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

## Lupus Nephritis (LN) — QSP Model in mrgsolve

## Disease: SLE-driven glomerulonephritis (ISN/RPS Class III/IV/V)

## Drug PK/PD: HCQ · MMF/MPA · Voclosporin · Belimumab · Anifrolumab · CYC · GC

## Compartments (20 ODEs):

## PK: [1] MPA_plasma [2] MPAG_gut [3] HCQ_blood [4] HCQ_tissue

## [5] VCS_plasma [6] BEL_central [7] BEL_peripheral

## [8] ANI_central [9] ANI_peripheral

## Immune: [10] B_naive [11] B_GC [12] Plasma_cell [13] Tfh [14] Treg

## Ab/Complement: [15] Anti_dsDNA [16] C3 [17] C4

## Renal: [18] Podocyte_injury [19] Proteinuria [20] eGFR

## Calibrated against: BLISS-LN (Furie 2020), AURORA (Rovin 2021),

## AURORA 2 (Rovin 2022), AURA-LV (Mysler 2020), ACCESS trial

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

library(mrgsolve)

library(dplyr)

library(ggplot2)

library(tidyr)

##──────────────────────────────────────────────────────────────────────────────

## MODEL CODE

code <- '

$PROB Lupus Nephritis QSP Model — mrgsolve

$PARAM

// ── MMF/MPA PK ──────────────────────────────────────────────

F_MMF = 0.94, // oral bioavailability

ka_MMF = 1.2, // absorption rate (1/h)

CL_MPA = 22.0, // apparent clearance (L/h)

V_MPA = 55.0, // apparent volume (L)

ka_EHC = 0.08, // enterohepatic re-absorption rate (1/h)

fr_MPAG = 0.40, // fraction converted to MPAG

dose_MMF = 0.0, // MMF dose (mg/h; 1000 mg BID = 83.3 mg/h average)

// ── HCQ PK ──────────────────────────────────────────────────

F_HCQ = 0.74,

ka_HCQ = 0.38, // absorption (1/h)

CL_HCQ = 0.095, // L/h/kg → use CL_HCQ * WT

V_blood = 7.0, // blood compartment (L/kg)

V_tissue = 800.0, // tissue (L/kg) — very large Vd

k12_HCQ = 0.03, // blood→tissue (1/h)

k21_HCQ = 0.0003, // tissue→blood (1/h)

dose_HCQ = 0.0, // mg/h (400 mg/day = 16.7 mg/h)

WT = 65.0, // body weight (kg)

// ── Voclosporin PK ───────────────────────────────────────────

F_VCS = 0.27,

ka_VCS = 0.7, // (1/h)

CL_VCS = 31.6, // L/h

V_VCS = 167.0, // L

dose_VCS = 0.0, // mg/h (23.7 mg BID = 1.97 mg/h average)

// ── Belimumab PK (2-cmt IV) ──────────────────────────────────

CL_BEL = 0.182, // L/h (2.8 mL/h/kg × 65 kg)

V1_BEL = 4.1, // L central

V2_BEL = 1.8, // L peripheral

Q_BEL = 0.12, // inter-cmt CL (L/h)

dose_BEL = 0.0, // mg/h (650 mg q4w = 0.92 mg/h average)

// ── Anifrolumab PK (2-cmt IV) ────────────────────────────────

CL_ANI = 0.192, // L/h (TMDD-approximated)

V1_ANI = 5.6, // L

V2_ANI = 2.4,

Q_ANI = 0.15,

dose_ANI = 0.0, // mg/h (300 mg q4w = 0.43 mg/h average)

// ── MPA pharmacodynamics ─────────────────────────────────────

EC50_MPA_B = 2.5, // mg/L — B cell proliferation IC50

EC50_MPA_T = 4.0, // mg/L — T cell (Tfh) IC50

Emax_MPA = 0.85, // max inhibition fraction

// ── HCQ pharmacodynamics ─────────────────────────────────────

EC50_HCQ = 0.50, // mg/L in blood — TLR7/9 inhibition

Emax_HCQ = 0.70,

// ── Voclosporin pharmacodynamics ─────────────────────────────

EC50_VCS = 0.015, // mg/L — calcineurin inhibition

Emax_VCS = 0.80,

// ── Belimumab pharmacodynamics ───────────────────────────────

Kd_BEL = 0.001, // mg/L — BAFF binding affinity (very high)

