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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
TEXTBOOK OF MEDICAL PHYSICS
FOREWORD
Many processes in the human body represent physical phenomena or have significant physical
aspect. Such processes will best be understood by means of the physical concepts and laws. These include
the flow of blood; perception of sound, light and heat signals; respiratory activity of lung; deformation of
various tissues; maintainence of constant body temperature, tissue damage by external physical factors,
the use of some physical factors for therapy and so on.
Studying Medical Physics, the student will be able to understand the basics of many new methods
of research, diagnosis and treatment that are physical in nature. These include the methods of spectral
analysis (absorption and fluorescence spectroscopy), X-ray microanalysis, mass spectroscopy,
measurement of biopotentials and electrode potentials, diagnostic methods using X-rays and ultrasound,
optical and electron microscopy, radioisotope diagnostics, laser methods for diagnosis and treatment,
methods of radiotherapy, differential scanning microcalorimetry, methods for separation of molecules
(electrophoresis, centrifugation, membrane technology) and so on.
The modern physician needs to know not only the structure and functions of the organs of the
human body and their pathological disturbances. He must know, to the necessary extent, the medical
instruments, devices and apparatus he uses to collect information about the structure and activities of the
various organs of the human body and to treat their diseases.
Electrocardiograph and electroencephalograph are examples of modern medical instruments
which measure the electrical activity of the heart and the brain, respectively, and help diagnose the
diseases of heart and brain. Spirometer measures the activity of the lungs and diagnoses diseases of the
respiratory system; X-ray machine produces radiographs of the internal organs; scintillation counter
detects tumors by measuring the disturbance in the uptake of radioisotopes by tissues. Computerized Xray tomography detects disorders in the structure of organs that are overshadowed by normal tissues and
therefore become invisible to conventional radiography. Ultrasonic devices register "echo" of the
ultrasonic waves passing through the human body enabling the physician to detect the position of the fetus
during pregnancy, disturbances in peripheral circulation and tumors in the brain. Endoscope allows both
observation and surgical procedures practically within every cavity of the body.
In modern hospitals for intensive care the hospitalized patients can be controlled automatically
through measurement systems allowing the electrocardiogram to be automatically obtained together with
the data for blood pressure, pulse, body temperature, respiratory rate and blood components. In some
monitoring systems, the information from a large number of patients is presented to a monitor in the nurse
central station. Once any of these important health indicators changes and comes out of the normal limits
an alarm is switched on.
In this textbook the usage of formulas is limited to the minimum. In spite, correlations between
different variables are explained in words and with the help of great number of graphics and drawings.
The discipline Medical Physics aims to provide basic physical knowledge for the medical
education of future medical professionals.
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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
CHAPTER 1. THERMODYNAMICS
1.1. Heat and temperature. Thermal and internal energy. Measurement of heat and
temperature in living organisms. Medical and biological applications
All bodies are made up of atoms, molecules or ions involved in an extremely intense movement
with chaotic character called thermal motion. At equilibrium, the temperature of the body is a measure of
the average kinetic energy of the constituent particles (molecules), i.e., a measure of the average speed of
their thermal motion. For monoatomic molecules this is the speed of their forward, translational
movement. In the case of two- or polyatomic molecules, besides the speed of forward movement, it
includes the speed of rotation and vibration of constituent atoms. Temperature is an intensive quantity. It
does not depend on the mass of the body and depends only on how great is the average speed for forward
displacement, vibration and rotation of molecules. Raising the temperature results in an increase of the
molecular motion and acceleration of the processes in which these molecules are involved. Therefore, the
temperature is an important physical parameter that affects many physical, chemical and biological
processes (diffusion, chemical reactions, cell metabolism).
Table 1.1.1. Temperature scales with practical signifficance
International practical
(European)
0 оС
100 оС
Number of divisions
between the reference
points
100 degrees Celsius оС
Thermodynamical
American
273,15 К
32 оF
373,15 К
212 оF
100 degrees Kelvin К
180 degrees Fahrenheit оF
Scale
Reference points
Ice melting
Boiling of water
Fig. 1.1.1. Relationship between the
most frequently used temperature scales.
The values of the temperature can be
determined using a reference body which,
depending on its temperature, could be found
in several well-defined and reproducible
states. Water is best suited for this aim as it
possesses two such states, boiling and
freezing. The measured temperature may be
represented by several temperature scales,
that of Celsius (C), Fahrenheit (F), Kelvin
(K) and others (table 1.1.1). Each scale
contains two key (reference) points
corresponding to the temperature of ice
melting and water boiling. The temperature
values of the reference points and the
distance between them are subject of choice
at the different scales. Conversion of the
temperature values from one scale to another
can be made graphically (Fig. 1.1.1) or using
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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
the following formulas: tC =T K - 273.15 = 5/9 tF – 32.
In many processes, temperature is an essential parameter and must be measured very accurately.
This is done with a suitable thermometer. To obtain reliable results it is of essential significance the
sensitive end of the thermometer to be in good contact with the tested body and its mass to be small
enough compared to the latter. The change in temperature causes a change in some physical parameter of
the thermometer - volume, pressure, etc. The magnitude of the temperature change can be judged by how
much the corresponding physical parameter has changed. In 1595 Galileo Galiley from the city of Pisa,
Italy, invented the first thermometer, which used the volume expansion of alcohol when heated.
Liquid thermometers use the extension of appropriate liquid placed in a thin capillary tube parallel
to a scale, graduated in the selected temperature units. The higher the temperature, the greater is the
expansion, and the readings are more. Liquid mercury is used to measure temperatures in a wide range
from -40°C to 356°C while organic solvents are suitable for much lower temperatures (ethyl alcohol to 80°C and pentane to -200°C). To measure the temperature of human body special mercury thermometers
are used having a larger reservoir of mercury and a thiner capillary tube. This increases the sensitivity and
accuracy and allows the measurement of temperature changes in a very narrow range around the
physiological temperature (35-42°C) with divisions as low as 0.1°C.
