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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
CHAPTER 4. ELECTRICITY. MEASURMENT OF BIOPOTENTIALS
4.1. Electric current - basic concepts. Active and reactive resistance. Electrical impedance
Each electric charge creates an electric field at its vicinity. Relying on this field the charge can
exersize a force, attractive or repulsive, on other charges well distanced from it. Electric field is a part of
the space around the charge, "filled" with electrical energy. A certain amount of electrical energy is
accumulated in every point of the field and this energy is expressed as electric potential, φ (volt, v). The
difference in the potentials, Δφ = φ1 - φ2, of each two points in the field is the electric voltage, U (volt, v)
between these points.
The electric field acts on charges by force and compels them to move. Depending on their
freedom of movement, the charges are free and bound.
The free (unbound) charges do not have an equilibrium position in the medium and are allowed to
move, under the action of the electric field, at large distances. A medium which contains free electric
charges (carriers of electric current) is called conductive medium. In biological objects each free hydrated
ion is a free charge.
The bound charges are elastically attached to certain points of the medium (equilibrium
possitions). Under the action of an electric field each bound charge can only be displaced at a little
distance around its equilibrium position. The bound charges in biological objects include the polar and
dissociable chemical groups attached to biomacromolecules. An important example of bound charge
represents the electric double layer arranged around the cell membranes and macromolecules.
The electric current arises in a conductive medium under the influence of an external electric
field. The electric current represents locomotion of electric charges in the conductive media under
the action of an external electric field. The driving force that causes electrical current is the electric
voltage applied at both ends of the conductive medium. The magnitude, I, of the current (Ampere, A)
means the amount of charge, Q (Coulomb, C), which passes through the cross section of the conductive
medium per unit time t (seconds, s), (I = Q/t). Electric current representing a motion of free charges is
called conduction current, Icon. Electric current representing displacement of bound charges is referred to
as a displacement current, Idis. In general, I = Icon + Idis.
Material medium which contains only free electric charges is called conductive medium or
conductor, while medium which contains only bound charges is dielectric. Most media, including the
biological tissues, contain both types of charges in different proportions.
Fig. 4.1.1. Time dependence of
the sinusoidally alternating electric
current.
Depending on the change of the
electric field over time, the electric current
can be alternating (when it changes in magnitude and direction, designated with the symbols ~ and AC),
direct (it varies in magnitude, preserving the same direction, DC) and constant (it does not change its
magnitude and direction, =). Most frequently, when we talk about an alternating current we mean a current
with sinusoidal form over time: I = Io.sin (2.t + ). Here Io is the amplitude,  is the frequency, (2.t +
) is the phase and  is the phase angle of the current. Fig. 4.1.1 shows how this current changes with
time, t. The period, T = 1/ and the circular frequency,  = 2.
When an electric current flows through a conductive medium (conduction current, displacement
current or both) the medium exerts opposition to the moving charges, thus spending the energy of the
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
electric field. The electric impedance (total resistance) of the medium, Z, is a measure of this opposition
and the loss of electrical energy. Impedance is given by the ratio of the electric voltage, U, between the
two ends of the conductive medium and the magnitude of current, I, through it, Z = U/I. If the voltage, U,
varies sinusoidally over time the current will changes in the same way and both variables will have the
same frequency. In general, the phase angles of the voltage and current may differ or not, depending on
the type of the medium, respectively, on the type of impedance. 1/Z is called admittance.
If the medium contains only free charges, only conduction current can flow through it. In their
movement the charges sustain friction with the molecules of the medium and convert the energy of the
field into heat, Q. In this case the impedance is called active resistance, R=U/I, and the phase angles of
current and voltage coincide to each other. 1/R = G is called conductance. According to the formule of
Joule the heat, Q = UI t, where t is the time interval when the current flows. Based on this the heat, Q,
released by the conductive current is called Joule΄s heat and its measurement allows the determination of
R (ohms, ).
Fig. 4.1.2. Flow of electric
current through a coil (A) and
electric capacitor (B).
Since U = I. R, it follows
that Q = I2. R. t, i.e., the Joule΄s heat depends on the square of the current. This relationship is used in the
electric scalpel and electrocoagulator, broadly used in surgery. In tissues the thermal effect of current
depends on the quadratic degree of current density. The current is supplied to the patient by means of two
electrodes. The first, stationary electrode has a large area. Hence, its current density is low and it does not
heat the underlying tissue. The second electrode is mobile and has sharp edge serving as a scalpel. The
current density through it is high and causes strong local heating to temperatures up to 100°C. This leads
to protein denaturation and evaporation of water, and the tissues could be cut by the sharp edge of the
electrode. The denatured proteins aggregate and adhere clogging the truncated blood vessels, hence, the
bleeding is small. This is the haemostatic effect. The same principle is used in the needle ablator and
bipolar electrocautery. At a density of 6-10 mA/mm2 the temperature under the electrode increases to a
point causing tissue coagulation (diathermocoagulation). At a density of 40 mA/mm2 the temperature is so
high that the tissue is carbonized and evaporated to yield pure cutting of the tissue (diathermotomy).
According to Ohm's formule, the active resistance, R, of a conductive medium is R = .L/S.
Apparently, the resistance, R, depends only on the parameters of the medium; cross-sectional area, S,
length, L and  - resistivity of medium. The 1/ = σ is called electric conductivity of the medium.
Depending on the value of σ, the media are divided into three groups; conductors, insulators and
dielectrics. In conductors (e.g., metal wires), the concentration of free charges is high and σ has a high
value. In nonconductive media σ is very low. These media include insulators (rubber, polyurethane)
lacking both free and bound charges, and dielectric materials (paper, mica, certain polymers and
biopolymers) in which there are only bound charges. In semiconductors σ has a value intermediate
between that of conductors and insulators. In addition, the σ of semiconductors strongly depends on some
physical factors (temperature, irradiation, ionizing radiation, the presence of admixtures) and this
dependence is used to monitor these factors.
Except through active resistance, R, the alternating electric current may flow through capacitors
and coils. The electric capacitor (Fig. 4.1.2 B) serves as a reservoir (storage, depot) for charges. It is
composed of two metal plates, most commonly with the same area, S, separated by a layer of nonconductive medium with a thickness, d. Let's have an electric circuit in which a capacitor is connected.
The electric sourse moves the free electrons and charges the one plate of capacitor with electric charge, +
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
Q, and the opposite plate with the charge, -Q. An electric field with the voltage, U, arises between the two
plates. The ratio Q / U = C = .S/d is a constant for this capacitor called capacitance of the capacitor. Here
 is the dielectric permittivity of the medium between the plates. For air or vacuum the permitivity has a
low value, marked with o. The  will be particularly high, respectively the capacitance, C, will be much
greater if a dielectric medium is placed between the metal plates. The more bound charges are present in
the dielectric, the greater will be  and C. Cell suspensions and tissues have the highest values of  due to
their cell membranes and biomacromolecules which possess a large number of bound charges. In
general, ε = ε0 εr, where εr is the relative permittivity of the dielectric medium.
A pure displacement current is only possible in an ideal dielectric placed between the plates of a
capacitor. This current is accompanied by a reorientation of the existing and creation of new electric
dipoles. The re-orientation of the electric dipoles is restricted by the friction with surrounding particles
resulting in the generation of heat. This energy loss is referred to as dielectric loss. At low frequencies of
the current there is sufficient time for the dipoles to re-orient in tact with the field. Consequently, the
dielectric energy loss is negligible in comparison with the conductive loss (Joule heat), which is due to
the free charge conduction, quantified by σ. Dielectric loss increase largly at a given high frequency, when
the dipoles rotate with different phases. Due to their inertia the dipoles ceace to rotate at even higher
frequencies and the released heat again diminishes. Of this type is the microwave heating of tissues.
Fig. 4.1.3. A circuit of serially connected
electrical
components
(left).
The
total
impedance of the circuit is obtained as the
vector sum of the impedances of all its
elements (right).
The coil (Fig. 4.1.2 A) consists of winded
wire into which a core could be placed. The current
flowing through the coil creates magnetic field into the core material. The strength (intensity), H, of the
magnetic field is proportional to the current, I. The proportionality coefficient contains a multiplication
factor called inductance, L = μ.V.n2, where V is the volume of the core, n is the number of turns of wire
per unit length and μ is the magnetic permeability of core material. Permeability, μ, expresses the
inductive (magnetic) properties of a given material. There are materials (iron alloys) with μ far exceeding
that of air. Most materials, including the biological media, however, do not practically differ in their
permeability, μ, from air. Thus, the magnetic properties of biological tissues are weekly demonstrated and
their total impedance has entirely capacitive character without inductive component. The magnetic
properties of biological tissues are important only in special cases when either the magnetic field strength
is very large or the impact of the field is very long.
There are three major differences between the impedances of the resistors, capacitors and electric
coils.
1. In contrast to the active resistance, the energy of electric field is not converted into heat when
alternating electric current flows through a capacitor with capacitance, C, and a coil with inductance, L. In
these cases, the energy is stored in the capacitor and the coil in the form of electric field and magnetic
field, respectively. After the current is stopped the stored energy entirely returns back keeping the current
flowing until the energy is entirely spent as active loss. Because the strored energy behaves like a
counteracting response or reaction, the impedance of these elements is purely reactive in nature and is
called reactance (marked with X). In case the current is alternating with circular frequency, , the
reactance of the capacitor will be XC = 1/(.C), and that of the coil will be XL = .L.
2. Based on the presented formulae it follows that while the active resistance, R, does not depend
on frequency, , the reactances XC and XL strongly depend, i.e., they have dispersive character.
Apparently, while the XC decreases, the XL increases with the frequency, . The latter fact is employed in
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
medical equipment where appropriate combinations of capacitors and inductors are used to construct
filters admitting currents with selective frequency. These filters allow the passage of electic currents with
appropriate frequency only and suppress the signals with other frequencies like the noice.
3. If the electric circuit contains an active resistor only, the current and potential difference
(voltage) are in phase, i.e.,  = 0. Any change in the current is accompanied by a corresponding change in
the voltage without delay, there is no inertia. In a circuit with reactive impedances, the current and voltage
are shifted by 90° to one another. Thereat, with coil the current leaves behind the voltage ( = + 90°),
while with capacitor the voltage exceeds current ( = - 90°). This means that reactances introduce inertia,
for example the presence of capacitor in the circuit makes the changes in voltage to lag behind the changes
in current.
