Dose prescription complexity versus tumor control probability in biologically conformal radiotherapy

Abstract

5Purpose: The technical feasibility and potential benefits of voxel-based non-uniform dose prescriptions for biologically heterogeneous tumors have been widely demonstrated. In some cases, an "ideal" dose prescription has been generated by individualizing the dose to every voxel within the target, but often this voxel-based prescription has been 10 discretized into a small number of compartments. The number of dose levels utilized, and the methods used for prescribing doses and assigning tumor voxels to different dose compartments have varied significantly. We present an investigation into the relationship between the complexity of the dose prescription and the tumor control probability (TCP) for a number of these methods. 15Methods: The linear quadratic model of cell killing was used in conjunction with a number of modelled tumors heterogeneous in clonogen density, oxygenation, or proliferation. Models based on simple mathematical functions, published biological data and biological image data were investigated. Target voxels were assigned to dose compartments using (i) simple rules based on the initial biological distribution; (ii) 20 iterative methods designed to maximize the achievable TCP; or (iii) methods based on an "ideal" dose prescription.Complexity versus efficacy in dose painting 2 Results: The relative performance of the simple rules was found to depend on the form of heterogeneity of the tumor, whilst the iterative and "ideal" dose methods performed comparably for all models investigated. In all cases the maximum achievable TCP was 25 approached within the first few (typically 2-5) compartments.Conclusion: Results suggest that irrespective of the pattern of heterogeneity, the optimal dose prescription can be well approximated using only a few dose levels, but only if both the compartment boundaries and prescribed dose levels are well chosen. 30

Functional Radiotherapy Targeting using Focused Dose Escalation

“…They reported that the optimal dose distribution for eradication of a heterogeneous tumour is proportional to the spatial variation of the D 0 value within the tumour (D 0 is the dose required to reduce the number of surviving clonogens to 37% of its previous value) and the logarithm of the tumour cell density. Other studies have modelled the benefits of dose painting based on particular biological characteristics, such as tumour hypoxia [57e59] or clonogen density [60]. Ultimately, the true benefit for non-uniform dose distributions will only be fully appreciated once we have evidence from a clinical trial.…”

Robust PET‐guided intensity‐modulated radiation therapy

“…A follow-up study by South et al [13] applied this theoretical framework to PET imaging using fluorodeoxyglucose 55 (FDG) as a tracer to ultimately describe a heterogeneous distribution reflecting radiosensitivity. We follow a similar framework as South et al [13] in this study to translate the PET image map to a desired heterogeneous dose distribution.…”

“…Our model uses a simplified treatment planning formulation that gives the treatment planner an adjustable parameter that can be used to adjust the conservatism of the resulting solution. The following theoretical framework, based on several models in the literature, [13] generates a heterogeneous desired dose distribution from PET SUV values and allows us to evaluate our models performance. This is not meant to represent a clinically validated function to map PET values to dose.…”

“…For this study, the intrinsic radiobiological parameters for the lung tumor were set as follows [13,49,50]: ρ = 10 7 clonogens/cm 3 , α = 0.35 Gy −1 , β = 0.035, α β = 10, T p = 3 days (equivalent to a cell proliferation rate of 0.1386 days −1 ), OER αmax = 2.5, OER βmax = 3, K m = 3.28, T k = 28 days. Partial oxygen pressure for a voxel was assumed to be bounded within the range p ∈ [1, 100] mmHg.…”

“…Partial oxygen pressure for a voxel was assumed to be bounded within the range p ∈ [1, 100] mmHg. [13] The treatment plan parameters were set as follows:…”