Economic Approach to Risk Analysis of Naturally Occurring Radioactive Materials (NORMs) in Dairy Milk Products Consumed in Nigeria

One of the UN SDGs is for sustainable food for all; thus the need for safety in milk consumption in Nigeria which is also consonant with the NAFDAC regulatory plan of safety of food in Nigeria. This research work examined the radioactivity content in milks (powdered and liquid) consumed in Nigeria using sodium iodide (7.6 cm (cid:1) 7.6 cm NaI(Tl)) detector. The estimated total cost of health detriment of consumption of the investigated milk products shows that the children age group has the highest cost health detriment per-caput dose with an estimated total cost of health detriment of US $17.26 million, followed by the adult age group with an estimated cost implication of US $11.86 million, and infants with the least computed cost implication of US $10.192 million. The overall results show that the milks consumed in Nigeria are radiologically safe and may not constitute any direct radiological health burden to consumers of these milk brands. Optimization of radiation protection mechanism for cost-benefit analysis is recommended.


Introduction
Radionuclide consequence recognizes no boundaries and therefore it is transborder in nature. It can migrate through food, air, and soil and be transported to faraway countries from where its pollution or contamination occurs. An assessment of any release of radioactivity to the environment is important for the protection of public health, especially if the released radionuclides can enter the food chain. Milk as a staple food may naturally represent a comprehensive radioactive food chain because cows consume grass and are exposed to the same radioactive elements as food crops and water supply.
Contamination pathway: emitted radionuclides go into the human body through multifaceted mechanisms which include the intake of foodstuffs via food chain from natural sources. Vegetables and green leafy are susceptible to exterior contamination during the growing season, whereas roots and tubers get contaminated through the ingestion of nutrient from the soil [1,2]. Grains are subjected to contamination mostly during storage or fallout may occur during the growing season as in the case of Fukushima Daiichi nuclear fallout. These liberated radionuclides may be transported into the grains and grasses through the plant growth process and find their way into the food chain when grazed by a cow [3]. Pollution of dairy products like milk is largely due to animal grazing and consumption of contaminated grass and drinking waters. Thus grass is essentially a direct source or pathway of radionuclides to animals and to man through meat and milk consumption. If dairy milk starts testing positive for high level of radioactive elements, this is indicative of radioactive contamination of the total food supply [4]. Milk samples that contain high levels of radioactivity when ingested by man could accumulate in certain parts of the body, for example, uranium-238 and radium-226 accumulates in human kidney and lungs, and thorium-232 accumulates in human liver, skeleton, tissue, and lungs, while potassium-40 accumulates in the muscles [5]. The accumulation of these radionuclides in any vital organs of the human body will affect the health condition that may cause various forms of diseases and weakening of the immune system and contribute to the increase in mortality rate [6].

Statement of the problem
Since the end of Second World War in 1948, research works on radionuclide contamination of food in the environment, and its transfer mechanism and pathway to animals and human population have been reported with vigor (ICPR, 1993(ICPR, & 2000, [2,[7][8][9][10][11]); milk has been one of the staple foodstuff products that was featured prominently in the food items studied [9]. This may be due to its vital position in a family's daily food consumption plan, thus a reliable indicator of natural radionuclides to man for its high consumption rate globally. It is one of the essential food for human nutrition and contains most of the macronutrients, namely, protein, carbohydrates, fat, vitamins (A, B, and D groups), and trace elements such as calcium, phosphate, magnesium, zinc, and selenium [7,12]. Milk is a rudimentary foodstuff for the infants compared to adults, on apparent body weight basis. Thus, milk consumed in Nigeria need to be assessed for radiological risk level for proper economic benefit analysis. It is therefore pertinent to set a radionuclide regulatory framework necessary in establishing guidelines relating to radiation protection in milk as a staple foodstuff. To the best of our knowledge, comprehensive data base on levels of radionuclides in staple foodstuffs and standard radionuclide regulatory framework for food imported and consumed in the country are inadequate, these lay credence to this research work.

