Optimal beam angle selection and knowledge-based planning significantly reduces radiotherapy dose to organs at risk for lung cancer patients.

BACKGROUND: Lung cancer patients struggle with high toxicity rates. This study investigates if IMRT plans with individually set beam angles or uni-lateral VMAT plans results in dose reduction to OARs. We investigate if introduction of a RapidPlan model leads to reduced dose to OARs. Finally, the model is validated prospectively. MATERIAL AND METHODS: Seventy-four consecutive lung cancer patients treated with IMRT were included. For all patients, new IMRT plans were made by an experienced dose planner re-tuning beam angles aiming for minimized dose to the lungs and heart. Additionally, VMAT plans were made. The IMRT plans were selected as input for a RapidPlan model, which was used to generate 74 new IMRT plans. The new IMRT plans were used as input for a second RapidPlan model. This model was clinically implemented and used for generation of clinical treatment plans. Dosimetric parameters were compared using a Wilcoxon signed rank test or a 1-sided student's t-test. p < .05 was considered significant. RESULTS: IMRT plans significantly reduced mean doses to lungs (MLD) and heart (MHD) by 1.6 Gy and 1.7 Gy in mean compared to VMAT plans. MLD was significantly (p < .001) reduced from 10.8 Gy to 9.4 Gy by using the second RapidPlan model. MHD was significantly (p < .001) reduced from 4.9 Gy to 3.9 Gy. The model was validated in prospectively collected treatment plans showing significantly lower MLD after the implementation of the second RapidPlan model. CONCLUSION: Introduction of RapidPlan and beam angles selected based on the target and OARs position reduces dose to OARs.

A joint physics and radiobiology DREAM team vision - Towards better response prediction models to advance radiotherapy.

Radiotherapy developed empirically through experience balancing tumour control and normal tissue toxicities. Early simple mathematical models formalized this practical knowledge and enabled effective cancer treatment to date. Remarkable advances in technology, computing, and experimental biology now create opportunities to incorporate this knowledge into enhanced computational models. The ESTRO DREAM (Dose Response, Experiment, Analysis, Modelling) workshop brought together experts across disciplines to pursue the vision of personalized radiotherapy for optimal outcomes through advanced modelling. The ultimate vision is leveraging quantitative models dynamically during therapy to ultimately achieve truly adaptive and biologically guided radiotherapy at the population as well as individual patient-based levels. This requires the generation of models that inform response-based adaptations, individually optimized delivery and enable biological monitoring to provide decision support to clinicians. The goal is expanding to models that can drive the realization of personalized therapy for optimal outcomes. This position paper provides their propositions that describe how innovations in biology, physics, mathematics, and data science including AI could inform models and improve predictions. It consolidates the DREAM team's consensus on scientific priorities and organizational requirements. Scientifically, it stresses the need for rigorous, multifaceted model development, comprehensive validation and clinical applicability and significance. Organizationally, it reinforces the prerequisites of interdisciplinary research and collaboration between physicians, medical physicists, radiobiologists, and computational scientists throughout model development. Solely by a shared understanding of clinical needs, biological mechanisms, and computational methods, more informed models can be created. Future research environment and support must facilitate this integrative method of operation across multiple disciplines.

Toxicity and outcome of pelvic IMRT for node-positive prostate cancer.

BACKGROUND AND PURPOSE: This study reports on the treatment techniques, toxicity, and outcome of pelvic intensity-modulated radiotherapy (IMRT) for lymph node-positive prostate cancer (LNPPC, T1-4, c/pN1 cM0). PATIENTS AND METHODS: Pelvic IMRT to 45-50.4 Gy was applied in 39 cases either after previous surgery of involved lymph nodes (n = 18) or with a radiation boost to suspicious nodes (n = 21) with doses of 60-70 Gy, usually combined with androgen deprivation (n = 37). The prostate and seminal vesicles received 70-74 Gy. In cases of previous prostatectomy, prostatic fossa and remnants of seminal vesicles were given 66-70 Gy. Treatment-related acute and late toxicity was graded according to the RTOG criteria. RESULTS: Acute radiation-related toxicity higher than grade 2 occurred in 2 patients (with the need for urinary catheter/subileus related to adhesions after surgery). Late toxicity was mild (grade 1-2) after a median follow-up of 70 months. Over 50% of the patients reported no late morbidity (grade 0). PSA control and cancer-specific survival reached 67% and 97% at over 5 years. CONCLUSION: Pelvic IMRT after the removal of affected nodes or with a radiation boost to clinically positive nodes led to an acceptable late toxicity (no grade 3/4 events), thus justifying further evaluation of this approach in a larger cohort.

