Calculation and Correction of Secondary Translation Deformities and Secondary Length Deformities

Transcription

1 Calculation and Correction of Secondary Translation Deformities and Secondary Length Deformities BRUNO GLADBACH, DMED*; ETIENNE HEIJENS, DMED*; JOACHIM PFEIL, PROFDMED*; DROR PALEY, MD abstract External fixation correction of angular deformities leads to secondary translation deformities when occurring around an axis located proximal or distal to the center of rotation of angulation (CORA); secondary length deformities result when correction occurs around an axis concave or convex to the CORA. With circular fixation, the hinge axis can be matched to the CORA. With monolateral fixation, the level of the hinge/angulator is not easily controlled. Axis of correction of angulation can be plotted graphically and secondary deformities calculated trigonometrically. Location of the hinge/angulator can be accurately planned and adjustments incorporated to compensate for expected secondary deformities. The principles and planning of deformity correction have been well described. 1-4 The nomenclature and abbreviations presented herein are adopted from the glossary by Paley. 1,5 The center of rotation of angulation (CORA) is the point of intersection of the proximal and distal axis lines of an angulated bone. The crossing of the axis lines produces a transverse angle and a longitudinal angle. A line dividing an angle in half is called a bisector line. Each angulation has a transverse bisector line (tbl) and a longitudinal bisector line (lbl). All points on the tbl are also considered CORA. The neutral CORA is located at the point of intersection of the proximal and distal axis lines of the bone. The axis of correction of angulation (ACA) is the imaginary axis line around which an angular deformity is corrected. It has been shown that when the ACA passes through a CORA, complete colinear realignment of the proximal and distal axis lines occurs. 1,2,4 When the ACA passes through a CORA concave or convex to the neutral CORA, secondary shortening or lengthening, respectively, of the bone ends results. When the ACA passes proximal or distal to the bisector line, a secondary translation deformity is produced. 1,2,4 When the ACA lies on the lbl, no secondary lengthening or shortening occurs. When the ACA lies on the tbl, no secondary translation occurs. The use of external fixation for limb realignment is well accepted. Principles of deformity correction with circular external fixation have been described based on the fundamental work of Ilizarov. 6 To achieve realignment of an angular deformity without creating a secondary translation deformity, the axis of the hinges of the Ilizarov apparatus is centered over a CORA on the tbl of the angular deformity. The circular Ilizarov fixator allows hinge placement at any level, including proximal or distal to any ring in a longitudinal direction and concave or convex to the bone in a transverse direction. If the hinge axis is placed at the tbl convex to the neutral CORA, lengthening of the bone ends occurs. If the hinge axis is placed at the tbl concave to the neutral CORA, shortening of the bone ends occurs. If the hinge axis is placed proximal or distal to the tbl, secondary translation of the bone axes occurs. If the hinge axis is located proximal or distal to the tbl and concave or convex to the lbl, secondary length change and secondary translation result. Unilateral external fixators are more limited regarding hinge or angulator axis placement. Uniplanar fixators use hinges and angulators to correct deformities. Uniplanar hinges are passive devices that require a change in length of the fixator From the *Orthopädische Klinik Wiesbaden, Wiesbaden, Germany; and Sinai Hospital, Rubin Institute for Advanced Orthopedics, International Center for Limb Lengthening, Baltimore, Md. Reprint requests: Dror Paley, MD, Sinai Hospital, Rubin Institute for Advanced Orthopedics, International Center for Limb Lengthening, 2401 W Belvedere Ave, Baltimore, MD ORTHOPEDICS

2 SECONDARY TRANSLATION AND LENGTH DEFORMITIES GLADBACH ET AL Figure 1: Calculation of secondary length and secondary translation. Tibial angulation of magnitude (A). The proximal and distal axis lines of the tibia intersect at the neutral CORA. The tbl and lbl are marked. The Heidelberg external fixator (Smith & Nephew Inc, Memphis, Tenn) with an angulator is templated on the convex side of the varus deformity. The axis of the angulator is the ACA. The tbl and lbl are measured as the perpendicular distance of the neutral CORA to the lbl and tbl, respectively (B). These distances are used in the trigonometric formulae to calculate the amount of secondary translation and secondary length, respectively. Abbreviations: ACA=axis of correction of angulation, lbl=longitudinal bisecting line, n-cora=neutral central of rotation of angulation, and tbl=transverse bisecting line. (Reprinted with permission from Paley D. Principles of Deformity Correction. Berlin, Germany: Springer-Verlag; Copyright 2002.) Figure 2: Graphic method to determine secondary length and secondary translation. Secondary translation is measured as the distance along the tbl between the arms of the angle. Secondary length is measured by drawing an angle, (angle rotated 90 ), centered on the tbl. The secondary length is measured as the distance between the arms of angle along the lbl. Abbreviations: lbl=longitudinal bisecting line, SL=secondary length, ST=secondary translation, and tbl=transverse bisecting line. (Reprinted with permission from Paley D. Principles of Deformity Correction. Berlin, Germany: Springer-Verlag; Copyright 2002.) 