Cardiac function estimation from MRI using a heart model and data assimilation: advances and difficulties.

In this paper, we present a framework to estimate local ventricular myocardium contractility using clinical MRI, a heart model and data assimilation. First, we build a generic anatomical model of the ventricles including muscle fibre orientations and anatomical subdivisions. Then, this model is deformed to fit a clinical MRI, using a semi-automatic fuzzy segmentation, an affine registration method and a local deformable biomechanical model. An electromechanical model of the heart is then presented and simulated. Finally, a data assimilation procedure is described, and applied to this model. Data assimilation makes it possible to estimate local contractility from given displacements. Presented results on fitting to patient-specific anatomy and assimilation with simulated data are very promising. Current work on model calibration and estimation of patient parameters opens up possibilities to apply this framework in a clinical environment.

Tissue deformation and shape models in image-guided interventions: a discussion paper.

This paper promotes the concept of active models in image-guided interventions. We outline the limitations of the rigid body assumption in image-guided interventions and describe how intraoperative imaging provides a rich source of information on spatial location of anatomical structures and therapy devices, allowing a preoperative plan to be updated during an intervention. Soft tissue deformation and variation from an atlas to a particular individual can both be determined using non-rigid registration. Established methods using free-form deformations have a very large number of degrees of freedom. Three examples of deformable models--motion models, biomechanical models and statistical shape models--are used to illustrate how prior information can be used to restrict the number of degrees of freedom of the registration algorithm and thus provide active models for image-guided interventions. We provide preliminary results from applications for each type of model.

Simulation of cardiac pathologies using an electromechanical biventricular model and XMR interventional imaging.

Simulating cardiac electromechanical activity is of great interest for a better understanding of pathologies and for therapy planning. Design and validation of such models is difficult due to the lack of clinical data. XMR systems are a new type of interventional facility in which patients can be rapidly transferred between X-ray and MR systems. Our goal is to design and validate an electromechanical model of the myocardium using XMR imaging. The proposed model is computationally fast and uses clinically observable parameters. We present the integration of anatomy, electrophysiology, and motion from patient data. Pathologies are introduced in the model and simulations are compared to measured data. Initial qualitative comparison on the two clinical cases presented is encouraging. Once fully validated, these models will make it possible to simulate different interventional strategies.

Measures of folding applied to the development of the human fetal brain.

Previous work has suggested the existence of differences between the cerebral cortex of normal individuals, and those of patients with diseases such as epilepsy and schizophrenia. These shape abnormalities may be of developmental origin. Improved shape measures could provide useful tools for neuroscience research and patient diagnosis. We consider the theoretically desirable properties of measures of brain shape. We have implemented seven measures, three from the neuroscience literature, and four new to this field. Three of the measures are zero-order and four are second-order with respect to the surface. We validate the measures using simple geometrical shapes, and a collection of magnetic resonance scans of ten histologically normal ex vivo fetal brains with gestational ages from 19-42 weeks. We then apply the measures to MR scans from two histologically abnormal ex vivo brains. We demonstrate that our implementation of the measures is sensitive to anatomical variability rather than to the discreteness of the image data. All the measures were sensitive to changes in shape during fetal development. Several of the measures could distinguish between the normal and abnormal fetal brains. We propose a multivariate approach to studying the shape of the cerebral cortex, in which both zero-order and second-order measures are used to quantify folding.

Measurement and analysis of brain deformation during neurosurgery.

Recent studies have shown that the surface of the brain is deformed by up to 20 mm after the skull is opened during neurosurgery, which could lead to substantial error in commercial image-guided surgery systems. We quantitatively analyze the intraoperative brain deformation of 24 subjects to investigate whether simple rules can describe or predict the deformation. Interventional magnetic resonance images acquired at the start and end of the procedure are registered nonrigidly to obtain deformation values throughout the brain. Deformation patterns are investigated quantitatively with respect to the location and magnitude of deformation, and to the distribution and principal direction of the displacements. We also measure the volume change of the lateral ventricles by manual segmentation. Our study indicates that brain shift occurs predominantly in the hemisphere ipsi-lateral to the craniotomy, and that there is more brain deformation during resection procedures than during biopsy or functional procedures. However, the brain deformation patterns are extremely complex in this group of subjects. This paper quantitatively demonstrates that brain deformation occurs not only at the surface, but also in deeper brain structure, and that the principal direction of displacement does not always correspond with the direction of gravity. Therefore, simple computational algorithms that utilize limited intraoperative information (e.g., brain surface shift) will not always accurately predict brain deformation at the lesion.

