1. Stereology Theory and
Experimental Design
Julie Korich, Ph.D.
Staff Scientist/Research Liaison

2. Demystifying Stereology

3. mbfbioscience.com
• What are you quantifying?
• How will you quantify it?
• How do you validate
results?
Basic Questions
Artwork by Sidney Harris

4. mbfbioscience.com
What are you quantifying?
• Need to quantify 3D structures in various brain regions
• How do you quantify volume of the cortex?
• How do you quantify motor neuron number in the spinal
cord?
• How do you quantify sprouting in the cerebellum?
Whole brain image courtesy of http://science.nationalgeographic.com/science/photos/brain/
Motorneurons image courtesy of MBF Bioscience
Cerebellum image courtesy of Dr. Tamily A. Weissman.

5. mbfbioscience.com
Sampling from Tissue Sections
• Measure 3D parameters (number, area, volume,
length)on tissue sections
http://www.boneclones.com/KO-515.htm

6. mbfbioscience.com
The How… Non-stereological Methods
• Profile counts
• Exhaustive Sampling-sample
every event in every section
through the region of interest
• Pitfalls:
• Inefficient
• Laborious
• Biases
• One representative section
• Pitfalls: Introducing Bias
www.PHDComics.com

7. Profile Counting: Size and
Orientation Bias
mbfbioscience.comC. Schmitz and P. R. Hof. Neuroscience 130 (2005) 813–831

8. Profile Counting: Double Counts
mbfbioscience.com
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Profile Counting
• Counter would report 20 cells. However, there are only 8 cells.
• Also, if using exhaustive sampling, it is necessary to count
EVERY cell in EVERY section.

9. mbfbioscience.com
‘One Representative Section’
Counts within a single field-of-view (white box) would lead to the
false impression that Animal 1 has fewer cells than Animal 2 in the
entire region of interest.
A
B
Animal 1
Animal 2

10. mbfbioscience.com
In Summary: Non-Stereological Methods
• Non-stereological sampling can be biased in
addition to laborious
• With stereological techniques sampling bias is
avoided – every event has an equal opportunity of
being sampled
• Stereology does not make assumptions regarding
size, shape, orientation or distribution
• Therefore, stereology is considered the gold
standard for quantification in neuroscience

11. Design-Based Stereology
• The sampling is performed on a
sub-fraction of the entire region
• Within each section, only a
subsample is evaluated
• Systematic sampling is highly
efficient and provides sampling
consistency across and within
sections
• A randomized offset ensures
unbiased measures

12. mbfbioscience.com
What is Stereology
• The process of obtaining unbiased, meaningful,
quantitative measurements of three dimensional
objectives from two dimensional information
• The geometrical properties of features in 3-D space can
be quantified by „throwing‟ random geometrical probes
into the space and recording the way in which they
intersect with the structures of interest.
• Unbiased Stereology, Second Edition, 2005, Howard, C.V. and
Reed, M.G., QTP Publications, Liverpool, page 8.

13. Geometric Probes
• Geometric probes used
for the sampling
• Points for volume
• Lines for surface area
• Planes for lengths
• Volume for numbers
• Geometric probes are
required to report 3D
data
mbfbioscience.comHoward CV, Reed MG: Unbiased Stereology. 2nd ed., Bios, Oxford, 2005

14. mbfbioscience.com
Design-Based Stereology
•Used to avoid sampling bias and error
• Sample whole region using systemic random
sampling
•Requires isotropy to prevent bias
• Ensures that all positions in the structure have the
same likelihood of being sampled
• How do you achieve isotropy
• Object Orientation
• Tissue Preparation
• Probe

15. Achieving Sampling Isotropy
Object Orientation
• Some objects are isotropic while others have a preferential
orientation
• If your object population of interest is anisotropic…
AnisotropicIsotropic
Wikimedia.org

16. Achieving Sampling Isotropy
• Isotropic tissue sections
• All three planes are randomized (3D spin) in
the tissue before sectioning
• Vertical tissue sections
• Two planes are randomized (2D spin) in the
tissue before sectioning
• Preferential tissue sections (e.g., coronal)
• Because the orientation of the tissue is
specified, the object or the probe must be
isotropic
Tissue Preparation
Allen Brain Atlas, http://www.brain-map.org/

17. Achieving Sampling Isotropy
• Using isotropic probes frees you from having to either
prove that your objects are isotropic or make your
tissue isotropic
Stereology Probe

