Recurrences and explicit formulae for the expansion and connection coefficients in series of ordinary Bessel polynomials

2008 ◽  
Vol 199 (2) ◽  
pp. 482-493 ◽  
Author(s):  
H.M. Ahmed ◽  
S.I. El-Soubhy
2020 ◽  
Vol 63 (9) ◽  
pp. 2921-2929
Author(s):  
Alan H. Shikani ◽  
Elamin M. Elamin ◽  
Andrew C. Miller

Purpose Tracheostomy patients face many adversities including loss of phonation and essential airway functions including air filtering, warming, and humidification. Heat and moisture exchangers (HMEs) facilitate humidification and filtering of inspired air. The Shikani HME (S-HME) is a novel turbulent airflow HME that may be used in-line with the Shikani Speaking Valve (SSV), allowing for uniquely preserved phonation during humidification. The aims of this study were to (a) compare the airflow resistance ( R airflow ) and humidification efficiency of the S-HME and the Mallinckrodt Tracheolife II tracheostomy HME (M-HME) when dry (time zero) and wet (after 24 hr) and (b) determine if in-line application of the S-HME with a tracheostomy speaking valve significantly increases R airflow over a tracheostomy speaking valve alone (whether SSV or Passy Muir Valve [PMV]). Method A prospective observational ex vivo study was conducted using a pneumotachometer lung simulation unit to measure airflow ( Q ) amplitude and R airflow , as indicated by a pressure drop ( P Drop ) across the device (S-HME, M-HME, SSV + S-HME, and PMV). Additionally, P Drop was studied for the S-HME and M-HME when dry at time zero (T 0 ) and after 24 hr of moisture testing (T 24 ) at Q of 0.5, 1, and 1.5 L/s. Results R airflow was significantly less for the S-HME than M-HME (T 0 and T 24 ). R airflow of the SSV + S-HME in series did not significant increase R airflow over the SSV or PMV alone. Moisture loss efficiency trended toward greater efficiency for the S-HME; however, the difference was not statistically significant. Conclusions The turbulent flow S-HME provides heat and moisture exchange with similar or greater efficacy than the widely used laminar airflow M-HME, but with significantly lower resistance. The S-HME also allows the innovative advantage of in-line use with the SSV, hence allowing concurrent humidification and phonation during application, without having to manipulate either device.


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