A clinical application of fair value estimate (FVE) for R50%: Separating overlapping 50% isodose volumes in single isocenter multiple targets SRS

In the treatment of single isocenter multiple targets (SIMT) stereotactic cranial cases with linac-based, multi-leaf collimated delivery, one encounters cases when the 50% isodose clouds (IDC50%s) of planning target volumes (PTVs) in close proximity overlap and cannot easily be separated. In such cases, it is difficult to assign an IDC50% to each individual PTV, which is necessary to allow evaluation of individual PTV intermediate dose spill for comparison to established intermediate dose spill metrics for plan quality assessment. The Fair Value Estimate (FVE) for R50% (R50%FVE ) is a method to unambiguously apportion the overlapping volume of IDC50% to allow calculation of the intermediate dose spill metric R50% (defined as volume of IDC50% / volume of PTV). Full application of R50%FVE requires knowing the surface area of the PTVs. Since surface area information is not always available, we develop a spherical PTV approximation to R50%FVE-sphere and compare this to R50%FVE . Then we apply the R50%FVE-sphere to clinical data from the University of Alabama, Birmingham (UAB) that catalogs 68 PTVs from various SIMT plans with overlapping IDC50%. The UAB dataset reports intermediate dose spill as Falloff Index. While Falloff Index looks mathematically equivalent to R50%, the Falloff Index attributes the "entire overlapping IDC50% of PTVs in close proximity" to each individual PTV in the cluster. R50%FVE-sphere provides a value that is conceptually correct and numerically smaller relative to the Falloff Index data reported by UAB in all cases. This reprocessing of the UAB data places many of the PTVs with very high intermediate dose spill within recently proposed R50% guidelines.

How to estimate R50% for cranial SRS/SRT cases with overlapping 50% isodose volumes: A proposed system

Inevitably in clinical stereotactic cranial single isocenter multiple target cases treated with linac‐based multi‐leaf collimated (MLC) delivery, one encounters planning target volumes (PTVs) in close proximity with overlapping 50% isodose clouds (IDC50%). In such cases, it is very difficult to separate the IDC50% attributable to each individual target and, thus, assess the intermediate dose conformality or R50%. Such scenarios happen regardless of what metric is used to measure intermediate dose spill. Now that universal standards for intermediate dose spill have been proposed, it is important to have a consistent method for apportioning these overlapping IDC50% volumes to allow comparison with the proposed standards when multiple PTVs have overlapping IDC50%. We propose a systematic method for apportioning the IDC50% of multiple targets with overlapping IDC50% based on the relative surface area of each target volume; we call this the fair value estimate (FVE). This FVE system of apportionment is tested for reasonableness by comparing the apportionment of multiple target single isocenter stereotactic treatment with widely spaced targets where the IDC50% can be obviously assigned to demonstrate that the FVE results are very similar to the actual R50% results. We then demonstrate how the FVE system would be applied to cases with overlapping IDC50%. We propose this FVE system for consideration by the cranial stereotactic community for apportioning the intermediate dose spill when that intermediate dose spill overlaps among multiple targets.

A measure of SRS/SRT plan quality: Quantitative limits for intermediate dose spill (R50%) in linac-based delivery

Stereotactic radiosurgery (SRS) and stereotactic radiotherapy (SRT) of multiple cranial targets using a single isocenter on conventional C‐arm linear accelerators are rapidly developing clinical techniques. However, no universal guidelines for acceptable intermediate dose spill limits are currently available or widely accepted. In this work, we propose an intermediate dose spill guidance range for cranial SRS/SRT delivered on C‐arm linacs with MLC collimation for single PTV plans and single isocenter multiple target plans with PTV volumes in the range 0.02–57.9 cm³. We quantify intermediate dose spill with the R50% metric (R50% = volume of 50% of prescription isodose cloud / volume of PTV) and test the proposed range using three clinical data sets, containing both 6 MV and 10 MV beams, previously published by other authors. Our proposed lower limit of R50% (LowerR50%) and upper limit of acceptable R50% (UpperR50%) bound over 90% of the clinical data used in this study, yet still provide a challenging benchmark for optimization and plan assessment of linac‐based, MLC collimated SRS/SRT.

