## Results: 9

2.

3.

ACA-CORA Rule 2. If the ACA is not located on the transverse bisection line (tBL) of the CORA, the secondary translation develops after angular correction. The fragment on the opposite side to the ACA moves toward the convex side of the angular deformity. ACA, axis of correction of angulation; lBL, longitudinal bisecting line; CORA, Center of Rotational Angulation.

4.

ACA-CORA Rule 1. If the ACA is located on the concave side of angular deformity, secondary lengthening at the corticotomy develops after angular correction (A) and if the ACA is located on the convex side, secondary shortening develops (B). ACA, axis of correction of angulation; lBL, longitudinal bisecting line; CORA, Center of Rotational Angulation; tBL, transverse bisection line; L, amount of secondary lengthening; S, amount of secondary shortening.

5.

Secondary length change after angular correction when the ACA is not on the CORA (C and G) can be calculated before angular correction (A, B, E, F) and be compensated during angular correction (D and H). To avoid abutment during angular correction, secondary length change to be compensated should be calculated at the convex side of the corticotomy. 1) Secondary lengthening when the ACA is on the convex side of the CORA (A-D). L=2×dt×tan (a/2). 2) Secondary shortening when the ACA is on the convex side of the CORA (E-H). S=2×dt×tan (a/2). L, the amount of lengthening to be compensated; dt, distance from the ACA to the convex side of the corticotomy over the tBL of the CORA; a, the amount of angular deformity to be corrected. S, the amount of shortening to be compensated. ACA, axis of correction of angulation; lBL, longitudinal bisecting line; CORA, Center of Rotational Angulation; tBL, transverse bisection line.

6.

Case 2. A 15-year-old girl with bilateral DDH. Despite several surgeries, the patient suffered genu valgum with shortening and hip subluxation on the left side (A). Gradual angular correction and lengthening on the femur and acute correction with shortening on the tibia were performed with Dyna-ATCs (B and C). At the time of removal of fixators, Chiari osteotomy was performed (D) and five months later, neck lengthening osteotomy with greater trochanter transfer was added for hip reconstruction (E).

7.

Correction rate calculation. During angular correction, secondary length change and translation are compensated continuously, therefore, correction rate can be calculated with the amount of displacement on the concave side of the corticotomy (D, G and H). 1) Even in cases which do not require lengthening, the concave side of the corticotomy should be open to correction angular deformity (C). The amount of distraction can be calculated with the distance between the convex and concave side of the corticotomy and the amount of angular correction. l=2×dcv×tan (a/2) (D). 2) If the corticotomy are on tBL of the CORA (E), as shown in Fig 5. additional translation is needed for exact realignment (F and G). In this case, although exact realignment is achieved, translation of the corticotomy site still remains after correction (G and H). This translation can be calculated with the distance between the corticotomy and the CORA over the lBL. t=2×da×tan (a/2) (F). 3) Overall displacement on the concave side of the corticotomy is D=(l

^{2}+t^{2})^{1/2}(H). 4) Daily amount of angular correction is the angle that make D=1 mm. D=(l^{2}+ t^{2})^{1/2}=1. D=[{2×dcv×tan (φ/2)}^{2}+{2×da×tan (φ/2)}^{2}]^{1/2}=1. D=2^{2}×dcv^{2}×{tan (φ/2)}^{2}+2^{2}×da^{2}×{tan (φ/2)}^{2}=1. D=2^{2}×(dcv^{2}+da^{2})×{tan (φ/2)}^{2}=1. {tan (φ/2)}^{2}=(dcv^{2}+da^{2})^{-1}×2^{-2}. tan (φ/2)=(dcv^{2}+da^{2})^{-1/2}×2^{-1}. φ=2×cot {(dcv^{2}+da^{2})^{-1/2}×2^{-1}}. l, the amount of lengthening on the concave side of the corticotomy; dcv, distance from the concave to the convex side of the corticotomy; a, the amount of angular deformity to be corrected; D, Overall displacement on the concave side of the corticotomy in mm; t, the amount of additional translation at the corticotomy site; da, distance from the corticotomy to the CORA over the lBL; φ, the amount of daily angular correction; cot, cotangent. tBL, transverse bisection line; CORA, Center of Rotational Angulation; lBL, longitudinal bisecting line.8.

