# Mathematical Calculation of Pedicle Subtraction Osteotomy Size to Allow Precision Correction of Fixed Sagittal Deformity

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### Abstract

Study Design.This is a retrospective review of 15 consecutive fixed sagittal plane deformity patients who have undergone pedicle subtraction osteotomies. The focus of this article is the application of a trigonometric equation that calculates the degree of correction needed to achieve sagittal balance. The intraoperative predictive accuracy and clinical radiographic results of using this mathematical equation are discussed.Objective.The need for a precise and reproducible planning tool for the correction of sagittal imbalance prompted us to apply a simple trigonometric equation to achieve the desired sagittal alignment of the spine.Summary of Background Data.Establishing sagittal balance has been widely recognized as one of the most important parameters in optimizing outcomes for spinal reconstruction patients. Preoperative planning for sagittal plane correction in adult spinal deformity has traditionally been done by estimation or with cumbersome film cutouts. To our knowledge, there has not been a consistent method of calculating the exact number of degrees needed to reestablish spinal balance.Methods.Patients’ C7 plumb lines are measured on a 36-inch radiograph to assess the degree of sagittal imbalance and determine how many degrees of correction (and subsequent millimeters of wedge resection) are needed. Applying a basic trigonometric formula for the tangent to the sagittal alignment is used to do this.Results.We have used this technique reliably in a series of 15 consecutive patients to reestablish sagittal balance. The predicted degree of correction was compared to the achieved degree of correction at the site of the osteotomy. This comparison was accurate to within 3° (the standard error of measurement for the method of Cobb) in all cases except 2.Conclusions.By using a simple mathematical equation, one can reliably determine the degree of pedicle subtraction osteotomy needed for correction of sagittal deformity. This technique is reproducible and has led to successful clinical outcomes.