Computational methods have complemented experimental and clinical neurosciences and led to improvements in our understanding of the nervous systems in health and disease. In parallel, neuromodulation in form of electrical and magnetic stimulation is gaining increasing acceptance in chronic and intractable diseases. First, we will present models of slow dynamics emerging on large cortical scales controlled by both subcortical networks and neurovascular coupling. The focus is on modeling migraine, though this approach is nested within the wider interest in modeling slow and large-scale dynamics in the brain. The aim is not only to better understand pain conditions and fluctuations in the resting state that causes these conditions but also to identify new opportunities to intervene with medical devices and implantable neuroprostheses. To this end, we then present the relevant state of the art of neuromodulation in migraine and approaches in fusion of both developments towards a translational computational neuroscience.

1. Slow and large
Dynamics in migraine and opportunities to intervene
Markus A. Dahlem
MPI of the Physics of Complex Systems, Dresden
B
C
activator, u
immobile inhibitor, v
long-range inhibitor, w
A
activator:
front
propagation
activator-inhibitor:
pulse propagation
(includes re-entry
patterns in 2D)
activator:
front
propagation
act.-2-inhibitors:
localized structures
(spots)
MPI Leipzig for Human Cognitive and Brain Sciences, August 26, 2014

2. Outline
Neuron: Electrophysiology with time-dependent ion concentrations
Vasculature: Regulation of cerebrovascular tone by nerves & blood
Application: Personalized and predictive medicine
Individal activity patterns in migraine
Non-drug treatment in migraine
Controlling the migraine generator network
Summary & Conclusion

3. Outline
Neuron: Electrophysiology with time-dependent ion concentrations
Vasculature: Regulation of cerebrovascular tone by nerves & blood
Application: Personalized and predictive medicine
Individal activity patterns in migraine
Non-drug treatment in migraine
Controlling the migraine generator network
Summary & Conclusion

4. HH-type conductance-based
C
∂V
∂t
= −INa − IK − Ileak +Iapp (1)
INa = ¯gNam3
h(V − ENa)
IK = ¯gK n4
(V − EK )
Ileak = gleak(V − Vrest)
∂n
∂t
= αn(1 − n) − βn,
∂h
∂t
· · · (2) − (4)
HH: Hodgkin-Huxley

5. From HH-type conductance-based to
conductance- & ion-based models (2nd
generation model)
ion
reservoirs
isolated boundary
system
surroundings
energy
source
extracellular
intracellular
C
∂V
∂t
= −INa − IK − Ileak−Ipump+Iapp (1)
INa = ¯gNam3
h(V − ENa)
IK = ¯gK n4
(V − EK )
Ileak = gleak(V − Vrest)
∂n
∂t
= αn(1 − n) − βn,
∂h
∂t
· · · (2) − (4)
∂[ion]e
∂t
= −
A
FVolo
Iion
∂[ion]i
∂t
=
A
FVoli
Iion (5) − · · ·
HH: Hodgkin-Huxley

6. From HH-type conductance-based to
conductance- & ion-based models (2nd
generation model)
ion
reservoirs
isolated boundary
system
surroundings
energy
source
extracellular
intracellular
Modeling new (mainly slow) phenomena
tissue energetics
ATP comsumption
Gibb’s free engergy
modeling oxygen glucose deprivation
tissue properties (neuropil vs granular)
neurovascular coupling
osmotic pressure (water homeostasis)
(temperature)
clinical comorbitities
seizure activity (epilepsy)
cortical spreading depression (migraine)
peri–infarct depolarization (stroke)
HH: Hodgkin-Huxley

7. Metabolically driven slow dynamics from sec to min
Bursting, tonic firing, spreading depression (SD)
in HH model with time-dependent ion concentrations.
• H¨ubel et al., PLOS Comp. Biology. 10, e1003551 (2014)
• H¨ubel & Dahlem, arXiv:1404.3031 (under review in PLOS Comp. Biology )

