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PubMed2003

Is self-mastery always a helpful resource? Coping wiith paradoxical findings in relation to optimism and abstinence self-efficacy.

This study investigated the relationship between three personal resources (self-mastery, optimism, and abstinence self-efficacy) and ways of coping among recovering substance abusers (n = 52) residing in Oxford Houses. Although residents' scores on optimism and abstinence self-efficacy were significantly correlated in a positive direction, residents' self-mastery scores were significantly and negatively related to both optimism and abstinence self-efficacy scores. However, residents reported using significantly more emotion-focused than problem-focused coping even though there was a significant positive relationship between emotion-focused coping and self-mastery. These paradoxical findings might be due to communal living and 12-step philosophy that is antithetical to a sense of control, which may have facilitated residents' emotional regulation to stress. Furthermore, significant relationships between coping strategies and personal resources imply that active coping strategies are instrumental in recovering substance abusers' use of optimism and abstinence self-efficacy, whereas passive coping strategies are involved with self-mastery. In addition, African American residents reported using significantly more wishful thinking coping, suggesting ethnicity might be an important aspect of the coping process. Overall, findings suggest that optimism and abstinence self-efficacy are effective personal resources for recovering substance abusers in 12-step programs.

Adaptation, Psychological↗

PubMed2003

Density dependence, territoriality, and divisibility of resources: from optimality models to population processes.

Species differ enormously in their territorial systems. Some species defend only small areas surrounded by undefended space, while others defend large contiguous territories. Using an optimization approach, we show that this variation can be explained from the density of two types of resources: divisible and nondivisible. We assume that benefits of territories are monotonously related to the defended amount of divisible resources (hereafter called food). In contrast, no benefits are obtained without a nondivisible resource (hereafter called nest site) in the territory, while more than one nest site does not further increase the benefits. The optimal territory size depends on the relative abundance of these resources. With a low density of nest sites, the optimal territory size is small and includes only the nest site. If the density of nest sites is relatively large, the optimal territory size is high, and territories are contiguous. Competition for these different resources yields contrasting patterns of how populations are regulated. If there is mainly competition for nest sites, we expect density-dependent exclusion through territoriality and no density-dependent reproduction. When competition is mainly for food, we expect density-dependent reproduction because optimal territory size will be compressed at higher densities, resulting in lower reproductive success. These predicted patterns indeed are observed in some well-studied passerine species for which both the territorial system and the occurrence of density dependence is known.

Animals↗

PubMed2003

Optimization, conflict, and nonoverlapping foraging ranges in ants.

An organism's foraging range depends on the behavior of neighbors, the dynamics of resources, and the availability of information. We use a well-studied population of the red harvester ant Pogonomyrmex barbatus to develop and independently parameterize models that include these three factors. The models solve for an allocation of foraging ants in the area around the nest in response to other colonies. We compare formulations that optimize at the colony or individual level and those that do or do not include costs of conflict. Model predictions were compared with data collected on ant time budgets and ant density. The strategy that optimizes at the colony level but neglects costs of conflict predicts unrealistic levels of overlap. In contrast, the strategy that optimizes at the individual level predicts realistic foraging ranges with or without inclusion of conflict costs. Both the individual model and the colony model that includes conflict costs show good quantitative agreement with data. Thus, an optimal foraging response to a combination of exploitation and interference competition can largely explain how individual foraging behavior creates the foraging range of a colony. Deviations between model predictions and data indicate that colonies might allocate a larger than optimal number of foragers to areas near boundaries between foraging ranges.

Animals↗

PubMed1991

Optimization by simulated annealing of three-dimensional conformal treatment planning for radiation fields defined by a multileaf collimator.

Three-dimensional conformal radiotherapy may be achieved by using a combination of geometrically shaped radiation fields from different orientations around the patient. A convenient method to shape the fields is to use a multileaf collimator. These fields are shaped to the beam's-eye-view of the target volume, at each orientation of the collimator, and may also encompass sensitive structure, i.e. organs at risk, if the target region has concavities in its outline within which such structure may reside. The term 'conformal therapy' is used in this paper to mean tailoring the high dose volume to the target volume whilst minimising dose to other normal structures (organs at risk) which may be irradiated by the treatment fields, shaped by a multileaf collimator. The question then arises of the optimum distribution of beam weights to apply to the fields to minimise dose to organs at risk whilst aiming towards a uniform dose distribution in the target volume. This paper provides a method of optimizing the choice of beamweights to achieve this. The method is based on the well known optimization technique of simulated annealing. Either an optimal set of beamweights, one weight per field, is generated or the intensity may be spatially modulated across the field at each orientation (two weights per field) depending on whether there is just target volume or both target volume and volume containing organs at risk in the line of sight. It is shown that the dose matrix resulting from the latter optimization is closer to the dose prescription than that obtained by using either an optimal set of single weights per field or uniform beamweights.

