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{SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT 257 49 "Mathematical Model of P
ethidine Flow Through Body" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 32 "Definition of the clinical data." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "cl
inical_data := [[0.5, 0.42], [1,0.29],[1.5,0.22],[2,0.18],[2.5,0.15],[
3,0.125],[4,0.096],[6,0.06],[8,0.038],[10,0.024]]:" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "unass
ign('x1','x2', 'k12', 'k21', 'k10');" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "Definition of Variables:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "x1 = the \+
concentration of Pethidine in the Blood Plasma" }}{PARA 0 "" 0 "" 
{TEXT -1 55 "x2 = the concentration of Pethidine in the Other Organs" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 74 "k12 = r
ate of flow of pethidine from the blood plasma to the other organs." }
}{PARA 0 "" 0 "" {TEXT -1 74 "k21 = rate of flow of pethidine from the
 other organs to the blood plasma." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 47 "C
oncentration of Pethidine in the blood stream." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "de1 := diff(x1(t),t
) = (-(k10+k12)*x1(t))+(k21*x2(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%$de1G/-%%diffG6$-%#x1G6#%\"tGF,,&*&,&%$k10G\"\"\"%$k12GF1F1F)F1!\"
\"*&%$k21GF1-%#x2GF+F1F1" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 47 "Concentration of Pethidine in the other o
rgans." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "de2 := diff(x2(t),t) = (k
12*x1(t))-(k21*x2(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$de2G/-%%d
iffG6$-%#x2G6#%\"tGF,,&*&%$k12G\"\"\"-%#x1GF+F0F0*&%$k21GF0F)F0!\"\"" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 73 "Solving the system of e
quations for both blood stream and other organs.  " }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 66 "sol := dsolve(\{de1, de2, x1(0) = .50, x2(0) = 0\},
 \{x1(t), x2(t)\}):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 74 "Solution for concentration of pethidine in the \+
blood plasma at any time t." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 16 "solx1 := sol[1];" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%&solx1G/-%#x1G6#%\"tG,$*&,2*&*&)%$k12G\"\"#\"\"\"-%$e
xpG6#,$*&,*F0F2%$k21GF2%$k10GF2*$-%%sqrtG6#,.*$F/F2F2*(F1F2F0F2F9F2F2*
(F1F2F0F2F:F2F2*$)F9F1F2F2*(F1F2F:F2F9F2!\"\"*$)F:F1F2F2F2FFF2F)F2#FFF
1F2F2*$-F=6#F?F2FF#F2F1*&#F2F1F2*&*(F0F2F3F2F9F2F2*$-F=6#F?F2FFF2FF*&*
*FMF2F0F2F3F2F:F2F2*$-F=6#F?F2FFF2*&#F2F1F2*&F0F2F3F2F2FF*&#F2F1F2*&*&
F/F2-F46#,$*&,*F0F2F9F2F:F2F;F2F2F)F2FIF2F2*$-F=6#F?F2FFF2FF*&**FMF2F0
F2F[oF2F9F2F2*$-F=6#F?F2FFF2*&#F2F1F2*&*(F0F2F[oF2F:F2F2*$-F=6#F?F2FFF
2FF*&#F2F1F2*&F0F2F[oF2F2FFF2F0FFFI" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 63 "Concentration of pethidine in the vital organs at any time t.  \+
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 
"solx2 := sol[2];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&solx2G/-%#x2G6
#%\"tG,&*&*&%$k12G\"\"\"-%$expG6#,$*&,*F-F.%$k21GF.%$k10GF.*$-%%sqrtG6
#,.*$)F-\"\"#F.F.*(F>F.F-F.F5F.F.*(F>F.F-F.F6F.F.*$)F5F>F.F.*(F>F.F6F.
