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Introduction and Clinical Overview of the DVH Risk Map
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Dose Volume Histogram (DVH) Clinical Overview: The DVH Risk Map Sucha O. Asbell MD, Jimm Grimm PhD, Jinyu Xue PhD, Meng-Sang Chew PhD, Tamara A. LaCouture MD
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S1053-4296(15)00115-0 http://dx.doi.org/10.1016/j.semradonc.2015.11.005 YSRAO50532
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Cite this article as: Sucha O. Asbell MD, Jimm Grimm PhD, Jinyu Xue PhD, Meng-Sang Chew PhD, Tamara A. LaCouture MD, Dose Volume Histogram (DVH) Clinical Overview: The DVH Risk Map, Semin Radiat Oncol , http://dx.doi.org/10.1016/j.semradonc.2015.11.005 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Dose Volume Histogram (DVH) Clinical Overview: The DVH Risk Map Sucha O. Asbell, MD1, Jimm Grimm, PhD2, Jinyu Xue, PhD1, Meng-Sang Chew, PhD3, and Tamara A. LaCouture, MD1
Radiation oncologists need reliable estimates of risk for various fractionation schemes for all critical anatomical structures throughout the body, in a clinically convenient format. Reliable estimation theory can become unduly complex, however, and estimates of risk continue to evolve as the literature matures. To navigate through this efficiently, a DVH Risk Map was created, which provides a comparison of radiation tolerance limits as a function of dose, fractionation, volume, and risk level. The graphical portion of the DVH Risk Map helps clinicians to easily visualize the trends, while the tabular portion provides quantitative precision for clinical implementation. The DVH Risk Map for rib tolerance from stereotactic ablative body radiotherapy (SABR) and stereotactic body radiation therapy (SBRT) is used as an example in this overview; the 5% and 50% risk levels for 1 to 5 fractions for five different volumes are given. Other articles throughout this issue of Seminars in Radiation Oncology present analysis of new clinical datasets including the DVH Risk Maps for other anatomical structures throughout the body. 1
Radiation Oncology, M.D. Anderson at Cooper University Hospital, Camden, NJ, USA Holy Redeemer Hospital, Bott Cancer Center, Meadowbrook, PA, USA 3 Packard Lab 256B, Lehigh University, Bethlehem, PA, USA 2
Conflict of Interests Notification: None of the authors has received any funding for this research. Dr. Grimm developed and holds intellectual property rights to the DVH Evaluator software tool which is an FDA-cleared product in commercial use, and which has been used for this analysis.
H
uman dose tolerance to conventionally fractionated radiation has been analyzed for many decades.
The development of isoeffect curves1, nominal standard dose (NSD)2, and time dose fractionation (TDF) tables3 eventually led to biological effective dose (BED)4 based on the linear quadratic (LQ) model5-9, and many other models for biological equivalence continue to be investigated10-17. Dose response modeling1829 provides a more explicit way to estimate the actual risk levels for each critical anatomical structure as a function of dose, fractionation, volume, and other parameters. Emami‟s 1991 work30 combined this theoretical framework with clinically usable dose tolerance limits like Rubin31-34 to provide 5% and 50% risk levels for 25 anatomical structures throughout the body. Ten years later the July 2001 issue of Seminars in Radiation Oncology35 presented a comprehensive update of the modeling results, and after about another 10 years, most of the lead authors from that work became
authors of QUANTEC36, which is currently the most accurate assessment of normal tissue complication probability (NTCP) for conventional fractionation. Dose tolerance for stereotactic ablative body radiotherapy (SABR) and stereotactic body radiation therapy (SBRT) is still much more uncertain. We began delivering CyberKnife treatments before most of the RTOG SABR/SBRT protocols37-40, before TG 10141, before QUANTEC36, and before the Timmerman 2008 issue of Seminars in Radiation Oncology42. Dose tolerance guidelines were extremely rare, and we began accumulating a simple spreadsheet of the sparsely published data. Over time it grew to 500 dose tolerance limits43 and as of 2016 there are well over 1000 published limits – but they are discordant, ever changing, and until now have lacked quantitative estimates of corresponding incidence of complication.
Dose Tolerance Limits Defined Much has been said about dose tolerance limits, but our formal definition may clarify:
Dose Tolerance Limit: A specified radiation dose, fractionation and volume, with an associated estimated risk of developing a complication of a specified endpoint within a specified followup time.
Human dose tolerance to radiation depends on many other factors, but a well-defined dose tolerance limit must specify at least the following: 1) Dose 2) Fractionation 3) Volume 4) Endpoint 5) Followup Time 6) Estimated Risk of the Endpoint occurring within the Followup Time The endpoint and length of followup must be clearly stated in order for the dose tolerance limit to be useful. Emami used 5 years as the followup period for every dose tolerance limit, and although this is convenient, there is not much 5-year quantitative data available yet in the SBRT literature. Note that a 5year followup period implicitly includes both early and late effects, but for SBRT in particular, there is much interest in distinguishing the timing of the onset of symptoms. Finally, for a dose tolerance limit to truly be useful in clinical decision making, it must include an estimate of the associated risk of the endpoint occurring within the specified time. The circumstances of each patient and each tumor are unique. We need reliable estimates of complication probability which will provide physicians with the information needed to make the most informed decisions.
