(Math and Biology) Can you do #1 a, b, and c step by step and show me how you did it?
1. Cilia in the ainivays beat rhythmically to move the liquid lining towards the mouth. This isan important defense mechanism for removing inhaled particles. Here is an abstract from a research paper on the influence of anesthesia delivered through breathinganesthetic gas (volatile anesthesia, SEVO group) as opposed to anesthesia given intravenously (TIVA group). WW zoom-1430. Bronchial Mucus Transport Velocity in Patients Receian Wandflewfeufanfl Versusamend W Anesthesia lhomastgdowaki, MUM, Michael J. Pagan, DM, FANZCAW, WPatel,MBBS,FRCA*, and Stephan A. Scam FANZCA, FFF’MANZCA’i *Department of anaesthesia, and Pain Medicine, Royal Perth Hospital; and tSchool of Medicineand Pharmacology The University of Western Australia, Perth, Australia Volatile anesthetics reduce m beat frequency in vitro. lt has been reported that impairedbronchial mucus transport velocity (B W) is associated with significantly increased pulmonary complications. ln this study, we sought to determine in vivo differences in BTV, comparingpatients having total l V anesthesia { Tl VA ) with propping! and mm to anesthesia with Wand WW Twenty-two patients scheduled for elective general surgery were randomized to one of two groups: Tl VA (WWW or SE V0{aevaflumue/cemiientaafl). Thirty minutes after tracheal intubation, BTV was assessed by Wobservation of the movement of methylene blue dye applied to the dorsal surface of the right main bronchus. BTV was significantly reduced in the SE V0 group compared with theTi VA group (mean, 1.5 i 0.7 [0—2. 3] versus 4.8 :I: 2.1 [2. 3—8. 8] mm/min; P < 0. 000 ‘l ). Anesthesia with semflwaae may lead to significantly impaired WWW clearance in comparison toTl VA. This could have implications for perioperative pulmonary complications, in particular in patients at risk for pulmonary complications. a. Assume that the relationship for ainnray diameter as aimay generation (n) is(1.1) where do=1.8 cm is the tracheal diameter (n=0). Plot the total perimeter of the ainNaytree as a function of n for 0 s n s 15. There are 2” tubes at each generation. b. Assume that the mucus volumetric flow rate, for the sum of all tubes at any generation n,is the constant Q=0.0001 cm3lsec. Now assume that the average mucus velocity, u, is the same for all generations, e.g. the TIVA group u=4.8 mmlmin, regardless of the valueof n. Plot the thickness of the liquid layer, the; as a function of n. c. Repeat "b.” for the SEVO group and discuss the difference.
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