Is the Cross-sectional Area after Unilateral Open Door Laminoplasty Wider than that after Midline Splitting Laminoplasty ? : Mathematical Approach

OBJECTIVE The aim of this study was to compare geometrically cross-sectional areas of two different laminoplasty techniques in same opening size. Some investigators have studied the expanded areas of the two different techniques using imaging study. Although it is unclear that postoperative spinal canal is correlated with the surgical outcome we just focused on mathematical and geometrical correlation of the expandable area with surgical opening size in different laminoplasty techniques. METHODS To predict the expandable area by a midline splitting technique and a unilateral open door technique, we placed an imaginary isosceles triangle in the spinal canal and drew graphs for the equation of the expandable areas in same opening size using the Pythagorean theorem and mathematical program. To substitute the constant figures of mathematical formula we estimated the normal cervical spine CT scans of 50 Korean adults. RESULTS We subtracted the imaginary triangle from the spinal canal and were left with the remaining area of the spinal canal that was not changed before and after surgery. In same opening size the expandable area by the midline splitting technique was same but slightly wider than the unilateral open door technique, irrespective of the triangular shape. For a normal isosceles triangle the results were the same. CONCLUSION Using mathematical proof, the expandable area after the midline splitting technique was same but slightly larger than that after the unilateral open door technique, irrespective of the size of the lamina opening.