Research article Special Issues

Tissue distribution patterns of solubilized metals from internalized tungsten alloy in the F344 rat

  • Because of its unique physical and chemical properties, tungsten has been increasingly utilized in a variety of civilian and military applications. This expanded use also raises the risk of human exposure through internalization by various routes. In most cases the toxicological and carcinogenic properties of these tungsten-based compounds are not known nor are the dissolution biokinetics and ultimate fate of the associated metals. Using a laboratory rodent model system designed to assess the health effects of embedded metals, and a tungsten alloy comprised of tungsten (91.1%), nickel (6.0%), and cobalt (2.9%), we investigated the tissue distribution patterns of the metals over a six month period. Despite its perceived insolubility, tungsten rapidly solubilized from the implanted metal fragments, as did nickel and cobalt. All three metals distributed systemically over time with extremely elevated levels of all three metals found in kidney, liver, and spleen. Unexpectedly, tungsten was found to cross the blood-brain and blood-testis barriers and localize in those tissues. These results, along with recent reports suggesting that tungsten is a tumor promoter, raises serious concerns as to the long-term health effects of exposure to tungsten and tungsten-based compounds.

    Citation: Vernieda B. Vergara, Christy A. Emond, John F. Kalinich. Tissue distribution patterns of solubilized metals from internalized tungsten alloy in the F344 rat[J]. AIMS Environmental Science, 2016, 3(2): 290-304. doi: 10.3934/environsci.2016.2.290

    Related Papers:

    [1] Pan Yang, Jianwen Feng, Xinchu Fu . Cluster collective behaviors via feedback pinning control induced by epidemic spread in a patchy population with dispersal. Mathematical Biosciences and Engineering, 2020, 17(5): 4718-4746. doi: 10.3934/mbe.2020259
    [2] Mingtao Li, Xin Pei, Juan Zhang, Li Li . Asymptotic analysis of endemic equilibrium to a brucellosis model. Mathematical Biosciences and Engineering, 2019, 16(5): 5836-5850. doi: 10.3934/mbe.2019291
    [3] Rajanish Kumar Rai, Pankaj Kumar Tiwari, Yun Kang, Arvind Kumar Misra . Modeling the effect of literacy and social media advertisements on the dynamics of infectious diseases. Mathematical Biosciences and Engineering, 2020, 17(5): 5812-5848. doi: 10.3934/mbe.2020311
    [4] Andrey V. Melnik, Andrei Korobeinikov . Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility. Mathematical Biosciences and Engineering, 2013, 10(2): 369-378. doi: 10.3934/mbe.2013.10.369
    [5] Yu Ji . Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection. Mathematical Biosciences and Engineering, 2015, 12(3): 525-536. doi: 10.3934/mbe.2015.12.525
    [6] Qiuyi Su, Jianhong Wu . Impact of variability of reproductive ageing and rate on childhood infectious disease prevention and control: insights from stage-structured population models. Mathematical Biosciences and Engineering, 2020, 17(6): 7671-7691. doi: 10.3934/mbe.2020390
    [7] Gang Huang, Edoardo Beretta, Yasuhiro Takeuchi . Global stability for epidemic model with constant latency and infectious periods. Mathematical Biosciences and Engineering, 2012, 9(2): 297-312. doi: 10.3934/mbe.2012.9.297
    [8] Ilse Domínguez-Alemán, Itzel Domínguez-Alemán, Juan Carlos Hernández-Gómez, Francisco J. Ariza-Hernández . A predator-prey fractional model with disease in the prey species. Mathematical Biosciences and Engineering, 2024, 21(3): 3713-3741. doi: 10.3934/mbe.2024164
    [9] Abdennasser Chekroun, Mohammed Nor Frioui, Toshikazu Kuniya, Tarik Mohammed Touaoula . Global stability of an age-structured epidemic model with general Lyapunov functional. Mathematical Biosciences and Engineering, 2019, 16(3): 1525-1553. doi: 10.3934/mbe.2019073
    [10] Yuhua Long, Yining Chen . Global stability of a pseudorabies virus model with vertical transmission. Mathematical Biosciences and Engineering, 2020, 17(5): 5234-5249. doi: 10.3934/mbe.2020283
  • Because of its unique physical and chemical properties, tungsten has been increasingly utilized in a variety of civilian and military applications. This expanded use also raises the risk of human exposure through internalization by various routes. In most cases the toxicological and carcinogenic properties of these tungsten-based compounds are not known nor are the dissolution biokinetics and ultimate fate of the associated metals. Using a laboratory rodent model system designed to assess the health effects of embedded metals, and a tungsten alloy comprised of tungsten (91.1%), nickel (6.0%), and cobalt (2.9%), we investigated the tissue distribution patterns of the metals over a six month period. Despite its perceived insolubility, tungsten rapidly solubilized from the implanted metal fragments, as did nickel and cobalt. All three metals distributed systemically over time with extremely elevated levels of all three metals found in kidney, liver, and spleen. Unexpectedly, tungsten was found to cross the blood-brain and blood-testis barriers and localize in those tissues. These results, along with recent reports suggesting that tungsten is a tumor promoter, raises serious concerns as to the long-term health effects of exposure to tungsten and tungsten-based compounds.


