Impact of balloon post-dilation on valve durability and long-term clinical outcomes after self-expanding transcatheter aortic valve implantation.

BACKGROUND: Balloon post-dilation (BPD) is a widely adopted strategy to optimize acute results of TAVI, with a positive impact on both paravalvular leak and mean gradients. On the other hand, the inflation of the balloon inside prosthetic leaflets may damage them increasing the risk of structural valve deterioration (SVD). Furthermore, the impact of BPD on long-term clinical outcomes and valve hemodynamics is yet unknown. AIMS: To evaluate the impact of BPD on valve durability and long-term clinical outcomes in patients undergoing self-expanding transcatheter valve implantation (TAVI). METHODS: Echocardiographic and clinical data from the ClinicalService (a nation-based data repository and medical care project) were analyzed. Patients were divided into two groups, those who underwent BPD after TAVI and those who did not. Coprimary endpoints were all-cause death and SVD. Cumulative incidence functions for SVD were estimated. RESULTS: Among 1835 patients included in the study, 417 (22.7%) underwent BPD and 1418 (77.3%) did not undergo BPD. No statistically significant differences at 6-year follow-up were found between groups in terms of all-cause mortality (HR: 1.05, 95% CI: 0.9-1.22; p = 0.557) and SVD (2.1% vs. 1.4%, p = 0.381). In addition, BPD did not predispose to higher risk of cardiovascular death, myocardial infarction, valve thrombosis, and endocarditis at 6-year follow-up. CONCLUSIONS: BPD following TAVI with a self-expanding prosthesis does not seem to be associated with an increased risk of adverse clinical outcomes or SVD at 6-year follow-up.

The Retinal Phenotype Associated with the p.Pro101Thr BEST1 Variant.

PURPOSE: To describe the retinal phenotype associated with the p.Pro101Thr BEST1 variant. DESIGN: Retrospective, observational case series. PARTICIPANTS: Patients diagnosed with bestrophinopathies in which molecular genetic testing identified the p.Pro101Thr BEST1 as well as healthy carriers among their first-degree relatives. METHODS: Medical records were reviewed to obtain data on family history and ophthalmic examinations, including retinal imaging. The imaging protocol included OCT and fundus autofluorescence using Spectralis HRA + OCT (Heidelberg Engineering). Genetic analysis was performed by next-generation sequencing. MAIN OUTCOME MEASURES: Results of ophthalmic examinations and multimodal imaging features of retinal phenotypes. RESULTS: The c.301C>A, p.Pro101Thr BEST1 missense variant was identified as the causative variant in 8 individuals (all men) from 5 families, accounting for 13% of cases (8/61) and 10% of pathogenic alleles (9/93) in our cohort of patients affected by bestrophinopathies. Seven individuals (14 eyes) had the variant in heterozygous status: all eyes had a hyperopic refractive error (median spherical equivalent of + 3.75 diopters [D]) and 4 individuals had a macular dystrophy with mildly reduced visual acuity (median of 20/25 Snellen), whereas the other 3 were asymptomatic carriers. On multimodal retinal imaging, 5 (36%) out of 14 eyes had subclinical bestrophinopathy, 4 (29%) had typical findings of adult-onset foveomacular vitelliform dystrophy (AOFVD), and the remaining 5 (36%) displayed a pattern dystrophy-like phenotype. Follow-up data were available for 6 subjects, demonstrating clinical stability up to 11 years, in both subclinical and clinical forms. An additional patient with autosomal recessive bestrophinopathy was found to harbor the p.Pro101Thr variant in homozygosity. CONCLUSIONS: The p.Pro101Thr BEST1 variant is likely a frequent cause of bestrophinopathy in the Italian population and can result in autosomal dominant macular dystrophies with incomplete penetrance and mild clinical manifestations as well as autosomal recessive bestrophinopathy. The spectrum of autosomal dominant maculopathy includes the typical AOFVD and a pattern dystrophy-like phenotype. FINANCIAL DISCLOSURE(S): Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Lumped-parameter model as a non-invasive tool to assess coronary blood flow in AAOCA patients.

