A New Linear Programming Approach to Radiation Therapy Treatment Planning Problems

Abstract

We consider the problem of radiation therapy treatment planning for cancer patients. During radiation therapy, beams of radiation pass through a patient, killing both cancerous and normal cells. Thus, the radiation therapy must be carefully planned so that a clinically prescribed dose is delivered to targets containing cancerous cells, while nearby organs and tissues are spared. Currently, a technique called intensity-modulated radiation therapy (IMRT) is considered to be the most effective radiation therapy for many forms of cancer. In IMRT, the patient is irradiated from several beams, each of which is decomposed into hundreds of small beamlets, the intensities of which can be controlled individually. In this paper, we consider the problem of designing a treatment plan for IMRT when the orientations of the beams are given. We propose a new model that has the potential to achieve most of the goals with respect to the quality of a treatment plan that have been considered to date. However, in contrast with established mixed-integer and nonlinear programming formulations, we do so while retaining linearity of the optimization problem, which substantially improves the tractability of the optimization problem. Furthermore, we discuss how several additional quality and practical aspects of the problem that have been ignored to date can be incorporated into our linear model. We demonstrate the effectiveness of our approach on clinical data.

Optimization of rotational arc station parameter optimized radiation therapy

“…The objective function f takes the form of a weighted linear function. 9 It consists of four parts: (1) Max (min) dose of OARs (PTV); (2) mean dose of OARs and PTV; (3) dose volume constraints modeled as piecewise linear functions; 10,11 and (4) maximum dose constraints for OARs. For the weights associated with items (1)-(3), we choose initial values in the range of 1-10 and allow these weights to be manually adjusted during the optimization.…”

Adaptive and robust radiation therapy optimization for lung cancer

“…In the case that p / ∈ P , it was shown empirically in Bortfeld et al [2008] that w * remains feasible with high probability. Due to the linearity of this model and the use of polyhedral uncertainty sets, this model is capable of accomodating robust versions of many other types of clinically relevant constraints, such as partial volume constraints based on conditional-value-at-risk (see Romeijn et al [2006]) or constraints involving αEUD (Thieke et al [2002]), which is a linear approximation to the popular equivalent uniform dose (EUD) metric. For simplicity, we consider only lower and upper dose bounds on the tumour.…”

Sampling issues for optimization in radiotherapy

“…These values can be set to approximate dose volume histogram constraints (see Langer et al, 1990), or other piecewise linearizations can be used to implement so-called CVAR constraints (Romeijn et al, 2006), or standard infinity or L 1 norm constraints. Further details on these choices are available in Lim et al (2006).…”