Non-rigid image registration: theory and practice.

Image registration is an important enabling technology in medical image analysis. The current emphasis is on development and validation of application-specific non-rigid techniques, but there is already a plethora of techniques and terminology in use. In this paper we discuss the current state of the art of non-rigid registration to put on-going research in context and to highlight current and future clinical applications that might benefit from this technology. The philosophy and motivation underlying non-rigid registration is discussed and a guide to common terminology is presented. The core components of registration systems are described and outstanding issues of validity and validation are confronted.

Deforming a preoperative volume to represent the intraoperative scene.

Soft-tissue deformation can be a problem if a preoperative modality is used to help guide a surgical or interventional procedure. We present a method that can warp a preoperative CT image to represent the intraoperative scene shown by an interventional fluoroscopy image. The method is a novel combination of a 2D-3D image registration algorithm and a deformation algorithm that allows rigid bodies to be incorporated into a nonlinear deformation based on radial basis functions. The 2D-3D registration algorithm is used to obtain information on relative vertebral movements between preoperative and intraoperative images. The deformation algorithm uses this information to warp the preoperative image to represent the intraoperative scene more accurately. Images from an aortic stenting procedure were used. The observed deformation in our experiment was 5 degrees flexion and 5 mm lengthening of the lumbar spine over a distance of four vertebrae. The vertebral positions in the warped CT volume represent the intraoperative scene more accurately than in the preoperative CT volume. Although we had no gold standard with which to assess the registration accuracy of soft-tissue structures, the position of such structures within the warped CT volume appeared visually realistic.

Reconstruction of undersampled dynamic images by modeling the motion of object elements.

Dynamic MRI is restricted due to the time required to obtain enough data to reconstruct the image sequence. Several undersampled reconstruction techniques have been proposed to reduce the acquisition time. In most of these techniques the nonacquired data are recovered by modeling the temporal information as varying pixel intensities represented in time or in temporal frequencies. Here we propose a new approach that recovers the missing data through a motion estimation of the object elements ("obels," or pieces of tissue) of the image. This method assumes that an obel displacement through the sequence has lower bandwidth than fluctuations in pixel intensities caused by the motion, and thus it can be modeled with fewer parameters. Preliminary results show that this technique can effectively reconstruct (with root mean square (RMS) errors below 4%) cardiac images and joints with undersampling factors of 8 and 4, respectively. Moreover, in the reconstruction process an approximation of the motion vectors is obtained for each obel, which can be used to quantify dynamic information. In this method the motion need not be confined to a part of the field of view (FOV) or to a portion of the temporal frequency. It is appropriate for dynamic studies in which the obels' motion model has fewer parameters than the number of acquired samples.

Anisotropic wave propagation and apparent conductivity estimation in a fast electrophysiological model: application to XMR interventional imaging.

Cardiac arrhythmias are increasingly being treated using ablation procedures. Development of fast electrophysiological models and estimation of parameters related to conduction pathologies can aid in the investigation of better treatment strategies during Radio-frequency ablations. We present a fast electrophysiological model incorporating anisotropy of the cardiac tissue. A global-local estimation procedure is also outlined to estimate a hidden parameter (apparent electrical conductivity) present in the model. The proposed model is tested on synthetic and real data derived using XMR imaging. We demonstrate a qualitative match between the estimated conductivity parameter and possible pathology locations. This approach opens up possibilities to directly integrate modelling in the intervention room.

Quantification of the shape of fiber tracts.

The fiber tracts generated using diffusion MRI are usually simply displayed and assessed visually for a specific clinical or medical research purpose. This paper proposes computational techniques that can be used to study the shape of the tracts and make interindividual comparisons. These methods make use of fundamental geometric invariants, such as curvatures and torsions, or Fourier descriptors, together with the link of a pair of curves. Intersubject comparisons only require that the starting and ending points of the tracts can be defined and do not require point-by-point correspondences such as obtained using image registration. Principal component analysis-based shape analysis is also investigated. The invariants are tested on simulations and in vivo datasets, and the scale dependence and noise sensitivity of the measures are assessed. The potential for these techniques to be used in neuroscience research and clinical applications is demonstrated.

