Ebook Principles of deformity correction: Part 2

1111

CHAPTER 12

Six-Axis Deformity Analysis and Correction

In previous chapters, we defined deformity components
and divided them into angulation, rotation, translation,
and length. Angulation and rotation are angular deformities, measured in degrees. Translation and length are
displacement deformities, measured in distance units
(e.g., millimeters, inches, etc.). In Chap. 9, we discussed
how angulation (axis in the transverse [x-y] plane) and
rotation (axial [z] axis) deformities can be resolved
three-dimensionally and characterized by a single vector (ACA) inclined out of the transverse plane (characterized by x,y,z coordinates). Similarly, translation
(displacement in the transverse plane) and length (displacement axially) can be combined into a single displacement vector inclined out of the transverse plane
(characterized by x,y,z coordinates).
Deformity between two bone segments can be fully
characterized by three projected angles (rotations) and
three projected displacements (translations). Therefore,
six deformity parameters are required to define a single
bone deformity. Mathematically, it is necessary to assign
positive and negative values to each rotation and each
translation, depending on the direction of rotation of
each angle and the direction of displacement of each
translation. The signs (+I-) of these angles and translations are determined by the mathematical convention of
coordinate axes and the right-hand rule.
The unique position of an object (bone segment) can
be determined by locating three non-collinear points on
that object. One segment can be moved with respect to
another by translating along three orthogonal axes and
rotating about these same three axes. The final position

after three orthogonal translations is independent of the
order undertaken. The final position after three orthogonal rotations is dependent on the order or sequence
undertaken (~ Fig. 12-1). Stated more formally, rotation
is not commutative.
Deformity analysis, as discussed in previous chapters, is conducted using AP and LAT view radiographs of
the bone deformity. Considering that a radiograph is an
X-ray projection of objects onto a plane (section), the
mathematical field concerning projection and section
(the plane of observation) is called projective geometry
(Klirre 1955). Projective geometry is the mathematical
basis of interpreting radiographs of bone deformities.

Yaw - Pitch - Roll

Fig.12-1

Although the order in which orthogonal translation is undertaken does not affect the final position of an object, the order
in which an object is rotated about orthogonal axes affects its
final spatial orientation. Three identical blocks are illustrated
(first column). Each of the blocks is shown as undergoing a 90°
rotation in yaw (Y), a 90° rotation in pitch (P), and a 90° rotation in roll (R), each in a different order. Note the very different
final orientations depending on the order in which the rotations were undertaken. Rotation is not commutative.

Gerard Desargues, a self-educated engineer, published the first known text on projective geometry in
1639. Blaise Pascal, a French mathematician and philosopher, added his theorem and published a text on
conic sections and projective geometry in 1640. All
printed copies of these works were lost. Fortunately, a
student of Desargues, Philippe de la Hire, made a manuscript copy of Desargues's book. Nearly 200 years later,
this copy was found serendipitously in a bookshop by
the geometer Michel Chasles (1793-1880). Along with

other 19th century geometers, Chasles rediscovered and
further developed projective geometry.
Chasles was the first to realize that the complex repositioning of an object in six axes (three translationsplus
three rotations) could be duplicated by rotation of a
threaded nut along a threaded shaft, the revolute. The
path of the nut in space is a curvilinear axis of correc-


IIEJI

CHAPTER 12 · Six-AxisDeformi!J AnalysisandCorrection

d.

tion of all the rotations (angulation and rotation deformities) and all the translations (translation and length
deformities). The central axis of this revolute in space is
the same as the vector that resolves the three rotations in
space. When rotation occurs in each reference axis, the
revolute will be inclined to all three reference axes. The
offset from the central axis (radius) of the revolute is
dependent on two translations, and the pitch of the
thread is dependent on the third translation.
The Chasles axis can be developed as a vector, with
direction and magnitude. The three contributions to the
vector are based on three angles (rotations): two from
radiographs (AP and LAT views of angulation) and the
third from clinical examination (axial rotation) or from
CT analysis of rotation deformity.
By treating the rotation or Chasles axis as a vector
quantity, one is able to exactly locate this axis in any of

eight octants. By invoking the right-hand rule, one can
readily determine the direction of rotation about this
axis to recreate the deformity. In addition to recreating
observed angulation and rotation with a single oblique
axis, Chasles showed that this same axis, if displaced
from the center of the fragment, can also provide translation in two planes. If the fragment is allowed to
progress along the shaft as it rotates (like a nut on a
threaded shaft), the third translation can be addressed.
The exact positioning of this shaft is beyond the scope of
this book, but a few conceptual examples are provided
(.... Fig. 12-2).

Fig. 12-2 a-f
Characterizing anatomic terms in their mathematical equivalents Ieads to improved understanding. Choose the point of
interest, or origin, as the zero position. Assuming you are working on yourself, anterior is positive, right is positive, and cephalad is positive. Positiverotation ab out each of the axes is shown.
The fragment is shown in reduced position (a). It is then
rotated ab out an oblique displaced axis and advanced along the
same axis. The fragment is shown in 40° and 2-cm increments
(b-f). This spiral or revolute motion can reproduce ( or correct)
a six-axis deformity.

The Taylor Spatial Frame Fixator
lntroduction

The Chasles axis can be applied to the real world to move
objects precisely through space. Moving objects through
space isaproblern encountered in many practical situations outside of orthopaedics. One of the most elegant
solutions was the fiight simulator developed in the early
1950s using the Stewart platform (Beggs 1966). This
same mechanism is used in amusement park rides. The

Stewart platform uses six struts of adjustable length to
move an object in any direction in space. It is not just
coincidental that the number of struts required corresponds to the number of axes of correction. If only five
struts are used, the system is unstable; when seven struts
are used, the system is overly constrained. The Stewart
platform also is used for the precise movements oflarge
telescopes and milling machines and has been used in
industry for years. It has now been applied to orthopaedics to allow simultaneous six-axis deformity correction.


