Fig. 1

A 42-year-old male patient with ankylosing spondylitis with rigid kyphotic deformity (RKD) for whom two-level pedicle subtraction osteotomy (PSO) was planned. A Preoperative three-dimensional computed tomographic scans of the full spine showed that AS caused a stiff spine and abdominal compression. X is the point of the xiphoid process, P is the point of the superior edge of the pubis, S is the point of the anterosuperior corner of the sacrum, T is the point of the anterosuperior edge of T12, and A_i and A_s are the points of the inferior PSO’s apex and superior PSO’s apex, respectively. The acreage of the abdominal median sagittal plane (a-AMSP) can be obtained by measuring the preoperative hexagon acreage consisting of X, P, S, A_i, A_s, and T. B Under the condition of RKD with pedicle subtraction closing-wedge osteotomy, little changes are observed in the triangle XA_sT and PSA_i area before and after the surgery. Meanwhile, the lengths of preoperative and postoperative XT, XA_s, TA_s, A_iA_s, PA_i, PS, and SA_i are assumed to remain unchanged. Thus, acreage change in the abdominal median sagittal plane (ac-AMSP) is the rough equivalent of the preoperative and postoperative acreage changes in the quadrilateral consisting of X, P, A_i, and A_s. C To simplify the calculation, the lengths of PA_i, A_iA_s, XA_s, and XP were defined as a, b, c, and d, respectively. The preoperative points of P, Ai, As, and X were labeled as A, B, C and D, respectively. The angles between beeline a and beeline b, and between beeline b and beeline c were called beta(β) and gamma (γ), respectively. D After two separate osteotomies were performed at surgical osteotomy points B and C, the angle of β and γ increased to β'(β + α₁) and γ'(γ + α₂), respectively. α₁ and α₂ are the planed inferior and superior osteotomized vertebra angles, respectively. The postoperative points of P, A_i, A_s, and X were called A', B', C', and D', respectively. E θ' is the angle between A'C' and B'D'. The acreage of the quadrilateral consisting of A', B', C', and D' can be obtained as \(S_{\left(A'B'C'D'\right)}=\frac{\sqrt{\left[a^2+b^2-2a\cdot b\cdot cos\;\left(\beta+\alpha 1\right)\right]\cdot\left[b^2+c^2-2b\cdot c\cdot cos\;\left(\gamma+\alpha 2\right)\right]-\left[b^2+a\cdot c\cdot cos\;\left(\beta+\gamma+\alpha 1+\alpha 2\right)-a\cdot b\cdot cos\;\left(\beta+\alpha 1\right)-b\cdot c\cdot cos\;\left(\gamma+\alpha 2\right)\right]^2}}2\), where \(S\left(A'B'C'D'\right)\) is the acreage of the quadrilateral consisting of A', B', C', and D'. F Postoperative three-dimensional computed tomographic scans of the full spine showed two-level pedicle subtraction closing-wedge osteotomy surgery was performed at the first and third lumbar levels, and the inferior(α₁) and superior(α₂) osteotomized vertebra angles were 50° and 45°, respectively. The data of a, b, and c remain unchanged, but the numerical increase in d is evident. ac-AMSP is the rough equivalent of the preoperative and postoperative acreage changes in the quadrilateral consisting of X, P, A_i, and A_s