Analysis of R50% location dependence on LINAC-based VMAT cranial stereotactic treatments

Stereotactic radiosurgery (SRS) and stereotactic radiation therapy (SRT) techniques are used to deliver high doses per fraction to various types of intra-cranial targets. LINAC-based solutions are growing in prevalence due to recent advances in technologies such as high-definition multi-leaf collimators and volumetric arc therapy radiation delivery. A wide variety of clinical pathologies including intracranial metastases, meningioma, glioblastoma, arteriovenous malformation, acoustic neuroma, and trigeminal neuralgia have been successfully treated using SRS/SRT techniques. These lesions can be in virtually at any location within the cranium. Several publications have shown a wide dispersion of intermediate dose conformality (intermediate dose spill) indices such as the Paddick Gradient Index or R50% for lesions of a specific volume. A complete explanation of this dispersion is lacking but location has been suggested as a contributing factor. While prior studies of PTV location in SRS/SRT are retrospective in nature, we have conducted a prospective study to ascertain the potential effects of location within the cranium on plan intermediate dose conformality as measured by R50% while controlling for lesion volume, lesion shape, prescription (Rx) dose, and Rx isodose surface. Lesion volumes utilized in this study are consistent with metastatic disease presentation. Results indicate only a weak relationship between intermediate dose conformality as measured by R50% and the lesion location when considering nine different, strategically placed lesions. Close proximity to critical structures can reduce the degree of conformality, but the effect appears to be minimal. Single isocenter multiple target cases were studied in addition to single target plans. All critical structure doses observed in this study were found to be within the recommendations of AAPM Task Group report 101. Lesion location does not appear to be a significant contributing factor to the observed variation of dose conformality seen in several SRS/SRT publications.

Efficient optimization of R50% when planning multiple cranial metastases simultaneously in single isocenter SRS/SRT

Simultaneous optimization of multiple Planning Target Volumes (PTVs) of varying size and location in the cranium is a non-trivial task. The rate of dose falloff around PTV structures is variable and depends on PTV characteristics such as the volume. The metric R50% is one parameter that can be used to quantify dose falloff achieved in a given treatment plan. An important treatment planning question is how to construct optimization conditions that result in the efficient production of acceptable plan outcomes considering metrics such as R50%. Guidance provided in literature suggests generating multiple shell control structures around each PTV. The constraints applied to these shells can vary significantly depending on PTV volume. Additionally, there is no clear guidance on how to prospectively determine objective constraints for the optimization shells to achieve a specified goal of R50%. Based on physical principles and empirical evidence, we provide clear quantitative guidance on how to translate the desired R50% outcome into appropriately sized optimization structures around PTVs via an equation that depends on a desired goal for R50% and the volume of PTV. Optimization schema are also provided that allow the goal R50% to be approached or achieved for all PTVs individually. We demonstrate the application of the methodology using commercially available treatment planning software and radiotherapy treatment equipment.

The surface area effect: How the intermediate dose spill depends on the PTV surface area in SRS

Purpose

Stereotactic radiosurgery (SRS) is rapidly becoming the standard of care for many intracranial targets. The characteristics of the planning target volume (PTV) can affect the intermediate dose spill and thus normal brain volume dose which is correlated with brain toxicity. R50% (volume receiving 50% of prescription dose divided by PTV volume) is a useful metric to quantify the intermediate dose spill. We propose a novel understanding of how the PTV surface area (SA_PTV) affects the intermediate dose spill of SRS treatments.