CHA PTE R 12 · Six-Axis Deformity Analysis and Correction

1111

Standard Struts
Mini 60-75 mm
X-short 75-96 mm
Short 90-125 mm
Medium 11 6--178 mm
Long 169-283 mm
Strut
Fast Fx Struts
X-short 91 - 121 mm
Short 116--152 mm
Medium 143-205 mm
Long 195- 311 mm

t

Anti-master

tab

Fig. 12·3

The Taylor spatial frame construct is always the same: six struts
connected to every other tab on a full ring. The master tab is
always on the proximal ring and faces anterior. Looking down
on the proximal ring,as ifto put the ring on one's leg, the numbered struts are attached 1 through 6 starting at the master tab
in a counterclockwise configuration. It is important to remember that this assembly does not change for either side of the

body or for proximal or distal reference frames. The anti-master tab is the empty distal tab between struts 1 and 2. This tab
is a virtual tab in a distal two-thirds ring construct. The available components consist of rings (full, half, and two-thirds),
struts (Fast Fx [Smith & Nephew) and standard), foot plates,
and butt plates.

b.

c.

Fig. 12-3

Taylor spatial frame adjusted to perform the same function as
the adjacent Ilizarov construct:

a Translation.
b Axial rotation.
c Angulation.
d Angulation-translation.

IlD CHAPTER 12 • Six-Axis Deformity Analysis and Correction
a. Anteroposterior plane
angulation

d. Anteroposterior plane translation
(proximal reference)

b. Lateral plane
angulation

e. Lateral plane translation
(proximal reference)

In Memphis, Tennessee, in 1994, J. Charles and Harold
S. Taylor first applied the Stewart platform and the
Chasles theorem to orthopaedics. They modified the
Ilizarov external fixation system by connecting six telescopic struts that are free to rotate at their connection
points to the proximal and distal rings. This external fixator is called the Taylor spatial frame. In Germany, a similar modification to the Ilizarov device, called the hexapod, was developed (Seide et al. 1999). By adjusting only
the strut lengths, one ring can be repositioned with
respect to the other. Using a computerprogram that calculates the strut lengths relative to deformity parameters, the frame can be preconstructed to mirnie any
deformity. A two-ring construct can simulate a singlelevel deformity, and a three-ring construct with six
struts between each pair of rings can be preconstructed
for a two-level deformity. Simple and complex deformities are treated with the same frame. The same frame
construct - two rings and six struts- can simulate various Ilizarov frame constructs (~ Figs. 12-3 and 12-4).
The multiple angles and translations of a particular
deformity are addressed simultaneously by adjusting
the lengths of the struts only. The Taylor spatial frame

c. Axial plane
angulation

I. Axial plane Iranslaiion

Fig.12-Sa-f

Six deformity parameters needed to fully define a dinical
deformity.
a Anteroposterior plane angulation.
b Lateral plane angulation.
c Axial plane angulation.
d Anteroposterior plane translation.
e Lateral plane translation.
f Axial plane translation.

fixator is capable of correcting all aspects of a six-axis
deformity simultaneously. This external fixator is very
streng. The angled six-strut construct Ioads each strut
axially without applying bending forces to the inclined
struts. If one Iooks at only the points of attachment of
the struts to the ring, the shape is a triangle instead of a
circle. The entire structure, including the side triangles
formed by the struts and the two end triangles, has the
same shape as the crystal structure of a diamond (octahedron). Not surprisingly, this is a very streng construct.
When compared with the Ilizarov external fixator, the
spatial frame was 1.1 tim es as axially stiff, was 2.0 tim es


CHAPTER 12 · Six-Axis Deformity Analysis and Correction
a. AP view frame offset

lllJI

b. Axial frame offset

c. LAT view frame offset

d. Rotary frame offset
(30° external rotation)
Anteroposterior Mastertab
30°

to origin

Fig. 12-6a-d

0

= Center of reference ring

as stiff in bending, and had 2.3 tim es the torsional stiffness. The computational accuracy of the computer program is 1/1,000,000 inch and 1/10,000°. The real
mechanical accuracy using manual adjustment of the
struts for even a full six-axis deformity correction has
been measured to within 0.7° and 2 mm.
To treat a specific deformity with the spatial frame,
one must determine the frame parameters, the deformity parameters, and the mounting parameters. The
frame parameters consist of the proximal and distal ring
diameters along with the strut type, sizes, and lengths.
The deformity parameters consist of the radiographic and clinical measurements of the three rotations and
three translations, defined relative to a point designated
as the origin on the reference segment and its corresponding point on the corresponding segment. We present an example of the six deformity parameters in

terms of a tibial model (..,. Fig. 12-5): (1) coronal plane

Four mounting parameters determine the position of the center of the reference ring in space with respect to the assigned
origin.
a AP view frame offset.
b Axial frame offset.
c LAI view frame offset.
d Rotary frame offset (30" external rotation).

angulation, varus or valgus; (2) sagittal plane angulation, procurvatum or recurvatum; (3) axial plane angulation, internal or external rotation; (4) anteroposterior
plane translation, medial or lateral; (5) lateral plane
translation, anterior or posterior; (6) axial plane translation, short or long. Measure the deformity parameters
by characterizing the fragment-to-fragment deformity.
This characterization is independent of the selected
frame size, but the translational parameters are depen dent on how the frame is oriented to the fragments.
Ei ther the proximal or distal fragment can be designated
as the reference fragment. The origin may be conveniently chosen as any point along the reference frag-


1111 CHAPTER 12 · Six-Axis Deformi!J Analysisand Correction
ment's axis, as long as its corresponding point can be
identified or determined. The CORA is a good choice for
the origin in many cases. Using the CORA as the origin
is the marriage of the CORA method to the method of
simultaneaus six-axis deformity correction. The corresponding point lies along the axis of the moving fragment and is determined by various planning methods
discussed later in the chapter.
The mounting parameters define the position of the
reference ring (proximal or distal) in space with respect
to the position of the origin. In other words, the mounting parameters determine the position of the center of
the reference ring in space to the position of the assigned origin. Once the mounting parameters have been

