Optimization of tumour control probability for heterogeneous tumours in fractionated radiotherapy treatment protocols

Robust PET-guided intensity-modulated radiation therapy

PURPOSE

Functional image guided intensity-modulated radiation therapy has the potential to improve cancer treatment quality by basing treatment parameters such as heterogeneous dose distributions information derived from imaging. However, such heterogeneous dose distributions are subject to imaging uncertainty. In this paper, the authors develop a robust optimization model to design plans that are desensitized to imaging uncertainty.

METHODS

Starting from the pretreatment fluorodeoxyglucose-positron emission tomography scans, the authors use the raw voxel standard uptake values (SUVs) as input into a series of intermediate functions to transform the SUV into a desired dose. The calculated desired doses were used as an input into a robust optimization model to generate beamlet intensities. For each voxel, the authors assume that the true SUV cannot be observed but instead resides in an interval centered on the nominal (i.e., observed) SUV. Then the authors evaluated the nominal and robust solutions through a simulation study. The simulation considered the effect of the true SUV being different from the nominal SUV on the quality of the treatment plan. Treatment plans were compared on the metrics of objective function value and tumor control probability (TCP).

RESULTS

Computational results demonstrate the potential for improvements in tumor control probability and deviation from the desired dose distribution compared to a nonrobust model while maintaining acceptable tissue dose.

CONCLUSIONS

Robust optimization can help design treatment plans that are more stable in the presence of image value uncertainties.

Molecular imaging-based dose painting: a novel paradigm for radiation therapy prescription

Dose painting is the prescription of a nonuniform radiation dose distribution to the target volume based on functional or molecular images shown to indicate the local risk of relapse. Two prototypical strategies for implementing this novel paradigm in radiation oncology are reviewed: subvolume boosting and dose painting by numbers. Subvolume boosting involves the selection of a "target within the target," defined by image segmentation on the basis of the quantitative information in the image or morphologically, and this is related to image-based target volume selection and delineation. Dose painting by numbers is a voxel-level prescription of dose based on a mathematical transformation of the image intensity of individual pixels. The quantitative use of images to decide both where and how to delivery radiation therapy in an individual case is also called theragnostic imaging. Dose painting targets are imaging surrogates for cellular or microenvironmental phenotypes associated with poor radioresponsiveness. In this review, the focus is on the following positron emission tomography tracers: FDG and choline as surrogates for tumor burden, fluorothymidine as a surrogate for proliferation (or cellular growth fraction) and hypoxia-sensitive tracers, including [(18)F] fluoromisonidazole, EF3, EF5, and (64)Cu-labeled copper(II) diacetyl-di(N(4)-methylthiosemicarbazone) as surrogates of cellular hypoxia. Research advances supporting the clinicobiological rationale for dose painting are reviewed as are studies of the technical feasibility of optimizing and delivering realistic dose painted radiation therapy plans. Challenges and research priorities in this exciting research field are defined and a possible design for a randomized clinical trial of dose painting is presented.

Feasibility of dose painting using volumetric modulated arc optimization and delivery

PURPOSE

Dose painting strategies are limited by optimization algorithms in treatment planning systems and physical constraints of the beam delivery. We investigate dose conformity using the RapidArc optimizer and beam delivery technique. Furthermore, robustness of the plans with respect to positioning uncertainties are evaluated.

METHODS

A head & neck cancer patient underwent a [(61)Cu]Cu-ATSM PET/CT-scan. PET-SUVs were converted to prescribed dose with a base dose of 60 Gy, and target mean dose 90 Gy. The voxel-based prescription was converted into 3, 5, 7, 9, and 11 discrete prescription levels. Optimization was performed in Eclipse, varying the following parameters: MLC leaf width (5 mm and 2.5 mm), number of arcs (1 and 2) and collimator rotation (0, 15, 30 and 45 degrees). Dose conformity was evaluated using quality volume histograms (QVHs), and relative volumes receiving within ±5% of prescribed dose (Q(0.95-1.05)). Deliverability was tested using a Delta4(®) phantom. Robustness was tested by shifting the isocenter 1 mm and 2 mm in all directions, and recalculating the dose.