In some pathological conditions body temperature varies between two limits, maximal and
minimal ones. To measure the achieved maximal and minimal temperatures special kinds of thermometers
are used called maximal and minimal thermometers. They are usually both combined in a single container.
Besides with liquid thermometers, the principle of thermal expansion is also applied in gas and
bimetallic thermometers. Gas thermometers consist of a metallic balloon filled with a suitable gas and a
manometer measuring the gas pressure. With increasing temperature, the gas pressure increases and
manometer readings indicate the values of temperature. The sensitive
element of the bimetallic thermometers comprises two plates made up
of different metal alloys. The plates are both attached to each other
using one of their ends; the other end is left free to expand in
accordance to temperature. When heated the plates expand differently.
This causes spacing of their free ends, which is taken as a measure of
the temperature.
Fig. 1.1.2. Schematic diagram of the calorimeter
The temperature can also be determined by measuring the
electric voltage of a thermocouple or the resistance of a resistor. The thermocouple consists of two wires
made up from different metals, metal alloys or semiconductors. The wires are connected at one end which
is the working or sensitive joint. For example, the iron-constantan thermocouple contains a wire made up
of iron and another wire of constantan alloy. If the working joint is placed at a temperature (t), higher than
the temperature (to) of the two free ends, an electrical voltage, U = k. (t - to), is generated between the free
ends of the thermocouple. This voltage is measured and presented directly in °C. The main advantage of
this thermometer is that the size and mass of the working joint are very small allowing the measurement of
the temperature of too small objects and measurement of surface temperature, e.g. the skin temperature of
human body, etc. Semiconductor thermocouples generate much higher voltage than the metal ones but can
not function at higher temperatures. For greater sensitivity, instead of a single thermocouple a bundle
containing great number of thermocouples is also used. They are connected in series to each other
(thermobatery) to increase the voltage responce. The semiconductor thermobateries generate yet higher
voltage than metal ones.
The resistance thermometers rely on the temperature dependence of electric resistance. Their
sensitive element is a metal or semiconductor resistor. Platinum resistor thermometer represents a thin
coiled platinum wire. Electrical resistance of this resistor increases with temperature virtually linear.
Measuring this resistance with the help of Wheatstone bridge (a sheme of four resistors, one of which is
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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
the platinum resistor), we get a value proportional to the magnitude of temperature in °C. This
thermometer allows measuring temperatures in a very wide range (from -100°C to + 1200°C) with
accuracy about ± 0.01°C. In some cases, instead of platinum, a semiconductor resistor (thermistor) is used,
which has a higher sensitivity.
The surface temperature of human body can be determined by applying a thin layer of liquid
crystal, usually composed of cholesterol esters. Depending on the local temperature, the liquid crystal of
thermometer changes its structure and, accordingly, its color. The resulting color picture can be
photographed and kept as a document.
Human physiological systems can function properly only in a narrow temperature range around
the normal body temperature of 36.7°C. Still tolerable for human life are the short time variations in body
temperature between 33 and 42°C – the temperature limits of life for human. At temperatures greater than
43°C cell death and tissue necrosis rapidly occur. Hyperthermia (43°C and more) is used as a technique
for local necrosis of tumor mass. Below 33°C (deep hypothermia) speech and hearing are distorted and the
contraction of heart and various other muscles is blocked. Below 20°C the conduction of nerve impulses is
interrupted. This temperature effect is applied for local anesthesis in the microsurgery of the eye, teeth,
nerve endings, and the like. Hypothermia slows down the metabolism and decreases the spending of
nutrients. This is used in the brain surgery, where it is necessary to suspend the brain blood circulation cryosurgery. For the purpose of blood transfusion, low temperatures (+4°C) are used for prolonged
storage of blood banks without cryoprotectants. Negative temperatures from -10°C to -30°C are used for
long term storage of cells (blood cells, germ cells), tissues and organs in non-freezing media containing
cryoprotectants (glycerol, DMSO, ethylene glycol). Ultra-low temperatures (liquid nitrogen) are applied
for local necrosis of superficial tumors.
Fig. 1.1.3. Schematic diagram of differential
calorimeter
Each body has its internal energy which is
additive (extensive) quantity. The more is the mass of
the body, the greater will be the number of constituent
particles and the greater will be the internal energy.
The latter is the sum of all energy contained in the
constituent particles (atoms and molecules) of the
body, i.e., it is the sum of:
a) Kinetic energy of all the constituent
particles, including the kinetic energy of the
translational movements, rotation and vibration of
molecules. This sum is also called thermal energy of the body;
b) Potential energy of all constituent particles. This sum depends on the forces acting between the
particles and the distances between them;
c) Chemical energy of all molecules, i.e., the energy stored in the chemical bonds which can be
released through chemical reactions;
d) Intraatomic energy, i.e., the energy of the electrons within the atoms and the energy of the
nuclei of the atoms. Usually it does not count because it changes only in special cases not related to life
processes.
When two bodies with different temperatures come in touch a portion of thermal energy called
heat is conveyed from the warmer body to the colder body. The transfer of heat continues until the
temperatures of the two bodies became equalized. This experiment allows define the term exchanged heat,
Q, and provides a method for its determination. Let us indicate one of the two bodies as a reference body
having mass, M, and initial temperature to. On completeness of the heat transfer and balancing the
temperatures of the two bodies, the temperature of the reference body becomes t. Then, the amount of heat
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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
exchanged is Q = M. C. (t -to), where C is called heat capacity of the reference body. As such, water is
usually selected. 1 cal of heat is exchanged when 1g of water is heated by 1 °C (between 15 and 16°C).
