Boosting in Nonlinear Regression Models with an Application to DCE-MRI Data

Parametric maps of spatial two-tissue compartment model for prostate dynamic contrast enhanced MRI - comparison with the standard tofts model in the diagnosis of prostate cancer

The spatial two-tissue compartment model (2TCM) was used to analyze prostate dynamic contrast enhanced (DCE) MRI data and compared with the standard Tofts model. A total of 29 patients with biopsy-confirmed prostate cancer were included in this IRB-approved study. MRI data were acquired on a Philips Achieva 3T-TX scanner. After T2-weighted and diffusion-weighted imaging, DCE data using 3D T1-FFE mDIXON sequence were acquired pre- and post-contrast media injection (0.1 mmol/kg Multihance) for 60 dynamic scans with temporal resolution of 8.3 s/image. The 2TCM has one fast ([Formula: see text] and [Formula: see text]) and one slow ([Formula: see text] and [Formula: see text]) exchanging compartment, compared with the standard Tofts model parameters (Ktrans and kep). On average, prostate cancer had significantly higher values (p < 0.01) than normal prostate tissue for all calculated parameters. There was a strong correlation (r = 0.94, p < 0.001) between Ktrans and [Formula: see text] for cancer, but weak correlation (r = 0.28, p < 0.05) between kep and [Formula: see text]. Average root-mean-square error (RMSE) in fits from the 2TCM was significantly smaller (p < 0.001) than the RMSE in fits from the Tofts model. Receiver operating characteristic (ROC) analysis showed that fast [Formula: see text] had the highest area under the curve (AUC) than any other individual parameter. The combined four parameters from the 2TCM had a considerably higher AUC value than the combined two parameters from the Tofts model. The 2TCM is useful for quantitative analysis of prostate DCE-MRI data and provides new information in the diagnosis of prostate cancer.

Spatially regularized estimation of the tissue homogeneity model parameters in DCE-MRI using proximal minimization

PURPOSE

The Tofts and the extended Tofts models are the pharmacokinetic models commonly used in dynamic contrast-enhanced MRI (DCE-MRI) perfusion analysis, although they do not provide two important biological markers, namely, the plasma flow and the permeability-surface area product. Estimates of such markers are possible using advanced pharmacokinetic models describing the vascular distribution phase, such as the tissue homogeneity model. However, the disadvantage of the advanced models lies in biased and uncertain estimates, especially when the estimates are computed voxelwise. The goal of this work is to improve the reliability of the estimates by including information from neighboring voxels.

THEORY AND METHODS

Information from the neighboring voxels is incorporated in the estimation process through spatial regularization in the form of total variation. The spatial regularization is applied on five maps of perfusion parameters estimated using the tissue homogeneity model. Since the total variation is not differentiable, two proximal techniques of convex optimization are used to solve the problem numerically.

RESULTS

The proposed algorithm helps to reduce noise in the estimated perfusion-parameter maps together with improving accuracy of the estimates. These conclusions are proved using a numerical phantom. In addition, experiments on real data show improved spatial consistency and readability of perfusion maps without considerable lowering of the quality of fit.

CONCLUSION

The reliability of the DCE-MRI perfusion analysis using the tissue homogeneity model can be improved by employing spatial regularization. The proposed utilization of modern optimization techniques implies only slightly higher computational costs compared to the standard approach without spatial regularization.

An Update on Statistical Boosting in Biomedicine

Statistical boosting algorithms have triggered a lot of research during the last decade. They combine a powerful machine learning approach with classical statistical modelling, offering various practical advantages like automated variable selection and implicit regularization of effect estimates. They are extremely flexible, as the underlying base-learners (regression functions defining the type of effect for the explanatory variables) can be combined with any kind of loss function (target function to be optimized, defining the type of regression setting). In this review article, we highlight the most recent methodological developments on statistical boosting regarding variable selection, functional regression, and advanced time-to-event modelling. Additionally, we provide a short overview on relevant applications of statistical boosting in biomedicine.