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PubMed2005

A fourier analysis of the dose grid resolution required for accurate IMRT fluence map optimization.

We present a theoretical and empirical analysis of the errors associated with the spatial discretization of the dose grid employed in optimized intensity modulated radiation therapy (IMRT) treatment plans. An information theory based Fourier analysis of the accuracy of discrete representations of three-dimensional dose distributions is presented. When applied to beamlet-based IMRT dose distributions, the theory produces analytic integrals that can bound worst case aliasing errors that can occur regardless of the location and orientation of the dose grid. The predictions of this theory are compared to empirical results obtained by solving a linear-programming based fluence-map optimization model to global optimality. A reasonable agreement between worst case estimates and the empirical results is attributed to the fact that the optimization takes advantage of aliasing to produce an optimal plan. We predicted and empirically demonstrated that an isotropic dose grid with <2.5 mm spacing is sufficient to prevent dose errors larger than a percent. However, we noted that in practice this resolution is mostly needed in high-dose target regions. Finally, a multiresolution 2-4-6 mm spacing model was developed and empirically tested where these spacings were applied to targets, structures, and tissue, respectively.

Algorithms↗

PubMed2006

Optimized approach to decision fusion of heterogeneous data for breast cancer diagnosis.

As more diagnostic testing options become available to physicians, it becomes more difficult to combine various types of medical information together in order to optimize the overall diagnosis. To improve diagnostic performance, here we introduce an approach to optimize a decision-fusion technique to combine heterogeneous information, such as from different modalities, feature categories, or institutions. For classifier comparison we used two performance metrics: The receiving operator characteristic (ROC) area under the curve [area under the ROC curve (AUC)] and the normalized partial area under the curve (pAUC). This study used four classifiers: Linear discriminant analysis (LDA), artificial neural network (ANN), and two variants of our decision-fusion technique, AUC-optimized (DF-A) and pAUC-optimized (DF-P) decision fusion. We applied each of these classifiers with 100-fold cross-validation to two heterogeneous breast cancer data sets: One of mass lesion features and a much more challenging one of microcalcification lesion features. For the calcification data set, DF-A outperformed the other classifiers in terms of AUC (p < 0.02) and achieved AUC=0.85 +/- 0.01. The DF-P surpassed the other classifiers in terms of pAUC (p < 0.01) and reached pAUC=0.38 +/- 0.02. For the mass data set, DF-A outperformed both the ANN and the LDA (p < 0.04) and achieved AUC=0.94 +/- 0.01. Although for this data set there were no statistically significant differences among the classifiers' pAUC values (pAUC=0.57 +/- 0.07 to 0.67 +/- 0.05, p > 0.10), the DF-P did significantly improve specificity versus the LDA at both 98% and 100% sensitivity (p < 0.04). In conclusion, decision fusion directly optimized clinically significant performance measures, such as AUC and pAUC, and sometimes outperformed two well-known machine-learning techniques when applied to two different breast cancer data sets.

Algorithms↗

PubMedDate not supplied

Application of fast simulated annealing to optimization of conformal radiation treatments.

Applications of simulated annealing to the optimization of radiation treatment plans, in which a set of beam weights are iteratively adjusted so as to minimize a cost function, have been motivated by its potential for finding the global or near-global minimum among multiple minima. However, the method has been found to be slow, requiring several tens of thousands of iterations to optimize 50 to 100 variables. A technique to improve the efficiency for finding a solution is reported, which is generally applicable to the optimization of continuous variables. In previous applications of simulated annealing to treatment planning optimization, only one or two weights are varied each iteration. This approach is to change all weights simultaneously, using random changes that are initially large to coarsely sample the cost function, then are reduced with iteration to probe finer structure. The performance of different methods are compared in optimizing a plan for treatment of the prostate, in which the search space consists of 54 noncoplanar beams and the cost function is based on tumor control and normal tissue complication probabilities. The proposed method yields solutions with similar values of the cost function in only a fraction of the iterations compared either to a fixed single weight adjustment technique, or to a method which combines the Nelder and Mead downhill simplex simulated annealing.

Humans↗

PubMed1994

A generalized pencil beam algorithm for optimization of radiation therapy.

