2. Literature:
1. Paul Davidovits. Physics in Biology and Medicine 5th Edition. Academic Press, 2018.
2. Irving P. Herman. Physics of the Human Body. Springer, 2016.
3. Muhammed Maqbool. An Introduction to Medical Physics. Springer, 2017.
4. J Šetrajčić, D Mirjanić. Biofizičke osnove tehnike i medicine. ANURS, Banja Luka, 2012.
5. D Ristanović, J Simonović, J Vuković, R Radovanović. Biofizika. Medicinska knjiga.
Beograd, 1981.
6. S Stanković. Fizika ljudskog organizma. PMF Novi Sad, 2006.
3. 1. Systemology
Biophysics-1892 English statistician Karl Pearson.
Science that uses physical laws to explain phenomena in biology.
The object of research in biophysics is a living or biological system and the
methodology of research is reduced to the methodology of physical sciences.
It is an interdisciplinary science. According to the object of research, biophysics
can be divided into three areas: molecular, cellular and system biophysics.
4. Basics of systemology
1. Concept and definition of system
By studying the common characteristics of all systems (nervous, cardiovascular,...) the so-
called systemology (general theory of systems) was born.
A system is a set of objects, living objects, processes or phenomena, which are arranged
in a certain way and interconnected as a whole with a certain function, different from
the function of individual elements.
System components:
- elements (fig.) that make up the material base of the system,
-channels of connection between elements and directions of
information transfer (action) between them and related to the
relational characteristic of the system,
-system boundary.
Example: CNS-system, neurons-elements that are
interconnected and can act on each other.
5. System and reality
There is only one universal system (universe) and partial systems that do not exist and that is
an approximation of reality.
The figure shows an isolated system that does not exist in nature (all systems in nature are
open).
In order for a set of elements to represent a system, there must be a function that the system
needs to achieve and a degree of mutual connection between the elements.
Example: Two oxygen atoms represent a system of oxygen molecules that have new
characteristics compared to the properties of individual oxygen atoms.
6. 2. System classification
a) According to the degree of complexity:
Simple systems - a small number of elements connected in a simple way
Complex systems - a large number of complexly connected elements
Complicated (very complex) - the current level of knowledge cannot describe them
b) According to the nature and behavior of the system in the future:
Deterministic systems-elements interact with each other in a precisely predictable way.
Probabilistic (probable) system - elements act so that in the same way they can predict
the behavior of the system in the future (with a certain probability).
7. c) Combined system classification:
1) A simple deterministic system - it contains few elements and mutual connections, it is easy to
describe and its behavior in the future is easy to predict (Typewriter).
2) A complex system with deterministic behavior has a relatively complex structure, but despite
that, its behavior in the future can be unambiguously predicted (PC).
3) Complicated system with determined behavior, rarely encountered (Cosmos).
4) A simple system with random behavior is a simple system whose behavior can be easily
predicted by the laws of probability (a tossed coin).
5) A complex system with random behavior - its behavior in the future can only be predicted on
the basis of probability. Many biological systems boil down to this. Conditioned reflex - complex
system - a large number of neurons, and it is probabilistic because the consequences are not
always the same (if a dog is offered a bone, it is not certain that he will always to take it).
6) Complicated system with random behavior - future behavior cannot be described or predicted
(the mammalian brain).
8. System inputs and outputs.
A real system is always open. With the environment is connected by inputs (x) through
which the environment affects on system and outputs (y) through which the system affects
the environment.
An effect (stimulus, impulse, cause, disorder) is an effect the environment whose change (at
the input) can be transmitted to the system while it is reaction (response, consequence)
property of the system that changes transmitted to the environment through the system
output.
In order for the examination of the system to have an exact character, it is necessary
that the actions and reactions of the system are physical quantities (properties of the
environment and the system are subject to physical measurements).
Let x1, x2, ..., xn be input and y1, y2, ...., ym output values.
9. 3. Terms that define the system
The “black box” is shown in the figure as a rectangle with inputs and outputs. It is
determined by:
a) Input quantities as a function of time: x1(t), x2(t),...
b) Output quantities as a function of time y1(t), ......
c) Parameters (const) characterize the properties of the system (or the
environment) a1, a2, ....
d) Transfer functions, which show the law of system behavior (dependence of
input x(t), output values y(t) and parameters a. f1, f2, ...
The law of system behavior can be presented in the form of a system of functions
y1=f1(x1,x2,x3; a1,a2), y2=f2(x1,x2,x3; a1,a2), ......
10. 4. Basic tasks of systemology
a) Direct task: x(t), f, and a are given, y(t) is required (simple).
b) Indirect task of the first type: given y(t), a and f, x(t) is required.
c) Indirect task of the second type: x(t), y(t) and f are given, a is sought.
The doctor takes the anamnesis of the disease (input), then examines the
patient and determines the symptoms (output) and, knowing the relationship
between effects and reactions (input and output, which represents the law of
behavior of the system-patient), draws conclusions about the type and nature
of the disease (system parameters).
d) The "black box" or induction problem: x(t) and y(t) are given, f and a are
required.
This task is the most difficult to solve. These systems are classified into the so-
called zero-, first-, and second - order systems whose properties are well
known.
11. 5. Zero order system
System with an elastic spring -
a force F (x-input) acts on the end of the spring. This force causes the spring to stretch
by a length l (y-output). According to Hook's law, the stretching of the body l is
proportional to the force F = - k l
k- is the coefficient of elasticity (a-parameter of the system)
If the law of system behavior can be represented as an algebraic equation (does not
contain differentials and integrals), it is a zero-order system ( x = a y, there is a linear
dependence).
12. 6. First order system
Spring box filled with viscous oil. By stretching the spring under the action of
force F, its threads meet the resistance force of the medium Fre (oil).
Fre is proportional to the speed v of the movement of the end of the spring A, i.e.
Fre = - r v = - r dl/dt
r is the system parameter (friction coefficient).
The force with which we act on the spring in order to stretch it (input) will be
F = k l + r dl/dt
is a first-order differential equation (x = a y + b dy/dt).
Any system whose behavior law (transfer function) can be represented by a
first-order differential equation (output quantity) is called a first-order
system.
13. 7. For the system to be of second order, the transfer function must contain the
second derivative of the output quantity
x = a y + b (dy/dt) + c (d2y/dt2) (a, b, c, are system parameters)
An example is the process of generating an action potential on the cell membrane.
Due to the external stimulus, the membrane will first depolarize (from: - 85 mV
to 40 mV). After that, the membrane repolarizes to the initial value through a
series of damped oscillations.
14. 8. Cybernetic systems
Cybernetics - the science of managing complex systems.
The elements of the cybernetic system are the control system (its action on the
control object leads to the desired changes in it) and the control object (the desired
changes are realized in it). They are connected by connection channels through
which the control system acts on the control object. They can be open and closed
systems.
8.1. Open cybernetic systems, information is brought to the input of the system and
the connection is one-way (automatic machines, computers). They are not of interest
in biomedicine.
15. 8.2. Closed cybernetic systems, there is also a feedback channel in the opposite
direction. It enables the feedback effect of the output value on the control system,
which is used to regulate it. They are widely used in biomedicine. They compensate for
a possible disturbance in the functioning of the system, caused by some undesirable
external effect.
Example:
Blood pressure is partly regulated by sensors in the kidney. Increased pressure
damages blood vessels also in the kidney where the sensors are. Damage reduces
pressure and an increase signal is sending again. Further increase leads to greater
damage to all vessels and to a new demands to increase the pressure. "Vicious Circle".
16. There are two types of feedback systems:
8.2.1. Tracking systems, pointer spring (control object) is stretched. The control
system is a person whose task is to position the pointer (output size Y) equate to
the position of the second pointer. The difference in the positions of the pointers
represents an error (noise, Y = Yi - Yo) which should be compensated. We stretch
the spring by hand and reduce the error. It is a cybernetic feedback system.
17. 8.2.2. Regulatory systems
Biological systems are open thermodynamic systems that communicate with the environment.
