Application of Maxwell Equations to Human Body Modelling
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1 Application of Maxwell Equations to Human Body Modelling Fumie Costen Room E, E0c at Sackville Street Building, The University of Manchester, U.K. February 5, 0 Fumie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
2 Outline Research background Research issues umie Costen Room E, E0c at Sackville Street Building, Application of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
3 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
4 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
5 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
6 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
7 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
8 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
9 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
10 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
11 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
12 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
13 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
14 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
15 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
16 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
17 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
18 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
19 Research background is a common form of heart disease Catheter ablation with RF radiation is a proven technique to remove Ideally ECG indicates the location of umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
20 Research background For emergency, electric shock is applied for defibrillation Not high success rate The optimum size, location of electrolodes are unknown and depends on age and sex. a Fumie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 4 /
21 Research background Brain disorders Amnesia, Alzehimer,Epilepsy, Parkinson s disease, Depression, Schizophrenia Medication and counselling for treatment a Fumie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 5 /
22 Research background Brain disorders Alternative treatment: deep brain stimulation Pacemaker implanted for treatment Fumie Costen Room E, E0c at Sackville Street Building, Application of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 6 /
23 Research background Brain disorders Literally Invasive treatment Non-invasive treatment desired Fumie Costen Room E, E0c at Sackville Street Building, Application of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 7 / a
24 Research background Needs of numerical simulation How ElectroMagnetic (EM) wave propagates from the electrolodes on the torso for successful defibrillation the electolodes on the skull to do the same effect as invasive treatment in the heart to the torso a electroconvulsive-therapy-is-like Fumie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 8 /
25 Numerical simulation tool development Maxwell s equation finite difference time domain (FDTD) most straightforward, robust, widely applicable 4 high accuracy possible with high computational cost umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 9 /
26 Numerical simulation tool development Maxwell s equation finite difference time domain (FDTD) most straightforward, robust, widely applicable 4 high accuracy possible with high computational cost umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 9 /
27 Numerical simulation tool development Maxwell s equation finite difference time domain (FDTD) most straightforward, robust, widely applicable 4 high accuracy possible with high computational cost umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 9 /
28 Numerical simulation tool development Maxwell s equation finite difference time domain (FDTD) most straightforward, robust, widely applicable 4 high accuracy possible with high computational cost umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 9 /
29 Many tissues involved in the computation Digital Human Phantom from mm resolution MRI under the non-disclosure agreement Fumie Costen Room E, E0c at Sackville Street Building, Application of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 0 /
30 Each tissue is frequency-dependent Measurement and data fitting by US Air Force Fumie Costen Room E, E0c at Sackville Street Building, Application of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
31 Wave propagation simulation inside human remeshing from mm resolution to 0. mm resolution loading of the fine geometrical detail to the Maxwell equation solver allocation of the frequency dependent characteristics to each tissue 4 load-balanced parallel computation on distributed memory architecture 5 hardware acceleration of computation umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
32 Wave propagation simulation inside human remeshing from mm resolution to 0. mm resolution loading of the fine geometrical detail to the Maxwell equation solver allocation of the frequency dependent characteristics to each tissue 4 load-balanced parallel computation on distributed memory architecture 5 hardware acceleration of computation umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
33 Wave propagation simulation inside human remeshing from mm resolution to 0. mm resolution loading of the fine geometrical detail to the Maxwell equation solver allocation of the frequency dependent characteristics to each tissue 4 load-balanced parallel computation on distributed memory architecture 5 hardware acceleration of computation umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
