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.

Mechanistic modelling of Virchows triad to assess thrombogenicity and stroke risk in atrial fibrillation patients

Background

Atrial fibrillation (AF) is responsible for almost one third of all strokes, with the left atrial appendage (LAA) being the primary thromboembolic source due to localised stimulation of prothrombotic mechanisms; blood stasis, hypercoagulability and endothelial damage, known as Virchow's triad.

Aim

We propose an in-silico modelling pipeline that leverages clinical imaging data to mechanistically assess patient thrombogenicity for all aspects of Virchow's triad to improve the prediction and prevention of AF-related stroke.

Methods

Two AF patients undergoing Cine magnetic resonance imaging (sinus rhythm (SR) N=1 or AF N=1 during imaging) were selected for 3D left atrial (LA) modelling with patient-specific myocardial deformation prescribed from image-derived wall motion. Blood stasis was quantified by computational fluid dynamics (CFD) simulations of 5 cardiac cycles [1]. Generation of three key coagulation proteins; thrombin, fibrinogen and fibrin, were modelled to represent thrombus growth and hypercoagulability [2]. Regions prone to thrombogenesis by endothelial damage were identified by the oscillatory shear index (OSI), time averaged wall shear stress (TAWSS) and endothelial cell activation potential (ECAP) metrics in the LAA [3].

Results

Patient-specific LA simulations enabled the assessment of differences between SR and AF conditions, quantified as numerical characteristics of each aspect of Virchow's triad.

In SR, blood flow velocities were in the range 0–2.6 m/s with mean of 0.85 m/s in the LA cavity, while AF had a range between 0–1.6 m/s with mean of 0.55 m/s. The peak and mean LAA velocities in SR were 0.85 m/s and 0.14 m/s, while AF had a peak LAA velocity of 0.32 m/s and mean of 0.09 m/s, showing a 38% decrease during AF.

The thrombin concentration reached its steady state at 1.26 mmol/m3 in the AF case after 4.7 seconds, while thrombin was washed away from the initial injury site in SR. After 5 cardiac cycles of thrombus growth dynamics, the peak fibrin concentration in the LAA was 1.3 mmol/m3 in SR and 3.8 mmol/m3 in AF, with the thrombus area in AF being 40% larger. Fibrinogen concentration decreased at a rate equal to fibrin generation in both SR and AF solely in the area of thrombus formation.

ECAP in the LAA had peak values of 2.9 in SR and 3.7 in AF, with the location at highest risk of thrombogenesis above the LAA entrance. LAA OSI had an average value of 0.45 in AF versus 0.36 in SR, showing a 26% increase. Similarly, the TAWSS was 3.5x10–3 Pa on average over the LAA in AF compared to 1.4x10–3 Pa in SR.

Conclusions

Patient-specific LA models combining these three quantitative characteristics can be used to predict the higher thrombogenic risk in AF. After further validation, this novel approach for quantitative assessment of AF patient thrombogenicity based on modelling all factors in Virchow's triad can personalise and improve management of AF patients with a risk of stroke.

Funding Acknowledgement

Type of funding sources: Public grant(s) – National budget only. Main funding source(s): UK Engineering and Physical Sciences Research Council

P588Flow profile for a better non-invasive pressure drop in CoA

Introduction

In cardiovascular obstructions, as Coarctation of the Aorta (CoA), guidelines recommend treatment based on a relevant pressure drop (ΔP). Diagnostic ΔP is estimated by simplified Bernoulli (SB) and is measured as peak-to-peak (PtP) ΔP via catheterization. The divergences amid methods are understood, but it is common practice to widely and positively accept both as valid diagnostic. Recently, simplified advective work-energy relative pressure (SAW) to correct SB by considering the full velocity profile for the ΔP computation.

Purpose

To verify the correctness of peak flow derived pressure drop via maximal velocity (SB), and full flow profile (SAW) versus clinical gold-standard PtP ΔP in a CoA phantom.

Methods

An MRI-compatible and pulsatile CoA phantom was built and tested in eight configurations, with four levels of obstruction (9, 11 and 13 mm CoA diameter and no CoA) under two flow regimes (stress and normal). The ΔP was measured via catheterization between ascending and in descending aorta (DA) as instantaneous and as PtP. Also, MRI 4D-flow velocity vector fields were acquired, enabling the ΔP estimation by SB and SAW at effective orifice area (EOA) and DA catheterization locations. at the point of the effective orifice area (EOA) and at DA catheterization location.

Results

The disparity in ΔP illustrate the fundamental differences between methods (figure and table). Catheterised instant and PtP ΔPs are similar for the CoA phantom configurations, where SB and SAW are valid. The lesser the obstruction, the greater is the temporal acceleration contribution to the ΔP and discrepancies between methods arise. As recognised, SB is an overestimation of the catheterization measurements. The most equivalent ΔPs are the catheterization PtP and SAW. Velocity-based ΔPs (SB and SAW) show a drop in performance when the velocity is captured at the DA instead of the right EOA point, illustrating the sensitivity to the acquisition location.

Peak ΔPs per method and per phantom 9mm CoA 11mm CoA 13mm CoA Normal R2 Linear eq. rest stress rest stress rest stress rest stress Instant ΔP 33.4 45.7 11.5 19.6 12.1 14.5 −2.7 −12.2 0.949 y=1.12x PtP ΔP 29.3 43.5 10.0 16.0 5.8 11.2 −1.8 -3.6 – – SB EOA 37.5 52.3 13.4 22.3 6.1 11.4 1.4 1.4 0.988 y=1.23x SB DA 22.6 59.8 10.7 18.6 5.2 8.5 0.9 1.2 0.893 y=1.15x SAW EOA 29.9 51.4 11.3 19.0 4.9 9.7 0.8 0.8 0.972 y=1.11x SAW DA 11.74 28.3 5.5 9.9 2.7 4.5 0.6 0.7 0.911 y=0.56x Linear comparisons were made against gold-standard catheterised PtP ΔP.

Velocity meshes and ΔPs in cardiac cycle

Conclusions

Initial phantom evidence suggests that the non-invasive ΔP assessments based on flow should consider the full flow profile and be acquired at the point of EOA.

Acknowledgement/Funding

PIC project, European Union's Horizon 2020 Marie Skłodowska-Curie ITN Project under grant agreement No 764738

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.

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.