Methods

Using a phantom model provided by a computed tomography (CT) of the IROC Head Phantom® and Eclipse® Treatment Planning System, we investigate the relationship of R50% and SA_PTV in single‐target SRS treatments. The planning studies are conducted for SRS treatments on a Varian TrueBeam® linear accelerator with high‐definition MLC and a 6 MVFFF beam mode. These data are analyzed to ascertain trends in R50% related to SA_PTV. Since SA_PTV is not available as a structure property in the Eclipse RTPS, we introduce an Eclipse script to extract PTV surface area of arbitrary‐shaped PTVs. We compare a physically reasonable theoretical prediction of R50%, R50%_Analytic, to the R50% achieved in treatment planning studies.

Results

The SRS phantom study indicates good correlation between the plan R50% and SA_PTV. A near‐linear relationship of plan R50% vs SA_PTV is observed as predicted by the R50%_Analytic model. Agreement between plan R50% values and R50%_Analytic predictions is good for all but the very smallest PTV volumes.

Conclusions

We demonstrate dependence of the intermediate dose spill measured by R50% on the SA_PTV. We call that dependence the surface area effect. This dependence is explicit in the R50%_Analytic prediction model. The predicted value of R50%_Analytic for a given PTV could be used for guidance during SRS treatment plan optimization, and plan evaluation for that PTV.

An analytical expression for R50% dependent on PTV surface area and volume: A cranial SRS comparison

The intermediate dose spill for a stereotactic radiosurgery (SRS) plan can be quantified with the metric R50%, defined as the 50% isodose cloud volume (V_IDC50% ) divided by the volume of the planning target volume (PTV). By coupling sound physical principles with the basic definition of R50%, we derive an analytical expression for R50% for a spherical PTV. Our analytical expression depends on three quantities: the surface area of PTV (SA_PTV ), the volume of PTV (V_PTV ), and the distance of dose drop-off to 50% (Δr). The value of ∆r was obtained from a simple set of cranial phantom plan calculations. We generate values from our analytical expression for R50% (R50%_Analytic ) and compare the values to clinical R50% values (R50%_Clinical ) extracted from a previously published SRS data set that spans the V_PTV range from 0.15 to 50.1 cm³ . R50%_Analytic is smaller than R50%_Clinical in all cases by an average of 15% ± 7%, and the general trend of R50%_Clinical vs V_PTV is reflected in the same trend of R50%_Analytic . This comparison suggests that R50%_Analytic could represent a theoretical lower limit for the clinical SRS data; further investigation is required to confirm this. R50%_Analytic could provide useful guidance for what might be achievable in SRS planning.

An analytical expression for R50% dependent on PTV surface area and volume: a lung SBRT comparison

In stereotactic body radiation therapy (SBRT), R50% is a common metric for intermediate dose spill and is defined in RTOG 0915 as the ratio of 50% isodose cloud volume (IDC50%) to the planning target volume (PTV). By coupling sound physical principles with the basic definition of intermediate dose spill, we derive an exact analytical expression for R50% for the case of a spherical volume. This expression for R50% depends on three quantities: the surface area of PTV (SA_PTV), the volume of PTV (V_PTV), and the dose gradient Δr. Validity of our analytical expression for R50% was confirmed via direct comparison to peer‐reviewed, multi‐institutional, diverse clinical data. The comparison of our R50% values computed from our analytical expression to the clinical data yielded an average percent difference of 3.8 ± 4.5%.

A physically meaningful relationship between R50% and PTV surface area in lung SBRT

Purpose

We propose a novel understanding of two characteristics of the planning target volume (PTV) that affect the intermediate‐dose spill in lung stereotactic body radiation therapy (SBRT) as measured by R50%. This phantom model research investigates two characteristics of the PTV that have a marked effect on the value of R50%: the mean dose deposited within the PTV (D_av) and the surface area of the PTV (SA_PTV).

Methods

Using a phantom model provided by a CT of the IROC Thorax‐Lung Phantom® (IROC Houston QA Center, Houston, TX) and Eclipse® Treatment Planning System (Varian Medical Systems, Palo Alto, CA), we investigate the two characteristics for spherical and cylindrical PTVs. A total of 135 plans with tightly controlled PTV characteristics are employed. A lower bound for R50% (R50%min_∆r) is derived and clearly establishes a relationship between R50% and SA_PTV that has not been fully appreciated previously.