1 2 body to change their angle. The ACA usually is one cortex of the bone rather than the axis of the hinge. Angulators are active devices that can be directly adjusted to change their angles. The ACA is the axis of rotation of the angulator. Hinges usually are used on the concave side of the deformity, whereas angulators can be used on the concave or convex side. It is difficult to align the hinge or angulator axis exactly on the tbl. When the unilateral fixator hinge or angulator axis is not on the tbl, a secondary translation deformity results. The secondary translation needs to be corrected with translation adjustments of the unilateral external fixator to avoid a fixed translation deformity of the bone axes. Even when the hinge or angulator axis of a unilateral fixator can be initially aligned on the tbl, it is difficult to maintain its level along the tbl To achieve realignment of an angular deformity without creating a secondary translation deformity, the axis of the hinges of the Ilizarov apparatus is centered over a CORA on the tbl of the angular deformity. when distraction or compression occurs on only one side of the hinge or angulator. Finally, even if the unilateral hinge or angulator can be located on the tbl, its location along the tbl is difficult to adjust, requiring additional length compensation by the fixator to correct for secondary lengthening or shortening of the bone. This article presents a simple method to determine the amount of secondary translation or secondary length change that results from different levels and locations of hinge or angulator placement. MATERIALS AND METHODS Bisector Coordinate System The tbl is perpendicular to the lbl. The neutral CORA is taken as the origin of the reference system. The neutral CORA also is the intersection of the neutral tbl and lbl, which is used as the reference lines for the x,y graphic coordinate system. With angulators used on the convex side, the ACA corresponds to the central axis of the angulator. With hinges used on the concave side, the ACA is the convex JULY 2004 Volume 27 Number 7 761

3 Figure 3: Compensation method for secondary length and secondary translation. These figures break up the correction and compensatory movements into sequential steps to better illustrate the process. Clinically, the gradual angular correction with its secondary deformities would be performed simultaneously with the compensatory translation and shortening adjustments. The threaded half-pins are in the angular deformity plane. Translation compensation is performed by attaching a second clamp to the proximal pins with a threaded rod attachment between the two pin clamps for gradual translation adjustment. The primary pin clamp must be left loose to allow the pins to slide through it (A). The translation compensation is simulated as if performed before angulation. The amount of compensatory translation is equal to the expected secondary translation because of the angulator location (B). Angulation alone would also produce undesired lengthening with excessive separation of the bone ends (C). To re-establish bone contact and avoid undesired lengthening, the telescopic segment of the fixator is shortened by the amount of the secondary length (D). Abbreviations: ACA=axis of correction of angulation, lbl=longitudinal bisecting line, n-cora=neutral central of rotation of angulation, SL=secondary length, ST=secondary translation, and tbl=transverse bisecting line. (Reprinted with permission from Paley D. Principles of Deformity Correction. Berlin, Germany: Springer-Verlag; Copyright 2002.) 3 cortex of the bone. Any ACA can be marked as a point on this graph. The coordinates of this ACA can be defined by two vectors, tbl and lbl. The plane of this two-dimensional graph represents the plane of the angular deformity. This corresponds to the radiograph obtained with the x-ray beam perpendicular to the true plane of angulation. The graph can be drawn directly on the radiograph (Figure 1). Using the tbl and lbl determined graphically, the secondary translation (ST) and secondary length (SL) can be calculated using trigonometric formulae modified from those presented by Ilizarov. 6 SL=2 tbl sin( /2) ST=2 lbl sin( /2) Using these formulae, it is possible to calculate every secondary translation and length for every ACA relative to the neutral CORA. The amount of secondary translation and length also can be determined graphically (Figure 2). The perpendicular lines from the ACA to the lbl and tbl are the tbl and lbl of the angulation, respectively (tbl and lbl, respectively), measured at the ACA (hinge axis). The distance between the central arms of a goniometer opened to the magnitude of angulation measured along the tbl at its intersection with the hinge lbl is the amount of secondary length. Similarly, the distance between the arms of a goniometer opened to the magnitude of angulation measured along the lbl at the intersection with the hinge tbl is the amount of secondary translation. Angulator Placement for Angular Deformity Correction Angulators can be used in any location convex to, concave to, or overlying the CORA. The axis of rotation of the angulator becomes the ACA for the bone deformity. The alignment achievable by this mechanism may need to be adjusted for secondary length and translation based on the preoperative planning. Standing long frontal and sagittal plane radiographs are obtained, and the malalignment test and CORA method are performed as pre- 762 ORTHOPEDICS

