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A quantitative method of assessing malalignment and joint space loss of the human knee
A QUANTITATIVE METHOD OF ASSESSING MALALIGNMENT AND JOINT SPACELOSSOF THE HUMAN KNEE H.W.
Wevers*,
D.W.
Siu+ and T.D.V. Cooke*
ABSTRACT Malalignment
and joint
space
loss in the arthritic
human
knee can be measured quantitatively by employing a frame that allows for parallax correction of radiographs taken from the weight bearing lower limb. This standardized method will assist pre-operative planning for osteotomies and postoperative follow-up of patients with surgically re-aligned
Keywords:
lower limbs. The procedure requires anatomically important points to be digitized, together with reference points built into the frame. Data are then processed automatically in a desk top computer, and the program provides for an easily understood diagram and listing of charactertitic indices of malalignment.
Skeletal system, radiograph, knee joint malalignments, osteomy, arthritis, parallax
INTRODUCTION
problems
Malalignment and joint space loss are common prob!ems in the arthritic knee. Varus (bow legged) and valgus (knock kneed) deformities may result from a variety of mechanisms acting singly or in combination. For example, rickets may result in a localized femoro-tibia1 deformity and obliquity of the joint resulting in valgus of the distal femur co-existing with tibia vara, and an inward medially sloping joint, Figure 1. More typical to osteoarthritis (OA) is the medial joint compartment degradation that occurs more rapidly on this side than on the lateral side’) 2. The loaded joint then shows a relative varus of the femur with tibia vara that is due to greater loss of cartilage of the medial femoral condyle and the plateau, Figure lc.
assessment of the deformity and accurate surgical techniques7. At present an anterior-posterior (A-P) weight bearing radiograph of the knee is generally used to provide an estimate of the knee varus/valgus deformity. It has been demonstrated that a knee joint at rest may have a normal alignment, yet weight bearing may show serious angular deformity, hence the need for frequent use of weight bearing radiographs.
In rheumatoid arthritis (RA) the loss of cartilage is more uniform. Deformity may be varus or valgus but usually tends toward the physiological shape present before the onset of arthritis. Patients with pain and deformity, unresponsive to conservative measures, are potential candidates for orthopaedic joint reconstruction. The principles involved in their surgical care depend on the cause. Osteoarthritis has had a high degree of successful treatment by bone realignment (osteotomy)3’ 4 and this has resulted in improvement of arthritic malalignment. In RA, osteotomy alone is seldom of lasting benefit ‘. Articular resurfacing, however, relieves pain, may be used to correct deformity and appears to lessen the local incidence of disease recurrence6. An optimal surgical solution to these *Department of Mechanical Engineering iDepartment of Mechanical Engineering, department of Surgery, Division of Orthopaedics, Queen’s University at Kingston, Ontario, K7L 3N6.
0141-5426/82/040319-06 $03.00 0 1982 Butterworth & Co. (Publishers) Ltd
depends upon a precise pre-operative
The medical radiographic criteria most commonly used for the assessment of femorotibial an ular deformity are those described by Ahlback B . A straight line is drawn through the tibial shaft to intersect a corresponding line drawn through the femoral shaft. The angle between these two lines is measured, (see Figures I and 2). In the normal person this coronal alignment between the femur and tibia with the knee extended is not normally a straight line. Depending upon body habitus, limb length and pelvic width, a coronal alignment or physiological valgus angle of between 0 and 10” may exist. The definition of a normal femorotibia1 alignment angle for a given patient is thus dependent upon anatomical variables. Optimally, this results in a horizontal joint with a straight line passing from the hip through the centre of the knee and ankle. The coronal alignment angle is not suitable for the objective assessment of leg alignment. Assessment of alignment is furthermore distorted by parallax factors and by malposition of the patient with respect to the X-ray film and of the X-ray source. These may each introduce significant errors into the measurements. Determination of the overall deformity expressed by assessment of the several contributing mechanisms becomes therefore even more difficult.
J. Biomed. Eng. 1982, Vol. 4, October 319
Malah’gnment and joint space toss in the knee: H. W. Wevers et al. LOAD
a
BEARING
AXIS
b
C.
