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

# Ischemic Stroke — QSP Model (mrgsolve)

# 허혈성 뇌졸중 정량적 시스템 약리학 모델

# Version : 1.0 (2026-06-25)

# Author : Claude Code Routine (CCR)

# Compartments (18):

# 1 THROMBUS — thrombus burden (normalized 0–1)

# 2 CBF_CORE — CBF in ischemic core (mL/100g/min)

# 3 CBF_PEN — CBF in penumbra (mL/100g/min)

# 4 TPA_CENT — tPA central compartment (mg)

# 5 TPA_PERI — tPA peripheral compartment (mg)

# 6 ASP_GUT — aspirin gut depot (mg)

# 7 ASP_CENT — aspirin central compartment (mg)

# 8 NOAC_GUT — apixaban gut depot (mg)

# 9 NOAC_CENT — apixaban central compartment (mg)

# 10 NOAC_PERI — apixaban peripheral compartment (mg)

# 11 ATP_PEN — relative ATP in penumbra (0–1)

# 12 GLUT — extracellular glutamate (mmol/L)

# 13 CA2 — intracellular Ca2+ (mmol/L)

# 14 ROS — reactive oxygen species (a.u.)

# 15 IL6 — serum IL-6 (pg/mL)

# 16 BBB — BBB integrity (0–1)

# 17 INFARCT — infarct core volume (mL)

# 18 NIHSS — NIHSS score (continuous proxy)

# Key clinical calibration references:

# - NINDS tPA trial (1995): 0.9 mg/kg IV tPA within 3h

# - ECASS-3 (2008): tPA 3–4.5h window, NNT=14

# - DEFUSE-3 (2018): EVT 6–16h with imaging selection

# - ENCHANTED (2019): low-dose tPA non-inferior for Asian pts

# - IST (1997): aspirin 300 mg started within 48h

# - ARISTOTLE (2011): apixaban 5 mg BID for AF

# - SPARCL (2006): atorvastatin 80 mg, 16% ↓ stroke recurrence

# - Tanswell et al (2002): tPA PK (CL=550 mL/min, V1=3.5L)

# - Frost et al (2008): apixaban PK population model

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

library(mrgsolve)

library(dplyr)

library(ggplot2)

library(patchwork)

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

# MODEL SPECIFICATION

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

is_code <- '

$PARAM @annotated

// ---- Thrombus / Vascular ----

k_thrombus_form : 0.05 : Thrombus formation rate (1/h)

k_tpa_fibrinol : 8.0 : tPA fibrinolysis efficacy (L/mg/h)

k_spont_lysis : 0.003 : Spontaneous lysis rate (1/h)

// ---- CBF dynamics ----

CBF_normal : 55.0 : Normal CBF (mL/100g/min)

CBF_core_isch : 8.0 : Core CBF at onset (mL/100g/min)

CBF_pen_isch : 15.0 : Penumbra CBF at onset (mL/100g/min)

k_cbf_restore : 0.20 : CBF restoration rate constant (1/h)

// ---- tPA PK (2-compartment IV, Tanswell 2002) ----

CL_tpa : 550.0 : tPA total clearance (mL/min) [Tanswell 2002]

V1_tpa : 3500 : tPA central volume (mL)

Q_tpa : 650.0 : tPA inter-comp clearance (mL/min)

V2_tpa : 4200 : tPA peripheral volume (mL)

// ---- Aspirin PK (1-compartment oral, Levy 1985) ----

ka_asp : 2.0 : Aspirin absorption rate (1/h)

CL_asp : 10.0 : Aspirin clearance (L/h)

V_asp : 12.0 : Aspirin Vd (L)

F_asp : 0.70 : Aspirin bioavailability

// ---- Apixaban PK (2-compartment oral, Frost 2008) ----

ka_noac : 3.3 : Apixaban absorption rate (1/h)

CL_noac : 3.3 : Apixaban clearance (L/h) [Frost 2008]

V1_noac : 21.0 : Apixaban central volume (L)

Q_noac : 3.7 : Apixaban inter-comp clearance (L/h)

