Using Virtual Reality to teach ultrasound-guided needling skills for regional anaesthesia: A randomised controlled trial.

STUDY OBJECTIVE: We previously designed and validated a virtual reality-based simulator to help train novices in ultrasound-guided needling skills necessary for safe and competent ultrasound-guided regional anaesthesia. This study was designed to compare the performance and error rates of novices trained by a human faculty aided with the assistance of this virtual reality simulator (virtual reality-assisted training), versus novices trained wholly by humans (conventional training). DESIGN, SETTING, AND PARTICIPANTS: In this single centre, randomised controlled study, we used a standardised teaching protocol, rigorous blinding, iterative training of assessors, and validated global rating scale and composite error score checklists to assess skills learning of novice participants. MAIN RESULTS: We recruited 45 novices and scored 270 assessments of performance and error rates. Inter-rater correlation coefficient of reliability of scoring between assessors for the global rating scale was 0.84 (95%CI 0.68-0.92) and for the composite error score checklist was 0.87 (95%CI 0.73-0.93). After adjustment for age, sex, Depression, Anxiety and Stress-21, and baseline score, there was no statistical difference for virtual reality-assisted training compared to conventional training in final global rating score (average treatment effect -3.30 (95%CI-13.07-6.48), p = 0.51) or in the final composite error score (average treatment effect 1.14 (95%CI -0.60-2.88), p = 0.20). Realism in the virtual reality simulator was similar to real-life when measured by the Presence Questionnaire, all components p > 0.79; and task workload assessed by the NASA-Task Load Index was not statistically different between groups, average treatment effect 5.02 (95%CI -3.51-13.54), p = 0.25. Results were achieved in the virtual reality-assisted group with half the human faculty involvement. CONCLUSION: Novices trained using a hybrid, virtual reality-assisted teaching program showed no superiority to novices trained using a conventional teaching program, but with less burden on teaching resources.

Craniocaudal spread and clinical translation for combined erector spinae plane block and retrolaminar block in soft embalmed cadavers: a randomised controlled equivalence study.

BACKGROUND: Erector spinae plane (ESP) block spread can be unpredictable. We previously improved the spread of ESP injection by addition of retrolaminar (RL) injection. However, it is not clear whether spread at high thoracic levels is similar to spread at midthoracic levels. Our primary objective was to demonstrate that craniocaudal dye spread was equivalent after combined ESP and RL injection using a 19 G Tuohy needle at the third (T3) and sixth (T6) vertebrae in soft embalmed Thiel cadavers. METHODS: We randomised 20 combined ESP and RL injections to the T3 and T6 vertebral levels on both sides of 10 prone Thiel cadavers. A 3-8 MHz transducer was placed in the paramedian sagittal plane and a single anaesthetist injected 10 ml dye onto the transverse process, then 10 ml dye onto the laminae of T3 or T6. Cadavers were dissected 24 h later. RESULTS: Mean (sd) craniocaudal spread of dye after combined ESP + RL injection at T3 and T6 vertebral levels was equivalent: 8.6 (1.8) vs 8.7 (2.3) levels, respectively; difference (90% confidence interval): -0.1 (-1.4 to 1.6), P=0.904. Dye extended uniformly, cranially and caudally, from the point of injection. A 3D prosection created from a Thiel cadaver confirmed that the dorsal ramus emerges from the costotransverse foramen deep to the intertransverse ligament within the retro-superior costotransverse ligament space. Combined ESP and RL block in six patients before mastectomy achieved extensive anterior, lateral, and posterior chest wall paraesthesia over four to six dermatomes. CONCLUSIONS: Combined ESP and RL injections showed equivalent and consistent spread at T3 and T6 injection sites. A pilot study confirmed translation to patients.

Nerve block, nerve damage, and fluid injection pressure: overturning the myth.

Histological and micro-ultrasound evidence rebuffs deep-rooted views on the nature of nerve block, nerve damage, and injection pressure monitoring. We propose that the ideal position of the needle tip for nerve block is between the innermost circumneural fascial layer and outer epineurium, with local anaesthetic passing circumferentially through adipose tissue. Thin, circumferential, subepineural expansion that is invisible to the naked eye was identified using micro-ultrasound, and could account for variability of outcomes in clinical practice. Pressure monitoring cannot differentiate between intrafascicular and extrafascicular injection. High injection pressure only indicates intraneural extrafascicular spread, not intrafascicular spread, because it is not possible to inject into the stiff endoneurium in most human nerves.

