Changing RxODE compartment numbers
2019-10-16
RxODE-cmt.Rmd
How RxODE assigns compartment numbers
RxODE automatically assigns compartment numbers when parsing. For example, with the Mavoglurant PBPK model the following model may be used:
library(RxODE)
pbpk <- RxODE({
KbBR = exp(lKbBR)
KbMU = exp(lKbMU)
KbAD = exp(lKbAD)
CLint= exp(lCLint + eta.LClint)
KbBO = exp(lKbBO)
KbRB = exp(lKbRB)
## Regional blood flows
CO = (187.00*WT^0.81)*60/1000; # Cardiac output (L/h) from White et al (1968)
QHT = 4.0 *CO/100;
QBR = 12.0*CO/100;
QMU = 17.0*CO/100;
QAD = 5.0 *CO/100;
QSK = 5.0 *CO/100;
QSP = 3.0 *CO/100;
QPA = 1.0 *CO/100;
QLI = 25.5*CO/100;
QST = 1.0 *CO/100;
QGU = 14.0*CO/100;
QHA = QLI - (QSP + QPA + QST + QGU); # Hepatic artery blood flow
QBO = 5.0 *CO/100;
QKI = 19.0*CO/100;
QRB = CO - (QHT + QBR + QMU + QAD + QSK + QLI + QBO + QKI);
QLU = QHT + QBR + QMU + QAD + QSK + QLI + QBO + QKI + QRB;
## Organs' volumes = organs' weights / organs' density
VLU = (0.76 *WT/100)/1.051;
VHT = (0.47 *WT/100)/1.030;
VBR = (2.00 *WT/100)/1.036;
VMU = (40.00*WT/100)/1.041;
VAD = (21.42*WT/100)/0.916;
VSK = (3.71 *WT/100)/1.116;
VSP = (0.26 *WT/100)/1.054;
VPA = (0.14 *WT/100)/1.045;
VLI = (2.57 *WT/100)/1.040;
VST = (0.21 *WT/100)/1.050;
VGU = (1.44 *WT/100)/1.043;
VBO = (14.29*WT/100)/1.990;
VKI = (0.44 *WT/100)/1.050;
VAB = (2.81 *WT/100)/1.040;
VVB = (5.62 *WT/100)/1.040;
VRB = (3.86 *WT/100)/1.040;
## Fixed parameters
BP = 0.61; # Blood:plasma partition coefficient
fup = 0.028; # Fraction unbound in plasma
fub = fup/BP; # Fraction unbound in blood
KbLU = exp(0.8334);
KbHT = exp(1.1205);
KbSK = exp(-.5238);
KbSP = exp(0.3224);
KbPA = exp(0.3224);
KbLI = exp(1.7604);
KbST = exp(0.3224);
KbGU = exp(1.2026);
KbKI = exp(1.3171);
##-----------------------------------------
S15 = VVB*BP/1000;
C15 = Venous_Blood/S15
##-----------------------------------------
d/dt(Lungs) = QLU*(Venous_Blood/VVB - Lungs/KbLU/VLU);
d/dt(Heart) = QHT*(Arterial_Blood/VAB - Heart/KbHT/VHT);
d/dt(Brain) = QBR*(Arterial_Blood/VAB - Brain/KbBR/VBR);
d/dt(Muscles) = QMU*(Arterial_Blood/VAB - Muscles/KbMU/VMU);
d/dt(Adipose) = QAD*(Arterial_Blood/VAB - Adipose/KbAD/VAD);
d/dt(Skin) = QSK*(Arterial_Blood/VAB - Skin/KbSK/VSK);
d/dt(Spleen) = QSP*(Arterial_Blood/VAB - Spleen/KbSP/VSP);
d/dt(Pancreas) = QPA*(Arterial_Blood/VAB - Pancreas/KbPA/VPA);
d/dt(Liver) = QHA*Arterial_Blood/VAB + QSP*Spleen/KbSP/VSP + QPA*Pancreas/KbPA/VPA + QST*Stomach/KbST/VST + QGU*Gut/KbGU/VGU - CLint*fub*Liver/KbLI/VLI - QLI*Liver/KbLI/VLI;
d/dt(Stomach) = QST*(Arterial_Blood/VAB - Stomach/KbST/VST);
d/dt(Gut) = QGU*(Arterial_Blood/VAB - Gut/KbGU/VGU);
