Radiofrequency ablation (RFA) has emerged as an alternative treatment modality for treating various tumors with minimum intervention. The application of RFA in treating breast tumor is still in its infancy stage. Nevertheless, promising results have been obtained while treating early stage localized breast cancer with RFA procedure. The outcome of RFA is tremendously dependent on the precise insertion of the electrode into the geometric center of the tumor. However, there remains plausible chances of inaccuracies in the electrode placement that can result in slight displacement of the electrode tip from the actual desired location during temperature-controlled RFA application. The present numerical study aims at capturing the influence of inaccuracies in electrode placement on the input energy, treatment time and damage to the surrounding healthy tissue during RFA of breast tumor. A thermo-electric analysis has been performed on three-dimensional heterogeneous model of multilayer breast with an embedded early stage spherical tumor of 1.5 cm. The temperature distribution during the RFA has been obtained by solving the coupled electric field equation and Pennes bioheat transfer equation, while the ablation volume has been computed using the Arrhenius cell death model. It has been found that significant variation in the energy consumption, time required for complete tumor necrosis, and the shape of ablation volume among different positions of the electrode considered in this study are prevalent.
Breast cancer is not only the most frequently diagnosed cancer among women, but is also the cause of greatest number of cancer-related deaths among women worldwide . In 2015, breast cancer resulted in 570,000 deaths that accounts to approximately 15% of all cancer-related deaths among women . In U.S., it has been estimated that about 252,710 women will be diagnosed with breast cancer in 2017, and 40,610 women are estimated to die from breast cancer . In India, breast cancer ranks first both in terms of incidences (1.4 million cases in 2012) as well as mortality (70,218 cases in 2012) among women . Although, India has much lower age-adjusted incidence rate (25.8 per 100,000) than U.S. (92.9 per 100,000) but the mortality rate is at par (15.9 versus 17.1 per 100,000) with the U.S. . According to WHO, Geneva, Switzerland prediction, the breast cancer burden in India will nearly double in next 20 years . It has been estimated that about 1.7 million breast cancer incidences will occur among Indian women with an estimated 85,869 deaths in 2020, that is estimated to increase to about 2.3 million incidences and 1.3 million deaths by the year 2035 .
With the advancement in modern imaging techniques, the detection rate of early, nonpalpable breast lesions has increased dramatically . In recent years, there has been a positive shift toward the minimally invasive treatment modalities, viz., radiofrequency ablation (RFA), laser ablation, microwave ablation, cryoablation and high-intensity focused ultrasound ablation. These minimally invasive treatment modalities result in lower treatment cost, reduction in morbidity and mortality rates, shorter recovery time and better cosmetic results as compared to surgical interventions . Among the different thermal ablative techniques, RFA is one of the frequently applied and best investigated treatment modality. RFA has already emerged as an alternative treatment modality for treating tumors in patients who are not candidate of surgery due to various reasons . During RFA, an electrode is inserted into the tumor through which electric current in the frequency range of 450–550 kHz is administered that induces resistive heating at the electrode–tissue interface . The generated heat results in the destruction of tumorous cells by instantaneous induction of protein coagulation that irreversibly damages key cytosolic and mitochondrial enzymes and nucleic acid histone complexes . Additionally, RFA is hindered if the tissue temperature rises above 100 °C, resulting in tissue carbonization and water vaporization. This can lead to noticeable increase in the electrical impedance of tissue, thus restricting further flow of the electric current . For successful ablation, the resulting ablation volume should encompass complete tumor along with a clinical safety margin of at least 5 mm, to avoid any chances of tumor recurrence .
Apart from clinical studies, several studies are available in the literature on mathematical modeling of RFA. The mathematical models could play a vital role in providing a priori information about the possible outcomes and risks involved to clinical practitioners before the onset of RFA. However, majority of the computational studies are mainly focused on liver cancer treatment investigating either one- or two-compartment models. Very limited studies are available on application of RFA in breast cancer due to the complexity associated in modeling heterogeneous breast model that comprises of varying concentrations of fat, glandular, and connective tissues [10–12]. Moreover, the application of RFA in treating breast cancer is still a developing area of research, although, breast as an organ seems to be an ideal case for RFA application because of its superficial location on the thorax and due to the absence of intervening organs . Also, due to the absence of any large blood vessels in the parenchyma of the breast, convectional heat loss is improbable to occur during RFA application.
The success rate of complete tumor necrosis during RFA is tremendously dependent on placing the electrode at the exact position predicted in the ablation protocol and that by itself is a research topic . The accurate and precise placement of electrode becomes even more challenging with early stage breast tumors that require placement accuracy of only a few millimeters. Further, the force of the electrode during insertion can easily deform the soft breast tissue and that may lead to tumor dislocation [14,15]. Generally, to circumvent this problem, the electrode insertion is done with the help of image-guided modalities. Usually, ultrasound imaging is preferred due to its capability of real-time visualization and cost effectiveness. During the RFA procedure, the clinician holds an ultrasound probe in one hand and inserts the radiofrequency electrode with the other hand. An excellent hand–eye coordination is often required for accurate and precise electrode insertion within the target tissue and to decrease the number of insertion attempts [14,15]. Thus, there remains a plausible possibility of slight discrepancy of the electrode position from the desired location during RFA application. In this regard, the present finite element method (FEM) study focusses at quantifying the effect of such errors in electrode placement on input energy, treatment time and damage to the surrounding healthy tissue during temperature-controlled RFA of breast tumor.
Problem Formulation and Mathematical Modeling
A computational three-dimensional models of breast comprising of fat, glandular, and muscular layer have been developed , as shown in Fig. 1. A spherical tumor of 1.5 cm has been embedded in the upper outer portion of the glandular tissue to mimic in situ tumor in early stages . A multitine RITA Starburst XL electrode (AngioDynamics, Inc., Latham, NY) deployed to 2 cm has been incorporated in the computational domain of the breast. The positioning of the electrode relative to the geometric center of the tumor is in agreement with the manufacturer's proposed protocol, i.e., the tip of the electrode is 1 cm proximal to the center of the tumor. This position is referred to as the perfect position of the electrode in the present study. However, in order to capture the influence of imperfect electrode insertion during clinical procedure, six different offset positions of the electrode have been considered relative to perfect position as shown in Fig. 2. The present numerical study considers a maximum offset of 5 mm from the actual perfect position of electrode, which is frequently encountered in clinical practice . In addition, an intermediate value of 2 mm offset of the electrode positioning has been considered to provide a priori information of possible outcome due to such minor discrepancies in electrode placement. The offset position of electrode with respect to the perfect position has been taken in both transverse (perpendicular to the electrode axis) as well as longitudinal directions (along the electrode axis). However, due to the symmetry in the transverse direction of the electrode axis (viz., right and left sides), the electrode position offset by 2 mm and 5 mm has been considered only on one side in the computational domain.
A 20 min temperature-controlled RFA of the breast tumor has been performed by incorporating the proportional–integral–derivative (PID) controller at the active tip of the electrode. The preset target temperature during temperature-controlled RFA has been considered to be 95 °C  to mitigate any adverse effect of tissue carbonization and charring. The initial voltage and initial temperature of the entire computational domain of the breast have been considered to be 0 V and 37 °C, respectively. The electric potential at the bottom surface of the breast has been considered to be zero in order to simulate dispersive ground pad. A variable voltage source V(t) computed by the PID controller has been applied on the boundaries of the multitine electrode whose initial temperature has been assumed to be 25 °C. All the remaining exterior boundaries of the computational domain were subjected to zero electric flux boundary conditions. Further, at each interface of numerical model, electrical and thermal continuity boundary conditions have been imposed. The outer surface of the breast model has been assumed to be exposed to ambience and is subjected to convective cooling condition (= h(T − T∞)). Here h is the convective heat transfer coefficient assumed to be 13.5 W m−2 K and T∞ is the surrounding ambient temperature considered to be 25 °C . The material properties considered in this computational study have been tabulated in Table 1 [19,20].
where T is the temperature, t is the ablation time, ρ is the density of tissue, c is the specific heat of tissue, k is the thermal conductivity of tissue, ρb is the blood density (=1050 kg m−3), cb is the blood specific heat (=3617 J kg−1 K−1), ωb is the blood perfusion rate, Qm is the volumetric heat generated due to tissue metabolism, Qp is the volumetric heating due to RFA and Tb is the blood temperature (=37 °C).
where σ0 and k0 are the constant electrical and thermal conductivities, respectively, at core body temperature (Tb = 37 °C) presented in Table 1.
where ωb,0 is the constant blood perfusion given in Table 1, and Ω(t) is the induced thermal damage.
where t is the ablation time, A is a frequency factor (=1.18 × 1044 s−1) , Ea is an activation energy for irreversible damage reaction (3.02 × 105 J mol−1)  and R is the universal gas constant (= 8.314 J mol−1 K−1). Further, this study considers damage integral value of Ω(t) = 1, that corresponds to 63% probability of cell death, as a critical threshold to represent tissue injury . All the cells below this critical threshold value have been considered to be alive.
where V is the applied voltage, e is the error between the preset tip temperature and current tip temperature at any instant, and Kp (0.02), Ki (0.01) and Kd (0.001) are the proportional, integral and derivative gains, respectively .
The FEM-based comsol mutiphysics software (COMSOL, Inc., AB, Stockholm, Sweden) has been used as a platform to solve the coupled electric–thermal problem of temperature-controlled RFA of breast tumor. The computational domain has been discretized into tetrahedral elements using comsol's built in free mesh generator that provides different meshing options based on number of mesh elements that range from extremely coarse (having low number of elements) to extremely fine (having high number of elements). A grid independence study has been conducted in order to determine the optimum mesh element size and reduce the computational cost. The mesh has been successively refined until the maximum error is less than 0.5% compared to the previous mesh. The final optimal mesh consists of 770,749 elements with a finer mesh at the electrode domain (where the highest electrical and thermal gradients are expected), fine mesh at the tumor and glandular domains, and normal mesh at the domain away from electrode, viz., muscle and fat layer. The relative tolerance for the electric field interface and the heat transfer interface has been set to 0.0001. The numerical convergence has been attained below the prespecified relative tolerance of the solvers for all simulations. The electric field has been solved by using multifrontal massively parallel sparse direct linear solver, while the temperature field has been solved using iterative conjugate gradient method. All numerical simulations have been performed on a Dell Precision Tower 7810 workstation with eight Core 3.1 GHz Xeon processor and 64 GB RAM.
Results and Discussion
The numerical model accuracy has been established by comparing the computational results with the experimental results obtained by conducting the temperature-controlled RFA on the polyacrylamide–based tissue-mimicking phantom gel, as reported in our previous study . A good agreement has been obtained between the temperature distribution obtained from numerical and experimental studies. Moreover, the time to reach the target temperature during temperature-controlled RFA has been found to be 2.95±0.3 min and 3.17 min from experimental and numerical studies, respectively. Further, the experimental validation has been extended to quantify the ablation volume during temperature-controlled RFA on the polyacrylamide–based tissue-mimicking phantom gel. The corresponding ablation volume attained from experimental and numerical studies have been found to be 17.36±1.86 cm3 and 17.61 cm3, respectively.
The variation of applied input voltage with ablation time due to different offset positions (refer Fig. 2) of electrodes relative to the perfect electrode position during temperature-controlled RFA of breast tumor have been presented in Fig. 3. It is evident from Fig. 3(a) that, very negligible variations prevail in the voltage requirement during incorrect placement of the electrode in the transverse direction (viz., cases 1 and 2) as compared to that of voltage requirement for the perfect electrode position. Further, for cases 3 and 4, the input voltage requirement during initial stage is slightly on the lower side as compared to that for the perfect electrode position, as shown in Fig. 3(b). However, on contrary, the input voltage requirement for cases 5 and 6 is considerably higher as compared to that for the perfect electrode position during temperature-controlled RFA, as depicted in Fig. 3(c). The maximum applied voltage values have been found to be 21.12 V, 22.35 V, and 24.49 V for the case of perfect electrode position, case 5 (i.e., 2 mm offset) and case 6 (i.e., 5 mm offset), respectively. The variation in applied input voltage requirement among different cases can be attributed to the variation of the electrode tip position, at which the temperature is being monitored, relative to the breast tumor during temperature-controlled RFA. Importantly, the active tip for perfect electrode position (as prescribed by manufacturer's protocol) lies just beneath the lower tumor boundary for the present scenario. Further, the blood perfusion rate of breast tumor is higher in comparison to the surrounding healthy glandular tissue (refer Table 1). Thus, active tip closer to the tumor will require more amount of energy to reach the preset target tip temperature and vice versa. Due to very small variation in the location of active tip and the tumor boundary for electrode positioning in transverse direction (viz., cases 1 and 2), negligible variation in the applied input voltage requirement prevails. But, for cases 3 and 4, the active tip shifts away from the tumor and results in lower input voltage requirement in comparison to the voltage requirement for perfect electrode position. However, for cases 5 and 6, the active tip is completely submerged within the highly perfused breast tumor that results in higher heat loss due to blood flow. Consequently, this requires more amount of input voltage to maintain the preset target temperature during RFA application.
The variation of tumor damage volume (corresponding to Ω = 1) with ablation time during temperature-controlled RFA for different cases, has been shown in Fig. 4. It is evident from Fig. 4(a) that the offset of electrode in transverse direction results in significant increase in the time required to attain complete ablation of 1.5 cm diameter breast tumor. The time required for attaining complete tumor necrosis increases from 7 min for perfect electrode position to 9 min for case 1 (i.e., 2 mm offset in transverse direction). However, for case 3 (i.e., 5 mm offset in transverse direction) approximately 99% tumor volume damage has taken place after performing temperature-controlled RFA for maximum preset ablation time of 20 min. Similarly, for offset in longitudinal (downward) direction, the time required for complete tumor necrosis increases by 3.67 min and 10.33 min for cases 3 and 4, respectively, as compared to that for perfect electrode position, as shown in Fig. 4(b). However, unanticipated results have been obtained for cases 5 and 6, whereby the time required to attain complete tumor necrosis actually decreases in comparison to that of perfect electrode position, as shown in Fig. 4(c). It has been found that the treatment time for complete tumor necrosis decreases to 4.67 min and 4.33 min for cases 5 and 6, respectively. This unexpected decrease in the treatment time can be attributed to the higher input voltage requirement for the cases 5 and 6 in comparison to the voltage requirement for the case of perfect electrode position, as explained in the preceding paragraph. The higher energy supplied to the electrode results in more tumor damage during temperature-controlled RFA application. However, it is important to mention that the success of RFA procedure is not only judged by the complete ablation of tumor alone. In addition, a clinical safety margin from tumor border also needs to be ablated to mitigate any chances of tumor recurrences. This numerical study assumes this clinical safety margin to be 5 mm for successful RFA application .
The damage field distribution at 5, 10, 15, and 20 min for different cases (refer Fig. 2) considered in this study during temperature-controlled RFA of breast tumor have been presented in Figs. 5–8, respectively. Importantly, the damage integral value of Ω = 1 has been considered for the prediction of damage volume during RFA application. These figures provide better visualization of the coagulation volume for different offset positions of electrode considered in this study. Figure 9 shows the shifting of ablation volume (corresponding to Ω = 1), along transversal line and longitudinal line, after 15 min of temperature-controlled RFA for different cases of electrode position. The selected ablation time of 15 min is in line with the time required for successful ablation of the entire tumor with perfect electrode position. It is evident from Figs. 9(a) and 9(b) that, any transverse variation in the electrode position (viz., cases 1 and 2) results in significant mismatch in the ablation volume produced after 15 min of RFA application. It can be seen from Fig. 9(a) that, for case 1, the ablation zone has not reached till the clinical safety margin of 5 mm along transverse line on one side. Further, it can be seen from Fig. 9(a) that, for case 2, one side of the tumor could not be ablated but an excessive damage of healthy tissue on the other side has occurred. Interestingly, ablation zone has almost reached the clinical safety margin for both cases 1 and 2 along the longitudinal line, as shown in Fig. 9(b).
The shifting of ablation zone for the offset of electrode position in longitudinally downward direction (viz., cases 3 and 4) has been shown in Figs. 9(c) and 9(d). It can be seen from Fig. 9(c) that, for both cases 3 and 4, the complete tumor has been ablated but the safety margin could not be ablated along the transverse line. Further, the ablation zone along the longitudinal line has reached the clinical safety margin for case 3 but not for case 4, as can be seen from Fig. 9(d). Additionally, the excessive damage to the healthy tissue is apparent along the longitudinal line for case 4 and is on the verge of damaging the muscular tissue.
The shifting of the ablation zone for offset of electrode in longitudinally upward direction (viz., cases 5 and 6) has been shown in Figs. 9(e) and 9(f). As was discussed earlier, the offset of electrode position compared to the perfect electrode position in longitudinally upward direction results in decrease in the treatment time required to attain complete tumor necrosis. However, extreme consequences of such scenarios can be clearly seen in Figs. 9(e) and 9(f). Even after attaining the complete tumor necrosis within first 5 min of RFA application, the clinical safety margin of 5 mm has not been completely attained even in next 10 min. Moreover, for case 5, very slight volume of safety margin has been spared during RFA along a transverse line (Fig. 9(e)). Further, as can be seen from Fig. 9(f), excessive damage of healthy tissue took place on one side along the longitudinal line for case 5. For case 6, ablation has reached the safety margin along the transverse line but not along the longitudinal line. Additionally, excessive damage of healthy tissue closer to the fat tissue can be clearly seen from Fig. 9(f) along the longitudinal line. Thus, it can be construed that, a slight deviation in the placement of electrode significantly affects the shape and size of the ablation volume produced during temperature-controlled RFA of breast tumor.
The variations of thermal damage (corresponding to Ω = 1) to the surrounding healthy tissue in close proximity of tumor for different electrode positions (shown in Fig. 2) have been shown in Fig. 10. It is evident from Fig. 10 that, for cases 2 and 4, the damage to the healthy tissue is below the clinical safety margin of 5 mm. While, for cases 5 and 6, excessive damage to the surrounding healthy tissue above 5 mm safety margin limit is apparent.
The effect of imperfect electrode placement during the temperature-controlled RFA of breast tumor has been studied. The flow of electric current and subsequent resistive heating and coagulation of the biological tissue during RFA have been modeled utilizing coupled electric field equation, Pennes bioheat equation, and Arrhenius rate equation. All the simulations have been done using FEM based comsol multiphysics commercial software. The ablation volume produced with the perfect electrode position as per the prescribed protocol during temperature-controlled RFA has been compared with different offset positions of the electrode in transverse and longitudinal directions. The study revealed that, the success rate of the RFA in breast tumor is significantly hampered due to the discrepancies in the electrode placement relative to the geometric center of the tumor. It has been observed that, the offset of electrode positioning by just 2 mm in transverse and longitudinal (downward) directions increases the time required for attaining complete tumor necrosis by 2 min and 10.33 min, respectively. Further, successful ablation has not been attained for 5 mm offset electrode positions in transverse and longitudinal (downward) directions even after 15 min of RFA application.
It has been found that even a slight error in positioning the electrode would result in significant mismatch in the shape of ablation volume produced during RFA application. Further, the damage to the healthy tissue has been quantified in order to provide a priori information to the clinicians about such possible scenarios during temperature-controlled RFA of breast tumor. The major limitation of this study is that, the experimental validation study has been conducted on homogeneous tissue-mimicking phantom gel in which the effect of blood perfusion has been ignored. This could bring in some errors during validation of the in vitro experimental results with the results obtained using numerical models of temperature-controlled RFA. The future work will be focussed on addressing the aforementioned issue by employing breast tumor phantom model for experimental validation and incorporating more realistic patient-specific models for numerical simulations.
The authors would like to acknowledge Indian Institute of Technology Ropar, India for providing necessary support and infrastructure for completion of the present research work.
• Science and Engineering Research Board (SERB), Department of Science and Technology, Government of India (Grant No. SB/FTP/ETA-0135/2013).
- A =
frequency factor (s−1)
- c =
specific heat capacity (J kg−1 K−1)
- e =
- Ea =
activation energy (J mol−1)
- k =
thermal conductivity (W m−1 K−1)
- Kd =
- Ki =
- Kp =
- Qm =
metabolic heat generation (W m−3)
- Qp =
radiofrequency heat source (W m−3)
- R =
universal gas constant (J mol−1 K−1)
- t =
ablation time (s)
- T =
temperature (°C or °K)
- V =
electric potential (V)