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235 "> " 0 "" {MPLTEXT 1 238 16 "mPsv := mPs-mPv:" }}}{EXCHG {PARA 235 "" 0 "" {TEXT 242 16 "Mean Resistances" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 18 "mRfs := mPfs/mQfs:" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 18 "mRfv := mPfv/mQfv:" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 18 "mRsv := mPsv/mQsv:" }}}{EXCHG {PARA 235 "" 0 "" {TEXT 242 13 "Forcing Terms" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 15 "Qinf := t -> 0:" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 17 "Pv := t -> mPv:" }}}{EXCHG {PARA 236 "> " 0 "" {MPLTEXT 1 239 25 "z := t -> Pv(t) - mPv:" }}}{EXCHG {PARA 235 "" 0 "" {TEXT 242 20 "Resistance Functions" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 11 "#m := .495:" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 8 "p := .2:" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 8 "q := 10:" }}} {EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 15 "Xup := (q-1)/m:" }}} {EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 17 "Xdown := (p-1)/m:" }}} {EXCHG {PARA 235 "" 0 "" {TEXT 242 11 "The Big One" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 24 "RsvFunction := (x,z) -> " }{MPLTEXT 1 238 67 "\npiecewise(x - z < Xdown, p*mRsv, x - z < Xup, (1 + m*(x - \+ z))*mRsv" }{MPLTEXT 1 238 10 ", q*mRsv):" }}}{EXCHG {PARA 235 "> " 0 " " {MPLTEXT 1 238 44 "#plot(RsvFunction(x,mPv),x=Xdown-5...Xup+5);" }}} {EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 17 "Rfs := t -> mRfs:" }}} {EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 17 "Rfv := t -> mRfv:" }}} {EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 35 "Rsv := t -> RsvFunction( x(t),z(t)):" }}}{EXCHG {PARA 235 "" 0 "" {TEXT 242 14 "Flow Functions" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 17 "Qcf := t -> mQcf:" } }}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 17 "Qcs := t -> mQcs:" }}} {EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 40 "Qfs := t -> (x(t) - y(t) + mPfs)/Rfs(t):" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 40 "Qfv := t -> (x(t) + mPf - Pv(t))/Rfv(t):" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 40 "Qsv := t -> (y(t) + mPs - Pv(t))/Rsv(t):" }}} {EXCHG {PARA 235 "" 0 "" {TEXT 242 13 "Compliances: " }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 20 "Cf := t -> .1333333:" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 13 "Cs := t -> 0:" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 20 "Cfs := t -> 1.87703:" }}}}{SECT 1 {PARA 238 "" 0 "" {TEXT 241 55 "2: The governing equations and graphs \+ of x(t) and y(t)." }}{EXCHG {PARA 235 "" 0 "" {TEXT 242 80 "Two forms \+ of Rate of volume change (RHS = right hand side, LHS = left hand side) " }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 54 "dVfRHS := t -> (Qin f(t) + Qcf(t)) - (Qfs(t) + Qfv(t)):" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 40 "dVsRHS := t -> Qcs(t) + Qfs(t) - Qsv(t):" }}} {EXCHG {PARA 239 "> " 0 "" {MPLTEXT 1 243 52 "detC := t -> Cf(t) * Cs( t) + Cfs(t)*(Cf(t) + Cs(t)):" }}}{EXCHG {PARA 239 "> " 0 "" {MPLTEXT 1 243 82 "dxRHS := t -> 1/detC(t) * (Cs(t) + Cfs(t))*dVfRHS(t) + \+ Cfs(t) *dVsRHS(t):" }}}{EXCHG {PARA 239 "> " 0 "" {MPLTEXT 1 243 82 "dyRHS := t -> 1/detC(t) * Cfs(t)*dVfRHS(t) + (Cf(t) + Cf s(t))*dVsRHS(t):" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 27 "dxL HS := t -> diff(x(t),t):" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 27 "dyLHS := t -> diff(y(t),t):" }}}{EXCHG {PARA 240 "> " 0 "" {MPLTEXT 1 244 31 "diffeq1 := dxLHS(t) = dxRHS(t):" }}}{EXCHG {PARA 240 "> " 0 "" {MPLTEXT 1 244 31 "diffeq2 := dyLHS(t) = dyRHS(t):" }}} {EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 9 "Xo := -1:" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 9 "Yo := -1:" }}}{EXCHG {PARA 236 " > " 0 "" {MPLTEXT 1 239 10 "m := .495:" }}}{EXCHG {PARA 235 "> " 0 "" {MPLTEXT 1 238 8 "soln := " }{MPLTEXT 1 238 42 "\ndsolve(\{diffeq1,dif feq2,x(0)=Xo,y(0)=Yo\}," }{MPLTEXT 1 238 13 "\{x(t),y(t)\}, " } {MPLTEXT 1 238 46 "numeric, output=listprocedure, maxfun=500000);" } {MPLTEXT 1 238 1 "\n" }}{PARA 241 "" 1 "" {XPPMATH 20 "6#>I%solnG6\"7% /I\"tGF%f*6#F(6%I$resGF%I%dataGF%I)solnprocGF%6#IaoCopyright~(c)~1993~ by~the~University~of~Waterloo.~All~rights~reserved.GF%F%C&>8%`6$I$GetG F%I$SetGF%b6#I+thismoduleGF%6#I%DataGF%F%F5F%F%F%F%I+_m22455732GF%F;>8 &-_F3F66#Q/soln_procedureF%@&-I'memberGI*protectedGFG6$9$7$Q%lastF%.I% lastGF%C$>8$-F?6#FK@$-I%typeGFG6$FP.I%listGFGO&FP6#\"\"\"3-FU6$FII\"=G FG-FF6$-I$lhsGFG6#FI7$Q(initialF%.I(initialGF%C$@%-FU6$-I$rhsGFGF_oFW> FP-F?6#/Fao7$\"\"!-I#opGFG6#Fho>FP-F?6#/Fao7$FfnFhoFSFIF%F%F%/-I\"xGF% F*f+F*6'F,F-F.I)outpointGF%I%x(t)GF%6#IinCopyright~(c)~2000~by~Waterlo o~Maple~Inc.~All~rights~reserved.GF%F%C)>I8_EnvDSNumericSaveDigitsGF%I 'DigitsGF%>Fdq\"#9@%/I-_EnvInFsolveGF%I%trueGFG>8'-&I&evalfGFG6#FcqF_o >F\\r-F_rF_oF2F>@$4-FU6$F\\r.I(numericGFGC$@.-FF6$FI7+Q&startF%.I&star tGF%Q'methodF%.I'methodGF%Q%leftF%Q&rightF%Q)leftdataF%Q*rightdataF%Q+ enginedataF%C$@%-FF6$FI7$F_sFbs>FP-F?6#-I(convertGFG6$FI.I'stringGFG>F P-F?F_o@&-FU6$FP.I&arrayGFGO-I%evalGFG6$FPFfn0FPQ)procnameF%OFP-FF6$FI 7$FKFaoC$Fft@$FTO&FP6#\"\"#-FF6$FI7$FLFboC$F^tFhu3-FU6$F\\rFjn-FF6$-F^ o6#F\\rF`oC$@%-FU6$-FioFgvFW>FP-F?6#/Fao7$F_p-Fap6#F\\w>FP-F?6#/Fao7$F \\vF\\wFhu/F\\rQ.solnprocedureF%O-F_u6#F?/F\\rQ(sysvarsF%O7%F(Fip-I\"y GF%F*@%09!I(unknownGF%O-.FfxF_oC$>8(-I(pointtoGFG6#&-FA6#Q0soln_proced uresF%F[vO-.F]yF_oZ%C$>FP-F?FgvFjuF%YF%F%F%F%F%/Fbxf+F*6'F,F-F.F]qI%y( t)GF%F_qF%C)FbqFeqFgqF2F>@$FdrC$@.F[sFisFduC$Fft@$FTO&FP6#\"\"$F]vC$F^ tFfzFavC$@%FjvF]w>FP-F?6#/Fao7$FjzF\\wFfzFiwF[xF^xF`x@%FexFhxC$>F]y-F_ y6#&FbyFizFeyZ%C$FjyFhzF%F\\zF%F%F%F%" }{TEXT 245 1 " " }}}{EXCHG {PARA 236 "> " 0 "" {MPLTEXT 1 239 209 "odeplot(soln,[[t,x(t),color = \+ red,style=point],[t,y(t),color = blue, thickness=2]],0..30,numpoints=1 50, labels=[\"time in min\",\"Red= x(CSF) and Blue = y(sinus) in mmHg \"],labeldirections =[horizontal,vertical]);" }}{PARA 242 "" 1 "" {GLPLOT2D 400 400 400 {PLOTDATA 2 "6&-%'CURVESG6%X,I)anythingGI*protec tedGF(6\"F)[gl'!%\"!!#g]l\"at\"#0000000000000000BFF00000000000003FC9C5 9579FC8FACBFFDEEE88652AF033FD9C59579FC8FACBFFDE2F5A7B67BF73FE354301B7D 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