M. Alber

Imaging oxygenation of human tumours

Tumour hypoxia represents a significant challenge to the curability of human tumours leading to treatment resistance and enhanced tumour progression. Tumour hypoxia can be detected by non-invasive and invasive techniques but the inter-relationships between these remains largely undefined. 18F-MISO and Cu-ATSM-PET, and BOLD-MRI are the lead contenders for human application based on their non-invasive nature, ease of use and robustness, measurement of hypoxia status, validity, ability to demonstrate heterogeneity and general availability, these techniques are the primary focus of this review. We discuss where developments are required for hypoxia imaging to become clinically useful and explore potential new uses for hypoxia imaging techniques including biological conformal radiotherapy.

Adapting inverse planning to patient and organ geometrical variation: algorithm and implementation.

Image guided radiotherapy has the potential to improve both tumour control and normal tissue sparing by including temporal patient specific geometry information into the adaptive planning process. In this study we present a practical method of image guided adaptive inverse planning based on computed tomography (CT) and portal image feedback during the treatment course. The method is based on a general description of the radiotherapy optimization problem subject to dynamic geometrical variations of the patient/organs. We will demonstrate the feasibility of off-line image feedback into the inverse planning process with the example of three prostate cancer patients. CT and portal images acquired during the early course of the treatment are used to predict the geometrical variation distribution of a patient and to re-optimize the treatment plan accordingly. We will study the convergence of the optimization problem with respect to the number of image measurements and adaptive feedback loops.

On biologically conformal boost dose optimization

A method is described that allows the inclusion of biological imaging data in the optimization of intensity-modulated radiotherapy to produce dose boosts that conform with target subvolumes of potentially reduced radiosensitivity. The biological image (e.g. PET, fMRI, etc) is transformed into a dose efficiency distribution using a piecewise linear calibration function with a prescribed maximum boost factor. Instead of dose alone, the cost function of the optimization algorithm depends on the product of the physical dose times dose efficiency. An example case of a base-of-tongue tumour which was imaged with the hypoxia tracer fluoro-misonidazole is presented, showing the excellent capability of IMRT to produce dose distributions that conform to spatially variable dose prescriptions.

Modelling individual geometric variation based on dominant eigenmodes of organ deformation: implementation and evaluation.

We present a method of modelling inter-fractional organ deformation and correlated motion of adjacent organ structures in terms of so-called eigenmodes. The method is based on a principal component analysis (PCA) of organ shapes and allows for reducing the large dimensionality of geometry information from multiple CT studies to a few-parametric statistical model of organ motion and deformation. Eigenmodes are 3D vectorfields of correlated displacements of the organ surface points and can be seen as fundamental modes of the patients geometric variability. The amount of variability represented by the eigenmodes is quantified in terms of corresponding eigenvalues. Weighted sums of eigenmodes describe organ displacements/deformations and can be used to generate new organ geometries. We applied the method to four patient datasets of prostate/rectum/bladder with N = 15-18 CTs to assess interfractional geometric variation. The spectrum of eigenvalues was found to be dominated by only few values, indicating that the geometric variability of prostate/bladder/rectum is governed by only few patient specific eigenmodes. We evaluated the capability of this approach to represent the measured organ samples by calculating the residual errors for the organ surface points, using a varying number of eigenmodes. The distribution of residual errors shows fast convergence with the number of eigenmodes. Using 4 dominating modes, the range of residual errors for the four patients was 1.3-2.0 mm (prostate), 1.4-1.9 mm (rectum) and 1.5-1.9 mm (bladder). Thus, individual geometric variation taken from multiple imaging data can be described accurately by few dominating eigenmodes, thereby providing the most important factors to characterize deformable organ motion, which can assist adaptive radiotherapy planning.

Non-coplanar beam direction optimization for intensity-modulated radiotherapy.

An algorithm for the optimization of the direction of intensity-modulated beams is presented. Although the global optimum dose distribution cannot be predicted, usually a large number of equivalent beam configurations exists. This degeneracy facilitates beam direction optimization (BDO) through a number of possible approximations and because the target set of good beam configurations is very large. Usually, the target volume is accessible through a finite number of paths of little resistance, which are defined by the properties of the objective function and the global optimum dose distribution. Since these paths can be occupied by a finite number of beams, it is reasonable to assume that a minimum number of beams for a configuration that is degenerate to the global optimum exists. Efficiency of the BDO will be characterized by detecting this degeneracy threshold. Beam configurations are altered by adding and deleting beams. A fast exhaustive (up to 3500 non-coplanar orientations) search finds beam directions that improve a configuration. Redundant beams of a configuration can be identified by a fast criterion based on second-order derivative information of the objective function. This offers a fast means of iteratively substituting redundant beams from a configuration. Inferior stationary states can be evaded by adding more beams than the desired number to the current configuration, followed by the subsequent cancellation of superfluous beams. The significance of BDO is examined in a coplanar and a non-coplanar test case. The existence of a threshold number for the minimum configuration and its dependence on the complexity of the problem are shown. BDO outperforms manual configurations and equispaced coplanar beam arrangements in both example cases.

Optimization of intensity modulated radiotherapy under constraints for static and dynamic MLC delivery

Multi-leaf collimators (MLCs) are emerging as the prevalent modality to apply intensity modulated radiotherapy (IMRT). Both the principle and the particular design of MLCs stipulate complex constraints on the practically applicable intensity modulated radiation fields. Most consequentially, the distribution of exposure times across the maximum field outline is either a piecewise constant function in the static mode or a piecewise linear function in the dynamic mode of driving an MLC. In view of clinical utility, the total leaf movement should be minimized, which requires that MLC-related constraints be considered in the dose optimization process. A method is proposed to achieve this for both static MLC fields and dynamic leaf close-in application. The method is an amendment to a generic gradient-based IMRT dose optimization algorithm and solves numerical problems related to the non-convexity of the MLC constraints, which can cause erratic behaviour of a gradient-based algorithm. It employs bistable penalty functions to select preferrable leaf configurations from the configuration space of the MLC, which is limited by specific design features. Together with an annealing escape mechanism from local minima, the algorithm is capable of finding the optimum of an IMRT problem as leaf sequences with minimized leaf travel. In particular, the efficiency of static IMRT can be raised to the levels of unmodulated fields with very few field segments, thereby increasing the utility of IMRT in clinical practice.

On the degeneracy of the IMRT optimization problem.

One approach to the computation of photon IMRT treatment plans is the formulation of an optimization problem with an objective function that derives from an objective density. An investigation of the second-order properties of such an objective function in a neighborhood of the minimizer opens an intuitive access to many traits of this approach. A general finding is that only a small subset of the parameter space has nonzero curvature, while the objective function is entirely flat in a neighborhood of the minimizer in most directions. The dimension of the subspace of vanishing curvature serves as a measure for the degeneracy of the solution. This finding is important both for algorithm design and evaluation of the mathematical model of clinical intuition, expressed by the objective function. The structure of the subspace of great curvature is found to be imposed on the problem by conflicts between objectives of target and critical structures. These conflicts and their corresponding modes of resolution form a common trait between all reasonable treatment plans of a given case. The high degree of degeneracy makes the use of a conjugate gradient optimization algorithm particularly favorable since the number of iterations to convergence is equivalent to the number of different eigenvalues of the curvature tensor and is hence independent from the number of optimization parameters. A high level of degeneracy of the fluence profiles implies that it should be possible to stipulate further delivery-related conditions without causing severe deterioration of the dose distribution.

Monte Carlo dose computation for IMRT optimization

A method which combines the accuracy of Monte Carlo dose calculation with a finite size pencil-beam based intensity modulation optimization is presented. The pencil-beam algorithm is employed to compute the fluence element updates for a converging sequence of Monte Carlo dose distributions. The combination is shown to improve results over the pencil-beam based optimization in a lung tumour case and a head and neck case. Inhomogeneity effects like a broader penumbra and dose build-up regions can be compensated for by intensity modulation.

IMRT optimization including random and systematic geometric errors based on the expectation of TCP and NTCP

The purpose of this work was the development of a probabilistic planning method with biological cost functions that does not require the definition of margins. Geometrical uncertainties were integrated in tumor control probability (TCP) and normal tissue complication probability (NTCP) objective functions for inverse planning. For efficiency reasons random errors were included by blurring the dose distribution and systematic errors by shifting structures with respect to the dose. Treatment plans were made for 19 prostate patients following four inverse strategies: Conformal with homogeneous dose to the planning target volume (PTV), a simultaneous integrated boost using a second PTV, optimization using TCP and NTCP functions together with a PTV, and probabilistic TCP and NTCP optimization for the clinical target volume without PTV. The resulting plans were evaluated by independent Monte Carlo simulation of many possible treatment histories including geometrical uncertainties. The results showed that the probabilistic optimization technique reduced the rectal wall volume receiving high dose, while at the same time increasing the dose to the clinical target volume. Without sacrificing the expected local control rate, the expected rectum toxicity could be reduced by 50% relative to the boost technique. The improvement over the conformal technique was larger yet. The margin based biological technique led to toxicity in between the boost and probabilistic techniques, but its control rates were very variable and relatively low. During evaluations, the sensitivity of the local control probability to variations in biological parameters appeared similar for all four strategies. The sensitivity to variations of the geometrical error distributions was strongest for the probabilistic technique. It is concluded that probabilistic optimization based on tumor control probability and normal tissue complication probability is feasible. It results in robust prostate treatment plans with an improved balance between local control and rectum toxicity, compared to conventional techniques.

A finite size pencil beam for IMRT dose optimization

Dose optimization for intensity modulated radiotherapy (IMRT) using small field elements (beamlets) requires the computation of a large number of very small, often only virtual fields of typically a few mm to 1 cm in size. The primary requirements for a suitable dose computation algorithm are (1) speed and (2) proper consideration of the penumbra of the fields which are composed of these beamlets. Here, a finite size pencil beam (fsPB) algorithm is proposed which was specifically designed for the purpose of beamlet-based IMRT. The algorithm employs an analytical function for the cross-profiles of the beamlets which is based on the assumption of self-consistency, i.e. the requirement that an arbitrary superposition of abutting beamlets should add up to a homogeneous field. The depth dependence is stored in tables derived from Monte Carlo computed dose distributions. It is demonstrated that the algorithm produces accurately the output factors and cross-profiles of typical multi-leaf-shaped segments. Due to the accurate penumbra model, the dose distribution features physically feasible gradients at any stage of the iterative optimization, which eliminates the problem of large discrepancies in normal tissue dose due to misaligned gradients between optimized and recomputed treatment plans.