Simple Graphs, Physical Dose If the information relating a range of dose tolerance limits and their respective risks could be arranged on a single graph it would help physicians make decisions about management. In an attempt to make sense of contradictory published SBRT constraints, simple graphs of the dose tolerance limits as a function of the number of fractions were made, which led to the creation of the DVH Risk Map44. Initially our tendency was to perform a BED conversion of the doses before plotting them. We quickly realized, however, that currently the BED conversions themselves were just one more confounding factor that made comparisons more difficult, since there are so many methods of BED conversion4-17. Due to lack of thorough reporting standards45 it has often not been feasible to unravel the conversions of one publication and recompute to the conversions of another. Therefore we tried simply plotting the dose tolerance limits on a linear scale; pure physical dose. Much to our surprise, we discovered that someone else must have already come to this realization, because as may be clearly seen by plotting the limits as in Fig. 1, many of the Timmerman 2008 limits are related by straight lines. It is not possible to express what a profound impact these few straight lines have had on the field of radiation oncology in SBRT – they may be simple, but they have been a remarkably useful starting point. Furthermore, the potential linearization of BED at high dose per fraction as expressed in the universal survival curve (USC)15 does provide a plausible theoretical justification, although, as with all BED conversions, there is some debate16,17.
In the DVH Risk Map graphs, dose is on the y-axis, each subplot is for a specific volume, and the number of fractions is on the x-axis of each subplot. There are many dose-volume metrics that combine dose and volume together, such as the inverse power law24, effective volume (Veff)46, effective dose (Deff)47, or equivalent uniform dose (EUD)48. Any of these metrics can be used to specify a dose tolerance limit, and any of these can be used as one of the five subplots in a DVH Risk Map.
Low-Risk and High-Risk Partition Every patient is unique, especially considering the variability of tumors and the proximity to critical structures, so a range of dose tolerance limits is needed. Over a period of more than twenty years, Rubin31-34 and Emami30,26 determined a unified format of low-risk and high-risk dose tolerance limits for conventionally fractionated radiation therapy, and twenty years later these were further refined by QUANTEC36. The Emami tables were specified in terms of tolerance dose (TD), with the TD 5/5 and the TD 50/5, the 5% and 50% risk levels of complication at 5 years. It would be easier to memorize 5% and 50% risk levels for most critical structures, but some structures like spinal cord or optic nerve require much lower complication rates than other structures such as ribs.
QUANTEC36 provided custom risk levels for each structure – in this issue of Seminars a compromise is sought between the unified structure of Emami and the precision of QUANTEC. The evolution of SBRT dose tolerance limits with Gamma Knife49, linac based radiosurgery50-55, the SBRT body frame56, and the CyberKnife57 all have had clinical usage for at least 20 years. We have attempted to consolidate some elements of that collective 20 year experience into a format comprehensive and convenient for clinical application. The simplified DVH Risk Map in Fig. 2 shows some of the variety in published dose tolerance limits for allowable Dmax to individual ribs; a blue diamond represents each published limit. The Pettersson 2009 data and dose response models58 has been used to estimate the risk levelfootnote 1 of each of the dose tolerance limits in Fig. 2. Limits close to the 5% or 50% risk level are circled, labeled, and shown numerically in the tabular portion of the DVH Risk Map. From the Dmax data in Pettersson 2009, the 50% risk level in three fractions was 60 Gy, so that was chosen as the high-risk limit, as seen by the “Pett. 2009” label in the graph in Fig. 2 and the “60 Gy (58), 49.9% Risk” text in the table at the bottom of Fig. 2. This strategy of notation is used throughout all the DVH Risk Maps, but in a more compressed form without the explanatory labels, wherein only the dose and risk would be shown, as “60.0, 49.9%”. The TG101 three-fraction 36.9 Gy Dmax limit had an estimated risk of 4.5%, which is close enough to 5% to be considered as the low-risk limit. Using linear quadratic (LQ) conversions with α/β=3 Gy enabled application of the same model to four fractions, and the 40 Gy Dmax limit of RTOG 0915 had 3.9% estimated risk so this also was deemed to be low-risk. The risk level of the 5-fraction TG101 limit was not estimated from this data because it would be too far to extrapolate from 3 fractions, so the 43.0 Gy dose was displayed in the table without an associated estimate of risk. For 4 and 5 fractions there were no published limits near the 50% risk level so in this example they have been left blank – typically they would be interpolated or extrapolated as preliminary estimates for limits and would be formatted in italics to emphasize the uncertainty. All these missing limits and estimates of risk can be established as more data is published and analyzed. In Fig. 2 it is apparent that the 5% and 50% risk level graphs are curved, instead of being straight lines as in Fig. 1. This is because the LQ model was used to convert the three-fraction dose limits into other fractionations. If a different BED model like USC or linear quadratic cubic (LQC)14 had been used the curve would have a different shape. In the DVH Risk Map three things have been done to alleviate the effects of this uncertainty: a) since the Pettersson 2009 dataset only has 3 fractions, in the table estimates of risk in 1 and 5 fractions were omitted, b) the numerical dose values in the table are all in terms of equivalent physical dose in Gy, not BED, and c) the y-axis in the graphs is still linear, raw physical dose, so the effects of the BED conversions may be observed. Even when BED conversions have been applied to the modeled results, the doses themselves can still be plotted on a linear scale as physical dose to alleviate the uncertainty. The red X‟s in DVH Risk Maps denote published complications for which there is insufficient data to know yet whether this is an acceptable risk level. In Fig. 2 the red X is a grade 3 rib fracture from 1
Figure 2 of the Pettersson 2009 article provides the DVH for each rib and we have digitized these to estimate TD50v=60.0564 Gy, γ50,V=2.4072 for Dmax, using the model in their Eq. 1. This model of the Pettersson 2009 data was used for all of the Dmax risk estimates.
