materials and methods

Huang-Wen Huang1*, Tzu-Ching Shih2, Chihng-Tsung Liauh3, Tzyy-Leng Horng4 1 Department of Software Engineering, Tamkang University, I-lan County, Taiwan

2 Department of Medical Radiology Technology, China Medical University, Taichung, Taiwan

3 Department of Mechanical Engineering, Kun-shan University of Science and Technology, Tainan, Taiwan

4 Department of Applied Mathematics, Feng Chia University, Taichung ,Taiwan

The objective of this paper is to investigate the optimization of applied thermal power in a

tumorous region which consists of thermally significant blood vessel(s) during hyperthermia.

Pennes’ bio-heat transfer equation (BHTE) was developed to model temperatures in the

living tissues, and other developed alternative equations having the same goal with

attempting to formulate a single, general field equation that could predict the overall

characteristics of the temperature distribution in tissues.

The present paper used a tissue heat transfer model which was not a general field

equation approximation, but which instead retained both the presence of the blood vessels

and the major, basic physics of the blood vessel/tissue heat transfer processes. It was called

a fully conjugated blood vessel network model (FCBVNM) or countercurrent blood vessel

network (CBVN) model which was published in 1996. Therefore, a tumor region situated in

cases of many thermally significant blood vessels nearby (or embedded) with attempts to

find therapeutic heating temperatures in tumor would be discussed. Optimization scheme of

applied thermal power on tissue and tumor regions in order to reach therapeutic tissue

temperatures was also studied and presented.

Figure 1(a) is a transparent view of parallelepiped showing internal heated tumor region

with 20 x 20 x 20 mm3. The level 1 largest blood vessel is running through the volume’s

edge from (42, 40, 40) mm to (62, 40, 40) mm. Figure 1(b) shows the location of the cubic

volume in a parallelepiped by indicating its 8 corners’ coordinates, and Figure 1(c) is a

dissecting transparent view of all associated arterial blood vessel paths in the cubic volume.

Veinous vessels do not appear in the figure, and within the volume, there are 2 branches of

level 5-6-7 blood vessels as expanded dissecting view indicates.

Figure 2 shows the flow chart of optimization scheme. The optimized thermal power

distribution in the treated cubic volume is computed in order to reach ideal therapeutic

tissue temperature distribution.

Figures 3(a-e) (top row from left to right) are temperature distributions at x = 38 mm (4 mm

away from the front boundary), x = 42 mm (the front boundary), x = 52 mm (middle of the

treated region), x = 62 mm (the back boundary) and x = 66 mm (4 mm away from the back

boundary) planes respectively with a perfusion rate of 0.5 kg·m-3s-1 after power optimization

scheme. The blood flow rate is about 320 mm/sec in level 1 branch vessel. Figures 3(a‘-e‘)

(bottom row from left to right) are thermal absorbed power distributions at the corresponding

planes respectively. No power presents on the planes at x=38 mm and 66 mm.

Optimization of Applied Thermal Power on Tumor Regions with Thermally Optimization of Applied Thermal Power on Tumor Regions with Thermally Significant Blood Vessels to Reach Therapeutic Tissue TemperaturesSignificant Blood Vessels to Reach Therapeutic Tissue Temperatures

At present results, cold spots and significant cooling effects of blood flow rate by vessels in

the treated region present vital characteristics in the CBVN model. These phenomena reveal

same critical situations during treatments. Unsuccessful hyperthermia treatments lead to

survival of cancerous tissues. Thus, insufficient net absorbed thermal energy in local tissue

region is one of the major problems.

Materials and Methods

(x, y, z)= (0, 40, 40)mm

(42,40,40)

(62,40,40)

(62,40,60)(62,60,60)

(62,20,40)

(42,60,40)

(42,40,60)

X=62 plane

X=0 plane

X=42 plane

(0, 0, 0)

(42,60,60)

(a)

(62,60,60)

(42, 60, 60)

(52, 60, 60)

(62,60,60)

(52,60,60)

(b)

1

1

1

3

2

4

56

7

4

56

7

4

56

7(c)

FIG. 1

Methods and Materials

P (x,y,z) =P(x,y,z) +Δ p(x,y,z)

Where Δ p=c*Δ T

Initial Condition: uniform power

Governing equation (FCBVNM) to estimate

the temperature

Temperature distribution

Comparison between estimated and ideal temperature.

Criteria <=10%

Typical initial and boundary conditions

applied

Ideal temperature distribution

Optimal power and temperature distributions

Adjust power distribution in tumor region

No

Yes

FIG. 2

FIG. 3

Power Absorption in Treated Tumor Region after Optimization

0

0.5

1

1.5

2

2.5

BHTE+w=0.5 BHTE+CBVN+W=0.123 BHTE+CBVN+W=0.5cases

Th

erm

al P

ower

Ab

sorb

ed (

Wat

t)

FIG. 4


Abstract


Results

Figures 4 shows comparison of power absorption in treated tumor region for different

thermal models after optimization. BHTE is the case when no blood vessel presents.

BHTE+CBVN+W=0.123 means that BHTE is having a countercurrent blood vessel network

present with blood flow rate at main artery (level 1 vessel) about 80 mm/sec and perfusion in

the tissue is 0.123 kg/(m3s). And BHTE+CBVN+W=0.5 is the same as previous case but with

blood flow rate about 320 mm/sec and the perfusion is 0.5 kg/(m3s) in tissues.


Conclusion