Coupled B-snake grids and constrained thin-plate splines for analysis of 2-D tissue deformations from tagged MRI

A novel thin plate spline methodology to model tissue surfaces and quantify tumor cell invasion in organ-on-chip models

Organ-on-chip (OOC) models can be useful tools for cancer drug discovery. Advances in OOC technology have led to the development of more complex assays, yet analysis of these systems does not always account for these advancements, resulting in technical challenges. A challenging task in the analysis of these two-channel microfluidic models is to define the boundary between the channels so objects moving within and between channels can be quantified. We propose a novel imaging-based application of a thin plate spline method - a generalized cubic spline that can be used to model coordinate transformations - to model a tissue boundary and define compartments for quantification of invaded objects, representing the early steps in cancer metastasis. To evaluate its performance, we applied our analytical approach to an adapted OOC developed by Emulate, Inc., utilizing a two-channel system with endothelial cells in the bottom channel and colorectal cancer (CRC) patient-derived organoids (PDOs) in the top channel. Initial application and visualization of this method revealed boundary variations due to microscope stage tilt and ridge and valley-like contours in the endothelial tissue surface. The method was functionalized into a reproducible analytical process and web tool - the Chip Invasion and Contour Analysis (ChICA) - to model the endothelial surface and quantify invading tumor cells across multiple chips. To illustrate applicability of the analytical method, we applied the tool to CRC organoid-chips seeded with two different endothelial cell types and measured distinct variations in endothelial surfaces and tumor cell invasion dynamics. Since ChICA utilizes only positional data output from imaging software, the method is applicable to and agnostic of the imaging tool and image analysis system used. The novel thin plate spline method developed in ChICA can account for variation introduced in OOC manufacturing or during the experimental workflow, can quickly and accurately measure tumor cell invasion, and can be used to explore biological mechanisms in drug discovery.

A novel thin plate spline methodology to model tissue surfaces and quantify tumor cell invasion in organ-on-chip models

Organ-on-chip (OOC) models can be useful tools for cancer drug discovery. Advances in OOC technology have led to the development of more complex assays, yet analysis of these systems does not always account for these advancements, resulting in technical challenges. A challenging task in the analysis of these two-channel microfluidic models is to define the boundary between the channels so objects moving within and between channels can be quantified. We propose a novel imaging-based application of a thin plate spline method - a generalized cubic spline that can be used to model coordinate transformations - to model a tissue boundary and define compartments for quantification of invaded objects, representing the early steps in cancer metastasis. To evaluate its performance, we applied our analytical approach to an adapted OOC developed by Emulate, Inc., utilizing a two-channel system with endothelial cells in the bottom channel and colorectal cancer (CRC) patient-derived organoids (PDOs) in the top channel. Initial application and visualization of this method revealed boundary variations due to microscope stage tilt and ridge and valley-like contours in the endothelial tissue surface. The method was functionalized into a reproducible analytical process and web tool - the Chip Invasion and Contour Analysis (ChICA) - to model the endothelial surface and quantify invading tumor cells across multiple chips. To illustrate applicability of the analytical method, we applied the tool to CRC organoid-chips seeded with two different endothelial cell types and measured distinct variations in endothelial surfaces and tumor cell invasion dynamics. Since ChICA utilizes only positional data output from imaging software, the method is applicable to and agnostic of the imaging tool and image analysis system used. The novel thin plate spline method developed in ChICA can account for variation introduced in OOC manufacturing or during the experimental workflow, can quickly and accurately measure tumor cell invasion, and can be used to explore biological mechanisms in drug discovery.

Using synthetic data generation to train a cardiac motion tag tracking neural network

A CNN based method for cardiac MRI tag tracking was developed and validated. A synthetic data simulator was created to generate large amounts of training data using natural images, a Bloch equation simulation, a broad range of tissue properties, and programmed ground-truth motion. The method was validated using both an analytical deforming cardiac phantom and in vivo data with manually tracked reference motion paths. In the analytical phantom, error was investigated relative to SNR, and accurate results were seen for SNR>10 (displacement error <0.3 mm). Excellent agreement was seen in vivo for tag locations (mean displacement difference = -0.02 pixels, 95% CI [-0.73, 0.69]) and calculated cardiac circumferential strain (mean difference = 0.006, 95% CI [-0.012, 0.024]). Automated tag tracking with a CNN trained on synthetic data is both accurate and precise.

A 3D Computational Head Model Under Dynamic Head Rotation and Head Extension Validated Using Live Human Brain Data, Including the Falx and the Tentorium

We employ an advanced 3D computational model of the head with high anatomical fidelity, together with measured tissue properties, to assess the consequences of dynamic loading to the head in two distinct modes: head rotation and head extension. We use a subject-specific computational head model, using the material point method, built from T1 magnetic resonance images, and considering the anisotropic properties of the white matter which can predict strains in the brain under large rotational accelerations. The material model now includes the shear anisotropy of the white matter. We validate the model under head rotation and head extension motions using live human data, and advance a prior version of the model to include biofidelic falx and tentorium. We then examine the consequences of incorporating the falx and tentorium in terms of the predictions from the computational head model.

An Overview on Image Registration Techniques for Cardiac Diagnosis and Treatment

Image registration has been used for a wide variety of tasks within cardiovascular imaging. This study aims to provide an overview of the existing image registration methods to assist researchers and impart valuable resource for studying the existing methods or developing new methods and evaluation strategies for cardiac image registration. For the cardiac diagnosis and treatment strategy, image registration and fusion can provide complementary information to the physician by using the integrated image from these two modalities. This review also contains a description of various imaging techniques to provide an appreciation of the problems associated with implementing image registration, particularly for cardiac pathology intervention and treatments.