d/dt(Bones) = QBO*(Arterial_Blood/VAB - Bones/KbBO/VBO);
d/dt(Kidneys) = QKI*(Arterial_Blood/VAB - Kidneys/KbKI/VKI);
d/dt(Arterial_Blood) = QLU*(Lungs/KbLU/VLU - Arterial_Blood/VAB);
d/dt(Venous_Blood) = QHT*Heart/KbHT/VHT + QBR*Brain/KbBR/VBR + QMU*Muscles/KbMU/VMU + QAD*Adipose/KbAD/VAD + QSK*Skin/KbSK/VSK + QLI*Liver/KbLI/VLI + QBO*Bones/KbBO/VBO + QKI*Kidneys/KbKI/VKI + QRB*Rest_of_Body/KbRB/VRB - QLU*Venous_Blood/VVB;
d/dt(Rest_of_Body) = QRB*(Arterial_Blood/VAB - Rest_of_Body/KbRB/VRB);
})If you look at the summary, you can see where RxODE assigned the compartment number(s)
summary(pbpk)#> RxODE 0.9.1-7 model named rx_a86b74039664d76045c0a466fe932da9 model (ready).
#> DLL: /tmp/RtmpbljJCY/.rxCache/rx_a86b74039664d76045c0a466fe932da9__.rxd/rx_a86b74039664d76045c0a466fe932da9_.so
#> -- User supplied parameters: ---------------------------------------------------
#> lKbBR lKbMU lKbAD lCLint eta.LClint lKbBO lKbRB
#> NA NA NA NA NA NA NA
#> WT BP fup
#> NA 0.610 0.028
#> -- User initial conditions: ----------------------------------------------------
#> Lungs Heart Brain Muscles Adipose
#> 0 0 0 0 0
#> Skin Spleen Pancreas Liver Stomach
#> 0 0 0 0 0
#> Gut Bones Kidneys Arterial_Blood Venous_Blood
#> 0 0 0 0 0
#> Rest_of_Body
#> 0
#> -- Compartments: ---------------------------------------------------------------
#> cmt=1 cmt=2 cmt=3 cmt=4
#> "Lungs" "Heart" "Brain" "Muscles"
#> cmt=5 cmt=6 cmt=7 cmt=8
#> "Adipose" "Skin" "Spleen" "Pancreas"
#> cmt=9 cmt=10 cmt=11 cmt=12
#> "Liver" "Stomach" "Gut" "Bones"
#> cmt=13 cmt=14 cmt=15 cmt=16
#> "Kidneys" "Arterial_Blood" "Venous_Blood" "Rest_of_Body"
#>
#> Calculated Variables:
#> [1] "KbBR" "KbMU" "KbAD" "CLint" "KbBO" "KbRB" "CO" "QHT" "QBR"
#> [10] "QMU" "QAD" "QSK" "QSP" "QPA" "QLI" "QST" "QGU" "QHA"
#> [19] "QBO" "QKI" "QRB" "QLU" "VLU" "VHT" "VBR" "VMU" "VAD"
#> [28] "VSK" "VSP" "VPA" "VLI" "VST" "VGU" "VBO" "VKI" "VAB"
#> [37] "VVB" "VRB" "fub" "KbLU" "KbHT" "KbSK" "KbSP" "KbPA" "KbLI"
#> [46] "KbST" "KbGU" "KbKI" "S15" "C15"
#> ______________________________ RxODE Model Syntax ______________________________
#> RxODE({
#> KbBR = exp(lKbBR)
#> KbMU = exp(lKbMU)
#> KbAD = exp(lKbAD)
#> CLint = exp(lCLint + eta.LClint)
#> KbBO = exp(lKbBO)
#> KbRB = exp(lKbRB)
#> CO = (187 * WT^0.81) * 60/1000
#> QHT = 4 * CO/100
#> QBR = 12 * CO/100
#> QMU = 17 * CO/100
#> QAD = 5 * CO/100
#> QSK = 5 * CO/100
#> QSP = 3 * CO/100
#> QPA = 1 * CO/100
#> QLI = 25.5 * CO/100
#> QST = 1 * CO/100
#> QGU = 14 * CO/100
#> QHA = QLI - (QSP + QPA + QST + QGU)
#> QBO = 5 * CO/100
#> QKI = 19 * CO/100
#> QRB = CO - (QHT + QBR + QMU + QAD + QSK + QLI + QBO + QKI)
#> QLU = QHT + QBR + QMU + QAD + QSK + QLI + QBO + QKI + QRB
