Tissue-specific compartmental analysis for dynamic contrast-enhanced MR imaging of complex tumors

Abstract

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) provides a noninvasive method for evaluating tumor vasculature patterns based on contrast accumulation and washout. However, due to limited imaging resolution and tumor tissue heterogeneity, tracer concentrations at many pixels often represent a mixture of more than one distinct compartment. This pixel-wise partial volume effect (PVE) would have profound impact on the accuracy of pharmacokinetics studies using existing compartmental modeling (CM) methods. We, therefore, propose a convex analysis of mixtures (CAM) algorithm to explicitly mitigate PVE by expressing the kinetics in each pixel as a nonnegative combination of underlying compartments and subsequently identifying pure volume pixels at the corners of the clustered pixel time series scatter plot simplex. The algorithm is supported theoretically by a well-grounded mathematical framework and practically by plug-in noise filtering and normalization preprocessing. We demonstrate the principle and feasibility of the CAM-CM approach on realistic synthetic data involving two functional tissue compartments, and compare the accuracy of parameter estimates obtained with and without PVE elimination using CAM or other relevant techniques. Experimental results show that CAM-CM achieves a significant improvement in the accuracy of kinetic parameter estimation. We apply the algorithm to real DCE-MRI breast cancer data and observe improved pharmacokinetic parameter estimation, separating tumor tissue into regions with differential tracer kinetics on a pixel-by-pixel basis and revealing biologically plausible tumor tissue heterogeneity patterns. This method combines the advantages of multivariate clustering, convex geometry analysis, and compartmental modeling approaches. The open-source MATLAB software of CAM-CM is publicly available from the Web.

Fig. 1.

Roadmap of the CAM-CM method (illustrated on the special case of J = 3). A hybrid multivariate clustering first groups the normalized pixel time courses into “local” clusters that correspond to either pure-volume or partial-volume pixels. The CAM-CM then separates the pure-volume clusters from partial-volume clusters by detecting the corners of the clustered convex hull. The identified pure-volume cluster centers and their associated pixels are further used to estimate the tissue-specific kinetic parameters within the tumor site by compartment modeling globally and locally.

Fig. 2.

Schematic diagram of parallel-mode J-tissue compartment model.

Fig. 3.

The spatial distributions of the compartments and TCs associated with the compartmental kinetic parameters used in the realistic DCE-MRI simulations. The nontumor background is denoted by “carpet texture” and the compartment pure-volume distributions are denoted by three partially-overlapped gray regions. The boundaries of the overlapping compartment pure-volume regions are also illustrated in “boundary map.”

Fig. 4.

Local volume transfer constants maps estimated by CAM-CM and IML-CM.

Fig. 5.

Model selection by MDL on different simulation data sets. MDL consistently indicates J = 3 as the optimum model order that is also consistent with the ground truth. (a) Scenario 1.SNR = 10dB (b) Scenario 2 SNR = 10 dB.(c) Scenario 3 SNR = 10 dB. (d) Scenario 4 SNR = 10 dB.

Fig. 6.

Model selection by MDL on real DCE-MRI data sets. MDL consistently suggests J = 3 as the optimum model order. (a) Typical case. (b) Longitudinal 1. (c) Longitudinal 2. (d) Longitudinal 3.

Fig. 7.

The experimental results of CAM-CM on a typical breast cancer DCE-MRI data. The estimated kinetic parameters are $K_f^{\text{trans}}=0.382/\text{min}$, $K_s^{\text{trans}}=0.017/\text{min}$, k_ep,f = 3.063/min, k_ep,s = 0.293/min. (a) The identified convex hull of clustered pixel TCs (Blue dots: normalized pixel TCs; Red circles: cluster centers; Blue lines: cluster memberships). (b) Normalized overall TC calculated from the entire tumor ROI. (c) Normalized compartment TCs estimated by CAM-CM (the discrete curves show the normalized TCs directly estimated via CAM; while the smooth curves show the normalized TCs which are fitted by the kinetic parameters estimated via CAM-CM). (d) Local volume transfer constant maps estimated by CAM-CM.

Fig. 8.

The results of CAM-CM on DCE-MRI data set 1 of the breast cancer longitudinal study. (a) Identified convex hull of clustered pixel TCs (Blue dots: normalized pixel TCs; Red circles: cluster centers; Blue lines: cluster memberships). (b) Normalized overall TC calculated from the entire tumor ROI. (c) Normalized compartment TCs estimated by CAM-CM. (d) Local volume transfer constant maps estimated by CAM-CM.

Fig. 9.

The results of CAM-CM on DCE-MRI data set 2 of the breast cancer longitudinal study.

Fig. 10.

The results of CAM-CM on DCE-MRI data set 3 of the breast cancer longitudinal study.