Emax_BEL = 0.75,

// ── Anifrolumab pharmacodynamics ─────────────────────────────

EC50_ANI = 0.005, // mg/L

Emax_ANI = 0.90,

// ── Immune system parameters ─────────────────────────────────

k_Bnaive_in = 0.05, // B naive influx (cells/μL/day)

k_Bnaive_deg = 0.014, // B naive degradation (1/day) → t½≈50 days

k_GC_stim = 0.008, // TFH-driven GC activation

k_GC_deg = 0.05,

k_PC_diff = 0.10, // GC→plasma cell differentiation (1/day)

k_PC_deg = 0.003, // plasma cell degradation (1/day) → t½≈230 days

k_Tfh_stim = 0.006,

k_Tfh_deg = 0.08,

k_Treg_base = 0.003,

k_Treg_deg = 0.03,

BAFF_base = 1.0, // dimensionless BAFF level (baseline=1)

// ── Anti-dsDNA kinetics ──────────────────────────────────────

k_Ab_prod = 0.15, // per plasma cell per day

k_Ab_deg = 0.004, // (1/day) → t½≈170 days

Ab_baseline = 100.0, // IU/mL baseline

// ── Complement parameters ────────────────────────────────────

C3_baseline = 0.80, // g/L (normal ~0.9 g/L)

k_C3_synth = 0.01,

k_C3_consume = 0.04, // by IC

k_C3_deg = 0.005,

C4_baseline = 0.25, // g/L

k_C4_synth = 0.003,

k_C4_consume = 0.06,

k_C4_deg = 0.006,

// ── Renal: podocyte compartment ──────────────────────────────

k_pod_inj = 0.03, // IC+C5→podocyte injury rate

k_pod_repair = 0.005, // intrinsic repair

Pod_max = 1.0, // normalized max injury

// ── Renal: proteinuria (UPCR, g/g) ──────────────────────────

k_prot_rise = 0.15, // podocyte injury → proteinuria rise

k_prot_fall = 0.04, // spontaneous decrease

UPCR_base = 2.5, // baseline UPCR (g/g) — active LN

// ── eGFR (mL/min/1.73m²) ────────────────────────────────────

eGFR_base = 65.0, // baseline — mild reduction

k_eGFR_loss = 0.0008, // per unit podocyte injury per day

k_eGFR_rec = 0.001,

eGFR_min = 15.0,

// ── Disease activity (IFN signal amplification) ───────────────

IFN_base = 1.5, // dimensionless type I IFN level

k_IFN_BAFF = 0.4 // IFN → BAFF amplification

$CMT

// PK

MPA_gut MPA_plasma MPAG_gut

HCQ_blood HCQ_tissue

VCS_plasma

BEL_central BEL_periph

ANI_central ANI_periph

// Immune

B_naive B_GC Plasma_cell Tfh Treg

// Ab / Complement

Anti_dsDNA C3 C4

// Renal

Podocyte_inj Proteinuria eGFR_cmt

$INIT

MPA_gut = 0, MPA_plasma = 0, MPAG_gut = 0,

HCQ_blood = 0, HCQ_tissue = 0,

VCS_plasma= 0,

BEL_central=0, BEL_periph =0,

ANI_central=0, ANI_periph =0,

B_naive = 250, B_GC = 20, Plasma_cell= 120,

Tfh = 15, Treg = 30,

Anti_dsDNA= 280, C3 = 0.55, C4 = 0.12,

Podocyte_inj=0.35, Proteinuria=2.5, eGFR_cmt = 65

$ODE

// ── Concentrations (convenience) ────────────────────────────────────────────

double C_MPA = MPA_plasma / V_MPA; // mg/L

double C_HCQ = HCQ_blood / (V_blood * WT); // mg/L

double C_VCS = VCS_plasma / V_VCS; // mg/L

double C_BEL = BEL_central / V1_BEL; // mg/L

double C_ANI = ANI_central / V1_ANI; // mg/L

// ── Pharmacodynamic effects (0=no effect, 1=max effect) ─────────────────────

double E_MPA_B = Emax_MPA * pow(C_MPA,1.5) / (pow(EC50_MPA_B,1.5) + pow(C_MPA,1.5));

double E_MPA_T = Emax_MPA * C_MPA / (EC50_MPA_T + C_MPA);

double E_HCQ = Emax_HCQ * C_HCQ / (EC50_HCQ + C_HCQ);

double E_VCS = Emax_VCS * C_VCS / (EC50_VCS + C_VCS);

double E_BEL = Emax_BEL * C_BEL / (Kd_BEL + C_BEL);

double E_ANI = Emax_ANI * C_ANI / (EC50_ANI + C_ANI);

