reentrant and retracting waves of cortical spreading depression in migraine

Reentrant and retracting waves of corticalspreading depression in migraine

Markus A. Dahlem

Research group: Nonlinear Dynamics in Physiology and Medicine

fragmentedlocalizedengulfing

berlin

Cardiovascular Research Lecture, UCLA, June 18, 2012

Markus A. Dahlem, TU Berlin

Confined 2D wave segments A pattern formation problem

Spatio-temporal patterns in the heart and brain

”Conduction in nervous tissue resembles that in somatic striated incardiac muscle. The laws which apply to the muscle fibers are alsoapplicable to the nerve fibers”

Wiener & Rosenblueth (1946)


Confined 2D wave segments A pattern formation problem

Spatio-temporal patterns in the heart and brain

A. Garfinkel et al. PNAS 97, 2000

(a) (b)

(c)

LS

CS

(d)

affected areatemporarily

Dahlem et al. Physcia D 239, 2010


Outline

1. Spreading depression: frommolecules to cell to tissue

2. Reentrant and retractingwaves in the cortex

3. Migraine as a dynamicaldisease: Towards therapy

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

Ca2+

Ca2+

Ca2+

Ca2+

Ca2+ Na

+Na

+

Ca2+

K+

Na+

Ca2+

Ca2+

K+

Swollen neuron during spreading depolarization

H2O

Nonspecific

cation channelsInsufficient

sodium pump

NMDAR

−gate deactivation Hopf

−gatemembrane voltage

SNIC

Hopf

SNIC

Recovery

eletrogenic pump

FoldSeizure−like activity

in ischaemic stroke

hypoxic tissue

Spreading depression

(ceiling level)

n

nV

Ipump[K+]o

[K+]o = 10mM

slow dynamicstransient and

positive (fender)

negative (saddle)

gyral crowns

entrance to sulci


Outline



3. Migraine as a dynamicaldisease: towards therapy

Iin

Iin

Iout

Iout


ECV 20%

ECV 5%

AMPA/kainate

–70 mV

–10 mV

SK

Na+

Na+

K+

Na+

DR

Ca2+

Ca2+

Ca2+

Ca2+

Ca2+ Na

+Na

+

Ca2+

K+

Na+

Ca2+

Ca2+

K+


H2O

Nonspecific


sodium pump

NMDAR



SNIC

Hopf

SNIC

Recovery

eletrogenic pump


in ischaemic stroke

hypoxic tissue


(ceiling level)

n

nV

Ipump[K+]o

[K+]o = 10mM


positive (fender)

negative (saddle)

gyral crowns

entrance to sulci


Spreading depression From molecules to cell to tissue

Migraine Types and subforms

from Migraine Aura Foundation

”Cortical spreading depression is key to the genesis of migraine”Michael Moskowitz (Harvard Medical School)



SD: From molecules to entire brain

Functional mutations Spreading depression (SD)

(e.g. FHM2: sodium-potassium pump)

cf.: Maagdenberg, et al., Ann. Neurol., 67 2010

Tottene, et al., Neuron, 61 2009

Freilinger, et al. Nature Genetics online 2012



SD: From molecules to entire brain

Electrophysiology Thermodynamics

break down of ion grandients

cell swelling

Iin

Iin

Iout

Iout


ECV 20%

ECV 5%

AMPA/kainate

–70 mV

–10 mV

SK

Na+

Na+

K+

Na+

DR

Ca2+

Ca2+

Ca2+

Ca2+

Ca2+ Na

+Na

+

Ca2+

K+

Na+

Ca2+

Ca2+

K+


H2O

Nonspecific


sodium pump

NMDAR

J.P. Dreier Nature Medicine 17 2011

massive release of Gibbs free energy

J.P. Dreier et al. Neuroscientist accepted


Spreading depression Local dynamics

Spreading depression wave: ion gradients breakdown

-1

-2

-3

-4-7

-8

1 min

20 mV

log [cat] , M

(mM)

VeNa+

Na+

K+

Ve

K+

Ca++

Ca++

H+

0 10 20 30 s

150

6050

31.5

0.08

unitact.

M. Lauritzen TINS 10:8 (1987)




-1

-2

-3

-4-7

-8

1 min

20 mV

log [cat] , M

(mM)

VeNa+

Na+

K+

Ve

K+

Ca++

Ca++

H+

0 10 20 30 s

150

6050

31.5

0.08

unitact.


