Hidenobu Suzuki, Yoshiki Kawata, Noboru Niki, Ryo Haraguchi and Katsuda Toshizo
Morphologic and Functional Modeling of the Heart
The heart functions by cycling through contraction and expansion. There is a close association between morphology and function. Electrophysiology is also important in cardiac function. The presence of a conduction system allows the heart to modify its output to react to different requirements. For computational modeling of the heart, it is necessary to consider both the morphological and functional anatomies; however, building a model that integrates all scales (from molecular to organ) and all phenomena (mechanics, fluid, electrophysiology, and molecular dynamics, among others) is impossible. Clarification of the functions of interest is important.
In clinical practice, assessment of the contractile function of the left ventricle (LV) is important for diagnosing cardiovascular disease. The most widely used index of the LV contractile function is the LV ejection fraction (LVEF). The LVEF is derived from end-diastolic volume (EDV) and end-systolic volume (ESV). The LVEF can be calculated using various noninvasive cardiac imaging modalities, including MRI, CT, SPECT, and echocardiography. Therefore, numerous segmentation techniques for the LV myocardium, including statistical techniques, have been proposed.
Much work is still required to gain an integrated understanding of the normal heart. The computational modeling of the diseased heart has just begun. Because of the complexities of cardiac structure, such as rotational myocardial fibers, and the conduction system, a shape model is not always sufficient to represent various disease states.
In this section, we provide some examples of morphologic and functional modeling of the heart.
Processing Algorithms and Imaging Specific to the Heart There are several noninvasive cardiac imaging modalities. In most modalities (CT, MRI, PET, and SPECT), data acquisition is performed over a few heartbeats with electrocardiographic (ECG) gating. Moving cardiac images can then be reconstructed using the gated data.
For segmentation of cardiac images, it is necessary to consider several points specific to the heart. Epicardial delineation is more difficult than endocardial delineation because of poor contrast and fuzzy boundaries between the heart and other tissues. Endocardial delineation needs intelligent processing because of the presence of the papillary muscles that control the valve leaflets, and myocardial trabeculation, which gives the endocardium its irregular surface. The right ventricle (RV) wall is thinner than the LV wall, making segmentation more difficult. In echocardiography, the limited field of view prevents acquisition of data including the entire organ.
Many methods have been proposed for computational morphologic and functional modeling of the heart. These methods are classified into four categories: (1) statistical models, (2) deformable models/level set, (3) biophysical models, and (4) nonrigid registration using basis functions [149, 284]. The use of statistical models for segmentation has some advantages, such as robustness for regional low contrast, intelligent processing that excludes the papillary muscles, and interpolation for outside the field of view.
Depending on the clinical question, other MR sequences such as DTI (assessing orientation of the myofibers), tagging imaging (assessing myocardial contraction), and velocity encoding imaging (motion of the blood/myocardium) can be performed.
Example 1: Active Appearance Motion Models Bosch et al.  proposed the active appearance motion model (AAMM) technique, which allows fully automated continuous delineation of LV endocardial contours over the heart cycle from echocardiographic images. The AAMM describes both image appearance and object shape within the dynamics of the heart cycle. The authors used 129 infarct patients’ echocardiographic transthoracic four-chamber sequences with manually defined LV contours. They split the datasets randomly into a training set of 65 patients and a testing set of 64 patients. The AAMM was generated from the training dataset. The generated AAMM was applied to segmentation of the 64 sequences and successfully matched 62 patients (97%). The example results are shown in Fig. 3.62. Statistical models built by machine learning (e.g., AAMM) are useful for automatic and robust segmentation of cardiac images.
Fig. 3.62 Fully automated segmentation results obtained by applying the AAMM to an echocar- diographic image sequence. (a) Initial AAMM model positioned on phase images 1, 9, and 16. (b) AAMM match after five iterations. (c) Final match after 20 iterations. (d) Manual contours for comparison 
Example 2: Modeling Contractility Wenk et al.  built a finite element model (FEM) of a patient’s beating infarcted LV and measured regional myocardial deformation with three-dimensional tagging MRI (Fig. 3.63). They showed evidence of depressed contractility in the border zone of a myocardial infarction by combining MR tagging imaging and computer simulation. The combination of biomechanical computational modeling and noninvasive functional imaging techniques can be a powerful methodology to clarify the mechanisms of cardiac diseases.
Example 3: Modeling Myofibers The spatial arrangement of myofibers within the myocardium, which is termed “fiber orientation,” must be taken into account for better understanding of cardiac electrophysiology patterns, mechanical function, and remodeling processes in the living/modeled heart. Lombaert et al.  built a statistical atlas of myofiber architecture with a human dataset of ten healthy ex vivo hearts (Fig. 3.64). The myofibers were imaged with diffusion tensor magnetic resonance imaging (DT-MRI). They used isolated hearts filled with hydrophilic gel to preserve the diastolic volume. In vivo DT-MRI of a beating heart is under
Fig. 3.63 (a) Short-axis view from 3D tagging MR image of patient LV. (b) Finite element model with infarct (brown) and border zone (green) regions 
Fig. 3.64 A statistical atlas of human myofiber architecture, (left) fiber tractography of the left ventricle, (center) close-up of the fiber orientations of a short-axis slice, (right) fiber tractography around the left ventricular blood pool 
development, though the availability of isolated human hearts is extremely rare. Therefore, their statistical myofiber model is valuable.
Example 4: Interactive Modeling for Congenital Heart Disease Congenital heart diseases (CHD) involve developmental abnormalities of the heart and/or great vessels present since before birth. Early treatment is often necessary. Because of its real-time imaging capabilities, 2D echocardiography is often used to diagnose CHD. CT and MRI are unsuitable for real-time diagnosis. 3D echocardiography is sometimes insufficient for detailed imaging of CHD. Only an experienced physician could diagnose from the 2D echocardiographic images based on a spatial perception of the 3D heart; however, it is difficult to transfer the specialist’s spatial perception of the 3D heart structure to other medical staff. There is no effective method of communicating the condition of an individual CHD patient, and sharing the special perception is difficult. Haraguchi and Nakao and Nakao et al. [115,213] proposed a
Fig. 3.65 The heart and great vessels interactive modeling system for CHD
3D heart and great vessels rapid modeling system using echocardiographic images with added simple interaction with the model by the operator (Fig. 3.65). They focused on the expression in a 3D format of the disease state as seen in a mental image by an experienced physician. Physicians can interactively construct patient- specific heart and great vessel models within a practical time frame and share the complex topology. This model cannot represent precise morphological information (e.g., vessel diameters). Nevertheless, it is an example of interactive modeling that may be useful in a particular application.
In the Future Several statistical models of the heart have been proposed for segmentation and registration. These computational models are useful for automation in determining clinically significant indices describing the disease state.
A shape model is not always sufficient to represent the various disease states (e.g., ischemic heart disease and dysrhythmia). The heart has a complex internal structure (e.g., myocardial fiber direction and trabeculation) and involves various phenomena (e.g. mechanics, fluid, and electrophysiology). Developing a biophysical model may help produce an integrated understanding of normal and diseased hearts [18, 129, 296].
To improve cardiac imaging, radiological technologist skills are also required [273, 274]. For example, in MRI, it is necessary to consider many parameters, physical conditions (e.g., quantity of the heterotopic fat) of the patient, heart rate, and breathing-related complicated movement, among other factors.