Figure 1 Examples of malalignment and joint deformation. Normal leg (a) and (b); dysplasia (c) and osteoarthritis (d).
The purpose of this paper is to describe an accurate method of determining quantitatively the joint space loss and malalignment which may combine to produce the lower limb deformity. This method, shown in Figure 3, requires the following variables: joint separation angle (v, tibia1 translocation angle (XT, transtibial angIe lSr femoral translocation angle c+, transcondylar angle &, lateral and medial joint space loss (b - CZ).To determine accurately these angles and the joint space loss, correction of the radiographic data for parallax must be made and standardization of the positions of patient, film and X-ray source undertaken. We describe the methods currently used for this correction. Digitization of the X-ray marker points and computer processing of the data result in a tabular output and a graphical display of the clinically relevant data.
ankle pad and the marker on the hip pad ensure that the ankle and the hip are vertical with respect to one another. The patient’s weight-bearing limb may be flexed due to malalignment, but this amounts to a secondary effect and does not influence the measurements significantly if flexion is < 25”, as is shown in the calibration of the instrument. The X-ray film is mounted vertically, first behind the hip and then the knee. The front of the frame has radiopaque ‘reference lines’ made up of steel balls mounted in a plexi-glass sub-frame. A ‘calibration ring’ and ‘calibration point’ establish a ‘calibration axis’ which is normal to the film surface. These are shown in detail in Figures 4 and 5. When the radiograph is taken, these radiopaque markers are projected onto the radiograph, digitized and processed to correct for parallax and X-ray source misalignment. Figure 6 illustrates, in the vertical or sagittal plane (y - z plane), images of the calibration ring, calibration point and one of several anatomical points. The real positions along the z axis of the X-ray source Z,, calibration ring 2~ (with diameter 4~ ), calibration point Zp and the anatomical point &, are also shown. By digitizing the calibration ring (diameter &y) on the film, the X-ray source distance 2s can be calculated [equation (l), Figure 71 and checked with the value measured during testing. For this calculation, triangles with ‘X-ray source’ at the top and $R and $y at the base are used. The distance 2s is further utilized for the correction of parallax of the anatomical features on the radiograph [equations (II) and (III)] . Equation (III) was derived using the vertically hatched triangle for calculating the first part of the equation representing the distance cu. The second part of the equation is derived using similar triangles within the horizontally hatched set and multiplying this with a ratio derived from the dotted set, yielding distance ab. The real and
FEMUR LONG AXIS
WEIGHT BEARING RADIOGRAPH To assess objectively knee malaligmnent, a standardization of the radiograph is achieved with a ‘standard knee radiograph frame’, as shown in Figure 4. The frame positions the patient’s lower limb in a true anterior-posterior (A-P) position, using the anterior-superior iliac spines (ASIS) to align the pelvis, by pointing the patella forward and placing each lateral malleolus against an ankle block. The ASIS pads can be adjusted vertically and horizontally to each patient’s anatomy. With the patient’s pelvis now oriented in a vertical plane, side to side fixation of the pelvis is achieved by positioning of the adjustable hip pads. The greater trochanter of the femur is positioned at a fixed distance from the plane of the X-ray film cassette by aligning with a marker on the hip pads. The lower limb is further positioned by aligning the lateral malleolus with an ankle pad fixed onto the floor of the frame. This
320
J. Biomed. Eng. 1982, Vol. 4, October
Figure 2 Coronal alignment angle for assessment of general malalignment according to Ahlback and others. (Redrawn from radiograph of deformed knee).
Malalignment
and joint
space loss in the knee: H. W. Wevers et al.
ASIS
Pad wth
Cassette holder
Width adjus
Htp pod lock
Verttcol adjustment
for knee and hip rodlographs
HIP , pad A-P ahgnment
Caibratlon Reference
IIne Ankle
V
iblock
Figure 4
Standard knee radiograph frame.
