reentrant and retracting waves of cortical spreading depression in migraine
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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)
Markus A. Dahlem, TU Berlin
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
Markus A. Dahlem, TU Berlin
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
Markus A. Dahlem, TU Berlin
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
Markus A. Dahlem, TU Berlin
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)
Markus A. Dahlem, TU Berlin
Spreading depression From molecules to cell to tissue
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
Markus A. Dahlem, TU Berlin
Spreading depression From molecules to cell to tissue
SD: From molecules to entire brain
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
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
J.P. Dreier Nature Medicine 17 2011
massive release of Gibbs free energy
J.P. Dreier et al. Neuroscientist accepted
Markus A. Dahlem, TU Berlin
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)
Markus A. Dahlem, TU Berlin
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)
“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
Markus A. Dahlem, TU Berlin
Spreading depression Local dynamics
Leao original demonstration of SD
Leao AAP (1944) J. Neurophysiol. 7:359
Markus A. Dahlem, TU Berlin
Spreading depression Local dynamics
SD in human cortex shown by ECoG
Fabricius et al. (2006) Brain 129:778
Markus A. Dahlem, TU Berlin
Spreading depression Local dynamics
SD in human cortex shown by ECoG
Fabricius et al. (2006) Brain 129:778
Markus A. Dahlem, TU Berlin
Spreading depression Local dynamics
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
Markus A. Dahlem, TU Berlin
Spreading depression Local dynamics
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
Markus A. Dahlem, TU Berlin
Spreading depression Local dynamics
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
Markus A. Dahlem, TU Berlin
Spreading depression Local dynamics
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
Markus A. Dahlem, TU Berlin
Spreading depression Local dynamics
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
Markus A. Dahlem, TU Berlin
Spreading depression Local dynamics
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
Markus A. Dahlem, TU Berlin
Spreading depression Local dynamics
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
Markus A. Dahlem, TU Berlin
Spreading depression Local dynamics
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.
Markus A. Dahlem, TU Berlin
Spreading depression Local dynamics
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
M. A. Dahlem, Models of cortical SD, Scholarpedia
Markus A. Dahlem, TU Berlin
Spreading depression Local dynamics
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.
Markus A. Dahlem, TU Berlin
Spreading depression Local dynamics
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,
Markus A. Dahlem, TU Berlin
Spreading depression Local dynamics
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
Markus A. Dahlem, TU Berlin
Spreading depression Spiral waves
Re-entrant SD waves with anatomical block
Reshodko, L. V. and Bures, J Biol. Cybern. 18,181 (1975)
Markus A. Dahlem, TU Berlin
Spreading depression Spiral waves
Experiments: open wave segments are unstable
Dahlem & Muller Exp. Brain Res. 115 (1997)
Markus A. Dahlem, TU Berlin
Spreading depression Spiral waves
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
Markus A. Dahlem, TU Berlin
Spreading depression Spiral waves
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
Markus A. Dahlem, TU Berlin
Spreading depression Spiral waves
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
Markus A. Dahlem, TU Berlin
Spreading depression Spiral waves
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
Markus A. Dahlem, TU Berlin
Spreading depression Spiral waves
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?
Markus A. Dahlem, TU Berlin
Spreading depression Spiral waves
Engulfing RD-wave: current paradigm of migraine attack
M. Lauritzen (1987) Trends in Neurosciences 10:8.
Markus A. Dahlem, TU Berlin
Spreading depression Spiral waves
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.
Markus A. Dahlem, TU Berlin
Spreading depression Spiral waves
What is a migraine aura?
Markus A. Dahlem, TU Berlin
Spreading depression Spiral waves
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.
Markus A. Dahlem, TU Berlin
Spreading depression Spiral waves
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.
Markus A. Dahlem, TU Berlin
Spreading depression Spiral waves
Tracking migraine aura symptoms
Vincent & Hadjikhani (2007) Cephalagia 27
Markus A. Dahlem, TU Berlin
Spreading depression Spiral waves
Tracking migraine aura symptoms
Vincent & Hadjikhani (2007) Cephalagia 27
Markus A. Dahlem, TU Berlin
Spreading depression Spiral waves
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.
