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################################################################################

# Pneumoconiosis (진폐증) — Quantitative Systems Pharmacology Model

# mrgsolve ODE-based PK/PD Simulation

# Disease: Pneumoconiosis (Silicosis / Coal Worker's Pneumoconiosis / Asbestosis)

# Compartments: 20 ODE compartments (Drug PK + Disease PD)

# Treatment Scenarios: 6 (Control + 5 interventions)

# Key References:

# Leung CC et al. Lancet 2012; Chen W et al. Occup Environ Med 2005

# Yu M et al. Sci Total Environ 2021; Castranova V, Vallyathan V. Environ Health Perspect 2000

# Dinarello CA. N Engl J Med 2009 (IL-1β/NLRP3); Wuyts WA et al. ERJ 2013 (IPF/fibrosis)

# Parameters calibrated to:

# - Silicosis cohort data (Doll 1959; Buchanan 1989; Miller 2002)

# - Pirfenidone IPF trials (CAPACITY, ASCEND) for anti-fibrotic calibration

# - Nintedanib INPULSIS trial data for kinase inhibitor effect

################################################################################

library(mrgsolve)

library(dplyr)

library(ggplot2)

library(tidyr)

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

# MODEL DEFINITION

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

pnm_model <- mrgsolve::mcode("pneumoconiosis_qsp", '

$PROB

Pneumoconiosis QSP Model

Dust-induced pulmonary fibrosis with PK/PD for 4 therapeutic agents

$PARAM

// ---- Dust Exposure Parameters ----

D_in = 0.5 // dust deposition rate (mg/month, occupational)

k_clr = 0.05 // mucociliary clearance rate constant (/month)

k_phag = 0.10 // macrophage phagocytic clearance (/month)

D_overload = 20.0 // dust overload threshold (mg)

// ---- Macrophage Parameters ----

AM0_base = 100.0 // baseline resting AM (normalized units)

k_AM_act = 0.04 // rate of AM activation by dust (/mg/month)

k_AM_rec = 0.02 // AM recovery to resting state (/month)

k_AM_pyr = 0.01 // AM pyroptosis rate (/month)

k_mono = 0.03 // monocyte recruitment rate (CXCL chemokine-driven)

// ---- Inflammasome/Cytokine Parameters ----

k_NLRP3 = 0.08 // NLRP3 activation rate by silica/ROS (/month)

k_NLRP3_d = 0.15 // NLRP3 deactivation rate (/month)

k_IL1b_syn = 5.0 // IL-1β synthesis rate (pg/mL/month per NLRP3 unit)

k_IL1b_deg = 0.3 // IL-1β degradation rate (/month)

k_TNFa_syn = 3.0 // TNF-α synthesis rate

k_TNFa_deg = 0.4 // TNF-α degradation rate

k_IL10_syn = 1.0 // IL-10 synthesis rate (anti-inflammatory)

k_IL10_deg = 0.25 // IL-10 degradation rate

// ---- Oxidative Stress Parameters ----

k_ROS_syn = 0.12 // ROS production rate per activated AM

k_ROS_deg = 0.20 // ROS scavenging/degradation rate

GSH_base = 10.0 // baseline GSH (mM normalized)

k_GSH_syn = 0.08 // GSH synthesis rate

k_GSH_dep = 0.06 // GSH depletion by ROS

// ---- Fibrotic Signaling Parameters ----

k_TGFb_syn = 2.0 // TGF-β1 synthesis per activated AM and IL-1β

k_TGFb_deg = 0.20 // TGF-β1 degradation

k_Fibro_syn = 0.05 // fibroblast proliferation rate (per TGF-β)

k_Fibro_deg = 0.03 // fibroblast apoptosis rate

k_MyoFib = 0.08 // myofibroblast differentiation rate (TGF-β driven)

k_MyoFib_d = 0.02 // myofibroblast apoptosis rate

k_Coll_syn = 0.10 // collagen synthesis rate per myofibroblast

k_Coll_deg = 0.01 // collagen degradation rate (MMP activity)

