades before each cut to ensure that no bone lodged between the two saw blades and that the blades did not diverge. We could not determine a predictor for this saw behavior. The divergence of the blades was observed for all the multiple blade combinations.

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Table 1:

Measured plantar inclination of metatarsals

Metatarsal	Mean	Minimum	Maximum
1	27.0	19	33
2	24.6	19	31
3	24.6	22	30
4	22.8	17	28
5	15.6	12	18

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Table 2:

Metatarsal head height

Metatarsal	Mean relative to foot	Minimum	Maximum	Mean relative to metatarsal	Minimum	Maximum
1	22.2	17.47	24.96	23.5	20.04	26.10
2	17.8	14.58	19.99	18.8	16.32	21.58
3	16.6	13.58	18.55	17.5	15.45	20.06
4	16.3	13.51	18.5	17.5	14.80	20.96
5	14.5	12.67	16.11	15.9	13.47	18.73

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Table 3:

Sawbones® results for single blades and two blades coupled

Blade name	Blade thickness mm	Mean cut mm	Standard deviation
2296-3-115	0.42	0.589	0.085697
2296-3-115 Doubled	0.81	1.252	0.305699
5400-33-115CPT	1.29	1.385	0.022592
5400-33-115CPT & 2296	1.58	1.674	0.022621
5400-33-116CPT	1.45	1.511	0.028497
5400-33-116CPT&2296	1.83	1.78	0.034681
5400-33-117CPT	1.61	1.69	0.039149
5400-33-117CPT&2296	1.97	2.038	0.057336

The effective kerf of the blades generally showed a higher variation when used on the cadaver specimens. The mean and standard deviation of each blade and blade combinations tested on cadaver specimens are reported in Table 4.

Geometric Analysis

The three variables the surgeon has control over while performing the osteotomy are the angle of the osteotomy, the thickness of the saw blade, and the amount of proximal displacement of the capital fragment. The key parameters that are modified by the osteotomy are the length of the metatarsal and the vertical position of the metatarsal head. The following analysis attempts to relate these two sets of parameters.

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Table 4:

Cadaver results for single blades and two blades coupled

Blade name	Mean cut mm	Standard deviation
2296-3-115	0.65	0.04
2296-3-115 Doubled	1.29	0.34
5400-33-115 CPT	1.31	0.10
5400-33-116 CPT	1.59	0.11
5400-33-117 CPT	1.76	0.14
5400-33-177 CPT & 2296	2.08	0.19

The observed plantar inclination of the metatarsal (I_MT) referenced by the surgeon intraoperatively is the dorsal surface of the specific metatarsal (Figure 2). This angle is measured using the surface of the foot as a reference plane. The osteotomy angle (α_ost) is referenced using the dorsal surface of the specific metatarsal. This angle also could be referenced off of the plantar surface of the foot (α_ost). The two osteotomy angles are directly related (Figure 5).

The surgeon controls the amount of displacement (D) of the capital segment along the osteotomy (Figure 3). The surgeon measures the proximal displacement (D) of the capital segment along the osteotomy line using the most distal edge of the proximal fragment as a reference. This displacement produces a shortening (S) of the bone along the longitudinal axis of the metatarsal, and displaces the metatarsal head in a plantar direction (P) (Figure 3). The shortening seen on anteroposterior radiographs (R) is the movement of the capital segment along the plantar reference plane. The use of thicker saw blades is intended to offset this plantar displacement of the distal fragment that accompanies the movement of the capital segment along the incline plane of the osteotomy.

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Fig. 2:

Relationship between the metatarsal osteotomy and the described directional planes. The observed metatarsal inclination (I_mt) is referenced off the plantar reference plane. The osteotomy angle (α_ost) is referenced off the dorsal diaphyseal surface.

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Fig. 3:

The displacement (D) of the capital fragment along the osteotomy at an angle (α_ost) to the metatarsal. Shortening (S) is along the metatarsal axis. Radiographic shortening (R) is along the plantar plane. Plantar displacement (P) is perpendicular to the plantar reference plane.

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Fig. 4:

The kerf (K) of the saw blade and its relationship to the metatarsal.

Because of the thickness of the saw blade, a kerf or segment of bone is resected with all saw cuts (Figure 4). When the Weil osteotomy is performed, the bone removed by the saw causes a gap between the capital fragment and the more proximal metatarsal. The capital fragment moves (S_K) toward the proximal fragment along the longitudinal axis of the bone. The distance the capital fragment travels is the same as the thickness of the missing material. This movement along the longitudinal axis also results in both the dorsal displacement (P_K) of the capital segment and shortening (R_K) of the metatarsal along the plantar plane. The dorsal movement of the capital segment due to the kerf is in direct opposition to the depression of the capital segment that results from the displacement along the osteotomy. By adjusting the amount of bone resected, the dorsal displacement of the capital segment due to the thickness of the saw blade can be changed.