Markus A. Dahlem, TU Berlin
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.
Markus A. Dahlem, TU Berlin
Spreading depression Open wave segments - fMRI evidence & retinal SD
Confined spatial patterns of spreading depression
neighboring points
collapse
?
16 min
31 min
1 cm
nucleationrecordedslice not
Hadjikhani et al. (2001) PNAS
Dahlem & Hadjikhani (2009) PLoS ONEDahlem & Muller (1997) Exp. Brain Res.
Markus A. Dahlem, TU Berlin
Spreading depression Open wave segments - fMRI evidence & retinal SD
Confined spatial patterns of spreading depression
23 min18 min.
28 min.
Hadjikhani et al. (2001) PNAS
Dahlem & Hadjikhani (2009) PLoS ONEDahlem & Muller (1997) Exp. Brain Res.
Markus A. Dahlem, TU Berlin
Spreading depression Open wave segments - fMRI evidence & retinal SD
Confined spatial patterns of spreading depression
23 min18 min.
28 min.
Open wave fronts move along
a rather straight line
preventing a reentry of SD
Hadjikhani et al. (2001) PNAS
Dahlem & Hadjikhani (2009) PLoS ONEDahlem & Muller (1997) Exp. Brain Res.
Markus A. Dahlem, TU Berlin
Spreading depression Open wave segments - fMRI evidence & retinal SD
Confined spatial patterns of spreading depression
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.
Markus A. Dahlem, TU Berlin
Spreading depression Open wave segments - fMRI evidence & retinal SD
Confined spatial patterns of spreading depression
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.
Markus A. Dahlem, TU Berlin
Spreading depression Open wave segments - fMRI evidence & retinal SD
Clinical evidence
Markus A. Dahlem, TU Berlin
Spreading depression Open wave segments - fMRI evidence & retinal SD
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.
Markus A. Dahlem, TU Berlin
Spreading depression Open wave segments - fMRI evidence & retinal SD
Mapped visual symptoms on cortex via fMRI retinotopy
23 min
21
19
17
17
15
1311
975
10°
1 cm
Visual hemifield Primary visual cortex
Dahlem & Hadjikhani (2009) PLoS ONE 4: e5007.
Markus A. Dahlem, TU Berlin
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
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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.
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Cortical homeostasis is stable
Hypothesis: Cortical susceptibility to SD depends on the size ofthe momentarily affected tissue.
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Yet, too big a perturbation triggers SD
Hypothesis: Cortical susceptibility to SD depends on the size ofthe momentarily affected tissue.
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Yet, too big a perturbation triggers SD
Hypothesis: Cortical susceptibility to SD depends on the size ofthe momentarily affected tissue.
nucleationcritical
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
But a global negative feedback keeps SD confined
Hypothesis: Cortical susceptibility to SD depends on the size ofthe momentarily affected tissue.
slow dynamicstransient and
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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.
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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.
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Nonlinear delayed transitions: saddle-node ghosts
homo.
stead
y stat
e
fast
fast
slow
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Nonlinear delayed transitions: saddle-node ghosts
homo.
stead
y stat
e
fast
fast
slow
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Simulation of transient SD wave segment
gray = cortical surface; red = SD wave
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Confined spatial patterns of spreading depression
neighboring points
collapse
?
16 min
31 min
1 cm
nucleationrecordedslice not
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Confined spatial patterns of spreading depression
neighboring points
0
4
8
12
16
20
32
28
24
time
16 min
31 min
1 cm
recordedslice not
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Confined spatial patterns of spreading depression
neighboring points 16 min
31 min
1 cm
recordedslice not
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Confined spatial patterns of spreading depression
neighboring points 16 min
31 min
1 cm
recordedslice not
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Confined spatial patterns of spreading depression
neighboring points 16 min
31 min
1 cm
recordedslice not
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Confined spatial patterns of spreading depression
5cm
00
0 0
32 16
6 24
time / m
in
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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
0 100 200
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
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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
0 250 500
0 150 300# Occurrences
β0 = 1.34
(1)
(2)
(3)
(4)
0 10 20 30 40 50 60 70 80 90time
1102030405060708090100110120130
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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.
