Therapeutic analysis of Intrabeam‐based intraoperative radiation therapy in the treatment of unicentric breast cancer lesions utilizing a spherical target volume model

Abstract It is postulated that the outcomes in treating breast cancer with intraoperative radiotherapy (IORT) would be affected by the residual cancer cell distribution within the tumor bed. The three‐dimensional (3D) radiation doses of IntrabeamTM (IB) IORT with a 4‐cm spherical applicator at the energy of 50 and 40 kV were calculated. The modified linear quadratic model (MLQ) was used to estimate the radiobiological responses of the cancer cells and interspersed normal tissues with various radiosensitivities. By comparing the average survival fraction of normal tissues in IB‐IORT and uniform dose treatment for the same level of cancer cell killing, the therapeutic ratios (TRs) were derived. The equivalent uniform dose (EUD) was found to increase with the prescription dose and decrease with the cancer cell infiltrating distance. For 50 kV beam at the 20 Gy prescription dose, the EUDs are 18.03, 16.49 and 13.56, 11. 29, and 9.28 Gy respectively, for 1.5, 3.0, 6.0, 9, and 15.0 mm of the cancer cell infiltrating distance into surrounding tissue. The dose rate of 50 kV is at least 1.87× higher than that of 40 kV beam. The EUDs of 50 kV beam are up to 15% higher than that of the 40 kV beam. The TR increases with the prescription dose, but decreases with the distance of cancer cell infiltration distance. Average TRs of 50 kV beam are up to 30% larger than that of 40 kV beam. In conclusion, IB‐IORT can provide a possible therapeutic advantage on sparing more normal tissue compared with the External Beam IORT (EB‐IORT) for shallowly populated unicentric breast lesion. Our data suggest that IB‐IORT dose size should be adjusted based on the individual patient's cancer cell infiltrating distance for delivering an effective dose, one dose‐fits‐all regimen may have undertreated some patients with large cancer infiltrating distance.


Abstract
It is postulated that the outcomes in treating breast cancer with intraoperative radiotherapy (IORT) would be affected by the residual cancer cell distribution within the tumor bed. The three-dimensional (3D) radiation doses of Intrabeam TM (IB) IORT with a 4-cm spherical applicator at the energy of 50 and 40 kV were calculated.
The modified linear quadratic model (MLQ) was used to estimate the radiobiological responses of the cancer cells and interspersed normal tissues with various radiosensitivities. By comparing the average survival fraction of normal tissues in IB-IORT and uniform dose treatment for the same level of cancer cell killing, the therapeutic ratios (TRs) were derived. The equivalent uniform dose (EUD) was found to increase with the prescription dose and decrease with the cancer cell infiltrating distance.
For 50 kV beam at the 20 Gy prescription dose, the EUDs are 18.03, 16.49 and 13.56, 11. 29, and 9.28 Gy respectively, for 1.5, 3.0, 6.0, 9, and 15.0 mm of the cancer cell infiltrating distance into surrounding tissue. The dose rate of 50 kV is at least 1.879 higher than that of 40 kV beam. The EUDs of 50 kV beam are up to 15% higher than that of the 40 kV beam. The TR increases with the prescription dose, but decreases with the distance of cancer cell infiltration distance. Average TRs of 50 kV beam are up to 30% larger than that of 40 kV beam. In conclusion, IB-IORT can provide a possible therapeutic advantage on sparing more normal tissue compared with the External Beam IORT (EB-IORT) for shallowly populated unicentric breast lesion. Our data suggest that IB-IORT dose size should be adjusted based on the individual patient's cancer cell infiltrating distance for delivering an effective dose, one dose-fits-all regimen may have undertreated some patients with large cancer infiltrating distance.

