BioMed Research International

Volume 2016 (2016), Article ID 2979081, 8 pages

http://dx.doi.org/10.1155/2016/2979081

## Depth Attenuation Degree Based Visualization for Cardiac Ischemic Electrophysiological Feature Exploration

^{1}School of Mechanical, Electrical & Information Engineering, Shandong University, Weihai 264200, China^{2}School of Art and Design, Harbin University, Harbin 150086, China^{3}Department of Educational Technology, Ocean University of China, Qingdao 266100, China^{4}Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China^{5}School of Computer Science and Technology, Harbin Institute of Technology, Harbin 150001, China^{6}School of Physics and Astronomy, University of Manchester, Manchester M139PL, UK

Received 3 June 2016; Revised 21 September 2016; Accepted 11 October 2016

Academic Editor: Qin Ma

Copyright © 2016 Fei Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Although heart researches and acquirement of clinical and experimental data are progressively open to public use, cardiac biophysical functions are still not well understood. Due to the complex and fine structures of the heart, cardiac electrophysiological features of interest may be occluded when there is a necessity to demonstrate cardiac electrophysiological behaviors. To investigate cardiac abnormal electrophysiological features under the pathological condition, in this paper, we implement a human cardiac ischemic model and acquire the electrophysiological data of excitation propagation. A visualization framework is then proposed which integrates a novel depth weighted optic attenuation model into the pathological electrophysiological model. The hidden feature of interest in pathological tissue can be revealed from sophisticated overlapping biophysical information. Experiment results verify the effectiveness of the proposed method for intuitively exploring and inspecting cardiac electrophysiological activities, which is fundamental in analyzing and explaining biophysical mechanisms of cardiac functions for doctors and medical staff.

#### 1. Introduction

Cardiac diseases have been the leading cause of death and disability in the world. Evidence has shown that functional abnormity of heart such as the heart failure may lead to the severe cardiac problem with increased mortality [1]. Heart failure manifests insufficient blood flow pumped for delivering oxygen, which generally appears as pulmonary edema and cardiogenic shock [2]. Cardiac researchers and medical staffs have put forward methods to analyze cardiac functional mechanism to understand and treat heart failure. Serpooshan et al. [3] analyzed the structure and function of the failing heart using the biomimetic three-dimensional technology to enhance cardiac healing after injury. Namazi et al. [4] presented an unusual case of amyotrophic lateral sclerosis (ALS) and the cardiac failure was diagnosed at the final stage of the ALS disease. Alickovic and Subasi [5] applied dwt and random forests classifier for analyzing the heart arrhythmia. Keller et al. [6] established a heterogeneous electrophysiological and three-dimensional anatomical model of human atria to explore atrial functional mechanism. Brocklehurst et al. [7] implied the discrete element method (DEM) to investigate the electromechanical mechanism for human atrial tissue. Then, mechanical contractions of cardiac tissues and their corresponding electrical waves’ conduction were successfully simulated. Salinet Jr. et al. [8] presented spectral analysis techniques to visualize intracardiac atrial fibrillation (AF) electrograms, helping guide catheter ablation procedures. Aslanidi et al. [9] constructed a 3D virtual human atria model using cell electrophysiological data with detailed DT-MRI anatomy, which provides a valuable way for investigating electrophysiological behavior in the arrhythmic atria during AF. Zhong et al. [2] discussed the utilization of extracorporeal membrane oxygenation (ECMO) for cardiogenic shock. Sala et al. [10] presented a new transgenic mouse model of to replicate the clinical findings of heart failure.