The movement of the capital segment caused by saw blade thickness (K)

Displacement along the longitudinal axis of the metatarsal (S) and the movement of the capital segment from the loss of bone due to the saw's kerf occur along the same plane. This shortening from the kerf (S_k) forms the hypotenuse of a right triangle (Figure 4). The hypotenuse intersects the plantar plane of the foot along the axis of the metarsal inclination (I_mt). The displacement dorsally of the capital fragment (P_K) and the radiographic shortening along the plantar surface (R_k) make up the other two legs of this triangle (Figure 4). The relationship of these variables to the kerf (K) is:

S K = K / sin ( α ost ) P K = K / sin ( α ost ) * sin ( I mt ) R k = K / sin ( α ost ) * cos ( I mt )

(Note: The K subscript indicates this movement is due to the kerf. The results will be added to the movement due to displacement at the end of the analysis.)

The movement of the capital segment caused by the displacement along the osteotomy

The relationship of the osteotomy to the plantar reference plane must be determined. The osteotomy, metatarsal inclination, and the plantar reference plane form a triangle (Figure 5). The sum of the vertices of a triangle equal 180 degrees. The missing angle of the triangle and the angle of the osteotomy add up to 180 degrees. If these equations are combined:

180 = β ost + I mt + ( 180 - α ost ) β ost = α ost - I mt

(Note: If the angle of the osteotomy is the same as the metatarsal inclination, then the osteotomy is parallel to the plantar reference plane, and there will be no plantar displacement.)

As the capital segment is displaced along the osteotomy at an angle of β_ost relative to the plantar surface of the foot, plantar displacement of the capital segment (P) forms the hypotenuse of a triangle. The displacement in the plantar direction of the capital fragment (P) and the radiographic shortening along the plantar surface (R) make up the other two legs of the triangle. The relationship of these variables is dependent on the angle of osteotomy relative to the plantar surface of the foot. (β_ost = α_ost - I_mt)

P = D * sin ( α ost - I mt ) R = D * cos ( α ost - I mt )

The actual shortening along the longitudinal metatarsal axis is described by the equation:

S = D * cos ( α ost )

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Fig. 5:

The angle of the osteotomy can be described by its relationship to the metatarsal (α_ost) or by its relationship to the plantar reference plane (β_ost).

The summation of movement from the kerf and the displacement

P = D * sin ( α ost - I mt ) - K / sin ( α ost ) * sin ( I mt ) S = D * cos ( α ost ) + K / sin ( α ost ) R = D * cos ( α ost - I mt ) + K / sin ( α ost ) * cos ( I mt )

The ranges and averages of metatarsal inclination obtained in the cadaver study were used to determine the limits of the calculated scenarios. The measured saw blade kerf was used in the calculations. The effect of saw blade selection on capital segment movement given a 5 mm displacement along an osteotomy at 45 degrees to the metatarsal is demonstrated in Table 5. This angle was selected to better demonstrate the effect of saw blade thickness on the movement of the capital segment. Table 6 and 7 illustrate the effect of displacement along the osteotomy on depression of the capital segment for the two extremes of saw blade thickness. (Note that the effect of the thicker blade is reduced for metatarsals with smaller inclinations.) The plantar displacements for various inclinations and saw blade thicknesses are illustrated in Figure 6.

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Table 5:

Calculated plantar displacement and shortening of the metatarsal for a 5-mm displacement, 45-degree osteotomy, and both the average and minimal metatarsal inclination

Saw blade	Kerf	Plantar displacement	Metatarsal shortening	Radiographic shortening
Inclination 25
2296-3-115	0.59	1.36	4.37	5.45
540-33-115CPT	1.39	0.88	5.50	6.48
540-33-117CPT	1.61	0.75	5.81	6.76
540-33-177CPT&2296	2.04	0.49	6.42	7.31
Inclination 19
2296-3-115	0.59	1.92	4.37	5.28
540-33-115CPT	1.39	1.55	5.50	6.35
540-33-117CPT	1.61	1.45	5.81	6.65
540-33-177CPT&2296	2.04	1.25	6.42	7.22

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Fig. 6:

Plantar displacement of the distal fragment based on a 25-degree osteotomy. The two extremes of effective kerf are shown over a range of metatarsal inclinations.

