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Model-based treatmentplanning
in reproductive medicine
Dr. Susanna Roblitz Zuse Institute Berlin
Computational Systems Biology Group
ZIB,FU
FU Berlin
September 14, 2015
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Motivation
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The human menstrual cycle
Exactly timed interplay ofphysiological processes
I follicle development
I ovulation and fertilization
I formation of corpus luteum
I embryonic attachment andgrowth in the uterus
⇒ coordination between neuraland endocrine systems
(http://www.websters-online-dictionary.org/definitions/Menstrual Cycle)
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Endocrine disorders
Unwanted childlessness among couples in Europe: 12-15%
Female health problems: 50%, thereof 40% endocrinological diseases
Infertility due to female problems
EU infertile couplesin reproductive age
Infertility due to endocrinological
diseases
I PCOS (Polyzystic Ovarian Syndrom):main cause for hyperandrogenism, leading to cycle disorders and infertility(4-12% of women in reproductive age)
I Endometriosis (uterine lining outside uterus):about 40% of women at reproductive age, thereof 30-50% infertility
I Hyperprolactinemia (increased blood levels of prolactin):in about 20% of women with reproductive disorders
I External factors: smoking, BMI, age
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Reproductive medicine
Increased chance for successful pregnancy by modern techniques:
I In-vitro fertilization (IVF)
I Intracytoplasmic sperm injection (ICSI)
Success rates: 8 - 35%
Depending on the clinic due to differenttreatment strategies!
Aim: supply of model-based clinical decision support system forreproductive endocrinologists
I better understanding of complex processes
I simulation and optimization of treatment strategies in silico(cost-saving and efficient)
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Virtual hospital
I input: patient data,treatment protocol
I output: actions to beperformed on thepatient
based on
I a population ofvirtual patients
I a virtual doctor
Patient-specific model
Treatment protocol
Physician Patient
Actions
Measurements
Actio
ns
Op
tio
ns
Individualised Treatment Protocol
Pass orFail + Counterexample
Mo
de
lling
+C
linic
al
exa
ms
Observable Outputs
Patient-specificmodel (plant)
Controllable Inputs(Controllable External Factors)
Treatment protocolmodel (controller)
Uncontrollable Inputs (Uncontrollable External Factors)
Model-Based Verification of Treatment Protocols
Observable Outputs
Patient-specificmodel (plant)
Controllable Inputs(Controllable External Factors)
Treatment protocolmodel (controller)
Uncontrollable Inputs (Uncontrollable External Factors)
Model-Based Design of Individualised Treatment Protocols
?
Modelling
Virtual Hospital
Parameter identification
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Experimental data in vivo
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Untreated cycles: healthy women
−10 0 10 20 30 400
20
40
60
80
100
IU/L
LH
−10 0 10 20 30 400
5
10
15
20
IU/L
FSH
−10 0 10 20 30 400
100
200
300
400
500
pg/m
l
E2
−10 0 10 20 30 400
5
10
15
20
25
30
ng/m
l
P4
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Untreated cycles: women with PCOS
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Treatment protocol data
0" 1" 2" 3" 4" 5" 6" 7" 8" 9" 10" 11" 12" 13" 14"
Fer0lity'treatment'
Downregula0on'with'GNrH''Analoga'(Long'protocol)''or'Primolut'N'(short'protocol)'
E2"P"PRL"T"A'
E2'P'T'
DHEAS'A'
UltraKsound'
' ' ' Daily' ' ' ' injec0on' ' ' ' of' ' ' ' FSH' ' ' or' ' ' HmG' ((9K' 14' days)' ' .''''
E2'T'
DHEAS'A'
UltraKsound'
Verfica0on'of'successful'
downregula0on'
Ovula0on'induc0on'between'day'9'and'day'14'(depending'on'follicles'size,'number'and'E2'level)'
E2'T'
DHEAS'A'
UltraKsound'
Individual'0ming'of'controls'every'1K2'(3)'days'
Egg're0reval'35h'aZer'ovula0on'induc0on'
Embryo'transfer'2K3'days'aZer'egg'
re0eval''
Ovarrechts Ovar links
GnRHa hMG/ Tag Datum BT E2 P4 < 10 12 14 16 18 ≥ < 10 12 14 16 18 ≥FSH pmol/L nmol/L 10 11 13 15 17 19 20 10 11 13 15 17 19 20
.