Regional cardiac function analysis from tagged MRI images. Comparison of techniques: Harmonic-Phase (HARP) versus Sinusoidal-Modeling (SinMod) analysis

Cardiac MRI tagging is a valuable technique for evaluating regional heart function. Currently, there are a number of different techniques for analyzing the tagged images. Specifically, k-space-based analysis techniques showed to be much faster than image-based techniques, where harmonic-phase (HARP) and sine-wave modeling (SinMod) stand as two famous techniques of the former group, which are frequently used in clinical studies. In this study, we compared HARP and SinMod and studied inter-observer variability between the two techniques for evaluating myocardial strain and apical-to-base torsion in numerical phantom, nine healthy controls, and thirty diabetic patients. Based on the ground-truth numerical phantom measurements (strain = -20% and rotation angle = -4.4°), HARP and SinMod resulted in overestimation (in absolute value terms) of strain by 1% and 5% (strain values), and of rotation angle by 0.4° and 2.0°, respectively. For the in-vivo results, global strain and torsion ranges were -10.6% to -35.3% and 1.8°/cm to 12.7°/cm in patients, and -17.8% to -32.7% and 1.8°/cm to 12.3°/cm in volunteers. On average, SinMod overestimated strain measurements by 5.7% and 5.9% (strain values) in the patients and volunteers, respectively, compared to HARP, and overestimated torsion measurements by 2.9°/cm and 2.5°/cm in the patients and volunteers, respectively, compared to HARP. Location-wise, the ranges for basal, mid-ventricular, and apical strain in patients (volunteers) were -8.4% to -31.5% (-11.6% to -33.3%), -6.3% to -37.2% (-17.8% to -33.3%), and -5.2% to -38.4% (-20.0% to -33.2%), respectively. SinMod overestimated strain in the basal, mid-ventricular, and apical slices by 4.7% (5.7%), 5.9% (5.5%), and 8.9% (6.8%), respectively, compared to HARP in the patients (volunteers). Nevertheless, there existed good correlation between the HARP and SinMod measurements. Finally, there were no significant strain or torsion measurement differences between patients and volunteers. There existed good inter-observer agreement, as all measurement differences lied within the Bland-Altman ± 2 standard-deviation (SD) difference limits. In conclusion, despite the consistency of the results by either HARP or SinMod and acceptable agreement of the generated strain and torsion patterns by both techniques, SinMod systematically overestimated the measurements compared to HARP. Under current operating conditions, the measurements from HARP and SinMod cannot be used interchangeably.

Phase Vector Incompressible Registration Algorithm for Motion Estimation From Tagged Magnetic Resonance Images

Tagged magnetic resonance imaging has been used for decades to observe and quantify motion and strain of deforming tissue. It is challenging to obtain 3-D motion estimates due to a tradeoff between image slice density and acquisition time. Typically, interpolation methods are used either to combine 2-D motion extracted from sparse slice acquisitions into 3-D motion or to construct a dense volume from sparse acquisitions before image registration methods are applied. This paper proposes a new phase-based 3-D motion estimation technique that first computes harmonic phase volumes from interpolated tagged slices and then matches them using an image registration framework. The approach uses several concepts from diffeomorphic image registration with a key novelty that defines a symmetric similarity metric on harmonic phase volumes from multiple orientations. The material property of harmonic phase solves the aperture problem of optical flow and intensity-based methods and is robust to tag fading. A harmonic magnitude volume is used in enforcing incompressibility in the tissue regions. The estimated motion fields are dense, incompressible, diffeomorphic, and inverse-consistent at a 3-D voxel level. The method was evaluated using simulated phantoms, human brain data in mild head accelerations, human tongue data during speech, and an open cardiac data set. The method shows comparable accuracy to three existing methods while demonstrating low computation time and robustness to tag fading and noise.

Myocardial motion estimation of tagged cardiac magnetic resonance images using tag motion constraints and multi-level b-splines interpolation

Myocardial motion estimation of tagged cardiac magnetic resonance (TCMR) images is of great significance in clinical diagnosis and the treatment of heart disease. Currently, the harmonic phase analysis method (HARP) and the local sine-wave modeling method (SinMod) have been proven as two state-of-the-art motion estimation methods for TCMR images, since they can directly obtain the inter-frame motion displacement vector field (MDVF) with high accuracy and fast speed. By comparison, SinMod has better performance over HARP in terms of displacement detection, noise and artifacts reduction. However, the SinMod method has some drawbacks: 1) it is unable to estimate local displacements larger than half of the tag spacing; 2) it has observable errors in tracking of tag motion; and 3) the estimated MDVF usually has large local errors. To overcome these problems, we present a novel motion estimation method in this study. The proposed method tracks the motion of tags and then estimates the dense MDVF by using the interpolation. In this new method, a parameter estimation procedure for global motion is applied to match tag intersections between different frames, ensuring specific kinds of large displacements being correctly estimated. In addition, a strategy of tag motion constraints is applied to eliminate most of errors produced by inter-frame tracking of tags and the multi-level b-splines approximation algorithm is utilized, so as to enhance the local continuity and accuracy of the final MDVF. In the estimation of the motion displacement, our proposed method can obtain a more accurate MDVF compared with the SinMod method and our method can overcome the drawbacks of the SinMod method. However, the motion estimation accuracy of our method depends on the accuracy of tag lines detection and our method has a higher time complexity.

Artifacts reduction in strain maps of tagged magnetic resonance imaging using harmonic phase

Tagged Magnetic Resonance Imaging (MRI) is a noninvasive technique for examining myocardial function and deformation. Tagged MRI can also be used in quasi-static MR elastography to acquire strain maps of other biological soft tissues. Harmonic phase (HARP) provides automatic and rapid analysis of tagged MR images for the quantification and visualization of myocardial strain. We propose a new artifact reduction method in strain maps. Image intensity of the DC component is estimated and subtracted from spatial modulation of magnetization (SPAMM) tagged MR images. DC peak interference in harmonic phase extraction is greatly reduced after DC component subtraction. The proposed method is validated using both simulated and MR acquired tagged images. Strain maps are obtained with better accuracy and smoothness after DC component subtraction.