// ── BAFF (boosted by IFN) ────────────────────────────────────────────────────

double IFN_cur = IFN_base * (1.0 - E_ANI) * (1.0 - 0.5*E_HCQ);

double BAFF = BAFF_base * (1.0 + k_IFN_BAFF * (IFN_cur - 1.0)) * (1.0 - E_BEL);

if(BAFF < 0) BAFF = 0.001;

// ── Immune complex load (proxy for IC) ──────────────────────────────────────

double IC_load = (Anti_dsDNA / Ab_baseline) * (C3_baseline / (C3 + 0.01));

// ── PK ODEs ─────────────────────────────────────────────────────────────────

// MMF/MPA

dxdt_MPA_gut = dose_MMF * F_MMF - ka_MMF * MPA_gut;

dxdt_MPA_plasma = ka_MMF * MPA_gut + ka_EHC * MPAG_gut

- (CL_MPA / V_MPA) * MPA_plasma

- (fr_MPAG * CL_MPA / V_MPA) * MPA_plasma;

dxdt_MPAG_gut = (fr_MPAG * CL_MPA / V_MPA) * MPA_plasma - ka_EHC * MPAG_gut;

// HCQ

dxdt_HCQ_blood = dose_HCQ * F_HCQ - (ka_HCQ + CL_HCQ * WT / (V_blood * WT)) * HCQ_blood

+ k21_HCQ * HCQ_tissue;

dxdt_HCQ_tissue = k12_HCQ * HCQ_blood - k21_HCQ * HCQ_tissue;

// Voclosporin

dxdt_VCS_plasma = dose_VCS * F_VCS * ka_VCS - (CL_VCS / V_VCS) * VCS_plasma;

// simplified 1-cmt for VCS

// Belimumab 2-cmt

dxdt_BEL_central = dose_BEL - (CL_BEL + Q_BEL) / V1_BEL * BEL_central

+ Q_BEL / V2_BEL * BEL_periph;

dxdt_BEL_periph = Q_BEL / V1_BEL * BEL_central - Q_BEL / V2_BEL * BEL_periph;

// Anifrolumab 2-cmt

dxdt_ANI_central = dose_ANI - (CL_ANI + Q_ANI) / V1_ANI * ANI_central

+ Q_ANI / V2_ANI * ANI_periph;

dxdt_ANI_periph = Q_ANI / V1_ANI * ANI_central - Q_ANI / V2_ANI * ANI_periph;

// ── Immune ODEs ─────────────────────────────────────────────────────────────

// B naive: BAFF-dependent survival, MPA inhibits proliferation

dxdt_B_naive = k_Bnaive_in * BAFF - k_Bnaive_deg * B_naive;

// GC B cells: Tfh-driven, MPA inhibits

dxdt_B_GC = k_GC_stim * Tfh * B_naive * (1 - E_MPA_B)

- k_GC_deg * B_GC;

// Plasma cells: from GC, very long-lived

dxdt_Plasma_cell = k_PC_diff * B_GC - k_PC_deg * Plasma_cell;

// Tfh: IFN-driven + GC BCR signal, VCS+MPA inhibit

dxdt_Tfh = k_Tfh_stim * IFN_cur * B_naive * (1 - E_MPA_T) * (1 - E_VCS)

- k_Tfh_deg * Tfh;

// Treg: GC-stabilized (VCS raises Treg through IL-2 reshaping in LN model)

dxdt_Treg = k_Treg_base * (1 + 0.3 * E_VCS) - k_Treg_deg * Treg;

// ── Anti-dsDNA antibody ──────────────────────────────────────────────────────

dxdt_Anti_dsDNA = k_Ab_prod * Plasma_cell - k_Ab_deg * Anti_dsDNA;

// ── Complement ───────────────────────────────────────────────────────────────

dxdt_C3 = k_C3_synth - k_C3_consume * IC_load * C3 - k_C3_deg * C3;

dxdt_C4 = k_C4_synth - k_C4_consume * IC_load * C4 - k_C4_deg * C4;

// ── Renal ODEs ───────────────────────────────────────────────────────────────

// Podocyte injury: driven by IC_load, C3(↓=worse), alleviated by VCS

double Pod_stim = k_pod_inj * IC_load * (C3_baseline / (C3 + 0.001));

double Pod_rep = k_pod_repair * (1 + E_VCS);

dxdt_Podocyte_inj = Pod_stim * (1 - Podocyte_inj) - Pod_rep * Podocyte_inj;

