Estimating the surface area of nonconvex particles from central planar sections

Area of Science:

• Stereology
• Biophysical imaging
• Computational geometry

Background:

• Accurate surface area estimation is crucial in various scientific fields.
• Existing local stereology estimators have limitations, particularly for non-convex objects.
• There is a need for robust and efficient surface area estimation techniques.

Purpose of the Study:

• To introduce a novel surface area estimator, the Morse-type estimator, for local stereology.
• To generalize existing pivotal estimators to accommodate non-convex structures.
• To demonstrate the estimator's utility in biological applications and computer-assisted microscopy.

Main Methods:

• A two-stage sampling procedure involving a plane section and a modified area tangent count method.
• Generalization of Cruz-Orive's pivotal estimator to include non-convex objects.
• Simulation studies to compare the Morse-type estimator with existing methods.

Main Results:

• The Morse-type estimator effectively generalizes to non-convex objects.
• Simulation studies show advantages over existing local surface area estimators.
• Demonstrated practicability in estimating the surface area of giant-cell glioblastoma nuclei from microscopy images.

Conclusions:

• The Morse-type surface area estimator is a valuable new tool in local stereology.
• It is well-suited for computer-assisted confocal microscopy and biological applications.
• An interactive software has been developed to facilitate its use.