2 symptom, 3 combinations: both or either of them
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Model-based hypothesis testing
1.1. 1.2.1
1.2.3Sub−threshold
Affe
cted
cor
tical
are
aSurvival time
SD in migraine attack
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Neuromodulation
”The headache future is bright for neuromodulation techniques ... if wemanage to understand how they work” (Jean Schoenen)
figure courtesy of Jean Schoenen
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Neuromodulation
”The headache future is bright for neuromodulation techniques ... if wemanage to understand how they work” (Jean Schoenen)
figure courtesy of Jean Schoenen
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Neuromodulation
”The headache future is bright for neuromodulation techniques ... if wemanage to understand how they work” (Jean Schoenen)
figure courtesy of Jean Schoenen
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Neuromodulation
”The headache future is bright for neuromodulation techniques ... if wemanage to understand how they work” (Jean Schoenen)
figure courtesy of Jean Schoenen
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Neuromodulation
”The headache future is bright for neuromodulation techniques ... if wemanage to understand how they work” (Jean Schoenen)
figure courtesy of Jean Schoenen
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Neuromodulation
”The headache future is bright for neuromodulation techniques ... if wemanage to understand how they work” (Jean Schoenen)
figure courtesy of Jean Schoenen
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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
Dynamical disease Towards therapeutical approaches
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
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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
noise!
model−based
stimulation strategiestherapeutic TMS
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Single-pulse transcranial magnetic stimulation
Lipton et al. Lancet Neurology 9,373, 2010
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
Single-pulse transcranial magnetic stimulation
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
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?
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
From bifurcation bench to bedside
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
From bifurcation bench to bedside
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
From bifurcation bench to bedside
Markus A. Dahlem, TU Berlin
Dynamical disease Towards therapeutical approaches
From bifurcation bench to bedside
Markus A. Dahlem, TU Berlin
Conclusion
Spatio-temporal waves needspatio-temporal control methods
Old paradigm
New paradigm: opens up new strategies, eg, transcranial randomnoise stimulation (tRNS) at special locations
Markus A. Dahlem, TU Berlin
Conclusion
(i) Persistent migraine w/o infarction, (ii) Migrainousinfarction, (iii) ischemia-induced migraine
Dahlem et al. Physica D 239, 889 (2010)
Markus A. Dahlem, TU Berlin
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
Markus A. Dahlem, TU Berlin
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!
−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
Balak and Elmaci (2005) European Journal of Neurology 12
Markus A. Dahlem, TU Berlin
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
Visual hemifield Primary visual cortex
Markus A. Dahlem, TU Berlin
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
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
maximal instantaneous area (MIA)
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
total affected area (TAA)
(1)
(2)
(3)
(4)
0
80
160
240
#O
ccu
rren
ces
0 250 500
0 150 300# Occurrences
β0 = 1.34
(1)
(2)
(3)
(4)
0 10 20 30 40 50 60 70 80 90time
1102030405060708090100110120130
Markus A. Dahlem, TU Berlin
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
Markus A. Dahlem, TU Berlin
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
Markus A. Dahlem, TU Berlin
Conclusion ¡
Peri-infarct depolarizations
Dahlem et al. Physica D 239, 889 (2010)
Markus A. Dahlem, TU Berlin
Conclusion ¡
Peri-infarct depolarizations
Dahlem et al. Physica D 239, 889 (2010)
Markus A. Dahlem, TU Berlin
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)
Markus A. Dahlem, TU Berlin
Conclusion ¡
Tangential cortical slice preparation
!
!"#$%&'$()'#"*(
+,-+,."(!"#$%&/*#(
0&1'2(3"'$#(
4#&5$1"(!"#$%&'$()'#"*( 6/&'7/2%1"(!"#$%&'$()'#"*(
Cooperation with Stephen Schiff & Bruce Gluckman
Markus A. Dahlem, TU Berlin
Conclusion ¡
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)
Markus A. Dahlem, TU Berlin
Conclusion ¡
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)
“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
Markus A. Dahlem, TU Berlin
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
2 symptom, 3 combinations: both or either of them
Markus A. Dahlem, TU Berlin
Conclusion Conducted orchestra or jazz?
