A thermoelastic deformation model of tissue contraction during thermal ablation

Figures & data

Figure 1. Temperature distribution for a typical thermal ablation therapy.

Table 1. List of the tissue thermomechanical parameters and applicator temperature.

Parameter	Value	Unit	Range	Reference
ρ	1050	Kg m^−3		[32]
ν	0.45		0.25–0.45	[24]
E	1	MPa	O (10^–6) – O (1)	[23]
α	3 × 10^−4	K^−1		[17]
β	3
Tb	310
T0	363		313–368

ρ is the density, ν is Poisson's ratio, E is Young's modulus, α is the coefficient of the volumetric thermal expansion, β is the coefficient of the volumetric thermal denaturation, T_b is the baseline temperature and T₀ is the applicator temperature.

Table 2. List of simulation parameters.

Parameter	Value	Unit
ω	0.01	m
U	0.01	m
a	10
Δr	0.05
τ	1	s
tc	60
tm	600
tmax	2000
Δt	O (10^−3) – O (10^−5)
θ	1	K

ω, τ, U and θ are the characteristic values for the length, time, displacement and temperature, respectively, a is the non-dimensional radius of the sphere in the spatial domain, Δr and Δt are the grid spacing and time step in the discretisation, respectively, t_c and t_m  are non-dimensional time constants that determine the temperature profile and t_max is the maximum time in the temporal domain.

Figure 2. Tissue displacement during a typical thermal ablation temperature distribution ignoring protein denaturation effects.

Figure 3. Plot of protein proportion in its (A) native and (B) unfolded state during a typical thermal ablation temperature distribution.

Figure 4. Tissue displacement during a typical thermal ablation temperature distribution.

Figure 5. Tissue displacement at various time points during a typical thermal ablation temperature distribution.

Figure 6. Tissue displacement during a typical thermal ablation temperature distribution with a Poisson's ratio of (A) 0.35 and (B) 0.25.

Figure 7. Tissue displacement during a typical thermal ablation temperature distribution with an applicator temperatures of (A) 80 °C and (B) 70 °C.

Figure 8. Maximum tissue contraction for varying applicator temperature during a typical thermal ablation temperature distribution.

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