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

## Sepsis & Septic Shock — QSP mrgsolve Model

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

## Disease : Sepsis / Septic Shock (Gram-negative bacteremia prototype)

## Framework : mrgsolve ODE (R)

## Compartments: 24 ODE compartments

## Scenarios : 7 treatment scenarios

## References : Singer 2016 (Sepsis-3), Rivers 2001 (EGDT), ADRENAL 2018,

## REMAP-CAP 2021, ATTACC/ACTIV 2021, Kumar 2006 (antibiotic timing)

## Author : Claude Code Routine (CCR) — 2026-06-24

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

library(mrgsolve)

library(dplyr)

library(ggplot2)

library(tidyr)

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

## MODEL DEFINITION

code <- '

$PROB

Sepsis & Septic Shock QSP Model

24-compartment ODE model integrating:

- Bacterial PK dynamics (pathogen burden)

- 2-cmpt antibiotic PK (meropenem prototype)

- Cytokine cascade: TNFalpha, IL6, IL10, IL1beta

- Innate immune: Neutrophils (blood/tissue), Macrophages

- Complement effector (C5a proxy)

- Coagulation: Thrombin, Fibrin, PAI1

- Endothelial damage index

- 6-domain SOFA (Lung, Renal, Liver, CNS, Cardio, Coag)

- Vasopressor (norepinephrine) PK/PD

- Corticosteroid (hydrocortisone) PK/PD

- IL-6R inhibitor (tocilizumab) PK/PD

- Lactate & Metabolic stress

$PARAM

// ── Bacterial dynamics ────────────────────────────────────────────────────────

kgrow = 1.2 // bacterial growth rate (1/h), ~doubling 35 min

kdeath0 = 0.05 // spontaneous bacterial death (1/h)

Bmax = 1e8 // maximum bacterial load (CFU/mL proxy)

B0 = 1e5 // initial inoculum (CFU/mL)

// ── Antibiotic PK (meropenem prototype, 1g q8h) ────────────────────────────

CL_abx = 10.0 // clearance (L/h)

V1_abx = 15.0 // central volume (L)

V2_abx = 20.0 // peripheral volume (L)

Q_abx = 8.0 // intercompartmental CL (L/h)

MIC = 0.5 // minimum inhibitory concentration (mg/L)

Emax_abx = 0.95 // maximum kill rate fraction

EC50_abx = 2.0 // EC50 for kill effect (mg/L above MIC)

kmax_abx = 5.0 // maximum antibiotic kill rate (1/h)

// ── Cytokine parameters ────────────────────────────────────────────────────

// TNFalpha

kprod_TNF = 0.8 // production (ng/mL/h stimulated)

kdeg_TNF = 0.6 // degradation (1/h, t1/2 ~70 min)

EC50_TNF = 1e4 // bacteria CFU for half-max TNF induction

kAmp_TNF = 0.3 // TNF autocrine amplification

TNF0 = 0.02 // baseline TNF (ng/mL)

// IL-6

kprod_IL6 = 1.2

kdeg_IL6 = 0.15 // t1/2 ~4.6 h

EC50_IL6 = 50.0 // TNF for IL-6 induction

IL6_0 = 0.01

// IL-10 (anti-inflammatory)

kprod_IL10 = 0.5

kdeg_IL10 = 0.2

EC50_IL10 = 5.0 // TNF for IL-10 induction

IL10_0 = 0.02

// IL-1beta

kprod_IL1b = 0.6

kdeg_IL1b = 0.8 // t1/2 ~50 min

EC50_IL1b = 2e4

IL1b_0 = 0.01

// ── Neutrophils ────────────────────────────────────────────────────────────

Neut_blood0 = 5000 // baseline circulating neutrophils (cells/uL)

krecruit_N = 0.4 // recruitment rate to tissue

kmarg_N = 0.2 // margination from blood to tissue

krestore_N = 0.3 // restoration toward baseline

kprod_N = 200 // bone marrow output (cells/uL/h)

kdeath_N = 0.08 // tissue neutrophil death

// Macrophages

Mac0 = 100 // baseline activated macrophages (arbitrary)

kact_Mac = 0.5 // LPS/cytokine activation rate

kdact_Mac = 0.1 // deactivation rate

kprod_Mac = 10 // monocyte-derived production

// ── Complement (C5a effector) ──────────────────────────────────────────────

kprod_C5a = 0.3

kdeg_C5a = 1.2 // rapid half-life (~10 min half-life)

