Localized transient waves of cortical spreading depression in migraine

Localized transient waves of cortical spreading
depression in migraine

Markus A. Dahlem

Research group: Nonlinear Dynamics in Physiology and Medicine

Visual hemifield Primary visual cortex

23 min
10°
21
critical
19
nucleation 5
17 7 9
11
13
15
17
1 cm

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


Neuromodulation


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

ﬁgure courtesy of Jean Schoenen Dahlem, TU Berlin
Markus A.

Stimulating the brain


Stimulating the brain

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


IHS Classiﬁcation ICHD-II – All Types

Migraine
1.
Subtypes

1.1. 1.2. 1.3. 1.4. 1.5. 1.6.
Subforms

1.2.1. 1.3.1. 1.5.1. 1.6.1.


IHS Classiﬁcation ICHD-II – Major Types

Migraine
1.
Subtypes

1.1. 1.2. 1.1. without aura
Subforms

1.2.1.
1.2.1. with aura

typical aura
1.2.3.
without headache

2 symptom, 3 combinations: both or either of them


Mainly two neural theories of migraine

”Migraine generator”-theory ”Spreading depression”-theory

S1
SMA

ACC PPC
Th
PFC
Amyg Insula

PAG


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


”Migraine generator” in the brainstem

trigger

SD

aura


”Migraine generator” in the brainstem

mysterious conductor
trigger A
trigger B
trigger C
trigger D
?
SD
?
?

prodrome aura headache postdrome
about 1 day < 60 min 4−72h about 1 day


A conductor of a neural orchestra playing migraine

trigger A
trigger B
trigger C
trigger D
?
SD
?
?



SD is playing jazz – self-organizing dynamics

heightened susceptibility

cortical homeostasis
prodrome

trigger
time

SD delay



Pathway of upstream and downstream events


trigger

SD delayed trigger

prodrome aura headache

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


Migraine full-scale attack is more conﬁned

(a) (b)
CS

LS

temporarily
affected area
(c) (d)

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


SD wave in the cortex

(mM)
Ve
+
Na 150
60
50
log [cat] , M +
Na
+
-1 K 3
1.5
Ca++
0.08
-2
+ 0 10 20 30 s
K

-3 Ca++

-4
-7 +
H

-8
Ve
20 mV

unit
act.

1 min

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.


What is a migraine aura?


Migraine visual field defects reported in 1941 by K. Lashley
visual field defect pattern on primary visual cortex

15 11min15min
9min
7min
10 5min

5

0
5min
7min
9min
11min

15min

0 10 20 30 40 50
mm

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



collapse

?
nucleation slice not
recorded

31 min

neighboring points 1 cm 16 min




28 min.
23 min
18 min.




28 min.
23 min
18 min.

Open wave fronts move along
a rather straight line
preventing a reentry of SD




28 min.
23 min
18 min.

Open wave fronts move along
a rather straight line
preventing a reentry of SD

Dahlem & Hadjikhani (2009) PLoS ONE



28 min.

33 min.

23 min
38 min.
18 min.

1 mm

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

Dahlem & Hadjikhani (2009) PLoS ONE
Dahlem & M¨ller (1997) Exp. Brain Res.
u


Clinical evidence


Mapped visual symptoms on cortex via fMRI retinotopy


1 cm
27 min
10°
25
23
21
1
3
5 19
17
7

15



Mapped visual symptoms on cortex via fMRI retinotopy


23 min
10°
21
19
5
17 7 9
11
13
15
17
1 cm



Mathematical models cells, circuits, and to tissue

Current distribution

I

Apical dendrite
IN a,P
II
IK,DR IN MDA
III IK,A

IV
Glia K+

V Soma
Osmotic force
IN a,T
VI Pump
[N a+ ]i

r
la
llu
ce
tra
[K + ]o

Ex


Local Dynamics during SD

∂V
C = −INa − IK − ICl + I pump + Iapp
∂t

Current distribution
Apical dendrite

IN a,P
IK,DR IN MDA
IK,A

Glia K+

Soma
Osmotic force
IN a,T
Pump
[N a+ ]i
r
la
llu
ce
tra

[K + ]o
Ex



∂V
∂t
3
INa = −m∞ h(ENa − V )
Current distribution IK = −n4 (EK − V )
Apical dendrite

