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Real-time 3D dose calculation and display: a tool for plan optimization.

PURPOSE: Both human and computer optimization of treatment plans have advantages; humans are much better at global pattern recognition, and computers are much better at detailed calculations. A major impediment to human optimization of treatment plans by manipulation of beam parameters is the long time required for feedback to the operator on the effectiveness of a change in beam parameters. Our goal was to create a real-time dose calculation and display system that provides the planner with immediate (fraction of a second) feedback with displays of three-dimensional (3D) isodose surfaces, digitally reconstructed radiographs (DRRs), dose-volume histograms, and/or a figure of merit (FOM) (i.e., a single value plan score function). This will allow the experienced treatment planner to optimize a plan by adjusting beam parameters based on a direct indication of plan effectiveness, the FOM value, and to use 3D display of target, critical organs, DRRs, and isodose contours to guide changes aimed at improving the FOM value. METHODS AND MATERIALS: We use computer platforms that contain easily utilized parallel processors and very tight coupling between calculation and display. We ported code running on a network of two workstations and an array of transputers to a single multiprocessor workstation. Our current high-performance graphics workstation contains four 150-MHz processors that can be readily used in a shared-memory multithreaded calculation. RESULTS: When a 10 x 10-cm beam is moved, using an 8-mm dose grid, the full 3D dose matrix is recalculated using a Bentley-Milan-type dose calculation algorithm, and the 3D dose surface display is then updated, all in < 0.1s. A 64 x 64-pixel DRR calculation can be performed in < 0.1 s. Other features, such as automated aperture calculation, are still required to make real-time feedback practical for clinical use. CONCLUSION: We demonstrate that real-time plan optimization using general purpose multiprocessor workstations is a practical goal. Parallel processing technology provides this capability for 3D planning systems, and when combined with objective plan ranking algorithms should prove effective for optimizing 3D conformal radiation therapy. Compared to our earlier transputer work, multiprocessor workstations are more easily programmed, making software development costs more reasonable compared with uniprocessor development costs. How the dose calculation is partitioned into parallel tasks on a multiprocessor work station can make a significant difference in performance. Shared-memory multiprocessor workstations are our first choice for future work, because they require minimum programming effort and continue to be driven to higher performance by competition in the workstation arena.

Computer Graphics↗

Intraoperative optimized inverse planning for prostate brachytherapy: early experience.

PURPOSE: To demonstrate the feasibility of an intraoperative inverse planning technique with advanced optimization for prostate seed implantation. METHODS AND MATERIALS: We have implemented a method for optimized inverse planning of prostate seed implantation in the operating room (OR), based on the genetic algorithm (GA) driven Prostate Implant Planning Engine for Radiotherapy (PIPER). An integrated treatment planning system was deployed, which includes real-time ultrasound image acquisition, treatment volume segmentation, GA optimization, real-time decision making and sensitivity analysis, isodose and DVH evaluation, and virtual reality navigation and surgical guidance. Ten consecutive patients previously scheduled for implantation were included in the series. RESULTS: The feasibility of the technique was established by careful monitoring of each step in the OR and comparison with conventional preplanned implants. The median elapsed time for complete image capture, segmentation, GA optimization, and plan evaluation was 4, 10, 2.2, and 2 min, respectively. The dosimetric quality of the OR-based plan was shown to be equivalent to the corresponding preplan. CONCLUSION: An intraoperative optimized inverse planning technique was developed for prostate brachytherapy. The feasibility of the method was demonstrated through an early clinical experience.

Algorithms↗

Optimization of planar high-dose-rate implants.

