Study of Stimulus Waveform Effect on Nerve Excitability and SENN - PowerPoint PPT Presentation

Biomedicine and Molecular Biosciences COST Action BM1309 EMF-MED COST EMF-MED European network for innovative uses of EMFs in biomedical applications Study of Stimulus Waveform Effect on Nerve Excitability and SENN model verification in Lumbricus Terrestris as a Convenient Animal Model Prof. Antonio Šarolić, PhD Zlatko Živković, PhD FESB Split 1

Biomedicine and Molecular Biosciences COST Action BM1309 EMF-MED Contents 1. Introduction 2. SENN model 3. Animal model 4. Measurement setup 4. Measurement/simulation results 5. Conclusion 2

Biomedicine and Molecular Biosciences COST Action BM1309 EMF-MED Contents 1. Introduction 2. SENN model 3. Animal model 4. Measurement setup 4. Measurement/simulation results 5. Conclusion 3

Introduction o single axon studies • effects of stimulus parameters • computational stimulation model • controllable measurements o transition ELF -> higher frequencies ( IF range ) • complex pulses (single or repetitive) • optimized biomedical effects (healing, pain relie f,…) • EMF safety (human exposure) • waveform effects (temporal and frequency parameters) 4

Terminology • Threshold level V th [mV] - the transmembrane voltage level that should be exceeded to excite the action potential. • Stimulus threshold level I TH [mA] - the minimum stimulus current magnitude (peak value) just sufficient to excite the nerve and initiate AP propagation. • Monopolar stimulation - the type of electrical stimulation with the active electrode positioned near the nerve that wants to be stimulated. • Bipolar stimulation - the type of stimulation where both the active and return electrode are placed in the close proximity to an axon • Monophasic stimulus - the stimulus with unidirectional current • Biphasic stimulus - the stimulus with bidirectional current 5

Biomedicine and Molecular Biosciences COST Action BM1309 EMF-MED Contents 1. Introduction 2. SENN model 3. Animal model 4. Measurement setup 4. Measurement/simulation results 5. Conclusion 6

McNeal’s and SENN model of myelinated axon d V          n I C I G V 2 V V m m i,n i i,n-1 i,n i,n+1 d t  π 2 d  G   i 4 L i i V n = V i,n - V e,n  INTRACELLULAR MEDIUM L 100 D i R i V i,n-1 R i V i,n R i V i,n+1 R i  d 0.7 D r m r m r m   d V 1 c m c m c m            n G V 2 V V V 2 V V I   i n-1 n n+1 e,n-1 e,n e,n+1 i,n d t C V r V r V r m Second spatial Second spatial difference of difference of unknown extracellural liqid potential V e,n-1 V e,n V e,n+1 transmembrane ( activation function ): EXTRACELLULAR MEDIUM potential Δ 2 V e,n => Δ 2 V e,n /Δx 2 =Δ E e,n /Δ x          π I d w J J J J i,n Na K P L    J G ( V V ) Na Na n Na    J G ( V V ) K K n K SENN model    J G ( V V ) P P n P    J G ( V V ) L L n L Activation function 7

SENN model parameters Parameter Value 20 µm 0,6 Fiber diameter ( D ) 0,5 0.7∙ D Axon diameter at node ( d ) 0,4 2.5 µm Nodal gap ( w ) σ e [S/m] 0,3 Axoplasmic resistivity ( ρ i ) 100 Ωm 0,2 External medium resistivity 300 Ωm 0,1 ( ρ e ) 0 2 µF/cm 2 Membrane capacitance ( c m ) 1 10 100 1000 f [kHz] Membrane conductivity 30.4 mS/cm 2 ( g m ) 100∙ D Internodal distance ( L i ) y A =5 mm L= 20∙ y A =10 cm N R =51 nodes 8

Equivalent time constant - τ Q   rb I rb approximate chronaxie ( τ c ) – equivalent time     ln 2 c constant ( τ ) relation τ=110 µs 9

