The Non-Paced 3-Minute Sit-to-Stand Test: Feasibility and Clinical Relevance for Pulmonary Rehabilitation Assessment.

Pulmonary rehabilitation (PR) improves health-related quality-of-life (HRQoL) in individuals with chronic obstructive pulmonary disease (COPD), notably by increasing exercise tolerance. Easy-to-implement sit-to-stand tests can facilitate the assessment of exercise tolerance in routine practice. This retrospective study conducted in a real-life setting was designed to describe the non-paced 3-min sit-to-stand test (3-STST) and to evaluate its relationship with HRQoL (VQ11 questionnaire) to identify the determinants of 3-STST performance and to analyze the evolution of 3-STST performance and HRQoL over the course of a community-based PR program. Seventy-one COPD patients (age 69 ± 10 years old; 51% with GOLD spirometric stages III-IV) were included. Mean ± SD 3-STST performance at the initial PR assessment was 43 ± 15 repetitions. This performance was significantly associated with HRQoL and other indicators of clinical severity (lung function, dyspnea, and functional capacities). During the multivariate analysis, younger age, exertional dyspnea with mMRC ≤ 1, and better HRQoL were significantly associated with better 3-STST performance. From the initial to second PR assessment, changes in 3-STST performance were significantly associated with changes in HRQoL. This study provides evidence that the non-paced 3-STST is feasible and might be clinically relevant in the assessment of patients with COPD referred for community-based PR. This test deserves to be prospectively validated.

Effect of Intensity of Home Noninvasive Ventilation in Individuals With Neuromuscular and Chest Wall Disorders: A Systematic Review and Meta-Analysis of Individual Participant Data

Introduction: Home noninvasive ventilation (NIV), targeting a reduction of carbon dioxide with a combination of sufficient inspiratory support and backup-rate improves outcomes in patients with chronic obstructive pulmonary disease. The aim of this systematic review with individual participant data (IPD) meta-analysis was to evaluate the effects of intensity of home NIV on respiratory outcomes in individuals with slowly progressive neuromuscular (NMD) or chest-wall disorders (CWD). Methods: Controlled, non-controlled and cohort studies indexed between January-2000 and December-2020 were sought from Medline, Embase and the Cochrane Central Register. Outcomes were diurnal PaCO2, PaO2, daily NIV usage, and interface type (PROSPERO-CRD 42021245121). NIV intensity was defined according to the Z-score of the product of pressure support (or tidal volume) and backup-rate. Results: 16 eligible studies were identified; we obtained IPD for 7 studies (176 participants: 113-NMD; 63-CWD). The reduction in PaCO2 was greater with higher baseline PaCO2. NIV intensity per se was not associated with improved PaCO2 except in individuals with CWD and the most severe baseline hypercapnia. Similar results were found for PaO2. Daily NIV usage was associated with improvement in gas exchange but not with NIV intensity. No association between NIV intensity and interface type was found. Conclusion: Following home NIV initiation in NMD or CWD patients, no relationship was observed between NIV intensity and PaCO2, except in individuals with the most severe CWD. The amount of daily NIV usage, rather than intensity, is key to improving hypoventilation in this population during the first few months after introduction of therapy. (AU)

Effect of Intensity of Home Noninvasive Ventilation in Individuals With Neuromuscular and Chest Wall Disorders: A Systematic Review and Meta-Analysis of Individual Participant Data.

INTRODUCTION: Home noninvasive ventilation (NIV), targeting a reduction of carbon dioxide with a combination of sufficient inspiratory support and backup-rate improves outcomes in patients with chronic obstructive pulmonary disease. The aim of this systematic review with individual participant data (IPD) meta-analysis was to evaluate the effects of intensity of home NIV on respiratory outcomes in individuals with slowly progressive neuromuscular (NMD) or chest-wall disorders (CWD). METHODS: Controlled, non-controlled and cohort studies indexed between January-2000 and December-2020 were sought from Medline, Embase and the Cochrane Central Register. Outcomes were diurnal PaCO2, PaO2, daily NIV usage, and interface type (PROSPERO-CRD 42021245121). NIV intensity was defined according to the Z-score of the product of pressure support (or tidal volume) and backup-rate. RESULTS: 16 eligible studies were identified; we obtained IPD for 7 studies (176 participants: 113-NMD; 63-CWD). The reduction in PaCO2 was greater with higher baseline PaCO2. NIV intensity per se was not associated with improved PaCO2 except in individuals with CWD and the most severe baseline hypercapnia. Similar results were found for PaO2. Daily NIV usage was associated with improvement in gas exchange but not with NIV intensity. No association between NIV intensity and interface type was found. CONCLUSION: Following home NIV initiation in NMD or CWD patients, no relationship was observed between NIV intensity and PaCO2, except in individuals with the most severe CWD. The amount of daily NIV usage, rather than intensity, is key to improving hypoventilation in this population during the first few months after introduction of therapy.

