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Kinetics of 210Po accumulation in moss body profiles


Radionuclide concentration analysis of total moss bodies often gave relatively different results than a separate analysis of each different morphological part of the same sample. The dynamics of the transfer of metals by dust uplifted from the soil and another approach, based on the diffusion of the two radionuclides to the moss, have been analyzed. In the proposed model, short- and long-term approaches have been applied. Each part of a moss’s profile can show different radionuclides accumulation ability, including both 210Pb and 210Po isotopes. A first-order kinetic model has been used for 210Po and 210Pb transport between three body components of mosses. This mathematical approach has been applied for 210Po activity concentration in the air estimation. For relatively clean deep forest region, calculated concentrations were from 17.2 to 43.8 μBqm−3, while for urban air concentrations were higher from 49.1 to 104.9 μBqm−3.


210Pb and 210Po are natural radionuclides present in the atmosphere in result of 222Rn exhalation from the ground. Both are widely used as markers of various atmospheric processes, and because of the disequilibrium between their activity, concentration in fresh aerosols are often use for aerosol residence time calculation method (Persson and Holm 2011; Papastefanou 2006; Długosz-Lisiecka and Bem 2012). Each year up to around 11 × 109 Bq of 210Po can be emitted to the urban air from the local coal power plants in Lodz city, Poland (Długosz-Lisiecka 2015b).

The 210Po radionuclide content in fresh outdoor living plants is the result of the adsorption process from atmospheric precipitation and ingrowth from 210Pb decay (Eq. 1) (Persson 2014).

$$ {}^{210} P{b}_{22.3\kern0.5em \mathrm{year}}\to {}^{210} B{i}_{5.03\kern0.5em \mathrm{days}}\to {}^{210} P{o}_{138\kern0.5em \mathrm{days}} $$

Mosses are common biomarkers mainly used for the quantitative determination of concentrations most spread pollutions (heavy metals, radionuclides) of the atmosphere. Because of their good adsorption capacity, the use of mosses as bioindicators of atmospheric metal or radionuclides deposition has been widely accepted (Agnan et al. 2015; Dołęgowska and Migaszewski 2013; Koz and Cevik 2014; Basile et al. 2001; Boquete et al. 2014).

The accumulation of 210Pb and 210Po in the moss body is generally characterized by two distinct processes: biosorption from dry or wet precipitation, or intake from soil, followed by internal transport. Firstly, a rapid radionuclides biosorption occurs to give a steady state, which is then followed by slower internal transport within the plant’s body (Basile et al. 2001; Boquete et al. 2014). This second, slow step is considered as decisive for the final total radionuclides uptake by moss cells (Długosz-Lisiecka 2016; Uğur et al. 2003, 2004; Brumelis and Brown 1997; Steinnes 1995; Krmar et al. 2009, 2016; Aleksiayenak et al. 2013). Passive deposition on the external parts of the moss body has also been taken into account (Kłos et al. 2012). It is generally assumed that the ectohydric mosses, represented by Pleurozium schreberi, take mineral components mainly from wet and dry deposition, so they are not greatly influenced by the soil composition (Fernández et al. 2005; Gjengedal and Steinnes 1990). Full analysis of the biosorption and accumulation of the metals should also take into account the translocation of the elements from the soil and their internal conduction by elongated cells, which promote the transport of water driven by surface tension (Kłos et al. 2012; Dołęgowska and Migaszewski 2013).

Both isotopes present in the air show different behaviors in the environment, including their transport and accumulation in plants, then can be transported between the annual increments of feather in the moss, and they are partially eluted due to leaching, depending on the meteorological conditions and the seasonal growth of the moss feather. Moreover, internal (vertical) transport of minerals within moss bodies, from leaves to rhizoids and vice versa, can also be enhanced by the presence of old dead tissue. Therefore, one should be aware that the rejection of dead fragments of stems or rhizoids can cause significant errors in the evaluation of the degree of air pollution by this method, thus, affecting the usefulness of moss as a biomarker.

