Add a Thermal Damage subnode under the
Biological Tissue node to calculate tissue damage.
is the ratio of the period of time when T > Td, h to the time limit
td, h, or the ratio of the period of time when
T < Td, c to the time limit
td, c. It gives an indication of damage state of the tissue. When it reaches 1, the tissue is necrotic. The fraction of necrotic tissue corresponds to the quantity
min(α, 1).
evaluates the period of time when T > Tn, h or the period of time when
T < Tn, c. If
αnecr > 0, the tissue is necrotic because it already reached the necrosis temperatures
Tn, h or
Tn, c at some time step of the simulation. Hence, the fraction of necrotic tissue due to immediate necrosis is equal to 1 if
αnecr > 0 and 0 otherwise.
Here, A is the frequency factor (SI unit: 1/s), and
ΔE is the activation energy for the irreversible damage reaction (SI unit: J/mol). The parameters
A and
ΔE are dependent on the type of tissue and have been characterized for liver tissues by Jacques et others (
Ref. 7) to be
A = 7.39 ⋅ 1039 s
–1 and
ΔE = 2.577 ⋅ 105 J/mol. See
Ref. 8,
Ref. 9, and
Ref. 10 for the characterization of these parameters for prostate, skin, and fat. See also
Ref. 11 and
Ref. 12 for more references on biological tissues material properties.
The material properties of the damaged tissue are redefined to take into account the influence of tissue injury. If ρd,
Cp, d,
and
kd denote the density, heat capacity at constant pressure, and thermal conductivity of the necrotic tissue, respectively, then two effective quantities are defined:
In these equalities, θd takes one of the two definitions given above in
Equation 4-38 or
Equation 4-39 according to the integral form chosen.