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## =============================================================================
## ntm_mrgsolve_model.R
## Nontuberculous Mycobacterial Lung Disease (Mycobacterium avium complex
## pulmonary disease, MAC-PD) — Quantitative Systems Pharmacology model
##
## 47 ODEs : macrolide / ethambutol / rifampicin / amikacin(IV) /
## amikacin-liposome-inhalation(ALIS) / clofazimine PK
## + CYP3A induction (the rifamycin DDI loop)
## + 4 bacterial niches, 3 of them mirrored by a resistant subpopulation
## + macrophage / Th1 / neutrophil / protease host arm
## + mucociliary clearance, bronchiectasis, cavitation
## + culture conversion, weight, QOL, and 5 toxicity endpoints
##
## -------------------------------------------------------------------------
## WHY THIS MODEL IS BUILT THE WAY IT IS (the two structural decisions)
## -------------------------------------------------------------------------
##
## DECISION 1 — Bacteria are indexed by PHYSICAL NICHE, not by phenotype.
##
## MAC in the lung is not one population with one drug exposure. It sits in
## four places that differ in (a) replication rate and (b) which drug can
## physically arrive:
##
## B_E extracellular planktonic, airway lumen / ELF — every drug arrives
## B_B biofilm inside bronchiectatic airway + mucus — EPS diffusion barrier
## B_I intracellular, macrophage phagosome, pH 5.2 — only cell-permeant drugs
## B_C cavity wall / caseum, non-replicating — only lipophilic drugs
##
## Every drug therefore carries FOUR effective concentrations, not one, each
## obtained from the ELF concentration by a niche-specific penetration factor
## (PBF_*, PCS_*) or by an explicit transport equation (intracellular).
## Cavitary vs nodular-bronchiectatic disease is then not a different model —
## it is the SAME model with a different initial B_C, and the well-documented
## conversion gap (~65-70% nodular vs <50% cavitary) falls out arithmetically.
##
## DECISION 2 — Phagosomal pH (5.2) is entered ONCE and drives TWO opposite
## consequences, so the central paradox is derived, not asserted.
##
## (i) Macrolides are weak bases (pKa ~8.7). Henderson-Hasselbalch ion
## trapping gives an equilibrium accumulation ratio
##
## R_trap = (1 + 10^(pKa - pH_in)) / (1 + 10^(pKa - pH_out))
## = (1 + 10^3.5)/(1 + 10^1.3) = 151x
##
## which is where the famous "100-1000x lung macrophage accumulation"
## of azithromycin comes from. It is computed here, not typed in.
##
## (ii) The SAME acid pH raises the macrolide MIC, because only the
## un-ionised species engages the 50S peptidyl-transferase centre:
##
## MIC_M(pH) = MIC_M0 * 10^(GM*(7.4 - pH)) = 12.6x at pH 5.2
##
## Net effective potency gain intracellularly is 151/12.6 = 12x, NOT 151x.
## The drug that best REACHES the phagosome is the drug most INACTIVATED
## there. That residual sub-MIC pressure in a compartment no companion drug
## reaches is exactly where the rrl A2058G mutant is selected — so R_I, the
## resistant intracellular pool, is *born* in this model rather than being
## switched on by a parameter.
##
## Amikacin loses activity at the same pH for the opposite biophysical
## reason — aminoglycoside uptake into the bacterium is proton-motive-force
## driven and collapses below pH 6 (GK > GM, a steeper penalty) — AND, being
## a polycation, free amikacin does not cross the macrophage plasma membrane
## at all. Which is the whole argument for ALIS: the liposome is
## phagocytosed intact, so the drug is delivered to the inside of the cell
## (barrier 3) after having been deposited straight into the lung
## (barrier 1), bypassing the plasma compartment that carries the
## ototoxicity. In this model ALIS efficacy is driven by KMAC/KELF and ALIS
## ototoxicity is driven by KPERI, which tracks KCEN — the decoupling is
## structural, so "high lung, low ear" is a consequence, not an assumption.
##
## -------------------------------------------------------------------------
## CALIBRATION ANCHORS (see ntm_references.md for the full citation list)
## -------------------------------------------------------------------------
## * CONVERT (Griffith 2018 AJRCCM): ALIS + guideline-based therapy in
## refractory MAC-PD -> culture conversion by month 6, 29.0% vs 8.9% GBT
## alone. Scenario 5 reproduces the direction and rough magnitude.
## * Wallace 1996 / Griffith 2001: macrolide-containing regimens convert
## ~ 60-80% of treatment-naive nodular-bronchiectatic disease; cavitary
## disease converts far less often. Scenarios 2 vs 3.
## * Griffith 2006 AJRCCM: macrolide monotherapy or functional monotherapy
## selects rrl mutants; acquired macrolide resistance carries ~47% 5-year
## mortality. Scenario 6.
## * Wallace 1995 / van Ingen 2012: rifampicin lowers clarithromycin AUC by
## ~70% via CYP3A induction; azithromycin is largely spared. Scenario 7.
## * Azithromycin alveolar-macrophage:plasma AUC ratio of order 10^2-10^3
## (Rodvold 1997, Olsen 1996) — reproduced by R_trap, not fitted.
## * ALIS lung/sputum amikacin >> systemic; systemic exposure ~ 1-2% of an
## equivalent IV dose (Zhang 2018) — reproduced by the deposition/release/
## uptake/absorption split, not fitted.
##
## DISCLAIMER: educational / research QSP model. Parameters are literature-
## informed approximations, not a validated population model. Not for clinical
## or regulatory use.
## =============================================================================
library(mrgsolve)
library(dplyr)
library(ggplot2)
library(tidyr)
ntm_code <- '
$PROB
# MAC-PD (Nontuberculous Mycobacterial Lung Disease) QSP model
- 47 ODEs; niche-resolved bacteriology with pH-derived macrolide paradox
- Drugs: azithromycin/clarithromycin, ethambutol, rifampicin,
amikacin IV, amikacin liposome inhalation suspension (ALIS),
clofazimine
$PARAM @annotated
// ---------------------------------------------------------------- switches
MACTYPE : 0 : Macrolide 0=azithromycin 1=clarithromycin (-)
WTBL : 52 : Baseline body weight, typical MAC-PD habitus (kg)
CAVFLAG : 1 : 1=cavitary phenotype, 0=nodular-bronchiectatic (-)
// ---------------------------------------------------------- macrolide PK
FMAC : 0.37 : Oral bioavailability, azithromycin (-)
KAM : 1.1 : Macrolide first-order absorption rate (1/hr equivalent, /d below)
VMC : 460 : Macrolide central volume (L)
VMP : 2500 : Macrolide peripheral volume (L)
QM : 200 : Macrolide intercompartmental clearance (L/d)
CLM : 900 : Macrolide baseline clearance (L/d)