DISCUSSION

The exact biomechanical effect of the Weil osteotomy is controversial. Studies examining plantar pressures after Weil osteotomies have not demonstrated significant changes ^6,11 . Sawbones® studies have shown depression of the capital fragment after proximal displacement, which should increase the plantar pressures ¹⁴ . While our calculations did not demonstrate the same magnitude of depression as reported by Trnka et al, ¹⁴ using their assumptions results in more than 1 mm dorsal displacement. The description of the Weil osteotomy suggests that the saw cut should be parallel to the plantar surface of the foot to prevent the plantar displacement of the capital segment ^4,13,15 . The removal of additional bone from the osteotomy site to compensate for this displacement has been described as well ¹⁰ . The angle of the osteotomy is limited by such practical factors as the length of the saw blade, geometry of the metatarsal head, inclination of the metatarsal, operative exposure, and need to exit the plantar surface of the bone distal to the metatarsal's blood supply ^4,14 . This limited ability to keep the osteotomy parallel to the plantar surface of the foot is particularly evident for metatarsals with small plantar inclinations.

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Table 6:

Displacement of capital fragment in plantar direction based on osteotomy of 25 degrees and 0.65 mm kerf

	Inclination of metatarsal
		15	17	19	21	23	25	27	29	31	33
Displacement of Fragment	1	−0.22	−0.31	−0.40	−0.48	−0.57	−0.65	−0.73	−0.82	−0.90	−0.98
	2	−0.05	−0.17	−0.29	−0.41	−0.53	−0.65	−0.77	−0.89	−1.00	−1.12
	3	0.12	−0.03	−0.19	−0.34	−0.50	−0.65	−0.80	−0.95	−1.11	−1.26
	4	0.30	0.11	−0.08	−0.27	−0.46	−0.65	−0.84	−1.02	−1.21	−1.39
	5	0.47	0.25	0.02	−0.20	−0.43	−0.65	−0.87	−1.09	−1.31	−1.53
	6	0.64	0.39	0.13	−0.13	−0.39	−0.65	−0.91	−1.16	−1.42	−1.67
	7	0.82	0.52	0.23	−0.06	−0.36	−0.65	−0.94	−1.23	−1.52	−1.81
	8	0.99	0.66	0.34	0.01	−0.32	−0.65	−0.98	−1.30	−1.63	−1.95
	9	1.16	0.80	0.44	0.08	−0.29	−0.65	−1.01	−1.37	−1.73	−2.09
	10	1.34	0.94	0.54	0.15	−0.25	−0.65	−1.05	−1.44	−1.84	−2.23

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Table 7:

Displacement of capital fragment in plantar direction based on osteotomy of 25 degrees and 2.08 mm kerf

	Inclination of metatarsal
		15	17	19	21	23	25	27	29	31	33
Displacement of Fragment	1	−1.10	−1.30	−1.50	−1.69	−1.89	−2.08	−2.27	−2.46	−2.64	−2.82
	2	−0.93	−1.16	−1.39	−1.62	−1.85	−2.08	−2.30	−2.53	−2.74	−2.96
	3	−0.75	−1.02	−1.29	−1.55	−1.82	−2.08	−2.34	−2.60	−2.85	−3.10
	4	−0.58	−0.88	−1.18	−1.48	−1.78	−2.08	−2.37	−2.67	−2.95	−3.24
	5	−0.41	−0.74	−1.08	−1.41	−1.75	−2.08	−2.41	−2.73	−3.06	−3.38
	6	−0.23	−0.60	−0.98	−1.35	−1.71	−2.08	−2.44	−2.80	−3.16	−3.52
	7	−0.06	−0.46	−0.87	−1.28	−1.68	−2.08	−2.48	−2.87	−3.27	−3.65
	8	0.12	−0.33	−0.77	−1.21	−1.64	−2.08	−2.51	−2.94	−3.37	−3.79
	9	0.29	−0.19	−0.66	−1.14	−1.61	−2.08	−2.55	−3.01	−3.48	−3.93
	10	0.46	−0.05	−0.56	−1.07	−1.57	−2.08	−2.58	−3.08	−3.58	−4.07

Previous authors have based their treatment of metatarsalgia and IPK on correcting the observed increased pressure beneath the metatarsal head. This has been accomplished by pads and orthotics or by metatarsal osteotomies that reduce the concentrated weightbearing under the metatarsal head ⁷ . Dreeben et al. ⁵ treated metatarsalgia with a dorsal wedge osteotomy to elevate the metatarsal head. Their results showed that 3.5 mm of elevation was required to provide relief of symptoms. They also noted that more than 4.5 mm of elevation resulted in transfer lesions. The current study indicates that the Weil osteotomy is unlikely to achieve this magnitude of elevation.

