Decomposition of a tissue into its constituent elements for specifying the

values of doses

SEYED ALIREZA MOUSAVI SHIRAZI

Department of Physics

South Tehran Branch, Islamic Azad University

Shahid Deh-Haghi AVE, Fifth Bridge, Abouzar Blvd, Pirouzi AVE, Tehran, Iran. Postal Code:

1777613651.

IRAN

Abstract: - In this research, a real tissue has been decomposed to its constituent materials and elements

applying its volumetric density and initial mass. This study has been carried out to obtain the exact amounts of

constituent elements existing in liver tissue as well as specify the absorbed dose because of the tissue getting

exposed to radiation in radiotherapy and radiography. In order, a medical model has been defined in a way that

its compositions are just like the materials existing in the tissue of a human. Then, the accurate mass, density,

and volume of every element in it are specified. In the next stage, the related tissue is exposed to a neutron

beam, and then the values of doses absorbed in the main constituent material namely water, and also the total

absorbed dose is obtained by the MCNP nuclear code. This study can be used to study the radiotherapy and

radiography scopes for obtaining the absorbed dose as a result of interaction between radiation beam and

biological cells. In this research, the values of absorbed doses have been obtained for a wide range of neutron

energies in a way that the absorbed doses can accurately be obtained.

Key-Words: - Constituent elements; Dose; Radiation; Tissue.

Received: May 21, 2021. Revised: March 14, 2022. Accepted: April 16, 2022. Published: May 7, 2022.

1 Introduction

In this investigation, the thickness of adipose

tissue, which has been considered for the

simulation, is 30 mm [1, 2]. One of the

compositions of adipose tissue is fat. The

chemical formula of fat is

CH2ORCHOR'CH2OR. Fat is not a compound.

It is a mixture of many esterified acids named:

fatty acids. The average skin thickness is

thicker in males than females. The average pure

skin thickness in males is average 1.5 mm. The

skin tissue and subcutaneous consist of some

portions such as the epidermis, dermis,

hypodermis, and fat [3]. Skin is not a single

substance, so it doesn't have a single formula. It

has largely been made of various proteins,

water, fat, and salt. Skin is a biological tissue

that consists of carbon, oxygen, and nitrogen

[4].

2 Materials and Methods

The correct representations of the geometry and

compositions of tissues, which are in front of the

liver tissue, have also accurately been considered

concerning an adult male liver tissue for this study.

Since, in this study, the calculation method and

simulation of tissues may slight difficult be to

understand, to better explain, all calculations

regarding tissues, which are in front of the liver

tissue, are expressed as below:

The distance from the body surface (nearest section

into the body for setting the neutron source) to the

liver is averagely considered 3 cm for a normal

body. If the diameter of the neutron source head is 3

cm, then the path, where the neutron beam crosses

to reach the liver, will almost be a cylinder with

MOLECULAR SCIENCES AND APPLICATIONS

DOI: 10.37394/232023.2022.2.6

Seyed Alireza Mousavi Shirazi

E-ISSN: 2732-9992

Volume 2, 2022

r=1.5 cm and h≈3 cm the volume of it will be: 21.20

cm3. This path plays the role of the collimator to

reach the neutron beam from the source. According

to the calculated volume and density of adipose

(0.905 g/cm3), the mass of adipose existing in the

mentioned path will be:

0.905 21.20 19.18mV g

=×= × =

According to the percentage of water, fat, and

protein in adipose, the mass of them (in this volume

of adipose) will be respectively:

For water: =× 18.19

100

2.10 1.95 g (H2O)

For fat: =× 18.19

100

2.87 16.72 g

(CH2ORCHOR'CH2OR)

For protein: =× 18.19

100

1.2 0.40 g

(C44189H71252N12428O14007S321)

The spatial average of the protein density can be

considered equivalent to 1.35 g/cm3, independent of

the nature of the protein and particularly

independent of its molecular weight. The density of

human body fat is also: 0.918 g/cm3 [5, 6, 7].

