1. Migraine: A dynamical disease Markus A. DahlemResearch group: Nonlinear Dynamics in Physiology and MedicineVisual hemifield Primary visual cortex23 min10 21critical195nucleation177 91113 15 17 1 cm FENS-IBRO-Hertie Winter School December, 2012Markus A. Dahlem, Humboldt-University of Berlin

2. Outline1 Overview of migraine research2 Migraine & mathematical models: mainly macroscopic3 Towards therapeutic interventionMarkus A. Dahlem, Humboldt-University of Berlin 3. Introduction to math of migraineOutline1 Overview of migraine research2 Migraine & mathematical models: mainly macroscopic3 Towards therapeutic interventionMarkus A. Dahlem, Humboldt-University of Berlin 4. Introduction to math of migraine OverviewDynamical disease Leon Glass and Michael Mackey coined the term dynamical disease to identify diseases that occur due to an abrupt change in the natural rhythms of the body and rhythms become abnormal. This is called a bifurcation. The signicance of identifying a dynamical disease is that it should be possible to develop therapeutic strategies based on our understanding of dynamics combined with manipulations of the physiological parameters back into the normal ranges. (Blair, Glass, an der Heiden, & Milton, Chaos, 5, 1995) eMarkus A. Dahlem, Humboldt-University of Berlin 5. Introduction to math of migraineMain research topics IMigraine pain: pathway & modulationmigraine generator (CPG) pain matrix PAGS1 S2SMALCACCSSN PPCPFC Th MRN AmygInsula TNC PAG C1 C2Network dynamics:x = Ax + Bu, e.g. synchronization a11 0 0 A=,B= structural controllabilitya21 a22 b2(CPG: central pattern generator) Markus A. Dahlem, Humboldt-University of Berlin 6. Introduction to math of migraine Main research topics IICortical architecture and visual hallucinationsa gfbcd e Cortical magnication tensor M (in terms of cont. mechanics,a pure stretch tensor) isMvr =(vr ) alternatively obtained from a Tpolar decomposition of J JgV 1 =J g R J Dahlem et al. Eur. J. Neurosci. 12,767 (2000). M =gV 1 . Dahlem & Tusch, accepted J. Math. Neurosci. Markus A. Dahlem, Humboldt-University of Berlin 7. Introduction to math of migraine Main research topics IIIMacroscopic reaction-diusion patterns in migraineCanonical reaction-diusion equations. 2 t u = f (u) k3 w k2 v k1 + u 2 t v= u v + Dv v 2 t w= u w + Dw w.Markus A. Dahlem, Humboldt-University of Berlin 8. Introduction to math of migraineMain research topics IVIon-based and conductance-based cellular models Current distributionN Wild-typeSCN5AIMutant GLN1478LysI05nA G Apical dendrite I N a,PS2mSII 1nAI N M DA I K ,DR 2mS PPP P PI K ,A 10IIIIIWild-typeMutant 08 NormalisedINaS 06 outside cellinside cell 04IVGlia K+02 00III1 10 100I Time(ms) 100S I SomaVOsmotic force I N a,TP fast (ms) 10Pump[N a+ ]iIV rlaI1 lluVI 120110 10090ce StraIVoltage(mV) [K + ]o Ex C 23V pumpKmKKmNaC = INa IK ICl + I + Iapp Ipump1 ([Na]i , [K ]o ) = Imax 1+1+t[K ]o[Na]i311INa = m h(ENa V ) Ipump2 ([Na]i , [K ]o ) = ImaxIK=4n (EK V )1 + e (25[Na]i /3) 1 + e (5.5[K ]o ) [ion]o Iion A= + Idi Alternatively (GHK currents) t FVolo [ion]i [ion]o e V Iion = V F Pion [ion]iIion A1 e V= t FVoli Dahlem & Hbel, Scholarpedia (invited, in preparation) unh= n (1 n) n,t t Markus A. Dahlem, Humboldt-University of Berlin 9. Introduction to math of migraine I-IV: Related also to seizure activity, stroke, and cluster headacheReseach interests overviewMacroscopic pattern in migraine Ion-based cellular modelsCurrent distributionN Wild-typeSCN5AIMutant GLN1478Lys I05nAG Apical dendriteI N a,PS2mSII 1nA I N M DA I K ,DR2mSP PPPPI K ,A 10III IIWild-typeMutant 08 NormalisedINaS 06outside cell inside cell 04+IVGlia K 02 00 III1 10 100I Time(ms) 100S I SomaV Osmotic forceI N a,TP fast (ms) 10Pump +[N a ]i IV rlaI1 lluVI 120110 10090ceStraIVoltage(mV) [K + ]oExCCortical architecture Pain pathways & modulation agfPAGS1 S2 SMA LC ACCSSN PPCPFCTh MRN AmygInsulaTNC b c PAGC1dC2 e Markus A. Dahlem, Humboldt-University of Berlin 10. Introduction to math of migraine From the International Headache Society (IHS)The International Headache Classication All Types Migraine1.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.Markus A. Dahlem, Humboldt-University of Berlin 11. Introduction to math of migraine From the International Headache Society (IHS)The International Headache Classication Major TypesMigraine 1. Subtypes1.1.1.2.1.1.w/o auraMO 70% Subforms1.2.1.1.2.1.with aura MA 30%typical aura1.2.3.without headache2 symptom, 3 combinations: both or either of them(64% only MO, 18% only MA, 13% MO and MA, 5% MA w/o pain) Markus A. Dahlem, Humboldt-University of Berlin 12. Introduction to math of migraine Open questionsCommon etiology or two mechanisms in MO and MA?heightened susceptibility trigger SDdelayed triggerprodromeauraheadache1. Only one upstream trigger?2. Silent aura? 3. Even prevalent? 