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PubMed1996

Optimal sample allocation in clinical trials designed to investigate relative risks.

Clinical trials with more than two groups are becoming increasingly common, especially trials with both active and placebo control groups. Equal allocation of subjects to each of the groups is the most common sample allocation, but in clinical trials where the purpose is to test hypotheses of relative risk, such as vaccine trials, equal allocation can be substantially sub-optimal. Optimal allocation for clinical trials has been considered previously, but not for trials with more than two groups. In this paper optimal sample allocation for relative risk trials is investigated in a variety of situations. The main results are as follows: (i) there are many situations where reductions of more than 20 per cent in sample size can be obtained by using optimal allocation instead of equal allocation; (ii) the optimal allocation for two group studies is not optimal in general; (iii) in many situations optimal allocation increases a subject's chances of being enrolled to a test treatment, and (iv) in most cases a grid search using the likelihood score asymptotic power function is the easiest method of finding an approximately optimal allocation. Extensions to situations more general than those covered here are sketched.

Case-Control Studies↗

PubMed1994

Optimization of the electrostatic interactions in proteins of different functional and folding type.

The 3-dimensional optimization of the electrostatic interactions between the charged amino acid residues was studied by Monte Carlo simulations on an extended representative set of 141 protein structures with known atomic coordinates. The proteins were classified by different functional and structural criteria, and the optimization of the electrostatic interactions was analyzed. The optimization parameters were obtained by comparison of the contribution of charge-charge interactions to the free energy of the native protein structures and for a large number of randomly distributed charge constellations obtained by the Monte Carlo technique. On the basis of the results obtained, one can conclude that the charge-charge interactions are better optimized in the enzymes than in the proteins without enzymatic functions. Proteins that belong to the mixed alpha beta folding type are electrostatically better optimized than pure alpha-helical or beta-strand structures. Proteins that are stabilized by disulfide bonds show a lower degree of electrostatic optimization. The electrostatic interactions in a native protein are effectively optimized by rejection of the conformers that lead to repulsive charge-charge interactions. Particularly, the rejection of the repulsive contacts seems to be a major goal in the protein folding process. The dependence of the optimization parameters on the choice of the potential function was tested. The majority of the potential functions gave practically identical results.

Computer Simulation↗

PubMed1977

A model of optimal voluntary muscular control.

In the absence of detailed knowledge of how the CNS controls a muscle through its motor fibers, a reasonable hypothesis is that of optimal control. This hypothesis is studied using a simplified mathematical model of a single muscle, based on A.V. Hill's equations, with series elastic element omitted, and with the motor signal represented by a single input variable. Two cost functions were used. The first was total energy expended by the muscle (work plus heat). If the load is a constant force, with no inertia, Hill's optimal velocity of shortening results. If the load includes a mass, analysis by optimal control theory shows that the motor signal to the muscle consists of three phases: (1) maximal stimulation to accelerate the mass to the optimal velocity as quickly as possible, (2) an intermediate level of stimulation to hold the velocity at its optimal value, once reached, and (3) zero stimulation, to permit the mass to slow down, as quickly as possible, to zero velocity at the specified distance shortened. If the latter distance is too small, or the mass too large, the optimal velocity is not reached, and phase (2) is absent. For lengthening, there is no optimal velocity; there are only two phases, zero stimulation followed by maximal stimulation. The second cost function was total time. The optimal control for shortening consists of only phases (1) and (3) above, and is identical to the minimal energy control whenever phase (2) is absent from the latter. Generalization of this model to include viscous loads and a series elastic element are discussed.

Biophysical Phenomena↗

PubMed1988

DESIGN: computerized optimization of experimental design for estimating Kd and Bmax in ligand binding experiments. I. Homologous and heterologous binding to one or two classes of sites.

We have developed a versatile computer program for optimization of ligand binding experiments (e.g., radioreceptor assay system for hormones, drugs, etc.). This optimization algorithm is based on an overall measure of precision of the parameter estimates (D-optimality). The program DESIGN uses an exact mathematical model of the equilibrium ligand binding system with up to two ligands binding to any number of classes of binding sites. The program produces a minimal list of the optimal ligand concentrations for use in the binding experiment. This potentially reduces the time and cost necessary to perform a binding experiment. The program allows comparison of any proposed experimental design with the D-optimal design or with assay protocols in current use. The level of nonspecific binding is regarded as an unknown parameter of the system, along with the affinity constant (Kd) and binding capacity (Bmax). Selected parameters can be fixed at constant values and thereby excluded from the optimization algorithm. Emphasis may be placed on improving the precision of a single parameter or on improving the precision of all the parameters simultaneously. We present optimal designs for several of the more commonly used assay protocols (saturation binding with a single labeled ligand, competition or displacement curve, one or two classes of binding sites), and evaluate the robustness of these designs to changes in parameter values of the underlying models. We also derive the theoretical D-optimal design for the saturation binding experiment with a homogeneous receptor class.