FCYP3A : 0.05 : Fraction of macrolide CL via CYP3A (AZM 0.05, CLR 0.70) (-)
PSMELF : 40 : Plasma<->ELF permeability-surface product, macrolide (L/d)
RMELF : 12 : ELF:plasma partition target, macrolide (-)
PSMMAC : 3.0 : ELF<->macrophage PS product, macrolide (L/d)
PKAM : 8.7 : Macrolide pKa, weak base (-)
// -------------------------------------------------------------- EMB PK
FEMB : 0.80 : Ethambutol oral bioavailability (-)
KAE : 1.6 : Ethambutol absorption rate (/d scaled) (-)
VEC : 240 : Ethambutol volume of distribution (L)
CLE : 400 : Ethambutol clearance (L/d)
PSEELF : 60 : Ethambutol plasma<->ELF PS (L/d)
REELF : 2.5 : ELF:plasma partition, ethambutol (-)
// -------------------------------------------------------------- RIF PK
FRIF : 0.70 : Rifampicin oral bioavailability (-)
KAF : 2.4 : Rifampicin absorption rate (/d scaled) (-)
VFC : 55 : Rifampicin volume of distribution (L)
CLF : 260 : Rifampicin baseline clearance (L/d)
PSFELF : 30 : Rifampicin plasma<->ELF PS (L/d)
RFELF : 0.45 : ELF:plasma partition, rifampicin (-)
KENZIN : 0.15 : CYP3A induction rate constant (L/mg/d)
KENZOUT : 0.10 : CYP3A enzyme degradation rate (1/d, t-half ~7 d)
EMAXENZ : 5.0 : Maximal fold CYP3A induction (-)
// ------------------------------------------------------- amikacin IV PK
VKC : 18 : Amikacin central volume (L)
VKP : 12 : Amikacin peripheral volume (L)
QK : 8 : Amikacin intercompartmental clearance (L/d)
CLK : 100 : Amikacin renal clearance (L/d)
KINELF : 0.0018: Plasma->ELF amikacin transfer rate constant (1/d)
RKELF : 0.20 : ELF:plasma amikacin partition implied by KINELF/(KABS+KMUCK) (-)
KPIN : 0.05 : Perilymph amikacin uptake rate (1/d)
KPOUT : 0.02 : Perilymph amikacin efflux rate (1/d)
KRIN : 0.60 : Renal cortex amikacin uptake (megalin) (1/d)
KROUT : 0.10 : Renal cortex amikacin efflux (1/d)
// --------------------------------------------------- ALIS (inhaled) PK
FDEP : 0.30 : Fraction of nominal ALIS dose deposited in lung (-)
KREL : 1.50 : Liposome amikacin release rate in ELF (1/d)
KUPT : 0.12 : Liposome phagocytic uptake into macrophage (1/d)
KLMUC : 1.50 : Liposome mucociliary removal rate (1/d)
KABS : 0.5 : Free ELF amikacin systemic absorption rate (1/d)
KMUCK : 6.0 : Free ELF amikacin mucociliary washout (1/d)
KMACOUT : 0.35 : Intracellular amikacin efflux/exocytosis rate (1/d)
VELF : 0.025: Epithelial lining fluid volume (L)
VMAC : 0.020: Total lung phagocyte intracellular volume (L)
// ------------------------------------------------------- clofazimine PK
FCFZ : 0.45 : Clofazimine oral bioavailability (-)
KAC : 1.0 : Clofazimine absorption rate (/d scaled) (-)
VCC : 60 : Clofazimine central volume (L)
VCT : 1200 : Clofazimine deep tissue volume (L)
QC : 45 : Clofazimine tissue distribution clearance (L/d)
CLC : 12 : Clofazimine clearance (L/d, t-half ~ weeks-months)
PCSC : 0.70 : Caseum:ELF partition, clofazimine (lipophilic) (-)
PBFC : 0.40 : Biofilm:ELF partition, clofazimine (-)
// ------------------------------------------- pH and niche penetration
PHPHAG : 5.2 : Phagosomal pH (arrested phagosome) (-)
PHREF : 7.4 : Reference extracellular pH (-)
GM : 0.50 : Macrolide log10 MIC shift per pH unit of acidification (-)
GK : 0.85 : Amikacin log10 MIC shift per pH unit (PMF-dependent uptake) (-)
PBFM : 0.50 : Biofilm:ELF penetration, macrolide (-)
PBFK : 0.15 : Biofilm:ELF penetration, free amikacin (-)
PBFL : 0.60 : Biofilm penetration, liposomal amikacin (engineered) (-)
PBFE : 0.55 : Biofilm:ELF penetration, ethambutol (-)
PCSM : 0.15 : Caseum:ELF penetration, macrolide (-)
PCSK : 0.02 : Caseum:ELF penetration, amikacin (polycation) (-)
PCSF : 0.30 : Caseum:ELF penetration, rifampicin (-)
// ---------------------------------------------------------- drug PD
MICM0 : 4.0 : Macrolide MIC at pH 7.4 (mg/L)
MICK0 : 16 : Amikacin MIC at pH 7.4 (mg/L)
MICF0 : 2.0 : Rifampicin MIC (mg/L)
MICC0 : 0.5 : Clofazimine MIC (mg/L)
EMAXM : 1.10 : Macrolide maximal kill rate (1/d)
EMAXK : 1.60 : Amikacin maximal kill rate (1/d, concentration-dependent)
EMAXF : 0.35 : Rifampicin maximal kill rate vs MAC (intrinsically weak) (1/d)
EMAXC : 0.45 : Clofazimine maximal kill rate (1/d)
EC50R : 1.5 : C/MIC ratio giving half-maximal kill (-)
HILLM : 1.6 : Hill coefficient, macrolide (time>MIC-like) (-)
HILLK : 2.4 : Hill coefficient, amikacin (Cmax/MIC-like) (-)
HILLF : 1.5 : Hill coefficient, rifampicin (-)
EC50EMB : 2.0 : Ethambutol ELF conc for half-maximal permeabilisation (mg/L)
EMAXPERM : 2.5 : Maximal fold increase in cell-wall permeability by EMB (-)
EMBKILL : 0.28 : Direct ethambutol kill rate - the companion-drug term (1/d)
TOLBF : 0.35 : Fractional kill retained in biofilm (persister tolerance) (-)
TOLCS : 0.10 : Fractional kill retained in caseum (non-replicating) (-)
// ------------------------------------------------------- bacteriology
KGE : 0.83 : Growth rate, extracellular planktonic (1/d)
KGB : 0.12 : Growth rate, biofilm (1/d)
KGI : 0.35 : Growth rate, intracellular (1/d)
KGC : 0.015: Growth rate, caseum / non-replicating (1/d)
BEMAX : 2e8 : Carrying capacity, extracellular (CFU)
BBMAX : 5e8 : Carrying capacity, biofilm (CFU)
BIMAX : 2e8 : Carrying capacity, intracellular (CFU)
BCMAX : 1e9 : Carrying capacity, caseum (CFU)
KBF : 0.20 : Planktonic -> biofilm adhesion rate (1/d)
KDISP : 0.06 : Biofilm -> planktonic dispersal rate (1/d)
KPHAG : 0.55 : Phagocytosis rate, planktonic -> intracellular (1/d)
KEGRESS : 0.18 : Macrophage lysis / bacterial egress rate (1/d)
KNECR : 0.03 : Intracellular -> caseum necrosis rate (1/d)
KSHED : 0.025: Caseum -> airway shedding / drainage base rate (1/d)
KMCCB : 0.90 : Maximal mucociliary bacterial clearance rate (1/d)
FBMCC : 0.35 : Fraction of MCC clearance that reaches biofilm-embedded MAC (-)
MU : 1e-8 : rrl point-mutation rate per replication (-)
EXFLOOR : 1.0 : Extinction floor: a pool below ~1 organism cannot regrow (CFU)
FITR : 0.97 : Relative fitness of rrl mutant (-)
// -------------------------------------------------------- host / immune
KMPHIN : 0.9 : Macrophage recruitment rate (1/d)
KMPHOUT : 0.7 : Macrophage turnover (1/d)
MPH0 : 1.0 : Baseline macrophage pool (relative)
KIFNIN : 0.45 : IFN-gamma production rate (1/d)
KIFNOUT : 0.9 : IFN-gamma elimination (1/d)
IFNCAP : 1.0 : Host Th1 capacity, 0-1 (anti-IFNg Ab / MSMD lowers it) (-)
KILLIFN : 0.55 : Maximal IFN-gamma-driven intracellular kill (1/d)
EC50IFN : 0.8 : IFN-gamma for half-maximal macrophage killing (rel units)
KTNFIN : 0.40 : TNF-alpha production rate (1/d)
KTNFOUT : 1.2 : TNF-alpha elimination (1/d)
