Stereology Theory and Experimental Design

Stereology Theory and Experimental Design

Julie Korich, Ph.D.Staff Scientist/Research Liaison

Demystifying Stereology

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• What are you quantifying?• How will you quantify it?• How do you validate

results?

Basic Questions

Artwork by Sidney Harris

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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 BioscienceCerebellum image courtesy of Dr. Tamily A. Weissman.

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Sampling from Tissue Sections

• Measure 3D parameters (number, area, volume, length)on tissue sections

http://www.boneclones.com/KO-515.htm

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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

Profile Counting: Size and Orientation Bias

mbfbioscience.comC. Schmitz and P. R. Hof. Neuroscience 130 (2005) 813–831

Profile Counting: Double Counts

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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.

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‘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.

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Animal 1

Animal 2

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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

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

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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.

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

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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

Achieving Sampling Isotropy

Object Orientation• Some objects are isotropic while others have a preferential

orientation• If your object population of interest is anisotropic…

Anisotropic Isotropic

Wikimedia.org

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/

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

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

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• Cell Size • Nucleator

Feature Anisotropic Probes

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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)

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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…

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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

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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

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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.

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

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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

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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

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Guard Zones

“Plucked Cell”

“Lost Cap”

Section Top

Section Bottom

Side View

DisectorHeight

TopGuard Zone

BottomGuard Zone

DisectorHeight

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• 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

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Section Sampling Fraction:

Lateral View

Dorsal View

In your experiments you will sample a subset of sections through the region of interest = section interval

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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

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• 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

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Area Sampling Fraction: asf

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= N∑Q- 1 Volume Fraction

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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!

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• 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

• 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

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True number

Accuracy vs. Precision

Know Your Question

• Shape of the region of interest

• Uniform in shape: fewer sections

• Non-uniform shape: more sections

mbfbioscience.comahappyvalentine.blogspot.comgeradandlauracoles.com

Know Your Question

• Are the objects normally distributed in your region?

• Evenly distributed in structure: fewer sections

• Unevenly distributed in structure: more sections

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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/

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

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

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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.

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.

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

Source of Methodological Errors

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• 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

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• 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

Coefficient of Error

OCV2 = CV2 OCE2+

Observed Group Variance

BiologicalVariabiliy

Methodologically Introduced Variance

Common CE equations: Gundersen (m=1),Schmitz-Hof

Why is the CE Important?

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• 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 2010Figure: Simpson, J. et. Devel Neurobio. 2013 Jan;73(1):45-59.

• 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

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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

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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

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Figures courtesy of MBF Bioscience

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

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Figure courtesy of MBF Bioscience

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Other ProbesCavalieri

Area Fraction FractionatorSpaceballsNucleator

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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

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Cavalieri Point Counting

Figures courtesy of MBF Bioscience

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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

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

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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

ssfva

Mouton PR, Gokhale AM, Ward NL, West MJ. Journal of Microscopy. 2002 Apr;206(Pt 1):54-64

Spaceballs

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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)

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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

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Learn More

• Visit www.stereology.info

• View practical demonstration webinars

www.mbfbioscience.com/webinars

• Email Julie at [email protected]