Predicting necrotising soft tissue infections in people who inject drugs: poor performance of the Laboratory Risk Indicator for Necrotising Fasciitis score and development of a novel clinical predictive nomogram in a retrospective cohort with internal validation.

INTRODUCTION: Necrotising soft tissue infections (NSTI) can threaten life and limb. Early identification and urgent surgical debridement are key for improved outcomes. NSTI can be insidious. Scoring systems, like the Laboratory Risk Indicator for Necrotising Fasciitis (LRINEC), exist to aid diagnosis. People who inject drugs (PWID) are high risk for NSTI. This study aimed to assess the utility of the LRINEC in PWID with lower limb infections and develop a predictive nomogram. METHODS: A retrospective database of all hospital admissions due to limb-related complications secondary to injecting drug use between December 2011 and December 2020 was compiled through discharge codes and a prospectively maintained Vascular Surgery database. All lower limb infections were extracted from this database, dichotomised by NSTI and non-NSTI with the LRINEC applied. Specialty management times were evaluated. Statistical analyses involved: chi-square; Analysis of "variance"; Kaplan-Meier, and receiver operating characteristic curves. Nomograms were developed to facilitate diagnosis and predict survival. RESULTS: There were 557 admissions for 378 patients, with 124 (22.3%; 111 patients) NSTI. Time from admission to: theatre and computed tomography imaging respectively varied significantly between specialties ( P =0.001). Surgical specialties were faster than medical ( P =0.001). Vascular surgery received the most admissions and had the quickest time to theatre. During follow-up there were 79 (20.9%) deaths: 27 (24.3%) NSTI and 52 (19.5%) non-NSTI. LRINEC ≥6 had a positive predictive value of 33.3% and sensitivity of 74% for NSTI. LRINEC <6 had a negative predictive value of 90.7% and specificity of 63.2% for non-NSTI. Area under the curve was 0.697 (95% CI: 0.615-0.778). Nomogram models found age, C-reactive protein, and non-linear albumin to be significant predictors of NSTI, with age, white cell count, sodium, creatinine, C-reactive protein, and albumin being significant in predicting survival on discharge. CONCLUSION: There was reduced performance of the LRINEC in this PWID cohort. Diagnosis may be enhanced through use of this predictive nomogram.

Accuracy of injection pressure measurement at peripheral nerves using high-resolution 40 MHz ultrasound in an anesthetized porcine model.

BACKGROUND: Fluid injection pressure measurement is promoted as a marker of needle tip position that discriminates between tissue layers. However, clinical ultrasound has insufficient resolution to identify the exact position of the needle tip. Our primary objective was to use 40 MHz ultrasound in anesthetized pigs in order to precisely locate the tip of the needle and measure opening injection pressure in muscle, at epineurium and in subepineurium. METHODS: We surgically exposed the axillae of four anesthetized pigs. Two operators placed a 40 MHz ultrasound transducer over the pectoral muscle and imaged axillary, median and radial nerves. Injections (0.5 mL) were randomized to in-plane and out-of-plane needle trajectories and flow rates of 1, 6 and 12 mL/min. RESULTS: We identified 541 fascicles in 23 nerves. The ratio of fascicle area to nerve area remained constant at ~0.30 for all nerves. Axillary nerves were smaller than median and radial nerves, difference in diameter (95% CI) 1.61 (0.87 to 2.36) mm, p<0.001 and 1.59 (0.82 to 2.36) mm, p=0.001, respectively. Axillary nerves had less fascicles per nerve than median nerves, difference 7.63 (2.43 to 12.83) and radial nerves, difference 9.02 (3.64 to 14.40). We visualized the circumneurium and injection within the subcircumneural compartment. Intraneural injection increased nerve area (SD) from 5.7 (2.2) mm2 to 13.7 (5.5) mm2, difference 8.0 (5.4-10.6) mm2, p<0.001. Mean injection pressure was greater in subepineurium compared with muscle, geometric ratio 2.29 (1.30 to 4.10), p<0.001; and greater on epineurium compared with muscle, geometric ratio 1.73 (1.03 to 3.00), p=0.01. Twenty-two out of 23 injections in muscle, 14 out of 23 injections at epineurium and 11 out of 22 injections in subepineurium were <138 kPa (20 psi). CONCLUSION: Needle tip position was not discernible using pressure monitoring. The circumneurium and subcircumneural injection compartment were observed but not intrafascicular injection.