Figure 3 Six indices defining malalignment objectively, including the separately contributing deformation mechanisms. (Redrawn from radiograph of a deformed knee).
corrected value for the anatomical point in the yz coordinate system is : Yi‘=ab +ca Similarly equation II can be derived in the xz or transverse plane. Note that all marker points on the radiograph are digitized with respect to the calibration point image yp, while the anatomical point is defined in the xyz coordinate system. In Figure 6, Ay; is the error in position of the anatomical point on the radiograph. The reference line of Figure 4, also shown on the radiograph in Figure 8, is mathematically transformed into a biomechanical load bearing axis through the hip and the ankle. To do this a hip radiograph of the patient aligned in the standard knee radiograph frame is necessary in addition to a knee radiograph. This hip X-ray will show the reference line with respect to the head of the femur. The calibration point and calibration ring and their images on this hip radiograph, enable correction for parallax and then transformation of the reference
Figure 5 Detail of calibration ring (a) and calibration point (b) Radiopaque steel balls embedded in a plexiglass frame with known distances from radiograph.
line to the load bearing axis. This latter axis is mathematically offset from the reference line, and positioned through the head of the femur. Similarly the offset is calculated at the knee. In this procedure the ankle pad is assumed to position the ankle sufficiently precisely so that the reference line, which is half a hypothetical average ankle width inside from the ankle pad, goes through the centre of the patient’s ankle. Statistical deviations from this average ankle width are of negligible influence on the calculation of the six knee deformity variables.
J. Biomed. Eng. 1982, Vol. 4, October
321
Malulignment
and joint space loss in the knee: H. W. Wevers et al.
Table 1 The six indices of malalignment, are the digitized and corrected values
numbers in brackets are pre-set and measured values; the first column of each case
Index no. Joint separation angle Tibial translocation angle Tram-tibia1 angle Femoral translocation angle Tram-condylar angle Medial joint space loss
1 2 3 5 6 4
Case 1 -0.0 6.3 82.8 5.3 92.9 0.1
Flexion angle
Case 2 3.6 6.8 82.6 5.7 95.7 2.7
(6.6) (7.6) (83) (6.4) $1
Case 3
(5.5) (6.9) (83) (5.8) ‘;$ 9
25
-2.5 3.0 84.8 2.6 94.5 -1.7
(-2.8) (3.3) (83) (2.8) I”:/ 11
y-AXIS
(VERTICAL)
ANATOMICAL
POINT
(HORIZONTAL)
LIBRATION
R
Figure 6 X-ray source, calibration ring and point, anatomical point and images on X-ray film; y: is corrected value of the y coordinate of the anatomical point; yi is the error due to parallax and misalignment of X-ray source
RESULTS The standard knee radiograph frame performance was validated by positioning a skeletal lower limb in a precisely known configuration in the frame, simulating three different flexion angles. Joint space loss was preset by spacers with radiopaque markers provided for calibration. After taking radiographs shown in Figure 8, the pertinent anatomical features and the radiopaque markers were digitized and processed with the help of a desk top computer. The results are shown in Table 1. Preset values of the variables are shown in paretheses. The largest variation is 1.7’ in the transcondylar angle. Average deviation in angle is < lo and in joint space loss < 0.5 mm. PRESENTATION USE
OF RESULTS
FOR CLINICAL
After X-ray pictures of the knee and hip are taken, relevant points are digitized by using a Hipad digitizer connected to a Hewlett Packard desk top computer. The digitization is performed as follows. With the radiograph positioned on the digitizer, the calibration point, reference line and calibration
322
J. Biomed. Eng. 1982, Vol. 4, October
ring are each digitized by locating the cursor on each point. Input of these data will determine the coordinates in the x-y plane and establish the reference axes for subsequent anatomical point digitization. A program stored on magnetic tape will automatically process these data along with known geometric information, make the required corrections and provide a plotter output (Figure 9). This plot shows schematically the alignment and joint space deformities of each knee. A table on the printout gives the numerical data related to indices 1 to 6, which in turn relates to the six variables of knee deformity, defined earlier (Figure 3).
ww zs= pjy-qJ
Figure 7 Equations for calculating the real x and y coordinates of an anatomical point.
I
Makzlignment and joint space loss in the knee: H. W. Weuers et al. Table 2 The six indices of malaligmnent, are the digitized and corrected values.
Joint separation angle Tibial translocation angle Tranotibial angle Femoral translocation angle Tnmscondylar angle Medial joint space loss Flexion Angle
FURTHER
CLINICAL
numbers
in brackets
Index no.
