Cardiac electrical activities are varying in both space and time. Human heart consists of a fractal network of muscle cells, Purkinje fibers, arteries and veins. Whole-heart modeling of electrical wave conduction and propagation involves a greater level of complexity. Our previous work developed a computer model of the anatomically realistic heart and simulated the electrical conduction with the use of cellular automata and parallel computing. However, simplistic assumptions and rules limit its ability to provide an accurate approximation of real-world dynamics on the complex heart surface, due to sensitive dependence of nonlinear dynamical systems on initial conditions. In this paper, we propose new reaction-diffusion methods and pattern recognition tools to simulate and model spatiotemporal dynamics of electrical wave conduction and propagation on the complex heart surface, which include (i) whole heart model; (ii) 2D isometric graphing of 3D heart geometry; (iii) reaction diffusion modeling of electrical waves in 2D graph, and (iv) spatiotemporal pattern recognition. Experimental results show that the proposed numerical solution has strong potentials to model the space-time dynamics of electrical wave conduction in the whole heart, thereby achieving a better understanding of disease-altered cardiac mechanisms.

1. Whole Heart Modeling – Spatiotemporal
Dynamics of Electrical Wave Conduction and
Propagation
Hui Yang
杨 徽
Associate Professor
Complex Systems Monitoring, Modeling and Control Lab
The Pennsylvania State University
University Park, PA 16802
November 25, 2017

2. Outline
1 Introduction
2 Research Methodology
Fractal surface simulation
Isometric graphing for surface characterization
Reaction-diffusion modeling in the reduced dimension
Spatiotemporal pattern recognition
3 Experimental Results
4 Conclusions and Future Directions

3. Introduction Research Methodology Experiments Conclusions
Introduction
Computer Simulation
Describe complex phenomena
Predict system behaviors
Optimize control action
Improve system performance
Whole-heart Modeling and Simulation
Overcome many practical and ethical limitations in real-world
biomedical experiments
Offer greater flexibility to test their hypothesis and develop new
hypotheses
Circulation Research - “Biophysics-based cardiac modeling has the
potential to dramatically change the 21st century cardiovascular
research and the field of cardiology.”
Yang, Hui (Penn State) Whole-Heart Modeling November 25, 2017 3 / 22

4. Introduction Research Methodology Experiments Conclusions
Challenges
Spatiotemporal dynamics
Reaction process: dynamic variables are interacting with each other
Diffusion process: dynamic variables spread out in space
High dimensionality
Approximately 2 billion heart muscle cells
Complex geometry
Euclidean vs. Fractal
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5. Introduction Research Methodology Experiments Conclusions
Fractal
Man made structures
Euclidean geometry ( > 2000 yrs ) : Triangles, circles, squares,
rectangles, trapezoids, pentagons, hexagons, octagons, cylinders
Natural objects
Fractal geometry (100 yrs)
Rough edges, non-uniform shapes
Self-similarity: human heart, flowers, trees, mountains, . . .
Yang, Hui (Penn State) Whole-Heart Modeling November 25, 2017 5 / 22

6. Introduction Research Methodology Experiments Conclusions
Literature - Fractal characterization and modeling
Mandelbrot - ”A rough or fragmented geometric shape that can be subdivided in
parts, each of which is (at least approximately) a reduced/size copy of the whole”
Characterization of fractal dimension
Monofractal - homogeneous self-similarity across scales, characterized by a single
fractal dimension.
Multifractal - non-homogeneous self-similarity across scales, singularity spectrum
to characterize scaling properties
Modeling the fractal object or process
Iterative or recursive function systems
Rough surfaces - shear displacement algorithm, diamond-square algorithm
Heart rate time series - random cascade model
Gaps
Little has been done to develop simulation model of spatiotemporal
dynamics on fractal geometry
Modeling differences between fractal and Euclidean geometry have not
been fully investigated before
Need to fill the gaps
Yang, Hui (Penn State) Whole-Heart Modeling November 25, 2017 6 / 22

