Inhomogeneous target-dose distributions: a dimension more for optimization?

PURPOSE: To evaluate if the use of inhomogeneous target-dose distributions, obtained by 3D conformal radiotherapy plans with or without beam intensity modulation, offers the possibility to decrease indices of toxicity to normal tissues and/or increase indices of tumor control stage III non-small cell lung cancer (NSCLC). METHODS AND MATERIALS: Ten patients with stage III NSCLC were planned using a conventional 3D technique and a technique involving noncoplanar beam intensity modulation (BIM). Two planning target volumes (PTVs) were defined: PTV1 included macroscopic tumor volume and PTV2 included macroscopic and microscopic tumor volume. Virtual simulation defined the beam shapes and incidences as well as the wedge orientations (3D) and segment outlines (BIM). Weights of wedged beams, unwedged beams, and segments were determined by optimization using an objective function with a biological and a physical component. The biological component included tumor control probability (TCP) for PTV1 (TCP1), PTV2 (TCP2), and normal tissue complication probability (NTCP) for lung, spinal cord, and heart. The physical component included the maximum and minimum dose as well as the standard deviation of the dose at PTV1. The most inhomogeneous target-dose distributions were obtained by using only the biological component of the objective function (biological optimization). By enabling the physical component in addition to the biological component, PTV1 inhomogeneity was reduced (biophysical optimization). As indices for toxicity to normal tissues, NTCP-values as well as maximum doses or dose levels to relevant fractions of the organ's volume were used. As indices for tumor control, TCP-values as well as minimum doses to the PTVs were used. RESULTS: When optimization was performed with the biophysical as compared to the biological objective function, the PTV1 inhomogeneity decreased from 13 (8-23)% to 4 (2-9)% for the 3D-(p = 0.00009) and from 44 (33-56)% to 20 (9-34)% for the BIM plans (p < 0. 00001). Minimum PTV1 doses (expressed as the lowest voxel-dose) were similar for both objective functions. The mean and maximum target doses were significantly higher with biological optimization for 3D as well as for BIM (all p values < 0.001). Tumor control probability (estimated by TCP1 x TCP2) was 4.7% (3D) and 6.2% (BIM) higher for biological optimization (p = 0.01 and p = 0.00002 respectively). NTCP(lung) as well as the percentage of lung volume exceeding 20 Gy was higher with the use of the biophysical objective function. NTCP(heart) was also higher with the use of the biophysical objective function. The percentage of heart volume exceeding 40 Gy tended to be higher but the difference was not significant. For spinal cord, the maximum dose as well as NTCP(cord) were similar for 3D plans (D(max): p = 0.04; NTCP: p = 0.2) but were significantly lower for BIM (D(max): p = 0.002; NTCP: p = 0.008) if the biophysical objective function was used. CONCLUSIONS: When using conventional 3D techniques, inhomogeneous dose distributions offer the potential to further increase the probability of uncomplicated local control. When using techniques as BIM that would lead to large escalation of the median and maximum target doses, it seems indicated to limit target-dose inhomogeneity to avoid dose levels that are so high that the safety becomes questionable.

3D conformal intensity-modulated radiotherapy planning: interactive optimization by constrained matrix inversion.

BACKGROUND AND PURPOSE: This paper presents a method for interactive optimization of 3D conformal intensity-modulated radiotherapy plans employing a quadratic objective that also contains dose limitations in the organs at risk. This objective function is minimized by constrained matrix inversion (CMI) that follows the same approach as the gradient technique using matrix notation. MATERIALS AND METHODS: Sherouse's GRATIS radiotherapy design system is used to determine the outlines of the target volume and the organs at risk and to input beam segments which are given by the beam segmentation technique. This technique defines the beam incidences and the beam segmentation. The weights of the segments are then calculated using a quadratic objective function and CMI. The objective function to be minimized consists of two components based on the planning target volume (PTV) and the organ at risk (OAR) with an importance factor w associated with the OAR. RESULTS: Optimization is tested for concave targets in the head and neck region wrapping around the spinal cord. For a predefined w-value, segment weights are optimized within a few seconds on a DEC Alpha 3000. In practice, 5-10 w-values have to be tested, making optimization a less than 5 min procedure. This optimization procedure predicts the possibility of target dose escalation for a tumour in the lower neck to 120-150 Gy without exceeding the spinal cord tolerance, whereas human planners could not increase the dose above 65-80 Gy. CONCLUSIONS: Treatment plans optimized using a quadratic objective function and the CMI algorithm are superior to those which are generated by human planners. The optimization algorithm is very fast and allows interactive use. Quadratic optimization by CMI is routinely used by clinicians at the Division of Radiotherapy, U.Z.-Gent.