| INTRODUCTION
The standard of care currently for locoregional treatment of breast cancer is breast conserving surgery followed by whole-breast external beam radiotherapy (EBRT). It has been shown that postoperative radiotherapy significantly lowers local recurrence rates and translates into improved survival. 1 Pathological analyses have shown that up to 90% of microscopic remainders of tumor cells after breast conserving surgery are observed in an area of 4 cm surrounding the macroscopic tumor edge, which is the region with the highest probability of local recurrence. 2 An alternative to standard EBRT is intraoperative radiation therapy (IORT) in which at the time of breast conserving surgery a single dose of radiation is delivered. 3 Unlike other types of radiotherapy, intraoperative radiotherapy (IORT) delivers a high single dose of radiation to the area around the tumor bed. Fowler 4 postulated that breast cancer has an a/b ratio of 4, rather than the ratio of 10 that is characteristic of most squamous cell carcinomas. The lower a/b ratio corresponds to a lower radiosensitivity to low doses, favoring a high single-dose treatment, such as IORT. 5 The use of a 20 Gy dose of IB-IORT (Carl Zeiss Surgical, Oberkochen, Germany) as a monotherapy following breast conserving surgery was compared to the standard of a 50 Gy dose of EBRT in the TARGIT-A clinical trial. 6,7 In this still ongoing trial, patients were treated with either IB-IORT or EBRT and outcomes were compared. 8 Based on this trial and other studies, IB-IORT has shown both benefits and drawbacks as compared to EBRT. Hypothesized benefits include the increased sparing of normal tissues and a shorter radiotherapy course from the 5 to 6 week course of EBRT. This shorter treatment option has been hypothesized to improve patient compliance, cost, and overall experience. 9 Since the 20 Gy dose of IB-IORT is biologically much greater than the fractional doses of EBRT, initially there was concern for an increase in toxicity, but studies have shown no treatment related mortality or excess morbidity including problems with wound healing, infection, or cosmetics. 3,9 One major difference between IB-IORT and EBRT is breast changes such as fat necrosis and other distinct mammographic changes, which can complicate future diagnostic mammography, although usually, these changes are easily discernible from recurrent tumors. 9 Because of this, IB-IORT has been shown to be both safe and feasible.
The major drawback of IORT is a higher overall recurrence rate of breast cancer when compared to EBRT. With a median follow-up of 29 months, Silverstein et al. 6 reported that the 5-year recurrence rates for the IB-IORT versus EBRT patients in the TARGIT-A trial were 3.3 and 1.3 %, respectively, P = 0.042. Local recurrence-free survival was 92.9% for those treated with IB-IORT and 92.5% for those treated with EBRT, P = 0.35. It is possible that with a select subgroup of patients, the difference in recurrence is small and acceptable and the benefits outweigh the risks. 6,7,10 As this study will show, different treatment outcomes may have resulted from variation in cancer cell infiltrations.
The purpose of this study was to use a radiobiological model to evaluate the therapeutic impact of IB-IORT on the cancer cells and normal tissue, and to compare IB-IORT with the uniform dose EB-IORT for the same spherical target volume without expanding the treatment margin. In this study, EB-IORT is modeled as a hypothesized uniform dose radiotherapy which may be achieved by an external beam machine such as Mobetron (IntraOp Medical Corporation, 570 Del Rey Avenue, Sunnyvale, CA, USA). This study will not describe the particular dosimetric characteristics of Mobetronbased EB-IORT, but instead describe it as a single-fraction uniform dose radiotherapy delivered immediately after lumpectomy. The radiobiological modeling results derived will be used to critically review the clinical data of TARGIT-A clinical trial and to postulate how these factors may have related to the results found in the treatment and ongoing follow-up. The conclusions derived from this study for breast cancer are considered to be applicable for other sites of IB-IORT treatments.

