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A Convolutional Neural Network for Accelerating the Computation of the Extended Tofts Model in DCE-MRI

Ke Fang¹, Zejun Wang^2,3, Zhaoqing Li^2,3, Bao Wang⁴, Guangxu Han^2,3, Zhaowei Cheng¹, Zhihong Chen¹, Chuanjin Lan⁵, Yi Zhang⁶, Peng Zhao⁷, Xinyu Jin¹, Yingchao Liu⁸, and Ruiliang Bai^2,3
¹College of Information Science & Electronic Engineering, Zhejiang University, Hangzhou, China, ²Department of Physical Medicine and Rehabilitation of The Affiliated Sir Run Run Shaw Hospital AND Interdisciplinary Institute of Neuroscience and Technology, School of Medicine, Zhejiang University, Hangzhou, China, ³Key Laboratory of Biomedical Engineering of Ministry of Education, College of Biomedical Engineering and Instrument Science, Zhejiang University, Hangzhou, China, ⁴Department of Radiology, Qilu Hospital of Shandong University, Jinan, China, ⁵School of Medicine, Shandong University, Jinan, China, ⁶Shandong Medical Imaging Research Institute, Shandong University, Jinan, China, ⁷Department of Neurosurgery, Provincial Hospital Affiliated to Shandong First Medical University, Jinan, China, ⁸Provincial Hospital Affiliated to Shandong First Medical University, Jinan, China

Synopsis

We proposed a customized conventional neural network (CNN) to fasten the computation time of non-linear pharmacokinetic models in DCE-MRI. The results demonstrated that the CNN could shorten the computation time of extended Tofts model of whole-brain data to less than a minute without sacrificing the agreements with conventional non-linear least square (NLLS) fitting. This CNN could serve as an alternative to conventional NLLS fitting for fast assessment of pharmacokinetic parameters in clinical practice.

Introduction

Dynamic contrast-enhanced MRI (DCE-MRI) is a widely used method for the study, diagnosis, and treatment evaluation of many diseases in vivo.^1–3 The pharmacokinetic parameters can be estimated through a number of tracer kinetic (TK) models, of which the Extended Tofts (eTofts) model ^4,5 is one of the most widely used for analysis of DCE-MRI data ⁶. However, the fitting of eTofts models is non-linear model and usually performed using a nonlinear-least-squares (NLLS) approach, which involves a large number of iterative operations ⁷ and is usually computationally expensive.

Convolutional neural networks (CNNs) have been shown to be promising tools to predict quantitative parameters from MRI data with the ability to provide compact representation of complicated functions^8–10. With the availability of graphical processing units (GPUs), which is able to implement basic operations in CNN parallelly, the computing speed of CNN algorithms have been greatly improved¹¹. In this study, we propose a customized CNN to accelerating the estimation the pharmacokinetic parameters of the eTofts model from DCE-MRI data without sacrificing the agreement with NLLS.

Methods

DCE-MRI data and double flip angle T1 map acquired at 3 T scanner (Magnetom Skyra, Siemens Healthcare, Erlangen, Germany) of 24 patients was used, of which 13 patients with brain glioma were used for training (75%) and validation (25%), and 11 patients (3 glioma, 4 brain metastases and 4 lymphoma) were used for testing. The temporal resolution of the DCE-MRI data was 4.5 s and the voxel size was 0.9 × 0.9 × 1.5 mm3. The total acquisition time for DCE-MRI was approximately 9 min. Sequence details could be found in reference ¹².

The venous input function (VIF) of each subject was taken from a region of interest (ROI) in the sagittal sinus drawn manually by two experienced investigators in neuroradiology together. For each patient’s data, two multiple slices ROIs with one encompassing most of the tumor and the other from normal-appearing brain tissue having a similar volume as the tumor ROI were also chosen used as training and test data.

A CNN with both local pathway and global pathway modules was designed to directly estimate pharmacokinetic parameters, the volume transfer constant ($$$K^{trans}$$$), blood volume fraction ($$$v_p$$$ ) and volume fraction of extracellular extravascular space ($$$v_e$$$), of the eTofts model from DCE-MRI data of tumor and normal-appearing voxels (Figure 1). The CNN was trained on mixed dataset consisting of both synthetic and patient data. Synthesized data was generated using MRI and physiological parameters mimicking in vivo conditions. The CNN result and computation speed were compared with NLLS fitting and the generalization to brain metastases and lymphoma data were also evaluated.

Student’s t-test on mean absolute error (MAE), concordance correlation coeﬃcient (CCC), and normalized root mean square error (NRMSE) was used to evaluate the agreement of the results of NLLS and CNN. A two-sided p-value <0.05 was considered significant.

Results

The fitting results of CNN maintain a high degree of agreement with NLLS (Figure 2). In comparison with results obtained with NLLS fitting, CNN yields an average CCC of greater than 0.985 for the estimation of $$$K^{trans}$$$, greater than 0.965 for $$$v_p$$$, and greater than 0.94 for $$$v_e$$$.

