BIOELECTRIC POTENTIALS Lecture 3 Generation and transfer of

BIOELECTRIC POTENTIALS Lecture 3

• Generation and transfer of the biopotentials appears to be one of the main functions of the biological membrane. This phenomenon lies at the basis of cells excitation, functioning of the nervous system, regulation of the intracellular processes, muscular constriction and reception. Modern medical diagnostical methods such as electrocardiography, electroen cephalography, electromyography, etc. are based on the investigation of the electrical fields, generated by the organs. Electrostimulation of tissues and organs is practiced: treatment by the external electrical impulses.

• Potential difference arises in the living cells and tissues during their vi tal activity: • Redoxy—potentials as the result of the electron transfer from one type of molecules to another; • Membrane potentials as a result of ion concentration gradient and transfer of the ions via membrane. • Biopotentials registered in the organism are mostly membrane potentials.

• Potential difference between the internal (cytoplasmic) and external membrane surfaces is called membrane potential:

• Progress in the biopotentials studies was achieved due to: • the development of the microelectrode method of the intracellular measuring of potentials; • the creation of special amplifiers of biopotentials (ABP); • the choice of good objects for the investigation — gigantic cells and among them — gigantic axon of (quick and dexterous cephalopoda mollusk). Diameter of this axon reaches 0, 5 mm that is 100— 1000 times larger than the diameter of the axons of vertebrates, including man. Gi gantic dimensions of the axon (in comparison with the vertebrates) are of the great physiological value; they provide quick transfer of the nervous im pulse along the nervous fiber.

• Gigantic axon of worked as the splendid mode! object of the • biopotentials study (not for nothing suggestions were done to erect a mon umentto this animal to which science is very much obliged; as the monu mentto the Frog in Paris and the Dog near Saint Petersburg). • One could insert the microelectrode into the gigantic axon of Calmari without significant damage of the axon structure.

Resting potential in the cells • Resting potential is the stationary electrical potential difference regis tered between the internal and external membrane surfaces in the non—ex cited state. • Resting potential is defined by the concentration difference of ions on different sides of the membrane and the ion diffusion via membrane.

• Resting potential is defined by the concentration difference of ions on different sides of the membrane and the ion diffusion via membrane. • In case when the intracellular concentration of the Cjn differs from its external the flow of charged particles begins across the membrane, which leads to the misbalance of the electrical neutrality of the system; equilib riumpotential difference inside and outside of the cell is formed , that will prevent further transitions of the ions via membrane. Set ting of the equilibrium levels the electrochemical potentials on both sides of membrane:

• If membrane potential is conditioned by the K+ ions transition for which |K+]jn > |K+]out and Z = +1, the equilibrium membrane potential is:

• Described concentration change is insignificant in comparison with intracellular potassium concentration (table 3. 1. ), being only 10~4 % of it. Thus to create Nernst equilibrium membrane potential negligibly low (in comparison with intracellular) ion concentration should pass through the membrane. • Table 3. 1. contains the values of membrane potential, calculated by Nernst formula for different cells and ions, and also experimentally ob taineddata of resting potential (p^for these cells.

• From comparison of calculated and experimentally obtained values of membrane potential one can see that resting potential does well agree with potential calculated by Nernst formula for K+ regarding Berstein assump tion that resting potential is potassium potential. At the same time attention is drawn to the efficient disagreement be tween experimental and theoretical data. Disagreement is caused by mem brane permeability to other ions not taken into account. • Simultaneous diffusion of K+, Na+ and Cl via membrane is consid ered by Goldman equation.

• Thus Nernst equation is the particular case of Goldman equation. • Absolute value of membrane potential calculated by the Goldman equation appeared to be smaller than membrane potential, calculated by Nernst formula and closer to the experimental data for the large cells.

