Talk at the Berlin Center for Studies of Complex Chemical Systems

1. Dynamical network biomarkers in migraine
(a)
mi
n
ths
on
cortex
magnetic
l
HY,TH
ele
(b)
PAG
(c)
p
ay
1d
e
e
r
rom
t
td
m
cle
in e c y
o
os
igr
a
e
4 -72h
dynamical
network
biomarkers
m
bone
cranial circulation
cranial innervation
ctr
ica
5-60
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Markus A. Dahlem (HU Berlin)
SPG
LC
SSN
RVM
ON
OFF
TG
TCC
a tt a c k
-fre
e
d a ys
to
Berlin Center for Studies of Complex Chemical Systems, Jan 24, 2014

2. Outline
Electrical & magnetic stimulation of the brain: Neuromodulation
Causality confusion in migraine: Dynamical network biomarkers
Mathematical migraine models: From genotype to phenotype
Towards therapeutic intervention
Conclusion

3. Outline
Electrical & magnetic stimulation of the brain: Neuromodulation
Causality confusion in migraine: Dynamical network biomarkers
Mathematical migraine models: From genotype to phenotype
Towards therapeutic intervention
Conclusion

4. History of electrical & magnetic stimluation
Non-drug treatment for headaches (AD 47)
Scribonius Largus, court physician to the Roman emperor Claudius 47 AD used
the black torpedo fish (electric rays) to treat migraine.

5. History of electrical & magnetic stimluation
Non-drug treatment for headaches (1788)
P. J. Koehler and C. J. Boes, A history of non-drug treatment in headache,
particularly migraine. Brain 133:2489-500. 2010

6. History of electrical & magnetic stimluation
Non-drug treatment for headaches (1887)
P. J. Koehler and C. J. Boes, A history of non-drug treatment in headache,
particularly migraine. Brain 133:2489-500. 2010

7. History of electrical & magnetic stimluation
Non-drug treatment for headaches (1896)

8. History of electrical & magnetic stimluation
Non-drug treatment for headaches (1961)
(1985) Zeitschrift EEG-EMG, Georg Thieme Verlag Stuttgart

9. History of electrical & magnetic stimluation
Non-drug treatment for headaches (2013)

10. Disclosure: Conflict of interest
Consulting services for Neuralieve Inc. (trading as eNeura
Therapeutics)

11. Modern neuromodulation (invasive)

12. Modern neuromodulation (invasive)

13. Modern neuromodulation (invasive)

14. Modern neuromodulation (invasive)

15. Modern neuromodulation (invasive)

16. Neuromodulation in migraine
hypothalamic deep brain stimulation (hDBS),
sphenopalatine ganglion stimulation (SPGS)
occipital nerve stimulation (ONS),
cervical spinal cord stimulation (cSCS),
hypothalamic deep brain stimulation (hDBS),
vagus nerve stimulation (VNS),
transcutaneous electrical nerve stimulation (TENS),
transcranial magnetic stimulation (TMS),
transcranial direct current stimulation (tDCS),
transcranial alternate current stimulation (tACS).

17. Long history in non-drug migraine treatment

18. Long history in non-drug migraine treatment

19. Old problems remain
¨
“Uber die physiologischen Wirkungen der elektrischen B¨der liegen eine Reihe von Angaben [...] vor.
a
[...]
Im allgemeinen haben faradische B¨der einen erfrischenden Einfluß, galvanische sollen m¨de machen.
a
u
Es kommt f¨r die Wirkung entschieden auf die Dauer der B¨der an, k¨rzere werden mehr anregend, l¨ngere mehr
u
a
u
a
erschlaffend wirken.
Durchsichtig ist jedenfalls die physiologische Begr¨ndung dieser B¨der durchaus nicht, man wird sich vorstellen,
u
a
daßsie im allgemeinen die eines indifferenten Bades, mit dem ein milder Hautreiz verbunden ist, haben.
Es m¨gen dadurch Aenderungen in unseren Allgemeingef¨hlen, also Wohlbehagen, Erfrischung oder M¨digkeit
o
u
u
bedingt werden. Nach meiner Ansicht liegt aber die Hauptwirkung dieser elektrischen B¨der in erster Linie auf
a
suggestivem Gebiete, und das rechtfertigt ihre Anwendung und ihre unleugbaren Erfolge auf dem Gebiete der
nerv¨sen Allgemeinleiden, wie Hysterie, Neurasthenie etc.”
o
(Lehrbuch der klinischen Hydrotherapie, Max Matthes)

20. Outline
Electrical & magnetic stimulation of the brain: Neuromodulation
Causality confusion in migraine: Dynamical network biomarkers
Mathematical migraine models: From genotype to phenotype
Towards therapeutic intervention
Conclusion

21. (i)
mi
n
ths
m
cortex
p
y
a
1d
magnetic
l
HY,TH
ele
ctr
(ii)
PAG
(iii)
e
r
rom
t
td
on
cle
in e c y
os
igr
a
e
4 -72h
dynamical
network
biomarkers
m
bone
cranial circulation
cranial innervation
ica
5-60
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
SPG
LC
SSN
RVM
ON
OFF
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).

22. 5-60
(i)
mi
n
ths
m
on
cle
in e c y
ay
bone
cranial circulation
cranial innervation
cortex
(ii)
(iii)
p
1d
e
r
rom
t
td
igr
a
os
m
e
4 -72h
dynamical
network
biomarkers
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).

23. 5-60
(i)
mi
n
ths
m
on
cle
in e c y
ay
bone
cranial circulation
cranial innervation
cortex
(ii)
(iii)
p
1d
e
r
rom
t
td
igr
a
os
m
e
4 -72h
dynamical
network
biomarkers
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).

24. 5-60
(i)
mi
n
ths
m
on
cle
in e c y
ay
bone
cranial circulation
cranial innervation
cortex
(ii)
HY,TH
(iii)
p
1d
e
r
rom
t
td
igr
a
os
m
e
4 -72h
dynamical
network
biomarkers
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).

