We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

OBJECTIVES: This revised clinical practice guideline, intended for use by primary care clinicians, provides recommendations for the diagnosis and management of the obstructive sleep apnea syndrome (OSAS) in children and adolescents. This practice guideline focuses on uncomplicated childhood OSAS, that is, OSAS associated with adenotonsillar hypertrophy and/or obesity in an otherwise healthy child who is being treated in the primary care setting. METHODS: Of 3166 articles from 1999–2010, 350 provided relevant data. Most articles were level II–IV. The resulting evidence report was used to formulate recommendations. RESULTS AND CONCLUSIONS: The following recommendations are made. (1) All children/adolescents should be screened for snoring. (2) Polysomnography should be performed in children/adolescents with snoring and symptoms/signs of OSAS; if polysomnography is not available, then alternative diagnostic tests or referral to a specialist for more extensive evaluation may be considered. (3) Adenotonsillectomy is recommended as the first-line treatment of patients with adenotonsillar hypertrophy. (4) High-risk patients should be monitored as inpatients postoperatively. (5) Patients should be reevaluated postoperatively to determine whether further treatment is required. Objective testing should be performed in patients who are high risk or have persistent symptoms/signs of OSAS after therapy. (6) Continuous positive airway pressure is recommended as treatment if adenotonsillectomy is not performed or if OSAS persists postoperatively. (7) Weight loss is recommended in addition to other therapy in patients who are overweight or obese. (8) Intranasal corticosteroids are an option for children with mild OSAS in whom adenotonsillectomy is contraindicated or for mild postoperative OSAS.

/pdf/diagnosis-and-management-of-childhood-obstructive-sleep-2wes17zrfk.pdf

Diagnosis and Management of Childhood Obstructive Sleep Apnea Syndrome

The safe sedation of children for procedures requires a systematic approach that includes the following: no administration of sedating medication without the safety net of medical supervision; careful presedation evaluation for underlying medical or surgical conditions that would place the child at increased risk from sedating medications; appropriate fasting for elective procedures and a balance between depth of sedation and risk for those who are unable to fast because of the urgent nature of the procedure; a focused airway examination for large tonsils or anatomic airway abnormalities that might increase the potential for airway obstruction; a clear understanding of the pharmacokinetic and pharmacodynamic effects of the medications used for sedation, as well as an appreciation for drug interactions; appropriate training and skills in airway management to allow rescue of the patient; age- and size-appropriate equipment for airway management and venous access; appropriate medications and reversal agents; sufficient numbers of people to carry out the procedure and monitor the patient; appropriate physiologic monitoring during and after the procedure; a properly equipped and staffed recovery area; recovery to presedation level of consciousness before discharge from medical supervision; and appropriate discharge instructions. This report was developed through a collaborative effort of the American Academy of Pediatrics and the American Academy of Pediatric Dentistry to offer pediatric providers updated information and guidance in delivering safe sedation to children.

https://pediatrics.aappublications.org/content/pediatrics/118/6/2587.full.pdf

Guidelines for Monitoring and Management of Pediatric Patients Before, During, and After Sedation for Diagnostic and Therapeutic Procedures.

Objective. Tonsillectomy is one of the most common surgical procedures in the United States, with more than 530 000 pr o- cedures performed annually in children younger than 15 years. Tonsillectomy is defined as a surgical procedure performed with or without adenoidectomy that completely removes the tonsil including its capsule by dissecting the peritonsil- lar space between the tonsil capsule and the muscular wall. Depending on the context in which it is used, it may indicate tonsillectomy with adenoidectomy, especially in relation to sleep-disordered breathing. This guideline provides evidence- based recommendations on the preoperative, intraoperative, and postoperative care and management of children 1 to 18 years old under consideration for tonsillectomy. In addition, this guideline is intended for all clinicians in any setting who interact with children 1 to 18 years of age who may be candi- dates for tonsillectomy. Purpose. The primary purpose of this guideline is to provide clinicians with evidence-based guidance in identifying children who are the best candidates for tonsillectomy. Secondary objectives are to optimize the perioperative management of children undergoing tonsillectomy, emphasize the need for evaluation and intervention in special populations, improve counseling and education of families of children who are con- sidering tonsillectomy for their child, highlight the manage- ment options for patients with modifying factors, and reduce inappropriate or unnecessary variations in care. Results. The panel made a strong recommendation that clinicians should administer a single, intraoperative dose of intravenous dexamethasone to children undergoing tonsillectomy. The panel made a strong recommendation against clinicians routinely admin- istering or prescribing perioperative antibiotics to children undergoing tonsillectomy. The panel made recommendations for

/pdf/clinical-practice-guideline-tonsillectomy-in-children-4fuvuegikz.pdf

Clinical practice guideline: tonsillectomy in children.

Tracheal pressure, central airflow, and alveolar capsule pressures in cardiac lobes were measured in open-chest dogs during 0.1- to 20-Hz pseudorandom forced oscillations applied at the airway open...