F5F.!\"\"*$)F6F>F.F.F.FDF.F)F.#FDF>F.F.*$-F96#F;F.FD#F.F>*&#F.F>F.*&*&
F-F.-F06#,$*&,*F-F.F5F.F6F.F7F.F.F)F.FGF.F.*$-F96#F;F.FDF.FD" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 223 "W
e now make the assumption that k12 < k21 < k10.  If Pethidine as enter
ing the other organs at a faster rate than it was re-entering the bloo
d plasma, the patient would remain permanently under the influence of \+
Pethidine.  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 193 "Rates at which Pethidine is absorbed is different for each per
son.  Therefore, k12, k21, and k10 will not have hard-fast numerical v
alues, but rather will differentiate from person to person.  " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 165 "We proce
ed to demonstrate how the solution behaves in comparison to the clinic
al data for different sets of absorption rates (k12, k21, and k10) and
 for values of t." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 520 "We estimate and t
hen assign k12, k21, and k10 with evenly spaced constants, graphing th
e resulting two-variable solution.  Thus we can compare the clinical d
ata with the predicted concentration in the blood stream and compare t
he collected clinical data for concentration of pethidine in the blood
 stream to the predicted concentration of pethidine in the blood strea
m.  Finally, we compare the predicted concentration of pethidine in th
e blood stream with the predicted concentration of pethidine in the ot
her organs.  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 74 "subn_value_3 := simplify(subs(\{k12 = 0.1, k21 = 0.20
, k10 = .35\}, solx1));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "subn_val
ue_3_2 := simplify(subs(\{k12 = 0.1, k21 = 0.20, k10 = 0.35\}, solx2))
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-subn_value_3G/-%#x1G6#%\"tG,&-
%$expG6#,$F)$!+\"RTDO\"!#5$\"+NbMV%)!#6*&$\"+[ambTF1\"\"\"-F,6#,$F)$!+
5'eu8&F1F8F8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/subn_value_3_2G/-%#
x2G6#%\"tG,&-%$expG6#,$F)$!+\"RTDO\"!#5$\"+dB`C8F1*&$\"+dB`C8F1\"\"\"-
F,6#,$F)$!+5'eu8&F1F7!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
158 "plot(\{rhs(subn_value_3), rhs(subn_value_3_2), clinical_data\}, t
=0..10, Concentration = 0..0.5, title = `Conc. vs. Time for k12 = 0.1,
 k21 = 0.2, k10 = 0.35`);" }}{PARA 13 "" 1 "" {GLPLOT2D 883 545 545 
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ABELSG6$Q\"t6\"Q.ConcentrationF^jl-%&TITLEG6#%TConc.~vs.~Time~for~k12~
