We propose a regularized least-squares method for reconstructing 2D velocity vector fields within the left ventricular cavity from single-view color Doppler echocardiographic images. Vector flow mapping is formulated as a quadratic optimization problem based on an [Formula: see text]-norm minimization of a cost function composed of a Doppler data-fidelity term and a regularizer. The latter contains three physically interpretable expressions related to 2D mass conservation, Dirichlet boundary conditions, and smoothness. A finite difference discretization of the continuous problem was adopted in a polar coordinate system, leading to a sparse symmetric positive-definite system. The three regularization parameters were determined automatically by analyzing the L-hypersurface, a generalization of the L-curve. The performance of the proposed method was numerically evaluated using (1) a synthetic flow composed of a mixture of divergence-free and curl-free flow fields and (2) simulated flow data from a patient-specific CFD (computational fluid dynamics) model of a human left heart. The numerical evaluations showed that the vector flow fields reconstructed from the Doppler components were in good agreement with the original velocities, with a relative error less than 20%. It was also demonstrated that a perturbation of the domain contour has little effect on the rebuilt velocity fields. The capability of our intraventricular vector flow mapping (iVFM) algorithm was finally illustrated on in vivo echocardiographic color Doppler data acquired in patients. The vortex that forms during the rapid filling was clearly deciphered. This improved iVFM algorithm is expected to have a significant clinical impact in the assessment of diastolic function.

Recent studies have suggested that intracardiac vortex flow imaging could be of clinical interest to early diagnose the diastolic heart function. Doppler vortography has been introduced as a simple color Doppler method to detect and quantify intraventricular vortices. This method is able to locate a vortex core based on the recognition of an antisymmetric pattern in the Doppler velocity field. Because the heart is a fast-moving organ, high frame rates are needed to decipher the whole blood vortex dynamics during diastole. In this paper, we adapted the vortography method to high-frame-rate echocardiography using circular waves. Time-resolved Doppler vortography was first validated in vitro in an ideal forced vortex. We observed a strong correlation between the core vorticity determined by high-frame-rate vortography and the ground-truth vorticity. Vortography was also tested in vivo in ten healthy volunteers using high-frame-rate duplex ultrasonography. The main vortex that forms during left ventricular filling was tracked during two-three successive cardiac cycles, and its core vorticity was determined at a sampling rate up to 80 duplex images per heartbeat. Three echocardiographic apical views were evaluated. Vortography-derived vorticities were compared with those returned by the 2-D vector flow mapping approach. Comparison with 4-D flow magnetic resonance imaging was also performed in four of the ten volunteers. Strong intermethod agreements were observed when determining the peak vorticity during early filling. It is concluded that high-frame-rate Doppler vortography can accurately investigate the diastolic vortex dynamics.

Persistence of external trunk asymmetry after scoliosis surgical treatment is frequent and difficult to predict by clinicians. This is a significant problem considering that correction of the apparent deformity is a major factor of satisfaction for the patients. A simulation of the correction on the external appearance would allow the clinician to illustrate to the patient the potential result of the surgery and would help in deciding on a surgical strategy that could most improve his/her appearance. We describe a method to predict the scoliotic trunk shape after a spine surgical intervention. The capability of our method was evaluated using real data of scoliotic patients. Results of the qualitative evaluation were very promising and a quantitative evaluation based on the comparison of the simulated and the actual postoperative trunk surface showed an adequate accuracy for clinical assessment. The required short simulation time also makes our approach an eligible candidate for a clinical environment demanding interactive simulations.Index Terms-Scoliosis, biomedical modeling, soft tissue deformation, interactive surgical planning systems.

One of the major concerns of scoliotic patients undergoing spinal correction surgery is the trunk's external appearance after the surgery. This paper presents a novel incremental approach for simulating postoperative trunk shape in scoliosis surgery. Preoperative and postoperative trunk shapes data were obtained using three-dimensional medical imaging techniques for seven patients with adolescent idiopathic scoliosis. Results of qualitative and quantitative evaluations, based on the comparison of the simulated and actual postoperative trunk surfaces, showed an adequate accuracy of the method. Our approach provides a candidate simulation tool to be used in a clinical environment for the surgery planning process. IntroductionAdolescent idiopathic scoliosis (AIS) is a complex three-dimensional deformation of the trunk. In severe cases, a spine surgery treatment is required. Most of the surgical procedures use specialized instrumentation attached to the spine to correct the deformities (Fig. 4.1). One 22of the concerns of the patient (and, in fact, a major factor of satisfaction) is the trunk's appearance after the surgery. In addition to the surgeon's priorities in the surgery planning process, a tool for simulating the trunk's postoperative appearance is of importance to take into account the patient's concerns in the treatment planning.Aubin et al. [4] have developed a spinal surgery simulation system in the context of the optimal planning of surgical procedures to correct scoliotic deformities. The overall goal of this biomechanical engineering research project is to develop a user-oriented simulator for virtual prototyping of spinal deformities surgeries: a fully operational, safe and reliable patient-specific tool that will permit advanced planning of surgery with predictable outcomes, and rationalized design of surgical instrumentation [3,4]. It addresses the problems faced by orthopedic surgeons treating spinal deformities when making surgical planning decisions. The developed system is, however, only concerned with the configuration of the spine, and does not furnish any estimate of the effects of the surgical treatment on the external appearance of the trunk. A desirable complement to this spine simulator would be to develop a full trunk model that would allow the propagation of the surgical correction on the spine toward the external trunk surface through the soft tissue deformation.Physics-based models of deformable objects have been studied since the early 80's and are common in animation where physical laws are applied to an object to simulate realistic movements. Deformable physics-based models are also used in biomedical applications, in particular for surgery simulation [30]. These applications require visual and physical realism, but the real biomechanical properties involved are not always well known. The two most popular approaches to physically modeling soft tissues are the Finite Element Method (FEM) and Mass-Spring Model (MSM). Commonly used in engineering to accurately analyze struct...