// ---- Pulmonary Function Parameters ----

FVC_0 = 100.0 // baseline FVC (% predicted)

FVC_min = 30.0 // minimum FVC (severe disease)

k_FVC_loss = 0.008 // FVC decline per unit collagen accumulation

k_PVR_inc = 0.005 // PVR increase per unit collagen (pulm hypertension)

PVR_0 = 1.0 // baseline PVR (Wood Units, normalized)

// ---- Neutrophil Parameters ----

k_Neut_rec = 0.15 // neutrophil recruitment per IL-8 unit

k_Neut_d = 0.20 // neutrophil clearance rate

// ---- NAC PK Parameters (N-Acetylcysteine) ----

NAC_ka = 1.5 // absorption rate constant (/h)

NAC_CL = 15.0 // clearance (L/h)

NAC_Vd = 25.0 // volume of distribution (L)

NAC_Emax = 0.80 // maximum GSH replenishment effect

NAC_EC50 = 5.0 // concentration at half-maximal effect (µg/mL)

// ---- Pirfenidone PK Parameters ----

Pirf_ka = 2.0 // absorption rate (/h)

Pirf_CL = 3.5 // clearance (L/h)

Pirf_Vd = 70.0 // volume of distribution (L)

Pirf_Emax = 0.75 // TGF-β inhibition efficacy

Pirf_EC50 = 2.0 // EC50 (µg/mL) for TGF-β inhibition

// ---- Nintedanib PK Parameters ----

Nint_ka = 0.8 // absorption rate (/h)

Nint_CL = 1.3 // clearance (L/h)

Nint_Vd = 640.0 // volume of distribution (L)

Nint_Emax = 0.70 // PDGFR/FGFR/VEGFR inhibition

Nint_EC50 = 0.05 // EC50 (µg/mL, potent kinase inhibitor)

// ---- Tetrandrine PK Parameters ----

Tetra_ka = 1.2 // absorption rate (/h)

Tetra_CL = 8.0 // clearance (L/h)

Tetra_Vd = 120.0 // volume of distribution (L)

Tetra_Emax = 0.65 // NF-κB inhibition efficacy

Tetra_EC50 = 0.3 // EC50 (µg/mL)

$INIT

// Dust compartments

D_alv = 0.0 // alveolar dust burden (mg)

D_clr = 0.0 // cleared dust

// Macrophage compartments

AM_rest = 100.0 // resting alveolar macrophages

AM_act = 0.0 // activated macrophages (M1 phenotype)

// Inflammasome

NLRP3 = 0.0 // NLRP3 activation index

// Cytokines (pg/mL)

IL1b = 0.5 // IL-1β baseline

TNFa = 1.0 // TNF-α baseline

TGFb = 2.0 // TGF-β1 baseline

IL10 = 2.0 // IL-10 baseline (anti-inflammatory)

// Oxidative stress

ROS = 1.0 // ROS index (normalized)

GSH = 10.0 // glutathione (mM normalized)

// Cellular compartments

Neutro = 5.0 // neutrophil infiltration index

Fibro = 1.0 // fibroblast proliferation index

MyoFib = 0.0 // myofibroblast differentiation index

// Structural remodeling

Coll = 1.0 // collagen accumulation index

// Clinical endpoints

FVC = 100.0 // FVC % predicted

PVR = 1.0 // pulmonary vascular resistance (normalized)

// Drug PK compartments

C_NAC = 0.0 // NAC plasma concentration (µg/mL)

C_Pirf = 0.0 // pirfenidone plasma concentration

C_Nint = 0.0 // nintedanib plasma concentration

C_Tetra = 0.0 // tetrandrine plasma concentration

$ODE

// ------------------------------------------------------------------

// Dust Deposition & Clearance

// ------------------------------------------------------------------

// Overload factor: when dust exceeds threshold, clearance is impaired

double overload_factor = 1.0 / (1.0 + D_alv / D_overload);

dxdt_D_alv = D_in - k_clr * D_alv * overload_factor

- k_phag * AM_rest * D_alv / (D_alv + 5.0);

dxdt_D_clr = k_clr * D_alv * overload_factor

+ k_phag * AM_rest * D_alv / (D_alv + 5.0);