Comparison of Four Mechanical Insufflation-Exsufflation Devices: Effect of Simulated Airway Collapse on Cough Peak Flow.

BACKGROUND: Mechanical insufflation-exsufflation (MI-E) devices are used to improve airway clearance in individuals with acute respiratory failure. Some MI-E devices measure cough peak flow (CPF) during MI-E to optimize pressure adjustments. The aim was to compare CPF and effective cough volume (ECV: volume expired/coughed > 3 L/s) measurements between 4 MI-E devices under simulated conditions of stable versus collapsed airway. METHODS: Four MI-E devices were tested on the bench. Each device was connected via a standard circuit to a collapsible tube placed in an airtight chamber that was attached to a lung model with adjustable compliance and resistance. Pressure was measured upstream and downstream the collapsing tube; air flow was measured between the chamber and the lung model. Each device was tested in 2 conditions: collapse condition (0 cm H2O) and no-collapse condition (-70 cm H2O). For each condition, 6 combinations of inspiratory/expiratory pressures were applied. CPF was measured at the "mouth level" by the device built-in flow meter and at the "tracheal level" by a dedicated pneumotachograph. Comparisons were performed with non-parametric tests. RESULTS: CPF values measured at the tracheal level and ECV values differed between devices for each inspiratory/expiratory pressure in the collapse and no-collapse conditions (P < .001). CPF values were significantly lower at the tracheal level in the collapse as compared with the no-collapse condition (P < .001 for each device), whereas they were higher at the mouth level (P < .05) for 3 of the 4 devices. CONCLUSIONS: CPF values differed significantly across MI-E devices, highlighting limitation(s) of using only CPF values to determine cough effectiveness. In simulated of airway collapse, CPF increased at the mouth, whereas it decreased at the tracheal level.

Quality of life in patients with slowly progressive neuromuscular disorders dependent on mechanical ventilation.

This cross-sectional study evaluated health-related quality of life (HRQoL) in patients with slowly progressive neuromuscular disorders dependent on mechanical ventilation (MV; ≥16 hours/day). 119 participants, with 9 years (25th-75th percentiles: 4-15 years) of MV dependence, were included. MV was applied via a tracheostomy in 80 participants (67.2%) and non-invasive interfaces in 39 participants (32.8%), including 28 participants (71.8%) with daytime mouthpiece ventilation. HRQoL was rated good or excellent by 81 participants (68.1%), independently from age, diagnosis or respiratory autonomy. On multivariate analysis, time since MV initiation, independence from family member(s), residence in a rural area, ability to go outdoors with MV and tracheostomy were associated with better HRQoL.

Noninvasive Ventilation Automated Technologies: A Bench Evaluation of Device Responses to Sleep-Related Respiratory Events.

BACKGROUND: Noninvasive ventilation (NIV) is the reference standard treatment for most situations of chronic respiratory failure. NIV settings must be titrated to both preserve upper-airway patency and control hypoventilation. Automatic adjustment of pressure support (PS) and expiratory positive airway pressure (EPAP) may facilitate the initiation and follow-up of domiciliary NIV. However, whether the automatic-adjustment algorithms embedded into current devices accurately detect, respond to, and score common sleep-related respiratory events remains unclear. METHODS: A bench was set up to simulate central hypopnea (CH), central apnea (CA), obstructive hypopnea (OH), and obstructive apnea (OA). Four home ventilators were evaluated, with their dedicated modes for automatic PS and EPAP adjustment. RESULTS: All 4 devices increased PS during CH, CA, and OH. However, PS adjustment varied widely in magnitude, with tidal volumes within 100 ± 20% of the target being provided by only 3 devices for CH, one for CA, and one for OH. Two devices increased EPAP for OH and 3 for OA, including one that also increased EPAP for CA. Only 2 devices scored residual hypopnea after simulated CA, and only one scored a residual event after OH. One device scored no event. CONCLUSIONS: Current NIV devices differed markedly in their responses to, and reporting of, standardized sleep-related respiratory events. Further improvements in embedded NIV algorithms are needed to allow more widespread out-of-laboratory initiation and follow-up of NIV.

