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PubMed2006

Optimization algorithms and weighting factors for analysis of dynamic PET studies.

Positron emission tomography (PET) pharmacokinetic analysis involves fitting of measured PET data to a PET pharmacokinetic model. The fitted parameters may, however, suffer from bias or be unrealistic, especially in the case of noisy data. There are many optimization algorithms, each having different characteristics. The purpose of the present study was to evaluate (1) the performance of different optimization algorithms and (2) the effects of using incorrect weighting factors during optimization in terms of both accuracy and reproducibility of fitted PET pharmacokinetic parameters. In this study, the performance of commonly used optimization algorithms (i.e. interior-reflective Newton methods) and a simulated annealing (SA) method was evaluated. This SA algorithm, known as basin hopping, was modified for the present application. In addition, optimization was performed using various weighting factors. Algorithms and effects of using incorrect weighting factors were studied using both simulated and clinical time-activity curves (TACs). Input data, taken from [(15)O]H(2)O, [(11)C]flumazenil and [(11)C](R)-PK11195 studies, were used to simulate time-activity curves at various variance levels (0-15% COV). Clinical evaluation was based on studies with the same three tracers. SA was able to produce accurate results without the need for selecting appropriate starting values for (kinetic) parameters, in contrast to the interior-reflective Newton method. The latter gave biased results unless it was modified to allow for a range of starting values for the different parameters. For patient studies, where large variability is expected, both SA and the extended Newton method provided accurate results. Simulations and clinical assessment showed similar results for the evaluation of different weighting models in that small to intermediate mismatches between data variance and weighting factors did not significantly affect the outcome of the fits. Large errors were observed only when the mismatch between weighting model and data variance was large. It is concluded that selection of specific optimization algorithms and weighting factors can have a large effect on the accuracy and precision of PET pharmacokinetic analysis. Apart from carefully selecting appropriate algorithms and variance models, further improvement in accuracy might be obtained by using noise reducing strategies, such as wavelet filtering, provided that these methods do not introduce significant bias.

Algorithms↗

PubMed2000

A simple iterative approach to parameter optimization.

Various bioinformatics problems require optimizing several different properties simultaneously. For example, in the protein threading problem, a scoring function combines the values for different parameters of possible sequence-to-structure alignments into a single score to allow for unambiguous optimization. In this context, an essential question is how each property should be weighted. As the native structures are known for some sequences, a partial ordering on optimal alignments to other structures, e.g., derived from structural comparisons, may be used to adjust the weights. To resolve the arising interdependence of weights and computed solutions, we propose a heuristic approach: iterating the computation of solutions (here, threading alignments) given the weights and the estimation of optimal weights of the scoring function given these solutions via systematic calibration methods. For our application (i.e., threading), this iterative approach results in structurally meaningful weights that significantly improve performance on both the training and the test data sets. In addition, the optimized parameters show significant improvements on the recognition rate for a grossly enlarged comprehensive benchmark, a modified recognition protocol as well as modified alignment types (local instead of global and profiles instead of single sequences). These results show the general validity of the optimized weights for the given threading program and the associated scoring contributions.

Algorithms↗

PubMed2003

A theoretically optimized method for cord blood stem cell cryopreservation.