Because each of the three impedances have its magnitude and phase angle, it can be represented as
a vector (or as a complex number) in a two-coordinate plot (Fig. 4.1.3). The horizontal axis of the plot is
referred to as axis of the current. The length of the vector will be equal to the magnitude of the impedance
and the angle of the vector towards the axis of current will be 0°, + 90° and -90° in case the impedance is
resistor, coil and capacitor, correspondingly. This presentation facilitates finding the total impedance in
case the circuit contains a number of impedances connected in series. In this case, under the rules of Ohm,
the total impedance will equal the vector sum of these impedances. If the circuit contains impedances
connected in parallel, then the parameter admittance, reciprocal to the impedance, is introduced and
represented as a vector in the same plot.
Let the current flows through a circuit containing a resistor with a pure resistance R, a
capacitor with reactance XC and a coil with reactance XL, connected in series (Fig. 4.1.3, left). The total
impedance, Z, of the circuit is a vector sum of the three impedances. According to the rules of vector
addition (Fig. 4.1.3 right), the total impedance will have a magnitude │Z│ = (R2 + (L - 1/C)2)1/2.
The phase angle, , of the impedance, equal to the phase angle between the current and the voltage is
also shown. If XC > XL, the phase angle  < 0 and the total impedance is capacitive in nature. The
impedance of biological objects always has capacitive nature, because they do not contain structures
with inductive properties, i.e., practically XL = 0 for all bioobects.
The bioelectrical impedance analysis (BIA) is a noninvasive and safe method for obtaining
diagnostic information by measurement of the impedance of human body at several frequencies. The
impedance is measured between the wrist of the hand and the sole of the foot. Thus, the active (resistive)
and reactive (capacitive) parts of the impedance, and the phase angle between them are measured. These
data are used to calculate, based on empirical formulae, body composition (fat mass, fat-free mass and
body water volume) in children and adults. On the other hand, these data are use to assess the health status
of the patient, his food regimen and the prognosis for its recovery.
4.2. Impedance of the electrolyte solutions, suspensions and tissues. Equivalent electric
scheme of tissue. Rheography of tissues and organs. Iontophoresis and electrophoresis.
Conductive cytometer.
Both types of electric charges, free and bound ones, are present in electrolytic solutions, cell
suspensions and tissues. The free charges of these media represent ions (cations and anions) produced in
the electrolytic dissociation of electrolytes (salts, acids and bases) present in the aqueous media. The
amount and type of the free charges determine the conductivity, σ, of medium. For a given electrolyte
solution σ =  Ci.i.Zi.Ui (the summation is on all types of ions in the medium). The electric conductivity
of medium, σ, depends proportionally on the concentration, Ci, of the i-th electrolyte, the degree i of its
electrolytic dissociation, charge, Zi, and mobility, Ui, of ions, present in medium. Strong acids and bases,
and their salts determine higher electrical conductivity because they have high, almost complete, degree of
dissociation, i.
According to their composition, blood and tissue fluids are highly conductive because they
contain many electrolytes. By contrast, cell membranes, fatty tissue, skin and bone are poor conductors of
electric current. The skin is a good electric insulator.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
The electrical conductivity of tissues is important for measuring the biopotential of organs (heart,
brain). For example, the biopotential of the heart varies with each contraction and relaxation of cardiac
muscle. Because tissues, nabouring to heart, are conductive this biopotential is carried to the surface of the
body and can be measured there via electrodes placed on the skin.
The quantity of divalent cations in drinking waters is referred to as hardness of water. This
parameter can be assessed quickly and accurately by measuring the electrical conductivity of the water
sample. For the distilled water, the conductivity is a measure of the concentration of the residual ions.
Fig.
4.2.1.
Presentation of various
biological tissues with
three types of equivalent
electrical circuits (A, B,
C). Given are the
frequency dependences
of the magnitude of their
impedances │Z│. Most
appropriate to represent
the electrical properties
of tissues is the circuit C.
Bound charges in liquids, solids and tissues are grouped in pairs, called electric dipoles. Each
dipole contains two charges with the same quantity, Q, but with opposite signs. At rest both charges are
merged, because a force of attraction acts between them. Under the influence of external forces, such as
electric field, the two charges are distanced from each other. The attractive force, however, increases with
the distance between the charges and balances the external force. With the elimination of external force
both charge again merge.
In some cases, the bound charges may be permanently distanced from each other even in the
absence of external forces. These are so called permanent dipoles. Under the action of external electric
field the permanent dipoles can only be rotated and aligned in the same direction as that of the field.
The appearence of electric dipoles in the medium is referred to as a dielectric polarization. Each
dipole creates an electric field, which is directed opposite to the incident field. Therefore, the resultant
electric field within the dielectric medium, which is equal to the sum of the incident field plus the field of
dipoles is less than the incident field. Therefore, dielectric polarization weakens both the resulting electric
field and the current flowing inside the medium and increases the impedance of the medium. When a
significant part of the impedance is due to the dielectric polarization, the impedance exhibits strong
dependence on frequency. In this case, the impedance is referred to as dispersive resistance.
When a layer of dielectric medium is positioned between the plates of a capacitor with
capacitance, Cо, the capacitance increases to C. The dielectric polarization of the medium is quantified by
the magnitude of the relative dielectric permittivity r = C/Cо.
Biological tissues have no specific inductive properties as there are no structures similar to coils
(solenoids) in them. However, they contain plenty of cell membranes and biopolymers, which stipulate
strong dielectric polarization in them. Thus, bioobjects possess only two types of resistances; active, R,
and capacitive, XC. The electric properties of bioobjects can be modeled with the equivalent electrical
circuits shown in fig. 4.2.1. Schemes A and B are not particularly useful, because in case A the
impedance│Z│tends to infinity at low frequencies, while in the case B the impedance│Z│tends to zero at
high frequencies. The scheme C is the most suitable to describe the passive electrical properties of a
bioobjects. In this scheme R1 is proportional to the resistance of the extracellular medium, and R2 depends
on the resistance of the cytoplasm of cells. The capacitance, C, is proportional to the capacity of cell
membranes due to their lipid bilayer. At low frequency it has naximal value called static capacity while at
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
high frequencies it decreases due to the elimination of the dielectric polarization of membranes. The
intrinsic resistance of plasma membranes is too great and coud be ignored.
The impedance Z (total resistance) of bioobjects has capacitive character as the phase angle, ,
between the current and voltage has negative values (from - 40° to -60° for different tissues). Therefore,
the tissue impedance decreases with the frequency of the current - dispersion of the impedance (Fig.
4.2.2). The ratio of the impedance at 103 Hz (Z1) to that at 105 Hz (Z2) is called coefficient of dispersion, k
= Z1/Z2. Upon damaging the cell membranes of bioobjects (e.g., after heating, irradiation with ionizing
radiation, inflammation), the coefficient of dispersion decreases. The phase angle is also reduced. This
finding allows the control of viability of isolated tissues and organs, stored for transplantation, by
measuring the coefficient of dispersion and phase angle of their impedance.
Fig. 4. 2. 2. Equivalent electric
scheme of bioobject (right), and frequency
dependence of the impedance of biobject
(left).
Rheography is a method for
monitoring the pulsative blood filling of
tissues and organs (limbs, muscles, liver,
brain), according to the changes in their
impedance. These changes are periodic and
occur in tact with the heart beats. Because the electrical conductivity of the blood (at 16-50 kHz) is much
higher than that of other tissues, the impedance of tissues decreases during the pulse wave (systole) and
grows during diastole. Fig. 4.2.3 shows a typical shape of the rheographic record of human hand. It
contains two phases, ascending (anacrotic phase, ἀνάκρουσις) and descending one (catacrotic phase,
κἀτάκρουσις). The initial phase of rapid increase in conductivity (AB) corresponds to the rapid filling of
the limb blood vessels due to the ejection of blood from the heart and the elastic expansion of large and
medium-sized arteries. At the top point B the blood pressure is equal to the maximal systolic pressure and
the blood flow is constant. Behind this point the conductivity decreases due to drainage of blood to veins.
In the middle of the discending phase, the blood pressure in the left ventricle of heart falls below a certain
value and the aortic valve closes down resulting in a slight increase in both the blood pressure and the
blood filling. This event is indicated by the point B (incisura), a notch in the downward curve caused by
the backflow of blood for a short time before the aortic valve closes. At the end of the descending phase,
when the blood pressure drops to its minimum diastolic value another peak (venous wave) may appear
indicating the reversal of blood flow due to the overfilling of the vein system with blood.
Based on the form of rheographic wave the hydraulic resistance of the vessels supplying blood to
a given tissue, including both hemispheres of brain, can be determined. The higher the hydraulic
resistance the smaller is the steepness of anacrotic phase. In addition, the A peak becomes more rounded
and the incisura rises. This method is especially useful in the study of blood flow to the two halves of the
brain.
Some medications (local anesthetics, antibiotics, anti-inflammatory and anti-cancer drugs)
dissociates to ions when dissolved in a polar media. Such drugs are frequently introduced through the
pores of skin directly to the disease site using the method of iontophoresis (electrophoresis). The drug
solusion is placed on the skin and direct electric current is allowed to flow from the solusion into the skin.
The amount of drug, delivered at the site of the disease and, accordingly, the therapeutic effect depends on
the current magnitude and on the duration of iontophoresis.
In a solution biomacromolecules generally represent ions (polyions) with large number of surface
charges. This is used for separation of a mixture of macromolecules into its fractions. For this purpose, the
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
macromolecules are driven through a suitable porous medium under the action of outside electric field
(electrophoresis). The greater is the charge of each molecule, the greater will be the driving force which
accelerates it. On the other hand, each moving molecule encounters a resistive force (force of Stokes),
which increases with its speed. As a result, the molecules initially accelerate to a point when they start to
move with constant velocities, each one depending on the charge and size of individual molecule. Thus,
starting from the same position, the individual fractions of macromolecules travel different distances and
separate into different groups (spaced zones). These zones can be isolated and used (preparative
electrophoresis) or fixed and stained (analytical electrophoresis).
