From: Assessing particle and fiber toxicology in the respiratory system: the stereology toolbox
Estimation (formula) | Counts (example)a | Results (example)a |
---|---|---|
Cavalieri (Fig. 4a) | \( \begin{array}{ll}\sum P\hfill & =125\hfill \\ {}a/p\hfill & ={\left(3.5\ mm\right)}^2\hfill \\ {}d=\hfill & 3\ mm\hfill \end{array} \) | \( \begin{array}{ll}V(lung)\hfill & =4594\ m{m}^3\hfill \end{array} \) |
V(lung) = ∑P x a/p x d | ||
Parenchymal Volume (Fig. 4b) | \( \begin{array}{ll}\sum P(par)\hfill & =218\times 4=872\hfill \\ {}\sum P(nonpar)\hfill & =107\hfill \\ {}\sum P(lung)\hfill & =\sum \left(P(par)+P(nonpar)\right)\hfill \\ {}\hfill & =979\hfill \end{array} \) | \( \begin{array}{ll}V\left(par, lung\right)\hfill & =4092\ m{m}^3\hfill \\ {}V\left( nonpar, lung\right)\hfill & =502\ m{m}^3\hfill \end{array} \) |
\( \begin{array}{ll}V\left(par, lung\right)\hfill & =\sum P(par)/\sum P(lung)\times V(lung)\hfill \\ {}V\left( nonpar, lung\right)\hfill & =\sum P(nonpar)/\sum P(lung)\times V(lung)\hfill \end{array} \) | ||
Alveolar volume, surface area and septal thickness (Fig. 4c) | \( \begin{array}{ll}\sum I\hfill & =394\hfill \\ {}\sum P(sept)\hfill & =94\hfill \\ {}\sum P(alv)\hfill & =333\hfill \\ {}\sum P(par)\hfill & =94+333=427\hfill \\ {}l/p\hfill & =35\ \mu m\hfill \end{array} \) | \( \begin{array}{ll}{V}_V\left( sept/par\right)\hfill & =0.22\hfill \\ {}{V}_V\left(alv/par\right)\hfill & =0.78\hfill \\ {}{S}_V\left( sept/par\right)\hfill & =527.3\ c{m}^{-1}\hfill \end{array} \) |
\( \begin{array}{ll}{V}_V\left( sept/par\right)\hfill & =\sum P(sept)/\sum P(par)\hfill \\ {}{V}_V\left(alv/par\right)\hfill & =\sum P(alv)/\sum P(par)\hfill \\ {}{S}_V\left( sept/par\right)\hfill & =\left(2\times \sum I\right)/\left(\sum P(par)\times l/p\right)\hfill \\ {}S\left( sept, lung\right)\hfill & ={S}_V\left( sept/par\right)\times V(par)\hfill \\ {}V\left(alv, lung\right)\hfill & ={V}_V\left(alv/par\right)\times V(par)\hfill \\ {}\tau (sept)\hfill & =2\times {V}_V\left( sept/par\right)/{S}_V\left( sept/par\right)\hfill \end{array} \) | \( \begin{array}{ll}V\left(alv, lung\right)\hfill & =3191.8\ m{m}^3\hfill \\ {}S\left( sept, lung\right)\hfill & =2158\ c{m}^2\hfill \\ {}\tau (sept)\hfill & =8.3\ \mu m\hfill \end{array} \) | |
Epithelial mucous cell metaplasia (Fig. 4d) | \( \begin{array}{ll}\sum I\hfill & =294\hfill \\ {}\sum P(muc)\hfill & =89\hfill \\ {}\sum P(epi)=\hfill & 245\hfill \\ {}\sum P(lung)\hfill & =396\times 50=19800\hfill \\ {}l/p\hfill & =35\ \mu m\hfill \end{array} \) | \( \begin{array}{ll}{V}_V\left(muc/ lung\right)\hfill & =0.0045\hfill \\ {}{V}_V\left(epi/ lung\right)\hfill & =0.012\hfill \\ {}{S}_V\left(bm/ lung\right)\hfill & =0.85\ m{m}^{-1}\hfill \end{array} \) |
\( \begin{array}{ll}{V}_V\left(muc/ lung\right)\hfill & =\sum P(muc)/\sum P(lung)\hfill \\ {}{S}_V\left(bm/ lung\right)\hfill & =\left(2\times \sum I\right)/\left(\sum P(lung)\times l/p\right)\hfill \\ {}V/S\left(muc/bm\right)\hfill & =\left(\sum P(muc)\times l/p\right)/\left(2\times \sum I\right)\hfill \\ {}\tau (epi)\hfill & ={V}_V\left(epi/ lung\right)/{S}_V\left(bm/ lung\right)\hfill \end{array} \) | \( \begin{array}{ll}V/S\left(muc/bm\right)\hfill & =5.3\ \mu {m}^3/\mu {m}^2\hfill \\ {}\tau (epi)\hfill & =14.1\ \mu m\hfill \end{array} \) | |
Cell numbers (Fig. 5a) | \( \begin{array}{ll}\sum {Q}^{-}\hfill & =107\ \left( both\ ways\right)\hfill \\ {}n\hfill & =53\hfill \\ {}A\hfill & =200\times 250\ \mu {m}^2\hfill \\ {}h\hfill & =5\ \mu m\hfill \end{array} \) | \( \begin{array}{ll}{N}_V\left( cell/ lung\right)\hfill & =4038\ m{m}^{-3}\hfill \\ {}N\left( cell, lung\right)\hfill & =18.5\times {10}^6\hfill \end{array} \) |
\( \begin{array}{ll}{N}_V\left( cell/ lung\right)\hfill & =\sum {Q}^{-}/\left(2\times n\times A\times h\right)\hfill \\ {}N\left( cell, lung\right)\hfill & =NV\left( cell/ lung\right)\times V(lung)\hfill \end{array} \) | ||
Alveolar number (Fig. 5b) \( \begin{array}{ll}N\left(alv, lung\right)\hfill & =\left(\sum B\right./\left.\left(2\times n\times A\times h\right)\right)\times V(lung)\hfill \end{array} \) | \( \begin{array}{ll}\sum B\hfill & =112\ \left( both\ ways\right)\hfill \\ {}n\hfill & =90\hfill \\ {}A\hfill & =200\times 250\ \mu {m}^2\hfill \\ {}h\hfill & =5\ \mu m\hfill \end{array} \) | \( \begin{array}{ll}{N}_V\left(alv/ lung\right)\hfill & =2489\ m{m}^{-3}\hfill \\ {}N\left(alv, lung\right)\hfill & =11.4\times {10}^6\hfill \end{array} \) |