Biomedicine and Molecular Biosciences COST Action BM1309 EMF-MED Contents 1. Introduction 2. SENN model 3. Animal model 4. Measurement setup 4. Measurement/simulation results 5. Conclusion 10

Lumbricus terrestris (Earthworm) Earthworm 11

Why Earthworm ( lat. Lumbricus Terrestris ) 12

Biomedicine and Molecular Biosciences COST Action BM1309 EMF-MED Contents 1. Introduction 2. SENN model 3. Animal model 4. Measurement setup 4. Measurement/simulation results 5. Conclusion 13

Measurement setup 14

Measurement setup (photo) 15

Biomedicine and Molecular Biosciences COST Action BM1309 EMF-MED Contents 1. Introduction 2. SENN model 3. Animal model 4. Measurement setup 4. Measurement/simulation results 5. Conclusion 16

Single/repetitive monophasic square pulses Single pulse t D =10 µs≈0.1τ t D =200 µs≈2τ I TH =24.75 mA I TH =4.15 mA 120 120 Transmembrane voltage Transmembrane voltage 100 100 change [mV] change [mV] 80 80 1.1*I_TH 60 60 1.1*I_TH I_TH I_TH 40 40 0.9*I_TH 0.8*I_TH 20 20 0.5*I_TH 0.5*I_TH 0 0 0 0.2 0.4 0.6 0.8 1 0 0,2 0,4 0,6 0,8 1 t [ms] t [ms] Repetitive pulses t D =200 µs≈2τ t D =10 µs≈0.1τ t P =200 µs≈2τ t P =200 µs≈2τ Case 3 120 I TH =3.21mA Transmembrane voltage 140 I TH =15 mA Transmembrane voltage 1.2 * I_TH 1.2 * I_TH 100 120 change [mV] I_TH I_TH 100 change [mV] 80 0.8 * I_TH 0.8 * I_TH 80 60 60 40 40 20 20 0 0 0 2 4 6 0 1 2 3 4 -20 -20 t [ms] t [ms] Case 2 120 t D =10 µs≈0.1τ 120 Transmembrane voltage Transmembrane voltage t P =10 µs≈0.1τ 100 1.2 * I_TH 100 I_TH 80 I TH =4.5 mA 80 change [mV] change [mV] 0.8 * I_TH 60 60 1.2 * I_TH t D =200 µs≈2τ 40 40 I_TH t P =10µs≈0.1τ 20 20 0.8 * I_TH I TH =2.21 mA 0 0 0 1 2 3 4 0 0,2 0,4 0,6 0,8 1 -20 -20 17 t [ms] t [ms]

Single/repetitive monophasic square pulses (2) single 20log I     TH dB SR repetitive I TH 14 tP=10 μs 12 tP=30 μs 10 tP=50 μs tP=100 μs 8 Δ SR [dB] tP=300 μs 6 4 2 0 10 100 1000 t D [ μ s] 18

Single/repetitive biphasic square pulses Single pulse D =100 µs D =10 µs 120 120 Transmembrane voltage change Transmembrane voltage change 100 90 80 60 60 I_TH=51.5 mA [mV] [mV] I_TH=4.68 mA 0.8*I_TH 40 30 0.8*I_TH 20 0 0 0 0,2 0,4 0,6 0,8 0 0,2 0,4 0,6 0,8 1 -20 -30 t [ms] t [ms] t D =1 00 µs≈τ t D =1 0 µs≈ 0.1 τ Repetitive pulses µs t D =100 µs 120 120 Transmembrane voltage change Transmembrane voltage change 100 I_TH=4.31 mA 90 80 0.8*I_TH I_TH=27 mA 60 60 [mV] 0.8*I_TH [mV] 40 30 20 0 0 0 0,2 0,4 0,6 0,8 1 0 0,5 1 1,5 2 2,5 -20 -30 t [ms] t [ms] t D =1 00 µs≈τ t D =1 0 µs≈ 0.1 τ 19

Single/repetitive biphasic square pulses (2) 60 Single monophasic pulse 50 Single biphasic pulse 10 monophasic pulses 10 biphasic pulses 40 I TH [mA] 30 20 10 0 10 100 1000 t D [µs] 20

Single cycle/continuous sinusoid Single cycle t D =100 µs t D =10 µs 120 120 Transmembrane voltage Transmembrane voltage 100 1.2*I_TH 100 80 80 I_TH change [mV] change [mV] 60 0.8*I_TH 60 1.2*I_TH 40 40 I_TH 20 20 0.8*I_TH 0 0 0 0,5 1 1,5 2 -20 0 0,2 0,4 0,6 0,8 -20 -40 -40 t [ms] t [ms] I TH =6.2 mA I TH =75 mA Continuous t D =100 µs t D =10 µs 1.2*I_TH 140 160 Transmembrane voltage I_TH 120 Transmembrane voltage 140 1.2*I_TH 120 0.8*I_TH 100 I_TH change [mV] 100 80 change [mV] 0.8*I_TH 80 60 60 40 40 20 20 0 0 -20 0 1 2 3 4 -20 0 0,2 0,4 0,6 0,8 1 -40 -40 t [ms] t [ms] I TH =5.6 mA I TH =36.5mA 21

Single cycle/continuous sinusoid (2) 80 70 Single monophasic pulse Single sinusoidal cycle 60 10 monophasic pulses 50 I TH [mA] 10 sinusoidal cycles 40 30 20 10 0 10 100 1000 t D [µs] 22

Equivalence between repetitive monophasic square pulses and continuous sinusoid - t D = t P 1  f  2 t D 100 Single monophasic pulse with tD=1/2fc (peak value) sine(rms) I Continuous sinusoid with   TH frequency fc (RMS value) I TH [mA] S/P pulse(peak) I 10  TH f 1/2 t c D 11 1 10 1 cycle 1 10 100 9 f c [kHz] 5 cycles 8 sine(rms) 10 cycles 7 I   TH 6 20 cycles ∆ S/P S/P pulse(peak) 5 I 50 cycles  TH 4 f 1/2 t c D 100 cycles 3 2 1 1 0 0.8 0.01 0.1 1 10 100 f [kHz] 0.6 ∆ S/P 0.4 0.2 23 0 1 10 100 fc [kHz]

Measurement results – SD curves 12 Worm 1 Worm 2 10 Worm 3 Worm 4 Worm 5 8 Chronaxie - τ c Time constant - I TH [mA] τ [ms] [ms] 6 Earthworm 1 1 1.44 Earthworm 2 1 1.44 4 Earthworm 3 1.05 1.51 Earthworm 4 0.5 0.72 Earthworm 5 0.55 0.8 2 SENN 0.078 0.11 0 24 t D [ms] 0 1 2 3 4 5

Measurement results – monophasic square pulse 100 Worm 3 Worm 1 Worm 2 100 100 SENN SENN SENN I TH /I rb I TH /I rb I TH /I rb 10 10 10 1 1 1 0.001 0.01 0.1 1 10 0.001 0.01 0.1 1 10 0.01 0.1 1 10 ϒ D =t D / τ ϒ D =t D / τ ϒ D =t D / τ 100 100 Worm 4 Worm 5 SENN SENN I TH /I rb I TH /I rb 10 10 1 1 0.01 0.1 1 0.01 0.1 1 10 ϒ D =t D / τ ϒ D =t D / τ 25

Measurement results – continuous sinusoid 10 Worm 1 Worm 2 Worm 3 Worm 4 I TH [mA] 1 Worm 5 0,1 0,1 1 10 f [kHz] 100 100 100 Worm 1 Worm 2 Worm 3 SENN SENN SENN I TH /I rb I TH /I rb I TH /I rb 10 10 10 1 1 1 0.01 0.1 1 10 0.01 0.1 1 10 0.01 0.1 1 10 ϒ D =t D / τ ϒ D =t D / τ ϒ D =t D / τ 100 100 Worm 4 Worm 5 SENN SENN I TH /I rb I TH /I rb 10 10 26 1 1 0.01 0.1 1 10 0.01 0.1 1 10 ϒ D =t D / τ ϒ D =t D / τ