PATIENT SPECIFIC MODELING OF INTERNAL DEFIBRILLATION USING THE FINITE VOLUME METHOD

 

 

Daniel Mocanu^*, M.S., Joachim Kettenbach^**, M.D., Michael O. Sweeney^***, M.D.,   Solomon R. Eisenberg, Sc.D^*.

 

^* Department of Biomedical Engineering, Boston University, U.S.A (mocanu@bu.edu)

^** Division of Radiology, University Hospital of Vienna, Austria

^*** Division of Cardiology, Brigham and Women’s Hospital, Boston, U.S.A.

 

 

Determination of the defibrillation threshold (DFT) during implantation of a cardioverter defibrillator (ICD) remains largely an empirical process. The goal of this research study is to investigate the predictive capacity of computational models of defibrillation by comparing patient-specific simulated and clinical defibrillation metrics. This paper describes the methods we used to construct patient specific 3-D computer models of the human thorax and to extract the defibrillation parameters specific to each individual. The finite volume models are constructed from segmented cross-sectional computerized tomographic (CT) images obtained post-implant from Brigham and Women's Hospital. The segmented data is imported into a computer-aided engineering package (I-DEAS) and two methods are used to generate the finite volume models. In the first method, the 3-D model of the patient's conductive anatomy is reconstructed using NURBS surfacing techniques and the resulting geometry is discretized using tetrahedral control volumes. In the second, the 3-D model is constructed with a structured meshing algorithm, in which a hexaedral control volume is associated to each voxel in the segmented image data set. I-DEAS uses a finite volume formulation to find the potential distribution within the human thorax. The defibrillation parameters were extracted based on Zipes’ critical mass criterion.

 

INTRODUCTION

 

Ventricular fibrillation (VF) is a condition marked by unsynchronized contractions of cardiac muscle cells. It has been suggested [1],[2] that the irregular and aperiodic electrical complexes observed in the electrocardiogram (ECG) are the representation of turbulent cardiac electrical activity where wandering wave fronts of electrical excitation (called “rotors”, “reverberators” or “vortices”) continually change in shape and direction. During VF, the heart rate is to high to allow adequate pumping of blood. The resulting lack of blood flow can cause brain damage or death if not promptly treated. With the advent of smaller defibrillation generators, catheter electrodes and "active can" technologies, implantable defibrillators (AICD) employing high-energy biphasic shocks have become the treatment of choice for patients with arrhythmias that do not respond to drug therapy. Determination of defibrillation energy (DFT) required to reset the heart to normal rhythm is mainly an empirical process. Therefore, to determine the DFT, fibrillation is induced and a defibrillation shock is delivered. This fibrillation/defibrillation sequence is repeated following an up-down protocol and the minimum energy shock sufficient to defibrillate is the DFT. This sequence of events imposes an immense strain on the myocardium and surrounding tissues.

Recent computer modeling studies in our laboratory of myocardial current distribution during defibrillation have shown a good correlation with the overall mean of reported clinical defibrillation metrics [3]. These findings suggest a possible use for computational models in the presurgical planning of AICD implantation. The goal of the current research study is to investigate the predictive capacity of such computational models by comparing patient-specific simulated and clinical defibrillation metrics. Ten subjects with implanted AICD have been recruited for this study. This paper reports the defibrillation metrics extracted for six of this patients. Models for the addition four patients recruited for the study have not yet been completed.

 

METHODS

 

Model Creation

      In order to model post-implantation patients, X-ray computer tomography (CT) is used to image the thorax anatomy. The acquisition of the cross-sectional data sets is performed using various slice width (from 1 mm to 3 mm) depending on patient characteristics. Every CT image is further processed to identify and classify the tissues. This procedure is called segmentation and is done semi-automatically using 3-D SLICER software package [5] at Brigham and Women’s Hospital , Boston.

Two methods are used to generate the finite volume models. In the first method, the  3-D model of the patient's conductive anatomy is reconstructed using NURBS surfacing techniques (fig.1) and the resulting geometry is discretized using tetrahedral volume elements. In the second, the 3-D model is constructed with a structured meshing algorithm, in which each voxel in the segmented image data set is defined as a volume element (fig.2).

