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OtherBASIC SCIENCE INVESTIGATIONS

Lognormal Distribution of Cellular Uptake of Radioactivity: Statistical Analysis of α-Particle Track Autoradiography

Prasad V.S.V. Neti and Roger W. Howell
Journal of Nuclear Medicine June 2008, 49 (6) 1009-1016; DOI: https://doi.org/10.2967/jnumed.107.048843
Prasad V.S.V. Neti
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Roger W. Howell
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  • FIGURE 1. 
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    FIGURE 1. 

    Statistical analysis of α-particle track distribution in V79 lung fibroblasts that were labeled in culture medium containing 0.52 kBq of 210Po-citrate per milliliter. (A–C) Vertical bars with SEs represent experimental track distributions (discrete) when scored after decays had been allowed to accumulate for 7, 26, and 52 d (7). (D) Data points represent normalized convolution of experimental track data obtained at 7 d (▴), 26 d (▪), and 52 d (•). Error bars represent SEs. In each panel, predicted probabilities based on Poisson, P-LN, and LN functions are represented by dashed step line, thick solid step line, and solid curve, respectively. Parameters of 3 probability density functions are enumerated in Table 1. Inset plots ordinates on log scale to compare trends of these probability functions relative to experimental data at high numbers of convolved tracks.

  • FIGURE 2. 
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    FIGURE 2. 

    Statistical analysis of α-particle track distribution in V79 lung fibroblasts that were labeled in culture medium containing 3.8 kBq of 210Po-citrate per milliliter. (A and B) Decays were allowed to accumulate for 0.67 d (A) and 4 d (B). (C) Data points represent normalized convolution of experimental track data obtained at 0.67 d (▴) and 26 d (•). Error bars represent SEs. In each panel, predicted probabilities based on Poisson, P-LN, and LN functions are represented by dashed step line, thick solid step line, and solid curve, respectively. Inset plots ordinates on log scale to compare trends of these probability functions relative to experimental data at high numbers of convolved tracks. Parameters of 3 probability density functions are enumerated in Table 1.

  • FIGURE 3. 
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    FIGURE 3. 

    Statistical analysis of α-particle track distribution in V79 lung fibroblasts that were labeled in culture medium containing 67 kBq of 210Po-citrate per milliliter. (A and B) Decays were allowed to accumulate for 0.25 d (A) and 1 d (B). (C) Data points represent normalized convolution of experimental track data obtained at 0.25 d (▴) and 1 d (•). Error bars represent SEs. In each panel, predicted probabilities based on Poisson, P-LN, and LN functions are represented by dashed step line, thick solid step line, and solid curve, respectively. Inset plots ordinate on log scale to compare trends of these probability functions relative to experimental data at high numbers of convolved tracks. Parameters of 3 probability density functions are enumerated in Table 1.

  • FIGURE 4. 
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    FIGURE 4. 

    LN σ for 3 different activity concentrations of 210Po-citrate. Open squares (□) represent values of σ obtained, when <n> was constrained, by LS fits of experimental track data corresponding to longest decay accumulation times (i.e., t2 > t1, Figs. 1C, 2B, and 3B) to LN distribution function. SEs of these fitted σ-values are indicated by vertical lines. Corresponding σ-values obtained for these same data using P-LN distribution function are shown as open circles (○). Open triangles (▵) correspond to LS fits of convolved data (Figs. 1D, 2C, and 3C) to LN function. Finally, dashed line passes through what are considered best σ-values as defined by lowest Embedded Image.

Tables

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    TABLE 1

    Statistical Analysis of 210Po α-Particle Track Distribution Data (7) Using Poisson, LN, and P-LN Functions

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    TABLE 2

    Relevant Parameters for β-Particle Tracks per Cell in Autoradiography Experiment Along with Quantities of Statistical Tests for Stirred and Unstirred Mixtures

    Statistical test
    Type and function<n>*σ†Embedded ImageEmbedded ImageR2
    Stirred mixture
     Poisson8.7—220.15—
     LN8.70.70200.0071—
     P-LN8.70.80200.0064—
     LS fit to LN12 ± 1.40.79 ± 0.075200.00480.79
    Unstirred mixture
     Poisson7.8—210.99—
     LN7.80.67200.0077—
     P-LN7.80.68200.0046—
     LS fit to LN8.2 ± 0.370.57 ± 0.033200.0180.93
    • ↵* SEs are provided by LS fit of data to LN function using SigmaPlot.

    • ↵† Optimized value of σ is obtained via minimization of Embedded Image procedure.

    • The <n> and σ are obtained from raw data based on Lehman and Scavia (18) and minimization of Embedded Image value.

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Journal of Nuclear Medicine: 49 (6)
Journal of Nuclear Medicine
Vol. 49, Issue 6
June 2008
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Lognormal Distribution of Cellular Uptake of Radioactivity: Statistical Analysis of α-Particle Track Autoradiography
Prasad V.S.V. Neti, Roger W. Howell
Journal of Nuclear Medicine Jun 2008, 49 (6) 1009-1016; DOI: 10.2967/jnumed.107.048843

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Lognormal Distribution of Cellular Uptake of Radioactivity: Statistical Analysis of α-Particle Track Autoradiography
Prasad V.S.V. Neti, Roger W. Howell
Journal of Nuclear Medicine Jun 2008, 49 (6) 1009-1016; DOI: 10.2967/jnumed.107.048843
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