// Proteinuria (UPCR g/g): rises with podocyte injury, slow resolution

dxdt_Proteinuria = k_prot_rise * Podocyte_inj - k_prot_fall * Proteinuria * (1 - 0.5*Podocyte_inj);

// eGFR: declines with sustained injury, slow partial recovery

dxdt_eGFR_cmt = k_eGFR_rec * (eGFR_base - eGFR_cmt)

- k_eGFR_loss * Podocyte_inj * eGFR_cmt;

$TABLE

capture C_MPA = MPA_plasma / V_MPA;

capture C_HCQ_b = HCQ_blood / (V_blood * WT);

capture C_VCS = VCS_plasma / V_VCS;

capture C_BEL = BEL_central / V1_BEL;

capture C_ANI = ANI_central / V1_ANI;

capture E_MPA_B = Emax_MPA * pow(C_MPA,1.5) / (pow(EC50_MPA_B,1.5) + pow(C_MPA,1.5));

capture E_VCS = Emax_VCS * C_VCS / (EC50_VCS + C_VCS);

capture E_BEL = Emax_BEL * C_BEL / (Kd_BEL + C_BEL);

capture E_ANI = Emax_ANI * C_ANI / (EC50_ANI + C_ANI);

capture BAFF_level= BAFF_base*(1.0+k_IFN_BAFF*(IFN_base*(1.0-E_ANI)*(1.0-0.5*E_HCQ)-1.0))*(1.0-E_BEL);

capture IC_load = (Anti_dsDNA/Ab_baseline)*(C3_baseline/(C3+0.01));

capture UPCR = Proteinuria;

capture eGFR = eGFR_cmt;

capture CRRP = (Proteinuria < 0.5 && eGFR_cmt >= 60) ? 1.0 : 0.0;

capture PRRP = (Proteinuria < 1.0 && eGFR_cmt >= 60) ? 1.0 : 0.0;

## COMPILE MODEL

mod <- mcode("LupusNephritis", code)

## DOSING HELPER FUNCTIONS

# Convert daily dose to continuous infusion rate (mg/h average)

mmf_rate <- function(daily_mg) daily_mg / 24

hcq_rate <- function(daily_mg) daily_mg / 24

vcs_rate <- function(bid_mg) (2 * bid_mg) / 24 # 2× daily

bel_rate <- function(mg_per_4w) mg_per_4w / (4 * 7 * 24)

ani_rate <- function(mg_per_4w) mg_per_4w / (4 * 7 * 24)

# Periodic bolus dosing for IV agents (belimumab, anifrolumab)

make_events <- function(agent, dose_mg, interval_days, n_doses,

cmt_name, bioavail = 1) {

times <- seq(0, by = interval_days * 24, length.out = n_doses)

ev(time = times, amt = dose_mg * bioavail, cmt = cmt_name)

}

## SCENARIO 1: Standard of Care — MMF + HCQ + GC (MMF induction)

cat("=== Scenario 1: MMF + HCQ (SoC) ===\n")

params_soc <- param(mod,

dose_MMF = mmf_rate(3000), # 3 g/day MMF

dose_HCQ = hcq_rate(400), # 400 mg/day HCQ

dose_VCS = 0, dose_BEL = 0, dose_ANI = 0

)

sim1 <- mrgsim(params_soc, end = 365, delta = 1) %>% as.data.frame()

## SCENARIO 2: AURORA Regimen — MMF + HCQ + Voclosporin (triple therapy)

cat("=== Scenario 2: Voclosporin triple therapy (AURORA) ===\n")

params_aurora <- param(mod,

dose_MMF = mmf_rate(2000),

dose_HCQ = hcq_rate(400),

dose_VCS = vcs_rate(23.7), # 23.7 mg BID

dose_BEL = 0, dose_ANI = 0

)

sim2 <- mrgsim(params_aurora, end = 365, delta = 1) %>% as.data.frame()

## SCENARIO 3: BLISS-LN — MMF + HCQ + Belimumab

cat("=== Scenario 3: Belimumab add-on (BLISS-LN) ===\n")

# Belimumab 10 mg/kg IV q4w (650 mg for 65 kg patient)

ev_bel <- make_events("BEL", 650, 28, 14, "BEL_central")

params_bliss <- param(mod,

dose_MMF = mmf_rate(3000),

dose_HCQ = hcq_rate(400),

dose_VCS = 0, dose_ANI = 0,

dose_BEL = 0 # use event-based dosing

)

sim3 <- mrgsim(params_bliss, events = ev_bel, end = 365, delta = 1) %>%

as.data.frame()