C5a_0 = 0.1

// ── Coagulation ────────────────────────────────────────────────────────────

kprod_Thr = 0.4 // thrombin generation rate

kdeg_Thr = 0.5

kprod_Fib = 0.2 // fibrin deposition

kdeg_Fib = 0.1

kprod_PAI = 0.3 // PAI-1 production

kdeg_PAI = 0.2

Thrombin0 = 1.0

Fibrin0 = 1.0

PAI1_0 = 1.0

// ── Endothelial damage ─────────────────────────────────────────────────────

kdam_End = 0.15 // endothelial damage rate (cytokine-driven)

krep_End = 0.05 // endothelial repair rate

Endot0 = 0.0 // initial damage (0 = intact)

// ── SOFA sub-scores dynamics ───────────────────────────────────────────────

// Lung (PaO2/FiO2 proxy): baseline 400 mmHg

PF_base = 400

kdam_lung = 0.02

krep_lung = 0.01

// Renal (Creatinine): baseline 0.9 mg/dL

Cr_base = 0.9

kprod_Cr = 0.05

kclr_Cr = 0.04

// Bilirubin: baseline 0.5 mg/dL

Bil_base = 0.5

kprod_Bil = 0.03

kclr_Bil = 0.04

// Lactate (mmol/L): baseline 1.0

Lac_base = 1.0

kprod_Lac = 0.08

kclr_Lac = 0.12

// MAP (mmHg): baseline 90

MAP_base = 90

kdam_MAP = 0.25 // cytokine-driven vasodilation

krep_MAP = 0.15 // autoregulatory recovery

// Platelet (×10^9/L): baseline 250

Plt_base = 250

kcons_Plt = 0.04 // consumptive drop (DIC)

kregen_Plt= 0.02 // megakaryocyte regeneration

// ── Vasopressor PK (norepinephrine, mcg/kg/min → simplified PK) ───────────

CL_NE = 120.0 // clearance (L/h) — very rapid

V1_NE = 18.0 // volume (L)

Emax_NE = 30.0 // max MAP increase (mmHg)

EC50_NE = 0.05 // plasma conc for half-max (mcg/mL equiv)

// ── Corticosteroid PK/PD (hydrocortisone 200 mg/day = 8.33 mg/h) ──────────

CL_HC = 25.0 // clearance (L/h)

V1_HC = 40.0 // volume (L)

Emax_HC = 0.65 // max cytokine suppression (fraction)

EC50_HC = 200.0 // conc for half-max (ng/mL)

// ── IL-6R inhibitor PK (tocilizumab 8 mg/kg IV) ───────────────────────────

CL_Toci = 0.28 // clearance (L/h)

V1_Toci = 4.2 // volume (L)

Emax_Toci = 0.90

EC50_Toci = 1.5 // mcg/mL

// ── Treatment switches (0 = off, 1 = on) ──────────────────────────────────

useAbx = 0

useNE = 0

useHC = 0

useToci = 0

useFluid = 0

// ── Fluid resuscitation (MAP boost, L in first 3h) ─────────────────────────

FluidBoost = 0.0 // L given (activates early MAP restoration)

$CMT

// Bacterial burden

BACT

// Antibiotic PK

ABX1 // central compartment (mg)

ABX2 // peripheral compartment (mg)

// Cytokines (ng/mL)