Fig. 4. 2. 3. A
change
in
the
impedance of a human
limb
during
the
passage of a pulse
wave of blood.
The
electric
properties of bone tissue
play an important role in
building the human
bones. If a direct current
is passed through aqueous solution of collagen a strip of concentrated collagen molecules forms around
the negative electrode (Fig. 2 4. 4). A little time after the current has stoped, the strip scatters, however, if
calcium salt was present in the solution, the strip remains as a permanent formation. This result explains
why flowing through a bone fracture, a direct electric current contributes to the deposition of collagen
molecules at the fracture spot and accelerate its healing.
Fig. 4. 2. 4. Electrophoresis of
collagen in solution (left). Right demonstration of the piezoelectric
properties of a hip bone.
Bone tissue is a dielectric material
that exhibits piezoelectric properties
(piezodielektric). Under the action of a force, F, an isolated femur deforms and electric charges appear at
the deformation site, which are negative at the place of contraction and positive at the place of stretching
(Fig. 2.4.4). This piezoelectricity is due to the displacement of charges from the inside to outside of
collagene macromolecules during the deformation of bone. These charges create electric voltage, and in
turn, the latter generates electric current inside the deformed bone. In human such a current is generated in
each bone subjected to deformation. In addition, calcium is present inside the bones. Provided this bone
deformation continuous for a long time, the induced current causes lasting deposition of collagen
molecules along the power lines of the inner mechanical stress and, hence, bone reshaping. Thus, the
piezoelectric properties of bones explain the famous law of Wolf, that at continuous mechanical strain, the
size and shape of bones are changed so that their resilience and ultimate tensile stress should be maximal.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
Conversely, in the absence of prolonged pressure, the bones lose mass and become brittle. This happens in
humans being sick and immobile for long time, and when astronauts spent a long time in weightlessness.
In a suspension of cells, the ratio of total cell volume to the volume of suspension is referred to as
cytocrit (cell volume fraction). The suspension resistance, measured at low frequencies (<10 kHz)
increases with cytocrit value. This is due to the plasma membrane of cells which have a very high intrinsic
resistance. Therefore, the resistance of separate cell is much greater than that of the suspension medium
and the current flows mainly in the suspension medium. There are precise formulae that allow the
calculation of suspension cytocrit after the determination of suspension conductivity at low frequencies.
Fig. 4. 2. 5. Schematic diagram of
conductometric cytometer.
The method of conductometric cytometry is based
on continuous measuring the electrical resistance of a thin
capillary tube through which the tested suspension of cells
(e.g. diluted blood) flows (Fig. 4.2.5). Each time a cell
passes through the capillary tube, the resistance will grow producing a drop in electrical current and a
negative impuse on the measuring resistance. The greater the cell volume the stronger will be the
magnitude of the impulse. Thus, by counting the number of pulses per unit of time we can determine the
concentration of cells in suspension. In addition, obtaining how the collected impulses are distributed by
amplitude we can found the distribution of cells by volume and, hence, by type. If we test the blood cells
of a patient, we could automatically determine the concentration and mean volume of the three main types
of blood cells - erythrocytes, leukocytes and platelets. Compared to other cells platelets have much smaller
volume. Hence, their signals are well discriminated by amplitude and are counted separately. To
enumerate the white blood cells a portion of blood is diluted in a vast hypotonic solution. At hypotonicity
the erythrocytes lyse and do not further affect the resistance of the capillary, while leukocytes remain
intact and are counted. Thus, conductometric cytometry allows rapid and fully automatic analysis of all
types of blood cells. A number of blood disorders, associated with variation in the average volume and
concentration of different types of blood cells, are established by this method.
4.3. Effects produced by the electric current in biological tissues. Physical basis of the
medical treatment procedures with electric current. Basic principles of electrical safety.
The electric current is often used as a treatment modality. Unlike drugs, the therapeutic action of
the electric current is not accompanied by side effects, toxicity, liver damage and induced allergy.
However, at improper handling of the current, it can cause damage to people. Therefore, to achieve a
therapeutic result, it is necessary to know and correctly apply the beneficial effects that electric current
induces in the tissues of human.
1. Main effects produced by electric currents flowing through tissues. In tissues, the electric
current interacts mainly with the free and bound charges, with cell membranes and electroexcitable cells.
Under the action of the electric field, the free charges (inorganic ions and macromolecules),
present in tissues, move in a direction determined by the direction of the field. This forced movement of
ions, called electrophoresis, in turn, gives rise to the movement of liquid medium, designated as
electroosmosis. Electrophoresis and electroosmosis represent forced transport of ions and dissolved nonelectrolyte substances in the liquid medium which contributes to the naturally occurring passive transport
like diffusion and osmosis. As a consequence the trophics of tissues improves, the acid-alkaline balance
changes, the metabolism speeds up and the harmful and waste products, released during the period of
disease, are removed.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
The movement of free charges (electric current) through a given tissue is accompanied by heat
release (Joule heating) and increase in temperature. This heating effect is stronger when the magnitude of
the current is greater, and the electrical conductivity of the tissue is higher. At moderate temperature rise
(1-3°C) the biological effect is useful (thermal activation of transport and metabolism, enhancement of the
immune response). Applying stronger current, the local heating could exceed 42°C (hyperthermia),
resulting in thermal death of cells and thermal necrosis of tissues. Thermal conductivity of tissues and heat
convection, due to blood circulation, cool down the heated tissue, hence, the hyperthermia is more intense
in poorly vascularized tissues.
Upon imposing electric field the bound charges of tissues become electric dipoles that create new
electric field, directed oppositely to the external one. This effect is called dielectric polarization of the
tissues. In general, the dielectric polarization of tissues weakens the resultant field and reduces the current
flowing in the tissue. Therefore, the dielectric polarization has beneficial effect protecting the tissues
against electric field and current. The greatest attenuation of the electric field and resulted currents is
caused by cell membranes and skin, because normally they are impermeable to the moving free charges.
Due to the dielectric polarization of cell membranes the cell cytosol is practically inaccessible for the
alternating electric fields with frequencies lower than 1 MHz. In this way, the plasma membrane protects
the cell nucleous and associated genetic apparatus from external electric fields.
The dielectric polarization, induced by high-frequency current, causes a change and rotation of
biomacromolecules in phase with the current, which is referred to as oscillatory effect of the current.
Assumingly, this effect is accompanied by resonance of the current with important biopolymers, cleavage
of hydrogen bonds, reorientation of the nucleic acids. At currents with greater magnitude, the oscillatory
effect and the dielectric polarization convert the energy of outside field into heat even in such tissues
where there are no free charges, like bones and fats. This is called dielectric heating.
The alternating electric field of high frequency increases the ion permeability of biomembranes
which strongly impacts the ionic imbalance and transport of ions in cells. The permeability of the wall of
blood capillaries is also increased which increases the flow of immune cells towards the inflammated
tissue. The enhancement of the active transport of ions across cell membranes is also established.
Excitable cells (muscle, nerve and receptor cells) have the ability to generate and transmit
transient electrical signals - nerve impulses along their membranes. The nerve impulses are generated in
specialized nerve nodes and then spread along the nerve cells. Reaching the muscles, they cause rhythmic
contractions (breathing, heart beat), shrinkage of pulmonary alveoli, blood and lymph vessels and opening
of blood capillaries. The same effects can be produced, however, with artificial electrical impulses having
such a shape, amplitude and frequency (electrostimulation effect). The latter impulses are generated in
electrical generators and applyed with suitable electrodes. To electrostimulate a given excitable tissue a
suitable pulsed current with frequency (50 - 500 Hz), close to that of their own nerve impulses, is passed
through the tissues.
The electric current increases the threshold of irritation of nerve endings. This is reffered to as
analgesic effect of the current and it is used as a means to suppress pain. The same effect, however, leads
to a gradual adaptation of tissues to the electrostimulatory action of alternating electric current.
2. Dependence of the effects, produced by the electric current, on the magnitude and
frequency of the current. Fig. 4.3.1 shows possible reactions of adult human to alternating current with
different frequency, , and magnitude, I. The adult is gripping a large electrode with one hand and the
other electrode is attached to his foot. The minimal magnitude of current producing feeling of irritation is
called sensory perception threshold or threshold twitch (around 1.0 mM). At much higher levels (around
10 mM), called tolerance threshold or let-go threshold, the human encounters grip tetanus, whereat the
hand “freezes” to the electrode.
In fig. 4.3.1 the perception threshold is shown by the curve (1). Under this curve there is no
perception of current. Curve (2) gives the let-go threshold for grip tetanus. At levels between the curves 1
and 2, the current causes relaxing grip, i.e., the patient may at will detach his hand from the electrode. In
this area the current is producing useful effects (electrodifusion, electroosmosis, dielectric polarization,
electrostimulation, ect) and the current exhibits a curative effect.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
The adverse effects of the current are exhibited above the curve (2) where the area of the lesion is
disposed. Immediately above the curve (2) the damage of tissues is small and reversible (treatable)
including defibrillation of muscles (tetanus, temporal interruption of breathing and heart activity).
Defibrillation occurs when separate muscle fibers do not contract at the same time under the influence of
innervation pulses. At a greater magnitude of current the tissue damage becomes irreversible, due to the
thermal necrosis. The necrosis has thermal character and is due to the heat-induced cell death. The thermal
effect of current is used in electrosurgery for electrocoagulation of superficial tumors, for hyperthermic
killing of internal tumors (e.g., prostate cancer).
Fig. 4. 3. 1. Frequency dependence of
the sensory perception threshold (curve 1) and
of tolerance threshold (curve 2) for human.
It is clear that the biological effect of the
current depends mainly on its strength, I, and to a
lesser degree to the frequency, . According to
Fig. 4.3.1 the greater magnitudes of the current
cause harmful effects instead of cure. When a
current of few mA flows through the human body
the related perception is very weak or absent.
Currents of about 10 mA cause a tetanic
contraction of the muscles of the limbs. Current of
about 20 mA disrupts breathing due to the tetanic contraction of respiratory muscles. Current of about 80
mA causes tetanus of miocardium. All these injuries are reversible and treatable, if the victim is given
immediate medical treatment after the interruption of the current - artificial breathing, massage and
fibrillation of the heart. In many cases the currents between 100 and 200 mA are lethal because of the
irreversible thermal damage to the heart muscle. Above 200 mA, the current damages the heart muscle
and the ventricular fibrillation is no more possible.