18. Stereology Probes
Feature
• Cell Population
• Regional Volume
• Area Fraction (fraction of
cortex occupied by
plaques)
• Fiber Length
Isotropic Probes
• Physical/Optical Fractionator
• Cavalieri
• Area Fraction Fractionator
• SpaceBalls
mbfbioscience.com
• Cell Size • Nucleator
Feature Anisotropic Probes

19. mbfbioscience.com
Physical Disector
• View 2 adjacent thin
sections. Sections need to
be thinner than the cells
being counted
• Count cells that appear in
one section (green inclusion
plane) but not the other (red
exclusion plane)
• Ideal for very small (e.g EM)
or very large structures (e.g.
kidney glomeruli)

20. mbfbioscience.com
Optical Disector
• Why not use thick sections and
focus through (optical sections)
rather than using two thin
adjacent sections?
• As focus through the tissue,
count cells as they appear
following specific counting rules
• Sections need to be thick…

21. mbfbioscience.com
Optical Disector
• Isotropy is ensured by
identifying and marking a
unique point
• The counting frame combined
with the fractionator improves
sampling efficiency
• Typically it is not required to
sample every cell within a
section

22. mbfbioscience.com
The Optical Fractionator
• Sampling is done following systematic random sampling
(SRS)
• The counting frame is laid down on a systematic grid that is
randomly placed on the anatomical area of interest

23. mbfbioscience.com
The Fractionator Overview:
A: Entire ROI
B: The region of interest has been
sectioned with an interval of 2 -
every other section will be sampled
C: Within each section, a fraction of
the tissue will be sampled using
the optical fractionator
D: 3D view of the optical
fractionator and disector
Anderson and Gundersen. Journal of Microscopy, Vol. 196, Pt 1, Oct1999, pp. 69±73.

24. Formula for the Optical Fractionator
The cell population is determined by sampling a
subset or subfraction of tissue within the region
of interest.
Population estimate, N, is equal to:
Reciprocal of Volume Fraction X Sum of Counts
= N∑Q-1
Volume Fraction
X
mbfbioscience.com

25. Three components constitute the volume fraction:
1. Height sampling fraction (hsf):
How much of the tissue (thickness) was sampled (e.g., 80%)
2. Section sampling fraction (ssf):
How many sections you examine (e.g., every 4th)
3. Area sampling fraction (asf):
How much of each section‟s area was sampled (e.g., 25%)
Calculating the Volume Fraction
mbfbioscience.com

26. mbfbioscience.com
Height Fraction:hsf
• Disector Height is the thickness of the tissue sampled
• Average Mounted Section Thickness is the thickness of the
tissue after processing
• The disector height ≠ average mounted thickness
• The cut surfaces of the tissue can be disturbed to the point that
counting is inaccurate. Therefore, only a portion of the tissue is
used for counting - disector height

27. mbfbioscience.com
Guard Zones
“Plucked Cell”
“Lost Cap”
Section Top
Section Bottom
Side View 
Disector
Height
Top
Guard Zone
Bottom
Guard Zone
Disector
Height

28. mbfbioscience.com
• Thickness should be measured at every sampling
site
• Assumptions pertaining to the post-processing
thickness can lead to sampling bias and error
• Processing of tissue results in shrinkage
• With some techniques, tissue can shrink 80%
• Avoid assuming shrinkage is homogenous across ages, groups,
etc.
• Processing can also result in uneven shrinkage – wavy tissue
Section Thickness

29. mbfbioscience.com
Section Sampling Fraction:
Lateral View
Dorsal View
In your experiments you will
sample a subset of sections
through the region of
interest = section interval

30. mbfbioscience.com
Section Sampling Fraction: ssf
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• The interval is systematic (e.g. every 5th section is sampled)
• The starting section needs to be random

31. mbfbioscience.com
• The counting frame ( ) ensures that objects are counted
once and only once
• The grid ensures that a fraction of the tissue is sampled in
a systematic and random manner
• Once defined, the grid spacing and counting frame size
cannot be changed
• Placement of the grid on the ROI is random (via Stereo
Investigator)
Area Sampling Fraction: asf

32. mbfbioscience.com
Area Sampling Fraction: asf

33. mbfbioscience.com
= N∑Q-1
Volume Fraction
X
Optical Fractionator: Recap
• Report the total cell population within the region of
interest independent of volume
• Important to understand the volume fraction and
its components: hsf, asf and ssf
• Stereology is not magic its math!

