Session U01: Focus Session: The Fluid Dynamics of Medical Imaging II

Physics-based enhancement of flow biomarkers quantification from 4D flow imaging

Four-dimensional magnetic resonance imaging ("4D flow") holds great promise towards the development of actionable flow-related biomarkers of disease and their implementation into clinical practice. Nonetheless, many of the flow metrics that have so far demonstrated correlation with pathophysiology have also shown severe sensitivity to the coarse 4D flow spatial/temporal resolution, and cannot be reliably estimated. In this work, we leverage the analogy between 4D flow imaging and unresolved computations of multi-scale flows to: i) propose a mathematical framework for the description of the evolution equations of the measured velocity fields, and ii) exploit this framework to augment the reconstruction of 4D flow velocity fields via physics-inspired modeling paradigms. Particularly, we focus on enhancing the quantification of two well-established flow metrics: the viscous dissipation rate (aka viscous energy losses), and the wall shear stress. The novel concepts are qualitatively and quantitatively demonstrated in the context of right-heart flow dynamics, and validated against synthetic datasets generated using computational fluid dynamics. The impact of the uncertainties related to the proposed methodology is also briefly discussed.   

Input parametrized physics-informed neural networks for super-resolution of hemodynamic flow images

Physics-informed neural networks (PINNs) have successfully been used for super-resolution of low resolution, artifact prone, and noisy blood flow images. PINNs do not require the labeled data sets (ground truth) for training. Furthermore, automatic differentiation (AD) enables accurate calculation of velocity and pressure gradients. However, the main drawback of PINNs is the lack of its ability to institute any kind of transfer learning. Consequently, PINNs take significant amount of time for processing new data sets. In this talk we present a scheme to parametrize the PINN solution with respect to the input data. Wavelet transform of the input followed by selection of k coefficients is used to reduce the input data cube to a latent parameter vector. The latent parameter vector is then appended to the spatio-temporal coordinate input of a fully connected network. The common loss function imposes data fidelity with the input data set as well as flow physics through regularization. Synthetic data from computational fluid dynamics (CFD) simulations as well as actual image data can be used to pre-train the network. The proposed scheme retains useful properties of PINNs, namely, computation of pressure and velocity gradients through AD and eliminates the need for expensive ab-initio training required for new data sets.

    

Use of 4D Murine Ultrasound to Estimate External Tissue Support Parameters from Fluid-Structure Interaction Models of the Murine Thoracic Aortae

Modeling of Fluid-structure interactions (FSIs) between the deformable arterial wall and blood ow is necessary to obtain physiologically realistic computational models of cardiovascular systems. However, lack of information on the nature of contact between the outer vessel wall and surrounding tissue presents challenges in prescribing appropriate structural boundary conditions. Imaging techniques used to visualize wall deformation in vivo may be useful for estimating simulation parameters that capture the effects of both vascular composition and surrounding tissue support on the vessel wall displacement. Here, we present a method to calibrate external tissue support parameters in FSI simulations against four-dimensional ultrasound (4DUS) of the murine thoracic aortae. We collected ultrasound, blood pressure, and histological data from several mice infused with angiotensin II (n = 4) and created a representative model of healthy and diseased (at 28 days post-angiotensin II infusion) murine aortae. We ran pulsatile FSI simulations after accounting for increased arterial wall stiffness with varying levels of tissue support, which demonstrated non-trivial variation in not only structural quantities, such as vessel wall deformation, but also hemodynamic quantities, such as wall shear stress across simulations. Furthermore, we compared simulation results with in vivo 4DUS imaging data and observed that the optimum range of the tissue support spring parameter was identical for both healthy and diseased states. This indicated that the same tissue support parameter estimates could be used for modeling the healthy and diseased states of the vessel, provided that changes in arterial wall stiffness had been considered. We anticipate this technique and the tissue support estimates reported herein will help inform computational models of blood ow and vasculature that incorporate the influence of external tissue.   

