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. 2013 Dec;10(4):237-41.
doi: 10.14245/kjs.2013.10.4.237. Epub 2013 Dec 31.

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

Sang-Hyuk Kim  1 , Eun-Sang Kim  2 , Whan Eoh  2 , Il Tae Jang  1 , Sang-Eun Choi  3
Affiliations

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

Sang-Hyuk Kim et al. Korean J Spine. 2013 Dec.

Abstract

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.

Keywords: Cervical Vertebrae; Laminoplasty; Ossification of Posterior Longitudinal Ligament; Spinal Canal; Spinal Cord Compression; Spinal Osteophytosis.

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Figures

Fig. 1
Fig. 1
Line X and Y of imaginary triangle.
Fig. 2
Fig. 2
(A) Line X, Y and D of isosceles trapezoid after MST. (B) After UODT, preoperative imaginary triangle was rotated posteriorly.
Fig. 3
Fig. 3
Panel (A) and (C) show the excluded area (black area) from imaginary triangle. After laminoplasty (panel (B): midline splitting technique, panel (D): unilateral open door technique) black area was moved, but not changed.
Fig. 4
Fig. 4
Graphs for expandable areas of real triangles. (A) highest triangle on C5 level, (B) triangle with mean height on C5 level, (C) lowest triangle on C5 level, (D) highest triangle on C5 foraminal level, (E) triangle with mean height on C5 foraminal level, (F) lowest triangle on C5 foraminal level, (G) difference between MST and UODT on C5 level, (H) difference between MST and UODT on C5 foraminal level.
Fig. 5
Fig. 5
Graphs for height and difference between expandable area of two techniques. If H is about 0.5, the line will be more flat (H=height/X, D'=D/X, Area'=area of MST-area of UODT).
See this image and copyright information in PMC

References

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