The mathematical description of all the processes that occur in the moss body after absorption of the metals is quite complicated and depends on the speed of various processes. Several papers describe biosorption processes using the linear forms of the Langmuir, Freundlich, and Dubinin-Radushkevich models (Olu-Owolabi et al. 2012). The aim of this study is to use this type of kinetic investigation to identity activity of the 210Po in the air. For characterization of the dynamics of the metal bioaccumulation in the moss plant, at three compartment model has been applied. For each compartment, a first-order kinetic equation was used for analyzing the 210Pb and 210Po radionuclides’ transport within the mosses.

Material and methods

Samples were collected in two different environments (Fernández et al. 2005). Three samples were collected from different city centers and, for comparison, five samples were collected from unpolluted deep forest. The #1, #2, and #3 samples were collected during the summer, while samples #4 and #5 were taken in winter, all from a deep forest area, for identification seasonal fluctuation of radionuclide uptake from the environment by mosses.

Three remaining samples, #6, #7, and #8, were taken from the three city centers. Samples were dried in room temperature by 2 or 3 days, and the cleaned from grass, tree trunk, or other. The samples of mosses were divided into three parts: stems leaves, stems, and rhizoids (Długosz-Lisiecka and Wróbel 2014). The sample weights ranged from 1 up to a maximum of 2 g. Only two subsamples were prepare for each moss body parts for analysis radionuclides. Various species of the moss have different biosorption dynamic and accumulation ability; therefore, only one type of moss samples P. schreberi were object for this study. Pleurozium species is wide spread in local environment and has satisfying biomonitor features (Długosz-Lisiecka and Wróbel 2014).

The 210Pb activities were determined by gamma spectrometry analysis in anticoincidence mode (Długosz-Lisiecka 2016). After instrumental 210Pb analysis, a radiochemical 210Po separation technique was applied before counting this radionuclide with α-spectrometry. Each sample was placed in a beaker filled with 2 and 5 ml of concentrated HNO3 and HCl, respectively. In order to calculate the 210Po separation efficiency, a known activity of 209Po isotope (NIST 4326a) was added to each sample as a marker. After digestion, the samples were evaporated and the dry residues were dissolved in 70 ml of 1 M HCl. Prior to the spectrometry measurement, the 210Po and 209Po present in the solution were separated by spontaneous deposition on silver discs (the average efficiency of deposition was equal 95%). The activities of 210Po and 209Po were determined using an α-spectrometry system with a PIPS (CANBERRA) detector (Długosz et al. 2010).

The kinetics of the210Po and 210Pb radionuclides’ translocation with dust uplifted from the soil was evaluated using the epigeal moss P. schreberi. The kinetic parameters for the radionuclide content of the three compartments of the moss are shown in Fig. 1.

Fig. 1

Three compartment models of moss body vertical profile for 210Pb and 210Po bioaccumulation

Radionuclide uptake kinetics can be described using an adjustment of the three compartment models: Eq. (2, 3, 4) and Eq. (5, 6, 7) for 210Pb and 210Po, respectively.

$$ \left\{\begin{array}{l}\frac{dC_{Pb1}}{dt}={\lambda}_{b1} B+{\lambda}_{c1}{C}_{Pb2}-\left({\lambda}_{y1}+{\lambda}_{Pb}+{\lambda}_{z1}\right){C}_{Pb1}- sB\\ {}\frac{dC_{Pb2}}{dt}={\lambda}_{b2}{C}_{Pb1}+{\lambda}_{c2}{C}_{Pb3}-\left({\lambda}_{y2}+{\lambda}_{Pb}+{\lambda}_{z2}\right){C}_{Pb2}- sB\\ {}\frac{dC_{Pb3}}{dt}={\lambda}_{b3}{C}_{Pb2}+{\lambda}_{c3} D-\left({\lambda}_{y3}+{\lambda}_{Pb}\right){C}_{Pb3}- sB\end{array}\right. $$
(2, 3, 4)
$$ \left\{\begin{array}{l}\frac{{ d C}_{Po1}}{ d t}={\lambda}_{a1} X+\Delta {C}_{Po1}+{\lambda}_{d1}{C}_{Po2}-\left({\lambda}_{Po}+{\lambda}_{w1}+{\lambda}_{t1}\right){C}_{Po1}- kX\\ {}\frac{{ d C}_{Po2}}{ d t}={\lambda}_{a2}{C}_{Po1}+\Delta {C}_{Po2}+{\lambda}_{d2}{C}_{Po3}-\left({\lambda}_{Po}+{\lambda}_{w2}+{\lambda}_{t1}\right){C}_{Po2}- kX\\ {}\frac{{ d C}_{Po3}}{ d t}={\lambda}_{a3}{C}_{Po2}+\Delta {C}_{Po3}+{\lambda}_{d3} P-\left({\lambda}_{Po}+{\lambda}_{w3}\right)\;{C}_{Po3}- kX\end{array}\right. $$
(5, 6, 7)


CPo1,2,3; CPb1,2,3 :

activity concentration of 210Po and 210Pb [Bq kg−1] in the moss body, in compartments 1,2, and 3, respectively,


210Po and 210Pb activity concentrations accumulated from the atmosphere [Bq kg−1],

λa1,2,3, λb1,2,3, :

210Po and 210Pb radionuclides’ accumulation rate (adsorption rate) (day−1) for compartments 1,2, and 3, respectively (vertical, down),

λt1,2,3;λz1,2,3 :

210Po and 210Pb elimination rate (desorption) from each compartment of the moss’s body (day−1) for compartments 1,2, and 3, respectively,

λd1,2,3;λc1,2,3 :

210Po and 210Pb accumulation rate taking into account transport to the top for each part of the moss’s body (day−1) for compartments 1, 2, and 3, respectively (vertical, up),

λw1,2,3;λy1,2,3 :

210Po and 210Pb washout rate from each compartment of the moss’s body (day−1) for compartments 1, 2, and 3, respectively, to the outside,

λPo,λBi :

210Po and 210Bi radionuclide decay constant [day−1],


coefficient resulting from uplifted soil particles deposited on the surfaces of the moss samples for 210Po and 210Pb, respectively,

ΔCPo1,2,3 :

210Po ingrowth from 210Pb decay at time t [days].

As a result, after the integration for a given accumulation time t, a set of equations for each compartment can be obtained. Particularly for leaves (compartment 1), these equations have the following forms (equations for next compartments would have similar form):

$$ 1-{ \exp}^{\left(-\left({\lambda}_{y1}+{\lambda}_{z1}+{\lambda}_{Pb}\right) t1\right)}=\frac{\left({\lambda}_{y1}+{\lambda}_{z1}+{\lambda}_{Pb}\right){A}_{Pb1}}{\lambda_{b1} B+{\lambda}_{c1}{A}_{Pb2}- sB}{\mathrm{for}\kern0.5em }^{210}\mathrm{Pb}\ \mathrm{radionuclide} $$
$$ 1-{ \exp}^{\left(-\left({\lambda}_{w1}+{\lambda}_{t1}+{\lambda}_{Po}\right) t1\right)}=\frac{\left({\lambda}_{w1}+{\lambda}_{t1}+{\lambda}_{Po}\right){A}_{Po1}}{\lambda_{a1} X+\Delta {C}_{Po1}+{\lambda}_{d1}{A}_{Po2}- kX}{\mathrm{for}\kern0.5em }^{210}\mathrm{Po}\kern0.5em \mathrm{radionuclide} $$


$$ \Delta {C}_{Po1}={A}_{Pb1}\left[\right(1- \exp \left(-{\lambda}_{Bi}{t}_1\right)+\frac{\lambda_{Bi}}{\left({\lambda}_{Bi}+{\lambda}_{Po}\right)}\left( \exp \left(-{\lambda}_{Bi}{t}_1\right)- \exp \left(-{\lambda}_{Po}{t}_1\right)\right)\Big] $$

Both Eqs. (8, 9) show the strong dependence of the APb1 and APo1 activities on the time of exposure. Both metals are incorporated into the moss’s body (e.g., via adsorption followed by internal transport); therefore, two processes, biosorption and radionuclide transportation, were considered. Firstly, a fast variant of the kinetics, describing the intensive processes of bioaccumulation and washout from compartments, was examined. Secondly, a long-term approach was used, describing the steady state conditions of the dynamics of bioaccumulation, taking into account 210Po ingrowth from 210Pb decay and its own radioactive decay.


The levels of 210Po and 210Pb activity concentration in the various components of the moss’s body depend on several factors, such as the initial content of both radionuclides in the local environment and their activity ratios in the air and soil, along with the total accumulation time, which plays a significant role in the internal transport of metals (Koz and Cevik 2014; Sert et al. 2011; Uğur et al. 2003, 2004). 210Pb activity concentration distributions in moss body profiles collected in various environments (forest air, urban air) seemed to be more stable than 210Po concentrations. Proposed method focused on the fluctuations of 210Po activity concentration distributions in the moss profiles. 210Pb distribution analysis at the same profiles is aimed to help in estimation of the real 210Po content in the air, only.

Short-term dynamics of 210Po radionuclide bioaccumulation

For a short period of the absorption process (t = 0–10 days), ΔCPo1,2,3, the ingrowth of 210Po values from 210Pb decay, has a negligible contribution towards the total estimation of APo activity and some simplification of the expressions (5–7) can be carried out. In the leaves, all the processes take place at their fastest rate; therefore, the 210Po decay constant λ Po  = 0.005 [day−1] only gives a small contribution to the exponent value and can be omitted (Ghaemian 1979). It has been assumed, if there is no rain during that time, which mechanically removes the heavy metals from the plant, Eq. 9 that it can be simplified to the form shown below (e.g., for compartment 1). The kX parameter describes the deposition of the uplifted soil particles onto the moss’s surface. Over a short period of time, the kX parameter can be considered to be negligible.

$$ 1-{ \exp}^{\left(-\left({\lambda}_{t1}\right) t\right)}=\frac{\lambda_{t1}{A}_{Po1}}{\lambda_{a1} X+{\lambda}_{d1}{A}_{Po2}} $$

Therefore, for a short term (t = <10 days), we can obtain the correlation:\( 1-{ \exp}^{\left(-\left({\lambda}_{t1}\right) t\right)}->0 \)

$$ {\lambda}_{t1}{A}_{Po1}<<{\lambda}_{a1} X+{\lambda}_{d1}{A}_{Po2} $$
$$ {\lambda}_{t1}<{\lambda}_{a1},{\lambda}_{d1} $$

This equation confirms that the uptake of metals from wet or dry deposition seemed to be greater than the amount released from these mosses (Ghaemian 1979). In general, λa1t1 exceeds a value of 1.

The ratio of factors, λat, for 210Po accumulation in moss describes the speed of two competing processes: accumulation from the atmosphere on the upper layer of the moss’s profile and downwards transport resulting from translocation in different parts of this plant (Olu-Owolabi et al. 2012). The λa1 factor in compartment 1 describes the very effective biosorption of metals by the leaves from the air, whereas -λt1 describes 210Po transport down to the stem. Effective 210Po sorption at compartment 1 results from well-developed leaf branches and their large surface for the sorption process. The λat factor ratio is rather typical for each moss species, while also depending on the effective surface of their leaves and local environmental pollution conditions.

Long-term dynamics of the210Po and 210Pb radionuclides’ bioaccumulation

Over longer period of time >10 days, the steady-state condition for compartment 1 can be settled and the expression \( 1-{ \exp}^{\left(-\left({\lambda}_{w1}+{\lambda}_{t1}+{\lambda}_{Po}\right) t1\right)}->1 \). In the long term, external and internal transport of 210Pb and 210Po radionuclides in the moss profile should be taken into account (Eqs. 14, 15).

$$ {\lambda}_{w1}+{\lambda}_{t1}+{\lambda}_{Po}={\lambda}_{a1}+{\lambda}_{d1}- k $$

As a result, Eq. 9 has the form:

$$ {\lambda}_{a1} X+\Delta {C}_{Po1}+{\lambda}_{d1}{A}_{Po2}- kX=\left({\lambda}_{w1}+{\lambda}_{t1}+{\lambda}_{Po}\right){A}_{Po1} $$

The ΔCPo1 parameter, a linear function of 210Pb, describes the ingrowth of 210Po from 210Pb decay. Over a long period (t > 1 year) of time, ΔCPo1 = APb1. For the sake of simplicity of calculation, a state of equilibrium for the activity of this parameter has been taken to apply. As a result, Eq. 15 has the simple, linear form y = ax-b (Eq. 16).

$$ {\mathrm{A}}_{\mathrm{Pb}1}=\left({\lambda}_{w1}+{\lambda}_{t1}+{\lambda}_{Po}\right){A}_{Po1}-{\lambda}_{a1} X-{\lambda}_{d1}{A}_{Po2}+ kX $$


$$ a={\lambda}_{w1}+{\lambda}_{t1}+{\lambda}_{Po};\kern0.5em \mathrm{and}\kern0.5em b={\lambda}_{a1} X+{\lambda}_{d1}{A}_{Po2}- kX $$

where the x and y coefficients are the 210Po and 210Pb activity concentrations in the compartments of the vertical moss profile (Eq. 17).

The settling of the steady-state conditions in the moss body takes a longer time in the case of rapid, mechanical, washout processes (Čučulović and Veselinović 2015; Čučulović et al. 2014) and seems to be different for each compartment. In general, saturation conditions cause a slowdown of the accumulation λa, λb and λt, λz internal transport parameters and change between each of the separate morphological moss parts, for the 210Po and 210Pb radionuclides. Other processes, such as 210Pb and 210Po radioactive decay and 210Po ingrowth from 210Pb, change both the rate and the accumulation process dynamics significantly. These low decay factors λPo = 0.005 [day−1] and λPb = 8.5 × 10−5 [day−1] became essential and should be considered in the long-term process (t > 10 days).

On the base of this simple, linear Eq. (15), estimations of the X parameter, which describes the 210Po activity concentration in the air, can be applied. Two sets of moss samples, representing two different environments, clean deep forest and city center, were collected. Let us assume the difference in the rate of deposition on the leaves surface and the accumulation in to the moss interior is linearly correlated, and their difference is constant. For simplicity of calculation, the k-λ a1 parameter was set at 0.3 [day−1]. The results obtained in taking into account this assumption are show in Table 1.

Table 1 Results of estimation of 210Po kinetic parameters X in [Bq kg−1] and [μBq m−3], in eight moss profiles (with assumption dust concentration equal 40 μgm−3)

There is a linear correlation between 210Pb and 210Po radionuclides in moss profiles. The 210Po and 210Pb activity concentrations in the moss profile can be applied for 210Po activity concentration estimation in the air. The results presented in Table 1 confirm that there is a significantly higher 210Po content in the urban air (samples 6, 7, and 8) than in the clean forest air (1, 2, and 3 for summer, and 4 and 5 for winter).

In relatively non-polluted air, the number of 210Po ions attached to particles is low and ranges from dozens to hundreds [Bq kg−1], while for polluted regions, the 210Po activity concentration attached to the aerosols can reach up to several thousands [Bq kg−1], depending on its origin and the particles’ size (Długosz et al. 2010). 210Po activity concentration analysis in Bq kg−1 units is more profitable for source pollution identification.

In this study, values the 210Po activity concentration has been re calculated for the concentration in the air, assuming dust concentration levels equal to 40 μg m−3 . Therefore, in Table 1, X parameter values in μBq m−3 units have been also present.

For relatively clean areas, the 210Po activity concentration ranges from 23 to 38 μBq m−3 for the Arctic (Persson 2014). For comparison, in urban air, its activity concentration varied between 9.44 and 136.9 μBq m−3(Długosz-Lisiecka 2015a). X parameter values obtained on the basis of the proposed method are within the range of values provided by other investigators for France, Italy, Germany, and other European countries (Nho et al. 1996; Jia and Jia 2014; UNSCEAR 2000).

In the case of polluted urban environments (air or soil), the activity ratios 210Po/210Pb ≥ 1 can even exceed unity. As a result, the 210Po total activity concentration depends on two processes: 210Po decay with a half-life T1/2 = 138 days and ingrowth from 210Pb (Fig. 2a). If the 210Po/210Pb initial activity ratio is equal to 0.1 in the different parts of the moss (as is the case for a relatively clean atmosphere), than the 210Po content results mostly from ingrowth from 210Pb decay (Fig. 2b). The same kinetics between 210Po and 210Pb radionuclide activities can be obtained for morphological moss parts. However, washout, downward internal transport processes, biosorption, and upward transport processes will all significantly change the dynamic of the steady-state condition.

Fig. 2

210Po activity changes in time a 210Po/210Pb = 1 b 210Po/210Pb = 0.1

The results confirmed observations that different fragments of mosses have different contents of 210Po and 210Pb radionuclides deposited from the local environment. Based on the analysis, it can be concluded that the concentration distributions undergo significant changes with the seasonal variation in their shares of the radionuclides from different emission sources, and the varying transport of minerals within the plant. Solving the first-order kinetic equation for compartment no. 1 (leaves) can give valuable information about the input of fresh atmospheric 210Po. Interesting differences have been noticed between samples collected in various locations with different contributions of atmospheric pollution sources. Because of the low number of the sample collected from high polluted regions this study has a preliminary character and will be continue.


The pollutants accumulated in the leaves of the moss tissues mostly come from atmospheric deposition, rather than from soil contamination. The increased activities of 210Po and 210Pb in moss body profiles confirm the significant contribution of 210Po activity in growth from 210Pb decay and aging of the moss tissue. The first-order kinetics of 210Po bioaccumulation in each of the morphological moss parts have been used as a method of estimating 210Po radionuclide activity concentration in the air.

Based on the radiometric analysis results, one can conclude that the 210Po and 210Pb concentration distributions depend on seasonal changes in the contributions of different emission sources, as well as the rate of the internal transport of minerals within the plants. The pollutants accumulated in the moss tissues come from sources of atmospheric deposition, rather than from contaminated soil. The disproportion in 210Po and 210Pb accumulation in different parts of the moss has been measured. Stems and rhizoids can be used for estimation of long-term pollution, while leaves be used for estimation short-term pollution in the air.


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This research work is supported by the National Science Centre under SONATA grant no. UMO-2012/07/D/ST10/02874.

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Correspondence to Magdalena Długosz-Lisiecka.

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210Po and 210Pb (as parent) activity distribution in vertical moss profiles have been analyzed.

• First-order kinetic have been applied for describing biosorption process.

• The highest content of both radionuclides was detected in rhizoids.

Responsible editor: Georg Steinhauser

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Długosz-Lisiecka, M. Kinetics of 210Po accumulation in moss body profiles. Environ Sci Pollut Res 24, 20254–20260 (2017).

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  • Biomarkers
  • Radionuclide distribution
  • First-order kinetic
  • Biosorption
  • 210Po and 210Pb in the air
  • Pleurozium schreberi
  • Accumulation rate
  • Low background spectrometry