[No abstract available]

14:S61

Ultrasound-Doppler assessment of diastolic function is subject to velocity errors caused by angle sensitivity and a fixed location of the sample volume. We used 3-dimensional phase contrast magnetic resonance imaging (MRI) to evaluate these errors in 10 patients with hypertension and in 10 healthy volunteers. The single (Doppler) and triple (MRI) component velocity was measured at early (E) and late (A) inflow along Doppler-like sample lines or 3-dimensional particle traces generated from the MRI data. Doppler measurements underestimated MRI velocities by 9.4% ± 8.6%; the effect on the E/A ratio was larger and more variable. Measuring early and late diastolic inflows from a single line demonstrated the error caused by their 3-dimensional spatial offset. Both errors were minimized by calculating the E/A ratio from maximal E and A values without constraint to a single line. Alignment and spatial offset are important sources of error in Doppler diastolic parameters. Improved accuracy may be achieved with the use of maximal E and A velocities from wherever they occur in the left ventricle.

BACKGROUND: Abnormal flow patterns in the left atrium in atrial fibrillation or mitral stenosis are associated with an increased risk of thrombosis and systemic embolisation; the characteristics of normal atrial flow that avoid stasis have not been well defined.

OBJECTIVES: To present a three dimensional particle trace visualisation of normal left atrial flow in vivo, constructed from flow velocities in three dimensional space.

METHODS: Particle trace visualisation of time resolved three dimensional magnetic resonance imaging velocity measurements was used to provide a display of intracardiac flow without the limitations of angle sensitivity or restriction to imaging planes. Global flow patterns of the left atrium were studied in 11 healthy volunteers.

RESULTS: In all subjects vortical flow was observed in the atrium during systole and diastolic diastasis (mean (SD) duration of systolic vortex, 280 (77) ms; and of diastolic vortex, 256 (118) ms). The volume incorporated and recirculated within the vortices originated predominantly from the left pulmonary veins. Inflow from the right veins passed along the vortex periphery, constrained between the vortex and the atrial wall.

CONCLUSIONS: Global left atrial flow in the normal human heart comprises consistent patterns specific to the phase of the cardiac cycle. Separate paths of left and right pulmonary venous inflow and vortex formation may have beneficial effects in avoiding left atrial stasis in the normal subject in sinus rhythm.

Numerous studies have shown a correlation between Wall Shear Stress (WSS) and atherosclerosis, but few have evaluated the reliability of estimation methods and measures used to assessWSS, which is the subject of this work. A subject specific vessel model of the aortic arch and thoracic aorta is created fromMRI images and used for CFD simulations with MRI velocity measurements as inlet boundary condition. WSS is computed from the simulation results. Aortic WSS shows significant spatial as well as temporal variation during a cardiac cycle, which makes circumferential values very uninformative, and approximate estimates using Hagen-Poiseuille fails predict the averageWSS. Highly asymmetric flow, especially in the arch, causes the spatial WSS variations.

Manual identification of structures and features in multidimensional images is at best time consuming and operator dependent. Feature identification need to be accurate, repeatable and quantitative. This thesis presents a unified approach for automatic feature detection in multidimensional scalar and vector fields. The basis for the feature detection is a tensor representation of multidimensional local neighborhoods, constructed from a filter response controlled linear combination of basis tensors. Using eigenvalue and eigenvector decomposition, local topology and local orientation can be estimated. With different filter sets the tensor representation can be used to find specific features in multidimensional images, such as planar structures in scalar fields or flow structures as vortices or parallel flow in vector fields.

The motivation for the unified approach for feature detection in both scalar and vector fields is to build a foundation to tackle the challenge of understanding the complex interaction between the cardiac walls and the blood flow in the human heart.

The heart wall consists of three distinct layers: the inner endocardium, the middle myocardium and the outer epicardium. The myocardium is the functional tissue that endows the heart with its ability to pump blood, and consists primarily of locally parallel muscle fibers. The orientation of these muscle fibers change with position in the wall. The myofibers have been shown to be arranged parallel in sheets that are rotated around the fiber direction relative to the radial direction of the left ventricle. During a cardiac beat there are local shortenings and lengthenings in the myocardium, both within and between myolaminar sheets. The mechanism by which the local shortening or lengthening is translated into the large and complex motions of the ventricle has to be studied on a local level, by studying deformation. A parameter that describes deformation is strain. The scope of the current project is to perform detailed studies of cardiac strain, particularly during diastole. There exist several definitions of strain tensors and the focus in this project is on the Lagrangian strain tensor.

The myocardial bead array gives kinematic measures of the myocardium toestimate strain in the left ventricular wall of the pumping heart. During surgery, radiopaque beads are inserted into the myocardium along three transmural columns, with typically four to six beads in each column. The 4D coordinates of the beads are acquired with high resolution using time-resolved biplane cineradiography.

This thesis presents a method for strain estimation from myocardial coordinate data. This strain estimation method is tailored for the transmural bead array and fits a polynomial to the bead coordinates. A benefit with the polynomial method is its ability to avoid loss of accuracy for the case of a missing bead, e.g. due to problems sometimes encountered during surgery or during the recovery period. The polynomial strain estimation method is applied to coordinate data from a transmural bead array to quantify diastolic myocardial strain in the ovine heart. This reveals transmural strain inhomogeneities during diastole in the ovine heart.

Rapid early filling requires a rapid shift to a very compliant left ventricle immediately after systole, allowing filling at low driving pressures. This compliance shift is manifested as changes in transmural strains: however its mechanistic basis is incompletely understood. Seven adult Dorsett hybrid sheep were anesthetized and radiopaque markers were surgically implanted to silhouette the LV chamber. Three transmural columns of four beads each were implanted into the lateral equatorial LV wall. Eight weeks after surgery, biplane videofluoroscopic images of all radiopaque markers were acquired at 60 Hz horn dosed-chest anesthetized animals. After data acquisition, hearts were arrested at the end-diastolic pressure aud quantitative hist.ology was used to determine fiber and sheet angles. Lagrangian strains in cardiac and liber-sheet coordinates were computed at end of early filling and end diastole with filling onset as reference at three transmural depths. Rapid early filling was dominated by subepicardial circumferential stretching (E_CC=0.08±0.02) and fiber lengthening (E_ƒƒ=0.03±0.01), midwall circumferential stretching (E_CC=0.07±0.02), and subendocardial wall thinning (E_RR=-0.05±0.01). Subepicardial strains achieved their ED values during early diastole, while mid wall and subendocardial straius reset during late diastole. Sheet-normal shear strain was a dominant contributor to wall thinning during diastole.

Background: Knowledge of normal cardiac kinematics is important when attempting to understand the mechanisms that impair the contractile function of the heart during disease. The complex kinematics of the heart can be studied by inserting radiopaque markers in the cardiac wall and study the pumping heart with biplane cineradiography. In order to study the local strain, the bead array was developed where small radiopaque beads are inserted along three columns transmurally in the left ventricle. Method: This paper suggests a straightforward method for strain computation, based on polynomial least-squares fitting and tailored for combined marker and bead array analyses. Results: This polynomial method gives small errors for a realistic bead array on an analytical test case. The method delivers an explicit expression of the Lagrangian strain tensor as a polynomial function of the coordinates of material points in the reference configuration. The method suggested in this paper is validated with analytical strains on a deforming cylinder resembling the heart, compared to a previously suggested finite element method, and applied to in vivo ovine data. The errors in the estimated strain components are shown to remain unchanged on an analytical test case when evaluating the effects of one missing bead. In conclusion, the proposed strain computation method is accurate and robust, with errors smaller or comparable to the current gold standard when applied on an analytical test case.

The field of topology optimization is well developed for load carrying trusses, but so far not for other similar network problems. The present paper is a first study in the direction of topology optimization of flow networks. A linear network flow model based on Hagen-Poiseuille's equation is used. Cross-section areas of pipes are design variables and the objective of the optimization is to minimize a measure, which in special cases represents dissipation or pressure drop, subject to a constraint on the available (generalized) volume. A ground structure approach where cross-section areas may approach zero is used, whereby the optimal topology (and size) of the network is found.A substantial set of examples is presented: Small examples are used to illustrate difficulties related to non-convexity of the optimization problem, larger arterial tree-type networks, with bio-mechanics interpretations, illustrate basic properties of optimal networks, the effect of volume forces is exemplified.We derive optimality conditions which turns out to contain Murray's law, thereby, presenting a new derivation of this well known physiological law. Both our numerical algorithm and the derivation of optimality conditions are based on an e-perturbation where cross-section areas may become small but stay finite. An indication of the correctness of this approach is given by a theorem, the proof of which is presented in an appendix. © 2003 Elsevier B.V. All rights reserved.