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Vascular and Interventional Radiology |
1 From the Department of Ultrasound, School of Clinical Oncology, Peking University, 52 Fu-cheng Rd, Hai-Dian District, Beijing 100036, China (M.H.C., W.Y., K.Y., Y.D.); Department of Mathematics, High School Affiliated to Capital Normal University, Beijing, China (M.W.Z.); Department of Radiology, Ospedale Generale, Busto Arsizio, Italy (L.S.); and Department of Radiology, Thomas Jefferson University Hospital, Philadelphia, Pa (J.B.L.). Received May 26, 2003; revision requested August 6; revision received October 15; accepted November 25. Address correspondence to M.H.C. (e-mail: minhuachen@vip.sina.com).
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODS RESULTSDISCUSSIONAPPENDIX REFERENCES |
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MATERIALS AND METHODS: A regular prism and a regular polyhedron model were used to develop a preoperative protocol for liver tumor ablation. This protocol enabled the authors to minimize the number of ablation spheres, optimize the overlapping mode, and determine the electrode placement process. One hundred ten patients with 121 liver tumors were treated by using this protocol. Sixty-nine patients had 74 hepatocellular carcinomas (HCCs), and 41 had 47 metastases to the liver (ie, metastatic liver carcinomas [MLCs]). Patients underwent follow-up helical computed tomography (CT) 1 month and every 2–3 months after RF ablation. Ablation was considered a success if no contrast enhancement was detected in the treated area on the CT scan obtained at 1 month.
RESULTS: A total of 536 ablations were performed in the 121 tumors. The ablation success rate was 87.6% (106 of 121 tumors); the local recurrence rate, 24.0% (29 of 121 tumors); and the estimated mean recurrence-free survival, 17.1 months. Twenty-five patients underwent 38 re-treatments for local tumor recurrence. Major complications occurred in seven patients. Of these patients, only one, who had a tumor close to the colon, had a colon perforation 1 week after RF and required surgical intervention.
CONCLUSION: The described protocol for treatment of large tumors had a success rate of 87.6% and a local recurrence rate of 24.0%.
© RSNA, 2004
Index terms: Liver neoplasms, 761.323, 761.33 • Liver neoplasms, CT, 761.12111, 761.12112, 76.12114, 76.12115 • Liver neoplasms, US, 761.12982, 761.12986, 761.12989 • Model, mathematical • Radiofrequency (RF) ablation, 761.1269
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTSDISCUSSIONAPPENDIX REFERENCES |
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However, moderate to high rates of local tumor recurrence, especially of large tumors, have been reported (12,15,16). A possible reason for failures in the treatment of large tumors is the inability to determine the optimal number of ablations and the exact location of electrode placement needed to completely destroy tumors larger than the size of a single ablation zone (17–19). Thus, an appropriate protocol to determine the correct number of RF ablations has been investigated (20,21). Dodd et al (22) reported their results of computer analysis of the thermal injury sizes created by overlapping ablations and proposed six- and 14-ablation models. Their results demonstrated the importance of performing these types of calculations to develop tumor ablation strategies.
Currently, the maximum diameter of the ablation sphere produced by most RF devices is 5 cm (2,20,23,24). Larger tumors should be treated with multiple overlapping ablations. The local recurrence rate for tumors larger than 3.5 cm was high in our early clinical experience (17). Thus, the purpose of our study was to develop a preoperative protocol for ultrasonographically (US) guided percutaneous RF ablation of hepatic tumors larger than 3.5 cm in diameter that is based on mathematic models and clinical experience and to evaluate the role of this protocol in RF ablation treatment.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTSDISCUSSIONAPPENDIX REFERENCES |
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These models allowed us to calculate the smallest number of ablation spheres and the optimal overlapping mode required to adequately ablate large spherical target lesions. The target volume consisted of the tumor plus at least a 0.5–1.0-cm tumor-free margin. The RF device (Model 1500; RITA Medical Systems, Mountain View, Calif) that we used could produce 5-cm ablation spheres. The numbers of ablation spheres and the overlapping modes of multiple ablations derived from the mathematic models are summarized in Table 1.
