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
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
Lecture 2 Measurement of Volume 1. Review of what is stereology? 2. Think 3-D 3. Volume-Cavalieri Principle 4. Volume Fraction-Delesse Principle
Review Organs, Tissues, Cells, Organelles are 3-Dimensional Objects
Review 3-D 2-D
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
Review 3-D 2-D Stereology
Review Stereology is founded on: 1. Geometrical probability 2. Statistics
Review Geometrical Probability
Review Stereology Parameters (geometrical structural characteristic) Volume 3-D Surface 2-D Length 1-D Number 0-D
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
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
Measurement of Volume
Volume of Rectangular Prism
Volume of Rectangular Prism Volume = H x Area
Volume of Cylinder
Volume of Cylinder Volume = H x area
Arbitrarily Shaped Object
Measurement of Volume of Arbitrarily Shape Objects: Cavalieri Principle -Italian mathematician and monk -1620 AD
Cavalieri Principle unbiased estimate Volume = H x Area
Cavalieri Principle unbiased estimate Volume = H x Area
Cavalieri Principle If you estimate the volume with 1 random section -Unbiased (Accurate) estimate -Not Precise estimate
Cavalieri Principle unbiased estimate Volume = h x Areas
Cavalieri Principle Estimate volume with several sections with random start -Unbiased (Accurate) estimate -Precise estimate
Cavalieri Principle Must be able to measure: 1. h 2. Areas
Cavalieri Principle 1. Measuring h A) Tissue Slicer
Cavalieri Principle 1. Measuring h A) Tissue Slicer B) Parallel Razor Blades Madsen K. J Am Soc Nephrol 1999
Cavalieri Principle 1. Measuring h A) Tissue Slicer B) Parallel Razor Blades
Cavalieri Principle 2. Measuring Areas A) Planimeter
Cavalieri Principle 2. Measuring Areas A) Planimeter
Cavalieri Principle 2. Measuring Areas A) Planimeter B) Digital Planimeter or Mouse
Cavalieri Principle 2. Measuring Areas A) Planimeter B) Digital Planimeter or Mouse C) Point Counting Grid
Where is the point?
Cavalieri Principle 2. Measuring Areas A) Planimeter B) Digital Planimeter or Mouse C) Point Counting Grid Area of 1 point = X * X mm 2
Cavalieri Principle
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
Cavalieri Principle
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.
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.
57 µm 47 µm 37 µm Cavalieri Principle 7 µm 17 µm 27 µm
Cavalieri Principle 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
Cavalieri Principle 7 µm 17 µm 27 µm 57 µm 47 µm 37 µm
Cavalieri Principle 7 µm 17 µm 27 µm 57 µm 47 µm 37 µm
57 µm 47 µm 37 µm Cavalieri Principle 7 µm 17 µm 27 µm
Cavalieri Principle 7 µm 17 µm 27 µm 57 µm 47 µm 37 µm
57 µm 47 µm 37 µm Cavalieri Principle 7 µm 17 µm 27 µm
57 µm 47 µm 37 µm Cavalieri Principle 7 µm 17 µm 27 µm
Cavalieri Principle Volume = h x areas
Cavalieri Principle Volume = h x areas Volume = h x (area 1 point x points )
Cavalieri Principle Volume = h x areas Volume = h x (area 1 point x points ) Volume = h x [(d/mag) 2 x points]
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]
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
Cavalieri Principle unbiased estimate Volume = h x Areas
Volume Fraction
Volume Fraction Volume Density Percent Volume V v (Particle Volume/Reference Volume)
Volume Fraction Reference Space Particles or Components V v (Basketball Volume/Reference Volume)
Volume Fraction V v (Basketball Volume/Reference Volume)
Volume fraction V v (Mitochondrial Volume/Heart Muscle Volume)
Volume fraction V v (Capillary Volume/Glomerular Volume)
Volume Fraction 3-D 2-D
Volume Fraction 3-D 2-D Delesse Principle
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.
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
Volume fraction Delesse Principle
Volume Fraction Must be able to measure: 1. Area of reference profile 2. Area of particle profile
Volume Fraction Must be able to Measure Areas A) Planimeter
Volume Fraction Must be able to Measure Areas A) Planimeter
Volume Fraction Must be able to Measure Areas A) Planimeter B) Digital Planimeter or Mouse
Volume Fraction Must be able to Measure Areas A) Planimeter B) Digital Planimeter or Mouse
Volume Fraction Must be able to Measure Areas A) Planimeter B) Digital Planimeter or Mouse C) Automatic Image Analysis
Volume Fraction Must be able to Measure Areas A) Planimeter B) Digital Planimeter or Mouse C) Automatic Image Analysis
Volume Fraction Must be able to Measure Areas A) Planimeter B) Digital Planimeter or Mouse C) Automatic Image Analysis D) Point Counting Grid
Volume Fraction
Volume Fraction V v (capillary/glom) = A A (capillary/glom) = P mes / P glom = 26 /65 = 0.400
Volume Fraction
Volume Fraction V v (capillary/glom) = FP capillary / (CP glom x 4) = 26 /(16 x 4) = 0.406
Volume Fraction V v (capillary/glom) = FP capillary / (CP glom x 4) = 9 /(16 x 4) = 0.406 41% of glomerular volume is capillary volume
Volume Fraction Which is best? A) Planimeter B) Digital Planimeter or Mouse C) Automatic Image Analysis D) Point Counting
Volume Fraction Which is best? A) Planimeter NO B) Digital Planimeter or Mouse C) Automatic Image Analysis D) Point Counting
Volume Fraction Which is best? A) Planimeter B) Digital Planimeter or Mouse Maybe C) Automatic Image Analysis D) Point Counting
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
Volume Fraction Which is best? A) Planimeter B) Digital Planimeter or Mouse C) Automatic Image Analysis D) Point Counting Maybe
Volume Fraction Digitizer Tracing vs Point Counting
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
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
Volume Fraction Which is best? A) Planimeter B) Digital Planimeter or Mouse C) Automatic Image Analysis D) Point Counting YES
Volume Fraction WARNING Be careful reporting Volume Fraction
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.
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 : 0.14 1,000,000 µm 3 140,000 µm 3 Experiment 1 : 0.28 2,000,000 µm 3 560,000 µm 3
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 : 0.14 1,000,000 µm 3 140,000 µm 3 Experiment 1 : 0.28 2,000,000 µm 3 560,000 µm 3 Experiment 2 : 0.28 500,000 µm 3 140,000 µm 3
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 : 0.14 1,000,000 µm 3 140,000 µm 3 Experiment 1 : 0.28 2,000,000 µm 3 560,000 µm 3 Experiment 2 : 0.28 500,000 µm 3 140,000 µm 3 Experiment 3 : 0.14 2,000,000 µm 3 280,000 µm 3
Volume Fraction WARNING Be careful reporting Volume Fraction Measure Reference Volume µm 3 REPORT Component Volume µm 3
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
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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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: johnbasgen@cdrewu.edu Skype: basijing