Rusthoven 200959 which became part of a subsequent multi-institutional analysis60. By itself, the datapoint with a complication is merely one case out of 38 and the dose to the rib in the other cases was not reported, so initially points like this were just marked with a red X to denote a caution. Now that models for dose tolerance are emerging, however, the risk level can be estimated, and this datapoint is above the 50% risk level for Grade 1-3 complications in most models. However, data in these high dose regions and data points for grade 3 and higher complications are still sparse, so it is still possible that this will become a usable dose level.
Volume Effects Emami et al. presented dose tolerance limits in terms of 100%, 67%, and 33% volumes for most critical structures in their table30 and as depicted by the diagram in Fig. 3a. These percent choices were convenient but obviously these volumes cannot be the most significant indicator of toxicity for every critical anatomical structure. For SBRT, the volumes of interest are usually much smaller as suggested in Fig. 3b, and there is considerable variation in the volume specified in the published SBRT dose tolerance limits. The main premise of SBRT is that only small volumes of healthy tissue will be allowed to receive the ablatively high dose per fraction, and in light of the bath and shower effects studied by van der Kogel and colleagues61-64, it is prudent to explicitly limit the low dose to the large volume, at least until the outcomes are better understood. Therefore a limit for the median dose (D50%)footnote 2 which corresponds to 50% volume is usually included. Instead of D33%, a smaller volume like D10% is more likely to be appropriate, and D10% has been used as an SBRT constraint by a wide variety of authors for various anatomical structures65-76,41. Absolute volume is generally expected to be more important for SBRT, particularly small absolute volumes like 1cc or 0.1cc. In addition to D50%, D10%, and Dmax, the DVH Risk Maps usually provide dose tolerance limits for two absolute volumes. These absolute volumes are chosen specific to each anatomical structure – for bowel a volume as large as 20cc is common41,42,67, and 1cc is suitable for the small volume, whereas for spinal cord and other neurological structures 1cc is the large volume and 0.1cc is more typical of the small volume41-42. The Dx definition is the same as the dose cursor in most treatment planning systems for scrolling back and forth across a DVH: with the dose cursor at a particular volume, the displayed dose on the cursor is the minimum dose corresponding to the highest-dose volume of the contoured tissue. This Dx notation means that volume x of the anatomical structure exceeds dose D. The volume x can be a percentage of the total volume, such as 50% or 10%, or it can be absolute volume like 1cc or 0.1cc. Within human tissue there is heterogeneity of dose: every voxel of the treatment plan can have a different dose. The D x notation takes this into account by incorporating dose and volume into the dose tolerance limit.
2
Dx = minimum dose received by the „„hottest‟‟ x% (or x cc‟s) of the organ36.
In most works on dose response modeling, it is called dose response for ease of explanation – but in radiation oncology, wherever there is a dose there is a corresponding volume, and wherever there is a volume there is a corresponding dose. The term “dose response” implies dose to a particular metric that quantifies the volume, such as Dx, Deff, EUD, etc. Likewise, the model could instead be in terms of volume response, with respect to a metric that quantifies the dose, such as Vx, Veff, etc. The most accurate terminology is dose-volume response, instead of dose response or volume response. However, it is easier to explain it as dose response when dose is on the x-axis, or to explain it as volume response when volume is on the x-axis, so most authors throughout this issue simply call it “dose response” and “dose tolerance limits”. This makes sense clinically, since physicians have more control over dose than volume.