Results

The study of PTV D_av revealed a local minimum for R50% as a function of the PTV D_av at D_av ≈ 110% of Rx dose. As PTV D_av increases above this local minimum, R50% increases; while for PTV D_av less than this local minimum, the R50% value also increases. The study of PTV surface area (SA_PTV) demonstrated that as the SA_PTV increases, the R50% increases if the PTV volume stays the same. The SA_PTV result is predicted by the theoretical investigation that yields the R50% lower bound, R50%min_∆r.

Conclusions

This research has identified two characteristics of the PTV that have a marked influence on R50%: PTV D_av and SA_PTV. These characteristics have not been clearly articulated in the vast body of previous research in SBRT. These results could help explain plans that cannot meet the RTOG criteria for R50%. With further development, these concepts could be extended to provide additional guidance for creating acceptable SBRT plans.

Induction of anti-DNA antibody with DNA-peptide complexes

Spontaneous anti-DNA antibodies in autoimmune mice have the characteristics of antibodies produced by antigen-specific, clonally selective B cell stimulation. The nature of the somatically derived antibody variable region structures recurrent among spontaneous anti-DNA antibodies suggests that DNA or DNA-protein complexes may provide the antigenic stimulus for autoimmune anti-DNA antibody. Previously we have demonstrated that native mammalian DNA in complexes with an immunogenic DNA-binding peptide Fus1 from Trypanosoma cruzi can induce anti-DNA antibody in mice not genetically prone to autoimmune disease. The induced anti-DNA has similar specificity, structure and immunopathological function as autoimmune anti-DNA. The present experiments were designed to further characterize the immune response to DNA-peptide complexes. There was considerable variation in the antibody responses of mice from different strains to DNA-Fus1 immunizations. The range was from virtually no response in C57BL/6 mice to most robust responses in NZW mice. The full-length 52 amino acid carboxy-extension protein of ubiquitin (CEP) in T. cruzi (TCEP) protein from which Fus1 was derived functions equally well as an immunogenic carrier for DNA. Anti-DNA responses were generally weak even though anti-Fus1 and anti-TCEP responses were very strong. The results are discussed with respect to the contrasting roles of T cell help and peripheral B cell tolerance in controlling immune and autoimmune antibody responses to DNA.

Immunoregulation of Th cells by naturally processed peptide antagonists

Th cells recognize protein Ags as short peptides bound to MHC class II molecules. Altered peptide ligands can antagonize (inhibit) T cell responses to stimulatory peptides. Peptides generated by APC may contain peptide flanking residues (PFR), which lie outside the minimal binding epitope and can be recognized by the TCR. Our data show that PFR-dependent T cells were found to be potently antagonized by peptides that lack PFR and responded poorly to native protein or the immunogenic epitope delivered by a recombinant influenza virus. These data provide the first evidence that Ag processing generates both stimulatory and antagonist peptides from a single immunogenic epitope, an observation that may have important implications for T cell immunoregulation and autoimmunity.

Expression of an anti-DNA-associated VH gene in immunized and autoimmune mice

The J558 family BW-16 VH gene is closely associated with the autoimmune response to DNA of lupus-prone mice. We have followed the expression of VHBW-16-encoded heavy chains in cDNA libraries prepared from unmanipulated normal (C3H, AKR) and autoimmune (New Zealand Black/New Zealand White F1) mice, and from mice immunized with a highly immunogenic peptide/DNA complex. The prevalence, clonal heterogeneity, and structural properties (somatic mutation, complementarity-determining region 3 composition) of these H chains were investigated, and the DNA affinity of VHBW-16-encoded hybridoma mAb was measured in solution. We find that H chains encoded by VHBW-16 are very rare in Igs of normal mice, but increase significantly in peptide/DNA-immunized mice, and dramatically in diseased mice. The experimentally induced VHBW-16-encoded H chains are clonally restricted, somatically mutated, partly switched from IgM to IgG, and give rise to anti-DNA Abs with low affinity. In contrast, the VHBW-16-encoded H chains from diseased New Zealand Black/New Zealand White mice are clonally heterogeneous, exclusively of the IgG isotype, and produce high affinity anti-DNA autoantibodies. We conclude that the experimentally induced and spontaneous immune responses to DNA are qualitatively similar, but quantitatively different, and may truly reflect the principles of self immunologic tolerance.