The CNN accelerated computation speed approximately 2000 times compared to NLLS (Figure 3). For example, the proposed CNN could shorten the computation time for whole-brain DCE-MRI data (matrix size is 192×192, 80 slices, about 1.2 million voxels in this study) from 1.3 hours with conventional NLLS fitting method (parallel computation with 32 CPU) to less than one minute (about 40 seconds) with CNN using a regular GPU (single CPU).

Including global pathway modules in the CNN significantly (P<0.05) improved the agreement of the estimation results of all the three parameters $$$K^{trans}$$$ , $$$v_p$$$ and $$$v_e$$$, from the metrics of both MAE, CCC and NRMSE (Figure 4).

In the statistics for all brain metastases and lymphoma subjects, the parameters estimated by CNN and NLLS maintain a high degree of agreement (NRMSE<1.5% for $$$K^{trans}$$$ , $$$v_p$$$ and $$$v_e$$$) and show no significant difference (P = 0.27 and P = 0.21, respectively) from glioma with respect to MAE (Figure 5).

Discussion

The fast computation speed of CNN is achieved by two factors. At first, CNN avoids the time-consuming, iterative calculations used in NLLS. Secondly, similar to the previous work¹³, the CNN method can achieve faster computation speed with the support of GPU.

Our study also confirmed that the long-term features obtained from the global pathway in CNN significantly improved the agreement in the estimation of $$$v_e$$$ and the other two PK parameters. These long-term time-domain features, such as the influence of contrast agent backflow^14,15, are more easily captured by the global pathway. On the other hand, the pre-injection (of contrast agent) DCE-MRI signal itself and the relative signal changes rather than the absolute signal changes after contrast agent injection contain important information. Global pathway allows CNN to fully consider the initial state of the signal and the relative signal changes in comparison with pre-injection signal, in the process of extracting data features.

Conclusion

The proposed neural network to estimate eTofts parameters showed comparable result as conventional NLLS fitting while significantly reducing the computation time.

Acknowledgements

No acknowledgement found.

References

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6. Sourbron SP, Buckley DL. On the scope and interpretation of the Tofts models for DCE-MRI. Magn Reson Med. 2011;66(3):735-745. doi:10.1002/mrm.22861

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12. Bai R, Wang B, Jia Y, et al. Shutter-Speed DCE-MRI Analyses of Human Glioblastoma Multiforme (GBM) Data. Journal of Magnetic Resonance Imaging. n/a(n/a). doi:10.1002/jmri.27118

13. Hsu Y-HH, Huang Z, Ferl GZ, Ng CM. GPU-Accelerated Compartmental Modeling Analysis of DCE-MRI Data from Glioblastoma Patients Treated with Bevacizumab. Cercignani M, ed. PLoS ONE. 2015;10(3):e0118421. doi:10.1371/journal.pone.0118421

14. Hansen MB, Tietze A, Haack S, et al. Robust estimation of hemo-dynamic parameters in traditional DCE-MRI models. Schmid VJ, ed. PLoS ONE. 2019;14(1):e0209891. doi:10.1371/journal.pone.0209891

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Figures

Figure 1. The proposed CNN architecture for the estimation of pharmacokinetic parameters in the eTofts model. The input data are the 1D DCE-MRI time series data, $$$C_p$$$ (contrast agent concentration in the blood plasma) and $$$T_{10}$$$ ( $$$T_{1}$$$ before contrast agent injection) for each voxel. The number of ﬁlters and output nodes in the network are provided at the bottom of each layer. The outputs from the proposed CNN are the three independent eTofts parameters: $$$K^{trans}$$$, $$$v_p$$$ and $$$v_e$$$.

Figure 2. Example of the results from conventional eTofts model fitting using nonlinear-least-squares (NLLS) and CNN trained on mixed data in the testing dataset. (a) The contrast-enhanced slice of one glioma subject, where the tumor is outlined by solid red curves. (b) The predicted DCE-MRI time series signal using parameters obtained from conventional NLLS fitting (blue curve) and the CNN (red curve). (c) Pharmacokinetic parameter maps obtained from NLLS and the CNN, along with the absolute difference (error map) between the results from these two methods.

Figure 3. Comparison of the time cost for whole-brain DCE-MRI data (matrix size is 192×192, 80 slices, about 1.2 million voxels) using the conventional NLLS method and the proposed CNN method under different computation hardware conditions.

Figure 4. The benefits of including the global pathway in the network. The global pathway in CNN significantly improved the agreement in the estimation of volume transfer constant $$$K^{trans}$$$, blood plasma volume fraction $$$v_p$$$ and extracellular extravascular space $$$v_e$$$. * P < 0.05.

Figure 5. Examples of pharmacokinetic parameter maps on a brain metastases subject (top) and a lymphoma subject (bottom) obtained from the proposed CNN method and conventional NLLS fitting. The NRMSE between results of CNN and NLLS (for voxels shown in the orange rectangle) were also shown in white color.

Proc. Intl. Soc. Mag. Reson. Med. 29 (2021)

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