Comparison between single- and dual-porosity models for fluid transport in predicting lesion volume following saline-infused radiofrequency ablation

Figures & data

Figure 1. (a) Geometry and dimensions of the liver model used in this study (the dimensions in brackets are in mm) and (b) the boundary conditions implemented. The red point in (b) indicates the point where the temperature is probed for the implementation of the PID controller.

Table 1. Hydraulic and transport parameters used in the present study.

Parameter	Value	Source
Interstitial space permeability, κi (m^2)	3.12 × 10^–17	[15]
Vascular space permeability, ${\kappa }_v$ (m^2)	1.56 × 10^–14	[35]
Dynamic viscosity of saline, μ (Pa⋅s)	0.0007	[36]
Vasculature hydraulic conductivity, $L_{p,v}$ (m/(Pa⋅s))	5.68 × 10^–11	[15]
Vascular surface area to volume ratio, $S_v/V$ (1/m)	7000	[9]
Lymphatics transfer coefficient, Lp,LSL/V (Pa⋅s)^– 1	4.43 × 10^–9	[15]
Vascular pressure, $p_v$ (Pa)${}^{\text{a}}$	2080	[9]
Lymphatics pressure, $p_L$ (Pa)	133.3	[9]
Vascular osmotic pressure, πv (Pa)	2666.67	[9]
Interstitial fluid osmotic pressure, πi (Pa)	1333.33	[9]
Osmotic reflection coefficient, σT	0.91	[9]
Vascular permeability coefficient, $P_v$ (m/s)	7.3 × 10^–12	[9]
Vascular space diffusion coefficient, $D_v$ (m^2/s)	4.2 × 10^–10	[37]
Interstitial space diffusion coefficient, $D_i$ (m^2/s)	1 × 10^–9	[38]
Solute retardation coefficient, σsol	0.90	[9]
Volume fraction of vascular space, $w_v$	0.143	[35]
Volume fraction of interstitial space, $w_i$	0.857	1-$w_v$
Tissue porosity, ${\varphi }_i$	0.6	[39]
Vasculature porosity, ${\varphi }_v$	1	[25]
Saline concentration in plasma, $c_{pl}$ (mol/m^3)	134
Saline concentration, $c_s$ (mol/m^3)	154

^a Value is used only for the SP model.

Table 2. Thermal, electrical and cell death parameters used in the present study.

Parameter	Value	References
Electrical model
Baseline liver electrical conductivity, σ0 (S/m)	0.33	[40]
Vapour electrical conductivity, σvap (S/m)	0.001σ0
Probe electrical conductivity, σprobe (S/m)	10^8
Shaft electrical conductivity, σshaft (S/m)	4 × 10^6
Thermal model
Liver thermal conductivity, κ (W/m⋅K)	0.512	[40]
Liver density, ρ (kg/m^3)	1060
Liver heat capacity, C (J/kg⋅K)	3600
Probe thermal conductivity, κprobe (W/m⋅K)	18
Probe density, ρprobe (kg/m^3)	6450
Probe heat capacity, $C_{probe}$ (J/kg⋅K)	840
Shaft thermal conductivity, κshaft (W/m⋅K)	71
Shaft density, ρshaft (kg/m^3)	21 500
Shaft heat capacity, $C_{shaft}$ (J/kg⋅K)	132
Blood density, ρb (kg/m^3)	1000
Blood heat capacity, $C_b$ (J/kg⋅K)	4180
Baseline blood perfusion rate, ωb (1/s)	0.0064
Latent heat of vapourisation, $h_{fg}$ (J/kg)	2.26 × 10^6	Assumed as water
Tissue water content, β	0.71	[32]
Heat capacity of water vapour,  ${\left(\rho c\right)}_{vap}$ (J/m^3· K)	6 × 10^5
Cell death model
Frequency factor, A (1/s)	7.395 × 10^39	[41]
Activation energy, $\Delta E$ (J/mol)	2.5775 × 10^5
Universal gas constant, R (J/mol⋅K)	8.314

Figure 2. Penetration depth of saline after 10 min of infusion in the SP and DP (interstitium and vasculature) models obtained for the pre-infusion mode.

Figure 3. Contours of the temperature distribution 10 min after pre-infused RFA of the (a) SP and (b) DP models. Regions within the white lines represent zones where tissue vapourisation occurs.

Figure 4. Coagulation zone formation following saline infused RFA with pre-infusion of saline obtained using the (a) SP and (b) DP models.

Table 3. Comparisons of the coagluation volumes (cm³) obtained using the SP, DP and SP (with vascular permeability) models.

	Pre-infusion			Simultaneous-infusion
Saline volume (ml)	SP	DP	SP (with κv)	SP	DP	SP (with κv)
2.5	26.01	35.74	27.78	25.48	29.05	28.86
5	26.64	41.03	28.62	25.75	32.97	31.91
10	27.16	48.79	29.53	26.11	38.81	32.65
15	27.45	53.20	30.85	26.39	44.56	34.14
20	28.09	56.29	31.37	26.66	48.26	36.87

Figure 5. Penetration depth of saline after 10 min of infusion in the SP and DP (interstitium and vasculature) models obtained for the simultaneous infusion mode. Color legend is similar to that in Figure 2.

Figure 6. Contours of the temperature distribution 10 min after simultaneous-infused RFA of the SP and DP models. Regions within the white lines represent zones where tissue vapourisation occurs.

Figure 7. Coagulation zone formation following saline infused RFA with simultaneous-infusion of saline obtained using the SP and DP models.

Figure 8. Comparison between the saline penetration depth obtained using the new SP model and the DP model (vasculature only) for (a) pre-infusion and (b) simultaneous-infusion protocols. Colour legend is similar to that in Figure 2.

Table 4. Comparison of the coagulation zone radius of the SP and DP model against experimental studies of Cha et al. [23].

	Coagulation zone			Mean percentage
	diameter (cm)			difference (%)
	SP model	DP model	^*Experiment	SP model	DP model
2 cm probe (Cha et al. [23])
Longitudinal diameter	3.00	4.00	5.07 (4.2–6.6)	40.8	21.1
Axial diameter	3.70	4.40	5.28 (4.3–7.0)	29.9	16.7
3 cm probe (Cha et al. [23])
Longitudinal diameter	3.20	4.20	5.66 (4.8–7.3)	43.5	25.8
Axial diameter	4.80	5.20	5.71 (4.8–7.0)	15.9	8.9

* Number in bracket represents the range of values obtained from experimental data.

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