An iterative pencil beam algorithm for optimization of multidimensional radiation therapy dose plans has been developed. The algorithm allows the use of both physical and radiobiological treatment objective functions and allows arbitrary sampling such as straight Cartesian grids with linear or nonlinear sampling functions or random sampling. The algorithm can account for and optimally combine almost all the degrees of freedom at an advanced radiotherapy clinic, such as different beam modalities and spectra, beam directions, beam fluence distributions, and time-dose fractionations. The algorithm allows for external charged and neutral beams as well as intracavitary and interstitial sources to be optimally combined. A quantity termed the generalized fluence vector is introduced, combining fluences and energy fluences from external beams as well as the radiation source densities of intracavitary and interstitial sources or external source distributions. The positivity constraint on the generalized fluence can therefore be applied directly during the optimization procedure. The convergence properties and the required iteration time of the algorithm are discussed. Several examples with combinations of photon and electron beams of different energies and directions of incidence are presented. The optimization has been made with the treatment objective to maximize the probability of achieving tumor control without causing severe complications in healthy normal tissues.

Algorithms↗

PubMed1994

A model for optimization of spectral shape in digital mammography.

X-ray mammography is the most sensitive imaging modality available for the detection of breast cancer. The highest performance can only be achieved, however, if the complete imaging system is optimized. The development of digital mammography offers an opportunity to obtain improved sensitivity in mammography. In such systems, the decoupling of the recording and display processes allows each component of the imaging system to be optimized separately. In this paper we describe a method for optimizing the recording process for digital mammographic techniques. Our method uses an energy transport model of the propagation of signal and noise through the imaging system. The computations make use of experimentally determined data wherever possible so that the number of assumptions in the model can be minimized. The model predicts the signal-to-noise ratio for a constant dose to the breast, and therefore allows comparison and optimization both for different x-ray spectra and for different imaging tasks. The major energy-dependent components of the model have been verified, and good agreement is demonstrated between predictions by the model of both contrast and SNR and experimentally measured values. Calculations for a particular imaging task, detection of a 200-microns cubic calcification in a 6-cm, 50% adipose-50% glandular breast, illustrate application of the model for optimization of spectral shape.

Breast Neoplasms↗

PubMed1995

Optimization of MR pulse sequences for Bayesian image segmentation.

A method for optimizing MR imaging pulse sequence parameters in a statistical framework is presented. Parameters are defined to be optimal when the resulting scalar images yield optimal image segmentations using Bayesian pixel classification. Thus, Bayes risk is used as the objective function to minimize. Approximations are made to give a tractable solution in a four-step procedure. A sample calculation is carried out to determine the optimal TR and flip angle for scalar SPGR imaging of the brain. Overall, this paper gives a new approach to optimize MRI pulse sequences for the specific objective of improved image segmentation.

Bayes Theorem↗

PubMed1995

The evaluation of optimized implants for idealized implant geometries.

The purpose of this paper is to investigate the utility of implant quality measures on single stepping-source brachytherapy treatment plans. Four dwell weight optimization algorithms were applied to four regular geometric implants: single plane, double plane, cuboid, and cylindrical. The dwell weight optimization schemes included equal weighing, two commercial optimization schemes (dose-point and geometric) and a variation of the Paterson-Parker distribution rules. The implant quality measures were investigated as a function of dose-per-integrated reference air kerma (IRAK) to eliminate bias resulting from a prescription choice. A particular dose per IRAK refers to a dose surface that is a function only of the relative dwell weight distribution and is therefore well suited to investigate dwell weight optimization schemes. The implant quality measures included the dose-nonuniformity ratio (DNR) developed by Saw and a coverage index to assess the isodose coverage relative to the implanted volume. These were termed direct quantities due to their clear clinical significance. Additional measures include the ratio of the implant dose-volume histogram (DVH) to that of a point source exhibiting the same IRAK (Rp) and the ratio of the optimized DVH to the equally weighted DVH (EWR). The widths of the Rp curves and depths of the EWR curves were used to characterize these indirect implant quality measures. To evaluate the effectiveness of both the direct and indirect measures, they were correlated with the DNR for an isodose surface that covered the implant (D0). The efficiency of the dwell weight distribution was examined by noting the dose-per-IRAK surface D0.(ABSTRACT TRUNCATED AT 400 WORDS)

Algorithms↗

PubMed1996

Genetic and geometric optimization of three-dimensional radiation therapy treatment planning.

