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

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

Outline

1 Introduction

Long history in non-drug migraine treatment

Berlin, Institute of Physiology

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

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

figure courtesy of Jean Schoenen

Neuromodulation

Homo Neuromodulandus

figure courtesy of Jean SchoenenMarkus A. Dahlem, TU Berlin

Stimulating the brain

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

IHS Classification ICHD-II – All Types

1.1. 1.2. 1.4. 1.5. 1.6.1.3.

1.2.1. 1.3.1. 1.5.1. 1.6.1.

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. 1.2.

1.2.1.

Migraine

Subtypes

1.2.1.

1.2.3.

Mainly two neural theories of migraine

”Migraine generator”-theory

Amyg Insula

”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

trigger

”Migraine generator” in the brainstem

trigger A

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

trigger A

trigger D

postdromeprodrome

headache

trigger C

trigger B

about 1 day about 1 day< 60 min 4−72h

trigger A

trigger B

trigger C

trigger D

SD is playing jazz – self-organizing dynamics

postdromeaura headache

delaytime

trigger

prodrome

heightened susceptibility

prodrome

Pathway of upstream and downstream events

headacheprodrome aura

trigger

edsusceptibility

delayed trigger

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

Outline

1 Introduction

Migraine full-scale attack is more confined

(a) (b)

affected areatemporarily

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

SD wave in the cortex

log [cat] , M

0 10 20 30 s

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)

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

(a) (b)

What is a migraine aura?

Migraine visual field defects reported in 1941 by K. Lashley

visual field defect pattern on primary visual cortex

5min7min

0 10 20 30 40 50mm

5min7min

9min11min

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

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.

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

27 min

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

Mapped visual symptoms on cortex via fMRI retinotopy

23 min

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

Outline

1 Introduction

Mathematical models cells, circuits, and to tissue

al dendrite

Current distribution

Osmotic force

[Na+]i

Local Dynamics during SDA

al dendrite

Osmotic force

[Na+]i

∂t= −INa − IK − ICl + I pump + Iapp

INa = −m3∞h(ENa − V )

IK = −n4(EK − V )

∂t= αn(1 − n) − βn,

∂t· · ·

∂[ion]o

FVolo+ Idiff

∂[ion]i

I pumpion (V ) = βionImax

)−2 (1 +

Alternatively (GHK currents)

Iion = V αF Pion[ion]i − [ion]oe

−αV

1 − e−αV

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

al dendrite

Osmotic force

[Na+]i

IK = −n4(EK − V )

∂t= αn(1 − n) − βn,

∂t· · ·

∂[ion]o

FVolo+ Idiff

∂[ion]i

)−2 (1 +

−αV

1 − e−αV

al dendrite

Osmotic force

[Na+]i

IK = −n4(EK − V )

∂t= αn(1 − n) − βn,

∂t· · ·

∂[ion]o

FVolo+ Idiff

∂[ion]i

)−2 (1 +

−αV

1 − e−αV

al dendrite

Osmotic force

[Na+]i

IK = −n4(EK − V )

∂t= αn(1 − n) − βn,

∂t· · ·

∂[ion]o

FVolo+ Idiff

∂[ion]i

)−2 (1 +

−αV

1 − e−αV

al dendrite

Osmotic force

[Na+]i

IK = −n4(EK − V )

∂t= αn(1 − n) − βn,

∂t· · ·

∂[ion]o

FVolo+ Idiff

∂[ion]i

)−2 (1 +

−αV

1 − e−αV

al dendrite

Osmotic force

[Na+]i

IK = −n4(EK − V )

∂t= αn(1 − n) − βn,

∂t· · ·

∂[ion]o

FVolo+ Idiff

∂[ion]i

)−2 (1 +

−αV

1 − e−αV

Tissue properties & engery state change time scales . . .

... otherwise robust!

0 1 2 3 4 5 6time (s)

0 5 10 15 20 25 30 35

time (s)

Parameters relevant for migraine aura–ischemic stroke continuum.

Possible bifurcations involved in local dynamics of SD

0 1 2 3 4 5 6time (s)

age (m

−gate deactivation Hopf

−gatemembrane voltage

Recovery

eletrogenic pump

FoldSeizure−like activity

in ischaemic stroke

hypoxic tissue

Spreading depression

(ceiling level)

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

currents

ion gradient

conductance

pumpsout in

activator−inhibitor dynamics

depolarization

firing rate

neurovascular coupling

neural network activity

Hodgkin-Huxley-Grafstein model

(1963) of SD

(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

1.3 1.32 1.34 1.36 1.38 1.4

torus outside

torus inside2

ring wave

∂P1D∂R∞

Nucleation of visual aura clusters in the visual field

23 min

Cooperation with Andrew Charles, UCLA.

27 min

Nucleation failure on torus

Transient times in flat and curved geometry

1.3 1.32 1.34 1.36 1.38

with controlwithout control

torus outside

torus inside

ring wave

∂R∞

0 10 20 30 40 50 60 70 80

outside

inside

outside

inside

torus, without controltorus, with control

flat, without control

Critical nucleation size varies with curvature

nucleationcritical

(a) (b)

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

stim. su

traveling wave

homo. steady state

phase space

threshold

Excitable media.