4. MO & MA share same pain phase?5. Delayed headache link? 6. Missing the pain phase?SD: Spreading Depression, see next slideMarkus A. Dahlem, Humboldt-University of Berlin 13. Introduction to math of migraine Current paradigm of full-scale attackEngulng Spreading Depression (SD)SD: massive perturbation of ion homeostasis in gray matter (mM)m Ve we any Na+ 150bs ite6050s log [cat] , M + Na + -1K31.5 Ca++0.08-2 + 0 10 20 30 s K-3 Ca++-4-7 +ooktextb Hany ~2004-8from Ve20 mVunitact. 1 minM. Lauritzen, Trends in Neurosciences 10,8 (1987).Markus A. Dahlem, Humboldt-University of Berlin 14. Introduction to math of migraine Current paradigm of full-scale attackWhat is a migraine aura?based on: Dahlem & Mller Biol. Cybern. 88,419 (2003)u Dahlem et. al. Eur. J. Neurosci. 12,767 (2000).Markus A. Dahlem, Humboldt-University of Berlin 15. Introduction to math of migraine Current paradigm of full-scale attackMigraine full-scale attack is more conned(a) (b)CS LStemporarilyaffected area(c) (d) Dahlem et al. 2D wave patterns ... . Physcia D 239 (2010) Special issue: Emerging Phenomena. Markus A. Dahlem, Humboldt-University of Berlin 16. Introduction to math of migraine Visual and other aura symptomsSD does not curl-in in human cortex 10 min1cmOnly about 2-10% but not 50% cortical surface area is aected!right: modied from Hadjikhani et al. PNAS 98:4687 (2001). Dahlem & Hadjikhani, PLoS ONE, 4: e5007 (2009). Markus A. Dahlem, Humboldt-University of Berlin 17. Introduction to math of migraine Visual and other aura symptomsSD does not curl-in in human cortex SD curls in to form spirals with T=2.45min! 1cm spiral core 10 min1cmOnly about 2-10% but not 50% cortical surface area is aected!right: modied from Hadjikhani et al. PNAS 98:4687 (2001). Dahlem & Hadjikhani, PLoS ONE, 4: e5007 (2009). Dahlem & Mller, Exp. Brain Res. 115,319, (1997).u Markus A. Dahlem, Humboldt-University of Berlin 18. Mathematical modelsOutline1 Overview of migraine research2 Migraine & mathematical models: mainly macroscopic3 Towards therapeutic interventionMarkus A. Dahlem, Humboldt-University of Berlin 19. Mathematical modelsMacroscopic RD patterns in 2DExcitable media Traveling wave solutionsCanonical RD eqs.(in weak limit, large but not too large)2 t u = f (u) v + u t v = (u + ) R 60 50 wave size S 40 30 20 10 01.31.321.34 1.361.381.4 Schenk et al. Phys. Rev. Lett. 78, 3781 (1997)threshold Markus A. Dahlem, Humboldt-University of Berlin 20. Mathematical modelsMacroscopic RD patterns in 2DExcitable media Traveling wave solutionsCanonical RD eqs.(in weak limit, large but not too large)2 t u = f (u) v + u t v = (u + ) ve wapr ang Rm . sueli 60 stitrav. sub 50mstite stathreshold wave size S 40y tead 30o.sm ho 20Dahlem & Isele, under review for J. Math. Neurosci. 10 01.31.321.34 1.361.381.4threshold Markus A. Dahlem, Humboldt-University of Berlin 21. Mathematical modelsMacroscopic RD patterns in 2DExcitable media Traveling wave solutionsCanonical RD eqs.(in weak limit, large but not too large)ve wa. sup raling m vesti tra2 t u = f (u) v + usti m. sub testa threshold t v = (u + )tea dy o.s m ho R 60 50 wave size S 40 30 20 10 01.31.321.34 1.361.381.4threshold Dahlem & Isele, under review for J. Math. Neurosci. Markus A. Dahlem, Humboldt-University of Berlin 22. Mathematical modelsMacroscopic RD patterns in 2DExcitable media Traveling wave solutionsCanonical RD eqs.(in weak limit, large but not too large)ve wa. sup raling m vesti tra 2 t u = f (u) v +u sti m. sub testa threshold t v = (u + )tea dy o.s m ho R 60 50 sub-excitable wave size S 40 30 20 10 01.31.321.34 1.36 1.38 1.4threshold Dahlem & Isele, under review for J. Math. Neurosci. Markus A. Dahlem, Humboldt-University of Berlin 23. Mathematical models Macroscopic RD patterns in 2DExcitable media Traveling wave solutionsCanonical RD eqs.(in weak limit, large but not too large) vewa . supra lingm ve sti tra 2 t u = f (u) v +ustim . subte sta threshold t v = (u + ) teadyo.smho RP1D 60 50 sub-excitable wave size S 40not excitable 30 20 10 01.31.321.34 1.36 1.381.4threshold Dahlem & Isele, under review for J. Math. Neurosci. Markus A. Dahlem, Humboldt-University of Berlin 24. Mathematical models Macroscopic RD patterns in 2DExcitable media Traveling wave solutionsCanonical RD eqs.