DYNAMIC MODELING OF THE RIGHT VENTRICLE FOR THE ANALYSIS OF CONGENITAL HEART DEFECTS

Unquestionably, the accurate clinical assessment and appropriate treatment of children with congenital heart defects, especially the timeliness with which needed clinical intervention is performed, are central to the survival these patients. In marked contrast to adult cardiology, which deals almost exclusively with the left ventricle (LV), the function of the right ventricle (RV) is associated with a number of life-threatening congenital defects in children. Because of its relative unimportance in adult cardiology, only limited work[1,2] has been done analyzing RV function.. Unfortunately, because of its different shape and pressures, much of the research on the LV cannot be easily transferred to the RV. This research is aimed at developing a novel method for modeling the clinical factors impacting RV function, which can lead to a more reliable, consistent, and comprehensive pre-operative treatment planning.

Unlike the prevalent literature[3] concerning the heart which either deal exclusively with modeling the heart wall or with analyzing the fluid dynamics of the blood pool[4], we present an interactive, physically based, nonlinear, elastically deformable model utilizing techniques that separately model the heart wall and blood pool in the RV.

Bag of Particles

The bag of particles (BOP) model[5] is initial method used for simulating ventricular behavior. The model borrows from both molecular dynamics (MD) methods and surface particle systems. The blood pool is composed of physically interacting, unoriented volume particles behaving like molecules in an MD simulation, but held within the ventricular wall. The ventricular wall is composed of oriented surface particles forming what may be viewed as a "bag" containing particles. The behavior of the model is controlled by a number of types of forces. All the particles experience volume forces that govern particle spacing. The ventricular wall particles undergo two additional types of forces: surface forces and torques are necessary to form surfaces and shaping forces and torques allow for the particles to assume the ventricular shape. Table 1 contains a description of the forces and torques used with this model.

Table 1. Bag of Particles Dynamics

 Hybrid Model

Limitations of the BOP to model the ventricular wall prompted the exploration of a new model. Specifically, the inability of BOP to measure strains in the heart wall and the inability of BOP to model the ventricular wall as a thick anisotropic surface. This new "hybrid" model retains the particle model to simulate the blood pool, but replaces the wall surface particles with a non-linear finite element model first reported by Terzopolis[7].

The interaction between the two models is accomplished by attaching particles at the nodes of the finite element mesh along the heart wall. This technique, adapted from the BOP, is based on the volume forces only. The surface particles will apply forces on the volume particles not allowing them to escape. The volume particles apply forces on the surface particles. The surface particles will transfer the force to the finite element mesh, with no need of surface or shape forces.

Figure 1. Model Dynamics (a) BOP (b) Hybrid Model.  Surface Particles correspond to the hart wall wall; volume particles, the blood pool

Results

The bag-of-particles approach has been applied to modeling a human heart left ventricle through a complete cardiac cycle (Fig. 2). Positron emission tomography (PET) images acquired at eight evenly spaced temporal intervals ("gated PET") were segmented to produce eight 3D voxel bitmaps of the LV endocardial volume.

Figure 2. Left Ventricle through one cardiac cycle.

Pressure values shown in Figure 3 have been scaled such that peak pressure is assumed to be a nominal systolic pressure of 120 mm Hg. Also plotted is a typical LV pressure curve. The difference between the bag-of-particles pressure and the typical curve is due to the absence of the LV aortic valve. With an anatomically complete model, it should be possible to accurately measure pressure as well as cardiac ejection

Figure 3. Ventricular pressure vs. time through one cardiac cycle.

Bag-of-particles has been demonstrated to model basic blood flow. Figure 4 shows the flow of blood particles through a simplified cylindrical artery.

Figure 4. Flow of blood particles through a cylindrical model of an artery.

Initial studies utilizing the hybrid model are currently underway. The model will be used to determine clinically useful parameters such as strain, strain rate, and thickening of the heart wall. Blood measurements such as ejection fraction, pressure and basic flow patterns can also be calculated. The model will be adapted to individual patient data to achieve an accurate representation of the RV for the given patient. Magnetic Resonance Imaging (MRI) datasets of healthy adult volunteers are being used as the preliminary test case of the RV. Once these tests are completed, the model will be used on existing MRI datasets of pediatric patients with Hypoplastic Left Heart Syndrome

References

[1] M.A.Fogel, K.B. Gupta, P.M. Weinberg, and E.A. Hoffman, "Regional wall motion and strain analysis across stages of Fontan reconstruction by magnetic resonance tagging," Am. J. Physiol., vol. 269, pp. H1132-1152, Sept. 1995.

[2] E. Haber, D.N. Metaxas, L. Axel, W.M. Wells, A. Colchester, and S. Delp, "Motion analysis of the right ventricle from MRI images," MICCAI ‘98, pp.177-88, 1998.

[3] A. Frangi, W. Niessen, and M. Viergever, "Three-dimensional modeling for functional analysis of cardiac images: a review," IEEE Trans. Med. Imag., vol. 20, pp. 2-25, Jan. 2001.

[4] N. Saber, A. Gosman, N. Wood, P. Kilner, C. Charrier, and D. Firmin, "Computational flow modeling of the left ventricle based on in vivo MRI data: initial experience," vol.29, no.4 pp. 275-83, 2001.

[5] D. Stahl and N. Ezquerra, "Bag of Particles Model for Simulating Tissue, Organs, and Flow," accepted MICCAI 2001.

[6] D. Frenkel and B. Smit, Understanding Molecular Simulation, From Algorithms to Applications, Chestnut Hill, MA: Academic Press, 1996.