Aim and objectives of the study
This research work was designed to examine the level of natural radionuclides present in liquid and powdered milk products consumed in Nigeria with a view to establishing their specific activities and compare same with values reported in other parts of the world. Assessment of the annual internal dose from the intake of the milk product will be determined, while the doses to the different sensitive human organs were estimated to establish their radiological risk to man. The result would be a contribution to the creation of a standard catalogue of natural radioactivity in foodstuff (milk) in Nigeria. This can serve as a baseline data for possible evaluation of future change in activity levels of these milk products due to environmental factors, ingredient composition, etc. The result obtained in this study will also be useful to the country food and drug regulatory body which has the obligation to protect the public health by ensuring that only the right quality of food and drugs are imported and consumed in the country.

Sample collection
To collect milk samples that represent a fair proportion of milk products consumed in Nigeria, a survey was carried out, which involves visiting homes, major supermarkets, fast food outlets, hotels, and major milk distributors throughout the six geopolitical zones in Nigeria. The survey revealed that the acceptability of brands of the milk (powdered or liquid) is dictated by its availability, cost, and social class of consumers. The availability of specific products in a region is closely related to the proximity to the manufacturer or key distributor and the awareness due to advertisement of the products in the area. This in situ assessment has shown that 10 leading powdered milk and 11 liquid milk brands were consumed by a large sector of the populace in the six geopolitical zones of the country in the following order: Peak > Cowbell > Coast > Loya > Nunu > Miksi > Dano > real milk for powdered milks and peak > Three Crown > Coast > Hollandia > Olympic > Nunu > Nutri milk > vital milk > Lady liberty > Bridel in liquid milks, of these Dano milk (Demark), Bridel milk (France), and Lady liberty (USA) are imported milk brands. These 10 powdered milk brands and 11 liquid milk brands were then sourced from various shopping malls and local markets. Two hundred (200) grams of the powdered milk collected was put in a cylindrical polystyrene container and sealed with tapes to prevent radon permeability, while for liquid milk, 200 cl of the homogenous samples was filled into a Marinelli beaker which was hitherto washed, rinsed with diluted H 2 SO 4 acid to prevent the samples from being contaminated, and sealed and weighed as samples for gamma spectroscopy analysis.

Gamma spectroscopy analysis
The collected sealed samples were left for a minimum of 4 weeks to allow secular equilibrium prior to the counting of the samples for radioactivity concentration. The counting for radioactivity was carried out using a 7:6cm Â 7:6cm NaI(Tl) detector for 10 h (Model Bircom, USA) housed in a 10-cm-thick lead shield to reduce background gamma radiation. The detector with energy resolution (FWHM) of 7.5% at 662 keV was coupled to a set of electronics which consist of pre-amplifier, main amplifier, analog-to-digital converter (ADC), and a Canberra Multichannel Analyzing (MCA) computer system. The integrated spectroscopy system was used for the power supply and the data acquisition of the energy spectra and utilized SAMPO S100 software package from Canberra (MAESTRO window USA). The energy calibration of the detector was performed between the gamma energy range of 83 keV and 1875 keV using International Atomic Energy Agency standard point sources ( 109 Cd, 57 Co, 137 Cs, 54 Mn, and 22 Na), the energy range of the radionuclide to be identified. To simulate the milk samples, 100 g of IAEA-375 reference sample was used. The radioactivity concentrations of 226 Ra/ 238 U were determined from the photopeaks of 609.32 keV ( 214 Bi), 1120.20 keV ( 214 Bi), and 352.6 keV ( 214 Pb) and that of 232 Th from 969.3 keV ( 228 Ac) and 583.78 keV ( 208 Tl), while the radioactivity of 40 K was evaluated from 1460.3 keV photopeak following the decay of 40 K. The background spectrum measured under the same settings for both the standard and sample measurement was used to correct the computed sample activity concentration in agreement with Arogunjo et al. [13].