assigned, the frame orientation to the limb can be anticipated. However, the frame usually is applied first and
the mounting parameters subsequently determined.
Four measurements defining the relationship of the reference ring to the origin determine the mounting parameters. The four mounting parameters are as follows:
(1) anteroposterior frame offset, medial or lateral offset
to the origin; (2) lateral frame offset, anterior or posterior offset of the center of the reference ring to the origin; (3) axial frame offset, proximal or distal offset of the
reference ring to the origin; and (4) rotational frame offset, the degree of rotation between the master tab (proximal reference) or anti-master tab (distal reference) to
the designated anteroposterior plane (usually patella
forward) (~ Fig. 12-6). The rotational offset is either
external or internal. With most applications, the intent is
to place the frame in a neutral position with no rotational offset. However, if rotational offset is present but
not accounted for, a secondary deformity will be created
during the initial correction. For example, if a varus
deformity is being corrected and the frame has been
mounted with an internal rotational offset, a secondary
recurvatum deformity will be created during the varus
deformity correction. This occurs because the frame is
correcting the varus deformity not in the anteroposterior plane but in an oblique plane because of the rotational offset that has not been accounted for. On the
other hand, a rotational offset allows the freedom to
mount a frame in a better position for soft tissue dearance or patient comfort. An external rotational offset of
90° in a proximal femoral two-thirds ring allows clearance for the opposite thigh and perineal area. This same
construct with a distal reference will result in a 60° external rotational frame offset due to the position of the distal anti-master tab (~ Fig. 12-7).

rotational offset
= goo

/

Distal reference
imaginary
anti-master tab

External
rotalienal offset
=

......

60°

_______ _
oo
Patella torward

Fig. 12-7

An external rotational offset of 90° in a proximal femoral twothirds ring allows clearance for soft tissues. The same construct
with a distal reference will result in a 60° external rotational
frame offset due to the position of the distal (imaginary) antimaster tab. The anti-master tab is imaginary in this construct
because the distal ring is a two-thirds ring.

Modes of Correction

Currently, three program modes of correction can be
accomplished with the Taylor spatial frame: chronic
deformity, residual deformity, and total residual deformity program modes. However, since the advent of the
Total Residual Program, the earlier Chronic and Residual Programs have been used less frequently and are
becoming of academic interest only. In this chapter, we
focus only on the total residual deformity mode.
For the total residual deformity mode, the rings are
applied independently of each other. Ideally, to facilitate
the planning, the reference ring should be applied perpendicular to the long axis of the reference bone seg-

CHAPTER 12 · Six·Axis Deformity Analysis and Correction

a.

IIfl

b.

Axial frame
offset =54 mm
proximal
to origin

I
AP view frame
I
offset = 10 mm __... :

LATERAL

to origin

ment. Nevertheless, the planning can compensate for
nonorthogonal mountings. After the two rings are applied, the six struts are connected to the rings and the
osteotomy is performed at a chosen Ievel. The deformity
is defined for the computer by six deformity parameters:
AP view angulation, LAT view angulation, axial view
angulation (rotation), AP view translation, LAT view

translation, and axial view translation (shortening or
lengthening). The three angulations (rotations) can be
measured independently of the orientation of the reference ring. The three translations are dependent on the
orientation of the reference ring. For orthogonal mountings of the reference ring, the measurement of translation can be made perpendicular to the long axis of the
bone for AP and LAT view translations and along the
long axis of the bone for axial translations. If the reference ring is nonorthogonal, the translations are measured according to a virtual grid of lines parallel and
perpendicular to the reference ring. The mounting parameters define the relationship of a chosen point on the
reference axis (origin) to the center of the reference ring.
These mounting parameters include offset of the center
of the reference ring from the origin in the anteroposterior and lateral planes, axial offset of the reference ring
from the origin, and rotational offset of the reference
ring to the anatomic or designated neutral rotation
(usually patella forward). The position of the corresponding or moving ring is defined by entering the moving ring size and strut length data into the computer. The
moving ring does not need to be perpendicular to the
long axis of the moving segment.
During surgery, the appropriate ring size (diameter)
and type (full, two-thirds, foot, etc.) are chosen for the
proximal and distal rings. Six struts that can connect the
two rings are attached between the two rings. The ring
size and type and the type and length of struts chosen
represent the frame parameters.

Fig. 12-Sa,b

The mounting parameters are influenced by the orientation of
the reference ring. The orange dots represent the center of the
reference ring. The green dots represent the corresponding
point.
a An orthogonal reference ring to the proximal hone axis
allows for easy determination of the mounting parameters.

b A non-orthogonal reference ring tilts the virtual grid and
significantly changes the AP frame offset.

To permit gradual correction of the deformity, the
computer prepares a schedule of correction based on the
rate of correction desired. The desired rate of correction
can be chosen arbitrarily or according to a predetermined rate at a chosen structure at risk (SAR). Orthogonal reference ring placement facilitates planning by
making the mounting parameter reference lines parallel
and perpendicular to the reference bone axis line. As
long as one is prepared to adjust the planning to a
nonorthogonal position of the reference ring, no difference in the ability of the computer to calculate a deformity correction solution is encountered (..,.. Fig. 12-8).
The recent advent of digital planning software (Spatial CAD; Orthocrat Ltd., Tel Aviv, Israel) automatically
takes the orientation of the reference ring into consideration, making planning with an orthogonal reference
ring as simple as with a nonorthogonal reference ring.
We prefer placing the reference ring as orthogonal as
possible for ease of non-digital planning. This might,
however, be a vestige of our bias based on extensive
experience with the Ilizarov device, with which orthogonal ring placement is critical.


1111

CHAPTER 12 · Six-Axis Deformity Analysis and Correction

Planning Methods

J. Charles Taylor developed the origin-corresponding
point method of planning (also called the fracture
method). It permits characterization of the deformity
and mounting parameters relative to two points in

space: the origin and its corresponding point. John E.
Herzenberg and Dror Paley simplified this method by
relating it to the CORA, coincidentally and conveniently
renaming these methods the CORAgin and CORAsponding point methods. Shawn C. Standard added the
virtual hinge method of planning. The most recent planning method developed by J. Charles Taylor is termed
the line of closest approach (LOCA). The LOCA is a
method of determining the location of osteotomy that
minimizes translation during the deformity correction.
The five methods of planning are as follows: ( 1) fracture method, (2) CORAgin method, {3) CORAsponding
point method, {4) virtual hinge method, and (5) LOCA.
With the fracture method, the surgeon chooses both the
origin and corresponding points as points on opposite
sides of the fracture. These designated points should
represent congruent points of the opposing fractured
fragments. With the CORAgin method, the surgeon
chooses the origin at the CORA and then finds the

Fig.12-9

Fracture method: two corresponding points (CP) on opposite
sides of the fracture (e. g., at the ends of a recognizable spike
and corresponding negative of the spike) are chosen as the origin and corresponding point.

corresponding point. With the CORAsponding point
method, the surgeon chooses the corresponding point
first, at a CORA, and then finds the origin. With the virtual hinge method, both the origin and corresponding
points are located at a CORA, on the convex edge of the
bone.

