Modeling Pharmacology - CVUT 2026 presentation

Created by Tomas Kulhanek

pharmacolibrary

#modelica, #pharmacolibrary

Modeling Pharmacology

Tomáš Kulhánek, Ph.D.

VITO, 1.LF UK

Filip Ježek, Ph.D.

Univ of Michigan, 1.LFUK

Agenda seminar:

00:00 - interactive intro - do it yourself

3 patients - same diagnosis, same pharmacotherapy, but ...

find optimal dose for each of them, continue at:

https://digital-biosystems.github.io/pharma/

and do Patient1, Patient2 and Patient 3 - not Patient 4

equation models and basic simulation, pharmacokinetics of gentamicin, dose adjustment / change regimen, caffeine → effect

Agenda lecture: Pharmacokinetics, PHarmacodynamics, Pharmacogenomics

Try patient 4: https://digital-biosystems.github.io/pharma/

PRIBE - personal reference intervals

brave ZR8tgl5Xml

RAIDO

DigiTwin4PH - PGx digital twin

VITO

Flemish Institute for Technological Research

Mol, Belgium

Environmental unit

Digital Precision Health group

ONCOSCREEN

Pharmacology

Pharmacokinetics (PK) body → drug

Pharmacodynamics (PD) drug → body

Pharmacogenomics (PGx) genetics→drug&body

pharmacokinetics(PK): body → drug

Administration(absorption), Distribution, Metabolism, Elimination(excretion)

observation - concentration of a drug during time among different patients

brave JW8Psddw3W

1-compartment PK model

$c = c_0 \times e^{-Cl.t}$

or derivative form:

$c=\frac{M}{V_d}$

$\frac{dM}{dt} = - Cl \times c$

2-compartment PK model

$C_1=\frac{M_1}{V_{d1}}$

$C_2=\frac{M_2}{V_{d2}}$

brave AYU2OQg3y6

3-compartment PK model

standard Modelica language

Commercial tools:

Dymola,

, …

Open-source:

software engineering principles in mathematical modeling

can write equations

can plug & play with well defined components

why Modelica?

model of complex system may lead to implementation errors

A C Guyton, T G Coleman, H J Granger, Circulation: overall regulation, Annu Rev Physiol.1972;34:13-46.doi: 10.1146/annurev.ph.34.030172.000305.

Correction of schema after reimplementation in 2010

J.Kofránek, et al., Restoration of Guyton‘s Diagram for Regulation of the Circulation ...Physiol Res. 2010;59(6):897-908.doi: 10.33549/physiolres.931838.

Guyton's original scheme part of circulatory dynamics

equivalent implementation in component and acausal modeling language

.

Frank-Starling law is much more visible in component model - "force of the heart muscle depends on pressure of incoming blood".

small models - equation based

VirtualBoxVM 4UK0GmE2mR

Readability & Plausability

medium/complex models- composition of smaller models as components (icons) in diagrams

Dymola 9CIA5zGnUy

pk1


model pk1
  Real C;
  Real M(start=dosage);
  parameter Real dosage = 400 / 1000000;
  parameter Real Vd = 17.5 / 1000;
  parameter Real Cl = 0.1 / 1000 / 60 ;
  parameter Real MIC = 2 / 1000000 * 1000; //mg/l -> kg/m3
equation
  C = M / Vd;
  der(M) = -Cl * C;
end pk1;

pk2


model pk2
  Real C;
  Real M(start=dosage);
  parameter Real dosage = 500 / 1000000;
  parameter Real t1 = 8 * 3600; //hour -> seconds
  parameter Real Vd = 17.5 / 1000;
  parameter Real Cl = 0.1 / 1000 / 60 ;
  parameter Real MIC = 2 / 1000000 * 1000; //mg/l -> kg/m3
equation
  C = M / Vd;
  der(M) = -Cl * C;
  when sample(t1,t1) then
    reinit(M,pre(M)+dosage);
  end when;
end pk2;

seminar task 1

create pharmacokinetic model pk1 of gentamicin (1 dosage=400mg, Vd=17.5 l, Cl=0.1 l/min)

one dosage - simulate 24h (86400 s)
create copy pk2 with dosage every 8 hours
what regimen/dosage lead the C > MIC (2mg/l) during treatment
simulate 10 days of treatment (864 000 s)

pk2

dosage> 400mg - e.g. 500

t1 = 8 hours

standard Modelica library 4.0.0

custom libraries for specific domains

Physiolibrary - for modeling physiology (v1.0.0 won 1st library award at Modelica conference, Lund, 2014)