25. 5-60
(i)
mi
n
ths
m
on
cle
in e c y
ay
bone
cranial circulation
cranial innervation
cortex
(ii)
HY,TH
(iii)
p
1d
e
r
rom
t
td
igr
a
os
m
e
4 -72h
dynamical
network
biomarkers
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).

26. 5-60
(i)
mi
n
ths
m
on
cle
in e c y
bone
cranial circulation
cranial innervation
cortex
(ii)
HY,TH
SPG
(iii)
SSN
p
y
a
1d
e
r
rom
t
td
igr
a
os
m
e
4 -72h
dynamical
network
biomarkers
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).

27. 5-60
(i)
mi
n
ths
m
on
cle
in e c y
bone
cranial circulation
cranial innervation
cortex
(ii)
HY,TH
SPG
(iii)
SSN
p
y
a
1d
e
r
rom
t
td
igr
a
os
m
e
4 -72h
dynamical
network
biomarkers
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).

28. (i)
mi
n
ths
m
cortex
p
y
a
1d
magnetic
l
HY,TH
ele
ctr
(ii)
PAG
(iii)
e
r
rom
t
td
on
cle
in e c y
os
igr
a
e
4 -72h
dynamical
network
biomarkers
m
bone
cranial circulation
cranial innervation
ica
5-60
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
SPG
LC
SSN
RVM
ON
OFF
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).

29. a ur a
(i)
m
on
cle
in e c y
cortex
p
y
a
1d
HY,TH
magnetic
ele
ctr
(ii)
PAG
(iii)
e
r
rom
t
td
igr
a
os
ths
e
4 -72h
(avg 2 we
e
a ch
m
bone
cranial circulation
cranial innervation
l
mi
n
ica
5-60
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
SPG
LC
SSN
RVM
ON
OFF
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
• M. A. Dahlem, S. Rode, A. May, N. Fujiwara, Y. Hirata, K. Aihara, J. Kurths, Towards dynamical network
biomarkers in neuromodulation of episodic migraine, Translational Neuroscience, 4,282-294 (2013).

30. (i)
mi
n
ths
m
cortex
p
y
a
1d
magnetic
l
HY,TH
ele
ctr
(ii)
PAG
(iii)
e
r
rom
t
td
on
cle
in e c y
os
igr
a
e
4 -72h
dynamical
network
biomarkers
m
bone
cranial circulation
cranial innervation
ica
5-60
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network & Dynamical Network Biomarker
SPG
LC
SSN
RVM
ON
OFF
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
• M. A. Dahlem, S. Rode, A. May, N. Fujiwara, Y. Hirata, K. Aihara, J. Kurths, Towards dynamical network
biomarkers in neuromodulation of episodic migraine, Translational Neuroscience, 4,282-294 (2013).

31. Early-warning signals for sudden deterioration of diseases
Dynamical Network Biomarkers

32. Early-warning signals for sudden deterioration of diseases
large fluctuations in
cerebreal blood
flow control
DNB
B
DN
Migraine generator network (MGN)
bone
cerebral blood flow
?
Which
subnetworks
drive the
transtions into
the pain
phase?
highly variable
pattern of free
energy stravation
prodrome
aura
headache
postdrome
1 day
5-60min
4-72h
1 day
cortex
subcortical
parasympathetic
control
ON
OFF
• M. A. Dahlem, S. Rode, A. May, N. Fujiwara, Y. Hirata, K. Aihara, J. Kurths, Towards dynamical network
biomarkers in neuromodulation of episodic migraine, Translational Neuroscience, 4,282-294 (2013).
cranial innervation
spreading
depression
(SD)
&
brainstem
modulatory network
Dynamical network biomarker (DNB)

33. Unitary hypothesis for multiple natural migraine triggers
light
bone
cerebral blood flow
exercise
foods (chocolate, wine, ...)
menstrual cycle
olfactory stimuli
cortex
subcortical
parasympathetic
control
...
All triggers originate or activate subnetwork: pre- and
postganglionic parasym- pathetic neurons in the
SPG
SSN
ON
OFF
superior salivatory nucleus (SSN) and sphenopalatine
ganglion (SPG).
R. Burstein and M. Jakubowski, Unitary hypothesis for multiple triggers of the pain and strain of migraine. J Comp
Neurol. 493,9-14 (2005).
cranial innervation
sleep deprevation
brainstem
modulatory network
stress

34. Causality confusion in migraine
pain phase
prodromal phase
attack-free interval
time
τ
Hougaard et al, Provocation of migraine with aura using natural trigger factors, Neurology 80,428-431 (2013)
• M.A. Dahlem, J. Kurths, A. May, K. Aihara, M. Scheffer, and M. D. Ferrari, Causality confusion in migraine: ,
Cephalalgia accepted

35. Outline
Electrical & magnetic stimulation of the brain: Neuromodulation
Causality confusion in migraine: Dynamical network biomarkers
Mathematical migraine models: From genotype to phenotype
Towards therapeutic intervention
Conclusion

36. Modeling pain initiation and sensitization
50
seizure-like
afterdischarges
V
EK
dominance
pump current
ENa
0
Iapp
depolarization block
50
100
transmembrane
b
voltage (mV)
inside cell
outside cell
towards genetics
a
c
I
II
III
IV
m-gate
begin
deactivation
INa -driven
repolarization
V
+
0
5
10
15
20
time (s)
25
30
VI
35
cortical tissue
d
bone
cranial circulation
cranial innervation
cortex
cortex
HY,TH
SD
ignition
PAG
HY,TH
HY,TH
behavior,
sensory
processing
SD
corticothalamic
action
PAG
SPG
f g
bone
cranial circulation
cranial innervation
cortex
SD
release
noxious
agents
PAG
SPG
e
bone
cranial circulation
cranial innervation
SPG
visual aura (0min)
LC
LC
SSN
RVM
off
TCC
on
LC
SSN
RVM
TG
off
on
TCC
• Dahlem et al. (2013) Translational Neuroscience, 4, 282
SSN
RVM
TG
off
TCC
on
TG
sensory aura (15min)