Humans↗

PubMed1995

Linear dimension reduction of sequences of medical images: I. Optimal inner products.

A general theory is presented for minimizing noise in linear dimension reduction of sequences of medical images when the factors and the covariance matrix and mean of the noise are given. A dimension reduction is optimal when all diagonal elements in the covariance matrix of the noise in the signal (factor) space are minimized. This occurs when the noise in the signal space is uncorrelated with the residual noise. Expressions are given for the resulting covariance matrix of the noise in the signal space. Many optimal inner products exist, which all result in the same optimal dimension reduction. Given any pair of inner products for signal space and residual space, a combined inner product exists that is also optimal. If the covariance matrices of the noise in different pixel vectors are not multiples of each other, different pixel vectors may have different optimal inner products. The averaging process in generating images from tomographic projections tends to make the covariance matrices more uniform.

Biophysical Phenomena↗

PubMed1998

An adaptive control algorithm for optimization of intensity modulated radiotherapy considering uncertainties in beam profiles, patient set-up and internal organ motion.

A new general beam optimization algorithm for inverse treatment planning is presented. It utilizes a new formulation of the probability to achieve complication-free tumour control. The new formulation explicitly describes the dependence of the treatment outcome on the incident fluence distribution, the patient geometry, the radiobiological properties of the patient and the fractionation schedule. In order to account for both measured and non-measured positioning uncertainties, the algorithm is based on a combination of dynamic and stochastic optimization techniques. Because of the difficulty in measuring all aspects of the intra- and interfractional variations in the patient geometry, such as internal organ displacements and deformations, these uncertainties are primarily accounted for in the treatment planning process by intensity modulation using stochastic optimization. The information about the deviations from the nominal fluence profiles and the nominal position of the patient relative to the beam that is obtained by portal imaging during treatment delivery, is used in a feedback loop to automatically adjust the profiles and the location of the patient for all subsequent treatments. Based on the treatment delivered in previous fractions, the algorithm furnishes optimal corrections for the remaining dose delivery both with regard to the fluence profile and its position relative to the patient. By dynamically refining the beam configuration from fraction to fraction, the algorithm generates an optimal sequence of treatments that very effectively reduces the influence of systematic and random set-up uncertainties to minimize and almost eliminate their overall effect on the treatment. Computer simulations have shown that the present algorithm leads to a significant increase in the probability of uncomplicated tumour control compared with the simple classical approach of adding fixed set-up margins to the internal target volume.

Algorithms↗

PubMed1999

Optimization of the arthroscopic indentation instrument for the measurement of thin cartilage stiffness.

Structural alterations associated with early, mostly reversible, degeneration of articular cartilage induce tissue softening, generally preceding fibrillation and, thus, visible changes of the cartilage surface. We have already developed an indentation instrument for measuring arthroscopic stiffness of cartilage with typical thickness >2 mm. The aim of this study was to extend the applicability of the instrument for the measurement of thin (<2 mm) cartilage stiffness. Variations in cartilage thickness, which will not be known during arthroscopy, can nonetheless affect the indentation measurement, and therefore optimization of the indenter dimensions is necessary. First, we used theoretical and finite element models to compare plane-ended and spherical-ended indenters and, then, altered the dimensions to determine the optimal indenter for thin cartilage measurements. Finally, we experimentally validated the optimized indenter using bovine humeral head cartilage. Reference unconfined compression measurements were carried out with a material testing device. The spherical-ended indenter was more insensitive to the alterations in cartilage thickness (20% versus 39% in the thickness range 1.5-5 mm) than the plane-ended indenter. For thin cartilage, the optimal dimensions for the spherical-ended indenter were 0.5 mm for diameter and 0.1 mm for height. The experimental stiffness measurements with this indenter correlated well with the reference measurements (r = 0.811, n = 31, p < 0.0001) in the cartilage thickness range 0.7-1.8 mm. We conclude that the optimized indenter is reliable and well suited for the measurement of thin cartilage stiffness.

