Determining normal tissue dose in intracranial stereotactic radiosurgery: A diameter-based predictive nomogram

Abstract

Purpose: A major factor in dose-fractionation selection for intracranial metastases in stereotactic radiosurgery (SRS) is the size of the target lesion and consequently the dose-volume to the surrounding normal brain tissue (NTV), as this has been correlated with brain radiation necrosis (RN). This study outlines the development and validation of a predictive model that can estimate the NTV for a range of dose-fractionation schemes based on target diameter from a patient’s MRI.

Methods: Data from a cohort of historical SRS clinical treatment plans were used to extract three key input parameters for the model – conformity index, gradient index, and a scaling factor which were then defined as a function of target volume. The relationship between the measured tumour diameter and the NTV was established by approximating the target to a spherical volume covered by the prescription dose. A scaling factor (λ_NTV) describes the non-linear fall-off of dose beyond the target. This was then used to provide a first-order approximation of the resulting NTV. The predictive model was retrospectively validated using linear regression against actual NTV values from 39 historical SRS plans which were independent to the derivation process. The model was validated for both three-dimensional (3D) target diameter and axial-only two-dimensional (2D) estimates of target diameter values.

Results: The prediction model directly relates lesion diameter to NTV volume (cc) and thus RN risk for a given dose-fractionation. The predicted NTV (cc) for both 3D- and 2D-based volume estimates could statistically significantly predict the actual NTV (cc): R²=0.942 (p<.0005) for 3D-based estimate, and R²=0.911 (p=<.0005) for axial-only 2D-based estimate.

Conclusion: This knowledge-based method for NTV prediction in intracranial SRS provides the clinician with a decision support tool to appropriately select dose-fractionation prior to treatment planning.

Introduction

Between 20 and 60% of patients with cancer will develop brain metastases during the course of their disease[1-3]. Stereotactic radiosurgery (SRS) is an established treatment option for selected patients with brain metastases, and its efficacy has been demonstrated in several randomised trials and multi-institutional studies[2, 4-16]. SRS allows delivery of highly conformal ablative doses to tumour with rapid dose fall-off thus optimally sparing surrounding normal tissue, and results in less neurocognitive toxicity compared to whole brain radiotherapy (WBRT)[13, 16, 17]. However, SRS is not without risk. Brain radiation necrosis (RN) is a well-recognised complication of this high dose treatment, and can result in significant morbidity[18]. Incidence of RN correlates with increasing SRS dose, target volume, and the dose-volume to normal brain tissue (NTV), known as V_xGy [19-26].

As SRS has been widely implemented over recent decades, frameless immobilisation techniques have also been developed meaning that patients eligible for treatment include not only those with small lesions amenable to single fraction schedules but also those with larger lesions (generally defined as >2cm diameter) which can now be treated with hypofractionation. Fractionation has been shown to reduce the incidence of RN compared to a single fraction approach while maintaining efficacy[26, 27]. V_12Gy (the volume of normal brain tissue receiving 12Gy or higher for single fraction treatments[19, 22, 25], and V_18Gy [26] and V_24Gy [28] for 3 fraction schedules, have been reported as being significant prognostic factors for RN. The optimal sparing of normal brain tissue relies on dosimetric characteristics and must be achieved by good dose conformity and a steep dose gradient, both of which vary with target volume and shape[29].

Current practice in many radiotherapy centres follows a stepwise planning approach where the prescription dose and fractionation schedule for an individual patient are recursively adjusted and finalised only during the planning stage when the target and normal tissue volumes are known. With short timelines from clinical assessment to simulation to treatment with SRS, it is desirable to have an estimation of NTV at the time of initial patient consultation when only the diagnostic MRI is available. This can facilitate clinical decision making, for example by allowing knowledge-based selection of dose and fractionation. This has two potential advantages in making optimal use of limited resources: 1) reduction in planning time by providing a clinically relevant knowledge-based starting point for dose-fractionation, and 2) allowing the treatment unit to confidently schedule an appropriate number of treatment slots for each patient in advance.

In the present study we outline the development and validation of a predictive model that can be used at the time of initial patient consultation to predict NTV, directly from target diameter measurement from the patients MRI, for a range of dose-fractionation schemes.

Methods and Materials

SRS planning process

At our institution, intravenous contrast enhanced CT planning scans are acquired using a frameless SRS mask with localiser box, on a 16-slice CT scanner (GE BJG Optima), with a slice thickness of 1.25mm. A T1 gadolinium contrast-enhanced planning MRI is acquired immediately afterward on a 1.5T scanner (GE 1.5HDXT Echospeed), with an axial slice thickness of 1mm. These images are transferred to iPlan (BrainLAB, Germany) for fusion, targeting and planning. Gross tumour volume (GTV) is contoured on the T1c dataset, and a 1mm margin to planning target volume (PTV) is added to account for geometric uncertainties. Planning consists of 3 to 5 non-coplanar dynamic conformal arcs of up to 110º at various couch angles (eg 30º, 90º, and 100º or 10º, 50º, 90º, 310º, and 350º), using 6-MV SRS beam (1000MU/min) with flattening filter. Treatment is delivered on Varian Trilogy with HD-MLC (leaf width of 2.5mm at isocentre) and ExacTrac positioning system. Plans are normalised such that the 80% isodose line covers at least 99% of the PTV. A pencil beam algorithm (BrainLAB) with an adaptive dose grid size was used for dose calculation. Plan quality is assessed according to several parameters, including:

the RTOG Conformity Index (CI) (equivalent to the CI provided by iPlan when the PTV is fully covered):

where V_p is the volume covered by the prescription dose (cc);

and the ICRU Gradient Index (GI)

where V_p/2 is the volume of the half prescription (ie when prescribing 20Gy/1 fraction to 80% isodose line, V_p=V_20Gy and V_p/2=V_10Gy).

NTV is defined as the normal brain tissue minus the GTV (ie it includes normal tissue within the PTV) as this is a more clinically relevant assessment of the true volume at risk of RN compared to brain tissue minus PTV. NTV is limited to V_12Gy <10cc for single fraction treatments, and V_18Gy <30cc and V_24Gy <16cc for 3 fraction treatments.

Derivation of the Normal Tissue Volume (NTV) Predictive Model

For this model, NTV is approximated as a function of target size, and requires three knowledge-based input parameters: Conformity Index (CI) (eqn 1), Gradient Index (GI) (eqn 2), and a scaling factor (λ_NTV) (Table 1) describing the relative dose gradient beyond the PTV. Data from a cohort of 62 historical SRS treatment plans (all in situ metastases with 1mm margin to PTV) were used to extract the terms for these 3 input parameters. Derivation of the model involves 5 steps, with a visual representation of the process shown in Figure 1. The purpose of using intermediary steps to build the relationship between target size and NTV is twofold. Firstly, to provide the model with the flexibility to calculate any NTV between V_p and V_p/2, thus avoiding numerous correlations between different NTV’s and target size. The model could also be used to solve the DVH in this region for a given dose level. Secondly, to allow the input parameters to be changed in order to assess their impact on the resulting NTV.

Table 1.

First order approximation of λ_NTV determined as a function of isodose level

IsoDose Level	λNTV
80% → p	0
60% →
40% →	1

λ_NTV=scaling factor, p = prescription isodose

Figure 1.

Summary of the method used to determine NTV as a function of target size. (1) the equivalent sphere diameter is measured prior to treatment planning (2) GTVm (3) PTVm with xmm expansion (4) approximated (5) 1^st order approximation of NTV (green ring).

Step 1: The diameter (d) is approximated before the planning stage by averaging the diameter of the target lesion using the three anatomical planes of the patient’s MRI scan.

Step 2: The modelled Gross Target Volume (GTVm) is the volume of the resulting sphere from the approximated diameter.

Step 3: The GTVm radius is expanded by x mm in order to approximate the modelled Planning Target Volume (PTVm).

Step 4: The PTVm is expanded to a volume defined by half the prescription dose, denoted , using values

for CI and GI extracted from historical plan data and defined as a function of target volume, where the prescription volume is defined as:

and

Step 5: As the dose gradient in tissue is not linear, A scaling factor, λ_NTV, is used to approximate the relative dose gradient between V_p and . It varies between 0 and 1 depending on the chosen isodose level (isl) and is defined by the ratio, , as shown in Table 1. Here, the volume defined by three quarters of the dose prescription is taken from historical plan data and p is the prescription isodose.

Finally, the NTV for the isodose level of interest, NTV_isl, is approximated as:

where, accounts for the difference between the prescription volume and the GTVm.

Validation of the NTV Predictive Model

The predictive model was validated retrospectively on 39 historical patient treatment plans, which followed the planning process as outlined above, providing NTV datapoints for V_12Gy for single fraction plans, and V_18Gy and V_24Gy for 3 fraction plans.

A 2-part validation process, using linear regression analyses, was performed to assess the ability of the predicted NTV (cc) for both 3D- and 2D-based volume estimates to predict the actual NTV volume (cc). Part 1 used an equivalent sphere (or three dimensional 3D) average lesion diameter approach (taking diameter measurements from the three anatomical planes of the MRI) for Step 1 of the above process (Figure 1). Part 2 used average lesion diameter (or two dimensional – 2D) obtained from axial images only (largest diameter and that perpendicular to it)[31]. The advantage of omitting the craniocaudal dimension, as in Part 2, is eliminating the dependence of the prediction on the slice thickness of the MRI. The average diameter was then used to obtain an estimation of the NTV V_12Gy, V_18Gy, and V_24Gy using the model described above, and the relationship between this and the actual NTV values obtained from the planning system was explored.

Results

Derivation of the NTV Predictive Model

Steps 1 to 3: The model was calculated for single targets with diameters up to 4cm and PTVm margin 1mm.

Steps 4 and 5: The 3 input parameters (CI, GI and λ_NTV) required for the model were derived from a cohort of previous SRS plans and are outlined in Table 2.

Table 2.

Input parameters derived as a function of target diameter from historical plan data

GI (all PTV’s)	CI (PTV<1cc)	CI (PTV>1cc)	α (all PTV’s)	λNTV (all PTV’s)
−0.2759398ln (PTV) + 3.0698	−0.31213ln (PTV) + 1.44250	1.42	2.19	0.00046875 (isl)2 − 0.08125 (isl) + 3.5

GI (Gradient Index), PTV (planning target volume), CI (conformity Index), λ_NTV (scaling factor) fitted to data from Figure 2

CI (Figure 2a), GI (Figure 2b) and α (Figure 2c) are shown as a function of PTV, and λ_NTV as a function of isodose level (Figure 2d). For PTV volumes less than 1cc, CI and GI change rapidly with change in volume and so a logarithmic fit was used for both parameters (figures 2a and 2b).

Figure 2.

Input parameters for the NTV model randomly selected from a cohort of as a function of 62 previous SRS plans (1 σ (stdev)) (a) Conformity index as a function of PTV, (b) GI as a function of PTV, (c) α as a function of PTV, (d) the scaling factor (λ_NTV) as a function of isodose level.

NTV_isl is calculated as a function of target diameter for multiple prescriptions in order to develop the predictive nomogram as shown in Figure 3.

Figure 3.

First order knowledge-based approximation of NTV plotted as a function of target diameter up to 4cm using standard SRS dose prescriptions.

Variability in NTV (ΔNTV) was demonstrated by changing CI and GI by one standard deviation (as CI and GI rise sharply below 1cc (Figure 2), data points below 1cc are not included in the calculation of standard deviation). As an example, for the 18Gy dose prescription the resulting change in the 12Gy NTV, ΔNTV, is summarised for several target diameters in Table 3. A sensitivity analysis near the NTV cut-off thresholds (V_12Gy, V_18Gy and V_24Gy) is shown in Table 4.

Table 3.

Change in normal tissue volume (ΔNTV) as a result of varying conformity index (CI) and gradient index (GI) by 1 standard deviation (where σ is calculated for PTV > 1cc)

Target Diameter/ ΔNTV	1.5cm	2.5cm	3.5cm	4cm
ΔNTV CI (Ơ=0.14)	±0.69cc	±2.47cc	±-5.88cc	±8.3cc
ΔNTV GI (Ơ=0.26)	+-0.48cc	+-1.9cc	+-4.9cc	+-7.2cc

Table 4.

Sensitivity analysis of ΔNTV at the NTV cut-off thresholds

Dose Prescription and NTV cut-off threshold	24 Gy in1# D=1.61cm (V12Gy=10cc)	18 Gy in1# D=2.0cm (V12Gy=10cc)	16 Gy in1# D=2.24cm (V12Gy=10cc)	27 Gy in3# D=3.2cm (V18Gy=30cc)	27 Gy in3# D=3.25cm (V24Gy=16cc)
ΔNTV CI (O’=0.14)	±1.23 cc	±1.35cc	±1.55cc	±4.55cc	±3.34cc
ΔNTV GI (O’=0.26)	±1.15cc	±1.04 cc	±0.88 cc	±3.8cc	±0.74cc

Validation of the NTV predictive model

The model was validated on 48 NTV datapoints from 39 historical patient plans independent of the derivation process. PTV coverage was >99% for all plans. The median CI and GI were 1.41 (SD 0.15) and 2.59 (SD 0.33), respectively, for a median tumor diameter of 1.5cm (range 0.47-3.31cm) and PTV volume of 2.06cc (range 0.08-20.57cc).