Ventricle fibrillation (VF) is a serious cardiac functional abnormality that can lead to myocardial infarction. Zhang and Hancox [12] improved Luo-Rudy ventricular action potential models by integrating I-Kr current and inactivation-deficient I-Kr into the previous model and verified that loss of inactivation of the I-Kr led to QT interval shortening. Adeniran et al. [13] further considered stretch-activated channel current (sac) in the single cell models and then incorporated the models into 3D human ventricular tissue models to explore the Short QT Syndrome (SQTS) which is associated with ventricular arrhythmias and sudden cardiac death. The symptom of ischemic greatly increases the probability of occurrence of ventricle fibrillation. It has important meaning to investigate the intricate mechanisms under an ischemic condition in order to better facilitate therapeutic interventions. Although a vast amount of experimental and clinical data of the ionic, cellular, and tissue substrates has been acquired, the precise cardiac mechanisms of ischemia are not well understood. Therefore, any advances in finding and tracking the pathophysiological feature, especially advances that might help analyze and treat the cardiac ischemia more effectively are of great significance. Trejos et al. [14] proposed a mechanism of automatic detecting ischemic events using ECG signals, which allows a better interpretation of cardiac ischemic behavior and results in an increase in the discrimination capability for ischemia detection. Cimponeriu et al. [15] developed a two-dimensional realistic ventricular tissue model. The capacity of the model in simulating pathological conditions was validated on exploring the determinants of electrocardiographic (ECG) morphology and tracking in the ECG pathologic changes of ischemic heart. The cardiac electrophysiological activity has been proven to be important in analyzing functional mechanisms under cardiac physiological and pathological condition. At present, researches have carried out the study on the modeling and simulation of cardiac ischemia based on the ventricular cell model [16–21]. Ten Tusscher and Panfilov [22] created a human ventricular cell model which contains all major ion channel currents and thus simulated the human cardiac electrophysiological properties in a closer way. Chinchapatnam et al. [23] used a fast electrophysiological (EP) model and proposed an adaptive algorithm to estimate cardiac local conduction velocity and apparent electrical conductivity. The method revealed hidden cardiac parameters and can help guide diagnosis and therapy of human left ventricle arrhythmia. A computational cardiac model was applied to simulate the electrophysiological action of two drugs of amiodarone and cisapride in healthy and ischemic ventricle cells for investigating the pharmacological effects, which is helpful to analyze the underlying arrhythmias mechanisms caused by the two drugs [24]. Lü et al. [25] developed a human ventricular cell and tissue ischemic model. Through the model, the functional consequences and mechanisms underlying the arrhythmias in early acute global ischemia are investigated to analyze the influence of acute global ischemia on cardiac electrical activity and subsequently on reentrant arrhythmogenesis. Lu et al. [26] further developed a 3D human ventricular ischemic model combining a detailed biophysical description of the excitation kinetics of human ventricular cells with an integrated geometry of human ventricular tissue. To analyze the spatiotemporal deformation parameters for the myocardial contraction, Han et al. [27] proposed the visualization tools and a strategy for the automatic detection of dysfunctional regions of cardiac ischemic pathologies, which is proved very useful for quantitatively demonstrating the main properties of the left ventricle myocardial contraction. Shenai et al. [28] presented the visualization of normal and ischemic propagation and found intra-QRS changes in and around the ischemic region, which proved that ischemia may cause depolarization changes detectable by both action potentials and unipolar leads. To exhibit the electrophysiological activities under the physiological and pathological condition within the authentic cardiac structure, Wang et al. presented a multivariate visualization method [29] and Zhang et al. proposed an interactive visualization algorithm [30] to visualize both the anatomical data and the electrophysiological data simultaneously. However, these methods cannot explore the hidden electrophysiological feature of pathological tissue in the 3D space.

In this paper, we proposed a visualization framework, which combines the human cardiac ischemic model with a novel depth weighted optic attenuation model, to inspect the occluded cardiac ischemia information with the complicated context of electrophysiological activities under cardiac ischemic condition. First the human ventricle ischemic data is acquired through the cardiac ischemic model. In the proposed depth weighted optic attenuation model, Euclidean Distance Transform (EDT) of each voxel is computed in the electrophysiological data, that is, the Euclidean distance from each voxel to the ventricle boundary, as the coefficient of the attenuation degree of the voxel. This model makes the voxel which is closer to the boundary of the ventricular tissue have the higher attenuation value. Thus, the region that contains the voxels is more transparent. The hidden feature of interest in the ischemic tissue can be revealed from complex overlapping electrophysiological information by the model. The paper is organized as follows. Section 2 presents the human cardiac tissue ischemic model and visualization framework which includes a novel depth weighted optic attenuation model construction. Section 3 provides experimental results and discussions. In Section 3, results of the experiments demonstrate that the method we presented can show the feature of cardiac action potential propagation during ischemia more effectively through surrounding complex information. Finally, our conclusions are given in Section 4.