The thesis of this report is that potentially useful treatment beams can be chosen based on geometric heuristics and that a genetic algorithm (GA) can be constructed to find an optimal combination of beams based on a formal objective function. The paper describes the basic principles of a GA and the particular implementation developed. The code represents each plan in the population as two paired lists comprised of beam identifiers and relative weights. Reproduction operators, which mimic sexual reproduction with crossover, mutation, cloning, spontaneous generation, and death, manipulate the lists to grow optimal plans. The necessary gene pool is created by software modules which generate beams, distribute calculation points, obtain clinical constraints, add wedges, and calculate doses. The code has been tested on a set of artificial patients and on four clinical cases: prostate, pancreas, esophagus, and glomus. All demonstrated consistent results, indicating that the code is a reliable optimizer. Additional experiments compared the results for a full set of open beams to the geometrically selected set and the GA code with simulated annealing. Geometric selection of beam directions did not significantly compromise optimization quality. Compared to simulated annealing, the genetic algorithm was equally able to optimize the objective function, and calculations suggest it may be the faster method when the number of beams to be considered exceeds approximately 70.

Algorithms↗

PubMed1996

A genetic algorithm for the optimization of prostate implants.

A genetic algorithm (GA) is presented for the optimization of template- and ultrasound-guided prostate implants. The end points for optimization are incorporated in an objective function of separable cardinal utility terms. As an application of the GA, the minimum 103Pd total source strength required to deliver a given dose was correlated with the average dimension for prostate implants carried out under the current template and seed spacing protocols. Significant improvements in quality were observed, in terms of both the minimum peripheral dose and tumor cell surviving fractions, when GA-optimized implants were compared to the corresponding unoptimized implants for given target volumes. In addition, numerical simulation of source displacements indicates that the dosimetric and radiobiologic advantages of GA optimization can tolerate a reasonable level of seed placement uncertainties observed clinically. In summary, the GA application provides an automated design strategy for prostate implant planning, and at the same time affords the potential for systematic optimization of a set of end points that can sustain practical variations.

Algorithms↗

PubMed1997

Multiobjective decision theory for computational optimization in radiation therapy.

Machine-guided iterative optimization in radiation oncology requires ordinal or cardinal ranking of competing treatment plans. When the clinical objectives are multifaceted and incommensurable, the ranking formalism must take into account the decision maker's tradeoff strategies in a multidimensional decision space. To capture the decision processes in treatment planning, a multiobjective decision-theoretic scheme is formulated. Ranking among a group of candidate plans is based on a generalized distance metric. A dynamic metric weighting function is defined based on the state energy of the decision system, which is assumed to undergo thermodynamic cooling with iteration time. The decision maker is required to specify a baseline ranking of the objectives, which is taken to be the ground state of the decision system. This decision-theoretic formalism was applied to idealized cases in stereotactic radiosurgery and prostatic implantation, using the genetic algorithm as the optimization engine. The optimization pathways and the outcome at limited horizons indicated that the combined scheme of decision-theoretic steering and iterative optimization was robust and produced treatment plans consistent with the user's expectation. The effect of treatment uncertainties was simulated using imperfect objectives; however, certain recurring plans could be identified as optimized baseline solutions. Overall, the present formalism provides a realistic alternative to complete utility assessment or human-guided exploration of the efficient solution set.

Algorithms↗

PubMed1999

Anatomy-based three-dimensional dose optimization in brachytherapy using multiobjective genetic algorithms.

In conventional dose optimization algorithms, in brachytherapy, multiple objectives are expressed in terms of an aggregating function which combines individual objective values into a single utility value, making the problem single objective, prior to optimization. A multiobjective genetic algorithm (MOGA) was developed for dose optimization based on an a posteriori approach, leaving the decision-making process to a planner and offering a representative trade-off surface of the various objectives. The MOGA provides a flexible search engine which provides the maximum of information for a decision maker. Tests performed with various treatment plans in brachytherapy have shown that MOGA gives solutions which are superior to those of traditional dose optimization algorithms. Objectives were proposed in terms of the COIN distribution and differential volume histograms, taking into account patient anatomy in the optimization process.

Algorithms↗

PubMed1999

Morphology-guided radiosurgery treatment planning and optimization for multiple isocenters.

This work merges two distinct fields, 3D morphology and ionizing radiation dosimetry, to solve the problem of 3D-treatment planning and optimization in stereotactic radiosurgery. In Leksell Gamma Knife radiosurgery, dose delivery is based on the unit "shot," a dose distribution approximately spherical in shape. Multiple shots, or isocenters, are used in Gamma Knife treatment to deliver a conformal dose to an irregular radiosurgical target. The medial axis transformation, or skeleton, of the target, which uniquely characterizes the target volume and shape, is used to determine the optimal shot positions (isocenters), sizes (collimator helmet size and dosimetric weight), and the total number of shots that will deliver a conformal dose distribution to the target. The skeletonization approach reduces a complicated 3D-optimization problem to 1D searching with potential savings in computation time and mathematical complexity. In addition, optimization based on target shape replicates and automates manual treatment planning. This approach makes the process easily understandable. The relationship between skeleton discs and the dose distributions they predict is discussed. Results of optimal plans and corresponding dose distributions are presented. This approach is generally applicable to other types of multi-isocentric stereotactic radiosurgery techniques.