“SD is such a drastic andextensive phenomenon thatalmost any speculation is safeconcerning probable involvementof all cortical elements”Marshall (1959) Physiol. Rev. 39:239.

SD: spreading depression



Leao original demonstration of SD

Leao AAP (1944) J. Neurophysiol. 7:359



SD in human cortex shown by ECoG

Fabricius et al. (2006) Brain 129:778



Mathematical models cells, circuits, and to tissue

I

II

III

IV

V

VI

Apic

al dendrite

Current distribution

Soma

Glia

Extra

cellu

lar

Osmotic force

Pump

INa,P

IK,DR

IK,A

INMDA

INa,T

K+

[K+]o

[Na+]i



Local Dynamics during SDA

pic

al dendrite

Current distribution

Soma

Glia

Extra

cellu

lar

Osmotic force

Pump

INa,P

IK,DR

IK,A

INMDA

INa,T

K+

[K+]o

[Na+]i

C∂V

∂t= −INa − IK − ICl + I pump + Iapp

INa = −m3∞h(ENa − V )

IK = −n4(EK − V )

∂n

∂t= αn(1 − n) − βn,

∂h

∂t· · ·

∂[ion]o

∂t=

IionA

FVolo+ Idiff

∂[ion]i

∂t=

IionA

FVoli

I pumpion (V ) = βionImax

(1 +

KmK

[K ]o

)−2 (1 +

KmNa

[Na]i

)−3

Alternatively (GHK currents)

Iion = V αF Pion[ion]i − [ion]oe

−αV

1 − e−αV

M. A. Dahlem, Models of cortical SD, Scholarpedia



Tissue properties & engery state change time scales . . .

... otherwise robust!

0 1 2 3 4 5 6time (s)

100

50

0

50

volt

age

(mV

)

V

EK

ENa

Iapp

0 5 10 15 20 25 30 35

time (s)

100

50

0

50

volt

age

(mV

)

V

EK

ENa

Iapp

Parameters relevant for migraine aura–ischemic stroke continuum.



Bifurcations involved in local dynamics of SD

0 1 2 3 4 5 6time (s)

100

50

0

50

volt

age (m

V)

V

EK

ENa

Iapp



SNIC

Hopf

SNIC

Recovery

eletrogenic pump


in ischaemic stroke

hypoxic tissue


(ceiling level)

n

nV

Ipump[K+]o

[K+]o = 10mM

M. A. Dahlem, Models of cortical SD, Scholarpedia



Migraine full-scale attack is more confined

(a) (b)

(c)

LS

CS

(d)


Dahlem et al. ”2D wave patterns ... ”. Physcia D 239 (2010) Special issue: Emerging Phenomena.



Macroscopic RD with augmented nonlocal transmission

ion

currents

ion gradient

ion

conductance

ion

pumpsout in

diffu

sion

activator−inhibitor dynamics

depolarization

firing rate

neurovascular coupling

neural network activity

The extended Hodgkin-Grafstein model (1963) of SD

u =

(u − u3

3− v

)+ D∇2u

(+ FHN inhibitor equations + nonlocal term)

ε−1v = u + β − γv + KF [u]

Global control

F [u] = Su(t)− S0

Su(t) =

∫H(u(r, t)− ue) dr,



Outline




Iin

Iin

Iout

Iout


ECV 20%

ECV 5%

AMPA/kainate

–70 mV

–10 mV

SK

Na+

Na+

K+

Na+

DR

Ca2+

Ca2+

Ca2+

Ca2+

Ca2+ Na

+Na

+

Ca2+

K+

Na+

Ca2+

Ca2+

K+


H2O

Nonspecific


sodium pump

NMDAR



SNIC

Hopf

SNIC

Recovery

eletrogenic pump


in ischaemic stroke

hypoxic tissue


(ceiling level)

n

nV

Ipump[K+]o

[K+]o = 10mM


positive (fender)

negative (saddle)

gyral crowns

entrance to sulci


Spreading depression Spiral waves

Re-entrant SD waves with anatomical block

Reshodko, L. V. and Bures, J Biol. Cybern. 18,181 (1975)



Experiments: open wave segments are unstable

Dahlem & Muller Exp. Brain Res. 115 (1997)



Spreading Depression: Reaction-diffusion in the brain

A nearly complete discharge and

recharge of chemical batteries in

neurons and glial cells

Dahlem & Muller (1997) Exp. Brain Res. 115:319



Spreading Depression: Reaction-diffusion in the brain

Z-type rotation causes a wave break in the spiral core.