• Nei ther Nernst formula, nor Goldman equation consider active transport of ions via membranes and presence of electrogenic (separating the charges and thus causing appearance of potential difference) ion pumps, playing an important role in the maintenance of ionic equilibrium in small cells. In cytoplasm membrane K+ , Na+ ATP ases work, pumping potassium into and sodium outside of the cell. Thomas equation for the membrane poten tialwas obtained due to consideration of the functioning of electrogenic pumps (Thomas, 1972):

Action potential • Information within living organism is transferred with the help of elec tric nervous impulses from receptors to the brain neurons and from neurons to the muscles. Living organism is fully electrified. There is no life without electricity.

• Action potential was discovered before resting potential. Animal elec tricity is known for a long time. Discharges of electric eel (voltage up to 600 V, electric current nearly 60 A, duration — milliseconds) were used in the Ancient World for treatment of gout, headache and epilepsy. Luidgi Gal vani, professor of anatomy in Bologna, discovered electric nervous im pulse. Results of his electrophysiologic experiments were published in his essay "Commentary on the Effect of Electricity on Muscular Motion" (1791). Galvani found that muscular movement of the prepared frog legs may be caused by the electric impulse and that the living system itself is the cause of it. The great discovery of Galvani played an outstanding role in the development of physics, electrotechnics, electrochemistry, physiology, bio physicsand medicine.

• But the great popularity of his ideas has lead to their profanation, and traces of it are found nowadays (galvanization of corpses, touch and look galvanism, etc. ), that caused disbelief among physicists to Galvani's experiments. Professor Alessandro Volta, junior contemporary of Galvani was fierce opponent of the animal electricity idea (excluding spe cial cases of electric fish: electric eel and electric ray). He excluded biolog icalobject from his experiments and showed that electric current can be re ceived by the contact of the composition of metals, separated by the elec trolyte (Volta's pole). In such a way chemical source of the electric current was discovered (called afterwards by the name of his scientific opponent — galvanic element).

• In XIXth century common was primitive conception of electric cur rentsspreading by nerves those being like wires. However Gelmgolz in the second half of XIX century showed that speed of nervous impulse spread ing is only 1 — 100 m/s; that is significantly lower than speed of electric im pulse spreading by wires — up to 3 • 10 s m/s. Therefore at the end of the XIX 1'1 century hypothesis of the electric nature of the nervous impulse was rejected by most physiologists. Assumption was made concerning spread ing of the chemical reaction by the nervous fibers.

Later it was shown, that slow spreading of the electric nervous impulse is really connected with slow overcharging of capacitors through large resistances; these capacitors being the cell membranes. Time constant of overcharging membrane t = RC is large due to the large values of membrane capacity C and resistance R of the nervous fiber. • The English physiologist A. Hodgkin with collaborators established that nervous impulse appears to be electric impulse only in the middle of the XXth century. Hodgkin, Huxley andg^/egwere awarded the Nobel Prize in medicine in 1963 "for the operation of the nervous cells".

• Electric impulse, conditioned by the change of ion permeability of membrane and connected with spreading of the excitation wave along the nerves and muscles is called action potential (AP). • Electric impulse, conditioned by the change of ion permeability of mem brane and connected with spreading of the excitation wave along the nerves and muscles is called action potential (AP).

• Experiments studying action potential were performed (mostly by Hodgkin and his collaborators) on gigantic axons of calmari by the micro electrode method using high ohm voltage meter and also by the method of labelled atoms. Scheme of the experiments and the results are shown in fig.

• In these studies a pair of microelectrodes were inserted into the axon. Impulse with the amplitude V from generator of rectangular impulses G, changing the membrane potential is sent to the first microelectrode. Mem brane potential is measured with the help of the second microelectrode by the high ohm voltage meter R.

• Excitation pulse causes only short time displacement of membrane po tential that quickly disappears and resting potential is restored. Negative (hyperpolarizing) excitation pulse leads to dislocation of membrane poten tial far to the negative side. Positive (depolarizing) excitation pulse also prevents formation of the action potential, but amplitude of this impulse is much lower than the threshold, Vth

However if the amplitude of the pos itive depolarizing pulse appears to be higher than Vth , jm becomes larger than (pmlh and the process beginning in the membrane after that results in abrupt increase of membrane potential and even alteration of the charge — membrane potential becomes positive: (pjn > pout).