KNEUIN : 0.9 : Neutrophil influx rate (1/d)
KNEUOUT : 1.1 : Neutrophil clearance (1/d)
KMMPIN : 0.5 : MMP-1/9 induction rate (1/d)
KMMPOUT : 0.7 : MMP turnover (1/d)
IMMUNOM : 0.35 : Macrolide anti-inflammatory (neutrophil/mucin) efficacy (-)
IC50IM : 1.0 : ELF macrolide for half-maximal immunomodulation (mg/L)
// ----------------------------------------------- airway / structure
KMUCIN : 0.55 : Mucus production rate (1/d)
KMUCOUT : 0.65 : Mucus clearance rate (1/d)
MCC0 : 0.75 : Baseline mucociliary clearance capacity (0-1)
KMCCREC : 0.05 : MCC recovery rate (1/d)
KMCCDMG : 0.09 : MCC loss per unit airway damage (1/d)
ACT : 0 : Airway clearance therapy on/off (HFCWO + hypertonic saline)
ACTEFF : 0.35 : Fractional MCC gain with airway clearance therapy (-)
KBROIN : 0.030: Bronchiectasis progression rate per unit protease (1/d)
KBROOUT : 0.004: Airway remodelling / partial recovery rate (1/d)
KCAVIN : 0.035: Cavity expansion rate per unit MMP x caseum load (1/d)
KCAVOUT : 0.004: Cavity closure rate (1/d)
CAV50 : 10.0 : Cavity volume halving caseum penetration and drainage (cm3)
SURG : 0 : Adjunctive surgical resection flag (-)
TSURG : 240 : Time of surgical resection (d)
SURGFRAC : 0.70 : Fraction of cavity+caseum removed by resection (-)
// --------------------------------------------------- outcome / toxicity
KSYMIN : 0.55 : Symptom generation rate (1/d)
KSYMOUT : 0.30 : Symptom resolution rate (1/d)
KWTLOSS : 0.30 : TNF-driven weight loss rate (kg/d per unit TNF)
KWTGAIN : 0.012: Weight recovery rate (1/d)
NUTR : 0 : Nutritional repletion support flag (-)
KOTOIN : 0.055: Cochlear damage rate per mg/L perilymph amikacin (dB/d)
KOTOREC : 0.004: Partial cochlear recovery rate (1/d)
KOPTIN : 0.012: Optic neuropathy accrual per mg/L ethambutol above threshold
EMBTHR : 2.5 : Ethambutol plasma threshold for optic risk (mg/L)
KOPTREC : 0.020: Optic recovery rate after withdrawal (1/d)
KNEPIN : 0.020: Tubular injury accrual per mg/L renal cortex amikacin (1/d)
KNEPREC : 0.030: Tubular recovery rate (1/d)
KHEPIN : 0.035: Hepatic injury accrual per mg/L rifampicin (1/d)
KHEPREC : 0.090: Hepatic recovery rate (1/d)
KQTIN : 3.0 : QTc effect-compartment equilibration rate (1/d)
QTSLP : 6.0 : QTc slope (ms per mg/L plasma macrolide) (-)
VSP : 100 : Sputum sampling scale factor (CFU -> CFU/mL) (-)
FSPB : 0.05 : Fraction of biofilm burden appearing in sputum (-)
FSPC : 0.02 : Fraction of caseum burden appearing in sputum (-)
LODCFU : 1.0 : log10 CFU/mL below which culture reads negative (-)
$CMT @annotated
MGUT : Macrolide gut depot (mg)
MCEN : Macrolide plasma central (mg)
MPER : Macrolide peripheral (mg)
MELF : Macrolide in epithelial lining fluid (mg)
MMAC : Macrolide intracellular, macrophage (mg)
EGUT : Ethambutol gut depot (mg)
ECEN : Ethambutol plasma (mg)
EELF : Ethambutol in ELF (mg)
FGUT : Rifampicin gut depot (mg)
FCEN : Rifampicin plasma (mg)
FELF : Rifampicin in ELF (mg)
ENZ : Relative CYP3A4 enzyme amount (-)
KCEN : Amikacin plasma central (mg)
KPER : Amikacin peripheral (mg)
KELF : Free amikacin in ELF (mg)
KLIP : Liposome-encapsulated amikacin in lung (mg)
KMAC : Intracellular (phagosomal) amikacin (mg)
KPERI : Perilymph amikacin concentration (mg/L)
KREN : Renal cortex amikacin concentration (mg/L)
CGUT : Clofazimine gut depot (mg)
CCEN : Clofazimine plasma (mg)
CTIS : Clofazimine deep tissue / caseum (mg)
BE : MAC extracellular planktonic, susceptible (CFU)
BB : MAC biofilm-embedded, susceptible (CFU)
BI : MAC intracellular (phagosome), susceptible (CFU)
BC : MAC caseum / cavity wall, non-replicating (CFU)
RE : MAC extracellular, macrolide-resistant rrl mutant (CFU)
RB : MAC biofilm-embedded, macrolide-resistant rrl mutant (CFU)
RI : MAC intracellular, macrolide-resistant rrl mutant (CFU)
MPH : Alveolar macrophage pool (relative)
IFNG : IFN-gamma tone (relative)
TNF : TNF-alpha tone (relative)
NEU : Neutrophil burden (relative)
MMP : MMP-1/9 protease activity (relative)
MUC : Mucus / biofilm matrix burden (relative)
MCC : Mucociliary clearance capacity (0-1)
BRO : Bronchiectasis / airway damage score (0-10)
CAV : Cavity volume (cm3)
SYM : Symptom score (0-10)
WT : Body weight (kg)
OTO : Cochlear threshold shift (dB)
OPT : Optic neuropathy index (0-1)
NEP : Renal tubular injury index (0-1)
HEP : Hepatic injury index (0-8, ALT-like scale)
QTE : QTc effect compartment (mg/L)
TNEG : Cumulative days of culture negativity (d)
AUCML : Cumulative macrophage macrolide exposure (mg/L*d)
$GLOBAL
#define HILLKILL(EMX,CR,EC,HH) ( (EMX) * pow((CR),(HH)) / (pow((EC),(HH)) + pow((CR),(HH))) )
// Values computed in $MAIN that $ODE must see
double RTRAP_, MICM_PH_, MICK_PH_, MICM_EX_, MICK_EX_;
double FMAC_, KAM_, VMC_, CLM_, FCYP_, QTSLP_, MICM0_;
double POS(double x){ return (x > 0.0) ? x : 0.0; }
$MAIN
// ---- macrolide identity: azithromycin (0) vs clarithromycin (1) ----------
// The two differ in exactly the places that matter downstream: how much of
// their clearance is CYP3A (i.e. how badly rifampicin eats them), how much
// hERG block they carry, and their MIC against MAC.
if(MACTYPE > 0.5){
FMAC_ = 0.55; // clarithromycin
KAM_ = 6.0; // /d
VMC_ = 250;
CLM_ = 700;
FCYP_ = 0.70; // heavily CYP3A-cleared -> rifampicin drops AUC ~70%
QTSLP_ = 14.0; // stronger hERG signal than azithromycin
MICM0_ = 2.0;
} else {
FMAC_ = FMAC; // azithromycin
KAM_ = 26.4; // /d (KAM 1.1 /hr)
VMC_ = VMC;
CLM_ = CLM;
FCYP_ = FCYP3A; // ~5% CYP3A -> largely spared by rifampicin
QTSLP_ = QTSLP;
MICM0_ = MICM0;
}
F_MGUT = FMAC_;
F_EGUT = FEMB;
F_FGUT = FRIF;
F_CGUT = FCFZ;
F_KLIP = FDEP; // inhaled: only the deposited fraction reaches lung
// ---- THE ONE INPUT, TWO CONSEQUENCES ------------------------------------
// (i) Henderson-Hasselbalch ion trapping -> intracellular ACCUMULATION
RTRAP_ = (1.0 + pow(10.0, PKAM - PHPHAG)) / (1.0 + pow(10.0, PKAM - PHREF));
// (ii) the same acid pH -> LOSS OF POTENCY at the ribosome
MICM_PH_ = MICM0_ * pow(10.0, GM * (PHREF - PHPHAG));
MICK_PH_ = MICK0 * pow(10.0, GK * (PHREF - PHPHAG));
MICM_EX_ = MICM0_; // extracellular / biofilm / caseum sit near pH 7
MICK_EX_ = MICK0;
// ---- initial conditions --------------------------------------------------
MPH_0 = MPH0;
MCC_0 = MCC0;
WT_0 = WTBL;
ENZ_0 = 1.0;
BE_0 = 1.0e7;
BB_0 = 1.0e8;
BI_0 = 1.0e7;
BC_0 = (CAVFLAG > 0.5) ? 1.0e8 : 3.0e5; // <- the ONLY phenotype switch
CAV_0 = (CAVFLAG > 0.5) ? 25.0 : 0.0;
BRO_0 = (CAVFLAG > 0.5) ? 5.0 : 3.5;
// Pre-existing mutants scale with the burden that generated them (MU x pool).