8. SD: Wave of massive ionic imbalance
-1
-2
-3
-4
-7
-8
1 min
20 mV
log [cat] , M
(mM)
Ve
Na
+
Na
+
K
+
Ve
K
+
Ca++
Ca++
H
+
0 10 20 30 s
150
60
50
3
1.5
0.08
unit
act.
Lauritzen, M., TINS 10,8 (1987)
Xenon 133 method, radionuclide
used to image brain’s blood flow.
Olesen, J. , Larsen, B. and Lauritzen, M., Ann. Neurol.
9, 344 (1981)

9. What is cortical spreading depression on macro-scale?
Homeostatic insult self-organzied as 2D patterns in gray matter.
-1
-2
-3
-4
-7
-8
1 min
20 mV
log [cat] , M
(mM)
Ve
Na
+
Na
+
K
+
Ve
K
+
Ca++
Ca++
H
+
0 10 20 30 s
150
60
50
3
1.5
0.08
unit
act.
any textbook
from ~2004
m
anywebsites
M. Lauritzen, Trends in Neurosciences 10,8 (1987).
A controversial debate but
“...essential view of a reaction-diffusion process still holds ...”
Herreras (2005) J. Neurophysiol. 94:3656
Somjen & Strong (2005) J. Neurophysiol. 94:3656

10. Principal mechanisms of slow and large–scale
reaction–diffusion patterns
B
C
activator, u
immobile inhibitor, v
long-range inhibitor, w
A
activator:
front
propagation
activator-inhibitor:
pulse propagation
(includes re-entry
patterns in 2D)
activator:
front
propagation
act.-2-inhibitors:
localized structures
(spots)

11. Historical note:
Macroscopic approach is non-reductionist, hence
various analogies to animate and inanimate systems

12. Outline
Neuron: Electrophysiology with time-dependent ion concentrations
Vasculature: Regulation of cerebrovascular tone by nerves & blood
Application: Personalized and predictive medicine
Individal activity patterns in migraine
Non-drug treatment in migraine
Controlling the migraine generator network
Summary & Conclusion

13. Duvernoy et al., 1981
Architecture of the cerebral vasculature
Blinder, Tsai, et al.,
Nature Neuro, 2013

14. Model of SD in gray matter
Cortex SD

15. Model of SD in gray matter or in the brain?
Cortex
circulation with innervation
bone
SD
Circulation outside the parenchyma
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013)
• M. A. Dahlem, Migraines and Cortical Spreading Depression, In: Jaeger D., Jung R. (Ed.) Encyclopedia of
Computational Neuroscience. Springer-Verlag Berlin Heidelberg, 2014.

16. Model of SD in gray matter or in the brain?
Cortex
circulation with innervation
bone
SD
release of
noxious agents
Circulation outside the parenchyma
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013)
• M. A. Dahlem, Migraines and Cortical Spreading Depression, In: Jaeger D., Jung R. (Ed.) Encyclopedia of
Computational Neuroscience. Springer-Verlag Berlin Heidelberg, 2014.

17. Model of SD in gray matter or in the brain?
SPG
SSN
TCC
TG
Cortex
circulation with innervation
bone
SD
release of
noxious agents
peripheralpathway
Circulation outside the parenchyma
parasympathetic control
TG: trigeminal ganglion
TCC: trigeminocervical complex
SSN: superior salivatory nucleus
SPG: sphenopalatine ganglion
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013)
• M. A. Dahlem, Migraines and Cortical Spreading Depression, In: Jaeger D., Jung R. (Ed.) Encyclopedia of
Computational Neuroscience. Springer-Verlag Berlin Heidelberg, 2014.

18. Model of SD in gray matter or in the brain?
off on
HY,TH
SPG
SSN
TCC
PAG
LC
RVM
TG
Cortex
circulation with innervation
bone
SD
cortico-
thalamic
action
release of
noxious agents
peripheralpathway
Circulation outside the parenchyma
parasympathetic control
TG: trigeminal ganglion
TCC: trigeminocervical complex
SSN: superior salivatory nucleus
SPG: sphenopalatine ganglion
decending modulatory control and
further subcortical structures
RVM: rostral ventromedial medulla
LC: locus coeruleus
PAG: periaqueductal gray
TH: thalamus
HY: hypothalamus
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013)
• M. A. Dahlem, Migraines and Cortical Spreading Depression, In: Jaeger D., Jung R. (Ed.) Encyclopedia of
Computational Neuroscience. Springer-Verlag Berlin Heidelberg, 2014.