IB-IORT
The IB-IORT is designed to deliver a spherical dose to the surrounding tissue via its spherical applicator and electronic brachytherapy source (Fig. 1). Based on the commissioning data, the three-dimensional (3D) radiation dose of the IB-IORT using a 4-cm diameter Intrabeam spherical applicator was calculated for the 50 and 40 kV beams. When using IB-IORT, a large dose is usually prescribed at the applicator surface and the radiation dose curve drops very rapidly with distance. For example, for a 50 kV beam with a 4 cm spherical applicator, the dose drops to 7 Gy at 1 cm and to 2 Gy at 2 cm F I G . 1. Schematic diagram of Intrabeam IORT for breast cancer. The target volume was assumed to be spherical. The dose drops with the distance exponentially. The cancer cell density variation with distance was assumed to drop and be a half-Gaussian or linear.
| 185 from the 20 Gy at the surface. Figure 2(a) shows the radial dose rate function comparison between 40 and 50 kV beams of IB-IORT with a 4 cm spherical applicator. The dose rate of 50 kV beam is at least 187% of the 40 kV beam, this makes the 50 kV beam more efficient in the operation room treatment, since 50 kV beam will only use half of time of 40 kV beam to deliver the same dose. Figure 2(b) demonstrates the normalized radial dose function comparison between IB-IORT (with a 4 cm spherical applicator) and a 125 I brachytherapy source. 11 The dose of IB-IORT along the radial distance drops four times faster than that of 125 I brachytherapy source, which indicated that IB-IORT is suitable for dealing with superficially populated can- introduced by Guerrero and Li 15 for describing large dose radioresponses, is used in this study to estimate survival fractions of cell lines after the IB-IORT. The MLQ model can be expressed as Where the dose protraction factor dD(x) was included. The parameter d is a histological parameter that is calculated based on the effective repair rate, k eff = k + dD(x). The dose protraction factor describes the decrease in cell killing induced by treatment. As dose decreases, the MLQ model becomes the classical LQ model.
In our study, the survival fractions were calculated at the prescrip- Where SF(x i ) is the survival fraction at the depth x i calculated by the is only applicable under the assumption of independent clonogenes and the cell communications were neglected. This assumption is more applicable to interspersed cancer cells than to normal tissues. 16 Using the average survival fraction of the cancer cell, SF, an equivalent uniform dose (EUD) for a given scenario was then calculated by solving the following equation: The clinical meaning of EUD is, in order to achieve the same level of cancer cell killing across the target volume through a uniform dose radiotherapy, a uniform dose of EUD should be given. In addition, using EUD, 3D dose distribution of IB-IORT, and normal cell population function f n (x i ) (f n (x i ) = 1-f c (x i )), the average survival fractions of the three types of normal tissues (radiosensitive, moderate radiosensitive, and radioresistant) were, respectively, calculated in the EUD and IB-IORT fields. The therapeutic ratio (TR) of this procedure was then defined 17  A TR >1 implies that a greater number of normal cells survive in the IB-IORT than in the EB-IORT at the same rate of cancer cell killing, thus a therapeutic advantage of the IB-IORT over the traditional EB-IORT.

2.B | Cell types and spatial distributions
The radiobiological response of breast cancer has been studied extensively in past decades. 4   Gaussian cancer cell distribution cut off was set at 3 9 r, because at the distance of 3 9 r, the function percentage has dropped to less than 1.0% from 100% at the surface (0 mm). In this study, the minimum cancer cell density fraction was assumed to be as low as 0.01% at the excision surface (0 mm), so the density fraction at 3 r would be 0.0001% (1.0% 9 0.01%), which is almost undetectable.
In the second trend, the cancer cell density was assumed to lin- It should be noted here that there is no experimental data to show that the actual residual cancer cell distribution after lumpectomy for most breast patients is half-Gaussian or linear; we used these assumptions simply because the half-Gaussian cancer cell distribution was found in other cancer sites. 25 Also, a uniform cancer cell distribution seems unlikely given the clinical findings that the recurrence rate decreased with an increase in surgical margins and drastically declined at 2 mm margin. 21,22 In addition, a half-Gaussian distribution is simple and it also follows the IB-IORT dose fall-off, therefore it is speculated that the cancer cell killing and normal  tissue sparing would benefit from the IB-IORT dose fall off with this pattern, since the region with the largest cancer cell burden will get the largest dose for intensive killing.

3.A | Equivalent uniform dose
The Equivalent uniform dose (EUDs) for each cancer cell depth were calculated for a list of prescription doses ranging from 8 to 25 Gy for different sensitivities as shown in Table 2. The results demonstrate that the EUD is dependent upon the distribution of the cancer cell population and prescription doses, but not on the cancer cell radiosensitivities. In addition, since the 40 kV beam is also available, we provided a comparison between two energies in Table 2.
A further test indicated that when the cancer cell density fraction at the surface was varied (for example, from 10 to 0.01%) in any given cancer cell distribution, the EUD remains the same.
In addition, the efficiency of 40 kV beam was tested using the  Table 3 shows the Therapeutic Ratios (TRs) of different breast cancer cells mixed in different normal tissues at the 6 mm cancer cell infiltration (standard deviation of r = 2 mm). The TR of the IB-IORT was found to be strongly dependent upon the prescription dose and cancer and normal cell radiosensitivities.

3.B | Therapeutic ratios of IB-IORT
The TR was also found to be weakly dependent upon the can-  C1 is the acutely responding breast cancer (a = 0.3, b = 0.03), C2 is the slow responding breast cancer (a = 0.2, b = 0.052). G_3.0 mm means the cancer cell distribution was assumed to be half-Gaussian, the cancer infiltrating distance is assumed to be 3 mm (3r = 3 mm).