Figure 4.

a). Scatterplot showing the predicted NTV volume (cc) and actual NTV volume (cc) extracted from 39 SRS plans based on 3D (AP, LR, CC) average lesion diameter estimate. R²=0.942 (p=<0.0005); b) scatterplot showing the predicted NTV volume (cc) and actual NTV volume (cc) extracted from 39 SRS plans based on 2D (axial only) average lesion diameter. R²=0.911 (p=<0.0005)

Figures 4a and 4b show the relationship between predicted NTV (cc) and actual NTV (cc) extracted from the plan dose volume histogram (DVH), using linear regression, for Part 1 (R²=0.942) and Part 2 (R²=0.911) of the validation process, respectively. The predicted 3D-based NTV volume (cc) could statistically significantly predict the actual NTV volume (cc), and explained 94.2% of the total variance, F(1, 46) = 753, p< .0005. The predicted 2D-based NTV volume (cc) could statistically significantly predict the actual NTV vol (cc), and explained 91.1% of the total variance, F(1, 46) = 471, p< .0005.

Discussion

SRS for brain metastases has been widely adopted, and its efficacy has been demonstrated in several studies. However, long term toxicity can include RN which is associated with several risk factors including the volume of normal brain tissue irradiated to a certain dose (NTV V_xGy). Historically, all lesions were treated with a single fraction approach that was tailored depending on lesion size. With the development of frameless immobilisation devices, the option now exists to provide fractionated SRS which is associated with both improved efficacy and reduced toxicity for larger lesions[26, 28]. In many departments dose and fractionation is decided only when the planning process has commenced and the actual target and normal tissue volumes are known.

Here, we have described a readily accessible model for predicting NTV volume based on target lesion diameter determined from an MRI scan. The primary value of this work is that it allows the clinician to estimate the NTV in the outpatient setting from information available on diagnostic MRI and thus provide a knowledge-based decision support tool for dose-fractionation selection and appropriate scheduling of treatment slots, thus optimising resources. We highlight that the nomogram presented here (Figure 3) is derived from data (CI, GI and λ_NTV) from cases within our clinic, and so is specific to the SRS planning technique and delivery system we use as described above. Conformity of dose around a target depends in part on MLC design, while the beam’s penumbra is a function of radiation focal spot size and source to collimator distance. We provide in our results the median and SD values of CI and GI from our clinic such that the reader can decide if the nomogram here is appropriate for use within their clinic or if a unique nomogram should be derived using the method described. Overall, this relatively simple model can be adopted and optimised in any radiation oncology department using data from previously planned cases to provide accurate estimation of NTV based on that centre’s planning technique.

Other knowledge-based prediction models for intra-cranial SRS have previously been reported, though none utilizes pre-planning data. Bohoudi et al published a prediction model tailored specifically for V_12Gy estimation based on PTV size[32]. Notably, their study defines normal tissue as brain tissue minus PTV, whereas in the present study normal tissue is defined as brain tissue minus GTV. Bo Zhao et al also developed a method to predict V_12Gy, and thus RN probability, as a function of target volume and found that NTV could be reduced by optimising the isodose line prescription[33]. Both of these methods are limited to prediction of V_12Gy only and are not general enough to be applied multiple NTV’s. Our model is also different from those studies exploring automated and machine-learning driven treatment planning which aim to improve plan consistency and quality, and may ultimately supplant manual planning in the future[34-39].

The NTV prediction model presented in this manuscript also has some limitations. It must be highlighted that target size, dose and NTV are only a subset of the known risk factors associated with development of RN following SRS. Clinicians also take into account other patient-specific risk factors including lesion location[20, 40], prior radiation[20], and the use of concurrent systemic therapies[3, 41-43] to inform their clinical management plan. While the input variables were limited here to as few as three parameters (CI, GI and λ_NTV), the model could be easily further refined by including other features which also impact on NTV including for example lesion shape/regularity[36]. It is worth noting that predicted NTV was sensitive to small changes in conformity and gradient, particularly for larger volumes . In our clinical experience, larger lesions have a greater tendency to be more irregular in shape than smaller lesions, which may explain this trend. The model has also been validated for single brain metastases, and while it could be extrapolated for use for multiple brain metastases that are not in close proximity, this has not been tested here.

The value of the proposed model stems from its simplicity and its applicability at the pre-planning stage. It can be used for a range of dose-fractionation schedules based on published NTV values that have been correlated with the risk of radiation necrosis. It allows for variations in CI, GI and PTV margins in driving the model and thus flexibility across institutions. The clinician is provided with a knowledge-based prediction tool that can be used in the outpatient setting to both inform the patient for the details of their treatment as well as aid in intradepartmental resource management.

Conclusion

This manuscript describes in detail a model developed and validated for NTV estimation based on target diameter from a patient’s MRI. It provides the clinician with a useful knowledge-based tool to support clinical decision making with respect to dose-fractionation selection for intracranial metastases.