TNF

IL6

IL10

IL1B

// Immune cells

NEUT_B // blood neutrophils (cells/uL)

NEUT_T // tissue neutrophils

MACS // activated macrophages

// Complement

C5A

// Coagulation

THROMBIN

FIBRIN

PAI1

// Endothelial damage index (0–1)

ENDOT

// Organ function endpoints

PF_RATIO // PaO2/FiO2 (mmHg)

CREATININE // mg/dL

BILIRUBIN // mg/dL

LACTATE // mmol/L

MAP_val // mmHg

PLT_COUNT // ×10^9/L

// Vasopressor plasma (mcg/mL equiv)

NE_C

// Corticosteroid plasma (ng/mL)

HC_C

// Tocilizumab plasma (mcg/mL)

TOCI_C

$INIT

BACT = 1e5

ABX1 = 0

ABX2 = 0

TNF = 0.02

IL6 = 0.01

IL10 = 0.02

IL1B = 0.01

NEUT_B = 5000

NEUT_T = 200

MACS = 10

C5A = 0.1

THROMBIN = 1.0

FIBRIN = 1.0

PAI1 = 1.0

ENDOT = 0.0

PF_RATIO = 400

CREATININE= 0.9

BILIRUBIN = 0.5

LACTATE = 1.0

MAP_val = 90.0

PLT_COUNT = 250.0

NE_C = 0.0

HC_C = 0.0

TOCI_C = 0.0

$MAIN

// ── Antibiotic concentration (mg/L) ──────────────────────────────────────

double Cp_abx = ABX1 / V1_abx;

// Antibiotic kill: sigmoidal Emax above MIC

double dC_abx = (Cp_abx > MIC) ? (Cp_abx - MIC) : 0.0;

double Ekill = kmax_abx * pow(dC_abx, 2.0) / (pow(EC50_abx, 2.0) + pow(dC_abx, 2.0));

// ── IL-10 inhibition of pro-inflammatory cytokines ─────────────────────────

double Inh_IL10 = 1.0 / (1.0 + IL10 / 5.0); // Hill inhibition

// ── Hydrocortisone effect ──────────────────────────────────────────────────

double E_HC = Emax_HC * HC_C / (EC50_HC + HC_C);

// ── Tocilizumab effect on IL-6 signaling ──────────────────────────────────

double E_Toci = Emax_Toci * TOCI_C / (EC50_Toci + TOCI_C);

// ── Vasopressor MAP effect ──────────────────────────────────────────────────

double E_NE = Emax_NE * NE_C / (EC50_NE + NE_C);

// ── Combined cytokine suppression (HC + IL-10) ────────────────────────────

double Inh_combined = (1.0 - E_HC) * Inh_IL10;

// ── Bacterial driven NF-kB signal ────────────────────────────────────────

double NFkB_signal = BACT / (BACT + 1e5);

// ── Cytokine inflammation index (drives organ damage) ─────────────────────

double CytokineIndex = (TNF / 10.0 + IL6 / 200.0 + IL1B / 5.0) / 3.0;

double CI_norm = CytokineIndex / (1.0 + CytokineIndex);

$ODE

// ─── BACTERIAL DYNAMICS ─────────────────────────────────────────────────────

double BactLogistic = kgrow * BACT * (1.0 - BACT / Bmax);

double BactPhago = 0.002 * NEUT_T * BACT / (BACT + 1e4); // neutrophil kill

double BactAbxKill = useAbx * Ekill * BACT;

dxdt_BACT = BactLogistic - kdeath0 * BACT - BactPhago - BactAbxKill;

if (BACT < 1.0) dxdt_BACT = -BACT; // floor

// ─── ANTIBIOTIC PK ──────────────────────────────────────────────────────────

// Dosing handled via ADDL/II in event table

dxdt_ABX1 = -CL_abx * Cp_abx - Q_abx * (ABX1/V1_abx - ABX2/V2_abx);

dxdt_ABX2 = Q_abx * (ABX1/V1_abx - ABX2/V2_abx);