Nasal High-Flow Therapy during Exercise in Patients with Chronic Obstructive Pulmonary Disease: A Systematic Review and Meta-Analysis.

Background: Several studies have evaluated the effect of nasal high-flow (NHF) therapy to enhance exercise performance and tolerance in patients with chronic obstructive pulmonary disease (COPD); however, results are disparate. Objective: The aim of this systematic review and meta-analysis was to assess the effect of NHF therapy as an adjuvant to exercise training on functional exercise capacity in patients with COPD. Data Sources: An electronic search was performed in the following databases: PubMed, the Cochrane Central Register of Controlled Trials, the Physiotherapy Evidence Database, ScienceDirect, the Web of Science, OpenGrey, ClinicalTrials.gov, and European Respiratory Society and American Thoracic Society databases. Data Extraction: Two authors independently selected relevant randomized trials (parallel-group or crossover design), extracted data, assessed the risk of bias, and rated the quality of the evidence. Synthesis: Eleven studies were included, involving 408 participants (eight full papers and three conference abstracts). Most studies had a high risk of bias or other methodological limitations. The use of NHF therapy during a single session increased functional exercise capacity (standardized mean difference, 0.36 [95% confidence interval (CI), 0.03 to 0.69]; P = 0.03, heterogeneity [I2 = 83%]). When conference abstracts were included in the pooled analysis, the estimated effect did not change (P = 0.006). The use of NHF therapy throughout a pulmonary rehabilitation program (parallel-group randomized controlled trials) increased functional exercise capacity at 4-12 weeks compared with training without NHF therapy (standardized mean difference, 0.34 [95% CI, 0.00-0.68]; P = 0.05, heterogeneity [I2 = 18%]). Conclusions: There is very-low-quality to low-quality evidence that NHF therapy improves functional exercise capacity. Patient responses to NHF therapy were highly variable and heterogeneous, with benefits ranging from clinically trivial to worthwhile.

Protective Recommendations for Non-invasive Ventilation During COVID-19 Pandemic: A Bench Evaluation of the Effects of Instrumental Dead Space on Alveolar Ventilation.

INTRODUCTION: With the current COVID-19 pandemic, concerns have raised regarding the risk for NIV to promote airborne transmission. In case of hospital admission, continuation of therapy in patients undergoing chronic NIV is necessary and several protective circuit configurations have been recommended to reduce the risk of aerosol dissemination. However, all these configurations increase instrumental dead space. We therefore designed this study to evaluate their effects on the tidal volume (VTE) required to preserve stable end-tidal CO2 partial pressure (PETCO2) with constant respiratory rate. METHODS: A bench consisting of a test lung connected to an adult-sized mannequin head was set up. The model was ventilated through usual domiciliary configuration (single limb circuit with facial vented mask) which was used as reference. Then, five different circuit configurations including non-vented facial mask with viral/bacterial filter, modification of leak position, and change from single to double-limb circuit were evaluated. For each configuration, pressure support (PS) was gradually increased to reach reference PETCO2. Resulting VTE was recorded as primary outcome. RESULTS: Reference PETCO2 was 38(0) mmHg, with a PS set at 10 cmH2O, resulting in a VTE of 432(2) mL. Compared to reference, all the configurations evaluated required substantial increase in VTE to preserve alveolar ventilation, ranging from +79(2) to +216(1) mL. CONCLUSIONS: Modifications of NIV configurations in the context of COVID-19 pandemic result in substantial increase of instrumental dead space. Re-evaluation of treatment efficiency and settings is crucial whenever protective measures influencing NIV equipment are considered.

