Die mikroskopische Bestimmung der Größenverteilung von Kugelelementen, die zufällig in gewisser Umwelt verstreut sind

Komenda, S; Peřinová, V.; Bayer, Andrea

doi:10.1002/bimj.19690110202

Cited by 8 publications

(7 citation statements)

References 1 publication

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“…--In the following paragraph, we saw that the image distribution obtained experimentally is identical to the one derived with our model and also to the one given by Lodin et al [8], Bach [1], and Komenda et al [5].…”

Section: Discussionsupporting

confidence: 82%

“…The final equation was found to be mathematically identical to the one derived by Lodin et al [8], Bach [1], and Komenda et al [5].…”

Section: Discussionmentioning

confidence: 71%

“…, Lodin et al [8], Komenda et al [5] The authors to whom we refer in this section arrive at identical integral equations. Several solutions to this equation are possible, we will quote only the more interesting ones as examples.…”

Section: The Theories Of Bach [I]mentioning

confidence: 97%

“…Though the thickness is introduced in the probability considerations of cutting a spherical element in a tissue, this theory is regarded incomplete since the thickness has to be introduced also in the probability term relating the apparent to the real diameters. We modified the mathematical formulations accordingly and arrived at equations identical to those resulting from a third class of models [1,8,5]. With this last class of theories, as was experimentally verified, the real distribution of elements in a volume can be determined with a high degree of confidence.…”

mentioning

confidence: 98%

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Theoretical and experimental derivation of the function relating the size distribution of spherical particles in a volume element to that obtained from images of sections taken through it

Bélanger

Seufert

1972

Biophysik

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Summary. The mathematical formulation of three classes of theories con cerning the problem outlined in the title of this study was critically assessed and experimentally evaluated. It was found that only one class of the theories describes the relation between the distribution of particles in a volume element to that observed in sections through this volume in a satisfactory way. The errors in the remaining two classes could be traced and the corrections made after a mathematically rigorous analysis brought these theories to comply with a model which, as we could prove experimentally, deserves a high level of confidence.A statistical analysis of the dimensions of particles contained at random in a volume element from images of sections through the specimen meets with considerable difficulties. It seems intuitively obvious that the function relating the size distribution observed in the projected images to that in the volume element depends on a variable into which enter the orientation of the particles as well as a term associating mean particle diameter with section thickness. If this latter factor is not taken into account, variations in size even of particles not giving the orientation problem as, e.g., of spherical organelles under anisotonic conditions, could be seriously misinterpreted.In this study, the mathematical approach of several authors to this statistical problem was critically appraised and the domain of validity of each of the theories determined experimentally. The fact that the available theoretical treatments can be classified in three groups greatly facilitated this task.The first class of models is based on the assumption that the section thickness be negligible as compared to the diameter of the elements contained in the sample [9,6,4,3]. A second class is represented by the work of Coup]and [2] who recently proposed a theory in which the section thickness is considered finite. Though the thickness is introduced in the probability considerations of cutting a spherical element in a tissue, this theory is regarded incomplete since the thickness has to be introduced also in the probability term relating the apparent to the real

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Section: Discussionsupporting

confidence: 82%

“…The final equation was found to be mathematically identical to the one derived by Lodin et al [8], Bach [1], and Komenda et al [5].…”

Section: Discussionmentioning

confidence: 71%

Section: The Theories Of Bach [I]mentioning

confidence: 97%

mentioning

confidence: 98%

See 2 more Smart Citations

Theoretical and experimental derivation of the function relating the size distribution of spherical particles in a volume element to that obtained from images of sections taken through it

Bélanger

Seufert

1972

Biophysik

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“…The first analytical solution for T = 0 and no truncation was published by Wicksell (1925), and the last one so far, with T > 0, overprojection and truncation, is that of Coleman (1980Coleman ( , 1982. Among the many papers in between, we can mention those of Reid (1955), Santalo (1955, Bach (1963, Goldsmith (1967), Sidak (1968), Komenda et al (1969) and Tallis (1970). Only Bach (1963) seems to deal with overprojection and truncation (in the form of a positive resolution threshold) simultaneously.…”

Section: Distribution-free Analytic Approuchmentioning

confidence: 99%

Distribution‐free estimation of sphere size distributions from slabs showing overprojection and truncation, with a review of previous methods

Cruz‐Orive

1983

Journal of Microscopy

181

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K E Y w O R D S.Particle size distributions, linear size properties, slab section, overprojection, resolution threshold, capping angle, unfolding algorithm, stereology. S U M M A R YA distribution-free method is presented for unfolding the size distribution of an aggregate of disjoint opaque spherical particles in a translucent medium, from the circular profiles observed in the orthogonal projection of sections of a certain thickness through the medium. This situation pertains especially to light and transmission electron microscopy.The model accounts for overprojection (or 'Holmes effect') due to section thickness, and for two forms of truncation (or 'missing profiles' mechanisms), simultaneously. The profile data may be grouped into an arbitrary class system, chosen by the user, and the procedure can be programmed in a medium-size desk calculator.In order to incorporate the above features, however, we had to choose a finite-difference unfolding algorithm, the advantages and disadvantages of which are discussed early in the paper in the context of the main alternative unfolding procedures hitherto available.The performance of the method is tested against three sets of real data previously analysed by a maximum likelihood method (Keiding er al., 1972).

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Bestimmung der Größenverteilung von Kugeln aus Schnittkreisradien

Giger

Riedwyl

1970

Biom. J.

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Die mikroskopische Bestimmung der Größenverteilung von Kugelelementen, die zufällig in gewisser Umwelt verstreut sind

Cited by 8 publications

References 1 publication

Theoretical and experimental derivation of the function relating the size distribution of spherical particles in a volume element to that obtained from images of sections taken through it

Theoretical and experimental derivation of the function relating the size distribution of spherical particles in a volume element to that obtained from images of sections taken through it

Distribution‐free estimation of sphere size distributions from slabs showing overprojection and truncation, with a review of previous methods

Bestimmung der Größenverteilung von Kugeln aus Schnittkreisradien

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