.
.1 225 Fr 07.06.13 8 2841 4 1 1 5 1 11 225 Sa 08.06.13 91 225 So 09.06.13 101 225 Mo 10.06.13 11 6062 2 1 1 1 2 3 5 3 3
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Treatment cycle: ultrasound measurements
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Drug data
Single dose Nafarelin (GnRH agonist)
4 5 6 7 8 90
0.5
1
1.5
2
2.5
4 5 6 7 8 90
50
100
150
4 5 6 7 8 95
10
15
20
25
30
35
40
4 5 6 7 8 90
50
100
150
200
250
300
Single and multiple dose Cetrorelix (GnRH antagonist)
0 20 40 600
5
10
15
20
25
0 20 40 60 800
2
4
6
8
0 20 40 602.5
3
3.5
4
4.5
5
5.5
6
6.5
0 20 40 60 800
50
100
150
measurements: drug, LH, FSH, E2
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Model development for thehuman menstrual cycle
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Conceptual model
Compartments: blood, ovaries,uterus, pituitary, hypothalamusComponents:
I Estradiol
I Progesterone
I Inhibin A and B
I LH + receptor binding
I FSH + receptor binding
I GnRH + receptor binding
I 6 follicular stages
I 6 luteal stages (corpusluteum)
HYPOTHALAMUS
PITUITARY
CORPUS LUTEUM
OVARIES
inhibin
activin
follistatin
FSH
LH
GnRH
estradiol
progesterone
estradiol
progesterone
TEUM
ovulation
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Model GynCycle
����
����
Lut1 Lut2Sc2OvFPrF
GnRH antagonist
CENTRAL COMPARTMENT
GnRH antagonist
DOSING COMPARTMENT
PERIPHERAL COMPARTMENT
GnRH antagonist
GnRH agonist
DOSING COMPARTMENT
GnRH Ant−RecComplex
inactive GnRH−Rec
complex
complex
active GnRH−Rec
active Ago−Rec
complex
GnRH agonist
CENTRAL COMPARTMENT
AF1 AF2 AF3 AF4 Sc1 Lut3 Lut4
inactive
GnRH Receptors
GnRH Receptors
active
inactive Ago−Rec
complex
GnRH (G)
Progesterone (P4)
Estradiol (E2)
Inhibin B (IhB)
Inhibin A (IhA)
effective IhA (IhA )e
free LH receptors
LH(R )
LH receptor complex
(LH−R)
desensitized rec.
LH,des
pit
pituitary LH
(LH )blood
serum LH
pit(FSH )pituitary FSH
blood(FSH )
serum FSH free FSH receptors
(R )FSH
FSH receptor complex
(FSH−R)
(R )
FSH,des(R )desensitized rec.
(LH )
(freq)
( s )
foll. LH sensitivity
(mass)GnRH mass
GnRH frequency
GynCycle: 33(+8) ODEs, 114 parameters [Roblitz et al. (2013)]
I a model for the idealized cycle of a healthy womanI computation of hormone profiles and follicle development over
time
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Submodel for follicular development
xi : radius of follicle i
dxi
dt= A(G − D), i = 1, . . . , n
A := µH+i (FSH)
G :=
νκH−(P4) + (ν + β)xi
n∑j=1
xj
xi
D :=
(νβ + x2i )
n∑j=1
xj + κxi
xi
H−(P4) := cη5
P4(t)5 + η5, H+
i (FSH) :=FSH(t)5
δi5 + FSH(t)5
initial FSH sensitivity: ∼ N (µ, σ)
# follicles created in a fixed time interval: ∼ Poisson
0 2 4 6 8 10 12 140
0.02
0.04
0.06
0.08
0.1
FSH Sensitivity Mean100 150 200 250 300 350
Ovu
l per
per
iod
0.5
1
1.5
2
2.5
3
3.5
4
Number of ovulations per period
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Parameter estimation
Model: y(t, θ) = (y1(t, θ), . . . , yn(t, θ)) ∈ Rn
Parameters: θ = (θ1, ..., θq) ∈ Rq
Data: zkl ≈ yk(tl , θ), k = 1, . . . , n, l = 1, . . . ,mk
(i) direct minimisation of least squares error
‖F (θ)‖22 =
n∑k=1
mk∑l=1
(zkl − yk(tl , θ))2
2σ2kl
θ−→ min
⇒ ill-posed problem(ii) computation of joint probability distributions according toBayes’ theorem P(θ|z) ∝ P(z |θ)P(θ) with likelihood
P(z |θ) ∝ exp(−‖F (θ)‖2
2
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Results of in silico experiments
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Generic model for normal cycles
Single parametrization from real patient normal cycle data.