Fracture Method

The fracture method brings two points in space (origin
and corresponding point) to the same location. This
method can be likened to docking a mobile object to a
stationary object in space. The fracture method is the
simplest method to learn.
Two corresponding points on opposite sides of the
fracture (e.g., at the ends of a recognizable spike and corresponding negative of the spike) are chosen as the ori-


CHAPTER 12 · Six-Axis Deformity Analysis and Correction
LAT view frame offsei

AP view frame offsei

posterior
to origin

Master Iab
oarotation

=

ß

Axial frame offset

Frame
proximal
to origin

Rolary frame offsei - - - - - - - - - ,
Mastertab
=30° rotation

Fig.12-10

The mounting parameters are calculated by determining the
position of the origin with respect to the center of the reference
ring. It is important to note that the mounting parameters are
always measured as perpendicular distances from the reference ring.

gin and corresponding point (JII> Fig. 12-9). The origin is
defined as the point on the reference fragment, and the
corresponding point is defined as the point on the moving segment. The deformity parameters are determined
by calculating the angulation in the coronal and sagittal
planes (from the midaxillary lines of the fragments), by
measuring the displacement or translation between the
origin and corresponding points (in the anteroposterior,
lateral, and axial planes), and by estimating the rotation
deformity based on clinical examination. The mounting
parameters are calculated by determining the position
of the origin with respect to the center of the reference
ring (JII> Fig. 12-10). Once these parameters are determined, the strut settings areentered into the Total Residual Program and the correction schedule is generated.
The new strut settings are gradually dialed into position
and the fracture deformity reduced (JII> Fig. 12-11).


B

CHAPTER 12 · Six·Axis Deformity Analysisand Correction

Fig.12·11
Once all the deformity, frame, and mounting parameters are
determined and entered into the Total Residual Program, the
struts are dialed to the new settings and the fracture deformity
is reduced. An important clinical strategy is to leave the fracture shortened and aligned. This reduces swelling, compartment pressures, and pain. Acute reductions with distraction
should be avoided. The spatial frame schedule will provide
gradual reduction that is weil tolerated by the patient.

CORAgin Method

In Situations in which no acute fracture with identifiable
bone ends that correspond to each other is present, the
fracture method cannot be used. Such deformities are
called chronic deformities and include congenital, developmental, and posttraumatic residual (nonunion, malunion) deformities. With the CORAgin method, the origin is chosen to be the CORA, and the corresponding
point is determined by using locallength analysis or by
adding extrinsic length data (e.g., limb length discrepancy data per radiograph; ~ Fig. 12-12). Local length
analysis is used when the desired correction is a pure
neutral wedge. This analysis permits calculation of the
amount of shortening that is present because of the

Fig.12·12
With the CORAgin method, the origin is assigned to the CORA.


CHAPTER 12 · Six-Axis Deformity Analysis and Correction

a.

IDII

c.

b.

AP view translation

111(

W = 13 mm

deformity. The amount is added to determine the location of the corresponding point. When limb length discrepancy data are chosen instead, this extrinsic information is added in the same manner that the local
length analysis adds length along the reference axis line.
Locallength analysis is conducted by measuring the
distance from the CORA to the convex surface of the
deformity (W line). This line segment, W, is then projected from the moving fragment's axis at a 90° angle
(..,.. Fig. 12-13a). The projected W line is then translated
down the moving fragment's axis until it contacts the
original W line. The point on the moving fragment's axis
at which the projected W line is contacting the original
W line is assigned to be the corresponding point. The
deformity parameters, especially the coronal, sagittal,
and axial plane translations, can then be determined
(..,.. Fig. 12-13 b,c}. The corresponding point in the sagittal plane is determined from the axial translation calculated from the coronal plane. In the sagittal plane, starting at the same level as the coronal CORAgin, the distance of the axial translation is measured on the proximal reference axis and a perpendicular line (line s) is
drawn. This marks the level of the corresponding point
in the sagittal plane. The point of intersection of the line
s and the moving axis is the corresponding point in the
sagittal plane(..,.. Fig. 12-13d).
An alternate way of determining the corresponding

point is by assigning a certain amount of length needed
during deformity correction. The amount of length
needed is determined by the amount of planned lengthening based on the safe limits of lengthening and the
limb length discrepancy. This is considered extrinsic
information because it is not inherently obvious from
the radiograph of the deformed bone. To factor in shortening of the bone with deformity correction, the amount
of shortening is added on the moving segment axis line
in a direction toward the reference fragment. In the
example shown (..,.. Fig. 12-14a), the shortening of the
moving segment is 20 mm. By marking the corresponding point as shown, it is as if the moving segment were

LAT

4 mm lateral
tra nslation

_!

7 mm axial

-__-ft

Fig.12-lla-d

a Local length analysis is conducted by measuring the dis-

tance from the CORA to the convex surface of the deformity
(W line). This line segment, W, is then projected from the
moving fragment's axis at a 90° angle.
b The projected W line is then translated down the moving

fragment's axis until it contacts the original W line. The
point on the moving fragment axis at which the projected W
line contacts the original W line is assigned the corresponding point (CP).
c The deformity parameters, especially the coronal, sagittal,
and axial plane translations, can then be determined.
d The corresponding point in the sagittal plane is determined
from the axial translation calculated from the coronal plane.
In the sagittal plane, starting at the same Ievel as the coronal
CORAgin, the distance of the axial translation is measured
on the proximal reference axis and a perpendicular line
(Line s) is drawn. The point of intersection of the Line s and
the moving axis is the corresponding point in the sagittal
plane.

7 mm axial
translation


m

CHAPTER 12 · Six-Axis Deformity Analysisand Correction

a.

b.