• Reaching some positive value of reverse potential (pmr£membrane po tentialreturns to the value of resting potential, performing something like damped oscillation. • Duration of the action potential in the nervous fibers and skeletal mus clesis about 1 ms (about 300 ms in the cardiac muscle, ). For 1— 3 seconds after the end of the exaltation some residual phenomena could be observed; in this period membrane is refracteric (cannot be excited).

• New depolarizing potential V > Vth may cause formation of the new action potential only after membrane returns to the resting state. Moreover action potential amplitude • does not depend on the depolarizing potential amplitude, if V > Vth. If in the resting state membrane is polarized (cytoplasmic potential is nega tivewith regard to the external medium), then excitation leads to mem brane depolarization — intracellular potential is positive and after removal of excitation repolarisation (restoration of membrane polarization) takes place.

• Special features of the action potential are: • the presence of the threshold value of the depolarizing potential; • "all or nothing” law. action potential develops when depolarizing po tential is higher than threshold (amplitude of the action potential does not depend on the amplitude of the excitation impulse; it does n't develop when depolarizing potential is lower than threshold;

• presence of the refracteric period (non excitation of the membrane during development of the action potential and residual phenomena after excitation removal); • abrupt decrease of membrane resistance at the moment of excitation ( Sf axon has 0, 1 ohm • m 2 in the resting period and up to • 0025 ohm • m 2 during excitation).

• Change of the sodium concentration in the external medium causes al teration of the amplitude of the action potential impulse. Reduction of ex ternal sodium concentration leads to the amplitude decrease of the action potential due to the reverse potential changes. Action potential doesn't de velopat all in case of complete sodium removal from the external medium.

• Experiments with the radioactive sodium isotope allowed to establish that sodium permeability abruptly increases in the excited state. In the rest ing state correlation between permeability coefficients of the caiman's axon for various types of ions is: • PK : PNa : Pci = 1 : 0, 04 : 0, 45 • and in the excited state it is: • Pk: PNa : Pci = 1 : 20 : 0, 45 • that is sodium permeability coefficient during excitation increases 500 times in comparison with the non—excited state.

• Membrane exaltation is described by the Hodgkin—Huxley equations. One of these equations looks like:

• Transmembrane electric current is formed by the ionic current of potassium — Ik+, sodium — Ina+ a other ions, including chlorine — Id ; the so called leakage current and capacitive current. The last is brought about by the overcharging of capacitor (membrane), that is by overflow of charges from one surface to the other. Its value is conditioned by the quantity of charges, overflowing from one capacitor plate to another in the period of time dq/dt;

• On the equivalent scheme Nernst equilibrium potentials are modeled by the voltage sources with electromotive forces and the conductivities of the membrane element for various types of ions are mod eled by resistors

Spreading of the nervous impulse along the excitable fiber. • Formation of the action potential in one of the sections of excitable membrane leads to membrane depolarization and excitation spreads to the other sections of membrane. Let's consider excitation spreading using spreading of the nervous impulse in axon as the example.

• Local currents appear both in axoplasm and in the surrounding solu tion: between the sections of membrane surface with high potential (posi tively charged) and low potential section (negatively charged). • Local currents form inside the axon and at the external surface. Local electric currents lead to the increase of the potential on the inner surface of the non excited section of membrane (pin and decrease of the external po tential of this section (pout, neighboring with the excited zone. Thus the ab solutevalue of negative resting potential cp, ^ decreases, that means its in crease. In sections nearest to the excited one (pm increases higher than threshold. Under the influence of membrane potential alteration sodium channels open and the following increase comes due to the sodium cur rents via membrane. •

• Membrane depolarization takes place, then action potential develops. Then excitation transfer farther on to the resting sections of membrane. • The question may arise why excitation spreads along the axon not in both direction from zone reached by excitation, you know local currents flow to both sides of the excited section. The thing is the excitation can spread only to the membrane section in the resting state, that is to the one side regarding the excited section. Nervous impulse cannot spread to the other side as the sec tions undergoing excitation are non— excitable refracteric for some time.