Expression of an anti-DNA-associated VH gene in immunized and autoimmune mice

The J558 family BW-16 VH gene is closely associated with the autoimmune response to DNA of lupus-prone mice. We have followed the expression of VHBW-16-encoded heavy chains in cDNA libraries prepared from unmanipulated normal (C3H, AKR) and autoimmune (New Zealand Black/New Zealand White F1) mice, and from mice immunized with a highly immunogenic peptide/DNA complex. The prevalence, clonal heterogeneity, and structural properties (somatic mutation, complementarity-determining region 3 composition) of these H chains were investigated, and the DNA affinity of VHBW-16-encoded hybridoma mAb was measured in solution. We find that H chains encoded by VHBW-16 are very rare in Igs of normal mice, but increase significantly in peptide/DNA-immunized mice, and dramatically in diseased mice. The experimentally induced VHBW-16-encoded H chains are clonally restricted, somatically mutated, partly switched from IgM to IgG, and give rise to anti-DNA Abs with low affinity. In contrast, the VHBW-16-encoded H chains from diseased New Zealand Black/New Zealand White mice are clonally heterogeneous, exclusively of the IgG isotype, and produce high affinity anti-DNA autoantibodies. We conclude that the experimentally induced and spontaneous immune responses to DNA are qualitatively similar, but quantitatively different, and may truly reflect the principles of self immunologic tolerance.

Monoclonal anti-DNA antibodies: structure, specificity, and biology

Anti-DNA antibodies are a major contributor to the pathogenesis associated with the autoimmune disease systemic lupus erythematosus in mice and human. The accumulation of a large body of structural information on autoimmune anti-DNA antibodies over the past several years, particularly from mice, has provided considerable insight into the structure, function, and biology of this important class of autoantibodies. Even though the germline repertoire of light and heavy chain variable regions that may encode DNA-specific antibodies is very large in mice, there are individual light and heavy chain variable region genes that have been recurrent and preferentially expressed among anti-DNA hybridomas. This has been particularly true for hybridomas producing antibodies that bind duplex, B-form, mammalian DNA (dsDNA). Recurrent somatically derived variable region structures, particularly arginines in the third complementary-determining region of the heavy chain (VH-CDR3), have also been recurrent and preferentially expressed among monoclonal anti-DNA antibodies. In fact specificity for dsDNA can be correlated to the relative amino acid position at which arginines are expressed within VH-CDR3 of anti-DNA. Most important from the results of structural analyses of monoclonal anti-DNA autoantibodies has been the realization that autoimmunity to DNA results from a clonally selective, antigen-specific immune response to DNA. Autoimmune antibodies to DNA have all of the characteristics of secondary immune antibodies. In further support of this hypothesis, we have been able to induce anti-DNA antibodies in normal, nonautoimmune mice by immunization with immunogenic DNA-peptide complexes. The induced antibodies have all of the structural and functional characteristics of autoimmune anti-DNA including the pathogenetic potential to induce glomerulonephritis. This review summarizes the results of research from our laboratory that support the above conclusions.