The objective of this study was to develop an optimal cryopreservation method for human umbilical cord blood hematopoietic progenitor cells as evidenced by improved retention of in vivo engraftment ability and multilineage differentiation. An extended understanding of the osmometric/permeability characteristics of cord blood stem cells was accomplished by measuring permeability of the cryoprotectant dimethyl sulfoxide (DMSO) at below-ambient temperatures (10 degrees and 3 degrees C). These data were combined with previously published osmotic and permeability data and the water-NaCl-DMSO phase diagram in conjunction with a mathematical model to determine an optimal initial DMSO concentration, cooling rate, and liquid nitrogen plunging temperature. Cells cryopreserved with the theoretically optimized procedure were then compared with cells frozen using standard methods for the ability to engraft in irradiated NOD/SCID mice. The optimal procedure was determined to include a 0.7 molal (approximately 5%) DMSO concentration at a cooling rate of 4 degrees C/min, and a plunging temperature of -44 degrees C. The optimized protocol resulted in significantly higher engraftment of human CD45(+) cells (17.2 +/- 1.6% vs. 8.4 +/- 1.6%), CD19(+) B lymphocytes (11.3 +/- 1.2% vs. 5.8 +/- 1.2%), and CD34(+) cells (1.9 +/- 0.09% vs. 0.6 +/- 0.09%) compared to cells frozen using a standard method. Engraftment of CD33(+) cells was not significantly different (4.0 +/- 0.3 vs. 3.2 +/- 0.6, respectively). This study demonstrated that the use of a theoretically determined optimal cryopreservation method is superior to standard methods for maintaining UCB PCBs with multilineage repopulation potential in NOD/SCID mice.

Antigens, CD↗

PubMed2004

Optimal photosynthetic characteristics of individual plants in vegetation stands and implications for species coexistence.

AIMS: This paper reviews the way optimization theory has been used in canopy models to analyse the adaptive significance of photosynthesis-related plant characteristics and their consequences for the structure and species composition of vegetation stands. SCOPE: In most studies simple optimization has been used with trait values optimal when they lead to maximum whole-stand photosynthesis. This approach is subject to the condition that the optimum for one individual is independent of the characteristics of its neighbours. This seems unlikely in vegetation stands where neighbour plants strongly influence each other's light climate. Not surprisingly, there are consistent deviations between predicted plant traits and real values: plants tend to be taller, distribute nitrogen more evenly among their leaves and produce more leaf area which is projected more horizontally than predicted by models. CONCLUSIONS: By applying game theory to individual plant-based canopy models, other studies have shown that optimal vegetation stands with maximum whole-stand photosynthesis are not evolutionarily stable. They can be successfully invaded by mutants that are taller, project their leaves more horizontally or that produce greater than optimal leaf areas. While these individual-based models can successfully predict the canopy structure of vegetation stands, they are invariably determined at unique optimal trait values. They do not allow for the co-existence of more than one species with different characteristics. Canopy models can contribute to our understanding of species coexistence through (a) simultaneous analysis of the various traits that determine light capture and photosynthesis and the trade-offs between them, and (b) consideration of trade-offs associated with specialization to different positions in the niche space defined by temporal and spatial heterogeneity of resources.

Adaptation, Physiological↗

PubMed2005

Optimality principle and determination of kinetic constants for biochemical reactions.

An optimality principle is applied to determine kinetic constants for biochemical (enzymatic and second-order) reactions involved in a physiological system, a minimum protein consumption criterion being adopted. A direct optimization problem is to determine optimal zymogen concentrations. An 'inverse' optimization problem is also considered; this problem is to determine the kinetic constants for the biochemical reactions involved in a physiological system such that the optimal and observed zymogen and procofactor concentrations coincide. In solving an 'inverse' optimization problem we assume that the scheme of biochemical reactions and zymogen and procofactor concentrations are known. Good agreement is observed between the model results for the extrinsic blood coagulation pathway and relevant biochemical data. The proposed method is also applicable to determining kinetic constants for other physiological biochemical-reaction systems.

Blood Coagulation↗

PubMed2002

Optimal transfection with the HK polymer depends on its degree of branching and the pH of endocytic vesicles.