Dahlem & Muller (1997) Exp. Brain Res. 115:319



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



Drugs adjust excitability:retracting & collapsing waves

What happens if SD wave fragments with open ende occur inhuman pathophysiology during migraine?

Do they form spirals?

Do fragments quickly retract?

Or: can wave fragments propagte some distance?



Engulfing RD-wave: current paradigm of migraine attack

M. Lauritzen (1987) Trends in Neurosciences 10:8.




(a) (b)

(c)

LS

CS

(d)





What is a migraine aura?



Visual migraine aura model

b

a

c

e

d

Dahlem et al. (2000) Eur. J. Neurosci. 12:767.

Dahlem and Chronicle (2004) Prog. Neurobiol. 74:351.



Migraine visual field defects reported in 1941 by K. Lashley

visual field defect pattern on primary visual cortex

0

5

10

15

5min7min

9min

11min

15min

0 10 20 30 40 50mm

5min7min

9min11min

15min

Only about 2-10% but not 50% cortical surface area is affected!Dahlem & Hadjikhani (2009) PLoS ONE 4: e5007.



Tracking migraine aura symptoms

Vincent & Hadjikhani (2007) Cephalagia 27




(a) (b)

(c)

LS

CS

(d)




Spreading depression Open wave segments - fMRI evidence & retinal SD

Confined spatial patterns of spreading depression

Hadjikhani et al. (2001) PNAS

Dahlem & Hadjikhani (2009) PLoS ONEDahlem & Muller (1997) Exp. Brain Res.




neighboring points

collapse

?

16 min

31 min

1 cm

nucleationrecordedslice not






23 min18 min.

28 min.






23 min18 min.

28 min.

Open wave fronts move along

a rather straight line

preventing a reentry of SD






23 min18 min.

28 min.

Open wave fronts move along

a rather straight line

preventing a reentry of SD

Hadjikhani et al. (2001) PNASDahlem & Hadjikhani (2009) PLoS ONE

Dahlem & Muller (1997) Exp. Brain Res.




18 min.

23 min

28 min.

33 min.

38 min.

1 mm

Spiral waves (reentry) observed in retinal SDwith a rotation period of 2.45 min

Hadjikhani et al. (2001) PNASDahlem & Hadjikhani (2009) PLoS ONEDahlem & Muller (1997) Exp. Brain Res.



Clinical evidence



Mapped visual symptoms on cortex via fMRI retinotopy

1 cm

10°

1 357

15

1719

2123

25

27 min

Visual hemifield Primary visual cortex

Dahlem & Hadjikhani (2009) PLoS ONE 4: e5007.



Mapped visual symptoms on cortex via fMRI retinotopy

23 min

21

19

17

17

15

1311

975

10°

1 cm


Dahlem & Hadjikhani (2009) PLoS ONE 4: e5007.


Outline




Iin

Iin

Iout

Iout


ECV 20%

ECV 5%

AMPA/kainate

–70 mV

–10 mV

SK

Na+

Na+

K+

Na+

DR

Ca2+

Ca2+

Ca2+

Ca2+

Ca2+ Na

+Na

+

Ca2+

K+

Na+

Ca2+

Ca2+

K+


H2O

Nonspecific


sodium pump

NMDAR



SNIC

Hopf

SNIC

Recovery

eletrogenic pump


in ischaemic stroke

hypoxic tissue


(ceiling level)

n

nV

Ipump[K+]o

[K+]o = 10mM


positive (fender)

negative (saddle)

gyral crowns

entrance to sulci


Dynamical disease Towards therapeutical approaches


(a) (b)

(c)

LS

CS

(d)





Cortical homeostasis is stable

Hypothesis: Cortical susceptibility to SD depends on the size ofthe momentarily affected tissue.



Yet, too big a perturbation triggers SD




Yet, too big a perturbation triggers SD


nucleationcritical



But a global negative feedback keeps SD confined





Threshold surface separates attractor basins

supra

stim.

stim. su

b

traveling wave

homo. steady state

ui(x)

ui+1

(x)

ui+2

(x)

phase space

threshold

Excitable media.



Solution on threshold surface

supra

stim.

stim. su

b

traveling wave

homo. steady state

ui(x)

ui+1

(x)

ui+2

(x)

phase space

threshold

Excitable media.