Case 1
1 2 3 5 6 4
-0.0 6.3 82.8 5.3 92.9 0.1 25
RESEARCH
This paper describes a technique for quantifying knee deformities in the frontal plane. In the presence of arthritis, knee deformity may include malrotation of the tibia along its long axis and rather severe degrees of flexion deformity. In order to surgically correct such a three-dimensional deformity, single, double or triple plane osteotomies may be required with a variety of bone wedges removed or placed for correction. In such instances there is a need for precise measurement of both tibial rotation and flexion. Our next step is to construct a reference line, calibration point and calibration ring in a sagittal plane beside the patient and to take radiographs with the film between the
are pre-set
(0.0) (7.6) (83) (6.4) (94) (0)
and measured
values; the first column
Case 2 3.6 6.8 82.6 5.7 95.7 27 9
of each case
Case 3
(5.5) (6.9) (83) (5.8) (94) (3)
-2.5 2.5 84.8 2.6 94.5 -1.7 11
(-2.8) (-3.3) (83) (2.8) (94) (-2)
patient’s legs. By digitizing the fibular prominence, comparing it to the normal position, and measuring with respect to normal saggital joint planes of the tibia, we hope to provide the surgeon with exact measurements and correction data. This method is also of great potential use in the determination of changes or progression associated with disease, as well as in the assessment of surgical efficacy.
CONCLUSIONS Knee deformity
can be assessed accurately
by
Figure 8 Reference line (vertical line of dots) as seen on the radiograph of the knee and hip. After digitization and correction the reference line can be transformed into the load bearing axis through the head of the femur and the ankle. a, calibration ring; b, calibration point.
J. Biomed. Eng. 1982, Vol. 4, October
323
Malalignment and joint space loss in the knee: H. W. Wevers et al.
ACKNOWLEDGEMENTS
1
1
Members of the Clinical Mechanics Group at Queen’s University have contributed at several stages of design and experimentation, in particular the ideas and work of P.J. Lowe, T. Chaykowski, J.T. Bryant and G.A.B. Saunders are acknowledged. The research was funded by a Queen’s University Development Grant and Program Grant PG17 of the Medical Research Council of Canada. REFERENCES
Figure 9 A patient’s record with a printout of the real, corrected values of indices l-6 showing normal knees.
positioning patients in a frame that has built-in radiopaque markers for mathematical correction of parallax and misalignment of the X-ray source. The method is relatively insensitive for knee flexion. The method provides an objective measurement of knee deformity for pre- and postoperative assessment or for long-term follow up studies. In precise and geometrically accurate osteotomies, predetermined correction of deformities may be achieved.
324
J. Biomed. Eng. 1982, Vol. 4, October
Harrington, I J., A Bioengineering Analysis of Force Actions at the Knee in Normal and Pathological Gait, J. Biomed. Eng., May 1976,167-172. Morrison, J.B., The Mechanics of the Knee Joint in Relation to Normal Walking, J. Biomech. 1970,3, 57-61. Jackson, J.P., Waugh, W., Tibia1 Osteotomy for Osteoarthritis of the Knee, J. Bone Jt. Surg. 1961, 43B, 746-851. Gariepy, R., Derome, A., Laurin, C.A., Tibial Osteotomy in the Treatment of Degenerative Arthritis of the Knee, in Surgical Management of Degenerative Arthritis of the Lower Extremity. (Eds R.L. Cruess and N.S. Mitchell) Lea and Febiger, Philadelphia, 1975, pp. 155-164. Benjamin, A., Double Osteotomy for the Painful Knee in Rheumatoid Arthritis and Osteoarthritis, J. Bone Jt Surg 1969,51B, 694-699. Gunston, F.H., Polycentric Knee Arthroplasty, J. Bone Jt Surg 1971,53B, 272-277. Myrnerts, R., The Saab Jig: An Aid in High Tibia1 Osteotomy, Acta Orthop. Stand., 1978,49 (l), 85-88. Ahlback, S., Osteoarthrosis of the Knee, A Radiographic Investigation, Acta Radiol. Supp. 1968, 277. Kapandji, I.A., in The Physiology of Joints, Vol. 2, Lower Limb, 2nd Edn, E & S Livingstone, 1970.
