With sampling, a given estimate of a population will vary from the true (and unknown) number. Sampling design can yield high accuracy but low precision so that each estimate varies from each other, yet are clustered at the true number…Or it can be highly precise but low in accuracy – so replication can yield similar estimates which are not close to the true numberOr…it can be both precise and accurate with the estimates clustered together near the true number. The goal of stereology is to ensure that the individual sampling error does not overshadow the difference due to experimental manipulation.
With sampling, a given estimate of a population will vary from the true (and unknown) number. Sampling design can yield high accuracy but low precision so that each estimate varies from each other, yet are clustered at the true number…Or it can be highly precise but low in accuracy – so replication can yield similar estimates which are not close to the true numberOr…it can be both precise and accurate with the estimates clustered together near the true number. The goal of stereology is to ensure that the individual sampling error does not overshadow the difference due to experimental manipulation.
Reduction of the sampling area of a section by a known area since counting all cells is prohibitive.Grid spacing is systematic, placement of grid is randomFor lung, often a technique call the Smooth Fractionator is performed instead of systematic random…
Section collection must be regularly sampled and available for analysisMaximize post-processing section thicknessMinimize damage due to processingStaining must penetrate the entire section thickness
Geometric probes are required to quantify 3D data Howard CV, Reed MG: Unbiased Stereology. 2nd ed., Bios, Oxford, 2005Sum up by sayinghtat remind the viewer that tissue + object + probe = isotropic to be unbiased. (so you can use a preferential section + a isotropic probe or vertical sections and a probe that is random in at least one dimension etc).
With sampling, a given estimate of a population will vary from the true (and unknown) number. Sampling design can yield high accuracy but low precision so that each estimate varies from each other, yet are clustered at the true number…Or it can be highly precise but low in accuracy – so replication can yield similar estimates which are not close to the true numberOr…it can be both precise and accurate with the estimates clustered together near the true number. The goal of stereology is to ensure that the individual sampling error does not overshadow the difference due to experimental manipulation.
Also – how many objects/cells do you expect to see? You’re going to approach your sampling differently if you’ve got a sparse population vs a common population!Structure difference: e.g., rostral to caudal, add more coronal sectionsSection difference: e.g., medial to lateral difference, add more sites to your coronal sectionWork on your SN example description…big effect, you can accept greater sampling error, or be less conservative in your sampling parameter design.
Also – how many objects/cells do you expect to see? You’re going to approach your sampling differently if you’ve got a sparse population vs a common population!Structure difference: e.g., rostral to caudal, add more coronal sectionsSection difference: e.g., medial to lateral difference, add more sites to your coronal sectionWork on your SN example description…big effect, you can accept greater sampling error, or be less conservative in your sampling parameter design.
Also – how many objects/cells do you expect to see? You’re going to approach your sampling differently if you’ve got a sparse population vs a common population!Structure difference: e.g., rostral to caudal, add more coronal sectionsSection difference: e.g., medial to lateral difference, add more sites to your coronal sectionWork on your SN example description…big effect, you can accept greater sampling error, or be less conservative in your sampling parameter design.
Also – how many objects/cells do you expect to see? You’re going to approach your sampling differently if you’ve got a sparse population vs a common population!Structure difference: e.g., rostral to caudal, add more coronal sectionsSection difference: e.g., medial to lateral difference, add more sites to your coronal sectionWork on your SN example description…big effect, you can accept greater sampling error, or be less conservative in your sampling parameter design.
SHRINKAGE!
SHRINKAGE!
Advanced reading:Weibel’s 2006 review on lung stereologyWest’s bookHoward and Reid
Transcript
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Stereology Theory andExperimental DesignJulie Korich, Ph.D.Staff Scientist/Research Liaison
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mbfbioscience.com• What are you quantifying?• How will you quantify it?• How do you validateresults?Basic QuestionsArtwork by Sidney Harris
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mbfbioscience.comWhat 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 spinalcord?• 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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mbfbioscience.comSampling from Tissue Sections• Measure 3D parameters (number, area, volume,length)on tissue sectionshttp://www.boneclones.com/KO-515.htm
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mbfbioscience.comThe How… Non-stereological Methods• Profile counts• Exhaustive Sampling-sampleevery event in every sectionthrough the region of interest• Pitfalls:• Inefficient• Laborious• Biases• One representative section• Pitfalls: Introducing Biaswww.PHDComics.com
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Profile Counting: Size andOrientation Biasmbfbioscience.comC. Schmitz and P. R. Hof. Neuroscience 130 (2005) 813–831
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Profile Counting: Double Countsmbfbioscience.com344333Profile Counting• Counter would report 20 cells. However, there are only 8 cells.• Also, if using exhaustive sampling, it is necessary to countEVERY cell in EVERY section.