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Overlapping Modes and Ablation Localization
According to the geometric features of relevant mathematic models, the overlapping modes of multiple ablations and the ablation locations were determined (Appendix). With two-dimensional US guidance, three-dimensional multiple overlapping ablations were achieved.
Regular tetrahedron overlapping mode.—For a target sphere with a diameter of between 5.0 and 5.3 cm, the regular tetrahedron model is required. The overlapping mode of multiple ablations is assembled with three spheres in the x-y plane, and a fourth sphere is set along the z axis. Localization of ablations is performed as follows: (a) The lower two-fifths of the tumor is divided into three equal fan-shaped regions, and each region is covered by one ablation sphere. The center of each ablation sphere should be 0.8 cm (ie, [
] · r) from the center of this section (Fig 1). (b) The center of the fourth ablation sphere is located directly above the ablated area in a perpendicular direction and is about 0.9 cm (ie, [21/2 · r] – R) from the center of the tumor (Fig 1). Then, the target sphere, which is superimposed over the imaginary regular tetrahedron, can be completely covered by these four ablation spheres.
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Regular dodecahedron mode (three-segment overlapping ablation).—For a target sphere with a diameter of between 6.7 and 7.5 cm, a three-segment overlapping model is required. The target sphere is divided into three segments—specifically, the deep (ie, left), middle, and superficial (right) segments—which are parallel to each other. The thickness of the middle segment is about 4.0 cm. The deep, middle, and superficial segments are encompassed by three, six, and three ablation spheres, respectively, so that an approximately 7.5-cm spherical ablation zone might be achieved. Localization of the ablations is conducted as follows: (a) To ablate the middle segment, the maximum section of the tumor is divided into six equal fan-shaped regions. Each region is covered by one ablation sphere (Fig 5). The distance between the center of the ablation sphere and the center of the tumor should be kept at about 2.5 cm. (b) The deep and superficial segments of the tumor are ablated by using three ablation spheres in a similar manner. Then, the target sphere can be completely treated with 12 ablations (Fig 5).
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Protocol for ellipsoidal and irregularly shaped tumors.—In cases of ellipsoidal and irregularly shaped tumors, the spherical tumor protocol can be modified as follows: When the two short axes of an ellipsoidal tumor are shorter than 4.0 cm, we use several 5-cm ablation spheres overlapped along the longest axis. When the two short axes are 4.0 cm or longer, we regard each tumor as a regular spherical tumor that has a diameter that is equal to the longest axis of the ellipsoidal tumor but reduce the number of ablations according to the short axis of the tumor. The tumors 6.6–7.0 cm in diameter that we encounter in our clinical practice usually are ellipsoidal.
We also adopted a three-segment overlapping or regular prism model to ablate these tumors. For irregularly shaped tumors, the main part of the tumor is ablated by using the spherical or ellipsoidal tumor protocol, whereas the remaining irregular and protruding parts of the lesion are treated by using some small supplementary ablation spheres. It is conceivable that fewer ablation spheres could be used to treat ellipsoidal and irregularly shaped tumors as compared with the number of spheres needed to treat spherical tumors of the same size.
Electrode Placement
One ablation sphere is produced by a single placement of the RF electrode. It should be noted that in our study, the actual site of the electrode tip was not exactly at the center of the ablation zone, but rather it was 1.5 cm from the center. The center of the ablation zone was considered the target site. Either the electrode tip was inserted 1.5 cm proximal to the target site or the tip was first placed at the target site and then withdrawn 1.5 cm along the scaled puncture line before the nine prongs were deployed. We usually inserted the electrode into the tumor surface and then deployed the prongs to ablate the superficial part of the tumor. The relationship between the target site and the actual site of the electrode tip may be different for different RF electrodes.