#> VLU = (0.76 * WT/100)/1.051
#> VHT = (0.47 * WT/100)/1.03
#> VBR = (2 * WT/100)/1.036
#> VMU = (40 * WT/100)/1.041
#> VAD = (21.42 * WT/100)/0.916
#> VSK = (3.71 * WT/100)/1.116
#> VSP = (0.26 * WT/100)/1.054
#> VPA = (0.14 * WT/100)/1.045
#> VLI = (2.57 * WT/100)/1.04
#> VST = (0.21 * WT/100)/1.05
#> VGU = (1.44 * WT/100)/1.043
#> VBO = (14.29 * WT/100)/1.99
#> VKI = (0.44 * WT/100)/1.05
#> VAB = (2.81 * WT/100)/1.04
#> VVB = (5.62 * WT/100)/1.04
#> VRB = (3.86 * WT/100)/1.04
#> BP = 0.61
#> fup = 0.028
#> fub = fup/BP
#> KbLU = exp(0.8334)
#> KbHT = exp(1.1205)
#> KbSK = exp(-0.5238)
#> KbSP = exp(0.3224)
#> KbPA = exp(0.3224)
#> KbLI = exp(1.7604)
#> KbST = exp(0.3224)
#> KbGU = exp(1.2026)
#> KbKI = exp(1.3171)
#> S15 = VVB * BP/1000
#> C15 = Venous_Blood/S15
#> d/dt(Lungs) = QLU * (Venous_Blood/VVB - Lungs/KbLU/VLU)
#> d/dt(Heart) = QHT * (Arterial_Blood/VAB - Heart/KbHT/VHT)
#> d/dt(Brain) = QBR * (Arterial_Blood/VAB - Brain/KbBR/VBR)
#> d/dt(Muscles) = QMU * (Arterial_Blood/VAB - Muscles/KbMU/VMU)
#> d/dt(Adipose) = QAD * (Arterial_Blood/VAB - Adipose/KbAD/VAD)
#> d/dt(Skin) = QSK * (Arterial_Blood/VAB - Skin/KbSK/VSK)
#> d/dt(Spleen) = QSP * (Arterial_Blood/VAB - Spleen/KbSP/VSP)
#> d/dt(Pancreas) = QPA * (Arterial_Blood/VAB - Pancreas/KbPA/VPA)
#> d/dt(Liver) = QHA * Arterial_Blood/VAB + QSP * Spleen/KbSP/VSP +
#> QPA * Pancreas/KbPA/VPA + QST * Stomach/KbST/VST + QGU *
#> Gut/KbGU/VGU - CLint * fub * Liver/KbLI/VLI - QLI * Liver/KbLI/VLI
#> d/dt(Stomach) = QST * (Arterial_Blood/VAB - Stomach/KbST/VST)
#> d/dt(Gut) = QGU * (Arterial_Blood/VAB - Gut/KbGU/VGU)
#> d/dt(Bones) = QBO * (Arterial_Blood/VAB - Bones/KbBO/VBO)
#> d/dt(Kidneys) = QKI * (Arterial_Blood/VAB - Kidneys/KbKI/VKI)
#> d/dt(Arterial_Blood) = QLU * (Lungs/KbLU/VLU - Arterial_Blood/VAB)
#> d/dt(Venous_Blood) = QHT * Heart/KbHT/VHT + QBR * Brain/KbBR/VBR +
#> QMU * Muscles/KbMU/VMU + QAD * Adipose/KbAD/VAD + QSK *
#> Skin/KbSK/VSK + QLI * Liver/KbLI/VLI + QBO * Bones/KbBO/VBO +
#> QKI * Kidneys/KbKI/VKI + QRB * Rest_of_Body/KbRB/VRB -
#> QLU * Venous_Blood/VVB
#> d/dt(Rest_of_Body) = QRB * (Arterial_Blood/VAB - Rest_of_Body/KbRB/VRB)
#> })
#> ________________________________________________________________________________In this case, it is assigned to compartment 15. Figuring this out can be inconvenient and also lead to re-numbering compartment in simulation or estimation datasets. While it is easy and probably clearer to specify the compartment by name, other tools only support compartment numbers. Therefore, having a way to number compartment easily can lead to less data modification between multiple tools.