[Neonatal intracerebral bleeding as initial symptom of gliomatosis cerebri WHO III--neurological outcome after partial hemispherectomy]. / Eine neonatale intrazerebrale Blutung als Initialsymptom einer Gliomatosis cerebri WHO III--neurologisches Outcome nach partieller Hemisphärektomie.

INTRODUCTION: Anaplastic astrocytomas presenting as gliomatosis cerebri in neonates are extremely rare. Tumours in newborns are mostly of neuroectodermal origin. CASE REPORT: We report about a female newborn at term [birth weight 3 600 g (P 90), head circumference 35 cm (P 95) APGAR 9/10/10] with an intracerebral partially clotted bleeding in the left parieto-occipital region. The bleeding was expansive leading to axial and lateral cerebral herniation. The intracerebral bleeding in the left occipital region was surgically removed. Macroscopically no solid tumour was seen, but small fragments of an anaplastic astrocytic tumour (WHO grade III) were diagnosed histologically. After surgery, no remaining tumour was visible in the MRI. 6 weeks later, a recurrent tumour (4×4 cm) was found in the area of the initial bleeding. Further treatment was initially refused by the parents. The child was readmitted to our hospital at the age of 11 months in good clinical condition and presented with left-sided hemiparesis, right-sided hemianopsia and intermittent strabismus convergens alternans. Because of the good clinical condition further therapeutic treatment was initiated. Due to the final extension of the tumour into the temporal, parietal and occipital lobes, a gliomatosis cerebri WHO III was diagnosed. An extended partial hemispherectomy was done. After neurosurgery, no further neurological failures occurred. In the follow-up examination, MRI showed no relapse of the tumour. Chemotherapy according to the HIT SKK protocol was initiated. A relapse did not occur over a follow-up of 2 years. CONCLUSION: This is a rare case report of a congenital gliomatosis cerebri WHO grade III, treated with partial hemispherectomy, leading to a good clinical and neurological long-term outcome.

Robust optimization based upon statistical theory.

PURPOSE: Organ movement is still the biggest challenge in cancer treatment despite advances in online imaging. Due to the resulting geometric uncertainties, the delivered dose cannot be predicted precisely at treatment planning time. Consequently, all associated dose metrics (e.g., EUD and maxDose) are random variables with a patient-specific probability distribution. The method that the authors propose makes these distributions the basis of the optimization and evaluation process. METHODS: The authors start from a model of motion derived from patient-specific imaging. On a multitude of geometry instances sampled from this model, a dose metric is evaluated. The resulting pdf of this dose metric is termed outcome distribution. The approach optimizes the shape of the outcome distribution based on its mean and variance. This is in contrast to the conventional optimization of a nominal value (e.g., PTV EUD) computed on a single geometry instance. The mean and variance allow for an estimate of the expected treatment outcome along with the residual uncertainty. Besides being applicable to the target, the proposed method also seamlessly includes the organs at risk (OARs). RESULTS: The likelihood that a given value of a metric is reached in the treatment is predicted quantitatively. This information reveals potential hazards that may occur during the course of the treatment, thus helping the expert to find the right balance between the risk of insufficient normal tissue sparing and the risk of insufficient tumor control. By feeding this information to the optimizer, outcome distributions can be obtained where the probability of exceeding a given OAR maximum and that of falling short of a given target goal can be minimized simultaneously. CONCLUSIONS: The method is applicable to any source of residual motion uncertainty in treatment delivery. Any model that quantifies organ movement and deformation in terms of probability distributions can be used as basis for the algorithm. Thus, it can generate dose distributions that are robust against interfraction and intrafraction motion alike, effectively removing the need for indiscriminate safety margins.

Tools for the analysis of dose optimization: III. Pointwise sensitivity and perturbation analysis.

The major challenge in intensity-modulated radiotherapy planning is to find the right balance between tumor control and normal tissue sparing. The most desirable solution is never physically feasible, and a compromise has to be found. One possible way to approach this problem is constrained optimization. In this context, it is worthwhile to quantitatively predict the impact of adjustments of the constraints on the optimum dose distribution. This has been dealt with in regard to cost functions in a previous paper. The aim of the present paper is to introduce spatial resolution to this formalism. Our method reveals the active constraints in a target subvolume that was previously selected by the practitioner for its insufficient dose. This is useful if a multitude of constraints can be the cause of a cold spot. The response of the optimal dose distribution to an adjustment of constraints (perturbation) is predicted. We conclude with a clinical example.

Energy layer optimization strategies for intensity-modulated proton therapy of lung cancer patients.

