Passive diastolic modelling of human ventricles : effects of base movement and geometrical heterogeneity

Left-ventricular (LV) remodelling, associated with diastolic heart failure, is driven by an increase in myocardial stress. Therefore, normalisation of LV wall stress is the cornerstone of many therapeutic treatments. However, information regarding such regional stress–strain for human LV is still limited. Thus, the objectives of our study were to determine local diastolic stress–strain field in healthy LVs, and consequently, to identify the regional variations amongst them due to geometric heterogeneity. Effects of LV base movement on diastolic model predictions, which were ignored in the literature, were further explored. Personalised finite-element modelling of five normal human bi-ventricles was carried out using subject-specific myocardium properties. Model prediction was validated individually through comparison with end-diastolic volume and a new shape-volume based measurement of LV cavity, extracted from magnetic resonance imaging. Results indicated that incorporation of LV base movement improved the model predictions (shape-volume relevancy of LV cavity), and therefore, it should be considered in future studies. The LV endocardium always experienced higher fibre stress compared to the epicardium for all five subjects. The LV wall near base experienced higher stress compared to equatorial and apical locations. The lateral LV wall underwent greater stress distribution (fibre and sheet stress) compared to other three regions. In addition, normal ranges of different stress–strain components in different regions of LV wall were reported for five healthy ventricles. This information could be used as targets for future computational studies to optimise diastolic heart failure treatments or design new therapeutic interventions/devices

Computational Modeling of Cardiac Biomechanics

The goal of this dissertation was to develop a realistic and patient-specific computational model of the heart that ultimately would help medical scientists to better diagnose and treat heart diseases. In order to achieve this goal, a three dimensional finite element model of the heart was created using magnetic resonance images of the beating pig heart. This model was loaded by the pressure of blood inside the left ventricle which was measured by synchronous catheterization. A recently developed structurally based constitutive model of the myocardium was incorporated in the finite element solver to model passive left ventricular myocardium. Additionally, an unloading algorithm originally designed for arteries was adapted to estimate the stress-free geometry of the heart from its partially-loaded geometry obtained from magnetic resonance imaging. Finally, a regionally varying growth module was added to the computational model to predict eccentric hypertrophy of the heart under various pathological conditions that result in volume overload of the heart. The computational model was validated using experimental data obtained from porcine heart such as in vivo strains measured from magnetic resonance imaging

MR imaging of left-ventricular function : novel image acquisition and analysis techniques.