Animals↗

PubMed1999

Optimization of importance factors in inverse planning.

Inverse treatment planning starts with a treatment objective and obtains the solution by optimizing an objective function. The clinical objectives are usually multifaceted and potentially incompatible with one another. A set of importance factors is often incorporated in the objective function to parametrize trade-off strategies and to prioritize the dose conformality in different anatomical structures. Whereas the general formalism remains the same, different sets of importance factors characterize plans of obviously different flavour and thus critically determine the final plan. Up to now, the determination of these parameters has been a 'guessing' game based on empirical knowledge because the final dose distribution depends on the parameters in a complex and implicit way. The influence of these parameters is not known until the plan optimization is completed. In order to compromise properly the conflicting requirements of the target and sensitive structures, the parameters are usually adjusted through a trial-and-error process. In this paper, a method to estimate these parameters computationally is proposed and an iterative computer algorithm is described to determine these parameters numerically. The treatment plan selection is done in two steps. First, a set of importance factors are chosen and the corresponding beam parameters (e.g. beam profiles) are optimized under the guidance of a quadratic objective function using an iterative algorithm reported earlier. The 'optimal' plan is then evaluated by an additional scoring function. The importance factors in the objective function are accordingly adjusted to improve the ranking of the plan. For every change in the importance factors, the beam parameters need to be re-optimized. This process continues in an iterative fashion until the scoring function is saturated. The algorithm was applied to two clinical cases and the results demonstrated that it has the potential to improve significantly the existing method of inverse planning. It was noticed that near the final solution the plan became insensitive to small variations of the importance factors.

Algorithms↗

PubMed1999

Stochastic optimization of intensity modulated radiotherapy to account for uncertainties in patient sensitivity.

The aim of the present work is to better account for the known uncertainties in radiobiological response parameters when optimizing radiation therapy. The radiation sensitivity of a specific patient is usually unknown beyond the expectation value and possibly the standard deviation that may be derived from studies on groups of patients. Instead of trying to find the treatment with the highest possible probability of a desirable outcome for a patient of average sensitivity, it is more desirable to maximize the expectation value of the probability for the desirable outcome over the possible range of variation of the radiation sensitivity of the patient. Such a stochastic optimization will also have to consider the distribution function of the radiation sensitivity and the larger steepness of the response for the individual patient. The results of stochastic optimization are also compared with simpler methods such as using biological response 'margins' to account for the range of sensitivity variation. By using stochastic optimization, the absolute gain will typically be of the order of a few per cent and the relative improvement compared with non-stochastic optimization is generally less than about 10 per cent. The extent of this gain varies with the level of interpatient variability as well as with the difficulty and complexity of the case studied. Although the dose changes are rather small (<5 Gy) there is a strong desire to make treatment plans more robust, and tolerant of the likely range of variation of the radiation sensitivity of each individual patient. When more accurate predictive assays of the radiation sensitivity for each patient become available, the need to consider the range of variations can be reduced considerably.

Dose-Response Relationship, Radiation↗

PubMed2001

Simultaneous optimization of cryoprobe placement and thermal protocol for cryosurgery.

We demonstrate that it is possible to simultaneously optimize multiple cryoprobe placements and their thermal protocol for one freeze-thaw cycle. A numerical optimization algorithm is used and three different forms of objective function are examined in terms of algorithm convergence rate, minimum value of the chosen objective function, temperature-volume histograms and isotherm distributions. The optimization results depend on the initial values of the variables, the form of the objective function, optimization goals and the mathematical method adopted for gradient calculation. The proposed optimization model offers significant advantages over the previously reported semi-empirical approach to conformal cryotherapy, such as the ability to handle an unlimited number of variables and eliminating the need for the user input between iterations, thereby reducing, if not removing, the subjectivity of cryosurgery treatment planning.

Algorithms↗

PubMed2002

Multiobjective anatomy-based dose optimization for HDR-brachytherapy with constraint free deterministic algorithms.