CP

l

17 mm
short

20mm

ot lengthen i n~

~~~

~~~ ~--------~--~~----~

Fig.12·14a,b

a The extrinsic information has determined that the shortening of the moving segment is 20 mm. By marking the corresponding point (CP) as shown, it is as if the moving segment
were 20 mm longer and shortened relative to the reference
segment.
b When entering the amount of axial translation, one has to
measure the distance of the perpendicular line from the reference line to the corresponding point to the origin. This will
be less than 20 mm.

20 mm Ionger and shortened relative to the reference
segment. When entering the amount of axial translation,
one has to measure the distance of the perpendicular
from the reference line to the corresponding point to the
origin. This will be less than 20 mm (.,. Fig. 12-14b).

CORAsponding Point Method

With the CORAsponding point method, the corresponding point is chosen first and is assigned tobe at the
CORA instead of the origin. This places the corresponding point on the reference line because the CORA is the

one point at which both the corresponding point and the
origin are on the reference line. This method is espe-

cially useful when extrinsic length needs to be added.
The length is added on the reference line by moving the
origin along the reference line toward the corresponding
fragment. This is referred to as the extrinsic origin
(.,. Fig. 12-15). One of the advantages of this method is
that it eliminates anteroposterior and lateral translation
deformity parameters. The one downside is that it
increases the distance of the origin to the reference ring,
increasing the axial frame offset. This becomes significant only if a large unaccounted for magnification error
is present. The extrinsic origin is still a reproducible
point in space because its distance from the CORAsponding point is known. The mounting parameters are
based on the position of the extrinsic origin relative to
the center of the reference ring (.,. Fig. 12-16).
With the deformity and mounting parameters
entered into the Total Residual Program, a correction
schedule can be generated and the deformity corrected.
Even with the CORAsponding point method of planning, some deformities include true translational deformities. These deformities must be taken into account
and entered into the deformity parameters. With careful
planning, these translational deformities will become
obvious, as in the example shown (.,. Fig. 12-17). Also,
another subtle sign of underlying translational deformity is a CORA point that is at different Ievels in the
coronal and sagittal planes. A CORA at different Ievels
signifies angulation and translation in different planes.


CHAPTER 12 · Six-Axis Deformity Analysis and Correction

EI

CORAsponamg po1n
\~~~------ EO ------~~·

AP

LAT

Fig. 12·15
The CORAsponding point is assigned to the CORA. This places
the CORAsponding point on the reference axis line, which
appears as a red Une in the figure. The CORA is the one point
that allows the CORAsponding point and the origin tobe positioned on the reference axis line. This method is especially useful when extrinsic length needs to be added. The length is

Axial frame offsei

added on the reference axis line by moving the origin along
the reference line toward the moving fragment. This can be
referred to as the extrinsic origin (EO). One of the advantages
of this method is that it eliminates anteroposterior and lateral
translation deformity parameters, provided the reference ring
is mounted orthogonally.

= posterior to EO

= proximal to EO

AP frame offsei
= Omm

AP

LAT

Fig. 12·16
The mounting parameters are based on the position of the extrinsic origin (EO) in relation to the center of the reference ring.


111

CHAPTER 12 · Six-Axis Deformity Analysis and Correction
a.
b.

I
AP

Fig. 12-17 a, b

True translational deformities will be encountered even with
the CORAsponding method of planning. With careful deformity analysis, these true translational deformities will be identified. EO, extrinsic origin.
a An example of a tibial malunion with varus and posterior
translational deformity is shown. Careful analysis of both
planes easily demonstrates the translational deformity.
Another subtle sign of underlying translational deformity is
a CORA point that is at different Ievels in the coronal and
sagittal planes.
b Detailed LAT view.

LAT

Virtual Hinge Method

The virtual hinge method places the origin and corresponding point at the same location in space. By placing
both the origin and corresponding point at the same
location, a virtual axis of rotational correction - or virtual hinge - is created. The ideal position of a virtual
hinge is at the CORA. The CORA at the intersection of
the proximal and distal midaxillary lines can be chosen,
or any other CORA point that lies along the transverse
bisector can be designated the virtual axis of rotational
correction point (~ Fig. 12-18).
This planning strategy has several advantages. By
placing the origin and corresponding point at the same
location, all translational deformities are eliminated.
Next, the virtual hinge can be used to create a pure opening wedge osteotomy when placed on the transverse
bisector line at the convex surface of the bone deformity
(~ Figs. 12-19 and 12-20).
The virtual hinge can also be placed at the center of
rotation of the knee or ankle joint. This allows the joint
to be rotated about its normal axis of rotation. The Taylor spatial frame can first be used to distract a joint with
subsequent rotation ab out the virtual hinge.
When planning Taylor spatial frame correction using
the virtual hinge method, certain concepts must be kept
in mind. First, when adding length with this method,
the planning becomes the CORAgin method. Second, if


CHAPTER 12 · Six·AxisDeformityAnalysisandCorrection

m

tBL

;J
CO~
.. o···

.o··

tBL

'(

.o··

Fig. 12·18
The CORA at the intersection of the proximal and distal
midaxillary lines can be chosen, or any other CORA point that
lies along the transverse bisector line (tBL) can be designated
the virtual axis of rotational correction point.

a.

___ _

Fig.12.19
The virtual hinge can be used to create a pure opening wedge
osteotomy when placed on the transverse bisector line (tBL) at
the convex surface of the hone deformity.

c.

b.

CP

and origin

the virtual hinge has been placed on the convex cortex
to create an opening wedge, concurrent axial rotation
should not be performed. If rotational correction is
performed about this point, secondary translation will
occur. Therefore, if secondary rotational correction is
needed after an opening wedge is completed, the origin
must be adjusted to the center of the reference fragm ent's axis by changing the mounting parameters.

Fig.12·20a- c
a The origin and corresponding points (CP) are placed at the
same position along the transverse bisector line (tBL) on the
convex surface of the deformed tibia. No translations or axial
rotation deformity parameters are entered into the program.
b The mounting parameters are crucial for this planning
method. The mounting parameters position the virtual
hinge in space. If the mounting parameters are incorrect, the
virtual hinge will be misplaced and secondary translation
will occur.
c The virtual hinge method allows for pure opening wedge
osteotomy correction.

lf1l

CHAPTER 12 • Six-Axis Deformity Analysis and Correction
Line of Closest Approach (LOCA)

LAT

AP

Reference
fragment

Fig.12-21
The first step with the LOCA method is to assign two Ievels in
the coronal and sagittal planes. These two Ievels are arbitrary
but should be reproducible to ensure the same Ievel in both the
coronal and sagittal radiographs. These points should be chosen at the ends of the bone.

