Standard compartment models for the analysis of Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) are based on one or two compartments, parts of the tissue, which exchange the contrast agent. However, these models are often to simplistic, especially when analysing DCE-MR images of cancerous tissue. On the other hand, models with more than two compartments suffer from redundancy issues, that is, the model parameters cannot be identified. Julia Sommer has worked on ways to make more-compartment-models identifiable by using spatial regularization methods. In two recent publications, she also shows how the number of compartments can be found.

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Spatial two-tissue compartment model for dynamic contrast-enhanced magnetic resonance imaging. By Julia Sommer, and Volker J Schmid. *Journal of the Royal Statistical Society: Series C. (LINK) *

In the quantitative analysis of dynamic contrast-enhanced magnetic resonance imaging compartment models allow the uptake of contrast medium to be described with biologically meaningful kinetic parameters. As simple models often fail to describe adequately the observed uptake behaviour, more complex compartment models have been proposed. However, the non-linear regression problem arising from more complex compartment models often suffers from parameter redundancy. We incorporate spatial smoothness on the kinetic parameters of a two-tissue compartment model by imposing Gaussian Markov random-field priors on them. We analyse to what extent this spatial regularization helps to avoid parameter redundancy and to obtain stable parameter point estimates per voxel. Choosing a full Bayesian approach, we obtain posteriors and point estimates by running Markov chain Monte Carlo simulations. The approach proposed is evaluated for simulated concentration time curves as well as for in vivo data from a breast cancer study.

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Spatially regularized estimation for the analysis of dynamic contrast-enhanced magnetic resonance imaging data. By Julia Sommer, Jan Gertheiss, and Volker J Schmid. Statistics in Medicine. (LINK)

Competing compartment models of different complexities have been used for the quantitative analysis of dynamic contrast-enhanced magnetic resonance imaging data. We present a spatial elastic net approach that allows to estimate the number of compartments for each voxel such that the model complexity is not fixed *a priori*. A multi-compartment approach is considered, which is translated into a restricted least square model selection problem. This is done by using a set of basis functions for a given set of candidate rate constants. The form of the basis functions is derived from a kinetic model and thus describes the contribution of a specific compartment. Using a spatial elastic net estimator, we chose a sparse set of basis functions per voxel, and hence, rate constants of compartments. The spatial penalty takes into account the voxel structure of an image and performs better than a penalty treating voxels independently. The proposed estimation method is evaluated for simulated images and applied to an *in vivo* dataset.