PURPOSE: Brachytherapy has long been used to deliver localized radiation to the breast and other cancer sites. For interstitial implants, proper source positioning is critical in obtaining satisfactory dose distributions. The present work examines techniques for optimizing source guide placement in high-dose-rate (HDR) biplanar implants, and examines the effects of suboptimal catheter placement. METHODS AND MATERIALS: Control of individual dwell times in HDR implants allows a high degree of dose uniformity in planes parallel to the implant planes. Biplanar HDR implants can be considered optimized when the dose at the implant center is equal to the dose at the symmetric target boundaries. It is shown that this optimal dose uniformity is achieved when the interplanar separation is related to the target thickness T through the direct proportionality, s = T/square root2. To quantify the significance of source positioning, the average dose and a related quantity, equivalent uniform dose (EUD), were calculated inside the treatment volume for two conditions of suboptimal catheter geometry. In one case, the interplanar spacing was varied from 1 cm up to the target thickness T, while a second study examined the effects of off-center placement of the implant planes. RESULTS: Both the average dose and EUD were minimized when the interplanar spacing satisfied the relationship s = T/square root2. EUD, however, was significantly smaller than the average dose, indicating a reduced relative cell killing in the high dose regions near the dwell points. It was also noted that in contrast to the average dose, the EUD is a relatively weak function of catheter misplacement, suggesting that the biological consequences of suboptimal implant geometry may be less significant than is indicated by the increase in average dose. CONCLUSION: A concise formula can be used to determine the interplanar separation needed for optimal dose uniformity in Manchester-type implants. Deviations from optimal source geometry result in an increase in the average dose inside the treatment volume, but the weaker dependence of the EUD suggests that the surviving fraction of cells may not be not strongly affected by suboptimal source geometry.

Algorithms↗

Treatable domain and optimal frequency for brain tumors during ultrasound hyperthermia.

PURPOSE: To examine the optimal ultrasound frequency and the treatable domain determined by the tumor size and tumor depth when an external ultrasound heating system is employed for the brain tumor hyperthermia. METHODS AND MATERIALS: This work employs a simplified model of a scanned ultrasound transducer power deposition (a cone with convergent/divergent shape) and a search algorithm to investigate the optimal frequency and the treatable domain. The distributions of temperature and SAR (specific absorption rate) ratio are used to determine the appropriateness of the acoustic window size and the input power level for a yielded set of tumor conditions. The factors considered are the acoustic window size, tumor size and depth, ultrasound frequency, and the acoustic absorption of the post-target bone behind the tumor. RESULTS: Simulation results demonstrate that the optimal frequency depends on the tumor depth and the acoustic absorption of the post-target bone. However, it is almost independent of the acoustic window size. The optimal frequency shifts to a higher level for a deeper tumor heating to reduce the effect of the high acoustic absorption of post-target bone. Moreover, the treatable domain is proportional to the acoustic window size and related to the ultrasound frequency. CONCLUSION: It may not be possible to deliver appropriate ultrasonic energy to heat a brain tumor without overheating the normal brain tissue and/or the post-target bone under the constraints of the available acoustic window size for the ultrasonic beam, ultrasonic attenuation of brain tissue, high absorption of post-target bone, and high blood perfusion rate. The results of this study can be a guideline for designing an optimal ultrasound heating system, arranging the transducers, and implementing further treatment planning for the brain tumor hyperthermia.

Acoustics↗

Didanosine extended-release matrix tablets: optimization of formulation variables using statistical experimental design.

Statistical experimental design was applied to evaluate the influence of some process and formulation variables and possible interactions among such variables, on didanosine release from directly-compressed matrix tablets based on blends of two insoluble polymers, Eudragit RS-PM and Ethocel 100, with the final goal of drug release behavior optimization. The considered responses were the percent of drug released at three determined times, the dissolution efficiency at 6 h and the time to dissolve 10% of drug. Four independent variables were considered: tablet compression force, ratio between the polymers and their particle size, and drug content. The preliminary screening step, carried out by means of a 12-run asymmetric screening matrix according to a D-optimal design strategy, allowed evaluation of the effects of different levels of each variable. The drug content and the polymers ratio had the most important effect on drug release, which, moreover, was favored by greater polymers particle size; on the contrary the compression force did not have a significant effect. The Doehlert design was then applied for a response-surface study, in order to study in depth the effects of the most important variables. The desirability function was used to simultaneously optimize the five considered responses, each having a different target. This procedure allowed selection, in the studied experimental domain, of the best formulation conditions to optimize drug release rate. The experimental values obtained from the optimized formulation highly agreed with the predicted values. The results demonstrated the reliability of the model in the preparation of extended-release matrix tablets with predictable drug release profiles.

Anti-HIV Agents↗

Level dependence of optimal stimulus level difference for evoking DPOAEs in the gerbil.