(in weak limit, large but not too large) vewa . supra lingm ve sti tra 2 t u = f (u) v +ustim . subte sta threshold t v = (u + ) teadyo.smho RP1D 60 50 sub-excitable wave size S 40not excitablecritical 30 nucleation 20 10 01.31.321.34 1.36 1.381.4threshold Dahlem & Isele, under review for J. Math. Neurosci. Markus A. Dahlem, Humboldt-University of Berlin 25. Mathematical models Macroscopic RD patterns in 2DFull parameter spacetime scale ratio index -ln 1 2 3 MC0.5 reentrant1 mm1.0 retracting threshold ACcollapsing M R P(modied from) Winfree, Chaos 1,301 (1991) Dahlem et al. Physica D 239,889 (2010),. (inset from) Dahlem & Mller, Exp. Brain Res. 129,778 (1997). u Markus A. Dahlem, Humboldt-University of Berlin 26. Mathematical models Macroscopic RD patterns in 2DMapped visual symptoms on cortex via fMRI retinotopyVisual hemifieldPrimary visual cortex 1 cm27 min1025 23 2113519 17715 Dahlem & Hadjikhani (2009) PLoS ONE 4: e5007.Markus A. Dahlem, Humboldt-University of Berlin 27. Mathematical models Macroscopic RD patterns in 2D RD models on realistic cortical geometries it ive posnega t ivePrinciplesValidate simulations on simpler shapes uploading patients MRI scanner readings analytical results with isothermal nite element analysiscoordiantes (toroidal coordinates) polygon mesh processingMarkus A. Dahlem, Humboldt-University of Berlin 28. Mathematical models Macroscopic RD patterns in 2DExcitation waves on curved surfacesFitzHugh Nagumo equations u11 u= u u 3 v + Du gij g i t3 g i v= (u + ) tWaves in weakly excitable curved media posses critical properties.Davydov et al. (2002) Europhys. Lett. 59:34Markus A. Dahlem, Humboldt-University of Berlin 29. Mathematical models Macroscopic RD patterns in 2DExcitation waves on curved surfacesFitzHugh Nagumo equations u11 u= u u 3 v + Du gij g i t3 g i v= (u + ) tFirst approximation: Wave follows shortest path.Markus A. Dahlem, Humboldt-University of Berlin 30. Mathematical models Macroscopic RD patterns in 2DThe surface of the brain (cortex) is curvedMarkus A. Dahlem, Humboldt-University of Berlin 31. Mathematical models Macroscopic RD patterns in 2DMinimum threshold in a at geometryRP1D6050wave size S403020torus inside1100 1.31.32 1.34 1.361.381.4threshold Markus A. Dahlem, Humboldt-University of Berlin 32. Mathematical models Macroscopic RD patterns in 2DMinimum threshold in a at geometryRP1D6050wave size S4030 torus outside20torus inside110 10 1.31.32 1.34 1.361.381.4threshold Markus A. Dahlem, Humboldt-University of Berlin 33. Mathematical models Macroscopic RD patterns in 2DMinimum threshold in a at geometryRP1D6050wave size S4030 torus outside20torus inside110 10 1.31.32 1.34 1.361.381.4threshold Markus A. Dahlem, Humboldt-University of Berlin 34. Mathematical models Macroscopic RD patterns in 2DMinimum threshold in a at geometryR P1D6050 ringwavewave size S4030 torus outside 120 torus inside 11010 1.31.32 1.34 1.36 1.381.4threshold Markus A. Dahlem, Humboldt-University of Berlin 35. Mathematical models Macroscopic RD patterns in 2DMinimum threshold in a at geometry R P1D6050 ring wav e 2wave size S4030 torus outside120torus inside1 210 120 1.3 1.32 1.34 1.36 1.381.4 threshold Markus A. Dahlem, Humboldt-University of Berlin 36. Mathematical modelsMacroscopic RD patterns in 2DEect of intrinsic curvature of the medium1. Lower threshold for SD if cortex is (intrinsically) negatively curved.2. Stable wave segments: center being at positive curvature while the open ends extend into negative curvature. bifucation analysis on torus pos. curvature neg. curvatureRP1D stabilizationlower threshold 60 50ring wave 2 40 wave size S 30torus outside critical1 nucleation 20 torus inside1 2 1012 0 1.3 1.321.34 1.361.381.4threshold Dahlem & Kneer, in preparation Markus A. Dahlem, Humboldt-University of Berlin 37. Mathematical models Macroscopic RD patterns in 2DLong-range inhibitionIs the BOLD signal in fMRI ... a 15 105 ... the SD signal? 0no oset b Or is it a more disperse 15 10 neuropretective signal.5 0 osetMarkus A. Dahlem, Humboldt-University of Berlin 38. Mathematical models Macroscopic RD patterns in 2DLong-range or mean eld inhibition reaction-diusion + curvaturepos. curvatureneg. curvaturestabilization lower threshold criticalcritical nucleationnucleation + mean eld inhibitiontraveling wavealso localized!Markus A. Dahlem, Humboldt-University of Berlin 39. Mathematical models Macroscopic RD patterns in 2DLong-range or mean eld inhibition reaction-diusion + curvaturepos. curvatureneg. curvaturestabilization lower threshold criticalcritical nucleationnucleation + mean eld inhibitionbehaves likeexcitable elementtraveling wavealso localized!only transient wavesMarkus A. Dahlem, Humboldt-University of Berlin 40. Mathematical models Macroscopic RD patterns in 2DTypical trajectory: fast growth and collapse & bottlenecknucleation modelbased cortical surface area invaded by SD 25 therapeutic TMS stimulation strategies 20CSD breakup 15long transient propagation 10 5collapse 00 510 15202530 35time Markus A. Dahlem, Humboldt-University of Berlin 41. Mathematical models Macroscopic RD patterns in 2DPain comes from the meninges not the cortexbone cortical surface area invaded by SD 25 duradural sinuses 20sensory innervation blood arachnoid 15piacortex 