Binding Sites↗

PubMed1996

Implementation of OSPOP, an algorithm for the estimation of optimal sampling times in pharmacokinetics by the ED, EID and API criteria.

The most common approach to optimize the sampling schedule in parameter estimation experiments is the D-optimality criterion, which consists in maximizing the determinant of the Fisher information matrix (max det F). In order to incorporate prior parameter uncertainty in the optimal design, other criteria have been proposed: The ED = max E (det F), EID = min E (l/det F) and API = max E (log det F) criteria, where the expectation is with respect to the given prior distribution of the parameters. Previously described algorithm for the estimation of optimal sampling times according to these criteria are adaptive random search (ARS), a robust and global but slow optimizer for API, and stochastic gradient (SG), a fast but local optimizer for ED and EID. We implemented an algorithm named OSPOP 1.0, based on non-adaptive random search (RS) followed by stochastic gradient to determine optimal sampling times for parameter estimation in various pharmacokinetic models according to ED, EID and API criteria. Prior distributions are allowed to be uniform, normal or lognormal. This algorithm combines the robustness of RS and the speediness of SG (convergence is obtained in a few minutes on a microcomputer). The results of the SG algorithm have been compared to those described in the literature using the ARS algorithm on a one compartment model with first- order absorption and were very similar. Also, the CPU time needed by SG and ARS algorithms were compared and the former proved to be much faster. Then, it has been applied to a five parameters stochastic model with zero-order absorption rate and Weibull-distributed residence times which was shown to describe adequately the kinetics of metacycline in humans. Population pharmacokinetic parameters of metacycline were estimated from a six subject pilot study, by the iterative two-staged method, using ADAPT II repeatedly. Optimal sampling times were determined with each criterion (ED, EID, API) with a multivariate normal prior parameter distribution. Six to seven distinct sampling times could be estimated. Higher numbers of samples revealed coalescing of design points.

Algorithms↗

PubMed1993

The optimality concept and its clinical value.

To verify the clinical usefulness of the optimality concept in general and its prognostic value for later outcome, all babies born at all 14 maternity hospitals in Slovenia in the period from 1987 to 1991 (124,759 newborns) have been screened. In order to get an estimate of their condition Prechtl's original list of optimality has been adapted to 51 items representing mostly obstetric variables. The median of perinatal optimality scores for all newborns was 45 (six negative points) in mature, and 41 (10 negative points) in premature infants. Girls born at term scored better than mature boys, whereas there was no sex difference in the median score in prematures. Analysis of the data has shown that the majority of items which were non-optimal and which were associated with the greatest number of other non-optimal factors had to do with disturbances in oxygen supply. Children who developed cerebral palsy had a lower optimality score at birth than the remainder of the newborns. In these children the difference between the sexes is even more pronounced, to the advantage of the girls. Prematurely born children with spastic diplegia had a lower optimality score than mature children with diplegia. The opposite was noticed in children born prematurely and at term who developed spastic tetraparesis or dyskinesia. The present follow-up study has shown that predictions of disability were most accurate in the group of newborns who were clinically at risk at birth and who also had a low optimality score. The combination of both appraisals is the best way to identify newborns who need special attention.

Apgar Score↗

PubMed2001

ROC optimization may improve risk stratification of prostate cancer patients.

