Image Anal Stereol 2024;43:221-237  doi: 105566/ias.2951 
Original Research Paper 
221 
 
TISSUE VOLUME AND SECTION AREA CHANGES OF PARAFFIN AND 
METHACRYLATE EMBEDDED TESTICULAR SECTIONS: AN UNBIASED 
DESIGN STUDY 
YANG GUO1, YU XIANG1, DAN WANG2, ZHENG-WEI YANG,1 
1Morphometric Research Laboratory, Research Institute of Basic Medicine and Forensics School, North Sichuan 
Medical College, Nanchong, Sichuan, China; 2The Affiliated Hospital of North Sichuan Medical College,  
Nanchong, Sichuan, China 
e-mail: 7827382@qq.com; 261009034@qq.com; 649150029@qq.com; zwyang@nsmc.edu.cn 
(Received June 17, 2023; revised September 8, 2024; accepted October 9, 2024) 
ABSTRACT 
For stereological estimates of structures in an organ such as total number (particles), length or surface area, 
the tissue change after processing (usually embedding of tissue blocks, sectioning of embedded blocks, and 
mounting and staining of sections) may need to be estimated to correct the results obtained on final sections 
so as to reflect the true results in the organ before processing. We proposed that the correction be made 
depending on the stereological principle used: correction for estimation with 3-dimensional and 2-dimen-
sional measurements be based on different tissue volume and section area changes. Previous researches on 
tissue changes were limited and overlooked different corrections. Using paraffin and methacrylate embed-
ded testicular sections, we studied, with an unbiased design, the tissue volume and section area changes 
after processing. The results demonstrated that the overall change of the actual tissue volume of paraffin 
sections was a marked shrinkage of 21%-23% while that of methacrylate sections was a small expansion 
almost negligible; compared with area of the embedded block face, the final section area had a 4% decrease 
in paraffin but an 8% increase in methacrylate. The results were tentatively used for correction of estimates 
in some of previous studies. The present study provides both methods and data for experiments involving 
the study of tissue change for better stereological estimation. 
Keywords: methacrylate sections, paraffin sections, section thickness, stereology, tissue shrinkage.
INTRODUCTION  
Stereological Background 
It is marvelous, which many histopathological re-
searchers must have been aware of for half a century, 
that microscopic structures can be quantitatively studied 
with mathematics- and statistics-based stereological 
methods, including computer assisted stereological tools 
(Weibel, 1979 & 1980; Gundersen et al., 1988a & 
1988b; Yang et al., 1990; Zhengwei et al., 1997; Nyen-
gaard, 1999; Yang, 2012). The principle is simple. Just 
by means of counting (on fields of view sampled on tis-
sue sections cut from an biological organ), for instance, 
we can estimate XV: the amount (e.g. volume, surface 
area, length or number) of any structures (including lin-
ear structures or discrete particles such as nuclei) per 
volume of (some part of the) organ (the so-called refer-
ence space that contains the structures concerned). Then 
by multiplying the density (XV) by the volume of the or-
gan (the reference volume V), we can estimate the total 
amount of the structures (X) in the organ: 
𝑋 = 𝑋 ×  𝑉    (1) 
This parameter of total amount, most valuable and 
commonly obtained in stereological practice, reflects the 
true, absolute amount of structures in the organ, unaf-
fected by the organ size, and can thus best reflect (i) the 
overall function of the structures in the organ and (ii) the 
quantitative changes of the structures between different 
experimental conditions or groups, avoiding the serious 
problem of reference trap (Braendgaard & Gundersen, 
1986; Nyengaard, 1999; Yang, 2012). 
That being said, many researchers may have been 
confused about or tended to ignore what the organ vol-
ume (V) should be and what the total amount (X) ob-
tained actually represents. In practice, we (should) usu-
ally obtain the volume of the fresh organ before tissue 
processing (usually slicing & embedding of tissue 
blocks, sectioning of embedded blocks, mounting of 
sections, and staining & coverslipping of mounted sec-
tions), the process of obtaining final sections (from the 
organ) ready for microscopic observation and 
 GUO Y ET AL.: Volume and area changes of tissue sections 
222 
 
measurement. This volume, designated as V(pre), can be 
readily obtained by using methods such as water dis-
placement (for large organs) or one (for small or large 
organs) based on weight and specific gravity (density) 
of the organ (Weibel, 1979; Gundersen et al., 1988a; 
Yang, 2012; Guo et al., 2019). However, stereological 
measurements are performed on final sections, i.e. the 
structural density (XV) is obtained after processing. So 
what we first estimate is in fact the total structural 
amount after processing: 𝑋 𝑝𝑜𝑠𝑡 =  𝑋   𝑉 𝑝𝑜𝑠𝑡      (2) 
where V(post) is the organ volume after processing, 
which is, unlike V(pre), somewhat difficult to under-
stand and estimate. 
V(post) can be imagined as volume of the processed 
organ, reconstructed from all the serial sections that can 
be cut from the whole fresh organ, and X(post) is the to-
tal amount of the structures in the processed organ. Take 
the estimation of particle number as an example, 𝑁 𝑝𝑟𝑒 =  𝑁 𝑝𝑜𝑠𝑡 =  𝑁 × 𝑉 𝑝𝑜𝑠𝑡     (3) 
where (i) N(pre) and N(post) are the total numbers of 
particles in the organ before and after processing, re-
spectively, the two numbers being equal assuming that 
processing does not affect the number of particles, and 
(ii) NV is the numerical density of particles obtained after 
processing. 
V(post) is usually estimated by the Cavalieri’s prin-
ciple (Gundersen et al., 1988a; Yang, 2012). (i) When 
the organ concerned is completely cut into serial sec-
tions, we have a direct estimate of V(post) with the fol-
lowing Cavalier’s estimator: 𝑉 𝑝𝑜𝑠𝑡 =  𝑡 × 𝑎          (4) 
where t is the thickness of serial sections and ∑ 𝑎 is the 
total area of all the serial sections. Sample some of the 
tissue blocks from the organ and sample some of the se-
rial sections from the blocks in a systematic (uniform) 
random manner (with known sampling fractions), we 
can also estimate (𝑡 × 𝑎) according to  the fractionator 
principle, without necessarily cutting the organ all into 
serial sections (Gundersen et al., 1988b; Yang, 2012; 
Sadeghinezhad & Nyengaard, 2019), see Equation 19 
below. (ii) In most cases, only some random, single sec-
tions are obtained from the organ for stereological study 
and the organ’s V(post) cannot be directly estimated 
from the sections. In many cases, we need to perform a 
separate study to estimate the ratio of tissue volume 
change (RVC), thus indirectly estimating V(post): 𝑉 𝑝𝑜𝑠𝑡 =  𝑉 𝑝𝑟𝑒 × 𝑅𝑉𝐶      (5) 
where RVC can be estimated by sampling some tissue 
blocks from an organ, preparing serial sections and esti-
mating the organ volumes before and after processing 
(as we do in Part "First Experiment: Study of Tissue 
Volume Change" below): 𝑅𝑉𝐶 =         (6) 
Note that the V(post) in Equation 3 (for estimation 
of total particle number) can be directly estimated by the 
Cavalier’s principle (Equation 4), or indirectly estimated 
using Equations 5 & 6 that also involve the Cavalier’s 
principle (Equation 4). Now comes a tricky part: the sec-
tion thickness (t) in Equation 4 should be considered in 
two ways depending on the stereological principle used 
for the number estimation. (i) When the number is esti-
mated with the physical or optical disector, i.e. the par-
ticles are counted in 3D (3-dimentional) space (Gunder-
sen et al., 1988b; Nyengaard, 1999; Yang, 2012; Xu et 
al., 2019), the section thickness should be the actual 
thickness – t(act) – measured thickness of the sections 
after processing irrespective of whether the processing 
leads to uniform or non-uniform shrinkage or expansion 
(Fig. 1). That is, the V(post) in Equation 3 should be the 
actual V(post): 𝑉 𝑝𝑜𝑠𝑡, 𝑎𝑐𝑡 =  𝑡 𝑎𝑐𝑡 ×  𝑎     (7) 
where t(act) is best measured directly using an electronic 
microcator while the section is being observed with an 
oil immersion lens (Dorph-Petersen et al., 2001; Xiang 
& Yang, 2014). (ii) When the number estimation is 
based on 2D (2-dimensional) counts of particle profiles 
on sectional planes (Weibel, 1979; Yang et al., 1990), 
however, the section thickness should be the virtual 
thickness – t(vir) – thickness of the section after uniform 
change in proportion to the section area change [Figs. 
1(2) & 1(4)]. In this case, the V(post) in Equation 3 
should the virtual V(post): 𝑉 𝑝𝑜𝑠𝑡, 𝑣𝑖𝑟 =  𝑡 𝑣𝑖𝑟 × 𝑎     (8) 
The t(vir) can be estimated by, 𝑡 𝑣𝑖𝑟 =  𝑡 𝑏𝑎 ×  𝑅𝐴𝐶       (9) 
where t(ba) is the block advance (i.e. thickness set by 
the microtome) and RAC is the ratio of section area 
change. RAC can be estimated by, 𝑅𝐴𝐶 =       (10) 
where a(post) is the area of the final section after pro-
cessing and a(eb) is the area of the embedded block face 
(cut-surface) from which the section is cut, see Part 
"Second Experiment: Study of Section Area Change" 
below. Of note, where serial sections are used for 
Image Anal Stereol 2024;43: 221-237 
 
223 
 
volume estimation (Equations 4, 7 and 8), a separate 
study is usually required for RAC estimation (Equation 
10) since it is practically impossible to estimate both 
a(post) and a(eb) while cutting serial sections. 
 
