.
1 RF Models
2. 2. Start with simple plane wave models
3. 3. Progress to figures of revolution
4. 4. Numerical Approaches
1.
1
Antennas
Near Field
Far Field
R
R
2D 2
2D 2
Transition Range from
0.2to0.4
D2
Short Dipole = λ/2π
2
Some Basic Definitions
1 Specific Absorption Rate (SAR) in W/kg
E 2
SAR
Where σ is the conductivity in S/m ρ is the density in
kg/m3 and E is the electric field V/m
For short pulses
cT
SAR
t
Where c is the specific heat capacity in J/kg oC
ΔT is the change in temperature
Δt is the length of the pulse
3
Thermal Relaxation Times
1. For a short pulse in a Sphere
a2
4k
Where a is the radius and
k
is the thermal diffusivity
And
k'
k
c
where k’ is the thermal conductivity.
Note for a long thin plate we get much faster thermal
relaxation times as the surface to volume ratio
increases as 1/t where t is the thickness.
4
Thermal vs. Non-thermal Biological Effects
1 Temperature is a convenient way to define a
distribution functions. The only case when you
have a non-thermal system is when you have only
one particle or one state.
2. The common Maxwell Boltzmann distribution is
given by
3 Another common distribution function is a FermiDirac
4. Different temperatures for electrons and lattice.
5
Plane Waves
1 This works for R/λ>> 1 R is the radius of curvature
and λ is the wave length
2 Important parameters are the frequency, f,
polarization, P, the angle of incidence,θ, σ, and ε
3 At normal incidence reflection coefficient 2 1
Where η1, η2 are impedances
2 1
The transmission coefficient is given by
2 2
Going from 1 to 2.
T
2 1
The power reflected is given by Г2
6
Reflection Coefficients E Field
7
Power Transmission Coefficients
8
Penetration of EMF vs Frequency
Power
9
Depth of Penetration for Some Bio Materials
10
Reflection as a Function of Angle and Polarization
From a Tissue Interface
11
Phase of Reflection
12
Multiple Layers
13
SAR In the Plane of the Fat and Muscle
14
Peak SAR
15
Distribution of E Field
16
Spherical Model For Brain of Cat 918Mhz
1
17
Spherical Model for Cat Brain at 2450Mhz
18
Absorption Characteristics Spherical Model
19
Frequency Dependent Spherical Model for Human
Absorption
20
Numerical Models
1 Quasi-static < 30 to 40Mhz
2 Method of Moments, MoM
3. Finite Element, FEM
4. Finite Difference Time Domain, FDTD
21
3D Impedance Models
1. Assumes the dimensions are small compared to the
wave length so that everything is at the same time.
zx
zz
Zy
22
Applications of Quasi-Static Method
23
See Jim Lin’s Book
Electromagnetic Fields In Biological Systems. CRC
press.
24
Volume Integral Method of Moments, VMoM
1 Transforms Integral Equations into a matrix
equations using the volume equivalence principle
2 Break into N simple cells
3. Satisfy the Boundary Conditions
4. Get full matrices
5. Takes lots of memory.
25
Surface Method of Moments, SMoM
26
Finite Element Method FEM
1. This has not been used much for biological
estimates of the fields in humans
2. It grows with the number of elements as N
3. The choice of the elements and their shape is
important.
4. Use to form a system of linear equations.
5. Satisfy the boundary conditions.
27
28
Finite Difference Time Domain
29
Finite Difference Time Domain
1. Establish values of σ and ε for each cell
2. Include the source.
3. The boundary conditions are generated from the
curl equations.
4. Establish the E,H, about the unit cell then evaluate
the values at alternate half time steps
5. This calculation grows linearly with N
6. This can be fast even for N = 106
7. This is the most commonly used approach.
30
Frequency –Dependent FDTD
1 Used for short pluses and wide band where ε and σ
vary with frequency.
2 Two approaches
A. convert ε and σ to the time domain
B. Add the differential equation for displacement vector
D Solve the equations simultaneously
31
Tissue Properties
32
Current Densities in the Body from the Magnetic Fields
of a low field Electric Blanket
33
Current Densities in the Body from the Magnetic Fields
of a Standard Electric Blanket
34
Current Densities in the Body from the Magnetic Fields of an
Electric Blanket
35
Electric Blanket Exposures
36
Power Line Exposure at 10kV/m
and H= 26.5 A/m
37
Cubic Cell Mode.