// Below ~1 organism the mutant does not exist - which is exactly why acquired
// macrolide resistance is a HIGH-BURDEN / cavitary phenomenon rather than an
// intrinsic property of the drug.
RE_0 = MU * BE_0;
RB_0 = MU * BB_0;
RI_0 = MU * (BI_0 + BC_0);
IFNG_0 = 0.35;
TNF_0 = 0.30;
NEU_0 = 0.40;
MMP_0 = 0.35;
MUC_0 = 0.60;
SYM_0 = (CAVFLAG > 0.5) ? 5.0 : 3.0;
$ODE
// ============================ CONCENTRATIONS ==============================
double CMP = MCEN / VMC_; // macrolide plasma (mg/L)
double CME = MELF / VELF; // macrolide ELF
double CMI = MMAC / VMAC; // macrolide intracellular
double CEP = ECEN / VEC; // ethambutol plasma
double CEE = EELF / VELF; // ethambutol ELF
double CFP = FCEN / VFC; // rifampicin plasma
double CFE = FELF / VELF; // rifampicin ELF
double CKP = KCEN / VKC; // amikacin plasma
double CKE = KELF / VELF; // free amikacin ELF
double CKI = KMAC / VMAC; // amikacin intracellular (ALIS only)
double CCP = CCEN / VCC; // clofazimine plasma
double CCT = CTIS / VCT; // clofazimine deep tissue
// ==================== ETHAMBUTOL AS A PERMEABILISER =======================
// EMB is modelled for what it actually contributes: it blocks arabinogalactan
// synthesis, which thins the cell wall and multiplies the entry of the OTHER
// two drugs. That is a SYNERGY multiplier on their effective concentration,
// not an additive kill term - and it is why dropping EMB silently converts
// the regimen into functional macrolide monotherapy.
double PERM = 1.0 + (EMAXPERM - 1.0) * CEE / (EC50EMB + CEE);
// =================== NICHE-SPECIFIC EFFECTIVE CONCENTRATIONS ==============
double CM_E = CME * PERM; // macrolide, planktonic (ELF)
double CM_B = CME * PBFM * PERM; // macrolide, biofilm
double CM_I = CMI * PERM; // macrolide, intracellular
double CM_C = CME * PCSM; // macrolide, caseum
// Liposome-associated fraction of the lung amikacin pool. The liposome's
// advantage in biofilm is a PENETRATION advantage, so it shifts the biofilm
// partition coefficient from PBFK (free polycation, 0.15) towards PBFL
// (engineered liposome, 0.60) - it never creates concentration out of nothing.
double FLIP = KLIP / (KLIP + KELF + 1e-9);
double CK_E = CKE * PERM; // amikacin, planktonic
double CK_B = CKE * (PBFK + FLIP*(PBFL - PBFK)) * PERM;
double CK_I = CKI * PERM; // amikacin intracellular = ALIS only
double CK_C = CKE * PCSK;
// LESION-SIZE PENALTY (Dartois 2014, Prideaux 2015): a large, avascular,
// thick-walled cavity is both penetrated and drained far worse than a small
// centrilobular nodule. ONE factor scales drug entry into caseum AND caseum
// drainage, so cavitary and nodular disease diverge by more than their
// initial B_C alone would predict.
double FCAS = 1.0 / (1.0 + CAV/CAV50);
CM_C = CM_C * FCAS;
CK_C = CK_C * FCAS;
double CF_E = CFE; // rifampicin
double CF_C = CFE * PCSF * FCAS;
double CC_E = CCP * 0.15 + CCT * 0.05; // clofazimine reaching airway
double CC_C = CCT * PCSC * FCAS; // clofazimine reaching caseum
double CC_B = CC_E * PBFC;
// ============================== KILL RATES ================================
// Susceptible organisms, per niche. Macrolide kill uses the pH-shifted MIC
// intracellularly and the neutral-pH MIC everywhere else.
double kM_E = HILLKILL(EMAXM, CM_E/MICM_EX_, EC50R, HILLM);
double kM_B = HILLKILL(EMAXM, CM_B/MICM_EX_, EC50R, HILLM) * TOLBF;
double kM_I = HILLKILL(EMAXM, CM_I/MICM_PH_, EC50R, HILLM); // <- the paradox
double kM_C = HILLKILL(EMAXM, CM_C/MICM_EX_, EC50R, HILLM) * TOLCS;
double kK_E = HILLKILL(EMAXK, CK_E/MICK_EX_, EC50R, HILLK);
double kK_B = HILLKILL(EMAXK, CK_B/MICK_EX_, EC50R, HILLK) * TOLBF;
double kK_I = HILLKILL(EMAXK, CK_I/MICK_PH_, EC50R, HILLK); // ALIS only
double kK_C = HILLKILL(EMAXK, CK_C/MICK_EX_, EC50R, HILLK) * TOLCS;
double kF_E = HILLKILL(EMAXF, CF_E/MICF0, EC50R, HILLF);
double kF_C = HILLKILL(EMAXF, CF_C/MICF0, EC50R, HILLF) * TOLCS;
double kC_E = HILLKILL(EMAXC, CC_E/MICC0, EC50R, 1.4);
double kC_B = HILLKILL(EMAXC, CC_B/MICC0, EC50R, 1.4) * TOLBF;
double kC_C = HILLKILL(EMAXC, CC_C/MICC0, EC50R, 1.4) * TOLCS;
double kEMB = EMBKILL * CEE / (EC50EMB + CEE);
// Companion (non-macrolide) kill, per niche - this is the denominator of the
// resistance-selection gate.
double kComp_E = kK_E + kF_E + kC_E + kEMB;
double kComp_I = kK_I + kEMB * 0.4; // rifampicin/CFZ contribute little here
double kComp_B = kK_B + kC_B + kEMB * 0.5;
double kComp_C = kK_C + kF_C + kC_C;
double kTot_E = kM_E + kComp_E;
double kTot_B = kM_B + kComp_B;
double kTot_I = kM_I + kComp_I;
double kTot_C = kM_C + kComp_C;
// Resistant organisms: rrl A2058G removes the macrolide term entirely
// (single-copy gene -> no gene-dosage buffering, MIC >= 32 mg/L).
double kRes_E = kComp_E;
double kRes_I = kComp_I;
// ============================ IMMUNE KILLING ==============================
double kIMM = KILLIFN * IFNG / (EC50IFN + IFNG);
double kMCCcl = KMCCB * MCC;
// ============================= BACTERIOLOGY ===============================
double bE = POS(BE), bB = POS(BB), bI = POS(BI), bC = POS(BC);
double rE = POS(RE), rB = POS(RB), rI = POS(RI);
// EXTINCTION FLOOR. A pool holding less than about one organism cannot regrow.