PURPOSE: When treating lung cancer patients with intensity-modulated proton therapy (IMPT), target coverage can only be guaranteed when utilizing motion mitigation. The three motion mitigation techniques, gating, breath-hold, and dose repainting, all benefit from a more rapid application of the treatment plan. A lower limit for the ungated treatment time is defined by the number of energy layers in the IMPT plan. By limiting this number during treatment planning, IMPT could become more viable for lung cancer patients. We investigate to what extend the number of layers can be reduced in single-field optimization (SFO) and multifield optimization (MFO) plans and which implications it has on the plan quality and robustness. METHODS: We have implemented three distinct layer-reducing strategies in the treatment planning system Hyperion; constant energy steps, exponential energy steps, and an adaptive strategy, where the spot weights are exposed to a group sparsity penalty in combination with layer exclusion during optimization. Four levels of increasing layer removal are planned for each strategy. SFO and MFO plans with three treatment fields are created for eleven locally advanced NSCLC patients on the midventilation 4DCT phase to simulate a breath-hold. A minimum dose to the target is ensured for each degree of layer reduction, reflecting the plan quality in the homogeneity index (HI). Plan quality was also assessed by a robustness evaluation, where the patient setup was shifted 2 mm or 4 mm in six directions. RESULTS: The three strategies result in very similar target coverages and robustness levels as a function of removed layers. The HI increases unacceptably for all the SFO plans after 50% layer removal as compared to the reference plan, while all the MFO plans are clinically acceptable with up to a highest removed percentage of 75%. The robustness level is constant as a function of removed layers. The SFO plans are significantly more robust than the MFO plans with all P-values below 0.001 (Wilcoxon signed-rank). The overall mean D98% CTV dose difference is at 2-mm setup error amplitude: 0.7 Gy (SFO) and 1.9 Gy (MFO), and at 4 mm: 3.2 Gy (SFO) and 5.4 Gy (MFO), respectively. CONCLUSIONS: The number of layers in MFO plans can be reduced substantially more than in SFO plans without compromising plan quality. Furthermore, as the robustness is independent of the number of layers, it follows that if the level of robustness is acceptable or enforced via robust optimization, MFO plans could be candidates for treatment time reductions via energy layer reductions.

A finite size pencil beam algorithm for IMRT dose optimization: density corrections.

For beamlet-based IMRT optimization, fast and less accurate dose computation algorithms are frequently used, while more accurate algorithms are needed to recompute the final dose for verification. In order to speed up the optimization process and ensure close proximity between dose in optimization and verification, proper consideration of dose gradients and tissue inhomogeneity effects should be ensured at every stage of the optimization. Due to their speed, pencil beam algorithms are often used for precalculation of beamlet dose distributions in IMRT treatment planning systems. However, accounting for tissue heterogeneities with these models requires the use of approximate rescaling methods. Recently, a finite size pencil beam (fsPB) algorithm, based on a simple and small set of data, was proposed which was specifically designed for the purpose of dose pre-computation in beamlet-based IMRT. The present work describes the incorporation of 3D density corrections, based on Monte Carlo simulations in heterogeneous phantoms, into this method improving the algorithm accuracy in inhomogeneous geometries while keeping its original speed and simplicity of commissioning. The algorithm affords the full accuracy of 3D density corrections at every stage of the optimization, hence providing the means for density related fluence modulation like penumbra shaping at field edges.

A virtual photon source model of an Elekta linear accelerator with integrated mini MLC for Monte Carlo based IMRT dose calculation.

A dedicated, efficient Monte Carlo (MC) accelerator head model for intensity modulated stereotactic radiosurgery treatment planning is needed to afford a highly accurate simulation of tiny IMRT fields. A virtual source model (VSM) of a mini multi-leaf collimator (MLC) (the Elekta Beam Modulator (EBM)) is presented, allowing efficient generation of particles even for small fields. The VSM of the EBM is based on a previously published virtual photon energy fluence model (VEF) (Fippel et al 2003 Med. Phys. 30 301) commissioned with large field measurements in air and in water. The original commissioning procedure of the VEF, based on large field measurements only, leads to inaccuracies for small fields. In order to improve the VSM, it was necessary to change the VEF model by developing (1) a method to determine the primary photon source diameter, relevant for output factor calculations, (2) a model of the influence of the flattening filter on the secondary photon spectrum and (3) a more realistic primary photon spectrum. The VSM model is used to generate the source phase space data above the mini-MLC. Later the particles are transmitted through the mini-MLC by a passive filter function which significantly speeds up the time of generation of the phase space data after the mini-MLC, used for calculation of the dose distribution in the patient. The improved VSM model was commissioned for 6 and 15 MV beams. The results of MC simulation are in very good agreement with measurements. Less than 2% of local difference between the MC simulation and the diamond detector measurement of the output factors in water was achieved. The X, Y and Z profiles measured in water with an ion chamber (V = 0.125 cm(3)) and a diamond detector were used to validate the models. An overall agreement of 2%/2 mm for high dose regions and 3%/2 mm in low dose regions between measurement and MC simulation for field sizes from 0.8 x 0.8 cm(2) to 16 x 21 cm(2) was achieved. An IMRT plan film verification was performed for two cases: 6 MV head&neck and 15 MV prostate. The simulation is in agreement with film measurements within 2%/2 mm in the high dose regions (> or = 0.1 Gy = 5% D(max)) and 5%/2 mm in low dose regions (<0.1 Gy).

