Modeling and Simulation of Bioheat Transfer

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Modeling and Simulation of Bioheat Transfer
Alex Hutson Elkhorn Area Middle
School Advisor Dr. Subha K. Kumpaty Research
Experience for Teachers (RET) Summer 2008
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Purpose
To gain experience in engineering and research
that will better prepare me to teach science in a
meaningful way to my students.
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Rationale

• Understanding heat flow mechanisms is of major
  importance in science and engineering.

• It is important to start teaching students these
  concepts as early as possible.

• Heat transfer relates to students daily lives in
  many ways Therefore, using relevant simulations
  and examples student interest for learning can be
  positively affected.

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Objectives

• Research bioheat transfer mechanisms, simulation
  equations, and parameters.

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Objectives
2. Create a simulation (MATLAB program) that
allows students to vary heat transfer parameters
and analyze the results.
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Objectives

• 3. Create a curriculum module that illustrates
  heat transfer principles reinforced by
  implementing the simulation.

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Objectives
4. Connect physics, biology, engineering and math
into a project that will motivate students to
pursue careers in STEM fields.
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In all aspects of life, the universe, and
everything, heat energy is transferred from
object to object by one or a combination of three
transport mechanisms.
Background Information

• Conduction via contact in solids
• Convection currents through liquids and gases
• Radiation through space as electromagnetic
  energy

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The three modes of heat transfer can be
mathematically represented by these equations.
Fouriers Law
Newtons Law of (Convective) Cooling
Stefan-Boltzmann Law
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Application into Biology
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• For the purpose of basic simulation, it is
  easier to look at energy flow in terms of
  heat-balance for a controlled volume in a steady
  state
• qin qout qgen 0
• qin heat energy in at the boundaries
• qout heat energy out at the boundaries
• qgen heat generated within the boundaries

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Thermal Process Through Biological Tissues of a
Human Forearm
h, Tinf
Tc
T2
T1
T6
T7
T9
T10
T11
T8
Skin/Fat 3mm
3mm
Muscle Tissue 30mm
Image adapted from
http//i.treehugger.com/images/2007/10/24/air-qual
ity-clouds.jpg
http//cytochemistry.net/Cell-biology/Medical/prac
ti14.jpg
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Energy Balance on Node 1
TC
T1
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Energy Balance on Node 1
TC
T1
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Energy Balance on Node 1
T1
TC
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Energy Balance at muscle- skin/fat interface
(Node 10)
T10
T11
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Energy Balance at muscle- skin/fat interface
(Node 10)
T10
T11
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Energy Balance at muscle- skin/fat interface
(Node 10)
T10
T11
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Energy Balance at muscle- skin/fat interface
(Node 10)
T10
T11
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Thus, giving energy balances on 11 nodes
(control volumes) give 11 simultaneous equations
which can be solved using matrix algebra.
T10
T11
T9
T8
T7
T6
T2
T1
In matrix form, A 11 X 11 T 11 X 1 B 11 X
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Solving, T inv (A) B
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Parameters
h qm w Tsf
8, 200 W/m2 K
700, 5600 W/m3
0 0.001 m3 s-1/m3
273, 288, 297, 303 K
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MatLab Program
One-dimensional heat transfer (Steady-state) h10
0 (W/m2 K) Check conv, rad boundary h values, of
air or water surrounding Dry air
8 (W/m2 K), Half submerged in water 100 (W/m2
K), Submerged in water 200 (W/m2 K) eps0.95
skin emissivity Tf297 (K) T_infinity
(environment temperature) Tc310 (K) Core
Temperature Ta310 (K) Arterial
Temperature Lm0.03 (m) muscle length Lsf0.003
(m) skin/fat layer dx0.003 (m) node
thickness km0.5 (W/m K) Thermal conductivity
of muscle tissue ksf0.3 (W/m K) Thermal
conductivity of skin/fat layer qmd5600 (W/m3)
metabolism rate Resting 700 (W/m3), Exercising
5600 (W/m3) w0.001 (s-1) Perfusion
rate rb1000 (kg/m3) blood density cb3600
(J/kg K) blood sp heat
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perfwrbcbdx condkm/dx condsfksf/dx meta
qmddx perfwrbcbdx condkm/dx condsfksf/
dx metaqmddx for i111 for j111
A(i,j)0 A(i,i)2condperf end end
A(10,10)condcondsfperf/2 A(11,11)condsfh A(
11,10)-condsf for i210 A(i-1,i)-cond end A
(10,11)-condsf for i210 A(i,i-1)-cond end
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for i19 B(i)metaperfTa end B(1)B(1)condTc
B(10)0.5(metaperfTa) B(11)hTf
Tssinv(A)B' for i111 t(i)Tss(i)-273.
L(i)i0.003 end
t' plot (L,t) xlabel('length, m') ylabel ('temp,
C') heat transfer A1.8 m2 R1Lsf/(ksfA) R21
/(hA) q1(t(11)-Tf)/R2 q2(t(10)-Tf)/(R1R2)
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Effect of Convective Boundary (h - coefficient)
On the Temperature Distribution
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Effect of perfusion rate on skin temperature for
dry air and water environments
Tinf 297 C
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-1
Energy (W) vs. Perfusion Rate (s
)
2
at T
for h 200 (W/m
K) and T
297 (K)
sf
inf
700
650
qm 700 W/m3
600
550
qm 5,600 W/m3
500
(W)
450
400
350
300
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.0010
-1
Perfusion Rate (s
)
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Temperature (C) vs. Tissue Depth (mm)
-1
2
3)
for w0.0005 (s
), h200 (W/m
K), q
700 (W/m
m
40
35
30
25
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Temperature (C)
15
10
5
0
9
6
3
0
33
30
27
24
21
18
15
12
Tissue Depth (mm)
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-1
Energy q (W) vs. Perfusion Rate (s
)
for q
m
2000
1500
Tinf 297 K
(W)
1000
q
500
0
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.0010
-1
Perfusion Rate (s
)
-1
Energy q (W) vs. Perfusion Rate (s
)
W/m2 K
3
for q
5600 (W/m
) and h 200 (W/m2 K)
m
1750
(W)
1250
q
750
250
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0.0010
-1
Perfusion Rate (s
)
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.
.
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Arm cross-section model
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Z Corporation 3D Printer Spectrum Z510 (Rapid
Prototyping Technology)

• A premium 3D Printer with
• the capability of printing
• in full-color
• Use parts directly or infiltrate them to serve a
  wide range of modeling needs
• Accepts solid models in STL, PLY, VRML (WRL) and
  SFX file formats as input

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Conclusion

• Have a working heat flow simulation
• The results generated can be used to teach heat
  transfer principles
• The results are meaningful to students daily
  lives, which will increase their interest and
  learning success.
• Have made connections between biology,
  engineering, and math

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Acknowledgments

• Advisor - Dr. Subha Kumpaty
• Ann Bloor, Maria Soto, other RET participants
• National Science Foundation
• My family

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Modeling and Simulation of Bioheat Transfer
For More InformationContact Me
Athutsal_at_elkhorn.k12.wi.us