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.

Synergy in the heart: RV systolic function plays a key role in optimizing LV performance during exercise.

The right ventricle (RV) is often overlooked in the evaluation of cardiac performance and treatment of left ventricular (LV) heart diseases. However, recent evidence suggests the RV may play an important role in maintaining systemic cardiac function and delivering stroke volume (SV). We used exercise cardiac magnetic resonance and biomechanical modeling to investigate the role of the RV in LV stroke volume regulation. We studied SV augmentation during exercise by pharmacologically inducing negative chronotropy (sHRi) in healthy volunteers and investigating training-induced SV augmentation in endurance athletes. SV augmentation during exercise after sHRi is achieved differently in the two ventricles. In the RV, the larger SV is driven by increasing contraction down to lower end-systolic volume (ESV; P < 0.001). In the LV, SV augmentation is achieved through an increase in end-diastolic volume (EDV; P < 0.001), avoiding contraction to a lower ESV. The same mechanism underlies the enhanced SV response observed in athletes. Changes in atrial area during SV augmentation suggest that the improved LV EDV response is sustained by the larger RV contractions. Using our biomechanical model, we explain this behavior by showing that the RV systolic function-driven regulation of LV SV optimizes the energetic cost of LV contraction and leads to minimization of the total costs of biventricular contraction. In conclusion, this work provides mechanistic understanding of the pivotal role of the RV in optimizing LV SV during exercise. It demonstrates why optimizing RV function needs to become a key part of therapeutic strategies in patients and training for athletes.NEW & NOTEWORTHY The right ventricle appears to have an important impact on maintaining systemic cardiac function and delivering stroke volume. However, its exact role in supporting left ventricular function has so far been unclear. This study demonstrates a new mechanism of ventricular interaction that provides mechanistic understanding of the key importance of the right ventricle in driving cardiac performance.

Experiment for validation of fluid-structure interaction models and algorithms.

In this paper a fluid-structure interaction (FSI) experiment is presented. The aim of this experiment is to provide a challenging yet easy-to-setup FSI test case that addresses the need for rigorous testing of FSI algorithms and modeling frameworks. Steady-state and periodic steady-state test cases with constant and periodic inflow were established. Focus of the experiment is on biomedical engineering applications with flow being in the laminar regime with Reynolds numbers 1283 and 651. Flow and solid domains were defined using computer-aided design (CAD) tools. The experimental design aimed at providing a straightforward boundary condition definition. Material parameters and mechanical response of a moderately viscous Newtonian fluid and a nonlinear incompressible solid were experimentally determined. A comprehensive data set was acquired by using magnetic resonance imaging to record the interaction between the fluid and the solid, quantifying flow and solid motion.

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 spatially-distributed computational model to quantify behaviour of contrast agents in MR perfusion imaging.

Contrast agent enhanced magnetic resonance (MR) perfusion imaging provides an early, non-invasive indication of defects in the coronary circulation. However, the large variation of contrast agent properties, physiological state and imaging protocols means that optimisation of image acquisition is difficult to achieve. This situation motivates the development of a computational framework that, in turn, enables the efficient mapping of this parameter space to provide valuable information for optimisation of perfusion imaging in the clinical context. For this purpose a single-compartment porous medium model of capillary blood flow is developed which is coupled with a scalar transport model, to characterise the behaviour of both blood-pool and freely-diffusive contrast agents characterised by their ability to diffuse through the capillary wall into the extra-cellular space. A parameter space study is performed on the nondimensionalised equations using a 2D model for both healthy and diseased myocardium, examining the sensitivity of system behaviour to Peclet number, Damköhler number (Da), diffusivity ratio and fluid porosity. Assuming a linear MR signal response model, sample concentration time series data are calculated, and the sensitivity of clinically-relevant properties of these signals to the model parameters is quantified. Both upslope and peak values display significant non-monotonic behaviour with regard to the Damköhler number, with these properties showing a high degree of sensitivity in the parameter range relevant to contrast agents currently in use. However, the results suggest that signal upslope is the more robust and discerning metric for perfusion quantification, in particular for correlating with perfusion defect size. Finally, the results were examined in the context of nonlinear signal response, flow quantification via Fermi deconvolution and perfusion reserve index, which demonstrated that there is no single best set of contrast agent parameters, instead the contrast agents should be tailored to the specific imaging protocol and post-processing method to be used.

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.