Mateják, M. (2023, December). Creating cardiovascular and respiratory models using Physiolibrary 3.0. In Modelica Conferences (pp. 463-468). https://doi.org/10.3384/ecp204463

Chemical - for modeling chemical processes (v1.0.0 won 1st library award at Modelica conference, 2015)

Mateják, M., Tribula, M., Ježek, F., & Kofránek, J. (2015, September). Free modelica library for chemical and electrochemical processes. In 11th International Modelica Conference, Versailles, France (Vol. 118, pp. 359-66). http://dx.doi.org/10.3384/ecp15118359

Pharmacolibrary

for modeling Pharmacology (v25.09 wan 1st library award at Modelica conference,Luzerne, 2025)

Kulhanek, T., Jezek, F., Kofránek, J., Mateják, M., & Rommes, S. (2025, October). Pharmacolibrary-Free Library to Model Pharmacology. In Modelica Conferences (pp. 61-72). https://doi.org/10.3384/ecp21861

class for compartment

class for elimination

class for administration

creating model = composing components

VirtualBoxVM SSD3EQXp9H

model of pharmacokinetics

1-compartment model Gentamicin (aminoglycoside antibacterials)

gentamicin - 1 day simulation

Hodiamont, Caspar J et al. (2022-08). “Clinical pharmacokinetics of gentamicin in various patient populations and consequences for optimal dosing for Gram-negative infections: An updated review”. en. In: Clin. Pharmacokinet. 61.8, pp. 1075–1094. ISSN: 0312-5963,1179-1926. DOI: 10.1007/s40262 - 022 - 01143 - 0. URL: http://dx.doi.org/10.1007/s40262-022-01143-0

gentamicin - 1 day simulation logscale

pk 1c simlog

2-compartment model Midazolam (hypnotics and sedatives)

midazolam - 12 h simulation

logscale - 12h with peripheral

pk2csimlog

Heizmann, P., Eckert, M. and Ziegler, W. (1983), Pharmacokinetics and bioavailability of midazolam in man.. British Journal of Clinical Pharmacology, 16: 43S-49S. https://doi.org/10.1111/j.1365-2125.1983.tb02270.x

3-compartment model Fentanyl (anesthetics)

fentanyl - 10h simulation

fentanyl - 10h simulation logscale

pk3csim

Kaneda, Kotaro and Tae-Hyung Han (2009-09). “Comparative population pharmacokinetics of fentanyl using non-linear mixed effect modeling: burns vs. non-burns”. en. In: Burns 35.6, pp. 790–797. ISSN: 0305-4179,1879-1409. DOI: 10.1016/j.burns.2008.12.006. URL: http://dx.doi.org/10.1016/j.burns.2008.12.006

class for compartment with blood flow

follows more physiology and anatomy of body parts and tissues

physiology based PK model - propranolol (beta blocker)

PBPK simulation - propranolol (beta-blocker)

5496 models of drugs by Anatomical Therapeutical Chemical (ATC) classification - knowledge base extracted and combined from Pubmed, Drugbank using LLM

ATC level 1

ATC level 3

ATC level 5

Drug model variants

caffeine

1-compartment model - caffeine

1 cup = 100 mg of caffeine in 8 hours

caffeine in 24 hours

seminar task

create model of pk of caffeine - using components fom Pharmacolibrary

oral intake - 95 mg(coffee) and 50 mg(tea)

Vd = 35 l Cl = 6.8 l/h ka=0.1 /min Tlag= 10 min

What is relation between concentration and effect?

linear effect

effectlin

Emax effect

effectemax

pharmacodynamics (PD): drug → body

What effect has a drug to body

dose/response relation ~ effect

irreversible effect

time dependent (R response, C concentration, k rate of irreversible effect)