Wevers*,
D.W.
Siu+ and T.D.V. Cooke*
ABSTRACT Malalignment
and joint
space
loss in the arthritic
human
knee can be measured quantitatively by employing a frame that allows for parallax correction of radiographs taken from the weight bearing lower limb. This standardized method will assist pre-operative planning for osteotomies and postoperative follow-up of patients with surgically re-aligned
Keywords:
lower limbs. The procedure requires anatomically important points to be digitized, together with reference points built into the frame. Data are then processed automatically in a desk top computer, and the program provides for an easily understood diagram and listing of charactertitic indices of malalignment.
Skeletal system, radiograph, knee joint malalignments, osteomy, arthritis, parallax
INTRODUCTION
problems
Malalignment and joint space loss are common prob!ems in the arthritic knee. Varus (bow legged) and valgus (knock kneed) deformities may result from a variety of mechanisms acting singly or in combination. For example, rickets may result in a localized femoro-tibia1 deformity and obliquity of the joint resulting in valgus of the distal femur co-existing with tibia vara, and an inward medially sloping joint, Figure 1. More typical to osteoarthritis (OA) is the medial joint compartment degradation that occurs more rapidly on this side than on the lateral side’) 2. The loaded joint then shows a relative varus of the femur with tibia vara that is due to greater loss of cartilage of the medial femoral condyle and the plateau, Figure lc.
assessment of the deformity and accurate surgical techniques7. At present an anterior-posterior (A-P) weight bearing radiograph of the knee is generally used to provide an estimate of the knee varus/valgus deformity. It has been demonstrated that a knee joint at rest may have a normal alignment, yet weight bearing may show serious angular deformity, hence the need for frequent use of weight bearing radiographs.
In rheumatoid arthritis (RA) the loss of cartilage is more uniform. Deformity may be varus or valgus but usually tends toward the physiological shape present before the onset of arthritis. Patients with pain and deformity, unresponsive to conservative measures, are potential candidates for orthopaedic joint reconstruction. The principles involved in their surgical care depend on the cause. Osteoarthritis has had a high degree of successful treatment by bone realignment (osteotomy)3’ 4 and this has resulted in improvement of arthritic malalignment. In RA, osteotomy alone is seldom of lasting benefit ‘. Articular resurfacing, however, relieves pain, may be used to correct deformity and appears to lessen the local incidence of disease recurrence6. An optimal surgical solution to these *Department of Mechanical Engineering iDepartment of Mechanical Engineering, department of Surgery, Division of Orthopaedics, Queen’s University at Kingston, Ontario, K7L 3N6.
0141-5426/82/040319-06 $03.00 0 1982 Butterworth & Co. (Publishers) Ltd
depends upon a precise pre-operative
The medical radiographic criteria most commonly used for the assessment of femorotibial an ular deformity are those described by Ahlback B . A straight line is drawn through the tibial shaft to intersect a corresponding line drawn through the femoral shaft. The angle between these two lines is measured, (see Figures I and 2). In the normal person this coronal alignment between the femur and tibia with the knee extended is not normally a straight line. Depending upon body habitus, limb length and pelvic width, a coronal alignment or physiological valgus angle of between 0 and 10” may exist. The definition of a normal femorotibia1 alignment angle for a given patient is thus dependent upon anatomical variables. Optimally, this results in a horizontal joint with a straight line passing from the hip through the centre of the knee and ankle. The coronal alignment angle is not suitable for the objective assessment of leg alignment. Assessment of alignment is furthermore distorted by parallax factors and by malposition of the patient with respect to the X-ray film and of the X-ray source. These may each introduce significant errors into the measurements. Determination of the overall deformity expressed by assessment of the several contributing mechanisms becomes therefore even more difficult.
J. Biomed. Eng. 1982, Vol. 4, October 319
Malah’gnment and joint space toss in the knee: H. W. Wevers et al. LOAD
a
BEARING
AXIS
b
C.
Figure 1 Examples of malalignment and joint deformation. Normal leg (a) and (b); dysplasia (c) and osteoarthritis (d).
