Considerations for theoretical modelling of thermal ablation with catheter-based ultrasonic sources: implications for treatment planning, monitoring and control

Abstract

Purpose: To determine the impact of including dynamic changes in tissue physical properties during heating on feedback controlled thermal ablation with catheter-based ultrasound. Additionally, we compared the impact of several indicators of thermal damage on predicted extents of ablation zones for planning and monitoring ablations with this modality.

Methods: A 3D model of ultrasound ablation with interstitial and transurethral applicators incorporating temperature-based feedback control was used to simulate thermal ablations in prostate and liver tissue. We investigated five coupled models of heat dependent changes in tissue acoustic attenuation/absorption and blood perfusion of varying degrees of complexity. Dimensions of the ablation zone were computed using temperature, thermal dose, and Arrhenius thermal damage indicators of coagulative necrosis. A comparison of the predictions by each of these models was illustrated on a patient-specific anatomy in the treatment planning setting.

Results: Models including dynamic changes in blood perfusion and acoustic attenuation as a function of thermal dose/damage predicted near-identical ablation zone volumes (maximum variation < 2.5%). Accounting for dynamic acoustic attenuation appeared to play a critical role in estimating ablation zone size, as models using constant values for acoustic attenuation predicted ablation zone volumes up to 50% larger or 47% smaller in liver and prostate tissue, respectively. Thermal dose (t(43) ≥ 240 min) and thermal damage (Ω ≥ 4.6) thresholds for coagulative necrosis are in good agreement for all heating durations, temperature thresholds in the range of 54°C for short (<5 min) duration ablations and 50°C for long (15 min) ablations may serve as surrogates for determination of the outer treatment boundary.

Conclusions: Accounting for dynamic changes in acoustic attenuation/absorption appeared to play a critical role in predicted extents of ablation zones. For typical 5-15 min ablations with this modality, thermal dose and Arrhenius damage measures of ablation zone dimensions are in good agreement, while appropriately selected temperature thresholds provide a computationally cheaper surrogate.

Figure 1

Catheter-based ultrasound applicators with tubular transducer segments for thermal ablation: (top) 2.4 mm OD applicator suitable for interstitial or percutaneous ablation of prostate and liver targets, (bottom) 10 mm OD transurethral applicator for ablation of prostate targets. Transducers may be modified to sonicate in 90°, 180°, or 270° sectors of the angular expanse, or left unmodified for 360° sonication. (Not to scale).

Figure 2

(a) Acoustic attenuation coefficient, α = k_α α₀, increases linearly with the logarithm of thermal dose, t₄₃, as described in [31] and employed in models 1—3 (b) Blood mass perfusion rate ṁ_bl = ṁ_0,blṁ_rel, varies as a function of degree of vascular stasis, computed using an Arrhenius model, as described in [29] and [37] and employed in model 1.

Figure 3

Radial depth of ablation zone after 15 min ablations in prostate and liver targets using interstitial applicators as predicted by thermal dose (t₄₃) and thermal damage (Ω₁ uses Arrhenius parameters reported in [66] and Ω₂ uses parameters reported in [70]) indicators. Error bars indicate ranges computed using higher (5 kg m⁻³ s⁻¹ in prostate, 20 kg m⁻³ s⁻¹ in liver) and lower (1 kg m−3 s−1 and 10 kg m⁻³ s⁻¹) values for the nominal (2.5 kg m⁻³ s⁻¹ in prostate, 15 kg m⁻³ s⁻¹ in liver) blood perfusion rate. (a) 360° applicator in prostate (b) 180° applicator in prostate (c) 90° applicator in prostate and (d) 360° applicator in liver.

Figure 4

(a) Radial depth of ablation zone after 15 min prostate ablations with a 90° transurethral applicator, as predicted by thermal dose (t₄₃) and thermal damage (Ω₁ uses Arrhenius parameters reported in [66] and Ω₂ uses parameters reported in [70]) indicators (b) Radial depth of the ablation zone as indicated by temperature, thermal dose (t₄₃) and thermal damage (Ω₁ and Ω₂) thresholds, over the course of a 15 min ablation with a 90° transurethral applicator in prostate and liver tissue.

Figure 5

Radial depth of the extents of thermal toxicity, as indicated by T = 43 °C isotherm, after 5—15 min thermal ablations with a 180° interstitial applicator in prostate target, simulated using tissue models 1—5.

Figure 6

(a) Transient evolution of maximum tissue temperature during 15 min ablations (with and without feedback control) using a 180° interstitial applicator in a prostate target. (b) Transient evolution of power applied to a 180° ultrasound sector as determined by the control algorithm simulated using tissue models 1—5.

Figure 7

Radial depth of the ablation zone as indicated by temperature, thermal dose (t₄₃) and thermal damage (Ω₁ and Ω₂) thresholds, over the course of a 15 min ablation with interstitial applicators in prostate and liver tissue. (a) 360° applicator in prostate (b) 180° applicator in prostate (c) 90° applicator prostate and (d) 360° applicator in liver.

Figure 8

Patient-specific treatment simulation and plan for targeting prostate cancer in the posterior gland using a directional (90°) interstitial ultrasound applicator, implanted in the peripheral gland and directed toward the urethra; (a) thermal damage (Ω ≥ 4.6) and temperature (T ≥ 52 °C) isosurfaces indicating coagulative necrosis, (b) thermal dose (t₄₃ ≥ 240 min) and temperature (T ≥ 52 °C) isosurfaces indicating coagulative necrosis, (c) temperature map in axial slice through the center of the applicator with critical temperature, thermal dose and thermal damage contours overlaid.

Figure 9

Patient-specific treatment simulation and plan for targeting focal prostate cancer in the posterior gland using a directional (90°) transurethral ultrasound applicator directing energy toward the periphery; (a) thermal damage (Ω ≥ 4.6) and temperature (T ≥ 52 °C) isosurfaces indicating coagulative necrosis, (b) thermal dose (t₄₃ ≥ 240 min) and temperature (T ≥ 52 °C) isosurfaces indicating coagulative necrosis, (c) temperature map in axial slice through the center of the applicator with critical temperature, thermal dose, and thermal damage contours overlaid.

Figure 10

Simulated temperature, thermal dose (t₄₃), and thermal damage (Ω) profiles after 15 min ablation with a 180° interstitial applicator in prostate tissue, showing sharp fall off of thermal dose and thermal damage profiles in regions close the boundary of the ablation zone.