INTRODUCCIÓN: Durante la actual pandemia de COVID-19 ha surgido la preocupación sobre el posible riesgo de que la ventilación no invasiva (VNI) promueva la transmisión aérea. En el caso de ingreso hospitalario, es necesario continuar con el tratamiento de aquellos pacientes tratados con VNI crónica y se han recomendado varias configuraciones protectoras de los circuitos para reducir el riesgo de diseminación por aerosoles. Sin embargo, todas estas configuraciones aumentan el espacio muerto instrumental. Así, diseñamos este estudio para evaluar los efectos de estas configuraciones sobre el volumen corriente (VCE) necesario para mantener estable la presión parcial de CO2 al final del volumen corriente espirado (PETCO2) con una frecuencia respiratoria constante. MÉTODOS: Se construyó un modelo experimental que constaba de un pulmón de prueba conectado a una cabeza de maniquí de tamaño adulto. El modelo recibió ventilación utilizando la configuración domiciliaria habitual (circuito de rama única con máscara facial ventilada), lo que se utilizó como referencia. Después se evaluaron cinco configuraciones diferentes del circuito, incluidas la máscara facial sin ventilación con filtro antiviral/antibacteriano, la modificación de la posición de la fuga y el cambio de circuito de rama única a doble rama. Para cada configuración, la presión de soporte (PS) se incrementó gradualmente hasta alcanzar la PETCO2 de referencia. El VCE resultante se registró como resultado primario. RESULTADOS: La PETCO2 de referencia fue de 38(0) mmHg, con una PS fijada en 10 cmH2O, lo que resultó en un VCE de 432(2) mL. En comparación con la referencia, todas las configuraciones evaluadas requirieron un aumento sustancial del VCE para preservar la ventilación alveolar, en un rango entre +79(2) mL y +216(1) mL. CONCLUSIONES: Las modificaciones de las configuraciones de VNI en el contexto de la pandemia de COVID-19 resultan en un aumento sustancial del espacio muerto instrumental. Reevaluar la eficacia y los ajustes del tratamiento es fundamental cuando se ponen en consideración unas medidas de protección que influyen en el equipo de VNI.

Short-term effects of menthol on walking dyspnoea in patients with COPD: a randomised, single blinded, cross-over study.

Chewing menthol gum prior to exercise is a safe, easy-to-implement, low-cost, non-pharmacologic intervention that provides a reduction in dyspnoea in a third of patients and decreases the perception of discomfort during exercise in two-thirds of patients https://bit.ly/3FoFHp1.

Respiratory rehabilitation for Covid-19 related persistent dyspnoea: A one-year experience.

BACKGROUND: Growing consideration is emerging regarding the burden of persisting sequelae after SARS-CoV-2 infection. Out-patients exhibiting long Covid may benefit from ambulatory rehabilitation which is, to date, poorly documented. METHODS: A longitudinal follow-up over a one-year period was conducted in two ambulatory rehabilitation structures in order to describe the characteristics of real-life patients referred with Covid-19 sequelae and their evolution over the course of rehabilitation. RESULTS: 39 consecutive patients were included from April 1st, 2020 to April 1st, 2021. Patients were middle-aged (48 ± 15yr), without comorbidities, and mostly mild to moderate SARS-CoV-2 infection (25(64%) not requiring hospitalisation). Rehabilitation referral was considered with a median delay of 73[34-178] days after disease onset. Most prevalent symptoms were dyspnoea (n = 35(90%)) and fatigue (n = 30(77%)). Hyperventilation syndrome was highly frequent (n = 12(34%)). 29(74%) patients presented with prolonged functional sequelae, which was associated with younger age (43 ± 14 vs. 50 ± 10yr; p = 0.002), greater prevalence of hyperventilation syndrome (n = 12(41%) vs. 0(0%); p = 0.255) and poorer quality of life (VQ-11; 31 ± 10 vs. 23 ± 9; p = 0.030). Over the course of rehabilitation, exertional dyspnoea, 6-min walking distance, 3-min sit-to-stand test, hyperventilation syndrome prevalence and quality of life significantly improved. CONCLUSION: Hyperventilation is frequent in long Covid and may explain persistent dyspnoea as well as altered quality of life. Our data support screening of hyperventilation syndrome and functional impairment in mild Covid-19 out-patients as both of these components may improve with ambulatory rehabilitation.

Hygrometric Performances of Different High-Flow Nasal Cannula Devices: Bench Evaluation and Clinical Tolerance.