Nonlinear delayed transitions: saddle-node ghosts

homo.

stead

y stat

e

fast

fast

slow



Bottleneck due to saddle-node bifurcation

(a) (b)

(a)

(c)

(b)

(d)(c)

stable wave segment

homo.

stead

y stat

e

homo.

stead

y stat

e

homo.

stead

y stat

e

homo. steady state

supra

stim.

fast

fast

slow

trave

ling w

ave

stim. su

b

traveling wave

w

ave

size

S

threshold β

∂R

∂R

threshold



Simulation of transient SD wave segment

gray = cortical surface; red = SD wave



Typical trajectory: fast growth and collapse & bottleneck

0

5

10

15

20

25

0 5 10 15 20 25 30 35time

collapse

cort

ical

sur

face

are

a in

vade

d by

SD nucleation

CSD break−up

long transient propagation

model−based

stimulation strategiestherapeutic TMS




neighboring points

collapse

?

16 min

31 min

1 cm

nucleationrecordedslice not




neighboring points

0

4

8

12

16

20

32

28

24

time

16 min

31 min

1 cm

recordedslice not




neighboring points 16 min

31 min

1 cm

recordedslice not




5cm

00

0 0

32 16

6 24

time / m

in



Varying contact to the ghost

0

50

100

150

200

250

300

350

400

450

tota

laff

ecte

dar

ea(T

AA

)

(1)

(2)

(3)

(4)

0 10 20 30 40 50 60

maximal instantaneous area (MIA)

0

50

100

150

200

250

300

exci

tati

on

du

rati

on(E

D)

(1)

(2)

(3)

(4)

0 50 100 150 200 250 300 350 400 450

total affected area (TAA)

(1)

(2)

(3)

(4)

0

80

160

240

#O

ccu

rren

ces

0 80 160240

0 80 160240# Occurrences

β0 = 1.32

(1)

(2) (3)

(4)

0 30 60 90 120150180210240270time

1

10

20

30

40

50

60

70

80




0

50

100

150

200

250

300

350

400

450

tota

laff

ecte

dar

ea(T

AA

)

(1)

(2)

(3)

(4)

0 10 20 30 40 50 60


0

50

100

150

200

250

300

exci

tati

on

du

rati

on(E

D)

(1)

(2)

(3)

(4)

0 50 100 150 200 250 300 350 400 450


(1)

(2)

(3)

(4)

0

80

160

240

#O

ccu

rren

ces

0 100 200

0 100200300# Occurrences

β0 = 1.33

(1)

(2)

(3)

(4)

0 20 40 60 80 100120140160180time

1

10

20

30

40

50

60

70

80

90




0

50

100

150

200

250

300

350

400

450

tota

laff

ecte

dar

ea(T

AA

)

(1)

(2)

(3)

(4)

0 10 20 30 40 50 60


0

50

100

150

200

250

300

exci

tati

on

du

rati

on(E

D)

(1)

(2)

(3)

(4)

0 50 100 150 200 250 300 350 400 450


(1)

(2)

(3)

(4)

0

80

160

240

#O

ccu

rren

ces

0 250 500


β0 = 1.34

(1)

(2)

(3)

(4)

0 10 20 30 40 50 60 70 80 90time

1102030405060708090100110120130



IHS Classification ICHD-II – All Types

1.

1.1. 1.2. 1.4. 1.5. 1.6.1.3.

1.2.1. 1.3.1. 1.5.1. 1.6.1.

Sub

form

s

Migraine

Subtypes

2 symptom, 3 combinations: both or either of them



IHS Classification ICHD-II – Major Types

with aura

without aura

typical aurawithout headache

1.

1.1. 1.2.

1.2.1.

Sub

form

s

Migraine

Subtypes

1.1.

1.2.1.

1.2.3.




Model-based hypothesis testing

1.1. 1.2.1

1.2.3Sub−threshold

Affe

cted

cor

tical

are

aSurvival time

SD in migraine attack



Neuromodulation

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

figure courtesy of Jean Schoenen



Homo Neuromodulandus

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

figure courtesy of Jean SchoenenMarkus A. Dahlem, TU Berlin


Control of spreading depression

From bench to bedside

!