// Without it a deterministic model relapses from 1e-3 CFU, which is not a real
// event. It is a deterministic surrogate for stochastic extinction - and it is
// also what makes mutant ESTABLISHMENT (rather than mere mutant generation)
// require a large enough parent population.
double eE = bE/(bE + EXFLOOR), eB = bB/(bB + EXFLOOR);
double eI = bI/(bI + EXFLOOR), eC = bC/(bC + EXFLOOR);
double eRE = rE/(rE + EXFLOOR), eRB = rB/(rB + EXFLOOR), eRI = rI/(rI + EXFLOOR);
double growE = KGE * bE * (1.0 - (bE + rE)/BEMAX) * eE;
double growB = KGB * bB * (1.0 - (bB + rB)/BBMAX) * eB;
double growI = KGI * bI * (1.0 - (bI + rI)/BIMAX) * MPH/(MPH + 0.4) * eI;
double growC = KGC * bC * (1.0 - bC/BCMAX) * eC;
double growRE = KGE * FITR * rE * (1.0 - (bE + rE)/BEMAX) * eRE;
double growRB = KGB * FITR * rB * (1.0 - (bB + rB)/BBMAX) * eRB;
double growRI = KGI * FITR * rI * (1.0 - (bI + rI)/BIMAX) * MPH/(MPH + 0.4) * eRI;
// Mutation: the mutant is generated in proportion to replication events in
// each niche. It is then SELECTED (or not) by the difference between
// kTot and kRes in that niche - the "gate" is arithmetic, not a switch.
double mutE = MU * growE;
double mutB = MU * growB;
double mutI = MU * growI;
double phag = KPHAG * bE * MPH/(MPH + 0.5);
double phagR = KPHAG * rE * MPH/(MPH + 0.5);
double egr = KEGRESS * bI;
double egrR = KEGRESS * rI;
double adh = KBF * bE * MUC/(MUC + 0.5);
double adhR = KBF * rE * MUC/(MUC + 0.5);
double disp = KDISP * bB;
double dispR = KDISP * rB;
double necr = KNECR * bI * TNF/(TNF + 0.5);
double shed = KSHED * (1.0 + 2.0*FCAS) * bC; // small lesions drain better
dxdt_BE = growE - mutE + disp - adh - phag + egr + shed
- (kTot_E + kMCCcl) * bE;
dxdt_BB = growB - mutB + adh - disp - (kTot_B + FBMCC*kMCCcl) * bB;
dxdt_BI = growI - mutI + phag - egr - necr - (kTot_I + kIMM) * bI;
dxdt_BC = growC + necr - shed - kTot_C * bC;
dxdt_RE = growRE + mutE + dispR - adhR - phagR + egrR - (kRes_E + kMCCcl) * rE;
dxdt_RB = growRB + mutB + adhR - dispR - (kComp_B + FBMCC*kMCCcl) * rB;
dxdt_RI = growRI + mutI + phagR - egrR - (kRes_I + kIMM) * rI;
double BTOT = bE + bB + bI + bC + rE + rB + rI;
double BSTIM = log10(BTOT + 1.0) / 10.0;
// =============================== HOST ARM =================================
dxdt_MPH = KMPHIN * BSTIM + 0.15 - KMPHOUT * MPH;
dxdt_IFNG = KIFNIN * BSTIM * IFNCAP - KIFNOUT * IFNG;
dxdt_TNF = KTNFIN * BSTIM * (1.0 + 0.5*CAV/50.0) - KTNFOUT * TNF;
// Macrolides are anti-inflammatory independent of their antibacterial effect
// (this is why symptoms and sputum volume improve before culture converts).
double immod = 1.0 - IMMUNOM * CME/(IC50IM + CME);
dxdt_NEU = KNEUIN * (BSTIM + 0.6*TNF) * immod - KNEUOUT * NEU;
dxdt_MMP = KMMPIN * (NEU + 0.7*TNF) - KMMPOUT * MMP;
dxdt_MUC = KMUCIN * (NEU + 0.5*BSTIM) * immod - KMUCOUT * MUC * (1.0 + ACT*0.8);
// ========================= AIRWAY & STRUCTURE =============================
double mcc_target = MCC0 * (1.0 + ACT*ACTEFF) * exp(-0.06 * BRO) / (1.0 + 0.25*MUC);
dxdt_MCC = KMCCREC * (mcc_target - MCC) - KMCCDMG * MMP * MCC * 0.1;
dxdt_BRO = KBROIN * MMP * (10.0 - BRO)/10.0 - KBROOUT * BRO;
dxdt_CAV = KCAVIN * MMP * log10(bC + 1.0)/8.0 * (1.0 - CAV/200.0)
- KCAVOUT * CAV * (1.0 - MMP/(MMP + 1.0));
// ======================== SYMPTOMS / WEIGHT / QOL =========================
dxdt_SYM = KSYMIN * (0.45*BSTIM + 0.30*NEU + 0.25*MUC + 0.20*TNF + 0.02*CAV/10.0)
- KSYMOUT * SYM;
dxdt_WT = -KWTLOSS * POS(TNF - 0.25) + KWTGAIN * (1.0 + NUTR*1.2)
* (WTBL - WT) * (1.0/(1.0 + 4.0*TNF));
// =============================== DRUG PK ==================================
// --- macrolide: CL scaled by induced CYP3A (this is the whole DDI) --------
double CLMi = CLM_ * (1.0 - FCYP_ + FCYP_ * ENZ);
dxdt_MGUT = -KAM_ * MGUT;
dxdt_MCEN = KAM_ * MGUT - CLMi*CMP - QM*(CMP - MPER/VMP)
- PSMELF*(CMP*RMELF - CME)/RMELF;
dxdt_MPER = QM*(CMP - MPER/VMP);
dxdt_MELF = PSMELF*(CMP*RMELF - CME)/RMELF - PSMMAC*(CME*RTRAP_ - CMI)/RTRAP_
- KMUCK*0.15*MELF;
dxdt_MMAC = PSMMAC*(CME*RTRAP_ - CMI)/RTRAP_ - 0.35*MMAC;
// --- ethambutol ----------------------------------------------------------
dxdt_EGUT = -KAE*24.0 * EGUT;
dxdt_ECEN = KAE*24.0 * EGUT - CLE*CEP - PSEELF*(CEP*REELF - CEE)/REELF;
dxdt_EELF = PSEELF*(CEP*REELF - CEE)/REELF - KMUCK*0.2*EELF;
// --- rifampicin + its own auto-induction and the CYP3A pool --------------
double CLFi = CLF * (0.55 + 0.45*ENZ);
dxdt_FGUT = -KAF*24.0 * FGUT;
dxdt_FCEN = KAF*24.0 * FGUT - CLFi*CFP - PSFELF*(CFP*RFELF - CFE)/RFELF;
dxdt_FELF = PSFELF*(CFP*RFELF - CFE)/RFELF - KMUCK*0.2*FELF;
dxdt_ENZ = KENZIN * CFP * (EMAXENZ - ENZ) - KENZOUT * (ENZ - 1.0);
// --- amikacin: IV plasma route ------------------------------------------
// NOTE ON STRUCTURE: plasma<->ELF amikacin exchange is written as explicit
// rate constants on AMOUNTS, not as a permeability-surface product on
// CONCENTRATIONS. With VELF = 25 mL, a PS term imposes an enormous first-order
// rate on the ELF amount and pumps inhaled drug straight back into plasma -
// destroying the very lung/plasma separation that ALIS depends on.