BACKGROUND: High-flow nasal cannula (HFNC) is increasingly used for the management of respiratory failure. Settings include [Formula: see text], total gas flow, and temperature target. Resulting absolute humidity (AH) at the nasal cannula may affect clinical tolerance, and optimal settings with respect to hygrometry remain poorly documented. METHODS: A bench study was designed to assess AH delivered by 4 HFNC devices (Optiflow, Airvo 2, Precision Flow, and Hydrate) according to flow, ambient temperature, and other available settings. Clinical tolerance of different levels of hygrometry (20, 30, and 40 mg H2O/L) was evaluated in 15 healthy volunteers. RESULTS: With [Formula: see text] set at 1.0, normal ambient temperature, and settings made accordingly to the manufacturers' recommendations, mean ± SD AH was 42.2 ± 3.1, 39.5 ± 1.8, 35.7 ± 2.0, and 32.9 ± 2.7 mg H2O/L for the Airvo 2, Optiflow, Hydrate, and Precision Flow, respectively, (P < .001). AH dropped from -3.5 to -10.7 mg H2O/L (P <. 001) with high ambient temperature, except for the Precision Flow. Increasing flow did not significantly affect AH except for the Precision Flow (from 36.4 ± 1.6 to 29.8 ± 0.2 mg H2O/L at 10 and 40 L/min, respectively, [P < .001]). The lowest AH was encountered with the Optiflow set with noninvasive ventilation (NIV) mode, without compensation algorithm, and at high ambient temperature (14.2 ± 1.5 mg H2O/L). In studied subjects, AH significantly affected breathing comfort, reduced from 7.0 ± 1.0 to 3.0 ± 2.0 at 40 and 20 mg H2O/L, respectively, (P < .001). Comfort was similar at 30 and 40 mg H2O/L. CONCLUSIONS: When used according to manufacturer's recommendations and at normal ambient temperature, all the HFNC devices evaluated achieved satisfactory hygrometric output with respect to breathing comfort evaluated in healthy subjects (≥ 30 mg H2O/L). Substantial differences exist between devices, and optimal knowledge of their working principles is required as inappropriate usage may dramatically alter efficacy and clinical tolerance.

Expiratory obstruction in patients with Duchenne muscular dystrophy under non-invasive ventilation: A step-by-step analysis of a new obstructive pattern.

PURPOSE: Non-invasive ventilation (NIV) is the reference standard for managing chronic hypoventilation in patients with Duchenne muscular dystrophy (DMD). In these patients, upper airway obstruction under NIV may compromise efficacy and adherence. We aim to describe a novel pattern of expiratory obstructive events occurring during nocturnal barometric NIV. METHODS: We retrospectively included all patients with DMD who underwent full-night polygraphy during NIV as part of their usual follow-up between May 2018 and July 2019. RESULTS: We provide a step-by-step description of this previously undescribed pattern of obstruction. Expiratory obstructions lead to end-inspiratory breath-holding and impossibility to take another inspiratory breath with a barometric mode until expiration occurs. These events were observed in 4 (36%) of 11 DMD patients under barometric NIV. CONCLUSION: Expiratory obstructions may be common in DMD patients receiving NIV and should be sought out routinely. This previously undescribed variant of obstructive event must be identified.

Physiologic Effects of High-Flow Nasal Cannula in Healthy Subjects.

BACKGROUND: High-flow nasal cannula (HFNC) is increasingly used in the management of acute and chronic respiratory failure. Little is known about the optimal settings for HFNC. This study was designed to assess the dose effect of HFNC on respiratory effort indexes and respiratory patterns in spontaneously breathing adults. METHODS: A randomized controlled crossover study was conducted in 10 healthy subjects. Five experimental conditions were evaluated: baseline with no therapy; 5 L/min with conventional nasal prongs; and HFNC at 20, 40, and 60 L/min. The primary outcomes were the indexes of respiratory effort (ie, esophageal pressure swing [ΔPes], esophageal pressure-time product, and work of breathing). Secondary outcomes included breathing pattern parameters and blood gases. Dead-space ventilation and washout were calculated based on minute ventilation, breathing frequency, and Radford equations. RESULTS: ΔPes increased from median (interquartile range [IQR] 3.2 (2.2-3.6) cm H2O at baseline to median (IQR) 5.7 (4.6-6.8) cm H2O at 60 L/min (P < .001). Neither esophageal pressure-time product nor work of breathing were modified during the tested conditions. The minute volume was significantly reduced at 40 and 60 L/min compared with baseline (P = .04), mostly driven by an important and dose-dependent reduction in breathing frequency, from median (IQR) 16 (15-18) breaths/min at baseline, to median (IQR) 8 (7-10) breaths/min at 60 L/min (P < .001). Capillary [Formula: see text] was stable in all the tested conditions. The calculated dead-space ventilation was reduced by half with HFNC. CONCLUSIONS: HFNC did not significantly modify work of breathing in healthy subjects. However, a significant reduction in the minute volume was achieved, capillary [Formula: see text] remaining constant, which suggests a reduction in dead-space ventilation with flows > 20 L/min. (ClinicalTrials.gov registration NCT02495675).

Generalized Arcsine Laws for Fractional Brownian Motion.