$\frac{dR}{dt}=-k\times C\times R$

with recovery growth factor ks

$\frac{dR}{dt}=k_s \times R - k\times C\times R$

sigmoid Emax effect

effectsigmoid

seminar task 3

create model of dose response effect for caffein

behavioural (excitacy) 0 - 100%

EC50 = 10ug/ml, hill coeff = 1.85

cardiac effect (increased heart rate) 0-100%

EC50 = 20ug/ml, ...

model/simulate effect curve after 1 cup of coffee (95mg) (12 hours)
model/simulate effect curve after 1 cup of black tea (50mg) (12 hours)

PK PD model digoxin on hemodynamics of cardiovascular system

PKPD HemodynamicsMeurs flatNorm

pressure volume (PV) diagram

simulation 2

Go to https://digital-biosystems.github.io/pharma/#hemo/hemo2.md

Can we predict individual drug dose → blood plasma concentration → effect/response?

individual co-variates:

age, weight, height, sex, ethnicity, …, genomics

Pharmacogenomics (PGx)

What is individual variability of PK and PD based on genotype and phenotype?

PK PGx model metoprolol - illustrative influence CYP2D6 & CYP3A4

metoprolol

PK PGx population of 4 different patients

PK PGx simulation (metoprolol)

VirtualBoxVM w1OLlExIsM

Zamir, A., Hussain, I., ur Rehman, A. et al. Clinical Pharmacokinetics of Metoprolol: A Systematic Review. Clin Pharmacokinet 61, 1095–1114 (2022). https://doi.org/10.1007/s40262-022-01145-y

Metabolismus

obecně, první průchod (first pass) přes játerní buňky

aktivní lék → neaktivní lék (paracetamol)

neaktivní lék → aktivní lék (aspirin)

aktivní lék → více aktivní lék

více toxický (ethanol)

lék → více rozpustný ve vodě

paracetamol

acetaminophen → sulfate_conjugate

metabolism paracetamol

12h simulation - paracetamol metabolites (NAPQI is toxic)

most common pharmacogenes and mutation in Europe

omprehensive clinical pharmacogenomic (PGx) resource

https://www.clinpgx.org/

CYP2D6

hepatic CYP450 enzyme, Metabolizes ~20–25% of drugs (antidepressants, antipsychotics, opioids like codeine/tramadol, beta‑blockers, antiarrhythmics)
Key variants (by function)
- No function: 3, 4, 5, 6
- Decreased function: 9, 10, 14, 17, 29, 41
- Increased function: gene duplications 1xN, 2xN (ultra‑rapid)
Drug consequences
- Poor metabolizers → toxicity risk for inactivated drugs; lack of effect for prodrugs (codeine, tramadol)
- Ultra‑rapid metabolizers → low effect for many substrates; codeine toxicity from rapid morphine formation
Labels / guidelines
- EMA / EU labels: warnings or contraindication of codeine in CYP2D6 ultra‑rapid metabolizers
- CPIC, DPWG: phenotype‑based dosing / alternative drug recommendations for multiple CYP2D6 substrates (opioids, antidepressants, others)

CYP2C19

Pharmacogene / function
- CYP2C19 → CYP450 enzyme
- Metabolizes: clopidogrel, PPIs, many SSRIs/TCAs, voriconazole
Key variants (by function)
- No function: 2, 3
- Increased function: *17
Drug consequences
- Poor metabolizers → clopidogrel treatment failure; ↑ exposure and side effects with PPIs, SSRIs, TCAs
- Rapid/ultra‑rapid metabolizers (*17) → reduced exposure for some substrates (e.g., PPIs)
Labels / guidelines
- Labels: reduced clopidogrel effect in CYP2C19 loss‑of‑function carriers
- CPIC, DPWG: alternative to clopidogrel in poor metabolizers; dose/choice adjustments for PPIs, SSRIs, TCAs, voriconazole

