Postoperative pain management and hospital outcomes following robotic-assisted thoracoscopic surgery for non-small cell lung cancer: a propensity score-matched study

Introduction

Lung cancer, the leading cause of cancer-related mortality in the United States, is expected to account for over 125,000 deaths in 2024, representing 1 in 5 cancer-related deaths (1). Since its introduction in 2002, robotic-assisted thoracoscopic surgery (RATS) has been increasingly utilized as an alternative to video-assisted thoracoscopic surgery (VATS) for minimally invasive surgical treatment of non-small cell lung cancer (NSCLC) (2,3). The demonstrated advantages of RATS with the current Da Vinci Xi Surgical System (Intuitive Surgical, Sunnyvale, CA, USA), owing in part to increased maneuverability and reduced fulcrum effects, include improved nodal dissection and reduced blood loss compared to VATS, which allow for improved staging and downstream treatment options (3-7). Robotic surgeries now constitute more than half of minimally invasive lobectomies performed in the United States (2-6,8).

As advancements in surgical techniques continue to evolve, understanding the impact of robotic surgery extends beyond oncological outcomes to include patient-centered measures, such as postoperative recovery experiences and pain management, which are increasingly prioritized in the era of personalized medicine (9). Nevertheless, patient-reported outcomes (PROs) related to postoperative pain control remain incompletely characterized (9). A 2017 study (6) found no significant difference in acute or chronic pain outcomes between RATS and VATS, although patients also perceived robotic surgery as less painful, potentially influenced by physician-patient discussions and marketing. Related studies identified no significant differences in postoperative numeric pain scores or chronic pain between RATS and VATS (10-12). However, these findings may have been impacted by the learning curve for performing robotic surgery, as reflected by increased operative times during early adoption (10). Conflicting results have also arisen from studies of postoperative opioid use: one study reported increased morphine use within 48 hours of RATS compared to VATS (13), while another found decreased inpatient opioid use for RATS (14).

A major challenge in studying postoperative pain is the discordance between patient-reported pain scores and opioid consumption, which may reflect not only individual pain experiences but also physician preferences or current prescribing guidelines (15-17). Given the critical role of pain management in shaping patient recovery and healthcare resource utilization, further comprehensive studies are warranted (14-16). To date, few studies (6,14,15) have investigated the direct relationship between patient pain scores and opioid consumption across inpatient recovery windows and outpatient follow-up visits. The objective of this study was to compare inpatient opioid and non-opioid analgesic medication use, patient-reported pain scores, and length of hospital stay for RATS and VATS in Stage I NSCLC resections. We present this article in accordance with the STROBE reporting checklist (available at https://ccts.amegroups.com/article/view/10.21037/ccts-25-27/rc).

Methods

Study design and participants

This study was a retrospective cohort study. All data collection and research procedures were compliant with the Health Insurance Portability and Accountability Act (HIPAA). The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. This retrospective cohort study was approved by the Institutional Review Board of Stony Brook University on March 8, 2024 (IRB2022-00493), which waived the requirement for written informed consent. The study sample size was determined by selection of all eligible patients undergoing thoracoscopic surgical resection of Stage 1 NSCLC with curative intent at our institution for sufficient statistical power. The Cerner Electronic Medical Record (EMR) case selection was reviewed to identify patients undergoing surgical treatment of Stage I NSCLC at Stony Brook University Hospital from January 1, 2016, to January 1, 2024, yielding 252 eligible patients. Patients who underwent conversion to thoracotomy (1.2%, n=3) or wedge resection (35.3%, n=89) were excluded. These exclusions yielded 160 remaining patients with Stage I NSCLC undergoing either lobectomy or segmentectomy.

Patients were assigned to either the VATS cohort or the RATS cohort based on the surgical technique used. Patients were followed up according to the interval between hospital discharge and subsequent outpatient follow-up visit for a median of 11.4 days (mean: 11.7 days; range, 1.51–55.4 days). While follow-up visits were generally intended to occur two weeks postoperatively, individual differences in patient and physician scheduling led to variability in the actual follow-up interval. Figure 1 provides a cohort construction flowchart.