Physics-enhanced velocimetry (PEV) for joint reconstruction and segmentation of noisy velocity images

We formulate and solve a generalized inverse Navier–Stokes boundary value problem for velocity field reconstruction and simultaneous boundary segmentation of noisy flow velocity images. We use a Bayesian framework that combines CFD, Gaussian processes, adjoint methods, and shape optimization in a unified and rigorous manner. With this framework, we find the velocity field and flow boundaries (i.e. the digital twin) that are most likely to have produced a given noisy image. We also calculate the posterior covariances of the unknown parameters and thereby deduce the uncertainty in the reconstructed flow. First, we verify this method on synthetic noisy images of 2-D flows. Then we apply it to experimental phase contrast magnetic resonance (PC-MRI) images of an axisymmetric flow at low (≃6) and high (>30) SNRs. We show that this method successfully reconstructs and segments the low SNR images, producing noiseless velocity fields that match the high SNR images, despite using 27 times less data. This framework also provides additional flow information, such as the pressure field and wall shear stress, accurately and with known error bounds. We demonstrate this on a synthetic 2-D representation of the flow through an aortic aneurysm to show its relevance to medical imaging.   

Physics-Informed Compressed Sensing (PICS) for joint reconstruction and segmentation of sparse PC-MRI signals: a digital-twin approach

Compressed sensing (CS) methods perform well at magnitude reconstruction, but accurate velocity (phase difference) reconstruction remains a challenge. We address this by extending the standard notion of sparsity used in CS methods to a more general notion of a structure, which is dictated by the Navier–Stokes (N-S) problem (physics-informed compressed sensing, PICS). We formulate PICS in a Bayesian framework, and use an inverse N-S problem to jointly reconstruct and segment the most likely velocity field, and at the same time infer hidden quantities such as the hydrodynamic pressure and the wall shear stress. We create an algorithm that solves this inverse problem, and test it for noisy/sparse k-space signals of the flow through a converging nozzle. We find that the method is capable of reconstructing/segmenting the velocity fields from sparsely-sampled, low signal-to-noise ratio (SNR) signals, and that the reconstructed velocity field compares well with that derived from fully-sampled high SNR signals of the same flow. Unlike CS methods, which only provide the reconstructed magnitude and velocity images, PICS learns the most likely digital twin of the measured flow. It can therefore be used to model new flow conditions, enabling patient-specific cardiovascular modelling.   

Preferential Flow Into Liver Tumors Based On Multimodal Image Analysis For Pre-treatment Planning Of Radioembolization Therapy

Transarterial radioembolization (TARE) is a key treatment for hepatic malignancies where radioactive particles are delivered intra-arterially to a tumor. Hepatic blood supply comes from a combination of the hepatic portal vein and the hepatic artery. Through angiogenesis, pathologic blood flow into liver tumors is increased in the tumor-feeding arteries, leading to an arterial flow shunting effect. Procedures like TARE rely on this preferential flow to deliver drug to the tumor. Thus, treatment accuracy can be improved with better characterization of this preferential arterial flow into the tumor. Here, we develop a methodology to estimate preferential flow into the tumor based on direct analysis of standard-of-care multi-modal imaging for TARE pre-treatment planning for liver tumors. A combination of CT Angiography, Cone-beam CT, and Digital Subtraction Angiography (DSA) images are used. Tumor location and tumor-feeding vessels are co-located across the three, following which an automatic registration and postprocessing of the identified region of interest in the DSA sequence is used to identify preferential flow ratios. We will end with demonstration of this methodology on sample patient cases, and discuss integration with high-resolution CFD models for hepatic tumor flow.   

Imaging and Enhancing Cerebrospinal Fluid Flow with In silico, In vitro and In vivo Studies

The roles of cerebrospinal fluid (CSF) are diverse and include cushioning the brain, regulating intracranial pressure, and clearing metabolic waste. Disruptions in CSF flow contribute to pathologies ranging from hydrocephalus to Alzheimer’s disease. Here, we study CSF flow using in silico computational fluid dynamic (CFD) based models, in vitro 4D Flow MRI of 3D printed models, and in vivo 4D Flow MRI in healthy individuals. Study of CSF flow using 4D Flow MRI has been limited by low spatiotemporal resolution and velocity-to-noise ratios. We examine the feasibility of physics-guided neural networks (PGNN) in super-resolving and denoising 4D Flow MRI within the cerebral ventricles. We show PGNNs can reconstruct dominant flow structures such as counter-rotating vortices in the 3rd ventricle from CFD based synthetic 4D Flow MRI. By incorporating divergence-based regularization in our loss function, the RMSE of near-wall velocities was reduced by 15%. We assess reconstruction accuracy by imaging 1-to-1 and scaled 2-to-1 phantoms while conserving voxel size and matching Reynolds and Womersley numbers in the larger phantom. Using PGNN may enable increased use of 4D Flow MRI for analysis of CSF flow dynamics in cerebroventricular and neurodegenerative disorders.   