CYP2C9

Pharmacogene / function
- CYP2C9 → CYP450 enzyme
- Metabolizes: warfarin, phenytoin, some NSAIDs, some ARBs and sulfonylureas
Key variants (by function)
- Reduced function: 2, 3 (Europe‑relevant)
- Other reduced‑function alleles more relevant outside Europe (e.g., 5, 6, 8, 11)
Drug consequences
- Warfarin: 2/3 → lower dose requirement, ↑ bleeding risk at standard dosing
- Similar pattern (↑ exposure, toxicity risk) for several CYP2C9‑cleared drugs (e.g., phenytoin, some NSAIDs)
Labels / guidelines
- Labels: acknowledge CYP2C9/VKORC1 influence on warfarin dosing
- CPIC, DPWG: genotype‑based warfarin dosing algorithms using CYP2C9 + VKORC1 (± CYP4F2)

DPYD

Pharmacogene / function
- DPYD → dihydropyrimidine dehydrogenase (DPD)
- Catabolizes: fluoropyrimidines (5‑FU, capecitabine, tegafur)
Key variants (by function)
- No / markedly reduced function: *2A (c.1905+1G>A), c.1679T>G
- Decreased function: c.2846A>T, c.1236G>A/HapB3
Drug consequences
- Intermediate / poor metabolizers → massive ↑ exposure to 5‑FU/capecitabine → high risk of severe or fatal toxicity (myelosuppression, mucositis, neurotoxicity)
Labels / guidelines
- Labels: EMA‑level warnings for DPYD variants and dose reduction/avoidance for fluoropyrimidines
- CPIC, DPWG: recommend large dose reductions or avoidance based on DPYD activity score; NCCN and EU oncology groups now endorse pre‑treatment testing

SLC01B1

Pharmacogene / function
- SLCO1B1 → OATP1B1 hepatic uptake transporter
- Handles hepatic uptake of several statins (esp. simvastatin, atorvastatin)
Key variants (by function)
- Decreased function: rs4149056 (c.521T>C, p.V174A, *5 allele)
Drug consequences
- Decreased‑function genotypes (e.g., TC/CC) → ↑ simvastatin (and some other statins) plasma levels → ↑ risk of myopathy/rhabdomyolysis
Labels / guidelines
- Labels: simvastatin product info highlights higher myopathy risk in rs4149056 carriers and suggests dose limitation
- CPIC, DPWG: recommend lower simvastatin doses or alternative statin in high‑risk genotypes

genetic impact for paracetamol

Genetic impact
- UGT1A6, UGT1A9, CYP2E1 polymorphisms alter paracetamol clearance / NAPQI formation (interindividual variability, mostly research‑grade).
- Glutathione pathway capacity modulates toxicity risk more than any single pharmacogene.
Guidelines
- No CPIC/DPWG pharmacogenetic dosing guideline for paracetamol.
- Existing guidelines: dose based on age, weight, liver function (not genotype)

Python workflow - fit to external data from PK-DB.com

VirtualBoxVM TIsoOjFLH2

howto find a drug

VirtualBoxVM quF8UzRISk

CA125 concentration based on tumor growth, interactive simulator - change growth factor (logistic function) and CA125 production rate

VR JIPKA - projekt 1.LFUK, FBMI ČVUT, VirtualLab s.r.o.

brave UOvACzHPK9

bring virtual reality to life

WebGL+WebXR Unity+WebView

VR JIPKA + eGolem monitor životních funkcí

brave 0Rks5PPqHX

léčiva podávána ve scénáři

anestetikum a sedativum: Např. Propofol nebo Midazolam
infůze fyziologického roztoku: Např. Lactated Ringer/Hartman solution
antibiotika pro léčbu zánětu: např. piperacillin-tazobactam

blood-gas exchange

Dymola qmDZxxtrfj

respiration

Dymola sdXGmJf24o

hemodynamics of cardiovascular system

Dymola 9CIA5zGnUy

Conclusion

Pharmacolibrary: https://github.com/digital-biosystems/Pharmacolibrary (fork)

components for modeling pharmacology

+ repository of drug models

pharmacokinetic: 5496 drugs models, 1st version parameters extracted from primary papers, Drugbank, Pubmed & LLM (GPT4.1)