 

                        

 

Fig.1 Geometry based model of the human thorax           Fig.2 Voxel based model (bones and lungs)

 

Computational Approach

            In the quasistatic limit, the electric potential distribution associated with the defibrillation shock is governed by an elliptic partial differential equation

                                                       (1)

subject to the following boundary conditions:

 

                                                       (2)

 

where f is the electric potential, s is the electrical conductivity,  is the surface normal, S_e is the electrode surface and S_t is the thoracic surface. The surface of the AICD’s metallic housing (placed subcutaneous in the left upper thorax) and the catheter electrodes in the superior vena cava and right ventricle are given a generic potential boundary of zero, zero and one, respectively. The finite volume method was used to solve the spatial distribution of electric potential in the three-dimensional models of human thorax. The numerical models contained between 350 000 and 450 000 elements. Solutions were obtained using IDEAS/TMG Thermal Analysis software [4] running on an SGI Origin 2000.

 

Solution interpretation

            Every simulation is assumed to correspond to a successful defibrillation with the minimum delivered current, or defibrillation current threshold, I_th. Zipes’ critical mass criterion is used to define successful defibrillation. To meet this criterion, 75% of the myocardium must be exposed to current densities with magnitudes equal to or greater than the inexcitability threshold, J_th=17.5 mA/cm², which is the minimum current density necessary to render a fibrillating myocyte inexcitable. Inter-electrode impedance Z and defibrillation threshold energy (DFT), current I_th and voltage V_th are standard clinical metrics. The inexcitability threshold and current density magnitudes in the elements of the heart were used to calculate the defibrillation metrics. The volumes of the heart elements were sorted in ascending order of current density magnitude. Starting at the lowest current density magnitude, the volumes of the heart elements were summed until the subtotal was equal to 25% of the total myocardial volume. All current density magnitudes and voltages were then scaled so that the value of the current density at the critical mass point was equal to the assumed inexcitability threshold (J_th) of 17.5 mA/cm². The defibrillation threshold current, I_th, was the scaled total current delivered by the electrodes, the defibrillation threshold voltage, V_th, was the scaled applied voltage. The impedance, Z, was the ratio between the voltage and current. The delivered energy, or the DFT, was computed by equation (3) considering a biphasic pulse (fig. 3). with 60% tilt in the positive phase and 50% tilt in the negative phase corresponding to the CPI Ventak model (Cardiac Pacemakers Inc.) used in clinical trials.

 

 

(3)

Fig. 3. An example of CPI biphasic waveform. The waveform has a 60% tilt in positive phase and 50% tilt in negative phase. The pulse width of the first (PW1) and second phase (PW2) is 60% and 40% respectively of the total length.

 

The AICD has a 150 mF capacitor from which the pulse was delivered. The total duration of the biphasic pulse can be determined considering the waveform characteristics, and it is T_total=1.61t, where t is the time constant of the ZC circuit.

  

RESULTS

 

Figure 4 and figure 5 show the current density and electric potential distributions obtained for one of the six patients reported here. The defibrillation metrics calculated for the six out of ten patients involved in this study are listed in table 1.

 

                               

 

Fig. 4 Current density distribution                                   Fig. 5 Electric potential distribution. (geometry-based model)                                    (voxel-based model)

 

	DFT [J]	Ith [A]	Vth [V]	Z [W]
Patient #1	12.4	9.6	415.9	43.2
Patient #2	8.6	8.2	346.6	41.9
Patient #3	6.4	7.6	299.9	39.3
Patient #4	4.6	6.4	253.1	39.0
Patient #5	10.8	9.35	388.7	41.5
Patient #6	10.4	10.9	380.6	34.7

 

Table 1. Model predicted values for defibrillation parameters

 

After completion of all ten patient-specific models, the calculated defibrillation parameters will be compared with the clinical metrics obtained during AICD implantation procedure. If model and clinical values are in good agreement then work can be pursue to use these type of models in pre-surgical planning of AICD implantation.

 

References:

 

[1] C.J. Wiggers, “The mechanism and nature of ventricular fibrillation,” Am. Heart J. 20, 399-412 (1940).

 

[2] A.T. Winfree, “Electrical turbulence in three-dimensional heart muscle,” Science 266, 1003-1006 (1994)

 

[3] T.F. Kinst, M.O. Sweeney, J.L. Lehr, S.R. Eisenberg, “Simulated internal defibrillation in humans using an

anatomically realistic three-dimensional finite element model of the thorax,”J. Cardiovasc. Electrophysiol. 8, 537-547 (1997).

 

[4] I-DEAS Master Series 6 Engineering Analysis Software, Structural Dynamics Research Corporation.

 

[5] http://splweb.bwh.harvard.edu:8000/pages/papers/slicer/index.html.