Fig. 1. Schematic illustration of tissue change: from 
original tissue before processing (1) to tissue after pro-
cessing (2-5). The original tissue shown is a projection 
of some cuboid-shaped tissue (pink) containing large 
and small spherical particles (blue). The tissue is di-
vided into “sections”, each with an upper surface 
(length and width unseen) area of “a” and a thickness 
of “t”. (2) & (4): uniform change in 3 dimensions 
(length, width and thickness); (3) & (5): non-uniform 
change. Of note, the thickness change is proportional to 
the area change in (2) & (4), not in (3) & (5). 
Of note, (i) the area in comparison with a(post) in 
Equation 10 is the area of the tissue block face after em-
bedding, not the area of the fresh tissue block face before 
embedding, (ii) the block advance is the thickness (of 
sectioning the embedded tissue) set at the step of sec-
tioning, and (iii) the RAC in Equation 9 is used to con-
sider the virtual thickness change in proportion to the 
section area change after sectioning, for the estimation 
of the virtual V(post) (see Equations 8, 9 and 10). 
The virtual V(post) obtained by Equations 8 -10 can 
be imagined as the volume of the embedded organ after 
a 3D uniform magnification or minification of the organ 
based on the scale of the sectional area (2D) change, like 
a 3D uniform zooming with a computer mouse, or as the 
organ space consisting of serial sectional planes, with 
the interval between planes being the virtual thickness. 
Since we have V(post, act) and V(post, vir), we also 
have a block advance based V(post): 𝑉 𝑝𝑜𝑠𝑡, 𝑏𝑎 =  𝑡 𝑏𝑎 ×  𝑎    (11) 
Based on Equations 6 and 11, we have a block ad-
vance based ratio of tissue volume change: 𝑅𝑉𝐶 𝑏𝑎 =  ,     (12) 
Then we can estimate the actual or virtual ratio of tissue 
volume change based on the ratio of the actual or virtual 
section thickness change by, 𝑅𝑉𝐶 𝑎𝑐𝑡 =  ,   =  𝑅𝑉𝐶 𝑏𝑎 ×     (13) 𝑅𝑉𝐶 𝑣𝑖𝑟 =  ,   =  𝑅𝑉𝐶 𝑏𝑎 ×    (14) 
Note, from Equation 13, we have,  =      (15) 
And from Equations 14 and 9, we have,  =   = 𝑅𝐴𝐶     (16) 
To summarize in a practical way, (i) for total parti-
cle number estimation based on particle counts in 3D 
space (using 3D probes - physical or optical disectors), 
we have: 𝑁 𝑝𝑟𝑒 = 𝑁 𝑝𝑜𝑠𝑡 = 𝑁 × 𝑉 𝑝𝑟𝑒 × 𝑅𝑉𝐶 𝑎𝑐𝑡  (17) 
And (ii) for total particle number estimation based on 2D 
counts (number of particle profiles per area of section), 
we have: 𝑁 𝑝𝑟𝑒 = 𝑁 𝑝𝑜𝑠𝑡 = 𝑁 × 𝑉 𝑝𝑟𝑒 × 𝑅𝑉𝐶 𝑣𝑖𝑟   (18) 
where RVC(act) and RVC(vir) can be estimated in a sep-
arate, comparable study (Equations 13 & 14). 
In essence, whether for global estimation (estima-
tion of total amounts) of particle numbers or other geo-
metric properties, the V(post) in Equation 2 should be 
(i) the actual reference volume reconstructed from all 
the serial sections with actual thickness when the stere-
ological estimation is based on measurement in 3D 
space - measurement results per volume of reference 
space, or (ii) the virtual reference volume reconstructed 
from all the serial sections with virtual thickness when 
the stereological estimation is based on measurement on 
2D plane - measurement results per area of section. The 
virtual reference volume is proportional to the section 
area and the virtual (not actual) section thickness, and 
the virtual section thickness is proportional to the block 
advance and the section area change (Equation 9), un-
related to the actual section thickness. 
 GUO Y ET AL.: Volume and area changes of tissue sections 
224 
 
Note that, unlike total particle number estimation, 
assumption of uniform tissue volume change after pro-
cessing [Figs. 1(2) & 1(4)] must be accepted, although 
it may not be valid in practice (Dorph-Petersen et al., 
2001; Zhao et al., 2010), for total volume, surface area 
or length estimation, otherwise we cannot determine, 
with observation and measurement on final sections, 
what has happened, during processing, to the structural 
amounts relative to the reference volume. Under the 
prerequisite of uniform change, (i) the volume fraction 
(volume of structures per volume of organ) estimated 
after processing can be taken as the volume fraction be-
fore processing, so we can obtain the total volume of 
any structures before processing by: (the volume frac-
tion estimated after processing) × V(pre). (ii) The total 
surface area of any structures before processing can be 
obtained by: (the surface area density estimated after 
processing) × V(pre) × RVC(vir)1/3; the total length of 
linear structures before processing can be obtained by: 
(the length density estimated after processing) × V(pre) × RVC(vir)2/3 (Yang, 2012). 
Study of Tissue Volume and Section Area 
Changes after Processing 
We perform stereological measurements on final 
sections that are originally cut from organs and then 
subjected to histopathological processing, a series of 
procedures such as tissue fixation & dehydration, tissue 
blocks’ sampling, embedding & sectioning, and tissue 
sections’ mounting, staining & coverslipping (Dorph-
Petersen et al., 2001). The processing may vary from 
researcher to researcher, from laboratory to laboratory, 
and from study to study, likely leading to variable tissue 
volume change and thus introducing variable system-
atic error. So it is better to correct the error, if the cor-
rection can be made by studying the changes properly 
and reliably, so that the corrected data can best repre-
sent the true value in the original organ. 
The core part of correction for the tissue volume 
change is to estimate V(post), the volume of organ (ref-
erence space) after processing. V(post) is mostly esti-
mated by the Cavalieri’s principle (Equation 4). Rarely 
was it pointed out, however, that this volume estimation 
should be considered in two ways (see Part "Stereolog-
ical Background"). In one way, V(post) should be the 
actual reference volume, i.e. the actual measured thick-
ness of sections should be used for the Cavalieri’s vol-
ume estimation. The volume estimated in this way is 
essential for total number estimation with the disector 
based on Equations 3, with the exception of total num-
ber estimation by the fractionator principle (Gundersen 
et al., 1988b; Nyengaard, 1999; Dorph-Petersen et al., 
2001; Yang, 2012). In the other way, V(post) should be 
the virtual reference volume, i.e. the section thickness 
for the Cavalieri’s volume estimation (Equation 4) 
should be the virtual thickness, one that is calculated 
from the block advance (thickness set by the micro-
tome) and the ratio of section area change (Equation 9). 
The virtual reference volume is used for correction of 
global estimates (e.g. total surface area, length or num-
ber per organ) based on 2D measurement, and for that 
of local size estimates (e.g. mean size of particles) based 
on 2D measurement as well, which is beyond the scope 
of the present paper. 
In previous studies dealing with the volume 
change, few actually estimated the V(post) with consid-
eration of the actual thickness of sections (best meas-
ured with a microcator). Many studies used tissue 
blocks for the volume change study and the linear 
(length or width) change of the blocks was used to re-
flect the volume change, with concerns over the accu-
racy of the blocks’ volume estimation. In previous stud-
ies dealing with the section area change, few actually 
measured the areas at different stages of processing. 
Concerns also include clear viewing and confident 
measurement of the block faces and sections. 
For examples, researcher ZWY (and co-authors), 
whose major interest of research is stereological study 
of reproductive organs using paraffin and resin sections 
with light microscopy, previously studied the tissue 
shrinkage of paraffin embedded (Yang & Cui, 1989) 
and Epon-Araldite embedded (Yang et al., 1990) testic-
ular sections, but neglected to study the actual section 
thickness (Yang & Cui, 1989) and the section area 
change or virtual section thickness (Yang et al., 1990). 
Then the tissue shrinkage of methacrylate testicular sec-
tions was studied, neglecting to study the actual section 
thickness as well (Zhengwei et al., 1997); effects of fix-
ation and dehydration on organ sizes were studied and 
paraffin and methacrylate sections were compared in a 
stereological study, both being unable to reflect the fi-
nal tissue volume change (Zhao et al., 2010). Thereafter 
attention was given to study of the section area change 
of paraffin testicular sections by using scan images 
(Xiang et al., 2018), but the area of fresh tissue block 
faces was not studied, and methacrylate sections were 
not included in the study due to difficulty in clear view-
ing of the methacrylate block faces and sections. 
Therefore, the present experiment was carefully de-
signed to study both the tissue volume change and the 
section area change of testicular sections. Specifically, 
testicular tissue blocks from rats of different ages or 
blocks of different sizes and shapes were compared; 
both paraffin and methacrylate sections were used; the 
volume of testis after processing was unbiasedly 
Image Anal Stereol 2024;43: 221-237 
 