OBJECTIVES: Rational treatment decision requires accurate projection of the clinical course of a patient. Current methods in clinical outcome analysis mostly focus on population data. We investigated the applicability and optimization of the widely used actuarial method to project individual clinical outcomes. METHODS: We designed and implemented a Clinical Outcome Prediction Expert (COPE) that performs, assesses, and optimizes actuarial prediction on individual cases. We analyzed a post-prostatectomy database, consisting of 1043 patients. Sixty percent of the database was used for training and 40% for validation. Stratified actuarial curves are used to project individual outcomes. The prostate-specific antigen (PSA) level, the Gleason score, and the clinical American Joint Commission on Cancer Staging T-stage before treatment were used as predictors. The area under the receiver operator characteristic (ROC) curve was used to measure predictive performance. RESULTS: We obtained simple optimized stratification of pretreatment PSA level of 10 ng/mL or less, or more than 10 ng/mL; Gleason score of 6 or lower, or higher than 6; and clinical AJCC T-stage of T2a or lower, or higher. The optimized univariate risk scores were used to generate a multivariate score. After optimization, we found the higher risk group consisted of patients with PSA more than 10 ng/mL, or with PSA of 10 ng/mL or less and Gleason score higher than 6 and clinical AJCC T-stage higher than T2a. The optimized multivariate risk score has the highest ROC area of 0.77 among all predictors. CONCLUSIONS: The best conditions to perform actuarial prediction on individual cases are not known a priori and require optimization. This study shows that ROC optimization simplifies risk stratification and may improve the accuracy of clinical outcome prediction.

Data Interpretation, Statistical↗

PubMed1998

3D conformal intensity-modulated radiotherapy planning: interactive optimization by constrained matrix inversion.

BACKGROUND AND PURPOSE: This paper presents a method for interactive optimization of 3D conformal intensity-modulated radiotherapy plans employing a quadratic objective that also contains dose limitations in the organs at risk. This objective function is minimized by constrained matrix inversion (CMI) that follows the same approach as the gradient technique using matrix notation. MATERIALS AND METHODS: Sherouse's GRATIS radiotherapy design system is used to determine the outlines of the target volume and the organs at risk and to input beam segments which are given by the beam segmentation technique. This technique defines the beam incidences and the beam segmentation. The weights of the segments are then calculated using a quadratic objective function and CMI. The objective function to be minimized consists of two components based on the planning target volume (PTV) and the organ at risk (OAR) with an importance factor w associated with the OAR. RESULTS: Optimization is tested for concave targets in the head and neck region wrapping around the spinal cord. For a predefined w-value, segment weights are optimized within a few seconds on a DEC Alpha 3000. In practice, 5-10 w-values have to be tested, making optimization a less than 5 min procedure. This optimization procedure predicts the possibility of target dose escalation for a tumour in the lower neck to 120-150 Gy without exceeding the spinal cord tolerance, whereas human planners could not increase the dose above 65-80 Gy. CONCLUSIONS: Treatment plans optimized using a quadratic objective function and the CMI algorithm are superior to those which are generated by human planners. The optimization algorithm is very fast and allows interactive use. Quadratic optimization by CMI is routinely used by clinicians at the Division of Radiotherapy, U.Z.-Gent.

Equipment Design↗

PubMedDate not supplied

Optimization of ion-exchange protein separations using a vector quantizing neural network.

In this work, a previously proposed methodology for the optimization of analytical scale protein separations using ion-exchange chromatography is subjected to two challenging case studies. The optimization methodology uses a Doehlert shell design for design of experiments and a novel criteria function to rank chromatograms in order of desirability. This chromatographic optimization function (COF) accounts for the separation between neighboring peaks, the total number of peaks eluted, and total analysis time. The COF is penalized when undesirable peak geometries (i.e., skewed and/or shouldered peaks) are present as determined by a vector quantizing neural network. Results of the COF analysis are fit to a quadratic response model, which is optimized with respect to the optimization variables using an advanced Nelder and Mead simplex algorithm. The optimization methodology is tested on two case study sample mixtures, the first of which is composed of equal parts of lysozyme, conalbumin, bovine serum albumin, and transferrin, and the second of which contains equal parts of conalbumin, bovine serum albumin, tranferrin, beta-lactoglobulin, insulin, and alpha -chymotrypsinogen A. Mobile-phase pH and gradient length are optimized to achieve baseline resolution of all solutes for both case studies in acceptably short analysis times, thus demonstrating the usefulness of the empirical optimization methodology.

Algorithms↗

PubMed2001

Optimal design of a population pharmacodynamic experiment for ivabradine.

PURPOSE: To design a parsimonious population pharmacodynamic experiment that has the same or greater efficiency than that provided by two phase I studies. METHODS: The design was based on optimization of the population Fisher information matrix. Options for optimization were (1) determination of the optimal sampling times for each group ("group" represents a group of subjects that have identical design characteristics), (2) determination of the optimal doses for each group, and (3) determination of the optimal group structure. RESULTS: (1) Optimizing the sampling times, while retaining only four unique times per group, provided a more parsimonious experiment with the same efficiency as the original "study" that involved on average 10 samples per subject. Splitting sampling times between the first dose and a steady-state dose gave the most informative design. (2) The optimal dose was the same in all groups and was the upper bound of the dose range. (3) The optimal population design consisted of only one group with four unique sampling times that are the same for all subjects. CONCLUSION: A population pharmacodynamic trial design is presented that is more parsimonious than the original study and would be appropriate for inclusion in a premarketing clinical study.