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mbfbioscience.com‘One Representative Section’Counts within a single field-of-view (white box) would lead to thefalse impression that Animal 1 has fewer cells than Animal 2 in theentire region of interest.ABAnimal 1Animal 2
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mbfbioscience.comIn Summary: Non-Stereological Methods• Non-stereological sampling can be biased inaddition to laborious• With stereological techniques sampling bias isavoided – every event has an equal opportunity ofbeing sampled• Stereology does not make assumptions regardingsize, shape, orientation or distribution• Therefore, stereology is considered the goldstandard for quantification in neuroscience
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Design-Based Stereology• The sampling is performed on asub-fraction of the entire region• Within each section, only asubsample is evaluated• Systematic sampling is highlyefficient and provides samplingconsistency across and withinsections• A randomized offset ensuresunbiased measures
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mbfbioscience.comWhat is Stereology• The process of obtaining unbiased, meaningful,quantitative measurements of three dimensionalobjectives from two dimensional information• The geometrical properties of features in 3-D space canbe quantified by „throwing‟ random geometrical probesinto the space and recording the way in which theyintersect with the structures of interest.• Unbiased Stereology, Second Edition, 2005, Howard, C.V. andReed, M.G., QTP Publications, Liverpool, page 8.
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Geometric Probes• Geometric probes usedfor the sampling• Points for volume• Lines for surface area• Planes for lengths• Volume for numbers• Geometric probes arerequired to report 3Ddatambfbioscience.comHoward CV, Reed MG: Unbiased Stereology. 2nd ed., Bios, Oxford, 2005
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mbfbioscience.comDesign-Based Stereology•Used to avoid sampling bias and error• Sample whole region using systemic randomsampling•Requires isotropy to prevent bias• Ensures that all positions in the structure have thesame likelihood of being sampled• How do you achieve isotropy• Object Orientation• Tissue Preparation• Probe
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Achieving Sampling IsotropyObject Orientation• Some objects are isotropic while others have a preferentialorientation• If your object population of interest is anisotropic…AnisotropicIsotropicWikimedia.org
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Achieving Sampling Isotropy• Isotropic tissue sections• All three planes are randomized (3D spin) inthe tissue before sectioning• Vertical tissue sections• Two planes are randomized (2D spin) in thetissue before sectioning• Preferential tissue sections (e.g., coronal)• Because the orientation of the tissue isspecified, the object or the probe must beisotropicTissue PreparationAllen Brain Atlas, http://www.brain-map.org/
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Achieving Sampling Isotropy• Using isotropic probes frees you from having to eitherprove that your objects are isotropic or make yourtissue isotropicStereology Probe
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mbfbioscience.comPhysical Disector• View 2 adjacent thinsections. Sections need tobe thinner than the cellsbeing counted• Count cells that appear inone section (green inclusionplane) but not the other (redexclusion plane)• Ideal for very small (e.g EM)or very large structures (e.g.kidney glomeruli)
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mbfbioscience.comOptical Disector• Why not use thick sections andfocus through (optical sections)rather than using two thinadjacent sections?• As focus through the tissue,count cells as they appearfollowing specific counting rules• Sections need to be thick…
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mbfbioscience.comOptical Disector• Isotropy is ensured byidentifying and marking aunique point• The counting frame combinedwith the fractionator improvessampling efficiency• Typically it is not required tosample every cell within asection
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mbfbioscience.comThe Optical Fractionator• Sampling is done following systematic random sampling(SRS)• The counting frame is laid down on a systematic grid that israndomly placed on the anatomical area of interest
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mbfbioscience.comThe Fractionator Overview:A: Entire ROIB: The region of interest has beensectioned with an interval of 2 -every other section will be sampledC: Within each section, a fraction ofthe tissue will be sampled usingthe optical fractionatorD: 3D view of the opticalfractionator and disectorAnderson and Gundersen. Journal of Microscopy, Vol. 196, Pt 1, Oct1999, pp. 69±73.