    We are concerned with Atangana-Baleanu variable order fractional problems:

    $ {Lu(x)=ABCDα(x)u(x)+a(x)u(x)=f(x,u),x[0,1],B(u)=0,
    $
    (1.1)

    where $ 0 < \alpha(x) < 1 $, $ ^{ABC}D^{\alpha(x)}(x) $ denotes the $ \alpha(x) $ order Atangana-Baleanu Caputo derivatives, $ B(u) $ is the linear boundary condition, which includes initial value condition, periodic condition, final value condition and so on.

    The $ \alpha(x)(0 < \alpha(x) < 1) $ order Atangana-Baleanu Caputo derivatives of a function $ u(x) $ is firstly defined by Atangana and Baleanu [1]

    $ ABCDα(x)u(x)=M(α(x))1α(x)x0Eα(x)(α(x)1α(x)(xt)α(x))u(t)dt,
    $
    (1.2)

    where $ E_{\alpha(x)}(x) $ is the Mittag-Leffler function.

    Fractional order differential equations (FDEs) have important applications in several fields such as materials, chemistry transmission dynamics, optimal control and engineering [2,3,4,5,6]. In fact, the classical fractional derivatives are defined with weak singular kernels and the solutions of FDEs inherit the weak singularity. The Mittag-Leffler (ML) function was firstly introduced by Magnus Gösta Mittag-Leffler. Recently, it is found that this function has close relation to FDEs arising in real applications.

    Atangana and Baleanu [1] introduced a new fractional derivative by using the ML function, which is nonlocal and nonsingular. The new fractional derivatives is very important and have been applied to several different fields (see e.g. [7,8,9]). Up to now, several numerical algorithms have been developed for solving Atangana-Baleanu FDEs. Akgül et al. [10,11,12] proposed effective difference techniques and kernels based approaches for Atangana-Baleanu FDEs. On the basis of the Sobolev kernel functions, Arqub et al. [13,14,15,16,17] proposed the numerical techniques for Atangana-Baleanu fractional Riccati and Bernoulli equations, Bagley-Torvik and Painlev equations, Volterra and Fredholm integro-differential equations. Yadav et al. [18] introduced the numerical algorithms and application of Atangana-Baleanu FDEs. El-Ajou, Hadid, Al-Smadi et al. [19] developed approximated technique for solutions of population dynamics of Atangana-Baleanu fractional order.

    Reproducing kernel Hilbert space (RKHS) is ideal for function approximation and estimate of fractional derivatives. In recent years, reproducing kernel functions (RKF) theory have been employed to solve linear and nonlinear fractional order problems, singularly perturbed problems, singular integral equations, fuzzy differential equations, and so on (see, e.g. [10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]). However, there exists little discussion on numerical schemes for solving variable order Atangana-Baleanu FDEs.

    In this paper, by using polynomials RKF, we will present a new collocation method for solving variable order Atangana-Baleanu FDEs.

    This work is organized as follows. We summarize fractional derivatives and RKHS theory in Section 2. In Section 3, we develop RKF based collocation technique for Atangana-Baleanu variable order FDEs. Numerical experiments are provided in Section 4. Concluding remarks are included in the last section.

    Definition 2.1. Let $ H $ be a Hilbert function space defined on $ E $. The function $ K: E\times E\rightarrow R $ is known as an RKF of space $ H $ if

    $ (1)K(,t)HforalltE,(2)w(t)=(w(),K(,t)),foralltEandallwH.
    $

    If there exists a RKF in a Hilbert space, then the space is a RKHS.

    Definition 2.2. Symmetric function $ K:E\times E\rightarrow R $ is known as a positive definite kernel (PDK) if $ \sum\limits_{i, j = 1}^nc_ic_jK(x_i, x_j)\geq 0 $ for any $ n\in N $, $ x_1, x_2, \ldots, x_n\in E, c_1, c_2, \ldots, c_n\in R $.

    Theorem 2.1. [36] The RKF of an RKHS is positive definite. Besides, every PDK can define a unique RKHS, of which it is the RKF.

    Definition 2.3. Let $ q > 0 $. The one parameter Mittag-Leffler function of order $ q $ is defined by

    $ Eq(z)=j=0zjΓ(jq+1).
    $
    (2.1)

    Definition 2.4. Let $ q_1, q_2 > 0 $. The two-parameter Mittag-Leffler function is defined by

    $ Eq1,q2(z)=j=0zjΓ(jq1+q2).
    $
    (2.2)

    For the domains of convergence of the Mittag-Leffler functions, please refer to the following theorem.

    Theorem 2.2. [37] For $ q_1, q_2 > 0 $, the two-parameter Mittag-Leffler function $ E_{q_1, q_2}(z) $ is convergent for all $ z\in \mathbb{C} $.

