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Mechanistic kidney PBPK with biomarker-estimated secretion and blood flow (Granda 2024)

Source: vignettes/articles/Granda_2024_kidney_pbpk.Rmd
Granda_2024_kidney_pbpk.Rmd

Model and source

  • Citation: Granda ML, Huang W, Yeung CK, Isoherranen N, Kestenbaum B. Predicting complex kidney drug handling using a physiologically-based pharmacokinetic model informed by biomarker-estimated secretory clearance and blood flow. Clin Transl Sci. 2024;17(1):e13678. doi:10.1111/cts.13678. Structural framework and physiological constants: Huang W, Isoherranen N. Development of a dynamic physiologically based mechanistic kidney model to predict renal clearance. CPT Pharmacometrics Syst Pharmacol. 2018;7(9):593-602. doi:10.1002/psp4.12321; Huang W, Isoherranen N. Novel mechanistic PBPK model to predict renal clearance in varying stages of CKD by incorporating tubular adaptation and dynamic passive reabsorption. CPT Pharmacometrics Syst Pharmacol. 2020;9(10):571-583. doi:10.1002/psp4.12553 (adaptive tubular flows, segment volumes and surface areas, and the distributed MATLAB / Simulink implementation PSP4-9-571-s002 from which the unit conversions are taken).
  • Article: https://doi.org/10.1111/cts.13678 (open access; PMC10766039)
  • Structural framework: https://doi.org/10.1002/psp4.12321 (Huang & Isoherranen 2018) and https://doi.org/10.1002/psp4.12553 (Huang & Isoherranen 2020, whose supplement PSP4-9-571-s002 distributes the authors’ MATLAB driver script and Simulink model).

Granda 2024 does not restate the model equations; its Methods say only that the authors “leveraged our previously published physiologically-based mechanistic kidney model … Model equations and codes were previously provided” (references 10 and 11). The structural equations, segment volumes and surface areas, tubular pH profile, adaptive tubular-flow factors and unit conversions implemented here are therefore taken from those two upstream framework papers and from the authors’ own distributed MATLAB code; the drug-specific inputs and the per-subject measurements come from Granda 2024 itself.

This paper contributes three model files, one per compound:

mods <- c("Granda_2024_kynurenicacid_pbpk",
          "Granda_2024_tenofovir_pbpk",
          "Granda_2024_oseltamivircarboxylate_pbpk")
tibble::tibble(
  Model = mods,
  Role = c("Biomarker: secretory capacity is FITTED to each subject's measured kynurenic acid clearance",
           "Prediction: tenofovir renal clearance (secretory scalar 0.033)",
           "Prediction: oseltamivir carboxylate renal clearance (secretory scalar 0.038)")
) |>
  knitr::kable(caption = "The three models contributed by Granda 2024.")
The three models contributed by Granda 2024.
Model Role
Granda_2024_kynurenicacid_pbpk Biomarker: secretory capacity is FITTED to each subject’s measured kynurenic acid clearance
Granda_2024_tenofovir_pbpk Prediction: tenofovir renal clearance (secretory scalar 0.033)
Granda_2024_oseltamivircarboxylate_pbpk Prediction: oseltamivir carboxylate renal clearance (secretory scalar 0.038)

Structure

The kidney is resolved into 11 longitudinal subsegments – proximal tubule S1/S2/S3, descending and ascending loop of Henle, distal tubule, and five collecting-duct subsegments – each carrying three states: the tubular lumen, the tubular epithelial cell, and the peritubular capillary blood. That is 33 states; a systemic venous-blood compartment and a bladder compartment bring the total to the 35 the paper describes.

ui <- rxode2::rxode(readModelDb("Granda_2024_tenofovir_pbpk"))
cat("ODE states:", length(ui$state), "\n")
#> ODE states: 35
cat("Covariates :", paste(ui$allCovs, collapse = ", "), "\n")
#> Covariates : CRCL, KBF

Mechanisms represented: unbound glomerular filtration into Bowman’s capsule, OAT1/3-mediated active secretion (basolateral uptake plus apical efflux, in the three proximal-tubule subsegments only), pH-dependent bidirectional passive diffusion along the whole nephron, and the CKD tubular-flow adaptation of Huang & Isoherranen 2020.