RESULTS

Good conformity was obtained using MLC leaf width 2.5 mm, two arcs, and collimators 45/315 degrees, with Q(0.95-1.05)=92.8%, 91.6%, 89.7% and 84.6%. Using only one arc or increasing the MLC leaf width had a small deteriorating effect of 2-5%. Small changes in collimator angle gave small changes, but large changes in collimator angle gave a larger decrease in plan conformity; for angles of 15 and 0 degrees (two arcs, 2.5 mm leaf width), Q(0.95-1.05) decreased by up to 15%. Consistency between planned and delivered dose was good, with ∼90% of gamma values <1. For 1 mm shift, Q(0.95-1.05) was decreased by 5-15%, while for 2 mm shift, Q(0.95-1.05) was decreased to 55-60%.

CONCLUSIONS

Results demonstrate feasibility of planning of prescription doses with multiple levels for dose painting using RapidArc, and plans were deliverable. Robustness to positional error was low.

The role of protons in modern and biologically-guided radiotherapy

With the introduction of new biologically based imaging possibilities, a higher degree of individualisation and adaptation of radiotherapy will be possible. Better knowledge of the biology of the target and its sub-volumes will enable dose prescriptions tailored to the individual patients, tissues and sub-volumes. Repeated imaging during the course of treatment will in addition enable adaptation of the treatment to cope with anatomical, as well as biological changes of the patient and of the target tissues. To translate these bright future perspectives into significant improvements in clinical outcome, advanced tools to tailor the physical dose distributions are needed. The most conformal radiotherapy technique known to mankind and clinically available today is proton therapy; in particular Intensity Modulated Proton Therapy (IMPT) with active spot scanning can not only tailor the dose to the desired target, but also effectively avoid sensitive structures in the proximity of the target to a degree far better than other conformal techniques such as Intensity Modulated Radiotherapy with photons (IMRT). The development of IMPT is now mature enough for clinical introduction on a broad scale. Proton therapy is still more expensive than conventional radiotherapy, but with the present rapid increase in the number of proton facilities worldwide and new initiatives to improve efficiency, the difference in affordability will continue to decrease and in comparison with the benefits, soon diminish even further. Contrary to what is sometimes claimed, the demands for better physical dose distributions and better avoidance of non-target tissue, has never been higher. Prolonged expected survival in many groups of patients emphasises the need to reduce late toxicities. The success of concomitant systemic therapies, with their tendency to cause higher morbidity stresses even further the increased need for subtle dose-sculpting methodologies and tools. There is no contradiction between striving for better physical dose distributions and a more biologically based approach. On the contrary, physical dose distributions are the tools to which achieve a treatment that can meet the biological demands.

Radioimmunotherapy with radioactive nanoparticles: biological doses and treatment efficiency for vascularized tumors with or without a central hypoxic area

PURPOSE

Radioactive atoms attached to monoclonal antibodies are used in radioimmunotherapy to treat cancer while limiting radiation to healthy tissues. One limitation of this method is that only one radioactive atom is linked to each antibody and the deposited dose is often insufficient to eradicate solid and radioresistant tumors. In a previous study, simulations with the Monte Carlo N-Particle eXtended code showed that physical doses up to 50 Gy can be delivered inside tumors by replacing the single radionuclide by a radioactive nanoparticle of 5 nm diameter containing hundreds of radioactive atoms. However, tumoral and normal tissues are not equally sensitive to radiation, and previous works did not take account the biological effects such as cellular repair processes or the presence of less radiosensitive cells such as hypoxic cells.

METHODS

The idea is to adapt the linear-quadratic expression to the tumor model and to determine biological effective doses (BEDs) delivered through and around a tumor. This BED is then incorporated into a Poisson formula to determine the shell control probability (SCP) which predicts the cell cluster-killing efficiency at different distances "r" from the center of the tumor. BED and SCP models are used to analyze the advantages of injecting radioactive nanoparticles instead of a single radionuclide per vector in radioimmunotherapy.

RESULTS

Calculations of BED and SCP for different distances r from the center of a solid tumor, using the non-small-cell lung cancer as an example, were investigated for 90Y2O3 nanoparticles. With a total activity of about 3.5 and 20 MBq for tumor radii of 0.5 and 1.0 cm, respectively, results show that a very high BED is deposited in the well oxygenated part of the spherical carcinoma.

CONCLUSIONS

For either small or large solid tumors, BED and SCP calculations highlight the important benefit in replacing the single beta-emitter 90Y attached to each antibody by a 90Y2O3 nanoparticle.

