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# =====================================================================

# Microscopic Colitis (LC + CC) — mrgsolve QSP Model

# ---------------------------------------------------------------------

# Drugs: Budesonide MMX, Cholestyramine, Mesalamine, Bismuth subsalicylate,

# Loperamide, Azathioprine, Infliximab, Vedolizumab, Adalimumab

# Disease compartments: CD8-IEL, IFN-γ, TNF-α, IL-6/IL-17, TGF-β,

# epithelial barrier integrity, collagen-band thickness,

# bile-acid load, mucosal Na+/H2O flux, stool frequency,

# Hjortswang score, HRQoL.

# Calibration sources:

# - BUC-60 / BUC-63 (Miehlke 2007, Münch 2014) : budesonide RCTs

# - COLAL-PRED (Bonderup 2009)

# - Cholestyramine open-label (Ung 2000)

# - VICTORIA-MC (Miehlke 2021) vedolizumab open

# - Riddell, Loftus epidemiology

# ---------------------------------------------------------------------

# Author: QSP Disease Model Library (Claude Code Routine)

# =====================================================================

library(mrgsolve)

code <- '

$PROB Microscopic Colitis QSP

$PARAM @annotated

// ---- Budesonide MMX (PO, pH-/time-release, ~3 h Tlag) ------------------

KA_BUD : 0.85 : Absorption rate constant (1/h)

F_BUD : 0.10 : Oral bioavailability after high first-pass

TLAG_BUD : 3.00 : Release lag (h)

VC_BUD : 240 : Central V (L)

Q_BUD : 45 : Inter-compartmental Q (L/h)

VP_BUD : 880 : Peripheral V (L)

CL_BUD : 98 : Plasma clearance (L/h)

KGUT_BUD : 0.30 : Mucosal degradation rate (1/h)

EC50_BUD_GR : 4.0 : Local conc for 50% GR effect (mucosal a.u.)

// ---- Cholestyramine (luminal, non-absorbed bile-acid sequestrant) ------

KA_CHOL : 6.0 : Apparent luminal mixing (1/h)

KGUT_CHOL : 0.50 : Loss with stool (1/h)

EC50_CHOL : 4.0 : Conc for 50% BA chelation (g equiv. luminal)

// ---- Mesalamine PO ------------------------------------------------------

KA_MES : 0.90

F_MES : 0.30

CL_MES : 20

VC_MES : 20

EC50_MES : 10 : Local conc (mg/L equiv.) for PPAR-γ effect

// ---- Bismuth subsalicylate -- modeled as luminal anti-secretory ---------

KA_BIS : 4.0

KGUT_BIS : 0.80

EC50_BIS : 3.0

// ---- Loperamide (mu-opioid, gut motility) -------------------------------

KA_LOP : 1.5

F_LOP : 0.40

CL_LOP : 60

VC_LOP : 300

EC50_LOP : 0.6

// ---- Azathioprine -> 6-TGN (RBC) ----------------------------------------

KA_AZA : 3.0

F_AZA : 0.47

CL_AZA : 50

VC_AZA : 90

KFORM_TGN : 0.10 : 6-TGN formation rate (proxy)

KDEG_TGN : 0.0035 : 6-TGN degradation (1/h)

EC50_TGN : 250 : pmol/8e8 RBC for 50% lymphocyte effect

// ---- Infliximab (IV, anti-TNF) ------------------------------------------

CL_IFX : 0.32 : Linear CL (L/day)

VC_IFX : 3.0

Q_IFX : 0.5

VP_IFX : 3.5

KD_IFX_TNF : 0.1 : nM

// ---- Adalimumab (SC, anti-TNF) ------------------------------------------

KA_ADA : 0.30 : 1/day

F_ADA : 0.64

CL_ADA : 0.30 : L/day

VC_ADA : 5.0

KD_ADA_TNF : 0.1

// ---- Vedolizumab (IV, anti-α4β7) ----------------------------------------

CL_VDZ : 0.16

VC_VDZ : 4.7

Q_VDZ : 0.30

VP_VDZ : 1.7

EC50_VDZ : 2.0 : mg/L for 50% gut homing block

// =====================================================================

// Disease parameters (rates per day unless noted)

// =====================================================================

KSYN_IEL : 0.10 : CD8+ IEL synthesis (a.u./day)

KDEG_IEL : 0.04 : CD8+ IEL turnover (1/day)

IEL_BASE : 35 : Active-disease baseline IEL (per 100 EC)

IEL_NORM : 8

KSYN_IFNG : 6.0 : IFN-γ production (pg/mL/day)

