2. Super-resolution, Denoising, and Phase Offset Errors Removal in Processing 3-point Encoded 4D-Flow MRI Using Input Parametrized Physics Informed Neural Nets (IP-PINN)

This research Project endeavors reside at the nexus of cardiovascular fluid dynamics and the burgeoning field of scientific machine learning, with a particular emphasis on enhancing the fidelity of time-resolved phase-contrast magnetic resonance imaging (4D Flow MRI) using physics-informed neural networks (PINN). we have introduced an innovative deep learning paradigm known as the Input-Parametrized Physics-Informed Neural Network (IP-PINN). This methodological breakthrough allows for the nuanced parametrization of the PINN solution with respect to the input data, characterized predominantly by low-resolution spatio-temporal complex Cartesian velocity encoded PCMR acquired images. This  framework synergizes convolutional neural network (CNN) layers, underpinned by a ResNet architecture, with a feedforward neural network (Multilayer Perceptron). This hybrid model is engineered to proffer a continuous, physics-constrained solution space. The ingenuity of the network design is augmented by the integration of a bespoke data loss function, which enables the precursory training of the network with either empirical low-resolution image data or synthetic datasets contrived from computational fluid dynamics (CFD) simulations. This approach not only retains the intrinsic benefits of PINNs but also circumvents the onerous and computationally intensive training typically requisite for new dataset assimilation. Key breakthroughs of the IP-PINN include:

• A harmonious blend of CNN-derived super-resolution techniques with PINN’s hallmark continuous field representation, enabling the computation of exact spatiotemporal derivatives through automatic differentiation—without truncation errors.
• The introduction of novel data fidelity terms within our loss function addresses common challenges in 4D-Flow MRI, such as velocity aliasing and phase offset artifacts, obviating the need for high-resolution ground truth data during training.
• My methodology innovatively eliminates the necessity of reference scans traditionally required for velocity determination in 4D-Flow MRI, thus streamlining the process to employ solely velocity-encoded scans to reconstruct high-resolution velocity and relative pressure fields.
• We have rigorously validated our model against existing PINN-based algorithms, specifically referencing the work by Fathi et al. (2020). Our findings demonstrate not only a marked acceleration in computational performance but also a substantial leap in solution accuracy.
• A noteworthy application of our technique is its ability to generate high-resolution magnitude images from low-resolution velocity scans, significantly enhancing the precision of lumen boundary segmentation—an essential step in diagnostic imaging.

The following results requires the 1.5 minute of fine-tunning the neural network for the new input data. This can be compared to 18 minutes of training time for a pure PINN algorithm.

3D velocity predictions of blood flow in a middle cerebral artery (MCA) aneurysm

The following results requires the 1.5 minute of fine-tunning the neural network for 6 crops of new input data. This can be compared to 18 minutes of training time of a pure PINN algorithm for a single crop.

MCA aneurysm lumen boundary segmentation results

In summary, this research project ushers in a transformative approach to 4D-Flow MRI analysis, setting a new standard for accuracy and efficiency in the characterization of cardiovascular flows, and paving the way for broader applications in medical imaging.