Figure 1 Flowchart of patient selection. NSCLC, non-small cell lung cancer; RATS, robotic-assisted thoracoscopic surgery; VATS, video-assisted thoracoscopic surgery.

Data sources and outcome variables

The primary outcomes for this study were hospital length of stay (LOS) and cumulative inpatient opioid usage. Secondary outcomes for this study were inpatient pain scores, outpatient opioid usage, and non-opioid analgesic usage inpatient and outpatient. All data were obtained from the Cerner EMR case selection, physician notes, and the Medication Administration Record (MAR). Patient-reported pain scores were obtained from EMR vitals as recorded by nursing staff. Information on intraoperative pain control techniques including intercostal nerve blocks, paraspinal blocks, and epidural placement, was obtained from surgeons’ operative reports.

Hospital LOS was calculated as time elapsed from surgery completion to hospital discharge. Inpatient opioid usage was recorded for the entirety of each patient’s hospital stay after surgery completion. To homogenize patient opioid usage, opioid dosages and routes of administration were converted to oral morphine milligram equivalents (OMME) according to the University of California, San Francisco Opioid Analgesic Conversion Scales based on prior research studies (18,19). Self-reported pain scores were recorded at 12, 24, 36, and 48 hours postoperatively using the standard numerical scale ranging from 0 to 10. Pain levels were averaged if multiple pain levels were reported within three hours of a time point of interest.

Patient opioid use at discharge, interim period, and follow-up visit was determined according to physician notes and discharge summary reports. Patient pain scores at follow-up visit, obtained from physician notes, were reported using a combination of the standard numerical scale ranging from 0 to 10 and the subjective pain scale (i.e., minor, moderate, severe). Recorded readings were included in the analysis if patients were discharged before the time point was reached.

Surgical technique

All procedures were performed by cardiothoracic surgeons with a range of expertise from three to 11 years of experience in performing VATS and RATS. All RATS cases were performed using the Da Vinci Xi Surgical System (Intuitive Surgical). For lobectomies, the entire lobe of interest was resected and delivered as a specimen. For segmentectomies, the fissure of interest was identified via pulmonary arteries that were clamped, and indocyanine green (ICG) was infused to identify the interlobar segments. The segment of interest was marked with electrocautery and stapled before being removed via one of the 12 mm port sites. Hilar and mediastinal lymph nodes were identified, resected, and sent for pathology. Chest tubes of 24- or 28-French size were then guided into the pleural space.

For RATS procedures, an initial incision was made in the intercostal space at the anterior axillary line. Four robotic ports were placed using 8- and 12-mm ports at the intercostal spaces in addition to a 12-mm assistance port below the robotic trocars. When retrieving the bagged specimen for RATS, the most anterior port site was used and enlarged to allow for extraction. For VATS procedures, an initial incision was made in the intercostal space at the anterior axillary line, and a thoracoscope was introduced into the cavity. Two to three thoracoscopic ports were placed at intercostal spaces. In the event of limited visualization with the thoracoscope, a small lateral thoracotomy was performed to allow better angulation by extending the length of the initial incision. The bagged specimen was removed from the axillary utility port in VATS procedures. A schematic of RATS and VATS incisions is provided in Figure S1.

For intraoperative pain control, intercostal blocks were performed posteriorly in the subpleural space using 0.25% Bupivacaine (Marcaine) solution. Cryoablation, when performed, was applied to the intercostal spaces, allowing for time to thaw the probe for 2-minute sessions at each site. Epidural catheters were placed preoperatively by anesthesia. When performed, 0.25% Bupivacaine solution (Marcaine) was also infused into port sites after surgery completion.

Statistical analysis

Statistical analysis was performed using R version 4.1.1. (Posit PBC, Boston, MA, USA). Chi-squared tests and Fisher’s exact tests were used to evaluate significance for baseline comorbid diagnoses, smoking status, and procedure type. Given the non-normal distribution of the data as verified by Shapiro-Wilks test, a two-tailed Mann-Whitney U test was used to compare postoperative opioid use between patients undergoing VATS or RATS.

