Cagdas Ulas^{1}, Michael J. Thrippleton^{2}, Ian Marshall^{3}, Mike Davies^{4}, Paul A. Armitage^{5}, Stephen D. Makin^{2}, Joanna M. Wardlaw^{2}, and Bjoern H. Menze^{1}

We propose a novel alternative approach to estimate pharmacokinetic (PK) parameters of dynamic contrast enhanced (DCE)-MRI. Our approach leverages machine learning field and mainly targets to automatically learn temporal patterns of the voxel-wise concentration-time curves (CTCs) from a large amount of training samples in order to make accurate parameter estimations. We consider the estimation of parameters as a regression problem and specifically use Random Forest (RF) regression. We demonstrate its potential and utility to improve the conventional model-fitting based quantitative analysis of DCE-MRI especially in various noise conditions, and validate our method on clinical brain stroke datasets.

**Dataset:** We perform experiments on fully-sampled DCE-MRI datasets acquired from three patients with
clinically evident mild ischaemic stroke. DCE-MRI was
acquired using a 1.5T clinical scanner with a 3D T1W spoiled gradient echo
sequence (TR/TE = 8.24/3.1 ms, flip angle = 12$$$^{\circ}$$$, FOV = 24×24 cm,
matrix = 256×192, slice thickness = 4 mm, 42 slices, 73 sec temporal
resolution). The total acquisition time for DCE-MRI was approximately 24
minutes. Two pre-contrast acquisitions were carried out at flip angles of
2$$$^{\circ}$$$ and 12$$$^{\circ}$$$ to calculate longitudinal relaxation times
($$$T_{10}$$$).

**Preprocessing: **To generate noisy data, the noise-free (reference) data was corrupted by (1) undersampling the k-space, or (2) adding zero-mean Gaussian noise in the image space. Undersampling was retrospectively done in the $$$k_x-k_y$$$ plane using a randomized golden-angle sampling pattern^{8}. Dynamic image intensities $$$S(\mathrm{r},t)$$$ were converted to contrast agent concentration $$$C(\mathrm{r},t)$$$ by the steady-state spoiled gradient echo (SGPR) signal equation^{9}. The Parker's population-based arterial input function^{10} (AIF) was generated to obtain PK parameters using Patlak model^{3}.

**Random Forest Regression:** The parameter estimation task is formulated as a regression problem which takes the voxel-wise $$$C(\mathrm{r},t)$$$ as input and generates the PK parameters ($$$K^{\text{trans}},v_p$$$) as output. In this work, we adopt the random forest (RF) regression that has been shown to be effective in a wide range of classification and regression problems^{11,12}. We train a separate RF model to estimate each PK parameter. The overall regression task is defined as, $$\mathcal{M}(C(\mathrm{r}_i,t))=y_i;\quad i\in[1,N],\qquad(1)$$ where $$$y_i$$$ is the target parameter value for voxel $$$i$$$, $$$N$$$ is the total number of training samples (voxels), and $$$\mathcal{M}$$$ is the trained RF model. The target (reference) PK parameter values were estimated on noise-free data using Patlak model.

**Training-Testing:** Training and testing were carried out based on leave-one-patient-out cross-validation. The RF model $$$\mathcal{M}$$$ was trained with almost 340K voxels to learn important features from the input data to attain better parameter estimation. The pipeline of training-testing of RF model is provided in Figure 1.

**Evaluation:** The parameter estimates of our RF based method was compared with the estimations obtained from Patlak model in both noise-free and different noise conditions. The root-mean-square-error (RMSE) was used for quantitative evaluations of parameter estimation based on the following formula, $$RMSE=\sqrt{\frac{1}{N_i}\sum_{i=1}^{N_i} (y_i-f_i)^2},\qquad(2)$$ where $$$y_i$$$ is the target value, $$$f_i$$$ is the estimated value, and $$$N_i$$$ is the number of test samples.

We have demonstrated a new machine learning based approach to directly estimate PK parameters in DCE-MRI. This approach leverages large cohort of training data to learn significant characteristics and features of CTCs. Extensive experiments validated its efficacy in parameter estimation and robustness to various noise conditions. The proposed method is considerably faster than conventional model fitting. Training more than 300K samples takes around 5 minutes while testing takes only 1 second per slice. Future studies will aim at improving the estimation performance of RF model for high subsampling rates to potentially enable accelerated acquisitions of DCE-MRI, and testing our model on different tracer kinetic models such as extended Tofts model^{2 }and two-compartment exchange model^{13}.

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