Magnetic Resonance Data Processing
by Piero Barone and Giovanni Sebastiani
Magnetic Resonance (MR) in biology and medicine is the main application
field of the Signal and Image Processing group of the 'Istituto per le
Applicazioni del Calcolo' (IAC) in Rome, the largest applied mathematics
institute of the Italian National Research Council (CNR). In the last ten
years, a number of collaborations between the IAC group and outstanding
MR laboratories have focused on the development of models and methods for
MR data processing. The activities include enhancing the resolution of
MR spectra used for tumour identification, the quantification of MR signals
from selected metabolites in brain pathologies, as well as MR image quality
improvement, MR image reconstruction, dynamic MR imaging for human brain
and lung pathologies, and functional MR imaging for the characterization
of the areas of brain functions. Models and methods have been developed
within either a classical or a Bayesian statistical framework, depending
on the specific problem.
The Magnetic Resonance technique enables us to acquire digital data
on the chemical and physical structure of a large variety of systems, including
living systems. MR is increasingly used for both routine investigations
and research purposes due to its very low degree of invasiveness. The analysis
of MR spectroscopy data makes it possible to identify and quantify the
chemical compounds in a given sample. MR image data processing provides
tomographic slices as well as three-dimensional pictures describing the
interior of physical objects.
Standard methods are available for MR data processing. However, such
methods generally present serious drawbacks, eg they often have limited
power as they do not always take into account information on both the physics
of the MR data acquisition and the quantities to be estimated. Moreover,
they are based on local optimization procedures. The aim of our current
research is thus to provide more powerful methods that overcome these limitations.
From the physics of the MR data acquisition it is usually possible to
derive a statistical model (the likelihood model) for the MR data, given
the quantities to be estimated. However, the estimation of the quantities
of interest very often involves the solution of an ill-posed problem, eg
the solution of a Fredholm integral equation, the estimation of parameters
of non-linear models.
In order to solve these problems, we have either developed robust methods
based on highly sophisticated mathematical procedures, and/or we have incorporated
into a Bayesian model some additional prior information about the quantities
to be estimated. The a priori models we developed within the Bayesian framework,
belong to the Markov random field model class. This choice has the advantage
of reducing the computational complexity of the algorithms involved in
the estimation. Special attention has been devoted to the problem of selecting
the so-called hyper-parameters of the Bayesian model. In fact only by solving
this problem is it possible to exploit the potential of the Bayesian approach
for image and signal processing.
The methods we have developed include an original approach for solving
super-resolution problems that permits the identification of unknown chemical
compounds even when the noise affecting the data is moderately large. This
method is based on simple statistical principles coupled with sophisticated
complex analysis techniques. An example of application of this method is
the identification and quantification of the beta-ATP region of in vivo
31P MR spectrum of human breast tumour implanted in mice, as shown in Figure
1. The dashed curve represents the Fourier spectrum, where the expected
triplet is hardly recognizable. The solid curves are the lorentian lines
of the triplet, obtained by estimating the spectral parameters from the
MR signal.
Figure 1: Beta-ATP region of
'in vivo' 31P MR spectrum of human breast tumour implanted in mice.
Another method estimates blood perfusion parameters from a temporal
series of dynamic MR images acquired following the injection of a contrast
agent. The method is based on local non-linear spatial filtering and on
non-parametric linear regression. The method is simple and fast. Furthermore,
it provides sufficiently accurate estimates of a few quantities, which
are easily interpreted by the medical practitioner. An example of results
using this method is shown in Figure 2. On the left of this figure, an
MR image from a dynamic series of 30 images of the head of an ischaemic
rat brain is shown. The oval region at the centre of the image is the brain
and regional ischaemia appears in its left part (in white). The image on
the right shows the result obtained by applying our method: the processed
map of the blood perfusion defect in the interior of brain is superimposed
upon the image on the left. The ischaemic region is better depicted in
the processed image, where the two sub-regions called core (in white) and
penumbra (in grey) also appear.
Figure 2: Dynamic MR imaging for diagnosis of ischaemia in the brain
of a rat.
This research has benefited from cooperations between the IAC group
and the Physics Laboratory of the Italian National Institute of Health
(Rome), the Department of Chemical Physics of the Weizmann Institute of
Science, Rehovot (Israel), the Istituto di Strutturistica Chimica of CNR
(Rome), the group of Statistics of the University of Tromsoe (Norway),
and the MR-Centre in Trondheim (Norway).
Please contact:
Giovanni Sebastiani - IAC-CNR
Tel: +39 6 88470236
E-mail: sebast@iac.rm.cnr.it