// ─── CYTOKINES ───────────────────────────────────────────────────────────────

// TNFalpha

double Stim_TNF = kprod_TNF * NFkB_signal * Inh_combined

+ kAmp_TNF * TNF * Inh_combined;

dxdt_TNF = Stim_TNF - kdeg_TNF * (TNF - TNF0);

if (TNF < 0) dxdt_TNF = 0;

// IL-6

double Stim_IL6 = kprod_IL6 * TNF / (EC50_IL6 + TNF) * Inh_combined * (1.0 - E_Toci);

dxdt_IL6 = Stim_IL6 - kdeg_IL6 * (IL6 - IL6_0);

if (IL6 < 0) dxdt_IL6 = 0;

// IL-10 (anti-inflammatory, induced by TNF and macrophages)

double Stim_IL10 = kprod_IL10 * TNF / (EC50_IL10 + TNF);

dxdt_IL10 = Stim_IL10 - kdeg_IL10 * (IL10 - IL10_0);

if (IL10 < 0) dxdt_IL10 = 0;

// IL-1beta

double Stim_IL1B = kprod_IL1b * NFkB_signal * Inh_combined;

dxdt_IL1B = Stim_IL1B - kdeg_IL1b * (IL1B - IL1b_0);

if (IL1B < 0) dxdt_IL1B = 0;

// ─── INNATE IMMUNE CELLS ────────────────────────────────────────────────────

// Blood neutrophils (recruitment to tissue driven by IL-8 proxy = IL6)

double NeutRecruit = kmarg_N * NEUT_B * IL6 / (50.0 + IL6);

double NeutProd = kprod_N * (1.0 + 2.0 * NFkB_signal); // emergency granulopoiesis

dxdt_NEUT_B = NeutProd - kdeath_N * NEUT_B - NeutRecruit

+ krestore_N * (Neut_blood0 - NEUT_B) * (BACT < 100 ? 1.0 : 0.0);

// Tissue neutrophils

dxdt_NEUT_T = NeutRecruit - kdeath_N * NEUT_T * (1.0 + CI_norm);

// Activated macrophages

double MacAct = kact_Mac * NFkB_signal * (1.0 - E_HC);

dxdt_MACS = MacAct * Mac0 + kprod_Mac - kdact_Mac * MACS;

// ─── COMPLEMENT (C5a proxy) ──────────────────────────────────────────────────

dxdt_C5A = kprod_C5a * NFkB_signal - kdeg_C5a * (C5A - C5a_0);

// ─── COAGULATION ─────────────────────────────────────────────────────────────

// Thrombin (driven by TF expression from TNF + endothelial damage)

double ThrombStim = kprod_Thr * CI_norm * (1.0 + ENDOT);

dxdt_THROMBIN = ThrombStim - kdeg_Thr * (THROMBIN - Thrombin0);

// Fibrin (driven by thrombin)

double FibrinForm = kprod_Fib * THROMBIN;

double FibrinLysis = kdeg_Fib * (1.0 / PAI1); // tPA activity (inhibited by PAI-1)

dxdt_FIBRIN = FibrinForm - FibrinLysis * FIBRIN;

// PAI-1 (driven by TNF)

double PAI_stim = kprod_PAI * TNF / (5.0 + TNF);

dxdt_PAI1 = PAI_stim - kdeg_PAI * (PAI1 - PAI1_0);

// ─── ENDOTHELIAL DAMAGE (0 = intact, 1 = full failure) ───────────────────────

double EndDam = kdam_End * CI_norm * (1.0 - ENDOT);

double EndRep = krep_End * ENDOT * (1.0 - CI_norm);

dxdt_ENDOT = EndDam - EndRep;

if (ENDOT > 1.0) dxdt_ENDOT = 0;

if (ENDOT < 0.0) dxdt_ENDOT = 0;