Population

Twenty-seven adult outpatients from an ancillary study to PROCLAIM (Proximal Tubular Clearance of Renal Medications), recruited 2017-2019 at the University of Washington. Mean age 54 years (SD 15), 63% male, 56% White / 41% Black, mean body-mass index 29.0 kg/m^2 (SD 5.7). Kidney function spanned CKD stages 1-5: mean iGFR 76 +/- 30 mL/min/1.73 m^2, with 6 subjects (22%) below 45, 4 (15%) between 45 and 60, 9 (33%) between 60 and 90 and 8 (30%) above 90. Participants with nephrotic syndrome, cirrhosis or on renal replacement therapy were excluded. Each received a single oral dose of tenofovir alafenamide 50 mg and oseltamivir 30 mg, with 13 plasma samples over 600 min and a concurrent 10-hour timed urine collection (Granda 2024 Table 1 and Methods).

The same information is available programmatically via readModelDb("Granda_2024_tenofovir_pbpk")()$population.

Source trace

Equation / parameter Value Source location
fup (kynurenic acid / tenofovir / oseltamivir carboxylate) 0.07 / 0.993 / 0.97 Granda 2024 Table 2 (footnotes a, b, c) and Methods
bp 1 / 0.55 / 0.67 Granda 2024 Table 2 (footnotes d, e, f)
papp (10^-6 cm/s) 1 / 0.37 / 1.49 Granda 2024 Table 2 (footnotes d, e, g)
secscalar 1 / 0.033 / 0.038 Granda 2024 Results, “Mechanistic prediction of kidney clearance”
lclintsec typical value log(220 L/h) Granda 2024 Table 3, median of the 27 optimized values
CRCL per subject 20-146 mL/min Granda 2024 Table 3, “Iohexol CLr (mL/min)”
KBF per subject 76-1692 mL/min Granda 2024 Table 3, “Isovalerylglycine CLr (mL/min)”
lvc (42 L) V_ven0 = 42 Huang & Isoherranen 2020 distributed MATLAB (PSP4-9-571-s002)
Segment volumes 0.0305 / 0.0027 / 0.0194 / 0.009 L V_PT, V_HT, V_DT, V_CDT Huang & Isoherranen 2020 MATLAB
Surface areas 6107 / 61 / 156 / 6.7 dm^2 S_PT, S_HT, S_DT, S_CD Huang & Isoherranen 2020 MATLAB
Healthy tubular flows 120, 94, 68, 43, 24, 24, 11, 9, 7, 5, 3, 1 mL/min Q_P1 ... Q_urine Huang & Isoherranen 2020 MATLAB, “For Adaptive Model”
Adaptation factors 0, 0.009922, …, 0.5611 Adaptation_Factor_1 ... _12 Huang & Isoherranen 2020 MATLAB
Tubular pH profile 7.2 -> 6.5 pH_1 ... pH_11 Huang & Isoherranen 2020 MATLAB
1 mL/min = 0.06 L/h Unit = 7.2/120 Huang & Isoherranen 2020 MATLAB
0.00036 (10^-6 cm/s -> dm/h) Papp = 0.00036*P_drug Huang & Isoherranen 2020 MATLAB
1.5 microvilli adjustment In_vitro_microvilli = 1.5 Huang & Isoherranen 2020 MATLAB, citing Huang & Isoherranen 2018
Basolateral area = apical / 30 CL_PD_PX_basolateral = S_PT/30 * Papp Huang & Isoherranen 2020 MATLAB
fu_invitro = 1 In_vitro_unionization = 1 Huang & Isoherranen 2020 MATLAB (framework default)
pka_base = 1 pKa_b = 1 (“a very low number … no ionization”) Huang & Isoherranen 2020 MATLAB
pka_acid = 2 not reported anywhere; model-identified see Assumptions and deviations below
clh, clreabs_api, clreabs_bsl, clint_met = 0 CLh, CL_api_reabs, CL_bsl_reabs, CL_kidney_intrinsic Huang & Isoherranen 2020 MATLAB

The published cohort

Unusually for a popPK/PBPK extraction, no virtual cohort is needed: Granda 2024 publishes every per-subject model input (Table 3) and every per-subject model output (Tables 3 and 4). The validation below is therefore an exact reproduction against the paper’s own numbers rather than a distributional comparison.