Different bodies have different heat capacities, C (Table 1.1.2.). The heat capacity of gases is defined at
constant pressure, Cp, and at constant volume, Cv. Bodies made up of polyatomic molecules have a greater
heat capacities compared to the bodies made up of single atoms.
Table 1.1.2. Specific heat capacity, Cp, of some substances at room temperature
Substance
Paraffin
Liquid paraffin
Plexiglass
Polyethylene
Gypsum
Glass windows
Concrete
Cp (kJ / (kg . K))
Substance
1,6
3,0
1,5
2,5
1,06
0,67
0,84
Paper
Wood
Bricks
River Sand
Glycerol
Sun flower oil
Water
Cp (kJ / (kg . K))
1,5
1,2
0,88
0,84
2,35
1,5 – 2,0
4,2
Chemical energy of a body changes during the chemical transformation of its molecules. Upon
changing of internal energy heat is released (or absorbed) and the temperature of the body changes. The
heat is measured with devices called calorimeters. They contain two compartments, A and B, contacting
each other and thermally insulated from the environment (Fig.1.1.2). The test body which emits the heat,
Q, is placed in the compartment A. The compartment B contains the reference body (usually water) which
takes up the heat, Q, and changes its temperature. The exchanged amount of heat, Q, is calculated through
measuring the temperature change of the reference body using the above mentioned equation. Using such
type of calorimeters the heats of complete combustion of foods to CO2, H2O and N2 in an oxygen
atmosphere has been measured. The same quantity is called specific heat of combustion when refered to a
test substance having unit mass of 1 kg and caloricity when the testing material is food. Table. 1.1.2
shows the caloricity values of certain foods.
Table 1.1.3. Calorific value of some foods compared to the specific heat of combustion of
gasoline.
Substance
Apples
White bread
Beef steak
Butter
Buttermilk
Roast chicken
Beans
Energy (kcal / kg)
Substance
580
2700
4730
7160
360
2490
3490
Lamb leg
Milk
Baked Potatoes
Pork
Spinach
Sugar
Gasoline
Energy (kcal/kg)
3130
650
930
4100
230
3850
11500
Another more sofisticated device for measuring heat quantities is the differential calorimeter. It
consists of two identical containers A and B, thermally isolated from each other and from the environment
(Figure 1.1.3). The tested body which emits the heat Q is placed in the A container. In the B container an
electric heater is placed emitting the same amount of heat Q such that the temperature difference between
the two containers is maintained zero. Q is calculated by measuring the electric current through the
resistive heater.
Using differential calorimeters it is found that living organisms, at a complete rest, emit heat,
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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
designated as primary heat production. During each muscle contraction living organisms emit an
additional, so called active heat production. The primary heat production is due to the metabolic
degradation of nutrients to end products that consist of huge molecules also containing significant
amounts of chemical energy. Therefore, the metabolic degradation of food is incomplete and the heat
released in vivo, designated as physiological heat of combustion is less than the heat of complete
combustion in vitro.
Differential scanning microcalorimeters are devices similar to the device shown in Figure 1.1.3.
In addition, the containers A and B, which have a volume of about 1 ml, are heated simultaneously at
the same heating rate. The tested polymer solusion is placed in the A contaner, while the B container
is filled with the solvent. Upon reaching a certain temperature, Tm, biopolymer molecules contemplate
structural change (conformational transitions) absorbing or releasing the heat Qm, which is
compensated by the electric heater. Thus, the temperature, Tm, inducing the phase transition and the
heat effect of the phase transition, Qm, are both registered. The Tm and Qm have characteristic values
for each biopolymer.
Table 1.1.3. Activation energy of various processes.
Type of the process
Free diffusion
Diffusion of ions across a lipid bilayer
Enzymatically catalized metabolic
reactions
Thermal denaturation of monomeric
proteins
Еаct (kJ/mol)
About 20
About 50
20-25
350 – 800
With increasing temperature T, the thermal motion of atoms and molecules is accelerated and,
consequently, all metabolic processes increase its rate. The temperature dependence of the rate of
many processes (physical, chemical and biological) is described by the Arrhenius equation К = А.ехр
(– Еаct / RT). In this equation, A is the frequency factor and Еаct is the activation energy of the process.
Thermal motion involves individual particles having various speeds, furthermore, the particles
constantly exchange energy through mutual collisions. Due to these collisions some particles
accumulate significantly more energy than the average one. Based on this, E act represents that
minimal energy that must be accumulated by a particle (atom or molecule) to bring it in an activated
state allowing the particle to be transported through a barrier or to undergo chemical conversion. On
the other hand, the frequency factor A is interpreted as the average number of collisions the particle
must sustain in order to become activated. The Arrhenius law predicts that a slight increase in the
temperature of the process will lead to a strong increase in the rate of the process as much as the E act
is greater. Eact is determined using the experimental values of the rate of the process, measured at two
different temperatures. The values of Eact for some important processes are given in Table. 1.1.3.
1.2. Mechanisms of heat exchange. Physical basis of thermoregulation in humans
Without external interference, heat is always transferred from the warmer portion of a body to the
colder one, or from the warmer body to another, colder body. The amount of heat, Q, which is conveyed
through a surface with a given area, S, per unit time, t, is called heat flux, F. The heat flux, F, that is
transferred through the unit area, i.e., H = Q / (S. t) is designated as density of the heat flow.
Metabolic processes have different rates in different tissues and organs of human body, hence, the
primary heat production varies throughout the human body. The greatest heat production takes place in the
liver, brain and heart, where the greater amounts of O2 and glucose are consumed. Additionally, during the
muscle contraction the active heat production dramatically increases. Nevertheless, at physiological rest
and during physical working, the human body is constantly in a steady state thermal condution. This
steady state condition is characterized by relative uniformity and constancy of temperature inside the body
and strict equality between the internal heat production and outward heat flow. For example, the
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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
temperature differences between the internal organs in healthy individuals are no more than 0.5 оС.
Maintaining body temperature at constant level is a vital process and its disturbance is life threatening.
Hence, it is required for a physician to know the mechanisms of heat transfer and maintenance of body
temperature within the normal range of 36.7  0.5оC.
The heat transfer between the bodies is done by means of the following four physical
mechanisms:
Fig. 1.2.1. Heat transfer by means of
thermal conductance.
1) Heat conduction. This is transfer of
molecular kinetic energy (thermal energy,
heat) by means of the random thermal motion of molecules. This is the principal mechanism for heat
transfer in liquid and solid bodies, especially in crystalline ones. Heat passes from the warmer end of the
body to the cooler end (Fig. 1.2.1). At molecular level heat is transmitted from one particle which vibrates
faster to the next slower one. During this process the particles don’t change their location they only
exchange motion and energy. So, thermal conduction is not accompanied by transfer of mass and material.
The constituent particles (molecules, atoms, ions) of crystalline bodies are located in the nodes of a
regular, hard crystalline lattice. At each temperature, these particles are involved in thermal motion
vibrating around their equilibrium positions in the crystalline lattice. The amplitude of vibration increases
with temperature, but is usually not more than 0.1Å, which is about 5% of the equilibrium distance
between nodes. Thermal vibration of the particles in the hotter end of the body is more intense and is
transmitted to neighboring particles due to the forces of interaction between the particles. This transfers
heat without moving substance. In the case of thermal conduction, H = k. T/x, where T/x = (T2 - T1)
/ (x2 - x1) is the temperature gradient and k is the coefficient of thermal conductivity (Figure 1.2.1.)
Table 1.2.1. Coefficient of heat conduction, K, for various substances at room temperature.
Substance
Ferroconcrete
Gypsum
Cardboard
Bricks
Wood
K in W/(m оC)
0.7
0.35
0.23
0.6
0.10
Substance
Plexiglas
Glass
Copper
Water
Air
K in W/(m оC)
0.17
0.8 - 1.0
400
1.0
0.03
Compared to crystal bodies the heat conductivity of liquids and water is considerably lower,
because the thermal vibration of each molecule affects very weakly surrounding molecules. In gases
energy can be transferred from one molecule to another, and not very effectively, only upon mutual
collisions between molecules. Thus, of all the materials gases and air have the lowest heat conductivity k,
because the distance between their molecules is so great that they rarely collide with each other. Gases, as
well as solid porous materials (fabrics, layers of feathers and fur, wood, construction materials),
containing plenty of air bubbles are used as heat insulators. Biological tissues have thermal conductivity
close to that of water. Adipose tissues have thermal conductivity three times lower than that of water they are heat insulators. Most metals have thermal conductivity hundred of times higher compared to
water. Free electrons, available in them, determine their high thermal and electrical conductivity.
Some substances (quartz sand, ezolit, melted paraffin) have a large heat capacity and low thermal
conductivity. The two properties in combination make these substances suitable for contact
thermotherapy, at which the substance is heated to about 70°C and placed adjacent to the patient's body.
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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
Due to its high heat capacity, the substance accumulates significant amount of heat; its low thermal
conductivity provides a slow and safe transmission of this heat through the skin of the patient.
2) Convection is the transfer of heat from one place to another by the displacement of constituent
particles from one place to another. This is the main mechanism for heat transfer in liquids and gases. If a
small volume within the material is warmed up its density decreases causing the displacement of the warm
volume by the colder volume lying beneath. The warmed volume moving up carries substance and heat,
so, convection is accompanied by transfer of heat and matter. Besides free or natural, convection may be
forced - when it is accompanied by artificially stirring by fans, pumps, etc. Blood circulation in human
plays the role of heat transfer by forced convection. Let the heat flows by convection from a hot body with
temperature T1 to the colder environment with temperature T2. According to the Newton`s formula the
heat flow density, H, will be H = h. (T1- T2). Here h is the heat transfer coefficient, and 1/h is the heat
resistance of the boundary layer between the body and the environment.
Fig. 1. 2. 2. Heat transfer through the
mechanism of heat radiation.
3) Heat radiation (Fig. 1. 2. 2). This mechanism
does not require material media for the transfer of heat,
because the heat is transferred from the body with higher
temperature, T1, to the cooler radiation screen with
temperature T2 by means of electromagnetic waves from the infrared range, known as thermal radiation.
For temperatures close to 37С, H = r. (T1 - T2). Here r is the coefficient of radiation transfer.
4) Evaporation. The evaporation of 1g water, placed on the surface of a hot body consumes 2520
J causing substantial cooling of the body. The withdrawal of heat heavily depends on the pressure, P, of
water vapor close to the surface of cooled body. For this mechanism, H = e. (P1 - P2), where P1 and P2 are
the partial pressures of water vapor at the surface of the body and away from this surface, respectively
(Fig. 1.2.3). This is the only mechanism which allows removal of the heat from a body being cooler than
its environment. In humid air (P1 < P2) evaporation is difficult or impossible. In this case, if the ambient
temperature is equal to, or greater than the physiological one, no mechanism of heat transfer will dissipate
the heat, generated within the body, and the body
temperature will raise leading to heat stroke.
Fig. 1.2.3. Heat transfer by the mechanism of
evaporation.
Let us denote by Q the heat amount released within
the human body for the time interval of t. Then Q/t will
be the rate of heat production within the human body. Let us
denot the heat flux transmitted from inside to the surface of
the body by Fin, and the external heat flux carried from the surface of the body to environment by Fex. The
human body is in perfect steady state, hence, these three values must be equal to each other, i.e.,
Q / t = Фin = Фex
This is the equation of heat balance in humans, ensureing body
temperature to be constant during life.
