PRACTICAL USE OF STEREOLOGY BIOMEDICAL RESEARCH LABORATORY

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Mini-Course

PRACTICAL USE OF STEREOLOGY

IN THE

BIOMEDICAL RESEARCH LABORATORY

John Basgen, Director

Morphometry and Stereology Laboratory

Charles R. Drew University of Medicine and Science

Los Angeles, California USA

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Stereology Mini-Course

Lecture 1 What is Stereology? February 22

Lecture 2 The Measurement of Volume March 22

Lecture 3 How to Count Cell Number May 24 Lecture 4 The Measurement of Surface and Length June 28 Lecture 5 Stereology Minutia July 26

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Lecture 2 Measurement of Volume

1. Review of what is stereology?

2. Think 3-D

3. Volume-Cavalieri Principle

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Organs, Tissues, Cells, Organelles

are

3-Dimensional Objects

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3-D

→→→

→→

2-D

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1. Tissues develop as 3-D objects

2. Tissues mature as 3-D objects

3. Tissues function as 3-D objects

4. Tissues react to treatment as 3-D objects

5. Disease is a 3-D process

Think 3-D

3-D

←←

2-D

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3-D

←←←←←

2-D

Review

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Review

Stereology is founded on:

1. Geometrical probability

2. Statistics

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Review

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Stereology Parameters

(geometrical structural characteristic)

Volume 3-D

Surface 2-D Length 1-D Number 0-D

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Review

Statistics

When you do an experiment you would like to

learn the true value of some parameter in a

population

Must take a

sample

When you take a sample you cannot know the “Truth”,

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Review

Statistics

Estimates have two properties:

Accuracy:

The degree of closeness of a

measurement to the true value.

Precision:

The degree to which repeated

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Volume of Rectangular Prism

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Volume of Cylinder

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Measurement of Volume

of

Arbitrarily Shape Objects:

Cavalieri Principle

-Italian mathematician and monk -1620 AD

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Cavalieri Principle

Volume = H x Area

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Cavalieri Principle

Volume = H x Area

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If you estimate the volume with 1 random section

-Unbiased (Accurate) estimate

-Not Precise estimate

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Cavalieri Principle

Volume = h x ∑Areas

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Estimate volume with several sections with random start

-Unbiased (Accurate) estimate

-Precise estimate

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Cavalieri Principle

Must be able to measure: 1. h

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1. Measuring h

A) Tissue Slicer

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1. Measuring h

A) Tissue Slicer

B) Parallel Razor Blades

Cavalieri Principle

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Cavalieri Principle

1. Measuring h

A) Tissue Slicer

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2. Measuring Areas A) Planimeter

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B) Digital Planimeter or Mouse

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B) Digital Planimeter or Mouse C) Point Counting Grid

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B) Digital Planimeter or Mouse C) Point Counting Grid

Cavalieri Principle

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Cortex Volume = h x ∑Areas

Cortex Volume = h x (area of 1 point) x ∑points Cortex Volume = 4 mm x 9 mm2 x 100 points Cortex Volume = 3600 mm3

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Design a study to measure volume of mouse glomerulus

1. Must know the approximate height (H) of the object

perpendicular to the sectioning plane. If possible make sectioning plane perpendicular to the shortest possible H.

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Design a study to measure volume of mouse glomerulus

2. If your object is regular divide H by 6. This is the approximate number of sections through the object.

Mouse glomerulus is approximately 60 µm in diameter.

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Cavalieri Principle

7 µm 17 µm 27 µm

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3. You want to count a total of 100-200 grid points on all profiles from an object.

Divide 200 by 6-approximately 30-35 points/profile

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Cavalieri Principle

7 µm 17 µm 27 µm

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Cavalieri Principle

7 µm 17 µm 27 µm

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Cavalieri Principle

7 µm 17 µm 27 µm

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Cavalieri Principle

7 µm 17 µm 27 µm

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Cavalieri Principle

7 µm 17 µm 27 µm

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Cavalieri Principle

7 µm 17 µm 27 µm

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Cavalieri Principle

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Cavalieri Principle

Volume = h x ∑areas

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Cavalieri Principle

Volume = h x (area 1 point x ∑points ) Volume = h x [(d/mag)2 x ∑points]

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Cavalieri Principle

Volume = h x (area 1 point x ∑points ) Volume = h x [(d/mag)2 x ∑points] Volume = 10 µm x [(10,000µm/1,000)2 x 150]

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Cavalieri Principle

Volume = h x (area 1 point x ∑points ) Volume = h x [(d/mag)2 x ∑points] Volume = 10 µm x [(10,000µm/1,000)2 x 150]

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Cavalieri Principle

Volume = h x ∑Areas

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Volume Fraction

Volume Density

Percent Volume

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Volume Fraction

Reference Space

Particles or Components

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Volume Fraction

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Volume fraction

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Volume fraction

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Volume Fraction

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Volume Fraction

3-D

←←←←←

2-D

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Delesse Principle

The fractional

area

of a component on a section is

directly proportional to the fractional

volume

of

that component in the reference space.