#### 2. Design Materials and Methods

To explore organs of interest from mass of cardiac tissues, Zhang et al. [31–33] proposed approaches for revealing detailed structures and further presented a cardiac visualization system, which can provide the user different levels of cardiac anatomy rendering [34]. Yang et al. [35] designed a multidimensional transfer function for visualizing the multiboundary cardiac volume data. Different from the cardiac anatomy characteristic, electrophysiological activities such as excitation propagation in the various human heart tissues are hard to be observed and analyzed in the 3D space. To address this issue, Zhang et al. proposed a GPU-based high performance wave propagation simulation with fine anatomical structure [36]. Based on their work [11, 37], a GPU-based framework for electrophysiological data simulation and visualization is proposed. To fuse cardiac anatomical and electrophysiological model together, Yang et al. [38] designed the fusion transfer function which demonstrated cardiac electrophysiological activity by adjusting the parameter opacity of transfer function.

However, these methods cannot directly explore those cardiac function features at pathological conditions occluded by the complex biophysical information. In this section, we first induce a human cardiac ischemic model to explore cardiac electrophysiological activity and generate the altered ischemic electrophysiology data. Then 3D Euclidean distance transform is implemented on the data, and the depth weighted optic attenuation model is consequently constructed based on the Euclidean distance transform for revealing the hidden cardiac ischemic action potential propagation feature.

##### 2.1. Cardiac Ischemic Electrophysiological Model

To explore the cardiac ischemic feature, in this work, the phase of ischemia is considered in the cardiomyocyte electrophysiological model, which describes the cardiac ischemic action potential (AP) generation through the monodomain reaction-diffusion equation as follows:where represents transmembrane potential and is the time. is the total ionic current depending on the voltage and time and indicates the externally applied stimulate current. is the transmembrane capacitance per unit membrane area. is the diffusion tensor for describing the tissue conductivity and is the gradient operator. The ionic current in is the ATP sensitive current which is calculated by the following equation [17]: where is the potassium ion equilibrium potential which is given by Nerst equation [18]:where is the fraction of opened channels and is the temperature dependent factor. and are correction factors caused by intracellular Mg^{2+} ions and intracellular Na^{+} ions. is the open probability of a channel in the absence of ATP. is the gate control variable of adenosine triphosphate (ATP) and represents the ratio of cell membrane surface area and volume.

is a Hill equation:where and are the nonlinear function of : is described by the temperature effect formula:where , , and represent the temperature coefficient, absolute temperature, and reference temperature, respectively, and , °C. is used to explain the inward rectification of intracellular magnesium ions, which is a Hill equation: Here is defined as follows:where and is defined bywhere is used to explain the inward rectifier ion induced cell Boehner, which is also a Hill equation:Here is defined as follows: where and mM. The parameter setting in the ischemic model can be found in [18, 19].

The electrophysiological data is acquired by implementing the ischemic model on the Visible Human ventricle data. The value of each voxel in the electrophysiological volume data is the action potential of the cardiac cell under the ischemia condition. Thus, the electrophysiological volume data can represent the ventricle action potential propagation during ischemia.

##### 2.2. Euclidean Distance Transform

Distance transform (DT) maps each point into its smallest distance to regions of interest [39]. The central problem of EDT (Euclidean Distance Transform) is to compute the Euclidean distance of each point to a given subset of a plane. Let be a binary image, . By convention, 0 is assigned to black and 1 to white. Hence, we have the set which is represented by all white pixels: , as shown in Figure 1. The set is called foreground and can consist of any subset in the image domain, including disjoint sets. The elements of its complement, , the set of black pixels in , are called background. From the DT point of view, the background pixels are called the interest points or feature points.