19. Neurovascular coupling:
Regulation of cerebrovascular tone by perivascular nerves
E. Hamel, Perivascular nerves and the regulation of cerebrovascular tone, J. Appl. Physiol, 1001059-1064, 2006

20. Neurovascular coupling:
Regulation of cerebrovascular tone by activity
B Pia
Z
X
Y
Spherical
treadmill
PMT
A
Imaging cortical vascular dynamics during
voluntary locomotion
Figures courtesy to Yurong Gao and Patrick Drew (Penn State)

21. Neurovascular coupling:
Regulation of cerebrovascular tone by activity
Hypothesis: Blood is oversupplied because targeted,
intracranial vessels cannot dilate adequately
Vasodilation
Brain tissue
resistance
CSF
Brain
Pial
funnel
Arteriole
Baseline
Active
Mechanical restriction of
dilation by brain tissue plays
an important role in shaping
the vasodilation pattern
Surface arteries dilate 2-4x more than
intracortical arteries
order-0
order-1
-1 0 1 2 3 4 5 -1 0 1 2 3 4 5
−5
0
5
10
15
20
25
Other regions
Time, sec Time, sec
Diameter
Change(%)
surface order 0
surface order 1
depth 50µm
depth 100µm
depth 150µm
depth 200µm
−5
0
5
10
15
20
25
F/H region
Figures courtesy to Yurong Gao and Patrick Drew (Penn State)

22. Neurovascular coupling:
Regulation of cerebrovascular tone by blood pressure
A B
D E
The ratio of vertices to edges is a measure of redund
network. The combined data from rats and mice is con
a ratio of 3 to 2 (r2
= 0.99, P < 0.001) (Fig. 2B). This edg
ratio coincides with that for a simple lattice in which
have a coordination number of 3, such as a hexagonal gr
comparison, the scaling is 1 for binary trees and buse
The observed edge-to-vertex ratio of 3 to 2 implies that
edges within backbone with N vertices, N/2 of the edge
redundant connections, or anastomoses. These anasto
stitute only 8.4 ± 0.2% (mean ± SE) and 6.2 ± 0.2% o
number of edges in the network for rats and mice, resp
A second issue is the size of the loops in the pial bac
each network, we calculated the set that contained the s
dependent loops, analogous to Kirchhoff loops in cir
(Fig. 2C). The number of such loops is 3.4 times larger f
mice. This finding is not inconsistent with the larger terr
MCA network in rats versus mice, by a factor of 2.8 (Ta
distribution of edges in loops that comprise the bac
a mode at four edges and is the same for rats and mic
(P > 0.1, KS-test). The predominance of four rather tha
per loop, together with a coordination number of 3 for e
implies that no obvious lattice captures all features
networks. Lastly, our measures indicate that the proba
sity of loops with a given area is observed to be ex
distributed with mean values of 0.94 ± 0.14 mm2
(me
confidence interval) and 0.72 ± 0.06 mm2
for rat an
A
D E
B C
Fig. 1. Complete mapping of the middle cerebral artery. (A) A flattened
cortical hemisphere from a fluorescent vascular fill, overlaid with a tracing of
all vessels within the middle cerebral artery network. (B) In each tracing, the
edges (green lines) connect vertices positioned at branches, with coordination
number of 3 (red circles), and vertices positioned at the location of penetrating
A B
Fig. 3. Structural robustness to cumulative edge removal for measure
networks and ideal lattices. (A) Average backbone robustness to ed
moval for networks for rat, mice, and honeycomb lattices of differen
Robustness is computed by progressively removing graph edges at ra
while computing the fractions of vertices that become isolated fro
A
C D
B
The surface artery network is an interconnected mesh
Blinder, Shih, et al., PNAS, 2010