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10 0 2 9 1 4 2 1.000000 45.000000 46.000000 0 1 "Clinical Data for Con
c. of Pethidine in Blood Plasma" "Conc. of Pethidine in Other Organs" 
"Conc. of Pethidine in Blood Plasma" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 59 "To see how pethidine behaves as we change our time window. " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "pl
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[s$\"3UBu\\1H*ps\"Ffo7$F`s$\"3]#G9O7]**f\"Ffo7$Fes$\"3MHMq9!)y\"[\"Ffo
7$Fjs$\"39XetZ:=w8Ffo7$F_t$\"37')Qg>g\"oG\"Ffo7$Fdt$\"3yKsDyL2)=\"Ffo7
$Fit$\"3!y?jC;x.6\"Ffo7$F^u$\"3l]fIWyOE5Ffo7$Fcu$\"3Md'Q;sTKd*Few7$Fhu
$\"3=+;)ppQ!p))Few7$F]v$\"3CZ?>MqnY#)Few7$Fbv$\"3r_9?\\j\"Qk(Few7$Fgv$
\"3#zc8)=!*4HrFew7$F\\w$\"3,at)zX#p7mFew7$Faw$\"3O@8E&pge6'Few7$Fgw$\"
3D,a8!\\eQr&Few7$F\\x$\"3>&=s`(GJ4`Few7$Fax$\"3Vb:l#eL9#\\Few7$Ffx$\"3
i<nx/dSpXFew7$F[y$\"3]Jteuvy_UFew7$F`y$\"3I^/S)fto#RFew7$Fey$\"3;I`*e)
eQbOFew7$Fjy$\"3=vcJC4?'Q$Few7$F_z$\"3!>*[!pBR%fJFew7$Fdz$\"3>![lz\"z'
)GHFew7$Fiz$\"3*[%Re)y0ts#Few7$F^[l$\"3,kA(e[F9`#Few7$Fc[l$\"3?=H\"Q\"
)GNN#Few7$Fh[l$\"3o)3*fQem!=#Few7$F]\\l$\"3h-3f`?>E?Few7$Fb\\l$\"3'=v:
bAJ&z=Few7$Fg\\l$\"3wc.SU6dW<Few7$F\\]l$\"3u*)z]>v6H;Few7$Fa]l$\"3G%>#
yM1;1:Few7$Ff]l$\"3OO8)o!*pSS\"Few7$F[^l$\"3ks.4Q1$GI\"Few7$F`^l$\"3'4
SSO'fx77Few7$Fe^l$\"3%pzg$4o#H7\"Few-Fhn6&FjnF[oF[oF]o-%+AXESLABELSG6$
Q\"t6\"Q.ConcentrationFghl-%&TITLEG6#%TConc.~vs.~Time~for~k12~=~0.1,~k
21~=~0.2,~k10~=~0.35G-%%VIEWG6$;FboFe^l;F]o$\"\"&!\"*" 1 2 0 1 10 0 2 
9 1 4 2 1.000000 45.000000 43.000000 0 1 "Curve 1" "Conc. of Pethidine
 in Other Organs" "Conc. of Pethidine in Blood Plasma" }}}}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 150 "We can see that when the rates of exchange are cl
ose together, the concentration of pethidine remains higher in the org
ans than in the blood stream.  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 71 "Ag
ain, we reset the constants, this time so that k21 & k12 are similar.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 
"subn_value_1 := simplify(subs(\{k12 = 0.1, k21 = 0.11, k10 = 0.3\}, s
olx1));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "subn_value_1_2 := simpli
fy(subs(\{k12 =0.1, k21 = 0.11, k10 = 0.3\}, solx2));" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 29 "unassign('k12','k21', 'k10');" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%-subn_value_1G/-%#x1G6#%\"tG,&-%$expG6#,$F)$!+I)pWg