In distortion product otoacoustic emission (DPOAE) measurements the ear is stimulated with two pure tones f1 and f2. To maximize DPOAE levels and hence increase the sensitivity of DPOAE measurements, the separation of the two primary tone levels has been shown to play a crucial role. In contrast to conventionally used paradigms where the difference between the stimulus levels L1 and L2 is constant, Whitehead et al. [Whitehead, M.L. et al., 1995. J. Acoust. Soc. Am. 97, 2359-2377] found a variable level separation L1-L2, which is increasing with decreasing overall stimulus levels, to be optimal for evoking maximal DPOAE levels. This optimal level separation was quantified by Kummer et al. [Kummer, P. et al., 2000. Hear. Res. 146, 47-56] for humans. The aim of our study was to find out if such optimal level differences also exist in the gerbil Meriones unguiculatus in order to obtain an adequate animal model for determination of auditory sensitivity and its pathologies. The results clearly indicate that, as in humans, a variable level separation L1-L2 is optimal for generation of maximal DPOAE levels in the gerbil. This level separation strongly depends on the frequency relation between f1 and f2 and the deviation of the optimal level difference from L1=L2 increases with the frequency ratio f2/f1.

Acoustic Stimulation↗

Application of linear optimization techniques to MRI phase contrast blood flow measurements.

The goal of this study was to use linear optimization techniques as a systematic method of cine phase contrast pulse sequence design and to apply this technique to the measurement of blood flow in vivo. The optimized waveforms were validated in a constant flow phantom with average velocities ranging from 5 to 50 cm/s. The same optimized sequence was also run in a segmented k-space variation with five phase encoding lines per segment. The magnetic resonance (MR) derived velocity measurements were accurate over the entire range of velocities tested (p < .05) in both cases. The same optimized pulse sequence was applied to the measurement of flow in main pulmonary artery of five normal volunteers and compared with stroke volumes and cardiac outputs calculated from right ventricular volume measurements. These measurements showed a mean difference between the MR phase contrast calculated stroke volume and the volumetric stroke volume measurement of 9.8 +/- 11.6%. The mean difference between the calculated phase contrast cardiac output and the volumetric cardiac output was 4.4 +/- 10%. These results imply that optimization techniques are an efficient method for designing cine phase contrast pulse sequences.

Adult↗

Two-point method for T1 estimation with optimized gradient-echo sequence.

Relaxation times estimation methods play a central role in various problems, such as magnetic resonance (MR) hardware calibration, tissue characterization, or temperature measurement. Previous studies have proposed optimization criteria to estimate the relaxation time T1 faster than with a multipoint method leading to two-point methods. In this paper, the class of optimized two-point methods is extended to gradient-echo (GE) sequence offering new advantages over spin-echo (SE) or inversion recovery (IR) sequences. Two GE acquisitions, with optimal flip angles theta1 and theta2 minimizing both the total scan time and the variance in the computed T1 image were applied to estimate T1, and the results were compared with those of SE sequence with optimized paired repetition times T(R1) and T(R2). First, phantom studies were carried out with five tissue-like samples on a 0.5T scanner. Then in vivo, human brain T1 image were calculated using both optimized GE and SE two-point methods. More precise T1 GE estimates than those for SE were found thanks to high signal-to-noise ratio (SNR) per unit of time, but with a small bias. These results also concern the temperature variation measurement methods, based on T1 estimation. Preliminary experimental data for temperature measurement are given.

Brain↗

Selectivity optimization for the separation of chlorophenols in an irregularly shaped experimental region in capillary electrophoresis.

The separation of seventeen chlorophenol congeners and phenol was studied as a function of several variables. The pH and the concentration of sodium dodecylsulphate (SDS) were found to be important. During the implementation of a central composite design for the optimization of the separation it appeared that a part of the domain was not feasible as it resulted in very long migration times and extremely deformed peaks. Therefore, a D-optimal design was selected within the boundaries of the feasible region. The optimization of the selectivity did not result in selective regions for a simultaneous separation. It was, however, possible to find a region for the simultaneous separation of 15 compounds. Further optimization at these optimal conditions resulted in a separation where 17 peaks could be observed.

Chlorophenols↗

Experimental design strategies in the optimization and robustness testing of adsorptive stripping voltammetric conditions for kynurenic acid determination.