Estimating dense cardiac 3D motion using sparse 2D tagged MRI cross-sections

In this work, we describe a new method, an extension of the Large Deformation Diffeomorphic Metric Mapping to estimate three-dimensional deformation of tagged Magnetic Resonance Imaging Data. Our approach relies on performing non-rigid registration of tag planes that were constructed from set of initial reference short axis tag grids to a set of deformed tag curves. We validated our algorithm using in-vivo tagged images of normal mice. The mapping allows us to compute root mean square distance error between simulated tag curves in a set of long axis image planes and the acquired tag curves in the same plane. Average RMS error was 0.31 ± 0.36(SD) mm, which is approximately 2.5 voxels, indicating good matching accuracy.

Semi-automatic segmentation for 3D motion analysis of the tongue with dynamic MRI

Dynamic MRI has been widely used to track the motion of the tongue and measure its internal deformation during speech and swallowing. Accurate segmentation of the tongue is a prerequisite step to define the target boundary and constrain the tracking to tissue points within the tongue. Segmentation of 2D slices or 3D volumes is challenging because of the large number of slices and time frames involved in the segmentation, as well as the incorporation of numerous local deformations that occur throughout the tongue during motion. In this paper, we propose a semi-automatic approach to segment 3D dynamic MRI of the tongue. The algorithm steps include seeding a few slices at one time frame, propagating seeds to the same slices at different time frames using deformable registration, and random walker segmentation based on these seed positions. This method was validated on the tongue of five normal subjects carrying out the same speech task with multi-slice 2D dynamic cine-MR images obtained at three orthogonal orientations and 26 time frames. The resulting semi-automatic segmentations of a total of 130 volumes showed an average dice similarity coefficient (DSC) score of 0.92 with less segmented volume variability between time frames than in manual segmentations.

Sparse deformable models with application to cardiac motion analysis

Deformable models have been widely used with success in medical image analysis. They combine bottom-up information derived from image appearance cues, with top-down shape-based constraints within a physics-based formulation. However, in many real world problems the observations extracted from the image data often contain gross errors, which adversely affect the deformation accuracy. To alleviate this issue, we introduce a new family of deformable models that are inspired from compressed sensing, a technique for efficiently reconstructing a signal based on its sparseness in some domain. In this problem, we employ sparsity to represent the outliers or gross errors, and combine it seamlessly with deformable models. The proposed new formulation is applied to the analysis of cardiac motion, using tagged magnetic resonance imaging (tMRI), where the automated tagging line tracking results are very noisy due to the poor image quality. Our new deformable models track the heart motion robustly, and the resulting strains are consistent with those calculated from manual labels.

Single syllable tongue motion analysis using tagged cine MRI

The complicated muscle activity of the human tongue and the resultant surface shapes can give us important clues about speech motor control and pathological tongue motion. This study uses tagged magnetic resonance imaging to provide a 2D surface deformation analysis of the tongue, as well as a 4D compression-expansion analysis, during utterances of four different syllables (/ba/, /ta/, /sha/ and /ga/). All speech tasks were performed several times to confirm the repeatability of the motion analysis. The results showed that the tongue has unique motion patterns for utterances of different syllables, and these differences, which may not be observed by a simple surface analysis, can be examined thoroughly by a 4D motion model-based analysis of the tongue muscles.

MR assessment of regional myocardial mechanics

Regional myocardial function can be measured by several MR techniques including tissue tagging, phase velocity mapping, and more recently, displacement encoding with stimulated echoes (DENSE) and strain encoding (SENC). Each of these techniques was developed separately and has undergone significant change since its original implementation. As a result, in the current literature, the common features and the differences between the techniques and what they measure are often unclear and confusing. This review article delivers an extensively referenced introductory text which clarifies the current methodology from the starting point of the Bloch equations. By doing this in a consistent way for each method, the similarities and differences between them are highlighted. In addition, their capabilities and limitations are discussed, together with their relative advantages and disadvantages. While the focus is on sequence design and development, the principal parameters measured by each technique are also summarized, together with brief results, with the reader being directed to the extensive literature on data processing and clinical applications for more detail.

IN-VIVOESTIMATION OF THE TIBIO-FEMORAL CONTACT AREA USING THIN-PLATE SPLINE TOOL

Interaction between articular surfaces at the knee joint allows movement and stability. The knowledge of how this mechanism works in physiological conditions could be very useful for the development of new clinical procedures. The objective of this study was to develop a subject-specific model able to estimate the articular contact area at the tibio-femoral joint avoiding any destructive measurements. Thin plate splines were used to describe articular surfaces and to allow an analytical estimation of the distance between the surfaces. The sensitivity of the model was evaluated and the tibio-femoral contact area was estimated in a living subject. Femoral contact area results were always smaller than the tibial one, whereas tibial contact area results were less repeatable. Increasing the distance threshold, the increase of the contact area was almost linear. High repeatability was obtained sampling each condyle with more than 60 steps. Contact areas, estimated with the loaded knee, were in accordance with physiology and literature showing a good repeatability. The devised model was suitably used to evaluate the articular contact at the knee joint of an healthy living subject and can be a useful clinical tool to suggest procedures aimed at restoring physiological conditions.

Accurate two-dimensional cardiac strain calculation using adaptive windowed Fourier transform and Gabor wavelet transform

PURPOSE

Cardiac strain calculated from tagged magnetic resonance (MR) images provides clinicians information about abnormalities of heart-wall motion in patients. It is important to develop an accurate method to determine the cardiac strain efficiently. An adaptive windowed harmonic phase (AWHARP) method is proposed for cardiac strain calculation.