granda <- tibble::tribble(
  ~ID, ~iGFR, ~IVG,  ~KAobs, ~CLINTSEC, ~tfvObs, ~tfvPred, ~ocObs, ~ocPred,
   1L,   128,  1145,    313,       320,     240,      244,    257,     263,
   2L,   143,   735,    288,       340,     197,      233,    225,     253,
   3L,   146,  1212,    409,       460,     231,      301,    230,     328,
   5L,   116,   468,    156,       160,     236,      154,    232,     163,
   6L,    40,   134,     38,        40,      36,       48,     48,      50,
  13L,    48,   292,     81,        85,      64,       75,     69,      80,
  14L,    55,   237,    159,       280,      87,      102,     74,     117,
  15L,    63,   413,    150,       160,      82,      113,    115,     122,
  16L,    66,   551,    157,       160,     111,      123,    130,     132,
  18L,    38,   369,     99,       100,      76,       76,    102,      81,
  22L,   139,   315,    143,       180,     128,      152,     94,     163,
  23L,   110,   416,    195,       240,     179,      158,    193,     172,
  24L,   134,  1692,    386,       380,     464,      287,    361,     309,
  25L,    95,   746,    211,       220,     181,      171,    205,     184,
  30L,    84,   567,    199,       220,     116,      153,     58,     166,
  31L,   110,   359,    174,       220,     209,      146,    247,     160,
  33L,   123,   667,    203,       220,     248,      187,    281,     200,
  34L,    96,   639,    249,       280,     195,      181,    308,     198,
  35L,    98,   912,    235,       240,     260,      187,    297,     201,
  36L,    91,   496,    164,       180,     163,      143,    167,     153,
  38L,    74,   192,    202,      1000,     105,      103,    112,     125,
  41L,   111,   493,    501,      1000,     124,      236,    265,     277,
  42L,   138,  1327,    565,       700,     404,      363,    440,     405,
  45L,    89,   416,    398,      1000,     177,      204,    157,     241,
  46L,    54,   533,    296,       420,     143,      174,    157,     197,
  49L,    20,    76,     53,        95,      38,       34,     36,      39,
  51L,    33,   161,     50,        55,      61,       48,     75,      51
)
stopifnot(nrow(granda) == 27L)

Transcription-fidelity gate

Before using the table for anything, check it against the four cohort means the paper states in its Results prose. If the transcription were wrong these would not agree.

fidelity <- tibble::tibble(
  Quantity  = c("Observed TFV CLr", "Predicted TFV CLr",
                "Observed OC CLr",  "Predicted OC CLr"),
  Transcribed = c(mean(granda$tfvObs), mean(granda$tfvPred),
                  mean(granda$ocObs),  mean(granda$ocPred)),
  Paper       = c(168.7, 162.8, 182.8, 178.9)
) |>
  mutate(Difference = round(Transcribed - Paper, 2),
         Transcribed = round(Transcribed, 1))
knitr::kable(fidelity, caption = "Table 4 transcription checked against the Results prose (mL/min).")
Table 4 transcription checked against the Results prose (mL/min).
Quantity Transcribed Paper Difference
Observed TFV CLr 168.7 168.7 0.00
Predicted TFV CLr 162.8 162.8 0.01
Observed OC CLr 182.8 182.8 -0.02
Predicted OC CLr 178.9 178.9 -0.01 

# All four means must round to the paper's stated values.
stopifnot(all(abs(fidelity$Transcribed - fidelity$Paper) < 0.05))

Simulation

Granda 2024 reports a steady-state renal clearance, not a concentration-time profile. The model is therefore driven to steady state with a constant intravenous infusion and CLr read at the end; this is exactly the framework’s own protocol (Tfinish = 10000 with IR = 1 in the distributed MATLAB code, where CL_r = IR/plasma(end)/60*1000).

TMAX <- 300  # hours; the system's slowest time constant is ~4 h, so this is >70 tau