Compression-induced structural and mechanical changes of fibrin-collagen composites.

Fibrin and collagen as well as their combinations play an important biological role in tissue regeneration and are widely employed in surgery as fleeces or sealants and in bioengineering as tissue scaffolds. Earlier studies demonstrated that fibrin-collagen composite networks displayed improved tensile mechanical properties compared to the isolated protein matrices. Unlike previous studies, here unconfined compression was applied to a fibrin-collagen filamentous polymer composite matrix to study its structural and mechanical responses to compressive deformation. Combining collagen with fibrin resulted in formation of a composite hydrogel exhibiting synergistic mechanical properties compared to the isolated fibrin and collagen matrices. Specifically, the composite matrix revealed a one order of magnitude increase in the shear storage modulus at compressive strains>0.8 in response to compression compared to the mechanical features of individual components. These material enhancements were attributed to the observed structural alterations, such as network density changes, an increase in connectivity along with criss-crossing, and bundling of fibers. In addition, the compressed composite collagen/fibrin networks revealed a non-linear transformation of their viscoelastic properties with softening and stiffening regimes. These transitions were shown to depend on protein concentrations. Namely, a decrease in protein content drastically affected the mechanical response of the networks to compression by shifting the onset of stiffening to higher degrees of compression. Since both natural and artificially composed extracellular matrices experience compression in various (patho)physiological conditions, our results provide new insights into the structural biomechanics of the polymeric composite matrix that can help to create fibrin-collagen sealants, sponges, and tissue scaffolds with tunable and predictable mechanical properties.

Cadherin composition and multicellular aggregate invasion in organotypic models of epithelial ovarian cancer intraperitoneal metastasis.

During epithelial ovarian cancer (EOC) progression, intraperitoneally disseminating tumor cells and multicellular aggregates (MCAs) present in ascites fluid adhere to the peritoneum and induce retraction of the peritoneal mesothelial monolayer prior to invasion of the collagen-rich submesothelial matrix and proliferation into macro-metastases. Clinical studies have shown heterogeneity among EOC metastatic units with respect to cadherin expression profiles and invasive behavior; however, the impact of distinct cadherin profiles on peritoneal anchoring of metastatic lesions remains poorly understood. In the current study, we demonstrate that metastasis-associated behaviors of ovarian cancer cells and MCAs are influenced by cellular cadherin composition. Our results show that mesenchymal N-cadherin-expressing (Ncad+) cells and MCAs invade much more efficiently than E-cadherin-expressing (Ecad+) cells. Ncad+ MCAs exhibit rapid lateral dispersal prior to penetration of three-dimensional collagen matrices. When seeded as individual cells, lateral migration and cell-cell junction formation precede matrix invasion. Neutralizing the Ncad extracellular domain with the monoclonal antibody GC-4 suppresses lateral dispersal and cell penetration of collagen gels. In contrast, use of a broad-spectrum matrix metalloproteinase (MMP) inhibitor (GM6001) to block endogenous membrane type 1 matrix metalloproteinase (MT1-MMP) activity does not fully inhibit cell invasion. Using intact tissue explants, Ncad+ MCAs were also shown to efficiently rupture peritoneal mesothelial cells, exposing the submesothelial collagen matrix. Acquisition of Ncad by Ecad+ cells increased mesothelial clearance activity but was not sufficient to induce matrix invasion. Furthermore, co-culture of Ncad+ with Ecad+ cells did not promote a 'leader-follower' mode of collective cell invasion, demonstrating that matrix remodeling and creation of invasive micro-tracks are not sufficient for cell penetration of collagen matrices in the absence of Ncad. Collectively, our data emphasize the role of Ncad in intraperitoneal seeding of EOC and provide the rationale for future studies targeting Ncad in preclinical models of EOC metastasis.