Anomalous aortic origin of the coronary artery (AAOCA) is a rare disease associated with sudden cardiac death, usually related to physical effort in young people. Clinical routine tests fail to assess the ischemic risk, calling for novel diagnostic approaches. To this aim, some recent studies propose to assess the coronary blood flow (CBF) in AAOCA by computational simulations but they are limited by the use of data from literature retrieved from normal subjects. To overcome this limitation and obtain a reliable assessment of CBF, we developed a fully patient-specific lumped parameter model based on clinical imaging and in-vivo data retrieved during invasive coronary functional assessment of subjects with AAOCA. In such a way, we can estimate the CBF replicating the two hemodynamic conditions in-vivo analyzed. The model can mimic the effective coronary behavior with high accuracy and could be a valuable tool to quantify CBF in AAOCA. It represents the first step required to move toward a future clinical application with the aim of improving patient care. The study was registered at Clinicaltrial.gov with (ID: NCT05159791, date 2021-12-16).

Morphological Changes of Anomalous Coronary Arteries From the Aorta During the Cardiac Cycle Assessed by IVUS in Resting Conditions.

BACKGROUND: Anomalous aortic origin of coronary artery (AAOCA) with intramural segment is associated with risk of sudden cardiac death, probably related to a compressive mechanism exerted by the aorta. However, the intramural compression occurrence and magnitude during the cardiac cycle remain unknown. We hypothesized that (1) in end diastole, the intramural segment is narrower, more elliptic, and has greater resistance than extramural segment; (2) the intramural segment experiences a further compression in systole; and (3) morphometry and its systolic changes vary within different lumen cross-sections of the intramural segment. METHODS: Phasic changes of lumen cross-sectional coronary area, roundness (minimum/maximum lumen diameter), and hemodynamic resistance (Poiseuille law for noncircular sections) were derived from intravascular ultrasound pullbacks at rest for the ostial, distal intramural, and extramural segments. Data were obtained for 35 AAOCA (n=23 with intramural tract) after retrospective image-based gating and manual lumen segmentation. Differences between systolic and end-diastolic phases in each section, between sections of the same coronary, and between AAOCA with and without intramural tract were assessed by nonparametric statistical tests. RESULTS: In end diastole, both the ostial and distal intramural sections were more elliptical (P<0.001) than the reference extramural section and the correspondent sections in AAOCA without intramural segment. In systole, AAOCA with intramural segment showed a flattening at the ostium (-6.76% [10.82%]; P=0.024) and a flattening (-5.36% [16.56%]; P=0.011), a narrowing (-4.62% [11.38%]; P=0.020), and a resistance increase (15.61% [30.07%]; P=0.012) at the distal intramural section. No-intramural sections did not show morphological changes during the entire cardiac cycle. CONCLUSIONS: AAOCA with intramural segment has pathological segment-specific dynamic compression mainly in the systole under resting conditions. Studying AAOCA behavior with intravascular ultrasound during the cardiac cycle may help to evaluate and quantify the severity of the narrowing.

Assessing Prevalence and Characteristics of Oro-bulbar Involvement in Children and Adults with SMA Type 2 and 3 Using a Multimodal Approach.

Bulbar and jaw muscles are impaired in patients with Spinal Muscular Atrophy (SMA) but the assessment of their severity and progression are limited by the lack of age-appropriate and disease-specific measures. We investigated mastication and swallowing in children and adults with SMA, sitters and walkers. In a 2-year multicentre cross-sectional prospective study, lip and tongue strength (Iowa Oral Performance Instrument), chewing and swallowing (Test of Masticating and Swallowing Solids), active mouth opening (aMMO) were compared to age-appropriate normative data. The perceived burden of oro-bulbar involvement (SMA-Health Index) was recorded. 78 patients were included, 45 children (median age 7.4 years),22 adults (median age 26.8 years) on nusinersen and 11 untreated (median age 32.7 years). Forty-three percent children had reduced mouth opening, 50% had prolonged total time to eat. These issues were more prominent in sitters than in walkers (p = 0.019, p = 0.014). Sixty-six percent needed increased swallows for bolus clearance. Nusinersen treated adults had median aMMO, tongue strength and total time at TOMASS values within normal range (z score: -1.40, -1.22, -1.32, respectively) whereas untreated adults had reduced aMMO (z score: -2.68) and tongue strength (z score: -2.20). Only a minority of children (2/17) and treated adults (5/21) reported burden in swallowing or mastication compared to all untreated adults (5/5). After 16 months, mastication and swallowing were stable in treated children and adults, whether sitters or walkers. The reported multimodal approach to assess oro-bulbar functions demonstrate that swallowing and mastication are impaired in SMA despite patients' perception. These results suggest a trend towards stabilization of oro-bulbar function in patients on long-term treatment with nusinersen.