Benzazepines↗

PubMed1997

Comparison of ED, EID, and API criteria for the robust optimization of sampling times in pharmacokinetics.

Optimization of the sampling schedule can be used in pharmacokinetic (PK) experiments to increase the accuracy and the precision of parameter estimation or to reduce the number of samples required. Several optimization criteria that formally incorporate prior parameter uncertainty have been proposed earlier. These criteria consist in finding the sampling schedule that maximizes the expectation (over a given parameter distribution) of det F (ED-optimality) or Log(det F) (API-optimality), or minimizes the expectation of 1/det F (EID-optimality), where F is the Fisher information matrix. The precision and the accuracy of parameter estimation after having fitted a PK model to a small number of optimal data points (determined according to D, ED, EID, and API criteria) or to a naive sampling schedule were compared in a Monte Carlo simulation study. A one-compartment model with first-order absorption rate (3 parameters) and a two-compartment model with zero-order infusion rate (4 parameters) were considered. Data were simulated for 300 subjects with both structural models, combined with several residual error models (homoscedastic, heteroscedastic with constant or variable coefficient of variation). Interindividual variabilities in PK parameters ranged from 25-66%. ED-, EID-, and API-optimal sampling times were calculated using the software OSP-Fit. Three or five samples were allowed for parameter estimation by extended least-squares. Performances of each design criterion were evaluated in terms of mean prediction error, root mean squared error, and number of acceptable estimates (i.e., with a SE less than 30%). Compared to the D-optimal design, the EID and API designs reduced the bias and the imprecision of the estimation of the parameters having a large interindividual variability. Moreover, the API design resulted in some cases in a higher number of acceptable estimates.

Models, Biological↗

PubMed1999

Optimization of phenytoin therapy in adults with epilepsy in the Western Cape, South Africa.

OBJECTIVE: To assess the extent to which adults with epilepsy were optimized and individualized on phenytoin monotherapy in the Western Cape, South Africa and to estimate the average optimized dose and serum phenytoin concentration, and the therapeutic range for this patient group. METHODS: Patients were considered to be optimized on phenytoin if they were seizure-free or the best compromise was achieved between seizure reduction and side-effects. RESULTS: 538 (233 black and 305 coloured) adult people with epilepsy were treated at nine epilepsy clinics as outpatients. Of these patients, 332 (226 male and 106 female, 149 black and 183 coloured) were included in the data analysis as they were considered to have reliable phenytoin levels. Phenytoin doses and steady-state serum concentrations were predicted using the Michaelis-Menten equation. Patients attended a clinical pharmacokinetic service for 7.7+/-5.3 (range 1-22) months. The average optimized dose was 305.8 (range 100-500) mg/day and the average optimized level was 62.7+/-23.9 (range 15-133) micromol/l. Most patients (61.9%) were optimized in the therapeutic range 40-79 micromol/l; 21.1% were optimized above and 17% below this range. In 1.6% of patients serum concentrations above 120 micromol/l were required. Dosage adjustments were made in 47.0% of patients, increased in 31.9% and reduced in 15.1%. CONCLUSION: These findings indicate that many patients (47%) attending outpatient clinics were not optimized on phenytoin therapy.

Adolescent↗

PubMed1999

Determination of the optimal atrioventricular delay in DDD pacing. Comparison between echo and peak endocardial acceleration measurements.