Traumatic needle damage to nerves during regional anesthesia: presentation of a novel mechanotransduction hypothesis.

Despite advances in needle positioning techniques, nerve damage still occurs after regional anesthesia. Recognized causes include local anesthetic toxicity, subperineural injection, high subepineural fluid injection pressures and subepineural hematoma after forceful needle--nerve contact.We hypothesize that subperineural injection is still possible, but less likely to be the cause of nerve damage because needle penetration of fascicles and mechanical damage is difficult to achieve. High-resolution (75 µm) 40 MHz micro-ultrasound images of pig axillae show short-bevelled 22 g, 0.7 mm wide block needles that are three times larger than the average fascicle. Fascicular bundles are extremely difficult to puncture because they spin away on needle contact. Histology from fresh cadavers after supposed intrafascicular injection shows fluid spread within perineurium and intrafascicular perineural septae, but no breach of endoneurium or axons.We propose that mechanotransduction, the cellular changes that occur in response to force, contributes to nerve damage. Piezo ion channel proteins transduce force into electrical activity by rapid entry of cations into cells. Excessive Ca2+ influx into cells has the potential to inhibit nerve regeneration. Cellular changes include regulation of gene expression. The forces associated with purposeful needle insertion are generally unknown. Our experiments in the soft embalmed Thiel cadaver showed a lognormal range of forces between 0.6 N and 16.8 N on epineural penetration.We hypothesize that forceful needle injury may cause nerve damage by activation of Piezo receptors and release of intracellular Ca2.

Patterns of Skills Acquisition in Anesthesiologists During Simulated Interscalene Block Training on a Soft Embalmed Thiel Cadaver: Cohort Study.

BACKGROUND: The demand for regional anesthesia for major surgery has increased considerably, but only a small number of anesthesiologists can provide such care. Simulations may improve clinical performance. However, opportunities to rehearse procedures are limited, and the clinical educational outcomes prescribed by the Royal College of Anesthesiologists training curriculum 2021 are difficult to attain. Educational paradigms, such as mastery learning and dedicated practice, are increasingly being used to teach technical skills to enhance skills acquisition. Moreover, high-fidelity, resilient cadaver simulators are now available: the soft embalmed Thiel cadaver shows physical characteristics and functional alignment similar to those of patients. Tissue elasticity allows tissues to expand and relax, fluid to drain away, and hundreds of repeated injections to be tolerated without causing damage. Learning curves and their intra- and interindividual dynamics have not hitherto been measured on the Thiel cadaver simulator using the mastery learning and dedicated practice educational paradigm coupled with validated, quantitative metrics, such as checklists, eye tracking metrics, and self-rating scores. OBJECTIVE: Our primary objective was to measure the learning slopes of the scanning and needling phases of an interscalene block conducted repeatedly on a soft embalmed Thiel cadaver over a 3-hour period of training. METHODS: A total of 30 anesthesiologists, with a wide range of experience, conducted up to 60 ultrasound-guided interscalene blocks over 3 hours on the left side of 2 soft embalmed Thiel cadavers. The duration of the scanning and needling phases was defined as the time taken to perform all the steps correctly. The primary outcome was the best-fit linear slope of the log-log transformed time to complete each phase. Our secondary objectives were to measure preprocedural psychometrics, describe deviations from the learning slope, correlate scanning and needling phase data, characterize skills according to clinical grade, measure learning curves using objective eye gaze tracking and subjective self-rating measures, and use cluster analysis to categorize performance irrespective of grade. RESULTS: The median (IQR; range) log-log learning slopes were -0.47 (-0.62 to -0.32; -0.96 to 0.30) and -0.23 (-0.34 to -0.19; -0.71 to 0.27) during the scanning and needling phases, respectively. Locally Weighted Scatterplot Smoother curves showed wide variability in within-participant performance. The learning slopes of the scanning and needling phases correlated: ρ=0.55 (0.23-0.76), P<.001, and ρ=-0.72 (-0.46 to -0.87), P<.001, respectively. Eye gaze fixation count and glance count during the scanning and needling phases best reflected block duration. Using clustering techniques, fixation count and glance were used to identify 4 distinct patterns of learning behavior. CONCLUSIONS: We quantified learning slopes by log-log transformation of the time taken to complete the scanning and needling phases of interscalene blocks and identified intraindividual and interindividual patterns of variability.