Fixation Location and Stability in Best Vitelliform Macular Dystrophy.

Purpose: To analyze fixation location and stability in best vitelliform macular dystrophy (BVMD) and test their association with best-corrected visual acuity (BCVA). Design: Observational, cross-sectional study. Participants: Thirty patients (55 eyes) affected by genetically confirmed BVMD were followed up at the Retinal Heredodystrophies Unit of IRCCS San Raffaele Scientific Institute, Milan. Methods: Patients underwent testing with macular integrity assessment (MAIA) microperimeter. Fixation location was measured as distance in degrees (°) between preferred retinal locus (PRL) and estimated fovea location (EFL); fixation was defined as eccentric when the distance between PRL and EFL exceeded 2°. Fixation stability was graded as stable, relatively unstable, or unstable and expressed as bivariate contour ellipse area (BCEA, °2). Main Outcome Measures: Fixation location and stability. Results: The median distance of the PRL from the anatomic fovea was 0.7°, and fixation location was eccentric in 27% of eyes. Fixation was graded as stable in 64% of eyes, relatively unstable in 13%, and unstable in 24%, with a median 95% BCEA of 6.2°2. The atrophic/fibrotic stage was associated with worse fixation parameters (all P < 0.01). Both PRL eccentricity and fixation stability were linearly associated with BCVA: every 1° increase in PRL eccentricity was associated with a 0.07 logarithm of the minimum angle of resolution (logMAR) worse BCVA (P < 0.0001) while every 1°2 increase in 95% BCEA was associated with a 0.01 logMAR worse BCVA (P < 0.001). No significant intereye correlation was found for PRL eccentricity and fixation stability, as well as no association between the patient's age and fixation parameters. Conclusions: We demonstrated that most eyes affected by BVMD retain a central stable fixation and provided evidence that both fixation eccentricity and stability are strongly associated with visual acuity in BVMD. These parameters may serve as secondary end points for future clinical trials. Financial Disclosures: Proprietary or commercial disclosure may be found after the references.

How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy.

Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies limit computable sets with respect to the number of mistakes that are needed to approximate them. Biacino and Gerla extended the Kleene Hierarchy to the realm of fuzzy sets, whose membership functions range in a complete lattice. In this paper, we combine the Ershov Hierarchy and fuzzy set theory, by introducing and investigating the Fuzzy Ershov Hierarchy.

Development of prediction models based on respiratory assessments to determine the need for non-invasive ventilation in patients with myotonic dystrophy type 1.

INTRODUCTION: Myotonic dystrophy type 1 is a slowly progressive, multisystem, autosomal dominant disorder, in which the impairments of respiratory systems represent one of the main causes of death. OBJECTIVE: The aim of our study is to develop prediction models to identify the most appropriate test(s) providing indication for NIV. METHODS: DM1 patients attending the NEMO Clinical Center (Milan) between January 2008 and July 2020, who had been subjected to a complete battery of respiratory tests, were retrospectively recruited. Demographic, clinical, and anthropometric characteristics were collected, as well as arterial blood gas (ABG) analysis, spirometry, respiratory muscle strength, cough efficacy, and nocturnal oximetry as respiratory assessments. Patients were stratified in those requiring NIV and those with normal respiratory function. RESULTS: Out of 151 DM1 patients (median age: 44 years [35.00-53.00]; male/female ratio: 0.80 (67/84)), 76 had an indication for NIV initiation (50.33%). ABG, spirometry, and nocturnal oximetry prediction models resulted in an excellent discriminatory ability in distinguishing patients who needed NIV from those who did not (AUC of 0.818, 0.808, and 0.935, respectively). An easy-to-use calculator was developed to automatically determine a score of NIV necessity based on the prediction equations generated from each aforementioned prediction model. CONCLUSIONS: The proposed prediction models may help to identify which patients are at a higher risk of requiring ventilator support and therefore help in defining individual management plans and criteria for specific interventions early in the disease course.