Many cardiac diseases, such as myocardial ischemia, secondary to coronary artery disease, may be identified and localized through the analysis of cardiac deformations. Early efforts for quantifying ventricular wall motion used surgical implantation and tracking of radiopaque markers with X-ray imaging in canine hearts [1]. Such techniques are invasive and affect the regional motion pattern of the ventricular wall during the marker tracking process and, clearly are not feasible clinically. Noninvasive imaging techniques are vital and have been widely applied to the clinic. MRI is a noninvasive imaging technique with the capability to monitor and assess the progression of cardiovascular diseases (CVD) so that effective procedures for the care and treatment of patients can be developed by physicians and researchers. It is 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 imaging sequences. In order to assess cardiac function, there are two categories of indices that are used: global and regional indices. Global indices include ejection fraction, cavity volume, and myocardial mass [2]. They are important indices for cardiac disease diagnosis. However, these global indices are not specific for regional analysis. A quantitative assessment of regional parameters may prove beneficial for the diagnosis of disease and evaluation of severity and the quantification of treatment [3]. Local measures, such as wall deformation and strain in all regions of the heart, can provide objective regional quantification of ventricular wall function and relate to the location and extent of ischemic injury. This dissertation is concerned with the development of novel MR imaging techniques and image postprocessing algorithms to analyze left ventricular deformations. A novel pulse sequence, termed Orthogonal CSPAMM (OCSPAMM), has been proposed which results in the same acquisition time as SPAMM for 2D deformation estimation while keeping the main advantages of CSPAMM [4,5]: i.e., maintaining tag contrast through-out the ECG cycle. Different from CSPAMM, in OCSPAMM the second tagging pulse orientation is rotated 90 degrees relative to the first one so that motion information can be obtained simultaneously in two directions. This reduces the acquisition time by a factor of two as compared to the traditional CSPAMM, in which two separate imaging sequences are applied per acquisition. With the application of OCSPAMM, the effect of tag fading encountered in SPAMM tagging due to Tl relaxation is mitigated and tag deformations can be visualized for the entire cardiac cycle, including diastolic phases. A multilevel B-spline fitting method (MBS) has been proposed which incorporates phase-based displacement information for accurate calculation of 2D motion and strain from tagged MRI [6, 7]. The proposed method combines the advantages of continuity and smoothness of MBS, and makes use of phase information derived from tagged MR images. Compared to previous 2D B-spline-based deformation analysis methods, MBS has the following advantages: 1) It can simultaneously achieve a smooth deformation while accurately approximating the given data set; 2) Computationally, it is very fast; and 3) It can produce more accurate deformation results. Since the tag intersections (intersections between two tag lines) can be extracted accurately and are more or less distributed evenly over the myocardium, MBS has proven effective for 2D cardiac motion tracking. To derive phase-based displacements, 2D HARP and SinMod analysis techniques [8,9] were employed. By producing virtual tags from HARP /SinMod and calculating intersections of virtual tag lines, more data points are obtained. In the reference frame, virtual tag lines are the isoparametric curves of an undeformed 2D B-spline model. In subsequent frames, the locations of intersections of virtual tag lines over the myocardium are updated with phase-based displacement. The advantage of the technique is that in acquiring denser myocardial displacements, it uses both real and virtual tag line intersections. It is fast and more accurate than 2D HARP and SinMod tracking. A novel 3D sine wave modeling (3D SinMod) approach for automatic analysis of 3D cardiac deformations has been proposed [10]. An accelerated 3D complementary spatial modulation of magnetization (CSPAMM) tagging technique [11] was used to acquire complete 3D+t tagged MR data sets of the whole heart (3 dynamic CSPAMM tagged MRI volume with tags in different orientations), in-vivo, in 54 heart beats and within 3 breath-holds. In 3D SinMod, the intensity distribution around each pixel is modeled as a cosine wave front. The principle behind 3D SinMod tracking is that both phase and frequency for each voxel are determined directly from the frequency analysis and the displacement is calculated from the quotient of phase difference and local frequency. The deformation fields clearly demonstrate longitudinal shortening during systole. The contraction of the LV base towards the apex as well as the torsional motion between basal and apical slices is clearly observable from the displacements. 3D SinMod can automatically process the image data to derive measures of motion, deformations, and strains between consecutive pair of tagged volumes in 17 seconds. Therefore, comprehensive 4D imaging and postprocessing for determination of ventricular function is now possible in under 10 minutes. For validation of 3D SinMod, 7 3D+t CSPAMM data sets of healthy subjects have been processed. Comparison of mid-wall contour deformations and circumferential shortening results by 3D SinMod showed good agreement with those by 3D HARP. Tag lines tracked by the proposed technique were also compared with manually delineated ones. The average errors calculated for the systolic phase of the cardiac cycles were in the sub-pixel range

Shape Analysis Based Strategies for Evaluation of Adaptations in In Vivo Right Ventricular Geometry and Mechanics as Effected by Pulmonary Hypertension

Pulmonary hypertension (PH) is a deadly disease, which as it progresses over time alters many aspects of the afflicted heart, and particularly the right ventricle (RV), such as its size, shape, and mechanical material properties. However, due to the limitations of what can be measured noninvasively in a standard clinical setting and the difficulty caused by the intrinsic complexity of the human RV, there has been little success to-date to identify clinically obtainable metrics of RV shape, deformation, or material properties that are quantitatively linked to the onset and progression of PH. Towards addressing this challenge, this work proposes the use of the shape and shape change of the RV, which is measurable from standard clinical imaging, along with statistical analysis and inverse material characterization strategies to identify new metrics of RV mechanical function that will be uniquely predictive of the state of the heart subject to PH. Thus, this thesis can be broken into two components: the first is statistical shape analysis of the RV, and the second is inverse characterization of heart wall mechanical material properties from RV shape change and measurable hemodynamics. For the statistical shape analysis investigation, a custom approach using harmonic mapping and proper orthogonal decomposition is applied to determine the fundamental components of shape (i.e., modes) from a dataset of 50 patients with varying states of PH, including some without PH at all. For the inverse characterization work, a novel method was developed to estimate the heterogeneous properties of a structure, given only the target shape of that structure, after a known excitation is applied to deform the structure. Lastly, the inverse characterization algorithm was extended to be applicable to actual in vivo cardiac data, particularly through the inclusion of a registration step to account for the organ-scale rotation and translation of the heart. Future work remains to expand on the computational efficiency of this inverse solution estimation procedure, and to further evaluate and improve upon the consistency and clinical interpretability of the material property estimates