37. From HH-type conductance-based to
conductance- & ion-based models (2nd generation model)
C
Extracellular Space
Cl
K+
-
Cl
K+
-
Na+
Na+
Neuron
3Na+
∂V
= −INa − IK − Ileak −Ipump −Iapp (1)
∂t
INa = gNa m3 h(V − ENa )
¯
IK
Ileak
= gK n4 (V − EK )
¯
= gleak (V − Vrest )
Diffusion
2K+
K+
Bath/Vasculature
∂n
∂t
∂[ion]o
∂t
∂[ion]i
∂t
= αn (1 − n) − βn,
A
Iion
FVolo
A
Iion
FVoli
∂h
· · · (2) − (4)
∂t
= −
=
(5) − · · ·
• N. H¨bel, E. Sch¨ll, M. A. Dahlem, Bistable dynamics underlying excitability of ion homeostasis in neuron
u
o
models under review

38. name
Cm
α
voltot
rn
A
Γ
R
T
F
Ipmax,1
Ipmax,2
gNamax
gKmax
gNal
gKl
gCl
ECl
value & unit
1µF/cm2
0.2
4/3π53 µm3
−15 3
√ 0.5236 × 10 m
3
5 1 − αµm≈4.6416µm
2
4πrn ≈ 270.73424µm2
≈ 2.7 × 10−6 cm2
A (αvoltot )−1 F−1
0.06698725858
8.3144621 JK−1 mol−1
293.5K
96 485.3415 sA/mol
5.14µA/cm2
matched Ipmax,1 at rest
120 mS/cm2
36 mS/cm2
0.12 mS/cm2
0.001 mS/cm2
0.5 mS/cm2
-65mV
description
conductance
volume fraction of ECS
total volume
total volume in m3
radius neural compartment
surface area
surface are in cm2
conversion factor
num. value (for given α, rn )
gas constant
temperatur
Faraday constant
pump rate
pump rate
conductance
conductance
leak conductance
leak conductance
leak conductance
initial reversal potential

39. FHM3 and spreading depression
60
V
EK
wild-type
20
V / mV
ENa
20
60
100
140
100%
20%
60
V
EK
mutant
20
V / mV
ENa
20
60
100
140
100%
20%
0
20
40
t/ s
60
80
100
• M.A. Dahlem, J. Schumacher, N. H¨bel, Linking a mutation in familial hemiplegic migraine type 3 to its
u
phenotype in spreading depression (in preparation)

40. FHM3 and action potential
40
40
oscillatory
wild-type
V / mV
HB2
50
70
0
50
40
60
excitatory
HB1
70
0
70
0
40
50
40
oscillatory
stable FP
unstable FP
30
100
150
Iapp / µ A cm−2
200
mutant
V / mV
HB2
50
70
0
50
40
60
excitatory
HB1
70
0
70
0
50
stable FP
unstable FP
30
100
Iapp / µA cm−2
150
200
• M.A. Dahlem, J. Schumacher, N H¨bel, Linking a mutation in familial hemiplegic migraine type 3 to its
u
phenotype in spreading depression (in preparation)

41. Multiscale disease: From molecules to entire brain
Functional mutations
Spreading depression (SD)
during a migraine attack
(e.g. FHM2: sodium-potassium pump)
cf.: Maagdenberg, et al., Ann. Neurol., 67 2010
Tottene, et al., Neuron, 61 2009
Atlas of Migraine and Other Headaches, Silberstein
Freilinger, et al. Nature Genetics 44 2012
et al (Editors)

42. Multiscale disease: From molecules to entire brain
Functional mutations
Spreading depression (SD)
during stroke
Subarachnoid space
Arachnoid
Ruptured
aneurysm
Dura mater
Blood clot
Arteriole
Neocortex
(e.g. FHM2: sodium-potassium pump)
Glutamate
K+
O2
Glucose
Delayed ischemic lesions
Energy
failure
Katie Vicari
Spreading
depolarization
Vasoconstriction
Microemboli
cf.: Maagdenberg, et al., Ann. Neurol., 67 2010
Tottene, et al., Neuron, 61 2009
Iadecola, ”Killer waves ...” Nature Medicine 15
Freilinger, et al. Nature Genetics 44 2012
(2009)

43. Neural dynamics during anoxia
membrane potential in mV
60
Wild-type
0
-60
60
Mutant
0
-60
24
28
32
36
40
time in s
van Rijn CM, et al. (2011) Decapitation in rats: latency to unconsciousness and the ‘wave of death’.
PLoS One 6, e16514.
Zandt B-J, et al. (2011), Neural Dynamics during Anoxia and the “Wave of Death”.
PLoS ONE 6, e22127.
Dichgans M, et al. (2005) Mutation in the neuronal voltage-gated sodium channel SCN1A in familial hemiplegic
migraine. Lancet 366, 371.

44. Neural dynamics during anoxia
membrane potential in mV
60
Wild-type
0
-60
60
Mutant
0
-60
24
28
32
36
40
time in s
van Rijn CM, et al. (2011) Decapitation in rats: latency to unconsciousness and the ‘wave of death’.
PLoS One 6, e16514.
Zandt B-J, et al. (2011), Neural Dynamics during Anoxia and the “Wave of Death”.
PLoS ONE 6, e22127.
Dichgans M, et al. (2005) Mutation in the neuronal voltage-gated sodium channel SCN1A in familial hemiplegic
migraine. Lancet 366, 371.