Reliability of dose volume constraint inference from clinical data.

Dose volume histogram points (DVHPs) frequently serve as dose constraints in radiotherapy treatment planning. An experiment was designed to investigate the reliability of DVHP inference from clinical data for multiple cohort sizes and complication incidence rates. The experimental background was radiation pneumonitis in non-small cell lung cancer and the DVHP inference method was based on logistic regression. From 102 NSCLC real-life dose distributions and a postulated DVHP model, an 'ideal' cohort was generated where the most predictive model was equal to the postulated model. A bootstrap and a Cohort Replication Monte Carlo (CoRepMC) approach were applied to create 1000 equally sized populations each. The cohorts were then analyzed to establish inference frequency distributions. This was applied to nine scenarios for cohort sizes of 102 (1), 500 (2) to 2000 (3) patients (by sampling with replacement) and three postulated DVHP models. The Bootstrap was repeated for a 'non-ideal' cohort, where the most predictive model did not coincide with the postulated model. The Bootstrap produced chaotic results for all models of cohort size 1 for both the ideal and non-ideal cohorts. For cohort size 2 and 3, the distributions for all populations were more concentrated around the postulated DVHP. For the CoRepMC, the inference frequency increased with cohort size and incidence rate. Correct inference rates >[Formula: see text] were only achieved by cohorts with more than 500 patients. Both Bootstrap and CoRepMC indicate that inference of the correct or approximate DVHP for typical cohort sizes is highly uncertain. CoRepMC results were less spurious than Bootstrap results, demonstrating the large influence that randomness in dose-response has on the statistical analysis.

An algorithm for automatic determination of the respiratory phases in four-dimensional computed tomography.

Recently, several techniques have been developed to improve the quality of computed tomography (CT) images of the thoracic and abdominal region that are degraded by the interference of the scanning process and respiration. Several devices for respiratory-correlated CT are available for clinical usage. They are based on the synchronization of the acquired CT image data with the respiratory motion using a signal from an external respiratory monitoring system. In this work, some practical aspects of clinical implementation of the multi-slice 4D CT scanner Somatom Sensation Open (Siemens Medical Solutions, Erlangen, Germany) equipped with a respiratory gating system (RGS) AZ-733V (Anzai Medical, Tokyo, Japan) are discussed. A new algorithm developed for automatic respiratory phase determination needed for the reconstruction of the 4D CT images is presented.

IMRT for breast. a planning study.

BACKGROUND AND PURPOSE: To evaluate the performance of ten different treatment-planning systems when intensity modulated (IMRT) plans are designed for breast treatments that include the irradiation of the internal mammary chain. PATIENTS AND METHODS: A dataset of five patients (CT images and volumes of interest) was distributed to design IMRT plans on the ten systems. To minimise biases, the same geometry and clinical planning aims were imposed on the individual plans. Results were analysed in terms of dose distributions and dose volume histograms. RESULTS AND CONCLUSIONS: For target coverage, the volume receiving more than 95% of the prescribed dose ranged from 77% (OTP) to 91% (Eclipse and Pinnacle), the volume receiving more than 107% ranged from 3.3% (Hyperion) to 23.2% (OTP). The mean dose to ipsilateral lung ranged from 13 Gy (Eclipse) to 18 Gy (OTP). The volume of the contralateral breast receiving more than 10 Gy ranged from 3% (Pinnacle) to 26% (Precise). The volume of heart receiving more than 20 Gy ranged from 7% (Eclipse) to 47% (Precise), the maximum significant dose to heart ranged from approximately 27 Gy (XiO) to approximately 49 Gy (Precise). The maximum significant dose to healthy tissue ranged from approximately 51 Gy (Eclipse) to approximately 62 Gy (OTP). It was also possible to show that the treatment geometry proposed here enables to minimise contralateral breast irradiation while keeping minimal ipsilateral lung (or heart) involvement and satisfactory target coverage.

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.

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 patient's 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.

On multiscale approaches to three-dimensional modelling of morphogenesis.

In this paper we present the foundation of a unified, object-oriented, three-dimensional biomodelling environment, which allows us to integrate multiple submodels at scales from subcellular to those of tissues and organs. Our current implementation combines a modified discrete model from statistical mechanics, the Cellular Potts Model, with a continuum reaction-diffusion model and a state automaton with well-defined conditions for cell differentiation transitions to model genetic regulation. This environment allows us to rapidly and compactly create computational models of a class of complex-developmental phenomena. To illustrate model development, we simulate a simplified version of the formation of the skeletal pattern in a growing embryonic vertebrate limb.

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.

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.