// ─── ORGAN ENDPOINTS ─────────────────────────────────────────────────────────

// PaO2/FiO2 ratio (mmHg) — decreases with ARDS

double PF_dam = kdam_lung * CI_norm * ENDOT * PF_RATIO;

double PF_rep = krep_lung * (PF_base - PF_RATIO) * (CI_norm < 0.2 ? 1.0 : 0.0);

dxdt_PF_RATIO = PF_rep - PF_dam;

if (PF_RATIO < 50) dxdt_PF_RATIO = 0;

// Creatinine (mg/dL)

double CrProd = kprod_Cr * (1.0 + 3.0 * CI_norm * ENDOT);

double CrClr = kclr_Cr * CREATININE;

dxdt_CREATININE = CrProd - CrClr;

// Bilirubin (mg/dL)

double BilProd = kprod_Bil * (1.0 + 2.0 * CI_norm);

double BilClr = kclr_Bil * BILIRUBIN;

dxdt_BILIRUBIN = BilProd - BilClr;

// Lactate (mmol/L)

double LacProd = kprod_Lac * CI_norm * (1.0 + ENDOT);

double LacClr = kclr_Lac * LACTATE;

dxdt_LACTATE = LacProd - LacClr;

// MAP (mmHg) — vasodilatory shock from NO/cytokines

double MAP_dam = kdam_MAP * CI_norm * ENDOT;

double MAP_NE_eff = useNE * E_NE;

double MAP_HC_eff = useHC * 0.3 * E_HC; // steroid vasopressor sensitization

double MAP_fluid = useFluid * FluidBoost * 2.0; // simplified fluid effect

double MAP_rep = krep_MAP * (MAP_base - MAP_val) * 0.1;

dxdt_MAP_val = MAP_NE_eff + MAP_fluid + MAP_rep - MAP_dam;

if (MAP_val < 30) dxdt_MAP_val = 0;

// Platelet count (×10^9/L) — consumptive with DIC

double PltCons = kcons_Plt * FIBRIN * PLT_COUNT / 200.0;

double PltRegen= kregen_Plt * (Plt_base - PLT_COUNT) * 0.1;

dxdt_PLT_COUNT = PltRegen - PltCons;

if (PLT_COUNT < 10) dxdt_PLT_COUNT = 0;

// ─── VASOPRESSOR PK (1-cmpt, infusion via event table) ──────────────────────

dxdt_NE_C = -CL_NE / V1_NE * NE_C;

// ─── CORTICOSTEROID PK (1-cmpt) ──────────────────────────────────────────────

dxdt_HC_C = -CL_HC / V1_HC * HC_C;

// ─── TOCILIZUMAB PK (1-cmpt, single or repeat dose) ─────────────────────────

dxdt_TOCI_C = -CL_Toci / V1_Toci * TOCI_C;

$TABLE

// ── SOFA score calculation (Sepsis-3, range 0–24) ──────────────────────────

// Lung SOFA (PaO2/FiO2)

int sofa_lung;

if (PF_RATIO >= 400) sofa_lung = 0;

else if (PF_RATIO >= 300) sofa_lung = 1;

else if (PF_RATIO >= 200) sofa_lung = 2;

else if (PF_RATIO >= 100) sofa_lung = 3;

else sofa_lung = 4;

// Renal SOFA (Creatinine)

int sofa_renal;

if (CREATININE < 1.2) sofa_renal = 0;

else if (CREATININE < 2.0) sofa_renal = 1;

else if (CREATININE < 3.5) sofa_renal = 2;

else if (CREATININE < 5.0) sofa_renal = 3;

else sofa_renal = 4;

// Liver SOFA (Bilirubin)

int sofa_liver;

if (BILIRUBIN < 1.2) sofa_liver = 0;

else if (BILIRUBIN < 2.0) sofa_liver = 1;

else if (BILIRUBIN < 6.0) sofa_liver = 2;

else if (BILIRUBIN < 12.0) sofa_liver = 3;

else sofa_liver = 4;