    Definition 2.5. The Sobolev space $ H^1(0, T) $ is defined as follows

    $ H^1(0,T) = \{u|\,u\in L^2(0,T),\,u^{\prime}\in L^2(0,T)\}. $

    Definition 2.6. The $ \alpha \in (0, 1) $ order Atangana- Baleanu fractional derivative of a function $ u\in H^1(a, b) $ is defined

    $ ABCDαu(x)=M(α)1αx0Eα(α1α(xt)α)u(t)dt,
    $
    (2.3)

    where $ M(\alpha) $ is the normalization term satisfying $ M(0) = M(1) = 1 $.

    Theorem 2.3. [38] The function $ k(x, y) = (xy+c)^m $ for $ c > 0, m\in N $ is a PDK.

    According to Theorem 2.1, there exists an associated RKHS $ Q_m $ with $ k $ as an RKF.

    To solve (1.1), we will construct the RKF which satisfies the homogenous boundary condition.

    Definition 3.1.

    $ Q_{m,0} = \{w(t)\mid w(t)\in Q_m,B(w) = 0\}. $

    Theorem 3.1. The space $ Q_{m, 0} $ is an RKHS and its RKF is expressed by

    $ K(x,y) = k(x,y)-\frac{B_xk(x,y)B_yk(x,y)}{B_xB_yk(x,y)}. $

    Proof. If $ B_yk(x, y) = 0 $ or $ B_xk(x, y) = 0 $, then

    $ K(x,y) = k(x,y). $

    If $ B_yk(x, y)\neq0 $, then

    $ BxK(x,y)=Bxk(x,y)Bxk(x,y)BxByk(x,y)BxByk(x,y),=0,
    $

    and naturally $ K(x, y)\in Q_{m, 0} $.

    For all $ u(y)\in Q_{m, 0} $, we have $ u(y)\in Q_{m} $ and $ B_yu(y) = 0. $

    We have

    $ (u(y),K(x,y))=(u(y),k(x,y))(u(y),Bxk(x,y)Byk(x,y)BxByk(x,y)=u(x)Byk(x,y)BxByk(x,y)(u(y),Bxk(x,y))=u(x)Byk(x,y)BxByk(x,y)Bx(u(y),k(x,y))=u(x)Byk(x,y)BxByk(x,y)Bxu(x)=u(x)0=0.
    $

    Thus, $ K(x, y) $ is the RKF of space $ Q_{m, 0} $ and the proof is complete.

    Suppose that $ L:Q_{m, 0}\rightarrow H^1 $ is a bounded linear operator. It is easy to proved that its inverse operator $ L^{-1} $ is also bounded since both $ Q_{m, 0} $ and $ H^1 $ are Banach spaces.

    Choose $ N $ distinct scattered points in $ [0, 1] $, such as $ \{x_1, x_2, \ldots, x_N\} $. Put $ \psi_i(x) = K(x, x_i), i = 1, 2, \ldots, N. $ By using RKF basis, the RKF collocation solution $ u_N(x) $ for (1.1) can be written as follows

    $ uN(x)=Ni=1ciψi(x),
    $
    (3.1)

    where $ \{c_i\}_{i = 1}^N $ are undetermined constants.

    Collocating (1.1) at $ N $ nodes $ x_1, x_2, \ldots, x_{N} $ provides $ N $ equations:

    $ LuN(xk)=Ni=1ciLψi(xk)=f(xk,uN(xk)),k=1,2,,N.
    $
    (3.2)

    System (3.3) of equations is simplified to the matrix form:

    $ Ac=f,
    $
    (3.3)

    where $ A_{ik} = L_x\psi_k(x)|_{x = x_i}, i, k = 1, 2, \ldots, N, $ $ {\bf{f}} = (f(x_1, u_N(x_1)), f(x_2, u_N(x_2)), \ldots, f(x_N, u_N(x_N)) $.

    Theorem 3.2. If $ \gamma > 0 $, then

    $ ^{ABC}D^{\alpha(x)}x^\gamma = \frac{M(\alpha(x))}{1-\alpha(x)}\Gamma(\gamma+1)x^\gamma E_{\alpha(x),\gamma+1}(-\frac{\alpha(x)}{1-\alpha(x)}x^{\alpha(x)}), $

    and therefore matrix $ A $ can be computed exactly.

    Proof. It is noticed that

    $ ABCDα(x)xγ=M(α(x))1α(x)x0Eα(x)(α(x)1α(x)(xt)α(x))γtγ1dt=M(α(x))1α(x)x0j=0(α(x)1α(x)(xt)α(x))jΓ(jα(x)+1)γtγ1dt=M(α(x))1α(x)γj=0(α(x)1α(x))jΓ(jα(x)+1)x0(xt)α(x)tγ1dt=M(α(x))1α(x)γj=0(α(x)1α(x))jΓ(jα(x)+1)Γ(jα(x)+1)Γ(γ)Γ(jα(x)+γ+1)xjα(x)+γ=M(α(x))1α(x)Γ(γ+1)xγj=0(α(x)1α(x)xα(x))jΓ(jα(x)+γ+1)=M(α(x))1α(x)Γ(γ+1)xγEα(x),γ+1(α(x)1α(x)xα(x)).
    $

    Since RKF $ K(x, y) $ is a polynomials, matrix $ A $ in (3.3) can be calculated exactly. The proof is complete.