10 5 00 5 10 15 20 25 3035 time Markus A. Dahlem, Humboldt-University of Berlin 42. Mathematical models Macroscopic RD patterns in 2DPain comes from the meninges not the cortexpeak value bone cortical surface area invaded by SD 25dura dural sinuses 20 sensory innervation blood SD is pronociceptive arachnoid 15piacortex 10 5 005 10 15 20 253035 time Markus A. Dahlem, Humboldt-University of Berlin 43. Mathematical models Macroscopic RD patterns in 2DPain comes from the meninges not the cortexpeak value bone cortical surface area invaded by SD 25dura dural sinuses 20 sensory innervation blood SD is pronociceptive arachnoid 15piacortex 10 5 005 10 15 20 253035 time Markus A. Dahlem, Humboldt-University of Berlin 44. Mathematical models Macroscopic RD patterns in 2DCommon etiology or two mechanisms in MO and MA?heightened susceptibilitytrigger SD delayed triggerprodromeaura headache1. Only one upstream trigger?2. Silent aura? 3. Even prevalent? 4. MO & MA share same pain phase?5. Delayed headache link? 6. Missing the pain phase?SD: Spreading Depression, see next slideMarkus A. Dahlem, Humboldt-University of Berlin 45. Mathematical models Macroscopic RD patterns in 2DHypoth.: pain instantaneous area, aura long durationtotal area aected (TAA)exct. duration (ED) classication1 #2k MAmean & STD w/oMA smooth histogram (solid lines) head- ache pain threshold3 0.532 2 1k4 aura threshold2 1 11 2 41MOSD (dotted)0 01MOSD MA2k1cmcorrelation large 0 TAA1k"aura" MOSD MIA IA"pain"MA10 00.2 0.4 0.6 0.8 1 00.20.4 0.6 0.8 1maximal instantaneous area (MIA)total aected area (TAA)Markus A. Dahlem, Humboldt-University of Berlin 46. Towards therapeutic interventionOutline1 Overview of migraine research2 Migraine & mathematical models: mainly macroscopic3 Towards therapeutic interventionMarkus A. Dahlem, Humboldt-University of Berlin 47. Towards therapeutic interventionLong history in non-drug migraine treatmentMarkus A. Dahlem, Humboldt-University of Berlin 48. Towards therapeutic interventionHistory of electrical stimuation (Dont 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. 2010Markus A. Dahlem, Humboldt-University of Berlin 49. Towards therapeutic interventionHistory of electrical stimuation (Dont 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. 2010Markus A. Dahlem, Humboldt-University of Berlin 50. Towards therapeutic interventionHistory of electrical stimuation (Dont try this at home!)Non-drug treatment for headaches.Markus A. Dahlem, Humboldt-University of Berlin 51. Towards therapeutic interventionHistory of electrical stimuation (Dont 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. 2010Markus A. Dahlem, Humboldt-University of Berlin 52. Towards therapeutic interventionHistory of electrical stimuation (Dont try this at home!)Non-drug treatment for headaches.Markus A. Dahlem, Humboldt-University of Berlin 53. Towards therapeutic interventionModern neuromodulation Markus A. Dahlem, Humboldt-University of Berlin 54. Towards therapeutic interventionModern neuromodulation Markus A. Dahlem, Humboldt-University of Berlin 55. Towards therapeutic interventionModern neuromodulation Markus A. Dahlem, Humboldt-University of Berlin 56. Towards therapeutic interventionModern neuromodulation Markus A. Dahlem, Humboldt-University of Berlin 57. Towards therapeutic interventionModern neuromodulation Markus A. Dahlem, Humboldt-University of Berlin 58. Towards therapeutic interventionHomo NeuromodulandusThe headache future is bright for neuromodulation techniques ... if wemanage to understand how they work (Jean Schoenen)Markus A. Dahlem, Humboldt-University of Berlin 59. Towards therapeutic interventionWhat are optimal stimulation protocols?software matters ...Markus A. Dahlem, Humboldt-University of Berlin 60. Towards therapeutic interventionTypical trajectory: fast growth and collapse & bottleneck nucleationmodelbased cortical surface area invaded by SD 25 therapeutic TMS stimulation strategies 20CSD breakup 15 long transient propagation 10 5 collapse 00 5 10 152025 3035 time Markus A. Dahlem, Humboldt-University of Berlin 61. Towards therapeutic interventionTypical trajectory: fast growth and collapse & bottleneck nucleationmodelbased cortical surface area invaded by SD 25 therapeutic TMS stimulation strategies 20CSD breakup 15 long transient propagation noise! 