To address potential bias, propensity score matching was performed between the VATS and RATS cohorts using an optimal matching algorithm in a 1:1 ratio without replacement and a caliper of 0.2 standard deviations (SDs) of the logit of the propensity scores. Patients were matched on variables expected to influence likelihood of undergoing robotic-assisted vs. video-assisted approaches: age, race, ethnicity, tumor laterality and location, and pulmonary function testing (PFTs) results [LV ejection fraction, forced expiratory volume in 1 second (FEV₁), forced vital capacity (FVC), and diffusion capacity of lung for carbon monoxide (DLCO)].

Kaplan-Meier curves for time to discharge were produced based on length of hospital stay (calculated as time from surgery completion to discharge). The 95% confidence intervals (CIs) for the discharge rates were calculated using a log-log transformation. A Cox proportional hazards model was used for further time-to-event analysis, with hospital discharge defined as the event of interest. Time-to-event analysis was performed with reference to VATS surgery; thus, a hazard ratio (HR) >1 indicated greater likelihood of discharge for the RATS cohort. The proportional hazards assumption was verified using Schoenfeld residuals. Statistical significance was assessed using a significance level of α=0.05 with P values obtained using two-sided tests.

Results

Patient characteristics

Table 1 provides a summary of the baseline characteristics of patients before and after propensity score matching. A total of 252 patients were eligible for inclusion in our study on the basis of surgical resection for Stage I NSCLC. Three patients (1.2%, n=3/252) were excluded for conversion to thoracotomy, yielding 249 surgical patients. Of these patients, 89 patients (35.7%) were excluded due to wedge resection and lack of comparability between cohorts; lobectomies and segmentectomies were included. Of 160 patients included before matching, 102 (63.8%) underwent RATS. Figure 1 provides a cohort construction flowchart. Before matching, the median follow-up time for VATS was 9.87 days (mean: 10.2 days; range, 1.51–22.3 days). The median follow-up time for RATS was 12.4 days (median: 13.7 days; range, 2.42–55.4 days). After propensity score matching, each cohort included 52 patients, for a total of 104 patients. For the propensity score-matched cohorts, the median follow-up time for VATS was 9.87 days (mean: 10.2 days; range, 1.51–22.3 days). The median follow-up time for RATS was 11.5 days (median: 13.2 days; range, 2.42–55.4 days).

Before matching, the average age at surgery was 69.3 years for the VATS cohort and 68.8 years for the RATS cohort. Patients were predominantly of White race (VATS: 96.6%, RATS: 93.1%) and non-Hispanic or Latino ethnicity (VATS: 93.1%, RATS: 96.1%). Tumor subtype was characterized as adenocarcinoma for 79.3% of patients in the VATS cohort and 77.5% of patients in the RATS cohort. Lobectomy was performed in 94.8% of the VATS cohort and 92.2% of the RATS cohort; segmentectomy was performed in 5.2% of the VATS cohort and 7.8% of the RATS cohort [standardized mean difference (SMD): 0.108]. Preoperative PFTs for patients were similar across cohorts for left ventricle ejection fraction (LVEF) (SMD: 0.087), FEV₁ (SMD: 0.105), FVC (SMD: 0.104), and DLCO (SMD: 0.026).

After propensity score matching, the average age at surgery was 69.5 years for the VATS cohort and 67.7 years for the RATS cohort. Patients were predominantly of White race (VATS: 98.1%, RATS: 98.1%). In the VATS cohort, 92.3% were of non-Hispanic or Latino ethnicity, compared to 98.1% in the RATS cohort. Tumor subtype was characterized as adenocarcinoma for 78.8% of patients in the VATS cohort and 82.7% of patients in the RATS cohort. Lobectomy was performed in 94.2% of the VATS cohort and 94.2% of the RATS cohort; segmentectomy was performed in 5.8% of the VATS cohort and 5.8% of the RATS cohort (SMD <0.001). Preoperative pulmonary function testing (PFTs) for patients were similar across cohorts for LVEF (SMD: 0.016), FEV₁ (SMD: 0.063), FVC (SMD: 0.108), and DLCO (SMD: 0.016).