23. Neurovascular coupling:
Regulation of cerebrovascular tone by blood pressure
Mass conservation, inlet conditions
(i.e., pressure at middle cerebral artery (MCA)),
and outlet conditions
(i.e., capillary pressure)
j=i
cji =
pi − pj
Rji
+ cii
pi − pc
Rci
= 0
⇒

 cii
Rci
+
j=i
cji
Rji

 pi −
j=i
cji
Rji
pj = cii
pc
Rci
⇒
Ap = b

24. Outline
Neuron: Electrophysiology with time-dependent ion concentrations
Vasculature: Regulation of cerebrovascular tone by nerves & blood
Application: Personalized and predictive medicine
Individal activity patterns in migraine
Non-drug treatment in migraine
Controlling the migraine generator network
Summary & Conclusion

25. Outline
Neuron: Electrophysiology with time-dependent ion concentrations
Vasculature: Regulation of cerebrovascular tone by nerves & blood
Application: Personalized and predictive medicine
Individal activity patterns in migraine
Non-drug treatment in migraine
Controlling the migraine generator network
Summary & Conclusion

26. Migraine = Headache

27. What is a migraine aura?
based on: • M. A. Dahlem & S. C. M¨uller Biol. Cybern. 88,419 (2003)
• M. A. Dahlem et. al. Eur. J. Neurosci. 12,767 (2000).

28. Mapped visual symptoms on cortex via fMRI retinotopy
1 cm
10°
1
3
5
7
15
17
19
21
23
25
27 min
Visual hemifield Primary visual cortex
• Dahlem & Hadjikhani (2009) PLoS ONE 4: e5007.

29. RD waves w/ global inhibitory coupling on curved media
Macroscopic SD model on gyrified cortex.
∂u
∂t
= u −
1
3
u3
− v + Du
1
√
g
∂
∂αi
gij
√
g
∂u
∂αi
∂v
∂t
= (u + β + K H(u)dαi
)
SD in the folded cortex posses critical properties.
First approximation: localized SD follows shortest path.

30. Hot spots left visual field
23 min
21
19
17
17
15
13
11
97
5
10°
1 cm
Visual hemifield Primary visual cortex
Cooperation with Andrew Charles, UCLA.

31. Hot spots right visual field
1 cm
10°
1
3
5
7
15
17
19
21
23
25
27 min
Visual hemifield Primary visual cortex

32. Labyrinth path in reverse direction
1 cm
10°
1
3
5
7
15
17
19
21
23
25
27 min
Visual hemifield Primary visual cortex

33. Observed wave forms of SD in gyrencephalic brain
• E. Santos, et al., Radial, spiral and reverberating waves of spreading depolarisation occur in the gyrencephalic
brain, NeuroImage 99:244-255 (2014).

34. Outline
Neuron: Electrophysiology with time-dependent ion concentrations
Vasculature: Regulation of cerebrovascular tone by nerves & blood
Application: Personalized and predictive medicine
Individal activity patterns in migraine
Non-drug treatment in migraine
Controlling the migraine generator network
Summary & Conclusion

35. 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.

36. 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

37. 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

38. History of electrical & magnetic stimluation
Non-drug treatment for headaches (1896)
First steps in miniaturization

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

40. History of electrical & magnetic stimluation
Non-drug treatment for headaches (2013)
Courtesy eNeura Inc. USA
Disclosure: Conflict of interest
Consulting services in 2013 for Neuralieve Inc. (trading as eNeura
Therapeutics)

41. History of electrical & magnetic stimluation
Non-drug treatment for headaches (2014)
Courtesy Cerbomed GmbH, Germany

42. Modern neuromodulation (invasive)

43. Modern neuromodulation (invasive)
Courtesy Autonomic Technologies, Inc.

44. Modern neuromodulation (invasive)
Courtesy Autonomic Technologies, Inc.

45. Modern neuromodulation (invasive)
Courtesy St. Jude Medical Inc.

46. Modern neuromodulation (invasive)
Courtesy St. Jude Medical Inc.

47. Past and modern neuromodulation in migraine

48. 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).

