ORGAN MODELLING 


     The most important biophysical cardiac processes at the organ level are:


     a) The generation of the electric signal and its propagation
     b) The mechanical movement of the heart (contraction)
     c) The blood flow in the cardiac vessels

     These physical processes i.e. electric current flow, mechanics, hydraylics are described by specific conservations laws and can be integrated in whole organ models following the approaches that were described in the tissue modelling section.

     Similarly to tissue modelling, for whole organ modelling a detailed morphological characterization is first required. Anatomically based models have been developed for different species.

     By using measurements from the left and right ventricle of pig heart Stevens, C., E. Remme, et al. (2003). J Biomech 36(5): 737-748 created a 3-D finite element model for the geometry of the ventricles as shown in their study available at the above link or alternatively in figure 6 of the review by Crampin, E. J., M. Halstead, et al. (2004), Exp Physiol 89(1): 1-26. In this case the elements use high order mathematical functions and therefore fewer are necessary in order to obtain an accurate description of ventricular morphology.

     Once the geometry of the organ is represented, the spatial variation of the tissue must also be described. In the heart tissue, cardiomyocytes (cardiac fibers) are bound by the glue-like material, collagen, in layers or sheets that are 4-5 cell thick and that are termed fibrous-sheets. The fibrous-sheet structure for the whole myocardium is demonstrated in figure 8 of the review by Crampin, E. J., M. Halstead, et al. (2004), Exp Physiol 89(1): 1-26


     Once the three-dimensional space has been characterized different processes can be modelled at the example mentioned in the tissue modelling section.

     In order to model the propagation of the electric signal in the tissue, or the ionic current flow, the reaction-diffusion equations that model current flow are solved with the diffusivity (i.e. conductivity) tensor which is based on the tissue structure. A model that was generated with this method is demonstrated in the study by Hunter, P. J. and T. K. Borg (2003) Nat Rev Mol Cell Biol 4(3): 237-243, in part a of the figure shown in Box 2 - The Cardiome Project or in figure 1a below and also in the study byCrampin, E. J., M. Halstead, et al. (2004), Exp Physiol 89(1): 1-26 in figure 9. Electrically active myocardium (anterior and posterior view in upper and lower panel respectively) is shown in yellow in different time points within one heart beat.

     In order to model the contraction of the heart, a similar approach is followed. The mechanics equations that incorporate information from cell models of sarcomere kinetics and calcium binding are solved with the elasticity tensor, which maps the mechanical behavior of different parts/points of the tissue.

     In order to model blood flow and oxygen delivery to the myocardium we must take into account the fact that the flow is influenced by the change of organ form. Therefore the equations of fluid flow in the vessels are coupled with the behavior of the compliant vessel wall to the stress that is associated with heart contraction.

     A model of cardiac mechanics, which inludes the coronary arteries, at four stages in the cardiac cycle, is demonstrated in the paper by Hunter, P. J. and T. K. Borg (2003) Nat Rev Mol Cell Biol 4(3): 237-243, in part b of the figure of Box 2 - The Cardiome Project or figure 1b below and also in the study by Crampin, E. J., M. Halstead, et al. (2004), Exp Physiol 89(1): 1-26 in figure 11. The contraction of the heart applies stress on the coronary vessels and thus affects flow. The color code assigns blue to minimal flow and red to maximal flow.

Figure 1: Figure of  Box 2 - The Cardiome Project from the paper by Hunter, P. J. and T. K. Borg (2003) Nat Rev Mol Cell Biol 4(3): 237-243 and legend of the publication figure

 

"Part a of the figure shows a model of myocardial activation. Wavefront locations are shown using an eikonal equation to simulate propagation from the distal ends of the Purkinje tree. For each sample time, anterior (top) and posterior (bottom) views are given. The endocardial surfaces of the left and right ventricles are coloured red. The regions of electrically activated myocardium at each time step are coloured yellow. Part b of the figure shows a model of cardiac mechanics, which includes the coronary arteries, at four stages in the cardiac cycle (from left to right: early in diastole, end-diastole, pre-ejection systole and end-systole). The colours (blue minimum to red maximum) indicate the flow reduction caused by compressive wall stresses acting on the coronary vessels. LV, left ventricle; RV, right ventricle."


References
Crampin, E. J., M. Halstead, et al. (2004). "Computational physiology and the Physiome Project." Exp Physiol 89(1): 1-26.
Hunter, P. J. and T. K. Borg (2003). "Integration from proteins to organs: the Physiome Project." Nat Rev Mol Cell Biol 4(3): 237-243
Stevens, C., E. Remme, et al. (2003). "Ventricular mechanics in diastole: material parameter sensitivity." J Biomech 36(5): 737-748