34. mbfbioscience.com
• What are you quantifying?
• Global measures – cell numbers,
volumes, area, lengths
• How will you quantify it?
• Non-stereological methods
• Stereology
• How do you validate results?
• Accuracy vs. Precision
• Experimental Design
• CE
• Pilot Study
Basic Questions
Artwork by Sidney Harris

35. • With sampling, a given estimate of a
population will vary from the true number
• The goal of stereology is to ensure that
the individual sampling error does not
overshadow the difference due to
experimental manipulation
• High Precision, Low Accuracy
• High Accuracy, Low Precision
• High Precision, High Accuracy
mbfbioscience.com
True
number
Accuracy vs. Precision

36. Know Your Question
• Shape of the region of interest
• Uniform in shape: fewer sections
• Non-uniform shape: more sections
mbfbioscience.comahappyvalentine.blogspot.com
geradandlauracoles.com

37. Know Your Question
• Are the objects normally
distributed in your region?
• Evenly distributed in
structure: fewer sections
• Unevenly distributed in
structure: more sections
mbfbioscience.com

38. Know Your Question
• How frequent are your objects?
• Dense population (more spots on the pup): fewer
sections
• Sparse populations (fewer spots on the pup): more
sections
mbfbioscience.commbfbioscience.comhttp://dalmatian-dog-lovers.blogspot.com/

39. Know Your Question
• Are the objects normally distributed within a
section?
• Evenly distributed in section: fewer disectors
• Unevenly distributed in section: more disectors
mbfbioscience.comImages courtesy of MBF Bioscience

40. Designing Your Study
• How do you plan to visualize the tissue?
• Brightfield
• Fluorescence
• Tissue collection
• Collect tissue through the entire ROI
• Different series can be used to label different
biological features
• Cut the tissue at the proper thickness for the
probe being used
• Same sections can be used for multiple probes
• Staining must penetrate entire thickness
• „Garbage in, Garbage out‟
1. www.randform.org; 2.www. brainmuseum.org; 3. Courtesy of Dr. Daniel Peterson
1.
2.
3.
mbfbioscience.com

41. Tissue Considerations
mbfbioscience.comDorph-Petersen,, K.A, Nyengaard, J.R., Gundersen, H.J. G... Journal of Microscopy, Vol. 204, Pt 3, December
2001, pp. 232±246.

42. Tissue Considerations
Dorph-Petersen,, K.A, Nyengaard, J.R., Gundersen, H.J. G... Journal of Microscopy, Vol. 204, Pt 3, December
2001, pp. 232±246.

43. Microscope Considerations
• High resolution and a thin depth
of field are required to
discriminate between objects
on top of each other
• Necessary for the Optical
Fractionator
Objective Approx. Depth of Field
40 x (NA 0.65) 1.84 m
40 x (NA 0.95) 0.98 m
60 x (NA 1.0) 0.68 m
100 x (NA 1.4) 0.58 m
Image courtesy of Chandra Avinash, http://photography.learnhub.com/lesson/page/41-understanding-depth-of-field

44. Source of Methodological Errors
mbfbioscience.com
• Observer
• Defining the ROI
• Properly counting cells using the counting rules
• This is always present
• Sampling
• Sampling within sections (noise) and across sections
• Number of animals
• Number of sections
• If enough sampling is performed, the error
introduced by your methods will be reduced
Modified from Mark West NeuroStereology Workshop 2010

45. • Coefficient of Error (CE) is an estimate of the precision of
the population size estimate
• Reported per animal
• A lower CE indicates less chance for sampling error and greater
chance for an accurate estimate
mbfbioscience.com
Coefficient of Error
OCV2 = CV2 OCE2+
Observed
Group Variance
Biological
Variabiliy
Methodologically
Introduced
Variance
Common CE equations: Gundersen (m=1),Schmitz-Hof

46. Why is the CE Important?
mbfbioscience.com
• If the results are not significant
(no difference between groups),
could increasing the precision
achieve the desired result?
• Increase precision (decrease the CE)
by sampling more
• Helps other researchers evaluate
the validity of the results
• Important for optimizing your
study
Modified from Mark West NeuroStereology Workshop 2010
Figure: Simpson, J. et. Devel Neurobio. 2013 Jan;73(1):45-59.