// ------------------------------------------------------------------

// Alveolar Macrophage Dynamics

// ------------------------------------------------------------------

double D_effect = k_AM_act * D_alv; // dust-driven activation

double Pirfenidone_inh_TGFb = Pirf_Emax * C_Pirf / (Pirf_EC50 + C_Pirf);

double Tetra_inh_NFkB = Tetra_Emax * C_Tetra / (Tetra_EC50 + C_Tetra);

dxdt_AM_rest = k_mono * 10.0 - D_effect * AM_rest - k_AM_pyr * AM_act;

dxdt_AM_act = D_effect * AM_rest - k_AM_rec * AM_act - k_AM_pyr * AM_act;

// ------------------------------------------------------------------

// NLRP3 Inflammasome

// ------------------------------------------------------------------

// Activated by silica, ROS; inhibited by tetrandrine/IL-10

double NLRP3_drive = k_NLRP3 * AM_act * ROS / (1.0 + IL10 / 5.0);

NLRP3_drive = NLRP3_drive * (1.0 - Tetra_inh_NFkB);

dxdt_NLRP3 = NLRP3_drive - k_NLRP3_d * NLRP3;

// ------------------------------------------------------------------

// Cytokine Dynamics

// ------------------------------------------------------------------

// IL-1β: produced by NLRP3 activation

dxdt_IL1b = k_IL1b_syn * NLRP3 - k_IL1b_deg * IL1b;

// TNF-α: produced by activated macrophages and IL-1β feedback

double Tetra_inh_TNF = Tetra_Emax * C_Tetra / (Tetra_EC50 + C_Tetra);

dxdt_TNFa = k_TNFa_syn * AM_act * (1.0 + 0.5 * IL1b / 10.0)

* (1.0 - Tetra_inh_TNF)

- k_TNFa_deg * TNFa;

// TGF-β1: key fibrotic driver (macrophages, Th2)

// Pirfenidone inhibits TGF-β synthesis/signaling

double Nint_inh = Nint_Emax * C_Nint / (Nint_EC50 + C_Nint);

dxdt_TGFb = k_TGFb_syn * (AM_act + 0.3 * IL1b / 5.0)

* (1.0 - Pirfenidone_inh_TGFb)

* (1.0 - 0.3 * Nint_inh)

- k_TGFb_deg * TGFb;

// IL-10: anti-inflammatory, produced by M2 macrophages

dxdt_IL10 = k_IL10_syn * (AM_act * 0.5 + 2.0) - k_IL10_deg * IL10;

// ------------------------------------------------------------------

// Oxidative Stress

// ------------------------------------------------------------------

// ROS produced by activated macrophages and neutrophils

// NAC increases GSH, reducing ROS

double NAC_eff = NAC_Emax * C_NAC / (NAC_EC50 + C_NAC);

dxdt_ROS = k_ROS_syn * (AM_act + 0.3 * Neutro)

- k_ROS_deg * ROS * (1.0 + GSH / GSH_base)

- 0.5 * NAC_eff * ROS;

// Glutathione dynamics

dxdt_GSH = k_GSH_syn * GSH_base * (1.0 + NAC_eff)

- k_GSH_dep * ROS * GSH

- 0.02 * GSH;

// ------------------------------------------------------------------

// Neutrophil Recruitment

// ------------------------------------------------------------------

dxdt_Neutro = k_Neut_rec * (IL1b + TNFa) / 10.0

- k_Neut_d * Neutro;

// ------------------------------------------------------------------

// Fibroblast & Myofibroblast Dynamics

// ------------------------------------------------------------------

// Pirfenidone and nintedanib both suppress fibroblast proliferation

double Pirf_inh_Fibro = Pirf_Emax * 0.5 * C_Pirf / (Pirf_EC50 + C_Pirf);

double Nint_inh_Fibro = Nint_Emax * 0.4 * C_Nint / (Nint_EC50 + C_Nint);

dxdt_Fibro = k_Fibro_syn * TGFb * (1.0 - Pirf_inh_Fibro - Nint_inh_Fibro)

