# A composite visualization method for electrophysiology-morphous merging of human heart

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## Abstract

### Background

Electrophysiological behavior is of great importance for analyzing the cardiac functional mechanism under cardiac physiological and pathological condition. Due to the complexity of cardiac structure and biophysiological function, visualization of a cardiac electrophysiological model compositively is still a challenge. The lack of either modality of the whole organ structure or cardiac electrophysiological behaviors makes analysis of the intricate mechanisms of cardiac dynamic function a difficult task. This study aims at exploring 3D conduction of stimulus and electrical excitation reactivity on the level of organ with the authentic fine cardiac anatomy structure.

### Methods

In this paper, a cardiac electrical excitation propagation model is established based on the human cardiac cross-sectional data to explore detailed cardiac electrical activities. A novel biophysical merging visualization method is then presented for biophysical integration of cardiac anatomy and electrophysiological properties in the form of the merging optical model, which provides the corresponding position, spatial relationship and the whole process in 3D space with the context of anatomical structure for representing the biophysical detailed electrophysiological activity.

### Results

The visualization result present the action potential propagation of the left ventricle within the excitation cycle with the authentic fine cardiac organ anatomy. In the visualized images, all vital organs are identified and distinguished without ambiguity. The three dimensional spatial position, relation and the process of cardiac excitation conduction and re-entry propagation in the anatomical structure during the phase of depolarization and repolarization is also shown in the result images, which exhibits the performance of a more detailed biophysical understanding of the electrophysiological kinetics of human heart in vivo.

### Conclusions

Results suggest that the proposed merging optical model can merge cardiac electrophysiological activity with the anatomy structure. By specifying the respective opacity for the cardiac anatomy structure and the electrophysiological model in the merging attenuation function, the visualized images can provide an in-depth insight into the biophysical detailed cardiac functioning phenomena and the corresponding electrophysiological behavior mechanism, which is helpful for further speculating cardiac physiological and pathological responses and is fundamental to the cardiac research and clinical diagnoses.

## Keywords

Computational cardiology Morphous Biophysical merging Cardiac biophysiological function Merging attenuation model## Abbreviations

- LTM
light transport model

- MAF
merging attenuation function

- LLUT
linear look up table

## Background

The cardiac disease, e.g., atrioventricular block, ventricular fibrillation and cardiomyopathy, is one of the most common causes of mortality in the world. It has been proven that cardiac functional abnormity may produce the serious problem of heart disability and are generally life-threatening [1]. Although there are considerable progresses have been achieved on conventional open-heart research and acquirement of experimental and clinical data, the cardiac mechanisms aren’t well understood. Increasing momentum is tending to study the cardiac biophysiological function noninvasively [2, 3, 4]. Serpooshan et al. [5] analyzed the structure and function of the failing heart to enhance cardiac healing after injury. Zhang et al. [6] visualized cardiac microvessels embolization in 3D space with X-ray phase contrast images. This method was beneficial to diagnoses and predicting and judging the prognosis in myocardial infarction (MI). Based on the surface shape space Taimouri and Hua [7] et al. defined two novel shape descriptors by the geodesic distance connecting two points in the two cardiac medial surfaces, which quantitatively analyzed the similarity and disparity of the 3D heart motions between the healthy and myopathic subjects and accurately detected myopathic regions on the left ventricle. Spicher et al. [8] proposed a new cardiac triggering method to estimate the cardiac cycle phase in real-time from videos captured with an in-bore camera. However, the function mechanisms and the underlying genesis of human heart still remain unclear.