4 SECONDARY TRANSLATION AND LENGTH DEFORMITIES GLADBACH ET AL viously described. 1,2,4 When both frontal and sagittal plane angulations are present, oblique plane analysis is conducted, using trigonometric formulae 1,7-9 or the graphic method. 1,10-12 The neutral CORA is identified as the intersection point of the proximal and distal anatomic or mechanical axis lines. The magnitude of the angulation (longitudinal angle) and its complement, the transverse angle (180 minus the magnitude), are measured. The tbl and lbl of these angles are drawn passing through the neutral CORA. They should be perpendicular to each other. The circular Ilizarov fixator allows hinge placement at any level, including proximal or distal to any ring in a longitudinal direction and concave or convex to the bone in a transverse direction. The Heidelberg external fixation system templates (Smith & Nephew Inc, Memphis, Tenn) (or, if another monolateral external fixator is used, the specific templates of that system are used) are used to draw the planned position of the external fixator and pins on the radiograph. The angulator is placed as close as possible to the tbl. Secondary length and translation can be determined by graphic or trigonometric analysis. For both analyses, the neutral CORA is considered the origin of the graph (0,0) and the perpendicular distance between the ACA and the tbl ( lbl ) and between the ACA and the lbl ( tbl ) are measured (Figure 1). The measurements lbl and tbl are used to calculate secondary length and translation using the Figure 4: Double angulation technique for correction of translation deformity. Pure translation deformity of the tibia is present. A fixator with two angulators is applied parallel to the tibia (A). The translation deformity can be resolved into two angular deformities by drawing a diagonal line between the proximal and distal axes of the tibia. The level of each angulator is projected to the tibia as a perpendicular line to the fixator passing through the axis point of the angulator. The diagonal line is drawn between the intersection points of the projected angulator lines with the tibial axis lines. The angle is measured between the diagonal line and each of the tibial axis lines. is the magnitude of angulation ( ) and counter angulation ( ) required by each of the angulators to realign the translation deformity (B). After the correction, the bone is straight and the fixator is zigzagged by equal and opposite angulation at the angulators (C). Abbreviations: ACA=axis of correction of angulation, D=distance between the two angulator levels, and ST=amount of translation required. (Reprinted with permission from Paley D. Principles of Deformity Correction. Berlin, Germany: Springer-Verlag; Copyright 2002.) What is already known on this topic External fixation correction of angular deformities leads to secondary translation deformities when occurring around an axis located proximal or distal to the center or rotation of angulation (CORA). Secondary length deformities result when correction occurs around an axis concave or convex to the CORA. With circular fixation, the hinge axis can be matched to the CORA. With monolateral fixation, the level of the hinge/angulator is not easily controlled, and in many cases, secondary translation deformity results. What this article adds The axis of correction of angulation can be plotted graphically, and secondary deformities can be calculated trigonometrically. Location of the hinge/angulator can be accurately planned and adjustments incorporated to compensate for expected secondary deformities. A simple method can be used to predetermine the amounts of secondary translation and length that need to be corrected for different hinge locations. It is possible to plan and perform gradual deformity correction using monolateral external fixation and achieve accuracy similar to that which previously was possible only with circular fixation. 4 JULY 2004 Volume 27 Number 7 763