225 
 
determined by the Cavalieri’s principle in combination 
with the fractionator principle; methods of observing 
block faces and sections were improved; the actual 
thickness of sections after processing were directly 
measured; and areas of the block faces and sections ob-
served at all major stages of tissue processing were un-
biasedly determined with the test-point counting 
method. With such a comprehensive, unbiased design, 
the present study aimed not only to clarify the testicular 
tissue change after processing but also provide both 
methods and data for experiments involving the study 
of tissue change for better stereological estimation. 
MATERIALS AND METHODS  
First Experiment: Study of Tissue Volume 
Change 
Three groups of 6 testes of different sizes from 
three groups of normal male Sprague–Dawley rats aged 
1 month (pubertal), 3 months (mature) and 5 months 
(adult), respectively, were obtained from the Animal 
Center of North Sichuan Medical College. After anaes-
thesia with intraperitoneal injection of pentobarbital so-
dium (50 mg/kg), one testis with its surrounding tissues 
was immediately removed from one rat and immersion 
fixed in Bouin's fluid. Two days later, the organs were 
stored in 70% ethanol, for a few months before further 
experiment. The samples were from an animal study by 
Guo et al. (2019) which was approved by the Ethics 
Committee of North Sichuan Medical College (CBY13-
A-ZP05). 
Sampling and embedding of tissue blocks 
Dissected from the surrounding tissues, each testis 
with a complete capsule (tunica albuginea) was weighed 
on an electronic balance (accuracy 0.1 mg) and its den-
sity (around 0.925 g/cm3) was determined in graded eth-
anol solutions of known densities (Yang, 2012; Guo et 
al., 2019). 
Each small testis (pubertal), with a height of about 
10 mm, was cut into 4 circular slices (blocks, thickness 
approximately equal) perpendicular to its long axis 
(height). Two alternate blocks, determined in a random 
manner, were used for paraffin embedding and the other 
2 blocks for methacrylate embedding. That is, the sam-
pling fraction of tissue blocks, SF(blo), for either paraf-
fin or methacrylate embedding was 1/2 (Table 1). 
Table 1: Tissue volume change related results obtained from the First Experiment 
 Paraffin embedding Methacrylate embedding 
 Small testes Medium testes Large testes Small testes Medium testes Large testes 
Volume (cm3) of fresh testisa 0.178 
(17.1%) 
1.387  
(8.1%) 
1.556  
(13.9 %) 
0.178 
(17.1%) 
1.387  
(8.1%) 
1.556  
(13.9 %) 
 a V(pre), volume of the testis before processing, estimated by weight and density of the fresh (intact) testis 
Sampling fraction of blocksb 0.500 0.167 0.063 0.500 0.167 0.063 
 b Fraction of the testicular tissue blocks sampled from the fresh testis (= Number of blocks sampled / Total number of blocks cut) 
Sampling fraction of sectionsc 0.067 0.067 0.067 0.100 0.100 0.100 
 c Fraction of the testicular sections sampled systematically from all serial sections cut from the testicular block 
Thickness (μm) of sectionsd       14.6 
(0.9%) 
      14.6  
(4.5%) 
     14.5  
(1.8%) 
     20.7  
(4.0%) 
       21.8  
(2.9%) 
     21.1  
(2.4%) 
d Actual thickness, t(act), of testicular sections after staining. [The thickness set by microtome: 14 (paraffin) and 25 (methacrylate).] 
Mean area (mm2) of sectionse       12.8 
(16.4%) 
      23.1  
(7.6%) 
     13.2  
(17.1%) 
     17.9  
(12.7%) 
      33.5  
(15.0%) 
    19.4  
(16.8%) 
e Average area of testicular sections (stained). [Average numbers of sections: 25, 35, 26, 24, 32 and 25, respectively, from left to right.] 
Volume (cm3) of processed tes-
tisf 
0.142 
(23.8%) 
1.061 
(9.5%) 
1.206 
(27.4%) 
0.178 
(15.2%) 
1.399 
(10.9%) 
1.603 
(18.5%) 
 f V(post, act), actual volume of the testis after processing, estimated by the Cavalieri’s principle (see Equation 7 in the text) 
RVC(act)g 0.793 
(12.0%) 
0.766 
 (7.7%) 
0.771 
(18.6%) 
1.005 
(10.8%) 
1.009 
(6.8%) 
1.034 
(14.3%) 
g Actual ratio of testicular tissue volume change, equal to [V(post, act) / V(pre)], see Equation 13 in the text 
RVC(ba)h 0.758 
(11.7%) 
0.732 
(6.0%) 
0.746 
(18.0%) 
1.213 
(8.8%) 
1.158 
(8.8%) 
1.227 
(14.5%) 
h Block advance based ratio of testicular tissue volume change, see Equation 12 in the text 
RVC(vir)i 0.760 
(11.7%) 
0.716 
(6.0%) 
0.730 
(18.0%) 
1.262 
(8.8%) 
1.221 
(8.8%) 
1.294 
(14.5%) 
i Virtual ratio of testicular tissue volume change, see Equation 14 in the text* 
Data shown as “x (%)”: “mean (coefficient of variation)” calculated from each sub-group (n=6). Three groups of testes (small, medium-
sized and large) were obtained from three groups (pubertal, mature and adult) of normal Sprague-Dawley rats (6 rats per group, with one 
testis being sampled from each rat). Four testicular tissue blocks were cut and sampled in a systematic random manner from each testis, 
with 2 systematic blocks being embedded in paraffin (sub-group) and the other 2 blocks in methacrylate (another sub-group). *The ratios 
of testicular section area change (RACs) necessary for the RVC(vir) estimation (see Equations 9, 10 & 14 in the text) were borrowed 
from Table 2, being 1.005, 0.957, 0.957, 1.083, 1.112 and 1.112, respectively, in the 6 sub-groups from left to right. 
 GUO Y ET AL.: Volume and area changes of tissue sections 
226 
 
 
Fig. 2. Serial sections of paraffin (1 & 3) and methacrylate (2 & 4) embedded testicular tissue blocks. Each embedded 
block contains two tissue blocks that were cut and sampled from one testis; the testes were obtained from normal 
male Sprague-Dawley rats aged one-month (1 & 2) or five-months (3 & 4). The tissue block is a circular slice of 
tissue (1 & 2) or a quarter of the slice (3 & 4) that was cut in a direction perpendicular to the testicular long axis. 
One out of every fifteen serial paraffin sections (thickness set by microtome 14 µm), or one out of every ten serial 
methacrylate sections (thickness set by microtome 25 µm), was sampled and stained with periodic acid-Schiff’s rea-
gent and hematoxylin, with the embedding medium being removed (paraffin) or not removed (methacrylate) during 
staining. The section image was scanned from the coverslipped section (stained) on glass slide, each (shown here) 
with an image processing (Photoshop) of automatic contrast (paraffin), or automatic contrast followed by an increase 
(+28) of brightness and an increase (+28) of contrast (methacrylate). *, non-intact tissue sections cut from the two 
ends of the tissue block; , an empty area (artifact) inside the tissue section. The width and height of each image 
(small rectangular panel in the figure): 7.5 and 14.5 mm. 
Each medium-sized testis (mature), with a height of 
about 21 mm, was first cut into 6 circular slices (thick-
ness approximately equal) perpendicular to its long axis. 
Two slices were sampled in a systematic random manner 
(Gundersen et al., 1988b; Nyengaard, 1999; Dorph-Pe-
tersen et al., 2001; Yang, 2012): the 1st & 4th, the 2nd 
& 5th, and the 3rd & 6th slices were sampled in turn 
from different testes. Each of the 2 slices sampled was 
then cut into 2 halves (semicircular blocks), with one 
block (randomly chosen) being used for paraffin and the 
other one for methacrylate. So the SF(blo) for either par-
affin or methacrylate was 1/(3×2) (Table 1). 
Each large testis (adult), with a height of about 22 
mm, was first cut into 8 circular slices (thickness ap-
proximately equal) perpendicular to its long axis. Two 
slices were sampled in a systematic random manner. 
Each of the 2 sampled slices was then cut into 4 quad-
rants (blocks), with one block (randomly chosen) being 
used for paraffin and another one (randomly chosen as 
well) for methacrylate. The SF(blo) for either paraffin or 
methacrylate was therefore 1/(4×4) (Table 1). 
The 2 tissue blocks obtained from each testis were 
embedded as one embedded block for either paraffin or 
methacrylate embedding (Fig. 2). 
For paraffin embedding of the tissue blocks, the wax 
used was Paraplast by Leica Biosystems Richmond 
(USA), melting point 56ºC. The basic embedding proce-
dures we worked out were dehydration in 100% ethanol 
for 3 × 1 hours (i.e. 1 hour for 3 changes), clearing in 1-
butanol for 1 hour plus 2 × 2 hours, infiltration first in 
butanol and melted paraffin (1:1) for 40 minutes and 
then in melted paraffin for 2 × 80 minutes in a container 
(60ºC), and finally embedded in a mould on a cooling 
table at room temperature. 
For methacrylate embedding, the resin used was a 
glycol methacrylate (2-hydroxyethyl methacrylate), 
Historesin by Leica Microsystems Nussloch GmbH 
(Germany). The embedding procedures, which, essen-
tially based on the manufacturer’s instruction, we have 
been following for years (Zhengwei et al., 1997; Zhang 
et al., 2002), were dehydration in 100% ethanol for 3 × 
1 hours, clearing in 1-butanol for 3 hours, infiltration in 
the infiltration solution [100 mL basic resin 
Image Anal Stereol 2024;43: 221-237 
 