KDEG_IFNG : 0.50

IFNG_BASE : 25

KSYN_TNF : 4.0

KDEG_TNF : 0.55

TNF_BASE : 18

KSYN_IL6 : 3.0

KDEG_IL6 : 0.70

IL6_BASE : 12

KSYN_IL17 : 2.5

KDEG_IL17 : 0.65

IL17_BASE : 9

KSYN_TGFB : 2.0

KDEG_TGFB : 0.20

TGFB_BASE : 15

// Barrier (0 = open, 1 = intact)

BAR_BASE : 0.55

KFORM_BAR : 0.05

KDEG_BAR : 0.05 : Driven by cytokines

// Collagen band thickness (μm) – CC subtype

COL_BASE : 18 : CC baseline (CC dx > 10)

COL_LC : 4 : LC baseline

KFORM_COL : 0.02

KDEG_COL : 0.02

EC50_TGFB_COL: 30

// Bile acid colonic load (a.u.)

BA_BASE : 2.5 : Baseline colonic BA load

KSYN_BA : 0.4

KDEG_BA : 0.15

// Net absorptive flux (mL water/day → -ve = secretory)

WAT_BASE : -350 : ml/day secretory in active disease

WAT_NORM : 200 : ml/day net absorption healthy

KFLX : 0.30

// Stool freq (stools/day)

STOOL_BASE : 6.0

STOOL_MIN : 1.5

KSTOOL : 0.5

// Hjortswang clinical-remission score (0 = remission, 1 = active)

HJ_BASE : 1.0

// HRQoL (SF-36 mental subscale-like, 0–100, 100 best)

QOL_BASE : 55

KQOL : 0.04

// Subtype switch (1 = CC, 0 = LC)

SUBTYPE_CC : 1

// Comorbidity flags

BMD_DECAY_GC: 0.0008 : 1/day BMD loss while on systemic GC

HPA_HALF : 60 : hours t1/2 for HPA suppression

$CMT @annotated

// PK compartments

GUT_BUD : Budesonide gut lumen

CENT_BUD : Budesonide central

PER_BUD : Budesonide peripheral

GUT_CHOL : Cholestyramine luminal

GUT_MES : Mesalamine gut

CEN_MES : Mesalamine plasma

GUT_BIS : Bismuth luminal

GUT_LOP : Loperamide gut

CEN_LOP : Loperamide plasma

GUT_AZA : Azathioprine gut

CEN_AZA : Azathioprine plasma

TGN : 6-TGN RBC pool

CEN_IFX : Infliximab central

PER_IFX : Infliximab peripheral

DEPOT_ADA : Adalimumab SC depot

CEN_ADA : Adalimumab plasma

CEN_VDZ : Vedolizumab central

PER_VDZ : Vedolizumab peripheral

// Disease compartments

IEL : CD8+ intraepithelial lymphocytes (per 100 EC)

IFNG : IFN-gamma (pg/mL)

TNF : TNF-alpha (pg/mL)

IL6 : IL-6 (pg/mL)

IL17 : IL-17A (pg/mL)

TGFB : TGF-beta (pg/mL)

BAR : Epithelial barrier integrity (0–1)

COL : Subepithelial collagen band (μm)

BA : Colonic bile-acid load (a.u.)

WAT : Net colonic water flux (mL/day)

STOOL : Stool frequency (stools/day)

HJ : Hjortswang active-disease score

QOL : HRQoL composite

BMD : Bone mineral density (T-score proxy)

HPA : HPA axis cortisol response (1=normal,0=suppressed)

$GLOBAL

double pos(double x){ return x<0 ? 0 : x; }

double sat(double C, double E){ return C/(C+E); }

$MAIN

GUT_BUD_0 = 0;

CENT_BUD_0 = 0;

PER_BUD_0 = 0;

GUT_CHOL_0 = 0;

GUT_MES_0 = 0;

CEN_MES_0 = 0;

GUT_BIS_0 = 0;

GUT_LOP_0 = 0;

CEN_LOP_0 = 0;

GUT_AZA_0 = 0;

CEN_AZA_0 = 0;

TGN_0 = 0;

CEN_IFX_0 = 0;

PER_IFX_0 = 0;

DEPOT_ADA_0= 0;

CEN_ADA_0 = 0;

CEN_VDZ_0 = 0;

PER_VDZ_0 = 0;

IEL_0 = IEL_BASE;

IFNG_0 = IFNG_BASE;

TNF_0 = TNF_BASE;

IL6_0 = IL6_BASE;