1
38
Cubic Cell Model of Human
39
Insert Virtual Family
40
See VF
1. See for Cell Phone Radiation into the Head.
IEEE Proc. Vol 83, Jan 1995 “Em Interaction of Handset
Antennas and a Human in Personal Communications”
Michael Jensen and Yahya Rahmat-Sami
41
Average Absorption
42
Average SAR vs Frequency at10W/m2 and
80MHz Vertical Polarization
43
Average SAR Whole Body
44
AVERAGE SAR
45
SAR Average for Children
46
2
10W/m
Whole Body SAR At
Plane Wave vs Frequency
47
Base Station Exposures
48
Cell Phone Exposures
49
Cell Phone Exposures
50
Ultra Wide Band EMP at 1.1V/m
51
Fourier Spectra UWB EMP
52
FTDT with Time Varying Dielectric Constant
Start with
D
xH
t
and
D * ( ) E
Using the Debye equations * ( ) o s1 s 2
1 j1
1 j 2
We get the following differential equation with the time
varying dielectric constant to be solved
2 D
D
E
2 E
1 2 2 ( 1 2 )
D o o E ( s1 2 s 2 1 )
1 2 2
t
t
t
t
53
Debye Constants
54
Induced Currents at V=1.1V/m
55
Peak Currents UWB Exposure
56
Bio Heat Equation
57
Heating of Body Tissue
1. Initial conditions Q=0
2 . Boundary conditions . Assume heat flow
perpendicular to skin.
58
Heat Flow
1. Radiation
2. Usually the surface temperature Ts and TA are close
enough together that this is not significant.
3. The body temperature is tightly temperature
regulated to near 37o C. Thus parameters vary with
temperature
4. The metabolic rate A depends on the local
Temperature as
59
Blood Profusion
1 Below 39o C
2. For
linear increase
3. For T> 44o the blood flow is at a maximum. C
4. Control with vasodilatation and profusion through
the skin.
60
Heat Flow
1. Heat is carried from the interior to the surface of the
skin. The blood temperature TB varies as
61
Numerical Calculations
1 Need to couple heat generation from the RF to the
basic heat equation.
2. The geometry is complicated and the coefficients
vary in time and space.
3. The usual approach is to use FDTD for calculating
the power distribution and a finite difference approach
for solving the heat diffusion equation.
4. The temperature difference is calculated at the
center of each cube with the heat gain or loss and
repeated at each time interval.
62
Skin Temperature
1. One signal for temperature control is the
hypothalamic temperature as an indicator of core body
temperature.
63
Temperature Values as
Considered for Standards
1. Threshold for nerve damage +4.5oC for 30 minutes
2. Lens of rabbit eye 3-5oC
3. Skin 8 to 10oC for damage
4. 1o to 2oC in the core can lead to physiological
changes
4. Other data shows threshold problems typically
about 41oC
5. All this data is exposure time dependent.
64
RF Protection
1 Guide lines set at SAR = 4W/kg for whole body
exposures with estimated core temperature rise of 1oC.
2. Local heating may be as much as 20: 1 for plain wave
exposures
3. There are a lot of variables here, position,
environment, humidity , temperature of the air, etc.
4. One model shows maximum ΔT = 0,72oC at 4oMHz
in the ankles where the estimated damage is at
ΔT =8oC
65
1
Plain Wave at 40MHz and
2
900MHz at 1mW/cm
66
Head and Cell Phone
1. Heating from RF
2. Cell phone blocking convection cooling
3. Heating from the power losses in the phone.
4. Example 250mW at 50% efficiency at 900MHz air at
24oC for 15 minutes.
Some results Brain ΔT= o,1oC from SAR
Contact heating with no RF to 1.5oC in the ear.
67
Table from Visible Human Model
1
68
Temperature in the Ear
1 Note cooling on contact.
69
ANSI/IEEE Guidelines
1
2. Note these guidelines only consider thermal effects.
70
Thermal Therapeutic Applications
1 Hyperthermia Therapies at ≈ 43oC
2. Ablations at ≈ 65oC
3. Microwave Applicator Power ~ 1/r2 Heating ~ 1/r4
Need to account for blood flow and prevent heat flow
along the wire for heart ablation. f= 2.45GHz Use chokes
to confine the power
71
Power Required for Lesion in
Cardiac Tissue
1.
2. Competition , Laser Surgery,
3. Single electrode and grounded back.
72
Slot Antenna
1
73
Depth of Heating to 75oC as a Function of
the Time and Power
1, Objective to get tumor T> 43oC and normal T< 42oC
74
Sleeved Slot Antenna
75
An Array For Heating a Larger Volume
1
76
0