227 
 
(methacrylate) plus 1 g activator containing dibenzo-
ylperoxide] overnight at 4ºC, and embedding (polymer-
ization) in the embedding solution (15 mL infiltration 
solution plus 1 mL hardener containing dimethyl sulfox-
ide) in a mould at room temperature. 
Sectioning, sampling and staining of tissue 
sections 
Attached to a rectangular plastic piece (supporting 
block) that was clamped to microtome, each embedded 
tissue block was serially and completely sectioned using 
the same semi-automatic microtome (RM2235, Leica 
Biosystems Nussloch GmbH, Germany). The knives for 
cutting paraffin sections were Leica high profile micro-
tome blades and those for methacrylate sections were 
Leica tungsten carbide knives; the section thickness set 
by the microtome [t(ba)] was 14 µm for paraffin and 
25 µm for methacrylate (Xu et al., 2019). 
One out of every 15 serial paraffin sections or 10 
serial methacrylate sections was sampled in a systematic 
random manner and stained for area measurement. Oc-
casionally, the sampled section was of poor quality and 
a nearest neighbor section was used instead. So the sam-
pling fraction of tissue sections, SF(sec), was 1/15 for 
paraffin and 1/10 for methacrylate (Table 1). 
All sections underwent procedures, including stain-
ing with periodic acid-Schiff’s reagent and hematoxylin, 
with a similar protocol we have been following for years 
(Zhang et al. 2002; Xiang & Yang, 2014; Guo et al., 
2016; Xiang et al., 2018; Xu et al., 2019). Briefly, (i) 
each section was floated onto an adhesive glass slide 
(with positively charged surface) from a distilled water 
bath, at 37°C for paraffin sections and at room tempera-
tures for methacrylate sections, and was left dried up: 
paraffin sections, placed vertically in a slides box at 
room temperature; methacrylate sections, placed flat on 
a hotplate at 80°C for a few minutes. (ii) Key staining 
steps for paraffin sections included: heating of sections 
in an incubator at 50°C (1 hour) for prevention of section 
detachment; dewaxing in xylene (2×3 minutes); staining 
in 1% periodic acid (15 minutes), Schiff's reagent (20 
minutes) and hematoxylin (90 seconds); dehydration in 
70% ethanol (2 minutes), 95% ethanol (2 minutes) and 
absolute ethanol (2×2 minutes); and clearing in xylene 
(2×2 minutes). Key staining steps for methacrylate sec-
tions included: heating of sections on a hotplate at 90°C 
(30 minutes) for prevention of section detachment; 
staining in 1% periodic acid (30 minutes), Schiff's rea-
gent (50 minutes) and hematoxylin (30 minutes); dehy-
dration in 95% ethanol (2 minutes) and absolute ethanol 
(2×2 minutes); and clearing in xylene (2×2 minutes). 
(iii) All sections after staining were mounted with a 
neutral balsam (refractive index ~1.52). Unlike paraffin 
sections, methacrylate sections did not have the embed-
ding medium (plastic) dissolved or removed in all pro-
cedures. 
Estimation of total section area 
Each of the testicular sections sampled and stained 
(21-36 paraffin and 22-37 methacrylate sections per tes-
tis) was observed on a computer screen through a × 1.25 
objective lens (PlanApo N, numerical aperture 0.04) of 
an Olympus BX53 microscope equipped with a stereol-
ogy system (newCAST, Visiopharm, Denmark). Evenly 
spaced, rectangularly distributed test-points (centers of 
cross-shaped lines) covering the whole section were 
generated and superimposed on screen. The area that 
each point occupied or was associated with, equal to the 
product of the horizontal and vertical distances between 
points along the X-axis and Y-axis respectively, was 
0.479 mm2 for smaller serial sections and 0.767 mm2 for 
larger serial sections. The total area of the serial paraffin 
or methacrylate sections from each testis was estimated 
by multiplying the area associated with each point by the 
total number of points hitting the sections, the total num-
ber being 499-1120 (paraffin) or 513-1693 (methacry-
late). 
Measurement of actual section thickness 
From the serial testicular sections for area measure-
ment (above), 3-4 paraffin and 6-8 methacrylate sections 
per testis were re-sampled in a systematic random man-
ner for thickness measurement. The sections were ob-
served and measured on a computer screen through a × 
100 immersion oil lens (PlanApo N, numerical aperture 
1.40) of an Olympus BX51 microscope equipped with a 
stereology system (newCAST, Visiopharm, Denmark), 
the refractive index of the immersion oil used (Olympus) 
being 1.518. Fields of view were sampled on the sec-
tions in a systematic random manner (meander sam-
pling) by means of a computer-assisted motorized stage 
(ProScan III, Prior Scientific Inc., USA); the fraction (in 
area) of fields sampled on each set of serial sections re-
mained unchanged during measurement, set at 
0.35%-0.90% (paraffin) or 0.25%-0.45% (methacry-
late). A frame (35 μm × 26 μm) was generated and su-
perimposed at the center of each field. The height of the 
testicular tissue in the frame, as measured between the 
top and bottom surfaces of the tissue section with an 
electronic microcator (Dr. Johannes Heidenhain GmbH, 
Germany; maximum position error: ± 0.13 µm within a 
distance of 12 mm), was taken as the actual section 
thickness at the field (Xiang & Yang, 2014; Xu et al., 
2019). Of note, the top or bottom surface was deter-
mined, in serially focusing up and down through the 
 GUO Y ET AL.: Volume and area changes of tissue sections 
228 
 
section, as the focal plane where the tissue structure (es-
pecially stained granules of nuclear chromatin) just be-
gan to appear or disappear. The average of the thick-
nesses measured was the mean actual thickness of the 
serial sections and the number of thicknesses measured 
was 21-38 (paraffin) or 24-58 (methacrylate) for each set 
of serial sections, with the average within-individual 
(set) CVs (coefficients of variation, for groups of testes 
shown in Table 1) being 2.7%-4.7% and 7.4%-11.9% for 
paraffin and methacrylate sections, respectively. 
Ratio of tissue volume change 
The volume of the testis before processing, V(pre), 
was directly calculated, equal to its weight divided by 
density. According to the Cavalieri’s principle (Equa-
tion 4) and the fractionator principle, the actual volume 
of the testis after processing (paraffin or methacrylate) 
was estimated by, 𝑉 𝑝𝑜𝑠𝑡, 𝑎𝑐𝑡 =    𝑎  𝑡 𝑎𝑐𝑡  (19) 
Dividing the V(post, act) by V(pre), we obtained the 
actual ratio of the testicular tissue volume change, 
RVC(act), for each sub-group (Equation 13 and Table 
1). Replacing the actual section thickness with the block 
advance or virtual section thickness - t(ba) or t(vir) - in 
the above calculations, we obtained the block advance 
based ratio or the virtual ratio of the testicular tissue vol-
ume change, RVC(ba) or RVC(vir), for each sub-group 
(Equations 11, 12 & 14 and Table 1). Of note, the ratios 
of the section area change (RACs) that were needed in 
the estimation of the virtual section thickness (Equation 
9) were from the Second Experiment (below) with sim-
ilar testicular sizes and block shapes (Part "Second Ex-
periment: Study of Section Area Change" and Table 2). 
Error analysis 
The total sampling error of the above stereological 
estimation of V(post) with Equation 19 arose mainly 
from the sampling of tissue blocks (i.e. estimation of the 
testis volume from the volume of the sampled blocks ac-
cording to the fractionator principle) and the Cavalieri’s 
estimation of the blocks’ volume. The error of blocks’ 
sampling, which people might be unconcerned with, was 
tentatively analyzed by the weights of tissue blocks. Af-
ter the 2 tissue blocks for paraffin and the 2 tissue blocks 
for methacrylate were cut (systematically sampled) from 
each testis (Part "Sampling and embedding of tissue 
blocks"), the tissue blocks and all other tissue blocks cut 
in the same way from the testis were weighed to obtain 
the weight fraction of the 2 tissue blocks (for paraffin or 
methacrylate), which should approximate the sampling 
fraction [SF(blo)] of the 2 tissue blocks (Part "Sampling 
and embedding of tissue blocks") assuming homogene-
ous specific gravity of the tissue blocks. The error of 
Cavalieri’s estimation, which people might be more con-
cerned with, was analyzed as previously described 
(Yang et al., 2000), without considering the error which 
the actual section thickness measurement might contrib-
ute. Briefly, each glass slide, on which there was 1 or 2 
tissue sections (Fig. 2), was regarded as “one section”. 
In this way, the sample of serial sections was divided 
into 2 systematic sub-samples, one including the first, 
third, … “sections” (odd numbers) while the other in-
cluding the second, fourth, … “sections” (even num-
bers). Summating the total numbers of test-points 
counted (Part "Estimation of total section area") on the 
sections of the 2 sub-samples, respectively, we had an 
approximate coefficient of error (CE) for the V(post) es-
timation: 𝐶𝐸 =      –       (20) 
where x1 & x2 are the total point numbers obtained from 
the 2 sub-samples, respectively. 
To determine if there was considerable systematic 
(machine) error in the section thickness set by the mi-
crotome [t(ba) in Part "Sectioning, sampling and stain-
ing of tissue sections"], another 18 testicular blocks em-
bedded in methacrylate, obtained from some other stud-
ies and prepared in the same way (Part "Sampling and 
embedding of tissue blocks"), were serially cut using the 
same microtome at thickness 25 µm [t(ba)] and this 
thickness was estimated by dividing the difference of the 
block heights, measured before and after serial section-
ing with a digital vernier caliper (Shanghai Meinaite In-
dustrial Company Ltd., China; accuracy 10 µm), by the 
total number (approximately 100-200) of serial sections 
cut (Xiang et al., 2018). Of note, to minimize error of 
this thickness estimation, the block heights were meas-
ured from a corner (edge) of the methacrylate block and 
the first section cutting the corner was taken as the first 
of the serial sections. 
Second Experiment: Study of Section Area 
Change 
Two groups of testes (12 per group) from 2 groups 
of normal pubertal and mature male Sprague–Dawley 
rats (6 per group) were obtained from the Animal Center 
of North Sichuan Medical College, the average testicu-
lar volume being 0.38 cm3 (CV, i.e. coefficient of vari-
ation, 4.8%) for the smaller testes and 1.30 cm3 (6.7%) 
for the larger testes. After fixation in the same way as 
described above, the testes were stored in 70% ethanol 
for 2 weeks before further experiment. 
Image Anal Stereol 2024;43: 221-237 
 