Dose Response Modeling A sufficiently high dose is guaranteed to kill the tumor and cause a complication, so dose response is widely understood. For many years, statistical models18-29 have been determined that relate dose to outcome in clinically useful ranges. As shown in Fig. 4, when the model is known, the estimated risk level for any dose tolerance limit can be interpolated from the model. For the rib fracture example, the dose response model for a volume of 2cc was determined in the threefraction Pettersson 2009 study58, and was superimposed in Fig. 4 for convenience. For the low risk limit, the 5% risk level can be interpolated from the graph as 27.2 Gy in 3 fractions. The high risk limit can similarly be interpolated, where 49.8 Gy in 3 fractions corresponds to 50% risk. The LQ model with α/β=3 Gy can be used to convert these doses to 2 fractions or 4 fractions, but to convert to more dramatically different fractionations it is advisable to re-analyze with more applicable clinical data. The Pettersson 2009 manuscript also provided models for Dmean and D20%, as well as DVH data that we used to generate a Dmax model. In this issue of Seminars, most papers use BED conversions both before and after NTCP. Prior to NTCP modeling, the doses from various fraction schemes are converted to some form of BED so they can all be analyzed together. After the NTCP analysis, they are converted back to their respective fractionations, and if the reliability of the data and model permits, possibly extended to other fractionations. Ideally the results would be extended to the full range of 1-5 fractions used in SBRT, or perhaps even up to 10 fractions, but frequently the data is too sparse and there is certainly much work to be done in future studies to fill in the remaining data.
DVH Risk Map Example, for Individual Ribs Based on the preceding explanations, the Pettersson 2009 dataset for individual ribs is displayed as a DVH Risk Map in Fig. 5. The median followup was 29 months (range: 15-69) and the endpoint was radiation induced rib fractures, mostly grade 1 and possibly up to CTCAE v4 grade 377. Clinical data from an institution may also be superimposed onto the graph of dose tolerance limits as a function of the number of fractions, with the green dots representing dose-volume points that fell below the low-risk limits, the red dots representing dose-volume above the high-risk limits, and yellow dots in between. The
red boxes denote the institutional data that had complications, for an early view of dose response as it occurs clinically. When sufficient data has accumulated to construct a dose response model, estimates of risk can be included in the tabular portion of the DVH Risk Map; in this case these percentage risk estimates are from the Pettersson 2009 data and corresponding models.
Conclusion Beginning with simplistic graphs of dose tolerance limits as a function of the number of fractions, the DVH Risk Maps have become a useful comparison of the range of clinical and published data. In an attempt to make safe decisions in the treatment of patients with SBRT, published data was accumulated and the DVH Risk Map was created to provide the physician with a range of comparisons of risk levels as a function of dose, fractionation, and volume.
Glossary
AAPM: American Association of Physicists in Medicine BED: Biological Effective Dose CTCAE: Common Terminology Criteria for Adverse Events Deff: Effective Dose DVH: Dose Volume Histogram Dx: minimum dose received by the „„hottest‟‟ x% (or x cc‟s) of the organ36 EUD: Equivalent Uniform Dose Fx: Fraction, one treatment session of the overall total dose Gy: Gray, the International System (SI) unit of dose, defined as the absorption of one Joule per kilogram LQ: Linear Quadratic, a model of BED LQC: Linear Quadratic Cubic, a model of BED NSD: Nominal Standard Dose NTCP: Normal Tissue Complication Probability QUANTEC: Quantitative Analysis of Normal Tissue Effects in the Clinic RTOG: Radiation Therapy Oncology Group
SABR: Stereotactic Ablative Body Radiotherapy SBRT: Stereotactic Body Radiation Therapy TD: Tolerance Dose TDF: Time Dose Fractionation TG 101: The report of AAPM Task Group 101 USC: Universal Survival Curve Veff: Effective Volume Vx: minimum volume received by the „„hottest‟‟ x% (or x Gy‟s) of the organ
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Figure 1 Simplified DVH Risk Map for Spinal Cord, for maximum point dose (Dmax) limits in 1, 3, and 5 fractions from Timmerman 2008, with a straight line interpolation from 1 to 5 fractions. The universal survival curve (USC)15 is linear at high dose per fraction.
Figure 2 DVH Risk Map for Individual Rib maximum point dose (Dmax). The blue diamonds are the published dose tolerance limits, the circled and labeled limits are near the 5% or 50% risk levels, the red X is the dose at which a published complication occurred, the solid red line is the 50% risk level and the dashed green line is approximately the 5% risk level. Estimates of risk in this example are from Pettersson 2009.
D100%
D67%
D33%
3/3 Volume
2/3 Volume
1/3 Volume
(a)
D50%
D10%
D30cc
D2cc
Dmax
1/2 Volume
10% Volume
30cc Volume
2cc Volume
“Zero” Volume
(b) Figure 3 Dose tolerance limits as a function of volume, (a) for conventional fractionation and (b) for SABR/SBRT. Low dose per fraction enables large volumes of critical structures to be irradiated, like D100%, D67%, and D33%, but SABR/SBRT requires smaller volumes like D50%, D10%, D30cc, D2cc and Dmax. The ideal volumes for each critical anatomical structure are being actively studied.
Figure 4 Creation of a DVH Risk Map: Interpolating risk level estimates from the published dose response model: the arrows show that for D2cc=27.2 Gy in 3 fractions the estimated risk level was 5%, and that for D2cc=49.8 Gy in 3 fractions the estimated risk level was 50%. All other dose-volume constraints were interpolated from corresponding models using the same methodology.
Figure 5 Full DVH Risk Map for Individual Ribs, with clinical data and estimates of risk from Pettersson 2009.