Electrophysiological behavior is of great importance for analyzing the functional mechanism under cardiac physiological and pathological condition. Noble [9] first applied the cell mathematical model-HH model to the purkinje fibre and pace-maker cells and started the research on cardiac function by modeling of cardiac electrophysiological activities. Zhang et al. [10] proposed mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node. Models of the ventricular action potential [11, 12] were constructed to describe the electrophysiological activity of the single ventricular cell in detail. Based on the experimental data of human heart, Priebe and Beuckelmann [13] established the first human ventricular cell model. ten Tusscher et al. [14] created a new human ventricular cell model which contains all major ion channel currents and thus is more close to the human heart’s real condition in the electrophysiological properties. Hilgemann et al. [15] constructed the first excitation–contraction model in the rabbit atrium. Nygren [16] and Courtemanche proposed [17] common human atrium cell models and the models were improved based on the recent experimental data [18, 19, 20]. Salinet et al. [21] presented the autoregressive (AR) spectral estimation techniques to produce 3D dominant frequency (DF) maps of atrial electrograms (AEGs) for persistent atrial fibrillation (persAF) study. Wang and Yang et al. [22, 23] implemented the ventricular ischemic model and visualized the electrophysiological activity. A framework to simulate multi-scale wave propagation of ischemia is proposed [24], which leverages the high-performance computing capacity of Graphic Processing Units (GPU).

Recently, visualization of cardiac models in the organ level have been developed to express the microscopic origin of electrophysiological mechanism in the three dimensional space. Rubio-Guivernau et al. [25] visualized myocardial substrate and located conducting channels for pre-planning and guidance of ablation procedures. Lu et al. [26, 27] developed and visualized the human ventricular ischemic model to analyze the influence of acute global ischemia on cardiac electrical activity and subsequently on reentrant arrhythmic genesis. Detailed structures of the human heart are revealed by visualizing the cardiac volume data [28, 29, 30, 31, 32, 33]. Seemann [34] established heterogeneous three-dimensional anatomical and electro-physiological model of human atria. Based on the novel fusion transfer function, Zhang and Wang et al. developed a platform integrating multi-volume visualization method for both heart anatomical data and electrophysiological data visualization [35, 36, 37]. However these methods did not demonstrate electrophysiological activity clearly with anatomy. Due to the mass of cardiac tissues and complicated cardiac functional mechanism, visualizing the biophysically detailed cardiac model becomes a more difficult task.

In this paper, firstly a cardiac electrical excitation propagation model is established based on the cardiac cross-sectional data to explore detailed cardiac electrical activities. Then a novel merging attenuation function (MAF) is proposed for the visualization of biophysical merging model of cardiac anatomy structure and electrical excitation reactivity conduction. The description of the cardiac excitation kinetics is thus coupled with a genuine fine anatomical geometry, which provides the corresponding position and 3D spatial relationship in the context of anatomical structure for representing the electrophysiological activity in vivo. By the biophysically detailed visualization image, medical staffs and cardiac researchers can obtain insight into underlying mechanisms by observing regions of particular interest of the biophysical area with real anatomical structure context from an arbitrary perspective, which gives a reliable and optimal pre-computed view for the cardiac research and clinical diagnoses.

The rest of the paper is organized as follows. In “Data and methods”, the human cardiac anatomical data and multicellular tissue action potential conduction model is described. Then the MAF is constructed for the cardiac electrophysiology-morphous merging visualization. Results and effectiveness of the proposed visualization method and discussion are shown in “Results and discussions”. And finally conclusion marks are provided in “Conclusion”.

## Data and methods

### Human cardiac cross-sectional data

The clinical general image modality such as MRI and CT are commonly used to generate 3D cardiac models [38, 39, 40, 41], which can provide the structural and functional information of cardiac tissue and is very practical in the clinical environment. Automatic segmentation of medical images and manual correction after the segmentation process are usually needed in most cases to construct the cardiac model.

### Cardiac electrophysiological model

*V*

_{ m }is the transmembrane potential and

*t*is the time.

*C*

_{ m }is the transmembrane capacitance per unit membrane area.

*I*

_{ stim }represents stimulus current which is externally applied on the cells, and

*I*

_{ ion }is the sum of all ionic currents. In this paper, according to the TNNP model [14], current

*I*

_{ ion }is acquired by:

*I*

_{Na}is fast Na

^{+}current,

*I*

_{K1}is inward rectifier K

^{+}current,

*I*

_{to}is transient outward current,

*I*

_{Kr}is rapid delayed rectifier current,

*I*

_{Ks}is slow delayed rectifier current,

*I*

_{CaL}is

*L*-type Ca

^{2+}current,

*I*

_{NaCa}is Na

^{+}/Ca

^{2+}exchanger current,

*I*

_{NaK}is Na

^{+}/K

^{+}pump current,

*I*

_{pCa}is plateau Ca

^{2+}currents,

*I*

_{pK}is plateau K

^{+}currents,

*I*

_{bCa}is background Ca

^{2+}current,

*I*

_{bNa}is background Ca

^{2+}current.