49. Outline
Neuron: Electrophysiology with time-dependent ion concentrations
Vasculature: Regulation of cerebrovascular tone by nerves & blood
Application: Personalized and predictive medicine
Individal activity patterns in migraine
Non-drug treatment in migraine
Controlling the migraine generator network
Summary & Conclusion

50. Migraine Generator Network & Dynamical Network Biomarker
attack-free
headache
prodrome
p
ostdrome
p
ostdrome
aura
magnetic
electrical
HY,TH
SPG
SSN
TCC
PAG
LC
RVM
TG
cortex
cranial circulation
bone
ON OFF
cranial innervation1 day 5-60min
4-72h
day
1
daysto
m
onths(avg2weeks
)
dynamical
network
biomarkers
m
igraine cycle
(i)
(ii)
(iii)
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).

51. Migraine Generator Network & Dynamical Network Biomarker
attack-free
headache
prodrome
p
ostdrome
p
ostdrome
aura
TCC
TG
cortex
cranial circulation
bone
cranial innervation1 day 5-60min
4-72h
day
1
daysto
m
onths(avg2weeks
)
dynamical
network
biomarkers
m
igraine cycle
(i)
(ii)
(iii)
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).

52. Migraine Generator Network & Dynamical Network Biomarker
attack-free
headache
prodrome
p
ostdrome
p
ostdrome
aura
TCC
TG
cortex
cranial circulation
bone
cranial innervation1 day 5-60min
4-72h
day
1
daysto
m
onths(avg2weeks
)
dynamical
network
biomarkers
m
igraine cycle
(i)
(ii)
(iii)
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).

53. Migraine Generator Network & Dynamical Network Biomarker
attack-free
headache
prodrome
p
ostdrome
p
ostdrome
aura
HY,TH
TCC
TG
cortex
cranial circulation
bone
cranial innervation1 day 5-60min
4-72h
day
1
daysto
m
onths(avg2weeks
)
dynamical
network
biomarkers
m
igraine cycle
(i)
(ii)
(iii)
• M. A. Dahlem, Migraine generator network and spreading depression dynamics as neuromodulation targets in
episodic migraine. Chaos, 23, 046101 (2013).

54. Migraine Generator Network & Dynamical Network Biomarker
attack-free
headache
prodrome
p
ostdrome
p
ostdrome
aura
HY,TH
TCC
TG
cortex
cranial circulation
bone
cranial innervation1 day 5-60min
4-72h
day
1
daysto
m
onths(avg2weeks
)
dynamical
network
biomarkers
m
igraine cycle
(i)
(ii)
(iii)
• 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).

55. Migraine Generator Network & Dynamical Network Biomarker
attack-free
headache
prodrome
p
ostdrome
p
ostdrome
aura
HY,TH
SPG
SSN
TCC
TG
cortex
cranial circulation
bone
cranial innervation1 day 5-60min
4-72h
day
1
daysto
m
onths(avg2weeks
)
dynamical
network
biomarkers
m
igraine cycle
(i)
(ii)
(iii)
• 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).

56. Migraine Generator Network & Dynamical Network Biomarker
attack-free
headache
prodrome
p
ostdrome
p
ostdrome
aura
HY,TH
SPG
SSN
TCC
TG
cortex
cranial circulation
bone
cranial innervation1 day 5-60min
4-72h
day
1
daysto
m
onths(avg2weeks
)
dynamical
network
biomarkers
m
igraine cycle
(i)
(ii)
(iii)
• 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, J. Kurths, M. D. Ferrari, K. Aihara, M. Scheffer, and A. May, Understanding Migraine using
Dynamical Network Biomarkers (accepted, Cephalalgia, 2 pages, 1 figure, arxiv pre-print before peer review) (2014).