Depending on the health, emotional status and the physical activity of the human, the rate of heat
production Q/t changes. In order to keep the temperature homeostasis (invariability of body
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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
temperature), the heat flows Fin and Fex must also be changed so that the heat balance equation should be
always valid.
Fin is transmitted via two mechanisms - heat conduction and convection, which are equivalent at
physiological rest (Fig. 1.2.4). The thermal conductivity of the internal media in humans is similar to that
of water which is sufficiently high. However, this thermal conductivity can not be changed in order to
convey the additional heat flux in the case of intense musle activity. The role of such regulator is taken up
by the second mechanism – forced convection, which is implemented by circulating blood.
Blood has a high heat capacity and thermal conductivity, moves in a highly branched system of
vessels and therefore accomplishs effective heat convection that equalizes the temperature of the internal
organs. In case of strenuous physical work the active heat production is accelerated and the temperature of
the blood increases. This irritates the nerve receptors for heat placed in hypothalamus and the receptors
generate more nerve impulses. As a result, cardiac function and blood flow are enhanced, and additional
blood capillaries are opened in the skin. These effects can increase Fin about 5 to 7 times, restoring the
heat balance (Fig.1.2.4).
Fig. 1. 2. 4. Changes in
the heat flows and heat
production in man at rest and
intense working.
During
hyperthermia
(e.g. at body temperatures above
38оС) another process takes place
in tissues – an increase in the
synthesis of nitric oxide NO, a
potent dilatant, increasing the
width of peripheral blood vessels.
This is an adaptive response
aimed at the increase in Fin. The
presence of anesthetics and
alcohol in the blood degrades the
performance of the nerve center for temperature regulation. This may disrupt the thermoregulation of
human leading to heat stroke at high ambient temperatures.
During prolonged hyperthermia, the blood flow near the skin is steadily increased at the
expense of the blood supplying internal organs (e.g. stomach). Continued reduction in blood flow to
the stomach can lead to impairment of his blood barrier and passage of bacteria from the stomach into
the blood (sepsis).
Fex is conveyed mainly via three mechanisms: thermal radiation, heat convection and evaporation.
At rest, Fex is exported mainly through heat radiation, while at active exersize - by evaporation (Fig.
1.2.4). In some cases, when a person is immersed in water or is in contact with a heat conductive medium
(metal, stone, water) thermal conductivity becomes involved, which is able to strongly disturb the heat
balance of the body in just a few hours. At humans the Fex flow is subjected to additional, behavioral
regulation in order to avoid direct heating of the body from the Sun and other heat sources or to utilize
additional thermal insulation (clothing) in case of large heat losses.
At low ambient temperatures and in the case of large heat losses, the temperature of internal
organs and blood drops. This triggers additional mechanisms for its recovery: additional heat production
by periodic muscle contractions (shivering, twitch); decomposition of fats; reduction in Fin by lowering
blood circulation (contraction of peripheral vessels, slow heart rate) and behavioral regulation. Children
have small mass and low heat capacity, hence, at low ambient temperatures they cool much faster than the
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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
adults. Moreover, the mechanism of thermoregulation is still not operating effectively in the babies of a
few months, and their cooling is extremely dangerous.
1.3. Basic thermodynamic quantities. First law of thermodynamics
Thermodynamics is a branch of physics that explores the general laws which govern the transfer
of energy from one body to another in the form of heat and work. It is a macroscopic science not
interested in the molecular structure of bodies and the mechanism of energy transfer. It is concered only
about the quantitative changes in energy during the transition between the initial and final state.
The first fundamental concept of thermodynamics is the thermodynamic (macroscopic) system
that is a geometrically shaped physical body, which is located close to an endless, unchangable
environment (surroundings). When the system is in equilibrium with the environment, we say the system
is in equilibrium state. The simplest thermodynamic system consists of a certain volume of gas or water
vapor. The equilibrium state of this sytem can be completely described using several experimentally
measurable quantities, called basic thermodynamic parameters; temperature T, pressure p and the volume
V of the system. Other parameters (density, specific heat, etc.) can be derived or calculated using these
basic parameters.
Energy and work are two other basic concepts of thermodynamics. Work is done when a force
moves certain body or when a system changes its volume against ouside force. Energy reflexes the ability
of a body to perform work as a concequence of its movement or position in respect to a force acting on it.
Energy associated with the movement of the body is referred to as kinetic energy and the energy
associated with the position of the body in respect to forces is called potential energy. Kinetic and
potential energy together constitute the so called mechanical energy. Except the mechanical energy we
know other forms of energy as well; thermal, chemical, electrical, atomic, and radiation ones. Energy can
be converted from one form to another by appropriate physical process, but this transformation obeys
certain general laws established by thermodynamics.
Thermodynamic systems are of three types:
a) isolated systems – those that do not exchange energy and substance with the environment;
b) closed systems – those that exchange energy but no substance with the environment;
c) open sytems – such that exchange both energy and substance with the environment. All living
organisms are open thermodynamic systems.
When a thermodynamic system goes from one equilibrium state to another, we say that it
performs thermodynamic process. Based on the large volume of empirical data gathered during the XIXth
century the thermodynamics has postulated five basic laws (postulates, principles) governing all
thermodynamic processes. These are as follows.
a) Zero law – it defines the parameter temperature as the degree to which the body is heated.