Therefore, both the total density and volume of

materials existing in the mentioned path, which is in

front of the liver tissue, are calculated as below:

1.95 16.72 0.40

1 0.918 1.35

19.07 19.07 0.93 /

1.95 18.21 0.29 20.45

Total

Water Fat otein

mmm

gr cm

ρρρ

===

5.20

93.0

07.19 cm

Total

Total ===

→

25.20)( cmhrr =×−×

Where:

r1=1.5cm (radius of neutron source head), h≈3 cm

(distance between body surface and liver)

Therefore:

cmrr 10.25.203)25.2( 2

2=→=×−×

Thus, in this modelling, the path, where the neutron

beam passes across it to reach the liver tissue, is

considered a cylinder that has an inside radius of

r1=1.5cm and an outside radius of r2=2.10cm [8, 9,

10].

The mass, thickness, and outside radius of every

layer and shell have accurately been calculated. It

meets actual dimensions, from which calculation of

various layers is filled up with them.

(I)

i) Since in this study a sample liver weighing 2kg

(for an adult male) has been considered, therefore:

ii) The weight of water existing in the mentioned

tissue will be [11, 12, 13]:

8.13932000

100

69.69 =× g (Water)

iii) Therefore, the weight of existent hydrogen in

water is:

=× 8.1393

015.18

016.2 155.975 g (H)

iv) Similarly, the weight of existent oxygen is also

calculated as below:

=× 8.1393

015.18

999.15 1237.824 g (O)

(II)

i) Then, a similar calculation is carried out for

glycogen existing in the sample liver [14, 15, 16].

The weight of 1 gram-molecular of glycogen

(C24H42O21) → 288.264 (C) + 42.336 (H) +

335.979 (O) =666.579 g

ii) The weight of glycogen existing in the mentioned

tissue will be:

72000

100

35.0 =× g (Glycogen)

MOLECULAR SCIENCES AND APPLICATIONS

DOI: 10.37394/232023.2022.2.6

Seyed Alireza Mousavi Shirazi

E-ISSN: 2732-9992

Volume 2, 2022

iii) Therefore, the weight of existent carbon in

glycogen is: =×7

579.666

264.288 3.027 g (C)

iv) Similarly, the weight of existent hydrogen and

oxygen are also calculated as below:

For hydrogen: =×7

579.666

42.336 0.444 g (H)

For oxygen: =× 7

579.666

335.979 3.528 g (O)

(III)

i) As two of the compositions of the liver tissue are

protein and glucose, the molecules of each of them

are decomposed to the related constituent elements,

and taking the molecule gram into consideration, the

amount of each atom existing in a molecule is

extracted based on the number of atoms and the

composition percentage of protein and glucose,

which are alike 29.9% of the liver tissue.

Thus, a similar calculation is carried out for protein

and glucose existing in the sample tissue. Due to the

same percentage of protein and glucose existing in

the liver (29.9%), the weight of 1 gram-molecular of

both proteins (C44189H71252N12428O14007S321)

and glucose (C6H12O6) is jointly calculated.

The number of common atoms between two

molecules namely: C, H, and O are: 44195, 71264,

and 14013 respectively [17, 18, 19].

The weight of 1 gram-molecular of both protein

(C44189H71252N12428O14007S321) and glucose

(C6H12O6) → 532864.58 (C) + 71834.112 (H) +

224193.99 (O) + 174079 (N) + 10291.26 (S) =

1013262.9 g

ii) The weight of protein and glucose existing in this

liver tissue is:

5982000

100

9.29 =× g (Protein and Glucose)

iii) The weight of existent carbon in glycogen is:

101326

532864

2.9

.58 598×=

315.116 g (C)

iv) Similarly, the weight of existent hydrogen,

oxygen, nitrogen, and sulphur are also calculated as

below:

For hydrogen: =× 598

5.1011224

112.71834 42.479 g (H)

For oxygen: =× 598

5.1011224

99.224193 132.579 g (O)

For nitrogen: =×598

5.1011224

174079 102.943 g (N)

For sulphur: =×598

5.1011224

26.10291 6.085 g (S)

(IV)

i) Therefore, the total mass of each element existing

in the mentioned tissue is shown below:

For hydrogen → 155.975 g + 0.444 g + 42.479 g =

198.898 g (H)

For oxygen → 1237.824 g + 3.528 g + 132.579 g =

1373.931 g (O)

For carbon → 3.027 g + 315.116 g = 318.143 g (C)

For nitrogen → 102.943 g (N)

For sulphur → 6.085 g (S)

ii) In this state, the amounts of H and O are

incorporated into the water:

1 H2O = 2H + O → the amount of water because

incorporating the hydrogen and oxygen will be:

85.876 g (H2O)

In this stage, the obtained results are defined for the

MCNP code, and are inputted to this code. On the

other hand, decomposed tissue gets virtually

irradiated by neutron beam, and the results are

specified for a wide range of energies [20, 21].