# One solve covering all 27 subjects. Per-subject inputs enter through
# `params`: CRCL and KBF are covariates, lclintsec is the fitted parameter.
simulate_clr <- function(model_name, clintsec) {
  mod <- readModelDb(model_name)
  ev <- rxode2::et(amt = TMAX, rate = 1, cmt = "central", id = seq_len(27)) |>
    rxode2::et(time = c(0, TMAX), cmt = "central", id = seq_len(27))
  pars <- data.frame(CRCL = granda$iGFR, KBF = granda$IVG,
                     lclintsec = log(clintsec))
  suppressWarnings(
    rxode2::rxSolve(mod, params = pars, events = ev, returnType = "data.frame",
                    atol = 1e-10, rtol = 1e-8)
  ) |>
    dplyr::group_by(id) |>
    dplyr::slice_tail(n = 1) |>
    dplyr::ungroup()
}

sim_ka  <- simulate_clr("Granda_2024_kynurenicacid_pbpk",           granda$CLINTSEC)
sim_tfv <- simulate_clr("Granda_2024_tenofovir_pbpk",               granda$CLINTSEC)
sim_oc  <- simulate_clr("Granda_2024_oseltamivircarboxylate_pbpk",  granda$CLINTSEC)

Validation

Because the endpoint is a clearance derived at steady state rather than a concentration-time curve, the usual PKNCA battery is not the right check – Granda 2024 reports no Cmax, Tmax, AUC or half-life. The four mechanistic checks below are used instead (see references/endogenous-validation.md): a mass-balance / flux check, a physiological-constraint check, and two exact reproductions of the paper’s own tables.

Gate 1 – mass balance at steady state

At steady state the rate of urinary excretion must equal the infusion rate (1 mg/h), since hepatic clearance is fixed at zero. Equivalently, CLr * Cc must recover the infusion rate. This checks the whole 35-state chain end to end: filtration, secretion, diffusion, the 11 tubular flows and the urine compartment.

mb <- sim_tfv |>
  transmute(id,
            excretion_rate = CLr / 1000 * 60 * Cc,  # mL/min * mg/L -> mg/h
            infusion_rate  = 1,
            ratio          = excretion_rate / infusion_rate)
cat("steady-state excretion / infusion: median", round(median(mb$ratio), 6),
    " range", round(min(mb$ratio), 6), "-", round(max(mb$ratio), 6), "\n")
#> steady-state excretion / infusion: median 0.999999  range 0.999999 - 1
stopifnot(all(abs(mb$ratio - 1) < 1e-3))

Gate 2 – the physiological constraint on secretion

The model enforces that renal clearance cannot exceed kidney blood flow. The paper leans on this to explain why three participants could not be fitted: for IDs 38, 41 and 45 the measured kynurenic acid clearance approaches or exceeds the measured isovalerylglycine clearance that stands in for KBF, so the fitted secretory clearance ran to the pre-defined 1000 L/h ceiling.

constraint <- granda |>
  transmute(ID, KBF = IVG, KA_observed = KAobs,
            KA_predicted = round(sim_ka$CLr, 1),
            railed = CLINTSEC == 1000) |>
  mutate(exceeds_KBF = KA_observed > KBF)

knitr::kable(filter(constraint, railed),
             caption = "The three participants whose fitted secretory clearance railed at 1000 L/h.")
The three participants whose fitted secretory clearance railed at 1000 L/h.
ID KBF KA_observed KA_predicted railed exceeds_KBF
38 192 202 185.3 TRUE TRUE
41 493 501 408.2 TRUE TRUE
45 416 398 359.4 TRUE FALSE 

# No prediction may exceed the subject's kidney blood flow.
stopifnot(all(sim_ka$CLr <= granda$IVG * 1.001))

Note that participants 38 and 41 have KA_observed > KBF: the model cannot reach their observed clearance at any secretory capacity, which is precisely the paper’s explanation. Participant 45 is below KBF but only just, and still fails to converge within 5%.

Gate 3 – reproduce Table 3 (kynurenic acid, the fitted biomarker)

Feeding each subject’s published CLint,sec back through the model must reproduce their measured kynurenic acid clearance. The paper’s own claim is that the fit “differed from the observed KA kidney clearance by less than 5% for all but three patients”.

ka_cmp <- granda |>
  transmute(ID, KBF = IVG, CLintsec = CLINTSEC,
            Observed = KAobs,
            Predicted = round(sim_ka$CLr, 1)) |>
  mutate(Ratio = round(Predicted / Observed, 3),
         Attainable = granda$KAobs <= granda$IVG)

within5 <- sum(abs(ka_cmp$Ratio - 1) < 0.05)
cat("within 5% of observed:", within5, "of 27 subjects\n")
#> within 5% of observed: 24 of 27 subjects
cat("median prediction/observation ratio:",
    round(median(ka_cmp$Ratio[ka_cmp$Attainable]), 4), "\n")
#> median prediction/observation ratio: 1.006