Results
The measured radioactivity levels of the three naturally occurring radionuclides, 226 Ra, 232 Th, and 40 K, identified in the sampled milk under investigation including their uncertainty are presented in Table 1.
The obtained results of the radioactivity concentration indicate that 226 Ra activity in powdered milk varied from 14.2 AE 5.9 Bq kg À1 to 26 232 Th samples had the least activity level. Evaluation of the three naturally occurring radionuclide concentrations in the milk samples with the UNSEAR 2000 permissible limit for powdered milks and liquid milk samples shows that all 226 Ra and 232 Th activity levels in both samples are well below the permissible limits, while 40 K exceeded the permissible limit in Peak milk, Peak Chocolate, Cowbell Chocolate, Loya, Miksi, Coast, Real, and Nunu milk for powdered milk and exceeded the permissible limit for liquid milk in Vital and Nutric milk. It is pertinent to note that the activity levels determined in the current study are above the values gotten for milk consumed in some countries like Saudi Arabia [7]; Iran/France [14]; Jordan [15]; Egypt [16]; and Syria [17], while the values are comparable to those milk consumed in other countries like New Zealand [14] and Brazil [18]. Conversely, this result shows that the mean activity concentrations in the various milk brands sampled are well within their international permissible limits. The difference in the radioactivity levels in the various brands of milk sampled suggests that the source of raw materials used for the production of the milks is a contributory factor.
The estimated Radium equivalent (Ra eq ), annual gonadal dose equivalent (AGED), internal hazard (H in ) indices, annual effective dose equivalent (AEDE) received, and excess lifetime cancer risk (ELCR) for the various milk products sampled are presented in Table 2.

Radium equivalent activity (Ra eq )
The model of the radium equivalent activity establishes the use of a single index to define the gamma output or compare the specific activities of materials containing 226 Ra, 232 Th, and 40 K by a single quantity, which takes into consideration the radiation risk associated with these NORMs [19][20][21][22]. The radium equivalent activity represents a weighted factor of activities of the three natural radionuclides measured and is based on the estimation that 1.0 Bqkg À1 of 226 Ra, 0.7 Bq kg À1 of 232 Th, and 13.0 Bq kg À1 of 40 K produce equal radiation dose rates [23,24].
The radium equivalent activity concentration is given as [23]: where C Ra, C Th, and C K are the radioactivity concentrations in Bq kg À1 of 226 Ra, 232 Th, and 40 K, respectively.
The consumption of any foodstuff whose Ra eq concentration exceeds 370 Bq kg À1 should be discouraged to avoid radiation hazards. The result of the estimated radium equivalent dose rates in Table 2 shows a value range of 60.6 AE 20.8 Bq kg À1 in Cowbell milk to 82.5 AE 24.3 Bq kg À1 in real milk with a mean value of 72.6 AE 19.7 Bq kg À1 in powdered milk brands, while in liquid milk brand, the range of value is 41.5 AE 12.9 Bq l À1 in Peak milk to 72.0 AE 20.3 Bq l À1 in Nutric milk with a mean value of 56.2 AE 17.0 Bq l À1 . All the values obtained are within the international acceptable limit for Ra eq and therefore comply with the radium equivalent standard for radioactivity concentration. The percentage contributions of the three naturally occurring radionuclides in the powdered and liquid milk samples are shown in Figures 1 and 2, respectively. These percentages were calculated based on the estimation that 1 Bq kg À1 of 226 Ra, 0.7 Bq kg À1 of 232 Th, and 13 Bq kg À1 of 40 K produce the same radiation dose rates in the radium equivalent [24]; the average percentage contribution of 40 K is 42%, and for 226 Ra the percentage contribution to the entire milk content is 20%, while 232 Th percentage contribution to the powdered milk samples is 38%. The percentage contribution of the three natural radionuclides ( 226 Ra, 232 Th, and 40 K) to the liquid milk samples were computed to be 24, 36, and 40%, respectively, which shows that 232 Th contributes the highest radioactivity dosage to both the powdered and liquid milk activity concentration.

Annual gonad equivalent dose (AGED)
The gonads, the active bone marrow, and the bone surface cells are classified as organs of interest by UNSCEAR (2003). The annual gonadal dose equivalent (AGED, mS vy À1 ) owing to the specific activities of 226 Ra, 232 Th, and 40 K was computed using [25]:  where C Ra , C Th , and C K represent the radioactivity levels of 226 Ra, 232 Th, and 40 K, respectively. If the radioactivity of the food source is higher than the world permissible value of 0.30 mSvy À1 , the model suggests that the food product is a potential source of radiological health risk to the consumer. In the studied powdered milk samples, AGED activity concentration varied from 208.3 μS vy À1 to 290.7 μS vy À1 , whereas in liquid milk samples analyzed, the estimated activity levels varied from 170.6 μS vy À1 to 256.4 μSvy À1 . Although the obtained 290.7 μS vy À1 activity concentration value in Real powdered milk is approximately the maximum permissible limit value, all other obtained estimated values in both liquid and powdered brands of milk sampled are well within the global maximum permissible values of 300 μS vy À1 [26]; thus the different milk samples examined may not cause any immediate radiological health side effects in terms of AGED index.