LOS

Figure 2 depicts the Kaplan-Meier curves for time to discharge for the propensity score-matched VATS and RATS cohorts. Overall likelihood of remaining in the hospital was lower for the RATS cohort than the VATS cohort at all time points upon visual inspection. The median LOS was 4.60 days [interquartile range (IQR), 3.96–7.11 days] for the VATS cohort and 2.98 days (IQR, 2.07–4.20 days) for the RATS cohort (P<0.001, Table 2). From the Cox proportional hazards analysis, patients in the RATS cohort were 1.88 times more likely to be discharged at any time postoperatively than patients in the VATS cohort (HR 1.88, 95% CI: 1.27–2.78, P=0.001).

Figure 2 Kaplan-Meier curve depicting time to discharge after surgery for propensity score-matched cohorts. RATS, robotic-assisted thoracoscopic surgery; VATS, video-assisted thoracoscopic surgery.

Postoperative pain management

Table 2 provides a comparison of postoperative patient-reported pain scores and medication administration for the propensity score-matched VATS and RATS cohorts. Opioid analgesic usage was converted to OMME and normalized by dividing the quantity by each patient’s LOS. Median daily OMME consumption was 22.52 mg/day (IQR, 12.33–34.63 mg/day) for the VATS cohort and significantly higher at 33.90 mg/day (IQR, 19.59–51.40 mg/day) for the RATS cohort (P=0.04). The specific opioid medications received by each patient were also reviewed; inspection revealed a greater daily median dosage of oral oxycodone in the RATS cohort compared to the VATS cohort (VATS: 2.09 mg/day, RATS: 13.71 mg/day, P<0.001). No significant differences in daily IV fentanyl, oral morphine, oral tramadol, or patient-controlled analgesia were observed. VATS patients received greater doses of IV hydromorphone per day than RATS patients (VATS: 0.47 mg/day, RATS: 0.20 mg/day).

Non-opioid analgesic usage was evaluated by recording oral and IV acetaminophen, IV bupivacaine, oral gabapentin, oral methocarbamol, oral ibuprofen, and IV ketorolac consumption. Oral acetaminophen usage was greater in the RATS cohort (median: 2.14 g/day, IQR, 1.54–3.12 g/day) than the VATS cohort (median: 1.00 g/day, IQR, 0.00–2.95 g/day) (P=0.002). The median IV bupivacaine usage was 117.2 mg/day for the VATS cohort, compared to 0 mg/day for the RATS cohort (P<0.001). No significant differences in methocarbamol, ibuprofen, or ketorolac usage were observed. Intraoperative characteristics are provided in Table S1.

A summary of postoperative inpatient pain management and patient-reported pain scores is provided in Figure 3. At 12 hours post-op, the average pain score was significantly higher in RATS patients than VATS patients (RATS: 5.28, VATS: 3.33, P<0.001). At 48 hours post-op, average pain scores were 3.75 for RATS and 2.90 for VATS (P<0.001). Visual inspection of the line plots showed patient-reported pain scores to be higher for RATS at all time points except for 36 hours postoperatively (VATS: 3.93, RATS: 4.36, P=0.40). In the VATS cohort, patients experienced a smaller reduction in pain (0.44) compared to RATS patients (1.65).

Figure 3 Pain levels and management trends for propensity score-matched cohorts. (A) Line plot of patient-reported pain scores (scale of 0–10) at 12, 24, 36, and 48 hours postoperatively. (B) Box plot of cumulative OMME usage normalized by hospital length of stay. *, P<0.05. OMME, oral morphine milligram equivalents; RATS, robotic-assisted thoracoscopic surgery; VATS, video-assisted thoracoscopic surgery.

Normalized OMME usage was higher in the RATS cohort compared to the VATS cohort, with an average daily usage of 33.2 mg/day (median: 22.52 mg/day, SD: 32.90) for the VATS cohort and 39.8 mg/day (median: 33.9 mg/day, SD: 29.0) for the RATS cohort (P=0.05, Figure 3B).