IL17_0 = IL17_BASE;

TGFB_0 = TGFB_BASE;

BAR_0 = BAR_BASE;

COL_0 = (SUBTYPE_CC>0.5 ? COL_BASE : COL_LC);

BA_0 = BA_BASE;

WAT_0 = WAT_BASE;

STOOL_0 = STOOL_BASE;

HJ_0 = HJ_BASE;

QOL_0 = QOL_BASE;

BMD_0 = 0.0;

HPA_0 = 1.0;

$ODE

// ====== Budesonide PK ======

double BUD_GUT_C = GUT_BUD / 0.4; // mucosal a.u.

double BUD_PLAS = CENT_BUD / VC_BUD;

dxdt_GUT_BUD = -KA_BUD * GUT_BUD - KGUT_BUD * GUT_BUD;

dxdt_CENT_BUD = F_BUD * KA_BUD * GUT_BUD - (CL_BUD/VC_BUD)*CENT_BUD

- (Q_BUD/VC_BUD)*CENT_BUD + (Q_BUD/VP_BUD)*PER_BUD;

dxdt_PER_BUD = (Q_BUD/VC_BUD)*CENT_BUD - (Q_BUD/VP_BUD)*PER_BUD;

// ====== Cholestyramine luminal ======

dxdt_GUT_CHOL = -KGUT_CHOL * GUT_CHOL;

double CHOL_LUM = GUT_CHOL;

// ====== Mesalamine ======

dxdt_GUT_MES = -KA_MES * GUT_MES;

dxdt_CEN_MES = F_MES * KA_MES * GUT_MES - (CL_MES/VC_MES) * CEN_MES;

double MES_LUM = GUT_MES;

// ====== Bismuth luminal ======

dxdt_GUT_BIS = -KGUT_BIS * GUT_BIS;

double BIS_LUM = GUT_BIS;

// ====== Loperamide ======

dxdt_GUT_LOP = -KA_LOP * GUT_LOP;

dxdt_CEN_LOP = F_LOP * KA_LOP * GUT_LOP - (CL_LOP/VC_LOP) * CEN_LOP;

double LOP_C = CEN_LOP / VC_LOP;

// ====== Azathioprine -> 6-TGN ======

dxdt_GUT_AZA = -KA_AZA * GUT_AZA;

dxdt_CEN_AZA = F_AZA * KA_AZA * GUT_AZA - (CL_AZA/VC_AZA) * CEN_AZA;

double AZA_C = CEN_AZA / VC_AZA;

dxdt_TGN = KFORM_TGN * AZA_C - KDEG_TGN * TGN;

// ====== Infliximab IV ======

dxdt_CEN_IFX = -(CL_IFX/24/VC_IFX) * CEN_IFX

- (Q_IFX/24/VC_IFX) * CEN_IFX + (Q_IFX/24/VP_IFX) * PER_IFX;

dxdt_PER_IFX = (Q_IFX/24/VC_IFX) * CEN_IFX - (Q_IFX/24/VP_IFX) * PER_IFX;

double IFX_C = CEN_IFX / VC_IFX;

// ====== Adalimumab SC ======

dxdt_DEPOT_ADA = -(KA_ADA/24) * DEPOT_ADA;

dxdt_CEN_ADA = F_ADA * (KA_ADA/24) * DEPOT_ADA - (CL_ADA/24/VC_ADA) * CEN_ADA;

double ADA_C = CEN_ADA / VC_ADA;

// ====== Vedolizumab IV ======

dxdt_CEN_VDZ = -(CL_VDZ/24/VC_VDZ) * CEN_VDZ

- (Q_VDZ/24/VC_VDZ) * CEN_VDZ + (Q_VDZ/24/VP_VDZ) * PER_VDZ;

dxdt_PER_VDZ = (Q_VDZ/24/VC_VDZ) * CEN_VDZ - (Q_VDZ/24/VP_VDZ) * PER_VDZ;

double VDZ_C = CEN_VDZ / VC_VDZ;

// ====== Drug-effect functions ======

double E_BUD = sat(BUD_GUT_C, EC50_BUD_GR); // mucosal GR transrepression

double E_CHOL = sat(CHOL_LUM, EC50_CHOL); // BA sequestration

double E_MES = sat(MES_LUM, EC50_MES); // PPAR-γ

double E_BIS = sat(BIS_LUM, EC50_BIS); // anti-secretory

double E_LOP = sat(LOP_C, EC50_LOP); // motility/secretion

double E_TGN = sat(TGN, EC50_TGN);

double E_TNF_b = sat(IFX_C + ADA_C, 5.0); // anti-TNF combined

double E_VDZ = sat(VDZ_C, EC50_VDZ);

