Seminar 4. Biophysical background of electrophysiology

Transcription

1 Seminar 4 Biophysical background of electrophysiology Electrical and magnetic properties of body tissues. Sources of biological potentials. Ion channels. Nerve conduction. Electrodes. Electroencephalographic (EEG) and electromyographic (EMG) signals. Electrocardiogram (ECG) - detection and analysis. S4 1

2 Electric properties of biological tissues Electric field Constant in time DC electric field Alternating in time AC electric field E electric field intensity vector [E] = V/m U electric potential scalar [U] = V = J/C Remark: Electric potential electric potential energy S4 2

3 Interaction of electric field with a biological material Biological material Conductor (resistor) body fluids Nonconductor (insulator, dielectric) cell membrane Remark: The division of biological objects into resistor and dielectric material is an approximation Remark: The separate description is necessary in case of AC or DC currents Conductor (resistor) Metallic conductor electric current electron current Ionic conductor (electrolyte solution) electric current electron and ion currents To facilitate description of the electric current flow, the biological tissue is approximated by the equivalent electric circuit 2 elements are important resistor and capacitor S4 3

4 Ohm s law identical relation for DC and AC currents U = R*I In the resistor a conversion of the electrical energy to thermal energy takes place. It is beneficially used, however it can also be a fire hazard. The rate at which electric energy is lost is given by the electric power (P) P = I*U = R*I 2 = U 2 /R [P] = W = J/s = A*V Symbols to mark resistor S4 4

5 Capacitor A capacitor consists of two conductors separated by a nonconductive region. The non-conductive region is called the dielectric (electrical insulator). Examples of dielectric mediums are glass, air, paper, vacuum. The conductors hold equal and opposite charges on their facing surfaces, and the dielectric develops an electric field. An ideal capacitor is wholly characterized by a constant capacitance C, defined as the ratio of charge ±Q on each conductive plates to the electric potential U between them C = Q U S4 5

6 Remark: Water tank analogy In SI units, a capacitance of 1 farad (F) means that 1 coulomb (C) of charge on each conductor causes an electric potential of 1 volt (V) across the device. [C] = F (farad) F = C/V The charged capacitor not only stores charge, but also energy The potential energy stored in the capacitor = 1/2*Q*U EP = 0.5*Q*U = 0.5*C*U 2 [EP] = J = C*V Remark: Application defibrillator S4 6

7 Capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass DC current does not flow across capacitor R = AC current flows across capacitor the maximum current is related to the maximum voltage by the factor 1/ωC ZC = 1/ωC = 1/(2π*ν*C) impedance ω = 2π*ν circular frequency U = (1/ωC)*I Ohm s law Remark: [1/ωC] = V/A = Ω Remark: Impedance is equivalent to resistance is the description of AC current flow Symbol to mark capacitor S4 7

8 Remark: Each conductor may be treated as capacitor in relation to ground Remark: Nonconductor (biological membrane) dielectric constant ε U' U = Q/C' Q/C = C C' = 1 ε Remark: Dielectric constant ε is dimensionless quantity S4 8

9 External electric field produces the polarization of the dielectric an additional electric filed is generated which compensates the external electric field Dielectric constant for water = ~80 Remark: In water solution electric forces decreases by the factor ~80 electrolytic dissociation of molecules in water solution (NaCl Na + + Cl - ) S4 9

10 Magnetic fields Magnetic fields are produced as a result of electric charge movement flow of an electric current magnetic moment (m ρ ) magnetic dipole Two types of electric current should be distinguished bound current (electrons in atoms) free current (electrons in a metal conductor) To describe the magnetic field produces by bound current the magnetization M ρ (the average magnetic moment per unit volume) is used = To describe the magnetic field produces by free current the magnetic field intensity H is used SI unit A/m S4 10

11 To describe the total magnetic field the magnetic induction B (magnetic field B) is also used += µ0 magnetic permeability of vacuum [B] = T tesla Remark: In vacuum B = µ0h Permanent magnet H = 0 A magnetic bacterium with small permanent magnets (~100 nm) called magnetosome (magnetite - Fe3O4) S4 11

12 It has been traditional to define magnetic permeability of a medium since B and H are proportional B = µh µ M µ r = = 1 + = 1 + µ H 0 χ m µr relative permeability dimensionless quantity χm magnetic susceptibility Diamagnetic material χm < 0 µr < 1 χm Paramagnetic material χm > 0 µr > 1 χm 10-4 Ferromagnetic material χm > 0 µr >> 1 χm 10 3 Diamagnetic material the orbital motion of electrons creates magnetic moment when an external magnetic field is applied magnetic moments will tend to align in such a way as to oppose the applied field Lenz's law induced magnetic fields tend to oppose the change which created them materials in which this effect is the only magnetic response are called diamagnetic Paramagnetic material each atom has permanent magnetic moment random orientation due to thermal motion alignment in external magnetic field Ferromagnetic material a set of randomly oriented magnetic domains (size ~( ) mm) alignment of domains in external magnetic field extremely big magnetic field is generated S4 12