34 Wave propagation simulation inside human remeshing from mm resolution to 0. mm resolution loading of the fine geometrical detail to the Maxwell equation solver allocation of the frequency dependent characteristics to each tissue 4 load-balanced parallel computation on distributed memory architecture 5 hardware acceleration of computation umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
35 Wave propagation simulation inside human remeshing from mm resolution to 0. mm resolution loading of the fine geometrical detail to the Maxwell equation solver allocation of the frequency dependent characteristics to each tissue 4 load-balanced parallel computation on distributed memory architecture 5 hardware acceleration of computation umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
36 How to solve partial differencial equations fast Original equation A φ = Bφ; B has spatial discretization t elements A φn+ φ n = B φn+ + φ n t (A tb)φ n+ = (A + tb)φ n Sparse matrix to handle Approximate factorization *example* to handle tridiagonal matrix (I X L )(I Y L )(I Z L )φ n+ = (I + X R )(I + Y R )(I + Z R )φ n how to factorise multiplicative solution additive solution umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
37 How to solve partial differencial equations fast Original equation A φ = Bφ; B has spatial discretization t elements A φn+ φ n = B φn+ + φ n t (A tb)φ n+ = (A + tb)φ n Sparse matrix to handle Approximate factorization *example* to handle tridiagonal matrix (I X L )(I Y L )(I Z L )φ n+ = (I + X R )(I + Y R )(I + Z R )φ n how to factorise multiplicative solution additive solution umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
38 How to solve partial differencial equations fast Original equation A φ = Bφ; B has spatial discretization t elements A φn+ φ n = B φn+ + φ n t (A tb)φ n+ = (A + tb)φ n Sparse matrix to handle Approximate factorization *example* to handle tridiagonal matrix (I X L )(I Y L )(I Z L )φ n+ = (I + X R )(I + Y R )(I + Z R )φ n how to factorise multiplicative solution additive solution umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
39 How to solve partial differencial equations fast Original equation A φ = Bφ; B has spatial discretization t elements A φn+ φ n = B φn+ + φ n t (A tb)φ n+ = (A + tb)φ n Sparse matrix to handle Approximate factorization *example* to handle tridiagonal matrix (I X L )(I Y L )(I Z L )φ n+ = (I + X R )(I + Y R )(I + Z R )φ n how to factorise multiplicative solution additive solution umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
40 How to solve partial differencial equations fast Original equation A φ = Bφ; B has spatial discretization t elements A φn+ φ n = B φn+ + φ n t (A tb)φ n+ = (A + tb)φ n Sparse matrix to handle Approximate factorization *example* to handle tridiagonal matrix (I X L )(I Y L )(I Z L )φ n+ = (I + X R )(I + Y R )(I + Z R )φ n how to factorise multiplicative solution additive solution umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
41 How to solve partial differencial equations fast Original equation A φ = Bφ; B has spatial discretization t elements A φn+ φ n = B φn+ + φ n t (A tb)φ n+ = (A + tb)φ n Sparse matrix to handle Approximate factorization *example* to handle tridiagonal matrix (I X L )(I Y L )(I Z L )φ n+ = (I + X R )(I + Y R )(I + Z R )φ n how to factorise multiplicative solution additive solution umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
42 Reduction of memory requirement by sophisticated boundary condition The normal wave propagation Boundary placed close to the signal source umie Costen Room E, E0c at Sackville Street Building, Application of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 4 /
43 Reduction of memory requirement by Subgridding Signal leaking at the interface between the fine mesh and the coarse mesh Filtering out the leaking signal for stability Independent fine mesh FDTD computation only for heart Communication between the coarse and fine mesh at the interface umie Costen Room E, E0c at Sackville Street Building, Application of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 5 /
44 Efficient computation on EUgrid and Supercomputers in RIKEN The production code requires more than 00 GB of memory for ECG simulation Each node can share upto GB of memory with the latest technology Distributed computing is essential 4 High scalability is aimed at with the sophisticated parallel computing umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 6 /
45 Efficient computation on EUgrid and Supercomputers in RIKEN The production code requires more than 00 GB of memory for ECG simulation Each node can share upto GB of memory with the latest technology Distributed computing is essential 4 High scalability is aimed at with the sophisticated parallel computing umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 6 /
46 Efficient computation on EUgrid and Supercomputers in RIKEN The production code requires more than 00 GB of memory for ECG simulation Each node can share upto GB of memory with the latest technology Distributed computing is essential 4 High scalability is aimed at with the sophisticated parallel computing umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 6 /
47 Efficient computation on EUgrid and Supercomputers in RIKEN The production code requires more than 00 GB of memory for ECG simulation Each node can share upto GB of memory with the latest technology Distributed computing is essential 4 High scalability is aimed at with the sophisticated parallel computing umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 6 /
48 Efficient computation on EUgrid The concept of computation on the distributed memory architecture machine OpenMP for speedup machine 4 GB shared memory CPU MPI for increase of memory usage CPU 4 GB shared memory CPU CPU4 Fumie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 7 /