3. Physiotherapeutic methods (techniques), which use the beneficial effects of the current.
The beneficial and healing effects of the electric current occur only at amplitudes and frequencies of the
current associated with the area between the curves (1) and (2) of fig.4.3.1. Electrical currents of low and
sound frequency exert a multitude of beneficial effects - electrostimulation, electrophoresis and
electroosmosis, analgesia. A major problem, however, is the passage of these currents through the skin of
the patient, which is a strong electrical insulator barrier.
Currents with low and sound frequency are transmitted through the patient using two contact
electrodes attached to the skin of patient. The penetration of current through the skin, however, is
hampered by the high electrical resistance and facilitated by the high capacitance of the skin. The stronger
currents have more prominent curative effect, however, they stronger irritate the skin. To penetrate the
skin, the electric current passes through the sweat and tallow glands and hair follicles. Further, the current
passes mainly through the intercellular spaces, because the resistance of the cells is very high. With
increasing frequency of the current, the impedance of the skin decreases, hence penetration of the current
increases. The impedance of the skin decreases strongly when the skin is wetted and cleaned with alcohol
and at higher blood filling of skin vessels. In order to distribute the current over a larger area and to
improve the contact between the electrode and the skin, a layer of highly conductive material (a
conductive paste, a gauze soaked with NaCl saline solution and the like) is placed between them.
Galvanization. In this method, the healing effect of the current is induced in pure form. For this
purpose a direct current is passed through the diseased tissue by means of two electrodes placed on the
skin, at a voltage of 60-80 v. The beneficial effect of the galvanization is mainly due to electrophoresis
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
and electroosmosis both taking place in the tissue. It is convenient to combine the galvanizing with the
iontophoresis of appropriate drug.
The technique of interference currents uses two sinusoidal currents with low frequency (50-100
Hz) and small amplitude in order to cause a slight and tolerable irritation in the skin of the patient. The
paths of the two currents intersect at the therapeutic area situated deep in the body. The currents both
interfere and the resulting current has larger amplitude and, hence, stronger healing effect in the
therapeutic area. Diadinamotherapy is a similar method, wherein two currents with semisinusoidal shape
and low frequencies (50 Hz and 100 Hz) and amplitudes pass through the skin of the patient. Currents
with such form manifest the electrostimulation effect; they induce rhythmic muscle contractions, increase
the number of open collateral capillaries of circulatory system. This method is used for anesthesia, for
electrostimulation of muscles and regeneration of wounds.
The problem with difficult passing of low frequency currents through the skin and underlying
tissues is avoided by the method of amplipulsotherapy. It uses sinusoidal current with higher frequency of
2 kHz to 5 kHz (carrier frequency) whose amplitude is modulated with a low frequency (10-150 Hz)
current. The depth of modulation can vary from 0 to 100%. The high carrier frequency of this current
provides easier penetration through the skin, while the biological effect is due to the low frequency
current, which affects mainly neuromuscular connections. With this method the rhythmic contraction of
muscles is stimulated, and the regional circulation is increased. In tissues this leads to enhanced transport
of substances and removal of the products of inflammatory process. The above two methods allow
appropriate drugs to be administered through the skin - diadynamoforesis and amplipulsoforesis.
The application of the above methods, however, leads to rapid adaptation of tissues to the
stimulatory action of the electric current. The reason for this is the increase in the thresholds of irritation
and stimulation caused by the prolonged flow of current with constant frequency, i.e., by the analgesic
effect of the current. This is avoided using a current with variable frequency. Fluktuorization is the
therapeutic usage of sinusoidal current with frequency which shifts randomly in the range 20 Hz - 20 kHz,
mostly between 1-2 kHz. This current causes rhythmic muscle contractions that enhance the regional flow
of blood and lympha subduing the inflammation. In addition the epithelialization of superficial wounds is
accelerated. This method is used in neuralgia, myositis, and dental diseases.
Electrostimulation, based on pulsed currents with appropriate frequency, is successfully applied to
restore damaged nerves and neuromuscular connections. One of the electrodes is placed in the engine
section of the damaged muscle and the other is placed at the spinal cord section which innervates the
muscle (unipolar method) or at the transition zone between the muscle and its tendon (bipolar method).
The applied current pulses have usually triangular or rectangular shape with steep front edge, similar to
that of the nerve impulses. Such type of impuses has strong stimulating effect, respectively, lower
threshold of stimulation. Therefore, electrostimulation of the heart, respiration, contraction of the uterine
musculature, electrogymnastics of body muscles is performed with such triangular pulses. Diseases of the
neuromuscular apparatus, disruption of the heart rhythm and breathing, paralysis of the stomach, loss of
contractile ability of smooth and striated muscles (paralysis, paresis, atrophy, atony) are treated by
rectangular or triangular electric impulses. Such a treatment method is successfully applied to treat
diseases of neurogenic origin (hypertension, ulcer, asthma). Neurogenic diseases of the central nervous
system (neuroses, insomnia) are treated by stimulation with rectangular impulses (electrosleep and
electronarcosis). For these cases pulsed currents with a frequency of 3.5 to 150 Hz, and pulse duration of
0.5 ms are used. Electrodes are placed adjacent to the patient's head as cups collected in one mask.
Through their action on the brain and sub-cortical compartments the impulses normalize the activity of the
autonomic nervous system.
Currents with high frequency (above 500 kHz) are devoid of the methodological difficulty related
to the nead to overcome the skin barrier. These currents easily penetrate the skin and cause small
displacement of tissue ions with amplitude comparable to their thermal fluctuations. Hence, at these
frequencies the current do not exhibit electrophoretic effect and electrostimulation. Nevertheless, these
currents produce therapeutic result, which is explained by the heating and oscillatory effect of the current.
At lower amplitudes predominates the oscillatory effect, while at greater amplitudes the thermal effect of
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
current is also demonstrated. In addition, this current increases ion permeability of plasma membranes and
the permeability of the wall of blood capillaries. Hence, it has demonstrated anti-inflammatory activity
and decreasing effect on the high blood pressure.
Diathermy is a therapy method whereby the heat is released in deep underlying tissues using
electric currents with frequency of 1-2 MHz, voltage of 100-150 v and strength of 1 – 1.5 A. The heat is
released due to the dielectric loss in tissues with low conductivity like bones, skin, fat, muscle. The tissue
temperature rises depending on how much heat is generated, and what is the rate of heat removal by
thermal conduction and convection. If the local temperature rises above 42oC, diathermy causes
irreversible damage to tissue. In human, the receptors for heat and temperature are mainly disposed in the
skin, consequently human may not be alerted by pain when the heat generation in its internal tissues
become overcritical. Consequently, tissues that have a low blood supply, such as the eye lens, are most
likely subjected to overheating by diathermy.
This method of treatment has a beneficial effect, for example in muscle pain and sprain. In
modern medicine, diathermy is used to produce local hyperthermia in order to kill tumor masses. With this
modality the high frequency electric field is concentrated in the tumor tissue and raises its temperature
above 43oC (mild hyperthermia) or 55-60oC which has a cytotoxic effect on tumor cells.
To apply the technique of ultrahigh frequency therapy ( = 30 to 300 MHz) the patient is placed
between the plates of a capacitor, with no contact between the patient and plates. The electric voltage is
applied between the plates of the capacitor creating an electric field, which penetrates the patient’body and
induces electric current in his tissues. Depending on the type of tissues - conductive (muscle, blood) or
dielectric (skin, bone), the current generates heat based on different mechanisms.
In conductive tissues, the thermal power, P, released for unit time (1 s) in a unit volume (l m3)
depends on the intensity of the electric field, E, and the electric conductivity, σ, of the tissue by the
formula P = 0,5.σ.E2. This power is related to the Joule heat and is maximal in tissues with high
conductivity (blood, lymph, urine, and tissues with good blood suply).
In dielectric tissues with low conductivity (adipose and connective tissue, nerves and bones)
the alternating current generates heat power, P, according to the so called dielectric heating (dielectric
losses). The dielectric polarization is accompanied by reorientation, rotation, and oscillation of the
electric dipoles. The heat is released due to the friction between the vibrating dipoles and surrounding
particles. In this case P = 0,5... Е2. tg (), where  is the angular frequency,  is the dielectric
permittivity of the medium and
current).
 is the angle of dielectric losses (the angle between voltage and
Another type of dielectric heating is obtained in tissues with greater water content using
microwave or millimeter radio waves (microwave therapy). In this type of heating the frequency is in the
GHz region (2.45 GHz), nevertheless, the electric field still penetrates deep into the tissues (10 - 20 cm).
Due to their high dielectric permittivity the tissues with high water content strongly absorb the
microwaves and are subjected to strong heating. Recently, the microwave radiation is used to irradiate
tumor tissues producing hyperthermia in them, which is an additional therapeutic modality for cancer
treatment. This method is based on the high water content of cancer cells compared to normal cells. For
example, melanoma cells contain 82% water in contrast to the 61% in the cells of normal epidermis. Thus,
under microwave irradiation (2.45 GHz) cancer cells are heated to 42-46 oС while normal skin cells are
heated to 38 oС.
Similar heating effect is obtained when the patient's body is placed in an alternating magnetic
field within the core of a coil - inductothermy. The patient is placed in the core of the coil and the
magnetic field induces an alternating electric field in the patient’tissues (Faraday effect, electromagnetic
induction). The electric field lines represent closed cicles. In the conductive tissues of the patient this
vortex electric field drives circular currents (Eddy currents) which release Joule heat, according to the
formule: Р = 0,5.С.2.B2. σ. Here, B is the magnetic induction, and C is a coefficient depending on the
geometry of the patient’body. The thermal effect is greater in the conductive tissues and at greater
frequency, , of the magnetic field.
The method of darsonvalization uses pulsed current with high frequency (100-400 kHz), high
voltage (20 kV) and low current (15-20 A). This current readily passes through the skin, reduces the
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
sensitivity of skin receptors and, hence, induces local analgesis. The current expands alveoli and opens
additional capillaries, improves the trophics of tissues. There is no thermal effect. Similar is the method of
ultratonotherapy, using sinusoidal current with a frequency of 22 kHz is supplied at electrode, slightly
distanced from the skin. The high voltage causes spark discharge between the electrode and the skin,
which is accompanied by heat. Like darsonvalization this method has predominantly local analgesic and
anti-inflammatory action.