5 Figure 5: Axis of correction of angulation (ACA) migration. The fixator is applied to the concave side of the bone with the hinge axis not aligned on the tbl. Because the ACA is not on the tbl, a secondary translation deformity is expected and occurs (A). The hinge level distance from the initial tbl (tbl i ) increases relative to the final tbl (tbl f ). This ACA migration contributes to the translation deformity (B). Abbreviations: lbl=longitudinal bisecting line, n-cora=neutral central of rotation of angulation, ST=secondary translation, and tbl=transverse bisecting line. (Reprinted with permission from Paley D. Principles of Deformity Correction. Berlin, Germany: Springer-Verlag; Copyright 2002.) 5 trigonometric formulae. To determine secondary length and translation from the graph, the base of the angles created by extending the arms of a goniometer from the neutral CORA to the lbl and tbl, respectively, are measured (Figure 2). Using the Heidelberg external fixation system, expected secondary translation in the plane of the pins can be corrected acutely or gradually using a second pin clamp secured to the pins (Figure 3). This correction can be performed after the secondary translation occurs (usually as an acute correction) or simultaneously with the angular correction (usually with gradual correction). In the latter situation, unwanted translation of the bone ends never occurs because it is corrected by the double clamp mechanism at the same rate as that at which it is produced by the angulator. Secondary length deformity correction must be combined with the angular correction. This length adjustment is accomplished by lengthening or shortening the telescopic body of the Heidelberg fixator (Figure 3). The amount of length adjustment required with the angular correction to maintain a neutral correction is equal to the secondary length calculation. Secondary translation also can be corrected using two angulators, making use of the geometric principle that two equal and opposite angulations have the net effect of translation (Figure 4). This method of translation correction can be used in any plane, including the plane of Gradual deformity correction is less limited by the soft tissues and is therefore safer in many situations. the pins. The amount of angulation and counterangulation ( ) at the two angulators can be determined graphically, or can be calculated trigonometrically knowing only the amount of translation required (ST) and the distance between the two angulators (D). =tan 1 (ST/D) Hinge Placement for Deformity Correction Hinges are used for deformity correction from the concave side. As the fixator body is distracted, a gradual opening wedge correction occurs, pivoting on the convex cortex. Therefore, the convex cortex is the ACA. If the hinge is placed off the bisector line, translation deformity is produced (Figure 5). Because of the translation, the convex cortex does not act as the ACA. The ACA is the hinge axis. If the hinge is placed on the tbl initially, the osteotomy remains aligned without translation by the end of correction. Between the beginning of correction and the end, the bisector line changes its position. At the end of correction, the bisector line is the bisector of the opening wedge angle. It has therefore moved up by an amount that is half the angle of correction. Relative to the final level of the bisector line, the hinge is as far away initially as it is at the end. This causes the bone ends to translate back and forth by the same amount, canceling out any translation deformity produced (Figure 6). RESULTS This study was conducted to find a simple objective method to predetermine the amounts of secondary translation and length that need to be corrected for different hinge locations. The trigonometric 764 ORTHOPEDICS

6 SECONDARY TRANSLATION AND LENGTH DEFORMITIES GLADBACH ET AL 6 Figure 6: To have the convex cortex and not the hinge act as the ACA, the hinge should be placed with the initial start position (hinge i ) on the initial tbl (tbl i ). During deformity correction, the hinge follows the telescopic axis. The hinge migrates proximally by the distance L, which is the length adjustment along the telescopic axis (A). A short translation occurs during hinge migration, caused by the straight path of the ACA migration along the telescopic axis (B). After half the correction, the secondary translation reaches its maximum; by the end of correction, which is half the corrective angle again, the secondary translation is completely corrected. The tbl migrates half the corrective angle to be the final tbl of the resulting opening wedge (C). This translation would not occur if the hinge followed the path of a circle drawn around the ACA instead of the path of a chord across the circle (D). Abbreviations: ACA=axis of correction of angulation, hinge f =final hinge, hinge i =initial hinge, n-cora=neutral center of rotation of angulation, and tbl=transverse bisecting line. (Reprinted with permission from Paley D. Principles of Deformity Correction. Berlin, Germany: Springer-Verlag; Copyright 2002.) and graphic methods described in this study accurately determined the best hinge location and amount of compensatory length and translation correction. Furthermore, with the methods developed by Gladbach et al, 13 Heijens et al, 14 and Pfeil et al, 15 and as illustrated in this study, it is possible to accurately plan and perform gradual deformity correction using monolateral external fixation. This accuracy is similar to that achieved previously with circular external fixation. The calculation and techniques reported in this study were clinically applied for 2 years and will be the subject of a future comparison with circular external fixation. Although the methodologies reported herein are specifically described for the Heidelberg external fixator, they are generic and can be modified for application with other monolateral external fixators that have hinge or angulator components (eg, Orthofix [Orthofix Inc, Bussellongo, Italy] and DynaFix [EBI Medical Systems, Parsippany, NJ]). DISCUSSION The CORA method of planning has revealed the relationships between the ACA, CORA, and osteotomy level. These are summarized as osteotomy rules 1 and 2 and a corollary to these rules. 