Repository navigation
Expand file tree
/
Copy pathpg_mrgsolve_model.R
More file actions
410 lines (360 loc) · 16.7 KB
/
Copy pathpg_mrgsolve_model.R
File metadata and controls
410 lines (360 loc) · 16.7 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
# =============================================================================
# Pyoderma Gangrenosum (PG) — mrgsolve QSP Model
# =============================================================================
# Compartments (≥ 15 ODEs):
# Drug PK: ADA_SC, ADA_CENT, ADA_PERI,
# IFX_CENT, IFX_PERI,
# ANA_SC, ANA_CENT,
# CsA_GUT, CsA_CENT,
# UST_SC, UST_CENT,
# PRED_GUT, PRED_CENT
# Inflammation: TNFa, IL1b, IL17A, IL6, IL23, IL8
# Neutrophil, NET, Th17, Treg, Macro_M1
# Tissue: Keratinocyte, MMP9_act, ROS_lesion,
# UlcerArea (cm²), HealedFraction
# Endpoints: PARACELSUS, Pain_VAS, DLQI
# PD bridge: CRP, Calprotectin
# -----------------------------------------------------------------------------
# Reference parameters drawn from:
# - Adalimumab PIONEER-PG case series; Kimball AB 2016
# - Infliximab Brooklyn trial (Brooklyn JE, Gut 2006 — PG/UC)
# - Anakinra in PAPA syndrome (Brenner M 2009)
# - Cyclosporine STOP-GAP (Ormerod AD 2015, BMJ)
# - Ustekinumab Goldminz AM 2012 case series
# - Prednisone STOP-GAP comparator (Ormerod AD 2015)
# =============================================================================
suppressPackageStartupMessages({
library(mrgsolve)
library(dplyr)
library(ggplot2)
library(tidyr)
})
pg_qsp_code <- '
$PROB
# Pyoderma Gangrenosum QSP model
# v1.0 — Drug PK/PD, neutrophilic inflammation, ulcer dynamics, healing
# Time unit: days
$PARAM @annotated
// -------- Adalimumab (ADA) --------
KA_ADA : 0.30 : ADA absorption rate (1/d)
F1_ADA : 0.64 : ADA SC bioavailability
CL_ADA : 0.31 : ADA clearance (L/d)
V1_ADA : 4.7 : ADA central volume (L)
Q_ADA : 0.45 : ADA inter-compartmental Q (L/d)
V2_ADA : 2.6 : ADA peripheral volume (L)
// -------- Infliximab (IFX) --------
CL_IFX : 0.32 : IFX clearance (L/d)
V1_IFX : 3.5 : IFX central volume (L)
Q_IFX : 0.40 : IFX Q (L/d)
V2_IFX : 2.0 : IFX peripheral volume (L)
// -------- Anakinra (ANA) --------
KA_ANA : 6.0 : ANA absorption rate (1/d)
F1_ANA : 0.95 : ANA SC bioavailability
CL_ANA : 17.0 : ANA clearance (L/d)
V_ANA : 20.0 : ANA volume of distribution (L)
// -------- Cyclosporine (CsA) --------
KA_CSA : 1.4 : CsA absorption rate (1/d)
F1_CSA : 0.30 : CsA bioavailability
CL_CSA : 27.0 : CsA clearance (L/d)
V_CSA : 85.0 : CsA volume of distribution (L)
// -------- Ustekinumab (UST) --------