IN a,P
IK,DR IN MDA
IK,A

Glia K+

Soma
Osmotic force
IN a,T
Pump
[N a+ ]i
r
la
llu
ce
tra

[K + ]o
Ex



∂V
∂t
3
∂n ∂h
= αn (1 − n) − βn, ···
∂t ∂t
Apical dendrite

IN a,P
IK,DR IN MDA
IK,A

Glia K+

Soma
Osmotic force
IN a,T
Pump
[N a+ ]i
r
la
llu
ce
tra

[K + ]o
Ex



∂V
∂t
3
∂n ∂h
= αn (1 − n) − βn, ···
∂t ∂t
Apical dendrite

IN a,P
IK,DR IN MDA ∂[ion]o Iion A
= + Idiﬀ
IK,A ∂t FVolo
∂[ion]i Iion A
K+ =
Glia
∂t FVoli
Soma
Osmotic force
IN a,T
Pump
[N a+ ]i
r
la
llu
ce
tra

[K + ]o
Ex



∂V
∂t
3
∂n ∂h
= αn (1 − n) − βn, ···
∂t ∂t
Apical dendrite

IN a,P
= + Idiﬀ
IK,A ∂t FVolo
∂[ion]i Iion A
K+ =
Glia
∂t FVoli
Soma
Osmotic force
IN a,T −2 −3
Pump pump KmK KmNa
[N a+ ]i
Iion (V ) = βion Imax 1+ 1+
r
la
llu

[K ]o [Na]i
ce
tra

[K + ]o
Ex



∂V
∂t
3
∂n ∂h
= αn (1 − n) − βn, ···
∂t ∂t
Apical dendrite

IN a,P
= + Idiﬀ
IK,A ∂t FVolo
∂[ion]i Iion A
K+ =
Glia
∂t FVoli
Soma
Osmotic force
IN a,T −2 −3
Pump pump KmK KmNa
[N a+ ]i
Iion (V ) = βion Imax 1+ 1+
r
la
llu

[K ]o [Na]i
ce
tra

[K + ]o
Ex

Alternatively (GHK currents)

[ion]i − [ion]o e −αV
Iion = V αF Pion
1 − e −αV

Tissue properties & engery state change time scales . . .

... otherwise robust!

50 V 50 V
EK EK
ENa ENa
0

voltage (mV)
0 Iapp Iapp
voltage (mV)

50
50

100
100

0 1 2 3 4 5 6 0 5 10 15 20 25 30 35
time (s) time (s)

Parameters relevant for migraine aura–ischemic stroke continuum.


Possible bifurcations involved in local dynamics of SD
50 V
EK
ENa
0 Iapp
voltage (mV)

50

100

0 1 2 3 4 5 6
time (s)

hypoxic tissue
Recovery in ischaemic stroke
+]
n−gate deactivation Hopf
[K o I
pump eletrogenic pump Hopf
SNIC
Spreading depression
Fold
Seizure−
like activ [K + ]o = 10mM
ity (ceiling level)

SNIC

V n −gate
membran
e voltage


Feedback control of spreading depression
From bench to bedside

!

Cooperation with Stephen Schiﬀ Bruce Gluckman Courtesy of Neuralieve


Macroscopic RD with nonlocal transmission

Hodgkin-Huxley-Grafstein model
neurovascular coupling
(1963) of SD
activator−inhibitor dynamics

ion gradient u3 2
diffusion

ion u =
˙ u− −v +D u
out in pumps 3
+ FHN inhibitor equations + ...
firing rate

ion
neural network activity ε−1 v
˙ = u + β − γv + KF [u]
depolarization
currents

global inhibitory control (mean ﬁeld)
ion
conductance F [u] = Su (t) − S0
Su (t) = H(u(r, t) − ue ) dr,


RD models on realistic cortical geometries

gyral crowns
gyral crowns
positive (fender)

entrance to sulci

entrance to sulci

negative (saddle)


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

∂R∞ ∂P1D
60

ring
wav
e 2
40
S

torus outside 1
flat
20
torus inside 1
2
1 2

0
1.3 1.32 1.34 1.36 1.38 1.4
β

Nucleation of visual aura clusters in the visual ﬁeld


23 min
10°
21
19
5
17 7 9
11
13
15
17
1 cm

Cooperation with Andrew Charles, UCLA.


Nucleation of visual aura clusters in the visual ﬁeld


1 cm
27 min
10°
25
23
21
1
3
5 19
17
7

15


Nucleation failure on torus


Transient times in ﬂat and curved geometry

30 torus, without control
torus, with control
flat, without control
∂R∞
50
with control
without control
ring
wave
40 outside
20
30
torus outside

S
S

flat inside
20
torus inside
outside
10
10 inside

0
1.3 1.32 1.34 1.36 1.38
β
0
0 10 20 30 40 50 60 70 80
t


Critical nucleation size varies with curvature

critical
nucleation


Cortical homeostasis is excitable (bistabe)

critical
nucleation


Long transient: ghost behavior, inhib. global feedback

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

transient and
slow dynamics


Threshold surface separates attractor basins
phase space
u i+2(x) traveling wave
ui+1 (x)

u i (x)

ra
. sup
m
sti
. sub
m
sti
threshold

homo. steady state
Excitable media.


