Cerebrovascular super-resolution 4D Flow MRI - Sequential combination of resolution enhancement by deep learning and physics-informed image processing to non-invasively quantify intracranial velocity, flow, and relative pressure.

The development of cerebrovascular disease is tightly coupled to regional changes in intracranial flow and relative pressure. Image-based assessment using phase contrast magnetic resonance imaging has particular promise for non-invasive full-field mapping of cerebrovascular hemodynamics. However, estimations are complicated by the narrow and tortuous intracranial vasculature, with accurate image-based quantification directly dependent on sufficient spatial resolution. Further, extended scan times are required for high-resolution acquisitions, and most clinical acquisitions are performed at comparably low resolution (>1 mm) where biases have been observed with regard to the quantification of both flow and relative pressure. The aim of our study was to develop an approach for quantitative intracranial super-resolution 4D Flow MRI, with effective resolution enhancement achieved by a dedicated deep residual network, and with accurate quantification of functional relative pressures achieved by subsequent physics-informed image processing. To achieve this, our two-step approach was trained and validated in a patient-specific in-silico cohort, showing good accuracy in estimating velocity (relative error: 15.0 ± 0.1%, mean absolute error (MAE): 0.07 ± 0.06 m/s, and cosine similarity: 0.99 ± 0.06 at peak velocity) and flow (relative error: 6.6 ± 4.7%, root mean square error (RMSE): 0.56 mL/s at peak flow), and with the coupled physics-informed image analysis allowing for maintained recovery of functional relative pressure throughout the circle of Willis (relative error: 11.0 ± 7.3%, RMSE: 0.3 ± 0.2 mmHg). Furthermore, the quantitative super-resolution approach is applied to an in-vivo volunteer cohort, effectively generating intracranial flow images at <0.5 mm resolution and showing reduced low-resolution bias in relative pressure estimation. Our work thus presents a promising two-step approach to non-invasively quantify cerebrovascular hemodynamics, being applicable to dedicated clinical cohorts in the future.

A novel methodology for personalized simulations of ventricular hemodynamics from noninvasive imaging data.

Current state-of-the-art imaging techniques can provide quantitative information to characterize ventricular function within the limits of the spatiotemporal resolution achievable in a realistic acquisition time. These imaging data can be used to personalize computer models, which in turn can help treatment planning by quantifying biomarkers that cannot be directly imaged, such as flow energy, shear stress and pressure gradients. To date, computer models have typically relied on invasive pressure measurements to be made patient-specific. When these data are not available, the scope and validity of the models are limited. To address this problem, we propose a new methodology for modeling patient-specific hemodynamics based exclusively on noninvasive velocity and anatomical data from 3D+t echocardiography or Magnetic Resonance Imaging (MRI). Numerical simulations of the cardiac cycle are driven by the image-derived velocities prescribed at the model boundaries using a penalty method that recovers a physical solution by minimizing the energy imparted to the system. This numerical approach circumvents the mathematical challenges due to the poor conditioning that arises from the imposition of boundary conditions on velocity only. We demonstrate that through this technique we are able to reconstruct given flow fields using Dirichlet only conditions. We also perform a sensitivity analysis to investigate the accuracy of this approach for different images with varying spatiotemporal resolution. Finally, we examine the influence of noise on the computed result, showing robustness to unbiased noise with an average error in the simulated velocity approximately 7% for a typical voxel size of 2mm(3) and temporal resolution of 30ms. The methodology is eventually applied to a patient case to highlight the potential for a direct clinical translation.

Towards a fast and efficient approach for modelling the patient-specific ventricular haemodynamics.

Computer modelling of the heart has emerged over the past decade as a powerful technique to explore the cardiovascular pathophysiology and inform clinical diagnosis. The current state-of-the-art in biophysical modelling requires a wealth of, potentially invasive, clinical data for the parametrisation and validation of the models, a process that is still too long and complex to be compatible with the clinical decision-making time. Therefore, there remains a need for models that can be quickly customised to reconstruct physical processes difficult to measure directly in patients. In this paper, we propose a less resource-intensive approach to modelling, whereby computational fluid-dynamics (CFD) models are constrained exclusively by boundary motion derived from imaging data through a validated wall tracking algorithm. These models are generated and parametrised based solely on ultrasound data, whose acquisition is fast, inexpensive and routine in all patients. To maximise the time and computational efficiency, a semi-automated pipeline is embedded in an image processing workflow to personalise the models. Applying this approach to two patient cases, we demonstrate this tool can be directly used in the clinic to interpret and complement the available clinical data by providing a quantitative indication of clinical markers that cannot be easily derived from imaging, such as pressure gradients and the flow energy.

