**4.1 Committed effective dose (CD)**

presents an optimized annual quantity of powdered milk to be consumed as 7 kg

**Organ or tissue Conversion factor (F)**

Lungs 0.64 Ovaries 0.58 Bone marrow 0.69 Testes 0.82 Whole body 0.68 Kidney 0.62 Liver 0.46

*Multifunctionality and Impacts of Organic and Conventional Agriculture*

recommended for children and infants, respectively, for liquid milk, while adult was not optimized because the value obtained was within the international permissible limit. Using the optimized quantity, the annual accrued values obtained for infants and children for powdered milk were 750.1 μSv and 755.9 μSv, respectively, while the accumulated values recorded for liquid milk were 717.6 μSv and 763.7 μSv for infants and children, respectively. The values recorded are well below the

**Table 6** presents the result of calculated effective dose rate to the different

**3.8 The effective dose rate (Dorgan) in mS vyr**�**<sup>1</sup> to different body organs or**

transported to a particular organ was calculated using the relation:

**Table 7** presents the average values of F, for different organ or tissue uses in the

The annual effective dose to organ models evaluates the total amount of radionuclides consumed by man over a period of 1 year that goes to and accumulate in the different sensitive organs and tissues of the human body. The effective dose rate

The parameter *ED* represents the annual effective dose, *O* represents the occupancy factor with a value of 0.8, and F is the conversion factor of organ dose from

**Table 6** presents the obtained computed values of the effective dose rate assim-

infants, children, and adults, respectively; meanwhile, the dose received by the liver

0.1 mS vy�<sup>1</sup> for infants, children, and adults, respectively, and the least dose intake

liquid milk follow the same trend with testes recording the highest radionuclide

ilated by the various organs evaluated, while **Table 7** presents the conversion factors and F values for the seven organs/ tissues. The computed dose values obtained in powdered milks revealed that the human testes (organ) received the

was established to be the least with average dose values of 0.6 mS vy�<sup>1</sup>

dose ingestion with average estimated dose levels of 0.9 mS vy�<sup>1</sup>

, 0.3 mS vy�<sup>1</sup>

Dorgan mSvy�<sup>1</sup> <sup>¼</sup> <sup>O</sup> � ED � <sup>F</sup> (7)

, 0.6 mS vy�<sup>1</sup>

, respectively. The computed results obtained from

, and 0.1 mS vy�<sup>1</sup> were detected in liver for

, and 0.1 mS vy�<sup>1</sup> for

,

, 0.5 mS vy�<sup>1</sup>

, and

and 11 kg for children and infants, respectively, and 8 kg and 13 kg were

800 μSv [26] yearly recommended permissible limit.

*Average values of F for different organs or tissues [33].*

human organs for consuming powdered and liquid milk.

computation of the effective dose rate of these organs.

**tissues**

**Table 7.**

consumption of the food.

0.4 mS vy�<sup>1</sup>

**72**

values of 0.5 mS vy�<sup>1</sup>

greatest dose of average values of 1.1 mS vy�<sup>1</sup>

, and 0.1 mS vy�<sup>1</sup>

The committed effective dose to an individual assessed for three age groups (0–1 yr infant, 1–7 yrs children, and >17 yrs age group for adults) over a typical lifetime of 50 years was computed using the formula:

$$\mathbf{C\_D = 50 \times E\_D} \tag{8}$$

The calculated committed effective doses to the various age groups are presented in **Table 8**. The obtained doses to infants and children were futuristic and a forecast of the probable dose to be committed to the individuals in the period of 50 years. The obtained dose values for adult over an average lifetime of 50 years for powdered milk and liquid milk were 9.3 mS vy�<sup>1</sup> and 9.1 mS vy�<sup>1</sup> doses, respectively. The committed doses obtained for children were 48.1 mS vy�<sup>1</sup> and 41.1 mS vy�<sup>1</sup> for powdered and liquid milk, respectively, while for infants it is 80.4 mS vy�<sup>1</sup> and 67.3 mS vy�<sup>1</sup> , respectively. The result obtained points to the fact that constant ingestion of the milk products may result to accumulation of radionuclides in some organs of the human, with more radionuclide dose intake in powdered milk than consuming liquid milk. Moreover, the values gotten are well within international standard.

**Table 8** presents the summary of the result of the risk analysis and health detriment effect values that may arise from the consumption of milk product samples investigated in this study.