7. Introduction Research Methodology Experiments Conclusions
Literature - Dimensionality reduction
High-dimensional data are difficult to visualize and interpret
Dimensionality reduction approaches
Principal component analysis (PCA)
Multidimensional scaling (MDS)
Self-organizing map (SOM)
Isometric feature mapping (ISOMAP)
Most of previous studies focused on the reduction of high-dimensional
data and then the extraction of useful information from the
low-dimensional data.
Gaps - Few previous approaches considered the construction of
simulation models in the low-dimensional space.
Need to fill the gaps
Yang, Hui (Penn State) Whole-Heart Modeling November 25, 2017 7 / 22

8. Introduction Research Methodology Experiments Conclusions
Fractal surface simulation
Random midpoint displacement algorithm
Yang, Hui (Penn State) Whole-Heart Modeling November 25, 2017 8 / 22

9. Introduction Research Methodology Experiments Conclusions
Isometric graphing for surface characterization
Isometric graphing algorithm*
Construct neighborhood graph
Compute shortest paths – geodesic distances: e.g., Dijkstra’s algorithm
Construct low dimensional embedding: classical MDS
Euclidean distance → Geodesic distance
*J. B.Tenenbaum et al., A Global Geometric Framework for Nonlinear Dimensionality Reduction, Science 290 (5500), 2000
Yang, Hui (Penn State) Whole-Heart Modeling November 25, 2017 9 / 22

10. Introduction Research Methodology Experiments Conclusions
Reaction-Diffusion Modeling
FitzHugh-Nagumo (FHN) model
∂u
∂t = c1u(1 − u)(u − a) − c2uv + 2u
∂v
∂t = b(u − dv)
where a = 0.13; b = 0.013; c1 = 0.26; c2 = 0.1; d = 1.0; u : membrane
voltage; v : recovery variable.
Yang, Hui (Penn State) Whole-Heart Modeling November 25, 2017 10 / 22

11. Introduction Research Methodology Experiments Conclusions
R-D Model on the Heart
Healthy heart
Near-periodic electrical impulse
Arrhythmia heart
Atrial fibrillation
Rapid, disorganized and irregular electrical impulse
https://youtu.be/bH vJfZzgOM
Yang, Hui (Penn State) Whole-Heart Modeling November 25, 2017 11 / 22

12. Introduction Research Methodology Experiments Conclusions
Spatiotemporal pattern recognition
Spatiotemporal data
Y (si, t), t = 1, ..., T
si - spatial location, i = 1, ..., N
Hyper-distance matrix: spatiotemporal dissimilarity
Yang, Hui (Penn State) Whole-Heart Modeling November 25, 2017 12 / 22

13. Introduction Research Methodology Experiments Conclusions
Self-Organizing Network Embedding
Spring-Electrical Model
Nodes − electrically charged particles
Edges − springs between nodes
The repulsive force exists between any pair of nodes
fr(l, m) = −
1
xl − xm
2
× eDT (l,m)
The attractive force exists only between two connected nodes
fa(l, m) = xl − xm
2
× e−DT (l,m)
, l ↔ m
The combined force at a node l: f(l, x)
l=m
−
(xl − xm)
xl − xm
3
×eDT (l,m)
+
l↔m
xl −xm ×(xl − xm)×e−DT (l,m)
Minimal energy network: x∗ = arg minx l=1,...,T f(l, x)2
Yang, Hui (Penn State) Whole-Heart Modeling November 25, 2017 13 / 22

