20,347 research outputs found
Breast Cancer: Modelling and Detection
This paper reviews a number of the mathematical models used in cancer modelling and then chooses a specific cancer, breast carcinoma, to illustrate how the modelling can be used in aiding detection. We then discuss mathematical models that underpin mammographic image analysis, which complements models of tumour growth and facilitates diagnosis and treatment of cancer. Mammographic images are notoriously difficult to interpret, and we give an overview of the primary image enhancement technologies that have been introduced, before focusing on a more detailed description of some of our own recent work on the use of physics-based modelling in mammography. This theoretical approach to image analysis yields a wealth of information that could be incorporated into the mathematical models, and we conclude by describing how current mathematical models might be enhanced by use of this information, and how these models in turn will help to meet some of the major challenges in cancer detection
Improving Fiber Alignment in HARDI by Combining Contextual PDE Flow with Constrained Spherical Deconvolution
We propose two strategies to improve the quality of tractography results
computed from diffusion weighted magnetic resonance imaging (DW-MRI) data. Both
methods are based on the same PDE framework, defined in the coupled space of
positions and orientations, associated with a stochastic process describing the
enhancement of elongated structures while preserving crossing structures. In
the first method we use the enhancement PDE for contextual regularization of a
fiber orientation distribution (FOD) that is obtained on individual voxels from
high angular resolution diffusion imaging (HARDI) data via constrained
spherical deconvolution (CSD). Thereby we improve the FOD as input for
subsequent tractography. Secondly, we introduce the fiber to bundle coherence
(FBC), a measure for quantification of fiber alignment. The FBC is computed
from a tractography result using the same PDE framework and provides a
criterion for removing the spurious fibers. We validate the proposed
combination of CSD and enhancement on phantom data and on human data, acquired
with different scanning protocols. On the phantom data we find that PDE
enhancements improve both local metrics and global metrics of tractography
results, compared to CSD without enhancements. On the human data we show that
the enhancements allow for a better reconstruction of crossing fiber bundles
and they reduce the variability of the tractography output with respect to the
acquisition parameters. Finally, we show that both the enhancement of the FODs
and the use of the FBC measure on the tractography improve the stability with
respect to different stochastic realizations of probabilistic tractography.
This is shown in a clinical application: the reconstruction of the optic
radiation for epilepsy surgery planning
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