I normal cycle simulation
0 10 20 300
50
100
150
mIU
/mL
LH
0 10 20 300
5
10
15
20
mIU
/mL
FSH
0 10 20 300
5
10
15
20
25
30
ng/m
L
P4
0 10 20 300
100
200
300
400
500
pg/m
L
E2
I simulating the effect ofbirth control pills
0 50 100 150 200 250 3000
20
40
60
80
100
120
day
LH P4 estrogens
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Validation of generic model
Validate generic model with real patient treatment data.
I single dose agonist (nafarelin)
−20 0 20 40 60 80 1000
50
100
150
200
day−20 0 20 40 60 80 1000
50
100
150
200
day−20 0 20 40 60 80 1000
50
100
150
200
day
I multiple dose agonist (nafarelin)
−20 0 20 40 60 80 100 120 1400
5
10
15
20
days
ng/m
L
datasimulated P4
[Roblitz et al. (2013)]
I single dose antagonist(cetrorelix)
−30 −20 −10 0 10 200
100
200
300
days
pg/m
L
dataE2
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Uncertainty quantification
0 20000 40000 6000021000
21500
22000
22500 par16
0 20000 40000 60000
9.2
9.4 par71
0 20000 40000 600004.2
4.3
4.4
4.5 par87
21000 21500 22000 225000.000
0.002
0.004
0.006 par16
9.2 9.40
5
10
15 par71
4.2 4.3 4.4 4.50
5
10
15 par87
I 82 random variables, uniform prior distribution
I posterior sampling: Metropolis-Hastings algorithm with lognormalproposal distribution
I alignment of LH peaks in each sample; only acceptance of periodicsolutions with cycle length 20-50 days
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Virtual patients
Generate model instances (parametrizations) compatible with realpatient data for the normal cycle [Mancini et al. (2014)].
finite set of biologically admissable parameter sets
Real Patient
Virtual patient
(a) Medical level
(b) Computation level
offline −→ online
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Virtual patients
Validate virtual patient models with real patient data fromtreatment cycles.
Long protocol: downregulation cycle days 23 to 50 with Triptoreline, then 14 days
stimulation, finally Ovitrelle (drug database!)
−→ model refinement −→
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Model-based treatment verification & design
I treatment verificationthe treatment model (closedloop system) reaches a statein which some desiredproperty is satisfied(treatment goals)
I treatment designfinding values for treatmentparameters (type, dose andtime of drug) that optimizesome key performanceindicators (KPIs): E2 levels,number and size of follicles,total amount of drug
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Model-based treatment verification
Verify that a given treatment protocol reachesits goal for the largest possible number of(virtual) patients → evaluate success rate
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Model-based treatment design
Synthesised generic down-regulation treatments require 40% of theinjections and <25% of the overall Decapeptyl amount required byreference treatment. Individualised treatments even lighter, stillachieving clinical goals!
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Model-based treatment design
incremental change oftreatment parameters:
I age class
I AMH level
I AFC class
I dose ofstimulation drug
→ set ofPareto-optimaltreatments, in which atleast one performanceindicator is better
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Conclusion
Benefit
I the virtual hospital as a trainingtool for physicians
I suggestions for new clinical studies
Future work
I improve the model
I improve the mathematicalalgorithms
I perform model-based comparisonof treatment protocols
I extend approach toendocrinological diseases
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Acknowledgement
Computational Systems Biology Grouphttp://www.zib.de/numeric/csb
in particular:
Thomas Dierkes, Rainald Ehrig, Stefan Schafer,
Claudia Stotzel
Contact: [email protected]
Partners in the EU-project PAEON-Model-Driven Computation ofTreatments for Infertility RelatedEndocrinological Diseases
I Enrico Tronci (La SapienzaRome)
I Brigitte Leeners (UniversityHospital Zurich)
I Tillmann Kruger (HannoverMedical School)
I Marcel Egli (University Lucerne)
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