frequency-domain response analysis for quantitative systems pharmacology models

Frequency-domain response analysis for quantitativesystems pharmacology modelsNovember 17, 2016

Pascal Schulthess

Systems PharmacologyLeiden Academic Centre for Drug Research (LACDR)Leiden University, The Netherlands

I’m an Control Engineer.

with a PhD in Theoretical Biophysics.now doing a PostDoc in Mathematical Pharmacology.

1

I’m an Control Engineer

.

with a PhD in Theoretical Biophysics.

now doing a PostDoc in Mathematical Pharmacology.

1

I’m an Control Engineer

.

with a PhD in Theoretical Biophysics

.

now doing a PostDoc in Mathematical Pharmacology.

1

A short excursion intoengineering

Mass-spring-damper system with base excitation

u

y

2

Mass-spring-damper system with base excitation

u

y

2

Mass-spring-damper system with base excitation

u

y

2

Mass-spring-damper system with base excitation

u

y

2

Mass-spring-damper system with base excitation

u

y

2

Mass-spring-damper system with base excitation

u

y

2

Mass-spring-damper system with base excitation

u

y

2

Frequency-domain response analysis

• How does a system respond to periodic inputs?

• Which input frequencies amplify/attenuate the output?

• Is there resonance?

3

Frequency-domain response analysis

• How does a system respond to periodic inputs?

• Which input frequencies amplify/attenuate the output?

• Is there resonance?

3

Frequency-domain response analysis

• How does a system respond to periodic inputs?

• Which input frequencies amplify/attenuate the output?

• Is there resonance?

3

Where’s the connection to pharmacology?

3

FdRA for QSP models

A tolerance and rebound PD model

4

A tolerance and rebound PD model

x1

u

x2

kin kout

ktol ktol

4

Response characteristic of the PD model

x1

u

x2

kin kout

ktol ktol

5

Response characteristic of the PD model

u G y

5

Response characteristic of the PD model

u G y

5

Response characteristic of the PD model

u G y

Input

u(t) = sin(ωt)

5

Response characteristic of the PD model

u G y

Input

u(t) = sin(ωt)

Output

y(t) = Asin(ωt+ φ)

5

Response characteristic of the PD model

u G y

Input

u(t) = sin(ωt)

Output

y(t) = Asin(ωt+ φ)

5

Frequency response of the PD model

x1

u

x2

kin kout

ktol ktol

Model equations

x(t) =[0 −koutktol −ktol

]x(t) +

[kin0

]u(t)

y(t) =[1 0

]x(t)

6

Frequency response of the PD model

Model equations

x(t) =[0 −koutktol −ktol

]x(t) +

[kin0

]u(t)

y(t) =[1 0

]x(t)

Transfer function

G(iω) =[1 0

] ([iω 00 iω

]−

[0 −koutktol −ktol

])−1 [kin0

]

=kin(ktol − iω)

ω2 − ktol(kout − iω)

6

Frequency response of the PD model

Model equations

x(t) =[0 −koutktol −ktol

]x(t) +

[kin0

]u(t)

y(t) =[1 0

]x(t)

Transfer function

G(iω) =[1 0

] ([iω 00 iω

]−

[0 −koutktol −ktol

])−1 [kin0

]=

kin(ktol − iω)

ω2 − ktol(kout − iω)

6

Frequency response of the PD model

Transfer function

G(iω) =[1 0

] ([iω 00 iω

]−

[0 −koutktol −ktol

])−1 [kin0

]=

kin(ktol − iω)

ω2 − ktol(kout − iω)

Magnitude

A = |G(iω)|

Phase shift

φ = argG(iω)

6

Frequency response of the PD model

Transfer function

G(iω) =kin(ktol − iω)

ω2 − ktol(kout − iω)

Magnitude

A = |G(iω)|

Phase shift

φ = argG(iω)

6

Alternative treatment scheme to optimise effect amplitude

7

Alternative treatment scheme to optimise effect amplitude

ResultTreatment every 8 hours minimises effect amplitude.