Bone and Bones↗

PubMed2002

On the selection of optimization parameters for an inverse treatment planning replacement of a forward planning technique for prostate cancer.

The influence of organ volume sampling, lateral scatter inclusion, and the selection of objectives and constraints on the inverse treatment planning process with a commercial treatment planning system is investigated and suitable parameters are identified for an inverse treatment planning replacement of a clinical forward planning technique for prostate cancer. For the beam geometries of the forward technique, a variable set of parameters is used for the calculation of dose from pencil beams. An optimal set is identified after the evaluation of optimized plans that correspond to different sets of pencil-beam parameters. This set along with a single, optimized set of objectives and constraints is used to perform inverse planning on ten randomly selected patients. The acceptability of the resulting plans is verified by comparisons to the clinical ones calculated with the forward techniques. For the particular commercial treatment planning system, the default values of the pencil beam parameters are found adequate for inverse treatment planning. For all ten patients, the optimized, single set of objectives and constraints results in plans with target coverage comparable to that of the forward plans. Furthermore inverse treatment planning reduces the overall mean rectal and bladder doses by 4.8% and 5.8% of the prescription dose respectively. The study indicates that (i) inverse treatment planning results depend implicitly on the sampling of the dose distribution, (ii) inverse treatment planning results depend on the method used by the dose calculation model to account for scatter, and (iii) for certain sites, a single set of optimization parameters can be used for all patient plans.

Dose Fractionation, Radiation↗

PubMed2002

Optimized planning for intraoperative planar permanent-seed implant.

We describe a fast, PC-based optimization planning system for a planar permanent-seed implant. Sites where this system is applicable include brain, lung, and head and neck. The system described here allows placing ribbons of different strengths and of different lengths along and across the implant plane. The program takes full advantage of the availability of different source strengths in inventory, and attempts to find configurations of ribbons that result in optimal dose uniformity over the prescription plane. Dosimetry is based on the AAPM TG 43 Report [R. Nath et al., Med. Phys. 22, 209-234 (1995)]. Compared with TG 43 parameters, the classical tables underestimate the I-125 source strengths needed by 40%. The use of several source strengths improves the plan. Typical optimization yields dose uniformity of 10%, and computing times are within 2-3 min. No further enhancement is obtained if ribbons are placed in a grid pattern as opposed to the (simpler) arrangement along parallel lines. Nor is it valuable to have variable ribbon lengths. For an I-125 implant the optimization system described here is a practical alternative to the (strictly speaking inapplicable) classical systems. It calculates correctly the total source strengths, and--most notably--generates plans with optimal dose uniformity. The fast computing time is well suited for planning during surgery in the operating room.

Brain Neoplasms↗

PubMed2006

Response surface optimization for joint contact model evaluation.

When optimization is used to evaluate a joint contact model's ability to reproduce experimental measurements, the high computational cost of repeated contact analysis can be a limiting factor. This paper presents a computationally-efficient response surface optimization methodology to address this limitation. Quadratic response surfaces were fit to contact quantities (contact force, maximum pressure, average pressure, and contact area) predicted by a discrete element contact model of the tibiofemoral joint for various combinations of material modulus and relative bone pose (i.e., position and orientation). The response surfaces were then used as surrogates for costly contact analyses in optimizations that minimized differences between measured and predicted contact quantities. The methodology was evaluated theoretically using six sets of synthetic (i.e., computer-generated) contact data, and practically using one set of experimental contact data. For the synthetic cases, the response surface optimizations recovered all contact quantities to within 3.4% error. For the experimental case, they matched all contact quantities to within 6.3% error except for maximum contact pressure, which was in error by up to 50%. Response surface optimization provides rapid evaluation of joint contact models within a limited range of relative bone poses and can help identify potential weaknesses in contact model formulation and/or experimental data quality.

Bone Screws↗

PubMed2003

Optimal sampling schedule design for populations of patients.