45. Outline
Electrical & magnetic stimulation of the brain: Neuromodulation
Causality confusion in migraine: Dynamical network biomarkers
Mathematical migraine models: From genotype to phenotype
Towards therapeutic intervention
Conclusion

46. Old problems remain
¨
“Uber die physiologischen Wirkungen der elektrischen B¨der liegen eine Reihe von Angaben [...] vor.
a
[...]
Im allgemeinen haben faradische B¨der einen erfrischenden Einfluß, galvanische sollen m¨de machen.
a
u
Es kommt f¨r die Wirkung entschieden auf die Dauer der B¨der an, k¨rzere werden mehr anregend, l¨ngere mehr
u
a
u
a
erschlaffend wirken.
Durchsichtig ist jedenfalls die physiologische Begr¨ndung dieser B¨der durchaus nicht, man wird sich vorstellen,
u
a
daßsie im allgemeinen die eines indifferenten Bades, mit dem ein milder Hautreiz verbunden ist, haben.
Es m¨gen dadurch Aenderungen in unseren Allgemeingef¨hlen, also Wohlbehagen, Erfrischung oder M¨digkeit
o
u
u
bedingt werden. Nach meiner Ansicht liegt aber die Hauptwirkung dieser elektrischen B¨der in erster Linie auf
a
suggestivem Gebiete, und das rechtfertigt ihre Anwendung und ihre unleugbaren Erfolge auf dem Gebiete der
nerv¨sen Allgemeinleiden, wie Hysterie, Neurasthenie etc.”
o
(Lehrbuch der klinischen Hydrotherapie, Max Matthes)

47. Feedback control of spreading depression (Talk 5. Feb!)
From bench
to bedside
!

48. Cooperation with Stephen Schiff Bruce Gluckman
Dept. Biomedical Engineering, Penn State (CRCNS)
Courtesy Neuralieve
Feedback control with Kalman filter
TMS (external forcing)

49. (i)
mi
n
ths
m
cortex
p
y
a
1d
magnetic
l
HY,TH
ele
ctr
(ii)
PAG
(iii)
e
r
rom
t
td
on
cle
in e c y
os
igr
a
e
4 -72h
dynamical
network
biomarkers
m
bone
cranial circulation
cranial innervation
ica
5-60
a ch
(avg 2 we
e
a ur a
ad
rome
od
pr
ay
1d
)
he
ks
Migraine Generator Network Dynamical Network Biomarker
SPG
LC
SSN
RVM
ON
OFF
TG
TCC
a tt a c k
-fre
e
d a ys
to
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).
Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
• M. A. Dahlem, S. Rode, A. May, N. Fujiwara, Y. Hirata, K. Aihara, J. Kurths, Towards dynamical network
biomarkers in neuromodulation of episodic migraine, Translational Neuroscience, 4,282-294 (2013).

50. Two tipping points
large fluctuations in
cerebreal blood
flow control
DNB
NB
D
Migraine generator network (MGN)
bone
cerebral blood flow
?
Which
subnetworks
drive the
transtions into
the pain
phase?
highly variable
pattern of free
energy stravation
prodrome
aura
headache
postdrome
1 day
5-60min
4-72h
1 day
cortex
subcortical
parasympathetic
control
ON
OFF
cranial innervation
spreading
depression
(SD)
brainstem
modulatory network
Dynamical network biomarker (DNB)

51. Modeling pain initiation and sensitization
50
seizure-like
afterdischarges
V
EK
dominance
pump current
ENa
0
Iapp
depolarization block
50
100
transmembrane
b
voltage (mV)
inside cell
outside cell
towards genetics
a
c
I
II
III
IV
m-gate
begin
deactivation
INa -driven
repolarization
V
+
0
5
10
15
20
time (s)
25
30
VI
35
cortical tissue
d
bone
cranial circulation
cranial innervation
cortex
cortex
HY,TH
SD
ignition
PAG
HY,TH
HY,TH
behavior,
sensory
processing
SD
corticothalamic
action
PAG
SPG
f g
bone
cranial circulation
cranial innervation
cortex
SD
release
noxious
agents
PAG
SPG
e
bone
cranial circulation
cranial innervation
SPG
visual aura (0min)
LC
LC
SSN
RVM
off
TCC
on
LC
SSN
RVM
TG
off
on
TCC
• Dahlem et al. (2013) Translational Neuroscience, 4, 282
SSN
RVM
TG
off
TCC
on
TG
sensory aura (15min)

52. Twist: A ‘ghost’ phathological state (waves)
d
postdrome
ictus
ictus
ictal
• Dahlem et al. (2013) Translational Neuroscience, 4, 282
f
+ aura
g chronification
ictus
c
ictus
interictal
ictus
a
prodrome
normal state
e
ictus
b
episodic manifestation
ictus
disease state

53. Phase-dependend neuromudulation
sensory innervation
blood
arachnoid
pia
cortex
SD
large MIA
blood
arachnoid
SD
small MIA
pia
cortex
depleted surface area
bone
dural sinuses
dura
5
y
IP: ignition phase AP: acute phase
x
a
MIA
4
b
3
c
2
d
1
0
e
f
slow dynamics
0
5
10
15
20
25
30
time
cf. Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
cf. Charles AC, Baca SM., Cortical spreading depression and migraine. Nat Rev Neurol. 9:637-44, (2013)
• M. A. Dahlem and T. Isele: Transient localized wave patterns and their application to migraine. J. Math.
Neurosci. 3,7 (2013).
35

54. Phase-dependend neuromudulation
sensory innervation
blood
arachnoid
pia
cortex
SD
large MIA
blood
arachnoid
SD
small MIA
pia
cortex
depleted surface area
bone
dural sinuses
dura
5
y
IP: ignition phase AP: acute phase
x
a
MIA
4
IP Stim.
b
AP Stim.
3
c
2
d
1
0
e
f
slow dynamics
0
5
10
15
20
25
30
time
cf. Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
cf. Charles AC, Baca SM., Cortical spreading depression and migraine. Nat Rev Neurol. 9:637-44, (2013)
• M. A. Dahlem and T. Isele: Transient localized wave patterns and their application to migraine. J. Math.
Neurosci. 3,7 (2013).
35