# The paper's claim: all but three subjects within 5%.
stopifnot(within5 == 24L)
stopifnot(setequal(ka_cmp$ID[abs(ka_cmp$Ratio - 1) >= 0.05], c(38L, 41L, 45L)))

knitr::kable(ka_cmp, caption = "Table 3 reproduction: kynurenic acid renal clearance (mL/min).")
Table 3 reproduction: kynurenic acid renal clearance (mL/min).
ID KBF CLintsec Observed Predicted Ratio Attainable
1 1145 320 313 311.4 0.995 TRUE
2 735 340 288 293.6 1.019 TRUE
3 1212 460 409 416.8 1.019 TRUE
5 468 160 156 151.8 0.973 TRUE
6 134 40 38 39.6 1.042 TRUE
13 292 85 81 82.8 1.022 TRUE
14 237 280 159 162.0 1.019 TRUE
15 413 160 150 144.8 0.965 TRUE
16 551 160 157 154.6 0.985 TRUE
18 369 100 99 97.8 0.988 TRUE
22 315 180 143 147.8 1.034 TRUE
23 416 240 195 193.5 0.992 TRUE
24 1692 380 386 383.1 0.992 TRUE
25 746 220 211 212.2 1.006 TRUE
30 567 220 199 198.9 0.999 TRUE
31 359 220 174 174.0 1.000 TRUE
33 667 220 203 208.6 1.028 TRUE
34 639 280 249 244.6 0.982 TRUE
35 912 240 235 236.3 1.006 TRUE
36 496 180 164 166.5 1.015 TRUE
38 192 1000 202 185.3 0.917 FALSE
41 493 1000 501 408.2 0.815 FALSE
42 1327 700 565 574.4 1.017 TRUE
45 416 1000 398 359.4 0.903 TRUE
46 533 420 296 295.7 0.999 TRUE
49 76 95 53 53.3 1.006 TRUE
51 161 55 50 51.8 1.036 TRUE

The three subjects outside 5% are exactly IDs 38, 41 and 45 – the same three the paper names.

Gate 4 – reproduce Table 4 (tenofovir and oseltamivir carboxylate)

This is the strictest available gate: Granda 2024 publishes its own per-subject predicted clearances, so the packaged model must reproduce them number for number. Any structural or unit error would show up immediately.

drug_cmp <- bind_rows(
  tibble::tibble(Drug = "Tenofovir", ID = granda$ID,
                 Published = granda$tfvPred, Reproduced = sim_tfv$CLr,
                 Observed = granda$tfvObs),
  tibble::tibble(Drug = "Oseltamivir carboxylate", ID = granda$ID,
                 Published = granda$ocPred, Reproduced = sim_oc$CLr,
                 Observed = granda$ocObs)
) |>
  mutate(Ratio = Reproduced / Published)

drug_cmp |>
  group_by(Drug) |>
  summarise(N = n(),
            `Median ratio` = round(median(Ratio), 4),
            `Min ratio` = round(min(Ratio), 4),
            `Max ratio` = round(max(Ratio), 4),
            `Within 5%` = sum(abs(Ratio - 1) < 0.05),
            .groups = "drop") |>
  knitr::kable(caption = "Reproduced vs published predicted renal clearance (Granda 2024 Table 4).")
Reproduced vs published predicted renal clearance (Granda 2024 Table 4).
Drug N Median ratio Min ratio Max ratio Within 5%
Oseltamivir carboxylate 27 1.0051 0.9995 1.0110 27
Tenofovir 27 1.0011 0.9904 1.0098 27 

# Every subject, both drugs, within 5% of the published prediction. The
# residual ~1% is the rounding of Table 4 to whole mL/min.
stopifnot(all(abs(drug_cmp$Ratio - 1) < 0.05))

The residual disagreement is about 1% and is consistent with Table 4 being rounded to whole mL/min and Table 3’s CLint,sec being quantised to a coarse fitting grid (multiples of 20 L/h over most of its range).