Pilot Project for a Web-Based Dynamic Nomogram to Predict Survival 1 Year After Hip Fracture Surgery: Retrospective Observational Study.

BACKGROUND: Hip fracture is associated with high mortality. Identification of individual risk informs anesthetic and surgical decision-making and can reduce the risk of death. However, interpreting mathematical models and applying them in clinical practice can be difficult. There is a need to simplify risk indices for clinicians and laypeople alike. OBJECTIVE: Our primary objective was to develop a web-based nomogram for prediction of survival up to 365 days after hip fracture surgery. METHODS: We collected data from 329 patients. Our variables included sex; age; BMI; white cell count; levels of lactate, creatinine, hemoglobin, and C-reactive protein; physical status according to the American Society of Anesthesiologists Physical Status Classification System; socioeconomic status; duration of surgery; total time in the operating room; side of surgery; and procedure urgency. Thereafter, we internally calibrated and validated a Cox proportional hazards model of survival 365 days after hip fracture surgery; logistic regression models of survival 30, 120, and 365 days after surgery; and a binomial model. To present the models on a laptop, tablet, or mobile phone in a user-friendly way, we built an app using Shiny (RStudio). The app showed a drop-down box for model selection and horizontal sliders for data entry, model summaries, and prediction and survival plots. A slider represented patient follow-up over 365 days. RESULTS: Of the 329 patients, 24 (7.3%) died within 30 days of surgery, 65 (19.8%) within 120 days, and 94 (28.6%) within 365 days. In all models, the independent predictors of mortality were age, BMI, creatinine level, and lactate level. The logistic model also incorporated white cell count as a predictor. The Cox proportional hazards model showed that mortality differed as follows: age 80 vs 60 years had a hazard ratio (HR) of 0.6 (95% CI 0.3-1.1), a plasma lactate level of 2 vs 1 mmol/L had an HR of 2.4 (95% CI 1.5-3.9), and a plasma creatinine level of 60 vs 90 mol/L had an HR of 2.3 (95% CI 1.3-3.9). CONCLUSIONS: In conclusion, we provide an easy-to-read web-based nomogram that predicts survival up to 365 days after hip fracture. The Cox proportional hazards model and logistic models showed good discrimination, with concordance index values of 0.732 and 0.781, respectively.

A paired comparison of nerve dimensions using B-Mode ultrasound and shear wave elastography during regional anaesthesia.

Introduction: Shear wave elastography (SWE) presents nerves in colour, but the dimensions of its colour maps have not been validated with paired B-Mode nerve images. Our primary objective was to define the bias and limits of agreement of SWE with B-Mode nerve diameter. Our secondary objectives were to compare nerve area and shape, and provide a clinical standard for future application of new colour imaging technologies such as artificial intelligence. Materials and Methods: Eleven combined ultrasound-guided regional nerve blocks were conducted using a dual-mode transducer. Two raters outlined nerve margins on 110 paired B-Mode and SWE images every second for 20 s before and during injection. Bias and limits of agreement were plotted on Bland-Altman plots. We hypothesized that the bias of nerve diameter would be <2.5% and that the percent limits of agreement would lie ±0.67% (2 SD) of the bias. Results: There was no difference in the bias (95% confidence interval (CI) limits of agreement) of nerve diameter measurement, 0.01 (-0.14 to 0.16) cm, P = 0.85, equivalent to a 1.4% (-56.6% to 59.5) % difference. The bias and limits of agreement were 0.03 (-0.08 to 0.15) cm2, P = 0.54 for cross-sectional nerve area; and 0.02 (-0.03 to 0.07), P = 0.45 for shape. Reliability (ICC) between raters was 0.96 (0.94-0.98) for B-Mode nerve area and 0.91 (0.83-0.95) for SWE nerve area. Conclusions: Nerve diameter measurement from B-Mode and SWE images fell within a priori measures of bias and limits of agreement.

Needle insertion forces and fluid injection pressures during targeting of nerves in a soft embalmed cadaver model.