The purpose of this paper is to describe an accurate method of determining quantitatively the joint space loss and malalignment which may combine to produce the lower limb deformity. This method, shown in Figure 3, requires the following variables: joint separation angle (v, tibia1 translocation angle (XT, transtibial angIe lSr femoral translocation angle c+, transcondylar angle &, lateral and medial joint space loss (b - CZ).To determine accurately these angles and the joint space loss, correction of the radiographic data for parallax must be made and standardization of the positions of patient, film and X-ray source undertaken. We describe the methods currently used for this correction. Digitization of the X-ray marker points and computer processing of the data result in a tabular output and a graphical display of the clinically relevant data.
ankle pad and the marker on the hip pad ensure that the ankle and the hip are vertical with respect to one another. The patient’s weight-bearing limb may be flexed due to malalignment, but this amounts to a secondary effect and does not influence the measurements significantly if flexion is < 25”, as is shown in the calibration of the instrument. The X-ray film is mounted vertically, first behind the hip and then the knee. The front of the frame has radiopaque ‘reference lines’ made up of steel balls mounted in a plexi-glass sub-frame. A ‘calibration ring’ and ‘calibration point’ establish a ‘calibration axis’ which is normal to the film surface. These are shown in detail in Figures 4 and 5. When the radiograph is taken, these radiopaque markers are projected onto the radiograph, digitized and processed to correct for parallax and X-ray source misalignment. Figure 6 illustrates, in the vertical or sagittal plane (y - z plane), images of the calibration ring, calibration point and one of several anatomical points. The real positions along the z axis of the X-ray source Z,, calibration ring 2~ (with diameter 4~ ), calibration point Zp and the anatomical point &, are also shown. By digitizing the calibration ring (diameter &y) on the film, the X-ray source distance 2s can be calculated [equation (l), Figure 71 and checked with the value measured during testing. For this calculation, triangles with ‘X-ray source’ at the top and $R and $y at the base are used. The distance 2s is further utilized for the correction of parallax of the anatomical features on the radiograph [equations (II) and (III)] . Equation (III) was derived using the vertically hatched triangle for calculating the first part of the equation representing the distance cu. The second part of the equation is derived using similar triangles within the horizontally hatched set and multiplying this with a ratio derived from the dotted set, yielding distance ab. The real and
FEMUR LONG AXIS
WEIGHT BEARING RADIOGRAPH To assess objectively knee malaligmnent, a standardization of the radiograph is achieved with a ‘standard knee radiograph frame’, as shown in Figure 4. The frame positions the patient’s lower limb in a true anterior-posterior (A-P) position, using the anterior-superior iliac spines (ASIS) to align the pelvis, by pointing the patella forward and placing each lateral malleolus against an ankle block. The ASIS pads can be adjusted vertically and horizontally to each patient’s anatomy. With the patient’s pelvis now oriented in a vertical plane, side to side fixation of the pelvis is achieved by positioning of the adjustable hip pads. The greater trochanter of the femur is positioned at a fixed distance from the plane of the X-ray film cassette by aligning with a marker on the hip pads. The lower limb is further positioned by aligning the lateral malleolus with an ankle pad fixed onto the floor of the frame. This
320
J. Biomed. Eng. 1982, Vol. 4, October
Figure 2 Coronal alignment angle for assessment of general malalignment according to Ahlback and others. (Redrawn from radiograph of deformed knee).
Malalignment
and joint
space loss in the knee: H. W. Wevers et al.
ASIS
Pad wth
Cassette holder
Width adjus
Htp pod lock
Verttcol adjustment
for knee and hip rodlographs
HIP , pad A-P ahgnment
Caibratlon Reference
IIne Ankle
V
iblock
Figure 4
Standard knee radiograph frame.