229 
 
Table 2: Section area and diameter related results obtained from the Second Experiment. 
 Paraffin embedding Methacrylate embedding 
 O-blocks (n=6) C-blocks (n=6) O-blocks (n=6) C-blocks (n=6) 
Study of smaller testes     
Area of FBs a (mm2) 38.9 (3.7%) 19.2 (14.8%)    40.6 (3.4%) 22.3 (8.5%) 
Ratio r of EB a to FB areas   0.887 (3.4%) f,o    0.927 (6.7%) f,c  1.052 (2.9%) f 1.078 (3.8%) f 
Ratio r of US a to EB areas   1.006 (3.8%) f,o    0.968 (7.1%) f,c  1.119 (5.5%) f,e   1.129 (4.8%) f,e 
Ratio r of SS a to EB areas (i.e. RAC)   1.005 (3.1%) f,o    0.952 (6.4%) f,c  1.083 (4.7%) f,e   1.098 (3.9%) f,e 
Mean diameter of FBs d (mm)    7.2 (1.5%)     5.9 (6.9%)      7.2 (1.2%)    5.8 (5.6%) 
Ratio r of EB d to FB mean diameters    0.946 (1.5%) f,o    0.944 (2.3%) f,c  1.017 (1.1%) f 1.028 (2.3%) f 
Ratio r of US d to EB mean diameters     0.980 (0.6%) f,e,o    0.988 (2.2%) f,c  1.060 (1.5%) f,e   1.082 (2.2%) f,e 
Ratio r of SS d to EB mean diameters     0.984 (0.9%) f,e,o    0.990 (2.4%) f,c  1.043 (1.3%) f,e,u,*   1.064 (1.9%) f,e 
Study of larger testes     
Area of FBs a (mm2)      90.8 (6.6%)   43.4 (10.7%)      88.8 (5.6%)     41.9 (14.6%) 
Ratio r of EB a to FB areas    0.888 (5.0%) f,o    0.905 (6.4%) f,c    1.037 (2.5%) 1.076 (8.2%) f 
Ratio r of US a to EB areas    0.929 (3.9%) f,e,o,l      0.929 (5.8%) f,e,c  1.039 (3.6%) f,*,l   1.138 (5.5%) f,e 
Ratio r of SS a to EB areas (i.e. RAC)   0.935 (4.7%) f,e,o,l    0.957 (6.5%) f,c    1.034 (4.2%) f,*   1.112 (3.4%) f,e 
Mean diameter of FBs d (mm)      10.7 (2.7%)     8.8 (3.5%)      10.7 (3.6%)    8.0 (5.5%) 
Ratio r of EB d to FB mean diameters    0.950 (0.7%) f,o    0.937 (2.3%) f,c    1.014 (2.2%) f, 0.994 (3.4%) 
Ratio r of US d to EB mean diameters    0.966 (0.6%) f,e,o,l      0.977 (2.0%) f,e,c    1.025 (1.6%) f,e,*,l    1.063 (2.3%) f,e 
Ratio r of SS d to EB mean diameters    0.968 (1.0%) f,e,o,l      0.972 (2.1%) f,e,c    1.011 (1.3%) f,u,*,l    1.053 (2.3%) f,e 
Data: mean (%, coefficient of variation) calculated from each sub-group (n=6). Design: 12 smaller testes from 6 normal pubertal Spra-
gue-Dawley rats and 12 larger testes from 6 normal mature Sprague-Dawley rats were used for study. From one testis (left or right 
alternately chosen) of each rat, 2 circular, central, adjacent tissue slices were cut perpendicular to the testicular long axis, with 1 slice (O-
block) and one half (C-block) of the other slice being embedded in paraffin; 1 O-block and 1 C-block were obtained in the same way 
from the other testis of the rat and were embedded in methacrylate. Sections were cut along the central cut-surface of the embedded tissue 
blocks. Abbreviations: FB, the fresh tissue block face; EB, the embedded tissue block face left after the unstained section was cut; US, 
the unstained section cut from the embedded block; SS, the stained section, after staining and coverslipping of the unstained section; 
RAC, the ratio of (testicular section) area change. Statistical tests results: significantly different (p < 0.05) from FB f, EB e or US u in 
comparison of the areas a (not ratios) or diameters d (not ratios) of FB, EB, US and SS (same column); p < 0.05 in comparison of the 
same ratios r between paraffin and methacrylate O-blocks o or C-blocks c (same line), between paraffin or methacrylate O-blocks and C-
blocks * (same line), or between smaller and larger testes l (same column). 
Slicing and embedding of tissue blocks 
Two circular, adjacent slices (thickness 2-3 mm) 
were cut from the middle of each testis, perpendicular to 
the long testicular axis (with an approximate length of 
13 mm and 20 mm for smaller and larger testes respec-
tively). One slice (circular O-block of testicular tissue) 
and one half (semi-circular C-block of tissue) of the 
other slice (chosen randomly and cut along the circular 
center) were embedded in a mould separately, with care 
being taken to ensure that the central cut-surface of ei-
ther tissue block was the cut-surface of the embedded 
block in sectioning with microtome. The O-block and C-
block obtained from one testis (left or right alternately 
chosen) of one rat were embedded in paraffin and the 2 
blocks obtained from the other testis of the rat were em-
bedded in methacrylate (see Table 2 for such grouping 
of blocks), using the same embedding mediums and 
methods described above (Part "Sampling and embed-
ding of tissue blocks"). 
Sectioning and staining of tissue sections 
Sections were cut and stained in the same way as 
described above, with e.g. the same microtome and 
knives, the same block advance (paraffin 14 µm, meth-
acrylate 25 µm), and the same mounting methods and 
staining protocols. Special attention paid or different 
treatment given included (i) a bit of the upper-right cor-
ner of the paraffin or methacrylate block was cut off be-
fore sectioning and the corner of the section cut from the 
block was placed at an upper-right position on the glass 
slide. Doing so was to better determine the cutting direc-
tion of sections (below). (ii) Only one section was ob-
tained from each block. Effort was made to ensure that 
the section was intact, well cut and complete, and it was 
the first intact section that was obtained. (iii) Sections 
were stained with hematoxylin only (without periodic 
acid or Schiff's reagent), and, in particular, methacrylate 
sections were slightly stained with hematoxylin (15 
minutes) so that the boundary of the tissue sections was 
clearer on the scan images (below). [The average actual 
section thickness, as measured in the same way as de-
scribed above, of the 12 stained sections (6 from O-
blocks and 6 from C-blocks for paraffin or methacrylate) 
was 14.5 µm (CV 7.2%) for paraffin and 20.0 µm (8.0%) 
for methacrylate.] 
Scanning of tissue blocks and sections  
The FB (fresh block face, central cut-surface of the 
testicular tissue block), EB (embedded block face left 
after the intact section was cut), US (unstained section, 
the intact section before staining) and SS (stained 
 GUO Y ET AL.: Volume and area changes of tissue sections 
230 
 