Generation of pharmacodynamic relationships in the clinical arena requires estimation of pharmacokinetic parameter values for individual patients. When the target population is severely ill, the ability to obtain traditional intensive blood sampling schedules is curtailed. Population modeling guided by optimal sampling theory has provided robust estimates of individual patient pharmacokinetic parameter values. Because of the wide range of parameter values seen in this circumstance, it is important to know how the range of parameter values in the population affects the timing of the optimal samples. We describe a new, simple technique to obtain optimal samples for a population of patients. This technique uses the nonparametric distribution associated with a nonparametric adaptive grid population pharmacokinetic analysis. We used the distribution from an analysis of 58 patients receiving levofloxacin for nosocomial pneumonia at a dose of 750 mg. The collection of parameter vectors and their associated probabilities were entered into a D-optimal design evaluation by using ADAPT II. The sampling times, weighted for their probabilities, were displayed in a frequency histogram (an expression of how system information varies with time for the population). Such an explicit expression of the time distribution of information allows rational sampling design that is robust not only for the population mean vector, as in traditional D-optimal design theory, but also for large portions of the total population. For levofloxacin, one reasonable six-sample design would be 1.5, 2, 2.25, 4, 4.75, and 24 h after starting a 90-min infusion. Such sampling designs allow informative population pharmacokinetic analysis with precise and unbiased estimates after the maximal a posteriori probability Bayesian step. This allows the highest probability of delineating a pharmacodynamic relationship.

Chromatography, High Pressure Liquid↗

PubMed2005

Type 1 immunity provides both optimal mucosal and systemic protection against a mucosally invasive, intracellular pathogen.

It has been hypothesized that optimal vaccine immunity against mucosally invasive, intracellular pathogens may require the induction of different types of immune responses in mucosal and systemic lymphoid tissues. Mucosal type 2/3 responses (producing interleukin-4 [IL-4], IL-6 and/or transforming growth factor beta) could be necessary for optimal induction of protective secretory immunoglobulin A responses. On the other hand, systemic type 1 responses (including gamma interferon [IFN-gamma], tumor necrosis factor alpha, and optimal cytotoxic T-cell responses) are likely to be critical for protection against the disseminated intracellular replication that occurs after mucosal invasion. Despite these predictions, we recently found that vaccines inducing highly polarized type 1 immunity in both mucosal and systemic tissues provided optimal mucosal and systemic protection against the protozoan pathogen Trypanosoma cruzi. To further address this important question in a second model system, we now have studied the capacity of knockout mice to develop protective immune memory. T. cruzi infection followed by nifurtimox treatment rescue was used to immunize CD4, CD8, beta2-microglobulin, inducible nitric oxide synthase (iNOS), IL-12, IFN-gamma, and IL-4 knockout mice. Despite the previously demonstrated importance of CD4(+) T cells, CD8(+) T cells, and nitric oxide for T. cruzi immunity, CD4, CD8, and iNOS knockout mice developed mucosal and systemic protective immunity. However, IL-12, IFN-gamma, and beta2-microglobulin-deficient mice failed to develop mucosal or systemic protection. In contrast, IL-4 knockout mice developed maximal levels of both mucosal and systemic immune protection. These results strongly confirm our earlier conclusion from studies with polarizing vaccination protocols that type 1 immunity provides optimal mucosal and systemic protection against a mucosally invasive, intracellular pathogen.

Animals↗

PubMed2002

Evaluation of the OptiMAL rapid antigen test and species-specific PCR to detect placental Plasmodium falciparum infection at delivery.

During pregnancy, Plasmodium falciparum infection of the placenta frequently occurs in the absence of parasites in peripheral blood. We investigated the abilities of the OptiMAL rapid immunochromatographic strip test for P. falciparum lactate dehydrogenase and species-specific PCR performed on peripheral blood to detect placental infection or malaria-associated low birth weight. Of 509 Malawian women screened by microscopy, 76 had malaria infection. Among these 509 women, the frequency of peripheral blood parasitemia was low. The OptiMAL test gave positive results in 37 of 171 women tested (one of whom had placental but not peripheral blood parasitemia) and had sensitivities of 71% for peripheral parasitemia and 38% for placental parasitemia compared to the microscopy values. The specificity for peripheral parasitemia was 94%. In 135 women, PCR had sensitivities of 94% for peripheral blood malaria detected by microscopy and 72% for placental infection. In samples examined by PCR, the prevalence of malaria in peripheral blood increased from 26.7% by microscopy to 51.9%. Women with placental malaria and women with malaria in peripheral blood samples by microscopy or OptiMAL testing, but not women with malaria detected only by PCR, had lower-birth-weight babies than did women without malaria by these criteria. Positive results by PCR in the absence of microscopic parasitemia were not associated with low birth weight. Neither OptiMAL nor PCR testing of peripheral blood is adequately sensitive to detect all placental malaria infection, but a positive result by OptiMAL testing identifies women with a high proportion of low-birth-weight babies.

Adolescent↗