    If $ f(x, u) $ is linear, then $ (3.3) $ is a system of linear equations and it is convenient to determine the value of the unknowns $ \{c_i\}_{i = 1}^N $. If $ f(x, u) $ is nonlinear, then (3.3) is a system of nonlinear equations, we solve it by using the tool "FindRoot" in soft Mathematica 11.0.

    The residual function is defined as

    $ R_{N}(x) = Lu_{N}(x)-f(x,u_N(x)). $

    Theorem 3.3. If $ a(x) $ and $ f(x, u)\in C^4[0, 1] $, then

    $ \parallel R_{N}(x)\parallel_\infty\triangleq\max\limits_{x\in[x_1,x_{N}]}\mid R_{N}(x)\mid\leq c\,h^4, $

    where $ c > 0 $ is a real number, $ h = \max\limits_{1\leq i \leq N}\mid x_{i+1}-x_i\mid $.

    Proof. For the proof, please refer to [22].

    Three experiments are illustrated in this section to show the applicability and effectiveness of the mentioned approach. We take $ M(\alpha) = 1 $ in the following experiments.

    Problem 4.1

    Solve fractional linear initial value problems (IVPs) as follows:

    $ \left \{ ABCDαu(x)+exu(x)=f(x),x(0,1],u(0)=1,
    \right. $

    where $ \alpha(x) = 0.5x+0.1 $, $ f(x) = e^x(x^2+x^3+1)+\frac{M(\alpha(x))}{1-\alpha(x)}2x^2 E_{\alpha(x), 3}(-\frac{\alpha(x)}{1-\alpha(x)}x^{\alpha(x)})++\frac{M(\alpha(x))}{1-\alpha(x)}6x^3 E_{\alpha(x), 4}(-\frac{\alpha(x)}{1-\alpha(x)}x^{\alpha(x)}) $. The true solution of this equation is $ u(x) = x^2+x^3+1 $.

    Selecting $ m = 8, N = 8 $, $ x_i = \frac{i}{N}, i = 1, 2, \ldots, N, $ we apply our new method to Problem 4.1. The obtained numerical results are shown in Tables 1. The Mathematica codes for Problem 4.1 is provided as follows:

    $ tru[x_]=x2+x3+1;p[x_]=Ex;α[x_]=0.5x+0.1;B[x_]=1;a[x_]=1Gamma[2α[x]];K[x_,y_]=(xy+1)8;R[x_,y_]=K[x,y]K[x,0]K[0,y]/K[0,0];w[x_,y_]=p[x]R[x,y];v[x_,d_]=B[α[x]]Gamma[d+1]xdMittagLefflerE[2,d+1,α[x]xα[x]/(1α[x])];fu[x_,y_]=8yv[x,1]+28y2v[x,2]+56y3v[x,3]+70y4v[x,4]+56y5v[x,5]+28y6v[x,6]+8y7v[x,7]+y8v[x,8];m=8;xx=Table[0,{i,1,m}];A=Table[0,{i,1,m},{j,1,m}];For[i=1,im,i++,xx[[i]]=i/m];For[i=1,im,i++,For[j=1,jm,j++,A[[i,j]]=w[xx[[i]],xx[[j]]]+fu[xx[[i]]+xx[[j]]]]];v[x_]=tru[0];f0[x]=p[x]tru[x]+v[x,2]+v[x,3];f[x]=f0[x]p[x]v[x];b=Table[f[xx[[k]]],{i,1,m}];c=LinearSolve[A,b];u[x_]=mi=1c[[i]]R[x,xx[[i]]];u[x_]=u[x]+v[x];
    $
    Table 1.  Errors of numerical results for Problem 4.1.
    Nodes $ x $ Exact solution Absolute error Relative error
    0.10 1.011 $ 1.88\times 10^{-13} $ $ 1.86\times 10^{-13} $
    0.20 1.048 $ 2.57\times 10^{-13} $ $ 2.45\times 10^{-13} $
    0.30 1.117 $ 9.50\times 10^{-14} $ $ 8.50\times 10^{-14} $
    0.40 1.224 $ 6.35\times 10^{-13} $ $ 5.19\times 10^{-13} $
    0.50 1.375 0 0
    0.60 1.576 $ 2.17\times 10^{-14} $ $ 1.38\times 10^{-14} $
    0.70 1.833 $ 7.65\times 10^{-13} $ $ 4.17\times 10^{-13} $
    0.80 2.152 $ 8.65\times 10^{-13} $ $ 4.02\times 10^{-13} $
    0.90 2.539 $ 2.40\times 10^{-13} $ $ 9.46\times 10^{-14} $
    1.00 3.000 $ 9.09\times 10^{-13} $ $ 3.03\times 10^{-13} $

     | Show Table
    DownLoad: CSV

    Problem 4.2

    Solve the variable order fractional linear terminal value problems

    $ \left \{ ABCDαu(x)+2u(x)=f(x),x[0,1),u(1)=3,
    \right. $

    where $ \alpha(x) = \sin x $, $ f(x) = 2(x^4+2)+\frac{M(\alpha(x))}{1-\alpha(x)}24x^4 E_{\alpha(x), 5}(-\frac{\alpha(x)}{1-\alpha(x)}x^{\alpha(x)}) $. The exact solution is $ u(x) = x^4+2 $.