Secondary translation after angular deformity when the ACA is not on the CORA (N and X) can be calculated before angular correction and should be compensated during angular correction. If the corticotomy is not performed on the CORA, zigzag deformity develops even after the compensation of the secondary translation (H and R). To avoid this zigzag deformity, additional translation is needed (I and S). The amount of additional translation also can be calculated before angular correction. 1) Secondary translation when the ACA is not on the CORA (A-D). T=2×dl×tan (a/2). 2) Secondary translation when the ACA is not on the CORA and corticotomy is not on the CORA but on the side of the ACA (E-N). The amount of translation at the corticotomy site can be calculated with the amount of the angular deformity to be corrected and the distance between the ACA and the corticotomy over the lBL (F, G, P, Q). However, after the compensation, zigzag deformity still remains (H and R) and additional compensatory translation to the same direction for the realignment of the corticotomy is needed (H and R). The additional translation can be calculated with the amount of angular deformity to be corrected and the distance between the corticotomy and the CORA (I and S). a) Secondary translation at the corticotomy site (E, F and G). Tc=2×dc×tan (a/2) (F). b) Additional translation to be compensated to avoid zigzag deformity (H and I). Ta=2 ×da×tan (a/2) (I). c) Overall translation to be compensated (K-N). If the corticotomy is not on the CORA but on the side of the ACA, additional translation should be compensated to the same direction to that for the corticotomy. To=Tc+Ta=2×dc×tan (a/2)+2×da×tan (a/2)=2×(dc+da)×tan (a/2)=2×dl×tan (a/2) (L and N). 3) Secondary translation when the ACA is not on the CORA and corticotomy is not on the CORA but on the other side of the ACA (O-X). The amount of translation at the corticotomy site and the amount of additional translation to avoid zigzag deformity also can be calculated with the amount of the angular deformity to be corrected and the distances between the ACA and the corticotomy and between the corticotomy and the CORA over the lBL. However, the direction of the compensatory additional translation is the opposite to that for the corticotomy site (Q, R and T). a) Secondary translation at the corticotomy site (O-Q). Tc=2×dc×tan (a/2) (P). b) Additional translation to be compensated to avoid zigzag deformity (R and S). Ta=2×da×tan (a/2) (S). c) Overall translation to be compensated (U-X). If the corticotomy is not on the CORA but on the side of the ACA, additional translation should be compensated to the opposite direction to that for the corticotomy (Q, R and T). To=Tc-Ta=2×dc×tan (a/2)-2×da×tan (a/2)=2×(dc-da)×tan (a/2)=2×dl×tan (a/2) (V and X). 4) Therefore, regardless of the location of the corticotomy, the overall amount of compensatory translation can be calculated with the amount of angular correction and the distance between the ACA and the CORA over the lBL (K-N, U-X). T, the amount of translation to be compensated; dl, distance from the ACA to the CORA over the longitudinal bisection line (lBL) of the CORA; a, the amount of angular deformity to be corrected. Tc, the amount of translation at the corticotomy site; dc, distance from the ACA to the corticotomy over the lBL; Ta, the amount of additional translation to avoid zigzag deformity; da, distance from the corticotomy to the CORA over the lBL; To, the overall amount of translation to be compensated. ACA, axis of correction of angulation; CORA, Center of Rotational Angulation.

9.

Case 1. A 7-year-old boy with Blount's disease. Despite previous treatments, proximal tibia vara on left side did not improve (A). Intraoperative valgus stress arthrogram showed mild dye pooling on medial side (B). Gradual angular correction with application of T-type Dyna-ATC was planned. First, proximal posterior screw was inserted parallel to the proximal tibial joint orientation line on coronal plane and on the proximally extended posterior cortical line of diaphysis in sagittal plane using cannulated drilling over the guide-wire technique (D and G). Then, distal screws were inserted (F and G). The proximal anterior screw was placed with about 5 degrees of convergent angle (C and G). Oblique type osteotomy was performed below the tibial tuberosity (E and G). Secondary deformities and the rate of angular correction were calculated with immediate postoperative radiographs (H). The ACA was located on the concave side of the angular deformity, therefore, fixator should be lengthened during angular correction to compensate secondary shortening. The amount of secondary shortening to be compensated during angular correction is S=2×dt (98 mm)×tan (a/2=26/2)=45.3 mm. The ACA was not on tBL of the CORA but distal to the CORA, therefore, the proximal tibia (the opposite fragment) would translate laterally (to the convex side of the deformity). Proximal tibia should be translated medially to compensate secondary translation during angular correction. The amount of secondary translation to be compensated was T=2×dl (59 mm)×tan (a/2=26/2)=27.2 mm. The rate of angular correction was calculated with the amount of secondary translation on the concave side of the corticotomy (I). The amount of daily angular correction was φ=2×cot [{dcv (25 mm)

^{2}+da (13 mm)^{2}}^{-1/2}×2^{-1}]=2.03°. Therefore, the rate of angular correction is 2 and total duration for angular correction was a/φ=26°/(2°/day)=13 days. Daily amount of compensatory lengthening was S=2×dt (98 mm)×tan (φ/2=2/2)=3.42 mm and the daily amount of compensatory translation was T=2×dl (59 mm)×tan (φ/2=2/2)=2.05 mm. After 5 days of latency period, 5 mm of pre-lengthening was performed to avoid impingement of convex side (J). Angular correction was performed for 13 days with the rate of 2°/day. The rate of compensatory lengthening was 3.5 mm/day and the rate of compensatory translation was 2 mm/day. 13 days later, angular correction was achieved (K and L). The fixator was removed 2 months later and the teleradiograph taken at postoperative 3.5 month showed successful realignment (M). ACA, axis of correction of angulation; tBL, transverse bisection line; CORA, Center of Rotational Angulation.