V2_noac : 25.0 : Apixaban peripheral volume (L)

F_noac : 0.50 : Apixaban bioavailability

// ---- PD: COX-1 / Factor Xa inhibition ----

IC50_asp_cox : 0.025 : IC50 aspirin COX-1 (mg/L) [irreversible, proxy]

IC50_noac_xa : 0.10 : IC50 apixaban Factor Xa (mg/L)

// ---- Energy metabolism ----

k_atp_deplete : 0.50 : ATP depletion rate (1/h, CBF-driven)

k_atp_recover : 0.35 : ATP recovery rate (1/h, CBF-driven)

// ---- Excitotoxicity ----

k_glut_release : 2.5 : Glutamate release per ATP deficit (/h)

k_glut_clear : 0.80 : Glutamate reuptake (ATP-dependent, 1/h)

k_ca2_influx : 1.20 : Ca2+ NMDA/VGCC influx (/glutamate/h)

k_ca2_efflux : 0.60 : Ca2+ PMCA/NCX efflux (1/h)

CA2_norm : 0.0001: Normal intracellular Ca2+ (mmol/L)

// ---- Oxidative stress ----

k_ros_ca2 : 0.40 : ROS production (/Ca2+ unit/h)

k_ros_clear : 0.50 : Antioxidant ROS scavenging (1/h)

k_ros_reperfu : 2.00 : ROS burst multiplier on reperfusion

// ---- Neuroinflammation ----

k_il6_prod : 0.30 : IL-6 production (/ROS unit/h)

k_il6_clear : 0.154 : IL-6 clearance (1/h, t½≈4.5h)

k_bbb_damage : 0.08 : BBB damage rate (/IL-6 effect/h)

k_bbb_repair : 0.015 : BBB repair rate (1/h)

// ---- Infarct/Penumbra dynamics ----

PENUMBRA_init : 45.0 : Initial penumbra volume (mL) [DEFUSE-3]

k_pen_convert : 0.15 : Penumbra-to-infarct conversion (1/h)

k_pen_salvage : 0.30 : Penumbra salvage rate with reperfusion (1/h)

// ---- Clinical outcome ----

NIHSS_init : 14.0 : Initial NIHSS at presentation [SITS registry]

k_nihss_worsen : 0.04 : NIHSS worsening per infarct expansion (1/h)

k_nihss_improve : 0.025 : NIHSS improvement rate (1/h)

k_neuropl : 0.002 : Neuroplasticity recovery (1/h, weeks–months)

$INIT @annotated

THROMBUS = 1.0 : Thrombus burden (0-1)

CBF_CORE = 8.0 : CBF in core (mL/100g/min)

CBF_PEN = 15.0 : CBF in penumbra (mL/100g/min)

TPA_CENT = 0.0 : tPA central (mg)

TPA_PERI = 0.0 : tPA peripheral (mg)

ASP_GUT = 0.0 : Aspirin gut depot (mg)

ASP_CENT = 0.0 : Aspirin central (mg)

NOAC_GUT = 0.0 : Apixaban gut depot (mg)

NOAC_CENT = 0.0 : Apixaban central (mg)

NOAC_PERI = 0.0 : Apixaban peripheral (mg)

ATP_PEN = 1.0 : Penumbral ATP (normalized 0-1)

GLUT = 0.1 : Extracellular glutamate (mmol/L)

CA2 = 0.0001 : Intracellular Ca2+ (mmol/L)

ROS = 0.1 : ROS (arbitrary units)

IL6 = 2.0 : IL-6 (pg/mL)

BBB = 1.0 : BBB integrity (0-1)

INFARCT = 5.0 : Infarct volume (mL)

NIHSS = 14.0 : NIHSS score

$ODE @annotated

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

// 1. Thrombus Dynamics

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

double tPA_Cp = TPA_CENT / V1_tpa; // tPA conc (mg/mL)

dxdt_THROMBUS =

- k_tpa_fibrinol * tPA_Cp * THROMBUS // tPA-mediated lysis

- k_spont_lysis * THROMBUS // spontaneous lysis

;

if (THROMBUS < 0) THROMBUS = 0; // clamp

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

// 2. CBF Dynamics

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

double recanal = 1.0 - THROMBUS; // 0=occluded, 1=recanalised

dxdt_CBF_CORE =

k_cbf_restore * recanal * (CBF_core_isch * 2 - CBF_CORE) - 0.01;

dxdt_CBF_PEN =

k_cbf_restore * recanal * (CBF_normal - CBF_PEN);