Thin Objects Are Not Transparent.

In this short paper, we analyse whether assuming that mathematical objects are "thin" in Linnebo's sense simplifies the epistemology of mathematics. Towards this end, we introduce the notion of transparency and show that not all thin objects are transparent. We end by arguing that, far from being a weakness of thin objects, the lack of transparency of some thin objects is a fruitful characteristic mark of abstract mathematics.

Computability theory as a philosophical achievement.

Artificial intelligence plays an important role in contemporary medicine. In this short note, we emphasize that philosophy played a role in the development of artificial intelligence. We argue that research in computability theory, the theoretical foundation of modern computer science, was motivated by a philosophical question: can we characterize precisely the class of problems that can be solved by algorithms? We suggest that reflecting on the connection between philosophy and artificial intelligence helps realize that philosophical and scientific progress are connected.

Myocardial infarction with non-obstructive disease and anomalous coronary origin: look for the common in the uncommon.

Management of congenital coronary artery anomalies (CAA) is not standardized due to the variety of conditions included and their rare prevalence. Detection of CAA during myocardial infarction with non-obstructive coronary arteries (MINOCA) may induce clinicians to address the patient for surgery as CAA is not included in any algorithm1,2 for the management of MINOCA and American Association for Thoracic Surgery evidence-based guidelines suggest surgical repair for patients with anomalous aortic origin of a coronary artery and symptoms compatible with myocardial ischaemia.3 We present the case of a 35-year-old man with an anomalous origin of left coronary artery from right Valsalva sinus with pre-pulmonic course detected during urgent coronary angiography for suspected myocardial infarction. Stress cardiac magnetic resonance did not show signs of ischaemia at high-dose dobutamine but did reveal a recent myocarditis. This clinical case highlights the need for accurate risk stratification in CAA especially when confounding clinical scenarios co-exist.

Assessment of Respiratory Function and Need for Noninvasive Ventilation in a Cohort of Patients with Myotonic Dystrophy Type 1 Followed at One Single Expert Center.

Introduction: Respiratory insufficiency is one of the main causes of death in myotonic dystrophy type 1 (DM1). Although there is general consensus that these patients have a restrictive ventilatory pattern, hypoventilation, chronic hypercapnia, and sleep disturbances, the prevalence of respiratory disease and indication for the effects of noninvasive ventilation (NIV) need to be further explored. Objectives: To describe respiratory function and need for NIV at baseline and over time in a cohort of adult patients with DM1. Methods: A total of 151 adult patients with DM1 were subjected to arterial blood gas analysis, sitting and supine forced vital capacity (FVC), peak cough expiratory flow (PCEF), nocturnal oximetry, and maximal inspiratory pressure and expiratory pressure (MIP/PEP). Results: On first assessment, 84 of 151 had normal respiratory function (median age: 38 years, median BMI: 23.9, and median disease duration: 11 years); 67 received an indication to use NIV (median age: 49 years, median BMI: 25,8, and median disease duration: 14 years). After a median time of 3.85 years, 43 patients were lost to follow-up; 9 of 84 required NIV; only 17 of 67 with the new NIV prescription were adherent. Conclusions: We provide additional data on the natural history of respiratory function decline and treatment adherence in a relatively large cohort of well-characterized patients with DM1. A high proportion (28%) was lost to follow-up. A minority (11%) required NIV, and only 25% were treatment adherent, irrespective of specific demographics and respiratory features. Our results also confirm previous findings, showing that age, disease duration, and higher BMIs are predisposing factors for respiratory impairment.

In-Hospital Outcomes and Predictors of Paravalvular Leak and Deep Implantation With the Evolut R 34-mm Device: A Comparison With Smaller Evolut R Sizes.