    Selecting $ m = 8, N = 8 $, $ x_i = \frac{i-1}{N}, i = 1, 2, \ldots, N, $ the obtained absolute and relative errors of numerical results using our method are listed in Tables 2.

    Table 2.  Errors of numerical results for Problem 4.2.
    Nodes $ x $ Exact solution Absolute error Relative error
    0.00 2.0000 $ 2.75\times 10^{-10} $ $ 1.37\times 10^{-10} $
    0.10 2.0001 $ 1.02\times 10^{-10} $ $ 5.14\times 10^{-11} $
    0.20 2.0016 $ 9.96\times 10^{-11} $ $ 4.97\times 10^{-11} $
    0.30 2.0081 $ 1.08\times 10^{-10} $ $ 5.39\times 10^{-11} $
    0.40 2.0256 $ 1.12\times 10^{-10} $ $ 5.56\times 10^{-11} $
    0.50 2.0625 $ 1.10\times 10^{-10} $ $ 5.37\times 10^{-11} $
    0.60 2.1296 $ 1.05\times 10^{-10} $ $ 4.96\times 10^{-11} $
    0.70 2.2401 $ 1.08\times 10^{-10} $ $ 4.83\times 10^{-11} $
    0.80 2.4096 $ 9.36\times 10^{-11} $ $ 3.88\times 10^{-11} $
    0.90 2.6561 $ 4.38\times 10^{-11} $ $ 1.64\times 10^{-11} $

     | Show Table
    DownLoad: CSV

    Problem 4.3

    We apply our method to the nonlinear variable order fractional IVPs as follows

    $ \left \{ ABCDαu(x)+sinhxu(x)+sin(u)=f(x),x(0,1],u(0)=1,
    \right. $

    where $ \alpha(x) = 0.5x+0.1 $, $ f(x) = \sinh x(x+x^3+1)+\frac{M(\alpha(x))}{1-\alpha(x)}x E_{\alpha(x), 2}(-\frac{\alpha(x)}{1-\alpha(x)}x^{\alpha(x)})+\frac{M(\alpha(x))}{1-\alpha(x)}6x^3 E_{\alpha(x), 4}(-\frac{\alpha(x)}{1-\alpha(x)}x^{\alpha(x)}) $. Its true solution is $ u(x) = x+x^3+1 $.

    Choosing $ m = 8, N = 8 $, $ x_i = \frac{i}{N}, i = 1, 2, \ldots, N, $ we plot the absolute and relative errors in Figure 1.

    Figure 1.  Absolute errors (left) and relative errors (right) for Problem 4.3.

    In this work, a new RKF based collocation technique is developed for Atangana-Baleanu variable order fractional problems. The proposed scheme is meshless and therefore it does not require any background meshes. From the numerical results, it is found that the accuracy of obtained approximate solutions is high and can reach to $ O(10^{-10}) $. Also, for nonlinear fractional problems, our method can yield highly accurate numerical solutions. Hence, our new method is very effective and easy to implement for the considered problems.

    The work was supported by the National Natural Science Foundation of China (No.11801044, No.11326237).

    All authors declare no conflicts of interest in this paper.

