A Mathematical Approach to Optimizing the Radiation dose Distribution in Heterogeneous Tumours

Stavreva, N; Stavrev, Pavel; Round, W. Howell

doi:10.3109/02841869609084006

Cited by 17 publications

(13 citation statements)

References 5 publications

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“…Because of the limitation of normal tissue dose tolerances, an arbitrarily high dose to the tumor cannot be achieved and certain constraints need to be imposed. [36][37][38][39][40][41] In line with previous researchers, 36,37,40 we restrict the integral dose to the tumor volume to a constant. Mathematically, the constraint is written as…”

Section: ͑2͒mentioning

confidence: 99%

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

Yang

Liu

2005

Medical Physics

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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.

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Section: ͑2͒mentioning

confidence: 99%

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

Yang

Liu

2005

Medical Physics

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“…The constraint on the total radiation dose (used in the paper) leads to a particular shape of the beam, which was also obtained in previous studies [9, 11, 12]. By contrast, a constraint on the ‘mean dose,’ weighted by the local cell density, leads to a uniform beam profile [10].…”

Section: Introductionmentioning

confidence: 61%

“…An interesting consequence of this optimal profile is that it leaves the resulting cell density as a uniform distribution. Stavreva et al [10] applied an extremization of TCP subject to a constraint on the mean dose defined as , i.e. weighting the dose according to the local cell density.…”

Section: Resultsmentioning

confidence: 99%

Spatial optimization for radiation therapy of brain tumours

et al. 2019

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Glioblastomas are the most common primary brain tumours. They are known for their highly aggressive growth and invasion, leading to short survival times. Treatments for glioblastomas commonly involve a combination of surgical intervention, chemotherapy, and external beam radiation therapy (XRT). Previous works have not only successfully modelled the natural growth of glioblastomas in vivo , but also show potential for the prediction of response to radiation prior to treatment. This suggests that the efficacy of XRT can be optimized before treatment in order to yield longer survival times. However, while current efforts focus on optimal scheduling of radiotherapy treatment, they do not include a similarly sophisticated spatial optimization. In an effort to improve XRT, we present a method for the spatial optimization of radiation profiles. We expand upon previous results in the general problem and examine the more physically reasonable cases of 1-step and 2-step radiation profiles during the first and second XRT fractions. The results show that by including spatial optimization in XRT, while retaining a constant prescribed total dose amount, we are able to increase the total cell kill from the clinically-applied uniform case.

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“…Similar results were also reported in other studies. 32,33 This result, however, was obtained with the use of the constraint of integral target dose. If this constraint is removed, the conclusion that homogeneous radiosensitivity leads to uniform dose distribution would not hold, as revealed from this study.…”

Section: Discussionmentioning

confidence: 91%

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

et al. 2007

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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.

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A Mathematical Approach to Optimizing the Radiation dose Distribution in Heterogeneous Tumours

Cited by 17 publications

References 5 publications

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

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

Spatial optimization for radiation therapy of brain tumours

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

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