Changing compartment numbers by pre-declaring the compartments
To add the compartments to the RxODE model in the order you desire you simply need to pre-declare the compartments with cmt. For example specifying is Venous_Blood and Skin to be the 1st and 2nd compartments, respectively, is simple:
pbpk2 <- RxODE({
cmt(Venous_Blood) ## Now this is the first compartment, ie cmt=1
cmt(Skin) ## Skin may be a compartment you wish to dose to as well, so it is now cmt=2
KbBR = exp(lKbBR)
KbMU = exp(lKbMU)
KbAD = exp(lKbAD)
CLint= exp(lCLint + eta.LClint)
KbBO = exp(lKbBO)
KbRB = exp(lKbRB)
## Regional blood flows
CO = (187.00*WT^0.81)*60/1000; # Cardiac output (L/h) from White et al (1968)
QHT = 4.0 *CO/100;
QBR = 12.0*CO/100;
QMU = 17.0*CO/100;
QAD = 5.0 *CO/100;
QSK = 5.0 *CO/100;
QSP = 3.0 *CO/100;
QPA = 1.0 *CO/100;
QLI = 25.5*CO/100;
QST = 1.0 *CO/100;
QGU = 14.0*CO/100;
QHA = QLI - (QSP + QPA + QST + QGU); # Hepatic artery blood flow
QBO = 5.0 *CO/100;
QKI = 19.0*CO/100;
QRB = CO - (QHT + QBR + QMU + QAD + QSK + QLI + QBO + QKI);
QLU = QHT + QBR + QMU + QAD + QSK + QLI + QBO + QKI + QRB;
## Organs' volumes = organs' weights / organs' density
VLU = (0.76 *WT/100)/1.051;
VHT = (0.47 *WT/100)/1.030;
VBR = (2.00 *WT/100)/1.036;
VMU = (40.00*WT/100)/1.041;
VAD = (21.42*WT/100)/0.916;
VSK = (3.71 *WT/100)/1.116;
VSP = (0.26 *WT/100)/1.054;
VPA = (0.14 *WT/100)/1.045;
VLI = (2.57 *WT/100)/1.040;
VST = (0.21 *WT/100)/1.050;
VGU = (1.44 *WT/100)/1.043;
VBO = (14.29*WT/100)/1.990;
VKI = (0.44 *WT/100)/1.050;
VAB = (2.81 *WT/100)/1.040;
VVB = (5.62 *WT/100)/1.040;
VRB = (3.86 *WT/100)/1.040;
## Fixed parameters
BP = 0.61; # Blood:plasma partition coefficient
fup = 0.028; # Fraction unbound in plasma
fub = fup/BP; # Fraction unbound in blood
KbLU = exp(0.8334);
KbHT = exp(1.1205);
KbSK = exp(-.5238);
KbSP = exp(0.3224);
KbPA = exp(0.3224);
KbLI = exp(1.7604);
KbST = exp(0.3224);
KbGU = exp(1.2026);
KbKI = exp(1.3171);
##-----------------------------------------
S15 = VVB*BP/1000;
C15 = Venous_Blood/S15
##-----------------------------------------
d/dt(Lungs) = QLU*(Venous_Blood/VVB - Lungs/KbLU/VLU);
d/dt(Heart) = QHT*(Arterial_Blood/VAB - Heart/KbHT/VHT);
d/dt(Brain) = QBR*(Arterial_Blood/VAB - Brain/KbBR/VBR);
d/dt(Muscles) = QMU*(Arterial_Blood/VAB - Muscles/KbMU/VMU);
d/dt(Adipose) = QAD*(Arterial_Blood/VAB - Adipose/KbAD/VAD);
d/dt(Skin) = QSK*(Arterial_Blood/VAB - Skin/KbSK/VSK);