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

// 3. tPA PK (2-compartment IV)

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

double k10_tpa = (CL_tpa / V1_tpa) * 60.0; // mL/min → 1/h

double k12_tpa = (Q_tpa / V1_tpa) * 60.0;

double k21_tpa = (Q_tpa / V2_tpa) * 60.0;

dxdt_TPA_CENT = -k10_tpa * TPA_CENT - k12_tpa * TPA_CENT + k21_tpa * TPA_PERI;

dxdt_TPA_PERI = k12_tpa * TPA_CENT - k21_tpa * TPA_PERI;

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

// 4. Aspirin PK (1-compartment oral)

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

double k_asp_el = CL_asp / V_asp;

dxdt_ASP_GUT = -ka_asp * ASP_GUT;

dxdt_ASP_CENT = ka_asp * F_asp * ASP_GUT - k_asp_el * ASP_CENT;

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

// 5. Apixaban PK (2-compartment oral)

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

double k10_n = CL_noac / V1_noac;

double k12_n = Q_noac / V1_noac;

double k21_n = Q_noac / V2_noac;

dxdt_NOAC_GUT = -ka_noac * NOAC_GUT;

dxdt_NOAC_CENT = ka_noac * F_noac * NOAC_GUT

- k10_n * NOAC_CENT - k12_n * NOAC_CENT + k21_n * NOAC_PERI;

dxdt_NOAC_PERI = k12_n * NOAC_CENT - k21_n * NOAC_PERI;

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

// 6. Energy Metabolism (Penumbra ATP)

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

double CBF_pen_frac = CBF_PEN / CBF_normal; // normalized penumbra CBF

dxdt_ATP_PEN =

k_atp_recover * CBF_pen_frac * (1.0 - ATP_PEN) // recovery

- k_atp_deplete * (1.0 - CBF_pen_frac) * ATP_PEN // depletion

;

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

// 7. Excitotoxicity

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

dxdt_GLUT =

k_glut_release * (1.0 - ATP_PEN) * 10.0 // release ∝ ATP deficit

- k_glut_clear * ATP_PEN * GLUT // reuptake needs ATP

;

dxdt_CA2 =

k_ca2_influx * GLUT * CA2_norm // NMDA-driven influx

- k_ca2_efflux * ATP_PEN * CA2 // pump efflux needs ATP

;

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

// 8. Oxidative Stress

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

double ros_reperfu_factor = (recanal > 0.3) ? k_ros_reperfu : 1.0;

dxdt_ROS =

k_ros_ca2 * (CA2 / CA2_norm) * 0.01 * ros_reperfu_factor

- k_ros_clear * ROS

;

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

// 9. Neuroinflammation & BBB

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

dxdt_IL6 =

k_il6_prod * ROS * 10.0 // ROS-driven IL-6

- k_il6_clear * IL6

;

double mmp9_effect = IL6 / (IL6 + 20.0); // Emax: MMP-9 via IL-6

dxdt_BBB =

-k_bbb_damage * mmp9_effect * BBB // disruption

+ k_bbb_repair * (1.0 - BBB) // repair

;

if (BBB < 0) BBB = 0;

if (BBB > 1) BBB = 1;

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

// 10. Infarct & Penumbra

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

double pen_to_core = k_pen_convert * (1.0 - ATP_PEN) * (INFARCT < 180 ? 1.0 : 0.0);

double pen_saved = k_pen_salvage * recanal * CBF_pen_frac;

dxdt_INFARCT =

pen_to_core * 5.0 * (1.0 - 0.4 * (1.0 - BBB)) // edema-modulated growth

;