Non-Invasive Assessment of the Lower Urinary Tract – MRI Urodynamics

Lower urinary track symptoms (LUTS) affect many older adults. Multi-channel urodynamics provides information about bladder pressure and urinary flow but offer little insight into changes in bladder anatomy and detrusor muscle function. Use of non-invasive methods for the study of lower urinary tract anatomy and function has been limited. Image based patient specific computational models have been extensively used for cardiovascular evaluation and personalized treatment planning. The objective of this study was to implement a magnetic resonance imaging (MRI) urodynamics method, as well as a patient specific MRI-based computational fluid dynamics (CFD) simulation of bladder voiding.

Three men with known LUTS (ages 73, 71, and 54) and three control subjects (ages 66, 42, and 44) were recruited under an IRB approved protocol. MRI was performed on a clinical 3T scanner using a high-density flexible surface coil array. A dynamic acquisition was performed using 3D Differential Subsampling with Cartesian Ordering (DISCO) with a temporal resolution of 3.7 seconds. 15 minutes prior to the MRI scans, 1/3 of a single weight-based dose (0.1 mmol/kg) of gadolinium-based contrast was hand injected intravenously allowing the visualization of bladder and urethral deformation and general LUT biomechanics. Images were imported into MIMICS (Materialise, Leuven, Belgium), where bladder facia and mucosa, and urethral mucosa are segmented to obtain 3D renderings. Three critical points during the voiding event were determined from the 3D segmentations, pre-void, maximum flow rate, and post-void phases.

A methodology to evaluate and characterize biomechanics of the bladder and uretrha during voiding in human subjects was successfully implemented. This MRI based techinique is an invaluable imaging modality that can be used to characterize anatomical and functional information of the LUT throughout the voiding cycle in a safe, accurate, and reproducible way   

Bayesian Segmentation of 4D Flow MRI Data Based on Flow Physics

4D flow MRI provides time-resolved, 3-directional measurements of cardiovascular flow in vivo. Improving the accuracy and repeatability of 4D flow data segmentation is critical for reliable assessment of hemodynamic metrics associated with cardiovascular disease, e.g., wall shear stress. We propose a Bayesian vessel segmentation algorithm that generates time-resolved volumetric masks of vessels by assessing the probability of fluid flow in each voxel and time frame. The flow likelihood is assessed using the normalized divergence, defined as the velocity divergence non-dimensionalized using the mean speed and the voxel size. The Bayesian vessel segmentation algorithm’s performance was demonstrated on in vivo 4D flow MRI measurements in the aorta of three patients. Manual segmentation is used as the benchmark for evaluating the performance of the proposed Bayesian vessel segmentation method. We quantify the performance of the vessel segmentation algorithm using the sensitivity metric computed as the ratio of true positives to the total number of manually segmented voxels. The sensitivity values ranged from 95.6% to ­­99.9% across all patients, with a root mean square of ­­98.4%. Efforts are ongoing to apply the Bayesian segmentation algorithm to different vascular territories.

    

Multitasks convolutional networks for medical image segmentation and regression.

The analysis of medical images consists of a number of tasks, some of which have significant mutual interaction. For example, predicting relative in-vivo pressures from velocity field measurements (we refer to this tasks as pressure prediction or simply regression) requires a preliminary characterization of the fluid domain through segmentation. In turn, image segmentation quality can be improved based on flow features, such as spatial velocity gradients and acceleration that can be captured by trainable convolution kernels. Therefore, instead of treating these two tasks independently, we investigate the accuracy of a number of multitask architectures designed to promote the exchange of information between the segmentation and regression tasks. We train these networks using realistic velocity fields, with a random field noise model resulting from the non linear reconstruction of undersampled single-coil k-space acquisitions. Finally, we consider various forms of physics-based regularization designed for convolutional network architectures.