• Increase of the membrane potential — value of the depolarized poten tial. V, transmitted from the excited sections along the membrane^ depends on the distance x (as it results from electrodynamics) due to the formula: • In this formula Vo is the increase of membrane potential in the excited zone, x — the distance from the excited section; A — constant of the nerv ous fiber length, equal to the distance on which depolarizing potential in creasese times.

• The farther membrane depolarization spreads, the less V decreases with the distance, that is the larger is the constant of the membrane length, the higher is the speed of nervous impulse spreading. The value of A in creases with the increase of the axon radius and the specific membrane ca pacity and with the reduction of specific resistance of cytoplasm.

• The high speed of nervous impulse spreading via axon is provided by their gigantic diameter compared with the vertebrates. The higher speed of the excitation transmittance in the nervous fibers of vertebrates is per formeddue to the other mechanisms. Their axons are covered by myelin envelope, that increase membrane resistance.

• Excitation in the myelin fiber spreads saltgtorly (spasmodically) from one Ranwie interception (section without myelin shell) to the other. Ner vous impulses are transferred in axons in some degree similar to the electric impulses transfer by the cable relax line. Electric impulse transmitted without damping due to its amplifying at the intermediate relay stations, role of which in the axons is played by the sections of excitable membrane, where action potentials are generated.

ELECTRICAL ACTIVITY OF HUMAN ORGANS

• As was shown in previous sections, in the process of cells electric func tioning biopotentials are generated. Therefore electrical activity of human organs is due to electrical activity of separate cells and their mutual action. Detecting parameters of electrical activity of different organs we can make up medical research and diagnostics.

• Method of studying organs functioning based on detecting their elec trical activity (distribution of electrical potential on the surface of human body and its time dependence) is called electrography. Two electrodes ap plied to different points of the human body surface detect time dependence of potential difference between those points. Time dependence of that po tentialdifference is called electrogram.

• There exist two main problems in electrography: • A) direct problem — calculation of electrical potential distribution on the surface of the human body based on parameters of emitted organ. • B) inverse problem — defining characteristics and parameters of the emitted organ parameters by measuring potential distribution on the hu man body surface.

• Inverse problem is a problem of diagnostics — detecting electrocardio gram doctor can determine conditions of functioning of the heart. • Considering electrical activity of the organs we need to solve a difficult problem — to describe potential distribution on the human body as a result of one by one excitation of cells.

• During living activity the state of organ and its electrical activity change with time. It is caused firstly by the penetration of excitation waves along nerve and muscle fibers. In clinical practice it is very difficult to measure potential difference directly — between two points of any organ.

• But even if this potential difference is detected it is very difficult to plot it and to describe time dependence of the electrical activity. Therefore in es timating functional state of the organ we use the principle of equivalent generator: instead of real organ consisting of many cells excited in different moments we use its model which is called equivalent generator. It is pro posed that this generator disposes within considered organ and creates electric field on the human body surface similar to those created by real or gan.

• For calculating electric potential of the field created by the generator in homogeneous electroconductive medium, generator is presented as cur rent electrical dipole — system of positive and negative poles disposed at small distance L. The main parameter of this dipole is D = J • L (dipole mo mentum). • This procedure is widely used in electrocardiography — a method of studying electrical activity of the human heart. According to the principle of equivalent generator we use equivalent current dipole which creates electrical field close to those formed by human heart.

Electrocardiography. • Studying electrical activity of the heart is very widely used in medicine. • Full description of electrical activity of the heart and mathematical presentation of distribution of membrane potentials for every point of the heart and presentation of time dependence of these potentials is impossi ble. Therefore heart is considered as electrical dipole of small size.

• After long computations it can be shown that potential difference be tween two point of electric field generated by electrical dipole (which are located at equal distances from the dipole) is directly proportional to the projection of the dipole momentum on the line to which these point be long.