Experimental design was used for the optimization and robustness testing of an adsorptive stripping voltammetric procedure for kynurenic acid determination. The optimization of the peak height response proceeded through a screening phase (D-optimal design strategy) followed by a response surface study (Doehlert design) applied to the variables pH, pulse amplitude and stirring rate. An interaction between pH and stirring rate was pointed out. The optimized method was validated and the variation of factors that was expected to occur in practice was simulated in a robustness test. A composite fractional matrix for the evaluation of method robustness was used and pH emerged as the only critical factor. The linear range found applying the optimized conditions was 2.5 x 10(-9) to 2.5 x 10(-7) M and the calculated limit of detection was 1.72 x 10(-9) M.

Adsorption↗

Coronary hemodynamics of stent implantation after suboptimal and optimal balloon angioplasty.

OBJECTIVES: This study was performed to evaluate hemodynamic alterations of stent implantation after Doppler flow-guided balloon angioplasty (BA). BACKGROUND: There is controversy regarding the effect of stent implantation on coronary hemodynamics after suboptimal and optimal BA. METHODS: A total of 523 of 620 patients underwent Doppler-guided BA in the setting of a multicenter study and were analyzed before and after additional stent implantation. Balloon angioplasty was considered optimal when the diameter stenosis (DS) was < or = 35% and coronary flow reserve (CFR) was >2.5 and suboptimal if these two criteria were not met. Coronary flow reserve was also measured in an angiographically normal artery to determine relative CFR. Patients were followed for 12 months to document major adverse cardiac events (MACE). RESULTS: The main difference between patients with suboptimal BA (n = 195 [51%]) and optimal BA (n = 184 [49%]) was a more pronounced increase in baseline blood flow velocity (15 +/- 8 to 22 +/- 11 vs. 14 +/- 8 to 16 +/- 10 cm/s, p < 0.01). Coronary flow reserve improved after stent implantation in both patient groups, owing to a reduction in residual lumen obstruction, as determined by angiographic (%DS) and Doppler flow criteria (hyperemic blood flow velocity, relative CFR), and was associated with a decrease in MACE (16% vs. 7% in optimal BA group, p = 0.08; and 27% vs. 11% in suboptimal BA group, p = 0.007). CONCLUSIONS: Stent implantation enhances CFR after suboptimal and optimal Doppler-guided BA, owing to a reduction in residual lumen obstruction-determined by angiographical and Doppler flow criteria-as the underlying mechanism for an improved clinical outcome.

Aged↗

High-dose nitrates in the immediate management of unstable angina: optimal dosage, route of administration, and therapeutic goals.

Nitrates are commonly used for rapid relief of ischemia in the initial management of unstable angina. However, their optimal dosage, route of administration, and therapeutic goals have not been fully established. This study was conducted to determine the optimal dosage and mode of administration (intravenous bolus versus sublingual spray) of nitrates and the therapeutic goals of their use in the immediate management of unstable angina. In a single-center prospective trial, 72 consecutive patients with unstable angina accompanied by typical ST-segment depression on electrocardiogram were randomly assigned to receive isosorbide dinitrate either as repeated intravenous boluses or as sublingual sprays while being delivered to the hospital by a mobile intensive care unit. Optimal nitrate dosage was tailored to pain relief while monitoring mean blood pressure reduction to an optimal range (5% to 20%) without dosage restriction. The mean nitrate dosage needed for ischemia control during the first hour of treatment was 7.8 +/- 3.8 mg. Optimal blood pressure reduction was achieved by significantly more intravenously treated patients than sublingually treated patients (68% v 41%, P = .037). Intravenously treated patients also experienced a more pronounced therapeutic effect, as assessed by reduction in chest pain score (67% v 39%, P = .0004) and decrease in ST-segment depressions (57% v 27%, P = .004). These results show that higher doses of nitrates than previously recommended are required for ischemia control during the initial management of unstable angina. The use of repeated intravenous boluses is safe and more easily controlled and, therefore, more efficacious than sublingual sprays in inducing the maximal anti-ischemic effect while avoiding significant hypotension.

Administration, Sublingual↗

Optimal control by least squares support vector machines.