Dose Volume Histogram (DVH) Clinical Overview: The DVH Risk Map Sucha O. Asbell MD, Jimm Grimm PhD, Jinyu Xue PhD, Meng-Sang Chew PhD, Tamara A. LaCouture MD
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S1053-4296(15)00115-0 http://dx.doi.org/10.1016/j.semradonc.2015.11.005 YSRAO50532
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Cite this article as: Sucha O. Asbell MD, Jimm Grimm PhD, Jinyu Xue PhD, Meng-Sang Chew PhD, Tamara A. LaCouture MD, Dose Volume Histogram (DVH) Clinical Overview: The DVH Risk Map, Semin Radiat Oncol , http://dx.doi.org/10.1016/j.semradonc.2015.11.005 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Dose Volume Histogram (DVH) Clinical Overview: The DVH Risk Map Sucha O. Asbell, MD1, Jimm Grimm, PhD2, Jinyu Xue, PhD1, Meng-Sang Chew, PhD3, and Tamara A. LaCouture, MD1
Radiation oncologists need reliable estimates of risk for various fractionation schemes for all critical anatomical structures throughout the body, in a clinically convenient format. Reliable estimation theory can become unduly complex, however, and estimates of risk continue to evolve as the literature matures. To navigate through this efficiently, a DVH Risk Map was created, which provides a comparison of radiation tolerance limits as a function of dose, fractionation, volume, and risk level. The graphical portion of the DVH Risk Map helps clinicians to easily visualize the trends, while the tabular portion provides quantitative precision for clinical implementation. The DVH Risk Map for rib tolerance from stereotactic ablative body radiotherapy (SABR) and stereotactic body radiation therapy (SBRT) is used as an example in this overview; the 5% and 50% risk levels for 1 to 5 fractions for five different volumes are given. Other articles throughout this issue of Seminars in Radiation Oncology present analysis of new clinical datasets including the DVH Risk Maps for other anatomical structures throughout the body. 1
Radiation Oncology, M.D. Anderson at Cooper University Hospital, Camden, NJ, USA Holy Redeemer Hospital, Bott Cancer Center, Meadowbrook, PA, USA 3 Packard Lab 256B, Lehigh University, Bethlehem, PA, USA 2
Conflict of Interests Notification: None of the authors has received any funding for this research. Dr. Grimm developed and holds intellectual property rights to the DVH Evaluator software tool which is an FDA-cleared product in commercial use, and which has been used for this analysis.
H
uman dose tolerance to conventionally fractionated radiation has been analyzed for many decades.
The development of isoeffect curves1, nominal standard dose (NSD)2, and time dose fractionation (TDF) tables3 eventually led to biological effective dose (BED)4 based on the linear quadratic (LQ) model5-9, and many other models for biological equivalence continue to be investigated10-17. Dose response modeling1829 provides a more explicit way to estimate the actual risk levels for each critical anatomical structure as a function of dose, fractionation, volume, and other parameters. Emami‟s 1991 work30 combined this theoretical framework with clinically usable dose tolerance limits like Rubin31-34 to provide 5% and 50% risk levels for 25 anatomical structures throughout the body. Ten years later the July 2001 issue of Seminars in Radiation Oncology35 presented a comprehensive update of the modeling results, and after about another 10 years, most of the lead authors from that work became
authors of QUANTEC36, which is currently the most accurate assessment of normal tissue complication probability (NTCP) for conventional fractionation. Dose tolerance for stereotactic ablative body radiotherapy (SABR) and stereotactic body radiation therapy (SBRT) is still much more uncertain. We began delivering CyberKnife treatments before most of the RTOG SABR/SBRT protocols37-40, before TG 10141, before QUANTEC36, and before the Timmerman 2008 issue of Seminars in Radiation Oncology42. Dose tolerance guidelines were extremely rare, and we began accumulating a simple spreadsheet of the sparsely published data. Over time it grew to 500 dose tolerance limits43 and as of 2016 there are well over 1000 published limits – but they are discordant, ever changing, and until now have lacked quantitative estimates of corresponding incidence of complication.
Dose Tolerance Limits Defined Much has been said about dose tolerance limits, but our formal definition may clarify:
Dose Tolerance Limit: A specified radiation dose, fractionation and volume, with an associated estimated risk of developing a complication of a specified endpoint within a specified followup time.
Human dose tolerance to radiation depends on many other factors, but a well-defined dose tolerance limit must specify at least the following: 1) Dose 2) Fractionation 3) Volume 4) Endpoint 5) Followup Time 6) Estimated Risk of the Endpoint occurring within the Followup Time The endpoint and length of followup must be clearly stated in order for the dose tolerance limit to be useful. Emami used 5 years as the followup period for every dose tolerance limit, and although this is convenient, there is not much 5-year quantitative data available yet in the SBRT literature. Note that a 5year followup period implicitly includes both early and late effects, but for SBRT in particular, there is much interest in distinguishing the timing of the onset of symptoms. Finally, for a dose tolerance limit to truly be useful in clinical decision making, it must include an estimate of the associated risk of the endpoint occurring within the specified time. The circumstances of each patient and each tumor are unique. We need reliable estimates of complication probability which will provide physicians with the information needed to make the most informed decisions.