Figure 3 Six indices defining malalignment objectively, including the separately contributing deformation mechanisms. (Redrawn from radiograph of a deformed knee).
corrected value for the anatomical point in the yz coordinate system is : Yi‘=ab +ca Similarly equation II can be derived in the xz or transverse plane. Note that all marker points on the radiograph are digitized with respect to the calibration point image yp, while the anatomical point is defined in the xyz coordinate system. In Figure 6, Ay; is the error in position of the anatomical point on the radiograph. The reference line of Figure 4, also shown on the radiograph in Figure 8, is mathematically transformed into a biomechanical load bearing axis through the hip and the ankle. To do this a hip radiograph of the patient aligned in the standard knee radiograph frame is necessary in addition to a knee radiograph. This hip X-ray will show the reference line with respect to the head of the femur. The calibration point and calibration ring and their images on this hip radiograph, enable correction for parallax and then transformation of the reference
Figure 5 Detail of calibration ring (a) and calibration point (b) Radiopaque steel balls embedded in a plexiglass frame with known distances from radiograph.
line to the load bearing axis. This latter axis is mathematically offset from the reference line, and positioned through the head of the femur. Similarly the offset is calculated at the knee. In this procedure the ankle pad is assumed to position the ankle sufficiently precisely so that the reference line, which is half a hypothetical average ankle width inside from the ankle pad, goes through the centre of the patient’s ankle. Statistical deviations from this average ankle width are of negligible influence on the calculation of the six knee deformity variables.
J. Biomed. Eng. 1982, Vol. 4, October
321
Malulignment
and joint space loss in the knee: H. W. Wevers et al.
Table 1 The six indices of malalignment, are the digitized and corrected values
numbers in brackets are pre-set and measured values; the first column of each case
Index no. Joint separation angle Tibial translocation angle Tram-tibia1 angle Femoral translocation angle Tram-condylar angle Medial joint space loss
1 2 3 5 6 4
Case 1 -0.0 6.3 82.8 5.3 92.9 0.1
Flexion angle
Case 2 3.6 6.8 82.6 5.7 95.7 2.7
(6.6) (7.6) (83) (6.4) $1
Case 3
(5.5) (6.9) (83) (5.8) ‘;$ 9
25
-2.5 3.0 84.8 2.6 94.5 -1.7
(-2.8) (3.3) (83) (2.8) I”:/ 11
y-AXIS
(VERTICAL)
ANATOMICAL
POINT
(HORIZONTAL)
LIBRATION
R
Figure 6 X-ray source, calibration ring and point, anatomical point and images on X-ray film; y: is corrected value of the y coordinate of the anatomical point; yi is the error due to parallax and misalignment of X-ray source
RESULTS The standard knee radiograph frame performance was validated by positioning a skeletal lower limb in a precisely known configuration in the frame, simulating three different flexion angles. Joint space loss was preset by spacers with radiopaque markers provided for calibration. After taking radiographs shown in Figure 8, the pertinent anatomical features and the radiopaque markers were digitized and processed with the help of a desk top computer. The results are shown in Table 1. Preset values of the variables are shown in paretheses. The largest variation is 1.7’ in the transcondylar angle. Average deviation in angle is < lo and in joint space loss < 0.5 mm. PRESENTATION USE
OF RESULTS
FOR CLINICAL
After X-ray pictures of the knee and hip are taken, relevant points are digitized by using a Hipad digitizer connected to a Hewlett Packard desk top computer. The digitization is performed as follows. With the radiograph positioned on the digitizer, the calibration point, reference line and calibration
322
J. Biomed. Eng. 1982, Vol. 4, October
ring are each digitized by locating the cursor on each point. Input of these data will determine the coordinates in the x-y plane and establish the reference axes for subsequent anatomical point digitization. A program stored on magnetic tape will automatically process these data along with known geometric information, make the required corrections and provide a plotter output (Figure 9). This plot shows schematically the alignment and joint space deformities of each knee. A table on the printout gives the numerical data related to indices 1 to 6, which in turn relates to the six variables of knee deformity, defined earlier (Figure 3).
ww zs= pjy-qJ
Figure 7 Equations for calculating the real x and y coordinates of an anatomical point.
I
Makzlignment and joint space loss in the knee: H. W. Weuers et al. Table 2 The six indices of malaligmnent, are the digitized and corrected values.
Joint separation angle Tibial translocation angle Tranotibial angle Femoral translocation angle Tnmscondylar angle Medial joint space loss Flexion Angle
FURTHER
CLINICAL
numbers
in brackets
Index no.