double CLKi = CLK * (1.0 - 0.55*NEP); // nephrotoxicity feeds back on CL
dxdt_KCEN = -CLKi*CKP - QK*(CKP - KPER/VKP)
- KINELF*KCEN + KABS*KELF;
dxdt_KPER = QK*(CKP - KPER/VKP);
// --- ALIS: deposited liposome splits three ways -------------------------
// release into ELF | phagocytic uptake | mucociliary removal
dxdt_KLIP = -(KREL + KUPT + KLMUC) * KLIP;
dxdt_KELF = KREL*KLIP + KINELF*KCEN - KABS*KELF - KMUCK*KELF;
dxdt_KMAC = KUPT*KLIP - KMACOUT*KMAC;
// --- amikacin toxicity driver compartments (concentrations) --------------
dxdt_KPERI = KPIN*(CKP - KPERI) - KPOUT*KPERI;
dxdt_KREN = KRIN*(CKP - KREN) - KROUT*KREN;
// --- clofazimine ---------------------------------------------------------
dxdt_CGUT = -KAC*24.0 * CGUT;
dxdt_CCEN = KAC*24.0 * CGUT - CLC*CCP - QC*(CCP - CCT);
dxdt_CTIS = QC*(CCP - CCT);
// ============================== TOXICITY ==================================
// Ototoxicity tracks PERILYMPH, which tracks PLASMA - not lung. This is the
// arithmetic reason ALIS separates efficacy from hearing loss.
dxdt_OTO = KOTOIN * KPERI - KOTOREC * OTO;
dxdt_OPT = KOPTIN * POS(CEP - EMBTHR) * (1.0 - OPT) - KOPTREC * OPT;
dxdt_NEP = KNEPIN * KREN * (1.0 - NEP) - KNEPREC * NEP;
dxdt_HEP = KHEPIN * CFP * (1.0 - HEP/8.0) - KHEPREC * (HEP);
dxdt_QTE = KQTIN * (CMP - QTE);
// ========================= ENDPOINT BOOKKEEPING ===========================
double SPUTC = (bE + rE + FSPB*bB + FSPC*bC) / VSP;
double LSPUT = log10(SPUTC + 1e-6);
// smooth culture-negativity indicator (steep logistic around the LOD)
double NEGIND = 1.0 / (1.0 + exp(4.0 * (LSPUT - LODCFU)));
dxdt_TNEG = NEGIND;
dxdt_AUCML = CMI;
$TABLE
double CMPo = MCEN / VMC_;
double CMEo = MELF / VELF;
double CMIo = MMAC / VMAC;
double CKPo = KCEN / VKC;
double CKEo = KELF / VELF;
double CKIo = KMAC / VMAC;
double CEPo = ECEN / VEC;
double CFPo = FCEN / VFC;
double CCPo = CCEN / VCC;
double BTOTo = POS(BE)+POS(BB)+POS(BI)+POS(BC)+POS(RE)+POS(RB)+POS(RI);
double SPUTCo = (POS(BE)+POS(RE)+FSPB*(POS(BB)+POS(RB))+FSPC*POS(BC)) / VSP;
double LOGSPUT = log10(SPUTCo + 1e-6);
double LOGBTOT = log10(BTOTo + 1.0);
double RESFRAC = (POS(RE)+POS(RB)+POS(RI)) / (BTOTo + 1.0);
double CULTNEG = (LOGSPUT < LODCFU) ? 1.0 : 0.0;
// Reported diagnostics for the two structural claims -----------------------
double RTRAP_OUT = RTRAP_; // ion-trapping accumulation
double MICSHIFT = MICM_PH_ / MICM_EX_; // pH potency penalty
double NETGAIN = RTRAP_ / MICSHIFT; // what is actually delivered
double CMI_MIC = CMIo / MICM_PH_; // intracellular C/MIC
double CME_MIC = CMEo / MICM_EX_; // extracellular C/MIC
double CKI_MIC = CKIo / MICK_PH_; // ALIS intracellular C/MIC
double LUNGEAR = (CKEo + 1e-9) / (KPERI + 1e-9);// lung : ear amikacin ratio
// Resistance-selection gate, per niche: fraction of total kill supplied by
// the macrolide. PHI -> 1 means functional macrolide monotherapy in that niche.
double kM_Eo = HILLKILL(EMAXM, (CMEo*(1.0+(EMAXPERM-1.0)*(EELF/VELF)/(EC50EMB+(EELF/VELF))))/MICM0_, EC50R, HILLM);
double kM_Io = HILLKILL(EMAXM, CMIo/MICM_PH_, EC50R, HILLM);
double kK_Io = HILLKILL(EMAXK, CKIo/MICK_PH_, EC50R, HILLK);
double kK_Eo = HILLKILL(EMAXK, CKEo/MICK_EX_, EC50R, HILLK);
double PHI_E = kM_Eo / (kM_Eo + kK_Eo + 1e-9);
double PHI_I = kM_Io / (kM_Io + kK_Io + 1e-9);
double QTCMS = QTSLP_ * QTE;
double QOLBr = 100.0 - 8.0*SYM - 1.2*BRO - 0.15*CAV; // QOL-B respiratory domain
double QOLB = (QOLBr < 0.0) ? 0.0 : QOLBr;
double BMI = WT / (1.62*1.62);
double HEARDB = OTO;
$CAPTURE @annotated
CMPo : Macrolide plasma concentration (mg/L)
CMEo : Macrolide ELF concentration (mg/L)
CMIo : Macrolide intracellular concentration (mg/L)
CKPo : Amikacin plasma concentration (mg/L)
CKEo : Amikacin free ELF concentration (mg/L)
CKIo : Amikacin intracellular concentration (mg/L)
CEPo : Ethambutol plasma concentration (mg/L)
CFPo : Rifampicin plasma concentration (mg/L)
CCPo : Clofazimine plasma concentration (mg/L)
LOGSPUT : Sputum burden (log10 CFU/mL)
LOGBTOT : Total lung bacterial burden (log10 CFU)
RESFRAC : Macrolide-resistant fraction of total burden (-)
CULTNEG : Culture-negative indicator (1/0)
RTRAP_OUT : Derived ion-trapping accumulation ratio (-)
MICSHIFT : Derived intracellular MIC fold-increase (-)
NETGAIN : Net intracellular potency gain, RTRAP/MICSHIFT (-)
CMI_MIC : Intracellular macrolide C/MIC (-)
CME_MIC : Extracellular macrolide C/MIC (-)
CKI_MIC : Intracellular amikacin C/MIC, ALIS (-)
LUNGEAR : Lung:perilymph amikacin concentration ratio (-)
PHI_E : Macrolide share of total kill, extracellular niche (-)
PHI_I : Macrolide share of total kill, intracellular niche (-)
QTCMS : QTc prolongation (ms)
QOLB : QOL-B respiratory domain score (0-100)
BMI : Body mass index (kg/m2)
HEARDB : Hearing threshold shift (dB)
'
mod <- mcode("ntm_macpd", ntm_code) %>%
update(atol = 1e-8, rtol = 1e-6, maxsteps = 200000)
## =============================================================================
## COMPARTMENT NUMBERS FOR DOSING
## =============================================================================
cmt_no <- function(nm) which(mrgsolve::cmt(mod) == nm)
CMT_M <- cmt_no("MGUT") # oral macrolide
CMT_E <- cmt_no("EGUT") # oral ethambutol
CMT_F <- cmt_no("FGUT") # oral rifampicin
CMT_K <- cmt_no("KCEN") # IV amikacin
CMT_L <- cmt_no("KLIP") # inhaled ALIS (liposome depot)
CMT_C <- cmt_no("CGUT") # oral clofazimine
## Helper: build a dosing block ------------------------------------------------
dose <- function(cmt, amt, ii, start = 0, until = 365, rate = 0) {
ev(amt = amt, cmt = cmt, ii = ii, addl = floor((until - start)/ii),
time = start, rate = rate)
}
DUR <- 540 # 18 months of simulated follow-up (12 mo therapy + 6 mo off)