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.
2 symptom, 3 combinations: both or either of them
Markus A. Dahlem, TU Berlin
Conclusion Conducted orchestra or jazz?
”Migraine generator” in the brainstem
SD
aura
trigger
Markus A. Dahlem, TU Berlin
Conclusion Conducted orchestra or jazz?
”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
Markus A. Dahlem, TU Berlin
Conclusion Conducted orchestra or jazz?
A conductor of a neural orchestra playing migraine
?
trigger A
?
trigger C
?
trigger D
postdromeprodrome headache
mysterious conductor
trigger B
SD
aura
about 1 day about 1 day4−72h< 60 min
Markus A. Dahlem, TU Berlin
Conclusion Conducted orchestra or jazz?
A conductor of a neural orchestra playing migraine
?
trigger A
?
trigger D
postdromeprodrome
mysterious conductor
headache
trigger C
?SD
trigger B
aura
about 1 day about 1 day< 60 min 4−72h
Markus A. Dahlem, TU Berlin
Conclusion Conducted orchestra or jazz?
SD is playing jazz – self-organizing dynamics
SD
postdromeaura headache
about 1 day about 1 day4−72h< 60 min
delaytime
trigger
prodrome
heightened susceptibility
cort
ical
hom
eost
asis
prodrome
Markus A. Dahlem, TU Berlin
Conclusion Conducted orchestra or jazz?
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
Markus A. Dahlem, TU Berlin
Conclusion Conducted orchestra or jazz?
Localized stimulation: sampling of phase space
Orientation selective
−π/2
0
π/2
Markus A. Dahlem, TU Berlin
Conclusion Conducted orchestra or jazz?
Localized stimulation: sampling of phase space
Orientation selective
−π/2
0
π/2
Markus A. Dahlem, TU Berlin
Conclusion Conducted orchestra or jazz?
Localized stimulation: sampling of phase space
Orientation selective
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Markus A. Dahlem, TU Berlin
Conclusion Conducted orchestra or jazz?
Localized stimulation: sampling of phase space
Orientation selective
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Markus A. Dahlem, TU Berlin
Conclusion Conducted orchestra or jazz?
Localized stimulation: sampling of phase space
Orientation selective
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Markus A. Dahlem, TU Berlin
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
Markus A. Dahlem, TU Berlin
Conclusion Open wave segments - fMRI evidence & retinal SD
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
Markus A. Dahlem, TU Berlin
Conclusion Open wave segments - fMRI evidence & retinal SD
Localized stimulation: sampling of phase space
Orientation selective
−π/2
0
π/2
Markus A. Dahlem, TU Berlin
Conclusion Open wave segments - fMRI evidence & retinal SD
Localized stimulation: sampling of phase space
Orientation selective
−π/2
0
π/2
Markus A. Dahlem, TU Berlin
Conclusion Open wave segments - fMRI evidence & retinal SD
Localized stimulation: sampling of phase space
Orientation selective
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Markus A. Dahlem, TU Berlin
Conclusion Open wave segments - fMRI evidence & retinal SD
Localized stimulation: sampling of phase space
Orientation selective
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Markus A. Dahlem, TU Berlin
Conclusion Open wave segments - fMRI evidence & retinal SD
Localized stimulation: sampling of phase space
Orientation selective
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Markus A. Dahlem, TU Berlin
Conclusion Open wave segments - fMRI evidence & retinal SD
Localized stimulation: sampling of phase space
”A”-”Z”,”0”-”9” (36 patterns), 4 sizes, 10 stimulation strengths =1440 stimulation patterns (elevation of activator concentration u)
12.56.25
Markus A. Dahlem, TU Berlin
Conclusion Open wave segments - fMRI evidence & retinal SD
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
Markus A. Dahlem, TU Berlin
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