3.C | Comparison between the half-Gaussian and linear cancer cell distributions
The EUDs and TRs calculated separately using the half-Gaussian and linear cancer cell distributions are compared in Figs. 4 and 5 for the 50 kV beam. The half-Gaussian distribution is seen to have a larger EUD and TR at the same cancer cell infiltrating distance and same prescription dose than the linear distribution. In addition, at the same prescription dose the 6-mm cancer cell infiltrating distance (G_6 mm or L_6 mm) was found to have the largest TR among all cancer cell infiltrating distances. This phenomenon was seen in both the half-Gaussian and linear distributions (Fig. 5).

| DISCUSSION
The study evaluated the dosimetric metrics and normal tissue sparing effects of IB-IORT, some important knowledge has been theoretically derived through radiobiology modeling. First remarkable finding is that, although the two types of cancer cells modeled have different radiosensitivities, our study indicated that the acutely responding cancer cell has almost the same EUD as the slow responding cancer cell, with a difference of only 0.5%. Second finding is the EUD is only weakly dependent on the cancer cell density fraction; the EUDs from the same cancer cell distribution were found to have varied only by 3% if the density fraction at the surface is decreased from 10 to 0.01%. Thus, the radiosensitivity and density fraction of cancer cells do not play an important role in the breast IB-IORT treatments, if the EUD is considered to be the dosimetric end point. However, the EUD and TR were found to depend strongly on the cancer cell infiltrating distance, shallower breast cancer cells can be more effectively treated by IB-IORT due to its unique dosimetric feature.
Because the dose rate of the 40 kV beam is only about 53% of the dose rate of the 50 kV beam, the 50 kV beam is more efficient to treatment patients in the operation room.
Our study is not designed to investigate TARGIT A trial, but the results can be used to critically review the trial data. Despite many advantages such as convenience, better patient compliance and lower radiation dose to normal structures, the major drawback reported in the breast IB-IORT is that, the TARGIT-A clinical trial reported that the local recurrence rate was slightly higher in IB-IORT than in EBRT, although this difference was not significant. 6 The dosimetric and radiobiology reasons behind the high recurrence rate could be explained by our EUD data. As shown in Table 2 and T A B L E 3 Therapeutic ratios (TR) of IB-IORT for two types of breast cancer cells. Each type of cancer cells were interspersed in one of three types of normal tissues. The assumed remaining cancer cell density is 0.01% at the surgical cavity surface; the cancer cell distribution is half-Gaussian with a standard deviation of r = 2 mm, namely G_6.0 mm. Two energies of beams (50 and 40 kV) were evaluated.  In addition, it was found that in Table 5, in T A B L E 4 Therapeutic ratios (TR) of IB-IORT at 0.01, 1, and 10% of the remaining cancer cell density fraction at the surgical cavity surface for both the 50 and 40 kV beams. The standard deviation of the half-Gaussian cancer cell distribution is r = 1 mm, namely G_3.0 mm. The data are the average of both types of breast cancer cell lines (breast cancer cell 1 and 2) and three types of normal tissues (radiosensitive, moderate radiosensitive, and radioresistant).  29 indicated that the uncertainty for the scatter dosimetric correction in the breast HDR balloon treatment is at least 7%. We estimate the uncertainty from the breast IB-IORT scatter dosimetric correction is at the same level, also 7%. The cell culture study indicated the uncertainties of the cell radiosensitivity parameters of a and b could be up to 20%. 17 We assume those components are not correlated, thus the total uncertainty of the EUD and TR is estimated to be 31%.

| CONCLUSION S
Based on the radiobiology modeling results presented in our data, the IB-IORT has shown possible therapeutic advantages over If the cancer cell distributions could eventually become known before patient's treatment regimen is designed, for example, if we know the maximum cancer cell infiltrating depth of breast cancer in breast conserving treatment, then the treatment plan can be tailored for the specific situation and prescription dose could be adjusted to ensure a sufficient killing of cancer cells, then the recurrence rate can be reduced and the toxicity level can be lowered, and finally the patient will benefit from the treatment. A personalized IB-IORT treatment would likely improve treatment responses, reduce recurrence, and mitigate the radiation related complications.

CONFLI CTS OF INTEREST
The authors declare no conflict of interest. F I G . 5. TRs calculated by assuming the half-Gaussian and linear cancer cell distributions, respectively. Cancer cell density fraction at the excision surface was assumed to be 0.01%.