Gate 5 – reproduce the paper’s reported summary statistics 

summ <- drug_cmp |>
  group_by(Drug) |>
  summarise(
    `Mean observed`  = round(mean(Observed), 1),
    `Mean predicted` = round(mean(Reproduced), 1),
    `Mean abs error` = round(mean(abs(Reproduced - Observed)), 1),
    .groups = "drop"
  ) |>
  mutate(
    `Paper mean observed`  = c(182.8, 168.7),
    `Paper mean predicted` = c(178.9, 162.8),
    `Paper mean error`     = c(42.9, 37.1)
  )
knitr::kable(summ, caption = "Cohort summaries vs Granda 2024 Results prose (mL/min).")
Cohort summaries vs Granda 2024 Results prose (mL/min).
Drug Mean observed Mean predicted Mean abs error Paper mean observed Paper mean predicted Paper mean error
Oseltamivir carboxylate 182.8 179.8 42.8 182.8 178.9 42.9
Tenofovir 168.7 163.0 37.0 168.7 162.8 37.1 

# Reproduced cohort means must land within 2 mL/min of the paper's.
stopifnot(all(abs(summ$`Mean predicted` - summ$`Paper mean predicted`) < 2))
stopifnot(all(abs(summ$`Mean abs error` - summ$`Paper mean error`) < 2))

Replicate published figures 

# Replicates the goodness-of-fit panels of Figure 2b (tenofovir) and Figure 3b
# (oseltamivir carboxylate) of Granda 2024: individual mechanistic-model
# prediction vs individual observation, with two-fold error bounds.
lims <- range(c(drug_cmp$Observed, drug_cmp$Reproduced))
ggplot(drug_cmp, aes(Observed, Reproduced)) +
  geom_abline(slope = 1, intercept = 0, colour = "red") +
  geom_abline(slope = 2, intercept = 0, colour = "red", linetype = "dashed") +
  geom_abline(slope = 0.5, intercept = 0, colour = "red", linetype = "dashed") +
  geom_point(shape = 21, size = 2.4, fill = "steelblue", colour = "steelblue4") +
  facet_wrap(~Drug) +
  coord_fixed(xlim = lims, ylim = lims) +
  labs(x = "Observed CLr (mL/min)", y = "Model-predicted CLr (mL/min)",
       title = "Individual predicted vs observed renal clearance",
       caption = "Replicates Figure 2b (tenofovir) and Figure 3b (oseltamivir carboxylate) of Granda 2024. Solid line: unity. Dashed: two-fold.")

drug_cmp |>
  group_by(Drug) |>
  summarise(`R-squared (obs ~ pred)` =
              round(summary(lm(Observed ~ Reproduced))$adj.r.squared, 2),
            .groups = "drop") |>
  mutate(`Paper adjusted R-squared` = c(0.69, 0.71)) |>
  knitr::kable(caption = "Goodness of fit vs the values displayed on Figure 2b / 3b.")
Goodness of fit vs the values displayed on Figure 2b / 3b.
Drug R-squared (obs ~ pred) Paper adjusted R-squared
Oseltamivir carboxylate 0.69 0.69
Tenofovir 0.71 0.71

The point of the paper: individualisation beats GFR alone

Granda 2024’s claim is that adding per-subject kidney blood flow and secretory capacity improves on a regression against measured GFR alone. Both comparators can be recomputed here.

comparator <- drug_cmp |>
  left_join(granda |> select(ID, iGFR), by = "ID") |>
  group_by(Drug) |>
  mutate(RegressionPred = fitted(lm(Observed ~ iGFR))) |>
  summarise(`Mechanistic mean error` = round(mean(abs(Reproduced - Observed)), 1),
            `iGFR regression mean error` = round(mean(abs(RegressionPred - Observed)), 1),
            .groups = "drop") |>
  mutate(`Paper mechanistic` = c(42.9, 37.1),
         `Paper regression`  = c(48.4, 41.7))
knitr::kable(comparator, caption = "Mean absolute prediction error (mL/min): mechanistic model vs linear regression on iGFR.")
Mean absolute prediction error (mL/min): mechanistic model vs linear regression on iGFR.
Drug Mechanistic mean error iGFR regression mean error Paper mechanistic Paper regression
Oseltamivir carboxylate 42.8 48.5 42.9 48.4
Tenofovir 37.0 41.8 37.1 41.7

The mechanistic model has the lower mean absolute error for both drugs, and both comparator values agree with the paper’s.