Matrix description of general motion correction applied to multishot images.

Motion of an object degrades MR images, as the acquisition is time-dependent, and thus k-space is inconsistently sampled. This causes ghosts. Current motion correction methods make restrictive assumptions on the type of motions, for example, that it is a translation or rotation, and use special properties of k-space for these transformations. Such methods, however, cannot be generalized easily to nonrigid types of motions, and even rotations in multiple shots can be a problem. Here, a method is presented that can handle general nonrigid motion models. A general matrix equation gives the corrupted image from the ideal object. Thus, inversion of this system allows us to get the ideal image from the corrupted one. This inversion is possible by efficient methods mixing Fourier transforms with the conjugate gradient method. A faster but empirical inversion is discussed as well as methods to determine the motion. Simulated three-dimensional affine data and two-dimensional pulsation data and in vivo nonrigid data are used for demonstration. All examples are multishot images where the object moves between shots. The results indicate that it is now possible to correct for nonrigid types of motion that are representative of many types of patient motion, although computation times remain an issue.

Localization of abnormal conduction pathways for tachyarrhythmia treatment using tagged MRI.

Tachyarrhythmias are pathological fast heart rhythms often caused by abnormally conducting myocardial areas (foci). Treatment by radio-frequency (RF) ablation uses electrode-catheters to monitor and destroy foci. The procedure is normally guided with x-rays (2D), and thus prone to errors in location and excessive radiation exposure. Our main goal is to provide pre- and intra-operative 3D MR guidance in XMR systems by locating the abnormal conduction pathways. We address the inverse electro-mechanical relation by using motion in order to infer electrical propagation. For this purpose we define a probabilistic measure of the onset of regional myocardial activation, derived from 3D motion fields obtained by tracking tagged MR sequences with non-rigid registration. Activation isochrones are then derived to determine activation onset. We also compare regional motion between two different image acquisitions, thus assisting in diagnosing arrhythmia, in follow up of treatment, and in determining whether the ablation was successful. Difference maps of isochrones and other motion descriptors are computed to determine abnormal patterns. Validation was carried out using an electromechanical model of the heart, synthetic data, a cardiac MRI atlas of motion and geometry, MRI data from 6 healthy volunteers (one of them subjected to stress), and an MRI study on a patient with tachyarrhythmia, before and after RF ablation. A pre-operative MRI study on a second patient with tachyarrhythmia was used to test the methodology in a clinical scenario, predicting the abnormally conducting region.

A fast-marching approach to cardiac electrophysiology simulation for XMR interventional imaging.

Cardiac ablation procedures are becoming more routine to treat arrhythmias. The development of electrophysiological models will allow investigation of treatment strategies. However, current models are computationally expensive and often too complex to be adjusted with current clinical data. In this paper, we have proposed a fast algorithm to solve Eikonal-based models on triangular meshes. These models can be used to extract hidden parameters of the cardiac function from clinical data in a very short time, thus could be used during interventions. We propose a first approach to estimate these parameters, and have tested it on synthetic and real data derived using XMR imaging. We demonstrated a qualitative matching between the estimated parameter and XMR data. This novel approach opens up possibilities to directly integrate modelling in the interventional room.

Anisotropic noise propagation in diffusion tensor MRI sampling schemes.

The subject of this study is the controversial choice of directions in diffusion tensor MRI (DT-MRI); specifically, the numerical algebra related to this choice. In DT-MRI, apparent diffusivities are sampled in six or more directions and a least-squares equation is solved to reconstruct the diffusion tensor. Numerical characteristics of the system are considered, in particular the condition number and normal matrix, and are shown to be dependent on the relative orientation of the tensor with respect to the laboratory frame. As a consequence, noise propagation can be anisotropic. However, the class of icosahedral direction schemes is an exception, and icosahedral directions have the same condition number and normal matrix for direction encoding as the ideal scheme with an infinite number of directions. This normal matrix and its condition number are rotationally invariant. Numerical simulations show that for icosahedral schemes with 30 directions the standard deviation of the fractional anisotropy is both low and nearly independent of fiber orientation. The recommended choice of directions for a DT-MRI experiment is therefore the icosahedral set of directions with the highest number of directions achievable in the available time.