1,4 Osteotomy rule 1 states that angular correction with the ACA and the osteotomy passing through the CORA leads to complete colinear realignment of the proximal and distal axes of the bone, without displacement of the bone ends. Osteotomy rule 2 states that when the ACA passes through the CORA but the osteotomy is at a different level, complete colinear realignment of the proximal and distal axis lines occurs, with displacement of the bone ends. Finally, the corollary to these osteotomy rules is that when the ACA and osteotomy do not pass through a CORA, a secondary translation deformity of the proximal and distal axis lines results. These geometric principles apply to osteotomy deformity correction irrespective of the hardware used. These principles have been applied to circular external fixation, and the technical details and consequences of hinge placement have been previously described. 1-4,16 Using these techniques, deformity correction with circular external fixation has been shown to be controllable. 17 Angular correction using monolateral fixators has also been previously described. 9,15,18 Price et al 18 recommend acute angular correction following the osteotomy rules. Acute correction with angulation alone or acute translation and angulation yielded excellent results. The limiting factor is the soft-tissue structure at risk. 19,20 Gradual deformity correction is less limited by the soft tissues and is therefore safer in many situations. Gradual deformity correction using monolateral external fixation has been reported. 21 Because of lack of consideration of the hinge level, in many cases, secondary translation deformity resulted. Pfeil et al 15 designed an external fixator that could perform gradual angular cor- JULY 2004 Volume 27 Number 7 765

7 rection. Pfeil et al 15 and Leyes et al 21 had the same early experience with secondary translation deformity caused by the hinge placement not coinciding with the tbl. To improve the alignment results, Pfeil et al 15 presented methods to compensate for secondary translation and length deformities. Although these methods permit correction of secondary deformities, they do not determine the amount of correction required. REFERENCES 1. Paley D. Principles of Deformity Correction. Berlin, Germany: Springer-Verlag; Paley D, Tetsworth K. Mechanical axis deviation of the lower limbs. Preoperative planning of uniapical angular deformities of the tibia or femur. Clin Orthop. 1992; 280: Paley D, Tetsworth K. Deformity correction by the Ilizarov technique. In: Chapman MW, ed. Operative Orthopaedics. 2nd ed. Philadelphia, Pa: JB Lippincott Co; 1993: Paley D, Herzenberg JE, Tetsworth K, McKie J, Bhave A. Deformity planning for frontal and sagittal plane corrective osteotomies. Orthop Clin North Am. 1994; 25: Paley D. Glossary and deformity correction principles. Gaslini. 1997; 29:1, Ilizarov G. Transosseous Osteosynthesis. Berlin, Germany: Springer-Verlag; Green SA, Gibbs P. The relationship of angulation to translation in fracture deformities. J Bone Joint Surg Am. 1994; 76: Green SA, Green HD. The influence of radiographic projection on the appearance of deformities. Orthop Clin North Am. 1994; 25: Taylor JC. Geometry of hinge placement. Techniques in Orthopaedics. 1990; 5: Bär HF, Breitfuss H. Analysis of angular deformities on radiographs. J Bone Joint Surg Br. 1989; 71: Paley D. Oblique plane deformity analysis. Bull Hosp Joint Dis. 1992; 52: Paley D, Tetsworth KD. Deformity correction by the Ilizarov technique. In: Chapman M, ed. Orthopaedic Surgery. Philadelphia, Pa: Lippincott Williams & Wilkins; 2001: Gladbach B, Pfeil J, Heijens E. Percutaneous epiphyseodesis. Correction of leg length inequalities and frontal plane deformities [German]. Orthopade. 2000; 29: Heijens E, Gladbach B, Pfeil J. Definition, quantification, and correction of translation deformities using long leg, frontal plane radiography. J Pediatr Orthop B. 1999; 8: Pfeil J, Grill F, Graf R. Extremitätenverlängerung, Deformitätenkorrektur, Pseudarthrosenbehandlung. Berlin, Germany: Springer-Verlag; Paley D. The principles of deformity correction by the Ilizarov technique: technical aspects. Tech Orthop. 1989; 4: Tetsworth K, Paley D. Accuracy of correction of complex lower-extremity deformities by the Ilizarov method. Clin Orthop. 1994; 301: Price CT, Bright R, Sproul JT, Lang L. Limb lengthening after immediate correction of deformity using the Orthofix unilateral fixator. Presented at: Annual Meeting of the American Academy of Orthopaedic Surgeons; March 6-12, 1991; Anaheim, Calif. 19. Dahl MT, Gulli B, Berg T. Complications of limb lengthening. A learning curve. Clin Orthop. 1994; 301: Green SA. Complications of external skeletal fixation. Clin Orthop. 1983; 180: Leyes M, Noonan KJ, Forriol F, Canadell J. Statistical analysis of axial deformity during distraction osteogenesis of the tibia. J Pediatr Orthop. 1998; 18: ORTHOPEDICS