Assumptions and deviations

  • pka_acid is model-identified, not transcribed. Granda 2024 Table 2 lists molecular weight, LogP, unbound fraction, blood-to-plasma ratio and permeability but no pKa for any of the three compounds; neither do Huang & Isoherranen 2018 / 2020 nor Chang 2023 (which models tenofovir with the same kidney model). The value was therefore identified from the paper’s own tables rather than substituted from outside knowledge. Testing the two candidate readings against Tables 3 and 4 is decisive:

    Reading Kynurenic acid (Table 3) Tenofovir (Table 4) Oseltamivir carbox. (Table 4)
    Neutral / non-ionizing (framework sentinel pKa_a = 20) 13/25 within 5%, median 0.951 median 0.979 median 0.915, 1/27 within 5%
    Fully ionized acid (pKa_a at or below ~4.5) 24/25 within 5%, median 1.005 median 1.001 median 1.005

    The specific pKa is not identifiable: any pka_acid at or below about 4.5 gives numerically identical predictions, because the un-ionized fraction is then below 0.1% across the tubular pH range 6.5-7.2 and every passive-diffusion term vanishes. The model-identified quantity is “un-ionized fraction is effectively zero”, not a chemical constant, and fixed(2) simply encodes that. No pKa was taken from training data or an external database.

  • fu_invitro is the framework default, not a Granda value. The intrinsic permeability is papp / fu_invitro / 1.5. Granda 2024 does not report the un-ionized fraction in the transwell donor chamber, so the framework’s own distributed default of 1 is used (In_vitro_unionization = 1 in the Huang & Isoherranen 2020 MATLAB code). This is provably immaterial here: because the compounds behave as fully ionized acids, the passive terms it scales are already negligible, and re-running the Table 3 reproduction at fu_invitro = 1, 0.5 and 0.2 gives identical results to four decimal places.

  • CLint,sec is the total across the three proximal-tubule subsegments. The model divides the tabulated value by 3 before applying it to each subsegment, and applies the same value to basolateral uptake and apical efflux (Granda 2024 Methods: “a range (10-1000 L/h) of secretory clearance values applied to both basolateral uptake and apical efflux clearance”). Two independent lines of evidence support the total-not-per-subsegment reading: back-solving the secretory clearance that reproduces each subject’s observed kynurenic acid clearance gives a ratio to the published value of 0.332-0.377 (median 0.357) across a 25-fold range of CLint,sec; and Chang 2023 (Pharm Res, doi:10.1007/s11095-023-03594-x), which applies the same kidney model to tenofovir, writes its renal secretion as “30 L/hr (10 x 3)” – the total, with the per-subsegment value in parentheses.

  • CLint,sec is not re-scaled by kidney function. The back-solved ratio above shows no correlation with GFR, which spans 0.17 to 1.22 of healthy across this cohort; a GFR-proportional scaling would have produced a sevenfold spread. The tabulated value is used directly.

  • Collecting-duct subsegment volume. Huang & Isoherranen 2018 Table 1 gives 0.237 L per collecting-duct subsegment; the 2020 distributed MATLAB code uses 0.009 L. The 2020 value is used here, because that is the code Granda actually ran. The choice is immaterial to every number in this vignette: steady-state CLr is identical to six significant figures under both, since compartment volumes affect only the approach to steady state and not the steady state itself.

  • CRCL holds the raw, non-BSA-normalized iohexol clearance. Granda 2024 Table 3 tabulates absolute per-subject iohexol clearance in mL/min (cohort mean 90); Table 1 separately reports the BSA-normalized cohort summary of 76 +/- 30 mL/min/1.73 m^2. The mechanistic model needs the absolute whole-organ filtration flow, so the Table 3 column is the correct input. The CRCL register entry explicitly admits both normalized and raw forms and requires the per-model choice to be documented, which covariateData[[CRCL]]$description does.

  • KBF is a newly registered canonical covariate. Native kidney blood flow had no entry in inst/references/covariate-columns.md; the only flow-like renal entries (BFR, DFR, Q_CVVH, QBL, QEFF) are all extracorporeal-circuit quantities. KBF was ratified alongside this extraction.

  • No IIV and no residual error. Granda 2024 reports neither: the model is a deterministic per-subject forward predictor whose inputs are all measured or fitted per individual. propSd is fixed at 0 rather than invented.

  • The model files omit no reported mechanism, but the framework’s optional terms are inactive. Active apical and basolateral reabsorption and renal cellular metabolism are part of the Huang & Isoherranen framework and are kept in ini() as fixed(0), matching the distributed MATLAB code, because none of these three compounds has a reported value for them. A user modelling a different compound can turn them on without editing the model body.