Fig.12-22 l'
The translational deformities between the two axis lines are
determined at each of the assigned Ievels and are plotted on a
graph representing the axial plane. The two points on the graph
are connected and represent the deformed fragment in the
axial plane with respect to the reference fragment.

In chronic fracture deformities (nonunion, malunion),
the CORA on the AP view radiograph does not necessarily correspond to the CORA on the LAT view radiograph. This is because angulation and translation are in
different planes. In Chap. 8, we considered various solutions to the level of osteotomy in such cases. One other
solution has been proposed by J. Charles Taylor: to correct the deformity at the level of the LOCA, which is the

level at which the translation between the fragments is
the least.
The LOCA can be determined by a graphic method.
First, two levels are designated in both the anteroposterior and lateral planes (111> Fig. 12-21). Second, the translations between the reference and deformed fragments
are determined at both levels. The two points are plotted
on a graph representing the axial plane (111> Fig. 12-22).
Third, a line is drawn from the reference fragment perpendicular to the deformed fragment on the axial graph.
This line is the LOCA, and the point of intersection of
this line with the deformed fragment is the LOCA point.
The translations of the new LOCA point are determined
and extrapolated to the anteroposterior and lateral
planes. These measurements from the LOCA point to the
reference fragment represent the translational deformity parameters (111> Fig. 12-23 a). The translations of
the new LOCA point are used to determine the level
of osteotomy (111> Fig. 12-23b). The points lying on the
LOCA are the origin and corresponding points. The
translational deformity parameters, along with the
other deformity parameters are now complete and can
be entered into the computer program. If length is
needed, the CORAgin method is used. The correspond-

AP

LAT

9 mm medial

2 mm anterior

APview

I

Level 1 - - - - Point 1

-

Point 1

LAT view

9 mm medial

2 mm anterior

Point 2 15 mm lateral 20 mm posterior
AXIAL VIEW

Anterior

Medial

Anterior

fragment

Level2 ------- - - - -

-+ I+-

Posterior


CHAPTER 12 · Six-Axis Deformity Analysis and Correction

AP

a.

I!JI

LAT
AP view
Point 3

3 mm medial

LATview

3 mm posterior

Anterior

AXIALVIEW
Medial

Point 2

Posterior

Level 2 - - - - - - - -

Deformity parameters
AP view angulation = 14° valgus
LAT view angulation = 8° apex anterior
AP view Iranslaiion = 3 mm medial
LAT view Iransialion = 3 mm posterior
Axial translation = Local length analysis
or extrinsic length data

AP

b.

LAT

...._

.......I

3 mm posterior

3 mm medial

I

AP view
• • • • • • ·- • ·- • • Point 3

3 mm medial

AXIAL VIEW

Anterior

LATview

3 mm posterior
Origin

Osteotomy __
Ievei

er

Osteotomy
• · · Ievei

Anterior

Medial

Lateral --~--:::'""""~•-::~~L----- Medial

Point 2

Level2------ - -

Fig. 12·23a-d
a A line is drawn from the reference fragment perpendicular

to the deformed fragment on the axial graph. This line represents the LOCA. The translations of the new LOCA point
(Point 3) from the reference fragment are measured- in this
example, 3 mm medialand 3 mm posterior. These measurements represent the translational deformity parameters. CP,
corresponding point.

Posterior

b The Ievel of osteotomy can be determined by using the
translations of the new LOCA point. In this example, a point
is placed 3 mm medial to the reference fragment in the
anteroposterior plane and another point 3 mm posterior
in the lateral plane along the designated Ievel 1. Lines are
subtended at 90°, and the point of intersection with the
deformed fragment's axis is the Ievel of osteotomy. Note that
the Ievel of osteotomy is the same in both the anteroposterior and lateral planes.


I!IJ

CHAPTER 12 • Six·Axis Deformity Analysis and Correction

c.

AP view
CP 5 mm medial

d.

LAT view
0 mm

2 cm of lengthening required
AP

LAT

5 mm medial

....,

of Iransialion

No Iransialion

I
Level 1 ------

Osteotomy
Ievei

Fig. 12-23a-d
c In this example, 2 cm of lengthening is desired. The new
deformity translation parameters are determined and
entered into the computer program.
d Correction after 2 cm of lengthening was performed.

Left AP view

Left LAT view

Left axial view

ing point is translated along the moving segment's axis
from the LOCA level to the point of desired lengthening
(~ Fig. 12-23c,d). Interestingly, the spatial frame program can be used to create the axial LOCA diagram
(~ Fig. 12-24). Also, the LOCA diagram can be used to
Medial Lateral
Medial
Posterior Anterior
Lateral
determine the magnitude of the oblique plane deformity (~ Fig. 12-25).
Most posttraumatic deformities can be defi.ned by
Moving
fragment
using the LOCA. In essence, the CORA is a special case
of a LOCA with the length of the LOCA equaling 0. However, when translational and angular deformities place
the CORA at different levels in the coronal and sagittal
planes, the LOCA is the level at which the origin and corFig.12-24
responding points are the closest, as stated above. The
By entering the angulation data from the same example into end points of the LOCA comprise one possible pair of
the Taylor spatial frame web-based program, a schematic dia- origin and corresponding points. Therefore, by defi.ning
gram of the deformity can be generated. The axial view is the the level of the LOCA, the origin can be placed on the refdiagram that was produced with the LOCA graphic method.
erence fragment at that level. If the osteotomy is chosen
at the level of the LOCA, the amount of translation correction is minimized. If length is needed, the corresponding point is translated along the moving fragment's axis and the CORAgin method is used.
Reference
fragment

\

CHAPTER 12 · Six-Axis Deformity Analysis and Correction ~~~

\.

\.

\.

\.

\.

h= Distance
between
\. Levels 1 and 2
\.

\.

\.