(!#6$\"+!4XNu%F1*&$\"+!\\Xc_%!#5\"\"\"-F,6#,$F)$!+<IbRVF7F8F8" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/subn_value_1_2G/-%#x2G6#%\"tG,&-%$e
xpG6#,$F)$!+I)pWg(!#6$\"+!*o*pR\"!#5*&$\"+!*o*pR\"F4\"\"\"-F,6#,$F)$!+
<IbRVF4F8!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 177 "plot(\{c
linical_data, rhs(subn_value_1), rhs(subn_value_1_2)\}, t=0..10, Conce
ntration=0..0.5, title = `Concentration of Pethidine vs. Time for k12 \+
= 0.1, k21 = 0.11, k10 = 0.3`);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 963 588 
588 {PLOTDATA 2 "6(-%'CURVESG6$7S7$$\"\"!F)$\"3#*******)*******\\!#=7$
$\"3emmm;arz@F,$\"3W$zX0AWPe%F,7$$\"3[LL$e9ui2%F,$\"3uny&eez<D%F,7$$\"
3nmmm\"z_\"4iF,$\"3V)=u]uk\"4RF,7$$\"39ommT&phN)F,$\"3Qjr\"z^AVf$F,7$$
\"3KLLe*=)H\\5!#<$\"3u1ri&)3E3LF,7$$\"3smm\"z/3uC\"FD$\"376*)zs3ElIF,7
$$\"3!****\\7LRDX\"FD$\"3,<MZ7wDMGF,7$$\"3%om;zR'ok;FD$\"3*)>k31)Rbh#F
,7$$\"33++D1J:w=FD$\"31YiLuE=;CF,7$$\"3oLLL3En$4#FD$\"3aG`\"e1V)GAF,7$
$\"3#pmmT!RE&G#FD$\"3%*)fF2[\\u2#F,7$$\"3D+++D.&4]#FD$\"3w>1f9O'4#>F,7
$$\"3;+++vB_<FFD$\"3K\"\\l=1Dux\"F,7$$\"33+++v'Hi#HFD$\"3-,4T\\+&3l\"F
,7$$\"3&om;z*ev:JFD$\"3E\\;\\&*\\0X:F,7$$\"3_LLL347TLFD$\"3uH=!fl;'H9F
,7$$\"3nLLLLY.KNFD$\"3Y!z&oP(**)R8F,7$$\"33++D\"o7Tv$FD$\"3uZP2\\5/W7F
,7$$\"3?LLL$Q*o]RFD$\"3k:u`X@=m6F,7$$\"3m++D\"=lj;%FD$\"3yXzoCql(3\"F,
7$$\"3S++vV&R<P%FD$\"3<6eFyX->5F,7$$\"3CML$e9Ege%FD$\"3esb!=@oC`*!#>7$
$\"3]LLeR\"3Gy%FD$\"3)Q$HO&opk(*)Ffr7$$\"3emm;/T1&*\\FD$\"3LC&>hkJRU)F
fr7$$\"3=nm\"zRQb@&FD$\"3;Z<RSES(*yFfr7$$\"3:++v=>Y2aFD$\"3;aIp\"eN]Z(
Ffr7$$\"3Znm;zXu9cFD$\"33IdY2!4L0(Ffr7$$\"34+++]y))GeFD$\"3?lqDyj0_mFf
r7$$\"3H++]i_QQgFD$\"3-$*[X&[u/H'Ffr7$$\"3b++D\"y%3TiFD$\"3Y#y-'[HInfF
fr7$$\"3+++]P![hY'FD$\"3:<p2*3qlj&Ffr7$$\"3iKLL$Qx$omFD$\"3a'Q*zpSYi`F
fr7$$\"3Y+++v.I%)oFD$\"3og+1fu\"=4&Ffr7$$\"3?mm\"zpe*zqFD$\"3as\"3&\\&
)ek[Ffr7$$\"3;,++D\\'QH(FD$\"3L>i//I7MYFfr7$$\"3%HL$e9S8&\\(FD$\"3$4K;
<X(*HV%Ffr7$$\"3s++D1#=bq(FD$\"3la>'\\t)pPUFfr7$$\"3\"HLL$3s?6zFD$\"3#
3bJU>..1%Ffr7$$\"3a***\\7`Wl7)FD$\"3!e4;'eCt()QFfr7$$\"3enmmm*RRL)FD$
\"3xfa!\\.\"=LPFfr7$$\"3%zmmTvJga)FD$\"31$=uFTmfe$Ffr7$$\"3]MLe9tOc()F
D$\"3q_:%[q'*)\\MFfr7$$\"31,++]Qk\\*)FD$\"34b<>6L(GL$Ffr7$$\"3![LL3dg6
<*FD$\"3V\"G6j'pT2KFfr7$$\"3%ymmmw(Gp$*FD$\"3!\\JWw^BC5$Ffr7$$\"3C++D
\"oK0e*FD$\"35\"p[#e:P(*HFfr7$$\"35,+v=5s#y*FD$\"3KH?fJ7'H!HFfr7$$\"#5
F)$\"3T?\"\\LCcw!GFfr-%'COLOURG6&%$RGBG$Ffz!\"\"F(F(-F$6$7,7$$\"3+++++
+++]F,$\"3%)*************>%F,7$$\"\"\"F)$\"3y**************GF,7$$\"3++
++++++:FD$\"3-+++++++AF,7$$\"\"#F)$\"3#**************z\"F,7$$\"3++++++
++DFD$\"3%**************\\\"F,7$$\"\"$F)$\"3+++++++]7F,7$$\"\"%F)$\"3?