Case 1
1 2 3 5 6 4
-0.0 6.3 82.8 5.3 92.9 0.1 25
RESEARCH
This paper describes a technique for quantifying knee deformities in the frontal plane. In the presence of arthritis, knee deformity may include malrotation of the tibia along its long axis and rather severe degrees of flexion deformity. In order to surgically correct such a three-dimensional deformity, single, double or triple plane osteotomies may be required with a variety of bone wedges removed or placed for correction. In such instances there is a need for precise measurement of both tibial rotation and flexion. Our next step is to construct a reference line, calibration point and calibration ring in a sagittal plane beside the patient and to take radiographs with the film between the
are pre-set
(0.0) (7.6) (83) (6.4) (94) (0)
and measured
values; the first column
Case 2 3.6 6.8 82.6 5.7 95.7 27 9
of each case
Case 3
(5.5) (6.9) (83) (5.8) (94) (3)
-2.5 2.5 84.8 2.6 94.5 -1.7 11
(-2.8) (-3.3) (83) (2.8) (94) (-2)
patient’s legs. By digitizing the fibular prominence, comparing it to the normal position, and measuring with respect to normal saggital joint planes of the tibia, we hope to provide the surgeon with exact measurements and correction data. This method is also of great potential use in the determination of changes or progression associated with disease, as well as in the assessment of surgical efficacy.
CONCLUSIONS Knee deformity
can be assessed accurately
by
Figure 8 Reference line (vertical line of dots) as seen on the radiograph of the knee and hip. After digitization and correction the reference line can be transformed into the load bearing axis through the head of the femur and the ankle. a, calibration ring; b, calibration point.
J. Biomed. Eng. 1982, Vol. 4, October
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Malalignment and joint space loss in the knee: H. W. Wevers et al.
ACKNOWLEDGEMENTS
1
1
Members of the Clinical Mechanics Group at Queen’s University have contributed at several stages of design and experimentation, in particular the ideas and work of P.J. Lowe, T. Chaykowski, J.T. Bryant and G.A.B. Saunders are acknowledged. The research was funded by a Queen’s University Development Grant and Program Grant PG17 of the Medical Research Council of Canada. REFERENCES
Figure 9 A patient’s record with a printout of the real, corrected values of indices l-6 showing normal knees.
positioning patients in a frame that has built-in radiopaque markers for mathematical correction of parallax and misalignment of the X-ray source. The method is relatively insensitive for knee flexion. The method provides an objective measurement of knee deformity for pre- and postoperative assessment or for long-term follow up studies. In precise and geometrically accurate osteotomies, predetermined correction of deformities may be achieved.
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Harrington, I J., A Bioengineering Analysis of Force Actions at the Knee in Normal and Pathological Gait, J. Biomed. Eng., May 1976,167-172. Morrison, J.B., The Mechanics of the Knee Joint in Relation to Normal Walking, J. Biomech. 1970,3, 57-61. Jackson, J.P., Waugh, W., Tibia1 Osteotomy for Osteoarthritis of the Knee, J. Bone Jt. Surg. 1961, 43B, 746-851. Gariepy, R., Derome, A., Laurin, C.A., Tibial Osteotomy in the Treatment of Degenerative Arthritis of the Knee, in Surgical Management of Degenerative Arthritis of the Lower Extremity. (Eds R.L. Cruess and N.S. Mitchell) Lea and Febiger, Philadelphia, 1975, pp. 155-164. Benjamin, A., Double Osteotomy for the Painful Knee in Rheumatoid Arthritis and Osteoarthritis, J. Bone Jt Surg 1969,51B, 694-699. Gunston, F.H., Polycentric Knee Arthroplasty, J. Bone Jt Surg 1971,53B, 272-277. Myrnerts, R., The Saab Jig: An Aid in High Tibia1 Osteotomy, Acta Orthop. Stand., 1978,49 (l), 85-88. Ahlback, S., Osteoarthrosis of the Knee, A Radiographic Investigation, Acta Radiol. Supp. 1968, 277. Kapandji, I.A., in The Physiology of Joints, Vol. 2, Lower Limb, 2nd Edn, E & S Livingstone, 1970.