Immunoglobulin variable-region structures in immunity and autoimmunity to DNA

Important to the immunopathology associated with the autoimmune disease systemic lupus erythematosus, is the production of autoantibody to DNA. Crucial to understanding the immunological basis for autoimmunity to DNA is knowing whether the anti-DNA autoantibody is the product of clonally-selective, antigen-specific B cell stimulation or non-selective, polyclonal B cell activation. Structural analyses of the immunoglobulin variable-regions of both early, IgM and late, IgG anti-DNA antibodies from lupus-prone (NZB x NZW) F1 mice have indicated that both IgM and IgG anti-DNA autoantibodies are generated by clonally-selective B cell stimulation. Within individual autoimmune mice the later appearing, IgG anti-DNA autoantibodies are structurally similar to the earlier appearing, IgM antibodies, and in some cases both IgM and IgG may be produced by the same B cell clones. The variable-region structural data also suggest that DNA or complexes containing DNA may be the immunogenic stimuli for autoantibody to DNA. In support of this conclusion, normal mice immunized with immunogenic peptide-DNA complexes produce anti-DNA antibodies with structural and serological characteristics similar if not identical to those of autoimmune anti-DNA antibodies. Normal mice immunized with peptide-DNA complexes eventually develop immunopathology that resembles lupus nephritis. These results suggest that autoimmunity to DNA and subsequent autoimmune disease in SLE may result from a specific immune response to DNA containing antigens.

Antigen-specific induction of antibodies against native mammalian DNA in nonautoimmune mice

Spontaneous anti-DNA antibodies in autoimmune mice have the characteristics of antibody produced by Ag-specific, clonally selective B cell stimulation. The nature of the somatically derived antibody V region structures recurrent among spontaneous anti-DNA antibodies suggests that DNA or DNA-protein complexes may provide the antigenic stimulus for autoimmune anti-DNA antibody. In order to test this hypothesis directly, we have immunized normal, nonautoimmune-predisposed mice with complexes formed with DNA and an immunogenic, DNA-binding peptide. The highly immunogenic peptide, Fus1, forms an internal domain of a 128-amino acid ubiquitin-fusion protein from Trypanosoma cruzi. DNA-Fus1 complexes formed with native calf thymus DNA induced anti-DNA antibody in normal, nonautoimmune-predisposed mice that is similar in isotype and specificity to spontaneous anti-DNA antibody in (NZB x NZW)F1 autoimmune mice. The progressive nature of the development of dsDNA specificity in the immunized mice was also analogous to what is observed in the spontaneous anti-DNA antibody response of autoimmune (NZB X NZW)F1 mice. DNA-Fus1 immunized mice that produced IgG that bound to dsDNA had low to moderate levels of proteinuria and glomerular deposits of IgG. This experimental immunization system may be useful for understanding the immunologic basis for autoimmunity to DNA.

Antigen-specific induction of antibodies against native mammalian DNA in nonautoimmune mice

Spontaneous anti-DNA antibodies in autoimmune mice have the characteristics of antibody produced by Ag-specific, clonally selective B cell stimulation. The nature of the somatically derived antibody V region structures recurrent among spontaneous anti-DNA antibodies suggests that DNA or DNA-protein complexes may provide the antigenic stimulus for autoimmune anti-DNA antibody. In order to test this hypothesis directly, we have immunized normal, nonautoimmune-predisposed mice with complexes formed with DNA and an immunogenic, DNA-binding peptide. The highly immunogenic peptide, Fus1, forms an internal domain of a 128-amino acid ubiquitin-fusion protein from Trypanosoma cruzi. DNA-Fus1 complexes formed with native calf thymus DNA induced anti-DNA antibody in normal, nonautoimmune-predisposed mice that is similar in isotype and specificity to spontaneous anti-DNA antibody in (NZB x NZW)F1 autoimmune mice. The progressive nature of the development of dsDNA specificity in the immunized mice was also analogous to what is observed in the spontaneous anti-DNA antibody response of autoimmune (NZB X NZW)F1 mice. DNA-Fus1 immunized mice that produced IgG that bound to dsDNA had low to moderate levels of proteinuria and glomerular deposits of IgG. This experimental immunization system may be useful for understanding the immunologic basis for autoimmunity to DNA.