10 5 collapse 00 5 1015 2025 3035 time Markus A. Dahlem, Humboldt-University of Berlin 62. Towards therapeutic interventionSpatio-temporal waves need spatio-temporal controlOld paradigmNew paradigm: opens up new strategies, eg, transcranial randomnoise stimulation (tRNS) at special locationsMarkus A. Dahlem, Humboldt-University of Berlin 63. Towards therapeutic interventionTangential cortical slice preparationHow-to control SD? We need physiologically detailed models onthe cellular scale. ! & 64. model-based Kalman lter control, cooperation with Stephen Schi & BruceGluckman Markus A. Dahlem, Humboldt-University of Berlin 65. Towards therapeutic interventionLocal Dynamics during SD V C=INa IK ICl + I pump + Iapp t 3INa =m h(ENa V )Current distribution IK =n4 (EK V ) n h=n (1 n) n,ttApical dendriteIN a,PIK,DRIN MDA[ion]o Iion A= + IdiIK,A tFVolo [ion]i Iion AK+= Gliat FVoliSomaOsmotic forceIN a,T 23Pump pumpKmK KmNa [N a+ ]i Iion (V ) =ion Imax 1+1+ r lallu [K ]o [Na]icetra [K + ]o Ex Markus A. Dahlem, Humboldt-University of Berlin 66. Towards therapeutic interventionLocal Dynamics during SD V C= INa IK ICl + I pump + Iapp t3INa = m h(ENa V )Current distribution IK = n4 (EK V ) nh= n (1 n) n,t tApical dendriteIN a,PIK,DRIN MDA[ion]oIion A=+ IdiIK,A t FVolo [ion]iIion AK+= GliatFVoliSomaOsmotic forceIN a,T23Pump pump KmK KmNa [N a+ ]i Iion (V ) =ion Imax 1+ 1+ r lallu[K ]o [Na]icetra [K + ]o ExAlternatively (GHK currents)[ion]i [ion]o e VIion= V F Pion1 e V Markus A. Dahlem, Humboldt-University of Berlin 67. Towards therapeutic interventionIonic changes produce long afterdischarge and SD 50V EK ENa0voltage (mV) Iapp50 100 051015 20 25 3035 time (s) Markus A. Dahlem, Humboldt-University of Berlin 68. Towards therapeutic interventionTissue properties & engery state change time scales . . . ... otherwise robust! 50V50 V EKEK ENa ENa0voltage (mV) Iapp0 Iapp voltage (mV)50 50 100100 05101520 2530350 1 23 4 56 time (s) time (s) Parameters relevant for migraine auraischemic stroke continuum. cf. Ionic models of ischemic ventricular muscle. eg. Arce, Xu, Gonzalez, Guevara (2000) Chaos. 10,411. Markus A. Dahlem, Humboldt-University of Berlin 69. Towards therapeutic interventionPossible bifurcations involved in local dynamics of SD 50 VEKENa0 Iappvoltage (mV)50 100 0 1 23 4 56 time (s)hypoxic tissueRecoveryin ischaemic strokengate deactivation Hopf [K +]o I pump eletrogenic pump Hopf SNIC Spreading depressionFold Seizure like activ[K + ]o = 10mM ity (ceiling level) SNIC V n gatemembran e voltage Markus A. Dahlem, Humboldt-University of Berlin 70. Towards therapeutic intervention I-IV: Related also to seizure activity, stroke, and cluster headacheReseach interests overviewMacroscopic pattern in migraine Ion-based cellular modelsCurrent distributionN Wild-typeSCN5AIMutant GLN1478Lys I05nAG Apical dendriteI N a,PS2mSII 1nA I N M DA I K ,DR2mSP PPPPI K ,A 10III IIWild-typeMutant 08 NormalisedINaS 06outside cell inside cell 04+IVGlia K 02 00 III1 10 100I Time(ms) 100S I SomaV Osmotic forceI N a,TP fast (ms) 10Pump +[N a ]i IV rlaI1 lluVI 120110 10090ceStraIVoltage(mV) [K + ]oExCCortical architecture Pain pathways & modulation agfPAGS1 S2 SMA LC ACCSSN PPCPFCTh MRN AmygInsulaTNC b c PAGC1dC2 e Markus A. Dahlem, Humboldt-University of Berlin 71. ConclusionConclusionsWe need more non-invasiveimaging data of migraine withaura!The predicted plateau (ghost ofsaddle-node) theory can be tested Visual hemifield Primary visual cortexclinically with non-invasive imaging 1 cmSef-organizing patterns provide a10 27 min 2523unifying concept including silent aura,1 321 519migraine w or w/o headache/aura717 15Insights pattern formation may reneneuromodulation strategies:Being close to a saddle-nodebifurcation (ghost plateau)Design (feedback) control tointelligently target certain propertiesof SD in migraineMarkus A. Dahlem, Humboldt-University of Berlin 72. ConclusionConclusionsWe need more non-invasiveimaging data of migraine withMAaura! w/o MAhead-achepain thresholdThe predicted plateau (ghost ofsaddle-node) theory can be tested aura thresholdclinically with non-invasive imaging MOSDSef-organizing patterns provide aunifying concept including silent aura,MOSD MAmigraine w or w/o headache/aura1cmInsights pattern formation may renelargeTAAneuromodulation strategies:"aura"Being close to a saddle-node MIAIA "pain"bifurcation (ghost plateau)Design (feedback) control tointelligently target certain propertiestotal aected area (TAA)of SD in migraineMarkus A. Dahlem, Humboldt-University of Berlin 73. ConclusionConclusionsWe need more non-invasiveimaging data of migraine withaura!The predicted plateau (ghost ofsaddle-node) theory can be testedclinically with non-invasive imagingSef-organizing patterns provide aunifying concept including silent aura,migraine w or w/o headache/auraInsights pattern formation may reneneuromodulation strategies:Being close to a saddle-nodebifurcation (ghost plateau)Design (feedback) control tointelligently target certain propertiesof SD in migraineMarkus A. Dahlem, Humboldt-University of Berlin 74. Conclusion Cooperation & Funding Frederike Kneer, Thomas Isele Paul Van Valkenburgh, Bernd Schmidt Nouchine Hadjikhani (EPFL & Martinos Center for Biomedical