The goal of this study was to compare two methods determining the optimal atrioventicular delay (AVD) in 19 patients implanted with the BEST-Living system for complete heart block. The definition of the optimal AVD was: the AVD with the echo method that provided the longest diastolic filling time without interruption of the A wave, and the AVD with the peak endocardial acceleration (PEA) method, corresponding to the knee of the PEA curve vs AV delay. The amplitude of the PEA was measured for every AVD programmed via an automatic scanner in steps of 60 to 300 ms (40 ms steps): in the VDD pacing mode with a low base rate, to obtain 100% sensed P waves; in DDD with a base rate = sinus rate + 20%, to obtain 100% paced P waves. Echocardiographic (Echo) measurement of the left ventricular filling time were performed in the same AV delay settings in VDD and DDD as the ones tested in the PEA method, which were manually programmed. The optimal AVDs obtained in DDD and those obtained in VDD were compared in the echo and the PEA tests by a paired Student's t-test. The optimal AVDs obtained by both Echo and by PEA were also compared by a paired Student's t-test in VDD and DDD. The r value of the correlation between the optimal AVDs obtained by Echo and those obtained by PEA was calculated. Similar values of optimal AVD were obtained with both methods. The optimal AVDs given by the Echo technique (179 +/- 25 ms in DDD and 124 +/- 18 ms in VDD) were slightly, but significantly shorter than the ones obtained with the PEA method (202 +/- 21 ms in DDD and 145 +/- 18 ms in VDD, P < 0.05). A highly significant difference between AVD VDD and AVD DDD was found with both methods (P < 0.001). The correlation between the AVDs obtained with the echo and the PEA methods was highly significant (r = 0.78, P < 0.01). Pacemaker software could be modified to determine automatically the optimal AVDs to be applied throughout the heart rate range.

Atrioventricular Node↗

PubMed2001

Optimal atrioventricular delay setting determined by evoked QT interval in patients with implanted stimulus-T-driven DDDR pacemakers.

Cardiac function is improved by optimizing the atrioventricular (AV) delay. An automatic optimizing function of AV delay may be necessary to achieve the most favourable haemodynamic state in paced patients. The QT interval may change when cardiac function is improved by optimizing the AV delay. The QT or stimulus-T interval is used as a sensor for rate-responsive pacemakers. Evoked (e) QT interval is measured as the time duration from the ventricular pace pulse (stimulus) and the T-sense point that is the steepest point of the intracardiac T wave (stimulus-T interval). The relationship between AV delay, eQT interval and cardiac function was studied in 10 patients (73 +/- 10 (SD) years old) with an implanted stimulus-T-driven DDDR pacemaker. Cardiac output (CO) and pulmonary capillary wedge pressure (PCWP) were measured by Swan-Ganz catheter. The AV delay was prolonged stepwise by 30 ms. Electrocardiogram event markers which indicated ventricular spike and sensed T wave were recorded, and the interval between two event markers was measured as eQT interval. When AV delay was changed from 240 ms to the AV delay at which CO was maximal (172 +/- 33 ms), eQT interval prolonged from 346 +/- 60 to 353 +/- 62 ms (P < 0.01). There was a significant positive correlation between the optimal AV delay at which CO was maximal (172 +/- 33 ms) and the optimal AV delay which was predicted from the maximum eQT interval (179 +/- 37 ms, r = 0.92, P < 0.001). When AV delay was changed from 240 ms to the predicted optimal AV delay, CO increased from 4.2 +/- 0.7 to 4.5 +/- 0.81.min-1 (P < 0.001) and PCWP was decreased from 7.1 +/- 4.0 to 5.7 +/- 3.1 mmHg (P < 0.05). In conclusion, the optimal AV delay can be predicted from the eQT interval which is sensed by an implanted pacemaker. Automatic setting of the optimal AV delay may be achieved by the QT sensor of an implanted pacemaker.

Aged↗

PubMed2001

Optimal continuous positive airway pressure in patients with obstructive sleep apnoea: role of craniofacial structure.

Although nasal continuous positive airway pressure (CPAP) is effective in improving nocturnal obstructive apnoea, daytime sleepiness and well-being in patients with obstructive sleep apnoea syndrome (OSAS), not all patients tolerate this treatment. Since optimal CPAP titration is essential to maintain compliance, it is important to elucidate the factors that help to determine the optimal pressure. However, the determinants of the optimal CPAP level are controversial. The subjects comprised 27 Japanese male patients with OSAS who underwent standard polysomnography (PSG), pulmonary function tests, arterial blood gas analysis, cephalometry and CPAP titration. Twenty normal controls also underwent cephalometric analysis. The apnoea-hypopnoea index (AHI), mean oxygen saturation (mean SaO2) and the lowest SaO2 during sleep were found to be 54.7+/-22.6, 89.0+/-5.6%, and 69.7+/-9.0%, respectively by PSG. The mean optimal CPAP was 9.6+/-1.8 cmH2O. The cephalometric angles (SNA, SNB and NSBa) were similar to those found in the control subjects. but MP-H, and PNS-P were significantly longer than those in the control subjects as shown by cephalometry. The optimal CPAP was correlated with the mean SaO2 (P<0.0001), neck circumference (P<0.05) and three cephalometric variables (NSBa: P<0.01, MP-H: P<0.05, PNS-P: P<0.05). Multiple, step-wise, regression analysis showed that the mean SaO2 and NSBa were independent variables that best predicted the optimal CPAP. These variables accounted for 57.5% of the total variance (R2=0.575, P<0.001). Optimal CPAP was closely correlated with oxygen desaturation during sleep. However, the craniofacial structure had additional effects such as an independent factor in determining the optimal CPAP level.

