Interaction models for the propagation of the e.m.f. in biological systems

1. Interaction models for the propagation of the e.m.f. in biological systems Francesca Apollonio, Micaela Liberti, Guglielmo d’Inzeo ICEmB at Department of Electronic Engineering, University "La Sapienza" of Rome E-mail: dinzeo@uniroma1.it

2. Physical Law Na K

3. Water dielectrical constant

4. Tissue Dielectric Constant

5. Polarization Effects • Electronic and Atomic polarization nearly instantaneous • (Resonant in the visible range) • Dipolar polarization (Debye): • Water (t =10-12) g • Big globular proteins (t = 10-6) b • Counter-ions diffusion (t = 10-4 ) a

6. Mobile phone and Head |H|2/|HMAX|2 0 0.2 0.4 0.6 0.8 1

7. Tissue Absorption SAR as a function of e” o DT/Dt SAR = w e e”E2/r [W/kg] = s E2/r r = mass density [kg /m3] Termoregulation? Skin sensors?

8. 150 V/m 100 V/m 100 V/m 50 V/m SARpeak = 1.5 W/kg SARpeak = 2.0 W/kg Exposure and Absorption Example

9. Field Distribution [mW/cm2] [mW/cm2] [W/kg] 510-3 10-3 10-4 10-5 10-6 (SAR) distribution Power distribution in presence of the exposed subjecy Plane-wave power distribution

10. Exposure (SAR, DT) Induced SAR and DT f = 900 MHz, Prad = 600 mW

11. Chiabrera & d’Inzeo 1993

12. WHERE?? k12 k12 k23 k23 S + E ES E + P S + E ES E + P Enzymatic reactions in external environment: kiEM fields k21 k32 k32 k21 + + + + - + + + - + - - - - - + - Product in extracellular space (i.e. free ions) Ligand [ ] & motion  EM fields Binding of ions on their specific receptors in membrane Binding  EM fields Ionic fluxes through the cell membrane I ions EM fields Cell to cell interaction Communication  EM fields K+ Na+ Ca++ + + + + + + + + + + + + + + + + + + + + + Enzymatic reactions in cytoplasm, linked to internal processes: Cell functions  EM fields The cell and its environment - - - - - - - - - - - - - - - - - - - - - - K+ Na+ Ca++

13. Proposed Methodology Effects on Physiological Parameters (e.g. Vm, ISI) EM Field Source Membrane Model Internal EM Field Effects on single channel currents Single Ionic Channel Model Microscopic EM Field Effects on ion binding probability Ligand Ion Receptor Site Model Local Microscopic EM Field

14. D •  [30 ÷0.01] m f  [10 ÷30000] MHz D  [3 ÷50] mm l >> D Quasi Statical Condition Laplace Equation: 2V=0 RF Microdosimetry

15. D •  [10 ÷0.01] mm f  [30 ÷30000] GHz D  [3 ÷50] mm l ”@ D Full wave approach 2V + k2V= 0 THz Dosimetry

16. II level Three Strates Sphere: - extracellular Medium - membrane - citoplasm Homogenous Sphere: First Approximation Level III level Five Strates Sphere : - extracellular Medium - external Bound water - membrane - internal Bound water - citoplasm Full Model: Five Strates Sphere + Involved cellular compartments IV level

17. Cytoplasmatic medium k Cytoplasmatic layer of bound water z y B y E x Cell membrane Extracellular layer of bound water x Microscopic Dosimetric Evaluation • The Model: • multilayered sphere • incident plane wave • Solved with Mie theory Results: Alta frequenza, Vol 11, n 3, 1999

18. Millimiter wave Range

19. Low THz Range

20. Low THz Range

21. |E |field in cell membrane vs frequency

22. MEMBRANE: percent variation at different angular positions

23. e2 e1 emix 2V+ k2V=0 + Boundary conditions for D at the interface among materials D1n=D2n Mixtures Scattering?