Imaging, MGH)berlin Andrew Charles (Headache Research and Treatment Program, UCLA School of Medicine) Steven Schi (Penn State Center for Neural Engineering) Jens Dreier (Department of Neurology, Charit; University Medicine, Berlin) e Migraine Aura Foundation Klaus Podoll (University Hospital Aachen)Markus A. Dahlem, Humboldt-University of Berlin 75. Conclusion Ionic modelConned spatial patterns of spreading depression collapse ? nucleationslice not recorded31 minneighboring points 1 cm 16 min Markus A. Dahlem, Humboldt-University of Berlin 76. Conclusion Ionic modelConned spatial patterns of spreading depression time3228242016 slice not12 recorded 831 min 4 0 neighboring points1 cm 16 minMarkus A. Dahlem, Humboldt-University of Berlin 77. Conclusion Ionic modelConned spatial patterns of spreading depression slice not recorded31 min neighboring points1 cm 16 minMarkus A. Dahlem, Humboldt-University of Berlin 78. Conclusion Ionic modelConned spatial patterns of spreading depression slice not recorded31 min neighboring points1 cm 16 minMarkus A. Dahlem, Humboldt-University of Berlin 79. Conclusion Ionic modelConned spatial patterns of spreading depression slice not recorded31 min neighboring points1 cm 16 minMarkus A. Dahlem, Humboldt-University of Berlin 80. Conclusion Ionic modelConned spatial patterns of spreading depression5cm 32 16 time / min 00 624 00Markus A. Dahlem, Humboldt-University of Berlin 81. ConclusionIonic modelVarying contact to the ghost: MA # Occurrences 240 (2)(3) 1600 = 1.3280 0 450 400(1)(1)total aected area (TAA) 350(2) 300(3) 250(4) 200 150 (4) 100500 30 60 90 120 150 180 210 240 270 time 00 80 160240 300 80(1)(1) 250 70excitation duration (ED)(2)(2) 60 200(3)(3) 50 150(4)(4) 40 100 30 2050 10 0 1 0 102030 40 5060 0 50 100 150 200 250 300 350 400 4500 80 160240maximal instantaneous area (MIA) total aected area (TAA)# OccurrencesMarkus A. Dahlem, Humboldt-University of Berlin 82. Conclusion Ionic modelVarying contact to the ghost: MO # Occurrences 240 160 (3) 0 = 1.3480 0 (2) 450 400(1)total aected area (TAA) 350(2) 300(3) (1) 250(4) 200 150 (4) 100500 10 20 30 40 50 60 70 80 90 time 0 0 250 500 300 130(1)(1) 120 250 110excitation duration (ED)(2)(2) 100 200 90(3)(3) 80 150(4)(4) 70 60 50 100 40 3050 20 10 0 1 0 102030 40 5060 0 50 100 150 200 250 300 350 400 4500 150 300maximal instantaneous area (MIA)total aected area (TAA) # OccurrencesMarkus A. Dahlem, Humboldt-University of Berlin 83. Conclusion Ionic modelNucleation failure on torusMarkus A. Dahlem, Humboldt-University of Berlin 84. Conclusion Ionic modelTransient times in at and curved geometry 30torus, without control torus, with control flat, without control R50 with controlwithout control ringwave40 outside 2030 torus outside SSflatinside20torus inside outside 1010 inside0 1.3 1.321.34 1.361.38 00 10 203040 5060 7080 tMarkus A. Dahlem, Humboldt-University of Berlin 85. Conclusion Ionic modelNucleation of visual aura clusters in the visual eldVisual hemifieldPrimary visual cortex 23 min1021 195 17 7 91113 15 171 cmCooperation with Andrew Charles, UCLA.Markus A. Dahlem, Humboldt-University of Berlin 86. Conclusion Ionic modelNucleation of visual aura clusters in the visual eld Visual hemifield Primary visual cortex 1 cm 27 min 10 252321 1 3 51917 7 15 Markus A. Dahlem, Humboldt-University of Berlin 87. Conclusion Ionic modelNucleation of visual aura clusters in the visual eld Visual hemifield Primary visual cortex 1 cm 27 min 10 252321 1 3 51917 7 15 Markus A. Dahlem, Humboldt-University of Berlin 88. Conclusion Ionic modelSimulation of transient SD wave segmentgray = cortical surface; red = SD waveMarkus A. Dahlem, Humboldt-University of Berlin 89. Conclusion Ionic modelSimulation of an engulng SD waveIn cooperation with Bernd Schmidt, In cooperation with Jens Dreier &MagdeburgDenny Milakara, Charit e Markus A. Dahlem, Humboldt-University of Berlin 90. Conclusion Ionic modelMigraine scotoma reveal functional propertiesPattern matchingA B47C913Dahlem & Tusch, revision J. Math Neuroscie.Markus A. Dahlem, Humboldt-University of Berlin 91. Conclusion Ionic modelMigraine scotoma reveal functional propertiesPattern matching Curved retinotopic mappingA B 47C913Dahlem & Tusch, revision J. Math Neuroscie.Markus A. Dahlem, Humboldt-University of Berlin 92. Conclusion Ionic modelMigraine scotoma reveal functional propertiesPattern matching Curved retinotopic mappingA Bamd e 479Cbc13 mDahlem & Tusch, revision J. Math Neuroscie.Markus A. Dahlem, Humboldt-University of Berlin 93. Conclusion Ionic modelMigraine scotoma reveal functional propertiesPattern matching Curved retinotopic mapping 1 0.8 0.6A B0.4 0.2 2 4 6 8 10 12 14 140 120 1008060402042 4 6 8 10 12 147 C0.390.213 0.1 2 4 6 8 10 12 14 Dahlem & Tusch, revision J. Math Neuroscie.Markus A. Dahlem, Humboldt-University of Berlin 94. Conclusion Ionic modelSD triggers trigeminal meningeal aerents, ie, headachesee e.g.: Bolay et al. Nature Medicine 8, 2002Review: Eikermann-Haerter & Moskowitz, Curr Opin Neurol. 