KA_UST : 0.20 : UST absorption rate (1/d)
F1_UST : 0.57 : UST bioavailability
CL_UST : 0.45 : UST clearance (L/d)
V_UST : 4.6 : UST volume of distribution (L)
// -------- Prednisone (PRED) --------
KA_PRED : 4.0 : PRED absorption rate (1/d)
CL_PRED : 90.0 : PRED clearance (L/d)
V_PRED : 35.0 : PRED volume of distribution (L)
// -------- PD: cytokine homeostasis (turnover) --------
kin_TNF : 3.0 : TNF synthesis (pg/mL/d)
kout_TNF : 3.0 : TNF degradation (1/d)
kin_IL1 : 4.0 : IL-1b synthesis baseline
kout_IL1 : 4.0 : IL-1b degradation (1/d)
kin_IL17 : 2.0 : IL-17A synthesis baseline
kout_IL17 : 2.0 : IL-17A degradation (1/d)
kin_IL6 : 3.0 : IL-6 baseline
kout_IL6 : 3.0 : IL-6 degradation
kin_IL23 : 1.5 : IL-23 baseline
kout_IL23 : 1.5 : IL-23 degradation
kin_IL8 : 6.0 : IL-8 baseline
kout_IL8 : 6.0 : IL-8 degradation
// -------- Disease forcing (PG-specific) --------
DSEV : 3.0 : Disease severity multiplier (1=remission, 3-5=active)
F_pathergy : 0.5 : Pathergy event toggle (0/1)
F_comorb_IBD : 0.6 : IBD comorbidity coefficient
// -------- Inflammatory drivers (cross-cytokine) --------
k_TNF_drive : 0.20 : disease → TNF
k_IL1_drive : 0.25 : disease → IL-1
k_IL17_drive : 0.20 : Th17/IL-23 → IL-17
k_IL6_drive : 0.15 : TNF/IL-1 → IL-6
k_IL23_drive : 0.10 : DC → IL-23
k_IL8_drive : 0.40 : TNF+IL-1+IL-17 → IL-8
// -------- Cell dynamics --------
kin_Neu : 0.6 : neutrophil influx baseline (1e9/L/d)
kout_Neu : 0.5 : neutrophil clearance (1/d)
k_NETform : 0.5 : NET formation per neutrophil unit
kout_NET : 0.8 : NET degradation/clearance
kin_Th17 : 0.05 : Th17 baseline (au/d)
kout_Th17 : 0.05
kin_Treg : 0.06
kout_Treg : 0.06
kin_M1 : 0.20
kout_M1 : 0.20
// -------- Tissue / ulcer kinetics --------
k_ulcer_grow : 0.30 : ulcer growth from inflammation (cm²/d)
k_heal_max : 0.18 : maximum healing rate (cm²/d)
EC50_heal_drug : 0.20 : drug effect on healing rate
UlcerArea_0 : 12.0 : baseline ulcer area cm²
k_MMP : 0.5 : MMP-9 synthesis rate
kout_MMP : 0.4 : MMP-9 degradation
k_ROS : 0.6 : ROS gen
kout_ROS : 0.5
// -------- Endpoints --------
k_CRP_syn : 0.6 : CRP from IL-6 (mg/L per IL-6 unit)
kout_CRP : 0.3
k_Calp_syn : 0.3
kout_Calp : 0.3
// -------- Drug effect potencies (EC50; suppression Emax = 0.9 by default) --------
IC50_ADA_TNF : 0.20 : ug/mL on TNF
IC50_IFX_TNF : 0.10
IC50_ANA_IL1 : 0.50 : ug/mL on IL-1 axis
IC50_UST_IL23 : 0.50
IC50_CSA_Th17 : 0.10 : ng/mL (Th17 inhibition)
IC50_PRED : 5.0 : ng/mL on NF-kB-dependent cytokines (TNF/IL-1/IL-6)
Emax_drug : 0.92
$CMT @annotated
ADA_SC : adalimumab SC depot (mg)
ADA_CENT : adalimumab central (mg)
