Ethical approval.

This was a prospective, randomized, double-blind, and up-and-down sequential allocation trial. The study protocol was approved by the Institutional Ethics Committee of the Suining Central Hospital (S4 Fig,approval no: LLSLH20220029) and registered in the Chinese Clinical Trials Registry in October 30th, 2022 (available at http://www.chictr.org.cn, identifier: ChiCTR2200065164), all methods were carried out in accordance with relevant guidelines and regulations. Participants were recruited between June 13, 2022, and December 31, 2022, from patients at the Suining Central Hospital.The study protocol, including the design, eligibility criteria, primary and secondary outcomes, and statistical analysis plan, was finalized prior to the enrollment of the first participant. The delay in registration was primarily due to administrative oversight during the early stage of the study initiation. The authors confirm that all ongoing and related trials for this drug/intervention are registered and all participants provided their written informed consent prior to participation in the study.

Participants.

In this study, we enrolled 50 patients who underwent arthroscopic shoulder surgery under general anesthesia. The inclusion criteria were 20–65 years of age, American Society of Anesthesiologists (ASA) physical status I–II, and body mass index (BMI) of 18–28 kg/m². We excluded patients with serious cardiopulmonary disease, abnormal liver and kidney function, skin infection at the site of nerve block, coagulation dysfunction, drug abuse,and known allergy to general anesthetics and research drugs. Furthermore, patients who did not cooperate during the trial, experienced adverse events (e.g., major bleeding and cardiac arrest), had insufficient postoperative follow-up time, or had incomplete data were considered for withdrawal.

Randomization and blinding.

Using a computer-generated random number sequence, the eligible patients were randomly divided into ropivacaine and butorphanol groups. Opaque sealed envelopes were used to conceal the allocation details. A research nurse prepared the study solutions in identical 20-mL syringes. The study solution for all patients was diluted with 0.9% normal saline to a final volume of 20 mL. For all patients in the butorphanol group, the quantity of butorphanol was 1 mg, and the final volume of butorphanol + ropivacaine was 20 mL. The concentration of ropivacaine for the first patient was 0.4% in both groups. The ropivacaine concentration for the next patient was determined on the basis of the response of the previous patient. All patients, surgeons, and other investigators were blinded to the group allocation.

Anesthesia.

All patients underwent routine 8-h fasting, and no preoperative medication was administered. After entering the operating room, electrocardiogram, pulse oximetry, systolic blood pressure, diastolic blood pressure, non-invasive mean arterial blood pressure (MAP), and heart rate (HR) were monitored. A peripheral venous channel was established and compound sodium chloride injection (6–8 mL/kg^-1·h^-1) was administered.

All patients were placed in a supine position, with their upper limbs on the surgical side closely attached to the trunk and the head slightly tilted to the opposite side. First, the location of the intermuscular sulcus was identified under ultrasound to determine the precise location of the brachial plexus nerve. The linear array probe was placed at the level of the cricoid cartilage and gradually advanced toward the outer edge of the sternocleidomastoid muscle. Several low-echoic structures were noted between the anterior and middle scalene muscles, and these structures appeared to be arranged in a string of beads. This was identified as the location of the brachial plexus (S1 Fig). The probe was slid up and down to identify the ideal section for puncture, and before puncture, it was differentiated from blood vessels using ultrasound color mode to avoid puncture injury and prevent the local anesthetic from erroneously entering the blood vessels. After identifying the precise location of the brachial plexus nerve, the intended puncture site was disinfected, and a 50-mm puncture needle was used to insert the needle at a distance of 1–1.5 cm outside the ultrasound probe. The puncture needle was advanced at a 45° angle to the skin, and an in-plane puncture technique was used (S2 Fig). When the tip of the puncture needle reached the vicinity of the nerve and there was no blood, gas, or cerebrospinal fluid in the syringe, the experimental drug was injected into the space between the two scalene muscles to completely surround the brachial plexus nerve with local anesthetic solution (S3 Fig). If the puncture needle position needs to be adjusted, the syringe must be drawn back again without blood before injection. Within 30 min of brachial plexus block injection, acupuncture using a 1-mL syringe needle was used every 5 min to evaluate skin pain in areas innervated by the musculocutaneous nerve, radial nerve, median nerve, ulnar nerve, and axillary nerve. Based on the degree of pain reduction, the level of pain was interpreted as follows: level I indicated normal or slightly reduced pain, level II indicated significantly reduced pain, and level III indicated no pain. Negative reactions are defined as Grade III (no pain) in all five innervated areas, whereas positive reactions are defined as Grade I–II (Grade I: normal or slightly reduced pain; Grade II: significantly reduced pain) in any part of the five innervated areas. When a negative reaction was noted in a patient, the concentration of ropivacaine was reduced by one level in the next patient, and when a positive reaction was noted in a patient, the concentration of ropivacaine was increased by one level in the next patient. The trial was terminated when seven negative vs. positive or positive vs. negative crossover points were obtained.