55. Phase-dependend neuromudulation
IP: ignition phase AP: acute phase
bone
sensory innervation
blood
arachnoid
any node in the
migraine generator
network is potential
target for
neuromodulation
pia
cortex
large MIA
blood
a
CC
aura
b
hypermia
HY,TH
oligemia +
CTX
HY,TH
vlPAG
vlPAG
SPG
LC
SuS
off
on
x
a
MIA
4
IP Stim.
b
AP Stim.
3
c
2
d
on
TG
0
e
f
slow dynamics
SuS
off
TCC
y
1
RVM
TG
5
SPG
LC
RVM
TCC
CC
pain
CTX w loc SD
depleted surface area
dural sinuses
dura
0
5
10
15
20
25
30
time
cf. Karatas H et al., Spreading depression triggers headache by activating neuronal Panx1 channels. Science,
339:1092-5 (2013).
cf. Charles AC, Baca SM., Cortical spreading depression and migraine. Nat Rev Neurol. 9:637-44, (2013)
• M. A. Dahlem and T. Isele: Transient localized wave patterns and their application to migraine. J. Math.
Neurosci. 3,7 (2013).
35

56. wave size
Single pulse stimulation (current TMS strategy)
25
noise sample 1 k=0.010
noise sample 1 k=0.100
noise sample 1 k=0.300
noise sample 2 k=0.010
noise sample 2 k=0.100
noise sample 2 k=0.300
without noise
20
15
10
noise on
5
0
0
5
10
15
20
25
30
time
35

57. wave size
Constant noise stimulation
25
noise sample 1 k=0.030
noise sample 1 k=0.040
noise sample 1 k=0.050
noise sample 2 k=0.030
noise sample 2 k=0.040
noise sample 2 k=0.050
without noise
20
15
10
noise on
5
0
0
5
10
15
20
25
30
time
35

58. Various SD patterns cause different migraine types?
a
pain onset
5 min
~20 min
~60 min (full-scale aura)
MA
TAA
MIA
aura
MO
MIA
TAA
b
• M. A. Dahlem et al., Spreading depression in migraine without aura: a model-based hypothesis. (in preparation)

59. Various SD patterns cause different migraine types?
total area affected (TAA)
exct. duration (ED)
1k
4
2
(dotted)
1
1
1
4
2
1
0
1
0
2k
0
1k
MWoA
MWA
−1
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
maximal instantaneous area (MIA)
0.8
1
MWA
aura threshold
MWoA
MWoA MWA
1cm
large
TAA
MIA
pain
aura
IA
correlation
3
2
2
w/o
headache
pain threshold
0.5
MxWA
smooth histogram (solid lines)
mean STD
2k
3
classification
#
1
0
total affected area (TAA)
• M. A. Dahlem et al., Spreading depression in migraine without aura: a model-based hypothesis. (in preparation)

60. Individual ‘hot spots’ and ‘labyrinth’ determine attack
e
iv
sit
po
ne
ga
t
ive
Principles
Validate
• simulations on simpler shapes
• analytical results with isothermal
• uploading patient’s MRI scanner readings
• finite element analysis
coordiantes (toroidal coordinates)
• polygon mesh processing

61. Excitation waves on curved surfaces
Paradigmatic SD model on gyrified cortex.
∂u
∂t
∂v
∂t
1
1 ∂
= u − u 3 − v + Du √
3
g ∂αi
=
√ ∂u
gij g i
∂α
(u + β)
SD in weakly excitable cortex posses critical properties.
First approximation: localized SD follows shortest path.

62. Outline
Electrical magnetic stimulation of the brain: Neuromodulation
Causality confusion in migraine: Dynamical network biomarkers
Mathematical migraine models: From genotype to phenotype
Towards therapeutic intervention
Conclusion

63. Modern neuromodulation

64. Modern neuromodulation

65. Modern neuromodulation

66. Modern neuromodulation

67. Modern neuromodulation

68. Modern neuromodulation
”The headache future is bright for neuromodulation techniques ... if we
manage to understand how they work” (Jean Schoenen)

69. Models fill the ‘gaps’ in the multiscale framework
seizure-like
afterdischarges
dominance
pump current
ENa
0
Iapp
depolarization block
50
100
c
V
EK
II
III
10
15
20
time (s)
cortex
HY,TH
V
25
30
35
balanced excitation and
inhibition in ion-based models
VI
e
behavior,
perception
sensory
processing
SD
corticothalamic
action
PAG
SPG
visual aura (0min)
LC
m-gate
begin
deactivation
INa -driven
repolarization
5
bone
cranial circulation innervation
release noxious agents
IV
+
0
d
I
organ level
50
transmembrane
cellular level
outside cell
inside cell
molecular level
genetics
b
voltage (mV)
a
RVM
off
on
SSN
TG
TCC
sensory aura (15min)
(a) Functional mutations, either FHM, CADASIL, ... or GWAS.
(b) Hodgkin-Huxley type, single cell electrophysiology models.
(c) Neural mass/fields population models, with subpopulations
having specific synaptic receptor distribution.
(d) Local circuits, in particular including the migraine generator
network in the brainstem
(e) Aura symptoms, mental dysfunctions, impared sensory and
cognitive processing