!"#$%&'$()'#"*(

+,-+,."(!"#$%&/*#(

0&1'2(3"'$#(

4#&5$1"(!"#$%&'$()'#"*( 6/&'7/2%1"(!"#$%&'$()'#"*(

Cooperation with Stephen Schiff & Bruce Gluckman Courtesy of Neuralieve




0

5

10

15

20

25

0 5 10 15 20 25 30 35time

collapse

cort

ical

sur

face

are

a in

vade

d by

SD nucleation

CSD break−up


model−based





0

5

10

15

20

25

0 5 10 15 20 25 30 35time

collapse

cort

ical

sur

face

are

a in

vade

d by

SD nucleation

CSD break−up


noise!

model−based




Single-pulse transcranial magnetic stimulation

Lipton et al. Lancet Neurology 9,373, 2010



Single-pulse transcranial magnetic stimulation



Double pulse stimulation (current TMS strategy)

0

5

10

15

20

25

0 5 10 15 20 25 30 35

noise sample 1 k=0.010noise sample 1 k=0.100noise sample 1 k=0.300noise sample 2 k=0.010noise sample 2 k=0.100noise sample 2 k=0.300

without noise

time

noise on

wav

e si

ze



Permanent noise stimulation

0

5

10

15

20

25

0 5 10 15 20 25 30 35

noise sample 1 k=0.030noise sample 1 k=0.040noise sample 1 k=0.050noise sample 2 k=0.030noise sample 2 k=0.040noise sample 2 k=0.050

without noise

time

noise on

wav

e si

ze



Single pulse vs. constant noise stimulation

0 5 10 15 20 25 30 35survival time of unstable solitons

0.0

0.1

0.2

0.3

0.4

0.5

pro

babili

ty



Single pulse vs. constant noise stimulation

0 5 10 15 20 25 30 35survival time

0.0

0.1

0.2

0.3

0.4

0.5

pro

babili

tyMigraine aura duration

without noiseon t=5, k = 0.050on t=5, k = 0.100noise 0.050pulse t=5, k = 0.100pulse t=5, k = 0.500



Noise sensitivity of transient wave segments

0

5

10

15

20

25

0 5 10 15 20 25 30 35

without noisenoise k=0.010noise k=0.015noise k=0.020noise k=0.025noise k=0.030noise k=0.035noise k=0.040

wav

e si

ze

time

How to escape quicklyfrom the ”ghost” plateau?



From bifurcation bench to bedside


Conclusion

Spatio-temporal waves needspatio-temporal control methods

Old paradigm

New paradigm: opens up new strategies, eg, transcranial randomnoise stimulation (tRNS) at special locations


Conclusion

(i) Persistent migraine w/o infarction, (ii) Migrainousinfarction, (iii) ischemia-induced migraine

Dahlem et al. Physica D 239, 889 (2010)


Conclusion

2D patterns with laser speckle-contrast imaging

SG

EG

KCLMG

(a)

(b) 5 min 37s (c) 9 min 07s

Dahlem et al. 239, 889 (2009) Physica D


Conclusion

Costs of disorders of the brain in Europe

55 Dementia

27 Migraines

22 Strokes

15.5 Epilepsy

10.5 Parkinson’s

billion Euro a year!



SNIC

Hopf

SNIC

Recovery

eletrogenic pump


in ischaemic stroke

hypoxic tissue


(ceiling level)

n

nV

Ipump[K+]o

[K+]o = 10mM

Balak and Elmaci (2005) European Journal of Neurology 12


Conclusion

Conclusions

The predicted plateau theory can betested clinically with non-invasiveimaging

Unifying concept including silent aura,migraine with or withoutheadache/aura

Insights into the self-organized patternformation may refine neuromodulationstrategies:

Being close to a saddle-nodebifurcation (”ghost” plateau)Design (feedback) control tointelligently target certain propertiesof SD in migraine

1 cm

10°

1 357

15

1719

2123

25

27 min



Conclusion

Conclusions





0

50

100

150

200

250

300

350

400

450

tota

laff

ecte

dare

a(T

AA

)

(1)

(2)

(3)

(4)

0 10 20 30 40 50 60


0

50

100

150

200

250

300

exci

tati

ond

ura

tion

(ED

)

(1)

(2)

(3)

(4)

0 50 100 150 200 250 300 350 400 450


(1)

(2)

(3)

(4)

0

80

160

240

#O

ccu

rren

ces

0 250 500


β0 = 1.34

(1)

(2)

(3)

(4)

0 10 20 30 40 50 60 70 80 90time

1102030405060708090100110120130


Conclusion

Conclusions






Conclusion ¡

Cooperation & Funding

Nouchine Hadjikhani(EPFL & Martinos Center for Biomedical Imaging, MGH)