MATERIALS AND METHODS

AWHARP is based on adaptive windowed Fourier transform (AWFT) and 2D Gabor wavelet transform (2D-GWT). The AWFT provides a spatially varying representation of the signal spectra, which allows the harmonic phase (HARP) image to be extracted with high accuracy. Instantaneous spatial frequencies are calculated using 2D-GWT, and the widths of the adaptive windows are then determined according to the instantaneous spatial frequencies for multi-resolution analysis of phase extraction. The proposed method was studied using simulated images and patients' MR images. Both single tagged images (SPAMM) and subtracted tagged images (CSPAMM) were generated using our simulation method, and their results calculated using AWHARP and HARP methods were compared. Normal and pathological tagged MR images were also processed to evaluate the performance of our method.

RESULTS

Our experimental results show that the accuracies of phase and strain images calculated using the AWHARP method are higher than that calculated using the HARP method especially for large tag line deformation. The improvement in accuracies can be up to 3.2 strain (E1) and 17.3 calculation from MR images reveals that the cardiac strain in the end-systolic state is significantly reduced for patients with hypertrophic cardiomyopathy (HCM) compared to that of healthy subjects.

CONCLUSION

The proposed AWHARP is an accurate and efficient method for cardiac strain estimation from MR images. This new algorithm can help clinicians to detect left ventricle dysfunctions and myocardial diseases with accurate cardiac strain analysis.

Cardiac motion and deformation recovery from MRI: a review

Magnetic resonance imaging (MRI) is a highly advanced and sophisticated imaging modality for cardiac motion tracking and analysis, capable of providing 3D analysis of global and regional cardiac function with great accuracy and reproducibility. In the past few years, numerous efforts have been devoted to cardiac motion recovery and deformation analysis from MR image sequences. Many approaches have been proposed for tracking cardiac motion and for computing deformation parameters and mechanical properties of the heart from a variety of cardiac MR imaging techniques. In this paper, an updated and critical review of cardiac motion tracking methods including major references and those proposed in the past ten years is provided. The MR imaging and analysis techniques surveyed are based on cine MRI, tagged MRI, phase contrast MRI, DENSE, and SENC. This paper can serve as a tutorial for new researchers entering the field.

Incompressible deformation estimation algorithm (IDEA) from tagged MR images

Measuring the 3D motion of muscular tissues, e.g., the heart or the tongue, using magnetic resonance (MR) tagging is typically carried out by interpolating the 2D motion information measured on orthogonal stacks of images. The incompressibility of muscle tissue is an important constraint on the reconstructed motion field and can significantly help to counter the sparsity and incompleteness of the available motion information. Previous methods utilizing this fact produced incompressible motions with limited accuracy. In this paper, we present an incompressible deformation estimation algorithm (IDEA) that reconstructs a dense representation of the 3D displacement field from tagged MR images and the estimated motion field is incompressible to high precision. At each imaged time frame, the tagged images are first processed to determine components of the displacement vector at each pixel relative to the reference time. IDEA then applies a smoothing, divergence-free, vector spline to interpolate velocity fields at intermediate discrete times such that the collection of velocity fields integrate over time to match the observed displacement components. Through this process, IDEA yields a dense estimate of a 3D displacement field that matches our observations and also corresponds to an incompressible motion. The method was validated with both numerical simulation and in vivo human experiments on the heart and the tongue.

Motion tracking and strain map computation for quasi-static magnetic resonance elastography

This paper presents a new imaging method for quasi-static magnetic resonance elastography (MRE). Tagged magnetic resonance (MR) imaging of human lower leg was acquired with probe indentation using a MR-compatible actuation system. Indentation force was recorded for soft tissue elasticity reconstruction. Motion tracking and strain map of human lower leg are calculated using a harmonic phase (HARP)-based method. Simulated tagged MR images were constructed and analyzed to validate the HARP-based method. Our results show that the proposed imaging method can be used to generate accurate motion distribution and strain maps of the targeted soft tissue.

Trans-dimensional MCMC methods for fully automatic motion analysis in tagged MRI

Tagged magnetic resonance imaging (tMRI) is a well-known noninvasive method allowing quantitative analysis of regional heart dynamics. Its clinical use has so far been limited, in part due to the lack of robustness and accuracy of existing tag tracking algorithms in dealing with low (and intrinsically time-varying) image quality. In this paper, we propose a novel probabilistic method for tag tracking, implemented by means of Bayesian particle filtering and a trans-dimensional Markov chain Monte Carlo (MCMC) approach, which efficiently combines information about the imaging process and tag appearance with prior knowledge about the heart dynamics obtained by means of non-rigid image registration. Experiments using synthetic image data (with ground truth) and real data (with expert manual annotation) from preclinical (small animal) and clinical (human) studies confirm that the proposed method yields higher consistency, accuracy, and intrinsic tag reliability assessment in comparison with other frequently used tag tracking methods.

Reversible jump MCMC methods for fully automatic motion analysis in tagged MRI

Tagged magnetic resonance imaging (tMRI) is a well-known noninvasive method for studying regional heart dynamics. It offers great potential for quantitative analysis of a variety of kine(ma)tic parameters, but its clinical use has so far been limited, in part due to the lack of robustness and accuracy of existing tag tracking algorithms in dealing with low (and intrinsically time-varying) image quality. In this paper, we evaluate the performance of four frequently used concepts found in the literature (optical flow, harmonic phase (HARP) magnetic resonance imaging, active contour fitting, and non-rigid image registration) for cardiac motion analysis in 2D tMRI image sequences, using both synthetic image data (with ground truth) and real data from preclinical (small animal) and clinical (human) studies. In addition we propose a new probabilistic method for tag tracking that serves as a complementary step to existing methods. The new method is based on a Bayesian estimation framework, implemented by means of reversible jump Markov chain Monte Carlo (MCMC) methods, and combines information about the heart dynamics, the imaging process, and tag appearance. The experimental results demonstrate that the new method improves the performance of even the best of the four previous methods. Yielding higher consistency, accuracy, and intrinsic tag reliability assessment, the proposed method allows for improved analysis of cardiac motion.