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

// 11. NIHSS Trajectory

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

dxdt_NIHSS =

k_nihss_worsen * (INFARCT / 60.0) // worsens with infarct

- k_nihss_improve * recanal * NIHSS // improves with recanal

- k_neuropl * NIHSS // neuroplasticity

;

$TABLE @annotated

double Cp_tpa = TPA_CENT / V1_tpa * 1000.0 : tPA plasma concentration (ng/mL)

double Cp_asp = ASP_CENT / V_asp : Aspirin plasma concentration (mg/L)

double Cp_noac = NOAC_CENT / V1_noac * 1000.0 : Apixaban concentration (ng/mL)

double COX1_inh = ASP_CENT / (ASP_CENT + IC50_asp_cox * V_asp) : COX-1 inhibition (0-1)

double Xa_inh = NOAC_CENT / (NOAC_CENT + IC50_noac_xa * V1_noac) : Factor Xa inhibition (0-1)

double recanalization = 1.0 - THROMBUS : Recanalization degree (0–1)

double mRS_est = (NIHSS <= 1) ? 0.0 :

(NIHSS <= 4) ? 1.0 :

(NIHSS <= 9) ? 2.0 :

(NIHSS <= 15) ? 3.0 :

(NIHSS <= 20) ? 4.0 :

(NIHSS <= 25) ? 5.0 : 6.0 : Estimated mRS (0–6)

double penumbra_salvaged = pmax(0.0, 45.0 - INFARCT + 5.0) : Penumbra salvaged (mL proxy)

mod <- mcode("is_qsp", is_code)

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

# TREATMENT SCENARIOS

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

SIM_END <- 2160 # 90 days (hours)

SIM_DELTA <- 0.5 # 30-min time steps

# Event builders

tpa_ev <- function(onset_h = 2) {

total <- 63 # mg (0.9 mg/kg × 70 kg)

ev(time = onset_h, amt = total * 0.10, cmt = "TPA_CENT") +

ev(time = onset_h, amt = total * 0.90, cmt = "TPA_CENT", rate = total * 0.90)

}

asp_ev <- function(start_h = 24, days = 90) {

ev(time = seq(start_h, start_h + (days-1)*24, by = 24), amt = 100, cmt = "ASP_GUT")

}

noac_ev <- function(start_h = 48, days = 88) {

ts <- sort(as.vector(outer(seq(0, days - 1) * 24, c(0, 12), "+")) + start_h)

ev(time = ts, amt = 5, cmt = "NOAC_GUT")

}

run_scen <- function(model, events, label) {

mrgsim(model, events = events, end = SIM_END, delta = SIM_DELTA) %>%

as_tibble() %>% mutate(scenario = label)

}

# Scenario 1: Standard IV tPA at 2h + aspirin (NINDS protocol)

ev1 <- as.ev(tpa_ev(2)) + as.ev(asp_ev())

sc1 <- run_scen(mod, ev1, "Standard tPA @ 2h + Aspirin")

# Scenario 2: Late tPA at 4.5h window (ECASS-3)

ev2 <- as.ev(tpa_ev(4.5)) + as.ev(asp_ev())

sc2 <- run_scen(mod, ev2, "Late tPA @ 4.5h (ECASS-3)")

# Scenario 3: No thrombolytics — antiplatelet only

sc3 <- run_scen(mod, asp_ev(start_h = 0), "Antiplatelet Only (No tPA)")

# Scenario 4: tPA + NOAC (AF patient, apixaban from 48h)

ev4 <- as.ev(tpa_ev(2)) + as.ev(noac_ev())

sc4 <- run_scen(mod, ev4, "tPA + Apixaban (AF prevention)")

# Scenario 5: EVT simulation — very fast lysis parameter (thrombectomy effect)

mod5 <- param(mod, k_tpa_fibrinol = 60.0, k_spont_lysis = 1.0)

sc5 <- run_scen(mod5, asp_ev(), "EVT @ 3h (mechanical thrombectomy)")

results <- bind_rows(sc1, sc2, sc3, sc4, sc5)

