# Generating anatomical models of the heart and the aorta from medical images for personalized physiological simulations

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DOI: 10.1007/s11517-012-1027-0

- Cite this article as:
- Weese, J., Groth, A., Nickisch, H. et al. Med Biol Eng Comput (2013) 51: 1209. doi:10.1007/s11517-012-1027-0

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## Abstract

The anatomy and motion of the heart and the aorta are essential for patient-specific simulations of cardiac electrophysiology, wall mechanics and hemodynamics. Within the European integrated project euHeart, algorithms have been developed that allow to efficiently generate patient-specific anatomical models from medical images from multiple imaging modalities. These models, for instance, account for myocardial deformation, cardiac wall motion, and patient-specific tissue information like myocardial scar location. Furthermore, integration of algorithms for anatomy extraction and physiological simulations has been brought forward. Physiological simulations are linked closer to anatomical models by encoding tissue properties, like the muscle fibers, into segmentation meshes. Biophysical constraints are also utilized in combination with image analysis to assess tissue properties. Both examples show directions of how physiological simulations could provide new challenges and stimuli for image analysis research in the future.

### Keywords

Physiological simulationPatient-specific anatomical modelHeart and aorta segmentationCoronary veinsHeart motionWall mechanicsPressure waveTissue properties## 1 Introduction

Physiological simulations have specific requirements regarding personalized anatomical models. These models must represent a variety of anatomical structures and functional information. For simulating the electrophysiology in cardiac resynchronization therapy (CRT) it is, for instance, desirable to have a model comprising the anatomy including part of the coronary veins, tissue motion and scar tissue distribution in the left ventricle (see e.g., [1, 46]). In addition, physiological simulations can have specific requirements for heart structures. The wall should, for instance, be represented by the epi- and endocardial borders to allow for a transmural signal propagation in the left atrium [16].

Apart from anatomical structures, tissue properties are important for physiological simulations. Information such as muscle fiber direction in the myocardium can hardly be obtained from clinical images. Given the patient’s heart anatomy, this information may be reconstructed by rule-based approaches [30, 51] or by mapping a specific atlas [43] to the patient’s heart anatomy. Tissue properties can also be linked to image analysis methods. They have, for instance, been used in image registration to tailor the properties of the deformation field [23, 27, 59] for a specific application. Vice versa, a physical constraint may be used in an image analysis algorithm to estimate a tissue’s material parameter.

This paper gives an overview over the image analysis methods developed in the euHeart project [22]. Section 2 summarizes the methods that have been developed to extract the heart anatomy (Sect. 2.1), vasculature (Sect. 2.2) and deformation (Sect. 2.3) from images. Section 3 describes two approaches for a closer integration of image analysis and physiological simulations. The first one integrates information for simulations in a generic anatomical model used in model-based segmentation (Sect. 3.1). The second approach uses the one-dimensional pressure equation to enforce a consistent time-series segmentation of the aorta, while measuring the speed of the pressure wave at the same time (Sect. 3.2). Section 4 illustrates use of the methods for two examples. A comprehensive heart model is generated by integrating anatomy, vasculature and deformation information (Sect. 4.1). Furthermore, the methods are used to set up and perform electrical signal propagation in the left atrium (Sect. 4.2). The paper concludes with a discussion of the results and an outlook.

## 2 Comprehensive anatomical models

### 2.1 Model-based heart segmentation

The resulting accuracy of the viability information depends to a large extent on the accuracy of both the anatomical model and the mapping of the model to the LE image. For the considered 3D SSFP MR images, the LV endocardium can be segmented robustly, but the epicardium is often hardly visible. To improve the segmentation, the epicardium is linked to the shape of the endocardium (cf. also [28]). To reflect the observed variability of inter-patient myocardium thickness, the myocardium thickness is corrected by a patient-specific factor measured at a reliable location like the interventricular septum. Thereby it is assumed that this deviation from the model is similar in all regions of a patient’s LV myocardium which might not hold under specific disease conditions. Using 20 clinical 3D SSFP MR data sets, it was shown that the proposed shape-bias for the epicardium reduces the segmentation error of the LV epicardium from 1.28 to 1.17 mm [24].

### 2.2 Vessel segmentation

Apart from shape of the whole heart including the four chambers also the supplying and draining vessels are essential for a comprehensive heart model. For example, for simulating the electrophysiology in CRT it is desirable to complement the anatomical heart model with the coronary venous system assuming a placement of LV lead through the coronary venous tree [13].

