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Changing rxode2 compartment numbers

2023-03-21

Source: vignettes/rxode2-cmt.Rmd
rxode2-cmt.Rmd

How rxode2 assigns compartment numbers

rxode2 automatically assigns compartment numbers when parsing. For example, with the Mavoglurant PBPK model the following model may be used:

#> rxode2 2.0.12 using 1 threads (see ?getRxThreads)
#>   no cache: create with `rxCreateCache()`
pbpk <- rxode2({
    KbBR = exp(lKbBR)
    KbMU = exp(lKbMU)
    KbAD = exp(lKbAD)
    CLint= exp(lCLint + eta.LClint)
    KbBO = exp(lKbBO)
    KbRB = exp(lKbRB)

    ## Regional blood flows
    # Cardiac output (L/h) from White et al (1968)
    CO  = (187.00*WT^0.81)*60/1000; 
    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;
    # Hepatic artery blood flow
    QHA = QLI - (QSP + QPA + QST + QGU); 
    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 rxode2 assigned the compartment number(s)

summary(pbpk)
#> rxode2 2.0.12 model named rx_900b20cb697e518e9a4805e6e356bb04 model (ready). 
#> DLL: /tmp/RtmpifGRUC/rxode2/rx_900b20cb697e518e9a4805e6e356bb04__.rxd/rx_900b20cb697e518e9a4805e6e356bb04_.so
#> NULL
#> 
#> 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"  
#> -- rxode2 Model Syntax --
#> rxode2({
#>     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, Venous_Blood 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 rxode2 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 <- rxode2({
  ## Now this is the first compartment, ie cmt=1
  cmt(Venous_Blood)
  ## Skin may be a compartment you wish to dose to as well,
  ##  so it is now cmt=2
  cmt(Skin) 
  KbBR = exp(lKbBR)
  KbMU = exp(lKbMU)
  KbAD = exp(lKbAD)
  CLint= exp(lCLint + eta.LClint)
  KbBO = exp(lKbBO)
  KbRB = exp(lKbRB)

  ## Regional blood flows
  # Cardiac output (L/h) from White et al (1968)m
  CO  = (187.00*WT^0.81)*60/1000; 
  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
#> rxode2 2.0.12 model named rx_0025a0fb31b1342271d5905c227ac64a 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, C15

The 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 <- rxode2({
    C2 = center/V;
    d / dt(depot) = -KA * depot
    d/dt(center) = KA * depot - CL*C2
    cmt(eff);
})
print(ode.1c.ka)
#> rxode2 2.0.12 model named rx_47d5daf8bd391d6b32add99095dfd2c9 model (ready). 
#> $state: depot, center
#> $stateExtra: eff
#> $params: V, KA, CL
#> $lhs: C2

But compartments defined before all the differential equations is not supported; So the model below:

ode.1c.ka <- rxode2({
    cmt(eff);
    C2 = center/V;
    d / dt(depot) = -KA * depot
    d/dt(center) = KA * depot - CL*C2
})

will give an error:

Error in rxModelVars_(obj) : 
  Evaluation error: Compartment 'eff' needs differential equations defined.