In high dose rate (HDR) brachytherapy, conventional dose optimization algorithms consider multiple objectives in the form of an aggregate function that transforms the multiobjective problem into a single-objective problem. As a result, there is a loss of information on the available alternative possible solutions. This method assumes that the treatment planner exactly understands the correlation between competing objectives and knows the physical constraints. This knowledge is provided by the Pareto trade-off set obtained by single-objective optimization algorithms with a repeated optimization with different importance vectors. A mapping technique avoids non-feasible solutions with negative dwell weights and allows the use of constraint free gradient-based deterministic algorithms. We compare various such algorithms and methods which could improve their performance. This finally allows us to generate a large number of solutions in a few minutes. We use objectives expressed in terms of dose variances obtained from a few hundred sampling points in the planning target volume (PTV) and in organs at risk (OAR). We compare two- to four-dimensional Pareto fronts obtained with the deterministic algorithms and with a fast-simulated annealing algorithm. For PTV-based objectives, due to the convex objective functions, the obtained solutions are global optimal. If OARs are included, then the solutions found are also global optimal, although local minima may be present as suggested.

Algorithms↗

PubMed2002

A unified model for the speed of sound in cranial bone based on genetic algorithm optimization.

The density and structure of bone is highly heterogeneous, causing wide variations in the reported speed of sound for ultrasound propagation. Current research on the propagation of high intensity focused ultrasound through an intact human skull for non-invasive therapeutic action on brain tissue requires a detailed model for the acoustic velocity in cranial bone. Such models have been difficult to derive empirically due to the aforementioned heterogeneity of bone itself. We propose a single unified model for the speed of sound in cranial bone based upon the apparent density of bone by CT scan. This model is based upon the coupling of empirical measurement, theoretical acoustic simulation and genetic algorithm optimization. The phase distortion caused by the presence of skull in an acoustic path is empirically measured. The ability of a theoretical acoustic simulation coupled with a particular speed-of-sound model to predict this phase distortion is compared against the empirical data, thus providing the fitness function needed to perform genetic algorithm optimization. By performing genetic algorithm optimization over an initial population of candidate speed-of-sound models, an ultimate single unified model for the speed of sound in both the cortical and trabecular regions of cranial bone is produced. The final model produced by genetic algorithm optimization has a nonlinear dependency of speed of sound upon local bone density. This model is shown by statistical significance to be a suitable model of the speed of sound in bone. Furthermore, using a skull that was not part of the optimization process, this model is also tested against a published homogeneous speed-of-sound model and shown to return an improved prediction of transcranial ultrasound propagation.

Algorithms↗

PubMed2003

A fast dose calculation method based on table lookup for IMRT optimization.

This note describes a fast dose calculation method that can be used to speed up the optimization process in intensity-modulated radiotherapy (IMRT). Most iterative optimization algorithms in IMRT require a large number of dose calculations to achieve convergence and therefore the total amount of time needed for the IMRT planning can be substantially reduced by using a faster dose calculation method. The method that is described in this note relies on an accurate dose calculation engine that is used to calculate an approximate dose kernel for each beam used in the treatment plan. Once the kernel is computed and saved, subsequent dose calculations can be done rapidly by looking up this kernel. Inaccuracies due to the approximate nature of the kernel in this method can be reduced by performing scheduled kernel updates. This fast dose calculation method can be performed more than two orders of magnitude faster than the typical superposition/convolution methods and therefore is suitable for applications in which speed is critical, e.g., in an IMRT optimization that requires a simulated annealing optimization algorithm or in a practical IMRT beam-angle optimization system.

Algorithms↗

PubMed2003

Thermal dose optimization method for ultrasound surgery.

In this paper, a model-based optimization method is derived to control the thermal dose in biological tissues for ultrasound surgery. The optimization method uses the bioheat equation as a system model and quadratic cost criteria for the desired thermal dose. Time-harmonic quasi-stationary ultrasound fields are used as the heat source. In this method the optimal phase and the amplitude trajectories are found directly by minimizing the associated cost function. The approach also allows for maximum input amplitude constraints. The method is based on the Hamiltonian form of the system and results in a large dimensional nonlinear optimization problem which is solved with a gradient-type iterative scheme. The performance of the optimization method is tested with 2D simulations and it is shown that the approach is able to yield a feasible nominal solution. This nominal evolution would then eventually be sought to be maintained with the help of a feedback controller during the actual sonication.

Algorithms↗

PubMed2004

Degeneracy, frequency response and filtering in IMRT optimization.