Support vector machines have been very successful in pattern recognition and function estimation problems. In this paper we introduce the use of least squares support vector machines (LS-SVM's) for the optimal control of nonlinear systems. Linear and neural full static state feedback controllers are considered. The problem is formulated in such a way that it incorporates the N-stage optimal control problem as well as a least squares support vector machine approach for mapping the state space into the action space. The solution is characterized by a set of nonlinear equations. An alternative formulation as a constrained nonlinear optimization problem in less unknowns is given, together with a method for imposing local stability in the LS-SVM control scheme. The results are discussed for support vector machines with radial basis function kernel. Advantages of LS-SVM control are that no number of hidden units has to be determined for the controller and that no centers have to be specified for the Gaussian kernels when applying Mercer's condition. The curse of dimensionality is avoided in comparison with defining a regular grid for the centers in classical radial basis function networks. This is at the expense of taking the trajectory of state variables as additional unknowns in the optimization problem, while classical neural network approaches typically lead to parametric optimization problems. In the SVM methodology the number of unknowns equals the number of training data, while in the primal space the number of unknowns can be infinite dimensional. The method is illustrated both on stabilization and tracking problems including examples on swinging up an inverted pendulum with local stabilization at the endpoint and a tracking problem for a ball and beam system.

Feedback↗

Optimization of olfactory model in software to give 1/f power spectra reveals numerical instabilities in solutions governed by aperiodic (chaotic) attractors.

We present a general connectionist model for an olfactory system. The dynamical behavior of each node (neural ensemble) of the model is governed by a second-order ordinary differential equation (ODE) followed by an asymmetric sigmoidal function, relating the aggregate activity of neurons to system parameters and stimuli from an outside environment. A digital implementation of the general connectionist model simulates the characteristics of a mammalian olfactory system having modifiable synaptic connections and spatio-temporal interactions among neural ensembles. Each of four distributed delay terms is represented by a second-order ODE. A parameter optimization algorithm is an integral component of the model. The parameter optimization discussed in this paper results in aperiodic oscillations having a near 1/f-type power spectrum with a peak in the gamma range, simulating the electro-encephalographic (EEG) potentials from the neural olfactory system. Random optimization is used for a rough search in a global parameter domain and the parameter self-adaptation rule serves for fine tuning within a local domain after the global search. By design the model is started from an unstable zero point by an external impulse input. It requires 650-850ms to pass through an initializing transient before settling into a strange attractor. The attractor persists for at least 1500ms, which is 7.5-20 times longer than the duration of the maximal stationary states observed in the EEGs and it is stable under perturbation by simulated sensory inputs giving response amplitudes less than 2 times the basal aperiodic activity. However, the optimization to 1/f-type activity reveals an inherent limit on digital simulation of chaotic states, owing to attractor crowding such that the size of basins decreases with increasing size of the model, until it approaches the size of digitizing step in computation, here a 64-bit word ( approximately 10(-16)). Outputs that are not optimized to approach 1/f-type power spectra transit earlier to limit cycle activity, usually well before 2000ms. The duration of stationarity is increased by randomizing the terminal bit of the 64-bit words representing the state variables. The 1/f-type solutions are also exquisitely sensitive to parameter truncation; parameter values must be saved in their full binary form for re-starting. The implications in terms of numerical instability, chaos, attractor crowding and the shadowing theorem are discussed.

Journal Article↗

Optimism, anxiety, and coping in parents of children hospitalized for spinal surgery.

Optimistic expectations about outcomes have significant implications for behaviors. Knowing the role that dispositional optimism plays in parents' anxiety and coping responses during their child's surgical experience is essential to aid professionals in bolstering parents' coping and providing support. Parental optimism, anxiety and coping, and whether optimism moderated (changed) the anxiety-coping relationship preoperatively and postoperatively were the factors evaluated in this study. Parents (N = 60) primarily white of middle and upper middle class, were administered the Life Orientation Test to assess optimism, Spielberger's State Anxiety Scale and the Ways of Coping Questionnaire. Parental anxiety decreased significantly from preoperative to postoperative levels but remained high, indicating that parents continue to be emotionally distressed during their child's recovery. Reappraising the situation more positively (positive reappraisal) was the most often used emotion-focused coping strategy and seeking social support was the most often used problem-focused coping strategy. The preoperative and postoperative anxiety-coping relationships also depended on parents' levels of optimism. The use of emotion-focused coping strategies was not effective for reducing anxiety in highly optimistic parents. Recommendations include continually assessing the parents' need for reassurance and support throughout the surgical experience. Professionals can bolster parental coping by stressing the benefits of surgery and encouraging parents to be actively involved in the child's care and progress.