7

Alternative treatment scheme to optimise effect amplitude

ResultTreatment every 24 hours maximises effect amplitude.

7

FdRA allows for

analyticaloptimisation of dosing frequency.

7

Influence of model parameters

8

Influence of model parameters

8

Influence of model parameters

8

FdRA highlights how

parametersinfluence treatment scheme.

8

Potential of FdRA in QSP

Frequency Dependence of Osmo-Adaptation in yeast

Mettetal et al., Science (2008) & Muzzey et al., Cell (2009) 9

Frequency Dependence of Osmo-Adaptation in yeast

Mettetal et al., Science (2008) & Muzzey et al., Cell (2009) 9

Frequency dependence of osmo-adaptation in yeast

Mettetal et al., Science (2008) & Muzzey et al., Cell (2009) 10

Frequency dependence of osmo-adaptation in yeast

Mettetal et al., Science (2008) & Muzzey et al., Cell (2009) 10

Frequency dependence of osmo-adaptation in yeast

− Mapk signalling& nuclear import

Hog1-independentmechanisms

Hog1-dependentmechanisms

+

Glycerolaccumulation

Osmext Hog1∗

Osmint

Mettetal et al., Science (2008) & Muzzey et al., Cell (2009) 10

FdRA enables

model identificationfrom experiments.

10

Conclusion & outlook

Conclusion

Frequency-domain response analysis

• allows for analytical dosing frequency optimisation

• highlights how parameters influence treatment scheme

• enables model identification from experiments

11

Conclusion

Frequency-domain response analysis

• allows for analytical dosing frequency optimisation

• highlights how parameters influence treatment scheme

• enables model identification from experiments

11

Conclusion

Frequency-domain response analysis

• allows for analytical dosing frequency optimisation

• highlights how parameters influence treatment scheme

• enables model identification from experiments

11

Conclusion

Frequency-domain response analysis

• allows for analytical dosing frequency optimisation

• highlights how parameters influence treatment scheme

• enables model identification from experiments

11

Outlook

Open questions

• Which systems give rise to which response behaviour?

• Can FdRA identify model structures from experiments?

• Is FdRA able to suggest (better) treatment schedules?

• Can FdRA be extended to allow combinatory treatments?

• How to incorporate FdRA into clinical practice?

12

Outlook

Open questions

• Which systems give rise to which response behaviour?

• Can FdRA identify model structures from experiments?

• Is FdRA able to suggest (better) treatment schedules?

• Can FdRA be extended to allow combinatory treatments?

• How to incorporate FdRA into clinical practice?

12

Outlook

Open questions

• Which systems give rise to which response behaviour?

• Can FdRA identify model structures from experiments?

• Is FdRA able to suggest (better) treatment schedules?

• Can FdRA be extended to allow combinatory treatments?

• How to incorporate FdRA into clinical practice?

12

Outlook

Open questions

• Which systems give rise to which response behaviour?

• Can FdRA identify model structures from experiments?

• Is FdRA able to suggest (better) treatment schedules?

• Can FdRA be extended to allow combinatory treatments?

• How to incorporate FdRA into clinical practice?

12

Outlook

Open questions

• Which systems give rise to which response behaviour?

• Can FdRA identify model structures from experiments?

• Is FdRA able to suggest (better) treatment schedules?

• Can FdRA be extended to allow combinatory treatments?

• How to incorporate FdRA into clinical practice?

12

Outlook

Open questions

• Which systems give rise to which response behaviour?

• Can FdRA identify model structures from experiments?

• Is FdRA able to suggest (better) treatment schedules?

• Can FdRA be extended to allow combinatory treatments?

• How to incorporate FdRA into clinical practice?

12

Acknowledgements

• Piet Hein van der Graaf (@certara, @lacdr.leidenuniv)

• James Yates (@astrazeneca)

• Teun Post (@lapp, @lacdr.leidenuniv)

• Vivi Rottschäfer (@math.leidenuniv)

13