Since the related simulation is associated with the

MCNP code and it is required a big data to be

illustrated, to better illustrate the simulation and its

results, a part of the results extracted from the

MCNP code are shown as follows.

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DOI: 10.37394/232023.2022.2.6

Seyed Alireza Mousavi Shirazi

E-ISSN: 2732-9992

Volume 2, 2022

Fig 1. A part of the results extracted from the

simulation of the research by MCNP code of

absorbed dose in the water of the tissue plotted by

MCNP code

As shown, in the first column of the results

extracted from the MCNP code, the energy groups

of neutron, and the correlated absorbed doses, and

the errors, respectively are illustrated.

3 Results and Discussion

As explained in the article, at first, a liver tissue was

decomposed to its constituent materials, and then

was simulated by the MCNP nuclear code, and was

virtually irradiated by neutrons. The function of the

MCNP code is that it applies MONTE-CARLO

method to generate random number, and simulating

a sample space, and using random processes. After

many computational mathematics based on the

transport equation, a population of particles like

neutrons are collided, and then, the amounts of

absorbed doses are obtained. The transport equation

is as follows.

''' ' ''

.(,,) (,)(,,)

(, , ) (, , ) (, , )

rE rE rE

dE d r E E r E S r E

µϕ

∞

Ω∇ Ω + Ω =

Ω→Ω→Ω Ω+Ω

∫∫

(1)

The type and values of elements existing in the

mentioned tissue are according to Table 1.

Table 1. The type and values of elements existing in

the tissue

The existing

elements

(in the tissue)

The

obtained

value (g)

Percentage of

the element (%)

sulphur 6.085 0.3

Carbon 318.143 15.9

Hydrogen 198.898 9.95

Oxygen 1373.931 68.7

Nitrogen 102.943 5.15

Total 2000 100

The amounts of absorbed dose are extracted by

MCNP code, and illustrated in Figures 2 and 3:

Fig 2. The amounts of absorbed dose in the water of

the tissue plotted by MCNP code

Fig 3. The total amounts of absorbed dose received

by the tissue plotted by MCNP code

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Seyed Alireza Mousavi Shirazi

E-ISSN: 2732-9992

Volume 2, 2022

According to Figs. 2 and 3, the amounts of absorbed

doses in water, and also the total absorbed doses are

linearly changed within the neutron energy range 0-

17 MeV, but there appears a sharp rise within the

energy range 15-17 MeV.

4 Conclusion

As observed in Figs. 2 and 3 (extracted from the

MCNP code), it can be inferred that by increasing

the incident neutron energy within the fast to

thermal neutron range, water receives large amounts

of absorbed dose.

The current research can be generalized for other

tissues like stomach and intestine.

In the ICRP report, for a wide range of energy, the

conversion coefficients of fluence to effective dose

have been derived from the obtained organ dose,

thereby the radiation weighting factor (WR) and the

tissue weighting factor (WT) are very important

parameters to be considered. For instance, the skin

equivalent dose conversion coefficients have been

obtained for electrons and alpha particles in a

parallel beam on a tissue. The high LET includes

protons resulting from the capture reaction of a

neutron with nitrogen, and recoil protons resulting

from the collision of fast neutrons with hydrogen.

The low LET of gamma rays is resulting from the

capture of thermal neutrons with normal tissue and

also hydrogen atoms [1H(n,γ)2H]. In addition, the

high LET of protons is produced by fast neutrons

scattering and also from the capture of thermal

neutrons by nitrogen atoms [14N(n,p)14C].

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Volume 2, 2022

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Contribution of individual authors to

the creation of a scientific article

(ghostwriting policy)

Seyed Alireza Mousavi Shirazi has carried out

all of the scientific works belonging to this

research consisting of calculations, simulation,

and extraction of the results. In addition, he has

authored and organized the paper.

Sources of funding for research

presented in a scientific article or

scientific article itself

There are no potential sources of funding for this

research.

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MOLECULAR SCIENCES AND APPLICATIONS

DOI: 10.37394/232023.2022.2.6

Seyed Alireza Mousavi Shirazi

E-ISSN: 2732-9992

Volume 2, 2022