+++++++'*Ffr7$$\"\"'F)$\"3y**************fFfr7$$\"\")F)$\"3#**********
****z$Ffr7$Fez$\"3/+++++++CFfr-Fjz6&F\\[lF(F][lF(-F$6$7W7$F(F(7$$\"3GL
LL3x&)*3\"F,$\"38F'ztRm-I&!#?7$F.$\"3d.(erk%>J5Ffr7$$\"3v***\\7y%*z7$F
,$\"3i!R*)\\zY[W\"Ffr7$F3$\"3>?&=gH^&Q=Ffr7$$\"3z***\\(oMrU^F,$\"3wPc(
*G4^eAFfr7$F8$\"3)oa!y)o9al#Ffr7$$\"3Unmmm6m#G(F,$\"3Zh,**)H_F.$Ffr7$F
=$\"3_#oR76k))Q$Ffr7$FB$\"3Oy6sB\"R%QSFfr7$FH$\"3=K6MlXYvXFfr7$FM$\"3a
6hxVFEr]Ffr7$FR$\"3QpM\"\\TV__&Ffr7$FW$\"3Twy#RS#pBfFfr7$Ffn$\"3?nN;%*
eW#G'Ffr7$F[o$\"3?:-![5$RflFfr7$F`o$\"36^*QJK49$oFfr7$Feo$\"3GF(y<$o/m
qFfr7$Fjo$\"3#oCaoG7\"fsFfr7$F_p$\"3,$=/x(e*)3uFfr7$Fdp$\"33K!=*))fIev
Ffr7$Fip$\"3c'Q)4hXqiwFfr7$F^q$\"3Ee7)4oA5w(Ffr7$Fcq$\"3,9D&G?H#HyFfr7
$Fhq$\"3eW'Rz+0d)yFfr7$F]r$\"3$zDzTpNL#zFfr7$Fbr$\"3/nM:38ZZzFfr7$Fhr$
\"3%[YXgI_t&zFfr7$F]s$\"3WT%=zCQh&zFfr7$Fbs$\"3C]y)HAcJ%zFfr7$Fgs$\"3
\"oGnG%p7BzFfr7$F\\t$\"3G^Kc#35L*yFfr7$Fat$\"31k-@J]]ayFfr7$Fft$\"3qc)
*3hh_4yFfr7$F[u$\"3-3WYW!G,w(Ffr7$F`u$\"3MR#)e8\"z#*p(Ffr7$Feu$\"3.PS9
89%)RwFfr7$Fju$\"3+V1lJv+svFfr7$F_v$\"3ok-nK&3r](Ffr7$Fdv$\"3-zW\"e9&*
GV(Ffr7$Fiv$\"3k\"\\b3Ua.O(Ffr7$F^w$\"3_dl#QV.@G(Ffr7$Fcw$\"32l4C=Pa.s
Ffr7$Fhw$\"3\"pj&HNuX>rFfr7$F]x$\"3nwSrsT)p.(Ffr7$Fbx$\"3qb;'Gw/9&pFfr
7$Fgx$\"3#3En[QSb'oFfr7$F\\y$\"35)*z$4xcfy'Ffr7$Fay$\"37;0PKZ9%p'Ffr7$
Ffy$\"3XUxNOyk6mFfr7$F[z$\"38'eYOC`M_'Ffr7$F`z$\"3I%QT,*e%*QkFfr7$Fez$
\"3!3vv'4X;[jFfr-Fjz6&F\\[lF][lF][lF(-%+AXESLABELSG6$Q\"t6\"Q.Concentr
ationFcil-%&TITLEG6#%coConcentration~of~Pethidine~vs.~Time~for~k12~=~0
.1,~k21~=~0.11,~k10~=~0.3G-%%VIEWG6$;F(Fez;F($\"\"&F^[l" 1 2 0 1 10 0 
2 9 1 4 2 1.000000 45.000000 45.000000 0 1 "Conc. of Pethidine in Bloo
d Plasma" "Clinical Data for Conc. of Pethidine in Blood Plasma" "Conc
. of Pethidine in Other Organs" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 179 "plot(\{clinical_data, rhs(subn_value_1), rhs(subn_value_1_2)
\}, t=40..50, Concentration=0..0.01, title = `Concentration of Pethidi
ne vs. Time for k12 = 0.1, k21 = 0.11, k10 = 0.3`);" }}{PARA 13 "" 1 "
" {GLPLOT2D 916 589 589 {PLOTDATA 2 "6(-%'CURVESG6$7S7$$\"#S\"\"!$\"3?
\"*QVH$H]E#!#?7$$\"3Rmm;arz@S!#;$\"3)3;EQj$zFAF-7$$\"35L$e9ui2/%F1$\"3
3Xv!p[$*e>#F-7$$\"3omm\"z_\"4iSF1$\"3!3fGY(Qcg@F-7$$\"3ummT&phN3%F1$\"
3^+jl#>ub7#F-7$$\"3CL$e*=)H\\5%F1$\"3iRJj\"\\884#F-7$$\"3Xm;z/3uCTF1$
\"31!pq<+V+1#F-7$$\"3;+]7LRDXTF1$\"3d?cP)*o:G?F-7$$\"3#om\"zR'ok;%F1$
\"3?Sg'\\M*p&*>F-7$$\"37+]i5`h(=%F1$\"3Y%*ojlG'Q'>F-7$$\"3bLL$3En$4UF1
$\"3\"[)3is\\kJ>F-7$$\"3#pm;/RE&GUF1$\"3K.SZXbq.>F-7$$\"3!)****\\K]4]U
