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PubMedDate not supplied

Optimization of temperature distributions in scanned, focused ultrasound hyperthermia.

Scanned, focused ultrasound systems (SFUS) have considerable flexibility in shaping the power deposition field during hyperthermia treatments. When utilizing this adaptability many complicated, interacting decisions must be made to obtain an optimal steady-state temperature distribution. This optimization problem is studied using a 3-D, radially symmetric simulation program which searches for a set of optimal scan parameters. The conjugate-gradient optimization technique with a golden section search was used to obtain the optimal temperature distributions attainable with a single circular scan of a tumour. The variable scan parameters of the single transducer heating system optimized (and under the control of the therapist) are: transducer tilt and rotation angles, focal depth, output acoustical power, and scan radius. This single scan study includes the effects of tumour and normal tissue blood perfusions, tumour depth, skin temperature boundary condition, as well as tumour size and shape. A similar, but less comprehensive, study was done for larger tumours using two concentric circular scans. The results show that (1) the optimization process can produce a set of scan parameters that give a considerably better temperature distribution than could be obtained ad hoc, and (2) the optimal scan parameter configuration obtained produces a close-to-ideal tumour temperature distribution for a wide variety of clinically relevant conditions. Thus, when extended to include data from individual patients such optimization should be a very useful tool in patient treatment planning, and should enhance the present capabilities of clinical scanned, focused ultrasound systems.

Body Temperature↗

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↗

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↗

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↗

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↗

PubMedDate not supplied

Optimized dynamic rotation with wedges.

Dynamic rotation is a computer-controlled therapy technique utilizing an automated multileaf collimator in which the radiation beam shape changes dynamically as the treatment machine rotates about the patient so that at each instant the beam shape matches the projected shape of the target volume. In simple dynamic rotation, the dose rate remains constant during rotation. For optimized dynamic rotation, the dose rate is varied as a function of gantry angle. Optimum dose rate at each gantry angle is computed by linear programming. Wedges can be included in the optimized dynamic rotation therapy by using additional rotations. Simple and optimized dynamic rotation treatment plans, with and without wedges, for a pancreatic tumor have been compared using optimization cost function values, normal tissue complication probabilities, and positive difference statistic values. For planning purposes, a continuous rotation is approximated by static beams at a number of gantry angles equally spaced about the patient. In theory, the quality of optimized treatment planning solutions should improve as the number of static beams increases. The addition of wedges should further improve dose distributions. For the case studied, no significant improvements were seen for more than 36 beam angles. Open and wedged optimized dynamic rotations were better than simple dynamic rotation, but wedged optimized dynamic rotation showed no definitive improvement over open beam optimized dynamic rotation.

Humans↗

PubMed1988

Matching between feline left ventricle and arterial load: optimal external power or efficiency.

We tested the hypothesis that the feline left ventricle normally works at optimal external power as opposed to optimal efficiency by (re)analyzing data from five isolated, blood-perfused cat hearts and 39 open-thorax cats. In the isolated hearts, we measured pump function, external steady power, myocardial oxygen consumption, and efficiency. Optimal external power and optimal efficiency were found at different left ventricular outputs (6.94 +/- 0.33 and 8.35 +/- 0.37 ml/s, respectively; P less than 0.001). In the in situ cat hearts the working point was found at an output of 4.72 +/- 0.32 ml/s, whereas optimal external power was found at 4.84 +/- 0.26 ml/s. These values were not significantly different. Assuming that the point of optimal efficiency was located at the same fraction of the maximal unloaded left ventricular output (Fmax) as in the isolated hearts, i.e., 0.7, we found the point of optimal efficiency for the in situ heart at a flow of 5.83 +/- 0.32 ml/s, which was significantly different (P less than 0.001) from the flow in the working point. Our data therefore indicate that the left ventricle in the open-thorax cat is matched to the arterial load such that its external power output rather than efficiency is optimized.

Algorithms↗

PubMed1993

Signal-averaged electrocardiogram. Improved identification of patients with ventricular tachycardia using a 28-lead optimal array.

