Mathematics and treatment of cancer

1. Mathematics and treatment of
cancer

2. Biology without Math, does it work ?
In not very distant times, a
new secondar y-school graduate
who had good results in a
learning, but didn't feel secure
in the area of mathematics
(being a key to technical,
economic and studies) - often
went to study medicine. There
the success depended on the
knowledge of biology,
chemistry, even physics - but
not mathematics. However,
everything is changing and at
present in the area of
examinations a demand for
mathematical perspectives
which are connected with
omnipresent computers, also
grows in medicine. We will talk
today about these connections
of mathematics and medicine.

3. Have you ever thought that ?
Many people think that mathematics is only a learning of
counting, but they are wrong. Mathematics is above all a
learning of the logical thinking which in biology is essential.

4. Mathematics in various areas of
biology
● biocomputing - is based on applying mathematical algorithms in the sequencing of genomes
● modelling of cancers and complicated relations acting in them (genetic changes, the
height, cell divisions, the morphology of cells and tissues) lets for drawing therapy up
● theoretical neuroscience- modelling of the relation between nerve cells, neural networks
● radiobiology- influence of the radiation on tissues, counting physics formulae
The synergy of sciences make you will take out audits of the most accurate application.

5. Statistics – the Key to the correct
diagnosis
It is necessary for
acquiring the scientific
confidence of basing the
inference on series of
observation.
Only when it will be
possible to observe the
specific phenomenon
repeatedly in the similar
form - it is possible to talk
about the scientifically
stated fact.
However, a problem
appears. How to learn a
lesson from examination,
based on the harvest of
observation, since each of
them is a bit different,
individual, unique?

6. And here we need statistics
Firstly, it is possible from many observations to list one
indicator which best represents all these observations.
An average, trimmed average, Winsor’s average, a median, a
mode can be an indicator but also a lot of others.
Secondly, statistics shows us whether an activity of the
examined phenomenon is a conditioned effect. It lets us
determine whether an activity of the examined object is only
an accidental effect.
Here helps a variance which determines the measure of the
scattering of real data around the chosen indicator.

7. How is created mathematical
oncological model ?
The majority of oncological therapies are directed to the definite activities
of tumors, such as invasive propensity
● bulding models on the basis of the precise biological question
● the construction of model is necessary to begin from the formulation of research problem
● on accessible base of biological data a mathematical model is constructed
● on the base of carried out experiments it is possible to formulate the new hypothesis (which is
necessary to be verified)
● on the base of the results of these experiments it is possible to make a perfect mathematical model
through the addition of new elements and the constant repetition of all legal procedure
● the co-operation of specialists from different spheres (construction and the verification of models on
the basis of the quantitative experimental data, the project of new experiences, the search of new
mathematical methods allowing the proper description of process and its analysis, but at last
numerical simulations and the optimalization of treatment.

8. What benefits result from
the mathematical modelling
in medicine, in particular
from the modelling of
processes of the
proliferation of cancers?

9. First Benefit Result
The structure of such a model is facilitating to understand the main mechanisms - biological
processes.
In view of complexities of arrangements of life forms, which are the chance to understand the
processes in them occurring, it is possible to see above all in supplementing experimental
traditional methods with mathematical models. Creating the simplest models helps to understand
difficult phenomena. Character multiscale of them is a significant feature of biological processes so
better explanation of observed phenomena requires construction of models linking the description
on the tissue level with the cellular and intracellular description of processes occurring on different
levels. We can widen formulating research hypotheses and our understanding the nature of
influences between individual processes.
In this way modelling simplifies the project of new experiences, but additionally, it can determine
alternatives for many experimental models.

10. Second Benefit Result
The optimalization of therapeutic legal procedures,
permisssion on the simulation of morbid process, in particular answers on the
treatment with the use of different schemas in medicine.

11. Mathematics and treatment of cancer
Most papers are devoted to mathematical structuring different types of
models of cancer, which may eventually lead to a better than before
treatment. Mathematical modeling used in biology and medicine is very
useful in treatment of various diseases, especially cancer. Due to
the complexity of the system, which is the human body, the chance for a
fuller understanding of those processes can be seen in complement
traditional methods of experimental, mathematical models.
Mathematical models should be understood as an attempt to represent
the biological system using a mathematical language, for
example, differential equations. It usually means reduction of complexity
of the original system to simpler system, which can be analyzed and
on the basis of which the original system can be concluded.
Mathematical modeling allows, among others, to simulate the disease
process (in particular the response to treatment), optimization of
therapeutic procedures and the creation of experimentally testable
hypotheses. In addition, modeling facilitates understanding of the main
mechanisms, complex biological processes, designing new
experiences, and in the future might be an alternative for many
experimental models.

12. The use of mathematical
models for cancer treatment
I. An important example of using mathematical methods in oncology are models of
cancer invasion. The prognosis in cancer depends largely on whether the cancer is
malignant, that is, whether the cancer cells have the ability to invase neighboring tissues
and metastasis formation. Individual phrases of model describe most processes
associated with tumor invasion, i.e. migration of tumor cells, tumor growth due to the
proliferation of tumor cells, and the production and diffusion of the enzymes that digest
the extracellular matrix and degradation of the matrix itself. Each of these processes is
described by the respective function.
II. Another use of mathematics to treat cancer is to create 3D models.
So-called "3D modeling" is based on advanced mathematical mechanisms presenting a
three-dimensional image of the reality on the computer screen. Performance of a full
and detailed 3D model of the human genome is - because of the level of
complexity - extremely difficult. Even more difficult it is to carry on this basis all kinds of
simulations.
It has been proven that the three-dimensionality of the genetic material of the cell – in
itself - has a huge impact on the probability of occurrence of these changes of cancers.
Thanks to a thorough analysis of the 3D model it has been proven, first of all, that
natural contact between two - or more - three-dimensional points of the genetic structure
increases the likelihood of duplication in this place or remove a portion of genetic
material. And this is a phenomenon characteristic just for cancer.

13. Thank you for your attention, we
hope you enjoyed it :)

14. CANCER UNDER MICROSCOPE