localized transient waves of cortical spreading depression in migraine

Localized transient waves of cortical spreadingdepression in migraine

Markus A. Dahlem

Research group: Nonlinear Dynamics in Physiology and Medicine

nucleationcritical

23 min

21

19

17

17

15

1311

975

10°

1 cm

Visual hemifield Primary visual cortex

The Dynamics of Disease, Manchester August 23, 2012

Markus A. Dahlem, TU Berlin

Outline

1 Introduction

2 Localized spots traveling in human cortex

3 Modeling migraine with aura


Long history in non-drug migraine treatment


Berlin, Institute of Physiology


Organic Physics – The Fab Four


Organic Physics – The Fab Four

Kymograph (Carl Ludwig)


History of electrical stimuation (Don’t try this at home!)

Non-drug treatment for headaches.

P. J. Koehler and C. J. Boes, A history of non-drug treatment in headache,particularly migraine. Brain 133:2489-500. 2010


History of electrical stimuation (Don’t try this at home!)

Non-drug treatment for headaches.


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

Stimulating the brain


Stimulating the brain

Neuralieve (California, USA) tests small, portable TMS device forpotentially treating migraine with aura ...


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.



Mainly two neural theories of migraine

”Migraine generator”-theory

S1

PFCTh

PPC

PAG

Amyg Insula

SMA

ACC

”Spreading depression”-theory


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


”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




?

trigger A

?

trigger D

postdromeprodrome


headache

trigger C

?SD

trigger B

aura

about 1 day about 1 day< 60 min 4−72h



?

trigger A

SD

trigger B

?

trigger C

?

trigger D





SD is playing jazz – self-organizing dynamics

SD

postdromeaura headache


delaytime

trigger

prodrome

heightened susceptibility

cort

ical

hom

eost

asis

prodrome


Pathway of upstream and downstream events

SD

headacheprodrome aura

trigger

heig

hten

edsusceptibility

delayed trigger

Only one upstream trigger?Silent aura?Delayed headache link?


Outline

1 Introduction




Migraine full-scale attack is more confined

(a) (b)

(c)

LS

CS

(d)

affected areatemporarily

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


SD wave in the cortex

-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.

Lauritzen (1994) Brain 117:199.


Engulfing SD wave: current paradigm of full-scale attack

Xenon 133 method, radionuclide 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)


Engulfing SD wave: current paradigm of full-scale attack

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



(a) (b)

(c)

LS

CS

(d)




What is a migraine aura?


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


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


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

1 Introduction




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.


Possible 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

−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


Feedback 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


Macroscopic RD with nonlocal transmission

ion

currents

ion gradient

ion

conductance

ion

pumpsout in

diffu

sion

activator−inhibitor dynamics

depolarization

firing rate

neurovascular coupling

neural network activity

Hodgkin-Huxley-Grafstein model

(1963) of SD

u =

(u − u3

3− v

)+ D∇2u

+ FHN inhibitor equations + ...

ε−1v = u + β − γv + KF [u]

global inhibitory control (mean field)

F [u] = Su(t)− S0

Su(t) =

∫H(u(r, t)− ue) dr,


RD models on realistic cortical geometries

positive (fender)

negative (saddle)

gyral crowns

entrance to sulci

gyral crowns

entrance to sulci


Traveling spots are unstable (w/o long-range inhibition)

Schenk, C. P. , Or-Guil, M. , Bode, M. and Purwins, H. -G. , Phys. Rev. Lett. 78, 3781 (1997)


The surface of the brain (cortex) is curved


Minimum threshold in a flat geometry

0

20

40

60

1.3 1.32 1.34 1.36 1.38 1.4

S

β

torus outside

flat

torus inside2

21

1

ring wave

1

2

∂P1D∂R∞


Nucleation of visual aura clusters in the visual field

23 min

21

19

17

17

15

1311

975

10°

1 cm


Cooperation with Andrew Charles, UCLA.


Nucleation of visual aura clusters in the visual field

1 cm

10°

1 357

15

1719

2123

25

27 min



Nucleation failure on torus


Transient times in flat and curved geometry

0

10

20

30

40

50

1.3 1.32 1.34 1.36 1.38

S

β

with controlwithout control

torus outside

flat

torus inside

ring wave

∂R∞

0

10

20

30

0 10 20 30 40 50 60 70 80

S

t

outside

inside

outside

inside

torus, without controltorus, with control

flat, without control


Critical nucleation size varies with curvature

nucleationcritical



(a) (b)

(c)

LS

CS

(d)




Cortical homeostasis is excitable (bistabe)

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

nucleationcritical


Long transient: ghost behavior, inhib. global feedback

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

slow dynamicstransient and


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



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



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

cort

ical

sur

face

are

a in

vade

d by

SD

sensory innervation

arachnoid

bone

blood

dura dural sinuses

cortex

pia



0

5

10

15

20

25

0 5 10 15 20 25 30 35time

cort

ical

sur

face

are

a in

vade

d by

SD

sensory innervation

arachnoid

bone

blood

dura

SD is pronociceptive

dural sinuses

cortex

pia

peak value



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



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?


