The Finite-Difference Time-Domain (FDTD) Method as the Most Practical Tool for Hyperthermia Planning?

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The Finite-Difference Time-Domain (FDTD) Method
as the Most Practical Tool for Hyperthermia
Planning?

• Dennis Sullivan, Ph.D.
• Professor of Electrical Engineering
• University of Idaho
• Moscow, ID USA
• 83844-1023

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Advantages of FDTD

• It is a direct implementation of Maxwells
• equations (or the bio-heat equation). There
  is no complicated additional mathematics, e.g.,
  matrix inversion, field singularities, etc.

2. There is no complicated mesh to generate.
FDTD uses cubes.

• The needed resources increase only linearly
• with the size of the problem space, e.g., a
  problem with 10,000 cells only takes twice as
  long as a problem with 5,000 cells.

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Advantages of FDTD (continued)

• It is a time-domain method. The actual radiation
  or temperature rise can be observed.
• Also, signal processing techniques can be
  brought to bear on simulation problems

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Possible Disadvantages of FDTD

1. The cubic structure can lead to stair-casing,

2. The problem space must be truncated properly
or reflections will give erroneous fields.
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Direct physics-based implementation
Electromagnetic radiation is governed by the
Maxwells equations
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Direct physics-based implementation
In one dimension in free space they become
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Direct physics-based implementation
To put these equations in a computer, take the
finite-difference approximations of the partial
derivatives in time and space




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Direct physics-based implementation
This is a time-domain method. Each new value of
the electric field E or the magnetic field H is
determined by the previous values
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Direct physics-based implementation
The k represents the location in an array in a
computer while n represents time
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Direct physics-based implementation
This results in the following two equations of
code in the C program language
exk exk 0.5( hyk-1 - hyk) hyk
hyk 0.5( exk - exk1)
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Direct physics-based implementation
nn1
Calculate En1/2
Calculate Hn1
Each time step represents an increment in the
total time T n Dt.
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Direct physics-based implementation
The following is a one-dimensional simulation of
an EM pulse propagation in free space. T
represents the number of time steps.
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