Adult↗

PubMed2000

Which factors determine the optimal pedaling rate in sprint cycling?

INTRODUCTION: Mechanical power output in sprint cycling depends on pedaling rate, with an optimum at around 130 revolutions per minute (rpm). In this study, the question is addressed if this optimal pedaling rate can be understood from a Hill-type description of muscular dynamics. In particular, it is investigated how 1) the power-velocity relationship that follows from Hill's force-velocity relationship and 2) activation dynamics (from the perspective of which the optimal pedaling rate is near-zero) affect the optimal pedaling rate. METHODS: A forward dynamics modeling/simulation approach is adopted in this study. The skeletal model is a 2D linkage of rigid segments; it is actuated by eight Hill-type "muscles." Input of the model is the neural stimulation of the muscles, output is the resulting movement and variables dependent thereupon, such as pedal forces. For a wide range of isokinetic pedaling rates, the neural stimulation is optimized with respect to the average mechanical power output. RESULTS: Correspondence between experimental data and simulation results regarding 1) the (pedaling-rate dependent) muscle phasing, 2) pedal forces, and 3) the power-pedaling rate relationship is good. At the optimal pedaling rate predicted by the model (120 rpm), muscles contract at velocities well below those that maximize their power output. Finally, when a model is considered that lacks activation dynamics, it is found that both the optimal pedaling rate and the maximal power output increase substantially. DISCUSSION: From the results pertaining to the standard model, it is concluded that the optimal pedaling rate is not uniquely specified by the power-velocity relationship of muscle, as suggested in literature. From the results pertaining to the model lacking activation dynamics, it follows that activation dynamics plays a surprisingly large role in determining the optimal pedaling rate. It is concluded that the pedaling rate that maximizes mechanical power output in sprint cycling follows from the interaction between activation dynamics and Hill's power-velocity relationship.

Bicycling↗

PubMed1997

Electrical defibrillation optimization: an automated, iterative parallel finite-element approach.

To date, optimization of electrode systems for electrical defibrillation has been limited to hand-selected electrode configurations. In this paper we present an automated approach which combines detailed, three-dimensional (3-D) finite-element torso models with optimization techniques to provide a flexible analysis and design tool for electrical defibrillation optimization. Specifically, a parallel direct search (PDS) optimization technique is used with a representative objective function to find an electrode configuration which corresponds to the satisfaction of a postulated defibrillation criterion with a minimum amount of power and a low possibility of myocardium damage. For adequate representation of the thoracic inhomogeneities, 3-D finite-element torso models are used in the objective function computations. The CPU-intensive finite-element calculations required for the objective function evaluation have been implemented on a message-passing parallel computer in order to complete the optimization calculations in a timely manner. To illustrate the optimization procedure, it has been applied to a representative electrode configuration for transmyocardial defibrillation, namely the subcutaneous patch-right ventricular catheter (SP-RVC) system. Sensitivity of the optimal solutions to various tissue conductivities has been studied. Results for the optimization of defibrillation systems are presented which demonstrate the feasibility of the approach.

Algorithms↗

PubMed2001

Optimization of wide-band linear arrays.

An optimization method is proposed for linear arrays to be used in ultrasound systems under wide-band operation. A fast algorithm, the threshold accepting, has been utilized to determine the element positions and weight coefficients of a linear array that generates a desired beam pattern. To reduce the computational burden in the optimization procedure, an efficient numerical routine for the beam pattern evaluation has been implemented. We address the optimization problem of both dense and sparse wide-band arrays. In the first case, the goal is to minimize the side-lobe energy by varying the element weights; we compare the optimized beam pattern with that obtained with classical shading functions, showing that better results can be achieved with a wide-band optimization. We also consider the optimization of the layout (positions and weights) of a sparse linear array to achieve a desired beam pattern with a fixed or minimum number of array elements. The comparison of the proposed method with a narrow-band optimization algorithm is presented, showing that better performances (about -7 dB further reduction of the side-lobe level) can be achieved with a wide-band sparse array optimization. Further numerical simulations are given, showing that the proposed method yields better results than wide-band sparse random arrays and periodic arrays with the same aperture width.

Journal Article↗