57. Migraine Generator Network & Dynamical Network Biomarker
attack-free
headache
prodrome
p
ostdrome
p
ostdrome
aura
magnetic
electrical
HY,TH
SPG
SSN
TCC
PAG
LC
RVM
TG
cortex
cranial circulation
bone
ON OFF
cranial innervation1 day 5-60min
4-72h
day
1
daysto
m
onths(avg2weeks
)
dynamical
network
biomarkers
m
igraine cycle
(i)
(ii)
(iii)
• 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, J. Kurths, M. D. Ferrari, K. Aihara, M. Scheffer, and A. May, Understanding Migraine using
Dynamical Network Biomarkers (accepted, Cephalalgia, 2 pages, 1 figure, arxiv pre-print before peer review) (2014).

58. Migraine Generator Network & Dynamical Network Biomarker
attack-free
headache
prodrome
p
ostdrome
p
ostdrome
aura
magnetic
electrical
HY,TH
SPG
SSN
TCC
PAG
LC
RVM
TG
cortex
cranial circulation
bone
ON OFF
cranial innervation1 day 5-60min
4-72h
day
1
daysto
m
onths(avg2weeks
)
m
igraine cycle
(i)
(ii)
(iii)
• 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, J. Kurths, M. D. Ferrari, K. Aihara, M. Scheffer, and A. May, Understanding Migraine using
Dynamical Network Biomarkers (accepted, Cephalalgia, 2 pages, 1 figure, arxiv pre-print before peer review) (2014).
• 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).

59. Migraine Generator Network & Dynamical Network Biomarker
attack-free
headache
prodrome
p
ostdrome
p
ostdrome
aura
magnetic
electrical
HY,TH
SPG
SSN
TCC
PAG
LC
RVM
TG
cortex
cranial circulation
bone
ON OFF
cranial innervation1 day 5-60min
4-72h
day
1
daysto
m
onths(avg2weeks
)
dynamical
network
biomarkers
m
igraine cycle
(i)
(ii)
(iii)
• 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, J. Kurths, M. D. Ferrari, K. Aihara, M. Scheffer, and A. May, Understanding Migraine using
Dynamical Network Biomarkers (accepted, Cephalalgia, 2 pages, 1 figure, arxiv pre-print before peer review) (2014).
• 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).

60. Tipping point behavior in migraine
magnetic
electrical
HY,TH
SPG
SSN
TCC
PAG
LC
RVM
TG
cortex
cranial circulation
bone
ON OFF
cranial innervation
τ
attack-free interval
prodromal phase
pain phase
time
• M. A. Dahlem et al. Understanding migraine using dynamical network biomarkers Cephalalgia in press (2014).

61. Pain comes from the meninges not the cortex
0
1
2
3
4
5
0 5 10 15 20 25 30 35
time
depletedsurfacearea slow dynamics
a
b
c
d e f
MIA
x
y

62. Pain comes from the meninges not the cortex
0
1
2
3
4
5
0 5 10 15 20 25 30 35
time
depletedsurfacearea slow dynamics
a
b
c
d e f
AP: acute phaseIP: ignition phase
MIA
x
y

63. Pain comes from the meninges not the cortex
0
1
2
3
4
5
0 5 10 15 20 25 30 35
time
depletedsurfacearea slow dynamics
a
b
c
d e f
AP: acute phaseIP: ignition phase
MIA
x
y
arachnoid
blood
arachnoid
blood
bone
sensory innervation
dura
small MIA
large MIA
SD
SD
dural sinuses
cortex
pia
cortex
pia
For example, can a sulcal pial siphoning of K+ lead to focally
raised concentration in the meninges?

64. Pain comes from the meninges not the cortex
0
1
2
3
4
5
0 5 10 15 20 25 30 35
time
depletedsurfacearea slow dynamics
a
b
c
d e f
AP: acute phaseIP: ignition phase
MIA
x
y
IP Stim.
AP Stim.
arachnoid
blood
arachnoid
blood
bone
sensory innervation
dura
small MIA
large MIA
SD
SD
dural sinuses
cortex
pia
cortex
pia
For example, can a sulcal pial siphoning of K+ lead to focally
raised concentration in the meninges?

