# br m br m br u br u br m

m

m

u

u

m

u

u

u

u

u

d

For Stage II,

r

Ste
2
dFo2
h2

r
r

Boundary condition Temozolomide II kind:

dFo2

u

dFo1

Ki
d2

are given as follows:

h
h
k
k

where

are given by:

m

u

m

m

u

u

N

m

u

N

N

N

For Stage II,

u

u

m

d
m

Ki

Ki

N

k

k

u

N

N

dFo2

m

m

m

m

u

N

u

u

N

u

N

are given as follows:

N

f

f

f

f

m

m

m

m

u

u

u

For Stage III,

dFo3

h

h
k

k

u

u

(74) Boundary condition of III kind: For Stage I,

Ste3

dFo3

dFo3

h

h

k

k

u

u

u

u

Table 1

Thermal-physical properties of tissues(Bischof et al.).

Parameter
unit of measurement
value

Density of unfrozen lung tissue
kg /m3
161
Density of frozen lung tissue
kg /m3
149
Density of unfrozen tumor tissue
kg /m3
998
Density of frozen tumor tissue
kg /m3
921
Density of blood
kg /m3
1005
Thermal conductivity of unfrozen lung tissue
W /m0C
0.11
Thermal conductivity of frozen lung tissue
W /m0C
0.38
Thermal conductivity of unfrozen tumor tissue
W /m0C
0.552
Thermal conductivity of frozen tumor tissue
W /m0C
2.25
Specific heat of unfrozen lung tissue
J /kg 0C
4174
Specific heat of frozen lung tissue
J /kg 0C
1221
Specific heat of unfrozen tumor tissue
J /kg 0C
4200
Specific heat of frozen tumor tissue
J /kg 0C
1230
Blood perfusion in lung tissue
ml /sl
0.0005
Blood perfusion in tumor tissue
ml /sl
0.002
Metabolic heat generation in lung
W /m3
42,000
Metabolic heat generation in tumor
W /m3
672
Latent heat
kJ /kg
333
Arterial blood temperature
°C
37

m

m

m

u

u

u

N

u

N

N

For Stage III,

dFo3

h

h

k

k

For Stage II,

Ste
3
dFo3

Ste2
dFo2

h

h

u

k

k

u

dFo3

dFo2

f

O

f

L

O

O

P

O

k

O

f

m

where

O

and

L

are
M M matrices
given
by
O

m

m

m

u

u

u

u

respectively. Integrating (85) over 0 to Fo1, we obtained

4. Modified Legendre wavelet Galerkin Method

dFo1

dFo1

We are using Legendre wavelet Galerkin method to solve our pro-

dFo1

where P is defined as

blem in all the stages with generalized boundary condition are as fol-

P

lows:

P

Boundary condition of I kind
P =

P

also

Let us assume that the unknown function
d2 u
is approximated by

Fo

C

where C is
unknown matrix of order N

matrix of order
defined by
CP¯
2

w
r
r

where d
=

and the elements of
( Fo) is defined by

m

k

k

1
and m is the order of

k

ˆ

m

Pm

where P if is the operational matrix of integration of order 2k 1M × 1,

Let us assume that the unknown functions dm and du are ap-

dFo2 dFo2
proximated by

dFo2

dFo2

m

u

Let us assume that the unknown functions
d f
,
d m
and
d u
are

approximated by

dFo3
dFo3

dFo3

dFo3

d
m

dFo3

d
u

dFo3

f

m

u

s

w

w

Ste3

w

Boundary condition of II kind

Stage 1