A

• Analysing changes of potential difference between two points on the human body surface we can find projections of the dipole momentum of heart and, consequently, make a conclusion about electrical potentials of the heart. It is the main idea of the Eintkhowen model (Dutch scientist, a founder of electrocardiography):

• This model states: • Electric field of the heart is considered as electric field small elec tric dipole which momentum is equal to geometrical sun of elementary momentumes of microareas of heart: E — (momentum of the dipole) is called integral electrical vector of the heart. •

• Integral electrical vector of the heart is placed in homogeneous electroconductive medium. • Integral electrical vector of the heart changes its value and direction. • It's initial point doesn’t move and located in auricular — ventricular node. It's end trajectory is spatial curve which projection on a frontal plane during one pulsation forms three finite curves which are called P; QRS; T.

Eintkhowen suggests to detect potential differences between the apexes of Eintkhowen triangular whose centre lies in auricular — ventricular node. It is traditional to attach three electrodes — one to each arm and one to the left foot

Electrocardiogram — is a graph representing time. dependence of po tential difference between two arbitrary points of Eintkhowen triang

• It has now become standard practice to attach 12 rather than three leads to the patient, the new method being called vector, as opposed to the old scalar, e. c. g. • The relationship between positions of the integral electrical vector of the heart and potential difference between two points of human body sur face could be presented in Fig. 4. 5.

• Eintkhowen model is not absolutely adequate to real process and when it was formulated some main proposals are taken into account. They are: • Human organism is not homogeneous electroconductive medium: blood, vessels, muscles and other tissues are differing in electrocon ductivity

• Integral electrical vector rotates and its end forms complex trajectory which projects not on the one plane only. • It is impossible to describe changes of vector E adequately with the use of only one dipole.

• But medical practice shows that these uncorrectnesses are not so great and Eintkhowen theory is used in electrocardiography with good effect. • Now is discovered more adequate model of the human heart electrical activity. It takes into account that heart has finite size and is presented by many dipoles.

• The electronic oscilloscope is used in this process: on the screen an ad dition of two perpendicular oscillations occurs. To the horizontal plates of capacitor the potential difference from the 1 st branch is applied. The sim ilar signal from another branch is applied to the vertical plates. This is a " method of detecting projection on the horizontal plane: for projections on the other planes another electrodes are used.

Electroencephalography. • Detection and analysing time dependence of potential differences of electric fields, generated by brain, is used for diagnosing different types of pathology: brain injury, brain infarction, psychic disorders, disturbing of the sleep and others. Detection and analyzing time dependence of potential differences of electric fields, generated by brain, is used for diagnosing different types of pathology: brain injury, brain infarction, psychic disorders, disturbing of the sleep and others.

• E. E. G is used in surgery for determination of brain area, which is necessary to be extracted, for determination functional con dition of brain before and after input drugs and so on. Metal electrodes are applied directly to skin. Detected potential differences are 100 times less than for e. e. g. : 0. 05 — 0. 001 m. V. Therefore amplifiers with high amplifica tion indexes (100000 — 1000000) are used in e. e. g. •

• Electroencephalogram — is a graph of time dependence of potential difference between two points of brain. In real practice are measured si multaneously with the use of many metal electrodes attached to several points of brain

• Each signal represents time dependence of potential difference de tected between arbitrary electrode and neutral (indifferent) electrode. The signal can be presented by the graph This representation can not be used for diagnostic interpretation and therefore Fourie decomposition is applied. For the signal spectrum can be drown on the graph : • In real practice spectral interval is divided into 5 subintervals, which are called rhythms:

• • • 0. 5 < v < 3 Hz 3<v<8 Hz 8 < v < 14 Hz 14 < v < 35 Hz 35 < v < 70 Hz δ - rhythm θ - rhythm α - rhythm β - rhythm γ - rhythm

• Fourie — decomposition is used simultaneously for the signals detected from all points to which metal electrodes are applied. After calculation of electrical power, for example, to a — rhythm for several points of brain a distribution of a — rhythm power on the surface of brain can be presented