section, the intact section after staining and coverslip-
ping) were scanned (resolution 1200 ppi) with the same 
scanner (MRS-4800U2, Microtek, China) (see Fig. 3). 
Of note, in order to get a better scan image (clearer 
boundary) of EB, the block face was immersed in hema-
toxylin and water (depth 1-2 mm) before scanning for a 
while: 10 minutes in hematoxylin, 5 minutes in tap water 
and 1 minute in distilled water for paraffin blocks, and 1 
minute in hematoxylin, 30 seconds in tap water and 30 
seconds in distilled water for methacrylate blocks. (The 
EB was also scanned before the immersion procedure 
and an analysis showed that the procedure did not affect 
the size or shape of the block face.) 
Fig. 3. Scanned pictures of testicular tissue blocks (be-
fore and after embedding in paraffin or methacrylate) 
and the sections cut from the blocks. The 2 O-shaped 
and 2 C-shaped blocks were obtained from smaller tes-
tes (pubertal rats) and larger testes (mature rats), re-
spectively. FB: a fresh block showing the testicular cut-
surface; EB: the embedded block showing the cut-sur-
face after the unstained section was cut; US: the un-
stained section on glass slide; SS: stained section, the 
US after staining with hematoxylin. Image processing of 
the scanned pictures with Photoshop: automatic con-
trast. The width and height of each small rectangular 
panel (pink background with a scanned picture placed 
on it): 12.5 and 10.1 mm. 
Measurement of scan images  
Using an Adobe Photoshop 8.0.1 software as we 
previously described (Xiang et al., 2018), the area of 
each scan image (Fig. 3), observed with a square grid 
(software generated) superimposed on it, was estimated 
by counting of test-points (intersections between the 
horizontal and vertical lines of the grid) as described 
above (Part "Estimation of total section area"). Different 
grids with different distances between the horizontal or 
vertical lines were used depending on the sizes of the 
images and an average of 40.3 (25-56) points were 
counted per image. 
To confirm the results of areas (above) and to 
demonstrate possible section compression along the cut-
ting direction, the diameters (length and width) of the 
images were also measured using the Photoshop (Xiang 
et al., 2018). Before the measurements, (i) the image of 
each EB was rotated according to the horizontal edge 
(perpendicular to the cutting direction) of the supporting 
block so that the X-axis of the rotated EB is perpendic-
ular to the cutting direction of sections. (ii) The image 
of each US was properly rotated according to the shapes 
of the US and the EB together with the edges of the em-
bedding medium so that the X-axis of the rotated US is 
also perpendicular to the cutting direction. (iii) The im-
age of each SS was properly rotated according to the 
SS’s and the US’s horizontal edges of the glass slide so 
that the X-axis of the rotated SS is perpendicular to the 
cutting direction as well. (iv) The image of each semi-
circular FB (C-block) was properly rotated according to 
the cut-edges of the fresh and embedded C-blocks so 
that the X-axis of the rotated FB is approximately per-
pendicular to its cutting direction after embedding. (v) 
The image of each circular FB (O-block) was rotated to 
an independent, uniform random angle between 0 and 
180 degrees (obtained with the Excel software) since it 
is difficult to determine which axis (direction) of the cir-
cular FB is perpendicular to its cutting direction after 
embedding. 
Error analysis and statistical tests 
To confirm accuracy of the above area estimation 
with the unbiased and efficient point counting method 
(Gundersen & Jensen, 1987), one stained section (SS) 
was arbitrarily chosen from each of the 8 sub-groups 
(Table 2) and its area was re-measured with the same 
method (above) for 2 times, independently and ran-
domly. Before each re-measurements, the section image 
was cut from the original file and pasted into another 
image file, with arbitrary widths between the image 
edges and section edges, and was then rotated an inde-
pendent uniform random angle between 0 and 180 de-
grees (obtained with the Excel). The CV (standard devi-
ation divided by mean) of the three measurements (the 
original measurement plus these 2 additional independ-
ent re-measurements) was regarded as the CE of the 
original measurement (Yang, 2012), as a reference sam-
pling error of the area estimation in the present study. 
To detect statistically significant difference (de-
fined as p < .05) between sub-groups, the one-way re-
peated measures analysis of variance was used for com-
parison of areas or diameters between FB, EB, US and 
Image Anal Stereol 2024;43: 221-237 
 
231 
 
SS representing tissue change at different stages of tis-
sue processing (Table 2 and Fig. 3). When significant 
difference was detected, the Student-Newman-Keuls 
method was further used for all pairwise multiple com-
parisons. 
The paired t test was used to compare area-to-area 
or diameter-to-diameter ratios (not absolute results - ar-
eas or diameters) between O-blocks and C-blocks from 
the same testes to detect difference of degrees of tissue 
change between shapes/sizes of blocks/sections (Table 
2). The paraffin O-blocks/C-blocks and the methacrylate 
O-blocks/C-blocks were from the same rats, and the 
paired t tests demonstrated that there were no significant 
differences (p > .08) between paraffin and methacrylate 
O-blocks’ or C-blocks’ FB areas (Table 2). So the paired 
t test was also used to compare results (ratios) between 
paraffin and methacrylate O-blocks or C-blocks to de-
tect difference of tissue change degrees between embed-
ding mediums (Table 2). 
In addition, the t test was used to compare results 
(ratios) between smaller and larger testes to detect dif-
ference of tissue change degrees between testicular (sec-
tion) sizes or textures (Table 2). 
The paired t test was also used to compare the di-
ameter ratio (ratio of the Y-axis diameter to the X-axis 
diameter) of SS and that of EB to determine if there was 
significant (p < .05) section compression along the cut-
ting direction of sections (Table 3) 
RESULTS 
On the whole, the overall change (after processing) 
of the actual tissue volume of paraffin sections was a 
marked shrinkage of 21%-23% while that of methacry-
late sections was a small expansion almost negligible 
(see RVC(act) in Table 1). The change of paraffin sec-
tions was largely contributed by tissue shrinkage at the 
process of embedding while that of methacrylate sec-
tions was first tissue swelling at the process of embed-
ding and then section expansion (in area) at the process 
of section preparation (after sectioning), with the overall 
expansion being largely counteracted by a 15% of sec-
tion compression in the actual thickness (Tables 1 & 2). 
Compared with area of the embedded block face, the fi-
nal section area had a 4% decrease in paraffin but an 8% 
increase in methacrylate (Table 2). 
Error Analysis 
In the First Experiment, the average weight frac-
tions of blocks sampled from the testes were 0.489 (CV 
8.9%, paraffin) and 0.511 (8.5%, methacrylate) for the 
pubertal testes, 0.163 (8.5%) and 0.176 (9.6%) for the 
mature testes, and 0.064 (18.9%) and 0.065 (13.3%) for 
the adult testes, approximating the sampling fractions 
[SF(blo)] of 0.500, 0.167 and 0.063 for the three groups 
of testes (Table 1), respectively.  
With respect to precision of the Cavalieri’s esti-
mates, the average CEs were 2.3% (CV 65.4%, paraffin) 
and 2.2% (54.2%, methacrylate), 1.2% (78.8%) and 
0.8% (112.0%), and 2.1% (60.5%) and 1.9% (41.3%) for 
the pubertal, mature and adult testes, respectively. 
As for the accuracy of the block advance (thickness 
set by the microtome), the average thickness of serial 
sections estimated by heights of the block and the num-
ber of serial sections was 24.94 µm (CV 2.4%) for the 
18 blocks, close to the 25.00 µm set by the microtome. 
In the Second Experiment, the CE of the area esti-
mation for the 8 sections was 2.5% (CV 32.0%) on av-
erage. 
Number of Non-intact Sections 
In the First Experiment, among the sections cut at 
the two ends of the blocks there were always some sec-
tions which were non-intact, incomplete or with empty 
area around (or inside) the tissue section (Fig. 2). Arti-
fact of apparent tissue detachment (Fig. 2) was not con-
sidered in this respect. Of the 25-35 serial sections sam-
pled and stained per sub-group (Table 1), the number of 
non-intact sections accounted for 23%-34% (paraffin) 
and 24%-29% (methacrylate), see Fig. 2. 
Table 3: Results indicating section compression along the cutting direction (Second Experiment) 
 Paraffin embedding Methacrylate embedding 
 O-blocks (n=6) C-blocks (n=6) O-blocks (n=6) C-blocks (n=6) 
Study of smaller testes     
Diameter ratio (Y/X) of SS 0.896 (5.6%) e 0.786 (23.5%) e 0.974 (3.6%) 0.577 (6.8%) 
Ratio of SS's to EB's diameter ratios 0.913 (2.8%) 0.911 (2.4%) 0.988 (3.8%) 0.963 (4.0%) 
Study of larger testes     
Diameter ratio (Y/X) of SS 0.926 (4.4%) e 0.973 (39.7%) e 0.999 (4.6%) 0.642 (5.6%) 
Ratio of SS's to EB's diameter ratios 0.916 (1.1%) 0.913 (3.9%) 0.983 (3.3%) 0.991 (1.8%) 
Data shown as mean (%, coefficient of variation). SS, the stained section; EB, the embedded block face; diameter ratio (Y/X), ratio of 
the Y-axis (cutting direction) diameter to the X-axis diameter of the SS or EB. eThe diameter ratio (Y/X) of SS significantly different (p 
< 0.05) from that of EB (this ratio not shown in the Table). See the footnote of Table 2 for the study design and other abbreviations. 
 