Well-known vessel segmentation techniques [34] are intensity-based methods [48], generalized cylinder approximations [56], multiscale [45, 52] and skeletonization [58] schemes, and deformable model approaches [25, 36] applied on successive 2D slices or on volume data. In our approach, a geometrical moment-based tracking algorithm is applied to magnetic resonance angiography (MRA) datasets to extract the coronary venous system. Initially, the algorithm was designed for the lower limb vessel extraction [54] and coronary arteries [10] in multi-slice CT angiography (MSCTA). Its principle is based on the assumption that a vessel can be locally approximated by a cylinder. Then, analytical expressions of 3D geometrical moments of up to order two are used in association with local intensity information to compute the local orientation of the cylinder axis and its diameter. The initialization of the tracking is performed from a list of seed points, interactively selected at a preliminary stage. From one seed point *P*_{i}, its position is first refined through an iterative process to make it converge towards the central axis. Then the local diameter is estimated using a multiscale local moment computation to take into account the size variation of the vessel. Afterwards, the tracking process is carried out by shifting a circular window towards a point *P*_{i} + 1 according to the estimated direction at point *P*_{i}. The incremental displacement between these two points is made adaptive and depends on the vessel size and curvature.

- 1.
The regularization of the tracking direction with the application of an infinite impulse response (IIR) filtering on the successive directions;

- 2.
The search for the optimal location of the centreline through the construction of a set of paths, based on a multiple hypothesis testing procedure [55];

- 3.
The selection of the optimal path for each coronary vein branch by means of a graph-based method: it consisted of the still-leaf of the graph, in applying a minimum spanning tree algorithm [20] followed by graph erosion [38].

Once the vein centerlines have been extracted, the vessel lumen was extracted from the local radius estimation at each central axis position. The latter one was computed using the cylinder equation, the background and vessel mean intensity computed inside and outside the vessel, and the zero order geometric moment.

### 2.3 Motion analysis

The quantification of cardiac motion and strain provides insight into cardiac function through the assessment of how a given pathology affects global and local deformation of the myocardium. For instance, the measurement of the relative timing of regional myocardial tissue motion helps to identify the type of dyssynchrony of each CRT candidate and the selection criteria for therapy [17]. Hence, personalized physiological simulations with comprehensive physiological heart models should be enriched by heart motion analysis.

Applying non-rigid registration for quantifying cardiac deformation has been thoroughly investigated both in tagged MR [57] and 3D ultrasound images [2, 21]. However, most of these approaches align images in a sequential manner, without exploiting the natural redundancy in the images sequence. Spatiotemporal registration methods solve for the full motion field, taking the whole image sequence as input [32, 37, 41]. In parallel, diffeomorphic registration techniques [7] substituted the classical representation of a non-rigid transformation using displacement fields by velocity fields. Diffeomorphic registration was first extended to temporal image sequences by [29].

Our temporal diffeomorphic free form deformation (TDFFD) algorithm [14] replaces the representation of the dense velocity field used in [29] by a B-spline representation continuous in space and time. Starting from a point in a reference frame (green point in Fig. 4), the point can be transported to other frames by following the flow of the velocity field and the interpolated intensities (red points in Fig. 4) can be matched to the intensity of the reference frame. Every pair of frames in the sequence can be seen as one observation channel to optimize the velocity field. Indeed, as suggested in Fig. 4, a variation of velocity in one frame modifies the interpolated intensities in all “channels”. Thus, when computing the metric gradient in the space of velocity parameters, e.g., for a specific time, derivative contributions from adjacent frames are transported to this time. This transport involves the parametric derivative of the velocity field at the transported time points and the volume change introduced by the transformation between the two considered instants.

The simultaneous use of multiple channels during motion estimation in combination with the B-spline representation of the velocity field that is continuous in space and time is expected to improve the robustness of the motion quantification algorithm. Indeed, it was shown in [14] that the TDFFD algorithm was more accurate at low levels of signal to noise ratios in synthetic ultrasound images with known ground truth motion compared to a classical pairwise approach.

## 3 Integration of image analysis and biophysical simulations

### 3.1 Encoding of structures for simulations

Personalized physiological simulations of the heart [50] often require knowledge about microstructures. This includes, for example, the atrial fast conduction tracts or muscle fiber directions [16]. Because such structures are hardly visible in clinical images, a direct, individualized segmentation is not feasible to date. However, these structures are visible in histological studies [26] or specialized measurements, such that their typical location can be defined in a simulation model.

*relative to*the segmentation mesh into the model prior to adaptation (Fig. 6). After adapting the model to the image [19], the mesh elements have been deformed and the relative coordinates of a structure with respect to a mesh element are used to reconstruct a specific location.

The approach assumes that the encoded structures show little anatomical variability between different individuals. In addition, the approach assumes that vertex positions of the generic model are mapped to corresponding anatomical positions in the adaptation process. To investigate to what extent the latter assumption is satisfied, *N* = 37 CT scans acquired at the same heart phase (diastasis/reduced filling) with very good segmentation quality were used and model-based segmentation has been performed with varying shape of the reference model. The resulting vertex displacements on the model surface has been measured after model adaptation leading to an average overall accuracy of \(1.6\,\text{mm}\) for corresponding vertex positions.