    [1] van der Voet GB, Todorov TI, Centeno JA, et al. (2007) Metals and health: a clinical toxicological perspective on tungsten and review of the literature. Mil Med 172: 1002-1005. doi: 10.7205/MILMED.172.9.1002
    [2] Agency for Toxic Substances and Disease Registry (ATSDR) (2005) Toxicological profile for tungsten. Atlanta, GA: U.S. Department of Health and Human Services, Public Health Service.
    [3] United States Fish and Wildlife Service, Nontoxic shot regulations for hunting waterfowl and coots in the U.S.. Available from: www.regulations.gov/#!documentDetail;D=FWS-R9-MB-2011-0077-0009.
    [4] Kraabel BJ, Miller MW, Getzy DM, et al. (1996) Effects of embedded tungsten-bismuth-tin shot and steel shot on mallards (Anas platyrhynchos). J Wildlife Dis 32: 1-8. doi: 10.7589/0090-3558-32.1.1
    [5] Kelly ME, Fitzgerald SD, Aulerich RJ, et al. (1998) Acute effects of lead, steel, tungsten-iron, and tungsten-polymer shot administered to game-farm mallards. J Wildlife Dis 34: 673-687. doi: 10.7589/0090-3558-34.4.673
    [6] Mitchell RR, Fitzgerald SD, Aulerich RJ, et al. (2001) Hematological effects and metal residue concentrations following chronic dosing with tungsten-iron and tungsten-polymer shot in adult game-farm mallards. J Wildlife Dis 37: 459-467. doi: 10.7589/0090-3558-37.3.459
    [7] Mitchell RR, Fitzgerald SD, Aulerich RJ, et al. (2001) Reproductive effects and duckling survivability following chronic dosing with tungsten-iron and tungsten-polymer shot in adult game-farm mallards. J Wildlife Dis 37: 468-474. doi: 10.7589/0090-3558-37.3.468
    [8] Mitchell RR, Fitzgerald SD, Aulerich RJ, et al. (2001) Health effects following chronic dosing with tungsten-iron and tungsten-polymer shot in adult game-farm mallards. J Wildlife Dis 37: 451-458.
    [9] Brewer L, Fairbrother A, Clark J, et al. (2003) Acute toxicity of lead, steel, and an iron-tungsten-nickel shot to mallard ducks (Anas platyrhynchos). J Wildlife Dis 39: 638-648.
    [10] Kerley CR, Easterly CE, Eckerman KF, et al. (1996) Environmental acceptability of high-performance alternatives for depleted uranium penetrators. ORNL/TM-13286. Oak Ridge National Laboratory. Available from: http://www.osti.gov/scitech/biblio/464128-environmental-acceptability-high-performance-alternatives-depleted-uranium-penetrators.
    [11] Kalinich JF, Emond CA, Dalton TK, et al. (2005) Embedded weapons-grade tungsten alloy shrapnel rapidly induces metastatic high-grade rhabdomyosarcomas in F344 rats. Environ Health Perspect 113: 729-734. doi: 10.1289/ehp.7791
    [12] Schuster BE, Roszell LE, Murr LE, et al. (2012) In vivo corrosion, tumor outcome, and microarray gene expression for two types of muscle-implanted tungsten alloys. Toxicol Appl Pharmacol 265: 128-138. doi: 10.1016/j.taap.2012.08.025
    [13] Emond CA, Vergara VB, Lombardini ED, et al. (2015) Induction of rhabdomyosarcoma by embedded military-grade tungsten/nickel/cobalt not by tungsten/nickel/iron in the B6C3F1 mouse. Int J Toxicol 34: 44-54. doi: 10.1177/1091581814565038
    [14] Koutsospyros A, Braida W, Christodoulatos C, et al. (2006) A review of tungsten: From environmental obscurity to scrutiny. J Hazard Mater 136: 1-19. doi: 10.1016/j.jhazmat.2005.11.007
    [15] Gbaruko BC, Igwe JC (2007) Tungsten: Occurrence, chemistry, environmental, and health exposure issues. Global J Environ Res 1: 27-32.
    [16] Ogundipe A, Greenberg B, Braida W, et al. (2006) Morphological characterization and spectroscopic studies of the corrosion behaviour of tungsten heavy alloys. Corr Sci 48: 3281-3297. doi: 10.1016/j.corsci.2005.12.004
    [17] Dermatas D, Braida W, Christodoulatos C, et al. (2004) Solubility, sorption, and soil respiration effects of tungsten and tungsten alloys. Environ Forensics 5: 5-13. doi: 10.1080/15275920490423980
    [18] Bednar AJ, Jones WT, Boyd RE, et al. (2008) Geochemical parameters influencing tungsten mobility in soils. J Environ Qual 37: 229-233. doi: 10.2134/jeq2007.0305
    [19] Strigul N (2010) Does speciation matter for tungsten ecotoxicology? Ecotoxicol Environ Safety 73: 1099-1113.
    [20] Institute of Laboratory Animal Resources (2010) Guide for the Care and Use of Laboratory Animals. 8th edition. Washington, DC: National Academy Press.
    [21] Rao GN (1996) New diet (NTP-2000) for rats in the National Toxicology Program toxicity and carcinogenicity studies. Fund Appl Toxicol 32: 102-108. doi: 10.1006/faat.1996.0112
    [22] Hockley AD, Goldin JH, Wake MJC, et al. (1990) Skull repair in children. Pediatric Neurosurg 16: 271-275.
    [23] Johansson CB, Hansson HA, Albrektsson T (1990) Qualitative interfacial study between bone and tantalum, niobium or commercially pure titanium. Biomaterials 11: 277-280. doi: 10.1016/0142-9612(90)90010-N
    [24] Strecker EP, Hagan B, Liermann D, et al. (1993) Iliac and femoropopliteal vascular occlusive disease treated with flexible tantalum stents. Cardiovasc Intervent Radiol 16: 158-164. doi: 10.1007/BF02641885
    [25] Emond CA, Vergara VB, Lombardini ED, et al. (2015) The role of the component metals in the toxicity of military-grade tungsten alloy. Toxics 3: 499-514. doi: 10.3390/toxics3040499
