Study of Stimulus Waveform Effect on Nerve Excitability and SENN model verification in Lumbricus Terrestris as a Convenient Animal Model

Transcription

1 Biomedicine and Molecular Biosciences COST Action BM39 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

2 Biomedicine and Molecular Biosciences COST Action BM39 EMF-MED Contents. Introduction 2. SENN model 3. Animal model 4. Measurement setup 4. Measurement/simulation results 5. Conclusion 2

3 Biomedicine and Molecular Biosciences COST Action BM39 EMF-MED Contents. Introduction 2. SENN model 3. Animal model 4. Measurement setup 4. Measurement/simulation results 5. Conclusion 3

4 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 relief, ) EMF safety (human exposure) waveform effects (temporal and frequency parameters) 4

5 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

6 Biomedicine and Molecular Biosciences COST Action BM39 EMF-MED Contents. Introduction 2. SENN model 3. Animal model 4. Measurement setup 4. Measurement/simulation results 5. Conclusion 6

7 McNeal s and SENN model of myelinated axon dv I C I G V 2V V dt n m m i,n i i,n- i,n i,n+ G i 2 π d L 4 i i Li D V n =V i,n -V e,n Ri INTRACELLULAR MEDIUM V i,n- Ri V i,n Ri V i,n+ Ri d.7d dv d n Gi Vn- 2V n Vn+ Ve,n- 2V e,n Ve,n+ Ii,n t C m cm rm Vr cm rm Vr cm rm Vr Second spatial Second spatial difference of difference of unknown extracellural liqid potential transmembrane (activation function): potential Δ 2 V e,n => Δ 2 V e,n /Δx 2 =ΔE e,n /Δx V e,n- V e,n V e,n+ EXTRACELLULAR MEDIUM I π 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 J G ( V V ) P P n P J G ( V V ) L L n L SENN model Activation function 7

8 σ e [S/m] SENN model parameters Parameter Value Fiber diameter (D) 2 µm,6 Axon diameter at node (d).7 D Nodal gap (w) 2.5 µm Axoplasmic resistivity (ρ i ) External medium resistivity (ρ e ) Ωm 3 Ωm Membrane capacitance (c m ) 2 µf/cm 2 Membrane conductivity (g m ) Internodal distance (L i ) 3.4 ms/cm 2 D,5,4,3,2, f [khz] y A =5 mm L=2 y A = cm N R =5 nodes 8

9 Equivalent time constant - τ Q I rb rb c ln 2 approximate chronaxie (τ c ) equivalent time constant (τ) relation τ= µs 9

10 Biomedicine and Molecular Biosciences COST Action BM39 EMF-MED Contents. Introduction 2. SENN model 3. Animal model 4. Measurement setup 4. Measurement/simulation results 5. Conclusion

11 Lumbricus terrestris (Earthworm) Earthworm

12 Why Earthworm (lat. Lumbricus Terrestris) 2

13 Biomedicine and Molecular Biosciences COST Action BM39 EMF-MED Contents. Introduction 2. SENN model 3. Animal model 4. Measurement setup 4. Measurement/simulation results 5. Conclusion 3

14 Measurement setup 4

15 Measurement setup (photo) 5

16 Biomedicine and Molecular Biosciences COST Action BM39 EMF-MED Contents. Introduction 2. SENN model 3. Animal model 4. Measurement setup 4. Measurement/simulation results 5. Conclusion 6

17 Single/repetitive monophasic square pulses Transmembrane voltage change [mv] 2 Transmembrane voltage change [mv] Single pulse td=2 µs 2τ ITH=4.5 ma 8 6.*I_TH I_TH 4.8*I_TH 2.5*I_TH td= µs.τ ITH=24.75 ma 8.*I_TH 6 I_TH 4.9*I_TH 2.5*I_TH,2,4 Repetitive pulses td=2 µs 2τ tp=2 µs 2τ Case ITH=3.2mA 2.2 * I_TH I_TH 8.8 * I_TH I_TH.8 * I_TH Case 4.2 * I_TH 8 I_TH 6.8 * I_TH t [ms] td=2 µs 2τ tp=µs.τ ITH=2.2 ma 3 4 Transmembrane voltage change [mv] Transmembrane voltage change [mv].2 * I_TH Case 2 t [ms] 2,8 td= µs.τ 3 tp=2case µs 2τ ITH=5 ma t [ms] -2,6 t [ms] Transmembrane voltage change [mv] Transmembrane voltage change [mv] t [ms] td= µs.τ tp= µs.τ ITH=4.5 ma * I_TH 4 I_TH 2.8 * I_TH -2,2,4,6 t [ms],8 7

18 Δ SR [db] Single/repetitive monophasic square pulses (2) SR db 2log I I single TH repetitive TH tp= μs tp=3 μs tp=5 μs tp= μs tp=3 μs 4 2 t D [μs] 8

19 Transmembrane voltage change [mv] Transmembrane voltage change [mv] Transmembrane voltage change [mv] Transmembrane voltage change [mv] Single/repetitive biphasic square pulses Single pulse t D = µs t D = µs I_TH=4.68 ma 3.8*I_TH,2,4,6,8-3 t [ms] t D = µs τ 8 6 I_TH=5.5 ma 4.8*I_TH 2-2,2,4,6,8 t [ms] t D = µs.τ Repetitive pulses 2 t D = µs 2 t D = µs I_TH=4.3 ma 8.8*I_TH ,5,5 2 2,5 t [ms] t D = µs τ 9 I_TH=27 ma 6.8*I_TH 3,2,4,6,8-3 t [ms] t D = µs.τ 9

20 I TH [ma] Single/repetitive biphasic square pulses (2) Single monophasic pulse Single biphasic pulse monophasic pulses biphasic pulses 3 2 t D [µs] 2

21 Transmembrane voltage change [mv] Transmembrane voltage change [mv] Transmembrane voltage change [mv] Transmembrane voltage change [mv] Single cycle/continuous sinusoid Single cycle t D = µs.2*i_th I_TH.8*I_TH,5,5 2 t [ms] I TH =6.2 ma t D = µs.2*i_th I_TH.8*I_TH,2,4,6,8 t [ms] I TH =75 ma Continuous t D = µs t [ms] I TH =5.6 ma.2*i_th I_TH.8*I_TH t D = µs,2,4,6,8 t [ms] I TH =36.5mA.2*I_TH I_TH.8*I_TH 2

22 I TH [ma] Single cycle/continuous sinusoid (2) Single monophasic pulse Single sinusoidal cycle monophasic pulses sinusoidal cycles t D [µs] 22

23 Equivalence between repetitive monophasic square pulses and continuous sinusoid - t D =t P I TH [ma] f 2 t D Single monophasic pulse with td=/2fc (peak value) Continuous sinusoid with frequency fc (RMS value) S/P I I sine(rms) TH pulse(peak) TH f /2t c D S/P f c [khz] S/P I I sine(rms) TH pulse(peak) TH f /2t c D S/P cycle 9 5 cycles 8 7 cycles 6 2 cycles 5 5 cycles 4 cycles f [khz].2 fc [khz] 23

24 I TH [ma] Measurement results SD curves Worm Worm 2 Worm 3 Worm 4 Worm 5 Chronaxie - τ c [ms] Time constant - τ [ms] Earthworm.44 Earthworm 2.44 Earthworm Earthworm Earthworm SENN t D [ms]

25 Measurement results monophasic square pulse Worm SENN Worm 2 SENN Worm 3 SENN I TH /I rb I TH /I rb I TH /I rb... ϒ D =t D /τ... ϒ D =t D /τ.. ϒ D =t D /τ Worm 4 SENN Worm 5 SENN I TH /I rb I TH /I rb.. ϒ D =t D /τ.. ϒ D =t D /τ 25

26 I TH [ma] Measurement results continuous sinusoid Worm Worm 2 Worm 3 Worm 4 Worm 5,, f [khz] Worm SENN Worm 2 SENN Worm 3 SENN I TH /I rb I TH /I rb I TH /I rb.. ϒ D =t D /τ.. ϒ D =t D /τ Worm 4 SENN.. ϒ D =t D /τ Worm 5 SENN I TH /I rb I TH /I rb.. ϒ D =t D /τ.. ϒ D =t D /τ 26

27 Comparison of the single monophasic square pulse and continuous sinusoid with equal t D (f c =/2t D ) I TH [ma] S/P Worm Worm 2 Worm 3 Worm 4 Worm 5 SENN,, ϒ D =t D /τ Comparison of the repetitive biphasic square pulses and continuous sinusoid with equal t D (f c =/2t D ) 8, Sinusoid Biphasic square wave S/P,8,6,4,2 Measurements SENN results,, f [khz],, ϒ D =t D /τ 27

28 I TH [ma] P/S (ϒ D,ϒ P ) Comparison of the repetitive monophasic square pulses and continuous sinusoid with equal t D and t P (f c =/2t D ) P/S (ϒ D,ϒ P ) P/S (ϒ D,ϒ P ), t D =t P Single pulse Repetitive pulses (tp=td),, ϒ=t D /τ [ms] Comparison of the repetitive monophasic square pulses with arbitrary phase/pause durations and continuous sinusoid with (f c =/2t D ) S/P t D =t P Measurement results SENN results,, ϒ D =t D /τ,2 t D =3τ,8,6,4 Measurement results,2 SENN results,,, ϒ P =t P /τ t D =τ,8,6,4,2 Measurement results SENN results,,, ϒ P =t P /τ t D =.τ,7,6 Measurement results,5 SENN results,4,3,2,,,, ϒ P =t P /τ 28

29 Conclusion The study produced a set of results that nicely agree both with the theory and with SENN model, proving that this setup could be conveniently used for following studies. 29

30 THANK YOU FOR YOUR ATTENTION! 3

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