It has been reported that *I* _{Ks} density is about 2 times and *I* _{to} density is 2.0–4.5 times larger in human right ventricle than in human left ventricle. As a result, in this study, the epicardial *I* _{Ks} and *I* _{to} densities of the right ventricle are set by a factor of 2 and 4, respectively [27].

The model in Eq. (3) is thus composed of two portions: the single cell model for describing the cellular electrical activity of cardiac cells and the intercellular electronic conductivity model for representing intercellular electronic interactions between cells. Thus the model consists of a number of ordinary differential equations (ODE) and the partial differential equation (PDE).

*n*, the ordinary differential equation has the following form:

*n*is obtained by integrating Eq. (5):

*f*(

*x*,

*y*,

*z*), \(V_{r} (\varsigma )\) indicates the resting potential. To describe the electrical conduction in the human heart, the finite difference method is used to solve the cardiac dynamics of transmembrane potential equation. In this work, the forward Euler finite difference method is extended to 3D space, as in Eq. (8):

*D*

_{ global }demonstrates the maximum electrical conductivity of 0.154 mm

^{2}/ms and

*d*is the spatial dimension. Here,

*d*= 3 for 3D ventricle models. Thus we have iterative time step Δ

*t*≤ 0.118 ms, i.e. the maximum stable time step

*Δt*

_{ max }is 0.118 ms. In this paper, we use \(\Delta t\) = 0.02 ms.

*n*is the vector normal to the surface, means that there is zero current flow normal to the ventricular tissue boundaries.

Equation (13) is integrated using the forward Euler method with ζ = 0.33 mm.

The 3D anatomical model of ventricle is constructed with 325 × 325 × 425 pixels, which is like a box includes the interior pixels i.e. the ventricular tissue points and the exterior pixels which are not ventricular tissue points. We see each interior pixel as a syncytium corresponds to ς in Eq. (7). And its space position is (x, y, z). By using the forward Euler difference method to solve Eq. (13) with ς = 0.33 mm, each syncytium’s action potential can be obtained. Combined with all syncytium’s action potential, then the electrical propagation of human ventricular tissue is formed.

### Merging attenuation function (MAF) for biophysical merging visualization

*x*is the position of a point t along the direction of the light, and

*L*(

*x*) is the light intensity at

*x*.

*L*(

*x*

_{0}) represents the intensity at

*x*

_{0}, where the ray enters the volume data.

*τ*(

*x*) is the absorption coefficient and depends on the location on the ray. Let \(\sigma (x_{1} ,x_{2} ) = - \int_{{x_{1} }}^{{x_{2} }} {\tau (t)} dt\), which is called the optical depth, the opacity is thus defined as:

*L*(

*s*) and to

*α*(

*s*), where

*s*is the scalar value of a point

*t*which is inside the data volume and on the ray passing through the volume. Considering all points

*t*on a ray, the total amount energy along the ray can be computed by:

*L*(

*x*) and

*α*(

*s*) of voxel sample pair, i.e.

*s*and it corresponding sample

*s’*in the two volumes can be obtained. The linear mapping which is achieved by each LLUP is as follows:

*s*in the volume of cardiac excitation conduction model respectively. \(\alpha_{a} (x')\) and \(L_{a} (x')\) are the analogous variables in anatomy structure volume. Thus the merging attenuation function (MAF) for the cardiac electrophysiology-morphous merging visualization is defined by:

Where *mef* is the merging factor, *N*(*x*) is the normalized normal vector and ||*N*(*x*)|| is the norm of *N*(*x*). *V* _{ e }(*x*) = −1 means that only cardiac tissue data exists at current *x* position on the ray. Otherwise both cardiac conduction data and tissue data are valid at the current position.

Here \(\alpha_{e} (x)\) and \(\alpha_{a} (x')\) are the weight factors. \(\sigma '\) is the merging optical depth which has the form of \(\sigma '(x_{1} ,x_{2} ) = - \int_{{x_{1} }}^{{x_{2} }} {\tau '(t)} dt\).

