■ Feature Article
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.
he 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
T
760
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 21215.
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SECONDARY TRANSLATION AND LENGTH DEFORMITIES | GLADBACH ET AL
2
1
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 兩tBL兩 and 兩lBL兩 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; 2002. 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;
2002. Copyright © 2002.)
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
JULY 2004 | Volume 27 • Number 7
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 com-
pensation 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
761
■ Feature Article
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; 2002.
Copyright © 2002.)
762
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, 兩tBL兩 and 兩lBL兩. 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 兩tBL兩 and 兩lBL兩 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⫻兩tBL兩⫻sin(␣/2)
ST=2⫻兩lBL兩⫻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-
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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 formulae1,7-9 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 (兩lBl兩) and
between the ACA and the lBL (兩tBL兩) are
measured (Figure 1). The measurements
兩lBL兩 and 兩tBL兩 are used to calculate secondary length and translation using the
JULY 2004 | Volume 27 • Number 7
4
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. 兩␣兩 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; 2002. 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.
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■ Feature Article
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 (tBLi) increases relative to the final tBL (tBLf).
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;
2002. 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 cor-
764
rected 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 correc-
tion 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
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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 (hingei) on the initial tBL (tBLi).
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,
hingef=final hinge, hingei=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; 2002. 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]).
JULY 2004 | Volume 27 • Number 7
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 prin-
ciples 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 al18 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 al15 designed an external fixator
that could perform gradual angular cor-
765
■ Feature Article
rection. Pfeil et al15 and Leyes et al21 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 al15
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.
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