Weak electric shock caused by static electricity in cold and dry weather (winter) is known to
everyone. This current is caused by the static potential of several thousand volts. However, it duration
is very short, thus, the total charge is very small. Although it causes muscle contraction, this shock is
usually harmless.
When working with electricity, it is necessary to observe the following electrical safety rules:
1. The most important precaution against electric shock is to avoid contact with metal parts,
conductors and wiring under voltage. Especially dangerous is the simultaneous contact of the body with a
pair of metal objects under voltage, such as wire and wet ground, wire and grounded metal object and
others.
2. If the casing of the electric machine is made up of metal, it must be protected by grounding,
since once damaged it may turn out under voltage. The protect ground is made up either by a separate wire
or using a power cord of schuko type. The schuko (short for protective contact) plug and socket are
equipped with protective-earth contacts. Recently, plastic casings are frequently used that are electrically
safe because they are insulators.
3. The electrical circuits of medical equipment are provided with suitable relays and switches,
which turn off the power supply to the working electrodes and the patient at danger.
4. As the voltages less than 36 v are considered safe the 36 v should be used when possible.
5. The risk of electrical shock increases when the skin is wet, because the electric resistance of
wet skin is a hundred of times lower than that of dry skin. When working with equipment under high
voltage the best protection remains the usage of gloves, boots and rugs made up of insulating materials.
4.4. Electrode potential. Electrochemical energy sources. Non-polarisable, pH-, ion-selective
and gas electrodes
Metal prostheses, pacemakers, dentures, fillings, crowns and more metallic bodies are frequently
used in traumatology, surgery and dentistry. Upon contact of each metal body with the tissue and aqueous
solutions electrode potentials arise, which represent an electric voltage between the metal and the media.
Such electrode potentials arise when measuring biopotentials using a metal electrode, when measuring the
concentration of ions in a solution, the pH and the redox potential of a redox system, and so on. Electrode
potentials are used in the chemical sources of direct current providing power supply to various devices.
The origine of the electrode potential can be explained by the following mechanism. Metals are
divided into two groups of precious and non-precious (base) ones. For the base metals (e.g., zinc, lead),
the bonds between the metal cations in their crystal lattice are weak. Upon contact of such a metal with
aqueous solution of its salt the metal ions on the contact interface are hydrated and dissolved into the
solution (Fig. 4.4.1). The metal acquires a negative charge, respectively negative electrical potential,
which prevents further dissolution and promotes the return of a part of the released cations to the
electrode. After initial increase, the potential reaches a maximum and constant value Eel, at a time when
the release rate and the absorbance rate of the metal cations equalize. Eel is the equilibrium electrode
potential, which is given by the Nernst equation:
Еel = Ео + (R. T / Z. F). ln (a) …………………. (1),
where a is the activity (concentration) of the metal cations in the solution, and E o is the standard
electrode potential equal to the equilibrium electrode potential at a = 1 mol. Eo depends on the type of
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
metal. In this formula, R is the gas constant, T is the temperature, Z is a valence of the metal ions, and F is
the number of Faraday.
At the precious metals (platinum, silver, copper), the bonds between the cations in their crystalline
lattice are much stronger. When such metal is immersed in a solution of its salt, its cations start to deposit
from the solution into the metal interface. This metal electrode also acquires equilibrium potential, E el,
expressed by the Nernst formula, but now its value is positive.
Fig. 4. 4. 1. Formation of equilibrium
electrode potential at Zn/Zn2+ electrode (left).
Constuction of the non-polarisable silver
chloride Ag/AgCl electrode (right).
The charged electrode attracts oppositely
charged ions of the medium, which form nearby
layer called a layer of counterions. The proximal
layer of counterions and the ions of the electrode
surface both form a structure called a double electric layer. It is similar to the electric capacitor; it stores a
certain amount of charges and possesses its own capacity.
The system consisting of a metal salt solution and an electrode immersed in the medium is called
galvanic half cell (half element). An electric voltage exists between the electrode and the surrounding
medium (electrode potential), however, it could not be measured directly. When two half elements are
galvanically connectied, that is, using a conductive medium in which the current can flow, a galvanic
element forms. The galvanic element is also called voltaic cell, electrochemical cell, electric battery,
chemical source of power. Practically only the voltage between the two electrodes of a galvanic element
can be measured and used. This potential difference is called electromotive force (EMF), which according
to the Nernst equation (1) is given by the formula U12 = Eel2 – Eel1 = E02 – E01 + (R.T/Z.F).ln(a2/a1). A
given amount of energy, in the form of electric current, may be elicited from such a galvanic cell. The
power capacity of each galvanic cell is given by the total amount of electric charge Q, which may be
extracted from it. Since Q = I. t, it is usually measured in ampere-hours (Ah).
In case the solutions around the two electrodes have the same concentrations (a 1 = a2), then U12 =
E02 - E01, and it is referred to as galvanic electromotive force. The reason for this potential difference is the
different nature of the two metal electrodes having different standard electrode potentials. Such potential
difference appears when two metal prostheses of different alloys are put in contact with the same body
fluid or tissue.
If two identical electrodes are immersed in solutions with different concentrations, then E01 = E02
and the Nernst equation is reduced to U12 = Eel2 – Eel1 = (R.T/Z.F).ln(a2/a1) - concentration electromotive
force. Such a potential difference will occur if two prostheses, made up of the same alloy, are immersed in
various body fluids or tissues. Both cases are, however, undesirable because the generated electromotive
force can irritate the adjacent nerves, muscles or glands and cause continuous secretion or paresis.
Various parameters of the electrolyte solution (electric conductivity, concentration of a particular
ionic species, pH) can be measured immersing two appropriate electrodes in them and measuring the
electric current between them. However, the current releases electrolytic products on the electrodes
changing the chemical composition of their surfaces. In addition, the electric double layer of each
electrode changes. As a result the Eel is reduced and this is called polarization of the electrodes. There are
several ways to eliminate the polarization of the electrodes:
A) If possible, a current with small magnitude is used for a short time;
B) Electrodes of chemically inert metals, usually made of platinum, are used;
C) The surface area of electrodes is increased, for example using electrodeposition of platinum
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
black on the electrode surface;
D) If possible, alternating current of high frequency is used;
E) The most frequently used method for reduction of polarization is to use electrodes with lower
polarizability (non-polarisable electrodes) (Fig. 4.4.1). For example, the silver/silver chloride nonpolarisable electrode comprises a glass tube filled with saturated solution of KCl in which a silver metal
electrode is immersed. There is a filter window at the bottom of the tube to allow galvanic contact with the
tested media. The silver electrode is covered with a layer of insoluble salt of the same metal (AgCl). The
electrode attracts the Ag+ ions when it is cathode (-). The Ag+ ions oxidize the electrode and became
deposited on the electrode surface as Ag atoms. If the electrode is an anode (+) it attracts Cl- and thereby it
becames reduced. The Cl- ions deposit on the electrode in the form of AgCl. In both cases, there is no
polarization as the electrolysis does not alter the chemical composition of the electrode surface.
Besides silver, the electrode can be of mercury, coated with a layer of calomel paste (Hg2Cl2).
This is the calomel electrode. In general, the non-polarisable electrodes are used as reference electrodes in
conjunction with appropreate measuring electrode. It is assumed that the electrode potential of the nonpolarisable, reference electrode is zero and does not vary when the chemical composition of the medium is
changed.
1. Determination of the activity of a specific ion in the medium. The ion-selective electrodes
are used to determine the activity of important biocations in media. The most important feature of the ionselective electrodes is their selective sensitivity. In other words their readings depend on the concentration
of a given ion species, without being influenced by the presence of other ions in solution. In medical
practice, these electrodes are used to measure the concentration of K+, Na+, Ca2+ and others ions. The ionselective electrode consists of housing, an ion-selective membrane and internal auxiliary electrode system
(Fig.4.4.2). The ion-selective membrane represents a polymer (polyvinyl chloride) containing molecules
of a substance (ionophore) that specifically captures and transfers respected ion. In the potassium
electrode, the membrane containes the K+ ionophore valinomycin, and in the calcium electrode the
membrane contains the ionophore A23187, which is a specific carrier for Ca2+. Thus, the specificity of the
ion-selective electrode is based on the selective permeability of the membrane to the given ion. The
auxiliary system is a 0.1 M solution of chloride salt of the determined cation and a non-polarisable
electrode immersed in the solution.
When the ion-selective electrode is immersed in a solution containing an unknown concentration,
C, of the determined ion an electric voltage, Eel, arises between the electrode membrane and the solution.
The Eel is the electrode potential of ion-selective electrode, also given by the formula of Nernst (1). The
determination of the ion concentration, C, is carried out measuring the membrane potential, Eel, of the ionselective electrode with the help of another non-polarisable electrode, called reference electrode. In fact,
what is measured is the potential difference between both electrodes, which is a function of the
concentration, C, using appropriate millivolt meter.
2. Measurement of the acidity, pH, of the solution. Molar concentration of hydrogen cations
[H+] in a solution is defined by the variable pH = - lg [H+]. For example, if the [H+] in a medium is 1 mM,
i.e., 10-3 M, the pH will be –lg(10-3) = - (-3) = 3. Of the variaty of methods for determination of pH the
potentiometric method, using an electronic pH meter, is sufficiently accurate, reliable and convenient. This
pH meter contains two electrodes, immersed in the medium, one of which is the measuring glass electrode
and the other is an auxiliary (comparative, reference) electrode. The mercury or calomel non-polarisable
electrode is most commonly used as reference electrode. Its electrode potential, relative to the medium, is
assumed zero and does not depend on the changes in the concentration of hydrogen cations. The
measuring electrode plays the role of an ion-selective electrode, whose electrode potential depends only
on the concentration of the hydrogen cations [H+]. The potential difference between the two electrodes
depends on the concentration of hydrogen cations and is measured by sensitive high-impedance
milivoltmer.