Myocardial tagging by cardiovascular magnetic resonance: evolution of techniques--pulse sequences, analysis algorithms, and applications

Cardiovascular magnetic resonance (CMR) tagging has been established as an essential technique for measuring regional myocardial function. It allows quantification of local intramyocardial motion measures, e.g. strain and strain rate. The invention of CMR tagging came in the late eighties, where the technique allowed for the first time for visualizing transmural myocardial movement without having to implant physical markers. This new idea opened the door for a series of developments and improvements that continue up to the present time. Different tagging techniques are currently available that are more extensive, improved, and sophisticated than they were twenty years ago. Each of these techniques has different versions for improved resolution, signal-to-noise ratio (SNR), scan time, anatomical coverage, three-dimensional capability, and image quality. The tagging techniques covered in this article can be broadly divided into two main categories: 1) Basic techniques, which include magnetization saturation, spatial modulation of magnetization (SPAMM), delay alternating with nutations for tailored excitation (DANTE), and complementary SPAMM (CSPAMM); and 2) Advanced techniques, which include harmonic phase (HARP), displacement encoding with stimulated echoes (DENSE), and strain encoding (SENC). Although most of these techniques were developed by separate groups and evolved from different backgrounds, they are in fact closely related to each other, and they can be interpreted from more than one perspective. Some of these techniques even followed parallel paths of developments, as illustrated in the article. As each technique has its own advantages, some efforts have been made to combine different techniques together for improved image quality or composite information acquisition. In this review, different developments in pulse sequences and related image processing techniques are described along with the necessities that led to their invention, which makes this article easy to read and the covered techniques easy to follow. Major studies that applied CMR tagging for studying myocardial mechanics are also summarized. Finally, the current article includes a plethora of ideas and techniques with over 300 references that motivate the reader to think about the future of CMR tagging.

Comparison of different grid of tags detection methods in tagged cardiac MR imaging

PURPOSE

Non-invasive imaging assessment of cardiac function is important in cardiovascular disease diagnosis, especially for evaluation of local cardiac motion. Tagged cardiac MRI has been developed for this purpose, but evaluation of the results requires quantification and automation.

METHODS

Two methods utilizing active contour modeling for wall motion extraction based on tagged cardiac MRI scans were evaluated based on properties of tracking methods in the image domain and frequency domain. Three criteria were used: accuracy, inter-subject and intra-subject sensitivity. The tracking results were evaluated by a medical expert. The evaluation methodology and its possible generalization to other diagnostic methods were considered.

RESULTS

Image domain and frequency domain analysis of tagged cardiac MRI data sets were evaluated demonstrating that the image domain method provides better results. The image domain method method is much more resistant to changes in the data, this time, due to a different subject being scanned. The frequency domain approach is not suitable for clinical applications, as the global error is significantly increased (more than 20%).

CONCLUSION

The image domain method was found most effective, and it can generate a set of clearly identified parameters. The evaluation approach can be an interesting alternative to classical psychovisual studies which are time-consuming and often fastidious for clinicians.

A multiresolution method for tagline detection and indexing

Tagline detection and indexing are challenging tasks due to complicated anatomical properties and imaging noise. In this paper, we will address the following two important issues in tagline detection: 1) an automatic method independent from imaging approaches with improved robustness and accuracy and 2) tagline indexing that matches taglines in task and reference images for postprocessing. Our method consists of two steps: First, a wavelet decomposition is performed on a tagged magnetic resonance (tMR) image. Subband correlation is used to dampen anatomical boundaries but enhance taglines. A tagline map is created by segmenting a reconstructed image using pseudowavelet reconstruction. Next, tagline pixels are grouped into clusters and isolated small line segments are eliminated. A snake method is then used to index and recover broken taglines. Our method has been validated with 320 tMR tongue images. Measurement of tagline accuracy was performed by computing tag pixel displacement. Without assumptions on tagline models, it detects taglines automatically. Comparison studies were conducted against the harmonic phase method. Our experiments resulted in a p-value of 1E-6 with one-way ANOVA, which indicates a significant improvement in accuracy and robustness.

Segmentation of myocardial boundaries in tagged cardiac MRI using active contours: a gradient-based approach integrating texture analysis

The noninvasive assessment of cardiac function is of first importance for the diagnosis of cardiovascular diseases. Among all medical scanners only a few enables radiologists to evaluate the local cardiac motion. Tagged cardiac MRI is one of them. This protocol generates on Short-Axis (SA) sequences a dark grid which is deformed in accordance with the cardiac motion. Tracking the grid allows specialists a local estimation of cardiac geometrical parameters within myocardium. The work described in this paper aims to automate the myocardial contours detection in order to optimize the detection and the tracking of the grid of tags within myocardium. The method we have developed for endocardial and epicardial contours detection is based on the use of texture analysis and active contours models. Texture analysis allows us to define energy maps more efficient than those usually used in active contours methods where attractor is often based on gradient and which were useless in our case of study, for quality of tagged cardiac MRI is very poor.