After completing the brachial plexus block and observing for 30 min (EC50 test completed), general anesthesia was induced. The patient was given oxygen via an oxygen mask for 3 min, and the oxygen flow rate was 6 L/min. Then, 0.4 µg/kg sufentanil, 2 mg/kg propofol, and 0.6 mg/kg rocuronium were administered intravenously to induce an appropriate depth of anesthesia with complete muscle relaxation, and mechanical ventilation was started through tracheal intubation. Respiratory parameters (tidal volume 6–8 mL/kg, respiratory rate 10–15 breaths/min) were adjusted to maintain the end-expiratory carbon dioxide partial pressure (PETCO₂) at 35–45 mmHg. Positive end-expiratory pressure was used where necessary. Intraoperative infusion of propofol and remifentanil was used to maintain anesthesia, with an electroencephalogram bispectral index value of 40–60. The patient’s body temperature was maintained between 36℃ and 37℃. Hypotension was defined as a > 20% drop in the MAP from the baseline and was treated with intravenous injection of 6-mg ephedrine or 20% μg deoxyepinephrine. When an increase of >20% relative to the baseline was noted in the MAP, 5-mg urapidil was intravenously administered. When the HR declined to <50 beats/min, atropine 0.3–0.5 mg was intravenously administered, and when it exceeded >130 beats/min, esmolol 10–20 mg was intravenously administered. Repeated administration may be necessary.

If symptoms indicative of local anesthetic poisoning, such as nausea, vomiting, increased breathing rate and HR, delirium, and convulsions, occurred during the nerve block, the use of the local anesthetic was immediately stopped, the patient was given oxygen inhalation, and respiratory tract patency was maintained. During tachycardia, esmolol was administered to normalize the HR. Ventricular arrhythmia was treated with amiodarone. If the patient started convulsing, propofol was administered, and if necessary, intralipid was used. If circulatory suppression was noted, intravenous infusion or the use of vasoactive drugs was accelerated. In the event of respiratory suppression, mask pressure was used to provide oxygen, and emergency tracheal intubation was performed if necessary. If allergic reactions occurred, corresponding treatments were carried out according to the grading of allergic reactions.

Remifentanil was stopped 30 min before the end of the surgery, and intravenous sufentanil was administered at 0.2 μg/kg for pain relief. Propofol was stopped at the end of suturing. After the surgery, we waited for the patient to wake up, recover spontaneous breathing and show stable circulation, and then, the patient was sent to the recovery room for observation after extubation and anesthesia recovery. After the surgery, celecoxib (0.2 g. bid) was administered orally.

Statistical analysis.

The EC50 of ropivacaine was determined using Dixon’s up-and-down sequential allocation method [15]. The data of sequential allocation method has two major characteristics: non independence and unknown distribution, so conventional sample size calculation methods are not suitable for sequential allocation methods. A simulation study shows that including at least 20–40 patients will provide a stable estimate of the target dose for most scenarios [16]. With a sample size of 22 cases, Tian et al [17]. used the sequential method to identify the EC50 of ropivacaine for brachial plexus block. Considering that the improved sequential method terminated the experiment at 6–7 crossovers, the final sample size was determined to be 25 patients in each group. We used the SPSS software (version 25; SPSS Inc., IBM Corp, Armonk, USA) to process the data. All data were subjected to normality tests, and normally distributed variables were described as mean ± standard deviation. The patient’s age, BMI, and visual analog scale (VAS) score were statistically analyzed using independent sample t-tests. Count data, such as patient’s sex and number of additional postoperative analgesics, were tested using chi-square tests or Fisher’s exact test. Multiple comparisons were adjusted using the Benjamini–Hochberg (BH) method. Given the nonindependent structure and unknown distributional properties of responses obtained from the up-and-down sequential allocation design, traditional parametric approaches such as probit regression may yield biased estimates. Therefore, EC50 was estimated using isotonic regression implemented via the pooled-adjacent-violators algorithm (PAVA), in accordance with the recommendations of Pace and Stylianou. Bootstrap resampling was applied to derive the mean EC50 and corresponding 95% confidence intervals (CIs), as well as to evaluate the between-group difference (contrast) in EC50. A sensitivity analysis was performed by re-including the excluded samples. Statistical significance was defined as a two-sided P value <0.05.