A key step in accomplishing multiple overlapping ablations is the accurate placement of the electrode. On the basis of the described mathematic models, we first identified the maximum section of the tumor and determined the target sites of the electrode in the middle part of the tumor. We then rotated the US scanning plane or performed perpendicular US scanning to determine the target sites in the deep and superficial parts of the tumor (Fig 3), which were considered the lateral parts of the tumor in different scanning planes.
When the ablation was started, we often ablated the deepest parts first and the superficial parts last to avoid imaging disturbances caused by hyperechogenic gas artifacts generated from boiling tissue. If the tumor was near major structures, such as the diaphragm, gallbladder, or bowel, we preferred to ablate the area adjacent to these structures first. After establishing that the prongs were placed in the appropriate positions, we activated the RF generator to begin the ablation. Generally, the extent of gas artifact generated from the RF ablation decreased 2–3 minutes after each ablation. After this period, we performed another ablation in the tumor. This strategy minimized disturbances from gas artifacts and facilitated precise electrode placement during RF ablation.
Other crucial factors for electrode placement were considered: (a) We aimed for precise placement of the electrode with reference to the surrounding anatomic structures during the RF procedure. In large tumors at the surface of the liver or tumors in which there was no marker for reference, we used adjuvant measures to achieve precise positioning of the RF electrode. For example, two or three very small needles were inserted into the target sites to serve as markers for the electrode placements (Fig 6). (b) We monitored the actual site of the electrode tip by performing multiplane scanning from different directions after placing the electrode. (c) Replacement electrodes or adding a number of electrode placements was required when tissue was insufficiently ablated because the electrode tip deviated from the predetermined position.
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Clinical Subjects
This clinical study was approved by the institutional review board of the School of Clinical Oncology, Peking University. Written informed consent was obtained from all patients prior to their treatment.
From December 1999 to February 2003, 212 outpatients with 422 hepatic tumors (247 HCCs and 175 MLCs) underwent US-guided percutaneous RF ablation in our US department. One hundred twenty-one tumors larger than 3.5 cm in diameter in 110 consecutive patients (mean age, 58.4 years ± 11.5 [SD]; age range, 24–78 years) who were treated by using the described mathematic ablation protocol were enrolled in this study. Sixty-seven patients were men (mean age, 57.9 years ± 12.4; age range, 24–78 years), and 43 were women (mean age, 60.3 years ± 8.6; age range, 47–77 years). According to unpaired t test results, there was no significant difference in mean age between the male and female patients (P = .227). The mean diameter of all tumors was 4.75 cm ± 0.93 (range, 3.6– 7.0 cm).
Of the 110 patients enrolled in the study, 69 had 74 HCCs and 41 had 47 MLCs. For all patients, proof of the malignancy of at least one hepatic lesion was obtained at US-guided fine-needle aspiration biopsy. Of the 69 patients with HCCs, 61 (88%) had stage III or IV tumors (TNM system). Twenty-six of these 69 patients had Child-Pugh class A; 38, Child-Pugh class B; and five, Child-Pugh class C cirrhosis. Of the 41 patients with MLCs, 24 (58%) had hepatic metastasis from colorectal carcinoma and 17 (41%) had hepatic metastasis from other primary cancers: six from gastric esophageal cancer, four from lung cancer, four from breast cancer, two from intestinal leiomyosarcoma, and one from pancreatic cancer.
Imaging and Ablation Techniques and Equipment
Two radiologists (M.H.C., K.Y.) performed pretreatment measurements of the malignant hepatic tumors by using US. The maximum height, maximum length, and maximum depth of the tumor were measured by using multiplane scanning, and the maximum size of the tumor was determined by consensus between the two radiologists. Tumor size was the most important parameter used for protocol selection.
All tumor measurements and RF treatments were performed by the same two radiologists (M.H.C., K.Y.), each of whom had more than 3 years of experience in RF ablation and 10 years of experience in US-guided liver interventions. The treatments were performed with conscious sedation (82 patients) or general anesthesia (28 patients). Conscious sedation was induced with intravenous administration of 2.5–5.0 mg of midazolam (Roche; Basel, Switzerland) and 50–100 µg of fentanyl (Fentaini; Renfu, Yichang, China). Local infiltration anesthesia was induced by using 5–15 mL of 1% lidocaine (Liduokayin; Yimin, Beijing, China). When the tumor was adjacent to the diaphragm or the liver surface, the patient was given an intravenous bolus of propofol (Diprivan; Zeneca, Macclesfield, United Kingdom) (1–2 mg/kg) and fentanyl (50–100 µg) to induce general anesthesia in combination with local anesthesia.
The patients were conscious when the electrode was placed. Their vital signs, such as blood pressure, heart rate, respiratory function, and oxygen saturation, were continuously monitored during the procedure. Twenty-six patients were hospitalized for 1–3 days after the procedure. The remaining patients were discharged since there was no evidence of active bleeding seen on the US scans obtained 2–4 hours after treatment.
The RF system used in this study was a 460-KHz generator unit (Model 1500) that is capable of delivering a maximum power of 150 W through a 14-gauge electrode. The electrode contained nine hook-shaped prongs that could be deployed from the central needle cannula. Five of the nine prongs contained a thermocouple at the tip, and this array-electrode (Starburst XL; RITA Medical Systems) enabled the ablation of a 5.0-cm region. A spherelike coagulation area of 5.0 cm in diameter could be produced when the electrode was inserted into the tumor and nine prongs were deployed from the cannula. The time required to produce a 5-cm ablation sphere ranged from 20 to 25 minutes (24). The entire RF procedure lasted 1–5 hours, depending on the tumor size.
Real-time US (Aloka SSD-2000; Tokyo, Japan) was performed by using 3.5–5.0-MHz small-sector convex probes equipped with attachments for biopsy and electrode insertion. A Technos US scanning unit (Esaote, Genoa, Italy) also was used in a few cases.
All CT examinations were performed by using a helical scanner (Plus 4; Siemens, Erlangen, Germany) with 5-mm collimation and 7.5-mm/sec table speed. A total of 100 mL of nonionic contrast material (iohexol, 300 mg of iodine per milliliter, Omnipaque; Nycomed Amersham, Shanghai, China) was administrated at a rate of 3 mL/sec with a power injector (OP 100; Medrad, Pittsburgh, Pa). The CT images were acquired before and 25 seconds (during the hepatic arterial phase) and 60 seconds (during the portal venous phase) after the iohexol injection.
Assessment of Therapeutic Efficiency
To evaluate the tumor response to RF therapy, contrast-enhanced CT was performed 1 month after the treatment. Two patients underwent magnetic resonance imaging because they were allergic to the CT contrast material. To evaluate the response of comparatively large tumors, additional CT scans were obtained within 1 day after the treatment to determine whether there was any remaining malignant tissue that would require a second ablation session. The ablation was considered a success on the basis of all of the following findings at follow-up CT: (a) no contrast enhancement was detected within or around the tumor, (b) the margins of the ablation zone were clear and smooth, and (c) the ablation zone extended beyond the tumor borders (19,26).
Subsequently, patients were followed up with repeat CT every 2–3 months during the first year and then every 4–6 months after the first year. Contrast enhancement that was detected in the ablation zone on follow-up CT scans was considered to represent local tumor recurrence. If the CT scan showed no contrast enhancement but there were abnormal tumor markers (ie, 
-fetoprotein or carcinoembryonic antigen) and an abnormal vascular area was detected at color Doppler US, a multiple-core-needle biopsy specimen was obtained to assess for possible tumor recurrence in the highly suspicious area. However, only a positive biopsy result was useful for diagnosis.
One author with more than 3 years experience in liver CT (Y.D.) and two other radiologists, who had more than 10 years experience in liver CT, retrospectively interpreted the CT images without knowledge of the patients’ clinical information. In all cases, consensus agreement among the three radiologists was used to determine the therapeutic efficiency of the ablation treatment. Residual tumor tissue and local tumor recurrence were re-treated if the patient’s physical condition was strong enough for him or her to safely undergo another RF ablation session.
Statistical Analyses
The Fisher exact test was used to analyze the effect of tumor type on local tumor recurrence rate. For each patient, the time from RF ablation treatment to first local tumor recurrence or death was modeled by using Kaplan-Meier analysis. The mean recurrence-free survival was estimated from the survival curve. The level of significance was set at .05 for all tests. SPSS statistical analysis software (SPSS, Chicago, Ill) was used.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTSDISCUSSIONAPPENDIX REFERENCES |
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Twenty-five patients underwent a total of 38 re-treatments for local tumor recurrence: 17 patients underwent one re-treatment, and eight underwent two to three re-treatments. Of these 25 patients, six with MLC and four with HCC died 6–22 months after the re-treatments owing to extrahepatic metastases or hepatic dysfunction. The remaining 15 patients were still alive with tumor necrosis at the time this article was submitted for publication.
Seven (6.4%) of the 110 patients had major complications. One patient had MLC, from pancreatic cancer, that was adjacent to the liver surface and developed bile leakage along the electrode track 1 week after treatment. One patient with HCC developed renal colic 2 days after treatment owing to a ureter stone, which the RF treatment may have caused to shift from the kidney to the ureter. One patient, who had gallbladder stones and HCC near the gallbladder, developed subacute cholecystitis after the RF treatment. Another patient with recurrent HCC had a subcapsular hemorrhage during the third ablation session. These four patients recovered spontaneously.
A hepatic abscess occurred in one patient, who had a cyst near the MLC. The cyst suppurated after the treatment and later was drained with US guidance. One patient with HCC had tumor seeding along the electrode track after RF treatment and subsequently received radiation therapy. One patient had a colon perforation 7 days after the treatment. In this patient, who was undergoing re-treatment for HCC recurrence, the hepatic flexure of the colon may have been damaged by the heat from the nearby focus during the RF ablation. This patient required surgical intervention.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTSDISCUSSIONAPPENDIX REFERENCES |
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Number of Electrode Placements
We used a protocol derived from a mathematic model to determine the number and position of electrode placements required to achieve a satisfactory result. The objective was to optimize complete ablation of the targeted lesion while the surrounding normal tissues remained minimally injured. Although this ablation protocol was developed on the basis of a theoretic 5.0-cm ablation sphere, the number of electrode placements can also be calculated by using mathematic formulas for a 3.0- or 4.0-cm ablation sphere.
In general, the mathematic results of the protocol should be considered an important reference, especially in cases of large spherical tumors, for which the number of electrode placements needs to be equivalent to the calculated theoretic result. In some cases, however, fewer electrodes were placed than were calculated mathematically because of particular characteristics of the tumors.
Overlapping Mode and Electrode Placement
It is very important to design an optimal overlapping mode of multiple ablations in RF treatment. Otherwise, there will be residual tumor after the ablation. For instance, our mathematically calculated results indicated that a tumor target of 5.0–5.3 cm in diameter could be completely treated with four ablation spheres if the overlapping mode of the regular tetrahedron was used. Before the mathematic protocol was developed, we used a quartering ablation mode, in which all of the centers of the four 5.0-cm spheres were distributed on the maximum section of the tumor to ablate a target sphere of 5.0–5.3 cm. This resulted in residual tumor tissue at the two poles of the target. Two of three sphere-like tumors 4.0–4.3 cm in diameter were incompletely ablated.
The treatment of spherical tumors larger than 5.6 cm remains a challenge: Usually with treatment some areas are not ablated while other areas are overablated. We created a model with a three-segment overlapping geometry, which was easier to use clinically and could yield a composite ablation volume similar to that yielded by using a regular dodecahedron with the aid of our clinical experience. With this model, we treated seven tumors 5.7–7.0 cm in diameter. Six of these tumors were successfully treated. Among these seven patients, three could not tolerate the ablation for the duration of the procedure (lasting 4–5 hours) and completed the treatment in multiple sessions performed within 2–6 days. For such large tumors, we advocate the use of transcatheter arterial chemoembolization or chemotherapy first to increase the effectiveness of RF ablation (27).
With regard to electrode placement, when treating tumors in the superficial area of the liver, it appears to be safer to use multiple skin punctures for electrode placement rather than perform multiple ablations through a single skin puncture. In our practice, five patients with tumors near the liver surface had four or five electrode insertions at only one skin puncture site, and complications were observed in two of these individuals. One of the two patients had electrode track seeding, and the other had a bile leakage.
Assessment of Clinical Application
The problems with ablating a large tumor are not trivial. Livraghi et al (15) described their experience treating 126 primary liver lesions 3.1 cm in diameter or larger (mean diameter, 5.4 cm) in 114 consecutive patients. On the basis of the CT results obtained at least 5 months after treatment, they reported achieving complete tumor necrosis in 60 (47.6%) of 126 lesions. Solbiati et al (6) reported that 13 (68%) of 19 MLCs 4.1 cm in diameter or larger had local recurrence during a follow-up period of 6–52 months. In the current study, we treated 121 hepatic tumors (mean diameter, 4.75 cm ± 0.93). According to the CT results obtained 1 month after the treatment, the ablation was successful in 106 (87.6%) of the 121 tumors. During the follow-up period of 3–26 months, the local recurrence rate was 24.0% (29 of 121 tumors). The potentially shorter period of assessment to determine successful ablation and the shorter follow-up may have contributed to the difference in results among these studies. Nevertheless, the results of our present study were more favorable than our early study results (17). The mathematic protocol seemed to have had a therapeutic benefit in the RF treatment of large liver tumors.
It has been reported that surgical excision that yields a treated region with a tumor-free margin of less than 1 cm may result in a higher rate of local tumor recurrence (28). Thus, many investigators believe that a 1-cm tumor-free margin should be achieved by using RF ablation. This means that the RF ablation device used in our study can safely destroy only a tumor that is no larger than 3.0 cm in diameter with a single electrode placement. Our experience in treating 121 tumors larger than 3.5 cm during the past 3 years showed that for tumors with a clear margin or capsule, ablation with at least a 0.5-cm "ablative margin" resulted in a high response rate. This can be achieved by using an optimal preoperative protocol and accurate electrode placements. However, for tumors with an unclear or irregular border or tumors with a rich blood supply, the ablative margin should be extended to 1 cm or greater. For example, most of the MLCs examined in the current study had indefinite borders or irregular shapes; therefore, the ablation zone was extended to 1 cm or more.
Limitations
The described RF ablation protocol was limited by the fact that it is not always easy to determine the accurate position and location for the precise placement of the electrode, especially when multiple ablations need to be performed on the same relatively large lesion. Thus, it is necessary to thoroughly understand the three-dimensional features of the tumor by adjusting the imaging angles to view different sections. Adequate skills to perform US-guided puncture for electrode placement also are important.
Tumor ablation protocols should be designed according to the various features of the tumors. Factors such as an abundant blood supply, an undesirable location (such as the subdiaphragmatic region), the rigid texture of some tumors, and limitations of the prong deployment due to adjacent major structures can contribute to the failure to achieve complete tumor ablation (17,22,29).
In summary, we developed a new mathematic model, an overlapping mode, and an electrode placement process to standardize protocols for the treatment of large liver tumors with RF ablation. It is hoped that this information will be helpful in improving the efficiency of RF treatment.
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APPENDIX |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTSDISCUSSIONAPPENDIX REFERENCES |
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In our calculations, it was assumed (a) that the diameter of a target sphere, including the tumor plus the surrounding 0.5-cm tumor-free margin, was 2R (with R being the radius of a target sphere and r being the radius of a single ablation sphere; in this study, r = 2.5 cm); (b) that the diameter of a single ablation sphere was 2r (in this study, 2r = 5.0 cm); and (c) that the number of ablation spheres required to completely ablate the target sphere was n. On the basis of the mathematic principle of overlapping spheres, a polyhedron was inscribed in the target sphere, and each side of the polyhedron was covered by one ablation sphere.