F1$\"3[&3N'[cts=F-7$$\"3;++]PAvrUF1$\"3t=GgLb9U=F-7$$\"3=++]nHi#H%F1$
\"3I!p2,>RJ\"=F-7$$\"3Qm;z*ev:J%F1$\"3_KYleX>(y\"F-7$$\"30LL$347TL%F1$
\"3!p0vIlEov\"F-7$$\"3?LLLjM?`VF1$\"3S\"R;n80:t\"F-7$$\"3)***\\7o7TvVF
1$\"3*f.g%R!4Dq\"F-7$$\"3OLLLQ*o]R%F1$\"3]f$z;*zCx;F-7$$\"32+]7=lj;WF1
$\"3'*G_,HO'*\\;F-7$$\"3J+]PaR<PWF1$\"3*)zIbL^RC;F-7$$\"3qLLe9EgeWF1$
\"3)4*zg!RR\")f\"F-7$$\"35L$eR\"3GyWF1$\"3_KlZ%R-Wd\"F-7$$\"3emmT5k]*
\\%F1$\"31(Qb3$R>\\:F-7$$\"3sm;zRQb@XF1$\"3j!GN1rOM_\"F-7$$\"3?+](=>Y2
a%F1$\"3Zdp)Q)QO,:F-7$$\"3%om;zXu9c%F1$\"3QW$*\\<P)yZ\"F-7$$\"35+++&y)
)Ge%F1$\"3gI]R\"*>,a9F-7$$\"3.++DE&QQg%F1$\"3qipD[8.J9F-7$$\"3C+]7y%3T
i%F1$\"3hSON!=U\"49F-7$$\"3#)***\\P![hYYF1$\"3Il<-U+B&Q\"F-7$$\"3iLLLQ
x$om%F1$\"39qrmM-4k8F-7$$\"3C++]P+V)o%F1$\"34rr=y\\(=M\"F-7$$\"3im;zpe
*zq%F1$\"3&Qe:5Fd?K\"F-7$$\"37++]#\\'QHZF1$\"3ElGjIgs+8F-7$$\"3cL$e9S8
&\\ZF1$\"3_5Q#oPp4G\"F-7$$\"3#)**\\i?=bqZF1$\"3;UVi&oQ1E\"F-7$$\"3-LL$
3s?6z%F1$\"30\\p/7P2T7F-7$$\"3y**\\7`Wl7[F1$\"3nu)3iE;4A\"F-7$$\"3%pmm
m*RRL[F1$\"3\"oI()3#=\"=?\"F-7$$\"3)pm;a<.Y&[F1$\"3G1qV,Re#=\"F-7$$\"3
kL$e9tOc([F1$\"3gp!*GL!>Q;\"F-7$$\"35+++&Qk\\*[F1$\"3Adr_$pQo9\"F-7$$
\"3mLL3dg6<\\F1$\"3vykh\"y\"oF6F-7$$\"3hmmmw(Gp$\\F1$\"3]*zkL()=36\"F-
7$$\"3')**\\7oK0e\\F1$\"3K#=&3ir6$4\"F-7$$\"3I+](=5s#y\\F1$\"33\\RPN'Q
k2\"F-7$$\"#]F*$\"39p*z%\\))ze5F--%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*F`[l
-F$6$7,7$$\"3++++++++]!#=$\"3%)*************>%Fg[l7$$\"\"\"F*$\"3y****
**********GFg[l7$$\"3++++++++:!#<$\"3-+++++++AFg[l7$$\"\"#F*$\"3#*****
*********z\"Fg[l7$$\"3++++++++DFb\\l$\"3%**************\\\"Fg[l7$$\"\"
$F*$\"3+++++++]7Fg[l7$$\"\"%F*$\"3?+++++++'*!#>7$$\"\"'F*$\"3y********
******fFi]l7$$\"\")F*$\"3#**************z$Fi]l7$$F^[lF*$\"3/+++++++CFi
]l-Fjz6&F\\[lF`[lF][lF`[l-F$6$7S7$F($\"3U*zA#GzdqmF-7$F/$\"3e<,jb3#4c'
F-7$F5$\"39/@,[k(pY'F-7$F:$\"31B_8$>KHO'F-7$F?$\"3C\"[$f)y)))fiF-7$FD$
\"3kagb)*>**ehF-7$FI$\"3Ih/)\\7,p1'F-7$FN$\"3cvGsDr*H(fF-7$FS$\"3?z:%=
15u(eF-7$FX$\"3#Rz3+\">l$y&F-7$Fgn$\"3[!*Hfi.x)o&F-7$F\\o$\"3&ebsLx)[1
cF-7$Fao$\"34lg#oM#G:bF-7$Ffo$\"3D'3d[F%>DaF-7$F[p$\"3(=>4)H.xR`F-7$F`
p$\"31R2o%3jLE&F-7$Fep$\"3Ej@9m\"HR<&F-7$Fjp$\"3GI[&[(oN*4&F-7$F_q$\"3
Z)>4j\"G'R,&F-7$Fdq$\"3xZyP'\\o&R\\F-7$Fiq$\"3#e<'))=a@f[F-7$F^r$\"3e#
GXKc:Ry%F-7$Fcr$\"3)R\"\\T-<f1ZF-7$Fhr$\"3)f?$[\"e&oOYF-7$F]s$\"3S)Q><
\"fWiXF-7$Fbs$\"3[6iv,,f'[%F-7$Fgs$\"3ju=L<\\e@WF-7$F\\t$\"3c4oYY]V_VF
-7$Fat$\"3!Gj<L*>8#G%F-7$Fft$\"3(3&p&o=`W@%F-7$F[u$\"3y,\\b$z))*\\TF-7
$F`u$\"3W:g(zlm&zSF-7$Feu$\"3)\\P))G74t,%F-7$Fju$\"3A^*=HL%)=&RF-7$F_v
