One to two decades before type II diabetes is diagnosed, reduced glucose clearance is already present. This reduced clearance is accompanied by compensatory hyperinsulinemia, not hypoinsulinemia, suggesting that the primary defect is in peripheral tissue response to insulin and glucose, not in the pancreatic beta cell.

We propose and study a unified model for handling dose constraints (physical dose, equivalent uniform dose (EUD), etc) and radiation source constraints in a single mathematical framework based on the split feasibility problem. The model does not impose on the constraints an exogenous objective (merit) function. The optimization algorithm minimizes a weighted proximity function that measures the sum of the squares of the distances to the constraint sets. This guarantees convergence to a feasible solution point if the split feasibility problem is consistent (i.e., has a solution), or, otherwise, convergence to a solution that minimally violates the physical dose constraints and EUD constraints. We present computational results that demonstrate the validity of the model and the power of the proposed algorithmic scheme.

Treatment plans optimized for intensity modulated proton therapy (IMPT) may be very sensitive to setup errors and range uncertainties. If these errors are not accounted for during treatment planning, the dose distribution realized in the patient may by strongly degraded compared to the planned dose distribution. The authors implemented the probabilistic approach to incorporate uncertainties directly into the optimization of an intensity modulated treatment plan. Following this approach, the dose distribution depends on a set of random variables which parameterize the uncertainty, as does the objective function used to optimize the treatment plan. The authors optimize the expected value of the objective function. They investigate IMPT treatment planning regarding range uncertainties and setup errors. They demonstrate that incorporating these uncertainties into the optimization yields qualitatively different treatment plans compared to conventional plans which do not account for uncertainty. The sensitivity of an IMPT plan depends on the dose contributions of individual beam directions. Roughly speaking, steep dose gradients in beam direction make treatment plans sensitive to range errors. Steep lateral dose gradients make plans sensitive to setup errors. More robust treatment plans are obtained by redistributing dose among different beam directions. This can be achieved by the probabilistic approach. In contrast, the safety margin approach as widely applied in photon therapy fails in IMPT and is neither suitable for handling range variations nor setup errors.

With the recent availability of 4D-CT, the accuracy of information on internal organ motion during respiration has improved significantly. We investigate the utility of organ motion information in IMRT treatment planning, using an in-house prototype optimization system. Four approaches are compared: (1) planning with optimized margins, based on motion information; (2) the 'motion kernel' approach, in which a more accurate description of the dose deposit from a pencil beam to a moving target is achieved either through time-weighted averaging of influence matrices, calculated for different instances of anatomy (subsets of 4D-CT data, corresponding to various phases of motion) or through convolution of the pencil beam kernel with the probability density function describing the target motion; (3) optimal gating, or tracking with beam intensity maps optimized independently for each instance of anatomy; and (4) optimal tracking with beam intensity maps optimized simultaneously for all instances of anatomy. The optimization is based on a gradient technique and can handle both physical (dose-volume) and equivalent uniform dose constraints. Optimization requires voxel mapping from phase to phase in order to score the dose in individual voxels as they move. The results show that, compared to the other approaches, margin expansion has a significant disadvantage by substantially increasing the integral dose to patient. While gating or tracking result in the best dose conformation to the target, the former elongates treatment time, and the latter significantly complicates the delivery procedure. The 'motion kernel' approach does not provide a dosimetric advantage, compared to optimal tracking or gating, but might lead to more efficient delivery. A combination of gating with the 'motion kernel' or margin expansion approach will increase the duty cycle and may provide one with the most efficient solution, in terms of complexity of the delivery procedure and dose conformality to the target.