Zen and the art of medical image registration: correspondence, homology, and quality.

Nonrigid registration (NRR) is routinely used in the study of neuroanatomy and function and is a standard component of analysis packages such as SPM. There remain many unresolved correspondence problems that arise from attempts to associate functional areas with specific neuroanatomy and to compare both function and anatomy across patient groups. Problems can result from ignorance of the underlying neurology which is then compounded by unjustified inferences drawn from the results of NRR. Usually the magnitude, distribution, and significance of errors in NRR are unknown so the errors in correspondences determined by NRR are also unknown and their effect on experimental results cannot easily be quantified. In this paper we review the principles by which the presumed correspondence and homology of structures is used to drive registration and identify the conceptual and algorithmic areas where current techniques are lacking. We suggest that for applications using NRR to be robust and achieve their potential, context-specific definitions of correspondence must be developed which properly characterise error. Prior knowledge of image content must be utilised to monitor and guide registration and gauge the degree of success. The use of NRR in voxel-based morphometry is examined from this context and found wanting. We conclude that a move away from increasingly sophisticated but context-free registration technology is required and that the veracity of studies that rely on NRR should be keenly questioned when the error distribution is unknown and the results are unsupported by other contextual information.

SMASH navigators.

The additional data acquired when using multiple receiver coils is commonly used to improve SNR or reduce acquisition times. It may also be used to remove image artifacts by selectively replacing corrupt data. In the present study, a correction scheme is presented based on simultaneous acquisition of spatial harmonics (SMASH) that enables detection and correction of motion artifacts caused by 2D translations. Newly measured data is compared with predictions from previously measured data by making negative and positive spatial harmonics. Differences are attributed to motion occurring in the interval between the acquisition of separate phase encode lines and correction parameters are determined. Two types of rigid body motion are considered: 1) object and coil array move, and 2) object only moves, since each causes different phase errors in k-space. Simulation, phantom, and volunteer experiments demonstrate the validity of the technique.

Three- and four-dimensional reconstruction of intra-cardiac anatomy from two-dimensional magnetic resonance images.

The present study was designed to evaluate the feasibility and clinical usefulness of three-dimensional (3D) reconstruction of intra-cardiac anatomy from a series of two-dimensional (2D) MR images using commercially available software. Sixteen patients (eight with structurally normal hearts but due to have catheter radio-frequency ablation of atrial tachyarrhythmias and eight with atrial septal defects (ASD) due for trans-catheter closure) and two volunteers were imaged at 1T. For each patient, a series of ECG-triggered images (5 mm thick slices, 2-3 mm apart) were acquired during breath holding. Depending on image quality, T1- or T2-weighted spin-echo images or gradient-echo cine images were used. The 3D reconstruction was performed off-line: the blood pools within cardiac chambers and great vessels were semi-automatically segmented, their outer surface was extracted using a marching cube algorithm and rendered. Intra- and inter-observer variability, effect of breath-hold position and differences between pulse sequences were assessed by imaging a volunteer. The 3D reconstructions were assessed by three cardiologists and compared with the 2D MR images and with 2D and 3D trans-esophagal and intra-cardiac echocardiography obtained during interventions. In every case, an anatomically detailed 3D volume was obtained. In the two patients where a 3 mm interval between slices was used, the resolution was not as good but it was still possible to visualize all the major anatomical structures. Spin-echo images lead to reconstructions more detailed than those obtained from gradient-echo images. However, gradient-echo images are easier to segment due to their greater contrast. Furthermore, because images were acquired at least at ten points in the cardiac cycles for every slice it was possible to reconstruct a cine loop and, for example, to visualize the evolution of the size and margins of the ASD during the cardiac cycle. 3D reconstruction proved to be an effective way to assess the relationship between the different parts of the cardiac anatomy. The technique was useful in planning interventions in these patients.