Simulation of an engulfing SD wave

In cooperation with Jens Dreier &

Denny Milakara, Charite

Folds

Bumbs


Localized waves hitting a bump

(a) (b)


Perturbed into boa of homogeneous steady state

(a) t=55 (b) t=80 (c) t=105

(d) t=130 (e) t=150 (f) t=165

(g) t=180 (h) t=200 (i) t=220


Waves are scattered

(a) t=65 (b) t=100 (c) t=125

(d) t=145 (e) t=175 (f) t=220


Scattering angle vs off set


Another question: Why is the cortex intrinsically curved?


Migraine scotoma reveal functional properties

Pattern matching

”Curved” retinotopic mapping

47

913

A B

C

Dahlem & Tusch, revision J. Math Neuroscie.



Pattern matching ”Curved” retinotopic mapping

47

913

A B

C

A

C

BHM

10Æ10Æ





47

913

A B

C

a d

b ce

m

m lv u10Ælingual gyrus uneus CS





47

913

A B

C

2 4 6 8 10 12 14

0.1

0.2

0.3

2 4 6 8 10 12 14

20406080

100120140

2 4 6 8 10 12 14

0.2

0.4

0.6

0.8

1a 60Æ6Æ M=(a�1 )

HM�=(%)K=(mm2 ) �=(rad)a�2 00:20:40:60:8

b d



Conclusion

Conclusions

We need more non-invasive magingdata of the aura!

The predicted plateau (”ghost ofsaddle-node”) theory can be testedclinically with non-invasive imaging

Sef-organizing patterns provide aunifying concept including silent aura,migraine w or w/o headache/aura

Insights pattern formation may refineneuromodulation strategies:

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






SD

headacheprodrome aura

trigger

heig

hten

ed

susceptibility

delayed trigger


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 ¡

Cooperation & Funding

Frederike KneerSebstian BoieNiklas HubelThomas Isele

Paul Van Valkenburgh

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

Andrew Charles(Headache Research and Treatment Program, UCLA School of

Medicine)

Steven Schiff(Penn State Center for Neural Engineering)

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

Klaus Podoll(University Hospital Aachen)

berlin

Migraine Aura Foundation


Conclusion ¡

2 symptoms, 3 combinations: both or either of them

SD ?

aura headache

trigger trigger


Conclusion ¡


SD ?

aura headache


trigger trigger


Conclusion ¡


?

trigger A

SD

trigger B

?

trigger C

?

trigger D





Conclusion ¡


?

trigger A

?

trigger C

?

trigger D



trigger B

SD

aura



Conclusion ¡


?

trigger A

?

trigger D

postdromeprodrome


headache

trigger C

?SD

trigger B

aura

about 1 day about 1 day< 60 min 4−72h


Conclusion ¡


SD



delaytime

trigger

prodrome


cort

ical

hom

eost

asis

prodrome


Conclusion ¡


SD


trigger

delayed trigger


heig

hten

ed

susceptibility


Conclusion ¡



trigger

delayed triggerSD


heig

hten

ed

susceptibility


Conclusion ¡



trigger

SD

?

delayed trigger


heig

hten

ed

susceptibility


Conclusion ¡

Orchestrated vs self-organizing dynamics


?

delayed trigger

about 1 day about 1 day4−72h

trigger

SD

< 60 min

aura

heig

hten

ed

susceptibility


Conclusion ¡

Orchestrated vs self-organizing dynamics

SD



delaytime

trigger

prodrome


cort

ical

hom

eost

asis

prodrome


Conclusion ¡

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


Conclusion ¡


Orientation selective

−π/2

0

π/2


Conclusion ¡



0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


Conclusion ¡

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.


Conclusion Open wave segments - fMRI evidence & retinal SD

Tracking migraine aura symptoms

Vincent & Hadjikhani (2007) Cephalagia 27



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



Re-entrant SD waves with anatomical block

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



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?



Parameter space of excitability

Classifications of excitabile elements and excitability in activemedia.

Schneider, Scholl & Dahlem, Chaos 19 015110, (2009)



Characteristic time scale due to bottleneck

Three spatiotempral SD patterns:2 short lasting patterns: large and low amplitude (∼90%)long lasting wave with characteristic shape (∼10%)

0 10 20 30 40 50 600

10

20

30

40

50

600.00.20.40.60.81.01.21.4

0.00.20.40.60.81.01.21.4



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?




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



fMRI patterns is more diffuse than SD patterns

reference (min 0)

start (min 20)

end (min 30)

What if the the blood flow provides along-range or global negative feedback?

modified from Hadjikhani et al. (2001) PNAS 98



fMRI patterns is more diffuse than SD patterns

reference (min 0)

start (min 20)

end (min 30)

What if the the blood flow provides along-range or global negative feedback?modified from Hadjikhani et al. (2001) PNAS 98




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

12.56.25


localized transient waves of cortical spreading depression in migraine

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