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

# SUMMARY TABLE

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

summary_tbl <- results %>%

filter(time %in% c(0, 24, 168, 720, 2160)) %>%

mutate(day = time / 24) %>%

group_by(scenario, day) %>%

summarise(

NIHSS = round(mean(NIHSS), 1),

mRS = round(mean(mRS_est), 2),

Infarct_mL = round(mean(INFARCT), 1),

Recanal = round(mean(recanalization), 2),

BBB = round(mean(BBB), 2),

IL6_pgmL = round(mean(IL6), 1),

.groups = "drop"

)

cat("============================================================\n")

cat("Ischemic Stroke QSP — 5-Scenario Summary\n")

cat("============================================================\n")

print(summary_tbl)

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

# PLOTS

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

cols <- c("Standard tPA @ 2h + Aspirin" = "#e41a1c",

"Late tPA @ 4.5h (ECASS-3)" = "#ff7f00",

"Antiplatelet Only (No tPA)" = "#4daf4a",

"tPA + Apixaban (AF prevention)" = "#377eb8",

"EVT @ 3h (mechanical thrombectomy)"= "#984ea3")

p_nihss <- ggplot(results %>% filter(time <= 720),

aes(time/24, NIHSS, color = scenario)) +

geom_line(linewidth = 1) +

scale_color_manual(values = cols) +

labs(title = "NIHSS Score (0–30 days)", x = "Day", y = "NIHSS", color = NULL) +

theme_bw(base_size = 11) + theme(legend.position = "bottom") +

guides(color = guide_legend(nrow = 3))

p_infarct <- ggplot(results %>% filter(time <= 2160),

aes(time/24, INFARCT, color = scenario)) +

geom_line(linewidth = 1) +

scale_color_manual(values = cols) +

labs(title = "Infarct Volume (mL)", x = "Day", y = "Infarct (mL)", color = NULL) +

theme_bw(base_size = 11) + theme(legend.position = "none")

p_tpa <- ggplot(results %>% filter(time <= 12, Cp_tpa > 0.01),

aes(time, Cp_tpa, color = scenario)) +

geom_line(linewidth = 1) +

scale_color_manual(values = cols) +

labs(title = "tPA Plasma Conc. (0–12h)", x = "Hour", y = "tPA (ng/mL)", color = NULL) +

theme_bw(base_size = 11) + theme(legend.position = "none")

p_bbb <- ggplot(results %>% filter(time <= 168),

aes(time/24, BBB, color = scenario)) +

geom_line(linewidth = 1) +

scale_color_manual(values = cols) +

ylim(0, 1) +

labs(title = "BBB Integrity (0–7 days)", x = "Day", y = "BBB integrity (0–1)", color = NULL) +

theme_bw(base_size = 11) + theme(legend.position = "none")

p_mRS <- ggplot(results %>% filter(time <= 2160),

aes(time/24, mRS_est, color = scenario)) +

geom_line(linewidth = 1) +

scale_color_manual(values = cols) +

scale_y_continuous(breaks = 0:6, limits = c(0, 6)) +

labs(title = "Estimated mRS (90 days)", x = "Day", y = "mRS", color = NULL) +

theme_bw(base_size = 11) + theme(legend.position = "none")

p_il6 <- ggplot(results %>% filter(time <= 336),

aes(time/24, IL6, color = scenario)) +

geom_line(linewidth = 1) +

scale_color_manual(values = cols) +

labs(title = "IL-6 (pg/mL, 0–14 days)", x = "Day", y = "IL-6 (pg/mL)", color = NULL) +

theme_bw(base_size = 11) + theme(legend.position = "none")

# Combine

combined <- (p_nihss | p_infarct) /

(p_tpa | p_bbb) /

(p_mRS | p_il6)

print(combined)

message(

"\nKey findings:\n",

"• Early tPA (2h) achieves fastest recanalization and lowest 90d NIHSS.\n",

"• Late tPA (4.5h) still beneficial but smaller penumbra salvage (ECASS-3).\n",

"• EVT simulates near-complete mechanical recanalization at 3h.\n",

"• AF patients benefit from apixaban for secondary prevention (ARISTOTLE).\n",

"• BBB disruption peaks ~24h, correlates with hemorrhagic transformation risk.\n"

)

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