Adaptation, Psychological↗

Optimization of selectivity in high-performance liquid chromatography using desirability functions and mixture designs according to PRISMA.

A computer program for the mobile phase optimization of high-performance liquid chromatography (HPLC) is described. The desirability function technique combined to the prisma mixture design was employed to enhance the quality of HPLC separations. The use of statistical models to predict the behaviour of retention times (tR) and band broadening at the different eluent compositions obtained by prisma was examined for dansyl amides and coumarins. The study showed that the dependence between the eluent composition and tR values of dansyl amides and coumarins can be expressed using quadratic regression models with a high degree of accuracy. Band broadening given by means of the band width at half-height (wh) was described by a linear regression model. Both models were used in calculating and predicting the resolution (Rs) in various solvent combinations. The desirability function converted the calculated (Rs) value into the desirability value (D), and the overall optimum was then defined by means of the overall desirability. The optimal eluent mixtures for the separation of compounds were easily read from the contour plot inside the horizontal plane of the prisma model. A good separation was achieved using the optimized solvent combination. Depending on the aims of the optimal separation, the program allows either optimization of critical pairs or achieving the overall optimum giving a reasonable separation for as many compounds as possible.

Chromatography, High Pressure Liquid↗

Bone strain gradients and optimization in vertebrate skulls.

It is often stated that the skull is optimally designed for resisting feeding forces, where optimality is defined as maximum strength with minimum material. Running counter to this hypothesis are bone strain gradients--variation in bone strain magnitudes across the skull--which in the primate skull have been hypothesized to suggest that different parts of the skull are optimized for different functions. In this paper strain gradients in the skulls of four genera of primates, Sus, and Alligator were documented and compared. Strain gradients were pervasive in all taxa sampled. Patterns of strain gradients showed inter-taxon differences, but strains in the mandible and zygomatic arch were always higher than those in the circumorbital and neurocranial regions. Strain magnitudes in Alligator were twice as high as those in mammals. Strain gradients were also positively allometric; i. e., larger primates show steeper gradients (larger differences) between the mandible and circumorbital region than smaller primates. Different strain magnitudes in different areas of the same animal are hypothesized to reflect optimization to different criteria. It is therefore hardly surprising that the skull, in which numerous functional systems are found, exhibits very steep gradients. Inter-specific differences in strain magnitudes at similar sites also suggest inter-specific differences in optimality criteria. The higher strain magnitudes in the Alligator skull suggest that the Alligator skull may be designed to experience extremely high strains less frequently whereas the primate skull may be designed to resist lower strains more frequently.

Alligators and Crocodiles↗

Airway length in adults: estimation of the optimal endotracheal tube length for orotracheal intubation.

STUDY OBJECTIVE: To estimate the optimal endotracheal tube (ETT) length in orotracheally intubated patients. DESIGN: Prospective study. SETTING: Operating room of a medical center hospital. PATIENTS: 293 ASA physical status I and II patients (150 male and 143 female), requiring general anesthesia and orotracheal intubation. INTERVENTIONS: We used fiberoptic bronchoscope within the ETT to identify the carina and vocal cords. MEASUREMENTS: The length from carina to vocal cords, vocal cords to right mouth angle (corner), and carina to right mouth angle were measured. The optimal ETT tip was defined as 5 cm above the carina. Patient's height and sternum length were recorded. MAIN RESULTS: The correlation between airway length and body height was significant. By linear regression, a formula was obtained to estimate the optimal ETT length in orotracheally intubated patients: the length from 5 cm above carina to right mouth angle (cm) =< body height (cm)/5> - 13. CONCLUSION: The optimal insertion length of the ETT for orotracheally intubated adult patients with the head placed in a neutral position is correlated with body height. The proposed formula can provide a useful guide to determine the optimal ETT tip position in most of the patients who required orotracheal intubation.

Adult↗