    [26] Witten ML, Sheppard PR, Witten BL (2012) Tungsten toxicity. Chemico-Biol Interact 196: 87-88. doi: 10.1016/j.cbi.2011.12.002
    [27] Rubin CS, Holmes AK, Belson MG, et al. (2007) Investigating childhood leukemia in Churchill County, Nevada. Environ Health Perspect 115: 151-157.
    [28] Kalinich JF, Vergara VB, Emond CA (2008) Urinary and serum metal levels as indicators of embedded tungsten alloy fragments. Mil Med 173: 754-758. doi: 10.7205/MILMED.173.8.754
    [29] Miller AC, Mog S, McKinney LA, et al. (2001) Neoplastic transformation of human osteoblast cells to the tumorigenic phenotype by heavy metal-tungsten alloy particles: induction of genotoxic effects. Carcinogenesis 22: 115-125. doi: 10.1093/carcin/22.1.115
    [30] Miller AC, Xu J, Prasanna PGS, et al. (2002) Potential late health effects of the heavy metals, depleted uranium and tungsten, used in armor piercing munitions: comparison of neoplastic transformation and genotoxicity using the known carcinogen nickel. Mil Med 167: 120-122.
    [31] Kalinich JF, Kasper CE (2014) Do metals that translocate to the brain exacerbate traumatic brain injury? Med Hypoth 83: 558-562.
    [32] Leggett RW (1997) A model of the distribution and retention of tungsten in the human body. Sci Total Environ 206: 147-165. doi: 10.1016/S0048-9697(97)80006-X
    [33] Emond CA, Kalinich JF (2012) Biokinetics of embedded surrogate radiological dispersal device material. Health Phys 102: 124-136.
    [34] Endoh H, Kaneko T, Nakamura H, et al. (2000) Improved cardiac contractile functions in hypoxia-reoxygenation in rats treated with low concentration Co2+. Am J Physiol Heart Circ Physiol 279: H2713-H2719.
    [35] Rakusan K, Cicutti N, Kolar F (2001) Cardiac function, microvascular structure, and capillary hematocrit in hearts of polycythemic rats. Am J Physiol Heart Circ Physiol 281: H2425-H2431.
    [36] Fastje CD, Harper K, Terry C, et al. (2012) Exposure to sodium tungstate and Respiratory Syncytial Virus results in hematological/immunological disease in C57BL/6J mice. Chemico-Biol Interact 196: 89-95. doi: 10.1016/j.cbi.2011.04.008
    [37] Kelly ADR, Lemaire M, Young YK, et al. (2013) In vivo tungsten exposure alters B-cell development and increases DNA damage in murine bone marrow. Toxicol Sci 131: 434-446. doi: 10.1093/toxsci/kfs324
    [38] Jalaguier-Coudray A, Cohen M, Thomassin-Piana J, et al. (2015) Calcifications and tungsten deposits after breast-conserving surgery and intraoperative radiotherapy for breast cancer. Eur J Radiol 84: 2521-2525. doi: 10.1016/j.ejrad.2015.10.004
    [39] Bolt AM, Sabourin V, Molina F, et al. (2015) Tungsten targets the tumor microenvironment to enhance breast cancer metastasis. Toxicol Sci 143: 165-177. doi: 10.1093/toxsci/kfu219
    [40] Harris RM, Williams TD, Hodges NJ, et al. (2011) Reactive oxygen species and oxidative DNA damage mediate the cytotoxicity of tungsten-nickel-cobalt alloys in vitro. Toxicol Appl Pharmacol 250: 19-28. doi: 10.1016/j.taap.2010.09.020
    [41] Bardack S, Dalgard CL, Kalinich JF, et al. (2014) Genotoxic changes to rodent cells exposed in vitro to tungsten, nickel, cobalt, and iron. Int J Environ Res Pub Health 11: 2922-2940. doi: 10.3390/ijerph110302922
    [42] Harris RM, Williams TD, Waring RH, et al. (2015) Molecular basis of carcinogenicity of tungsten alloy particles. Toxicol Appl Pharmacol 283: 223-233. doi: 10.1016/j.taap.2015.01.013
    [43] Laulicht F, Brocato J, Cartularo L, et al. (2015) Tungsten-induced carcinogenesis in human bronchial epithelial cells. Toxicol Appl Pharmacol 288: 33-39. doi: 10.1016/j.taap.2015.07.003
    [44] Guandalini GS, Zhang L, Fornero E, et al. (2011) Tissue distribution of tungsten in mice following oral exposure to sodium tungstate. Chem Res Toxicol 24: 488-493. doi: 10.1021/tx200011k
    [45] McInturf SM, Bekkedal MYV, Wilfong E, et al. (2011) The potential reproductive, neurobehavioral and systemic effects of soluble sodium tungstate exposure in Sprague-Dawley rats. Toxicol Appl Pharmacol 254: 133-137. doi: 10.1016/j.taap.2010.04.021
    [46] Radcliffe PM, Leavens TL, Wagner DJ, et al. (2010) Pharmacokinetics of radiolabeled tungsten (188W) in male Sprague-Dawley rats following acute sodium tungstate inhalation. Inhalation Toxicol 22: 69-76. doi: 10.3109/08958370902913237
    [47] McDonald JD, Weber WM, Marr R, et al. (2007) Disposition and clearance of tungsten after single-dose oral and intravenous exposure in rodents. J Toxicol Environ Health A 70: 829-836. doi: 10.1080/15287390701211762
    [48] NTP Range-Finding Report: Immunotoxicity of Sodium Tungstate Dihydrate in Female B6C3F1/N Mice (CASRN: 10213-10-2) National Toxicology Program, U.S. Department of Health and Human Services. Available from: ntp.niehs.nih.gov/testing/types/imm/abstract/i03038/index.html.
    [49] U.S. Environmental Protection Agency (2008) Emerging contaminant tungsten. Fact sheet 505-F-070-005. Available from: http://nepis.epa.gov/Exe/ZyPDF.cgi/P1000L3K.PDF?Dockey=P1000L3K.PDF.
  • This article has been cited by:

    1. Yuexia Zhang, Ziyang Chen, SETQR Propagation Model for Social Networks, 2019, 7, 2169-3536, 127533, 10.1109/ACCESS.2019.2939150
    2. Anarul Islam, Haider Ali Biswas, Modeling the Effect of Global Warming on the Sustainable Groundwater Management: A Case Study in Bangladesh, 2021, 19, 2224-2880, 639, 10.37394/23206.2020.19.71
    3. Rong Hu, Lili Liu, Xinzhi Ren, Xianning Liu, Global stability of an information-related epidemic model with age-dependent latency and relapse, 2018, 36, 1476945X, 30, 10.1016/j.ecocom.2018.06.006
    4. R. Arazi, A. Feigel, Discontinuous transitions of social distancing in the SIR model, 2021, 566, 03784371, 125632, 10.1016/j.physa.2020.125632
    5. Magdalena Ochab, Piero Manfredi, Krzysztof Puszynski, Alberto d’Onofrio, Multiple epidemic waves as the outcome of stochastic SIR epidemics with behavioral responses: a hybrid modeling approach, 2023, 111, 0924-090X, 887, 10.1007/s11071-022-07317-6
    6. Alberto d'Onofrio, Piero Manfredi, Behavioral SIR models with incidence-based social-distancing, 2022, 159, 09600779, 112072, 10.1016/j.chaos.2022.112072
    7. Sileshi Sintayehu Sharbayta, Bruno Buonomo, Alberto d'Onofrio, Tadesse Abdi, ‘Period doubling’ induced by optimal control in a behavioral SIR epidemic model, 2022, 161, 09600779, 112347, 10.1016/j.chaos.2022.112347
    8. Wu Jing, Haiyan Kang, An effective ISDPR rumor propagation model on complex networks, 2022, 37, 0884-8173, 11188, 10.1002/int.23038
    9. D. Ghosh, P. K. Santra, G. S. Mahapatra, Amr Elsonbaty, A. A. Elsadany, A discrete-time epidemic model for the analysis of transmission of COVID19 based upon data of epidemiological parameters, 2022, 231, 1951-6355, 3461, 10.1140/epjs/s11734-022-00537-2
    10. Lili Liu, Jian Zhang, Yazhi Li, Xinzhi Ren, An age-structured tuberculosis model with information and immigration: Stability and simulation study, 2023, 16, 1793-5245, 10.1142/S1793524522500760
    11. Roxana López-Cruz, Global stability of an SAIRD epidemiological model with negative feedback, 2022, 2022, 2731-4235, 10.1186/s13662-022-03712-w
    12. Ruiqing Shi, Yihong Zhang, Cuihong Wang, Dynamic Analysis and Optimal Control of Fractional Order African Swine Fever Models with Media Coverage, 2023, 13, 2076-2615, 2252, 10.3390/ani13142252
    13. Shaday Guerrero‐Flores, Osvaldo Osuna, Cruz Vargas‐De‐León, Periodic solutions of seasonal epidemiological models with information‐dependent vaccination, 2023, 0170-4214, 10.1002/mma.9728
    14. Wanqin Wu, Wenhui Luo, Hui Chen, Yun Zhao, Stochastic Dynamics Analysis of Epidemic Models Considering Negative Feedback of Information, 2023, 15, 2073-8994, 1781, 10.3390/sym15091781
    15. Yau Umar Ahmad, James Andrawus, Abdurrahman Ado, Yahaya Adamu Maigoro, Abdullahi Yusuf, Saad Althobaiti, Umar Tasiu Mustapha, Mathematical modeling and analysis of human-to-human monkeypox virus transmission with post-exposure vaccination, 2024, 2363-6203, 10.1007/s40808-023-01920-1
    16. Ruiqing Shi, Yihong Zhang, Stability analysis and Hopf bifurcation of a fractional order HIV model with saturated incidence rate and time delay, 2024, 108, 11100168, 70, 10.1016/j.aej.2024.07.059
    17. James Andrawus, Yau Umar Ahmad, Agada Apeh Andrew, Abdullahi Yusuf, Sania Qureshi, Ballah Akawu Denue, Habu Abdul, Soheil Salahshour, Impact of surveillance in human-to-human transmission of monkeypox virus, 2024, 1951-6355, 10.1140/epjs/s11734-024-01346-5
  • Reader Comments
  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(6258) PDF downloads(1194) Cited by(5)

Figures and Tables

Tables(7)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog