Microwave ablation of lung tumors: A probabilistic approach for simulation-based treatment planning

Abstract

Purpose:

Microwave ablation (MWA) is a clinically established modality for treatment of lung tumors. A challenge with existing application of MWA, however, is local tumor progression, potentially due to failure to establish an adequate treatment margin. This study presents a robust simulation-based treatment planning methodology to assist operators in comparatively assessing thermal profiles and likelihood of achieving a specified minimum margin as a function of candidate applied energy parameters.

Methods:

We employed a biophysical simulation-based probabilistic treatment planning methodology to evaluate the likelihood of achieving a specified minimum margin for candidate treatment parameters (i.e., applied power and ablation duration for a given applicator position within a tumor). A set of simulations with varying tissue properties was evaluated for each considered combination of power and ablation duration, and for four different scenarios of contrast in tissue biophysical properties between tumor and normal lung. A treatment planning graph was then assembled, where distributions of achieved minimum ablation zone margins and collateral damage volumes can be assessed for candidate applied power and treatment duration combinations. For each chosen power and time combination, the operator can also visualize the histogram of ablation zone boundaries overlaid on the tumor and target volumes. We assembled treatment planning graphs for generic 1, 2, and 2.5 cm diameter spherically shaped tumors and also illustrated the impact of tissue heterogeneity on delivered treatment plans and resulting ablation histograms. Finally, we illustrated the treatment planning methodology on two example patient-specific cases of tumors with irregular shapes.

Results:

The assembled treatment planning graphs indicate that 30 W, 6 min ablations achieve a 5-mm minimum margin across all simulated cases for 1-cm diameter spherical tumors, and 70 W, 10 min ablations achieve a 3-mm minimum margin across 90% of simulations for a 2.5-cm diameter spherical tumor. Different scenarios of tissue heterogeneity between tumor and lung tissue revealed 2 min overall difference in ablation duration, in order to reliably achieve a 4-mm minimum margin or larger each time for 2-cm diameter spherical tumor.

Conclusions:

An approach for simulation-based treatment planning for microwave ablation of lung tumors is illustrated to account for the impact of specific geometry of the treatment site, tissue property uncertainty, and heterogeneity between the tumor and normal lung.

1. INTRODUCTION

Microwave ablation (MWA) is a minimally invasive modality employing non-ionizing radiation for thermal treatment of malignant nodules in lungs. Thermal ablation of lung tumors via a percutaneous approach has an established role in the clinical setting. Technologies employing a variety of ablative energy modalities have been developed and are in clinical use.^1–3 The most common serious complication associated^4,5 with transthoracic insertion of thermal ablation applicators is pneumothorax. Systems enabling delivery of flexible MWA applicators to lung tumor targets via a bronchoscopic approach are under development,^6–8 and offer the potential for reduced risk of pneumothorax.

The clinical goal of MWA is to heat the volume of tumor and a surrounding margin of normal tissue to cytotoxic temperatures (~55–60 °C), while maximally sparing nontargeted tissue outside of this zone.^2,9 It is believed that the higher rates of tumor recurrence are associated with inadequate delivery of thermal dose to tumors, resulting in smaller achieved margins.¹⁰ Inaccurate positioning of the MWA applicator with respect to the tumor may also lead to the failure to achieve an adequate treatment margin.¹¹ Robust treatment planning tools^12–14 that provide physicians with guidance on the relationship between applied energy delivery parameters, applicator position relative to the tumor and surrounding tissues, and anticipated treatment outcome have the potential to increase the likelihood of achieving a successful treatment with adequate treatment margins.¹⁵

Currently available tools for planning and guiding thermal ablation procedures provide an estimate of the extent of the ablation zone based on a candidate set of energy delivery parameters (applied power and ablation duration). These data are provided by MWA device manufacturers and are based on a priori heating experiments in ex vivo and in vivo tissues of various types.¹⁶ While early MWA systems relied on operators to use data provided in a look-up table in user documentation, some contemporary MWA systems enable the operator to visualize the ablation zone extents overlaid on the target tumor as viewed on imaging.¹⁷ The operator may then consider this information when selecting treatment parameters — applied power, treatment duration, and applicator position – that are likely to yield an ablation zone that encompasses the tumor and margin, and to limit thermal damage to surrounding tissue.

However, such treatment planning approaches do not consider the patient-specific anatomy of the patient, such as irregular shape of the tumor and proximity to surrounding structures (e.g., blood vessels and airways), and the impact they may have on thermal profiles. These approaches also do not account for the impact of the variability in tissue biophysical properties (dielectric, thermal, and perfusion), which may vary both between patients, as well as within patients (i.e., variations in biophysical properties between normal tissue and tumor¹⁸). Furthermore, tissue biophysical properties may spatially vary within a tumor as a function of disease pathology.¹⁹ These factors might result in ablation outcomes which can differ substantially from the data provided by MWA equipment manufacturers, which are typically derived from experiments in relatively homogeneous ex vivo or in vivo normal tissue. Consequently, the disconnect between anticipated and achieved ablation zones may lead to incomplete ablation of the tumor and/or failure to achieve an adequate treatment margin, as well as extraneous thermal damage to surrounding healthy tissue.

Several studies have proposed the use of computational modeling of bioheat transfer for patient-specific planning of thermal ablation procedures.^18,20–27 In a prior study,²⁸ we presented a method of accounting for tissue variability when predicting the extent of ablation in homogeneous liver tissue by running multiple simulations with a range of tissue properties and presenting ablation outcomes as a nonparametric distribution of potential outcomes rather than a deterministic result. This prior work was restricted to a single ablation power and duration, and did not consider any heterogeneity between normal and tumor tissue. Furthermore, while previous studies have investigated the impact of contrast in physical properties between parenchyma and normal tissue on ablation outcome for liver ablation,¹⁸ there are few studies reporting on dielectric and thermal properties of lung tumors. Joines et al presented dielectric properties of normal and lung tumors at frequencies up to 900 MHz.²⁹ Recently, Yu et al reported on the dielectric properties of lymph nodes resected during lung cancer surgeries.³⁰ The manner in which dielectric and thermal properties of lung tumors vary as a function of temperature has not been reported in the literature, thus presenting a considerable source of uncertainty in model predictions of lung ablation outcome.

Here, we present a framework for simulation-based planning of lung microwave ablation procedures for guiding the selection of treatment delivery parameters while considering the likelihood of achieving an adequate treatment margin, including methods for accounting for variability in tissue properties. For a specified MWA applicator position within a tumor and applied power level and ablation duration, a set of models is evaluated with varying tissue properties. Such an approach allows us to provide the operator with recommendations for energy delivery parameters considering patientspecific anatomy, including varying levels of heterogeneity in tissue physical properties between normal and tumor tissue. Moreover, instead of providing deterministic predictions of ablation size and shape, our approach provides the operator with a range of possible outcomes across patients and disease state. We further applied this method to investigate the range of lung tumors of various sizes that could be ablated with an adequate treatment margin using a flexible microwave lung ablation catheter under development for bronchoscopic ablation of lung tumors.⁷

2. MATERIALS AND METHODS

The objective of the ablation treatment planning method presented herein is to provide ablation operators with guidance on selecting the applied microwave power and ablation duration for a given procedure, based on the likelihood of successful coverage of the target area and extent of ablation in non-target tissue, termed as collateral damage. The target is defined as the volume of tumor plus a surrounding circumferential margin of normal tissue. The contrast between tissue properties — dielectric, thermal, and perfusion — of normal and malignant lung tissue is incompletely understood. Furthermore, lung tumor properties are likely dependent on tumor type and stage. Here, we further expand the probabilistic treatment planning approach initially proposed in Ref. [28] by investigating multiple scenarios of tissue heterogeneity between lung and tumor and apply this framework to illustrate the impact of applied power and time on the likelihood of achieving the desired margin.

2.A. Treatment planning methodology

For a candidate applied power and ablation duration, we performed a total of N simulations, with each simulation considering a set of tissue biophysical properties sampled from the distribution of anticipated values for that property. Let us denote the spatial temperature profile at the end of the i-th ablation simulation as T_P,t,i(x,y,z), where P is applied power at the tip of the ablation catheter [W] (i.e., after accounting for losses in the applicator), t is ablation duration [min], i =1, …, N is the index of simulation, N is the number of simulations, and x, y, and z are spatial coordinates. From each temperature map, we can estimate the extent of the ablation zone by either finding coordinates where the Arrhenius thermal damage integral exceeds the ablative threshold:

$$D_{P,t,i}(x,y,z)=\left\{\left[{\int }_{\tau =0}^{t}A\cdot \exp \left(\frac{-E_a}{R\cdot T_{P,\tau ,i}(x,y,z)}\right)d\tau \right]\ge 1\right\},$$ (1)

where D_P,t,i(x,y,z) is a binary map with unit values denoting thermal damage above the ablative threshold and a value of zero denoting sub-ablative thermal damage, A is frequency factor (1.61×10⁴⁵[s⁻¹]), E_a is an energy barrier (3.06×10⁵[J mol⁻¹]), R is the gas constant (8.3143 [J mol⁻¹ K⁻¹]), and τ is the time for which the thermal damage was accumulated in the tissue. Values of A and E_a parameters were chosen to represent the thermal damage process of collagen shrinkage during ablation.³¹ A value of 1 for the Arrhenius integral in (1), corresponding to ~63% completion of thermal damage process, was chosen as a threshold for estimating the extent of the ablation zone.

From the terms D_P,t,i(x,y,z) evaluated for each i-th simulation, an ablation histogram can be assembled for specific power P and duration t according to the following equation:

$$C_{P,t}(x,y,z)=\frac{1}{N}\sum _{i=1}^N{D}_{P,t,i}(x,y,z).$$ (2)

For each voxel x,y,z in the simulation space, the ablation histogram yields values in the range 0–1, representing the fraction of N simulations where that voxel accrued thermal damage exceeding the ablative threshold. For example, contours which encompass areas with ablation histogram C_P,t(x,y,z) ≥ 0.1, ≥ 0.5, and ≥ 1 represent a 10%, 50%, and 100% chance, respectively, of tissue regions within them being ablated.

Based on (2), we can further compute two treatment metrics, namely minimum margin and collateral damage, to quantitatively assess the simulated ablation outcome for a candidate set of applied power and ablation durations, considering a specified applicator position within the tumors, as earlier defined by Kaye et al.³² These metrics are illustrated in Fig. 1.

FIG. 1.

Illustration of metrics for characterizing simulated ablation zones relative to the tumor geometry. Minimum margin represents the minimum distance between the estimated ablation zone extent and the tumor boundary along the entire tumor boundary. Collateral damage represents the volume of ablated tissue outside of the target area (i.e. tissue ablated beyond the tumor and surrounding margin).

To define the minimum margin and collateral damage metrics, we first denote the tumor mask and margin mask as S_tumor(x, y, z), where

$$S_{tumor}(x,y,z)=\{\begin{array}{ll}0,\hfill & \text{if}[x,y,z]\text{is}\text{inside}\text{tumor,}\hfill \\ 1,\hfill & \text{if}[x,y,z]\text{is}\text{outside}\text{tumor,}\hfill \end{array}$$ (3)

and S_margin,m(x,y,z), where

$$S_{margin,m}(x,y,z)=\{\begin{array}{ll}0,\hfill & \text{if}[x,y,z]\text{is}\text{inside}\text{margin,}\hfill \\ 1,\hfill & \text{if}[x,y,z]\text{is}\text{outside}\text{margin,}\hfill \end{array}$$ (4)

where m is the desired margin in mm specified by the operator (e.g., 5 mm). A margin m = 0 implies that S_margin,0(x,y,z) = S_tumor(x,y,z). With the defined tumor and margin masks from (3) and (4), we can define the minimum margin M_P,t,i [mm] as the smallest margin m, for which Eq. (5), that is, ablation fully covers margin, holds.

$$\frac{{\sum }_{x,y,z}{D}_{P,t,i}(x,y,z)\cdot S_{margin,m}(x,y,z)}{{\sum }_{x,y,z}{S}_{margin,m}(x,y,z)}=1.$$ (5)

Collateral damage G_P,t,i,m [cm³] is defined as follows:

$$G_{P,t,i,m}=\sum _{x,y,z}{D}_{P,t,i}(x,y,z),\text{where}{S}_{margin\text{,}m}(x,y,z)=0.$$ (6)

The proposed treatment planning methodology is based on evaluation of the distribution of minimum margin and collateral damage metrics, and histogram of ablation zone boundaries, resulting from N simulations for each considered combination of input power P and treatment time t. The operator can thus evaluate each potential [P, t] combination by considering the predicted minimal value of achieved minimum margins, their distribution across N simulations, and the value of maximum observed collateral damage. If multiple [P, t] combinations yield similar minimum margin distributions and same minimum of minimum margin, then the combination with lowest maximum collateral damage may be preferable. Finally, the treatment outcome of the chosen [P, t] combination can be visualized by overlaying the ablation histograms C_P,t(x,y,z) on the target.

In the present study, we limit applied power to the range 10 W < P < 70 W with 10 W sampling step, as assessed at the catheter tip, and ablation duration to the range 2 < t < 10 min with 1 min sampling step consistent with the anticipated use settings for bronchoscopic microwave ablation.⁷ Furthermore, collateral damage values are computed with respect to the maximum evaluated minimum margin, which is 5 mm. The total number of simulations for each [P, t] combination was N = 20 to provide reasonable compromise between sufficient sampling of minimum margin statistical distribution and overall computation time.

2.B. Microwave ablation applicator

The MWA applicator modeled in this study is similar to the flexible applicator described in.⁷ Briefly, the applicator consists of a 2.45-GHz antenna with a balun, integrated within a custom catheter-extrusion through which chilled water is circulated. The outer diameter of the catheter is 2 mm, and it is suitable for deployment via the instrument channel of a flexible bronchoscope.

2.C. Computational model

To simulate the distribution of electromagnetic field, power absorption, and bioheat transfer, we employed an approach similar to our previous studies^28,33 and that has been experimentally validated against volumetric MRI thermometry data in ex vivo tissue.³⁴ Specifically, we utilized the finite element method (FEM) to solve the coupled electromagnetic and bioheat transfer equations during MWA. At each time-step of the transient bioheat transfer model, the following sequence of equations was solved. The spatial distribution of the electric field was determined by solving the time-harmonic Helmholtz electromagnetic wave equation:

$${\nabla }^2\mathbf{E}+{\beta }_0^2\left({\epsilon }_r-\frac{j\sigma }{\omega {\epsilon }_0}\right)\cdot \mathbf{E}=0,$$ (7)

where E is electric field [V m⁻¹], β₀ is the wavenumber in free space [m⁻¹], ɛ_r is relative permittivity, σ is effective electric conductivity [S m⁻¹], ω is angular frequency [rad s⁻¹], and ɛ₀ is the permittivity of free space [F m⁻¹]. From the solution of (7), the time-averaged electromagnetic losses can be evaluated using

$$Q_{mw}=\frac{1}{2}\sigma \Vert \mathbf{E}{\Vert }^2.$$ (8)

Finally, the temperature profile within the tissue was computed using the Pennes’ bioheat equation, including an additional term ω_air(T) added to approximate the heat transfer due to evaporation within alveoli³⁵:

$$\rho c(T)\frac{\partial T}{\partial t}=\nabla \cdot k(T)\nabla T+Q_{mw}-{\omega }_{bl}(T)\cdot \left(T-T_{bl}\right)-{\omega }_{air}(T),$$ (9)

where ρc is the volumetric heat capacity [J m⁻³ K⁻¹], T is the temperature [K], k is the thermal conductivity [W m⁻¹K⁻¹], ω_bl is the blood perfusion [W m⁻³K⁻¹], and T_bl is the physiologic temperature of the blood (i.e., 37 °C). The initial temperature was set to 37 °C in the whole simulation domain.

Equations (7) and (8) were solved subject to the following boundary conditions. The Sommerfeld radiation condition, as approximated by the first order scattering boundary condition, was used at all outer boundaries of simulated space.

$$\mathbf{n}\times (\nabla \times \mathbf{E})-jk\mathbf{n}\times (\mathbf{E}\times \mathbf{n})=0,$$ (10)

where n is a unit vector perpendicular to the specific boundary. A thermal insulation boundary condition was set at the outer simulation boundaries.

$$\mathbf{n}\cdot (k\nabla T)=0,$$ (11)

To approximate the effects of circulating water through the applicator shaft, a fixed temperature boundary condition (T = 20 °C) was employed along the applicator shaft.

The models considered herein include a tumor region distinct from background normal tissue. Two types of tumors were considered: generic, spherically shaped tumors for demonstrating the modeling and treatment planning methodology and assessing range of tumors that could be treated with the simulated applicator, as well as irregularly shaped tumors as segmented from CT scans of candidate lung tumors. The computational model as well as treatment planning methodology was implemented with COMSOL Multiphysics (v5.4, COMSOL Inc., Burlington, MA) and MATLAB (R2018a, The MathWorks Inc., Natick, MA).

The computational model was validated by comparing ablation zone extents from in vivo experiments in normal porcine lung against a corresponding simulation where tumor and normal tissue regions were assigned identical tissue properties (i.e., applicator was surrounded by lung parenchyma only). In vivo experiments were conducted under a protocol approved by the KSU Institutional Animal Care and Use Committee. Anesthesia was induced with Telazol (4.4 mg/kg, IM) and Xylazine (2.2 mg/kg, IM). Following induction of anesthesia, atropine (0.05 mg/kg, IM) was administered, and pigs were mechanically ventilated at 6–8 breaths/min. A ventral midline thoracotomy was performed from the manubrium to the xyphoid cartilage, and the pleural cavity was exposed. Ablation applicators were inserted into the lung parenchyma under visual guidance via direct puncture of the lungs. Once positioned, power was applied from a solid-stage 2.45-GHz generator (Sairem GMS 200 W) with cooling water circulated through the applicator by a peristaltic pump (Masterflex L/S7015–20). Following completion of ablations, animals were euthanized, and the lungs were harvested and sectioned. The extents of the ablation zone on gross pathology were measured after staining tissue sections with a triphenyl tetrazolium chloride viability stain, as detailed in Ref. [7]. Data from three in vivo experiments in porcine lungs were utilized for this illustration of model precision, one with P = 30 W and t = 10 min, and the other two experiments with P = 60 W and t = 10 min. In one of the 60 W, 10 min ablations, no ventilation was observed, and thus no air ventilation heat sink term (i.e., ω_air(T) = 0) was included. Experimental ablation zone extent following tissue sectioning and viability staining with TTC were estimated from photos, with the use of a two-stage segmentation algorithm utilizing k-means technique and area significancebased denoising.

2.D. Tissue properties and their variability

Average, standard deviation, and range of tissue biophysical properties used for normal lung are listed in Table I, and were taken from the Information Technologies in Society (IT’IS) tissue properties database.³⁶ When setting up the model for i-th simulation, baseline tissue properties at physiologic temperature were randomly sampled from within the range of values listed in Table I, using the listed parameters of the distribution (i.e. average and standard deviation). Dynamic changes in tissue biophysical properties during heating were then updated as temperature increased during the course of the ablation using the temperature dependency listed in the fourth column of Table I.

Table I.

Lung tissue biophysical properties employed in fem simulations

Parameter	Unit	Mean, Std., Min., Max.	Temperature dependency
Relative permittivity, εr	-	40.5, 5.6, 28.1, 51 (at 2.45GHz)	Piecewise linear 37
Effective conductivity, σef	S/m	1.47, 0.22, 0.9, 1.88 (at 2.45GHz)	Piecewise linear 37
Volumetric heat capacity, ρc	MJ m−3K−1	1.53, 0.67, 0.99, 2.34	Piecewise constant 38
Thermal conductivity, k	W m−1K−1	0.39, 0.09, 0.28,0.48	Piecewise linear 38
Blood perfusion rate, ωbl	kW m−3K−1	26.5, 23.6, 11.9, 38.4	Smoothed step 38
Air ventilation rate, ωair	kW m−3	105 (at 50°C), -,-,-	Exponential with cutoff 35

Due to the lack of lung tumor properties in literature, the tumor tissue was approximated by muscle as previously suggested.³⁹ Specific baseline values at physiologic temperature were again taken from the IT’IS database and temperature dependencies of thermal properties from the literature, as noted in the fourth column of Table II. Dielectric properties of tumors were approximated in few different ways to study the impact of contrast between tumor and background tissue to resulting ablation and treatment plan, as described in the following subsection.

Table II.

Muscle tissue biophysical properties employed in fem simulations

Parameter	Unit	Mean, STD, Min., Max.	Temperature dependency
Volumetric heat capacity, ρc	MJ m−3K−1	3.73, 0.024, 2.73, 4.48	Piecewise constant 38
Thermal conductivity, k	W m−1K−1	0.49, 0.04, 0.42, 0.56	Piecewise linear 38
Blood perfusion rate, ωbl	W m−3K−1	Perfusion is set to same value as in background lung.
Air ventilation rate, ωair	W m−3	No air ventilation heat sink

2.E. Models of heterogeneity between tumor and normal lung

We investigated four scenarios describing plausible dielectric and thermal contrast between tumor and background lung tissue properties.

Scenario 1:

This scenario represents a tumor with a central hypoxic necrotic core, often observed in established tumors.⁴⁰ A central zone of diameter 5 mm with decreased blood perfusion 11 kWm⁻³K⁻¹ was included to mimic a necrotic central core or volume with decreased perfusion of the tumor as can be identified in recent perfusion mapping studies.^41,42 Small value of decreased perfusion was chosen to correspond with the minima of perfusion maps and their ratios to average values. We modeled dielectric contrast between the tumor and surrounding parenchyma. Dielectric properties of the tumor were set to the upper envelope of lung dielectric properties in Table I for each simulation; for background lung parenchyma, dielectric properties were sampled from within the ranges listed in Table I. Thermal properties of the tumor were randomly sampled from the distribution listed in Table II. There was no ventilation heat sink modeled throughout the tumor region.

Scenario 2:

This scenario includes a 5-mm diameter central necrotic core with reduced perfusion of 11 kWm⁻³ K⁻¹. However, this scenario assumes no contrast in dielectric and thermal properties between all regions of the tumor and the normal lung. Specifically, dielectric properties of the tumor were the same as the properties of background lung tissue, which were randomly sampled from within the ranges listed in Table I. There was no ventilation heat sink modeled throughout the tumor region.

Scenario 3:

This scenario illustrates the impact of homogenous perfusion throughout the tumor region (i.e., no necrotic core). Dielectric and thermal properties of the tumor and normal lung regions were the same as in Scenario 1.

Scenario 4:

This scenario presents the extreme case of maximum contrast in dielectric properties between tumor and background lung tissue. For each simulation, dielectric properties of the tumor and background lung were set to the upper and lower envelope, respectively, of the ranges listed in Table I. Thermal properties of tumor were set to mimic those of muscle, and randomly sampled from within the ranges specified in Table II. Furthermore, a 5-mm diameter central region with decreased blood perfusion of 11 kWm^−3.K⁻¹ was modeled to mimic a necrotic core.

These scenarios are summarized in Table III.

Table III.

Contrast in biophysical properties between tumor and normal lung considered in simulations under scenarios 1 – 4

Scenario	Background lung		Tumor
	Dielectric	Thermal	Dielectric	Thermal	Necrotic core
1	Random sampling (Table I)		Upper Envelope (Table I)	Random sampling (Table II)	Yes
2	Random sampling (Table I)		Same as background lung		Yes
3	Random sampling (Table I)		Upper Envelope (Table I)	Random sampling (Table II)	No
4	Lower envelope (Table I)	Random sampling (Table I)	Upper Envelope (Table I)	Random sampling (Table II)	Yes

To study the effect of tissue variability on final treatment plans, we generated plans for 2-cm diameter spherical tumors for each of the above-considered scenarios. CT scans were obtained from the Lung Image Database Consortium (LIDC-IDRI) image collection with marked up annotations.⁴³ The LIDC-IDRI consortium is made up of seven academic centers and eight medical imaging companies that contributed to the dataset which is composed of 1018 actual patient cases. We further generated ablation histograms and computed planning features for three spherical tumors of diameter 1, 2, and 2.5 cm, under scenario 1 to illustrate the range of tumor sizes, which can be adequately ablated with the desired margin. Scenario 1 was also utilized to generate the treatment plans for two non-spherical shaped tumors, identified from example patient CT images, to demonstrate the proposed methodology.

3. RESULTS

3.A. Model accuracy illustration

Figure 2 shows an example comparison between an ablation zone observed following in vivo experiments in normal porcine lung and simulated minimum, average, and maximum ablation zones for [P, t] = [30 W, 10 min]. Thermal profiles and ablation zones are shown in an axial plane (perpendicular to the applicator axis) located in the middle of the ablation. These simulations were performed within homogeneous normal lung tissue to mimic the experimental setting.

FIG. 2.

Sample temperature map overlaid with contours of estimated ablation boundaries (a) following P = 30 W, t = 10 min ablations. The black contour depicts the observed ablation boundary following experimental ablations in normal porcine lung in vivo. The yellow, red and blue contours represent the maximum, average, and minimum ablation extent predicted from simulations respectively. Estimated contour of ablation overlaid on a tissue gross section (b).

Table IV provides the extent of the experimentally observed and simulated ablation dimensions – diameter (D) and height (H) – following three experimental ablations in normal porcine lung in vivo. For experimental ablations, the diameter was estimated as average of all diameters measured along the circumference of the observed ablation zone.

Table IV.

Ablation dimensions from in vivo experiments and simulations.

Power, time	Experiment		Simulation
			Minimum		Average		Maximum
	D [mm]	H [mm]	D [mm]	H [mm]	D [mm]	H [mm]	D [mm]	H [mm]
30 W, 10 min	15	-	12.5	26	16.8	27.2	18.2	28
60 W, 10 min	30	35	28.8	35.8	30.6	37	31.7	37.8
60 W*, 10 min	36	42	33	39	38	42	44	48

^*ω_air = 0 W/m³

3.B. Effect of tumor size on predicted ablationoutcome for generic spherical tumors

Figure 3 shows treatment planning graphs and accompanying ablation histograms for sample [P, t] combinations for spherical tumors of diameter 1 and 2.5 cm, when using scenario 1. In the treatment planning graphs, the color-coded thick horizontal bars represent the fraction of N simulations at each displayed [P, t] combination that yields a minimum margin corresponding to the color of the bar. For instance, for [P, t] = [20 W, 5 min], the horizontal bars colored red and orange, respectively, represent the fraction of N simulations that yielded 3 and 4 mm margins. Since both bars are of equal length, this indicates 10 of the N = 20 simulations yielded a minimum margin of at least 3 mm, and the remaining 10 simulations yielded a minimum margin of 4 mm. Similarly, the planning graph indicates [P, t] = [30 W, 6 min] yields a single horizontal bar in green, indicating all N = 20 simulations yielded a minimum margin of 5 mm. The thick colored lines identify [P, t] combinations that yield equal minimum margins across all N = 20 simulations. Finally, the dashed contours identify [P, t] combinations that yield equal maximum collateral damage values. The specific value for each contour is annotated at the top of the graph. In this manner, for a given applicator position, tumor geometry, and tissue property scenario (1–4), the treatment planning graph displays the relationship between candidate [P, t] combinations and treatment outcome, as assessed by minimum margin and collateral damage, including the impact of uncertainty in tissue physical properties. Thermal profiles relative to the tumor and target (i.e., tumor + 5 mm margin) boundaries for any [P, t] combination can then be generated to visualize the simulated treatment profile [Figs 3(c) and 3(d)]. Importantly, the extent of the ablation zones is presented as C_P,t(x,y,z) contours, thereby illustrating the ablation zone extent as a distribution – attributed to uncertainty in tissue properties – rather than as a deterministic boundary.

FIG. 3.

Treatment planning graph (a) and ablation histogram (c) for 1 cm spherical tumor. Treatment planning graph (b) and ablation histogram (d) for 2.5 cm spherical tumor. Solid black lines in Figures (c) and (d) represent tumor boundary and black dotted lines the boundary of 5 mm margin around tumor. The yellow, red and blue contours represent the maximum, average, and minimum ablation extent predicted from simulations respectively.

For the 1-cm spherical tumor, Fig. 3(c) illustrates the thermal profile and ablation zone histogram for [P, t] = [30 W, 6 min]. Figure 3(a) indicates [30 W, 6 min] yields a minimum margin of 5 mm in all N = 20 simulations; this is evident in Fig. 3(c), where all the C_P,t(x,y,z) contours extend beyond the target (i.e., tumor + 5 mm margin) boundary. Similarly, in the case of the 2.5-cm spherical tumor, a 5-mm minimum margin was not achieved in any of the N = 20 simulations even when using the highest power and ablation duration [70 W, 10 min] as seen in Fig 3(b); the thermal profile and ablation histogram shown in Fig 3(d) is for [70 W, 10 min] illustrating the average minimum margin from N = 20 simulations is less than the desired 5-mm margin, and even the largest of the 20 simulated ablation zones does not achieve the desired 5-mm margin. For this 2.5-cm spherical tumor, the minimum margin across all N = 20 simulations was 2 mm.

3.C. Effect of tumor–normal tissue contract on predicted ablation outcome for generic spherical tumors

Figure 4 illustrates longitudinal planes of ablation histograms overlaid on contours of the tumor and desired 5-mm margin contours, for each of the four tissue property scenarios, when considering a spherical 2-cm diameter tumor. For scenarios 1, 2, 3, and 4, temperature profiles and ablation zone extents are presented for combinations of [70W, 6 min], [70 W, 7 min], [70 W, 8 min], and [70 W, 8 min] respectively, as suggested by treatment planning graphs presented in Fig. 5.

FIG. 4.

Ablation zone histograms plotted over tumor and wanted margin contours for scenario 1,2,3 and 4. Solid black lines represent the tumor boundary and black dotted lines represent the boundary of 5 mm margin around the tumor. The yellow, red and blue contours represent the maximum, average, and minimum ablation extent, respectively, predicted by simulations.

FIG. 5.

Treatment plans for 2 cm diameter sphere tumor and tissue properties scenarios (1), (2), (3) and (4). Proportion of a given color, which stands for specific minimum margin, in each bar denotes how many simulations achieved this minimum margin. Solid contour lines encompass all [P, t] combinations where no single minimum margin was smaller than he color of the line.

Figure 5 shows the effect of tissue properties scenarios on treatment plans for a 2-cm diameter spherical tumor.

3.D. Treatment plan for sample irregular-shaped tumor, case 1

Figure 6(a) shows a treatment planning graph for an irregularly shaped tumor, segmented from an example patient imaging dataset. The [P, t] = [45 W, 5 min] combination was chosen as a first option, where each simulation achieved at least 5 mm minimum margin. This choice also minimized the maximum observed collateral damage, when compared with other combinations providing the same minimum margin histogram. The assembled ablation histogram for this power/duration combination with overlaid tumor and margin is shown in various planes in Figs. 6(b) and 6(c).

FIG. 6.

Treatment planning graph (a) for case 1 of tumor with irregular shape. Sample XY (b) and DZ cut-planes (c) of real tumor with ablation zone histogram for advised power 45W and duration 5 min. Axis d is a diagonal in XY plane. Black solid contour stands for tumor. Dashed black contour denotes margin. Blue, red and yellow contours denote 100%, 50%, and 10% probability of ablating space inside the respective contour.

3.E. Treatment plan for sample irregular-shaped tumor, case 2

Figure 7(a) shows a treatment planning graph for the second case of an irregular tumor, segmented from an example patient CT scan. The [P, t] = [70 W, 10 min] combination was selected for illustrating sample thermal profiles; this [P, t] provides the highest probability of achieving a 5-mm minimum margin. The assembled ablation histogram for this [P, t] combination with overlaid tumor and margin is shown in various planes in Figs. 7(b) and 7(c).

FIG. 7.

Treatment planning graph (a) for case 2 of tumor with irregular shape. Sample XY (b) and DZ cut-planes (c) of real tumor with ablation zone histogram for advised power 70W and duration 10 min. Axis d is a diagonal in XYplane. Black solid contour stands for tumor. Dashed black contour denotes margin. Blue, red and yellow contours denote 100%, 50%, and 10% probability of ablating space inside the respective contour.

4. DISCUSSION

There is a need to develop treatment planning and visualization tools that may help MWA operators comparatively assess candidate applied power and treatment durations based on predicted treatment profiles. Operators seek to identify applied energy settings that are likely to yield adequate treatment margins beyond the tumor boundary, while limiting collateral damage to tolerable ranges. The present study describes an approach for model-guided assessment of candidate applied power settings, including a method to account for uncertainty in tissue biophysical properties. Specifically, for a given tumor geometry, applicator position within the tumor, and candidate energy settings, we run N simulations with tissue biophysical properties sampled from within the range of anticipated values that have been previously reported in the literature. Consequently, predicted ablation outcomes can be presented as a distribution of ablation zone boundaries.

Figure 2 and Table IV present experimentally observed and simulated ablation zone dimensions for two power levels, illustrating good accuracy of the computational model. Importantly, experimentally observed ablation zones were largely within the range of minimum and maximum extents of the ablation zone computed using tissue physical properties corresponding to the extrema of the ranges considered in Tables I and II. The small region of the experimental ablation zone that extended beyond the simulation bounds may be attributed to heterogeneity within the lung parenchyma due to discrete structures such as airway walls and do not exceed 1.6% of area of experimental ablation extents, which are contained within the simulated maximum ablation extent. The maximum deviation of predicted average ablation diameter between simulation and experiment is 2 mm.

The applicator modeled in this study is similar to a flexible microwave ablation catheter under development for bronchoscopic applications.⁷ Simulations predicted that 1-cm diameter tumors could be ablated with a 5-mm circumferential margin across 100% of N = 20 simulations considered under scenario 1. For 2-cm diameter tumors, a 5-mm circumferential margin could be achieved in 65% of simulations, and a 4-mm margin could be achieved across 100% of simulations. For 2.5-cm diameter tumors, a 3-mm or bigger minimum margin could be achieved across 90% of simulations. These simulations illustrate the potential for this applicator to treat up to 2.5-cm tumors with a 3- to 5-mm margin, across a broad range of tissue physical properties.

Previous studies have illustrated that contrast in biophysical properties between background parenchyma and tumor tissue may considerably influence ablation profiles.^18,44 There is limited published literature on the biophysical properties of lung tumors relative to normal parenchyma, and how these differences vary as a function of tumor type and pathology (e.g., squamous cell carcinoma vs adenocarcinoma). Thus, we considered four scenarios describing plausible heterogeneity in biophysical properties between normal lung and tumor. As shown in Figs. 4 and 5, the nature of the heterogeneity between normal lung and tumor affects predicted ablation extent, and thus the choice of suitable [P, t] combinations. For the simulations with 2-cm tumors, Fig. 4 illustrates the thermal profiles and histograms of ablation zones for the [P, t] combinations that yielded the largest minimum margin for the least collateral damage (circled [P, t] combinations on planning graphs in Fig. 5). Across all considered scenarios, the maximum difference between the contours representing 100% probability of ablation zone was 2 mm. Specifically, scenario 1, [P, t] = [70 W, 6 min] was selected as it provided more than 50% probability of achieving 5-mm minimum margin and 100% probability of achieving 4-mm minimum margin. When simulating scenario 2, combination [P, t] = [70 W, 7 min] was selected as it provided a 100% probability of ablating the target area with a minimum margin of 5 mm. The more favorable performance with scenario 2, when compared to scenario 1, may be attributed to the tissue volumetric heat capacity in the tumor area (modeled as being similar to normal lung), which was on average less than half of that of the value simulated in scenario 1 (modeled as being similar to muscle), which resulted in a more rapid heating within the tumor area. For scenario 3, more energy than in the case of other scenarios was required to achieve an adequate margin, since the absence of a necrotic core translated to a larger perfusion-related heatsink. In this case, input parameter combination 70 W and 8 min was identified as yielding 100% probability of ablating the target area with a 4-mm minimum margin and more than 50% probability of achieving a 5-mm minimum margin. In case of scenario 4, there were three [P, t] combinations with 100% probability of ablation with a 4-mm minimum margin and ~25%, ~45%, and ~60% probability of ablating a 5-mm minimum margin for 70 W and 8, 9, and 10 min respectively. [P, t] combination [70 W, 8 min] could be in this case chosen for treatment to minimize collateral damage or combination [70 W, 10 min] for maximizing a 5-mm margin coverage with slight increase in collateral damage. Overall, simulations under all scenarios resulted in treatment planning suggesting 70 W value of input power and the ablation duration in range 7 to 9 min.

The above-discussed results apply to spherical shaped tumors as can be seen in Figs. 3 and 4, which can be an oversimplification of the geometry of the actual tumor. As can be seen on tumors identified from patient-images in Figs. 6 and 7, lung tumor geometries can have irregular shapes with extensions emanating from a central body. Depending on the biophysical properties (i.e., dielectric properties, thermal properties, and perfusion) of tumor extensions, which are currently unknown, and surrounding normal lung, higher power and/or ablation duration might be necessary to allow the ablation zone to grow and achieve an adequate minimum margin along the entire tumor boundary. Future studies investigating the impact of heterogeneity between normal lung parenchyma and extensions from the tumor on ablation outcome are warranted. This may come at a cost of considerably increased collateral damage. Planning for specific tumor geometries is therefore crucial for successful treatment planning, allowing physicians to consider the impact of applicator positioning and [P, t] choices on minimum margin and collateral damage. Furthermore, the treatment planning methodology presented in this work could be extended to include constraints for maximum tolerable thermal dose in critical structures and other organs at risk.

This work has some limitations. Dielectric and thermal properties of lung tumors were approximated as being similar to muscle, due to the lack of published studies reporting tissue properties for lung tumors. Furthermore, due to the lack of knowledge of tissue biophysical properties as a function of tumor type/pathology, we considered four scenarios approximating plausible variations in tissue biophysical properties between tumor and normal lung parenchyma. Establishment of datasets linking tumor pathology, imaging characteristics, and biophysical properties relevant for MWA and other ablation modalities, are warranted, and would considerably enhance the development of personalized thermal ablation planning techniques. Our simulations also did not account for tissue shrinkage, which may not necessarily be consistent across patients and tumor types.⁴⁵ For both generic spherically shaped tumors and irregular geometries from candidate patient images, this work considered central placement of the applicator through the tumor structure. In clinical practice, central applicator placement may not always be possible. Future efforts should consider applicator position and alignment within the tumor as additional parameters during treatment planning. While the current work allows the operator to assess thermal ablation profiles and corresponding metrics for a wide range of [P, t] combinations, the technique could be extended to incorporate optimization techniques that present the operator with a selection of the most promising treatment delivery parameters (i.e., [P, t], combinations). Ultimately, it would be important to develop rapid computation and visualization approaches so the treatment planning methodology presented in this work could be readily integrated within the routine clinical workflow.

5. CONCLUSION

We have proposed an approach for lung MWA treatment planning, which addresses the specific geometry of the treatment site as well as the impact of tissue property variability on the predicted ablations by employing a set of simulations for each assumed combination of power and ablation duration for a given microwave applicator. The operator can employ the treatment planning charts, which are assembled for each case individually, to assess the likelihood of achieving a specified minimum margin. Finally, while this approach is illustrated on a set of simulations in the lung, it may be extended to simulation-based planning of ablative treatments in other organs.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.