We then deduced the following mathematic calculation: If the diameter of each ablation sphere (2r) equals the diameter of a circle circumscribing the largest side of the polyhedron and the center of an ablation sphere is placed on the center of each side of this polyhedron, then the target sphere circumscribing the imaginary polyhedron could be completely covered. The diameter of this circumscribed sphere represents the size (2R) of the largest possible target sphere that could be adequately treated by performing multiple overlapping ablations (Fig 2).
A regular prism and a regular polyhedron with fewer sides and a regular geometric configuration are two ideal mathematic models that can be used to derive a protocol for the ablation of different-sized spherical tumors.
Calculation of Number of Ablation Spheres
The number of ablation spheres was calculated by using a regular prism model. With a 5-cm ablation device, as the diameter of the target sphere (2R) increases from 5.6 to 6.6 cm, the ablation sphere number (n) increases accordingly from five to eight, with n being almost linearly proportional to 2R. When the diameter of the target sphere increases from 6.6 to 7.0 cm, the number of ablations increases dramatically, from eight to 18. These calculations suggest that the overlapping of adjacent ablation spheres increases to such an extent that the regular prism model becomes no longer suitable for a target sphere larger than 6.6 cm in diameter. Therefore, other models need to be considered. By using the regular polyhedron model, target spheres ranging from 5.0 to 5.3 cm in diameter and from 6.7 to 7.5 cm in diameter would be completely treated by performing four and 12 ablations, respectively.
Formula of the regular tetrahedron model.—For four ablation spheres, the following equation can be used:
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Formula of the regular prism model.—To determine the required number of ablation spheres (n) of different sizes (2r) when the target size (2R) is given, the following equation can be used:
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Formula of the regular dodecahedron model.— For 12 ablation spheres, the following equation can be used: 2R = 1.5 · 2r. This means that the largest size of a target sphere that could be completely treated with 12 ablation spheres would be 7.5 cm.
Principles of Overlapping Target Spheres
Once an appropriate polyhedron is selected, the next step is to precisely superimpose the spherical target over this imaginary polyhedron. If an ablation is performed on each side of this polyhedron, then the center of the ablation sphere should be the same as the center of the side so that the target sphere can be completely ablated.
Regular tetrahedron.—A regular tetrahedron has four sides. The centers of three sides are located in the same section, and the center of the fourth side is directly above or below that section (Fig 1). An overlapping mode was designed accordingly for this three-dimensional feature.
Regular prism.—The geometric structure of the regular prism is perfectly symmetric. The centers of all sides of a regular prism are located in two planes that are perpendicular to each other. This means that the centers of the spheres on all lateral sides of the regular prism are located in the same plane and the other two centers on the upper and lower sides are located in the perpendicular plane (Fig 2).
Regular dodecahedron (three-segment overlapping).—The regular dodecahedron model is technically impossible to execute clinically by using RF ablation because its three-dimensional structure is very complex. On the basis of both clinical experiences and computer aid, we designed a three-segment overlapping model that has proved to be more applicable for treating target spheres with diameters of 6.7–7.5 cm.
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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Author contributions: Guarantor of integrity of entire study, M.H.C.; study concepts, M.H.C., W.Y., K.Y.; study design, M.H.C., W.Y.; literature research, M.H.C., Y.D.; clinical studies, M.H.C., K.Y.; data acquisition, M.H.C., M.W.Z., W.Y.; data analysis/interpretation, M.H.C., Y.D., M.W.Z., W.Y.; statistical analysis, W.Y., J.B.L., Y.D.; manuscript preparation, M.H.C., K.Y., J.B.L., L.S.; manuscript definition of intellectual content, M.H.C., Y.D.; manuscript editing, M.H.C., W.Y.; manuscript revision/review, M.H.C., W.Y., J.B.L., L.S.; manuscript final version approval, all authors
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REFERENCES |
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