In general, the most accurate measuring electrode for [H+] is the so called standart hydrogen
electrode. It consists of a platinum wire, immersed in the solution, which is continuously bubbled with
hydrogen gas at one atmospheric pressure. According to the Nernst equation (1), the electrode potential of
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
this electrode depends logarithmically on the concentration of the hydrogen cations [H +], i.e., on the pH
of the solution. Since it is very difficult to maintain and calibrate such a hydrogen electrode another type
of pH-sensitive electrode is used with similar properties. This is the glass pH electrode, whose
construction is shown in Fig. 4.4.2.
Fig. 4. 4. 2. The structure of ionselective electrode (left) and pH-sensitive glass
electrode (right).
The glass pH-electrode comprises a glass tube and a membrane, sealed at its bottom. The
membrane is made up of very thin, lithium containing glass. This glass membrane allows selective
diffusion of hydrogen cations through it while, at the same time, prevents the transfer of other ions. The
inside auxilliary electrode system represents a solution of 0.1 M HCl and a silver non-polarisable
electrode. In respect to the medium the glass pH-electrode has an electrode potential, Eel, which depends
on the activity, аН+, of hydrogen ions according to the formula of Nernst: Eel = Eelo + (RT/F).ln (аН+). Here
Eelo is the standard electrode potential, corresponding to the standard activity of hydrogen cations, аН+ = 1
mol.
According to the above formula the electrode potential of the glass pH-electrode depends on the
temperature of tested medium, due to the multiplier RT/F. In electronic pH-meters, this temperature
dependence is compensated automatically or manually, by seting up the temperature value by a variable
potentiometer.
When the activity аН+ is low it is equal, with sufficient accuracy, to the concentration of the
hydrogen cations [H+]. Using decimal, instead of natural logarithm, the Nernst formula for the electrode
potential of the glass pH-electrode at 20°C yields:
Еel = Еelo + 0.058 lg [H+] = Еelo - 0.058.pH
Eel is actually the electric voltage between the glass and reference electrode, measured with
millivolt meter calibrated directly in the units of pH. For example, when the pH of the solution increases
by a unit, the potential of the glass electrode will decrease by 58 mv. In this way, the pH of the solutions
can be measured in the range from pH 1 to pH 14.
Many modern pH-meters use the so called combined electrode, which represents a glass and
reference electrodes both mounted in a common body. This allows reduction in the volume of the tested
sample.
The glass electrode is widely used in the measurement of pH, due to its accuracy and
convenience. Furthermore, its indication does not depend on the presence of additional dissolved
substances – electrolites, oxidants, reducing agents, colloids. Its main drawback is the very high
electric resistance of the glass membrane reaching the value of 1000 M. This requires the
measurement of the electrode potential to be conducted using special amplifiers with high-impedance
input.
3. Determination of the gas concentration in a liquid media and blood using gas electrode.
The gas electrodes are similar to the ion-selective electrodes. They also consist of a housing, selectively
permeable membrane and internal auxiliary electrode system. The housing contains a suitable solution in
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
which two electrodes are immersed - measuring and reference (comparative, non-polarisable) electrode.
At the bottom of the housing a thin membrane is attached contacting the tested (blood) sample. The
membrane is made up of a special polymer which selectively permeates the tested gas. For example, the
polyethylene membrane is permeable for O2, while the teflon membrane permeates CO2. In the oxygen
electrode, known as Clark electrode (Fig. 4.4.3), the oxigene passes from the sample liquid through the
polyethylene membrane and oxidizes the measuring electrode which is made up of platinum. This
generates a direct electric current between the two inner electrodes, which is measured with a sensitive
microampermeter. The amount of current is proportional to the concentration of O2 in the sample. In the
electrode for CO2 (Fig.4.4.3), the gas passes through the teflon membrane and forms carbonic acid in the
internal solution. In turn the carbonic acid dissociates and acidifies the internal solution. The two inner
electrodes represent a glass and reference electrodes which measure the change in the pH of inner
solution. The latter value depends on the concentration of carbonic acid formed, respectively, of CO2 in
the blood sample. Such gas electrode is used to determine the gas content of the blood as a small volume
of blood sample is brought into contact with the teflon membrane of the electrode.
Fig. 4. 4. 3. Oxygen electrode
(right) and gass electrode for CO2
(left).
Hyperbaric oxygenation is
applied for people with insufficient
oxygen supply in their blood (coronary
disease, radiculitis, bleeding in the
brain). The patient is placed in a
pressure chamber with a increased
pressure of oxygen in order to more intensely saturate its blood with oxygen. In these case, the oxygen
content of the blood is controlled by the above described Clark electrode.
Microelectrodes are used for measuring biopotentials of cells with larger dimensions (animal
cells, plant cells) with the exeption of smaller sized mammal erythrocytes and bacteria. Microelectrodes
are constructed similarly to the non-polarisable silver electrode (Fig. 4.4.1) and contain external glass tube
and internal non-polarisable Ag+/AgCl electrode. The front end of the glass tube is thined and resembles a
highly tapered glass capillary with diameter of several μm. Under microscope and using a
micromanipulator this sharp end pierces the plasma membrane of tested cell. Accordingly, the electric
potential of the cytoplasm becomes equal to the potential of the silver electrode. This potential is
measured in respect to a ususal, non-polarisable electrode placed in the extracellular medium.
The measurement of redox (oxidation-reduction) potentials is important for biochemistry. Assume
a redox system is formed consisting of a couple of substances (oxidant and oxidizable substances),
dissolved in a solution. A large number of biochemical processes are of this kind, for example the transfer
of electrons in the oxidation chain of mitochondria. Electrons will constantly pass from the oxidizable
substance to the oxidant. If a suitable metal electrode is immersed in this solution, its contact surface will
acquire an electrode potential corresponding to the ability of the redox couple to release electrons. The
potential of this electrode (redox potential) is measured with the help of additional non-polarisable
electrode.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
4.5. Physical bases of passive and active electrodiagnosis. Electrography and evoked
potentials
The cytoplasm of cells has an electrical potential which differs greatly from that of the
extracellular medium. The electrical voltage across the both sides of plasma membranes is equal to the
difference between these two potential. Historicallly, the transmembrane electric voltage is denoted as
biopotential of cells. The main reason for the generation of this electrical voltage is the higher
concentration of potassium ions (K+) into the cells compared to the concentration outside the cell. In nonexcitable cells and in excitable cells at rest the biopotential is constant and equals about 60-70 mv being
negative in the cytoplasm. The biopotential of cells with larger dimensions can be measured with a
microelectrode inserted in their cytoplasm, with respect to an external reference electrode.
Excitable cells (nerve, muscle and receptor cells) may briefly change their biopotential. Upon
irritation the excitable cells change their biopotential which become abount +30 mv with positive sign (+)
in the cytoplasm. This change in transmembrane voltage is referred to as electrical depolarization of cell.
The depolarization of cells is very important event because it reflects the change in their biological
activity.
Fig. 4. 5. 1. Generation of the
biopotential of excitable tissue. The left
side of the tissue is depolarized and
negatively charged, the right side is at
rest and positively charged.
In tissues and organs, consisting
of a large number of excitable cells (heart
muscle, brain) the depolarization may
take place in an isolated group of cells
located in distinct, separate parts of the
body (Fig. 4.5.1). Thus, at a given moment the body is divided into two parts, one being irritated and the
other at rest. Electric voltage arises between the two parts of the body, which generates electric current.
Cell membranes, however, are electrical insulators, so only electrical charges located outside the cells are
of importance for this voltage and current. Only they participate in the flow of electric current through the
tissues. Viewed from the outside, the excited part of the body is loaded with negative electric charge -Q,
and the resting part with a positive charge + Q. The potential difference that arises between both parts of
the body has a significant value of about 100 mv and is called biopotential of tissue (organ). This spatial
separation of electric charges inside the body can be represented by an electric dipole. This is a vector
with magnitude P = Q.d and direction from (-) to (+), i.e., from the excited to the resting part of the body
(Fig. 4.5.1). In this formule, d is the distance between the excited and a resting part of the tissue.
The electric dipole of the tissue represents a source of electric voltage (something like a battery or
accumulator). Both spatially separated charges of the dipole generate strong electric field within the space
both at close distance and far away from the dipole. Especially strong is the electric dipole of the heart,
because the heart muscle contains a large number of excitable cells. Because the tissues surrounding the
heart are electrically conductive, this voltage is transmitted from the heart to the surface of the body where
it can be measured with two electrodes contacting the skin. The voltage between these electrodes is low (1
mv or less), therefore, its power must be amplified using appropriate electronic amplifier before it can be
registered.
Depending on the functional activity of the body, the local depolarization moves from one part of
the tissue to another. Accordingly, the biopotential of the tissue varies in magnitude and direction over
time. This means that the electric dipole, P, of the tissue and the electric voltage between the two outer
electrodes will also change over time. Fig. 4.5.2 shows how the local excitation of a tissue (organ) moves
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
and, accordingly, the electric voltage between the two outer electrodes E1 and E2 varies. E1 is the
supporting or comparative electrode, while E2 is the measuring electrode. When the front of excitement is
approaching the measuring electrode, E2, the potential of this electrode becomes more and more positive,
and when the front is distancing the potential of E2 decreases and turns negative. The electrodes E1 and E2
are termed as electrical leads.
Thus, the electrical activity of an organ carries clinical information for the status and function of
this organ. For diagnostic purposes, the biopotentials of individual organs (heart, muscle, stomach, brain,
eye) are recorded as a function of time. The shapes of the resulting curves contain information about the
status of these organs. This method for electrodiagnosis of organs is known as passive electrography.
The passive electrography of heart (electrocardiography, ECG) is based on a similar method of
measurement. The periodic contractions of the heart are caused by regular electrical impulses generated in
its sino-atrial node (point A in Fig. 4.5.3). For a specified time (40 ms) the generated impulse reaches the
atrioventricular node (point 1 in Fig. 4.5.3) and continues to spread along the conductive tissue of the
heart. Fig. 4.5.3 shows the time in ms, which the pulse spent to travel from the sino-atrial node to the
various points of the heart and their depolarization.
Fig. 4. 5. 2. Change in the
biopotential of excitable tissue.