Balanced left ventricular myocardial SSFP-tagging at 1.5T and 3T

The purpose of the study was to evaluate the performance of steady-state free precession (SSFP)-tagging at 1.5T and 3T and to define the ideal settings with respect to optimized tag contrast throughout the cardiac cycle for both field strengths. To identify optimal imaging parameters data acquisition was repeated for different flip angles. Left ventricular tag-tissue contrast, tag fading times, tag persistence, and myocardial signal-to-noise ratio (SNR) were quantified in basal, mid-ventricular, and apical slice locations. To assess the effect of field strength on image quality and artifact level, additional semiquantitative image grading was performed by two experienced readers. SSFP-tagging at 3T proved superior to 1.5T and provided significantly enhanced tag persistence and myocardial SNR while maintaining overall image quality and artifact level. The definition of a tag quality index demonstrated optimal SSFP-tagging performance for a flip angle of 20 degrees . Diastolic tag visibility was improved at 3T and resulted in enhanced average tag persistence of 789 +/- 128 ms compared to 523 +/- 40 ms at 1.5T. For SSFP-tagging at 3T the combination of T(1) lengthening and superior myocardial SNR is highly promising and has the potential to improve the depiction of tagged myocardial function throughout the entire cardiac cycle.

Preliminary validation of angle-independent myocardial elastography using MR tagging in a clinical setting

Myocardial elastography (ME), a radio-frequency (RF) based speckle tracking technique, was employed in order to image the entire two-dimensional (2D) transmural deformation field in full echocardiographic views and was validated against tagged magnetic resonance imaging (tMRI) in normal as well as reperfused (i.e., treated myocardial infarction [MI]) human left ventricles. RF ultrasound and tMRI frames were acquired at the papillary muscle level in 2D short-axis (SA) views at the frame rates of 136 (fps; real-time) and 33 fps (electrocardiogram [ECG]-gated), respectively. In ME, in-plane, 2D (lateral and axial) incremental displacements were iteratively estimated using one-dimensional (1D) cross-correlation and recorrelation techniques in a 2D search with a 1D matching kernel. In tMRI, cardiac motion was estimated by a template-matching algorithm on a 2D grid-shaped mesh. In both ME and tMRI, cumulative 2D displacements were obtained and then used to estimate 2D Lagrangian finite systolic strains, from which polar (i.e., radial and circumferential) strains, namely angle-independent measures, were further obtained through coordinate transformation. Principal strains, which are angle-independent and less centroid-dependent than polar strains, were also computed and imaged based on the 2D finite strains using methodology previously established. Both qualitatively and quantitatively, angle-independent ME is shown to be capable of (1) estimating myocardial deformation in good agreement with tMRI estimates in a clinical setting and of (2) differentiating abnormal from normal myocardium in a full left-ventricular view. The principal strains were concluded to be a potential diagnostic measure for detection of cardiac disease with reduced centroid dependence.

Automatic 3D tracking of cardiac material markers using slice-following and harmonic-phase MRI

A method to track a grid of cardiac material points in three dimensions using slice-following (SF) tagged magnetic resonance imaging (MRI) and harmonic-phase MRI is presented. A three-dimensional grid of material points on the lines of intersections of short-axis (SA) and long-axis (LA) planes is automatically tracked by combining two-dimensional pathlines that are computed on both SA and LA image planes. This process yields the true three-dimensional motion of points originating on the image plane intersections. Experimental data from normal volunteers, each obtained in four short breath-holds using the SF harmonic phase MRI pulse sequence, is presented. A validation of two-dimensional in-plane tracks using this pulse sequence on a moving phantom is also presented.

Advances in MRI tagging techniques for determining regional myocardial strain

MRI of the heart with magnetization tagging provides a potentially useful new way to assess cardiac mechanical function, through revealing the local motion of otherwise indistinguishable portions of the heart wall. Although still an evolving area, tagged cardiac MRI is already able to provide novel quantitative information on cardiac function. Exploiting this potential requires developing tailored methods for both imaging and image analysis. In this article, we review some of the progress that has been made in developing imaging methods for tagged cardiac MRI.

Biventricular myocardial strains via nonrigid registration of anatomical NURBS model [corrected]

We present research in which both left and right ventricular deformation is estimated from tagged cardiac magnetic resonance imaging using volumetric deformable models constructed from nonuniform rational B-splines (NURBS). The four model types considered and compared for the left ventricle include two Cartesian NURBS models--one with a cylindrical parameter assignment and one with a prolate spheroidal parameter assignment. The remaining two are non-Cartesian, i.e., prolate spheroidal and cylindrical each with their respective prolate spheroidal and cylindrical parameter assignment regimes. These choices were made based on the typical shape of the left ventricle. For each frame starting with end-diastole, a NURBS model is constructed by fitting two surfaces with the same parameterization to the corresponding set of epicardial and endocardial contours from which a volumetric model is created. Using normal displacements of the three sets of orthogonal tag planes as well as displacements of contour/tag line intersection points and tag plane intersection points, one can solve for the optimal homogeneous coordinates, in a weighted least squares sense, of the control points of the deformed NURBS model at end-diastole using quadratic programming. This allows for subsequent nonrigid registration of the biventricular model at end-diastole to all later time frames. After registration of the model to all later time points, the registered NURBS models are temporally lofted in order to create a comprehensive four-dimensional NURBS model. From the lofted model, we can extract three-dimensional myocardial deformation fields and corresponding Lagrangian and Eulerian strain maps which are local measures of nonrigid deformation. The results show that, in the case of simulated data, the quadratic Cartesian NURBS models with the cylindrical and prolate spheroidal parameter assignments outperform their counterparts in predicting normal strain. The decreased complexity associated with the Cartesian model with the cylindrical parameter assignment prompted its use for subsequent calculations. Lagrangian strains in three canine data, a normal human, and a patient with history of myocardial infarction are presented. Eulerian strains for the normal human data are also included.