A computationally efficient framework for the simulation of cardiac perfusion using a multi-compartment Darcy porous-media flow model.

We present a method to efficiently simulate coronary perfusion in subject-specific models of the heart within clinically relevant time frames. Perfusion is modelled as a Darcy porous-media flow, where the permeability tensor is derived from homogenization of an explicit anatomical representation of the vasculature. To account for the disparity in length scales present in the vascular network, in this study, this approach is further refined through the implementation of a multi-compartment medium where each compartment encapsulates the spatial scales in a certain range by using an effective permeability tensor. Neighbouring compartments then communicate through distributed sources and sinks, acting as volume fluxes. Although elegant from a modelling perspective, the full multi-compartment Darcy system is computationally expensive to solve. We therefore enhance computational efficiency of this model by reducing the N-compartment system of Darcy equations to N pressure equations, and N subsequent projection problems to recover the Darcy velocity. The resulting 'reduced' Darcy formulation leads to a dramatic reduction in algebraic-system size and is therefore computationally cheaper to solve than the full multi-compartment Darcy system. A comparison of the reduced and the full formulation in terms of solution time and memory usage clearly highlights the superior performance of the reduced formulation. Moreover, the implementation of flux and, specifically, impermeable boundary conditions on arbitrarily curved boundaries such as epicardium and endocardium is straightforward in contrast to the full Darcy formulation. Finally, to demonstrate the applicability of our methodology to a personalized model and its solvability in clinically relevant time frames, we simulate perfusion in a subject-specific model of the left ventricle.

Patient specific fluid-structure ventricular modelling for integrated cardiac care.

Cardiac diseases represent one of the primary causes of mortality and result in a substantial decrease in quality of life. Optimal surgical planning and long-term treatment are crucial for a successful and cost-effective patient care. Recently developed state-of-the-art imaging techniques supply a wealth of detailed data to support diagnosis. This provides the foundations for a novel approach to clinical planning based on personalisation, which can lead to more tailored treatment plans when compared to strategies based on standard population metrics. The goal of this study is to develop and apply a methodology for creating personalised ventricular models of blood and tissue mechanics to assess patient-specific metrics. Fluid-structure interaction simulations are performed to analyse the diastolic function in hypoplastic left heart patients, who underwent the first stage of a three-step surgical palliation and whose condition must be accurately evaluated to plan further intervention. The kinetic energy changes generated by the blood propagation in early diastole are found to reflect the intraventricular pressure gradient, giving indications on the filling efficiency. This suggests good agreement between the 3D model and the Euler equation, which provides a simplified relationship between pressure and kinetic energy and could, therefore, be applied in the clinical context.

A novel porous mechanical framework for modelling the interaction between coronary perfusion and myocardial mechanics.

The strong coupling between the flow in coronary vessels and the mechanical deformation of the myocardial tissue is a central feature of cardiac physiology and must therefore be accounted for by models of coronary perfusion. Currently available geometrically explicit vascular models fail to capture this interaction satisfactorily, are numerically intractable for whole organ simulations, and are difficult to parameterise in human contexts. To address these issues, in this study, a finite element formulation of an incompressible, poroelastic model of myocardial perfusion is presented. Using high-resolution ex vivo imaging data of the coronary tree, the permeability tensors of the porous medium were mapped onto a mesh of the corresponding left ventricular geometry. The resultant tensor field characterises not only the distinct perfusion regions that are observed in experimental data, but also the wide range of vascular length scales present in the coronary tree, through a multi-compartment porous model. Finite deformation mechanics are solved using a macroscopic constitutive law that defines the coupling between the fluid and solid phases of the porous medium. Results are presented for the perfusion of the left ventricle under passive inflation that show wall-stiffening associated with perfusion, and that show the significance of a non-hierarchical multi-compartment model within a particular perfusion territory.

Coupling multi-physics models to cardiac mechanics.

We outline and review the mathematical framework for representing mechanical deformation and contraction of the cardiac ventricles, and how this behaviour integrates with other processes crucial for understanding and modelling heart function. Building on general conservation principles of space, mass and momentum, we introduce an arbitrary Eulerian-Lagrangian framework governing the behaviour of both fluid and solid components. Exploiting the natural alignment of cardiac mechanical properties with the tissue microstructure, finite deformation measures and myocardial constitutive relations are referred to embedded structural axes. Coupling approaches for solving this large deformation mechanics framework with three dimensional fluid flow, coronary hemodynamics and electrical activation are described. We also discuss the potential of cardiac mechanics modelling for clinical applications.