When a thermodynamic system is in contact with the environment, the state of thermal equilibrium is
reached after a while. In this state the temperature attains a same value in all the points of the system,
equal to that of the ambient temperature. When two systems are in thermal equilibrium with each other,
they have the same temperatures. The zero law states that when two systems are in thermal equilibrium
with a third one (called thermometer), they are in thermal equilibrium with each other.
b) First law – it defines the important consepts heat and internal energy. Heat is not a material
substance (invisible gas, liquid or fluid), as it has long been thought about. Heat is a form of energy
exchage. It can be converted into mechanical energy (work) or acumulated as internal energy. The essence
of this law is explained in detail beneath separately.
c) Second law – it defines the important notion of entropy and associates its changes with the
direction of evolution of thermodynamic processes. The essence of this law is explained in a separate
topic.
d) Third law. On the basis of the known gas laws the thermodynamic scale of absolute
temperatures is introduced. The value of -273.15 оС, called absolute zero temperature, is obtained as
starting point of this scale. At this temperature, all of the atoms and molecules are expected to be at a
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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
complete rest, i.e., they can not vibrate and move. Therefore, the third law postulates that at the absolute
zero temperature, the entropy of the system is zero. Absolute zero temperature can be approached, but not
achieved with a finite number of steps.
e) The fourth law states that all processes in an isolated thermodynamic system end at reaching
such an equilibrium state in which all types of energy are degraded to heat and no more changes are
possible. This final state is called thermodynamic equilibrium, or in philosophy, heat death of the system.
A detailed description of the first law of thermodynamics follows.
The internal energy, U, of a thermodynamic system is the sum of the kinetic, potential and
chemical energy of all the molecules that form the system. It depends on the state of the system, i.e., on
the number of molecules, their speeds and mutual dispositions. It does not depend on the path (or process)
used to get the system to that state. From the presented definition it is obvious that the internal energy is a
function of the state in which the system is placed. In other words, each state of the system is
characterized by its own value of the internal energy. For example, in the state (1) the system will have an
internal energy U1, and in the state (2), respectively, U2. If the system passes from the initial state (1) to
the final state (2), the change of internal energy will be dU = U2 - U1. The U2 - U1 change, expressed by
the differential d (e.g. dU) will be the same regardless of the type of the transition from the state (1) to the
state (2). By contrast, all changes indicated by  (e.g. Q) depend on the type and path of the transition.
Theoretically many different thermodynamic processes are possible each one transfering the
system from the initial state (1) into the final state (2) - Fig.1.3.1. Let the system make the transition from
the state (1) into the state (2) by means of one of these possible processes. In this transition the system will
perform mechanical work, А1, and will exchange heat, Q1, with environment. Note that the heat, Q1,
and the work, А1, both depend on the particular process, i.e., on the way in which the system switches
from the first to the second state. During the same transition (1)  (2), but performed using another
process, the work and heat will have other values, А2 and Q2, using third process, А3 and Q3, and so
on (Fig.1.3.1).
Fig. 1.3.1. Illustrated are
three possible ways to transfer the
system from one state (1) into
another state (2). Each transfer is
accompanied by exchange of energy,
Q, and work, А, between the
system and the environment.
According to the first law of
thermodynamics, the sum of the
exchanged heat, Q, and the work
done, A, during each process the system uses to pass from the state (1) into the state (2), must equal the
change in the internal energy of the system, U2 - U1. In other words, Q + A have a constant value equal
to dU, i.e., Q + A = dU = U2 - U1. The first law postulates a path independence of the internal energy
and its changes.
The first law of thermodynamics actually confirms the law of conservation of energy which states
that energy can not be created or destroyed, it can only be converted from one form to another. According
to this law, the heat and work are equivalent forms of energy because both quantities produce the same
outcome, they both change the internal energy. Heat and work are two mechanisms by which systems
exchange energy. Before the establishment of their equivalence, the heat and work were measured in
different units, the heat in calories (cal), and the work in Joules (J). Based on the equivalence of heat and
work, it is experimentally obtained that 1 cal = 4,186 J.
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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
Machines are devices that convert some form of energy (chemical and electrical energy, heat,
radiation, etc.) into mechanical work. According to the first law of thermodynamics, there can be no
machine (called a perpetuum mobile of the first kind) that will work forever without consuming external
energy. Without the input of external energy (Q) the system can transform into work (A) as much
energy as that stored inside it as internal energy (U). When considering the second law of
thermodynamics, we will see that even not all of the internal energy can be converted into work, but only
a portion of it, the so called free energy.
In chemistry the Hess' law states that at constant volume, the chemical effect (heat released or
absorbed) during a chemical reaction does not depend on the intermediate steps, it only depends on the
initial and final state. This is because at constant volume A = 0 and, according to the first law, the
chemical effect Q is equal to the total change of internal energy dU = U2 - U1. In living organisms, the
Hess' law has the following equivalent - at rest (A = 0), they release as much heat (Q) into the
environment, as much energy they produced by the in vivo physiological oxidation of consumed nutrients
(i.e. Q = U2 - U1). This indicates that in living systems, there are no other forms of energy than those
known in physics.
Generally, the work, A, performed by a thermodynamic system is expressed by the change in its
volume, V, i.e. A = - p.V, where p is the pressure and V is the volume. The sign convention for this
equation reflects the fact that the internal energy of the system decreases when the system does work on
its surroundings. Therefore, the first law can be expressed as: dU = Q + A = Q - p.V. Hence, Q =
dU + p.V. Using infinitesimal changes of the system we could transform the last equation as Q = U +
p.V = (U + pV). The expression U + pV = H, called enthalpy, represents the total amount of energy
stored in the system, which can be transferred as heat to the environment. The total enthalpy, H, of a
system cannot be measured directly, therefore, what we measure is the change in enthalpy, ΔH. The
change ΔH is positive in endothermic or heat-absorbing reactions, and negative in heat-releasing
exothermic processes. Usually, in biological systems V and p are invariable parameters and then H =
U, i.e., the change in enthalpy coincides with the change in the internal energy of the system. The
enthalpy of nutrients, also called heat content or energy content is an important quantity for medicine and
its determination is a subject of dietetics, a modern branch of medicine.
In the course of chemical reactions the change in enthalpy is given by the heat which is
removed or absorbed at constant volume. It is the same and for the physical processes, for example
for phase transitions. In particular, the change in enthalpy during the transition from solid crystalline
state to liquid one is given by the latent heat of the transition. Upon heating each body increases its
enthalpy, for example an increase in body temperature by 1°C increases the enthalpy by a value equal
to the specific capacity of the body.
1.4. Second law of thermodynamics. Entropy, free energy and order.
Thermodynamic systems can be in a state of equilibrium or in a state of non-equilibrium. In the
state of equilibruium, each parameter of the system (temperature, pressure, etc.) has the same value in all
the points of the system and remains constant over time. In this state the system is in equilibrium with the
environment and does not interact with it. When the system makes a transition from one state of
equilibrium to another, we say that an equilibrium process is carried out. The equilibrium processes are
actually very slow ones, so the changes they produce are infinitesimal by rate. Each equilibrium process is
also a reversible one, because it may spontaneously (without external support and energy) be conducted in
the opposite direction. At the end of each equilibrium process both the system and its surroundings are
restored to their initial state without producing a change in them. The real processes, in particular those
conducted at a very high rate, are actually irreversible.
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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
In the state of non-equilibrium, at least one of the parameters of the system, e.g. temperature, has
different values in the different points of the system, i.e. the parameter has a gradient. Each of these
gradients serves as a driving force for respective non-equilibrium process (diffusion, heat exchange,
dissipation of energy by friction, viscosity). Non-equilibrium processes are irreversible because they can
not run in the opposite direction independently, without outside interference.
A cyclic process is a process in which the system is returned to its initial state after completion of
the cycle. For example, the system will perform a cyclic process when it forcibly passes from the state (1)
into the state (2) and then spontaneously reverts back to its initial state (1). If the energy supplied by the
environment during the forced transition (1)  (2) returns back entirely after the completion of the
reverse transition (2)  (1), this process is reversible. If the spended energy returns only partially, the
process is irreversible. In fact, only a small part of the processes can be considered reversible provided the
accompanying irreversible processes such as friction, resistance, viscosity, etc. could be ignored.
Fig. 1.4.1. Changes in the
entropy, S, of a closed system during a
cyclic process.
The first law of thermodynamics
postulates that after the completeness of
each thermodynamic process, the total
amount of energy before and after the process should be the same. However, this law does not indicate the
direction in which the process will occur. The second law of thermodynamics imposes another restriction
on the thermodynamic processes. It postulates a particular asymmetry in the processes, namely, they can
occur spontaneously only in a specific direction. There are several formulations of the second law:
1) The heat is not allowed to pass alone, without outside help, from a colder to a warmer body. It
would be possible, but only forcibly using an external mechanical work, as it happens in refrigerators.
2) When a thermodynamic system completes a cyclic process, it is not possible the net result to be
production of work and generation of heat. Machine that would constantly draw energy from a colder
body to produce work in a hot environment is called perpetuum-mobile of second kind. Under this
formulation, such a machine is impossible to build.
The other formulations have quantitative form and they use the new term entropy. The entropy, S,
of a thermodynamic system is a state function and, therefore, it changes when the system shifts to another
state. Let a closed thermodynamic system passes from the state (1) to the state (2) and then returns back to
the state (1), i.e., it carries out a cyclic process (Fig.1.4.1). Let the temperature of the system is T1 and Q1
is the heat exchanged between the system and the environment during the transition 12. Accordingly, T2
and Q2 are the temperature and the exchanged heat, respectively, during the opposite transition 2  1.
Historically the ratios Q1/T1 and Q2/T2 are firstly called “reduced amounts of heat” and later, „changes
in entropy” during the forward and reverse process, respectively. Thus, the term ‘reduced amount of heat”
(Q/T) represents the change of entropy, S, of the system and is designated as S. So, Q1/T1 = S12 and
Q2/T2 = S21 represent the changes in the entropy, S, of the system during the forward and reverse
processes, respectively. Upon completion of the cyclic process, the total entropy change will be S = S21
- S12.
3) The third formulation of the second law (in Clausewitz) states that in an isolated
thermodynamic system any cyclic process will either increase the entropy or preserve it the same.
So, the total entropy change will be S ≥ 0, whereat the sign ">" is valid for irreversible and the sign "="
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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
for the reversible processes. Since the real processes are always irreversible, the direction of each process
in the isolated systems will be such that the entropy should always be greater at the end of the process.
Let us substitute Q = T. S in the equation dU = A + Q, expressing the first law. Then we get
U = A + T. S. Hence, A = U - T. S = (U - T.S) = F. The expression F = U - T.S has the
meaning of work (A) and is called free energy. The free energy, F, represents that portion of the internal
energy, U, of the system, which can be converted into useful work. In turn, the term T.S is called bound
energy, this is the remaing portion of the internal energy of the system that can not be utilized as work.
The greater the entropy of the system, the higher will be the bound energy and the less will be the ability
of system to do work.
Table 1.4.1. Using the second law of thermodynamics to estimate the possibility of
a given process to ocurre.
Н
S
G
-
+
< 0 at any temperature
-
-
< 0 at low temperatures
> 0 at high temperatures
Assessment of the opportunity the process to
take place
The process can be performed at any
temperature
This process is possible only at low
temperatures
+
+
> 0 at low temperatures
< 0 at high temperatures
The process is only possible at high
temperatures
+
-
> 0 at any temperature
The process is not possible in any
temperature
Let us assume an isolated system performed a cyclic process, then F = U - T. S. Since the
process is cyclic one, U = 0, therefore F = -T. S. According to the second law, S ≥ 0, therefore F
≤0. Hence, a more general formulation of the second law originates, namely, in an isolated
thermodynamic system only such processes are allowed which increase the entropy, decrease the
free energy and reduce the ability of system to do usful work. Table. 1.4.1 shows the possibility of
spontaneous occurrance of a process depending on the changes in entropy, free energy and enthalpy
of the system.