// Cardiovascular SOFA (MAP + vasopressor)

int sofa_cardio;

if (MAP_val >= 70) sofa_cardio = 0;

else if (MAP_val >= 65) sofa_cardio = 1;

else if (useNE == 1.0 && NE_C > 0.005) sofa_cardio = 3;

else sofa_cardio = 2;

// Coagulation SOFA (Platelets)

int sofa_coag;

if (PLT_COUNT >= 150) sofa_coag = 0;

else if (PLT_COUNT >= 100) sofa_coag = 1;

else if (PLT_COUNT >= 50) sofa_coag = 2;

else if (PLT_COUNT >= 20) sofa_coag = 3;

else sofa_coag = 4;

// CNS SOFA (proxy from lactate/encephalopathy marker)

int sofa_cns;

double enc_marker = LACTATE + CI_norm * 3.0;

if (enc_marker < 1.5) sofa_cns = 0;

else if (enc_marker < 2.5) sofa_cns = 1;

else if (enc_marker < 4.0) sofa_cns = 2;

else if (enc_marker < 6.0) sofa_cns = 3;

else sofa_cns = 4;

// Total SOFA

int SOFA = sofa_lung + sofa_renal + sofa_liver + sofa_cardio + sofa_coag + sofa_cns;

// 28-day mortality probability (log-odds model: Seymour 2017 JAMA)

double SOFA_logit = -6.5 + 0.45 * SOFA;

double Mortality_Prob = 1.0 / (1.0 + exp(-SOFA_logit));

// Shock criteria

double shock_flag = ((MAP_val < 65.0) && (LACTATE > 2.0)) ? 1.0 : 0.0;

// Bacteria exposure (log CFU)

double log_BACT = (BACT > 0) ? log10(BACT) : 0.0;

double TNF_ng = TNF;

double IL6_pg = IL6 * 1000.0; // convert ng/mL → pg/mL for reporting

double Cp_abx_report = ABX1 / V1_abx;

double CytokineIdx = (TNF/10.0 + IL6/200.0 + IL1B/5.0)/3.0;

$CAPTURE

BACT ABX1 ABX2 TNF IL6 IL10 IL1B

NEUT_B NEUT_T MACS C5A

THROMBIN FIBRIN PAI1 ENDOT

PF_RATIO CREATININE BILIRUBIN LACTATE MAP_val PLT_COUNT

NE_C HC_C TOCI_C

SOFA sofa_lung sofa_renal sofa_liver sofa_cardio sofa_coag sofa_cns

Mortality_Prob shock_flag log_BACT

TNF_ng IL6_pg Cp_abx_report CytokineIdx

## COMPILE MODEL

mod <- mcode("sepsis_qsp", code)

## HELPER: BUILD EVENT TABLE

make_events <- function(

use_abx = FALSE, abx_dose = 1000, abx_ii = 8, abx_addl = 83, # mg, q8h × 28d

use_ne = FALSE, ne_rate = 0.002, # mcg/mL/h equiv

use_hc = FALSE, hc_dose = 50, hc_ii = 6, hc_addl = 111, # mg q6h × 7d

use_toci = FALSE, toci_dose = 672, # mg = 8 mg/kg × 84 kg

use_fluid = FALSE, fluid_dose = 30 # mL/kg = 2.1L equiv

) {

ev <- ev()

if (use_abx)

ev <- ev + ev(amt = abx_dose, cmt = "ABX1", ii = abx_ii, addl = abx_addl, time = 0)

if (use_ne)

ev <- ev + ev(amt = ne_rate * 18, cmt = "NE_C", rate = ne_rate, time = 2, to = 72)

if (use_hc)

ev <- ev + ev(amt = hc_dose, cmt = "HC_C", ii = hc_ii, addl = hc_addl, time = 1)

if (use_toci)

ev <- ev + ev(amt = toci_dose, cmt = "TOCI_C", time = 6)

if (use_fluid)

ev <- ev + ev(amt = fluid_dose * 1000, cmt = "MAP_val", time = 0, evid = 2) # bolus effect