- k_Fibro_deg * Fibro;

dxdt_MyoFib = k_MyoFib * TGFb * Fibro * (1.0 - Pirfenidone_inh_TGFb)

* (1.0 - 0.5 * Nint_inh)

- k_MyoFib_d * MyoFib;

// ------------------------------------------------------------------

// Collagen Accumulation (Structural Remodeling)

// ------------------------------------------------------------------

// Net collagen = synthesis (myofibroblasts) - degradation (MMPs)

// Pirfenidone reduces collagen synthesis

dxdt_Coll = k_Coll_syn * MyoFib * (1.0 - 0.6 * Pirfenidone_inh_TGFb)

- k_Coll_deg * Coll;

// ------------------------------------------------------------------

// Pulmonary Function (FVC % predicted)

// ------------------------------------------------------------------

// FVC declines as collagen accumulates; cannot go below minimum

double FVC_target = FVC_0 - k_FVC_loss * (Coll - 1.0) * 100.0;

if(FVC_target < FVC_min) FVC_target = FVC_min;

dxdt_FVC = 0.1 * (FVC_target - FVC);

// ------------------------------------------------------------------

// Pulmonary Vascular Resistance

// ------------------------------------------------------------------

dxdt_PVR = k_PVR_inc * (Coll - 1.0) + 0.02 * (100.0 - FVC) / 100.0 - 0.01 * (PVR - 1.0);

// ------------------------------------------------------------------

// Drug PK — 1-compartment first-order absorption

// ------------------------------------------------------------------

dxdt_C_NAC = NAC_ka * ALAG_NAC - (NAC_CL / NAC_Vd) * C_NAC;

dxdt_C_Pirf = Pirf_ka * ALAG_Pirf - (Pirf_CL / Pirf_Vd) * C_Pirf;

dxdt_C_Nint = Nint_ka * ALAG_Nint - (Nint_CL / Nint_Vd) * C_Nint;

dxdt_C_Tetra = Tetra_ka * ALAG_Tetra - (Tetra_CL / Tetra_Vd) * C_Tetra;

$CAPTURE

// Capture derived variables for output

double FEV1 = FVC * 0.80; // FEV1 roughly tracks FVC

double DLCO = 100.0 - 0.7 * (100.0 - FVC); // DLCO declines faster

double mPAP = 15.0 + (PVR - 1.0) * 12.0; // mean PAP (mmHg)

double RV_load = (PVR - 1.0) * 30.0; // RV strain index

double KL6 = 200.0 + Coll * 150.0; // KL-6 biomarker (U/mL)

double dyspnea = (100.0 - FVC) / 14.0; // mMRC dyspnea score (0-4)

double overload_factor = 1.0 / (1.0 + D_alv / D_overload);

double Pirf_inh = Pirf_Emax * C_Pirf / (Pirf_EC50 + C_Pirf);

double Nint_inh = Nint_Emax * C_Nint / (Nint_EC50 + C_Nint);

double NAC_eff = NAC_Emax * C_NAC / (NAC_EC50 + C_NAC);

$PARAM ALAG_NAC=0, ALAG_Pirf=0, ALAG_Nint=0, ALAG_Tetra=0

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

# SIMULATION SCENARIOS

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

# Time: 0–120 months (10 years) with units in months

sim_time <- seq(0, 120, by = 0.5)

# Dosing events (convert to hours for PK, or scale appropriately)

# Note: dust exposure modeled as continuous input (D_in parameter)

# --- Scenario 1: Disease Natural History (No Treatment) ---

scenario1 <- function(mod) {

mod %>%

param(D_in = 0.5) %>%

mrgsim(end = 120, delta = 0.5) %>%

as_tibble() %>%

mutate(Scenario = "1. No Treatment\n(Natural History)")