**Table 9** presents the population of the three age groups under examination in this study, obtained from the National Population Commission report [37], and the computed two-thirds (2*=*3Þ of this population used for the evaluation of the collective effective dose equivalent.

#### **4.2 Collective effective dose equivalent**

It is insufficient that the risk to individuals is set at an adequately low level in radiation protection, but the total detriment to the public resulting from exposure to radiation should be kept as low as is reasonably achievable (ALARA) for health, economic, and social factors. The evaluation of the collective/total detriment to health for the public is the sum of detriments to the individuals making up the



*Summary of risk analysis of radiation dose from milk products.* public due to a level of radiation exposure. The statement of proportionality between stochastic biological effects and dose equivalent also applies to the collective detriment to health being directly proportional to the collective effective dose equivalent [38]. Hence the collective effective dose equivalent, SE in a population

**Age Population (Pi) Two-thirds of the population (2**

*Economic Approach to Risk Analysis of Naturally Occurring Radioactive Materials (NORMs)…*

Infant (0–1 yr) 7,771,348 5,180,899 Children (7–12 yrs) 21,763,942 14,509,295 Adult (>17 yrs) 72.660,755 48,440,503

where SE represents the collective effective dose equivalent (person, Sv) and N*<sup>i</sup>* is the number of persons in a population that are exposed to the radiation, while HE*<sup>i</sup>*

The Nigerian Population Commission [37] puts the population figure of people living in Nigeria as 140,431,790 with the age groups of 0–1 year, 7–12 years, and >17 years having population figures of 7,771,348; 21,763,942; and 72,660,755, respec-

In Nigeria, approximately two-thirds of the population are expected or projected to make one brand of milk or the other as staple food; consequently two-thirds of the population of the different age ranges/groups are probable to have a radiation

The formula for collective effective dose equivalent was accordingly modified to

3

**Table 9** presents the population of three age group brackets being studied in Nigeria. Since two-thirds of the estimated population of Nigerian projected to consume one brand of milk or the other, it is estimated that the 5,180,899 infants, 14,509,295 children, and 48,440,503 adults signifying 48.5% of the total population of Nigeria consume milk products. The estimated collective effective dose equivalent SE obtained revealed that the value for infants is 5551.5man-Sv in powdered milk and 4640.9man-Sv in liquid milk. In the children age bracket, the values obtained are 9305.8man-Sv for powdered milk and 7950.3man-Sv for liquid milk. Similarly, in the adult age bracket, the collective effective dose equivalent values obtained are 6023.1man-Sv for powdered milk and 5840.7man-Sv for liquid milk. The values obtained revealed that the children population is probable to have the

The objective gross or total health detriment also known as collective health

detriment "G" (man), resulting from exposure to gamma radiation in an environment or ingestion of irradiated products by man, is evaluated using the

SE <sup>¼</sup> <sup>X</sup><sup>2</sup>

SE <sup>¼</sup> <sup>X</sup>*NiHEi* (9)

**<sup>3</sup> Pi)**

).

ð Þ *NiHEi* (10)

comprising of Ni individuals, is evaluated as [39]:

*Nigeria population in different age groups [37].*

*DOI: http://dx.doi.org/10.5772/intechopen.92279*

represents the mean effective dose equivalent (μS vy�<sup>1</sup>

tively.

**Table 9.**

read:

dose intake from milk products.

highest radionuclide dose from milk intake.

**4.3 Total health detriment**

formula [38]:

**75**

*Economic Approach to Risk Analysis of Naturally Occurring Radioactive Materials (NORMs)… DOI: http://dx.doi.org/10.5772/intechopen.92279*


**Table 9.**

*Nigeria population in different age groups [37].*

public due to a level of radiation exposure. The statement of proportionality between stochastic biological effects and dose equivalent also applies to the collective detriment to health being directly proportional to the collective effective dose equivalent [38]. Hence the collective effective dose equivalent, SE in a population comprising of Ni individuals, is evaluated as [39]:

$$\mathbf{S}\_{\text{E}} = \sum N\_{i} H\_{\text{E}i} \tag{9}$$

where SE represents the collective effective dose equivalent (person, Sv) and N*<sup>i</sup>* is the number of persons in a population that are exposed to the radiation, while HE*<sup>i</sup>* represents the mean effective dose equivalent (μS vy�<sup>1</sup> ).