 GUO Y ET AL.: Volume and area changes of tissue sections 
232 
 
In the 8 sub-groups of the Second Experiment, the 
average number of testicular sections (counting from the 
first section cutting the testicular tissue) discarded be-
fore the first intact section was obtained for study was 
15-20 (O-blocks and C-blocks) and 25-36 for paraffin 
sections from smaller and larger testes and 36-37 and 
60-87 for methacrylate sections from smaller and larger 
testes, respectively. 
Comparison of Section Sizes between Un-
stained and Stained Sections 
In general, there were not marked differences be-
tween the areas or mean diameters of stained sections 
(SSs) and those of the unstained sections (USs), as can 
be seen in the ratios of SS or US sizes to those of EB 
(embedded block face) sizes (Table 2). Significant dif-
ference was detected only in the diameters of the 2 sub-
groups of methacrylate O-blocks: the mean diameter ra-
tios of SS to EB were 1.4%-1.6% smaller than those of 
US to EB (Table 2). 
Section Diameters and Compression along 
the Cutting Direction 
As can be seen in the size ratios between EB and 
FB, US and EB, and SS and EB (Table 2), the mean di-
ameter changes were generally consistent with the area 
changes. An exception was found only in the sub-group 
of paraffin O-blocks (smaller testes) where the diame-
ters of USs or SS were 1.6%-2.0% smaller (with statis-
tical significance) than those of EBs whereas there were 
not significant differences in the areas between US (or 
SS) and EB (Table 2). 
In the 4 sub-groups of paraffin sections, the Y-axis 
(cutting directions of sections) diameter to X-axis diam-
eter ratios of SSs were 8.4%-8.9% smaller (with statisti-
cal significance) than those of EBs, indicating a 
8.4%-8.9% linear compression of sections along the cut-
ting direction (Table 3). In methacrylate sections, how-
ever, significant section compression along the cutting 
direction was not detected (Table 3). 
Paraffin Sections: Tissue Volume and Sec-
tion Area Changes 
The actual ratio of volume change [RVC(act)] of 
testicular tissue after paraffin processing was 0.77-0.79 
(a change from beginning to end of processing, Table 1), 
which indicated a 21%-23% tissue shrinkage (in vol-
ume) after processing, without significant difference be-
tween the 3 groups of testes (one-way analysis of vari-
ance). Considering an increase of ~4% in the actual sec-
tion thickness (compared with block advance), the over-
all volume shrinkage not considering the thickness 
change would be ~25%, as indicated by the block 
advance based ratio of volume change [RVC(ba)] in Ta-
ble 1. The ratio of section area change (RAC) was around 
0.96 (0.94-1.00) overall (a change after cutting) in the 4 
paraffin sub-groups (Table 2), indicating a 4% decrease 
of the section area compared with the area of the embed-
ded block face. This areal decrease, which we assume 
herein was a result of uniform volume (virtual) shrink-
age, would induce a volume decrease of ~6% [=1–
(0.963/2)], which suggests that the change after cutting 
(areal shrinkage) and the change after embedding (vol-
ume shrinkage from beginning to embedding) accounted 
for approximately 1/5 and 4/5 of the 25% volume 
shrinkage, respectively, if we assume results in Tables 1 
and 2 are mutually explainable. 
The area ratio of the embedded block (EB) to the 
fresh block (FB) was around 0.90 (0.89-0.93) for the 4 
paraffin sub-groups (Table 2), indicating a 10% areal 
shrinkage after embedding (from fresh block to embed-
ding). This areal shrinkage would induce a volume de-
crease of ~15% [=1–(0.903/2)], slightly smaller than the 
20% volume shrinkage from beginning to embedding 
(4/5 of the 25% overall volume shrinkage above). This 
might suggest that the fresh block obtained might have 
~5% of shrinkage once cut from the testis. 
As a result of the section area change, the virtual 
ratio of volume change [RVC(vir)] was approximately 
2% smaller than the block advance based ratio of vol-
ume change [RVC(ba)], see Table 1. 
Methacrylate Sections: Tissue Volume and 
Section Area Changes 
The RVC(act) of testicular tissue after methacrylate 
processing was 1.01-1.03 (Table 1), which indicated a 
1.6% (on average) tissue expansion (an almost negligi-
ble tissue change) in volume after processing, without 
significant difference between the 3 groups of testes 
(one-way analysis of variance). If not considering a 
marked decrease of ~15% in the actual section thickness 
compared with block advance, the volume change would 
be a marked expansion of 20% (16%-23%) as indicated 
by the RVC(ba) in Table 1. The RAC of methacrylate 
sections was around 1.08 (1.03-1.11) overall (a change 
after cutting) in the 4 sub-groups (Table 2), indicating 
an 8% increase of the section area compared with the 
area of the embedded block face. This areal increase, 
which we assume was a result of uniform volume (vir-
tual) expansion, would induce a volume increase of 
~12% [=(1.083/2)-1), which suggests that the change af-
ter cutting (areal expansion) and the change after em-
bedding (volume swelling from beginning to embed-
ding) accounted for approximately 2/3 and 1/3 of the 
20% volume expansion, respectively. 
Image Anal Stereol 2024;43: 221-237 
 
233 
 
The area ratio of EB to FB was around 1.06 (1.04-
1.08) for the 4 methacrylate sub-groups (Table 2), indi-
cating a 6% areal expansion after embedding (from fresh 
block to embedding). This areal expansion would induce 
a volume increase of ~9% [=(1.063/2)-1], slightly larger 
than the ~7% volume expansion from beginning to em-
bedding (1/3 of the 20% overall volume expansion 
above). This might indicate a slight shrinkage of the 
fresh block once cut from the testis. 
Note, if the section area increase (8%) was associ-
ated with a proportional decrease of the section thick-
ness (i.e. assuming that the area increase was not associ-
ated with the volume change), the thickness decrease 
would be about ~7.5% [≈1-(1/1.08)]. So the decrease of 
15% in the actual section thickness (above) might be 
equally contributed by section flattening due to areal ex-
pansion of the elastic plastic section and by section com-
pression (in thickness) due to other factors such as heat-
ing on hot plate. 
As a result of the section area change, the RVC(vir) 
was approximately 5% larger than the RVC(ba), see Ta-
ble 1. 
Factors Affecting the Section Area Change 
As can be seen in the area ratios of EB to FB, or SS 
to EB (Table 2), (i) paraffin and methacrylate tissue 
changes during processing were markedly different, 
with paraffin embedded tissue showing essentially 
shrinkage while the methacrylate embedded tissue 
showing expansion. (ii) There were not significant dif-
ferences between O-blocks and C-blocks (paraffin or 
methacrylate) except that the methacrylate RAC of C-
blocks was significantly larger than that of O-blocks, 
suggesting that methacrylate sections or blocks without 
a complete capsule might have a larger expansion. (iii) 
There were not significant differences between smaller 
and larger testes or sections (O-blocks or C-blocks) ex-
cept that the larger testis’s RAC of paraffin O-blocks was 
significantly smaller than the smaller testis’s RAC, sug-
gesting that larger paraffin O-blocks from larger testes 
might have a larger shrinkage. 
DISCUSSION 
Theoretical Consideration 
Stereological (quantitative) estimation is performed 
on final tissue sections that have undergone a series of 
tissue processing from the original organ. For global es-
timates of structures in an organ such as total number, 
length or surface area, the change of the tissue volume 
or section area after processing may need to be estimated 
to correct the results obtained on sections so as to reflect 
the true results in the original organ (Part "Stereological 
Background"). The present study proposed that the cor-
rection be based on the stereological principle used for 
the estimation and the actual or virtual ratio of volume 
change be estimated for the correction. The actual and 
virtual ratios, or the virtual thickness and volumes 
(Equation 8), are new concepts proposed in the present 
study, but not very difficult to understand (see Part "Ste-
reological Background"). 
Specifically, for total number (of particles) estima-
tion with disectors (based on 3D measurements), the ac-
tual tissue volume change (or the actual ratio of volume 
change) should be estimated for correction (Equation 
17); for total number estimation, or total length or sur-
face area estimation, based on 2D measurements, the 
virtual volume change (or the virtual ratio of volume 
change) should be estimated for correction (see Equa-
tion 18 and the last paragraph in Part "Stereological 
Background"). Of note, both tissue volume change (the 
block advance based ratio of volume change, to be pre-
cise) and section area change (or the ratio of section area 
change) are needed for estimation of the virtual volume 
change (see Equations 10, 14 & 16). 
Methodological Consideration 
Using paraffin and methacrylate embedded testicu-
lar sections, the present study estimated the actual and 
virtual ratios of the tissue volume change. Based on ex-
perience from previous researches (see the second last 
paragraph in Part "Study of Tissue Volume and Section 
Area Changes after Processing"), the present study was 
designed not only comprehensively but also in an unbi-
ased way. The unbiasedness consists mainly (i) in the 
use of the stereological Cavalieri’s principle combined 
with the fractionator (for volume estimation), in the 
combined use of the actual section thickness (measured 
directly with a microcator), and in the careful design that 
enabled estimation of the overall change from the origi-
nal organ in the First Experiment, and (ii) in the same 
way of clearly observing and measuring section images 
(Fig. 3), in the area estimation with point counting, and 
in the careful design that included all major steps of tis-
sue processing in the Second Experiment. 
“There is no ‘smart’ unbiased way to obtain infor-
mation about tissue deformation during tissue fixation 
and processing” (Nyengaard, 1999). Complete serial 
sections of embedded blocks (Fig. 2) are often needed to 
estimate the volume of organ after processing, which is 
essential for tissue volume change study. Use of serial 
sections means the need for more experience in histo-
logical technique and also more time and effort. In addi-
tion, serial sections are not all perfect, with at least many 
intact sections (see Fig. 2 and Part "Number of Non-
 GUO Y ET AL.: Volume and area changes of tissue sections 
234 
 