On the sensitivity of IMRT dose optimization to the mathematical form of a biological imaging-based prescription function

Voxel-based prescriptions of deliberately non-uniform dose distributions based on molecular imaging, so-called dose painting or theragnostic radiation therapy, require specification of a transformation that maps the image data intensities to prescribed doses. However, the functional form of this transformation is currently unknown. An investigation into the sensitivity of optimized dose distributions resulting from several possible prescription functions was conducted. Transformations between the radiotracer activity concentrations from Cu-ATSM PET images, as a surrogate of tumour hypoxia, and dose prescriptions were implemented to yield weighted distributions of prescribed dose boosts in high uptake regions. Dose escalation was constrained to reflect clinically realistic whole tumour doses and constant normal tissue doses. Optimized heterogeneous dose distributions were found by minimizing a voxel-by-voxel quadratic objective function in which all tumour voxels were given equal weight. Prescriptions based on a polynomial mapping function were found to be least constraining on their optimized plans, while prescriptions based on a sigmoid mapping function were the most demanding to deliver. A prescription formalism that fixed integral dose was less sensitive to errors in the choice of the mapping function than one that boosted integral dose. Integral doses to normal tissue and critical structures were insensitive to the shape of the prescription function. Planned target dose conformity improved with smaller beamlet dimensions until the inherent spatial resolution of the functional image was matched. Clinical implementation of dose painting depends on advances in absolute quantification of functional images and improvements in delivery techniques over smaller spatial scales.

A theoretical framework for prescribing radiotherapy dose distributions using patient-specific biological information

We present a formalism for using functional imaging both to derive patient-specific radiobiological properties and consequently to prescribe optimal nonuniform radiotherapy dose distributions. The ability to quantitatively assess the response to an initial course of radiotherapy would allow the derivation of radiobiological parameters for individual patients. Both an iterative optimization and an analytical approach to this problem were investigated and illustrated by application to the linear-quadratic model of cell killing using simulated parametric data for a modeled tumor. Potential gains in local control were assessed by comparing uniform dose distributions with optimized dose distributions of equal integral dose. The effect on local prescribed dose of variations in effective radiosensitivity, tumor burden, and proliferation rate was investigated, with results suggesting that dose variations would be significant but clinically achievable. The sensitivity of derived parameters to image noise and the effect of varying the initial fractionation and imaging schedule were assessed. The analytical approach proved remarkably robust, with 10% image noise resulting in dose errors of approximately 1% for a clinically relevant set of parameters. Potential benefits were demonstrated by using this formalism to prescribe nonuniform dose distributions for model tumors using a range of literature-derived parameters. The redistribution of dose improved tumor control probability by factors between 1.03 and 4.27 for a range of model tumors.

Intensity-modulated x-ray (IMXT) versus proton (IMPT) therapy for theragnostic hypoxia-based dose painting

In this work the abilities of intensity-modulated x-ray therapy (IMXT) and intensity-modulated proton therapy (IMPT) to deliver boosts based on theragnostic imaging were assessed. Theragnostic imaging is the use of functional or molecular imaging data for prescribing radiation dose distributions. Distal gradient tracking, an IMPT method designed for the delivery of non-uniform dose distributions, was assessed. Dose prescriptions for a hypoxic region in a head and neck squamous cell carcinoma patient were designed to either uniformly boost the region or redistribute the dose based on positron emission tomography (PET) images of the (61)Cu(II)-diacetyl-bis(N(4)-methylthiosemicarbazone) ((61)Cu-ATSM) hypoxia surrogate. Treatment plans for the prescriptions were created for four different delivery methods: IMXT delivered with step-and-shoot and with helical tomotherapy, and IMPT delivered with spot scanning and distal gradient tracking. IMXT and IMPT delivered comparable dose distributions within the boost region for both uniform and redistributed theragnostic boosts. Normal tissue integral dose was lower by a factor of up to 3 for IMPT relative to the IMXT. For all delivery methods, the mean dose to the nearby organs at risk changed by less than 2 Gy for redistributed versus uniform boosts. The distal gradient tracking method resulted in comparable plans to the spot scanning method while reducing the number of proton beam spots by a factor of over 3.