21, 2008Figure: Dodick & Gargus SciAm, August 2008Markus A. Dahlem, Humboldt-University of Berlin 95. Conclusion Ionic modelOrganic PhysicsMarkus A. Dahlem, Humboldt-University of Berlin 96. Conclusion Ionic modelOrganic PhysicsMarkus A. Dahlem, Humboldt-University of Berlin 97. Conclusion Spiral wavesRe-entrant SD waves with anatomical blockReshodko, L. V. and Bure, J Biol. Cybern. 18,181 (1975)sMarkus A. Dahlem, Humboldt-University of Berlin 98. Conclusion Spiral wavesExperiments: open wave segments are unstableDahlem & Mller Exp. Brain Res. 115 (1997)uMarkus A. Dahlem, Humboldt-University of Berlin 99. Conclusion Spiral wavesSpreading Depression: Reaction-diusion in the brainA nearly complete discharge and recharge of chemical batteries in neurons andglial cellsDahlem & Mller (1997) Exp. Brain Res. 115:319u Markus A. Dahlem, Humboldt-University of Berlin 100. Conclusion Spiral wavesSpreading Depression: Reaction-diusion in the brainZ-type rotation causes a wave break in the spiral core.Dahlem & Mller (1997) Exp. Brain Res. 115:319uMarkus A. Dahlem, Humboldt-University of Berlin 101. Conclusion Spiral wavesDrugs adjust excitability:retracting & collapsing waves a b c d e f g h ijk lDahlem et al. 2D wave patterns ... . (2010) Physcia DMarkus A. Dahlem, Humboldt-University of Berlin 102. Conclusion Spiral wavesDrugs adjust excitability:retracting & collapsing wavesWhat 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, Humboldt-University of Berlin 103. Conclusion Spiral wavesLocalized stimulation: sampling of phase spaceRetinotopicA-Z,0-9 (36 patterns), 4 sizes, 10 stimulation strengths =33 420 stimulation patterns (elevation of activator concentration u)6.2512.5Markus A. Dahlem, Humboldt-University of Berlin 104. Conclusion Spiral wavesLocalized stimulation: sampling of phase spaceOrientation selective/20/2Markus A. Dahlem, Humboldt-University of Berlin 105. Conclusion Spiral wavesLocalized stimulation: sampling of phase spaceOrientation selective/20/2Markus A. Dahlem, Humboldt-University of Berlin 106. Conclusion Spiral wavesLocalized stimulation: sampling of phase spaceOrientation selective0.90.80.70.60.50.40.30.20.10.0Markus A. Dahlem, Humboldt-University of Berlin 107. Conclusion Spiral wavesLocalized stimulation: sampling of phase spaceOrientation selective0.90.80.70.60.50.40.30.20.10.0Markus A. Dahlem, Humboldt-University of Berlin 108. Conclusion Spiral wavesLocalized stimulation: sampling of phase spaceOrientation selective0.90.80.70.60.50.40.30.20.10.0Markus A. Dahlem, Humboldt-University of Berlin 109. Conclusion Spiral wavesVisual migraine aura modelaeb c dDahlem et al. (2000) Eur. J. Neurosci. 12:767.Dahlem and Chronicle (2004) Prog. Neurobiol. 74:351.Markus A. Dahlem, Humboldt-University of Berlin 110. Conclusion Spiral wavesParameter space of excitabilityClassications of excitabile elements and excitability in activemedia.Schneider, Schll & Dahlem, Chaos 19 015110, (2009)oMarkus A. Dahlem, Humboldt-University of Berlin 111. Conclusion Spiral wavesParameter space of excitabilityClassications of excitabile elements and excitability in activemedia.Schneider, Schll & Dahlem, Chaos 19 015110, (2009)oMarkus A. Dahlem, Humboldt-University of Berlin 112. Conclusion Spiral wavesCerebral blood ow in migraineRadionuclide xenon 133 method, used to image brains blood owOlesen, J. , Larsen, B. and Lauritzen, M., Focal hyperemia followed byspreading oligemia and impaired activation of rCBF in classic migraine, Ann.Neurol. 9, 344 (1981)Markus A. Dahlem, Humboldt-University of Berlin 113. Conclusion Spiral wavesTracking migraine aura symptomsVincent & Hadjikhani (2007) Cephalagia 27Markus A. Dahlem, Humboldt-University of Berlin 114. Conclusion Spiral wavesTracking migraine aura symptomsVincent & Hadjikhani (2007) Cephalagia 27Markus A. Dahlem, Humboldt-University of Berlin 115. Conclusion Spiral wavesfMRI patterns is more diuse than SD patterns end (min 30) start (min 20) reference (min 0)modied from Hadjikhani et al. (2001) PNAS 98 Markus A. Dahlem, Humboldt-University of Berlin 116. Conclusion Spiral wavesfMRI patterns is more diuse than SD patterns end (min 30) start (min 20) reference (min 0)What if the the blood ow provides along-range or global negative feedback?modied from Hadjikhani et al. (2001) PNAS 98 Markus A. Dahlem, Humboldt-University of Berlin 117. ConclusionSpiral wavesVarying contact to the ghost # Occurrences 240 (2)(3) 1600 = 1.3280 0 450 400(1)(1)total aected area (TAA) 350(2) 300(3) 250(4) 200 150 (4) 100500 30 60 90 120 150 180 210 240 270 time 00 80 