PURPOSE: Forceful needle-nerve contact and high subepineural pressures and are recognised causes of nerve damage. Pressure and force measurements are necessary to inform the mechanisms of nerve injury, build virtual simulator environments and provide operator feedback during simulation training. However, the range of pressures and forces encountered at tissue layers during targeted needle insertion and fluid injection are not known. METHODS: We built a needle that recorded in-line pressure during fluid injection and continuously measured force at the needle tip. Two anaesthetists were randomised to insert a 21 g block needle at 48 nerve sites on both sides of 3 soft embalmed Thiel cadavers. Our objective was to measure pressure and force during the course of targeted nerve injection at epimysium, in perineural tissue, on epineurium and during subepineural injection. At each interface, we infused a 0.5 ml bolus of embalming solution at a rate of 12 ml min-1 and recorded the pressure response. Force was measured continuously in the background throughout the procedure. RESULTS: Pressure was greater at epineurium and within subepineurium than perineural tissue, geometric ratio (95% CI) 4.7 (3.0-7.3) kPa and 3.8 (2.5-5.7) kPa, respectively, both P < 0.0001. Force on nerve contact and on nerve penetration was greater than force in perineural tissue, geometric ratios (95% CI) 3.0 (1.9-4.7) N and 3.6 (2.2-7.5) N, respectively, both P < 0.0001. On nerve contact, 1 in 6 insertions were ≥ 5 N CONCLUSIONS: Despite valid infusion pressures, anaesthetists exerted excessive force on nerves.

Randomized trial comparing the spread of erector spinae block with the combination of erector spinae block and retrolaminar block in soft embalmed Thiel cadavers.

BACKGROUND: Erector spinae plane (ESP) and retrolaminar (RL) blocks show unreliable spread. We hypothesize that the combination of ESP and RL blocks provides more extensive and reliable spread of dye than single ESP blocks. Our primary objective was to compare the spread of dye to the paravertebral spaces after the combination block and ESP block in Thiel embalmed cadavers. Spread, the primary end point, was defined as the number of paravertebral spaces colored with dye per injection. MATERIALS AND METHODS: A single anesthetist performed ultrasound-guided ESP (20 mL) and combination of ESP and RL (10 mL each) blocks at the third thoracic vertebra of eight soft embalmed Thiel cadavers. Tissue displacement was visualized on an adjacent strain elastography image. Cadavers were dissected 24 hours later and anatomical structures were inspected for the presence of dye. FINDINGS: Dye was visualized in more paravertebral spaces with the combination block (median 3 (IQR 3-5 (range 0-8)) vs 1.5 (IQR 0.25-2.75 (range 0-3) and difference (1.5 (0-4), p=0.04). Six out of seven (86%) combined erector spinae and RL blocks spread to at least three paravertebral spaces compared with two out of eight (25%) ESP blocks (RR 3.4, 95% CI 1.0 to 11.8; p=0.04). Contralateral spread occurred in three combination blocks and in one ESP block (OR 9.0, 95% CI 4.0 to 21.1; p<0.001). CONCLUSIONS: In conclusion, the combination of ESP and RL blocks was more extensive and reliable than ESP block alone.

Standardizing nomenclature in regional anesthesia: an ASRA-ESRA Delphi consensus study of abdominal wall, paraspinal, and chest wall blocks.

BACKGROUND: There is heterogeneity in the names and anatomical descriptions of regional anesthetic techniques. This may have adverse consequences on education, research, and implementation into clinical practice. We aimed to produce standardized nomenclature for abdominal wall, paraspinal, and chest wall regional anesthetic techniques. METHODS: We conducted an international consensus study involving experts using a three-round Delphi method to produce a list of names and corresponding descriptions of anatomical targets. After long-list formulation by a Steering Committee, the first and second rounds involved anonymous electronic voting and commenting, with the third round involving a virtual round table discussion aiming to achieve consensus on items that had yet to achieve it. Novel names were presented where required for anatomical clarity and harmonization. Strong consensus was defined as ≥75% agreement and weak consensus as 50% to 74% agreement. RESULTS: Sixty expert Collaborators participated in this study. After three rounds and clarification, harmonization, and introduction of novel nomenclature, strong consensus was achieved for the names of 16 block names and weak consensus for four names. For anatomical descriptions, strong consensus was achieved for 19 blocks and weak consensus was achieved for one approach. Several areas requiring further research were identified. CONCLUSIONS: Harmonization and standardization of nomenclature may improve education, research, and ultimately patient care. We present the first international consensus on nomenclature and anatomical descriptions of blocks of the abdominal wall, chest wall, and paraspinal blocks. We recommend using the consensus results in academic and clinical practice.