47. • Perform a Pilot Study and check the CE
• Understand the cellular distribution
• Even distribution and/or high density: visit fewer sites per section
• Uneven distribution and/or low density: visit more sites per section
• It is more efficient to visit more sites per section than increase the
number of sections
From Theory to Practice
mbfbioscience.com

48. The pilot study is designed to select sampling
parameters that obtain accurate data with low sampling
error and the greatest amount of efficiency. It takes into
account:
• Probe choice
• Region of interest
• Section thickness & histology
• Object distribution
The Pilot Study
mbfbioscience.com

49. Interpreting the Pilot Study
• Oversample one animal
• Recalculate the estimations using
MBF‟s resampling, oversample
• Look for the „sweet spot‟
• If visit fewer sites per section, what
happens to the estimation
• If visit few sections, what happens to
the estimations
• Optimize the section interval and
SRS grid dimensions for remaining
study
mbfbioscience.com
20000
30000
40000
50000
60000
70000
80000
0 1 2 3 4 5 6
Section Interval
CellEstimation
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
SRS Site Interval
CellEstimation
Figures courtesy of MBF Bioscience

50. Pilot Study for Thin Tissue
• Tissue is thinner than recommended
• Sample pilot study animal without guard zones
• Measure the section thickness at every site
• Count cells through the entire thickness
• Run the data file though MBF‟s resample disector
mbfbioscience.com
0
5000
10000
15000
20000
25000
1 2 3 4 5 6 7
Guard Zone Height ( m)
CellEstimation
Figure courtesy of MBF Bioscience

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Other Probes
Cavalieri
Area Fraction Fractionator
Spaceballs
Nucleator

52. mbfbioscience.com
Area and Volume Estimation: Cavalieri
Point Counting
• Area of an object is estimated by point counting
• Volume of the object is estimated by summing the areas and
multiplying by the slice thickness
• Used for volume measurements of anatomical regions
• Done at low magnification on a single plane
Howard CV, Reed MG: Unbiased Stereology. 2nd ed., Bios, Oxford, 2005

53. mbfbioscience.com
Cavalieri Point Counting
Figures courtesy of MBF Bioscience

54. mbfbioscience.com
Planimetry
• Planimetric data is given to
users along with Optical
Fractionator Results
• The volume is correct provided
that the user defined the ROI
accurately
• Can be used to generate
density measures
• Not Stereology, it can be
considered biased
Figure courtesy of MBF Bioscience

55. mbfbioscience.commbfbioscience.com
Estimating Area/Volume Fraction
Area Fraction Fractionator
• Cavalieri estimate of area performed on a
systematically selected fraction of tissue
• Sampling is done at low magnification and
on one plane
• Place marker for subregion (e.g. lesion,
non-parenchyma)
• Place marker for area within the contour
(e.g. lung)
area fraction = area of subregion
area of total region
Figure courtesy of MBF Bioscience

56. mbfbioscience.com
Estimation of Length: Spaceballs
• Report total length of all the processes in the ROI
• Uses a SRS sampling
• Instead of a counting frame, a sphere is placed at the sampling sites
• Mark processes that intersect the sphere as focus through the tissue
• To maximize the diameter of the spherical probe, use hemispheres
• Length = 2 (∑Q) x x
1
ssf
v
a
Mouton PR, Gokhale AM, Ward NL, West MJ. Journal of Microscopy. 2002 Apr;206(Pt 1):54-64

57. Spaceballs

58. mbfbioscience.com
Area and Volume Estimation:
Nucleator
• Use in conjunction with the Optical Fractionator
• Measure cell size (area & volume) and number
• Uses one optical plane
• Cells and/or sections need to be isotropic
• If the cells and sections have a preferred orientation, Nucleator can
only be used to report cross sectional area, not volume (e.g., nerve
profiles in ventral root)
*
X
X X
X
X
X
X
X

59. In Conclusion
• Today we discussed stereology theory and
discussed the importance of using geometric
probes to quantify 3D events
• We discussed some rules for achieving unbiased
estimates
• SRS sampling
• Isotropy
• Discussed experimental design and sampling
strategies to ensure efficiency, precision and
accuracy
• We also introduced the Optical Fractionator for
counting cells and briefly discussed other probes
mbfbioscience.com

60. Learn More
• Visit www.stereology.info
• View practical demonstration webinars
www.mbfbioscience.com/webinars
• Email Julie at julie@mbfbioscience.com