Introduction

Dynamic Susceptibility Contrast MRI (DSC-MRI) provides crucial insights into cerebrovascular hemodynamics, aiding in the diagnosis and monitoring of conditions like stroke, tumors^1,2, and neurodegenerative diseases^3,4 by quantifying cerebral blood flow and blood volume⁵. Nevertheless, achieving high spatial and temporal resolutions concurrently remains challenging, restricting the detailed capture of perfusion dynamics⁶.
To overcome these limitations, we propose a novel deep learning framework that represents data within a continuous spatio-temporal domain, integrating implicit neural representation (INR) in the spatial domain and neural ordinary differential equations⁷ (Neural ODE) in the temporal domain.

Method

Problem Statement
Given a set of \(N\) sequences in low-resolution DSC-MRI, represented as \(I_{LR}\in\mathbb{R}^{N\times H\times W}\), the corresponding high spatio-temporal resolution image is represented as \(I_{HR}\in\mathbb{R}^{N\prime\times H\prime\times W\prime}\). Our objective is to reconstruct a high spatio-temporal resolution DSC-MRI, represented as \({\hat{I}}_{HR}\in\mathbb{R}^{N\prime\times H\prime\times W\prime}\). To achieve this, we generate an intermediate high-resolution MR image at time \(t\), denoted as \({\hat{I}}_{{HR}_t}\), using the low-resolution frames \(I_{{LR}_0}\) and \(I_{{LR}_1}\) as inputs, where \(0\le t\le1\).

Deep learning-based algorithm
As depicted in Figure 1, our proposed architecture comprises three main stages: Oriented Latent Feature Embedding, Continuous Temporal Trajectory Calculation, and Implicit Spatial Representation. In the Oriented Latent Feature Embedding stage, initial latent feature and directional information are generated when low-resolution images corresponding to time 0 and 1 are provided as inputs. This initial feature is subsequently combined with the directional information as follows: \[{\widetilde{Z}}_{{LR}_{\widetilde{t}}}=\left[Z_{{LR}_{\widetilde{t}}};d\right],\] where, the semicolon ; denotes the concatenation operator, \(Z_{{LR}_{\widetilde{t}}}\in\mathbb{R}^{c\times h\times w}\) represents the initial latent feature of size \(h\times w\) with \(c\) channels at \(\widetilde{t}\), for \(\widetilde{t}\in{0,1}\), and \({\widetilde{Z}}_{{LR}_{\widetilde{t}}}\in\mathbb{R}^{c\prime\times h\times w} \)represents the oriented latent feature with \(c\prime\) channels obtained by concatenating the latent feature \(Z_{{LR}_{\widetilde{t}}}\) with an additional \(d\).
Within the trajectory of the Neural ODE, the oriented initial features are subsequently calculated at the time correspond target. The bi-directional Neural ODE is composed of a forward flow and a backward flow. This design is aimed at efficiently capturing representations from the features of the two input time points. Formally, the bi-directional Neural ODE is formulated as follows: \[Z_{{LR}_{0\rightarrow t}}=ODESolve\left(f_\theta,{\widetilde{Z}}_{{LR}_0},\left(0,t\right)\right)\simeq{\widetilde{Z}}_{{LR}_0}+\int_{0}^{t}{f_\theta\left({\widetilde{Z}}_{{LR}_\tau},\tau\right)d\tau},\] \[Z_{{LR}_{0\rightarrow t}}=ODESolve\left(f_\theta,{\widetilde{Z}}_{{LR}_0},\left(0,t\right)\right)\simeq{\widetilde{Z}}_{{LR}_0}+\int_{0}^{t}{f_\theta\left({\widetilde{Z}}_{{LR}_\tau},\tau\right)d\tau},\] where, \(Z_{{LR}_{0\rightarrow t}}\) and \(Z_{{LR}_{1\rightarrow t}}\) respectively represent latent features at time \(t\) obtained from both the forward and backward flows. The functions \(f_\theta\), \(f_\phi\) are convolutional neural networks used to approximate \(\frac{{\widetilde{Z}}_{{LR}_\tau}}{d\tau}\) within these flows. These features are then integrated through feature fusion, resulting in a new feature vector \(Z_{{LR}_t}\).
Finally, this feature vector is employed to decode the signal intensity correspond with the target MRI coordinates via Local Implicit Image Function⁸ (LIIF). \[{\hat{I}}_{{HR}_t}\left(x_q\right)=\sum_{\gamma\in00,01,10,11}\frac{S^\gamma}{S}\bullet g_\psi\left(z_{{LR}_t}^\gamma,x_q-v^\gamma,\left(\frac{1}{s},\frac{1}{s}\right)\right),\]
where implicit function \(g_\psi\) is parameterized as MLPs (with \(\psi\) as its parameter), \(v^\gamma\) is the coordinate of the nearest latent feature sub-spaces, surrounding \(x_q, z_{{LR}_t}^\gamma\) is the nearest latent feature at \(v^\gamma\) in \(Z_{{LR}_t}\), and \(S^\gamma\) is the opposite area of the rectangle between \(x_q\) and \(v^\gamma\). The weights are normalized by \(S=\sum_{\gamma} S^\gamma\).

Results

We utilized DSC-MRI data from 41 adult diffuse glioma patients, with 32 for training and 9 for validation. DSC-MRI was performed with specific parameters: TR/TE of 1500/30-40 ms, FA of 35-90°, a matrix of 256×256, and a section thickness of 5 mm. Each section produced 60 images at intervals. A gadobutrol bolus was injected at a dose of 0.1 mmol/kg of body weight and a rate of 4 mL/sec.
We used the original DSC-MRI as ground truth and created low-resolution DSC images through 2×2 spatial and 4× temporal under-sampling for input. Our approach was compared to VIDEOINR⁹, a method employing INR for spatio-temporal super-resolution, using NMSE, PSNR, and SSIM metrics.
Figures 2 depicts reconstructed DSC-MRI examples, showing input and ground truth images. The proposed method is better than VIDEOINR in restoring spatiotemporal information, as shown in the difference map. In Figure 3, the cerebral blood volume (CBV) and cerebral blood flow (CBF) maps from our method closely matches the ground truth. Table 1 summarizes the metric results.

Conclusions

In this study, we proposed the novel deep learning architecture for spatio-temporal super-resolution in DSC-MRI, thereby addressing challenges associated with the inherent trade-off problem. Reconstructed results have shown better performance than comparative methods in terms of NMSR, PSNR, and SSIM, and provided visual support to robustly approximated MR signals but also accurately computed perfusion parameters. The spatiotemporal super-resolution of DSC-MRI with deep learning allows for more accurate assessment of perfused tissue dynamics and tumor habitat, as well as more freedom in choosing acquisition weights between spatial and temporal during MRI acquisition.

Acknowledgements

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. RS-2023-00251022) (K.S.C); the Phase III (Postdoctoral fellowship) grant of the SPST (SNU-SNUH Physician Scientist Training) Program (K.S.C); the SNUH Research Fund (No. 04-2023-2050) (K.S.C.); the Bio & Medical Technology Development Program of National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2021M3E5D2A01022493) (I.H); and the Technology Innovation Program (20011878, Development of Diagnostic Medical Devices with Artificial Intelligence Based Image Analysis Technology) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea) (J.W.C).