24. Proposed Methodology Effects on Physiological Parameters (e.g. Vm, ISI) EM Field Source Membrane Model Internal EM Field Effects on single channel currents Single Ionic Channel Model Microscopic EM Field Effects on ion binding probability Ligand Ion Receptor Site Model Local Microscopic EM Field

25. Non thermal (Blackman, 1982) Effect of an EM field (147 MHz), sinusoidally amplitude modulated, on 45Ca2+ fluxes in chick brain embrio. (*: p<0.05; **: p<0.01)

26. Bioem interaction Besides the experimental evidence, scattered in the scientific literature, of the biological effects of low-intensity electromagnetic exposure, there is a lack of both understanding and consensus about the underlying interaction mechanisms. Therefore, there are no well established guidelines for identifying all the important variables to be kept under control during the experiments, for designing the optimal experimental conditions, for fitting theories to experimental data, for predicting, on a theoretical ground, the bioeffects and the exposure conditions to be experimentally tested. In attempting to elucidate the mechanisms, most researchers have concentrated their experimental and theoretical efforts on the early steps of the electromagnetic interaction, at molecular level. Chiabrera et al., 1999

27. more than 140 articles reviewed • around 15 journals involved • around 40 main authors Attemping to organize….. History ‘70s 2002

28. More recent papers at higher levels, new tecniques Attention to network of cells Direct E-B action: First papers followed “classical” models. All recent papers moved to quantistic ones

29. physiological EM field source Neuronal Network model Effects??? Membrane voltage Membrane model Internal EM field exposed biological system Channel currents Single Channel Model EM field on microscopic structure Binding probability Ligand Ion Receptor Site local EM field on microscopic structure Apollonio et al., 2000

30. Whole Membrane Model Transmembrane Voltage time (ms)

31. NonThermal Effect

32. Effects on single channel currents Single Ionic Channel Model Ion binding model Pb Ligand dependent channel Effects on ion binding probability Fbm Ligand Ion Receptor Site Model Fbm(Vm) NEURONAL Model Local Microscopic EM Field METHODOLOGY

33. Binding Sites Calmodulin S-K Channel The S-K Channel Single Channel Model: Ligand-Dependent Channels Need of integration with more microscopic level An example: The Small Conductance Potassium Channel (Calcium controlled)

34. Molecular Simulations Protoporphirin IX Hemoglobin

35. Ligand Ion - Receptor Site

36. Calmoduline site (empty)

37. Calmoduline Site (bound)

38. Binding Sites Calmodulin S-K Channel The S-K Channel Single Channel Model: Ligand-Dependent Channels Need of integration with more microscopic level An example: The Small Conductance Potassium Channel (Calcium controlled)

39. [Ca2+ ] Popen Ca2+ -CaM Zeeman-Stark model SK channel model T D K+ DK- binding probability SAR=0.8 W/kg SAR=0.2 W/kg SAR=0.05 W/kg time (psec) First Step EM field

40. Single Ionic Channel 10ms 0

41. Single ChannelPhysics

42. 4 qji 0 3 CA* CA 2 qij 1 CA2 CA*2 closed open FINITE STATE MARKOV MODEL • The model is defined by N states, and it is characterised by: • Pi(t)  occupation probability of state i • qij(t)  transition coefficents from states i to j • The system evolves in time following the markovian equation: • dP(t) / dt = P(t) Q(t) • In the protein channel model: • each state corresponds to the channel open or closed • transition coefficents are affected by the exogenous e.m. field

43. Analytical solution

44. Model cascade [Ca2+ ] Ca2+ -CaM Zeeman-Stark model Popen SK channel model T D K+ DK- EM field

45. [Ca2+ ] Popen Ca2+ -CaM Zeeman-Stark model SK channel model T D K+ DK- %effect binding probability SAR=0.8 W/kg SAR=0.8 W/kg SAR=0.2 W/kg SAR=0.05 W/kg intracellular Ca2+ [mM] time (psec) Second Step EM field

46. Single Channel Model: Voltage-Dependent Channels 100 ms

47. physiological EM field source Neuronal Network model Membrane voltage Membrane model Channel currents Single Channel Model Binding probability Ligand Ion Receptor Site local EM field on microscopic structure Apollonio et al., 2000

48. Membrane potential T0 = ISI Vm

49. OUTSIDE I I I I I I I I Na KC P Ca Ka KK PM B M Whole Membrane Model: Neuron Basic Model (D’Inzeo et al., 1994) INSIDE HH like Model

50. Whole Membrane Model: Analytical Representation