// ====== Disease ODEs ======

// CD8+ IEL — driven by IL-15/IFN-γ, suppressed by GC, TPMT, anti-α4β7

double IEL_SS = IEL_NORM + (IEL_BASE - IEL_NORM) * (1 - 0.55*E_BUD - 0.25*E_TGN - 0.40*E_VDZ);

dxdt_IEL = KSYN_IEL*(IEL_SS) - KDEG_IEL * IEL;

// IFN-γ

dxdt_IFNG = KSYN_IFNG * (IEL/IEL_NORM) * (1 - 0.60*E_BUD - 0.30*E_TGN - 0.20*E_VDZ)

- KDEG_IFNG * IFNG;

// TNF-α — anti-TNF combo plus GC

dxdt_TNF = KSYN_TNF * (1 - 0.55*E_BUD - 0.35*E_TGN - 0.85*E_TNF_b)

- KDEG_TNF * TNF;

// IL-6

dxdt_IL6 = KSYN_IL6 * (1 - 0.50*E_BUD - 0.20*E_MES) - KDEG_IL6 * IL6;

// IL-17

dxdt_IL17 = KSYN_IL17 * (1 - 0.55*E_BUD - 0.40*E_TGN) - KDEG_IL17 * IL17;

// TGF-β — driven by mast cells / collagen feedback

dxdt_TGFB = KSYN_TGFB * (1 - 0.45*E_BUD) * (1 + 0.4*(COL/(COL+5.0)))

- KDEG_TGFB * TGFB;

// Barrier integrity: declines with TNF, IFN-γ, IL-17 + BA

double CYTO_BURDEN = (TNF/TNF_BASE) + (IFNG/IFNG_BASE) + 0.4*(IL17/IL17_BASE) + 0.3*(BA/BA_BASE);

dxdt_BAR = KFORM_BAR*(1 + 0.4*E_BUD + 0.2*E_TNF_b + 0.1*E_MES)*(1 - BAR)

- KDEG_BAR * CYTO_BURDEN * BAR;

// Collagen band — CC: TGF-β builds, GC degrades

dxdt_COL = KFORM_COL * sat(TGFB, EC50_TGFB_COL) * (SUBTYPE_CC>0.5 ? 1.0 : 0.3)

- KDEG_COL * COL * (1 + 0.8*E_BUD);

// Colonic bile-acid load

dxdt_BA = KSYN_BA * (1 + 0.4*(1-BAR)) - KDEG_BA * BA - 1.5 * E_CHOL * BA;

// Net colonic water flux (negative = secretion)

double WAT_TARGET = WAT_BASE

+ (WAT_NORM - WAT_BASE) * (0.40*E_BUD + 0.25*E_CHOL + 0.20*E_BIS

+ 0.15*E_LOP + 0.10*E_MES + 0.10*E_TNF_b

+ 0.10*E_VDZ + 0.10*E_TGN);

WAT_TARGET = WAT_TARGET + 200*pos(BAR-0.6) - 80*(BA/BA_BASE - 1);

dxdt_WAT = KFLX * (WAT_TARGET - WAT);

// Stool frequency — softplus driven by inverse of WAT

double drive = (WAT_BASE - WAT) / (WAT_BASE - WAT_NORM + 1e-3); // 0 = active, 1 = normal

double STOOL_TARGET = STOOL_BASE - (STOOL_BASE - STOOL_MIN) * drive;

dxdt_STOOL = KSTOOL * (STOOL_TARGET - STOOL);

// Hjortswang score — soft indicator: <3 stools/day & WAT recovering → remission

double HJ_TARGET = 1 / (1 + exp(-2*(STOOL - 3.0)));

dxdt_HJ = 0.5 * (HJ_TARGET - HJ);

// HRQoL — improves as stools, urgency, fatigue drop

double QOL_TARGET = 90 - 30*HJ - 5*(STOOL-1.5);

QOL_TARGET = QOL_TARGET < 30 ? 30 : QOL_TARGET;

dxdt_QOL = KQOL * (QOL_TARGET - QOL);

// BMD loss while on systemic GC (BUD_PLAS) above a threshold

dxdt_BMD = - BMD_DECAY_GC * (BUD_PLAS > 0.5 ? 1.0 : 0.0) - 0.0003 * (BUD_PLAS); // small effect

