Optimal increase in the sagittal diameter in DDCL
Itoh and Tsuji [20] noted that a 4.1-mm enlargement of the spinal canal was ideal and could be achieved by opening the separated lamina by 8 mm. Hirabayashi [1] stated that widening of the AP diameter by approximately 4 or 5 mm is sufficient for obtaining good operative result. Kohno [21] stated that good recovery group showed optimal widening by 5 mm in the diameter and by 95 mm2 in the canal area.
How to use this formula in the clinical practice?
Now, we make two examples in the following text. The preoperative distances from points A to B and from points E to F, and the laminar angle (α) were measured using picture archiving and communication system (PACS) software on axial CT cuts made at C5 pedicle level before surgery (Fig. 1a).
Example 1: (1) Measurement: the distances from points A to B is 4.84 mm, and from points E to F is 16.52 mm, and the laminar angle (α) is 30.35. (2) The calculation of γ (LOA): If the intended LOS is 12.0 mm, on the basis of the formula F–G = 2 × F–M = 2 × E–F × sin(γ/2), 12.0 = 2 × 16.52 × sin(γ/2), sin(γ/2) = 0.3632, γ/2 = 21.2969, γ = 42.59. (3) The calculation of d: Using the formula d = h × [tan(γ + α − γ × α/60)/tanα − 1] = 4.84 × [tan(42.59 + 30.35 − 42.59 × 30.35/60)/tan30.35 − 1], we get the value of d, d = 5.51. In other words, when the LOS is 12 mm, LOA is 42.59, and d is 5.51 mm.
Example 2: (1) Measurement: the distance from points A to B is 6.10 mm, and from points E to F is 18.84 mm, and the laminar angle (α) is 32.91. (2) The calculation of γ (LOA): if the intended increase in sagittal canal diameter after surgery is 5.0 mm, that is, d = 5.0 mm. Using the formula d = h × [tan(γ + α – γ × α/60)/tanα – 1], 5.0 = 6.10 × [tan(γ + 32.91 – γ × 32.91/60)/tan32.91 – 1], we get the value of γ, γ = 37.12. (3) The calculation of LOS: on the basis of the formula F–G = 2 × F–M = 2 × E–F × sin(γ/2) = 2 × 18.84 × sin(37.12/2), LOS = 12.0 mm. In other words, when the intended value of d is 5.0 mm, LOA is 37.12, and LOS is 12.0 mm.
The above-mentioned formula would help us plan precisely the LOS to return to approximately normal dimensions of the spinal canal on the basis of preoperative measured E–F, α and h. Because individual E–F, α and h value is variable, the above-mentioned formula enables ODCLs to be individualized based on an accurate size of the laminoplasty opening, preventing inadequate or excessive opening.
Influence of increased size of the postsurgical SCD
On the basis of the formula d = h × [tan(γ + α − γ × α/60)/tanα − 1] and the formula F–G = 2 × F–M = 2 × E–F × sin(γ/2), the d value (postsurgical increase in SCD) was directly proportional to the values of h and γ and varied inversely with α. For ODCL within the same vertebral segment, the values of h and α were the same, and the increase in postsurgical SCD was dependent on the LOS. The greater the LOS, the greater was the increase in SCD.
For ODCL of the same segment in different patients or different segments in the same patient, the values of h, α, and the distance between points E and F varied. Therefore, the increase in SCD after laminoplasty differed even when the LOS was the same. In this study, when the LOS was 12 mm, increases in the SCD of C3–C7 differed (values were 5.20, 5.39, 5.31, 5.35, and 5.27 mm, respectively). The largest increase in SCD was at C4–C6. The smallest increase was at C3 and C7 because of the smaller distance between points E and F and the greater preoperative laminar angle.
The position of the lateral hinges is closely related to the α value, h value, and distance between points E and F. As these three values changed with the position of the lateral hinges, the SCD was affected. For same-segment ODCL with the same LOS, the closer was the position of the lateral hinges to the inside of the lamina, the lower were the α and h values, the less was the distance between points E and F, and the smaller was the increase in SCD. As most authors believe that the lateral hinges should be positioned at the medial border of the lamina–lateral mass junction [15, 22–24], we followed this positioning in the current study.
Optimal LOS following ODCL
In this study, when the C3–C7 LOS was 10 mm, the increase in the SCD was 4.1 mm, and the increase in the cross-sectional area of the spinal canal in C3–C6 was 88 mm2, and the increase in the cross-sectional area of the spinal canal in C7 was 80 mm2.
The optimal increase in the sagittal diameter of the stenotic canal by laminoplasty is >4–5 mm [1, 21]. Therefore, when the LOS was <10 mm at C3–C7, the postoperative SCD and canal volume increases were inadequate and would not relieve spinal cord compression.
While devising the formula, we found that the increase in the SCD reached the maximum value when the LOA was 60° or when the LOS equal the distance between points E and F. The SCD obtained when the LOA was >60° or when the LOS was greater than the distance between points E and F was less than that when the LOA was 60° or when the LOS equal the distance between points E and F (Fig. 1). Therefore, the LOA cannot exceed 60° (the LOS cannot exceed the distance between points E and F) for ODCL.
Maezumi [25], using intraoperative ultrasonography, showed that anteriorly the spinal cord was separated from the osteophyte and that the ossification in the narrowest level of the spinal canal was decompressed successfully in most cases if the angle of the lamina was ≤45°. Tsuzukil et al. [26] noted that a smaller laminar opening might suppress posterior shift of the dural tube. Such suppression with balanced traction forces on the bilateral roots might reduce the traction effect of the bulging dural tube on the roots, which can prevent postoperative C5 root injury. We think that if spinal cord compression was alleviated completely, the spinal cord would have a greater chance to recover its functions. There is a positive correlation between the chance for the spinal cord to recover its functions and the degree of spinal cord decompression. However, it is not to say that if the LOS was larger the spinal cord would have a greater chance to recover its functions. In this study, when the C3–C7 LOS was 12 mm, the increase in the SCD was >5.2 mm, and the increase in the cross-sectional area of the spinal canal in C3–C6 was >104 mm2, and the increase in the cross-sectional area of the spinal canal in C7 was >94 mm2.
In conclusion, widening of the AP diameter by approximately 4.1–5.2 mm is obtained when LOS of 10–12 mm at C3–C7 is made, which is sufficient for obtaining good operative result [1, 21]. But, in some patients who suffered from serious ossification of the posterior longitudinal ligament, the greater opening size should be used to achieve a wider spinal canal than used in patients with cervical spondylotic myelopathy.
Study limitations
There are some limitations in this study. When the LOA was ≤60° and the lateral gutter positioning was symmetrical, the formula d = h × [tan(γ + α − γ × α/60)/tanα − 1] accurately revealed the correlation between the LOA and the SCD increase needed during ODCL. If the lateral gutter positioning was asymmetrical, there was a small difference from the calculated result.
An additional variable is the amount of bone removed when the laminae are opened. The surgeon, the technique, and instruments used influence the quantity of bone lost. The amount of bone removed is transverse of width of the cutting laminae. The removed bone was not taken into account in the current study. In reality, the size of the laminoplasty opening should equal the value calculated by the formula plus the diameter of the removed bone.