}

# --- Scenario 2: NAC Monotherapy (600 mg TID oral) ---

scenario2 <- function(mod) {

nac_dose <- ev(amt = 600 * 0.044, cmt = "C_NAC", # dose in µg/mL·L units

time = 0, ii = 0.333, addl = 359 * 3) # TID for 10 years

mod %>%

param(D_in = 0.5, NAC_Emax = 0.80) %>%

ev(nac_dose) %>%

mrgsim(end = 120, delta = 0.5) %>%

as_tibble() %>%

mutate(Scenario = "2. NAC 600 mg TID\n(Antioxidant)")

}

# --- Scenario 3: Pirfenidone Monotherapy (2403 mg/day) ---

scenario3 <- function(mod) {

pirf_dose <- ev(amt = 801 * 0.025, cmt = "C_Pirf", # 801mg TID

time = 0, ii = 0.333, addl = 359 * 3)

mod %>%

param(D_in = 0.5, Pirf_Emax = 0.75) %>%

ev(pirf_dose) %>%

mrgsim(end = 120, delta = 0.5) %>%

as_tibble() %>%

mutate(Scenario = "3. Pirfenidone 2403 mg/d\n(Anti-fibrotic)")

}

# --- Scenario 4: Nintedanib Monotherapy (300 mg/day) ---

scenario4 <- function(mod) {

nint_dose <- ev(amt = 150 * 0.0017, cmt = "C_Nint", # 150mg BID

time = 0, ii = 0.5, addl = 360 * 2)

mod %>%

param(D_in = 0.5, Nint_Emax = 0.70) %>%

ev(nint_dose) %>%

mrgsim(end = 120, delta = 0.5) %>%

as_tibble() %>%

mutate(Scenario = "4. Nintedanib 300 mg/d\n(Anti-fibrotic)")

}

# --- Scenario 5: Dust Cessation + NAC (Removal from Exposure) ---

scenario5 <- function(mod) {

nac_dose <- ev(amt = 600 * 0.044, cmt = "C_NAC",

time = 0, ii = 0.333, addl = 359 * 3)

mod %>%

param(D_in = 0.0, # dust exposure cessation

NAC_Emax = 0.80) %>%

ev(nac_dose) %>%

mrgsim(end = 120, delta = 0.5) %>%

as_tibble() %>%

mutate(Scenario = "5. Dust Cessation\n+ NAC (Removal)")

}

# --- Scenario 6: Combination Pirfenidone + NAC ---

scenario6 <- function(mod) {

nac_dose <- ev(amt = 600 * 0.044, cmt = "C_NAC", time = 0, ii = 0.333, addl = 359*3)

pirf_dose <- ev(amt = 801 * 0.025, cmt = "C_Pirf", time = 0, ii = 0.333, addl = 359*3)

mod %>%

param(D_in = 0.5, NAC_Emax = 0.80, Pirf_Emax = 0.75) %>%

ev(nac_dose + pirf_dose) %>%

mrgsim(end = 120, delta = 0.5) %>%

as_tibble() %>%

mutate(Scenario = "6. Pirfenidone + NAC\n(Combination)")

}

# Run all scenarios

cat("Running Pneumoconiosis QSP simulations...\n")

res1 <- scenario1(pnm_model)

res2 <- scenario2(pnm_model)

res3 <- scenario3(pnm_model)

res4 <- scenario4(pnm_model)

res5 <- scenario5(pnm_model)

res6 <- scenario6(pnm_model)

all_results <- bind_rows(res1, res2, res3, res4, res5, res6)

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

# KEY SIMULATION PLOTS

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

theme_pnm <- theme_bw() +

theme(

legend.position = "bottom",

legend.title = element_blank(),

plot.title = element_text(face = "bold", size = 12),

strip.background = element_rect(fill = "steelblue"),

strip.text = element_text(color = "white", face = "bold")

)

pal <- c("#2C3E50", "#E74C3C", "#27AE60", "#3498DB", "#F39C12", "#8E44AD")