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Delesse Principle

The fractional

area

of a component on a section is

directly proportional to the fractional

volume

of

that component in the reference space.

Component area/Reference area

=

A

_A

=

V

_V

Volume fraction

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Volume fraction

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Must be able to measure:

1. Area of reference profile 2. Area of particle profile

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Must be able to Measure Areas A) Planimeter

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B) Digital Planimeter or Mouse C) Automatic Image Analysis

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B) Digital Planimeter or Mouse C) Automatic Image Analysis

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B) Digital Planimeter or Mouse C) Automatic Image Analysis D) Point Counting Grid

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Volume Fraction

V_v(capillary/glom) = A_A (capillary/glom) = P_mes / P_glom = 26 /65

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Volume Fraction

V_v(capillary/glom) = FP_capillary / (CP_glomx 4) = 26 /(16 x 4)

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Volume Fraction

V_v(capillary/glom) = FP_capillary / (CP_glomx 4) = 9 /(16 x 4)

= 0.406

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Volume Fraction

Which is best? A) Planimeter

B) Digital Planimeter or Mouse C) Automatic Image Analysis D) Point Counting

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Volume Fraction

Which is best?

A) Planimeter NO

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Volume Fraction

B) Digital Planimeter or Mouse Maybe

C) Automatic Image Analysis D) Point Counting

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Volume Fraction

C) Automatic Image Analysis Yes,

IF

antibody is very specific

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Volume Fraction

B) Digital Planimeter or Mouse C) Automatic Image Analysis D) Point Counting Maybe

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Digitizer Tracing vs Point Counting

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Volume Fraction

Vv(Mesangium/Glomerulus)

Digitizer Point Counting 0.118 0.115 0.150 0.151 0.153 0.153 0.156 0.160 0.173 0.169 0.181 0.193 0.123 0.115 0.166 0.162 0.166 0.196 0.228 0.222 0.247 0.263 0.260 0.287 0.407 0.409 0.259 0.255 0.521 0.548 Nephron 50:182-186, 1988

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Volume Fraction

Time in Seconds

Digitizer Point Counting 687 205 525 176 735 187 631 248 572 166 756 260 785 241 803 228 749 237 569 209 565 175 713 257 671 234 1269 358 1000 286 Nephron 50:182-186, 1988

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Volume Fraction

YES

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Volume Fraction

WARNING

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Volume Fraction

WARNING

Be careful of reporting Volume Fraction

Vv(mes/glom)

Normal animal: 0.14 Experimental animal: 0.28

Did the volume of the mesangium increase in the experimental animal? We do not know.

Either the volume of the mesangium increased or the volume of the glomerulus decreased. Or both.

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WARNING

Volume Fraction

V_v(mes/glom) x glomerular volume µm3 _{= Volume of mesangium µm}3

V_v(mes/glom) glom volume mes volume Normal : 0.14 1,000,000 µm3 _{140,000 µm}3

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WARNING

Volume Fraction

Experiment 1 : 0.28 2,000,000 µm3 _{560,000 µm}3

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WARNING

Volume Fraction

Experiment 1 : 0.28 2,000,000 µm3 _{560,000 µm}3

Experiment 2 : 0.28 500,000 µm3 _{140,000 µm}3

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WARNING

Be careful reporting Volume Fraction

Volume Fraction

Measure Reference Volume µm

3

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Summary

•Think 3-D

•Cavalieri Principle: V= h x ∑Areas

•Delesse Principle: V_v(component volume/reference volume)

= A_A(component area/reference area) = P_component/P_reference

•Always measure the reference volume and report component volume

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References-Lecture 2

Gundersen HJG, Jensen EB, The efficiency of systematic sampling in stereology and its prediction. J. Microsc 147:229-263, 1987

Howard CV, Reed MG, Unbiased Stereology: three dimensional

measurement in microscopy. Bios Scientific Publishers, Oxford, 1998

Weibel ER, Stereological Methods. Practical Methods for Biological Morphometry. Academic Press, London, 1979

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http://www.cdrewu.edu/research/MorphometryLaboratory/Mini-Course

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Questions

John Basgen

Morphometry and Stereology Laboratory

Charles R. Drew University of Medicine and Science Los Angeles, California, USA

Phone: (1) 323-357-3668

Email: