Comparison of Ray Tracing and Monte Carlo Calculation Algorithms for Thoracic Spine Lesions Treated With CyberKnife-Based Stereotactic Body Radiation Therapy

Abstract

Stereotactic body radiation therapy (SBRT) is an emerging technology for the treatment of spinal metastases, although the dosimetric impact of the calculation method on spinal dose distribution is unknown. This study attempts to determine whether CyberKnife (CK)-based SBRT using a Ray Tracing (RyTc) algorithm is comparable dosimetrically to that of Monte Carlo (MC) for thoracic spinal lesions. Our institutional CK-based SBRT database for thoracic spinal lesions was queried and a cohort was generated. Patients were planned using RyTc and MC algorithms using the same beam angles and monitor units. Dose–volume histograms of the planning target volume (PTV), spinal cord, esophagus, and skin were generated, and dosimetric parameters were compared. There were 37 patients in the cohort. The average percentage volume of PTV covered by the prescribed dose with RyTc and MC algorithms was 91.1% and 80.4%, respectively (P < .001). The difference in average maximum spinal cord dose between RyTc and MC plans was significant (1126 vs 1084 cGy, P = .004), with the MC dose ranging from 18.7% below to 13.8% above the corresponding RyTc dose. A small reduction in maximum skin dose was also noted (P = .017), although no difference was seen in maximum esophageal dose (P = .15). Only PTVs smaller than 27 cm³ were found to correlate with large (>10%) changes in dose to 90% of the volume (P = .014), while no correlates with the average percentage volume of PTV covered by the prescribed dose were demonstrated. For thoracic spinal CK-based SBRT, RyTc computation may overestimate the MC calculated average percentage volume of PTV covered by the prescribed dose and have unpredictable effects on doses to organs at risk, particularly the spinal cord. In this setting, use of RyTc optimization should be limited and always verified with MC.

Keywords

Ray Tracing Monte Carlo stereotactic body radiation therapy inhomogeneous tissue density lung–tumor interface

Introduction

Spinal metastases frequently occur in patients with disease from a variety of cancers and can lead to significant morbidity as well as adversely affect quality of life.¹ In this setting, external beam radiation therapy (EBRT) techniques have been used to target spinal disease to treat or prevent tumor-related complications, most importantly spinal cord compression, but also to palliate pain and prevent spine destabilization.² Fractionated EBRT is typically delivered through posterior beams, with or without supplemental anterior beams. Therefore, further dose escalation is limited by the tolerances to surrounding critical structures, particularly the spinal cord.³ In addition, significant numbers of patients may develop recurrence or progression after such treatment.⁴

Although EBRT is the standard treatment for spinal metastases in many cases, there are instances where stereotactic body radiation therapy (SBRT) techniques may be preferred. In the reirradiation setting, advances in image guidance and dose delivery have allowed SBRT techniques to safely deliver a second course of radiation therapy to spinal segments that have progressed after initial EBRT.⁵ In addition, primary treatment with SBRT may be considered in particular subsets of patients, including those with an isolated/limited spinal metastasis, patients with radioresistant tumor types, selected patients with postoperative residual disease, or when patients need to be treated quickly between cycles of systemic therapy.^2,6,7 In light of the encouraging data on pain control and quality of life,⁸ prospective randomized studies, including Radiation Therapy Oncology Group (RTOG) 0631, are systematically evaluating spinal SBRT to delineate the specific benefits, differences, and drawbacks of such techniques.

CyberKnife (CK)-based SBRT has emerged as an effective method to deliver ablative radiotherapy to extracranial sites,^3,9 particularly with its ability to minimizing target uncertainty through fiducial or bony landmark localization and real-time tracking.^10,11 Accurate dose–volume analysis ensures critical structures are adequately spared while delivering ablative doses to the areas at risk. However, additional uncertainty may be introduced by the inaccuracy of computational methods. In lung cancer, Ray Tracing (RyTc) algorithm has been shown to be less accurate than Monte Carlo (MC) algorithm in terms of dose calculation, primarily due to the inhomogeneous tissue density at the lung–tumor interface and the small fields employed.^11
–13 In response to these limitations, RTOG has mandated MC calculations in all further trials.

Unknown, however, is how calculation methods may affect other SBRT sites, including spinal metastases in the thoracic region. Quantifying the degree of error RyTc may introduce in treatment planning of spinal metastases is very important, particularly given the delicate balance between tumor coverage and organs at risk (OARs). Thoracic spinal disease may be particularly vulnerable to changes in calculation methods due to the proximity of lung–tissue interfaces. However, given the central location and size of some of these lesions, a significant dosimetric difference between RyTc and MC may not be appreciable.¹⁴ At the same time, MC optimization is computationally cumbersome, requiring significantly more time to carry out, particularly with lower uncertainty levels.¹⁴ With this in mind, we reviewed our institutional experience with thoracic spine SBRT to determine the impact of RyTc versus MC planning on tumor coverage and dose exposure to OARs.

Materials and Methods

Prior to initiating our study, approval was obtained from the institutional review board of our hospital system. Our departmental CK-based SBRT database was queried for patients treated for lesions involving the spine or paraspinal regions from July 2007 through December 2012.

All patients were deemed appropriate candidates for spinal SBRT by a multidisciplinary team, which included medical, surgical, and radiation oncologists. Of the 106 spinal lesions treated, 45 were outside the thoracic spine, 23 lesions were treated with a previous version of CK and were thus not analyzable, and 1 patient’s thoracic spine lesion treatment data were irretrievable, leaving 37 lesions available for this analysis. Two patients had separate lesions treated with CK and whose plans were optimized independently, each of which are included in this analysis.

The median patient age was 62 years, with a variety of tumor types, the most prevalent of which were nonsmall cell lung (25.7%), breast (14.3%), and colon cancer (11.4%; Table 1). Traditionally, radioresistant histological tumor types (renal cell carcinoma, sarcoma, and melanoma; total 8.6%) and nonmalignant tumors (hemangioma and schwannoma; total 8.6%) made up a minority of the population. Disease was isolated to the spine in 21.9% of patients with malignant histology.

Table 1.

Demographics.

Patient Characteristics	Patients (n = 35)
Age, years
Median	62
Range	(19, 92)
Karnofsky performance status (KPS)
Median	80
Range	(60, 100)
Origin
NSCLC	9 (25.7%)
Breast	5 (14.3%)
Colon	4 (11.4%)
H&N	4 (11.4%)
Noninvasive	3 (8.6%)
Radioresistant	3 (8.6%)
Other	7 (20.0%)
Extraspinal disease
Yes	25 (78.1%)
No	7 (21.9%)
Nonmalignant	3

Abbreviations: H&N, head and neck; NSCLC, nonsmall cell lung cancer.

Subsequently, all patients underwent CT-based planning, with scans spanning the entire area of interest, including the at-risk spinal segments. These images were then fused with a recent spine MRI using MIMvista (MIMvista Corp, Cleveland, Ohio). Treatment target volumes, including gross tumor volume, clinical target volume (CTV), planning target volume (PTV), and OARs, were contoured according to consensus guidelines.¹⁵ Specifically, a uniform expansion of the CTV of up to 3 mm was used to generate the corresponding PTV, with modifications made when adjacent to critical structures at the discretion of the treating physicians. Prescription doses were then determined by the treating physicians (Table 2), and dose constraints limited according to departmental guidelines. All plans were optimized, evaluated, peer reviewed, and approved based on RyTc methods derived on the Multiplan treatment planning system. All cases utilized Xsight spine (Accuray, Sunnyvale, California) for tumor tracking during treatment delivery.

Table 2.

Treatment Characteristics.

Previous Treatment	Lesions (n = 37)
Previous spine surgery
Yes	10 (27.0%)
No	27 (73.0%)
Previous EBRT
Yes	20 (54.1%)
No	17 (45.9%)
Dose, median	3750 cGy (range: 300-4500)
Current treatment
SBRT location
T1-T4	9 (24.3%)
T5-T8	4 (10.8%)
T9-T12	17 (45.9%)
Multiple levels	7 (18.9%)
Epidural disease present
Yes	24 (64.9%)
No	13 (35.1%)
SBRT prescription
Dose, median	1950 cGy (range: 1200-3500)
Prescription IDL	74% (range: 70-82)
# of beams, median	157 (range: 99-220)
Fractionation
# of fractions, median	3 (1, 5)
Single	15 (40.5%)
Daily	16 (43.2%)
Every other day	6 (16.2%)
PTV volume
Median	61.53 cm³ (range 1.83-332)

Abbreviations: EBRT, external beam radiation therapy; SBRT, stereotactic body radiation therapy; IDL, isodose line.

At the initiation of this study, all patient plans were uploaded back on the Multiplan (Accuray, Sunnyvale, California) treatment planning station. Plans optimized prior to 2010 could not be evaluated due to hardware and software upgrades to the CK machine, resulting in changes to the machine calibrations that could not be accurately reconstructed. Available plans were recalculated using an MC algorithm, with a clinically meaningful uncertainty level of 1.5% while maintaining the same beam arrangement and corresponding monitor units. Collimator sizes used during plan optimization included 7.5, 10, 12.5, 15, 20, 25, 30, 35, 40, 50, and 60 mm, though 50 and 60 mm collimators were used sparingly. Subsequently, the resulting dose–volume histograms (DVHs) were evaluated based on the original target volumes and OARs to determine the dose received, with particular attention to the PTV, spinal cord, esophagus, and skin.

Comparisons between the dose parameters generated by the RyTc and MC algorithms were made via t tests and chi-square testing, where appropriate. Parameters included the dose to 90% of the target volume (D₉₀), volume receiving prescription (V_p) dose, and maximum doses to the spinal cord, esophagus, and skin. Exploratory analyses were undertaken to determine which, if any, tumor-related characteristics would correlate with clinically significant changes in D₉₀ or V_p. The parameters tested included PTV touching lung surface, size of lesion, location within thoracic spine, and presence of epidural disease. Clinically significant changes were defined as reductions by more than 10% in either D₉₀ or V_p as well as any increase in spinal cord dose. A size cutoff of 27 cm³ was set based on work done by other investigators evaluating lung treatment plans.^14,16 P values of less than .05 were considered statistically significant.

Results

CyberKnife Treatment Characteristics

Although a minority of lesions received prior spine surgery (27.1%), consisting exclusively of laminectomy with or without spinal fusion, a majority of patients received prior EBRT to the targeted spinal segment (54.1%) with a median prescription dose of 3750 cGy in 15 fractions (Table 2). When subsequently treated with CK-based SBRT, patients were treated to a median dose of 1950 cGy in 3 fractions, via a median of 157 noncoplanar beams. Single-fraction SBRT was delivered in 40.5% of lesions.

Dose–Volume Comparisons Between RyTc and MC Calculations

Dose–volume histogram parameters for RyTc and MC calculations are presented in Table 3. Significant differences between RyTc and MC plans were noted in PTV parameters including the D₉₀ and V_p, where 10% or greater reductions in these metrics were seen in 27.0% and 35.1% of MC plans relative to RyTc, respectively. Differences were also noted in maximum spinal cord doses, where 19.4% and 8.3% of MC-planned cases showed a 10% reduction and 10% increase in spinal cord dose relative to the corresponding RyTc plans, respectively.

Table 3.

DVH Parameters.

	Ray Tracing (95% CI)	Monte Carlo (95% CI)	P Value
Planning target volume
D90, mean, cGy	1982 (1792-2172)	1843 (1651-2035)	<.001
Range,^a %		(−27.6%, 0.9%)
5%-10% loss^b		8 (21.6%)
>10% loss^b		10 (27.0%)
V_p, %	91.1 (88.9-93.3)	80.4 (76.2-84.7)	<.001
Range,^a %		(−53.2%, 1.9%)
5%-10% loss		6 (16.2%)
>10% loss		13 (35.1%)
Spinal cord^c
Max dose, cGy	1126 (971-1279)	1084 (933-1236)	.004
Range,^a %		(−18.7%, 13.8%)
>10% reduction^d		7 (19.4%)
5%-10% reduction^d		12 (33.3%)
Within 5%^d		12 (33.3%)
5%-10% increase^d		2 (5.6%)
>10% increase^d		3 (8.3%)
Esophagus
Max dose, cGy	1520 (1291-1749)	1535 (1304-1767)	.15
Range,^a %		(−14.1%, 18.2%)
>10% reduction^d		1 (2.7%)
5%-10% reduction^d		2 (5.4%)
Within 5%^d		28 (75.7%)
5%-10% increase^d		5 (13.5%)
>10% increase^d		1 (2.7%)
Skin
Max dose, cGy	1429 (1208-1651)	1406 (1192-1620)	.017
Range,^a %		(−7.0%, 6.4%)
>10% reduction^d		0 (0%)
5%-10% reduction^d		4 (10.8%)
Within 5%^d		32 (86.5%)
5%-10% increase^d		1 (2.7%)
>10% increase^d		0 (0%)

Abbreviations: CI, confidence interval; DVH, dose–volume histogram; D₉₀, the dose to 90% of the target volume; V_p, volume receiving prescription.

^aRange: indicates span doses as a percentage of the corresponding Ray Tracing dose.

^b5% and 10% loss refer to the number of cases where a difference in D₉₀ by 5% or 10% is seen between RyTc and MC plans.

^cOne spinal lesion had only spinal canal contoured and was excluded from analysis.

^dNumber of cases and percentage of cases where reported difference is seen as a percentage of the corresponding Ray Tracing dose.

The only plan characteristic significantly correlating with large (>10%) reductions in D₉₀ between RyTc and subsequent MC calculated plans was lesion size, both as a continuous variable (P = .042) and with a cutoff of size greater than 27 cm³ (15.4% vs 54.5%, P = .014; Table 4). No treatment characteristics were able to correlate with large differences in volume receiving prescription dose or higher spinal cord doses. Given the number of patients with an increase in spinal cord dose of greater than 5% was limited (n = 5), no specific analysis could be completed on this cohort, although the evaluated characteristics were similar to the remaining cohort.

Table 4.

Large (>10%) Loss in PTV Coverage or V_p, Any Increase Spinal Cord Dose: Univariate Analysis.

	>10% Loss D₉₀ (95% CI)	P Value	>10% Loss V_p (95% CI)	P Value	Any Increase Cord Dose (95% CI)	P Value
PTV touching lung surface
Yes	23.8% (0.11-0.45)	.614	33.3% (0.17-0.55)	.793	23.8% (0.11-0.45)	.367
No	31.3% (0.14-0.56)	.614	37.5% (0.18-0.61)	.793	37.5% (0.18-0.61)	.367
Size of lesion
<27 cm³	54.5% (0.28-0.79)	.014	54.5% (0.28-0.79)	.108	36.4% (0.15-0.65)	.566
>27 cm³	15.4% (0.06-0.34)	.014	26.9% (0.14-0.46)	.108	26.9% (0.14-0.46)	.566
Size of lesion (continuous)^a
Yes	40.9 cm³ (12.9-68.8)	.042	80.5 cm³ (32.2-128.8)	.854	78.8 cm³ (25.4-132.2)	.806
No	99.7 cm³ (68.3-131.1)	.042	85.6 cm³ (55.6-115.6)	.854	85.9 cm³ (56.9-114.9)	.806
Location of lesion within thoracic spine
Upper (T1-T4)
Yes	11.1% (0.02-0.43)	.207	11.1% (0.02-0.43)	.091	44.4% (0.19-0.73)	.258
No	33.3% (0.17-0.55)	.207	42.8% (0.24-0.63)	.091	23.8% (0.11-0.45)	.258
Middle (T5-T8)
Yes	50.0% (0.15-0.85)	.257	50.0% (0.15-0.85)	.448	0% (0-0.49)	.160
No	23.1% (0.11-0.42)	.257	30.8% (0.17-0.50)	.448	34.6% (0.19-0.54)	.160
Lower (T9-T12)
Yes	29.4% (0.13-0.53)	.697	41.2% (0.22-0.64)	.297	29.4% (0.13-0.53)	.936
No	23.1% (0.08-0.50)	.697	23.1% (0.08-0.50)	.297	30.8% (0.13-0.58)	.936
Presence of epidural disease
Yes	25.0% (0.12-0.45)	.706	33.3% (0.18-0.53)	.755	25.0% (0.12-0.45)	.392
No	30.8% (0.13-0.58)	.706	38.5% (0.18-0.64)	.755	38.5% (0.18-0.64)	.392
Number of beams (continuous)^a
Yes	169.5 (153.2-185.8)	.264	164.2 (150.9-177.4)	.706	158.8 (149.8-167.9)	.607
No	159.3 (150.4-168.2)	.264	160.9 (151.0-170.9)	.706	164.4 (152.9-174.0)	.607

Abbreviations: CI, confidence interval; D₉₀, dose received to 90% of PTV; V_p, volume receiving prescription dose.

^aYes and no refer to patients with and without the above characteristic; for example, yes refers to patients who have had any increase in spinal cord dose.

Discussion

Stereotactic body radiation therapy is an emerging strategy for treating spinal metastases, allowing highly precise radiation treatments to be delivered with a hypofractionated approach.² Although this technology has been developed relatively recently, several institutions have published on their experiences using stereotactic techniques in the upfront,⁷ postoperative,¹⁷ and reirradiation settings.¹⁸ These techniques have generally reported to be safe, with minimal associated morbidity, respectable tumor control rates, and having a meaningful impact on pain control and quality of life.⁸ However, the safety and efficacy of these treatments depend on the ability to accurately determine the dose delivered to the tumor and at-risk structures.

Computational algorithms for treatment planning have developed substantially since the introduction of CK. Initially, the only algorithm through the CK Multiplan platform was RyTc, which utilizes a path length correction algorithm to compute the dose deposition characteristics. Central axis effective depth calculations account for tissue heterogeneity, and further adjustments of the anticipated dose distribution are made for off-axis calculations and differences in collimation. Although these methods are sufficient for treating relatively homogeneous structures and large field sizes, limitations in accuracy do exist. In particular, when modeling dose distributions in areas of high tissue heterogeneity, the RyTc methodology is unable to account for changes in the lateral range, scatter, and final dose deposition of liberated electrons, resulting in an overestimation of the deposited dose.¹⁹ Additionally, the smaller field sizes used in CK-based SBRT cause the dose distributions to become increasingly field size dependent, and accurate modeling of the electronic disequilibrium at the field border is necessary to predict the deposited dose.^20,21

In response, new algorithms have been developed based on MC techniques, which combine known machine-related factors, such as beam profiles, central axis depth dose measurements, and collimator factors, with a large number of individually simulated particle interactions. Given MC simulations evaluate individual particles, interactions occurring in areas of electronic disequilibrium can be modeled more accurately with the resulting dose distributions more closely resembling measured values when compared to RyTc.²⁰ However, MC requires a large number of simulations to reduce the uncertainty and improve the accuracy of the dose distribution, which can be computationally cumbersome and time consuming. Currently, it is unclear whether the benefit of improved accuracy justifies the additional computational cost of MC-based treatment planning, which is what we aimed to determine through our analysis.

In reviewing our cohort of patients, baseline characteristics demonstrate that patients receiving spinal SBRT are a highly selected group. The spine was the only site of disease in 21.9% of patients with malignant histology, which emphasizes the importance of achieving local control, prevention of neurologic sequelae of disease progression and/or treatment, and improving quality of life. Compared to all patients with spinal metastases, those receiving spinal SBRT likely represent a subset of patients with aggressive disease. In our cohort, this is evidenced by 27% having received previous spinal surgery due to symptomatic cord compression, 62.2% of patients having epidural disease at the time of SBRT treatment, and 54.1% having received prior fractionated EBRT. Accordingly, it is imperative to deliver the highest safe dose possible to the tumor while minimizing dose to the surrounding critical structures, particularly the spinal cord.

When comparing plans calculated with RyTc and MC algorithms, several DVH parameters were noted to have changed. With regard to the target structures, calculated MC plans resulted in an average loss in D₉₀ of 7.0%, with 27% of plans losing over 10% and up to a maximum loss of 27.4%. Similarly, target volume covered by the prescription dose was also reduced using MC, by an average of 11.7% and up to 53.2%. Similar changes were noted in patients with lung cancer; in a comparative study by Sharma et al,²⁰ target coverage was reduced from 97.7% to 69.2% and significant differences in conformality were noted when MC-optimized plans were compared to previous RyTc plans. Consequently, it is plausible this degree of change in calculated dose and coverage could lead to in-field and marginal treatment failures, which is of particular relevance in a cohort of patients with minimal salvage therapeutic options should disease control be compromised.

With regard to OARs, differences between RyTc and MC calculated plans varied widely with respect to spinal cord maximum doses, with less variation among maximum esophageal and skin doses. Specifically, although average maximum spinal cord doses only differed by 3.7%, increases in spinal cord dose by 10% or more were seen in 8.3% of cases, and decreases in spinal cord dose by 10% or more were seen in 19.4% of cases. Although overestimation of the spinal cord dose may not lead to any significant treatment-related morbidity, it may reduce the effective tumor dose one can provide to at-risk tumor volumes, taking into account normal tissue tolerances. At the same time, underestimation of the dose could have severe consequences, particularly in the reirradiation setting where spinal cord tolerances may already be reaching their upper limits. Absolute differences among calculated maximum esophagus and skin doses were much less, and the magnitudes of such differences are unlikely to be of any clinical consequence.

Interestingly, the only tumor characteristic that correlated with adverse changes in PTV coverage (D₉₀) was the size of the lesion, both as a continuous variable and dichotomized to size <27 cm³, similar to other investigators evaluating lung targets.^14,16 In our series, even among larger lesions, 15.4% of these patients still had decrements in D₉₀ of at least 10%, with clinically unacceptable reductions in coverage ranging up to 24.2%. Although no clear method for systematically reducing these discrepancies is evident from our data, some literature suggests that the coverage may be improved by minimizing beam angles traversing the lung.^22,23 Additionally, use of larger size collimators is expected to improve dosimetric computational accuracy. However, the degree to which this may improve the accuracy of RyTc calculations is unclear. Other tumor characteristics, including the presence of PTV touching the lung surface, the location of lesion within thoracic spine, and the presence of epidural disease, were unable to predict significant differences in RyTc and MC calculated treatment plans. Ultimately, there may not be any particular subset of patients receiving SBRT to the thoracic spine for which RyTc calculation methods are reliably accurate, similar to another report evaluating calculation methods in lung cancer.²⁰

Although our results demonstrate clinically meaningful changes in CK-based spinal SBRT by calculation method, there are several limitations. Limited patient numbers might have reduced the power to detect predictors of poor correlation between RyTc and MC on univariate analysis. Plans were not subsequently optimized based on MC planning, and thus the degree to which dosimetric improvements can be made utilizing this algorithm in DVH parameters is unknown. Finally, given the dosimetric focus of this study, the clinical impact of such differences in planning algorithms is presumed but to date remains unquantified.

Conclusion

In patients treated for thoracic spinal disease using CK-based SBRT, treatment plans generated through RyTc calculation methods generally overestimate target dose and coverage, as well as underestimate doses to at risk structures, including the spinal cord. Only plans with larger treatment targets were found to correlate with better concordance between RyTc and MC calculated plans, although unacceptably high reductions in coverage could still occur in this cohort. No consistent or reliable determinant of RyTc accuracy relative to MC could be found. The use of RyTc as a sole method to optimize dose distributions should be minimized in this setting and, if used, should be complemented by MC verification.

Footnotes

Abbreviations

Declaration of Conflicting Interests

The author(s) declared the following potential conflicts of interest with respect to the research, authorship, and/or publication of this article: Dr Simon S. Lo has received support for travel expenses and honorarium for speaking in a symposium from Varian Medical Systems and has received partial research support from Elekta AB in the context of International Oligometastasis Consortium.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

References

Levack

Graham

Collie

. Don’t wait for a sensory level—listen to the symptoms: a prospective audit of the delays in diagnosis of malignant cord compression. Clin Oncol (R Coll Radiol). 2002;14(6):472–480.

Expert Panel on Radiation Oncology-Bone Metastases. Lo

SS-M

Lutz

Chang

. ACR Appropriateness Criteria^® spinal bone metastases. J Palliat Med. 2013;16(1):9–19.

Gerszten

Burton

Ozhasoglu

Welch

. Radiosurgery for spinal metastases: clinical experience in 500 cases from a single institution. Spine (Phila Pa 1976). 2007;32(2):193–199.

Maranzano

Latini

. Effectiveness of radiation therapy without surgery in metastatic spinal cord compression: final results from a prospective trial. Int J Radiat Oncol Biol Phys. 1995;32(4):959–967.

Hall

Stapleford

Hadjipanayis

Curran

Crocker

Shu

H-KG

. Stereotactic body radiosurgery for spinal metastatic disease: an evidence-based review. Int J Surg Oncol. 2011;2011:979214.

Chang

Lee

. Stereotactic radiosurgery for spinal neoplasms: current status and future perspective. J Neurosurg Sci. 2013;57(2):87–101.

Gill

Oermann

. Fiducial-free CyberKnife stereotactic body radiation therapy (SBRT) for single vertebral body metastases: acceptable local control and normal tissue tolerance with 5 fraction approach. Front Oncol. 2012;2:39.

Degen

Gagnon

Voyadzis

J-M

. CyberKnife stereotactic radiosurgical treatment of spinal tumors for pain control and quality of life. J Neurosurg Spine. 2005;2(5):540–549.

Gagnon

Nasr

Liao

. Treatment of spinal tumors using cyberknife fractionated stereotactic radiosurgery: pain and quality-of-life assessment after treatment in 200 patients. Neurosurgery. 2009;64(2):297–306; discussion 306-307.

10.

Antypas

Pantelis

. Performance evaluation of a CyberKnife G4 image-guided robotic stereotactic radiosurgery system. Phys Med Biol. 2008;53(17):4697–4718.

11.

Ding

Duggan

. Impact of inhomogeneity corrections on dose coverage in the treatment of lung cancer using stereotactic body radiation therapy. Med Phys. 2007;34(7):2985–2994.

12.

Das

Ding

Ahnesjö

. Small fields: nonequilibrium radiation dosimetry. Med Phys. 2008;35(1):206–215.

13.

Wilcox

Daskalov

Lincoln

Shumway

Kaplan

Colasanto

. Comparison of planned dose distributions calculated by Monte Carlo and Ray-Trace algorithms for the treatment of lung tumors with cyberknife: a preliminary study in 33 patients. Int J Radiat Oncol Biol Phys. 2010;77(1):277–284.

14.

Tam

Tong

. Evaluation of the influence of tumor location and size on the difference of dose calculation between Ray Tracing algorithm and Fast Monte Carlo algorithm in stereotactic body radiotherapy of non-small cell lung cancer using CyberKnife. J Appl Clin Med Phys. 2013;14(5):68–78.

15.

Cox

Spratt

Lovelock

. International Spine Radiosurgery Consortium consensus guidelines for target volume definition in spinal stereotactic radiosurgery. Int J Radiat Oncol Biol Phys. 2012;83(5):e597–e605.

16.

van der Voort van Zyp

Hoogeman

van de Water

. Clinical introduction of Monte Carlo treatment planning: a different prescription dose for non-small cell lung cancer according to tumor location and size. Radiother Oncol. 2010;96(1):55–60.

17.

Rock

Ryu

Shukairy

. Postoperative radiosurgery for malignant spinal tumors. Neurosurgery. 2006;58(5):891–898; discussion 891-898.

18.

Sahgal

Ames

Chou

. Stereotactic body radiotherapy is effective salvage therapy for patients with prior radiation of spinal metastases. Int J Radiat Oncol Biol Phys. 2009;74(3):723–731.

19.

Wilcox

Daskalov

. Accuracy of dose measurements and calculations within and beyond heterogeneous tissues for 6 MV photon fields smaller than 4 cm produced by Cyberknife. Med Phys. 2008;35(6):2259–2266.

20.

Sharma

Ott

Williams

Dickow

. Clinical implications of adopting Monte Carlo treatment planning for CyberKnife. J Appl Clin Med Phys. 2010;11(1):3142.

21.

Haedinger

Krieger

Flentje

Wulf

. Influence of calculation model on dose distribution in stereotactic radiotherapy for pulmonary targets. Int J Radiat Oncol Biol Phys. 2005;61(1):239–249.

22.

Altman

Jin

Kim

. Practical methods for improving dose distributions in Monte Carlo-based IMRT planning of lung wall-seated tumors treated with SBRT. J Appl Clin Med Phys. 2012;13(6):4007.

23.

Jin

Wang

Luo

Feigenberg

. Investigation of optimal beam margins for stereotactic radiotherapy of lung-cancer using Monte Carlo dose calculations. Phys Med Biol. 2007;52(12):3549–3561.