Despite the limited elevation of the metatarsal head, the Weil osteotomy has a good clinical record. Previous reports showed good clinical results in 76% to 90% of patients ^4,9,13,15,17 and Weil ¹⁷ reported 95% resolution of metatarsalgia in 69 feet after the Weil osteotomy. Vandeputte et al. ¹⁵ suggested that the advantage of metatarsal shortening is that the metatarsal head is displaced proximally away from the inflammed tissues and placed above a healthy fat pad.

They concluded that this results in reduced pain without changing the load bearing of the metatarsal.

It may be that the effect of plantar pressures cannot be adequately measured in static models. Bojsen-Moller ¹ discussed the effect of a long second metatarsal on the dynamic loading of the lesser metatarsals. In 56% of feet that had a long second metatarsal, ¹⁶ no common axis for flexion of the metatarsophalangeal joints during toe-off was thought to exist. This foot configuration, referred to as index minus, was thought to lead to a dynamic increase in pressure beneath the second metatarsal head. This may explain the high incidence (up to 87%) of second metatarsalgia in index minus feet ⁵ . If the foot is index plus, described as a metatarsal cascade of lengths of 1 > 2 > 3 > 4 > 5, a common axis can exist that allows all of the metatarsals to share in weightbearing. By operatively converting an index minus to an index plus foot, the Weil osteotomy may reduce the dynamic loads experienced by the second metatarsal during gait.

Despite the lack of clinical data on the effect of plantar displacement of the metatarsal head after a Weil osteotomy, a surgeon should be hesitant to excessively alter the weightbearing pattern of the lesser metatarsals. The ideal result for a Weil osteotomy appears to be the establishment of an index plus foot with minimal depression or even some elevation of the metatarsal head. The elevation of the metatarsal head is likely to be more important in the treatment of intractable plantar keratosis.

Examination of the various saw blades demonstrated the effective kerf or thickness of each blade. It was noted that the effective kerf had a greater variability in the cadaver bone when compared to the Sawbones® models. It also should be noted that some power saw heads will not accept double-loaded blades, limiting the choices of the surgeon. The use of multiple blades coupled together was effective in increasing the effective kerf of the saw; however, this technique introduced a significant variance to the size of the kerf. The thick blades increased the kerf without an increase in variance. It is our recommendation that a blade be sized to allow sufficient shortening of the metatarsal with minimal plantar displacement of the capital segment.

From the results of the calculated displacement of the capital segment of the metatarsal in this small number of specimens, we recommend that a standard thin saw blade be used for patients with a high arch that allows a 25-degree or larger osteotomy to be parallel to the plantar surface of the foot. For feet with a metatarsal inclination of 25 degrees or less, a thicker blade should be selected. A kerf of just over 1 mm should be sufficient for most osteotomies unless the required shortening is more than 5 mm or the inclination of the metatarsal is less than 19 degrees. In these unusual cases, we prefer a saw blade with a kerf of 2 mm. This blade will allow up to 8 mm of shortening for a metatarsal with a 19-degree metatarsal plantar inclination when a 25-degree osteotomy is performed with less than 1 mm of depression. If the treatment of an intractable plantar keratosis is the primary goal, this blade may be useful.

The measurement of the cadaver metatarsal inclination did not match the commonly reported inclination of 15 degrees for the second metatarsal ^14,16 . This may be because of the use of the dorsal surface of the metatarsal as a reference plane and the small number of specimens. We selected this reference point because the dorsal surface is normally the only part of the metatarsal that the surgeon has available to judge the angle of the osteotomy. There was a large variance noted in the plantar inclination of the metatarsals in a relatively small number of specimens. Given the variety of arch heights from those with pes planus to pes cavus, it was not surprising that the lesser metatarsal plantar inclination would be highly variable. Because of this variety, no one osteotomy angle is ideal. In planning a Weil osteotomy, a surgeon should attempt to approximate the weightbearing plantar plane of the foot when possible. For metatarsals with smaller plantar inclinations, an osteotomy angle of 25 degrees and a thicker blade should be considered.

The measured size of the metatarsal heads provides some guidance to the length of internal fixation that can be used for a Weil osteotomy. Failure of the Weil osteotomy has been linked to prominent implants protruding on the plantar metatarsal surface ¹² . The length of the implant is related in part to the angle of fixation. A 12-mm implant should be acceptable for the second, third, and fourth metatarsals in all but the smallest individuals. If maximizing the fixation of the osteotomy is important, a depth gauge should be used to insure that the implant is not prominent on the plantar surface.