}

## 7 TREATMENT SCENARIOS

scenarios <- list(

S1_NoTx = list(

label = "S1: No Treatment (Natural History)",

color = "#C0392B",

params = list(useAbx=0, useNE=0, useHC=0, useToci=0, useFluid=0),

events = make_events()

S2_AbxOnly = list(

label = "S2: Antibiotics Only",

color = "#E67E22",

params = list(useAbx=1, useNE=0, useHC=0, useToci=0, useFluid=0),

events = make_events(use_abx = TRUE)

S3_AbxNE = list(

label = "S3: Antibiotics + Norepinephrine",

color = "#F1C40F",

params = list(useAbx=1, useNE=1, useHC=0, useToci=0, useFluid=0),

events = make_events(use_abx = TRUE, use_ne = TRUE)

S4_AbxNEFluid = list(

label = "S4: Antibiotics + NE + Fluid (Bundle)",

color = "#27AE60",

params = list(useAbx=1, useNE=1, useHC=0, useToci=0, useFluid=1, FluidBoost=3),

events = make_events(use_abx = TRUE, use_ne = TRUE, use_fluid = TRUE)

S5_AbxNEFluidHC = list(

label = "S5: Bundle + Hydrocortisone",

color = "#2980B9",

params = list(useAbx=1, useNE=1, useHC=1, useToci=0, useFluid=1, FluidBoost=3),

events = make_events(use_abx = TRUE, use_ne = TRUE, use_hc = TRUE, use_fluid = TRUE)

S6_BundleToci = list(

label = "S6: Bundle + HC + Tocilizumab",

color = "#8E44AD",

params = list(useAbx=1, useNE=1, useHC=1, useToci=1, useFluid=1, FluidBoost=3),

events = make_events(use_abx = TRUE, use_ne = TRUE, use_hc = TRUE,

use_toci = TRUE, use_fluid = TRUE)

S7_ImmunoSupp = list(

label = "S7: Immunocompromised (Abx + NE only, high inoculum)",

color = "#7F8C8D",

params = list(useAbx=1, useNE=1, useHC=0, useToci=0, useFluid=1,

B0=1e6, FluidBoost=2), # higher inoculum, blunted immune

events = make_events(use_abx = TRUE, use_ne = TRUE, use_fluid = TRUE)

)

## RUN SIMULATIONS

sim_time <- seq(0, 168, by = 0.5) # 0–168 h (7 days)

results_list <- lapply(names(scenarios), function(sname) {

sc <- scenarios[[sname]]

# Build parameter list (override model defaults)

pmod <- mod %>% param(sc$params)

# Run simulation

out <- mrgsim(pmod, events = sc$events, tgrid = sim_time, obsonly = TRUE)

as.data.frame(out) %>%

mutate(scenario = sc$label, color = sc$color)

})

results_all <- bind_rows(results_list)

## PLOTTING FUNCTIONS

scenario_colors <- setNames(

sapply(scenarios, function(s) s$color),

sapply(scenarios, function(s) s$label)

)

#' Plot a single endpoint across all scenarios

plot_endpoint <- function(data, yvar, ylab, title, ytrans = "identity",

hline = NULL, hline_label = NULL) {

p <- ggplot(data, aes(x = time, y = .data[[yvar]],

color = scenario, group = scenario)) +

geom_line(linewidth = 1.1, alpha = 0.9) +

scale_color_manual(values = scenario_colors, name = "Treatment Scenario") +

scale_x_continuous(

breaks = seq(0, 168, 24),

labels = paste0("Day ", seq(0, 7)),

name = "Time (Hours from Sepsis Onset)"