pharmacodynamics: various effects <10 models

pharmacogenomics: various genotype/phenotype influence <10 models

near future:

knowledge base from sources EMA, FDA, ClinPGx, Drugbank, Pubmed
informed update of PK, PD and PGx models with evidence score powered by LLM (evaluating GPT 5, GPT-OSS, Claude 4.6, ...)
integrate other modeling repos (SBML, physiomeproject, ...)
add toxicology models, food, biomarkers

co-simulation of multiple models via FMI in static web app with bodylight.js

https://egolem.online/demo/

hemodynamics of cardiovascular system

Dymola 9CIA5zGnUy

blood-gas exchange

Dymola qmDZxxtrfj

respiration

Dymola sdXGmJf24o

Physiomodel

firefox SHzAoizS4q

Complex model of physiology in Modelica and Physiolibrary

https://physiomodel.org

1-compartment PK model in Modelica (text variant)

1-compartment PK model

$c = c_0 \times e^{-Cl.t}$

or derivative form:

$c=\frac{M}{V_d}$

$\frac{dM}{dt} = - Cl \times c$

1-compartment PK model in component diagram

equations are behind each component

connecting components → equations among variables

compartment

$q_m =\frac{dM}{dt}$

$c=\frac{M}{V_d}$

elimination

q_m=Cl*c

connectors

$qm_1 +qm_2 = 0\$

c_1 = c_2

logscale - 12h simulation

comprehensibility

Chemical 2.0

modeling physical chemistry

Physiolibrary 3.0.0

www.physiolibrary.org

Dymola qmDZxxtrfj

Distribution

simplified - ideal mixing, no volume flow rate, compartment (Vd volume of distribution)

$q_m =\frac{dM}{dt}$

$c=\frac{M}{V_d}$

and 1st order kinetics

q_m=Cl_a*c_a-Cl_b*c_b

Metabolism

generally, first pass

active drug → inactive drug (paracetamol)

inactive drug → active drug (aspirin)

active drug → more active drug

make drug more toxic (ethanol)

make drug more water soluble

1st order kinetics between compartments

paracetamol

acetaminophen → sulfate_conjugate

for more complex - use Chemical library (https://www.physiolibrary.org)

equivalent 1-compartment model (in equations)

VirtualBoxVM 4UK0GmE2mR

1-compartment model

parameters for intravenous administration of gentamicin, type of antibiotic against bacterial infections

2-compartment model

parameters for intravenous administration of midazolam, a short-acting benzodiazepine used for sedation, anesthesia, ...

Distribution - physiology based

compartment - with concentration mixing based on volumetric flow through organs and tissues:

$\frac{dM}{dt} = q_{v_{a}}*actualStream(c_a)+q_{v_{b}}*actualStream(c_b)+q_m$

fixed volumetric flow component:

Elimination

via kidney or liver using clearance rate Cl

q_m=Cl*c

computed half life

$t_{1/2} = \frac{ln(2) \times V_d}{Cl}$

seminar task 2

create derived pharmacokinetic model of gentamicin.

Patient has chronic kidney disease (clearance is 20% of norm)

what is maximum peak concentration
adjust regimen/dosage so C>MIC(2mg/l) and C<Ctox (35 mg/l)

pk3, pk4

dosage < 400 mg or t1 = 24 hour or combination

Administration (absorption) - route

parenteral (e.g. intravenous, intraarterial (rare), main parameters: F bioavailability (almost 100%), adminMass, adminDuration):

enteral (e.g. oral, main parameters: F bioavailability, adminMass, Tlag, ka absorption rate)

Administration (absorption kinetics)

instanteous (e.g. intravenous, intraarterial, main parameters: bolus injection adminMass):

Zero-order (e.g. continuous infusion, main parameter: adminDuration):

First-order (rate proportional to the amount of drug remaining to be absorbed, main parameters: adminMass, ka (absorption rate))