Simple Graphs, Physical Dose If the information relating a range of dose tolerance limits and their respective risks could be arranged on a single graph it would help physicians make decisions about management. In an attempt to make sense of contradictory published SBRT constraints, simple graphs of the dose tolerance limits as a function of the number of fractions were made, which led to the creation of the DVH Risk Map44. Initially our tendency was to perform a BED conversion of the doses before plotting them. We quickly realized, however, that currently the BED conversions themselves were just one more confounding factor that made comparisons more difficult, since there are so many methods of BED conversion4-17. Due to lack of thorough reporting standards45 it has often not been feasible to unravel the conversions of one publication and recompute to the conversions of another. Therefore we tried simply plotting the dose tolerance limits on a linear scale; pure physical dose. Much to our surprise, we discovered that someone else must have already come to this realization, because as may be clearly seen by plotting the limits as in Fig. 1, many of the Timmerman 2008 limits are related by straight lines. It is not possible to express what a profound impact these few straight lines have had on the field of radiation oncology in SBRT – they may be simple, but they have been a remarkably useful starting point. Furthermore, the potential linearization of BED at high dose per fraction as expressed in the universal survival curve (USC)15 does provide a plausible theoretical justification, although, as with all BED conversions, there is some debate16,17.
In the DVH Risk Map graphs, dose is on the y-axis, each subplot is for a specific volume, and the number of fractions is on the x-axis of each subplot. There are many dose-volume metrics that combine dose and volume together, such as the inverse power law24, effective volume (Veff)46, effective dose (Deff)47, or equivalent uniform dose (EUD)48. Any of these metrics can be used to specify a dose tolerance limit, and any of these can be used as one of the five subplots in a DVH Risk Map.
Low-Risk and High-Risk Partition Every patient is unique, especially considering the variability of tumors and the proximity to critical structures, so a range of dose tolerance limits is needed. Over a period of more than twenty years, Rubin31-34 and Emami30,26 determined a unified format of low-risk and high-risk dose tolerance limits for conventionally fractionated radiation therapy, and twenty years later these were further refined by QUANTEC36. The Emami tables were specified in terms of tolerance dose (TD), with the TD 5/5 and the TD 50/5, the 5% and 50% risk levels of complication at 5 years. It would be easier to memorize 5% and 50% risk levels for most critical structures, but some structures like spinal cord or optic nerve require much lower complication rates than other structures such as ribs.
QUANTEC36 provided custom risk levels for each structure – in this issue of Seminars a compromise is sought between the unified structure of Emami and the precision of QUANTEC. The evolution of SBRT dose tolerance limits with Gamma Knife49, linac based radiosurgery50-55, the SBRT body frame56, and the CyberKnife57 all have had clinical usage for at least 20 years. We have attempted to consolidate some elements of that collective 20 year experience into a format comprehensive and convenient for clinical application. The simplified DVH Risk Map in Fig. 2 shows some of the variety in published dose tolerance limits for allowable Dmax to individual ribs; a blue diamond represents each published limit. The Pettersson 2009 data and dose response models58 has been used to estimate the risk levelfootnote 1 of each of the dose tolerance limits in Fig. 2. Limits close to the 5% or 50% risk level are circled, labeled, and shown numerically in the tabular portion of the DVH Risk Map. From the Dmax data in Pettersson 2009, the 50% risk level in three fractions was 60 Gy, so that was chosen as the high-risk limit, as seen by the “Pett. 2009” label in the graph in Fig. 2 and the “60 Gy (58), 49.9% Risk” text in the table at the bottom of Fig. 2. This strategy of notation is used throughout all the DVH Risk Maps, but in a more compressed form without the explanatory labels, wherein only the dose and risk would be shown, as “60.0, 49.9%”. The TG101 three-fraction 36.9 Gy Dmax limit had an estimated risk of 4.5%, which is close enough to 5% to be considered as the low-risk limit. Using linear quadratic (LQ) conversions with α/β=3 Gy enabled application of the same model to four fractions, and the 40 Gy Dmax limit of RTOG 0915 had 3.9% estimated risk so this also was deemed to be low-risk. The risk level of the 5-fraction TG101 limit was not estimated from this data because it would be too far to extrapolate from 3 fractions, so the 43.0 Gy dose was displayed in the table without an associated estimate of risk. For 4 and 5 fractions there were no published limits near the 50% risk level so in this example they have been left blank – typically they would be interpolated or extrapolated as preliminary estimates for limits and would be formatted in italics to emphasize the uncertainty. All these missing limits and estimates of risk can be established as more data is published and analyzed. In Fig. 2 it is apparent that the 5% and 50% risk level graphs are curved, instead of being straight lines as in Fig. 1. This is because the LQ model was used to convert the three-fraction dose limits into other fractionations. If a different BED model like USC or linear quadratic cubic (LQC)14 had been used the curve would have a different shape. In the DVH Risk Map three things have been done to alleviate the effects of this uncertainty: a) since the Pettersson 2009 dataset only has 3 fractions, in the table estimates of risk in 1 and 5 fractions were omitted, b) the numerical dose values in the table are all in terms of equivalent physical dose in Gy, not BED, and c) the y-axis in the graphs is still linear, raw physical dose, so the effects of the BED conversions may be observed. Even when BED conversions have been applied to the modeled results, the doses themselves can still be plotted on a linear scale as physical dose to alleviate the uncertainty. The red X‟s in DVH Risk Maps denote published complications for which there is insufficient data to know yet whether this is an acceptable risk level. In Fig. 2 the red X is a grade 3 rib fracture from 1
Figure 2 of the Pettersson 2009 article provides the DVH for each rib and we have digitized these to estimate TD50v=60.0564 Gy, γ50,V=2.4072 for Dmax, using the model in their Eq. 1. This model of the Pettersson 2009 data was used for all of the Dmax risk estimates.