$\"3A>310/_$*QF-7$Fdv$\"3-8e,\\!*pIQF-7$Fiv$\"3-$f(z,\\^sPF-7$F^w$\"3$
**)==!=SEr$F-7$Fcw$\"3Gu0_=0-bOF-7$Fhw$\"3qAuy\"*fl&f$F-7$F]x$\"3GO^V(
e#RRNF-7$Fbx$\"3c,AnQbw#[$F-7$Fgx$\"3>q8t)=-vU$F-7$F\\y$\"3yoxZYV\\xLF
-7$Fay$\"3:%R'*zRw5K$F-7$Ffy$\"3a>c5'Q99F$F-7$F[z$\"3_0OFd?G>KF-7$F`z$
\"3Mj`I[I;qJF-7$Fez$\"3x$4kO38#=JF--Fjz6&F\\[lF][lF][lF`[l-%+AXESLABEL
SG6$Q\"t6\"Q.ConcentrationFfhl-%&TITLEG6#%coConcentration~of~Pethidine
~vs.~Time~for~k12~=~0.1,~k21~=~0.11,~k10~=~0.3G-%%VIEWG6$;F(Fez;F`[l$F
\\\\l!\"#" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 1 "Co
nc. of Pethidine in Blood Plasma" "Conc. of Pethidine in Other Organs
" "Conc. of Pethidine in Other Organs" }}{TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 219 "We can s
ee that when we set the rate of flow in and out of the other organs re
latively close to each other, the concentration of pethidine in the ot
her organs remains higher than in the blood plasma for over two days. \+
 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
256 158 "We examine the behaviour for when pethidine is leaving the bl
oodstream at nearly the same rate as it is returning from the other or
gans (k21 is close to k10)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 75 "subn_value_2 := simplify(subs(\{k12 = 0.1
, k21 = 0.29, k10 = 0.30\}, solx1));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 77 "subn_value_2_2 := simplify(subs(\{k12 = 0.1, k21 = 0.29, k10 = 0
.30\}, solx2));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "unassign('k12','
k21', 'k10');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-subn_value_2G/-%#x
1G6#%\"tG,&-%$expG6#,$F)$!+$)pWg;!#5$\"+5<lJ<F1*&$\"+*G[$oKF1\"\"\"-F,
6#,$F)$!+:IbR_F1F7F7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%/subn_value_
2_2G/-%#x2G6#%\"tG,&-%$expG6#,$F)$!+$)pWg;!#5$\"+!*o*pR\"F1*&$\"+!*o*p
R\"F1\"\"\"-F,6#,$F)$!+:IbR_F1F7!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 172 "plot(\{rhs(subn_value_2), rhs(subn_value_2_2), clini
cal_data\}, t=0..10, Concentration = 0..0.5, title = `Conc. of Pethidi
ne vs. Time for k12 = 0.1, k21 = 0.29, k10 = 0.30`);" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 941 597 597 
{PLOTDATA 2 "6(-%'CURVESG6$7X7$$\"\"!F)F(7$$\"3GLLL3x&)*3\"!#=$\"3%y*3
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~Time~for~k12~=~0.1,~k21~=~0.29,~k10~=~0.30G-%%VIEWG6$;F(F]\\l;F($\"\"
&Ff\\l" 1 2 0 1 10 0 2 9 1 4 2 1.000000 43.000000 42.000000 0 1 "Conc.
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