Quantitative methods for diffusion measurements in fluorescence microscopy
Doctoral thesis, 2019

In this work, statistical methods are developed for mapping mass transport locally based on images collected using a confocal laser scanning microscope. Besides presenting raster image correlation spectroscopy as an established method in fluorescence microscopy, we introduce a single particle tracking method which takes advantage of the raster scanning of the image in a confocal microscope. In single particle tracking, particles are identified and followed in consecutive frames of a video to measure their diffusive mobility. Both a maximum likelihood and a centroid-based method have been developed to locate the particles and hence to estimate the diffusion coefficient. The method is generalized to analyse mixtures of particles having different diffusion coefficients. The proposed method allows us to study the entire distribution of diffusion coefficients, enabling the characterization of heterogeneous systems. Motivated by experiments with particle mixtures, we investigate the use of cross-validation to perform model selection, i.e. to select the number of mixture components, and compare it to some existing model selection criteria. In the specific case of normal mixtures, we prove a bound on the error between the cross-validated conditional risk and an oracle benchmark conditional risk, which assumes the knowledge of the true density generating the data. Furthermore, a detailed statistical analysis of the raster image correlation spectroscopy method is presented, uncovering the relationship between molecular and experimental parameters and the estimated diffusion coefficient. We propose a statistical method to compare different experimental conditions and apply it to find the optimal parameters to perform an experiment. The methods and models investigated and developed in this thesis are of general interest. In particular, the quantitative methods considered to study confocal images can be used in a wide range of applications, while the use of crossvalidation to perform model selection of mixture models is a valuable contribution to the statistical literature.


single particle tracking

Confocal laser scanning microscopy

raster scan

correlation spectroscopy

mixture models


room Pascal, MV Huset, Hörsalsvägen 1, Chalmers
Opponent: Rolf Sundberg, Matematiska institutionen, Stockholms universitet, Stockholm, Sweden


Marco Longfils

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Single particle raster image analysis of diffusion

Journal of Microscopy,; Vol. 266(2017)p. 3-14

Journal article

Single particle raster image analysis of diffusion for particle mixtures

Journal of Microscopy,; Vol. 269(2018)p. 269-281

Journal article

Longfils, M., Röding, M., Lorén, N., Särkkä, A., and Rudemo, M. Identification of mixture models with an application to diffusing particles.

Longfils, M., Smisdom, N., Ameloot, M., Rudemo, M., Lemmens, V., Fernández, G.S., Röding, M., E., Lorén, N., Hendrix, J. and Särkkä, A. Raster image correlation spectroscopy performance evaluation.

Diffusion is a general term to refer to the random movement of molecules from a region to another and finds a large number of applications. For example, a cell uses diffusion as a way to transport nutrients. The transportation of important materials such as proteins and amino acids to their correct destination within a cell is necessary for the correct functioning of the cell. The aim of this work is to develop new methods for measuring diffusion from experiments performed with a microscope. The diffusion coefficient is a measure of the speed at which the molecules move, and is often used to estimate diffusion. An experiment often consists of a large number of microscopy images. The sequence of images forms a video, where each image is a photo of the sample we want to study at a certain time. In a frame, the molecules appear as bright points and we can locate their position. We can follow the molecules in the video and measure how fast they are moving with the help of statistical models. The methods and models developed and studied in this thesis are of general interest and can be used in a wide range of applications. The results can be useful to study and understand diffusion in biology and material science.

Material structures seen through microscopes and statistics

Swedish Foundation for Strategic Research (SSF) (AM13-0066.020), 2014-04-01 -- 2019-06-30.

Subject Categories

Probability Theory and Statistics

Areas of Advance

Materials Science



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4579



room Pascal, MV Huset, Hörsalsvägen 1, Chalmers

Opponent: Rolf Sundberg, Matematiska institutionen, Stockholms universitet, Stockholm, Sweden

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