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SUMMARY:Optimal amplitude and frequency of breathing
DTSTART;VALUE=DATE-TIME:20180709T094500Z
DTEND;VALUE=DATE-TIME:20180709T100000Z
DTSTAMP;VALUE=DATE-TIME:20241107T220041Z
UID:indico-contribution-36@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Faheem Zaidi (Institute of Natural and Mathematical
Sciences\, Massey University\, Auckland\, New Zealand)\nPhysiological leve
ls of oxygen and carbon dioxide in the blood are tightly regulated by vary
ing the pattern of breathing\, but this can be achieved with different com
binations of amplitude and frequency. Why a specific combination of amplit
ude and frequency of breathing is observed remains a mystery. The aim of t
his study is to explore the hypothesis that the particular combination rea
lised is optimal with respect to some objective function. Several objectiv
e functions have been suggested in the literature\, such as the rate of wo
rk during inhalation\, the average force exerted by the respiratory muscle
s\, and the weighted sum of volumetric acceleration and work during inhala
tion\; all of these objective functions provide physiologically acceptable
minima under normal conditions. Resolving this issue requires optimal sol
utions of mathematical models that reflect more accurately the complex int
eraction between lung mechanics and gas exchange\, but this in turn requir
es the development of new computational methodologies. To help achieve thi
s goal\, we constructed a simple mathematical model\, consisting of two pi
ecewise linear differential equations\, that mimics gas exchange in the lu
ngs. By using concepts from optimal control theory\, we found the necessa
ry conditions that minimise a given objective function subject to several
constraints\, such as satisfying the differential equations and maintainin
g one of the variables at a given average value. We could then solve the
optimal control problem both analytically and numerically. Our method can
be extended to models with higher dimensions.\n\nhttps://conferences.maths
.unsw.edu.au/event/2/contributions/36/
LOCATION:University of Sydney Holme Building/--The Refectory
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/36/
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