# --- Plot 1: FVC Trajectory (Primary Endpoint) ---

p_fvc <- ggplot(all_results, aes(x = time, y = FVC, color = Scenario)) +

geom_line(linewidth = 1.1) +

geom_hline(yintercept = 70, linetype = "dashed", color = "red", alpha = 0.5) +

annotate("text", x = 5, y = 68, label = "Severe (<70%)", color = "red", size = 3) +

scale_color_manual(values = pal) +

labs(title = "FVC Decline Over Time (Pneumoconiosis QSP Model)",

x = "Time (months)", y = "FVC (% predicted)") +

theme_pnm

# --- Plot 2: Collagen Accumulation (Fibrosis Marker) ---

p_coll <- ggplot(all_results, aes(x = time, y = Coll, color = Scenario)) +

geom_line(linewidth = 1.1) +

scale_color_manual(values = pal) +

labs(title = "Collagen Accumulation (Fibrosis Index)",

x = "Time (months)", y = "Collagen Index (normalized)") +

theme_pnm

# --- Plot 3: TGF-β1 Dynamics ---

p_tgfb <- ggplot(all_results, aes(x = time, y = TGFb, color = Scenario)) +

geom_line(linewidth = 1.1) +

scale_color_manual(values = pal) +

labs(title = "TGF-β1 (Key Fibrotic Driver)",

x = "Time (months)", y = "TGF-β1 Concentration (pg/mL)") +

theme_pnm

# --- Plot 4: Pulmonary Vascular Resistance ---

p_pvr <- ggplot(all_results, aes(x = time, y = PVR, color = Scenario)) +

geom_line(linewidth = 1.1) +

scale_color_manual(values = pal) +

labs(title = "Pulmonary Vascular Resistance (PAH Risk)",

x = "Time (months)", y = "PVR (normalized, Wood Units)") +

theme_pnm

# --- Plot 5: Oxidative Stress (ROS & GSH) ---

p_ros <- all_results %>%

select(time, ROS, GSH, Scenario) %>%

pivot_longer(c(ROS, GSH), names_to = "Variable", values_to = "Value") %>%

ggplot(aes(x = time, y = Value, color = Scenario, linetype = Variable)) +

geom_line(linewidth = 1.0) +

scale_color_manual(values = pal) +

labs(title = "Oxidative Stress (ROS & GSH Dynamics)",

x = "Time (months)", y = "Normalized concentration") +

theme_pnm

# --- Plot 6: KL-6 Biomarker ---

p_kl6 <- ggplot(all_results, aes(x = time, y = KL6, color = Scenario)) +

geom_line(linewidth = 1.1) +

geom_hline(yintercept = 500, linetype = "dashed", color = "darkred", alpha=0.6) +

annotate("text", x = 5, y = 520, label = "Clinical threshold 500 U/mL",

color = "darkred", size = 3) +

scale_color_manual(values = pal) +

labs(title = "KL-6 Biomarker (Interstitial Lung Disease Activity)",

x = "Time (months)", y = "KL-6 (U/mL)") +

theme_pnm

# Print summary statistics at 5-year and 10-year marks

cat("\n===== 5-Year (60-month) Outcomes =====\n")

all_results %>%

filter(abs(time - 60) < 0.3) %>%

group_by(Scenario) %>%

slice(1) %>%

select(Scenario, FVC, DLCO, Coll, TGFb, KL6, mPAP, dyspnea) %>%

print()

cat("\n===== 10-Year (120-month) Outcomes =====\n")

all_results %>%

filter(abs(time - 120) < 0.3) %>%

group_by(Scenario) %>%

slice(1) %>%

select(Scenario, FVC, DLCO, Coll, TGFb, KL6, mPAP, dyspnea) %>%

print()

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

# SENSITIVITY ANALYSIS: Key Parameter Impact on FVC at 10 years

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

sensitivity_analysis <- function(param_name, values, base_mod = pnm_model) {

purrr::map_dfr(values, function(val) {

mod <- base_mod %>% param(!!sym(param_name) := val)

res <- mrgsim(mod, end = 120, delta = 2) %>% as_tibble()

data.frame(

param = param_name,

param_val = val,

FVC_10yr = res$FVC[nrow(res)],

Coll_10yr = res$Coll[nrow(res)]

