Model-based treatment planning in reproductive medicine

Model-based treatmentplanning

in reproductive medicine

Dr. Susanna Roblitz Zuse Institute Berlin

Computational Systems Biology Group

ZIB,FU

FU Berlin

September 14, 2015

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: susanna.roeblitz@zib.de

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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