intact Sections"). Sadeghinezhad & Nyengaard (2019) 
used single sections to represent tissue blocks, a simple 
method of avoiding the use of serial sections, but appar-
ently a biased method. We may also obtain the areal 
change of tissue before and after processing to estimate 
the tissue volume change (Nyengaard, 1999). This is an-
other simple method often used to avoid serial sections, 
but apparently a biased method as well. Nevertheless, 
the average area ratio of the stained section (SS) to the 
fresh block face (FB) for paraffin in the Second Experi-
ment (Table 2) was 0.87 (0.83-0.89), therefore the vol-
ume shrinkage estimated with this areal method would 
be ~19% [=1-(0.87)3/2], which happened to be close to 
the actual volume shrinkage of 21%-23% we estimated 
in the First Experiment (Table 1). This suggests that the 
tissue change in paraffin was relatively consistent at dif-
ferent steps of processing, especially in embedding 
where the major change occurred. So this areal method 
may be tentatively used for approximate estimation of 
tissue shrinkage of paraffin sections. Apparently this 
method is not suitable for methacrylate sections where 
the actual volume change was a marked tissue expansion 
during processing (Table 2) neutralized by a marked tis-
sue shrinkage due to reduction in the actual section 
thickness (Table 1). 
Linear change (change of length or width) of tissue 
blocks or sections was also used previously to reflect tis-
sue change (Weibel, 1979; Gerrits et al., 1992). This is 
more unadvisable as it is difficult to measure them (at all 
steps of processing), its results are affected by non-uni-
form change of the tissue, and its error, if any, will be 
augmented when converted to volume change. Take the 
diameter measurement in the present study as an exam-
ple, we were confident to determine the cutting direction 
(Y-axis) of the embedded block, but this axis might be 
different or deformed for the fresh block, unstained sec-
tion or stained section and could not be determined with 
full confidence. Measurement or comparison of diame-
ters was only an approximation, for confirmation of the 
area results. 
Measurement of actual section thickness is im-
portant for estimation of the actual ratio of volume 
change. There are no other measurement methods that 
are simpler or better than the one with a microcator (Part 
"Measurement of actual section thickness"). Our experi-
ence for accurate measurement is that (i) the top or bot-
tom surface of the tissue section is determined while the 
serial optical focal planes are moving up or down slowly 
and smoothly (through the thick section) with turning of 
the microscope adjustment knob, and (ii) the tissue 
structure which begins to appear or disappear on the top 
or bottom surface includes not only nuclei but also their 
surrounding tissue, with granules of nuclear chromatin 
being the key reference structure no matter whether they 
are darkly or lightly stained. In the present study, the 
mean actual thickness of methacrylate sections (with the 
same block advance) was 6% smaller in the Second Ex-
periment (Part "Sectioning and staining of tissue sec-
tions") than that in the First Experiment (Table 1), prob-
ably because of the markedly lighter staining in the Sec-
ond Experiment. Interestingly, we additionally tried and 
measured a few methacrylate sections (with the same 
block advance) which we used in other studies years 
ago, and obtained a result of the actual section thickness 
comparable with the present study. 
Previously tissue blocks cut from organs were often 
used to estimate tissue volume change, i.e. the volumes 
of the blocks before and after processing were taken as 
the V(pre) and V(post) in Equation 6 (e.g. Zhengwei et 
al., 1997). In this case, attention should be paid to accu-
racy of the weight and density measurements (to esti-
mate the volume before processing) for small blocks or 
blocks without a complete capsule. In particular, the pre-
sent study demonstrated with both paraffin and methac-
rylate sections that the volume of fresh tissue blocks cut 
from a testis was a few percents smaller than the volume 
of the “original” blocks within the original testis (Parts 
"Paraffin Sections: Tissue Volume and Section Area 
Changes" and "Methacrylate Sections: Tissue Volume 
and Section Area Changes"). This may be explained by 
the fact that the testis is of considerable intratesticular 
pressure (Ma et al., 2016), thus once the testis is cut into 
blocks, the blocks (or the “testis” reconstructed from 
these blocks) may shrink to some degree. 
For estimation of tissue volume change in the pre-
sent study, the volume of testis after processing was 
compared with the volume before processing. But the 
so-called “volume before processing” herein was actu-
ally a volume at the stage of storage in 70% ethanol after 
fixation (Part "First Experiment: Study of Tissue Vol-
ume Change"), not the volume of the in vivo testis or the 
original fresh testis before any processing. But this is out 
of practical consideration: at the stage of storage in 70% 
ethanol researchers can have more time and be more fo-
cused on the works of organ dissection and measure-
ments. Moreover, we previously demonstrated that vol-
ume of the fresh testis (just removed from rats) did not 
change markedly after immediate fixation in Bouin’s 
fluid and dehydration in 70% ethanol (Zhao et al., 2006). 
Tissue Changes 
We previously demonstrated that paraffin embed-
ded testicular sections (block advance 5 or 10 µm) had 
an areal shrinkage (SS compared with EB) of 
Image Anal Stereol 2024;43: 221-237 
 
235 
 
5.5%−8.6% and a linear section compression (along the 
cutting direction) of 5.9%−8.9% (Xiang et al., 2018). In 
the present study (block advance 14 µm), the shrinkage 
and compression results were ~0-6.5% and 8.4%-8.9%, 
respectively. This might suggest that thinner paraffin 
sections had a slightly larger areal shrinkage. In contrast, 
the present study demonstrated marked areal expansions 
with methacrylate sections (Table 2): expansion by 3%-
11% (SS compared with EB) or 7%-19% (SS compared 
with FB). Marked areal expansion of methacrylate sec-
tions was previously noted during section stretching and 
mounting, but with final section size being comparable 
with that of the original block face (Gerrits et al., 1992). 
It was thought that paraffin sections might have vol-
ume shrinkages up to 50% (Dorph-Petersen et al., 2001; 
Yang, 2012). Such large shrinkage might be possible 
with some paraffin or knives used previously (e.g. Yang 
& Cui, 1989), but the present study using the Leica par-
affin and knives together with an unbiased design 
demonstrated a much smaller shrinkage: 21%-23% (as 
indicated by RVC(act) in Table 1). With paraffin sec-
tions of renal tissues, a volume shrinkage of 17% was 
found by Akbari, Goodarzi & Tavafi (2017) using the 
areal method (Nyengaard, 1999) and a volume shrinkage 
of 25% was shown by Sadeghinezhad & Nyengaard 
(2019) using single sections. 
It was concluded from a limited study that tissue 
(actual volume) shrinkage of methacrylate sections was 
negligible (Zhengwei et al., 1997; Yang, 2012). And in-
deed, as demonstrated in the present study of methacry-
late sections, the actual tissue volume change was al-
most negligible. But the overall change was a volume 
expansion (indicated by a section area expansion of 7%-
19%, see above) counteracted by a volume shrinkage 
(indicated by a section thickness compression of 15%, 
Table 1), and 2/3 of the area expansion was contributed 
by expansion after cutting (Part "Methacrylate Sections: 
Tissue Volume and Section Area Changes"). So it seems 
that the tissue change of methacrylate sections is more 
“manipulable”, thus more attention should be paid to 
“standard” cutting, mounting and staining of methacry-
late sections in practice 
Implications 
Considerable volume changes of paraffin and meth-
acrylate embedded testicular sections shown in the pre-
sent study, especially the actual volume changes of par-
affin sections and the virtual volume changes of both 
paraffin and methacrylate sections (Table 1), indicate 
the importance of study of tissue changes and correction 
of stereological results in practical stereological studies. 
Some of previous studies by ZWY and co-authors 
(e.g. Zhengwei et al., 1997; Zhang et al., 2002) esti-
mated (total) nuclear numbers per testis by “the numer-
ical density × the volume of fresh testis” where the den-
sity was obtained with the optical disector using meth-
acrylate sections. Assuming the actual volume change of 
the testicular tissues after processing in the studies to be 
similar to the change shown in the present study, the 
number estimation could be tentatively corrected by 
multiplying the RVC(act): ~1.016 (Table 1), almost neg-
ligible. For estimation of the total area of alveolar sur-
face per lung with paraffin sections by “the surface den-
sity × the volume of fresh lung” (Yang et al., 2002), the 
result could be tentatively corrected by multiplying 
“RVC(vir)1/3” where RVC(vir) is ~0.74 (Table 1). For es-
timation of the total length of renal tubules per kidney 
with methacrylate sections by “the length density × the 
volume of fresh kidney” (Wang et al., 2021), the result 
could be tentatively corrected by multiplying 
“RVC(vir)2/3” where RVC(vir) is ~1.26 (Table 1). That 
is, the total surface area and length estimates could be 
multiplied by 0.90 and 1.17 respectively for correction. 
Not many applied researches with stereological 
methods addressed the potential effects of tissue volume 
change after processing on the results, probably because 
of ignorance, tolerance or inability (e.g. without a stere-
ology system equipped with a microcator to measure ac-
tual section thickness), because of difficulty in under-
standing or design, or because of need for much more 
time, effort or cost. Our suggestions are: (i) For compar-
ative studies, use of materials and methods, even includ-
ing the size and shape of tissue blocks, should be stand-
ardized for all groups. (ii) Methods used, even including 
the section heating and staining, should be clearly stated, 
leaving the tissue change issue open for discussion. (iii) 
Correction coefficients (ratios of volume change) may 
be tentatively cited for correction if the tissue processing 
procedures are similar. Tissue volume change after his-
tological processing is essentially mechanical or physi-
cal, perhaps without marked difference between studies 
if the materials and methods used (such as organ or tis-
sue blocks, embedding medium, cutting instruments and 
section thickness & staining) are comparable. (iv) If a 
series of (stereological) studies are being conducted by 
a lab or group, at least one study may be considered for 
estimation of tissue volume change. (v) For estimation 
of total particle number, a method of disector combined 
with fractionator may be used, where the reference vol-
ume need not be known, thus a correction of tissue vol-
ume change is not necessary (Gundersen et al., 1988b; 
Nyengaard, 1999; Dorph-Petersen et al., 2001; Yang, 
2012). Such fractionator method requires the strictest 
sampling design in stereology and such design usually 
 GUO Y ET AL.: Volume and area changes of tissue sections 
236 
 
involves serial sections. (vi) Volume is a basic, universal 
property of any structures and the total volume estima-
tion does not need a correction for tissue volume change 
(see the last paragraph in Part "Stereological Back-
ground"). So when study objective could be realized 
with the parameter of total volume, it is advisable to fo-
cus on volume estimation. And when many stereological 
parameters are obtained (e.g. Ma et al., 2016; Guo et al., 
2019; Wang et al., 2021) we may pay more attention to 
the parameter of total volume. 
ACKNOWLEDGMENTS 
The study was supported by North Sichuan Medical 
College. The author ZWY would like to express his grat-
itude to stereologists ER Weibel and HJ Gundersen for 
their works that let him like, learn and use stereology. 
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