2010 4 0817-2242778 2242778 E-mail zwyang@nsmc.edu.cn http://www.nsmc.edu.cn/forum/stereology www.nsmc.edu.cn/forum/stereology/
Essential procedures of stereological (morphometric( morphometric) ) study / / / / / / /
1 = / Random Sampling / Stereological Test / / : (Uniform Random Sampling) : (Isotropic Random Sampling) Isotropic Uniform Random (IUR)
Uniform random sampling: Each location has the same chance to be sampled 1 2 3 4 5 6 7 8 9 10 1 1 1~10 Simple - Excel =10*RAND()+0.5 Random 0 Sampling
1 2 3 4 5 6 7 8 9 10 2 1 1~5 r Systematic 2 r+5 Random Sampling 2~3 1 1~4 r 2 r+4 3 r+4+4 ( ( )
1 2 3 4 5 6 7 8 9 10 1 5 6 9 10 2 4 7 8 3 1 2 3 4 5 6 7 8 9 10
- 1 1 2 3 4 5 6 7 8 9 9 3 3 9 1 4 7 1 2 5 8 1 3 6 9
- 2 2 4 6 1 5 9
- 3 48.4 cm 3 48.4/3 = 16.1 cm 1 Excel 1 0~16.1 =16.1*rand() 4.4 2 20.5 (=4.4+16.1) 36.6 (=4.4+16.1+16.1) 4.4 20.5 36.6 cm 1
- 4 8 3 3 8 1 1 2 2
- 5 A B A B 2 1
- 1
- 2 V V S V V V S V L V N V
1. 2.
V V 1 2 V V V V
1 A A B V V B Sertoli
: Isotropic random sampling: Each direction has the same chance to be sampled ( ): / ( ): ( ) ( ) ( ) ( )
isotropic sections : IUR (isotropic uniform random) test
Isotropic Random Directions in 3D Space φ = 360 r 1 θ = arccos r 2 [r 1 /r 2 0-1 ] Excel Excel φ =360*RAND() θ =ACOS(RAND())*180/PI()
Isotropic Sectioning: Orientator 1 ϕ = 180r 1 Excel Excel =180*RAND() 2 θ=arccos(1 2r 2 ) Excel Excel =ACOS(1-2*RAND())*180/PI()
Isotropic sectioning: Isector 1 2
/ α: : 0~180 Excel: =180*RAND()
?
/ vertical sections : VUR (vertical uniform random) test
/ / / ϕ = 180*RAND()
= =
(Cycloid) / (sine-weighted) θ = arccos r Excel Excel =ACOS(RAND())*180/PI()
Y 4 2 p l =
1. 1 1 Excel =ACOS(RAND())*180/PI() 2. 2 2
Commonly seen stereological concepts Design-based / Model-based / Classical stereology / Modern stereology / Unbiased / Biased /
2 / / Ratio Estimates / ΣP 2ΣI 2ΣQ ΣQ V V = S V = L V = N V = - ΣP ref ΣL ref ΣA ref ΣV ref = The Reference Trap
??!?!
30%? ( = ) : 30% 30%
. / /?,.,? =
x N A = 1 (u -2 ) y N A = 2 (u -2 )
y N A = 2 (u -2 )
:
? /kg
The reference trap
The Reference Trap! = /
3 / Sampling Error + - / - - sample size
9.4% 9.4% 4.1% 4.1% 60 60 0.027 0.027 639 639 0.653 0.653 625 625 0.55 0.55 6 603 603 0.62 0.62 5 462 462 0.66 0.66 4 578 578 0.68 0.68 3 662 662 0.66 0.66 2 906 906 0.75 0.75 1 cm cm 3 SE SE CE CE
s 2 n Os 2 i : 1 s 2 i n i n i n ii n iii n iv s 2 i s 2 ii s 2 iii s 2 iv 2 Do more less well /
- - CE / CE < 0.05 - n > 1 M --- ---
- -- 100 ~ 200 (0.5) 5 < 0.05 -- / 5 ~ 10 ---, n = 5 ---
4 Effects of Tissue Processing on Stereological Estimates CT
topological property metric property / /
/ Tissue shrinkage d 3 = 0.6 D 3 = 1 - (d 3 /D 3 ) = 40.0% = 1 - (d 2 /D 2 ) = 28.9% / = 1 - (d/d) = 15.7%
? 1.! 2. 3.
V b b before V a a after C v coefficient of volume change C v = V a / V b
- V V V V b C 0/3 V = V V V b - S S V V b C 1/3 V - L L V V b C 2/3 V L L V V a - N = N V V b C 3/3 V = N V V a
? 4. fractionator 500
1/a 1/b 1/c n a b c n
blocks blocks 1/b 1/b b sections sections 1/s 1/s s 1/f 1/f f fields fields 1/d 1/d d depth depth n b s f d n +
5 / / Section Thickness / Overprojection / Underprojection NA x4 0.13 x10 x20 x40 x100 0.30 0.50 0.75 1.30 d (µm)( 32.27 5.83 1.91 0.65 0.25 d = λ (n 2 NA 2 ) 1/2 / NA 2
25 25µm 10 10 71.1% 40 40 71.5% 100 100 72.1%. 2010;15(2):191-4
6 Problem of Subjectivity
7 Preparation of Test Grids /
8 / Image Analysis /
- - (1) (2) - ( ) V V S V L N V V = Feret
1. 1 2. 3. 5 cm 3