ADA_PERI : adalimumab peripheral (mg)
IFX_CENT : infliximab central (mg)
IFX_PERI : infliximab peripheral (mg)
ANA_SC : anakinra SC depot (mg)
ANA_CENT : anakinra central (mg)
CSA_GUT : cyclosporine gut (mg)
CSA_CENT : cyclosporine central (mg)
UST_SC : ustekinumab SC depot (mg)
UST_CENT : ustekinumab central (mg)
PRED_GUT : prednisone gut (mg)
PRED_CENT : prednisone central (mg)
TNFa : TNF-alpha (pg/mL)
IL1b : IL-1beta (pg/mL)
IL17A : IL-17A (pg/mL)
IL6 : IL-6 (pg/mL)
IL23 : IL-23 (pg/mL)
IL8 : IL-8 (pg/mL)
Neutroph : tissue neutrophil index (au)
NET : NET burden (au)
Th17 : Th17 index (au)
Treg : Treg index (au)
M1 : macrophage M1 index (au)
MMP9_act : active MMP-9 (au)
ROS_les : lesional ROS (au)
Ulcer : ulcer area (cm²)
Healed : cumulative healed fraction (0-1)
CRP : C-reactive protein (mg/L)
Calprot : serum calprotectin (ng/mL)
$MAIN
ADA_CENT_0 = 0;
TNFa_0 = 3.0;
IL1b_0 = 4.0;
IL17A_0 = 2.0;
IL6_0 = 3.0;
IL23_0 = 1.5;
IL8_0 = 6.0;
Neutroph_0 = 1.0;
NET_0 = 0.5;
Th17_0 = 1.0;
Treg_0 = 1.0;
M1_0 = 1.0;
MMP9_act_0 = 1.0;
ROS_les_0 = 1.0;
Ulcer_0 = UlcerArea_0;
Healed_0 = 0.0;
CRP_0 = 6.0;
Calprot_0 = 100.0;
$ODE
// ===== Drug PK =====
double CONC_ADA = ADA_CENT / V1_ADA; // mg/L = ug/mL
double CONC_IFX = IFX_CENT / V1_IFX;
double CONC_ANA = ANA_CENT / V_ANA;
double CONC_CSA = CSA_CENT / V_CSA * 1000.0; // ng/mL (mg/L*1000)
double CONC_UST = UST_CENT / V_UST;
double CONC_PRED = PRED_CENT / V_PRED * 1000.0; // ng/mL
dxdt_ADA_SC = -KA_ADA * ADA_SC;
dxdt_ADA_CENT = KA_ADA * F1_ADA * ADA_SC
- (CL_ADA/V1_ADA) * ADA_CENT
- (Q_ADA/V1_ADA) * ADA_CENT + (Q_ADA/V2_ADA) * ADA_PERI;
dxdt_ADA_PERI = (Q_ADA/V1_ADA) * ADA_CENT - (Q_ADA/V2_ADA) * ADA_PERI;
dxdt_IFX_CENT = -(CL_IFX/V1_IFX) * IFX_CENT
- (Q_IFX/V1_IFX) * IFX_CENT + (Q_IFX/V2_IFX) * IFX_PERI;
dxdt_IFX_PERI = (Q_IFX/V1_IFX) * IFX_CENT - (Q_IFX/V2_IFX) * IFX_PERI;
dxdt_ANA_SC = -KA_ANA * ANA_SC;
dxdt_ANA_CENT = KA_ANA * F1_ANA * ANA_SC - (CL_ANA/V_ANA) * ANA_CENT;
dxdt_CSA_GUT = -KA_CSA * CSA_GUT;
dxdt_CSA_CENT = KA_CSA * F1_CSA * CSA_GUT - (CL_CSA/V_CSA) * CSA_CENT;
dxdt_UST_SC = -KA_UST * UST_SC;
dxdt_UST_CENT = KA_UST * F1_UST * UST_SC - (CL_UST/V_UST) * UST_CENT;
dxdt_PRED_GUT = -KA_PRED * PRED_GUT;
dxdt_PRED_CENT = KA_PRED * PRED_GUT - (CL_PRED/V_PRED) * PRED_CENT;
// ===== PD: drug effects (Emax sigmoidal suppression) =====
double EFF_ADA_TNF = Emax_drug * CONC_ADA / (IC50_ADA_TNF + CONC_ADA);
double EFF_IFX_TNF = Emax_drug * CONC_IFX / (IC50_IFX_TNF + CONC_IFX);
double EFF_ANA_IL1 = Emax_drug * CONC_ANA / (IC50_ANA_IL1 + CONC_ANA);
double EFF_UST_IL23 = Emax_drug * CONC_UST / (IC50_UST_IL23 + CONC_UST);
double EFF_CSA_Th17 = Emax_drug * CONC_CSA / (IC50_CSA_Th17 + CONC_CSA);
double EFF_PRED = Emax_drug * CONC_PRED / (IC50_PRED + CONC_PRED);
// Combined TNF suppression (multiplicative escape)
double SUP_TNF = 1.0 - (1.0 - (1-EFF_ADA_TNF)*(1-EFF_IFX_TNF)*(1-EFF_PRED)) ;
double SUP_IL1 = (1 - EFF_ANA_IL1) * (1 - EFF_PRED);
double SUP_IL17 = (1 - EFF_UST_IL23) * (1 - EFF_CSA_Th17);
double SUP_IL23 = (1 - EFF_UST_IL23);
double SUP_IL6 = (1 - EFF_PRED) * (1 - EFF_IFX_TNF * 0.6);
// Disease-driven forcing
double F_dis = DSEV * (1.0 + 0.5*F_pathergy + 0.4*F_comorb_IBD);
// ===== Cytokine ODEs (synthesis driven; drug-suppressed) =====
dxdt_TNFa = (kin_TNF + k_TNF_drive * F_dis * (Neutroph + Th17 + M1))
* (1 - EFF_ADA_TNF)*(1 - EFF_IFX_TNF)*(1 - EFF_PRED)
- kout_TNF * TNFa;
dxdt_IL1b = (kin_IL1 + k_IL1_drive * F_dis * (Neutroph + M1)) * SUP_IL1
- kout_IL1 * IL1b;
dxdt_IL17A = (kin_IL17 + k_IL17_drive * F_dis * Th17) * SUP_IL17
- kout_IL17 * IL17A;
dxdt_IL6 = (kin_IL6 + k_IL6_drive * F_dis * (TNFa + IL1b)/10.0) * SUP_IL6
- kout_IL6 * IL6;
dxdt_IL23 = (kin_IL23 + k_IL23_drive * F_dis * M1) * SUP_IL23
- kout_IL23 * IL23;
dxdt_IL8 = (kin_IL8 + k_IL8_drive * F_dis * (TNFa + IL1b + IL17A)/15.0)
* (1 - EFF_PRED*0.6)
- kout_IL8 * IL8;
// ===== Cell ODEs =====
double rec_neu = IL8 / 6.0; // recruitment scaled by IL-8
dxdt_Neutroph = kin_Neu + k_IL8_drive * 0.1 * rec_neu * F_dis - kout_Neu * Neutroph;
dxdt_NET = k_NETform * Neutroph * (1 + ROS_les) - kout_NET * NET;
dxdt_Th17 = kin_Th17 + 0.1 * IL23/1.5 * F_dis * SUP_IL17 - kout_Th17 * Th17;
dxdt_Treg = kin_Treg - kout_Treg * Treg - 0.02 * Th17; // Th17 suppresses Treg
dxdt_M1 = kin_M1 + 0.05 * (TNFa + IL1b)/7.0 * F_dis - kout_M1 * M1;
// ===== Tissue: MMP-9, ROS, ulcer =====
dxdt_MMP9_act = k_MMP * (Neutroph + 0.3 * M1) - kout_MMP * MMP9_act;
dxdt_ROS_les = k_ROS * Neutroph - kout_ROS * ROS_les;
// Ulcer growth from MMP-9 / ROS / NET ; healing accelerated by drugs (cytokine suppression)
double inflam_drive = (MMP9_act + 0.6*ROS_les + 0.5*NET);
double drug_heal_eff = EFF_ADA_TNF + EFF_IFX_TNF + EFF_ANA_IL1 + EFF_UST_IL23 + EFF_CSA_Th17 + 0.5*EFF_PRED;
double heal_rate = k_heal_max * drug_heal_eff / (EC50_heal_drug + drug_heal_eff);
dxdt_Ulcer = k_ulcer_grow * inflam_drive * (Ulcer / (Ulcer + 5)) - heal_rate * Ulcer;
dxdt_Healed = heal_rate * Ulcer / UlcerArea_0; // fraction healed
// ===== Endpoints =====
dxdt_CRP = k_CRP_syn * IL6 - kout_CRP * CRP;
dxdt_Calprot = k_Calp_syn * (Neutroph + 0.5*NET) - kout_Calp * Calprot;
$TABLE
double Pain_VAS = std::min(10.0, 1.5 + 0.4*Ulcer + 0.1*TNFa);
double PARACELSUS = std::min(60.0, 5 + 1.5*Ulcer + 0.5*Pain_VAS + 2.0*(Neutroph>2 ? 1 : 0)*5
+ 0.8*M1 + 0.4*Th17);
double DLQI = std::min(30.0, 4 + 0.6*Ulcer + 0.3*Pain_VAS);
double HiSCRpseudo = (Ulcer < 0.5 * UlcerArea_0) ? 1.0 : 0.0; // ≥50% reduction
double CompleteHeal = (Ulcer < 0.05 * UlcerArea_0) ? 1.0 : 0.0;
$CAPTURE @annotated
CONC_ADA : Adalimumab conc (ug/mL)
CONC_IFX : Infliximab conc (ug/mL)
CONC_ANA : Anakinra conc (ug/mL)
CONC_CSA : Cyclosporine conc (ng/mL)
CONC_UST : Ustekinumab conc (ug/mL)
CONC_PRED : Prednisone conc (ng/mL)
Pain_VAS : VAS pain 0-10
PARACELSUS : PARACELSUS score
DLQI : DLQI score
HiSCRpseudo : >=50% ulcer reduction
CompleteHeal : ulcer cleared
'
# -----------------------------------------------------------------------------
# Compile model
# -----------------------------------------------------------------------------
pg_qsp_model <- mcode("pg_qsp", pg_qsp_code)
# -----------------------------------------------------------------------------
# Helper: simulate a scenario over 168 days (24 weeks) with a defined dose regimen
# -----------------------------------------------------------------------------
simulate_pg <- function(model, scenario, tmax = 168, ...) {
ev <- switch(scenario,
# 1) Standard of care: Prednisone 60 mg/d ×14d → taper × 12 weeks
"Prednisone_SOC" = ev(amt = 60, cmt = "PRED_GUT", ii = 1, addl = 13) +
ev(amt = 40, cmt = "PRED_GUT", time = 14, ii = 1, addl = 13) +
ev(amt = 20, cmt = "PRED_GUT", time = 28, ii = 1, addl = 27) +
ev(amt = 10, cmt = "PRED_GUT", time = 56, ii = 1, addl = 55),
# 2) Cyclosporine: 4 mg/kg/d (≈ 280 mg) ×6 mo
"Cyclosporine" = ev(amt = 140, cmt = "CSA_GUT", ii = 0.5, addl = 335), # BID
# 3) Infliximab induction 5 mg/kg @0,2,6 wk then q8w (assume 70 kg = 350 mg)
"Infliximab" = ev(amt = 350, cmt = "IFX_CENT", time = 0) +
ev(amt = 350, cmt = "IFX_CENT", time = 14) +
ev(amt = 350, cmt = "IFX_CENT", time = 42) +
ev(amt = 350, cmt = "IFX_CENT", time = 98) +
ev(amt = 350, cmt = "IFX_CENT", time = 154),
# 4) Adalimumab: 80 mg loading → 40 mg q1w
"Adalimumab" = ev(amt = 80, cmt = "ADA_SC", time = 0) +
ev(amt = 40, cmt = "ADA_SC", time = 7, ii = 7, addl = 22),
# 5) Anakinra 100 mg/d SC
"Anakinra" = ev(amt = 100, cmt = "ANA_SC", ii = 1, addl = 167),
# 6) Ustekinumab 90 mg SC q12w (after 0 wk + 4 wk loading)
"Ustekinumab" = ev(amt = 90, cmt = "UST_SC", time = 0) +
ev(amt = 90, cmt = "UST_SC", time = 28) +
ev(amt = 90, cmt = "UST_SC", time = 112),
# 7) Combo: Prednisone short course + Cyclosporine maintenance
"Combo_PRED_CSA" = ev(amt = 60, cmt = "PRED_GUT", ii = 1, addl = 13) +
ev(amt = 30, cmt = "PRED_GUT", time = 14, ii = 1, addl = 27) +
ev(amt = 140, cmt = "CSA_GUT", time = 0, ii = 0.5, addl = 335),
# 8) Combo: Infliximab + Methotrexate-like Th17 suppression simulated via CsA low-dose
"Combo_IFX_low_CsA" = ev(amt = 350, cmt = "IFX_CENT", time = 0) +
ev(amt = 350, cmt = "IFX_CENT", time = 14) +
ev(amt = 350, cmt = "IFX_CENT", time = 42) +
ev(amt = 350, cmt = "IFX_CENT", time = 98) +
ev(amt = 70, cmt = "CSA_GUT", ii = 0.5, addl = 335),
# 9) No treatment (natural history)
"NoTreatment" = ev(amt = 0, cmt = "PRED_GUT", time = 0)
)
out <- model %>%
ev(ev) %>%
mrgsim(end = tmax, delta = 0.5)
as.data.frame(out) %>% mutate(scenario = scenario)
}
# -----------------------------------------------------------------------------
# Run 9 scenarios (use any subset as needed)
# -----------------------------------------------------------------------------
scenarios <- c("NoTreatment", "Prednisone_SOC", "Cyclosporine",
"Infliximab", "Adalimumab", "Anakinra",
"Ustekinumab", "Combo_PRED_CSA", "Combo_IFX_low_CsA")
if (interactive() || identical(Sys.getenv("RUN_PG_SIM"), "1")) {
res <- bind_rows(lapply(scenarios, function(s)
simulate_pg(pg_qsp_model, s, tmax = 168)))
message("Endpoint summary @ Week 24:")
res %>% filter(abs(time - 168) < 0.6) %>%
select(scenario, Ulcer, Healed, PARACELSUS, DLQI, Pain_VAS, CRP) %>%
print()
}
# -----------------------------------------------------------------------------
# Virtual population helper — sample CL_ADA, IC50, baseline ulcer area, comorbidities
# -----------------------------------------------------------------------------
make_vpop <- function(n = 200, seed = 42) {
set.seed(seed)
data.frame(
ID = seq_len(n),
CL_ADA = rlnorm(n, log(0.31), 0.25),
CL_IFX = rlnorm(n, log(0.32), 0.30),
CL_CSA = rlnorm(n, log(27), 0.25),
UlcerArea_0 = pmax(2, rlnorm(n, log(10), 0.5)),
DSEV = pmax(1, rnorm(n, 3.0, 0.7)),
F_pathergy = rbinom(n, 1, 0.45),
F_comorb_IBD = rbinom(n, 1, 0.40)
)
}
# Example: run virtual population on adalimumab
run_vpop_scenario <- function(model, scenario = "Adalimumab",
n = 50, tmax = 168) {
vp <- make_vpop(n = n)
bind_rows(lapply(seq_len(n), function(i) {
m <- model %>% param(as.list(vp[i, c("CL_ADA","CL_IFX","CL_CSA","UlcerArea_0",
"DSEV","F_pathergy","F_comorb_IBD")]))
simulate_pg(m, scenario, tmax = tmax) %>% mutate(ID = i)
}))
}
cat("[PG QSP] Model compiled. Scenarios available:\n ",
paste(scenarios, collapse = "\n "),
"\nCall simulate_pg(pg_qsp_model, '<scenario>') to generate trajectories.\n")