Solution on threshold surface
phase space
u i+2(x) traveling wave
ui+1 (x)

u i (x)

ra
. sup
m
sti
. sub
m
sti
threshold

homo. steady state
Excitable media.


Nonlinear delayed transitions: saddle-node ghosts

st
fa

w
te slo
sta
ady
ste st
o. fa
m
ho


Bottleneck due to saddle-node bifurcation

(a) (b) stable wave segment
e
w av
ra ng
m
. sup
veli
sti tra
. sub
m
sti
te
sta Ø Ö × ÓÐ
y
ad te
ste sta ∂R
o. ad
y
m te
ho .s
o
ho
m (a) ∂R (b)
(c)
st
(d) traveling wave
fa (c)

Û Ú ×Þ S
w
te slo
sta
y
ad
ste st
o. fa homo. steady state
h om
Ø Ö × ÓÐ β


Simulation of transient SD wave segment

gray = cortical surface; red = SD wave


Typical trajectory: fast growth and collapse bottleneck

nucleation model−based
cortical surface area invaded by SD

25
therapeutic TMS
stimulation strategies
20
CSD break−up

15
long transient propagation

10

5
collapse
0
0 5 10 15 20 25 30 35
time



collapse

?
nucleation slice not
recorded

31 min




time
32
28
24

20
16
slice not
12 recorded

8 31 min
4
0




slice not
recorded

31 min




5cm

32 16

time / min
0 0

6 24

0 0


Varying contact to the ghost

# Occurrences
240
(2) (3)
160
β0 = 1.32
80
0
450
400 (1) (1)
total aﬀected area (TAA)

350 (2)
300 (3)
250
(4)
200
150
(4)
100
50 0 30 60 90 120 150 180 210 240 270
time
0
0 80 160240
300
80
(1) (1)
250 70
excitation duration (ED)

(2) (2)
60
200 (3) (3)
50
150 (4) (4) 40

100 30
20
50
10
0 1
0 10 20 30 40 50 60 0 50 100 150 200 250 300 350 400 450 0 80 160240
maximal instantaneous area (MIA) total aﬀected area (TAA) # Occurrences



# Occurrences
240
160 (3)
β0 = 1.33
80
0 (2)
450
400 (1)

350 (2)
300 (3)
(1)
250
(4)
200
150
(4)
100
50 0 20 40 60 80 100120140160180
time
0
0 100 200
300 90
(1) (1) 80
250

(2) (2) 70
200 (3) (3) 60

(4) (4) 50
150
40
100 30
20
50
10
0 1
0 10 20 30 40 50 60 0 50 100 150 200 250 300 350 400 450 0 100200300



# Occurrences
240
160 (3)
β0 = 1.34
80
0
(2)
450
400 (1)

350 (2)
300 (3)
(1)
250
(4)
200
150
(4)
100
50 0 10 20 30 40 50 60 70 80 90
time
0
0 250 500
300 130
(1) (1) 120
250 110

(2) (2) 100
200 90
(3) (3)
80
150 (4) (4) 70
60
50
100
40
30
50 20
10
0 1
0 10 20 30 40 50 60 0 50 100 150 200 250 300 350 400 450 0 150 300


Model-based hypothesis testing

1.1. 1.2.1

Affected cortical area
Sub−
threshold 1.2.3

SD in migraine attack

Survival time



bone

25
dura dural sinuses

20 sensory innervation
blood

arachnoid
15 pia

cortex
10

5

0
0 5 10 15 20 25 30 35
time



peak value
bone

25
dura dural sinuses

20 sensory innervation
blood
SD is pronociceptive

arachnoid
15 pia

cortex
10

5

0
0 5 10 15 20 25 30 35
time



nucleation model−based

25
therapeutic TMS
stimulation strategies
20
CSD break−up

15
long transient propagation
noise!
10

5
collapse
0
0 5 10 15 20 25 30 35
time


Double pulse stimulation (current TMS strategy)

25
wave size
noise sample 1 k=0.010
20 noise sample 2 k=0.010
15 without noise

10
noise on

5

0
0 5 10 15 20 25 30 35
time


Permanent noise stimulation

25
wave size
20 noise sample 2 k=0.030
15 without noise

10
noise on

5

0
0 5 10 15 20 25 30 35
time


Single pulse vs. constant noise stimulation

0.5

0.4

0.3
probability

0.2

0.1

0.00 5 10 15 20 25 30 35
survival time of unstable solitons

Single pulse vs. constant noise stimulation

Migraine aura duration
0.5
without noise
on t=5, k = 0.050
0.4 on t=5, k = 0.100
noise 0.050
pulse t=5, k = 0.100
pulse t=5, k = 0.500
0.3
probability

0.2

0.1

0.00 5 10 15 20 25 30 35
survival time

Noise sensitivity of transient wave segments

25
wave size

without noise
noise k=0.010
noise k=0.015 How to escape quickly
20 noise k=0.020 from the ”ghost” plateau?
noise k=0.025
noise k=0.030
15 noise k=0.035
noise k=0.040

10

5

0
0 5 10 15 20 25 30 35
time


Simulation of an engulﬁng SD wave

Folds

Bumbs

In cooperation with Jens Dreier
Denny Milakara, Charit´
e


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
A B

4
7
C
9
13

Dahlem Tusch, revision J. Math Neuroscie.



Pattern matching ”Curved” retinotopic mapping

A B
½¼Æ
ÀÅ

½¼Æ

4
7
C
9
13





A B a m
d
Ú

ÙÒ Ù× Ù
Ë Ð
Ð Ò Ù Ð ÝÖÙ×

e ½¼Æ
4
7

9
C b c
13
m





´ ½µ
1
¼Æ 0.8
0.6

Å
A B 0.4
0.2

Æ 2 4 6 8 10 12 14

´±µ
140
120

¯
100

ÀÅ
80
60
40
20
4 2 4 6 8 10 12 14
7

´ÑÑ¾µ
C 0.3
9 0.2
13

Ã
0.1
¾ ¼
2 4 6 8 10 12 14
¼ ¼ ¼ ¼¾ ´Ö µ



Conclusion

Conclusions

We need more non-invasive maging
data of the aura!
The predicted plateau (”ghost of
saddle-node”) theory can be tested
clinically with non-invasive imaging
Sef-organizing patterns provide a 10°
27 min
1 cm

unifying concept including silent aura, 25
23
21

migraine w or w/o headache/aura 1
3
5
7
17
19

Insights pattern formation may reﬁne 15

neuromodulation strategies:
Being close to a saddle-node
bifurcation (”ghost” plateau)
Design (feedback) control to
intelligently target certain properties
of SD in migraine

Conclusion

Conclusions

data of the aura!
clinically with non-invasive imaging
susceptibility

Sef-organizing patterns provide a

heightened
trigger

unifying concept including silent aura, SD delayed trigger

migraine w or w/o headache/aura prodrome aura headache

Insights pattern formation may reﬁne
neuromodulation strategies:
of SD in migraine

Conclusion

Conclusions

data of the aura!

# Occurrences
240
160 (3)
β0 = 1.34
80
0
(2)

clinically with non-invasive imaging 450
400 (1)

350 (2)
300 (3)

Sef-organizing patterns provide a 250
200
150
(4)
(4)
(1)

unifying concept including silent aura, 100
50
0
0 10 20 30 40 50 60 70 80 90
time
0 250 500
300

migraine w or w/o headache/aura 250
(1) (1)
130
120
110

(2) (2) 100
200 90
(3) (3)
80

Insights pattern formation may reﬁne 150

100
(4) (4) 70
60
50
40

neuromodulation strategies: 50

0
30
20
10
1
0 10 20 30 40 50 60 0 50 100 150 200 250 300 350 400 450 0 150 300
# Occurrences

maximal instantaneous area (MIA) total aﬀected area (TAA)

of SD in migraine

Conclusion ¡

Cooperation Funding
Frederike Kneer
Sebstian Boie
Niklas H¨bel
u
Thomas Isele
Paul Van Valkenburgh
berlin
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 Migraine Aura Foundation
(Department of Neurology, Charit´; University Medicine, Berlin)
e

Klaus Podoll
(University Hospital Aachen)


Conclusion ¡

2 symptoms, 3 combinations: both or either of them

trigger
trigger

SD
?

aura headache


Conclusion ¡



trigger
trigger

SD
?

aura headache


Conclusion ¡


trigger A
trigger B
trigger C
trigger D
?
SD
?
?

about 1 day 60 min 4−72h about 1 day


Conclusion ¡



cortical homeostasis
prodrome

trigger
time

SD delay



Conclusion ¡


susceptibility
heightened

trigger

SD delayed trigger



Localized transient waves of cortical spreading depression in migraine

Localized transient waves of cortical spreading depression in migraine

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