A non-rigid registration approach for quantifying myocardial contraction in tagged MRI using generalized information measures

We address the problem of quantitatively assessing myocardial function from tagged MRI sequences. We develop a two-step method comprising (i) a motion estimation step using a novel variational non-rigid registration technique based on generalized information measures, and (ii) a measurement step, yielding local and segmental deformation parameters over the whole myocardium. Experiments on healthy and pathological data demonstrate that this method delivers, within a reasonable computation time and in a fully unsupervised way, reliable measurements for normal subjects and quantitative pathology-specific information. Beyond cardiac MRI, this work redefines the foundations of variational non-rigid registration for information-theoretic similarity criteria with potential interest in multimodal medical imaging.

Tagged magnetic resonance imaging of the heart: a survey

Magnetic resonance imaging (MRI) of the heart with magnetization tagging provides a potentially useful new way to assess cardiac mechanical function, through revealing the local motion of otherwise indistinguishable portions of the heart wall. While still an evolving area, tagged cardiac MRI is already able to provide novel quantitative information on cardiac function. Exploiting this potential requires developing tailored methods for both imaging and image analysis. In this paper, we review some of the progress that has been made in developing such methods for tagged cardiac MRI, as well as some of the ways these methods have been applied to the study of cardiac function.

Analysis of 3-D myocardial motion in tagged MR images using nonrigid image registration

Tagged magnetic resonance imaging (MRI) is unique in its ability to noninvasively image the motion and deformation of the heart in vivo, but one of the fundamental reasons limiting its use in the clinical environment is the absence of automated tools to derive clinically useful information from tagged MR images. In this paper, we present a novel and fully automated technique based on nonrigid image registration using multilevel free-form deformations (MFFDs) for the analysis of myocardial motion using tagged MRI. The novel aspect of our technique is its integrated nature for tag localization and deformation field reconstruction using image registration and voxel based similarity measures. To extract the motion field within the myocardium during systole we register a sequence of images taken during systole to a set of reference images taken at end-diastole, maximizing the normalized mutual information between the images. We use both short-axis and long-axis images of the heart to estimate the full four-dimensional motion field within the myocardium. We also present validation results from data acquired from twelve volunteers.

Spatial transformation of motion and deformation fields using nonrigid registration

In this paper, we present a technique that can be used to transform the motion or deformation fields defined in the coordinate system of one subject into the coordinate system of another subject. Such a transformation accounts for the differences in the coordinate systems of the two subjects due to misalignment and size/shape variation, enabling the motion or deformation of each of the subjects to be directly quantitatively and qualitatively compared. The field transformation is performed by using a nonrigid registration algorithm to determine the intersubject coordinate system mapping from the first subject to the second subject. This fixes the relationship between the coordinate systems of the two subjects, and allows us to recover the deformation/motion vectors of the second subject for each corresponding point in the first subject. Since these vectors are still aligned with the coordinate system of the second subject, the inverse of the intersubject coordinate mapping is required to transform these vectors into the coordinate system of the first subject, and we approximate this inverse using a numerical line integral method. The accuracy of our numerical inversion technique is demonstrated using a synthetic example, after which we present applications of our method to sequences of cardiac and brain images.

Measurement of strain in physical models of brain injury: a method based on HARP analysis of tagged magnetic resonance images (MRI)

Two-dimensional (2-D) strain fields were estimated non-invasively in two simple experimental models of closed-head brain injury. In the first experimental model, shear deformation of a gel was induced by angular acceleration of its spherical container In the second model the brain of a euthanized rat pup was deformed by indentation of its skull. Tagged magnetic resonance images (MRI) were obtained by gated image acquisition during repeated motion. Harmonic phase (HARP) images corresponding to the spectral peaks of the original tagged MRI were obtained, following procedures proposed by Osman, McVeigh and Prince. Two methods of HARP strain analysis were applied, one based on the displacement of tag line intersections, and the other based on the gradient of harmonic phase. Strain analysis procedures were also validated on simulated images of deformed grids. Results show that it is possible to visualize deformation and to quantify strain efficiently in animal models of closed head injury.

In vivo strain and stress estimation of the heart left and right ventricles from MRI images

Mechanical properties of the myocardium have been investigated intensively in the last four decades. Many complex strain energy functions have been used to estimate the stress-strain relationship of myocardium because the heart muscle is an inhomogeneous, anisotropic, and nearly incompressible material, which undergoes large deformations. These functions can be effective for fitting in vitro experimental data from myocardial stretch testing. However, it is difficult to model in vivo myocardium using these strain energy functions. Moreover, such estimates have so far been carried out almost exclusively on the left ventricle, because of the relative thinness and complex geometry of the right ventricle. Previous work from our research group has successful estimated the motion and deformation of both the left and the right ventricles, using data from noninvasive tagged magnetic resonance imaging. In this paper, we present a novel statistical model to estimate the in vivo material properties and strain and stress distribution in both ventricles, using such data. Two normal hearts and two hearts with right-ventricular hypertrophy (RVH) were studied and noticeable differences were found between the strain and stress distributions for normal volunteers and RVH patients. Compared to the strain energy function approach, our model is more intuitively understandable.

Harmonic phase MR tagging for direct quantification of lagrangian strain in rat hearts after myocardial infarction

The utility of harmonic phase (HARP) analysis was recently demonstrated in humans and large animals as a technique for rapid and automatic analysis of tagged magnetic resonance images. In the current study, the applicability and accuracy of HARP analysis for automatic strain quantification in small animals were investigated. A validation study was performed on seven postinfarct rats and seven age-matched controls. A method for direct computation of 2D Lagrangian strain fields from spatial derivatives of HARP images was also developed in this paper. The results of HARP analysis were evaluated by comparison with those of homogeneous strain analysis employing finite element method and manual tag tracking. Both methods were validated with simulated digital images. Compared to conventional homogeneous strain analysis, HARP analysis yielded similar results in the assessment of regional strain patterns in both control and infarct rats. Both methods detected a reduction in maximal stretch and shortening in infarct rats. Our results suggest that HARP analysis can also be applied to quantify alterations in regional myocardial wall motion in small animals.