160240 300 80(1)(1) 250 70excitation duration (ED)(2)(2) 60 200(3)(3) 50 150(4)(4) 40 100 30 2050 10 0 1 0 102030 40 5060 0 50 100 150 200 250 300 350 400 4500 80 160240maximal instantaneous area (MIA) total aected area (TAA)# OccurrencesMarkus A. Dahlem, Humboldt-University of Berlin 118. Conclusion Spiral wavesVarying contact to the ghost # Occurrences 240 160(3)0 = 1.3380 0(2) 450 400(1)total aected area (TAA) 350(2) 300(3) (1) 250(4) 200 150 (4) 100500 20 40 60 80 100120140160180 time 00 100 200 300 90(1)(1) 80 250excitation duration (ED)(2)(2) 70 200(3)(3) 60(4)(4) 50 150 40 100 30 2050 10 0 1 0 102030 40 5060 0 50 100 150 200 250 300 350 400 4500 100200300maximal instantaneous area (MIA) total aected area (TAA)# OccurrencesMarkus A. Dahlem, Humboldt-University of Berlin 119. Conclusion Spiral wavesVarying contact to the ghost # Occurrences 240 160 (3) 0 = 1.3480 0 (2) 450 400(1)total aected area (TAA) 350(2) 300(3) (1) 250(4) 200 150 (4) 100500 10 20 30 40 50 60 70 80 90 time 0 0 250 500 300 130(1)(1) 120 250 110excitation duration (ED)(2)(2) 100 200 90(3)(3) 80 150(4)(4) 70 60 50 100 40 3050 20 10 0 1 0 102030 40 5060 0 50 100 150 200 250 300 350 400 4500 150 300maximal instantaneous area (MIA)total aected area (TAA) # OccurrencesMarkus A. Dahlem, Humboldt-University of Berlin 120. Conclusion Two neural theories of migraineMainly two neural theories of migraineMigraine generator-theory Spreading depression-theory S1SMAACCPPCThPFC Amyg Insula PAGMarkus A. Dahlem, Humboldt-University of Berlin 121. ConclusionTwo neural theories of migraineSD: Wave of massive ionic imbalance (mM)Ve +Na 150 60 50log [cat] , M +Na+-1K3 1.5Ca++ 0.08 -2+ 0 10 20 30 sK -3 Ca++ -4 -7+H -8Ve 20 mV unit act.1 minLauritzen (1994) Brain 117:199. Markus A. Dahlem, Humboldt-University of Berlin 122. Conclusion Two neural theories of migraineMigraine generator in the brainstem trigger SDauraMarkus A. Dahlem, Humboldt-University of Berlin 123. Conclusion Two neural theories of migraineMigraine generator in the brainstemmysterious conductortrigger A trigger Btrigger Ctrigger D? SD??prodromeauraheadache postdromeabout 1 day < 60 min 472h about 1 dayMarkus A. Dahlem, Humboldt-University of Berlin 124. Conclusion Two neural theories of migraineA conductor of a neural orchestra playing migraine70%mysterious conductortrigger A trigger Btrigger Ctrigger D? SD??prodromeauraheadache postdromeabout 1 day < 60 min 472h about 1 dayMarkus A. Dahlem, Humboldt-University of Berlin 125. Conclusion Two neural theories of migraineA conductor of a neural orchestra playing migrainerarely(but: unreported cases)mysterious conductortrigger A trigger Btrigger Ctrigger D? SD??prodromeauraheadache postdromeabout 1 day < 60 min 472h about 1 dayMarkus A. Dahlem, Humboldt-University of Berlin 126. Conclusion Two neural theories of migraineA conductor of a neural orchestra playing migrainemysterious conductortrigger A trigger Btrigger Ctrigger D? SD??prodromeauraheadache postdromeabout 1 day < 60 min 472h about 1 dayMarkus A. Dahlem, Humboldt-University of Berlin 127. Conclusion Two neural theories of migraineSD is playing jazz self-organizing dynamicsheightened susceptibility cortical homeostasis prodrome trigger time SD delayprodromeauraheadache postdromeabout 1 day < 60 min472habout 1 dayMarkus A. Dahlem, Humboldt-University of Berlin 128. Conclusion Two neural theories of migraineCommon etiology or two mechanisms in MO and MA?heightened susceptibilitytrigger SDdelayed triggerprodromeauraheadache1. Only one upstream trigger?2. Silent aura? 3. Even prevalent? 4. MO & MA share same pain phase?5. Delayed headache link? 6. Missing the pain phase?SD: Spreading Depression, see next slideMarkus A. Dahlem, Humboldt-University of Berlin 129. Conclusion Two neural theories of migraineEngulng SD wave: current paradigm of full-scale attackM. Lauritzen (1987) Trends in Neurosciences 10:8.Markus A. Dahlem, Humboldt-University of Berlin 130. Conclusion Two neural theories of migraineEngulng SD wave: current paradigm of full-scale attackM. Lauritzen (1987) Trends in Neurosciences 10:8.Markus A. Dahlem, Humboldt-University of Berlin 131. ConclusionTwo neural theories of migraineMigraine full-scale attack is more conned(a)(b)CS LStemporarilyaffected area(c)(d) Dahlem et al. 2D wave patterns ... . Physcia D 239 (2010) Special issue: Emerging Phenomena. Markus A. Dahlem, Humboldt-University of Berlin 132. Conclusion Two neural theories of migraineMigraine visual eld defects reported in 1941 by K. Lashleyvisual eld defect pattern on primary visual cortex1511min15min9min 7min10 5min50 5min 7min 9min11min15min 01020304050mmOnly about 2-10% but not 50% cortical surface area is aected!Dahlem & Hadjikhani (2009) PLoS ONE 4: e5007. Markus A. Dahlem, Humboldt-University of Berlin