Doctor of Philosophy

dissertationImage-based biomechanics, particularly numerical modeling using subject-specific data obtained via imaging, has proven useful for elucidating several biomechanical processes, such as prediction of deformation due to external loads, applicable to both normal function and pathophysiology of various organs. As the field evolves towards applications that stretch the limits of imaging hardware and acquisition time, the information traditionally expected as input for numerical routines often becomes incomplete or ambiguous, and requires specific acquisition and processing strategies to ensure physical accuracy and compatibility with predictive mathematical modeling. These strategies, often derivatives or specializations of traditional mechanics, effectively extend the nominal capability of medical imaging hardware providing subject-specific information coupled with the option of using the results for predictive numerical simulations. This research deals with the development of tools for extracting mechanical measurements from a finite set of imaging data and finite element analysis in the context of constructing structural atlases of the heart, understanding the biomechanics of the venous vasculature, and right ventricular failure. The tools include: (1) application of Hyperelastic Warping image registration to displacement-encoded MRI for reconstructing absolute displacement fields, (2) combination of imaging and a material parameter identification approach to measure morphology, deformation, and mechanical properties of vascular tissue, and (3) extrapolation of diffusion tensor MRI acquired at a single time point for the prediction the structural changes across the cardiac cycle with mechanical simulations. Selected tools were then applied to evaluate structural changes in a reversible animal model for right ventricular failure due to pressure overload

Will the real ventricular architecture please stand up?

Ventricular twisting, essential for cardiac function, is attributed to the contraction of myocardial helical fibers. The exact relationship between ventricular anatomy and function remains to be determined, but one commonly used explanatory model is the helical ventricular myocardial band (HVMB) model of Torrent-Guasp. This model has been successful in explaining many aspects of ventricular function, (Torrent-Guasp et al. Eur. J. Cardiothorac. Surg., 25, 376, 2004; Buckberg et al. Eur. J. Cardiothorac. Surg., 47, 587, 2015; Buckberg et al. Eur. J. Cardiothorac. Surg. 47, 778, 2015) but the model ignores important aspects of ventricular anatomy and should probably be replaced. The purpose of this review is to compare the HVMB model with a different model (nested layers). A complication when interpreting experimental observations that relate anatomy to function is that, in the myocardium, shortening does not always imply activation and lengthening does not always imply inactivation

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

Modelling mitral valvular dynamics–current trend and future directions

Dysfunction of mitral valve causes morbidity and premature mortality and remains a leading medical problem worldwide. Computational modelling aims to understand the biomechanics of human mitral valve and could lead to the development of new treatment, prevention and diagnosis of mitral valve diseases. Compared with the aortic valve, the mitral valve has been much less studied owing to its highly complex structure and strong interaction with the blood flow and the ventricles. However, the interest in mitral valve modelling is growing, and the sophistication level is increasing with the advanced development of computational technology and imaging tools. This review summarises the state-of-the-art modelling of the mitral valve, including static and dynamics models, models with fluid-structure interaction, and models with the left ventricle interaction. Challenges and future directions are also discussed

Modified mass-spring system for physically based deformation modeling

Mass-spring systems are considered the simplest and most intuitive of all deformable models. They are computationally efficient, and can handle large deformations with ease. But they suffer several intrinsic limitations. In this book a modified mass-spring system for physically based deformation modeling that addresses the limitations and solves them elegantly is presented. Several implementations in modeling breast mechanics, heart mechanics and for elastic images registration are presented