Discharge and outpatient opioid use

A summary of patient outcomes after surgery and hospital discharge is provided in Table 3. The mean follow-up interval was 13.20 days for RATS patients and 10.18 days for VATS patients (P=0.02). While no significant differences in the distribution of pain levels at follow-up visits were observed between cohorts (P=0.06), raw counts demonstrated 51.9% of VATS patients to have no pain at follow-up visit compared to 26.9% of RATS patients. At day of discharge, near-equivalent proportions of RATS and VATS patients were still using opioid medications (VATS: 73.1%, RATS: 76.9%). During the interim period at home following discharge, 67.3% of VATS patients and 59.6% of RATS patients continued to require opioids for pain (P=0.54). At the first postoperative follow-up visit, no significant differences in opioid usage were detected, with 46.2% of VATS patients continuing to require opioids compared to 32.7% of RATS patients (P=0.23). A visual representation of the proportion of patients requiring opioids at each time point after hospital discharge is also provided in Figure 3A.

Discharge prescriptions for opioid and non-opioid medications were also reviewed. A five-day course of oral oxycodone (5 mg) was prescribed to 86.5% of RATS patients, compared to 67.3% of VATS patients (P=0.04). For non-opioid medications, RATS patients were more frequently prescribed acetaminophen 325 mg (RATS: 90.4%, VATS: 69.2%; P=0.02) and methocarbamol 500 mg (RATS: 75.0%, VATS: 46.2%; P=0.005). No significant differences in rates of gabapentin, ibuprofen, or naproxen prescription at discharge were observed.

Discussion

In this retrospective, propensity score-matched cohort study of patients with Stage I NSCLC, RATS was associated with significantly shorter hospital LOS by a median of 1.62 days compared to VATS. However, RATS patients required higher median inpatient opioid consumption and reported greater pain scores in the first 48 hours postoperatively. Despite these early differences, outpatient opioid use and pain levels at follow-up became comparable between cohorts.

The growing adoption of RATS for minimally invasive NSCLC treatment has been supported by numerous studies demonstrating its oncological non-inferiority compared to VATS (3,4,9,20). However, the full scope of its benefits regarding critical PROs, including symptom severity and functional status, remains under-characterized (9). Our findings of greater postoperative pain in the first 48 hours for RATS compared to VATS align with those reported by Qu et al., who described RATS patients with higher numerical pain scores on postoperative day 1 compared to VATS (21). However, other studies (9) have reported milder pain for RATS compared to VATS during the first week after surgery. One explanation for increased acute pain in RATS patients in our study may be the increased number of ports used in RATS, causing increased acute tissue injury (21). Reduced haptic feedback in RATS may also increase unperceived torque on ribs, contributing to immediate postoperative pain (22). Once pain from initial tissue injury subsides, however, the improved flexibility of robotic arms likely minimizes long-term injury to intercostal nerves and surrounding musculature via reduced fulcrum effects (9,14,23).

Shorter hospital stays observed in the RATS cohort align with prior studies (9), suggesting faster recovery and earlier discharge with robotic approaches, potentially due to improved visualization and precision afforded by the robotic platform. Although a higher proportion of RATS patients were prescribed opioids at discharge (86.5% vs. 67.3%, P=0.04), fewer continued to require opioids at follow-up visits (VATS: 46.2%, RATS: 32.7%, P=0.23). While this difference was not statistically significant, it may reflect a signal of improved functional recovery following RATS that should be investigated in future studies with larger cohorts. RATS patients also received more adjunct non-opioid medications at discharge, including acetaminophen and methocarbamol, suggesting greater attention to multimodal pain control in the RATS cohort or institutional changes in prescribing practices over time. While factors driving hospital LOS are likely multifactorial, we postulate that differences were primarily driven by patient-related factors, including pain and opioid use, and physician discretion regarding the timing of weaning from intravenous to oral analgesia.

Notably, inpatient opioid consumption remained higher in the RATS cohort even when normalized by hospital LOS, suggesting greater analgesic requirements for these patients during the early recovery period. This observation aligns with previous findings reporting increased morphine use on postoperative day 2 in RATS patients compared to VATS patients (13,14). Therefore, the increased opioid use observed in RATS patients may be concentrated during the initial phase of hospitalization when postoperative pain is most intense.

Our findings challenge assumptions that RATS is universally associated with less pain or reduced opioid need in the immediate postoperative setting. Instead, RATS may initially require more intensive pain control that is followed by faster tapering and recovery. These pain management trends highlight the importance of evaluating both inpatient and outpatient opioid use over time, rather than relying on a single time point. Furthermore, prescribing practices may not fully align with patient needs—RATS patients were prescribed opioids at higher rates, despite a shorter recovery period—potentially due to cautious physician practices or evolving institutional guidelines (15,16). Given the high rate of persistent opioid use among thoracic surgery patients, this issue is particularly important for future considerations (14,15).