The error of encoded structures has been determined by averaging the errors in the respective area on the model surface. The average positional deviation along the surface of the left ventricle was around \(1.5\,\text{mm}\) allowing to encode muscle fiber directions without much loss of precision. For sinus node, crista terminalis, pectinate muscles, Bachmann’s bundle, and right atrial inferior isthmus in the atria, the error was below \(2\,\text{mm}.\)

### 3.2 Aorta segmentation with pressure constraint

Various approaches exist with respect to vessel segmentation [34]. Most approaches for aorta segmentation have been developed for 3D CT or MR images, but also aorta segmentation in 3D + T image time-series has been considered [9, 60]. Segmentation of the aorta is of special interest in the context of arterial hemodynamics. However, patient-specific calculation of blood flow through the aorta as a function of time requires the simultaneous mechanical modeling of the vessel walls as well as flow within the lumen of the vessel. Especially, the dimensions and patient-specific material properties of the wall are required, but these physiological constraints are difficult to obtain. This section outlines how information about the material properties of the wall, as a function of distance along the vessel, can be extracted from 4D images of the aorta. The material properties can then be used in the fluid structure interaction (FSI) computation.

Arterial hemodynamics and especially the blood pressure and flow-velocity wave forms have been studied for a long time [3]. For an idealized cylindrical axi-symmetric vessel with linear wall material, the pressure in the vessel as a function of distance along the vessel and time obeys the 1D wave equation. The pressure difference with respect to a reference point is proportional to the associated fractional radius change (FRC). The proportionality factor can be either related to Young’s modulus describing tissue stiffness or to the pressure wave velocity. Measuring the FRC can therefore supply information about the variation of these properties along the vessel.

To determine the FRC between the image slice of the reference segment and the image slice of another segment at a distinct time point, an optical flow approach as in [5] restricted to a radial transform and simple translation can be used. The optical flow approach leads to one equation for every pixel, and the resulting set of simultaneous equations can be robustly solved for the unknown FRC and translation.

The equations for all slice pairs can be aggregated together in matrix vector form and solved simultaneously. However, even if aggregated the values of the FRC as function of distance along the vessel and time are determined independently of the others. The computed values are therefore inevitably corrupted by noise in the image data. Since for the ideal cylinder the FRC obeys the wave equation, this fact can be imposed as a Tikhonov regularization on the solution of the set of simultaneous equations. To this end, a constraint is derived from the form of the wave equation [6], ensuring that the resulting values of the FRC (Fig. 8b) satisfy both the data and the constraint.

Aorta segmentation with pressure constraint requires an estimate of wave-speed. Initially, the registration can be performed using literature values (normal ranges are 5-10 m/s) to obtain a first approximation of the wave speed curve. In a second iteration, an updated version of the wave speed curve is obtained using the data from the first run.

This algorithm has been validated using idealized cylindrical data, with and without a radius changing along the vessel, and using an FSI simulation on a patient’s anatomy.

## 4 Examples

### 4.1 Comprehensive model for a CRT case

### 4.2 Simulation of anisotropic excitation propagation

## 5 Discussion and conclusion

Heart chamber segmentation, vessel segmentation and deformation estimation algorithms have been developed in the European integrated project euHeart. Particular attention was paid to needs that are relevant for physiological simulations such as the integration of scar tissue information in the context of CRT. In addition, two approaches to closely link image processing and simulations have been presented. The first one allows to encode structures and information for simulations into segmentation meshes and to efficiently set up simulations. The second one directly integrates biophysical constraints with image analysis.

The direct integration of biophysical constraints with image analysis looks promising. The example of aorta segmentation from time-series of images using a pressure constraint shows the potential to assess tissue properties and improve data interpretation. This approach seems to be an alternative to simulation-based methods for the characterization of tissue properties, where simulation parameters are adapted to match medical images or other bio-signals. Such a parameter adaptation approach was used in [8] to estimate the artery wall stiffness in an idealized abdominal aortic aneurysm and in [11] to determine tissue stiffness and contractility in the left ventricular myocardium from tagged MR.

Physiological simulations rely often on a sophisticated and complex processing pipeline. Application in a clinical context requires, however, efficient and largely automated processing pipelines. Encoding of structures and information for simulations into segmentation meshes may help to simplify and automate processing pipelines as has been illustrated in the example of excitation propagation in the left atrium. Linking of this mechanism to evolving standards like the FieldML (field modelling/mark-up language) description [12] may be considered in the future.

Both approaches for closely linking image processing and simulations show directions of how physiological simulations provide new stimuli and challenges for future image analysis research. The use of biophysical or physiological constraints in image analysis has the potential to improve data interpretation in many cases. Efficient approaches for patient-specific model building are essential to pave the way of virtual physiological simulations for clinical use on a large number of cases.

## Acknowledgments

The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement number 224495 (euHeart project).