Rusthoven 200959 which became part of a subsequent multi-institutional analysis60. By itself, the datapoint with a complication is merely one case out of 38 and the dose to the rib in the other cases was not reported, so initially points like this were just marked with a red X to denote a caution. Now that models for dose tolerance are emerging, however, the risk level can be estimated, and this datapoint is above the 50% risk level for Grade 1-3 complications in most models. However, data in these high dose regions and data points for grade 3 and higher complications are still sparse, so it is still possible that this will become a usable dose level.
Volume Effects Emami et al. presented dose tolerance limits in terms of 100%, 67%, and 33% volumes for most critical structures in their table30 and as depicted by the diagram in Fig. 3a. These percent choices were convenient but obviously these volumes cannot be the most significant indicator of toxicity for every critical anatomical structure. For SBRT, the volumes of interest are usually much smaller as suggested in Fig. 3b, and there is considerable variation in the volume specified in the published SBRT dose tolerance limits. The main premise of SBRT is that only small volumes of healthy tissue will be allowed to receive the ablatively high dose per fraction, and in light of the bath and shower effects studied by van der Kogel and colleagues61-64, it is prudent to explicitly limit the low dose to the large volume, at least until the outcomes are better understood. Therefore a limit for the median dose (D50%)footnote 2 which corresponds to 50% volume is usually included. Instead of D33%, a smaller volume like D10% is more likely to be appropriate, and D10% has been used as an SBRT constraint by a wide variety of authors for various anatomical structures65-76,41. Absolute volume is generally expected to be more important for SBRT, particularly small absolute volumes like 1cc or 0.1cc. In addition to D50%, D10%, and Dmax, the DVH Risk Maps usually provide dose tolerance limits for two absolute volumes. These absolute volumes are chosen specific to each anatomical structure – for bowel a volume as large as 20cc is common41,42,67, and 1cc is suitable for the small volume, whereas for spinal cord and other neurological structures 1cc is the large volume and 0.1cc is more typical of the small volume41-42. The Dx definition is the same as the dose cursor in most treatment planning systems for scrolling back and forth across a DVH: with the dose cursor at a particular volume, the displayed dose on the cursor is the minimum dose corresponding to the highest-dose volume of the contoured tissue. This Dx notation means that volume x of the anatomical structure exceeds dose D. The volume x can be a percentage of the total volume, such as 50% or 10%, or it can be absolute volume like 1cc or 0.1cc. Within human tissue there is heterogeneity of dose: every voxel of the treatment plan can have a different dose. The D x notation takes this into account by incorporating dose and volume into the dose tolerance limit.
2
Dx = minimum dose received by the „„hottest‟‟ x% (or x cc‟s) of the organ36.
In most works on dose response modeling, it is called dose response for ease of explanation – but in radiation oncology, wherever there is a dose there is a corresponding volume, and wherever there is a volume there is a corresponding dose. The term “dose response” implies dose to a particular metric that quantifies the volume, such as Dx, Deff, EUD, etc. Likewise, the model could instead be in terms of volume response, with respect to a metric that quantifies the dose, such as Vx, Veff, etc. The most accurate terminology is dose-volume response, instead of dose response or volume response. However, it is easier to explain it as dose response when dose is on the x-axis, or to explain it as volume response when volume is on the x-axis, so most authors throughout this issue simply call it “dose response” and “dose tolerance limits”. This makes sense clinically, since physicians have more control over dose than volume.