Internal gamma indices
The internal hazard (H in ) index is defined according to Zarie and Al-Mugren [27] as: where C Ra , C Th , and C K represent the radioactivity levels of 226 Ra, 232 Th, and 40 K correspondingly. H in should be less than the unity for the radiation risk to be insignificant.
The internal hazard index (H in ) estimates the internal exposure rate to oncogenic radon nuclides and its short-lived progeny. The mean radioactivity values of the computed H in for powdered and liquid milk products are 0.3 and 0.2, respectively, which are well below the unity value recommended as the permissible limit. It is observed from the values obtained that powdered milks contain more of the natural radionuclides than liquid milk samples, which may be a result of the activity concentration through evaporation to dryness of the raw liquid milk. But all the milk samples analyzed met the minimum internal gamma index requirement for consumption.

Annual effective dose equivalent (AEDE)
The annual effective dose equivalent received was computed from absorbed dose rate by applying a dose conversion factor of 0.7 Sv Gy À1 and the occupancy of 0.8 (19/24) recommended by UNSCEAR [26] and Veiga et al. [28]. Therefore, the annual effective dose equivalent (μS vy À1 ) was calculated using the formula [26]: The estimated annual effective dose equivalent obtained for the powdered and liquid milk brands analyzed is shown in Table 2. The values obtained for the powdered milk varied from 146.2 μS vy À1 to 202.6 μS vy À1 with a mean activity dose level of 178.4 μS vy À1 , while in the liquid milk, the activity dose levels ranged from 99.6 μS vy À1 to 177.1 μS vy À1 with a mean activity concentration of 135.9 μS vy À1 . The obtained result shows that the milk samples surveyed have their annual effective dose equivalent values lower than the world average values of 450 μS vy À1 [26,[29][30][31]. This result shows that the various sampled milk brands are radiologically safe going by the global recommended permissible limit of annual effective dose rate.

Excess lifetime cancer risk
Excess life cancer risk predicts the likelihood of developing cancer over a lifetime at a certain exposure rate. It is a value representing the number of extra cancers expected in a given number of people on exposure to a carcinogen at a given dose.
Excess lifetime cancer risk is given as Taskin et al. [32]: The parameters used are defined; thus AEDE is the annual effective dose equivalent, DL is average duration of life (estimated to be 70 years), and RF is the risk factor (S/v), i.e., fatal cancer risk per Sievert. ICRP uses a RF of 0.05 for the public for stochastic effects [32]. The intake of milk containing an elevated level of radionuclide may increase the chance of cancer risk. If the radioactivity in the milk is higher than the world average, it could be a source of radiation to the human body and some specific organs, in that their ELCR would be greater than the world average of 0.29 mS vy À1 in such body. The estimated ELCR obtained in all the measured samples is lower than the international standard limit. Table 3 presents the estimated values of the annual effective dose of the three age groups of infants, children, and adult represented in this evaluation. Table 4 shows the dose conversion factor for the three different age groups used in estimating the annual effective dose rate to individual consumption of the various milk samples in Nigeria.

Annual effective dose for different age groups
"The annual effective dose E D to individuals due to the ingestion of the radionuclides in powder and liquid milk is estimated using the equation.
where the parameters; E D is the annual effective dose in (Svy À1 ), A c is the activity concentration of the radionuclides in milk; E is the dose conversion factor and I in is the annual intake of milk with respect to the age group" [15]. Table 3 presents the result of the computed annual ingestion dose to the three age groups (infants, children, and adults), with an estimated annual milk intake of 15 kg, 14 kg, and 10 kg, respectively, and using the conversion factor values in Table 4. The results obtained indicate that the infants' accumulated maximum and minimum effective dose values are 1743.0 μS vy À1 and 892.7 μS vy À1 , respectively, with an average dose rate of 1345.4 μS vy À1 . For the children, the obtained values for the annual accumulated maximum and minimum effective ingestion doses are 1048.9 μS vy À1 and 546.8 μS vy À1 , respectively, with an average dose rate of 822.5 μS vy À1 . The accumulated maximum and minimum annual effective ingestion doses obtained for adults are 235.1 μS vy À1 and 122.3 μS vy À1 , respectively, with an average annual dose rate of 181.1μSvy À1 . The obtained dose rates in the three different age groups show that the annual ingestion dose exceeded the UNSCEAR [26], maximum permissible limit by 68% for the infants, and 2.8% for the children; however, the adult value is 22.6% below the recommended maximum permissible limit. This obtained result indicates that the ingestion rate of milk by infants and children should be reduced to avoid any future amassed radiological health side effect [34]; accordingly an optimized amount of milk is required to be recommended as a yearly permissible limit for consumption.  [33]. Table 5 shows the optimized annual consumption rate to stay within the international recommended range.
Following the exceeding of the UNSCEAR [26] μSvy À1 permissible limit from the recommended quantity of milk to be consumed by the three age groups, presents an optimized annual quantity of powdered milk to be consumed as 7 kg and 11 kg for children and infants, respectively, and 8 kg and 13 kg were 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 800 μSv [26] yearly recommended permissible limit. Table 6 presents the result of calculated effective dose rate to the different human organs for consuming powdered and liquid milk. Table 7 presents the average values of F, for different organ or tissue uses in the computation of the effective dose rate of these organs.