This biopotential equals the
difference between the electric
potentials of the two electrodes, E1
and E2. The different phases of the
excitement wave are shown at left,
from top to bottom. The measured
biopotential
is
shown
as
dependent on the phase of
excitement at the right.
For each cardiac cycle, the
electric dipole of the heart varies in
direction and size, as its head
describes the complex spatial
trajectory - vectorcardiogram (Fig.
4.5.3).
The
vectorcardiogram
contains two circles. The inner circle
is due to the depolarization and
contraction of the atria and the
external circle corresponds to the
depolarization and contraction of the
chambers. The projection of this
vector on the spatial axis linking two
outer
measuring
electrodes
represents electrical voltage that can
be amplified and recorded as a
function of time – bipolar
electrocardiogram. Fig. 4.5.4 shows a bipolar electrocardiogram obtained by measuring the electric
voltage between two electrodes (leads), one placed on the left hand and the other on the right hand of the
patient (Ist electrocardiographic limb lead). Fig. 4.5.4 also shows the conventionally defined segments on
this electrocardiogram and their time intervals who have clinical significance. All three
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
electrocardiographic limb leads (I: left hand - right hand, II: right hand-left foot and III: left foot - left
hand) form the so called Einthoven's triangle. The registration of the three linear electrocardiograms on
these three axes allows obtain the vector cardiogram of the heart.
The fig. 4.5.4 indicates several peaks with clinical importance. The peak P corresponds to the
electric excitation (depolarization) and contraction of the atrium; QRS - complex corresponds to the
depolarization and contraction of the myocardium and both chambers. It has been found that the T-peak
describes the recovery of the rest potential (repolarization) of the heart. In some cases, an additional peak
is registered after the T peak, denoted by the letter U.
An important variable in the passive electrodiagnosis of heart is so called electrical vector of the
heart. Conventionally, this variable means the vector of the electric dipole of the heart at the moment of
strongest depolarization of the heart muscle. In fig. 4.5.3 it is the vector OR (the segment connecting
points A and R). The direction defined by this vector is called electrical axis of the heart. It is defined by
the angle that the electric vector of heart concludes with an imaginary horizontal line passing through the
heart (fig. 4.5.5). With a normal heart it is directed from the right shoulder to the left leg (an angle of
about +30°). At some patients this angle may have strongly different values in case the heart is displaced
or rotated compared to its normal position, or one of its walls has greater thickness.
The biopotentials of muscle tissues, brain, stomach, and the eye retina are registered in similar
way.
Fig. 4. 5. 3. Cross section of the heart (left) and the movement of the excitement in different
parts of the heart, numbered as points 0 to 4. The vectorcardiogram of the heart (right) indicats the
change of the electric dipole of the heart over time. The digits in the circles show the time (in ms)
when the excitement reachs the given part of the heart.
The activity of brain cells is also accompanied by a change in the polarity on the brain surface
(wave of electrical activity) and generation of electrical currents. These brain biopotentials are registered
by electrodes placed firmly on the patient's head and connected to electroencephalograph (EEG). The
latter enhances the potential differences and presents them as a function of time on screen. The registered
potentials have different amplitudes (between 1 and 10 μv) and frequencies. Depending on their
frequencies the brain potentials were initially designated as alpha waves (8-13 Hz) and beta waves (14-40
Hz) (Fig. 4.5.6). Very fast waves up to 100 Hz are rarely registered and referred to as gamma waves.
Later, waves with very low frequencies have been registered, referred to as theta (4-8 Hz) and delta waves
(below 4 Hz).
The electroencephalography measures the level of electrical activity of various areas of the brain.
The pulses with lower frequencies have greater amplitudes and cover wider area of the brain. The brain
areas with increased amplitude of the brain waves are presented on screen with a different color in respect
to the areas where these waves are absent. Alpha waves are generated in a state of sensory rest, relaxation
of the mental activity and in a sense of wellbeing and comfort. Their absence is a sign of stress and
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
anxiety. Beta waves are influenced by the stimulation of various sensory organs and brain activity.
Absence of beta waves is a sign of depression, poor attention and poor memory. Theta waves are
characteristic of the state of hypnosis and sleep with dreams. Delta waves are recorded in deep dreamless
sleeps. It was found that the EEG recording has a characteristic shape in some conditions and diseases,
such as fear and anxiety, poor sleep, epilepsy, stroke, brain tumor. EEG also allows definition of brain
death in patients, which may serve as a donor of organs.
Fig. 4. 5. 4. Bipolar electrocardiogram in electrocardiographic limb lead I: left hand - right
hand. For one cardiac cycle the electrocardiogram contains five points, marked with the letters P,
Q, R, S and T. The points 0, 1, 2, 3 and 4 correspond to the moments of excitement, shown in Fig. 4.
5. 3. Right: normal values of the indicated time intervals and the linear segments.
Exept the biopotentials of muscle and nerve cells, additional slowly varying potential differencies,
sometimes called direct current biosignals can be measured in tissues. Such biosignals occur in following
cases: in damaged tissues where potassium ions out leak from the cells (up to 50 mv), between the
different parts of the brain (less than 1 mv), skin (up to 10 mv), inner ear (about 80 mv), and endocrine
glands, such as thyroid gland (60 mv).
Fig. 4.5.5. Electric vector (electrical axis) of the
heart and its determination by the angle, he concludes with
the horizontal axis.
The electrography of different of organs (heart, lung,
brain) which can not be controlled by the human will is used in
criminology to test the possible implication of the person in
certain outlaw activities (lie detector). During the test the
person is asked a question or a picture is displayed to him,
revealing this activity. If the person is involved in this acitivy, the electrical signals of its brain, heart and
breathing change unconsciously. These changes can be used to substantiate the participation of the tested
person in a particular crime.
In cells with larger dimensions (nerves and muscles) the depolarization may be restricted in a
local area. Thus, at a given moment a local depolarization of the nerve cell can arise, generating local
electric impulse (nerve impulse). Starting from a given place, the nerve impulse subsequently spreads
along the stem of nerve cell (the nerve axon) at a certain speed. As the nerve cell ends at a particular
innervated organ (muscle, gland) the nerve impulses reach the organ and controls its function. Similarly,
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
the connection between a nerve cell and its innervated organ can be tested by the method of
electrostimulation using artifitial signals instead of nerve impulses. This method represents an active
electrodiagnosis and it is usually applied to organs (e.g. skeletal muscles), whose function is controlled by
the nerve impulses generated in distant nerve center located in the brain or spinal cord. The method
includes initial irritation of the nerve center with suitable external physical stimulus and subsequent record
of the elicited electrical response (evoked potentials) of the innervated organ.
Two types of stimulation which use electric and magnetic impulses are known in the medical
practice. The electric stimulation uses electrical stimulus signals of high amplitude (up to 2000 v) and
short duration (10 ms) which are fed by surface contact electrodes (Fig. 4.5.7). These signals stimulate
nerve centers in the brain or spinal cord to generate nerve impulses. These impulses travel down the
prolonged nerve axon to the corresponding muscle of a given limb causing its depolarization (evoked
potentials) and contraction with time delay, t. The respective evoked potentials, also known as motor
potential or M-response are registered with additional local electrodes (e.g. needle electrodes). In a similar
manner, a given site of the nerve can be irritated and the evoked response be registered at the distant end
of the nerve with time delay, t. If L is the distance between the irritated and tested sites of the nerve, then
the v = L/t is the speed of propagation of the
nerve impulses. The time delay, t, and
propagation
speed
present
important
information in a number of diseases.
Fig. 4.5.6. Different types of waves,
describing the electrical activity of the
brain.
The evoked potentials of the limb
muscles may also be registered by irritation of
the respective centers of the spinal cord
through pulsed magnetic field. This is called
transcrenial magnetic stimulation. The
stimulating magnetic pulse has a duration of
about 50-100 s and is produced by
electromagnet under a voltage 200 v. After
the magnetic stimulation a nerve impulse is generated in the pyramidal cortex of the brain which reaches
the distal sections of the arm and leg for about 20 ms. This is the central motor conduction time. The
parameters of evoked potentials (M-response) in norm are: amplitude about 1-5 mv and time delay
(latency) of about 30 ms.
Fig. 4.5.7. Position of electrodes in the electrical stimulation of
motor potentials in limbs.
The human eye has an electric potential with positive (+) sign on its
front side and a negative sign (-) at its back surface. The potential difference,
referred to as biopotential of the retina, can be measured and recorded. When the eye is irritated with
pulsed light, the retinal potential will periodically change. The form of the registered visual evoked
potential has an important diagnostic value in eye diseases.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
4.6. Elements of bioelectronic devices: electronic amplifiers of biopotentials, differential
amplifiers, converters. Generators of discrete electrical signals. Pacemakers and defibrillators.
Systems for recording and visualization.
Biopotentials are electrical voltages that arise between two metal electrodes in contact with a
bioobject, e.g. human body, neural and muscle tissue. They reflect the electrical activity of the bioobject
providing information about its function and status. The diseased organs (heart, brain) change their
biopotentials in a characteristic way. The measurement of biopotentials provides valuable clinical
information.
The biopotentsials are measured by two electrodes attached to the patient's body; one is the
measuring (active) electrode and the second is comparative (passive, ground) electrode. Most often, these
electrodes have flat surfaces and contact the skin through a layer of conductive paste. This type of contact
reduces the contact resistance between the skin and the electrode subduing the amplitude of electrical
noise. The motor potentials are measured with needle electrodes, inserted into the tested muscle. The
electrodes are most often made of stainless steel and silver alloys.
Measurement of biopotentials however represents a serious technical problem in view of the
following circumstances:
1. Biopotentials are electrical signals with very small magnitude (from 10 V to a few mV or tens
of mv). By amplitude they are comparable to electrical noises, which are unnecessary impulses transferred
from the electrical sets and mains. This requires separation of the signals from the noise and their
enhancing through appropriate electronic amplifiers to improve the signal / noise ratio.
2. Biopotentials are slowly varying, low frequency signals, similar to the electrical noises, and
3. The tested bioobjects usually have very large internal resistances, Rin, hence, only a small part
of their biopotentials can be extracted and measured (see Fig. 4.6.3).
These difficulties are overcome using suitable electronic amplifiers of biopotentials.
Fig. 4.6.1. Block diagram of
electronic amplifier.
