Intracardiac blood flow is driven by differences in relative pressure, and assessing these is critical in understanding cardiac disease. Non-invasive image-based methods exist to assess relative pressure, however, the complex flow and dynamically moving fluid domain of the intracardiac space limits assessment. Recently, we proposed a method, νWERP, utilizing an auxiliary virtual field to probe relative pressure through complex, and previously inaccessible flow domains. Here we present an extension of νWERP for intracardiac flow assessments, solving the virtual field over sub-domains to effectively handle the dynamically shifting flow domain. The extended νWERP is validated in an in-silico benchmark problem, as well as in a patient-specific simulation model of the left heart, proving accurate over ranges of realistic image resolutions and noise levels, as well as superior to alternative approaches. Lastly, the extended νWERP is applied on clinically acquired 4D Flow MRI data, exhibiting realistic ventricular relative pressure patterns, as well as indicating signs of diastolic dysfunction in an exemplifying patient case. Summarized, the extended νWERP approach represents a directly applicable implementation for intracardiac flow assessments.

Vascular pressure differences are established risk markers for a number of cardiovascular diseases. Relative pressures are, however, often driven by turbulence-induced flow fluctuations, where conventional non-invasive methods may yield inaccurate results. Recently, we proposed a novel method for non-turbulent flows, νWERP, utilizing the concept of virtual work-energy to accurately probe relative pressure through complex branching vasculature. Here, we present an extension of this approach for turbulent flows: νWERP-t. We present a theoretical method derivation based on flow covariance, quantifying the impact of flow fluctuations on relative pressure. νWERP-t is tested on a set of in-vitro stenotic flow phantoms with data acquired by 4D flow MRI with six-directional flow encoding, as well as on a patient-specific in-silico model of an acute aortic dissection. Over all tests νWERP-t shows improved accuracy over alternative energy-based approaches, with excellent recovery of estimated relative pressures. In particular, the use of a guaranteed divergence-free virtual field improves accuracy in cases where turbulent flows skew the apparent divergence of the acquired field. With the original νWERP allowing for assessment of relative pressure into previously inaccessible vasculatures, the extended νWERP-t further enlarges the method's clinical scope, underlining its potential as a novel tool for assessing relative pressure in-vivo.

MR angiography (MRA) and phase-contrast MRA (PC-MRA) generation methods that facilitate blood flow assessment in the heart and thoracic vessels typically lead to the compression of data from all the timeframes of a cardiac cycle into one 2D or 3D image. This process, however, results in information loss from individual timeframes. We propose a new method for PC-MRA data generation from 4D flow MRI, which uses registration between the timeframes of the 4D acquisition to create a “four-dimensional PC-MR CardioAngiography (4D PC-MRCA)” that retains vascular and cardiac blood flow information over the entire cardiac cycle. When evaluated on 10 4D flow MRI datasets, 4D PC-MRCA outperformed 3D PC-MRA, especially when cardiac or vessel motion was present. Consequently, the proposed method improves the existing PC-MRA generation techniques by effectively utilizing spatial as well as temporal blood flow information on both the heart and thoracic vasculature from 4D flow MR images. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The inverse gradient problem, finding a scalar field f with a gradient near a given vector fieldgon some bounded and connected domain Ω ϵ R𝓃, can be solved by means of a Poisson equation with inhomogeneous Neumann boundary conditions. We present an elementary derivation of this partial differential equation and an efficient multigrid-based method to numerically compute the inverse gradient on non-rectangular domains. The utility of the method is demonstrated by a range of important medical applications such as phase unwrapping, pressure computation, inverse deformation fields, and fiber bundle tracking.

This paper describes a novel method for regional characterization of three-dimensional vector fields using a pattern matching approach. Given a three-dimensional vector field, the goal is to automatically locate, identify, and visualize a selected set of classes of structures or features. Rather than analytically defining the properties that must be fulfilled in a region in order to be classified as a specific structure, a set of idealized patterns for each structure type is constructed. Similarity to these patterns is then defined and calculated. Examples of structures of interest include vortices, swirling flow, diverging or converging flow, and parallel flow. Both medical and aerodynamic applications are presented in this paper.

While many methods exist for visualising scalar and vector data, visualisation of tensor data is still troublesome. We present a method for visualising second order tensors in three dimensions using a hybrid between direct volume rendering and glyph rendering. An overview scalar field is created by using three-dimensional adaptive filtering of a scalar field containing noise. The filtering process is controlled by the tensor field to be visualised, creating patterns that characterise the tensor field. By combining direct volume rendering of the scalar field with standard glyph rendering methods for detailed tensor visualisation, a hybrid solution is created. A combined volume and glyph renderer was implemented and tested with both synthetic tensors and strain-rate tensors from the human heart muscle, calculated from phase contrast magnetic resonance image data. A comprehensible result could be obtained, giving both an overview of the tensor field as well as detailed information on individual tensors.

A four-dimensional mapping (three spatial dimensions + time) of myocardial strain-rate would help to describe the mechanical properties of the myocardium, which affect important physiological factors such as the pumping performance of the ventricles. Strain-rate represents the local instantaneous deformation of the myocardium and can be calculated from the spatial gradients of the velocity field. Strain-rate has previously been calculated using one-dimensional (ultrasound) or two-dimensional (2-D) magnetic resonance imaging) techniques. However, this assumes that myocardial motion only occurs in one direction or in one plane, respectively. This paper presents a method for calculation of the time-resolved three-dimensional (3-D) strain-rate tensor using velocity vector information in a 3-D spatial grid during the whole cardiac cycle. The strain-rate tensor provides full information of both magnitude and direction of the instantaneous deformation of the myocardium. A method for visualization of the full 3-D tensor is also suggested. The tensors are visualized using ellipsoids, which display the principal directions of strain-rate and the ratio between strain-rate magnitude in each direction. The presented method reveals the principal strain-rate directions without a priori knowledge of myocardial motion directions.