The intercristal line-based palpation protocol followed the rule described by Kim et al[19], with minor modifications to accommodate the flexed lateral decubitus position: Select the interspinous space that is either intersected by the intercristal line or lies immediately below it.

The PSIS line-based palpation protocol stipulated targeting the L3/4 interspinous space within the an interval using hierarchical rules: single spaces are labeled L3/4; for two spaces, L3/4 is the intercristal line-intersected one (or lower if neither); for rare three spaces, the lowest is L3/4

Based on an interim analysis of Phase 1 data, we established the following decision protocol for L3/4 interspinous space localization:

1. PI ≥9 cm: Select the interspace at or immediately below the PI line.

2. PI ≤7 cm: Select the interspace at or immediately above the PI line.

3. PI 7-9 cm: Apply a 6.5-10 cm target window from the PSIS point.

   • If one interspace lies within this window, select it.
   • If multiple interspaces are present, choose the most caudal one.

PSIS line was defined as an intercristal line drawn between the the final posterior superior iliac spine point.Use a ruler to measure the distance between the PSIS line and each midddle- interspinous space （L1/2 through L5/S1）and record. The mean of distances and 95% confidence interval are calculated.

The L3-L4 intervertebral space was detected using intercristal line and the PSIS line in a random order by 2 experienced anesthesiologists. After determining the L3-L4 intervertebral space using each method alternately, horizontal skin marks were created with an erasable pen. Then, another experienced anesthesiologist for ultrasonographic examination assessed the intervertebral spaces.After identifying the sacrum, the investigator moved the probe in a cephalad direction, counted the intervertebral spaces and assessed the actual intervertebral spaces of the 2 skin marks.

palpated intercristal line line was identified and marked by bilateral palpation of the iliac crest summits.

Subsequently, two reference points were defined: "point PSIS" (intersection of the PSIS line with the spinal midline) and "point PI" (intersection of the PI line with the spinal midline). We then calculated the following three distances: the "L3/4 distance" (from the L3/4 interspinous space midpoint to point PSIS), the "PI distance" (from point PI to point PSIS) The experienced anesthesiologist for ultrasonographic examination assessed the actual interspinous space of the intercristal line.