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Analysis of Spatial Patterns in Tissue Samples using Spectral Analysis and GMRF Modelling

Blomstrand, Simon and Bro, Viktor (2015) FMS820 20151
Mathematical Statistics
Abstract
Biotechnology company Medetect AB has developed a technology for staining
of multiple cell types in the same tissue sample enabling positioning of cells as
well as giving a way to distinguish between cell types. With new methods of
visualising human tissue at a cellular level, comes a need to analyse this data. In
this thesis, we therefore investigate some new methods, spectral non-parametric
as well as spatial and parametric, of analysing the structure of possibly mul-
tivariate point sets. Both spatial structure of univariate point data as well as
covariation of bivariate point data are analysed.
An approach using the raw periodogram is presented, followed by an application
of the Thomson multitaper method on point data and on... (More)
Biotechnology company Medetect AB has developed a technology for staining
of multiple cell types in the same tissue sample enabling positioning of cells as
well as giving a way to distinguish between cell types. With new methods of
visualising human tissue at a cellular level, comes a need to analyse this data. In
this thesis, we therefore investigate some new methods, spectral non-parametric
as well as spatial and parametric, of analysing the structure of possibly mul-
tivariate point sets. Both spatial structure of univariate point data as well as
covariation of bivariate point data are analysed.
An approach using the raw periodogram is presented, followed by an application
of the Thomson multitaper method on point data and on quadrat sampled
data. A third method is also presented, where quadrat sampled data is used
to construct a Gaussian Markov random eld (GMRF), using a conditional
autoregressive (CAR) model. The parameters of the CAR models are then
studied to see if it is possible to draw some conclusions about the underlying
point patterns from these.
Simulation studies are performed for each method, demonstrating that the pe-
riodogram { although noisy { may be used to estimate spatial structure and
covariation between point types. Furthermore we show that using a multitaper
spectral estimate on quadrat sampled data can be used to gain a better under-
standing of the spatial structure and covariation of point sets. We also found
that while some parameters of a CAR(1) model may be used to infer spatial
structure in univariate point sets, using our method, it is generally outperformed
by the spectral methods presented.
Lastly, cells from human intestinal and tonsil tissue are analysed using the pre-
sented techniques. Small subsections of the intestinal tissue were analysed, as
it is not very homogenous. It was difficult to nd subsections which were both
homogenous and contained a sufficent number of cells for spectral analysis. No
clear evidence for spatial structure was found for any cell type, nor any proof
of covariation between cell types. The tonsil tissue, being more homogeneous,
allowed for slightly larger analysis regions, giving more reliable results. The
analysis of the tonsil tissue showed some possible clustering of macrophages,
thymocytes and the protein Interleukin 33. Some evidence for clustering covari-
ation was found for T lymphocytes and thymocytes, as was inhibitory covaria-
tion for Interleukin 33 and the protein KI-67.
The usefulness of the methods used in this thesis seems limited when analysing
human intestinal and tonsil tissue but may be of use in other areas where spatial
point data are considered. (Less)
Please use this url to cite or link to this publication:
author
Blomstrand, Simon and Bro, Viktor
supervisor
organization
course
FMS820 20151
year
type
H2 - Master's Degree (Two Years)
subject
language
English
id
5472682
date added to LUP
2015-06-12 07:47:02
date last changed
2015-06-12 07:47:02
@misc{5472682,
  abstract     = {Biotechnology company Medetect AB has developed a technology for staining
of multiple cell types in the same tissue sample enabling positioning of cells as
well as giving a way to distinguish between cell types. With new methods of
visualising human tissue at a cellular level, comes a need to analyse this data. In
this thesis, we therefore investigate some new methods, spectral non-parametric
as well as spatial and parametric, of analysing the structure of possibly mul-
tivariate point sets. Both spatial structure of univariate point data as well as
covariation of bivariate point data are analysed.
An approach using the raw periodogram is presented, followed by an application
of the Thomson multitaper method on point data and on quadrat sampled
data. A third method is also presented, where quadrat sampled data is used
to construct a Gaussian Markov random eld (GMRF), using a conditional
autoregressive (CAR) model. The parameters of the CAR models are then
studied to see if it is possible to draw some conclusions about the underlying
point patterns from these.
Simulation studies are performed for each method, demonstrating that the pe-
riodogram { although noisy { may be used to estimate spatial structure and
covariation between point types. Furthermore we show that using a multitaper
spectral estimate on quadrat sampled data can be used to gain a better under-
standing of the spatial structure and covariation of point sets. We also found
that while some parameters of a CAR(1) model may be used to infer spatial
structure in univariate point sets, using our method, it is generally outperformed
by the spectral methods presented.
Lastly, cells from human intestinal and tonsil tissue are analysed using the pre-
sented techniques. Small subsections of the intestinal tissue were analysed, as
it is not very homogenous. It was difficult to nd subsections which were both
homogenous and contained a sufficent number of cells for spectral analysis. No
clear evidence for spatial structure was found for any cell type, nor any proof
of covariation between cell types. The tonsil tissue, being more homogeneous,
allowed for slightly larger analysis regions, giving more reliable results. The
analysis of the tonsil tissue showed some possible clustering of macrophages,
thymocytes and the protein Interleukin 33. Some evidence for clustering covari-
ation was found for T lymphocytes and thymocytes, as was inhibitory covaria-
tion for Interleukin 33 and the protein KI-67.
The usefulness of the methods used in this thesis seems limited when analysing
human intestinal and tonsil tissue but may be of use in other areas where spatial
point data are considered.},
  author       = {Blomstrand, Simon and Bro, Viktor},
  language     = {eng},
  note         = {Student Paper},
  title        = {Analysis of Spatial Patterns in Tissue Samples using Spectral Analysis and GMRF Modelling},
  year         = {2015},
}