The Nigerian Population Commission [37] puts the population figure of people living in Nigeria as 140,431,790 with the age groups of 0–1 year, 7–12 years, and >17 years having population figures of 7,771,348; 21,763,942; and 72,660,755, respectively.

In Nigeria, approximately two-thirds of the population are expected or projected to make one brand of milk or the other as staple food; consequently two-thirds of the population of the different age ranges/groups are probable to have a radiation dose intake from milk products.

The formula for collective effective dose equivalent was accordingly modified to read:

$$\mathbf{S}\_{\mathrm{E}} = \sum \frac{2}{3} (N\_i H\_{\mathrm{E}i}) \tag{10}$$

**Table 9** presents the population of three age group brackets being studied in Nigeria. Since two-thirds of the estimated population of Nigerian projected to consume one brand of milk or the other, it is estimated that the 5,180,899 infants, 14,509,295 children, and 48,440,503 adults signifying 48.5% of the total population of Nigeria consume milk products. The estimated collective effective dose equivalent SE obtained revealed that the value for infants is 5551.5man-Sv in powdered milk and 4640.9man-Sv in liquid milk. In the children age bracket, the values obtained are 9305.8man-Sv for powdered milk and 7950.3man-Sv for liquid milk. Similarly, in the adult age bracket, the collective effective dose equivalent values obtained are 6023.1man-Sv for powdered milk and 5840.7man-Sv for liquid milk. The values obtained revealed that the children population is probable to have the highest radionuclide dose from milk intake.

#### **4.3 Total health detriment**

The objective gross or total health detriment also known as collective health detriment "G" (man), resulting from exposure to gamma radiation in an environment or ingestion of irradiated products by man, is evaluated using the formula [38]:

**Age group**

**74**

 **Annual Effective dose**

**Committed**

**dose CD (mS vy1**

**)**

**dose equivalent**

 **SE**

**(G) (man)**

**(man-Sv)**

 **effective**

**Collective effective**

**Total health detriment**

**Mean THD (G)**

**Total cost of detriment (man-Sv)**

**(man)**

**\$million**

*Multifunctionality and Impacts of Organic and Conventional Agriculture*

**ED (μSv)**

**Powdered**

**Liquid**

**Powdered**

**Liquid**

**Powdered**

**Liquid**

**Powdered**

**Liquid**

**milk**

Infant (0–1 yr)

Children

962.0

 822.5

 48.1

 41.1

 9,305.8

 7,950.3

 153.5

 131.2

285

> (7–12 yrs)

Adult (>17 yrs)

**Table 8.** *Summary of risk analysis of radiation dose from milk products.*

 186.5

 181.1

 09.3

 9.1

 6,023.1

 5,840.7

 99.4

 96.4

196

11.9

 1607.3

 1345.4

 80.4

 67.3

 5,551.5

 4,640.9

 91.6

 76.6

168

10.2

17.3

**milk**

**milk**

**milk**

**milk**

**milk**

**milk**

**milk**

$$\mathbf{G} = \mathbf{R}\_{\mathbf{T}} \mathbf{S}\_{\mathbf{E}} \tag{11}$$

**5. Conclusion**

*DOI: http://dx.doi.org/10.5772/intechopen.92279*

(1.0 Sv y<sup>1</sup>

**Author details**

ezek64@yahoo.com

**77**

This investigation presents the gamma spectrometry evaluation of the natural radioactivity in powdered and liquid milk consumed in Nigeria. The radionuclide concentration of the milk samples was found to be dictated by the source the milks products were derived. Although the specific activity concentration of milk samples varied, their mean activities were less than the world permissible dose limit for the public. The radium equivalent activities obtained for all the milk samples (powdered or liquid) considered were all below the criterion limit of radiation dose

*Economic Approach to Risk Analysis of Naturally Occurring Radioactive Materials (NORMs)…*

milk samples exceeded their recommended allowable level. It was however found from the annual effective dose calculation that the consumption of powder and liquid milk by infants and children at the rate of 14 kg y<sup>1</sup> and 15 kg y<sup>1</sup>

tively, may lead to a radiation dose to vital organs of the body above normal recommended values, but optimized quantity was suggested for the group to stay within the recommended permissible limit. On the cost-benefit analysis, the estimated collective effective equivalent dose values obtained show that the children population receives the highest dose. The total health detriment values obtained revealed a low detrimental effect to consumers of these milk brands. The calculated values of the total cost of health detriment revealed that the children age group has the highest cost health detriment per-caput dose, followed by adults, while infants have the least; these values obtained are observed to be low. The overall result therefore shows that the powdered and liquid milks consumed in Nigeria are radiologically safe and may not cause immediate or significant radiation health hazard to consumers of the examined milk brands. However, optimizing radiation protection

by means of this cost-benefit analysis is recommended.

