Super-resolution is widely used in medical imaging to enhance low-quality data, reducing scan time and improving abnormality detection. Conventional super-resolution approaches typically rely on paired datasets of downsampled and original high resolution images, training models to reconstruct high resolution images from their artificially degraded counterparts. However, in real-world clinical settings, low resolution data often arise from acquisition mechanisms that differ significantly from simple downsampling. As a result, these inputs may lie outside the domain of the training data, leading to poor model generalization due to domain shift. To address this limitation, we propose a distributional deep learning framework that improves model robustness and domain generalization. We develop this approch for enhancing the resolution of 4D Flow MRI (4DF). This is a novel imaging modality that captures hemodynamic flow velocity and clinically relevant metrics such as vessel wall stress. These metrics are critical for assessing aneurysm rupture risk. Our model is initially trained on high resolution computational fluid dynamics (CFD) simulations and their downsampled counterparts. It is then fine-tuned on a small, harmonized dataset of paired 4D Flow MRI and CFD samples. We derive the theoretical properties of our distributional estimators and demonstrate that our framework significantly outperforms traditional deep learning approaches through real data applications. This highlights the effectiveness of distributional learning in addressing domain shift and improving super-resolution performance in clinically realistic scenarios.
Cerebral aneurysms, prevalent in approximately 6% of the general population, pose significant clinical challenges due to their potential for rupture, leading to high morbidity and mortality. Fortunately, most unruptured intracranial aneurysms (UIAs) rarely cause symptoms and do not require an invasive treatment that may itself causes severe cerebrovascular disorders. However, it is very difficult to predict which UIAs will rupture. Recent evaluations of the hemodynamic features of UIAs, using 4D Flow MRI (4DF), have shown promising results that suggest specific hemodynamic variables may have a great impact on aneurysm growth or rupture (Hope et al. 2010, Futami et al. 2016, Ferdian et al. 2020).
4DF offers direct in vivo blood flow measurements. It captures the actual hemodynamics during the scan, so it inherently includes the true physiological conditions, which makes 4DF highly valuable for patient-specific assessment. However, the quality of the 4DF data is constrained by measurement noise and imaging artifacts (Rutkowski et al. 2021). In addition, the spatial resolution of 4DF data is limited due to compromises made to ensure patient comfort during scanning. As a result, small-scale flow characteristics, especially those near vessel walls, are often overlooked (Callaghan & Grieve 2017), limiting the accuracy of estimating the critical metrics such as wall shear stress and the shear concentration index (Cebral et al. 2011). In contrast, computational fluid dynamics (CFD) has been the predominant methodology used to study hemodynamics in cerebral aneurysms. By applying the Navier-Stokes equations to patient-derived vascular geometry, CFD enables the simulation of high resolution, noise-free velocity fields that can be used to derive flow variables of interest (Karabasov & Goloviznin 2009). However, CFD is a simulation-based method that strongly depends on the accuracy of modeling assumptions and the initial conditions applied to the Navier-Stokes equations. Therefore, using CFD in clinical practice is less feasiable given that there is open lack of expertise to process the simulation and outcomes are highly sensitive to patient-specific conditions and require careful validation.
These differences highlight a strong motivation to leverage carefully modeled CFD data to enhance 4DF image resolution. A widely adopted approach involves training superresolution deep learning models on synthetic 4DF data derived from CFD simulations (Ferdian et al. 2020, 2023, Long et al. 2023, Shone et al. 2023). Beyond deep learning-based frameworks, Perez-Raya et al. (2020) leverage proper orthogonal decomposition (POD) to extract dominant flow features from patient-specific CFD data, subsequently employing generalized dynamic mode decomposition (DMD) for 4DF super-resolution. Additionally, flow data assimilation methods employing Kalman filtering (Habibi et al. 2021, Gaidzik et al. 2021) have also demonstrated efficiency in achieving 4DF super-resolution.
Due to challenges in data harmonization, paired 4DF and CFD datasets are limited.
Consequently, most super-resolution methods are developed exclusively using CFD data, assuming that downsampled CFD can approximate the distribution of 4DF data. Models trained on downsampled and original CFD pairs are then directly applied to upsample 4DF data. While these approaches have demonstrated promising results on synthetic 4DF datasets, their performance on real 4DF data remains largely underexplored. A critical yet often overlooked issue is the domain discrepancy between downsampled CFD and actual 4DF data. For example, downsampled CFD still follows the physical principles such as mass conservation, whereas real 4DF data often violates these constraints. Moreover, variations in acquisition protocols and physiological conditions further exacerbate the distributional gap between the two domains (Cherry et al. 2022, Black et al. 2023). This domain mismatch can significantly impair the performance of super-resolution models when using on clinical 4DF data (Shit et al. 2022).
In this paper, we propose a Distributional Super-Resolution (DSR) model aimed at enhancing the resolution of 4DF data. The DSR model demonstrates strong domain extrapolation capabilities, effectively handling scenarios where the input domain in the testing data deviates from that in the training data. Specifically, we employ a pre-additive model to capture the relationship between low-resolution (X) and high-resolution (Y) data through Building on the DSR model, we present the first comprehensive 4DF super-resolution framework validated on real intracranial 4DF data. We propose a local, patch-based super-resolution strategy specifically designed to enhance resolution on complex, irregular three-dimensional vascular geometries. This patch-based strategy ensures broad applicability across diverse structures. In addition, we implement a pre-training and fine-tuning paradigm that achieves superior performance even
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