Real-time visualisation of peripheral nerve trauma during subepineural injection in pig brachial plexus using micro-ultrasound.

BACKGROUND: Nerve damage is consistently demonstrated after subepineural injection in animal studies, but not after purposeful injection in patients participating in clinical studies. There is a need to better visualise nerves in order to understand the structural changes that occur during subepineural injection. METHODS: We scanned the brachial plexuses of three anaesthetised pigs using micro-ultrasound imaging (55-22 MHz probe), inserted 21 gauge block needles into the radial, median, and axillary nerves, and injected two 0.5 ml boluses of saline into nerves at a rate of 12 ml min-1. Our objectives were to measure the area and diameter of nerves and fascicles, and to describe changes in nerve anatomy, comparing our findings with histology. RESULTS: Images were acquired at 42 sites across 18 nerves in three pigs and compared dimensions (geometric ratio; 95% confidence interval; P value). As expected, the nerve cross-sectional area was greater in the proximal brachial plexus compared with the mid-plexus (2.10; 1.07-4.11; P<0.001) and the distal plexus (2.64; 1.42-4.87; P<0.001). Nerve area expanded after 0.5 ml injection (2.13; 1.48-3.08; P<0.001). Using microultrasound, subepineural injection was characterised by nerve and fascicle rotation, uniform, or localised swelling and epineural rupture. Micro-ultrasound revealed a unique pattern suggestive of subperineural injection after a median nerve injection, and good face validity with histology. Histology showed epineural trauma and inflammation to the perineurium. CONCLUSION: We accurately identified fascicles and real-time structural changes to peripheral nerves using micro-ultrasound. This is the first study to visualise in vivo and in real-time the motion of nerves and fascicles in response to anaesthetic needle insertion and fluid injection.

Validation of the soft-embalmed Thiel cadaver as a high-fidelity simulator of pressure during targeted nerve injection.

INTRODUCTION: Although administration of regional anesthesia nerve blocks has increased during the COVID-19 pandemic, training opportunities in regional anesthesia have reduced. Simulation training may enhance skills, but simulators must be accurate enough for trainees to engage in a realistic way-for example, detection of excessive injection pressure. The soft-embalmed Thiel cadaver is a life-like, durable simulator that is used for dedicated practice and mastery learning training in regional anesthesia. We hypothesized that injection opening pressure in perineural tissue, at epineurium and in subepineurium were similar to opening pressures measured in experimental animals, fresh frozen cadavers, glycol soft-fix cadavers and patients. METHODS: We systematically reviewed historical data, then conducted three validation studies delivering a 0.5 mL hydrolocation bolus of embalming fluid and recording injection pressure. First, we delivered the bolus at 12 mL/min at epimysium, perineural tissue, epineurium and in subepineurium at 48 peripheral nerve sites on three cadavers. Second, we delivered the bolus at using three infusion rates: 1 mL/min, 6 mL/min and 12 mL/min on epineurium at 70 peripheral nerve sites on five cadavers. Third, we repeated three injections (12 mL/min) at 24 epineural sites over the median and sciatic nerves of three cadavers. RESULTS: Mean (95%) injection pressure was greater at epineurium compared with subepineurium (geometric ratio 1.2 (95% CI: 0.9 to 1.6)), p=0.04, and perineural tissue (geometric ratio 5.1 (95% CI: 3.7 to 7.0)), p<0.0001. Mean (95%) injection pressure was greater at 12 mL/min compared with 1 mL/min (geometric ratio 1.6 (95% CI: 1.2 to 2.1), p=0.005). Pressure measurements were similar in study 3 (p>0.05 for all comparisons). DISCUSSION: We conclude that the soft-embalmed Thiel cadaver is a realistic simulator of injection opening pressure.

Erratum: Jiang et al. Localization Accuracy of Ultrasound-Actuated Needle with Color Doppler Imaging. Diagnostics 2020, 10, 1020.

The authors wish to correct the following erratum in this paper [...].