In order to avoid permanent disturbances, biological systems neutralize these influences
through regulatory systems. They achieve this through numerous regulatory systems.
Example: The hypothalamus ("thermostat") regulates the temperature in the body (37 0.5 oC).
If the thermostat is "set" to a higher temperature (by introducing toxic substances), a feeling of
coldness appears until we reach it.
By returning the thermostat to normal function (medicaments), the body is released from excess
heat until it reaches a normal temperature that corresponds to the state of homeostasis.
If the organism is in a state of low temperature, the hypothalamus activates shaking and thus
increases the temperature.
If the hypothalamus is not able to keep body
temperatures at very low temperatures, it will
protect vital organs (brain, heart) in that way,
reducing blood flow through the extremities.
18. At the cellular level, regulatory systems play a vital role in homeostasis (maintenance
of constant conditions in the environment of the cell-extracellular fluid).
A disturbance in the composition of this liquid leads to the destruction of the cell. That
is why a large number of regulatory systems neutralize changes.
The respiratory system regulates the concentration of carbon dioxide
Liver and pancreas regulate glucose concentration
Kidneys regulate the concentration of hydrogen ions, potassium (K), sodium (Na),
phosphorus (P), ...
19. Example: Regulation of the opening of the pupil of the eye.
The pupil changes its diameter L depending on the amount of light falling on the retina.
If is the amount of light reaching the retina, I is the light intensity and S is the area
of the pupil opening, then = a I S where a is the proportionality coefficient. The
response of the eye to an increase in light intensity is to reduce the pupil opening so
that the amount of light on the retina does not change, which means that there is a
feedback loop.
20. 9. Examination of Biological Systems
Basic principles and steps in system testing
The first step is to observe the biological system and
observe the behavioral characteristics.
Then, by induction (from the individual to the general),
we isolate the general characteristics of the structure
and behavior of the system, after which a hypothesis is
put forward that predicts the behavior of the system
under certain conditions.
After the hypothesis, an experiment should be
performed on the system to test the hypothesis.
Biological systems are very complicated, so we will
not do the tests right away on a living organism.
A system is designed on which an experiment is
performed to test the hypothesis. The results often
indicate incorrect settings, which leads to the
redesign of the experimental system. The system
obtained in this way represents the final model of the
biological system that we are examining, and the
procedure for obtaining the model is modeling. Only
now we can look for answers to the questions raised,
by numerical simulation or experimentally, then by
testing on animals and only at the end of clinical trials.
21. 10. Definition of the model. Principles of modeling.
Models are systems with all system characteristics. They are used to test the
functioning of real systems. The process of constructing a model, which is analogous
to a real system under investigation, is modeling.
The basic principles in the modeling process are: the principle of isomorphism, the
principle of homomorphism and the principle of analogy.
The principle of isomorphism. Two systems of an different nature are said to be
isomorphic, if when replacing one system with another, it gets the same answer for any
input quantity. It does not exist in the living world.
The principle of homomorphism. If systems have the same behavior with respect to
a finite number of properties, they are isomorphic with respect to those properties, but
may differ with respect to other properties. Such two partially identical systems are
homomorphic. Application in complicated biological systems when monitoring the
response of a part of the organism to the effect of an input quantity.
Principle of analogy. Various systems can function in the same way (the working
principle is the same). Analogy - a mechanical pump that causes fluid to circulate
through a tube and a heart that forces blood to circulate through blood vessels. The
results obtained in one system can be used to forecast another analog system.
22. Classification of models
Descriptive models - the simplest class that describes the system qualitatively. They
are divided into verbal and pictorial.
Mathematical models-data are in the form of equations and mathematical
expressions. If we mathematically express the transfer function of a system, then the
response that that system gives to a certain input quantity must have the same value as
the mathematically obtained solution of the equation representing the transfer function.
Physical models are material models that are realized in the form of a machine,
electrcircuit, etc. An example of a physical model is a electrical circuit that simulates
the behavior of a biogenerator of electric current in the human body.