13 Remark: All materials are inherently diamagnetic, but if the atoms have some net magnetic moment as in paramagnetic materials, or if there is long-range ordering of atomic magnetic moments as in ferromagnetic materials, these stronger effects are always dominant Relative permeability Material µr Cu H2O Air Al Electrical steel 4000 Soft tissue S4 13

14 Electrophysiology 1. Determination of the electric field (potential) which is generated inside the human body for diagnostic purposes 2. The use of the external electric field for diagnostic or/and therapeutic purposes The use of an external source of the electric potential for diagnostic purposes bioelectrical impedance analysis (BIA) determination of the fat content Electrical model of the tissue equivalent electric circuit Remark: RC approximates resistance of the cell membrane and cytoplasm Remark: The model above is the simplest possible approximation of the electrical property of the human body S4 14

15 Mass of the body MB FFM Fat-free mass FM Fat mass Empirical observation MB = FFM + FM FFM = Function(age, mass, height, TBW) TBW total body water TBW = ICW + ECW ICW intra-cellular water ECW extra-cellular water Electrical resistance of the body = Function(TBW) FFM = Function(age, mass, height, resistance) Empirical formula non-linear regression analysis FFM[female (50 70) y] = *Ht 2 /R *W FFM[male (18 29)y] = *Ht 2 /R *W FFM kg Ht height cm R50 resistance at 50 khz Ω W mass kg %FM = 100*(W - FFM)/W S4 15

16 Measurement of the tissue resistance four electrode system Ohm s law R = U/I Rough estimation Seminar 1 Men: fat (% of the body weight) = 1.28*BMI Women: fat (% of the body weight) = 1.48*BMI Recommended values (mean ± SD) Female (%) = 31.2 ± 7.8 Male (%) = 20.1 ± 7.6 S4 16

17 Source of biological potentials The origin of almost every electrical potential within the body is a semi-permeable membrane Na +, Cl -, K +, Ca 2+ can pass more freely in one direction through the membrane than the other potential ~0.1 V is generated across the membrane changes in potentials of this type are the origin of signals such as the ECG, EEG and EMG Electrophysiological measurements B brain, H heart, M muscle, S skin, E electrode, EF extra-cellular fluid S4 17

18 The nervous system The brain is supplied with information by afferent nerves (are affected by conditions they are sensed) the brain makes the decision the instruction is sent by the brain via efferent nerves to produce an effect (they effect the change) transmission in two directions Action potential excitation e.g. external stimulus membrane potential is changed threshold potential voltage-gated ion channels an avalanche effect (Na + enter, K + leave) depolarization S4 18

19 Action potential is the impulse of depolarization followed by re-polarization that travels along the nerve Remark: The nerve fibre are immersed in the conducting fluid ionic current will flow around it from the polarized to the depolarized parts the only external evidence that the action potential is present the external currents give rise to the bioelectric signals which can be recorded e.g. heart external currents amount to ~100 µa and give rise to ECG signals S4 19

20 Equivalent electrical circuit of the axon Parameter Myelinated Non-myelinated R0 i Ri (Ω/m) 6.4* *10 9 Cm (F/m) 8* *10-7 Rm (Ω/m) 3*10 6 8*10 3 Myelin electrical insulator nodes of Ranvier speed up transmission (about 10 times i.e. ~50 m/s) the nerve action potential jump from one node to the next Fast nerve fibre myelinated fibre Slow nerve fibre non-myelinated fibre S4 20

21 Muscle action potentials similar to nerve action potential 1) smooth (involuntary) artery wall, stomach 2) striated (voluntary) heart, skeleton Remark: Smooth muscle can produce electrical signals without any neural or hormonal trigger Two striated muscle fibres that are supported from one motor nerve fibre Contraction of muscle fibre needs additionally Ca 2+ current Remark: A muscle action may be induced using an external device S4 21

22 Muscle stimulation using external electrical pulses A nerve will be stimulated when the trans-membrane potential is reversed by an externally applied current Example Sem4/2 TENS trans-cutaneous electrical nerve stimulation S4 22

23 Membrane has capacitance a finite charge is required to change trans-membrane potential current must flow for a certain time nerve stimulation depends on current frequency A stimulus depolarized the cell by causing charge to flow across the membrane minimal charge is needed to produce the effect Charge = current*time Strong stimulus (big current) depolarizes membrane quickly - weak stimulus (small current) must be applied longer Muscle stimulation using electrical pulses strengthduration curve Rheobase the minimum current which will stimulate the muscle whatever the width of the stimulating pulse Chronaxie the pulse width such that the threshold current is twice the rheobase Remark: A very weak stimulus will not cause an effect even if applied for very long time S4 23

