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  • br m br m br u br u br m

    2020-03-17


    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