\.

h
\

\.

\.

e = Oblique plane

angulation of the
deformity = 37°

\.

,,.-.
\.
',

e

Fig.12-2S

The oblique plane angulation is calculated by forming a triangle. The height of the triangle equals the distance between the two
designated Ievels. The base of the triangle equals the length of the deformed fragment in the axial plane graph. The triangle is
completed by drawing a hypotenuse and the angle measured (angle 9). The angle equals the oblique plane angular deformity.

Taylor Computer-assisted Design (CAD) Software

A CAD program for Taylor spatial frame planning was
recently developed by Orthocrat Ltd. (Tel Aviv, Israel).
This program allows for detailed and accurate deformity
and mounting parameter analysis using digital radiographic images. The information can be uploaded to
the Taylor spatial frameweb site to generate a deformity
correction schedule. The CAD program also allows for
manipulation of the digital images for preoperative
"paper doll" planning. A complete description and
demo version can be found at www.ortho-crat.com.

AP view

Reference Concepts

During the planning of a Taylor spatial frame correction, the surgeon decides on the reference fragment and
reference ring. The reference ring is critical when determining the mounting parameters and when positioning
the frame in space as it relates to the designated origin.
The translational mounting parameters relate to the
center of the reference ring. The rotational mounting
parameter relates to the master tab for proximal reference cases and the anti-master tab for distal reference
cases. The decision for proximal or distal referencing is
based on certain standard concepts. The juxta-articular
ring usually is the reference ring. The most orthogonal
ring may also be a good choice for referencing. The decision for distal referencing creates a problern of perspective for orthopaedic surgeons. Orthopaedic surgeons are
trained to describe deformities from a proximally based
perspective. However, with distal referencing, this per-

LATview

Proximal reference
o Lateral translation
• Varus angulalion
o Axial shortening

Proximal reference
• Posterior Iranslaiion
• Procurvatum angulation
• Axial shortening

Distal reference
o Medial Iransialion
o Varus angulation
o Axial shortening

Distal reference
• Anterior translation
• Procurvatum angulation
o Axial shortening

Fig. 12-26

With distal referencing, the standard orthopaedic perspective
is reversed, resulting in opposite translational deformity descriptions. When the same deformity is characterized from two
different perspectives, different descriptions occur. This is
termed parallactic homologues. The example shows a distal tibial fracture that is displaced in a posterolateral direction. This
deformity would be described differently from a distal reference perspective. If the distal tibia and foot were looking at the
rest of the body (a distal perspective), the foot would describe
the body as being both anterior and medial. Therefore, a distal
reference would describe these translational deformities as a
medial translation in the coronal plane and an anterior translation in the sagittal plane. Angulation, rotation, and axial
translation deformities are unaltered by distal referencing.


m

CHAPTER 12 · Six-AxisDeformi~AnalysisandCorrection

spective is reversed, resulting in opposite translational
deformity descriptions. When the same deformity is

characterized from two different perspectives, different
descriptions occur. This is termed parallactic homologues and is discussed in further detail later in the
chapter. For example, a distal tibial fracture that is displaced in a posterolateral direction will be described differently from a distal reference perspective. Using this
example, if the distal tibia and foot were looking at the
rest of the body, the foot would describe the body as
being both anterior and medial. Therefore, a distal reference would describe these translational deformities as
a medial translation in the coronal plane and an anterior
translation in the sagittal plane. Angulation, rotation,
and axial translation deformity parameters are unaltered by distal referencing (..,. Fig. 12-26).

Rate of Correction and Structure at Risk (SAR)

As with the Ilizarov system, the rate of correction is
based on the biology of distraction of the bone and
soft tissues. With the spatial frame, this analysis can
be taken to a more sophisticated Ievel. The surgeon has
the opportunity to determine the SAR and the rate of
distraction of the SAR. The SAR might be the concave
side of the bone on the osteotomy line or the peroneal
nerve at the neck of the fibula, for example. With the
Ilizarov method, we approximated the ideal correction
rate so that the SAR would not distract faster than 1 mm
per day. This calculation was based on the arc length (arc
length = 2nnx/360, where a is the magnitude of angula-

Fig.12-27a-g
Mai-nonunion of the tibia and fibula in a 55-year-old male
patient.
a AP view of tibia, orthogonal to knee forward. The varus
deformity measures 44°.

b AP view of tibia, orthogonal to ankle forward. The varus
deformity measures 41°. The CORA is at a Ievel different
from that shown in a.
c LAT view of tibia, orthogonal to knee forward. The procurvatum deformity measures 25°.
d LAT view of tibia, orthogonal to ankle forward. The procurvatum deformity measures 20°.

tion). Are length probably overestimates the amount of
lengthening occurring at the SAR. The shortest length or
chord length between the SAR in the deformed state and
the normal state is calculated by using the following formula: chord length = 2rsina/2. These calculations are
adequate when only the three rotations are considered.
When displacement of the bone segments will occur, the
totallinear displacement also should be considered: displacement = V(anteroposterior translation)2 + (lateral
translation)2 + (axial translation)2. With the spatial
frame calculations, the computer considers the SAR
parameters and then determines the nurober of days of
correction. It will also generate an adjustment schedule
for the patient, from the start position to the end position of the frame. The designation of the SAR is not
mandatory. The surgeon has the option of determining
the rate of deformity correction by entering the desired
distraction rate or the nurober of days over which the
correction will be achieved. Three clinical examples of
the use of the spatial frame are shown in ..,. Figs. 12-27
and 12-28.


CHAPTER 12 · Six·Axis Deformi!Y Analysis and Corrertion

Fig. 12·27 a-g

e AP view of tibia with a pre-constructed spatial frame
mounted. The proximal segment was used as the reference fragment.
f AP view of final correction. The complex tibial deformity
was corrected, but the nonunion was not fully healed. It
was therefore treated by intramedullary nailing, as shown
in Fig. 8-18.
g LAT view of final correction.

Fig. 12·28a- l

a AP view of tibial varus and rotational malunion with concurrent distal femoral valgus deformity.
b Clinical photograph of thigh-foot axis viewed from foot end.
c Preoperative AP view radiograph.