70. Recent papers
M.A. Dahlem, J. Kurths, A. May, K. Aihara, M. Scheffer, and M. D.
Ferrari, Causality Confusion in Migraine Cephalalgia, (accepted).
M. A. Dahlem, Migraines and Cortical Spreading Depression,
Encyclopedia of Computational Neuroscience, Springer. (accepted)
M. A. Dahlem, S. Rode, A. May, N. Fujiwara, Y. Hirata, K. Aihara, J.
Kurths, Towards dynamical network biomarkers in neuromodulation of
episodic migraine, Translational Neuroscience, 4,282-294 (2013).
M. A. Dahlem: Migraine generator network and spreading depression
dynamics as neuromodulation targets in episodic migraine. Chaos, 23,
046101 (2013).
M. A. Dahlem and T. Isele: Transient localized wave patterns and their
application to migraine. J. Math. Neurosci. 3,7 (2013)
J. P. Dreier, T. Isele, C. Reiffurth, N. Offenhauser, S. A. Kirov, M. A.
Dahlem, and O. Herrars: Is spreading depolarization characterized by an
abrupt, massive release of Gibbs free energy from the human brain
cortex? The Neuroscientist 19,25-42 (2012).
M. A. Dahlem and J. Tusch: Cortical magnification tensor predicts a
virtual visual streak in humans waves, J. Math. Neurosci. 2,14 (2012)

71. Manuscripts in preparation
N. H¨bel, E. Sch¨ll, and M. A. Dahlem, Bistable dynamics underlying
u
o
excitability of ion homeostasis in neuron models (revised and under
review, 14 pages, 7 figures, 3 tables, ms on arxiv)
F. Kneer, E. Sch¨ll, and M.A. Dahlem, Nucleation of reaction-diffusion
o
waves on curved surfaces. (submitted, 23 pages, 11 figures, 4 movies)
M. A. Dahlem, F. Kneer, E. Sch¨ll, B. Schmidt, I. Bojak, and J. Kurths,
o
Personalized treatment strategies in episodic migraine by
neuromodulation devices. (12 pages, 5 figures, 1 movie)
M. A. Dahlem, Julia Schumacher, N. H¨bel, Linking a mutation in
u
familial hemiplegic migraine type 3 to its phenotype in spreading
depression, 4 figures, 8 pages
F. Kneer, K. Obermayer, M. Dahlem, Analyzing critical propagation in a
reaction-diffusion-advection model using unstable slow waves.
(submitted)
M. A. Dahlem, et al. Spreading depression in migraine without aura: a
model-based hypothesis. (in preparation)

72. Conclusions
We need more non-invasive
imaging data of migraine with aura
to test predictions.
Sef-organizing patterns provide a
unifying concept including silent aura,
migraine w or w/o headache/aura
Dynamical cocepts may refine
neuromodulation strategies:
Being close to a saddle-node
bifurcation (”ghost” plateau)
Design (feedback) control to
intelligently target certain properties
of SD in migraine
Visual hemifield
Primary visual cortex
1 cm
27 min
10°
25
23
21
1
3
5
7
17
15
19

73. Conclusions
Sef-organizing patterns provide a
unifying concept including silent aura,
migraine w or w/o headache/aura
Dynamical cocepts may refine
neuromodulation strategies:
Being close to a saddle-node
bifurcation (”ghost” plateau)
Design (feedback) control to
intelligently target certain properties
of SD in migraine
(1)
(2)
no attack
MWoA
(a)
cortex
top view
y
(3)
MWA
x
(4)
to ta l a ff e cte d a re a TAA
We need more non-invasive
imaging data of migraine with aura
to test predictions.
50 (1)
(2)
(3)
25
(4)
(b)
above
pain
threshold
6.25
time
0 3 6 9 12 15 18 21 24 27
0
2.5
6.25
maximal instantaneous area MIA

74. Conclusions
We need more non-invasive
imaging data of migraine with aura
to test predictions.
Sef-organizing patterns provide a
unifying concept including silent aura,
migraine w or w/o headache/aura
Dynamical cocepts may refine
neuromodulation strategies:
Being close to a saddle-node
bifurcation (”ghost” plateau)
Design (feedback) control to
intelligently target certain properties
of SD in migraine

75. Cooperation Funding
Frederike Kneer, Niklas H¨bel, Julia
u
Schumacher, Thomas Isele
Paul Van Valkenburgh, Bernd Schmidt
Nouchine Hadjikhani
(Martinos Center for Biomedical Imaging, MGH)
Steven Schiff
berlin
(Penn State Center for Neural Engineering)
Andrew Charles
(Headache Research and Treatment Program, UCLA School of
Medicine)
Jens Dreier
(Department of Neurology, Charit´; University Medicine, Berlin)
e
Klaus Podoll
(University Hospital Aachen)
Migraine Aura Foundation

76. Mainly two neural theories of migraine
”Migraine generator”-theory
S1
SMA
PPC
ACC
Th
PFC
Amyg
Insula
PAG
”Spreading depression”-theory

77. SD: Wave of massive ionic imbalance
(mM)
Ve
+
Na
log [cat] , M
150
60
50
+
Na
+
-1
K
Ca++
3
1.5
0.08
-2
+
0 10 20 30 s
K
-3
-4
-7
Ca++
+
H
-8
20 mV
Ve
unit
act.
1 min
Lauritzen (1994) Brain 117:199.

78. SD does not curl-in in human cortex
10 min
1cm
Only about 2-10% but not 50% cortical surface area is affected!
right: modified from Hadjikhani et al. PNAS 98:4687 (2001).
• Dahlem Hadjikhani, PLoS ONE, 4: e5007 (2009).