The physical sense of the term entropy can be derived based on the molecular structure of the
systems. Each thermodynamic system is composed of a vast number of molecules of one or more different
types. These molecules may have different locations and arrangements, hence, the system may has
different microstates. In many of these arrangements, however, the properties of the system will be the
same, i.e., a part of the microstates will bring about a same macrostate. Let W denotes the number of those
arrangements of the molecules of the system in which the system has the same macrostate. It can be
deduced that the entropy S = k. lnW, where k is the Boltzmann constant. In systems with more ordered
structure (unique systems with greater complexity), the W is less, and the entropy, S, is low. In this sense,
entropy is a measure of the disorder and reduced complexity of the internal structure of the system. The
moving of the isolated systems towards the states with greater entropy means that if the system can choose
one of several possible macrostates, it most likely will be found in the state with the greatest W.
Therefore, W is called thermodynamic probability.
The entropy, S, and free energy, F, are associated with the internal energy, U, and therefore are
also state functions. These state functions all depend on the state (temperature, pressure, and volume) in
which the system is located and do not depend on the path the system has used to reach this state.
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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
According to the third
law of thermodynamics, at the
absolute zero temperature (273.15 оС) the entropy of each
Substance
S (J / K.mol)
body is equal to zero. This
allows the determination of the
Crystal
Fluid
Gas
entropy of the body at any
other state. For the crystal
Diamond
2.44
158
bodies the more complex is the
Graphite
5.69
158
crystal lattice, the lower will be
Alluminium
28.3
37.8
164.4
the entropy. Table 1.2.4 and the
Water
43.9
66.9
188.7
Fig. 1.4.2 both ilustrate the
importance of entropy to
express the amount of order or disorder (chaos) in the structure of bodies. Most often, we are interested in
how much the entropy changes during the phase transition between two states. During processes
decreasing the complexity of structure, entropy increases, S > 0. Such processes are melting,
evaporation, dissolution, heating, formation of gaseous products and precipitate. Conversely, at processes
causing growth in orderliness, the entropy decreases, S < 0. These include condensation, crystallization,
cooling, reduction of gas components.
Table 1. 2. 4. Specific entropy of various substances and its change after
the phase transition.
Fig. 1.4. 2 Change in the entropy of water
upon heating. Dotted lines indicate the changes in its
physical state, melting point (273 K) and evaporation
(373 K).
It can be deduced from the formula F = U - TS
that the free energy, F, is also a measure of the order
(complexity) of the system. It is clear that the ordered
systems will have lower entropy, more free energy and a
greater ability to do useful work. Exactly such are the
living organisms, considered as thermodynamic systems.
They have high internal order and unique structure,
which is sometimes referred to as aperiodic crystal.
The second law of thermodynamics indigates that the entropy could be used as a measure of how
close the system is to the thermo-dynamic equilibrium. According to this law entropy, i.e., the disorder, is
always increasing in an isolated system. Thus, when a system reaches its maximal entropy, it can no
longer be changed because it has reached the thermo-dynamic equilibrium. By this law the nature shows
that it "prefers" the clutter to the orderliness.
The free energy finds particularly important application for descibing chemical and biochemical
reactions. Let the reaction A + B  C + D occurs spontaneously to reaching a state when the
concentrations of the precursors (A and B) and products (C and D) will remain constant in time. The
equilibrium constant K for this reaction is defined as the ratio of the equilibrium concentrations of the
substances involved K = [C].[D]/[A].[B]. Clearly K > 1, because at the end of the reaction, the
concentrations of precursors [A] and [B] will be lower than the concentrations of the products [C] and
[D]. If the reaction has occured at standard conditions, the change of in the free energy of the reaction
shold be F = - RT ln K, where R is the gas constant and T is the absolute temperature. Fom the
condition K > 1 it follows that F < 0, which is in agreement with the second law of thermodynamics.
In addition, this shows that there are less free energy and more entropy in the obtained products than
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Medical Physics. Ivan Tanev Ivanov. Thracian University. 2016
in the initial precursors. The difference in energy is released as heat, which appears as degraded and
unusable energy. If K < 1, it follows that F > 0 and the reaction could go in the opposite direction
only under external influence.
Bioenergetics studies processes by which cells accumulate, use and release energy. During
these processes the energy passes from one form into another, hence, these processes must obey the
laws of thermodynamics. As the life processes occur at constant pressure and temperature, the living
organisms can not convert heat into useful work.
The living organisms can use only the chemical energy and the energy of the light photons.
Chemical energy in the chemical bonds of nutrients is the only source of energy for those organisms
which can not photosynthesize. Therefore, the first law of thermodynamics for these organisms has to
be formulated as follows: the energy they need to perform all kinds of work is obtained by oxidation of
the chemical bonds in organic matter. In this sense, these organisms could be considered as chemical
machines that convert the chemical energy of the nutrients into work and partly into heat, according to
the laws of physics.
The second type of organisms, plant cells, uses the energy of sunlight to synthesize
carbohydrates from simple inorganic substances. So, the radiant energy of light is converted into
stockpile of chemical energy, decreased entropy and increased free energy. From plants these
chemical energy, low entropy and free energy all pass into animals where they become converted into
a movement (kinetic energy), body heat (thermal radiation), active transport of substances, nerve
impulses (electrical energy) or new chemical bonds (synthesis). In each of these conversions, a part of
the energy is lost in the form of primary heat to the environment resulting in the increase of entropy.
This lost energy can not be utilized because it has become a disordered form. The second law of
thermodynamics states that every system tends to fall apart and become more chaotic with time. This
requires a constant flow of solar light whose energy, through photosynthesis, can be converted into
new chemical bonds and negative entropy firstly in plants and later in animals.
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