65. Outline
Neuron: Electrophysiology with time-dependent ion concentrations
Vasculature: Regulation of cerebrovascular tone by nerves & blood
Application: Personalized and predictive medicine
Individal activity patterns in migraine
Non-drug treatment in migraine
Controlling the migraine generator network
Summary & Conclusion

66. Disability and burden in migraine
“[...] migraine alone is responsible of almost 3% of disability attributable to a
specific disease worldwide [...]. This places migraine as the eighth most
burdensome diseases, the seventh among non-communicable diseases and the
first among the neurological disorders ranked in the GBD report.” GBD =
Global Burden of Disease (WHO report)
Leonardi, M. and Raggi, A., Burden of migraine: international perspectives, Neurol. Sci., 34, 2013.

67. Summary & Conclusions
HH model with time-dependet ion concentrations
4 variables & time scales (AP/SD),
complete bifurcation analysis,
correct slow-fast analysis.

68. Summary & Conclusions
HH model with time-dependet ion concentrations
4 variables & time scales (AP/SD),
complete bifurcation analysis,
correct slow-fast analysis.
Thermodynamic foundation, e.g. appropriately
defining a free energy function, cyclic processes
(analogy: steam engine) and more.
−60 −40 −20 0 20 40
0
10
20
30
40
50
60
A B
[K ]gain
+ / mM
[K]e
+/mM
clearance
reuptakereuptake
trans-
membrane
activator(u)
inhibitor (v)
innersolutioninnersolution
outer solution

69. Summary & Conclusions
HH model with time-dependet ion concentrations
4 variables & time scales (AP/SD),
complete bifurcation analysis,
correct slow-fast analysis.
Thermodynamic foundation, e.g. appropriately
defining a free energy function, cyclic processes
(analogy: steam engine) and more.
This leads to macroscopic phenomenological
description—pattern formation principles than
guide us to look for missing mechanism, such as
long-range/global/fast diffusion inhibition.
B
C
activator, u
immobile inhibitor, v
long-range inhibitor, w
A
activator:
front
propagation
activator-inhibitor:
pulse propagation
(includes re-entry
patterns in 2D)
activator:
front
propagation
act.-2-inhibitors:
localized structures
(spots)

70. Summary & Conclusions
HH model with time-dependet ion concentrations
4 variables & time scales (AP/SD),
complete bifurcation analysis,
correct slow-fast analysis.
Thermodynamic foundation, e.g. appropriately
defining a free energy function, cyclic processes
(analogy: steam engine) and more.
This leads to macroscopic phenomenological
description—pattern formation principles than
guide us to look for missing mechanism, such as
long-range/global/fast diffusion inhibition.
Inhibition (likely) implementet by regulation of
cerebrovascular tone by perivascular
nerves—extrinsic (TG, SPG) or intrinsic
(conductive response of penetrating arterioles).

71. Summary & Conclusions
HH model with time-dependet ion concentrations
4 variables & time scales (AP/SD),
complete bifurcation analysis,
correct slow-fast analysis.
Thermodynamic foundation, e.g. appropriately
defining a free energy function, cyclic processes
(analogy: steam engine) and more.
This leads to macroscopic phenomenological
description—pattern formation principles than
guide us to look for missing mechanism, such as
long-range/global/fast diffusion inhibition.
Inhibition (likely) implementet by regulation of
cerebrovascular tone by perivascular
nerves—extrinsic (TG, SPG) or intrinsic
(conductive response of penetrating arterioles).
Whole brain model of migraine dynamics opens
up model-based control for predictive (hot spots
& labyrinths) and personalized medicine.
attack-free
headache
prodrome
p
ostdrome
p
ostdrome
aura
magnetic
ele
ctr
ica
l
HY,TH
SPG
SSN
TCC
PAG
LC
RVM
TG
cortex
cranial circulation
bone
ON OFF
cranial innervation1 day 5-60min
4-72h
day
1
daysto
m
onths(avg2weeks
)
dynamical
network
biomarkers
m
igraine cycle
(i)
(ii)
(iii)