The electronic amplifier is a
device that receives electric signals on its input and transmits them to its output in unchanged form with
increased amplitude (power amplification without distortion) (Fig. 4.6.1). The input and output signals are
usually of analog type, i.e., not coded in digitized form. Let us denote the amplitude of the input signal by
Uinput and the amplitude of the amplified output signal by Uoutput. The gain by voltage is defined as: Ко =
Uoutput /Uintput. Similarly defined are the gains by current and power. The amplifier contains active elements
(semiconductor transistors, operational integrated circuits, vacuum-tube valves), which are able to amplify
the electrical signals at the expense of the energy of the direct current. This energy is taken from the
accumulators, batteries but most frequently from the so called alternating current rectifiers.
Amplifiers that maintain its gain, Ко, at constant level in wide frequency range are called broad
band amplifiers. Depending on the frequency domain, where they amplificate they are designated as audio
amplifiers (20 Hz - 30 kHz) and video amplifiers (20 Hz -5 MHz).
Amplifiers that can amplify only signals with a given frequency and suppress the signals (noises)
with other frequencies are called resonance amplifiers.
Medical electronic equipment often includes the so called direct current (DC) amplifiers which
can only amplify signals of very low frequency including DC signals.
Modern electronic amplifiers are most frequently made as miniaturized integrated circuits, which
include dozens of transistors, but have dimensions of a few millimeters.
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
The properties and function of a given electronic amplifier can be improved applying a feedback
in it (Fig. 4.6.2). This means a part of the enhanced output voltage to be returned back to the input of the
amplifier. Lets  (a number between 0 and 1) is the portion of the returned output voltage. In case this
portion is added to (or subtructed from) the input signal, we have positive (respectively negative)
feedback. Although the negative feedback reduces the gain, the amplifier functions much better because
its input resistance increases, its working frequency range expands and the distortion of the signal is
reduced. When  = -1 (full negative feedback) К = Ко/(Ко+1), and the amplifier operates as a voltage
follower, it provides no voltage gain. However, the input resistance of this amplifier strongly increases:
Rinput = Rinputo .(1 + Ко), which in many cases is very useful. In these formulas, Ко and Rinputo are the
voltage gain and the input resistance, correspondingly, in the absence of feedback. By applying a deep
negative feedback, amplifiers with very high input resistance are obtained. Such are the amplifiers used in
the measurement of biopotentials and the pH with glass electrodes.
Fig. 4.6.2. Implementation of
feedback
in
the
electronic
amplifiers.
Nevertheless
the
gain
increases with positive feedback it is
used very rarely, because the ampifier becomes unstable. When  = +1 (full positive feedback), K  
and the amplifier becomes a voltage generator. All generators of electrical signals represent electronic
amplifiers, in which a full positive feedback is introduced. In addition, the voltage generators contain a
resonant circuit (capacitor, C, connected in parallel with a coil, L), which amplifys only signals with a
certain frequency (resonance frequency) suppressing all others. At their output these amplifiers elicit
alternating voltage with a frequency equal to the natural frequency of the resonant circuit.
Fig. 4.6.3. Schematic electrical circuit
for measurement of biopotential.
Fig. 4.6.3 shows the block diagram for
measurement and amplification of the biopotential, ε, where Rin is the internal resistance of the bioobject
and Rinput is the input resistance of the amplifier. Applying the Ohm's law for the input circuit of the
amplifier we obtain Uinput = I.Rinput = ε.Rinput/(Rin +Rinput) = ε /(1+ Rin/Rinput). When Rin /Rinput   then
Uinput  0, which is highly undesirable because the biopotential wont be amplified. It is desirable that Rin /
Rinput 0, then Uinput  ε and the biopotential will be amplified. In this case we say that the amplifier is
accommodated well with the biobject. Such amplifiers having high Rinput (several G) contain deep
negative feedback and are designed with difficulty. In electrophysiology it is considered optimal when
Rinput is 10-20 times greater than Rin.
Biopotentials are measured and amplified by means of appropriate, two step bioamplifiers. These
amplifiers contain differential amplifier, consequent to a voltage follower. In order to obtain very high
Rinput, the first step of amplifier represents a voltage follower. To improve the signal to noise ratio, the
second step contain a differential voltage amplifier. This step is the most important part of the amplifier,
because it enhances the useful signal (the tested biopotential) and suppresses noise signals.
The differential amplifier (Fig. 4.6.4) has two symmetric inputs, one inverting (INPUT1) and the
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other non-inverting (INPUT2). A signal fed to the non-inverting input does not change its phase when
coming out of the amplifier, while a signal fed to the inverting input changes its phase to 180° when it
comes out of the amplifier. There will be amplification when two, out-of-phase signals are fed to these
inputs, because the inverting input will reverse the phase of the signal and two amplified, in-phase signals
will appear at the output (Fig. 4.6.4). The measurement and amplification of the biopotentials of heart,
brain and others parts of human body is carried out in this way. By contrast, there will be no amplification
when an electrical noise is submitted to the inputs of the differential amplifier, because such noise
represents two in-phase signals (Fig. 4.6.4). Thus, the differential amplifier enhances the useful signal and
attenuates the noise. In the past, the patient was placed in a grounded Faraday cage in order to suppress the
noise, which is now unnecessary.
Fig. 4. 6. 4. Diagram of a differential amplifier built with transistors (left). Selective
amplification of two out-of-phase signals and inhibition of two in-phase signals (right).
The bioamplifiers usually contain third final step, which is a power amplifier enhancing the power
of output signal. This step enables the biosignals to be processed, registered and stored. In the past the
biopotentials were registered by ink pen, writing on a moving paper tape, using a fast-acting chart recorder
which produces minimal distortion of the time profile of the signal. Another way of registering used
thermal recording, in which the paper tape was coated by a wax layer and the stylus was heated above the
melting temperature of the wax (around 70°C). When the stylus touched the paper, the wax melted and a
point was scored.
Fig. 4.6.5. Cross-section of the
cathode ray tube.
Another way of processing
biopotentials is to show them as a function
of time on the screen of an electron-ray
tube. This method ensures fast performance
and lack of distortion.
Electron-ray tube (cathode-ray
tube) represents vacuumized (air evacuated)
glass tube with a screen, coated by a layer of zinc sulfide (Fig. 4.6.5). A source of focused beam of
accelerated electrons (electron gun) is mounted inside the tube. The beam falls on the screen and causes a
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
point to glow due to the cathode luminescence. X-plates and Y-plates are two electrical capacitors that
deflect the beam in the horizontal and vertical directions, respectively. An increasing voltage is fed to Xplates, causing the beam (luminescent point on the screen) to move horizontally with constant speed.
Meanwhile, the amplified biopotential is fed to the Y-plates, causing the illuminating point to describe the
change of biopotential with time.
In some cases two increasing voltages are fed to the X- and Y-deflection plates, causing the beam
to describe any point on the screen line by line. At the same time, the tested signal changes the intensity of
the beam, respectively, the brightness of the illuminating point on the screen. Thus, a picture of bright and
dark spots is created on the screen. These cathode-ray tubes are used in computer tomography, in scanning
electron microscopes and more.
Recently, the electron-ray tubes are replaced by the much more convenient liquid crystal screens.
Monitors with liquid crystal are flat, take up much less space and are much lighter than those with
cathode-ray tube.
In modern electromedical apparatus the biopotentials obtained at the output of bioamplifiers are
further converted in digitized form. This digitalization consists in transforming the analog (continuous)
type signal into a consequence of electric impulses. At any moment the amplitude of the analog
biopotential is coded as frequency of the produced pulses. This coding is performed by analog-to-digital
converters (ADCs). The amplified and digitized biopotentials are finally fed to a computer for processing,
presentation and storage of information they contain.
Fig. 4.6.6. Shape of the commonly used in medicine impulse currents - exponential,
rectangular, and amplitude-modulated.
In modern electrocardiographs the biopotentials are digitized and processed by means of
integrated computer. An appropriate program is installed in the computer that measures the amplitudes of
the peaks and the time intervals between them, and reports on the possible deviations in the obtained
values from the norm.
For medical purposes different types of generators are used which produce electrical signals with
the required shape, frequency and amplitude. Conventional generators produce sinusoidal voltage while so
called pulse generators generate pulses of rectangular, triangular and other shapes (Fig. 4.6.7). They are
used for treatment in physiotherapy, as well as for electrical stimulation.
An important example of pulse generators is the pacemaker (cardiostimulator) which generates
electrical impulses with rectangular shape, duration 0.8 - 3 ms, frequency 1 - 1.2 Hz and amplitude of 1-3
V. The pacemaker has two output electrodes, the positive "+" electrode represents a spring, which is
inserted into the aorta, and the negative "-" electrode touchs the human body. The generated signals
supplied to the positive electrode cause synchronous contractions of the heart muscle. Pacemakers are
implanted subcutaneously in patients whose sinus node generates nerve signals with subcritical frequency
(less than 40 beats per minute). The main function of pacemaker is to increase and stabilize the heart rate.
There is possibility for changing the heart rate depending on the physical activity. Pacemakers are
Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
powered by lithium-iodine batteries with electromotive voltage 5 v. Their energy capacity of about 1.5 Ah
is sufficient for a period of 6 to 10 years.
Fig. 4.6.7. A pacemaker, used to stabilize cardial rhythm.
In some cases (heart arrhythmia, electrical and lightning shock,
heart surgery), the synchronous contractions of individual heart muscle
fibrils is disrupted. This condition is called fibrillation of the heart, whereat
the stroke volume of ejected blood is greatly reduced. This dangerous condition can be terminated using a
defibrillator, which generates a single electric impulse with short duration (8-16 ms) and great power
(amplitude 500-700 v, current 15-20 A). The defibrillator consists of capacitor with a capacity, C,
connected in series to a coil with inductance, L, and two terminal electrodes. To apply the defibrilatying
pulse, the capacitor is firstly charged to the specified voltage and then, when necessary, discharged
through the coil by manually touching the two electrodes to the patient's chest. The discharge elicits a
power current pulse with duration (time constant), τ = 1/LC. This impulse passes through the chest region
of the patient and causes simultaneous depolarization of all the fibrils with subsequent synchronization of
their contractions.