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MIE520 Term Project: 0-D Model of Cardiovascular System

Due: December ! 20" at t#e be$i%%i%$ of class

I%troductio%:

This project is intended to be done in a spreadsheet, such as Microsoft Excel, LibreOffice Calc,

etc. Please provide your solutions calculated fro the spreadsheet for each of the ! probles. "naddition, for each of the five odels #probles $, %, &, ', and !( please include a list of the

)overnin) e*uations as +ell as the steps used to solve the in the spreadsheet.

&efere%ce:

ran- C. oppensteadt and Charles /. Pes-in. 0Modelin) and /iulation in Medicine and the

Life /ciences,1 2nd Ed., 3e+ 4or-: /prin)er, 2552, Chapter $, /ections $.26$.' and $.7.

8vailable online throu)h the 9. of T. library at:http:lin-.library.utoronto.caeirE";detail.cf

8/14/2019 MIE520TermProject.pdf

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' "n this *uestion, +e are )oin) to ta-e into account the effects of the intrathoracic pressure,

Pthorax, +hich +e previously ne)lected in the odel. /tartin) fro the baseline case in

*uestion $, a-e the follo+in) odifications to the syste of e*uations:

QR=K

R P

/P

thorax) QL=KL PPPthorax)VP8=CP8(PP8Pthorax) VP=CP(PPPThorax)

a' /olve the odified syste of e*uations forPthorax? 5, 6$, 62,H untilP/I5.b' Plot QandP/as functions ofPthorax.

c' 9sin) Joal /ee- in Excel, find the value ofPthoraxatP/? 5. Ge +ill call this value

Pthorax=transition.

5' 8t sufficiently ne)ative values ofPthorax, the systeic veins under)o partial collapse as theyenter the thorax. This partial collapse preventsP/fro becoin) ne)ative #i.e.P/? 5(.

To ipleent this chan)e into the odel defined in *uestion &, a variable resistance,RC, is

added bet+een the systeic veins and the ri)ht atria. This leads to the follo+in) chan)es inthe odel:

QSR

C=P

SVP

RA=5P

RA

QR=K

R (PRAPthorax)a' /olve the odified syste of e*uations for ne)ative values of Pthoraxstartin) fro

Pthorax=transitionand continuin) untilPthorax? 6$& ).

b' erify that atPthorax=transitionthe values of Q, ViandPiare the sae at those found in

*uestion &c(.

c' urther, verify that K is no+ independent ofPthorax.d' Modify the plots ade in *uestion & to account for these odel chan)es.

1' utore$ulatio%: This *uestion is related to the odel chan)es discussed in the

autore)ulation section of the notes.

Let [O

2]a=5.2,M

=5.2'L:in, R

5=$$2.!& ):#L:in(,

andP=P

saP

sv .a' Calculate O2vb' /ho+ that, for constant values of ;/and NP, if O2adecreases to 5.$, K increases such

that the value of KO2a reains constant.

c' /tartin) fro the baseline case in *uestion $, odify the syste of e*uations to include

autore)ulation. 3ote that the calculated flo+ rate, volues, and pressures are identical to

the values found in *uestion $. One of the stated behaviours of this odel is that thesensitivity of the flo+ to pressure chan)es is less than in the baseline case. This is

e*uivalent to statin) that the sensitivity of the pressure to flo+ chan)es is )reater than in

the baseline case. erify this stateent by sho+in) that by chan)in) K to & Lin, the

present odel sho+s lar)er chan)es in NPthan the baseline case.

d' 8neia is a condition in +hich there is a reduction in the aount of heo)lobin in theblood, +hich in turn leads to a reduction in O2a. One of the syptos of aneia is lo+

blood pressure. 9sin) the autore)ulation version of the odel, sho+ that by reducin)O2aby2'D, this causes a substantial decrease in blood pressure, notin) that the odel

)ives steady state values of pressure and easured blood pressure is best represented in

the odel by systeic blood pressure.