Enhanced recovery after surgery (ERAS) protocols emphasize opioid-sparing multimodal pain management, favoring oral acetaminophen over IV acetaminophen when possible (24,25). In our study, RATS patients received greater quantities of oral acetaminophen and opioids but significantly less IV acetaminophen and bupivacaine, suggesting a potential shift toward simplified oral regimens. While earlier studies reported no difference in acute or chronic pain between RATS and VATS, more recent evidence suggests that robotic approaches permit lower postoperative opioid administration rates (6,11,14). There remains a lack of evidence directly relating pain scores with opioid use, and therefore, patient-reported pain scores may not always accurately reflect opioid requirements (6,14,15). Furthermore, we found that operative time was slightly shorter in RATS cases (not statistically significant), which may reflect institutional experience with robotic surgery (4,7,26). Since shorter operative times have been linked to lower postoperative pain, reduction in the learning curve may also contribute to observed recovery trends (27).

Limitations of our study include a retrospective, single-center design, and a relatively small sample size after propensity score matching. Although matching was performed using key preoperative variables, unmeasured confounding from postoperative complications and differences in intraoperative pain control techniques remains possible. Differences in pain scores and opioid use, while statistically significant, may not always reflect clinically meaningful differences in prescribing practices or patient experience depending on effect size. Additionally, pain was not always reported as directly from the port site, incision site, or extraction site due to patient medical literacy and therefore introduces additional variability into our study. Patients also received differing intraoperative pain management techniques, including intercostal nerve blocks and cryoablation over the study time period; the indications for cryoablation could not be reliably assessed within the constraints of a retrospective study design and therefore may dampen the effect size for the robotic-assisted approach. Patients chosen for RATS over VATS may also be of higher socioeconomic status, which may indirectly improve their outcomes over VATS. Despite these limitations, our study offers a detailed, unique comparison of inpatient and outpatient pain control by incorporating opioid and non-opioid analgesic usage alongside patient-reported pain scores.

Future directions include prospective, multicenter studies assessing pain at port, incision, and extraction sites, quantifying chronic opioid use beyond 90 days, and integration of patient-reported outcomes measures (PROMs) to fully capture functional recovery. Furthermore, a comprehensive investigation into the cost-effectiveness of RATS compared to VATS with respect to opioid use, LOS, and short-term readmission rates will be critical for understanding the broader impact of robotic surgery on healthcare delivery. Our investigation highlights a reduction in hospital LOS for RATS over VATS but with higher inpatient opioid consumption, thus providing valuable insights into further investigations regarding the utility of robotic surgery in clinical practice.

Conclusions

In this propensity score-matched study of 104 patients with Stage I NSCLC, RATS was associated with higher patient-reported pain scores in the first 48 hours postoperatively and greater inpatient opioid consumption compared to VATS. However, these effects were offset by a significantly shorter hospital stay (1.62 days shorter) and greater use of multimodal non-opioid analgesics. Our findings suggest that while RATS may require more intensive early pain management, the robotic approach may also facilitate faster recovery. Future studies are needed to evaluate long-term opioid dependence, functional recovery times, and cost-effectiveness to fully characterize the long-term benefits of robotic surgery over conventional techniques.

Acknowledgments

None.

Footnote

Reporting Checklist: The authors have completed the STROBE reporting checklist. Available at https://ccts.amegroups.com/article/view/10.21037/ccts-25-27/rc

Data Sharing Statement: Available at https://ccts.amegroups.com/article/view/10.21037/ccts-25-27/dss

Peer Review File: Available at https://ccts.amegroups.com/article/view/10.21037/ccts-25-27/prf

Funding: None.

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://ccts.amegroups.com/article/view/10.21037/ccts-25-27/coif). A.D. has proctored other surgeons on the Intuitive Da Vinci Robotic platform for payment over the last 36 months. The other authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by institutional review board of Stony Brook University (IRB2022-00493) and individual consent for this retrospective analysis was waived.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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