Dose Response Modeling A sufficiently high dose is guaranteed to kill the tumor and cause a complication, so dose response is widely understood. For many years, statistical models18-29 have been determined that relate dose to outcome in clinically useful ranges. As shown in Fig. 4, when the model is known, the estimated risk level for any dose tolerance limit can be interpolated from the model. For the rib fracture example, the dose response model for a volume of 2cc was determined in the threefraction Pettersson 2009 study58, and was superimposed in Fig. 4 for convenience. For the low risk limit, the 5% risk level can be interpolated from the graph as 27.2 Gy in 3 fractions. The high risk limit can similarly be interpolated, where 49.8 Gy in 3 fractions corresponds to 50% risk. The LQ model with α/β=3 Gy can be used to convert these doses to 2 fractions or 4 fractions, but to convert to more dramatically different fractionations it is advisable to re-analyze with more applicable clinical data. The Pettersson 2009 manuscript also provided models for Dmean and D20%, as well as DVH data that we used to generate a Dmax model. In this issue of Seminars, most papers use BED conversions both before and after NTCP. Prior to NTCP modeling, the doses from various fraction schemes are converted to some form of BED so they can all be analyzed together. After the NTCP analysis, they are converted back to their respective fractionations, and if the reliability of the data and model permits, possibly extended to other fractionations. Ideally the results would be extended to the full range of 1-5 fractions used in SBRT, or perhaps even up to 10 fractions, but frequently the data is too sparse and there is certainly much work to be done in future studies to fill in the remaining data.
DVH Risk Map Example, for Individual Ribs Based on the preceding explanations, the Pettersson 2009 dataset for individual ribs is displayed as a DVH Risk Map in Fig. 5. The median followup was 29 months (range: 15-69) and the endpoint was radiation induced rib fractures, mostly grade 1 and possibly up to CTCAE v4 grade 377. Clinical data from an institution may also be superimposed onto the graph of dose tolerance limits as a function of the number of fractions, with the green dots representing dose-volume points that fell below the low-risk limits, the red dots representing dose-volume above the high-risk limits, and yellow dots in between. The
red boxes denote the institutional data that had complications, for an early view of dose response as it occurs clinically. When sufficient data has accumulated to construct a dose response model, estimates of risk can be included in the tabular portion of the DVH Risk Map; in this case these percentage risk estimates are from the Pettersson 2009 data and corresponding models.
Conclusion Beginning with simplistic graphs of dose tolerance limits as a function of the number of fractions, the DVH Risk Maps have become a useful comparison of the range of clinical and published data. In an attempt to make safe decisions in the treatment of patients with SBRT, published data was accumulated and the DVH Risk Map was created to provide the physician with a range of comparisons of risk levels as a function of dose, fractionation, and volume.
Glossary
AAPM: American Association of Physicists in Medicine BED: Biological Effective Dose CTCAE: Common Terminology Criteria for Adverse Events Deff: Effective Dose DVH: Dose Volume Histogram Dx: minimum dose received by the „„hottest‟‟ x% (or x cc‟s) of the organ36 EUD: Equivalent Uniform Dose Fx: Fraction, one treatment session of the overall total dose Gy: Gray, the International System (SI) unit of dose, defined as the absorption of one Joule per kilogram LQ: Linear Quadratic, a model of BED LQC: Linear Quadratic Cubic, a model of BED NSD: Nominal Standard Dose NTCP: Normal Tissue Complication Probability QUANTEC: Quantitative Analysis of Normal Tissue Effects in the Clinic RTOG: Radiation Therapy Oncology Group
SABR: Stereotactic Ablative Body Radiotherapy SBRT: Stereotactic Body Radiation Therapy TD: Tolerance Dose TDF: Time Dose Fractionation TG 101: The report of AAPM Task Group 101 USC: Universal Survival Curve Veff: Effective Volume Vx: minimum volume received by the „„hottest‟‟ x% (or x Gy‟s) of the organ
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Figure 1 Simplified DVH Risk Map for Spinal Cord, for maximum point dose (Dmax) limits in 1, 3, and 5 fractions from Timmerman 2008, with a straight line interpolation from 1 to 5 fractions. The universal survival curve (USC)15 is linear at high dose per fraction.
Figure 2 DVH Risk Map for Individual Rib maximum point dose (Dmax). The blue diamonds are the published dose tolerance limits, the circled and labeled limits are near the 5% or 50% risk levels, the red X is the dose at which a published complication occurred, the solid red line is the 50% risk level and the dashed green line is approximately the 5% risk level. Estimates of risk in this example are from Pettersson 2009.
D100%
D67%
D33%
3/3 Volume
2/3 Volume
1/3 Volume
(a)
D50%
D10%
D30cc
D2cc
Dmax
1/2 Volume
10% Volume
30cc Volume
2cc Volume
“Zero” Volume
(b) Figure 3 Dose tolerance limits as a function of volume, (a) for conventional fractionation and (b) for SABR/SBRT. Low dose per fraction enables large volumes of critical structures to be irradiated, like D100%, D67%, and D33%, but SABR/SBRT requires smaller volumes like D50%, D10%, D30cc, D2cc and Dmax. The ideal volumes for each critical anatomical structure are being actively studied.
Figure 4 Creation of a DVH Risk Map: Interpolating risk level estimates from the published dose response model: the arrows show that for D2cc=27.2 Gy in 3 fractions the estimated risk level was 5%, and that for D2cc=49.8 Gy in 3 fractions the estimated risk level was 50%. All other dose-volume constraints were interpolated from corresponding models using the same methodology.
Figure 5 Full DVH Risk Map for Individual Ribs, with clinical data and estimates of risk from Pettersson 2009.