24 Example Sem4/3 The mechanism of the electric shock DC and AC V = R*I R = 2*(skin) + (inner part of the body) R(skin) ~50 kω (normal) R(inner part of the body) 50 Ω V = 240 V I = 240/( ) = ~ A Power at the normal skin = 0.2 W After short time (part of second) skin carbonization R(skin) 0 Ω current ~4.5 A Additional effect AC The longer you re being shocked, the more chance there is for your heart to begin fibrillation. Fibrillation is the shocking of your heart into a useless flutter. Most people who die from electric shock die from fibrillation. S4 24

25 Example Sem4/4 Defibrillator a device to apply a large electric shock to the heart used to restore a normal sinus rhythm to a heart ~50 A of current is required for defibrillation across the chest the resistance of the chest ~50 Ω Power for defibrillation = ~100 kw Voltage for defibrillation = ~5000 V S4 25

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27 Artificial pacemaker a device which uses electrical impulses to regulate the beating of the heart X-ray image of installed pacemaker S4 27

28 Modern pacemaker is a processor-controlled device control of ventricles and atria rate responsive pacing allows the device to sense physical activity combination of pacemaker and defibrillator in a single device Three electrodes are used Black arrow right atrium Dashed arrow right ventricle (thickened parts mark a defibrillator) Red arrow left ventricle (coronary sinus wraps around the outside of the left ventricle) S4 28

29 Electrodes Before any physiological signal can be recorded it is necessary to make electrical contact with the body through an electrode 1) microelectrodes single cell (~0.5 µm) 2) needle electrodes pass through the skin (~1 mm) 3) surface electrodes ECG, EEC Surface electrodes contact (polarization) potential Metal electrode in a solution metal ions diffuse into solution Me Me + + e The process will reach an equilibrium similarity to Nernst s law electric potential Ψ Nernst s equation for metal electrode Metal Ψ 0 (mv) Iron Lead Copper +337 Platinum S4 29

30 By international agreement the electrode potential is measured with reference to a standard hydrogen electrode ( Ψ 0 = 0) These potentials are very much larger than electrophysiological signals Typical amplitude of some bioelectric signals Type of bioelectric Amplitude signal ECG 1 mv ECC 100 µv Electro-myogram (EMG) 300 µv To cancel the electrode potential two identical electrodes have to be used (reference electrode) Remark: Battery two different electrodes S4 30

31 Electric signals use for diagnostic purposes 1. Heart ECG 2. Brain EEG 3. Muscle EMG 4. Eye electro-oculogram 5. Eye electro-retinogram 6. Stomach electro-gastrogram Electro-oculogram is a recording of potential changes due to eye movement Electro-retinogram the changes of the potential produced by the eye when the retina is exposed to a flash of light Electrocardiography LAB S4 31

32 Electrocardiography Einthoven (1895) measurements of the electric potential generated during the heart operation Lab Advanced analysis of the ECG long-term monitoring (Holter system N. J. Holter 1949) chest electrode small digital recorder 24 h corresponds to ~ contractions Remark: New technology big pen-drive S4 32

33 Electroencephalographic (EEG) signals (Berger 1929) EEG arises from the neuronal potentials of the brain but signals are reduced by bone, muscle and skin which lie between electrodes and brain normal amplitude (10 300) µv and frequency (0.5 40) Hz Electrodes skullcap 21 electrodes Positions of electrodes system, i.e. spacing of the electrodes is based on 10% and 20% of the distance between specified points on the head 21 surface electrodes + 2 reference electrodes (sometimes additional electrodes are used) A1 and A2 attached to the ears are reference electrodes S4 33

34 In routine 8 or 16 channels are recorded simultaneously S4 34

35 Remark: The systems with 256 channels are now available S4 35

36 General classification frequency 1) Delta (δ) slow (0.5 4) Hz 2) Theta (Θ) intermediate slow (4 8) Hz 3) Alpha (α) (8 13) Hz 4) Beta (β) fast (13 30) Hz S4 36

37 EEG signals when the brain receives stimuli (light flashes, pulses of sound) evoked response Sound stimuli ~100 times EEG responses are averaged by the computer Random signals from the normal EEG tend to average to a background signal and the evoked response becomes clear S4 37

38 Electro-myographic (EMG) signals The electrical source is the muscle membrane potential of about -90 mv. Measured EMG potentials range between less than 50 µv and up to 20 to 30 mv, depending on the muscle under observation Functional unit of the muscle is one motor unit needle electrode Example of EMG measured with the needle electrode of weekly contracting muscle puncture Remarks: Large spike is the summation of the muscle action potentials from the fibres of the motor unit, which are closest to the tip of the needle electrode S4 38

39 Oscilloscope CRT cathode ray tube S4 39