Paul Van Valkenburgh

Jens Dreier(Department of Neurology, Charite; University Medicine, Berlin)

Steve Schiff(Penn State Center for Neural Engineering)

Klaus Podoll(University Hospital Aachen)

Thomas Isele

berlin

Migraine Aura Foundation


Conclusion ¡

Peri-infarct depolarizations

Dahlem et al. Physica D 239, 889 (2010)


Conclusion ¡

Clinical evidence for localized SD

Cortical perfusion measurement by indocyanine-green videoangiography inpatients undergoing hemicraniectomy for malignant stroke

cf. Woitzik J et al., Stroke 37,1549 (2006)


Conclusion ¡

Tangential cortical slice preparation

!

!"#$%&'$()'#"*(

+,-+,."(!"#$%&/*#(

0&1'2(3"'$#(

4#&5$1"(!"#$%&'$()'#"*( 6/&'7/2%1"(!"#$%&'$()'#"*(

Cooperation with Stephen Schiff & Bruce Gluckman


Conclusion ¡


-1

-2

-3

-4-7

-8

1 min

20 mV

log [cat] , M

(mM)

VeNa+

Na+

K+

Ve

K+

Ca++

Ca++

H+

0 10 20 30 s

150

6050

31.5

0.08

unitact.



Conclusion ¡


-1

-2

-3

-4-7

-8

1 min

20 mV

log [cat] , M

(mM)

VeNa+

Na+

K+

Ve

K+

Ca++

Ca++

H+

0 10 20 30 s

150

6050

31.5

0.08

unitact.


“SD is such a drastic andextensive phenomenon thatalmost any speculation is safeconcerning probable involvementof all cortical elements”Marshall (1959) Physiol. Rev. 39:239.

SD: spreading depression


Conclusion Conducted orchestra or jazz?

IHS Classification ICHD-II – All Types

1.

1.1. 1.2. 1.4. 1.5. 1.6.1.3.

1.2.1. 1.3.1. 1.5.1. 1.6.1.

Sub

form

s

Migraine

Subtypes




IHS Classification ICHD-II – Major Types

with aura

without aura

typical aurawithout headache

1.

1.1. 1.2.

1.2.1.

Sub

form

s

Migraine

Subtypes

1.1.

1.2.1.

1.2.3.




”Migraine generator” in the brainstem

SD

aura

trigger



”Migraine generator” in the brainstem

?

trigger A

SD

trigger B

?

trigger C

?

trigger D

postdromeprodrome aura headache

mysterious conductor

about 1 day about 1 day4−72h< 60 min



A conductor of a neural orchestra playing migraine

?

trigger A

?

trigger C

?

trigger D

postdromeprodrome headache


trigger B

SD

aura




A conductor of a neural orchestra playing migraine

?

trigger A

?

trigger D

postdromeprodrome


headache

trigger C

?SD

trigger B

aura

about 1 day about 1 day< 60 min 4−72h



SD is playing jazz – self-organizing dynamics

SD

postdromeaura headache


delaytime

trigger

prodrome

heightened susceptibility

cort

ical

hom

eost

asis

prodrome



Localized stimulation: sampling of phase space

Retinotopic”A”-”Z”,”0”-”9” (36 patterns), 4 sizes, 10 stimulation strengths =33 420 stimulation patterns (elevation of activator concentration u)

12.56.25




Orientation selective

−π/2

0

π/2





0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


Conclusion Open wave segments - fMRI evidence & retinal SD

2D patterns with laser speckle-contrast imaging

SG

EG

KCLMG

(a)

(b) 5 min 37s (c) 9 min 07s

Dahlem et al. 239, 889 (2009) Physica D




Retinotopic”A”-”Z”,”0”-”9” (36 patterns), 4 sizes, 10 stimulation strengths =33 420 stimulation patterns (elevation of activator concentration u)

12.56.25





−π/2

0

π/2





0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




”A”-”Z”,”0”-”9” (36 patterns), 4 sizes, 10 stimulation strengths =1440 stimulation patterns (elevation of activator concentration u)

12.56.25



SD triggers trigeminal meningeal afferents, ie, headache

see e.g.: Bolay et al. Nature Medicine 8, 2002Review: Eikermann-Haerter & Moskowitz, Curr Opin Neurol. 21, 2008

Figure: Dodick & Gargus SciAm, August 2008