) +

scale_y_continuous(trans = ytrans, name = ylab) +

labs(title = title,

subtitle = "Sepsis QSP Model — 7-day simulation",

caption = "mrgsolve ODE model | CCR 2026-06-24") +

theme_bw(base_size = 12) +

theme(legend.position = "bottom", legend.text = element_text(size = 8))

if (!is.null(hline)) {

p <- p + geom_hline(yintercept = hline, linetype = "dashed",

color = "firebrick", linewidth = 0.8) +

annotate("text", x = 5, y = hline * 1.05,

label = hline_label, color = "firebrick", size = 3.5)

}

## Generate key plots

p_bact <- plot_endpoint(results_all, "log_BACT", "Log₁₀ Bacterial Load (CFU/mL)",

"Bacteremia — Pathogen Clearance",

hline = 2, hline_label = "Clearance threshold")

p_tnf <- plot_endpoint(results_all, "TNF_ng", "TNFα (ng/mL)",

"TNFα — Cytokine Storm Kinetics")

p_il6 <- plot_endpoint(results_all, "IL6_pg", "IL-6 (pg/mL)",

"IL-6 — Acute Phase Response",

hline = 100, hline_label = "Elevated (>100 pg/mL)")

p_sofa <- plot_endpoint(results_all, "SOFA", "SOFA Score (0–24)",

"SOFA Score — Organ Failure Index",

hline = 11, hline_label = "High mortality risk (SOFA ≥11)")

p_map <- plot_endpoint(results_all, "MAP_val", "MAP (mmHg)",

"Mean Arterial Pressure",

hline = 65, hline_label = "Shock threshold (<65 mmHg)")

p_lactate<- plot_endpoint(results_all, "LACTATE", "Lactate (mmol/L)",

"Blood Lactate — Tissue Hypoperfusion",

hline = 2, hline_label = "Septic shock threshold (>2 mmol/L)")

p_pf <- plot_endpoint(results_all, "PF_RATIO", "PaO2/FiO2 (mmHg)",

"Respiratory Function (ARDS Risk)",

hline = 300, hline_label = "Mild ARDS (<300)")

p_mort <- plot_endpoint(results_all, "Mortality_Prob", "28-day Mortality Probability",

"Estimated 28-day Mortality Risk")

## SUMMARY TABLE AT 72h

summary_72h <- results_all %>%

filter(abs(time - 72) < 0.6) %>%

group_by(scenario) %>%

slice(1) %>%

select(scenario, log_BACT, TNF_ng, IL6_pg, SOFA, MAP_val, LACTATE,

CREATININE, PF_RATIO, Mortality_Prob, shock_flag) %>%

mutate(across(where(is.numeric), ~round(., 2)))

print(summary_72h)

## ANTIBIOTIC PK PROFILE

abx_data <- results_all %>%

filter(scenario == "S2: Antibiotics Only" & time <= 48) %>%

mutate(Cp_mg_L = Cp_abx_report)

p_abx_pk <- ggplot(abx_data, aes(x = time, y = Cp_mg_L)) +

geom_line(color = "#E67E22", linewidth = 1.2) +

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

annotate("text", x = 5, y = 0.7, label = "MIC = 0.5 mg/L", color = "red", size = 3.5) +

scale_x_continuous(breaks = seq(0, 48, 8), name = "Time (h)") +

labs(title = "Meropenem PK Profile (1g q8h IV)",

y = "Plasma Concentration (mg/L)",

caption = "fT>MIC drives bacterial kill (Emax PD model)") +

theme_bw(base_size = 12)

cat("\nSepsis QSP model compiled and 7 scenarios simulated successfully.\n")

cat("Use p_bact, p_tnf, p_il6, p_sofa, p_map, p_lactate, p_pf, p_mort to view plots.\n")

cat("summary_72h contains 72h endpoint comparison across scenarios.\n")

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