BACKGROUND: Although the signal-averaged ECG (SAECG) is currently the best noninvasive test to identify patients with ventricular tachycardia (VT) following myocardial infarction (MI), it is still a relatively insensitive test. Body surface mapping has improved the sensitivity of ECG in detecting various cardiac diseases. This study applied body surface mapping to the SAECG in the form of a clinically practical, 28-lead optimal array and compared its sensitivity and specificity with those of an orthogonal array. METHODS AND RESULTS: Two hundred twenty-three patients with previous MI (82 with inducible VT) underwent SAECG using 28 surface electrodes from which were obtained a three-lead orthogonal array and a 28-lead optimal array (optimal). From the orthogonal array, two QRS durations (QRSd) were obtained using the combined vector magnitude method (CVM) and the earliest onset to latest offset of the three individually filtered leads (individual). From the optimal array, 28 QRSd were obtained, each defined as the duration from the earliest onset of any of the 28 leads to the offset of each individually filtered lead. QRSd > 120 msec in > or = 3 leads was considered abnormal. For CVM and individual, QRSd of > 120 msec were considered abnormal. While the specificity of each method was comparable (84%, 86%, and 84% for CVM, individual, and optimal, respectively), the sensitivity of optimal (70%) was significantly greater than the sensitivity of CVM (54%) (p = 0.001) or individual (59%) (p = 0.004). The magnitude of improvement in sensitivity, 16% and 15%, respectively, was equal for anterior (n = 120) and inferior (n = 103) infarctions. CONCLUSIONS: Body surface mapping using the 28-lead optimal array significantly improved the sensitivity of the SAECG without loss of specificity. The increased sensitivity was of equal magnitude for inferior and anterior infarctions. The superiority and practicality of the 28-lead optimal array make it worth pursuing as an option for further refinement in SAECG:

Aged↗

PubMedDate not supplied

Evaluation of nonlinear optimization for scheduling of follow-up cystoscopies to detect recurrent bladder cancer. The Bladder Cancer follow-up Group.

Standard recommendations for patients who have had superficial bladder cancer are inspection by cystoscopy quarterly for a year or two after tumor removal, then half-yearly and yearly. The authors assessed the potential for improvement in scheduling cystoscopies according to probabilistic optimization techniques. Eight hypothetical practices were created, based on retrospective analysis of 918 bladder-cancer-patient charts. Standard and alternative recommendations for the interval to next cystoscopy were compared. The alternatives were derived from patient-specific predictions of future tumor risks (based on the patient's prior recurrence rate and tumor stage and grade) and a nonlinear optimization approach to allocation of the same number of cystoscopies as were available for standard follow-up. The optimization proposed longer intervals between visits for low-risk patients and shorter intervals for high-risk patients. Overall, optimization reduced expected tumor detection delays by 30%, from 12.6 to 8.7 weeks. When optimization intervals were shorter than standard, cancer was found more often at subsequent cystoscopies (34% vs 27%, p less than 0.05), suggesting that the optimization was a better predictor of cancer recurrence. If reduction in tumor-detection delay is the goal of follow-up for recurrent cancers, then urologists can improve monitoring by using probabilistic optimization methods for scheduling cystoscopies. Further understanding of the accuracy of predictive models for bladder-cancer recurrence rates is desirable. Subsequently, the optimization method developed here may be tested prospectively.

Aftercare↗

PubMed1999

Geometric optimization of a tissue pattern for semilunar valve reconstruction.

BACKGROUND AND AIM OF THE STUDY: A novel geometric trefoil pattern has been suggested for semilunar valve reconstruction. Optimization of the geometry must rely on an appreciation of normal anatomy and knowledge of the mechanical properties of the tissue used for the reconstruction. METHODS: Computer-assisted design (CAD) was used to create an optimized leaflet geometry based on published dimensions for normal human aortic valves. The optimized leaflet geometry was subjected to finite element analysis (FEA) to study stress distribution with pressure loading of the leaflet. In vitro function of the optimized trefoil tissue pattern is being studied by static testing initially, with physiological saline. RESULTS: An optimized leaflet geometry has been developed by CAD, and further refined by FEA. Static testing of the optimized trefoil tissue pattern shows near-normal anatomy, with no prolapse or pin wheeling, and full valve competence to 90 mmHg pressure. CONCLUSIONS: An initial optimized geometry has been developed for a two-dimensional tissue pattern that can be used to reconstruct diseased semilunar heart valves with human pericardium. Optimization studies are based on the mechanical properties of the tissue, CAD to mimic normal anatomy, FEA to study stress distribution, and static load testing to confirm function.

Animals↗

PubMed1993

Genetic algorithms-based design and optimization of statistical quality-control procedures.

In general, one cannot use algebraic or enumerative methods to optimize a quality-control (QC) procedure for detecting the total allowable analytical error with a stated probability with the minimum probability for false rejection. Genetic algorithms (GAs) offer an alternative, as they do not require knowledge of the objective function to be optimized and can search through large parameter spaces quickly. To explore the application of GAs in statistical QC, I developed two interactive computer programs based on the deterministic crowding genetic algorithm. Given an analytical process, the program "Optimize" optimizes a user-defined QC procedure, whereas the program "Design" designs a novel optimized QC procedure. The programs search through the parameter space and find the optimal or near-optimal solution. The possible solutions of the optimization problem are evaluated with computer simulation.

Algorithms↗