This paper attempts to provide an answer to some questions that remain either poorly understood, or not well documented in the literature, on basic issues related to intensity modulated radiation therapy (IMRT). The questions examined are: the relationship between degeneracy and frequency response of optimizations, effects of initial beamlet fluence assignment and stopping point, what does filtering of an optimized beamlet map actually do and how could image analysis help to obtain better optimizations? Two target functions are studied, a quadratic cost function and the log likelihood function of the dynamically penalized likelihood (DPL) algorithm. The algorithms used are the conjugate gradient, the stochastic adaptive simulated annealing and the DPL. One simple phantom is used to show the development of the analysis tools used and two clinical cases of medium and large dose matrix size (a meningioma and a prostate) are studied in detail. The conclusions reached are that the high number of iterations that is needed to avoid degeneracy is not warranted in clinical practice, as the quality of the optimizations, as judged by the DVHs and dose distributions obtained, does not improve significantly after a certain point. It is also shown that the optimum initial beamlet fluence assignment for analytical iterative algorithms is a uniform distribution, but such an assignment does not help a stochastic method of optimization. Stopping points for the studied algorithms are discussed and the deterioration of DVH characteristics with filtering is shown to be partially recoverable by the use of space-variant filtering techniques.

Algorithms↗

PubMed2004

Optimization of standard patient radiographic images for chest, skull and pelvis exams in conventional x-ray equipment.

Optimized radiographic techniques for clinical images of chest, skull and pelvis using conventional single-phase, three-phase and high-frequency x-ray units for a standard patient have been developed. Optimization of image contrast and optical density was obtained by using a homogeneous phantom (PEP) and an Anderson Rando anthropomorphic phantom. Image quality was evaluated by nine radiologists in independent analyses, leading to the choice of the optimized technique. A course of action to implement and validate these techniques in other radiographic systems has also been introduced. A realistic-analytic phantom (RAP) was constructed to certify the validation process. The optimized radiographic technique was implemented in the routine of our home hospital radiodiagnostic routine, enabling a reduction in patient doses around 25, 14 and 72%, respectively, for chest, skull and pelvis exams when compared with the previously used techniques. In addition, a corresponding reduction in the x-ray tube load of 68, 14 and 62% for the respective mentioned exams has been observed. In conclusion, implemented optimal techniques can lead to a reduction in the rate of film rejection, thus contributing to a better risk-benefit relationship for the patient and cost-benefit for the radiodiagnostic facility.

Humans↗

PubMed2006

Direct aperture optimization of breast IMRT and the dosimetric impact of respiration motion.

We have studied the application of direct aperture optimization (DAO) as an inverse planning tool for breast IMRT. Additionally, we have analysed the impact of respiratory motion on the quality of the delivered dose distribution. From this analysis, we have developed guidelines for balancing the desire for a high-quality optimized plan with the need to create a plan that will not degrade significantly in the presence of respiratory motion. For a DAO optimized breast IMRT plan, the tangential fields incorporate a flash field to cover the range of respiratory motion. The inverse planning algorithm then optimizes the shapes and weights of additional segments that are delivered in combination with the open fields. IMRT plans were generated using DAO with the relative weights of the open segments varied from 0% to 95%. To assess the impact of breathing motion, the dose distribution for the optimized IMRT plan was recalculated with the isocentre sampled from a predefined distribution in a Monte Carlo convolution/superposition dose engine with the breast simulated as a rigid object. The motion amplitudes applied in this study ranged from 0.5 to 2.0 cm. For a range of weighting levels assigned to the open field, comparisons were made between the static plans and the plans recalculated with motion. For the static plans, we found that uniform dose distributions could be generated with relative weights for the open segments equal to and below 80% and unacceptable levels of underdosage were observed with the weights larger than 80%. When simulated breathing motion was incorporated into the dose calculation, we observed a loss in dose uniformity as the weight of the open field was decreased to below 65%. More quantitatively, for each 1% decrease in the weight, the per cent volume of the target covered by at least 95% of the prescribed dose decreased by approximately 0.10% and 0.16% for motion amplitudes equal to 1.5 cm and 2.0 cm, respectively. When taking into account the motion effects, the most uniform and conformal dose distributions were achieved when the open segment weights were in the range of 65-80%. Within this range, high-quality IMRT plans were produced for each case. The study demonstrates that DAO with tangential fields provides a robust and efficient technique for breast IMRT planning and delivery when the open segment weight is selected between 65% and 80%.

Breast Neoplasms↗

PubMed2007

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.

Algorithms↗