Comparison of intensity modulated x-ray therapy and intensity modulated proton therapy for selective subvolume boosting: a phantom study

Selective subvolume boosting can theoretically improve tumour control probability while maintaining normal tissue complication probabilities similar to those of uniform dose distributions. In this work the abilities of intensity-modulated x-ray therapy (IMXT) and intensity-modulated proton therapy (IMPT) to deliver boosts to multiple subvolumes of varying size and proximities are compared in a thorough phantom study. IMXT plans were created using the step-and-shoot (IMXT-SAS) and helical tomotherapy (IMXT-HT) methods. IMPT plans were created with the spot scanning (IMPT-SS) and distal gradient tracking (IMPT-DGT) methods. IMPT-DGT is a generalization of the distal edge tracking method designed to reduce the number of proton beam spots required to deliver non-uniform dose distributions relative to IMPT-SS. The IMPT methods were delivered over both 180 degrees and 360 degrees arcs. The IMXT-SAS and IMPT-SS methods optimally satisfied the non-uniform dose prescriptions the least and the most, respectively. The IMPT delivery methods reduced the normal tissue integral dose by a factor of about 2 relative to the IMXT delivery methods, regardless of the delivery arc. The IMPT-DGT method reduced the number of proton beam spots by a factor of about 3 relative to the IMPT-SS method.

Development of an inverse optimization package to plan nonuniform dose distributions based on spatially inhomogeneous radiosensitivity extracted from biological images

An inverse optimization package which is capable of generating nonuniform dose distribution with subregional dose escalation is developed to achieve maximum equivalent uniform dose (EUD) for target while keeping the critical structure doses as low as possible. Relative cerebral blood volume (rCBV) maps obtained with a dynamic susceptibility contrast-enhanced MRI technique were used to delineate spatial radiosensitivity distributions. The voxel rCBV was converted to voxel radiosensitivity parameters (e.g., alpha and alpha/beta) based on previously reported correlations between rCBV, tumor grade, and radiosensitivity. A software package, DOSEPAINT, developed using MATLAB, optimizes the beamlet weights to achieve maximum EUD for target while limiting doses to critical structures. Using DOSEPAINT, we have generated nonuniform 3D-dose distributions for selected patient cases. Depending on the variation of the pixel radiosensitivity, the subregional dose escalation can be as high as 35% of the uniform dose as planned conventionally. The target dose escalation comes from both the inhomogeneous radiosensitivities and the elimination of integral target dose constraint. The target EUDs are found to be higher than those for the uniform dose planned ignoring the spatial inhomogeneous radiosensitivity. The EUDs for organs at risk are found to be approximately equal to or lower than those for the uniform dose plans. In conclusion, we have developed a package that is capable of generating nonuniform dose distributions optimized for spatially inhomogeneous radiosensitivity. Subregional dose escalation may lead to increased treatment effectiveness as indicated by higher EUDs. The current development will impact biological image guided radiotherapy.

Towards biologically conformal radiation therapy (BCRT): Selective IMRT dose escalation under the guidance of spatial biology distribution

It is well known that the spatial biology distribution (e.g., clonogen density, radiosensitivity, tumor proliferation rate, functional importance) in most tumors and sensitive structures is heterogeneous. Recent progress in biological imaging is making the mapping of this distribution increasingly possible. The purpose of this work is to establish a theoretical framework to quantitatively incorporate the spatial biology data into intensity modulated radiation therapy (IMRT) inverse planning. In order to implement this, we first derive a general formula for determining the desired dose to each tumor voxel for a known biology distribution of the tumor based on a linear-quadratic model. The desired target dose distribution is then used as the prescription for inverse planning. An objective function with the voxel-dependent prescription is constructed with incorporation of the nonuniform dose prescription. The functional unit density distribution in a sensitive structure is also considered phenomenologically when constructing the objective function. Two cases with different hypothetical biology distributions are used to illustrate the new inverse planning formalism. For comparison, treatments with a few uniform dose prescriptions and a simultaneous integrated boost are also planned. The biological indices, tumor control probability (TCP) and normal tissue complication probability (NTCP), are calculated for both types of plans and the superiority of the proposed technique over the conventional dose escalation scheme is demonstrated. Our calculations revealed that it is technically feasible to produce deliberately nonuniform dose distributions with consideration of biological information. Compared with the conventional dose escalation schemes, the new technique is capable of generating biologically conformal IMRT plans that significantly improve the TCP while reducing or keeping the NTCPs at their current levels. Biologically conformal radiation therapy (BCRT) incorporates patient-specific biological information and provides an outstanding opportunity for us to truly individualize radiation treatment. The proposed formalism lays a technical foundation for BCRT and allows us to maximally exploit the technical capacity of IMRT to more intelligently escalate the radiation dose.