/pdf/input-impedance-and-peripheral-inhomogeneity-of-dog-lungs-55tmpg9fj9.pdf

Input impedance and peripheral inhomogeneity of dog lungs

Objective. Obstructive sleep apnea (OSA) in children is usually effectively treated by adenotonsillectomy (TA 22%) had no additional sleep studies before T&A. Timing of T&A was based on oximetry score, leading to a significant reduction in waiting time for surgery for those with higher oximetry scores. Postoperative respiratory complications were more common with increasing oximetry score. Conclusions. Overnight pulse oximetry can be used to estimate the severity of OSA, to shorten the diagnostic and treatment process for those with more severe disease, and to aid clinicians in prioritization of T&A and planning perioperative care.

https://pediatrics.aappublications.org/content/pediatrics/113/1/e19.full.pdf

Planning Adenotonsillectomy in Children With Obstructive Sleep Apnea: The Role of Overnight Oximetry

Background:Postsurgical administration of opiates in patients with obstructive sleep apnea (OSA) has recently been linked to an increased risk for respiratory complications. The authors have attributed this association to an effect of recurrent oxygen desaturation accompanying OSA on endogenous opio

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Recurrent Hypoxemia in Children Is Associated with Increased Analgesic Sensitivity to Opiates

The interrupter method for measuring respiratory system resistance involves rapidly interrupting flow at the mouth while measuring the pressure just distal to the point of interruption. The pressure signal observed invariably exhibits two distinct phases. The first phase is a very rapid jump, designated delta Pinit, which occurs immediately on interruption of flow. The second phase is designated delta Pdif and is a further pressure change in the same direction as delta Pinit but evolving over several seconds. The physiological interpretations of delta Pinit and delta Pdif have been somewhat unclear. Delta Pinit has been taken to equal the pressure drop across the pulmonary airways, possibly with a contribution from the tissues of the respiratory system. Delta Pdif can arise, in principle, from two sources: gas redistribution throughout the lung after interruption of flow and stress recovery within the tissues. To resolve these issues we performed interruption experiments on anesthetized paralyzed, tracheotomized, open-chest normal dogs during passive expiration while measuring alveolar pressures at three sites with alveolar capsules. We found that, in the absence of the chest wall, delta Pinit reflects only the resistance of the airways and that delta Pdif can be ascribed almost entirely to the stress recovery properties of lung tissues.

Interrupter resistance elucidated by alveolar pressure measurement in open-chest normal dogs

Background: The aim of this study was to determine the frequency and type of respiratory complications after adenotonsillectomy in children. A second aim was to assess the ability of preoperative sleep studies to identify children at risk for respiratory complications. Methods: Children referred for sleep studies between 1992 and 1998, who underwent adenotonsillectomy within 6 months of the preoperative study, were reviewed. The study focused on two variables: the obstructive apnea and hypopnea index and the oxygen saturation nadir. Medical charts were reviewed for postoperative respiratory complications. Results: Three hundred forty-nine children were referred for sleep studies, and 163 met the inclusion criteria. Thirty-four children (21%) had postoperative respiratory complications requiring a medical intervention. Children experiencing respiratory complications were younger (aged < 2 yr; adjusted odds ratio, 4.3; 95% confidence interval, 1.7-11) and had an associated medical condition (odds ratio, 3; 95% confidence interval, 1.4-6.5). A preoperative obstructive apnea and hypopnea index of 5 or more events per hour increased the chance of postoperative respiratory complications (odds ratio, 7.2; 95% confidence interval, 2.7-19.3), as did a preoperative oxygen saturation nadir of 80% or less (odds ratio, 6.4; 95% confidence interval, 2.8-14.5). A preoperative oxygen saturation nadir of 80% or less had a likelihood ratio of 3.1, increasing the probability of postoperative respiratory complications from 20 to 50%. Conclusions: The data suggest, but do not prove, that preoperative nocturnal oximetry could be a useful preoperative test to identify children who are at increased risk for postoperative respiratory complications.

Can assessment for obstructive sleep apnea help predict postadenotonsillectomy respiratory complications

Background Obstructive sleep apnea (OSA) in children is often associated with recurrent hypoxemia during sleep. In developing animals, central opioid neuropeptide content is high, and opioid receptors are up-regulated after recurrent hypoxia. The authors hypothesized that children with recurrent hypoxemia due to OSA might have altered central opioid functionality that could affect their responsiveness to opioid drugs. Using a retrospective database, we assessed the relation of age and preoperative oxygen saturation to the cumulative postoperative morphine dose administered for analgesia in children with OSA undergoing adenotonsillectomy. Methods Inclusion criteria were (1) adenotonsillectomy for OSA; (2) no concomitant pathology; (3) intraoperative administration of short-acting opioid drugs; (4) endotracheal extubation on awakening in the operating room; and (5) morphine as the parenteral, postoperative analgesic. Results Forty-six children (16 girls) fulfilled the inclusion criteria. Age and preoperative arterial oxygen saturation (SaO2) nadir, either individually (P = 0.023, P = 0.0003, respectively) or in combination (P = 0.00009), exhibited a significant correlation to the morphine dose required for analgesia. Four of these children, aged 26.5 +/- 13.2 months, with a preoperative SaO2 nadir of 70.3 +/- 12.9%, did not require any postoperative morphine for analgesia at all. Conclusions The authors speculate that the reduced morphine requirement for analgesia in children displaying oxygen desaturation associated with severe OSA may be related to their young age and to an up-regulation of central opioid receptors consequent to recurrent hypoxemia. In evaluating OSA in children, preoperative determination of the SaO2 nadir is important for predicting the postoperative opioid dosage required for analgesia.

Karen A. Brown

Papers

Planning Adenotonsillectomy in Children With Obstructive Sleep Apnea: The Role of Overnight Oximetry

Recurrent Hypoxemia in Children Is Associated with Increased Analgesic Sensitivity to Opiates

Interrupter resistance elucidated by alveolar pressure measurement in open-chest normal dogs

Can assessment for obstructive sleep apnea help predict postadenotonsillectomy respiratory complications

Recurrent hypoxemia in young children with obstructive sleep apnea is associated with reduced opioid requirement for analgesia.