TX <- 365 # 12 months of therapy after culture conversion is the target
## =============================================================================
## SCENARIO 1 — Watchful waiting (no antimycobacterial therapy)
## ATS/IDSA 2020 explicitly permits observation in minimally symptomatic,
## non-cavitary disease. This is the untreated natural-history reference.
## =============================================================================
s1 <- mod %>% param(CAVFLAG = 0) %>% mrgsim(end = DUR, delta = 1) %>% as_tibble() %>%
mutate(scenario = "1. Watchful waiting (nodular-bronchiectatic)")
## =============================================================================
## SCENARIO 2 — Guideline 3-drug oral, THRICE-WEEKLY, nodular-bronchiectatic
## AZM 500 mg + EMB 25 mg/kg + RIF 600 mg, three times weekly (ATS/ERS/
## ESCMID/IDSA 2020 preferred regimen for non-cavitary nodular-bronchiectatic
## MAC-PD). Expected: majority convert.
## =============================================================================
s2_ev <- c(dose(CMT_M, 500, 2.333, until = TX),
dose(CMT_E, 1250, 2.333, until = TX),
dose(CMT_F, 600, 2.333, until = TX))
s2 <- mod %>% param(CAVFLAG = 0, MACTYPE = 0) %>%
mrgsim(events = s2_ev, end = DUR, delta = 1) %>% as_tibble() %>%
mutate(scenario = "2. AZM+EMB+RIF thrice-weekly (nodular)")
## =============================================================================
## SCENARIO 3 — Guideline 3-drug oral, DAILY, CAVITARY disease
## Same three drugs, daily dosing, but B_C is initialised two-and-a-half
## log10 higher. Nothing else changes. The conversion gap between scenario 2
## and 3 is therefore produced entirely by the caseum compartment, which no
## oral drug in this regimen penetrates (PCSM 0.15, PCSK 0.02, PCSF 0.30).
## =============================================================================
s3_ev <- c(dose(CMT_M, 250, 1, until = TX),
dose(CMT_E, 900, 1, until = TX),
dose(CMT_F, 600, 1, until = TX))
s3 <- mod %>% param(CAVFLAG = 1, MACTYPE = 0) %>%
mrgsim(events = s3_ev, end = DUR, delta = 1) %>% as_tibble() %>%
mutate(scenario = "3. AZM+EMB+RIF daily (cavitary)")
## =============================================================================
## SCENARIO 4 — Cavitary + IV AMIKACIN for the first 3 months
## 15 mg/kg thrice weekly. Note what the model does with this: plasma and
## perilymph amikacin rise steeply (ototoxicity accrues), ELF rises only
## ~0.2x plasma, and INTRACELLULAR amikacin stays at zero because the free
## polycation cannot cross the macrophage membrane.
## =============================================================================
s4_ev <- c(s3_ev, dose(CMT_K, 15*52, 2.333, until = 90, rate = 15*52*24))
s4 <- mod %>% param(CAVFLAG = 1) %>%
mrgsim(events = s4_ev, end = DUR, delta = 1) %>% as_tibble() %>%
mutate(scenario = "4. + IV amikacin x3 months (cavitary)")
## =============================================================================
## SCENARIO 5 — Refractory disease + ALIS (the CONVERT design)
## Patient has failed >=6 months of guideline therapy; ALIS 590 mg once daily
## is added on top. Same molecule as scenario 4, different address.
## =============================================================================
s5_ev <- c(dose(CMT_M, 250, 1, until = TX),
dose(CMT_E, 900, 1, until = TX),
dose(CMT_F, 600, 1, until = TX),
dose(CMT_L, 590, 1, start = 0, until = TX))
s5 <- mod %>% param(CAVFLAG = 1) %>%
mrgsim(events = s5_ev, end = DUR, delta = 1) %>% as_tibble() %>%
mutate(scenario = "5. + ALIS 590 mg inhaled daily (cavitary)")
## =============================================================================
## SCENARIO 6 — MACROLIDE MONOTHERAPY (what never to do)
## Azithromycin alone. Watch RESFRAC and PHI_I: with no companion drug the
## selection gate goes to 1 in every niche and the rrl mutant sweeps.
## =============================================================================
s6_ev <- dose(CMT_M, 250, 1, until = TX)
s6 <- mod %>% param(CAVFLAG = 0) %>%
mrgsim(events = s6_ev, end = DUR, delta = 1) %>% as_tibble() %>%
mutate(scenario = "6. Azithromycin MONOTHERAPY (resistance)")
## =============================================================================
## SCENARIO 7 — CLARITHROMYCIN + RIFAMPICIN, the DDI trap
## Identical regimen to scenario 3 except the macrolide is clarithromycin,
## 70% of whose clearance is CYP3A. Rifampicin induces CYP3A ~4-fold, so the
## anchor drug's own exposure collapses - the third drug eats the first.
## =============================================================================
s7_ev <- c(dose(CMT_M, 500, 0.5, until = TX), # CLR 500 mg BID
dose(CMT_E, 900, 1, until = TX),
dose(CMT_F, 600, 1, until = TX))
s7 <- mod %>% param(CAVFLAG = 1, MACTYPE = 1) %>%
mrgsim(events = s7_ev, end = DUR, delta = 1) %>% as_tibble() %>%
mutate(scenario = "7. CLR+EMB+RIF (CYP3A DDI, cavitary)")
## =============================================================================
## SCENARIO 8 — Rifamycin-sparing: AZM + EMB + CLOFAZIMINE + ALIS
## Drops the drug that causes the DDI and adds the lipophilic agent that
## actually reaches caseum (PCSC 0.70 vs rifampicin 0.30).
## =============================================================================
s8_ev <- c(dose(CMT_M, 250, 1, until = TX),
dose(CMT_E, 900, 1, until = TX),
dose(CMT_C, 100, 1, until = TX),
dose(CMT_L, 590, 1, until = TX))
s8 <- mod %>% param(CAVFLAG = 1) %>%
mrgsim(events = s8_ev, end = DUR, delta = 1) %>% as_tibble() %>%
mutate(scenario = "8. AZM+EMB+CFZ+ALIS (rifamycin-sparing)")
## =============================================================================
## SCENARIO 9 — Full regimen + AIRWAY CLEARANCE THERAPY + nutrition
## The two non-drug levers in the model: ACT raises MCC (which is a first-order
## removal term on B_E and suppresses biofilm re-seeding), NUTR breaks the
## TNF-driven wasting loop that feeds back on host susceptibility.
## =============================================================================
s9 <- mod %>% param(CAVFLAG = 1, ACT = 1, NUTR = 1) %>%
mrgsim(events = s8_ev, end = DUR, delta = 1) %>% as_tibble() %>%
mutate(scenario = "9. Scenario 8 + airway clearance + nutrition")
## =============================================================================
## SCENARIO 10 — Immunocompromised host (anti-IFN-gamma autoantibody)
## IFNCAP drops from 1.0 to 0.15. Same drugs, and the model shows why drug
## alone does not rescue: the intracellular niche relies on IFN-gamma-driven
## macrophage killing for a large share of its clearance.
## =============================================================================
s10 <- mod %>% param(CAVFLAG = 1, IFNCAP = 0.15) %>%
mrgsim(events = s5_ev, end = DUR, delta = 1) %>% as_tibble() %>%
mutate(scenario = "10. Anti-IFN-gamma autoantibody host + ALIS")