79. SD does not curl-in in human cortex
SD curls in to form
spirals with T=2.45min!
spiral
core
1cm
10 min
1cm
Only about 2-10% but not 50% cortical surface area is affected!
right: modified from Hadjikhani et al. PNAS 98:4687 (2001).
• Dahlem Hadjikhani, PLoS ONE, 4: e5007 (2009).
• Dahlem M¨ller, Exp. Brain Res. 115,319, (1997).
u

80. Re-entrant SD waves with functional block
Z-type rotation causes a wave break in the spiral core.
Dahlem M¨ller (1997) Exp. Brain Res. 115:319
u

81. Re-entrant SD waves with anatomical block
Reshodko, L. V. and Bureˇ, J Biol. Cybern. 18,181 (1975)
s

82. Drugs adjust excitability:retracting collapsing waves
a
b
c
d
e
f
g
h
i
j
k
l
Dahlem et al. 2D wave patterns ... . (2010) Physcia D

83. Nucleation failure on torus

84. Transient times in flat and curved geometry
torus, without control
torus, with control
flat, without control
30
∂R∞
50
ring
40
outside
20
S
torus outside
S
30
with control
without control
wave
inside
flat
20
torus inside
outside
10
inside
10
0
1.3
1.32
1.34
β
1.36
1.38
0
0
10
20
30
40
t
50
60
70
80

85. Simulation of transient SD wave segment
gray = cortical surface; red = SD wave

86. Simulation of an engulfing SD wave
In cooperation with Bernd Schmidt,
In cooperation with Jens Dreier
Magdeburg
Denny Milakara, Charit´
e

87. SD triggers trigeminal meningeal afferents, ie, headache
see e.g.: Bolay et al. Nature Medicine 8, 2002
Review: Eikermann-Haerter Moskowitz, Curr Opin Neurol. 21, 2008
Figure: Dodick Gargus SciAm, August 2008

88. Organic Physics

89. Organic Physics

90. Organic Physics

91. Organic Physics

92. Cerebral blood flow in migraine
Radionuclide xenon 133 method, used to image brain’s blood flow
Olesen, J. , Larsen, B. and Lauritzen, M., Focal hyperemia followed by
spreading oligemia and impaired activation of rCBF in classic migraine, Ann.
Neurol. 9, 344 (1981)

93. Tracking migraine aura symptoms
Vincent Hadjikhani (2007) Cephalagia 27

94. Tracking migraine aura symptoms
Vincent Hadjikhani (2007) Cephalagia 27

95. fMRI patterns is more diffuse than SD patterns
end (min 30)
start (min 20)
reference (min 0)
modified from Hadjikhani et al. (2001) PNAS 98

96. fMRI patterns is more diffuse than SD patterns
end (min 30)
start (min 20)
reference (min 0)
What if the the blood flow provides a
long-range or global negative feedback?
modified from Hadjikhani et al. (2001) PNAS 98

97. ”Migraine generator” in the brainstem
trigger
SD
aura

98. ”Migraine generator” in the brainstem
mysterious conductor
trigger A
trigger B
trigger C
trigger D
?
prodrome
about 1 day
SD
?
?
aura
headache
postdrome
60 min
4−72h
about 1 day

99. A conductor of a neural orchestra playing migraine
70%
mysterious conductor
trigger A
trigger B
trigger C
trigger D
?
prodrome
about 1 day
SD
?
?
aura
headache
postdrome
60 min
4−72h
about 1 day

100. A conductor of a neural orchestra playing migraine
rarely
(but: unreported cases)
mysterious conductor
trigger A
trigger B
trigger C
trigger D
?
prodrome
about 1 day
SD
?
?
aura
headache
postdrome
60 min
4−72h
about 1 day

101. A conductor of a neural orchestra playing migraine
mysterious conductor
trigger A
trigger B
trigger C
trigger D
?
prodrome
about 1 day
SD
?
?
aura
headache
postdrome
60 min
4−72h
about 1 day

102. heightened susceptibility
trigger
SD
prodrome
about 1 day
cortical homeostasis
SD is playing jazz – self-organizing dynamics
prodrome
time
delay
aura
headache
postdrome
60 min
4−72h
about 1 day

103. Common etiology or 2 mechanisms in MWoA and MWA?
heightened
susceptibility
trigger
SD
prodrome
aura
delayed trigger
headache
1. Only one upstream trigger?
2. MWoA MWA share same pain phase? 3. Silent aura? 4. Even prevalent?
5. Delayed headache link? 6. Missing the pain phase?
SD: Spreading Depression, see next slide

104. Unified Minimal (4D) Model of
Spiking, Seizures and Spreading Depression
e xtra c e llula r pota s s ium
pe riodic SD
uns ta ble lim it c yc le
s ta ble e q uilibrium
70
60
Kex,max in mMol/ l
50
40
30
20
TR?LP
LP
HB
TR
10
LP?
HB
0
4
6
8
10
14
12
Kbath in mMol/ l
16
18
20
22

105. Unified Minimal (4D) Model of
Spiking, Seizures and Spreading Depression
m e m bra ne pote ntia l
60
LP?
40
TR
Vmax in mVolt
20
0
ENa
V
0
20
EK
-100
LP
1min
HB
40
LP
HB
HB
LP
HB LP
TR?
60
80
4
6
8
10
14
12
Kbath in mMol/ l
16
18
20
22

106. Additional slides

107. Excitable media – Traveling wave solutions
Canonical RD eqs.
(in weak limit, β large but not too large)
∂t u = f (u) − v +
∂t v
= ε(u + β)
2
u

108. Excitable media – Traveling wave solutions
Canonical RD eqs.
(in weak limit, β large but not too large)
∂t u = f (u) − v +
∂t v
2
u
= ε(u + β)
Schenk et al. Phys. Rev. Lett. 78, 3781 (1997)

109. Excitable media – Traveling wave solutions
Canonical RD eqs.
(in weak limit, β large but not too large)
∂t u = f (u) − v +
∂t v
2
traveling
wave
u
= ε(u + β)
sup
sh
sh
o
st
ld imula
t
50
40
io
n
wave size S
hre
sub-thre
∂R∞
60
er-t
s
old
30
ula
ti m
ti o
n
critical
nucleaction
solution
threshold
homogeneous
steady state
20
10
0
1.3
1.32
1.34
1.36
threshold β
1.38
1.4