49 Efficient computation on EUgrid The directory information tree User Element site information Computing Element Storage Element Network information between this and other sites status supported protocols file statistics umie Costen Room E, E0c at Sackville Street Building, Application of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 8 /
50 General Purpose computing on Graphics Processing Units How do we change the computational strategy suitable for GPU? How much computational gain do we get over the computation with MPI? umie Costen Room E, E0c at Sackville Street Building, Application of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 9 /
51 General Purpose computing on Graphics Processing Units How do we change the computational strategy suitable for GPU? How much computational gain do we get over the computation with MPI? umie Costen Room E, E0c at Sackville Street Building, Application of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 9 /
52 General Purpose computing on Graphics Processing Units SM CPU Bridge System Streaming I Cache Host Interface Memory Processors MT Cache Input Viewport/clip/setup/ in C Cache Assembler raster/zcull SP SP Vertex work Pixel work Compute work Streaming SP SP distribution distribution distribution Multiprocessors are SP SP SP SP SM SM SM SM SM SM SM SM going to SFU SFU perform the Shared Interconnection network calculation Memory DRAM DRAM DRAM DRAM Memory operation (not arithmetic operation) dominates umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 0 /
53 General Purpose computing on Graphics Processing Units CUDA grid organization Host Device Grid Block (0,) Kernel Kernel Kernel Block (0,0) Grid Block (,) Block (,0) Block(,0) (0,,) (,,) (,,) Thread Thread Thread (0,0,) (,0,) (,0,) Thread Thread Thread (0,0,) (,0,) (,0,) Thread Thread Thread (0,0,0) (,0,0) (,0,0) umie Costen Room E, E0c at Sackville Street Building, Application of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
54 General Purpose computing on Graphics Processing Units Kernel 4 The domain decomposition of the D FDTD Kernel 0 A thread z y space in (,0,,0) the first in Kernel x approach. (a, b, c, d) means (block- Idx.x,blockIdx.y, threadidx.x, threadidx.y). sequential kernel invocation umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
55 General Purpose computing on Graphics Processing Units A thread with(,,,) The domain decomposition of the z y D FDTD space in x the second A thread with (,0,,0) approach. (a, b, c, d) means (block- Idx.x,blockIdx.y, threadidx.x, threadidx.y). umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
56 General Purpose computing on Graphics Processing Units A block [5, ] The domain decomposition of the z y Thread D FDTD Thread 0 space in Thread in Block [5, 0] the third approach. A block [5, 0] [a, b] means [blockidx.x, blockidx.y]. x umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 4 /
57 General Purpose computing on Graphics Processing Units Our approach Flexibility in the workload of each thread Flexible on the way to minimize the time to fetch data from global memory (DRAM) A block[,4] Thread Thread Thread 0 Thread Thread Thread 0 x z y A block [,0] umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 5 /
58 Streaming SIMD Extensions instructions SSE function is available in the ordinary computers Without any hardware purchase, speed up of 4 is achievable How we should use SSE effectively X X X X4 Register Y Y Y Y4 OP OP OP OP Register X OP Y X OP Y X OP Y X4 OP Y4 Register Behaviour of a packed SSE instruction Each rectangle has single precision. X and Y are -bit operands and OP means operation umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 6 /
59 Imaging detection of what you cannot see Ultrasound Infrared Magnetic resonance imaging 4 X-ray 5 Microwave imaging Cheap Non-invasive Easy to apply umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 7 /
60 Procedure of microwave imaging Launch a microwave signal from an array of antennas Detect the signal reflected from an object Analyze the reflected signal to understand the characteristics of the object. umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 8 /
61 Method of the microwave imaging projects Understand the software we use for the simulation of the wave propagation Investigate the geometry you need to model such as cancerous cells, metal or water under the ground Model the object in the software and apply the time reversal method ( imaging technique ) 4 Analyze the results and if possible improve the algorithm for the specific target. umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 9 /
62 Objects of the microwave imaging projects Cancer in breast, lung, bowel, brain, stomach Stone in kidney Metal under the ground or in the sea 4 Water under the ground in North Africa umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 0 /
63 Finally... Merci beaucoup Many thanks for your attention umie Costen Room E, E0c at Sackville Street Building, Application of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
64 Finally... Welcome to Computation in Electromagnetics Hope you like our research domain/activity ( biomedical modelling, parallel computing in Beowulf clusters, parabolic partial differential equations, programming, shell-scripting ) Please talk to me for the detail with your future plan umie Costen Room E, E0c at Sackville Street Building, Application fc@cs.man.ac.uk of Maxwell equations The University to Human of Manchester, Body U.K. ( ) February 5, 0 /
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