PRACTICAL USE OF STEREOLOGY BIOMEDICAL RESEARCH LABORATORY
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1 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
2 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
3 Lecture 2 Measurement of Volume 1. Review of what is stereology? 2. Think 3-D 3. Volume-Cavalieri Principle 4. Volume Fraction-Delesse Principle
4 Review Organs, Tissues, Cells, Organelles are 3-Dimensional Objects
5 Review 3-D 2-D
6 Review 3-D 2-D 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
7 Review 3-D 2-D Stereology
8 Review Stereology is founded on: 1. Geometrical probability 2. Statistics
9 Review Geometrical Probability
10 Review Stereology Parameters (geometrical structural characteristic) Volume 3-D Surface 2-D Length 1-D Number 0-D
11 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, You make estimates of the Truth
12 Review Statistics Estimates have two properties: Accuracy: The degree of closeness of a measurement to the true value. Precision: The degree to which repeated measurements have the same value
13 Measurement of Volume
14 Volume of Rectangular Prism
15 Volume of Rectangular Prism Volume = H x Area
16 Volume of Cylinder
17 Volume of Cylinder Volume = H x area
18 Arbitrarily Shaped Object
19 Measurement of Volume of Arbitrarily Shape Objects: Cavalieri Principle -Italian mathematician and monk AD
20 Cavalieri Principle unbiased estimate Volume = H x Area
21 Cavalieri Principle unbiased estimate Volume = H x Area
22 Cavalieri Principle If you estimate the volume with 1 random section -Unbiased (Accurate) estimate -Not Precise estimate
23 Cavalieri Principle unbiased estimate Volume = h x Areas
24 Cavalieri Principle Estimate volume with several sections with random start -Unbiased (Accurate) estimate -Precise estimate
25 Cavalieri Principle Must be able to measure: 1. h 2. Areas
26 Cavalieri Principle 1. Measuring h A) Tissue Slicer
27 Cavalieri Principle 1. Measuring h A) Tissue Slicer B) Parallel Razor Blades Madsen K. J Am Soc Nephrol 1999
28 Cavalieri Principle 1. Measuring h A) Tissue Slicer B) Parallel Razor Blades
29 Cavalieri Principle 2. Measuring Areas A) Planimeter
30 Cavalieri Principle 2. Measuring Areas A) Planimeter
31 Cavalieri Principle 2. Measuring Areas A) Planimeter B) Digital Planimeter or Mouse
32 Cavalieri Principle 2. Measuring Areas A) Planimeter B) Digital Planimeter or Mouse C) Point Counting Grid
33 Where is the point?
34 Cavalieri Principle 2. Measuring Areas A) Planimeter B) Digital Planimeter or Mouse C) Point Counting Grid Area of 1 point = X * X mm 2
35 Cavalieri Principle
36 Cavalieri Principle Cortex Volume = h x Areas Cortex Volume = h x (area of 1 point) x points Cortex Volume = 4 mm x 9 mm 2 x 100 points Cortex Volume = 3600 mm 3
37 Cavalieri Principle
38 Cavalieri Principle 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.
39 Cavalieri Principle 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.
40 57 µm 47 µm 37 µm Cavalieri Principle 7 µm 17 µm 27 µm
41 Cavalieri Principle 3. You want to count a total of grid points on all profiles from an object. Divide 200 by 6-approximately points/profile
42 Cavalieri Principle 7 µm 17 µm 27 µm 57 µm 47 µm 37 µm
43 Cavalieri Principle 7 µm 17 µm 27 µm 57 µm 47 µm 37 µm
44 57 µm 47 µm 37 µm Cavalieri Principle 7 µm 17 µm 27 µm
45 Cavalieri Principle 7 µm 17 µm 27 µm 57 µm 47 µm 37 µm
46 57 µm 47 µm 37 µm Cavalieri Principle 7 µm 17 µm 27 µm
47 57 µm 47 µm 37 µm Cavalieri Principle 7 µm 17 µm 27 µm
48 Cavalieri Principle Volume = h x areas
49 Cavalieri Principle Volume = h x areas Volume = h x (area 1 point x points )
50 Cavalieri Principle Volume = h x areas Volume = h x (area 1 point x points ) Volume = h x [(d/mag) 2 x points]
51 Cavalieri Principle Volume = h x areas 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]
52 Cavalieri Principle Volume = h x areas 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] Volume = 150,000 µm 3
53 Cavalieri Principle unbiased estimate Volume = h x Areas
54 Volume Fraction
55 Volume Fraction Volume Density Percent Volume V v (Particle Volume/Reference Volume)
56 Volume Fraction Reference Space Particles or Components V v (Basketball Volume/Reference Volume)
57 Volume Fraction V v (Basketball Volume/Reference Volume)
58 Volume fraction V v (Mitochondrial Volume/Heart Muscle Volume)
59 Volume fraction V v (Capillary Volume/Glomerular Volume)
60 Volume Fraction 3-D 2-D
61 Volume Fraction 3-D 2-D Delesse Principle
62 Volume fraction 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.
63 Volume fraction 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
64 Volume fraction Delesse Principle
65 Volume Fraction Must be able to measure: 1. Area of reference profile 2. Area of particle profile
66 Volume Fraction Must be able to Measure Areas A) Planimeter
67 Volume Fraction Must be able to Measure Areas A) Planimeter
68 Volume Fraction Must be able to Measure Areas A) Planimeter B) Digital Planimeter or Mouse
69 Volume Fraction Must be able to Measure Areas A) Planimeter B) Digital Planimeter or Mouse
70 Volume Fraction Must be able to Measure Areas A) Planimeter B) Digital Planimeter or Mouse C) Automatic Image Analysis
71 Volume Fraction Must be able to Measure Areas A) Planimeter B) Digital Planimeter or Mouse C) Automatic Image Analysis
72 Volume Fraction Must be able to Measure Areas A) Planimeter B) Digital Planimeter or Mouse C) Automatic Image Analysis D) Point Counting Grid
73 Volume Fraction
74 Volume Fraction V v (capillary/glom) = A A (capillary/glom) = P mes / P glom = 26 /65 = 0.400
75 Volume Fraction
76 Volume Fraction V v (capillary/glom) = FP capillary / (CP glom x 4) = 26 /(16 x 4) = 0.406
77 Volume Fraction V v (capillary/glom) = FP capillary / (CP glom x 4) = 9 /(16 x 4) = % of glomerular volume is capillary volume
78 Volume Fraction Which is best? A) Planimeter B) Digital Planimeter or Mouse C) Automatic Image Analysis D) Point Counting
79 Volume Fraction Which is best? A) Planimeter NO B) Digital Planimeter or Mouse C) Automatic Image Analysis D) Point Counting
80 Volume Fraction Which is best? A) Planimeter B) Digital Planimeter or Mouse Maybe C) Automatic Image Analysis D) Point Counting
81 Volume Fraction Which is best? A) Planimeter B) Digital Planimeter or Mouse IF C) Automatic Image Analysis Yes, antibody is very specific D) Point Counting
82 Volume Fraction Which is best? A) Planimeter B) Digital Planimeter or Mouse C) Automatic Image Analysis D) Point Counting Maybe
83 Volume Fraction Digitizer Tracing vs Point Counting
84 Volume Fraction Vv(Mesangium/Glomerulus) Digitizer Point Counting Nephron 50: , 1988
85 Volume Fraction Time in Seconds Digitizer Point Counting Nephron 50: , 1988
86 Volume Fraction Which is best? A) Planimeter B) Digital Planimeter or Mouse C) Automatic Image Analysis D) Point Counting YES
87 Volume Fraction WARNING Be careful reporting Volume Fraction
88 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.
89 Volume Fraction WARNING Be careful of reporting Volume Fraction V v (mes/glom) x glomerular volume µm 3 = Volume of mesangium µm 3 V v (mes/glom) glom volume mes volume Normal : ,000,000 µm 3 140,000 µm 3 Experiment 1 : ,000,000 µm 3 560,000 µm 3
90 Volume Fraction WARNING Be careful of reporting Volume Fraction V v (mes/glom) x glomerular volume µm 3 = Volume of mesangium µm 3 V v (mes/glom) glom volume mes volume Normal : ,000,000 µm 3 140,000 µm 3 Experiment 1 : ,000,000 µm 3 560,000 µm 3 Experiment 2 : ,000 µm 3 140,000 µm 3
91 Volume Fraction WARNING Be careful of reporting Volume Fraction V v (mes/glom) x glomerular volume µm 3 = Volume of mesangium µm 3 V v (mes/glom) glom volume mes volume Normal : ,000,000 µm 3 140,000 µm 3 Experiment 1 : ,000,000 µm 3 560,000 µm 3 Experiment 2 : ,000 µm 3 140,000 µm 3 Experiment 3 : ,000,000 µm 3 280,000 µm 3
92 Volume Fraction WARNING Be careful reporting Volume Fraction Measure Reference Volume µm 3 REPORT Component Volume µm 3
93 Summary Think 3-D Cavalieri Principle: Delesse Principle: V= h x Areas 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 Don t count more than 200 points per animal
94 References-Lecture 2 Gundersen HJG, Jensen EB, The efficiency of systematic sampling in stereology and its prediction. J. Microsc 147: , 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
95 Download copy of the slides
96 Questions John Basgen Morphometry and Stereology Laboratory Charles R. Drew University of Medicine and Science Los Angeles, California, USA Phone: (1) Skype: basijing
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