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Formula for the Optical FractionatorThe cell population is determined by sampling asubset or subfraction of tissue within the regionof interest.Population estimate, N, is equal to:Reciprocal of Volume Fraction X Sum of Counts= N∑Q-1Volume FractionXmbfbioscience.com
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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 Fractionmbfbioscience.com
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mbfbioscience.comHeight Fraction:hsf• Disector Height is the thickness of the tissue sampled• Average Mounted Section Thickness is the thickness of thetissue after processing• The disector height ≠ average mounted thickness• The cut surfaces of the tissue can be disturbed to the point thatcounting is inaccurate. Therefore, only a portion of the tissue isused for counting - disector height
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mbfbioscience.com• Thickness should be measured at every samplingsite• Assumptions pertaining to the post-processingthickness 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 tissueSection Thickness
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mbfbioscience.comSection Sampling Fraction:Lateral ViewDorsal ViewIn your experiments you willsample a subset of sectionsthrough the region ofinterest = section interval
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mbfbioscience.comSection Sampling Fraction: ssf|A|A|A|A|A|B|B|B|B|B|C|C|C|C|C|D|D|D|D|D|E|E|E|E|E1|2|3|4|5|6|7|8|9|10|11|12|13|15|14|16|17|18|19|21|20|22|23|24|25|• The interval is systematic (e.g. every 5th section is sampled)• The starting section needs to be random
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mbfbioscience.com• The counting frame ( ) ensures that objects are countedonce and only once• The grid ensures that a fraction of the tissue is sampled ina systematic and random manner• Once defined, the grid spacing and counting frame sizecannot be changed• Placement of the grid on the ROI is random (via StereoInvestigator)Area Sampling Fraction: asf
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mbfbioscience.com= N∑Q-1Volume FractionXOptical Fractionator: Recap• Report the total cell population within the region ofinterest independent of volume• Important to understand the volume fraction andits components: hsf, asf and ssf• Stereology is not magic its math!
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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 StudyBasic QuestionsArtwork by Sidney Harris
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• With sampling, a given estimate of apopulation will vary from the true number• The goal of stereology is to ensure thatthe individual sampling error does notovershadow the difference due toexperimental manipulation• High Precision, Low Accuracy• High Accuracy, Low Precision• High Precision, High Accuracymbfbioscience.comTruenumberAccuracy vs. Precision
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Know Your Question• Shape of the region of interest• Uniform in shape: fewer sections• Non-uniform shape: more sectionsmbfbioscience.comahappyvalentine.blogspot.comgeradandlauracoles.com
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Know Your Question• Are the objects normallydistributed in your region?• Evenly distributed instructure: fewer sections• Unevenly distributed instructure: more sectionsmbfbioscience.com
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Know Your Question• How frequent are your objects?• Dense population (more spots on the pup): fewersections• Sparse populations (fewer spots on the pup): moresectionsmbfbioscience.commbfbioscience.comhttp://dalmatian-dog-lovers.blogspot.com/
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Know Your Question• Are the objects normally distributed within asection?• Evenly distributed in section: fewer disectors• Unevenly distributed in section: more disectorsmbfbioscience.comImages courtesy of MBF Bioscience
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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 differentbiological features• Cut the tissue at the proper thickness for theprobe 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 Peterson1.2.3.mbfbioscience.com
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Tissue Considerationsmbfbioscience.comDorph-Petersen,, K.A, Nyengaard, J.R., Gundersen, H.J. G... Journal of Microscopy, Vol. 204, Pt 3, December2001, pp. 232±246.
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Tissue ConsiderationsDorph-Petersen,, K.A, Nyengaard, J.R., Gundersen, H.J. G... Journal of Microscopy, Vol. 204, Pt 3, December2001, pp. 232±246.
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Microscope Considerations• High resolution and a thin depthof field are required todiscriminate between objectson top of each other• Necessary for the OpticalFractionatorObjective Approx. Depth of Field40 x (NA 0.65) 1.84 m40 x (NA 0.95) 0.98 m60 x (NA 1.0) 0.68 m100 x (NA 1.4) 0.58 mImage courtesy of Chandra Avinash, http://photography.learnhub.com/lesson/page/41-understanding-depth-of-field
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Source of Methodological Errorsmbfbioscience.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 errorintroduced by your methods will be reducedModified from Mark West NeuroStereology Workshop 2010
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• Coefficient of Error (CE) is an estimate of the precision ofthe population size estimate• Reported per animal• A lower CE indicates less chance for sampling error and greaterchance for an accurate estimatembfbioscience.comCoefficient of ErrorOCV2 = CV2 OCE2+ObservedGroup VarianceBiologicalVariabiliyMethodologicallyIntroducedVarianceCommon CE equations: Gundersen (m=1),Schmitz-Hof
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Why is the CE Important?mbfbioscience.com• If the results are not significant(no difference between groups),could increasing the precisionachieve the desired result?• Increase precision (decrease the CE)by sampling more• Helps other researchers evaluatethe validity of the results• Important for optimizing yourstudyModified from Mark West NeuroStereology Workshop 2010Figure: Simpson, J. et. Devel Neurobio. 2013 Jan;73(1):45-59.
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• 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 thenumber of sectionsFrom Theory to Practicembfbioscience.com
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The pilot study is designed to select samplingparameters that obtain accurate data with low samplingerror and the greatest amount of efficiency. It takes intoaccount:• Probe choice• Region of interest• Section thickness & histology• Object distributionThe Pilot Studymbfbioscience.com
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Interpreting the Pilot Study• Oversample one animal• Recalculate the estimations usingMBF‟s resampling, oversample• Look for the „sweet spot‟• If visit fewer sites per section, whathappens to the estimation• If visit few sections, what happens tothe estimations• Optimize the section interval andSRS grid dimensions for remainingstudymbfbioscience.com200003000040000500006000070000800000 1 2 3 4 5 6Section IntervalCellEstimation01000020000300004000050000600007000080000900000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21SRS Site IntervalCellEstimationFigures courtesy of MBF Bioscience
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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 disectormbfbioscience.com05000100001500020000250001 2 3 4 5 6 7Guard Zone Height ( m)CellEstimationFigure courtesy of MBF Bioscience
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mbfbioscience.comArea and Volume Estimation: CavalieriPoint Counting• Area of an object is estimated by point counting• Volume of the object is estimated by summing the areas andmultiplying by the slice thickness• Used for volume measurements of anatomical regions• Done at low magnification on a single planeHoward CV, Reed MG: Unbiased Stereology. 2nd ed., Bios, Oxford, 2005
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mbfbioscience.comCavalieri Point CountingFigures courtesy of MBF Bioscience
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mbfbioscience.comPlanimetry• Planimetric data is given tousers along with OpticalFractionator Results• The volume is correct providedthat the user defined the ROIaccurately• Can be used to generatedensity measures• Not Stereology, it can beconsidered biasedFigure courtesy of MBF Bioscience
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mbfbioscience.commbfbioscience.comEstimating Area/Volume FractionArea Fraction Fractionator• Cavalieri estimate of area performed on asystematically selected fraction of tissue• Sampling is done at low magnification andon 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 subregionarea of total regionFigure courtesy of MBF Bioscience
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mbfbioscience.comEstimation 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 x1ssfvaMouton PR, Gokhale AM, Ward NL, West MJ. Journal of Microscopy. 2002 Apr;206(Pt 1):54-64
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mbfbioscience.comArea 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 canonly be used to report cross sectional area, not volume (e.g., nerveprofiles in ventral root)*XX XXXXXX
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In Conclusion• Today we discussed stereology theory anddiscussed the importance of using geometricprobes to quantify 3D events• We discussed some rules for achieving unbiasedestimates• SRS sampling• Isotropy• Discussed experimental design and samplingstrategies to ensure efficiency, precision andaccuracy• We also introduced the Optical Fractionator forcounting cells and briefly discussed other probesmbfbioscience.com
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