Solution on threshold surface

stim. su

traveling wave

homo. steady state

phase space

threshold

Excitable media.

Nonlinear delayed transitions: saddle-node ghosts

y stat

Nonlinear delayed transitions: saddle-node ghosts

y stat

Bottleneck due to saddle-node bifurcation

(a) (b)

(d)(c)

stable wave segment

y stat

homo. steady state

ling w

stim. su

traveling wave

threshold β

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 30 35time

collapse

SD nucleation

CSD break−up

long transient propagation

model−based

stimulation strategiestherapeutic TMS

neighboring points

collapse

16 min

31 min

nucleationrecordedslice not

neighboring points

16 min

31 min

recordedslice not

neighboring points 16 min

31 min

recordedslice not

31 min

recordedslice not

31 min

recordedslice not

time / m

Varying contact to the ghost

0 10 20 30 40 50 60

maximal instantaneous area (MIA)

0 50 100 150 200 250 300 350 400 450

total affected area (TAA)

0 80 160240

0 80 160240# Occurrences

β0 = 1.32

(2) (3)

0 30 60 90 120150180210240270time

0 10 20 30 40 50 60

0 50 100 150 200 250 300 350 400 450

0 100 200

0 100200300# Occurrences

β0 = 1.33

0 20 40 60 80 100120140160180time

0 10 20 30 40 50 60

0 50 100 150 200 250 300 350 400 450

0 250 500

β0 = 1.34

0 10 20 30 40 50 60 70 80 90time

1102030405060708090100110120130

IHS Classification ICHD-II – All Types

1.1. 1.2. 1.4. 1.5. 1.6.1.3.

1.2.1. 1.3.1. 1.5.1. 1.6.1.

Migraine

Subtypes

IHS Classification ICHD-II – Major Types

with aura

without aura

typical aurawithout headache

1.1. 1.2.

1.2.1.

Migraine

Subtypes

1.2.1.

1.2.3.

Model-based hypothesis testing

1.1. 1.2.1

1.2.3Sub−threshold

aSurvival time

SD in migraine attack

0 5 10 15 20 25 30 35time

collapse

SD nucleation

CSD break−up

model−based

0 5 10 15 20 25 30 35time

sensory innervation

arachnoid

dura dural sinuses

cortex

0 5 10 15 20 25 30 35time

sensory innervation

arachnoid

SD is pronociceptive

dural sinuses

cortex

peak value

0 5 10 15 20 25 30 35time

sensory innervation

arachnoid

SD is pronociceptive

dural sinuses

cortex

peak value

0 5 10 15 20 25 30 35time

collapse

SD nucleation

CSD break−up

model−based

0 5 10 15 20 25 30 35time

collapse

SD nucleation

CSD break−up

noise!

model−based

Double pulse stimulation (current TMS strategy)

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

noise on

Permanent noise stimulation

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

noise on

Single pulse vs. constant noise stimulation

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

babili

Single pulse vs. constant noise stimulation

0 5 10 15 20 25 30 35survival time

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 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

How to escape quicklyfrom the ”ghost” plateau?

Simulation of an engulfing SD wave

In cooperation with Jens Dreier &

Denny Milakara, Charite

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

Dahlem & Tusch, revision J. Math Neuroscie.

Pattern matching ”Curved” retinotopic mapping

10Æ10Æ

m lv u10Ælingual gyrus uneus CS

2 4 6 8 10 12 14

20406080

100120140

2 4 6 8 10 12 14

1a 60Æ6Æ M=(a�1 )

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

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

27 min

Conclusion

Conclusions

headacheprodrome aura

trigger

susceptibility

delayed trigger

Conclusion

Conclusions

0 10 20 30 40 50 60

0 50 100 150 200 250 300 350 400 450

0 250 500

β0 = 1.34

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

aura headache

trigger trigger

Conclusion ¡

aura headache

trigger trigger

Conclusion ¡

trigger A

trigger B

trigger C

trigger D

Conclusion ¡

trigger A

trigger C

trigger D

trigger B

Conclusion ¡

trigger A

trigger D

postdromeprodrome

headache

trigger C

trigger B

about 1 day about 1 day< 60 min 4−72h

Conclusion ¡

delaytime

trigger

prodrome

Conclusion ¡

trigger

delayed trigger

susceptibility

Conclusion ¡

trigger

delayed trigger

susceptibility

Conclusion ¡

trigger

delayed triggerSD

susceptibility

Conclusion ¡

trigger

delayed trigger

susceptibility

Conclusion ¡

Orchestrated vs self-organizing dynamics

delayed trigger

about 1 day about 1 day4−72h

trigger

< 60 min

susceptibility

Conclusion ¡

Orchestrated vs self-organizing dynamics

delaytime

trigger

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

Conclusion ¡

−π/2

Conclusion ¡

Visual migraine aura model

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

2D patterns with laser speckle-contrast imaging

(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

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)

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

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 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

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

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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