Accelerated brain DCE-MRI using Contrast Agent Kinetic Models as Temporal Constraints

Sajan Goud Lingala^{1}, Yi Guo^{1}, Yinghua Zhu^{1}, Naren Nallapareddy^{1}, R. Marc Lebel^{2}, Meng Law^{3}, and Krishna Nayak^{1}

** Construction of temporal dictionary:** As depicted in Fig.1,
we simulate
concentration vs. time profiles for a broad range of physiological kinetic parameters
(K

**
Noise sensitivity analysis: ** We analyzed the
statistics of kinetic parameter estimation from 100 realizations of
concentration profiles corrupted by white Gaussian noise (zero mean,
standard deviation=0.001). From Fig.2, note that as k is
increased the error statistics in estimating the kinetic parameters from noisy
data converge towards error statistics of kinetic parameter mapping with the
e-Tofts model. For low values of k ≤ 2,
we observed bias, and reduced variance, and for high values of k > 10 (not shown), we observe
increased uncertainty. k=3 or 4 provided
the best compromise, closely mimicking e-Tofts modeling.

** Reconstruction: **We estimate concentration time profiles X

* *** Analysis:**
We perform retrospective under-sampling experiments on
fully-sampled DCE-MRI data sets (3T, Cartesian T1 weighted spoiled
gradient echo, FOV: 22x22x4.2cm

[1] RM Lebel, J Jones, JC Ferre, M Law, KS Nayak. Highly accelerated dynamic contrast enhanced imaging. Magnetic Resonance in Medicine. 71(2):635-644. February 2014.

[2] H. Wang, Y. Miao, K. Zhou, Y. Yu, S. Bao, Q. He, Y. Dai, Feasibility of high temporal resolution breast DCE-MRI using compressed sensing theory, Med. Phys. 37(9), p. 4971, 2010.

[3] Y Guo, Y Zhu, SG Lingala, RM Lebel, KS Nayak. "Highly Accelerated Brain DCE MRI with Direct Estimation of Pharmacokinetic Parameter Maps." Proc. ISMRM 23rd Scientific Sessions, Toronto, June 2015, p573.

[4] SG Lingala, Y Guo, Y Zhu, S Barnes, RM Lebel, KS Nayak. "Accelerated DCE MRI Using Constrained Reconstruction Based On Pharmaco-kinetic Model Dictionaries." Proc. ISMRM 23rd Scientific Sessions, Toronto, June 2015, p196

[5] Parker et al, " Experimentally-Derived Functional Form for a Population-Averaged High-Temporal-Resolution Arterial Input Function for Dynamic Contrast-Enhanced MRI ". Magnetic Resonance in Medicine; 56: 993-1000.

[6] S.P. Sourbron, DL Buckley. "On the scope and interpretation of the Tofts models for DCE-MRI" Magnetic Resonance in Medicine; 66, 735-45, 2011

[7] M. Aharon, et al, "k-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation" IEEE Trans. Sign Processing; 54 (11): 4311-4322, 2006,

[8] Y Zhu, Y Guo, RM Lebel, M Law, KS Nayak. "Randomized Golden Ratio Sampling for Highly Accelerated Dynamic Imaging." Proc. ISMRM 22nd Scientific Sessions, Milan, May 2014, p4365.

Figure 1: Construction of temporal basis functions
(in a dictionary) from a specified tracer kinetic model. Basis functions
derived from the e-Tofts model are considered, and are used as temporal
constraints to enable accelerated DCE-MRI.

Figure 2: Error statistics in estimating kinetic
parameters using the e-Tofts model from the (a) noisy, (b-e) 1 to 4 sparse
projected concentration time profiles. Estimating (top row) K^{trans} with v_{p} =0.04, K^{ep}=0.2 min^{-1}, (middle row) K^{ep} with v_{p}=0.2, K^{trans}=0.2 min^{-1}, (bottom row) v_{p} with K^{trans}=0.2 min^{-1}, K^{ep}=0.4 min^{-1} .

Fig.3: Comparison of parameter
maps from (left) fully-sampled reference, (middle) fully sampled with
dictionary modeling, (right) 20x undersampled with dictionary modeling. Note
the extremely low nMSE from the (x1)
dictionary approach. At x 20, the nMSE is increased, however the thin tumor margins
are depicted with good fidelity (see arrows).

Comparison of
K^{trans} maps from two glioblastoma tumors with different shape and heterogeneity. Similar to the previous figure, note the low nMSE with the (x1) dictionary approach, and good fidelity of mapping the tumor shape and heterogeneity at (x20); see arrows.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

0651