## SCENARIO 4: High IFN Signature — Anifrolumab + MMF + HCQ

cat("=== Scenario 4: Anifrolumab (high IFN-sig) ===\n")

ev_ani <- make_events("ANI", 300, 28, 14, "ANI_central")

params_ani <- param(mod,

dose_MMF = mmf_rate(2000),

dose_HCQ = hcq_rate(400),

dose_VCS = 0, dose_BEL = 0,

dose_ANI = 0,

IFN_base = 3.0 # high IFN subgroup

)

sim4 <- mrgsim(params_ani, events = ev_ani, end = 365, delta = 1) %>%

as.data.frame()

## SCENARIO 5: Euro-Lupus CYC Induction → MMF Maintenance + HCQ

cat("=== Scenario 5: CYC induction (Euro-Lupus) → MMF maintenance ===\n")

# Euro-Lupus: CYC 500 mg IV q2w × 6 doses, then switch to MMF

# Simulate CYC as a transient lymphodepletion (Plasma_cell reset approach)

params_cyc_induction <- param(mod,

dose_MMF = 0,

dose_HCQ = hcq_rate(400),

dose_VCS = 0, dose_BEL = 0, dose_ANI = 0

)

# Phase 1: CYC induction (simulate via parameter override)

# Use lymphodepletion effect: CYC lowers Plasma_cell by ~70% at nadir (day ~84)

params_cyc <- param(mod,

dose_MMF = 0,

dose_HCQ = hcq_rate(400),

dose_VCS = 0, dose_BEL = 0, dose_ANI = 0,

k_PC_deg = 0.03 # CYC greatly accelerates plasma cell turnover

)

sim5_induction <- mrgsim(params_cyc, end = 84, delta = 1)

# Switch to MMF maintenance at week 24 (day 84 end of 6 doses)

init_m <- as.list(tail(as.data.frame(sim5_induction), 1)[, -c(1,2)])

init_m_clean <- init_m[names(formals(init_mod <- mod@mod))]

params_mmf_maint <- param(mod,

dose_MMF = mmf_rate(2000),

dose_HCQ = hcq_rate(400),

dose_VCS = 0, dose_BEL = 0, dose_ANI = 0

)

sim5_maint <- mrgsim(params_mmf_maint, end = 281, delta = 1,

idata = NULL) %>% as.data.frame()

sim5_maint$time <- sim5_maint$time + 84

sim5_induction_df <- as.data.frame(sim5_induction)

sim5 <- bind_rows(sim5_induction_df, sim5_maint)

## COMBINE RESULTS

results <- bind_rows(

mutate(sim1, Scenario = "SoC: MMF+HCQ"),

mutate(sim2, Scenario = "Triple: MMF+HCQ+VCS"),

mutate(sim3, Scenario = "BEL: MMF+HCQ+Belimumab"),

mutate(sim4, Scenario = "ANI: MMF+HCQ+Anifrolumab"),

mutate(sim5, Scenario = "CYC→MMF (Euro-Lupus)")

)

## PLOTS

theme_set(theme_bw(base_size = 12))

pal <- c("#2196F3","#4CAF50","#FF5722","#9C27B0","#FF9800")

## Figure 1: Proteinuria (UPCR) over 52 weeks

p1 <- ggplot(results, aes(time / 7, UPCR, color = Scenario)) +

geom_line(linewidth = 1.1) +

geom_hline(yintercept = c(0.5, 1.0), linetype = "dashed", color = "grey50") +

annotate("text", x = 53, y = 0.45, label = "CRR (<0.5)", size = 3) +

annotate("text", x = 53, y = 0.95, label = "PRR (<1.0)", size = 3) +

scale_color_manual(values = pal) +

scale_x_continuous(breaks = seq(0, 52, 4)) +

labs(title = "Proteinuria (UPCR) — 5 Treatment Scenarios",

x = "Week", y = "UPCR (g/g)", color = NULL) +

theme(legend.position = "bottom")

## Figure 2: eGFR

p2 <- ggplot(results, aes(time / 7, eGFR, color = Scenario)) +

geom_line(linewidth = 1.1) +

geom_hline(yintercept = 60, linetype = "dashed", color = "grey50") +

scale_color_manual(values = pal) +

scale_x_continuous(breaks = seq(0, 52, 4)) +

labs(title = "eGFR Trajectory Over 52 Weeks",

x = "Week", y = "eGFR (mL/min/1.73m²)", color = NULL) +

theme(legend.position = "bottom")

## Figure 3: Anti-dsDNA antibody

p3 <- ggplot(results, aes(time / 7, Anti_dsDNA, color = Scenario)) +

geom_line(linewidth = 1.1) +

scale_color_manual(values = pal) +

labs(title = "Anti-dsDNA Antibody Level",

x = "Week", y = "Anti-dsDNA (IU/mL)", color = NULL) +

theme(legend.position = "bottom")

## Figure 4: Complement C3

p4 <- ggplot(results, aes(time / 7, C3, color = Scenario)) +

geom_line(linewidth = 1.1) +

geom_hline(yintercept = 0.9, linetype = "dashed", color = "grey50") +

annotate("text", x = 2, y = 0.92, label = "Normal C3 lower limit", size = 3) +

scale_color_manual(values = pal) +

labs(title = "Complement C3 Recovery",

x = "Week", y = "C3 (g/L)", color = NULL) +

theme(legend.position = "bottom")

## Figure 5: Complete Renal Response rate at Week 52

wk52 <- results %>%

filter(abs(time - 364) < 1) %>%

group_by(Scenario) %>%

summarise(CRRP_rate = mean(CRRP), PRRP_rate = mean(PRRP))

p5 <- ggplot(wk52 %>%

pivot_longer(c(CRRP_rate, PRRP_rate), names_to = "Endpoint", values_to = "Rate"),

aes(Scenario, Rate * 100, fill = Endpoint)) +

geom_col(position = "dodge") +

scale_fill_manual(values = c("#1565c0","#42a5f5"),

labels = c("CRR (UPCR<0.5+eGFR≥60)", "PRR (UPCR<1.0+eGFR≥60)")) +

labs(title = "Renal Response Rates at Week 52",

x = NULL, y = "Response Rate (%)", fill = NULL) +

theme(axis.text.x = element_text(angle = 25, hjust = 1),

legend.position = "top")

print(p1)

print(p2)

print(p3)

print(p4)

print(p5)

## CLINICAL SUMMARY TABLE

cat("\n=== Week-52 Clinical Summary ===\n")

summary_tbl <- results %>%

filter(abs(time - 364) < 1) %>%

select(Scenario, UPCR, eGFR, Anti_dsDNA, C3, C4, CRRP, PRRP) %>%

mutate(

`UPCR (g/g)` = round(UPCR, 2),

`eGFR (mL/min)` = round(eGFR, 1),

`Anti-dsDNA (IU/mL)` = round(Anti_dsDNA, 0),

`C3 (g/L)` = round(C3, 3),

`C4 (g/L)` = round(C4, 3),

`CRR (%)` = CRRP * 100,

`PRR (%)` = PRRP * 100

) %>%

select(Scenario, `UPCR (g/g)`, `eGFR (mL/min)`, `Anti-dsDNA (IU/mL)`,

`C3 (g/L)`, `C4 (g/L)`, `CRR (%)`, `PRR (%)`)

print(summary_tbl, n = 20)

## PARAMETER SENSITIVITY ANALYSIS

cat("\n=== Sensitivity: MMF dose on Week-52 UPCR ===\n")

mmf_doses <- c(500, 1000, 1500, 2000, 2500, 3000)

sens_results <- lapply(mmf_doses, function(d) {

p <- param(mod, dose_MMF = mmf_rate(d), dose_HCQ = hcq_rate(400))

s <- mrgsim(p, end = 365, delta = 1) %>% as.data.frame()

s$MMF_dose_g <- d / 1000

}) %>% bind_rows()

p_sens <- sens_results %>%

filter(abs(time - 364) < 1) %>%

ggplot(aes(MMF_dose_g, UPCR)) +

geom_line(linewidth = 1.2, color = "#1565c0") +

geom_point(size = 3, color = "#1565c0") +

geom_hline(yintercept = 0.5, linetype = "dashed") +

labs(title = "Dose-Response: MMF Daily Dose vs Week-52 UPCR",

x = "MMF Dose (g/day)", y = "UPCR at Week 52 (g/g)")

print(p_sens)

cat("\nLupus Nephritis QSP model simulation complete.\n")

cat("Key references: AURORA (Rovin 2021), BLISS-LN (Furie 2020),\n")

cat(" ACCESS (Appel 2009), AURA-LV (Mysler 2020)\n")

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