72. Cooperation & Funding
Niklas H¨ubel, Frederike Kneer,
Thomas Isele, Julia Schumacher,
Bernd Schmidt
(TU Berlin, HU Berlin, Magdeburg)
Nouchine Hadjikhani
(Martinos Center for Biomedical Imaging, MGH)
Steven Schiff
Patrick Drew, Yurong Gao
(Penn State Center for Neural Engineering)
Huaxiong Huang
(York Uni, Toronto)
Timothy David
(Uni of Canterbury, NZ)
Kazuyuki Aihara
(Uni of Tokyo, Japan)
Arne May
(Uni Hamburg, Germany)
Jens Dreier
(Department of Neurology, Charit´e; Berlin, Germany)
Edgar Santos, Oliver W. Sakowitz
(Department of Neurosurgery, Heidelberg, Germany)
berlin
Migraine Aura Foundation

73. Additional slides

74. 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

75. Including cell swelling
Electrophysiology Thermodynamics
break down of ion grandients
cell swelling
Iin
Iin
Iout
Iout
Normal neuron in healthy brain
ECV 20%
ECV 5%
AMPA/
kainate
–70 mV
–10 mV
SK
Na
+
Na
+
K+
Na+
DR
Ca
2+
Ca
2+
Ca
2+
Ca
2+
Ca
2+ Na
+Na
+
Ca2+
K+
Na+
Ca2+
Ca
2+
K
+
Swollen neuron during spreading depolarization
H2O
Nonspecific
cation channelsInsufficient
sodium pump
NMDAR
J.P. Dreier Nature Medicine 17 2011
massive release of Gibbs free energy
J.P. Dreier et al. Neuroscientist 19 2012

76. Modeling the migraine aura–ischemic stroke continuum
0 1 2 3 4 5 6
time (s)
100
50
0
50
voltage(mV)
V
EK
ENa
Iapp
−gate deactivation Hopf
−gate
membrane voltage
SNIC
Hopf
SNIC
Recovery
eletrogenic pump
Fold
Seizure−like activity
in ischaemic stroke
hypoxic tissue
Spreading depression
(ceiling level)
n
nV
Ipump
[K+]o
[K+
]o = 10mM

77. Modeling the migraine aura–ischemic stroke continuum
Ischemia-induced
migraine,
Migrainous infarction,
Persistent migraine w/o
infarction (see below).
Dahlem et al. Physica D 239, 889 (2010)
0 1 2 3 4 5 6
time (s)
100
50
0
50
voltage(mV)
V
EK
ENa
Iapp
−gate deactivation Hopf
−gate
membrane voltage
SNIC
Hopf
SNIC
Recovery
eletrogenic pump
Fold
Seizure−like activity
in ischaemic stroke
hypoxic tissue
Spreading depression
(ceiling level)
n
nV
Ipump
[K+]o
[K+
]o = 10mM

78. Common etiology or 2 mechanisms in MWoA and MWA?
SD
headacheprodrome aura
trigger
heightened susceptibility
delayed trigger
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

79. SD does not curl-in in human cortex
1cm
10 min
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).

80. SD does not curl-in in human cortex
1cm
10 min
1cm
SD curls in to form
spirals with T=2.45min!
spiral
core
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¨uller, Exp. Brain Res. 115,319, (1997).

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

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

83. 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

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

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

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

87. Migraine scotoma reveal functional properties
Pattern matching ”Curved” retinotopic mapping
4
7
9
13
A B
C
2 4 6 8 10 12 14
0.1
0.2
0.3
2 4 6 8 10 12 14
20
40
60
80
100
120
140
2 4 6 8 10 12 14
0.2
0.4
0.6
0.8
1
¼Æ
Æ
Å´ ½µ
ÀÅ
¯´±µÃ´ÑѾµ
´Ö µ
¾ ¼
¼ ¾¼¼¼
• Dahlem & Tusch, J. Math Neuroscie. 2,14 (2012)