// HPA suppression first-order recovery + suppression

double k_hpa = log(2)/HPA_HALF; // per hour

double HPA_target = 1 - 0.6 * (BUD_PLAS / (BUD_PLAS + 1.0));

dxdt_HPA = k_hpa * 24 * (HPA_target - HPA); // convert to per day

$TABLE

double BUD_CONC = CENT_BUD / VC_BUD;

double STOOL_CLIP = STOOL < 0 ? 0 : STOOL;

double REMIT = (STOOL_CLIP < 3.0 ? 1.0 : 0.0);

$CAPTURE BUD_CONC IFX_C ADA_C VDZ_C TGN STOOL_CLIP HJ QOL BMD HPA BAR COL BA WAT IEL IFNG TNF IL6 IL17 TGFB REMIT

# Compile and quick smoke-test

mod <- mcode("microscopic_colitis_qsp", code)

# =====================================================================

# Treatment Scenarios

# =====================================================================

# Scenario 1: Natural history (no treatment), 365 days

s1 <- expand.ev(amt = 0)

# Scenario 2: Budesonide MMX 9 mg PO daily x 8 weeks induction + 6 mg taper x 6 mo

s2_ind <- ev(time = 0, amt = 9, cmt = "GUT_BUD", ii = 24, addl = 55) # 8 weeks

s2_main <- ev(time = 24*56,amt = 6, cmt = "GUT_BUD", ii = 24, addl = 180) # ~6 months

s2 <- c(s2_ind, s2_main)

# Scenario 3: Cholestyramine 4 g PO TID x 6 months

s3 <- ev(amt = 4, cmt = "GUT_CHOL", ii = 8, addl = 540)

# Scenario 4: Mesalamine 2.4 g PO daily x 8 weeks

s4 <- ev(amt = 2400, cmt = "GUT_MES", ii = 24, addl = 55)

# Scenario 5: Bismuth subsalicylate 524 mg PO QID x 8 weeks

s5 <- ev(amt = 524, cmt = "GUT_BIS", ii = 6, addl = 224)

# Scenario 6: Loperamide 4 mg PO BID prn (chronic) — symptomatic

s6 <- ev(amt = 4, cmt = "GUT_LOP", ii = 12, addl = 720)

# Scenario 7: Azathioprine 2 mg/kg (140 mg) PO QD — refractory

s7 <- ev(amt = 140, cmt = "GUT_AZA", ii = 24, addl = 360)

# Scenario 8: Infliximab 5 mg/kg (350 mg) IV at 0, 2, 6 weeks then q8w

ifx_doses <- c(0, 14*24, 42*24, seq(98*24, 365*24, by = 56*24))

s8 <- do.call(c, lapply(ifx_doses, function(t) ev(time = t, amt = 350, cmt = "CEN_IFX")))

# Scenario 9: Vedolizumab 300 mg IV at 0, 2, 6 weeks then q8w

vdz_doses <- ifx_doses

s9 <- do.call(c, lapply(vdz_doses, function(t) ev(time = t, amt = 300, cmt = "CEN_VDZ")))

# Scenario 10: Budesonide + Cholestyramine combo (refractory CC w/ BAM)

s10 <- c(s2, s3)

scenarios <- list(

"01_natural_history" = ev(amt = 0),

"02_budesonide_taper" = s2,

"03_cholestyramine" = s3,

"04_mesalamine" = s4,

"05_bismuth" = s5,

"06_loperamide_symp" = s6,

"07_azathioprine" = s7,

"08_infliximab_q8w" = s8,

"09_vedolizumab_q8w" = s9,

"10_bud_chol_combo" = s10

)

run_scenario <- function(label, evd, subtype = c("CC", "LC"), tend = 365*24) {

subtype <- match.arg(subtype)

pset <- if (subtype == "LC") list(SUBTYPE_CC = 0) else list(SUBTYPE_CC = 1)

out <- mod %>% param(pset) %>% mrgsim(events = evd, end = tend, delta = 24)

df <- as.data.frame(out)

df$scenario <- label

df$subtype <- subtype

}

if (FALSE) {

# Demo / verification – uncomment to execute

out_all <- do.call(rbind, lapply(names(scenarios), function(n) run_scenario(n, scenarios[[n]])))

head(out_all)

with(subset(out_all, scenario == "02_budesonide_taper"),

plot(time/24, STOOL_CLIP, type = "l", ylim = c(0, 8),

xlab = "Days", ylab = "Stools/day",

main = "Budesonide MMX induction + taper (CC)"))

}

# Export for Shiny app re-use

mc_model <- mod

mc_scenarios <- scenarios

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