Ezekiel O. Agbalagba\* and Hannah O. Agbalagba Federal University of Petroleum Resources, Nigeria

provided the original work is properly cited.

\*Address all correspondence to: agbalagba.ezekiel@fupre.edu.ng;

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

). All the calculated radiological risk parameters show that none of the

, respec-

From Eq. (11), RT represents the total risk factor the body organs are exposed to, as recommended by the International Commission on Radiological Protection, ICRP [39], where these risk factors are used in assessing the fatal radiation-induced cancers and severe hereditary effects in the first two generations. It has a gross value of 1.65 � <sup>10</sup>�<sup>2</sup> Sv�<sup>1</sup> , with 1.25 � <sup>10</sup>�<sup>2</sup> Sv�<sup>1</sup> representing the value for fatal radiation-induced cancers and 0.4 � <sup>10</sup>�<sup>2</sup> Sv�<sup>1</sup> representing the value for severe hereditary effects, for the first two generations, while SE is the collective effective dose equivalent (man–Sv) [38].

The estimation of the total health detriment is vital and necessary because any health detriment on this populace will impact negatively on the entire population.

The total health detriment for the three age brackets computed in the different milk products examined is presented in **Table 8**. The total health detriment to man obtained for powdered milk are 91.6 for infants, 153.5 for children, and 99.4 for adults. In the liquid milks, the values obtained for the age groups are 76.6 for infants, 131.2 for children, and 96.4 for adults. This calculated total health detriment indicates that for every 5,180,899 Nigerian infants consuming milk products, 168 of them have the probability to have radiological health-related side effects from the intake of milk products. Similarly, the evaluation of the gross health detriment indicates that for every 14,509,295 Nigerian children consuming milk products, 285 are likely to have a radiological health risk from the intake of milk, while of the estimated 48,440,503 Nigerian adults that consume milk products, 196 are likely to have a radiological health hazard, with fatal radiation-induced cancers the most probable, going by the risk factor of 1.25 � <sup>10</sup>�<sup>2</sup> Sv�<sup>1</sup> . The radiological index obtained shows a ratio of 1:30,839 for infants, 1:50,910 for children, and 1:247,145 for adults, with infants' radiological index ratio being the highest. This indicates that the infants are most vulnerable radiologically in milk intake.

#### **4.4 Cost of detriment**

The correlation between the cost of the health detriment and collective effective dose equivalent is a linear one. It is expressed as [38]:

$$Y\_{\mathbb{C}} = a \mathbb{S}\_{\mathbb{E}} \tag{12}$$

where *YC* is the cost of health detriment, SE is the collective effective dose equivalent (man-Sv), and *α* is the collective dose equivalent constant. If it were possible to arrive at a common monetary value for the cost of radiation harmful stochastic health effects, then *α* would have a unique value. But it is not practically possible due to socioeconomic considerations that vary from country to country and from time to time. A review of literatures indicates a wide range of *α* values ranging from 1000 to 100,000 US dollars [38]. Considering the low per capita income of African countries including Nigeria which is below US \$100 per day, the cost of detriment analysis value of US \$1000 was assigned to human life. This value does not necessarily mean a real monetary value of life but rather is proposed to provide measures by which fair and consistent resources are allocated to radiation protection [21]. From the computed result of the total cost of health detriment from the collective effective dose equivalent to the different age group in **Table 8**, it was observed that children age group has the highest cost health detriment per-caput dose with an estimated total cost of health detriment of US \$17.256 million, followed by adults with an estimated cost implication of US \$11.864 million, while infants have the least with an estimated cost implication of US \$10.192.

*Economic Approach to Risk Analysis of Naturally Occurring Radioactive Materials (NORMs)… DOI: http://dx.doi.org/10.5772/intechopen.92279*