14. Introduction Research Methodology Experiments Conclusions
Low-dimensional Pattern
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15. Introduction Research Methodology Experiments Conclusions
GPGPU Acceleration
Computer Setting
Intel dual core i3-2100 CPU @ 3.10GHz with 16G DDR3 memory,
Nvidia Telsa C2075 graphic card with 6GB global memory, Window 7
(64 bit) operating system
GPU - NVidia CUDA platform and OpenGL - rendering loop iteration
and GUI mechanism
CPU-based simulation
The algorithm traverses through all cells in the 3D heart model to
finish one iteration, and determine the status (timer value) of each cell.
Then, OpenGL is called to render the whole heart according to the
status of cells.
GPU-based simulation
Instead of iterating through the heart, we issue every cell a thread,
which will increase the timer of the thread, look up the neighbors, and
calculate and store the states for the cell if applicable. We, then,
launch 148516 threads to the GPU multicore processors and run these
threads in parallel.
Yang, Hui (Penn State) Whole-Heart Modeling November 25, 2017 15 / 22

16. Introduction Research Methodology Experiments Conclusions
GPU vs. CPU
GPU Case 1 - OpenGL/CUDA coop
GPU Case 2 - fast data transferring within shared memory
728,321 cells in the whole-heart model,
Improve the speed of computing by approximately 30-fold
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17. Introduction Research Methodology Experiments Conclusions
GPU Simulation Demo
https://youtu.be/7MGA9r9A- A
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18. Introduction Research Methodology Experiments Conclusions
Summary
Challenges
Complex geometry: Fractal nature of high-dimensional systems
Geometric preservation: Geodesic distances vs. Euclidean distances
Large-scale simulation of complex biological systems
Spatiotemporal dynamics of electrical conduction and propagation
Methodology - spatiotemporal dynamics on fractal surfaces
Characterization and modeling of fractal geometry
Fractal-based simulation and modeling of spatiotemporal dynamics
Recognizing and quantifying spatiotemporal patterns.
Parallel computing - GPGPU
GPU yields 30 times faster than CPU-based simulation models
Yang, Hui (Penn State) Whole-Heart Modeling November 25, 2017 18 / 22

19. References
H. Yang*, Y. Chen, and F. M. Leonelli, “Whole Heart Modeling – Spatiotemporal
Dynamics of Electrical Wave Conduction and Propagation,”Proceedings of 2016
IEEE Engineering in Medicine and Biology Society Conference (EMBC), August
16-20, 2016, Orlando, FL, United States, DOI: 10.1109/EMBC.2016.7591990
Y. Chen and H. Yang*, “Numerical simulation and pattern characterization of
spatiotemporal dynamics on fractal surfaces for the whole-heart modeling
applications,”European Physical Journal B, p. 1-16, 2016, DOI:
10.1140/epjb/e2016-60960-6
D. Yu, D. Du, H. Yang*, and Y.C. Tu, “Parallel Computing Simulation of
Electrical Excitation and Conduction in the 3D Human Heart,”Proceedings of
2014 IEEE Engineering in Medicine and Biology Society Conference (EMBC), p.
4315-4319, August 26-30, 2014, Chicago, IL, United States. DOI:
10.1109/EMBC.2014.6944579

20. Introduction Research Methodology Experiments Conclusions
Acknowledgements
NSF CAREER Award
NSF CMMI-1617148
NSF CMMI-1646660
NSF CMMI-1619648
NSF IOS-1146882
James A. Haley Veterans’ Hospital
Yang, Hui (Penn State) Whole-Heart Modeling November 25, 2017 20 / 22

21. Introduction Research Methodology Experiments Conclusions
Contact Information
Hui Yang, PhD
Associate Professor
Complex Systems Monitoring Modeling and Control Laboratory
Harold and Inge Marcus Department of Industrial and Manufacturing
Engineering
The Pennsylvania State University
Tel: (814) 865-7397
Fax: (814) 863-4745
Email: huy25@psu.edu
Web: http://www.personal.psu.edu/huy25/
Yang, Hui (Penn State) Whole-Heart Modeling November 25, 2017 21 / 22

22. Introduction Research Methodology Experiments Conclusions
Questions?
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