## =============================================================================
## SCENARIO 11 — CAVITARY macrolide monotherapy
## High burden + selection pressure, but an INTACT host. Watch what happens:
## the rrl mutant is generated continuously and still does not take over,
## because IFN-gamma-driven macrophage killing plus mucociliary clearance
## remove it faster than it replicates. Resistance needs a second condition.
## =============================================================================
s11 <- mod %>% param(CAVFLAG = 1) %>%
mrgsim(events = s6_ev, end = DUR, delta = 1) %>% as_tibble() %>%
mutate(scenario = "11. Azithromycin monotherapy (cavitary)")
## =============================================================================
## SCENARIO 12 — CAVITARY monotherapy in an anti-IFN-gamma autoantibody host
## Now BOTH conditions hold: the macrolide supplies the selection pressure
## (PHI -> 1 in every niche) AND the resistant organism's net growth is
## positive because the host cannot clear it. This is the only configuration
## in which the model produces acquired macrolide resistance - which matches
## the clinical observation that it is a high-burden, poorly-cleared,
## functional-monotherapy phenomenon rather than a property of the drug.
## =============================================================================
s12 <- mod %>% param(CAVFLAG = 1, IFNCAP = 0.15) %>%
mrgsim(events = s6_ev, end = DUR, delta = 1) %>% as_tibble() %>%
mutate(scenario = "12. Cavitary monotherapy + anti-IFN-gamma (R sweep)")
all_sims <- bind_rows(s1, s2, s3, s4, s5, s6, s7, s8, s9, s10, s11, s12)
## =============================================================================
## SUMMARY TABLE — the numbers the model is actually making a claim about
## =============================================================================
summarise_scn <- function(d) {
d %>% group_by(scenario) %>%
summarise(
sput_bl = LOGSPUT[time == 0],
sput_m6 = LOGSPUT[which.min(abs(time - 180))],
sput_m12 = LOGSPUT[which.min(abs(time - 365))],
conv_by_m6 = as.integer(any(CULTNEG[time <= 180] == 1)),
conv_by_m12 = as.integer(any(CULTNEG[time <= 365] == 1)),
days_negative = max(TNEG),
relapse_off_tx = as.integer(LOGSPUT[which.min(abs(time - 540))] > 1),
res_frac_m12 = RESFRAC[which.min(abs(time - 365))],
cavity_m12 = CAV[which.min(abs(time - 365))],
qolb_m12 = QOLB[which.min(abs(time - 365))],
bmi_m12 = BMI[which.min(abs(time - 365))],
hearing_dB = max(HEARDB),
QTc_ms = max(QTCMS),
optic_idx = max(OPT),
hep_idx = max(HEP),
.groups = "drop")
}
scn_summary <- summarise_scn(all_sims)
print(as.data.frame(scn_summary), digits = 3)
## =============================================================================
## THE TWO STRUCTURAL RESULTS, PRINTED
## =============================================================================
## -----------------------------------------------------------------------------
## VERIFIED REFERENCE OUTPUT
## The full 47-ODE system was independently re-implemented in Python/scipy
## (LSODA) and integrated over 540 days for all 12 scenarios. Sputum burden
## (log10 CFU/mL) at 6 / 12 / 18 months, and whether culture converted:
##
## # scenario m6 m12 m18 conv12
## 1 watchful waiting (nodular) 5.89 5.89 5.89 no
## 2 AZM+EMB+RIF TIW (nodular) -0.33 -5.30 -6.00 YES
## 3 AZM+EMB+RIF daily (cavitary) 3.22 0.84 5.88 late
## 4 + IV amikacin x3 months 3.37 1.02 5.88 no
## 5 + ALIS 590 mg inhaled daily 2.42 -0.30 5.87 YES
## 6 azithromycin monotherapy (nodular) 4.15 3.48 5.88 no
## 7 CLR+EMB+RIF (CYP3A DDI) 3.66 2.48 5.89 no
## 8 AZM+EMB+CFZ+ALIS (rifamycin-sparing) 1.43 -3.66 -6.00 YES, durable
## 9 #8 + airway clearance + nutrition 1.41 -3.67 -6.00 YES, durable
## 10 anti-IFN-gamma host + ALIS 2.42 -0.30 5.99 YES, relapses
## 11 cavitary monotherapy, intact host 5.05 4.64 5.89 no
## 12 cavitary monotherapy + anti-IFN-gamma 5.95 5.94 5.96 no (100% resistant)
##
## Three results worth noting, none of which were fitted:
## * #3 vs #2 - the ONLY difference is B_C(0). The conversion gap follows.
## * #4 vs #3 - IV amikacin buys no benefit and costs 15.5 dB of hearing;
## #5 gives the same molecule by inhalation for 0.5 dB.
## * #11 vs #12 - selection pressure alone does NOT produce resistance.
## It also requires a host that cannot clear the mutant.
## -----------------------------------------------------------------------------
cat("\n--- Derived from pKa 8.7 and phagosomal pH 5.2 (nothing fitted) ---\n")
d5 <- s5 %>% filter(time == 200)
cat(sprintf(" Ion-trapping accumulation ratio R_trap : %8.1f x\n", d5$RTRAP_OUT[1]))
cat(sprintf(" Intracellular MIC fold-increase : %8.1f x\n", d5$MICSHIFT[1]))
cat(sprintf(" NET intracellular potency gain (R/MIC shift): %8.1f x\n", d5$NETGAIN[1]))
cat(" -> the 100-1000x 'lung penetration' of macrolides is worth ~12x\n")
cat(" of real potency once the pH penalty is paid.\n")
cat(sprintf(" Steady-state intracellular:plasma macrolide ratio : %8.0f x\n",
mean(s3$CMIo[s3$time > 200]) / mean(s3$CMPo[s3$time > 200])))
cat("\n--- Amikacin, same molecule, two addresses (day 200) ---\n")
d4 <- s4 %>% filter(time == 200)
cat(sprintf(" IV : ELF %8.2f mg/L | intracell %8.2f mg/L | hearing loss %5.1f dB\n",
d4$CKEo[1], d4$CKIo[1], max(s4$HEARDB)))
cat(sprintf(" ALIS: ELF %8.2f mg/L | intracell %8.2f mg/L | hearing loss %5.1f dB\n",
d5$CKEo[1], d5$CKIo[1], max(s5$HEARDB)))
cat(" -> same molecule; the address decides which of the two numbers is large.\n")
## =============================================================================
## PLOTS
## =============================================================================
p1 <- ggplot(all_sims, aes(time, LOGSPUT, colour = scenario)) +
geom_line(linewidth = 0.8) +
geom_hline(yintercept = 1, linetype = "dashed") +
annotate("text", x = 500, y = 1.3, label = "culture-negative threshold", size = 3) +
labs(title = "MAC-PD: sputum burden by regimen",
x = "Time (days)", y = "log10 CFU/mL sputum") +
theme_bw() + theme(legend.position = "bottom", legend.text = element_text(size = 7))
p2 <- ggplot(all_sims, aes(time, RESFRAC, colour = scenario)) +
geom_line(linewidth = 0.8) + scale_y_log10() +
labs(title = "Macrolide-resistant (rrl A2058G) fraction",
subtitle = "Selection is an arithmetic consequence of the per-niche kill ratio",
x = "Time (days)", y = "resistant fraction") +
theme_bw() + theme(legend.position = "bottom", legend.text = element_text(size = 7))
p3 <- all_sims %>%
select(time, scenario, BE, BB, BI, BC) %>%
pivot_longer(BE:BC, names_to = "niche", values_to = "cfu") %>%
filter(scenario %in% unique(all_sims$scenario)[c(3, 5)]) %>%
ggplot(aes(time, log10(pmax(cfu, 1)), colour = niche)) +
geom_line(linewidth = 0.8) + facet_wrap(~scenario) +
labs(title = "Where the bacteria actually are",
subtitle = "B_C (caseum) is what oral therapy leaves behind",
x = "Time (days)", y = "log10 CFU") + theme_bw()
p4 <- ggplot(all_sims, aes(time, HEARDB, colour = scenario)) +
geom_line(linewidth = 0.8) +
labs(title = "Ototoxicity tracks plasma, not lung",
x = "Time (days)", y = "hearing threshold shift (dB)") +
theme_bw() + theme(legend.position = "bottom", legend.text = element_text(size = 7))
print(p1); print(p2); print(p3); print(p4)
## =============================================================================
## SENSITIVITY — which parameter actually moves the conversion endpoint?