PURPOSE: To compare in-hospital outcome of Evolut-R 34 mm vs. smaller Evolut-R devices and to identify predictors of paravalvular leak (PVL) and deep implantation specific for Evolut-R 34 mm. METHODS: This single-center retrospective study included 359 consecutive patients undergoing transcatheter aortic valve replacement (TAVR) with Evolut-R 34 mm (N = 84,23.4%) and Evolut-R 23/26/29 mm (N = 275,76.6%) between 2016 and 2019. RESULTS: Patients in Evolut-R 34 mm group were more frequently males, had lower STS score, ejection fraction, and mean aortic gradient compared to the Evolut-R 23/26/29 mm group. Horizontal aorta and large LVOT were more frequent findings in the Evolut-R 34 mm group, whereas calcium volume was comparable among the groups. During TAVR, mean implantation depth and contrast volume were greater in the Evolut-R 34 mm group, compared to the Evolut 23/26/29 mm group. Post-procedurally, 30-day mortality, ≥moderate PVL, device success and pacemaker implantation (PM) rates were comparable between groups. Among independent predictors of ≥moderate PVL, calcium volume (OR:1.04; p < 0.001) was predictive with different thresholds in both groups, whereas aortic angulation (OR:1.40; p = 0.005) was predictive only in Evolut-R 34 mm group at a cutoff of 60° (AUC:0.73; p = 0.043). Body weight (OR:1.03; p = 0.027), left ventricular outflow tract (LVOT) diameter (OR:1.34; p = 0.001), and mean aortic gradient (OR:0.96; p = 0.006) were independent predictors of deep implantation (mean depth ≥ 6 mm), with LVOT>27 mm being predictive specifically for Evolut-R 34 mm (AUC:0.66; p = 0.024). CONCLUSIONS: TAVR with Evolut-R 34 mm and Evolut-R 23/26/29 mm showed comparable in-hospital outcome. Aortic angulation >60° and LVOT >27 mm were predictive respectively of ≥moderate PVL and deep implantation specifically in Evolut-R 34 mm patients.

The actigraphic documentation of circadian sleep-wake rhythm dysregulation in myotonic dystrophy type 1.

STUDY OBJECTIVES: The present study aimed at identifying the sleep-wake rhythm in patients with myotonic dystrophy type 1 (DM1) compared to healthy controls. METHODS: Patients with genetic diagnosis of DM1 and healthy controls underwent a 7-day actigraphic recording and filled out a daily sleep diary to evaluate the sleep-wake rhythm. All participants underwent a physical and neurological examination to exclude conditions interfering with the sleep-wake cycle. Daytime activity, nocturnal sleep, and non-parametric circadian rhythm activity (NPCRA) were analysed. RESULTS: Twenty-nine patients affected by DM1 were included in the present study and were compared to 16 controls. Considering nocturnal actigraphic data, DM1 patients showed a longer time in bed, sleep period time, actual sleep time, and sleep latency compared to controls. Central phase measurement was significantly longer in DM1 patients than controls. At NPCRA analysis patients showed a lower degree of regularity in the activity-rest pattern compared to controls. Moreover, DM1 patients showed reduced motor activity during daytime and a lower synchronization of the rest-activity rhythm than controls. CONCLUSIONS: This study documented that patients with DM1 not only present the impairment of nocturnal sleep, but also show a dysregulation of the sleep-wake circadian rhythm; moreover, reduced amplitude of the circadian rhythmicity was also evident in comparison to controls, probably in relation to the reduced diurnal motor activity of patients. These findings add further evidence to the already documented sleep impairment and excessive daytime sleepiness in DM1 patients.

On logicality and natural logic.

In this paper we focus on the logicality of language, i.e. the idea that the language system contains a deductive device to exclude analytic constructions. Puzzling evidence for the logicality of language comes from acceptable contradictions and tautologies. The standard response in the literature involves assuming that the language system only accesses analyticities that are due to skeletons as opposed to standard logical forms. In this paper we submit evidence in support of alternative accounts of logicality, which reject the stipulation of a natural logic and assume instead the meaning modulation of nonlogical terms.

Assessment of self-reported and objective daytime sleepiness in adult-onset myotonic dystrophy type 1.