Estimating Motion From MRI Data

INVITED PAPER: Magnetic resonance imaging (MRI) is an ideal imaging modality to measure blood flow and tissue motion. It provides excellent contrast between soft tissues, and images can be acquired at positions and orientations freely defined by the user. From a temporal sequence of MR images, boundaries and edges of tissues can be tracked by image processing techniques. Additionally, MRI permits the source of the image signal to be manipulated. For example, temporary magnetic tags displaying a pattern of variable brightness may be placed in the object using MR saturation techniques, giving the user a known pattern to detect for motion tracking. The MRI signal is a modulated complex quantity, being derived from a rotating magnetic field in the form of an induced current. Well-defined patterns can also be introduced into the phase of the magnetization, and could be thought of as generalized tags. If the phase of each pixel is preserved during image reconstruction, relative phase shifts can be used to directly encode displacement, velocity and acceleration. New methods for modeling motion fields from MRI have now found application in cardiovascular and other soft tissue imaging. In this review, we shall describe the methods used for encoding, imaging, and modeling motion fields with MRI.

Construction of a statistical model for cardiac motion analysis using nonrigid image registration

In this paper we present a new technique for tracking the movement of the myocardium using a statistical model derived from the motion fields in the hearts of several healthy volunteers. To build the statistical model we tracked the motion of the myocardium in 17 volunteers using a nonrigid registration technique based on free-form deformations and mapped the motion fields obtained into a common reference coordinate system. A principal component analysis (PCA) was then performed on the motion fields to extract the major modes of variation in the fields between the successive time frames. The modes of variation obtained were then used to parametrize the free-form deformations and build our statistical model. The results of using our model to track the motion of the heart in normal volunteers are also presented.

A global method based on thin-plate splines for correction of geometric distortion: an application to fluoroscopic images

Quantitative analysis of biomedical images needs a careful correction of geometric distortion. To avoid the discontinuities of the local correction techniques and achieve good accuracy in the presence of global and local distortion, a novel global correction technique based on thin-plate splines is proposed. The technique approximates the grid points by a thin plate minimizing the weighted sum of the bending energy and the mean squared residual errors. The method proposed is compared with three traditional correction techniques: two local and one global. One local technique is linear and takes into account translation, rotation, and scaling, the other is nonlinear and includes skewing. The global technique is based on a two-dimensional polynomial model. Computer-based simulations and experimental tests on fluoroscopic images were carried out. The local techniques were sensitive to both sigmoidal and radial distortion. The polynomial and thin-plate splines global techniques were found sensitive only to sigmoidal distortion and to radial distortion, respectively. The two global techniques showed better performances with respect to any local on synthetic and real images. Where the distortion is predominantly radial or high computational efficiency is required, the polynomial global correction technique should be preferred. Where the distortion has a local nature or is predominantly sigmoidal, the thin-plate splines global correction technique should be chosen.

Exploratory analysis of the spatio-temporal deformation of the myocardium during systole from tagged MRI

Myocardial contractile function is, with perfusion, one of the main affected factors in ischemic heart diseases. In this paper, we propose an original framework based on functional data analysis for the quantitative study of spatio-temporal parameters related to the myocardial contraction mechanics. The mechanical strains in the left-ventricular (LV) myocardium are computed from tagged magnetic resonance imaging cardiac sequences. A statistical functional model of the normal contractile function of the LV is build from the study of eight examinations on healthy subjects. We show that it is possible to detect abnormal strain patterns comparatively to this model, by generating distance maps at rest and under pharmacological stress. We demonstrate the consistency of the results for the circumferential deformation parameter on healthy and pathological data sets.

A MAP framework for tag line detection in SPAMM data using Markov random fields on the B-spline solid

Magnetic resonance (MR) tagging is a technique for measuring heart deformations through creation of a stripe grid pattern on cardiac images. In this paper, we present a maximum a posteriori (MAP) framework for detecting tag lines using a Markov random field (MRF) defined on the lattice generated by three-dimensional (3-D) and four-dimensional (4-D) (3-D + t) uniform sampling of B-spline models. In the 3-D case, MAP estimation is cast for detecting present tag features in the current image given an initial solid from the previous frame (the initial undeformed solid is manually positioned by clicking on corner points of a cube). The method also allows the parameters of the solid model, including the number of knots and the spline order, to be adjusted within the same framework. Fitting can start with a solid with less knots and lower spline order and proceed to one with more knots and/or higher order so as to achieve more accuracy and/or higher order of smoothness. In the 4-D case, the initial model is considered to be the linear interpolation of a sequence of optimal solids obtained from 3-D tracking. The same framework proposed for the 3-D case can once again be applied to arrive at a 4-D B-spline model with a higher temporal order.

Estimation of 3-D left ventricular deformation from medical images using biomechanical models

The quantitative estimation of regional cardiac deformation from three-dimensional (3-D) image sequences has important clinical implications for the assessment of viability in the heart wall. We present here a generic methodology for estimating soft tissue deformation which integrates image-derived information with biomechanical models, and apply it to the problem of cardiac deformation estimation. The method is image modality independent. The images are segmented interactively and then initial correspondence is established using a shape-tracking approach. A dense motion field is then estimated using a transversely isotropic, linear-elastic model, which accounts for the muscle fiber directions in the left ventricle. The dense motion field is in turn used to calculate the deformation of the heart wall in terms of strain in cardiac specific directions. The strains obtained using this approach in open-chest dogs before and after coronary occlusion, exhibit a high correlation with strains produced in the same animals using implanted markers. Further, they show good agreement with previously published results in the literature. This proposed method provides quantitative regional 3-D estimates of heart deformation.