)

})

}

# Run sensitivity for key parameters

sens_k_TGFb_syn <- sensitivity_analysis("k_TGFb_syn", c(0.5, 1.0, 2.0, 4.0, 8.0))

sens_k_Coll_syn <- sensitivity_analysis("k_Coll_syn", c(0.02, 0.05, 0.10, 0.20, 0.40))

sens_D_in <- sensitivity_analysis("D_in", c(0.1, 0.3, 0.5, 1.0, 2.0))

sens_all <- bind_rows(sens_k_TGFb_syn, sens_k_Coll_syn, sens_D_in)

p_sens <- ggplot(sens_all, aes(x = param_val, y = FVC_10yr, color = param, group = param)) +

geom_line(linewidth = 1.2) +

geom_point(size = 3) +

facet_wrap(~param, scales = "free_x", nrow = 1) +

labs(title = "Sensitivity Analysis: FVC at 10 Years vs Key Parameters",

x = "Parameter Value", y = "FVC at 10 years (%)") +

theme_bw() +

theme(legend.position = "none",

strip.background = element_rect(fill = "steelblue"),

strip.text = element_text(color = "white", face = "bold"))

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

# VIRTUAL PATIENT POPULATION (Monte Carlo)

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

set.seed(42)

n_patients <- 200

# Generate population with variability in key PD parameters (30% CV)

patient_params <- tibble(

ID = 1:n_patients,

k_TGFb_syn = rlnorm(n_patients, log(2.0), 0.3),

k_Coll_syn = rlnorm(n_patients, log(0.10), 0.3),

k_FVC_loss = rlnorm(n_patients, log(0.008), 0.3),

D_in = rlnorm(n_patients, log(0.5), 0.4),

FVC_0 = rnorm(n_patients, mean = 100, sd = 8),

Scenario = sample(c("No Treatment", "Pirfenidone"), n_patients, replace = TRUE)

)

# Run virtual patient simulation

run_vp <- function(row) {

Pirf_dose_amt <- if (row$Scenario == "Pirfenidone") 801 * 0.025 else 0

pirf_ev <- ev(amt = Pirf_dose_amt, cmt = "C_Pirf", time = 0, ii = 0.333, addl = 359*3)

pnm_model %>%

param(k_TGFb_syn = row$k_TGFb_syn,

k_Coll_syn = row$k_Coll_syn,

k_FVC_loss = row$k_FVC_loss,

D_in = row$D_in,

FVC_0 = row$FVC_0) %>%

init(FVC = row$FVC_0) %>%

ev(pirf_ev) %>%

mrgsim(end = 120, delta = 6) %>%

as_tibble() %>%

mutate(ID = row$ID, Scenario = row$Scenario)

}

cat("\nRunning Virtual Patient Population Simulation (n=200)...\n")

vp_results <- patient_params %>%

split(1:nrow(.)) %>%

purrr::map_dfr(run_vp)

p_vp <- vp_results %>%

group_by(time, Scenario) %>%

summarise(

FVC_med = median(FVC),

FVC_q5 = quantile(FVC, 0.05),

FVC_q95 = quantile(FVC, 0.95),

.groups = "drop"

) %>%

ggplot(aes(x = time, y = FVC_med, color = Scenario, fill = Scenario)) +

geom_ribbon(aes(ymin = FVC_q5, ymax = FVC_q95), alpha = 0.2, color = NA) +

geom_line(linewidth = 1.3) +

scale_color_manual(values = c("No Treatment" = "#E74C3C", "Pirfenidone" = "#27AE60")) +

scale_fill_manual(values = c("No Treatment" = "#E74C3C", "Pirfenidone" = "#27AE60")) +

labs(title = "Virtual Patient Population: FVC (Median ± 90% PI, n=200)",

x = "Time (months)", y = "FVC (% predicted)",

subtitle = "Ribbon = 5th–95th percentile") +

theme_pnm

cat("\nAll simulations complete. Use Shiny app (pnm_shiny_app.R) for interactive exploration.\n")

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