STUDY OBJECTIVES: Excessive daytime sleepiness (EDS) in myotonic dystrophy type 1 is mostly of central origin but it may coexist with sleep-related breathing disorders. However, there is no consensus on the sleep protocols to be used, assessments vary, and only a minority of patients are regularly tested or are on treatment for EDS. Our study presents data on self-reported and objective EDS in adult-onset myotonic dystrophy type 1. METHODS: Sixty-three patients with adult-onset DM1 were subjected to EDS-sleep assessments (polysomnography, Multiple Sleep Latency Test, Epworth Sleepiness Scale). Correlation coefficients were computed to assess the relationship between sleep and sleepiness test results, fatigue, and quality of life. RESULTS: 33% and 48% of patients had EDS based, respectively, on the Epworth Sleepiness Scale and the Multiple Sleep Latency Test, with a low concordance between these tests (k = 0.19). Thirteen patients (20%) displayed 2 or more sleep-onset rapid eye movement periods on Multiple Sleep Latency Test. Patients having EDS by Multiple Sleep Latency Test had a shorter disease duration (P < .05), higher total sleep time and sleep efficiency and lower wake after sleep onset on polysomnography. Patients with self-reported EDS reported significantly higher fatigue score compared with patients without EDS (P < .05). No other difference was found in demographic, clinical, and respiratory features. CONCLUSIONS: EDS test results are contradictory, making treatment options difficult. Combining quantitative tests and self-reported scales may facilitate physicians in planning EDS care with patients and families. CITATION: Sansone VA, Proserpio P, Mauro L, et al. Assessment of self-reported and objective daytime sleepiness in adult-onset myotonic dystrophy type 1. J Clin Sleep Med. 2021;17(12):2383-2391.

Neurophysiological indices in amyotrophic lateral sclerosis correlate with functional outcome measures, staging and disease progression.

OBJECTIVE: This study examined neurophysiological (NI), split-hand (SI) and split-leg (SLI) index in patients with amyotrophic lateral sclerosis (ALS), and their correlation with functional status, disease duration, staging and survival. METHODS: Eighty-two patients underwent nerve conduction study to analyze NI, SI and SLI. Amyotrophic Lateral Sclerosis Functional Rating Scale-Revised (ALSFRS-R), disease progression rate (ΔFS), Milano-Torino (MiToS) and King's staging systems, Forced Vital Capacity (FVC), and survival data were collected. RESULTS: Both NI and SI indices were significantly associated with ALSFRS-R, MiToS, King's and FVC. Slow progressor patients (ΔFS < 0.5) reported a significantly higher NI and SI values compared to both normal (0.5 ≤ ΔFS < 1.00) and fast progressors (ΔFS ≥ 1.0). After dichotomizing patients in slow progressors (ΔFS < 0.5) and not-slow progressors (ΔFS ≥ 0.5), a combination of SI index and disease duration revealed to be the best prediction model to discriminate patients in accordance with their disease progression (c-index: 0.92), leading to a new prognostic index: the 'Split-Hand prognostic index' (SHpi). CONCLUSION: SI and NI are correlated with functional status and FVC. SHpi index could represent an useful tool to discriminate patients in accordance with their disease progression. SIGNIFICANCE: These data provide novel evidence of neurophysiological indices as promising biomarkers in ALS.

The Spinal Muscular Atrophy Health Index: Italian validation of a disease-specific outcome measure.

Patient report outcome measures in Spinal Muscular Atrophy (SMA) represent a potential complement to observer rated scales which can be used to better understand treatment response. We developed, translated and validated an Italian version of the Spinal Muscular Atrophy Health Index (SMAHI), a disease-specific, patient reported outcome measure questionnaire, designed to estimate the patients' perception of disease burden. Test-retest reliability was assessed in 37 patients (16 children aged 12-17 and 21 adults) and was excellent in both cohorts. Internal consistency in an additional 98 patients (24 children, 74 adults) was also excellent (Cronbach's alpha = 0.93 and 0.91 respectively). In children the highest level of disease burden was generated from lower limb dysfunction and fatigue as well as their perception of decreased performance in social situations. Most patients in the adult cohort were sitters and complained of problems with upper limb functions as well as of fatigue. The SMAHI-IT was also able to differentiate between SMA types according to diseases severity. The results of our study demonstrate that the SMAHI can be considered a marker of disease-specific burden in patients with SMA with a high test-retest reliability and internal validity in Italian patients aged 12 and older.

Classifying equivalence relations in the Ershov hierarchy.

Computably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility ⩽ c . This gives rise to a rich degree structure. In this paper, we lift the study of c-degrees to the Δ 2 0 case. In doing so, we rely on the Ershov hierarchy. For any notation a for a non-zero computable ordinal, we prove several algebraic properties of the degree structure induced by ⩽ c on the Σ a - 1 \ Π a - 1 equivalence relations. A special focus of our work is on the (non)existence of infima and suprema of c-degrees.