## Results and discussions

In this section, cardiac excitation conduction model is constructed and implemented on the female cross-sectional cardiac data. Then the performance of the presented MAF based cardiac biophysical merging visualization is assessed on the same data. Experiments were carried out on a 3.70 GHz Intel E5-1620 computer with 16.0G RAM and NVIDIA Quadro k4000 graphics.

The time consumption of the proposed method includes the time of computing cardiac excitation conduction model data and implementing the merging visualization of this data and cardiac structure data with the proposed merging attenuation function. Computing cardiac ventricle excitation conduction model data took 2 min 40 s for the simulation at a certain moment within the excitation cycle. The merging visualization for the ventricle structure data which has the size of 325 × 325 × 425 took 1 min 30 s. The total consuming time is 4 min 10 s. With the increased degree of the complication of the image set, the proposed method will take more computing time. When we implemented the merging visualization method on the whole heart geometry data of 469 × 325 × 487, it took 2 min 50 s to produce the heart image. The total consuming time became 5 min 30 s.

Since it is very difficult to observe the cardiac electrical activities in the tissue level, generally the open chest surgery is carried out and an electrode array is placed on the heart surface to monitor the electrical activities. However the experiment in vivo is infeasible for mankind. As an alternative method, a large number of animal patch clamping experiments were used. Based on the experimental data, the computational models were built to simulate the above activities. Here some classical and authoritative articles are available that cover models from cellular electrophysiology to models of cardiac anatomy. In our manuscript, the TNNP06 model is used, which can in detail describe different aspects of human ventricular electrophysiological function and dysfunction. It is constructed with 12 major ionic currents, and fits the experimentally measured APDR properties of human myocardium and the CVR properties for currently only available for dog and guinea pig model and so on. The model is also able to reproduce the APs of endo-, m-, and epimyocardial regions of the ventricles and their different rate dependencies. The methodology in this work is implemented on the electrophysiological data generated by the TNNP06 model and the real anatomical data. Therefore it can explore the cardiac action potential and other necessary electrophysiological characteristics which fit the experimental data.

## Conclusion

In this paper, we introduce a novel exploratory method for cardiac biophysical merging visualization of biophysical coupling of electrophysiological activity and cardiac anatomy structure. Compared to previous methods, the proposed approach comprehensively highlights certain features of interest of cardiac electrophysiological property in the authentic fine organ anatomy context. In order to explore detailed cardiac electrical activity, firstly a cardiac electrical excitation propagation model is implemented on the cardiac cross-sectional data and the volume of cardiomyocytes electrical excitation conduction is obtained. Then the MAF is constructed to integrate cardiac anatomy with electrophysiological volume and visualize a biophysically detailed merging heart.

The method presented in this work is a useful way for providing detailed electrophysiological behavior information while delivering detailed anatomical circumstance, which allows researchers to explore intricate functional mechanisms, which can further help speculate cardiac physiological and pathological properties for cardiac research and clinical diagnoses. Practical applications of our work will be the platform for having insights into cardiac disorders such as mechanisms of arrhythmia, and accordingly be the tools to aid in the prevention, diagnosis and treatment of cardiac diseases.

## Notes

### Authors’ contributions

FY carried out cardiac coupling visualization. WL was responsible for carrying out the modeling of excitation propagation of the ventricle. LZ and YZ participated in performing the experiments. WZ, KW and HZ designed the workflow of the cardiac model coupling and provided the manuscript revise suggestion. All authors read and approved the final manuscript.

### Acknowledgements

Not applicable.

### Competing interests

The authors declare that they have no competing interests.

### Availability of data and materials

The data supporting the conclusions of this article are included within the article. Any queries regarding these data may be directed to the corresponding author.

### Consent for publication

Authors have agreed to submit it in its current form for consideration for publication in the Journal.

### Ethics approval and consent to participate

Not applicable. No tests, measurements or experiments were performed on humans as part of this work.

### Funding

This work was supported by a Grant from the National Natural Science Foundation of China (NSFC) No. 61502275 and the Fundamental Research Funds for the Central Universities No. 2015ZQXM004. This work was also supported in part by the National Natural Science Foundation of China (NSFC) Grants No. 61571165.

### Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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