3-compartment model

connectors

web simulator - 10 minutes

try by yourself https://digital-biosystems.github.io/pharma/

PK PD model Midazolam on EEG activity

midazolam

PK PD simulation

Pharmacolibrary / GITHUB

https://github.com/creative-connections/Pharmacolibrary

acknowledgment

ONCOSCREEN project, funded by the European Union’s Horizon Europe grant No. 101097036.

subaward to R01 HL173346. funded by NIH

RAIDO

PRIBE - personal reference intervals

brave ZR8tgl5Xml

RAIDO

PRIBE - personal reference intervals

brave ZR8tgl5Xml

PRIBE - personal reference intervals

brave ZR8tgl5Xml

RAIDO

optimal dose of lithium carbonate

brave OZ24t5RrJ2

VITO

Flemish Institute for Technological Research

Mol, Belgium

Environmental unit

Digital Precision Health group

DigiTwin4PH - PGx digital twin

VITO

Flemish Institute for Technological Research

Mol, Belgium

Environmental unit

Digital Precision Health group

VITO

Flemish Institute for Technological Research

Mol, Belgium

Environmental unit

Digital Precision Health group

DigiTwin4PH - PGx digital twin

ONCOSCREEN

DigiTwin4PH - PGx digital twin

ONCOSCREEN

iron metabolism visualisation

brave 5rh0hlzHNL

eGolem powered by bodylight.js

https://egolem.online/irm/ https://bodylight.physiome.cz

PRIBE - personal reference intervals

brave ZR8tgl5Xml

RAIDO

PRIBE - personal reference intervals

brave ZR8tgl5Xml

VITO

Flemish Institute for Technological Research

Mol, Belgium

Environmental unit

Digital Precision Health group

VITO

Flemish Institute for Technological Research

Mol, Belgium

Environmental unit

Digital Precision Health group

co-simulace a bodylight.js - simulace v prohlížeči (WebAssembly)

DigiTwin4PH - PGx digital twin

ONCOSCREEN

bring virtual reality to life

WebGL+WebXR Unity+WebView

bring virtual reality to life

WebGL+WebXR Unity+WebView

VR JIPKA - nastavení a připojení

brave UOvACzHPK9

VR JIPKA - nastavení a připojení

brave UOvACzHPK9

VR JIPKA + eGolem monitor životních funkcí

brave 0Rks5PPqHX

VITO

Flemish Institute for Technological Research

Mol, Belgium

Environmental unit

Digital Precision Health group

bring virtual reality to life

WebGL+WebXR Unity+WebView

VR JIPKA - nastavení a připojení

brave UOvACzHPK9

VR JIPKA + eGolem monitor životních funkcí

brave 0Rks5PPqHX

VR JIPKA + eGolem monitor životních funkcí

brave 0Rks5PPqHX

co-simulace a bodylight.js - simulace v prohlížeči (WebAssembly)

léčiva podávána ve scénáři

anestetikum a sedativum: Např. Propofol nebo Midazolam
infůze fyziologického roztoku: Např. Lactated Ringer/Hartman solution
antibiotika pro léčbu zánětu: např. piperacillin-tazobactam

blood-gas exchange

Dymola qmDZxxtrfj

blood-gas exchange

Dymola qmDZxxtrfj

co-simulace a bodylight.js - simulace v prohlížeči (WebAssembly)

léčiva podávána ve scénáři

anestetikum a sedativum: Např. Propofol nebo Midazolam
infůze fyziologického roztoku: Např. Lactated Ringer/Hartman solution
antibiotika pro léčbu zánětu: např. piperacillin-tazobactam

léčiva podávána ve scénáři

anestetikum a sedativum: Např. Propofol nebo Midazolam
infůze fyziologického roztoku: Např. Lactated Ringer/Hartman solution
antibiotika pro léčbu zánětu: např. piperacillin-tazobactam

blood-gas exchange

Dymola qmDZxxtrfj

respiration

Dymola sdXGmJf24o

respiration

Dymola sdXGmJf24o

hemodynamics of cardiovascular system

Dymola 9CIA5zGnUy

hemodynamics of cardiovascular system

Dymola 9CIA5zGnUy

respiration

Dymola sdXGmJf24o

hemodynamics of cardiovascular system

Dymola 9CIA5zGnUy