110. Excitable media – Traveling wave solutions
traveling
wave
Canonical RD eqs.
(in weak limit, β large but not too large)
su
ol
es h
- th r
p er
sub-thre
n
= ε(u + β)
sub-excitable
wave size S
50
40
30
20
10
0
1.3
1.32
1.34
1.36
threshold β
ula
ti m
ti o
n
critical
nucleaction
solution
threshold
homogeneous
steady state
∂R∞
60
ti o
∂t v
u
o
st
ld imula
∂t u = f (u) − v +
2
sh
ds
1.38
1.4

111. Excitable media – Traveling wave solutions
traveling
wave
Canonical RD eqs.
(in weak limit, β large but not too large)
su
ol
es h
- th r
p er
sub-thre
n
= ε(u + β)
∂P1D
30
20
not excitable
sub-excitable
wave size S
50
40
10
0
1.3
1.32
1.34
1.36
threshold β
ula
ti m
ti o
n
critical
nucleaction
solution
threshold
homogeneous
steady state
∂R∞
60
ti o
∂t v
u
o
st
ld imula
∂t u = f (u) − v +
2
sh
ds
1.38
1.4

112. Excitable media – Traveling wave solutions
traveling
wave
Canonical RD eqs.
(in weak limit, β large but not too large)
su
ol
es h
- th r
p er
sub-thre
n
= ε(u + β)
ula
ti m
ti o
n
critical
nucleaction
solution
threshold
homogeneous
steady state
∂R∞
60
ti o
∂t v
u
o
st
ld imula
∂t u = f (u) − v +
2
sh
ds
∂P1D
40
30
20
not excitable
sub-excitable
wave size S
50
10
0
1.3
1.32
1.34
1.36
threshold β
1.38
1.4
critical
nucleation

113. Current and pump equations
Two pump types
Iion,pumped,1 ([K ]o , [Na]i ) = Imax
Iion,pumped,2 ([K ]o , [Na]i ) = Imax
K0 fixed 3.5mM
1
1
2
0.8
1
2
0.8
0.02
0.4
0.4
8
10 12
0
20
25
30
1
2
35
40
10
15
20
25
30
35
40
1
2
3
3.5
4
4.5
0.2
0.1
0.4
0
0
8
Ko
10
12
14
25
30
35
40
5
10
15
20
25
30
35
40
Nai
Nai fixed 40mM
1
1
2
1
2
0.8
0.6
0.6
0.4
0.4
0.2
0
6
20
0 2 4 6 8 10 12 14
0.2
4
15
Nai fixed 30mM
1
0.8
0.2
0.6
0
2
10
Nai
0.3
0.02
0.6
0
0
5
Nai fixed 20mM
1
0.8
2.5
0.2
0
5
Nai
0.04
0.4
0.4
0.2
Nai fixed 10mM
1
0.6
0.4
Nai
0.8
1
2
0.8
0.6
0
15
K0 fixed 55mM
1
1
2
0.8
0.2
10
−3
KmNa
[Na]i
1
5 10 15 20 25 30 35 40
0.2
5
1+
Ko fixed 10mM
1
5
4
3
2
1
0
0.6
0
−2
KmK
[K ]o
1
1 + e (25−[Na]i /3) 1 + e (5.5−[K ]o )
K0 fixed 8mM
1
0.04
0.6
1+
0.2
0
0
2
4
6
8
Ko
10
12
14
0
0
2
4
6
8
Ko
10
12
14
0
2
4
6
8
Ko
10
12
14

114. Minimum threshold in a flat geometry
∂R∞
60
∂P1D
wave size S
50
40
30
torus inside
1
20
10
0
1.3
1.32
1.34
1.36
threshold β
1.38
1.4

115. Minimum threshold in a flat geometry
∂R∞
60
∂P1D
wave size S
50
40
30
torus outside
torus inside
1
20
10
1
0
1.3
1.32
1.34
1.36
threshold β
1.38
1.4

116. Minimum threshold in a flat geometry
∂R∞
60
∂P1D
wave size S
50
40
30
torus outside
torus inside
1
20
10
1
0
1.3
1.32
1.34
1.36
threshold β
1.38
1.4

117. Minimum threshold in a flat geometry
∂R∞
60
wave size S
50
ring
40
30
∂P1D
wav
e
torus outside
1
torus inside
1
20
10
1
0
1.3
1.32
1.34
1.36
threshold β
1.38
1.4

118. Minimum threshold in a flat geometry
∂R∞
60
wave size S
50
ring
40
30
wav
e
∂P1D
2
torus outside
20
2
10
1
1
torus inside
1
2
0
1.3
1.32
1.34
1.36
threshold β
1.38
1.4

119. Migraine scotoma reveal functional properties
Pattern matching
A
B
4
7
13
C
9
• Dahlem Tusch, J. Math Neuroscie. 2,14 (2012)

120. Migraine scotoma reveal functional properties
Pattern matching
”Curved” retinotopic mapping
A
B
a
ÙÒ Ù×
Ð Ò Ù Ð ÝÖÙ×
13
9
Ë
C
b
c
m
• Dahlem Tusch, J. Math Neuroscie. 2,14 (2012)
Ú
Ð
e
4
7
d
m
Ù
½¼Æ

121. Migraine scotoma reveal functional properties
´ ½µ
”Curved” retinotopic mapping
Pattern matching
A
Å
¼Æ
B
1
0.8
0.6
0.4
0.2
Æ
¯
´±µ
2
ÀÅ
4
C
9
Ã
13
6
8
10 12 14
2
´ÑѾµ
7
4
140
120
100
80
60
40
20
¾
¼
¼
¼
¼
• Dahlem Tusch, J. Math Neuroscie. 2,14 (2012)
¼¾
4
6
8
10 12 14
2
4
6
8
10 12 14
0.3
0.2
0.1
´Ö µ