111

CHAPTER 12 · Six-AxisDeformi~AnalysisandCorrection

Fig. 12-28a-l

d Preoperative LAT view radiograph.
e Long standing AP view radiograph.
f Clinical AP photograph of tibial correction and simultaneous six-axis deformity correction using the Taylor spatial
frame.
g AP view radiograph shows the correction.
h Long standing AP view radiograph shows the correction.

AP view radiograph shows fixator-assisted nailing of the distal femoral valgus deformity. Note that the mechanical axis
is properly aligned.

j LAT view radiograph shows results.
k Clinical photograph of the thigh-foot axis viewed from the
foot end shows results afterfemoral and tibial correction.
I Clinical photograph shows final correction.


Parallactic Homologues of Deformity:
Proximal versus Distal Reference Perspective

In previous chapters we considered the projection of
angulation, translation, and rotation independently of
each other. However, projective geometry is not so simple (Kline 1955). Taylor has observed that the six-axis
deformity parameters viewed from one reference perspective differ from those seen from another reference
perspective (Taylor 2004). In the example of a tibial
deformity, the deformity parameters viewed relative to
the anatomic frontal, sagittal, and axial planes of the
knee differ from those seen relative to the anatomic
frontal, sagittal, and axial planes of the ankle. Both the
proximal and the distally referenced deformity parameters accurately describe the same deformity. The key is
that both sets of parameters are referenced to different
coordinate planes. Taylor calls these parallactic homologues. The amount and even direction of the different
rotations and translations can differ when viewed from
different perspectives (~ Figs. 12-29 and 12-30).
From a practical standpoint, it is important to keep
the reference segment in mind when evaluating and
operating on a deformity. For example, the tibial deformity associated with Blount's disease usually is described as varus, procurvatum, and internal rotation of
the distal segment relative to the proximal segment. The
magnitude of these deformities will differ if viewed relative to the knee or relative to the ankle. The dinical
examination of rotation, AP and LAT view radiography,
and surgery all should be performed from the same perspective, namely the perspective of the reference fragment. The thigh-foot axis of tibial torsion should be

measured from the knee looking toward the foot. If one
were to measure the torsion from the foot looking
toward the knee, one would measure a different amount
of tibial torsion. If computed tomographic scans are
used to assess rotation deformity, they should be
obtained perpendicular to the knee segment. The radiographs should be obtained as AP and LAT views of the
knee to include the tibia. When operating in such a case,
the knee forward position should be the reference of the
leg during surgery. For distal deformities, a distal reference segment is preferred. For proximal deformities, a
proximal reference segment is preferred. Fora distal tibial deformity, the thigh-foot axis is measured prone and
a computed tomographic scan should be obtained perpendicular to the distal segment and not the proximal
segment. The radiographs should be AP and LAT views
of the ankle to include the tibia. The deformity seen
from the ankle is the parallactic homologue of the deformity seen from the knee (~ Fig. l2-30e,f).
This concept is relevant to surgery irrespective of the
correction method used. For example, if one is using a
circular external fixator, such as the Ilizarov or spatial
frames, the frame must be preconstructed and applied
to the limb relative to the reference perspective used for
the evaluation of the deformity. If the radiographs are
obtained from a proximal segment reference perspective but the frame is applied from a distal reference perspective, the magnitude and sometimes even the direction of the deformity parameters will be different from
those built into the frame. The frame will seem not to
match the deformity of the leg. If using a monolateral
external fixator, this problern is addressed by inserting
the proximal pins relative to the reference planes of the


Fig. 12-30a-f ...
Clinical example of parallactic homologues in a case of proximal tibial deformity associated with congenital pseudarthrosis

of the tibia. The deformity parameters measured from the knee
reference perspective are different from those measured from
the ankle reference perspective.
a AP view radiograph of the lower limb obtained perpendicular to the distal segment. The magnitude of angulation measures 13° valgus.
b AP view radiograph of the tibia obtained perpendicular to
the proximal segment. The magnitude of angulation measures 1oo valgus.
c LAT view radiograph of the tibia obtained perpendicular to
the distal segment. The magnitude of angulation measures
43° recurvatum.
d LAT view radiograph of the tibia obtained perpendicular to
the proximal segment. The magnitude of angulation measures 52° recurvatum.

Fig.12-29a b

a Projectional difference in measurements caused by different
reference perspectives. The two different representations of
the deformity are called parallactic homologues. In the AP
view relative to the knee forward reference segment (vertical
left), the model of the left tibia appears to have 4.75° of varus.
In the AP view relative to the foot forward reference segment
( vertical right), the model of the tibia appears to have 5.5° of
valgus. In the LAT view relative to the knee forward reference
segment (horizontal top), the model tibia shows 33.5° of
extension. In the LAT view relative to the foot forward reference segment (horizontal bottom), the model tibia shows
33.0° of extension.
b Tibial model showing clinical measurement of rotation from
foot to knee (left limb) and from knee to foot. The foot-toknee measurement shows 21.5° of internal rotation. The
knee-to-foot measurement shows 22° of internal rotation.

proximal segment and the distal pins relative to the reference planes of the distal segment. For example, to

insert the proximal pins, the knee is oriented forward
and the pins are inserted in the frontal plane of the knee,
either perpendicular to the tibial shaft proximal to the
CORA or approximately 3° to the knee joint line. For the
distal pins, the ankle is oriented forward and the pins are
inserted in the frontal plane of the ankle, perpendicular
to the shaft of the tibia distal to the CORA or parallel to
the ankle joint line. After the osteotomy is made, the pins
are brought parallel to each other. This method takes
into consideration the reference coordinates ofboth the
proximal and distal ends.
With internal fixation using closing wedge osteotomies, a similar approach can be used by making each
bone cut perpendicular to its respective bone segment
in the same manner in which the half-pins were inserted
perpendicular to their bone segment in the previous
example. When an oblique plane closing wedge osteotomy is planned, it is essential to obtain the radiographs
from one perspective and to reference the oblique plane
wedge with reference to the same perspective. If angulation is eliminated by osteotomy and only axial rotation
remains, no difference exists in the amount of rotation
measured from the proximal or the distal end. In other
words, the parallactic homologues of rotation deformity
in the absence of angulation are the same as seen from


CHAPTER 12 · Six-Axis Deformity Analysis and Correction

m