d/dt(Spleen) = QSP*(Arterial_Blood/VAB - Spleen/KbSP/VSP);
d/dt(Pancreas) = QPA*(Arterial_Blood/VAB - Pancreas/KbPA/VPA);
d/dt(Liver) = QHA*Arterial_Blood/VAB + QSP*Spleen/KbSP/VSP + QPA*Pancreas/KbPA/VPA + QST*Stomach/KbST/VST + QGU*Gut/KbGU/VGU - CLint*fub*Liver/KbLI/VLI - QLI*Liver/KbLI/VLI;
d/dt(Stomach) = QST*(Arterial_Blood/VAB - Stomach/KbST/VST);
d/dt(Gut) = QGU*(Arterial_Blood/VAB - Gut/KbGU/VGU);
d/dt(Bones) = QBO*(Arterial_Blood/VAB - Bones/KbBO/VBO);
d/dt(Kidneys) = QKI*(Arterial_Blood/VAB - Kidneys/KbKI/VKI);
d/dt(Arterial_Blood) = QLU*(Lungs/KbLU/VLU - Arterial_Blood/VAB);
d/dt(Venous_Blood) = QHT*Heart/KbHT/VHT + QBR*Brain/KbBR/VBR + QMU*Muscles/KbMU/VMU + QAD*Adipose/KbAD/VAD + QSK*Skin/KbSK/VSK + QLI*Liver/KbLI/VLI + QBO*Bones/KbBO/VBO + QKI*Kidneys/KbKI/VKI + QRB*Rest_of_Body/KbRB/VRB - QLU*Venous_Blood/VVB;
d/dt(Rest_of_Body) = QRB*(Arterial_Blood/VAB - Rest_of_Body/KbRB/VRB);
})You can see this change in the simple printout
pbpk2#> RxODE 0.9.1-7 model named rx_89cc6331729db8dc6c6a6937d0262fa8 model (ready).
#> x$state: Venous_Blood, Skin, Lungs, Heart, Brain, Muscles, Adipose, Spleen, Pancreas, Liver, Stomach, Gut, Bones, Kidneys, Arterial_Blood, Rest_of_Body
#> x$params: lKbBR, lKbMU, lKbAD, lCLint, eta.LClint, lKbBO, lKbRB, WT, BP, fup
#> x$lhs: KbBR, KbMU, KbAD, CLint, KbBO, KbRB, CO, QHT, QBR, QMU, QAD, QSK, QSP, QPA, QLI, QST, QGU, QHA, QBO, QKI, QRB, QLU, VLU, VHT, VBR, VMU, VAD, VSK, VSP, VPA, VLI, VST, VGU, VBO, VKI, VAB, VVB, VRB, fub, KbLU, KbHT, KbSK, KbSP, KbPA, KbLI, KbST, KbGU, KbKI, S15, C15The first two compartments are Venous_Blood followed by Skin.
Appending compartments to the model
You can also append “compartments” to the model. Because of the ODE solving internals, you cannot add fake compartments to the model until after all the differential equations are defined.
For example this is legal:
ode.1c.ka <- RxODE({
C2 = center/V;
d / dt(depot) = -KA * depot
d/dt(center) = KA * depot - CL*C2
cmt(eff);
})
print(ode.1c.ka)#> RxODE 0.9.1-7 model named rx_58f98fc216f2216ae3872ad873435a6b model (ready).
#> $state: depot, center
#> $stateExtra: eff
#> $params: V, KA, CL
#> $lhs: C2Where as this is not:
ode.1c.ka <- RxODE({
cmt(eff);
C2 = center/V;
d / dt(depot) = -KA * depot
d/dt(center) = KA * depot - CL*C2
})Which gives an error:
Error in rxModelVars_(obj) :
Evaluation error: Compartment 'eff' needs differential equations defined.