The effective dose rate (D organ ) in mS vyr À1 to different body organs or tissues
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 transported to a particular organ was calculated using the relation: The parameter E D 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 consumption of the food. Table 6 presents the obtained computed values of the effective dose rate assimilated 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 greatest dose of average values of 1.1 mS vy À1 , 0.6 mS vy À1 , and 0.1 mS vy À1 for infants, children, and adults, respectively; meanwhile, the dose received by the liver was established to be the least with average dose values of 0.6 mS vy À1 , 0.4 mS vy À1 , and 0.1 mS vy À1 , respectively. The computed results obtained from liquid milk follow the same trend with testes recording the highest radionuclide dose ingestion with average estimated dose levels of 0.9 mS vy À1 , 0.5 mS vy À1 , and 0.1 mS vy À1 for infants, children, and adults, respectively, and the least dose intake values of 0.5 mS vy À1 , 0.3 mS vy À1 , and 0.1 mS vy À1 were detected in liver for  Table 7. Average values of F for different organs or tissues [33].
infants, children, and adults, respectively. It was observed from the results that the dose ingestion to infants' testes exceeded the world acceptable limit of 1.0 mSv annually to the human-sensitive organs/tissues. The relatively higher dose to the testes and low-dose intake to the liver are justifiable from food nutrient absorption rate [15,31]. The high radiological dose to the testes may justify the rampant rate of prostate cancer among young men which may be linked to accumulated effects of the dose intake over time, which need further clinical investigation [34].

Risk factors and cost-benefit analysis
Cost-benefit analysis in radiation protection is the projection of radionuclide injection effects of consumption of food product versus the nutritional benefits derived from the intake of the food at low individual doses, below the dose limits. Applying the direct relationship between dose and effect, the health impairment is directly proportional to the effective dose-equivalent occasioned by the consumption of milk product. The proportionality element is termed the risk factors [35,36].

Committed effective dose (C D )
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: 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 À1 and 9.1 mS vy À1 doses, respectively. The committed doses obtained for children were 48.1 mS vy À1 and 41.1 mS vy À1 for powdered and liquid milk, respectively, while for infants it is 80.4 mS vy À1 and 67.3 mS vy À1 , 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.

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 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, S E in a population comprising of N i individuals, is evaluated as [39]: where S E represents the collective effective dose equivalent (person, Sv) and N i is the number of persons in a population that are exposed to the radiation, while H Ei represents the mean effective dose equivalent (μS vy À1 ).
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: 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 S E 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.

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]:  Table 9.
Nigeria population in different age groups [37].
From Eq. (11), R T 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 Â 10 À2 Sv À1 , with 1.25 Â 10 À2 Sv À1 representing the value for fatal radiation-induced cancers and 0.4 Â 10 À2 Sv À1 representing the value for severe hereditary effects, for the first two generations, while S E 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 Â 10 À2 Sv À1 . 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.

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]: where Y C 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.

Conclusion
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 (1.0 Sv y À1 ). All the calculated radiological risk parameters show that none of the 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 À1 and 15 kg y À1 , respectively, 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.

Author details
Ezekiel O. Agbalagba* and Hannah O. Agbalagba Federal University of Petroleum Resources, Nigeria *Address all correspondence to: agbalagba.ezekiel@fupre.edu.ng; ezek64@yahoo.com © 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, provided the original work is properly cited.