The three arcsine laws for Brownian motion are a cornerstone of extreme-value statistics. For a Brownian B_{t} starting from the origin, and evolving during time T, one considers the following three observables: (i) the duration t_{+} the process is positive, (ii) the time t_{last} the process last visits the origin, and (iii) the time t_{max} when it achieves its maximum (or minimum). All three observables have the same cumulative probability distribution expressed as an arcsine function, thus the name arcsine laws. We show how these laws change for fractional Brownian motion X_{t}, a non-Markovian Gaussian process indexed by the Hurst exponent H. It generalizes standard Brownian motion (i.e., H=1/2). We obtain the three probabilities using a perturbative expansion in ϵ=H-1/2. While all three probabilities are different, this distinction can only be made at second order in ϵ. Our results are confirmed to high precision by extensive numerical simulations.

Effects of High-Flow Nasal Cannula on the Work of Breathing in Patients Recovering From Acute Respiratory Failure.

OBJECTIVES: High-flow nasal cannula is increasingly used in the management of respiratory failure. However, little is known about its impact on respiratory effort, which could explain part of the benefits in terms of comfort and efficiency. This study was designed to assess the effects of high-flow nasal cannula on indexes of respiratory effort (i.e., esophageal pressure variations, esophageal pressure-time product/min, and work of breathing/min) in adults. DESIGN: A randomized controlled crossover study was conducted in 12 patients with moderate respiratory distress (i.e., after partial recovery from an acute episode, allowing physiologic measurements). SETTING: Institut Universitaire de Cardiologie et de Pneumologie de Québec, QC, Canada. SUBJECTS: Twelve adult patients with respiratory distress symptoms were enrolled in this study. INTERVENTIONS: Four experimental conditions were evaluated: baseline with conventional oxygen therapy and high-flow nasal cannula at 20, 40, and 60 L/min. The primary outcomes were the indexes of respiratory effort (i.e., esophageal pressure variations, esophageal pressure-time product/min, and work of breathing/min). Secondary outcomes included tidal volume, respiratory rate, minute volume, dynamic lung compliance, inspiratory resistance, and blood gases. MEASUREMENTS AND MAIN RESULTS: Esophageal pressure variations decreased from 9.8 (5.8-14.6) cm H2O at baseline to 4.9 (2.1-9.1) cm H2O at 60 L/min (p = 0.035). Esophageal pressure-time product/min decreased from 165 (126-179) to 72 (54-137) cm H2O • s/min, respectively (p = 0.033). Work of breathing/min decreased from 4.3 (3.5-6.3) to 2.1 (1.5-5.0) J/min, respectively (p = 0.031). Respiratory pattern variables and capillary blood gases were not significantly modified between experimental conditions. Dynamic lung compliance increased from 38 (24-64) mL/cm H2O at baseline to 59 (43-175) mL/cm H2O at 60 L/min (p = 0.007), and inspiratory resistance decreased from 9.6 (5.5-13.4) to 5.0 (1.0-9.1) cm H2O/L/s, respectively (p = 0.07). CONCLUSIONS: High-flow nasal cannula, when set at 60 L/min, significantly reduces the indexes of respiratory effort in adult patients recovering from acute respiratory failure. This effect is associated with an improvement in respiratory mechanics.

Extreme-value statistics of fractional Brownian motion bridges.

Fractional Brownian motion is a self-affine, non-Markovian, and translationally invariant generalization of Brownian motion, depending on the Hurst exponent H. Here we investigate fractional Brownian motion where both the starting and the end point are zero, commonly referred to as bridge processes. Observables are the time t_{+} the process is positive, the maximum m it achieves, and the time t_{max} when this maximum is taken. Using a perturbative expansion around Brownian motion (H=1/2), we give the first-order result for the probability distribution of these three variables and the joint distribution of m and t_{max}. Our analytical results are tested and found to be in excellent agreement, with extensive numerical simulations for both H>1/2 and H<1/2. This precision is achieved by sampling processes with a free end point and then converting each realization to a bridge process, in generalization to what is usually done for Brownian motion.

Perturbative expansion for the maximum of fractional Brownian motion.

Brownian motion is the only random process which is Gaussian, scale invariant, and Markovian. Dropping the Markovian property, i.e., allowing for memory, one obtains a class of processes called fractional Brownian motion, indexed by the Hurst exponent H. For H=1/2, Brownian motion is recovered. We develop a perturbative approach to treat the nonlocality in time in an expansion in ɛ=H-1/2. This allows us to derive analytic results beyond scaling exponents for various observables related to extreme value statistics: the maximum m of the process and the time t_{max} at which this maximum is reached, as well as their joint distribution. We test our analytical predictions with extensive numerical simulations for different values of H. They show excellent agreement, even for H far from 1/2.