We have recently reported that liposomes in combination with histidine (HK)-containing polymers enhanced the expression of luciferase in transfected cells. In transformed or malignant cell lines, branched HK polymers (combined with liposome carriers) were significantly more effective than the linear HK polymer in stimulating gene expression. In the current study, we found that the linear HK polymer enhanced gene expression in primary cell lines more effectively than the branched polymers. The differences in the optimal carrier (linear versus branched) were not due to initial cellular uptake, size of the complexes or level of gene expression. There was, however, a strong association between the optimal type of HK polymer and the pH of endocytic vesicles (P = 0.0058). By altering the percentage of histidines carrying a positive charge, the endosomal pH of a cell may determine the amount of DNA released from the linear or branched HK polymer. In the two cell lines in which the linear HK was the optimal polymer, the endocytic vesicles were strongly acidic with a pH of <5.0. Conversely, in the four cell lines in which the branched polymers were optimal transfection agents, the pH of endocytic vesicles was >6.0. Furthermore, binding data support the relationship between DNA release from the optimal HK polymer and endosomal pH. The interplay between optimal HK polymers and the endosomal pH may lead to improved gene-delivery polymers tailored to a particular cell.

Animals↗

PubMed2005

D-optimal experimental designs to test for departure from additivity in a fixed-ratio mixture ray.

Traditional factorial designs for evaluating interactions among chemicals in a mixture may be prohibitive when the number of chemicals is large. Using a mixture of chemicals with a fixed ratio (mixture ray) results in an economical design that allows estimation of additivity or nonadditive interaction for a mixture of interest. This methodology is extended easily to a mixture with a large number of chemicals. Optimal experimental conditions can be chosen that result in increased power to detect departures from additivity. Although these designs are used widely for linear models, optimal designs for nonlinear threshold models are less well known. In the present work, the use of D-optimal designs is demonstrated for nonlinear threshold models applied to a fixed-ratio mixture ray. For a fixed sample size, this design criterion selects the experimental doses and number of subjects per dose level that result in minimum variance of the model parameters and thus increased power to detect departures from additivity. An optimal design is illustrated for a 2:1 ratio (chlorpyrifos:carbaryl) mixture experiment. For this example, and in general, the optimal designs for the nonlinear threshold model depend on prior specification of the slope and dose threshold parameters. Use of a D-optimal criterion produces experimental designs with increased power, whereas standard nonoptimal designs with equally spaced dose groups may result in low power if the active range or threshold is missed.

Animals↗

PubMed2000

A direct search procedure to optimize combinations of epidural bupivacaine, fentanyl, and clonidine for postoperative analgesia.

BACKGROUND: The authors applied an optimization model (direct search) to find the optimal combination of bupivacaine dose, fentanyl dose, clonidine dose, and infusion rate for continuous postoperative epidural analgesia. METHODS: One hundred ninety patients undergoing 48-h thoracic epidural analgesia after major abdominal surgery were studied. Combinations of the variables of bupivacaine dose, fentanyl dose, clonidine dose, and infusion rate were investigated to optimize the analgesic effect (monitored by verbal descriptor pain score) under restrictions dictated by the incidence and severity of side effects. Six combinations were empirically chosen and investigated. Then a stepwise optimization model was applied to determine subsequent combinations until no decrease in the pain score after three consecutive steps was obtained. RESULTS: Twenty combinations were analyzed. The optimization procedure led to a reduction in the incidence of side effects and in the mean pain scores. The three best combinations of bupivacaine dose (mg/h), fentanyl dose (microg/h), clonidine dose (microg/h), and infusion rate (ml/h) were: 9-21-5-7, 8-30-0-9, and 13-25-0-9, respectively. CONCLUSIONS: Given the variables investigated, the aforementioned combinations may be the optimal ones to provide postoperative analgesia after major abdominal surgery. Using the direct search method, the enormous number of possible combinations of a therapeutic strategy can be reduced to a small number of potentially useful ones. This is accomplished using a scientific rather than an arbitrary procedure.

Adrenergic alpha-Agonists↗

PubMed2004

Combinations of bupivacaine, fentanyl, and clonidine for lumbar epidural postoperative analgesia: a novel optimization procedure.

BACKGROUND: The authors developed and applied a method to optimize the combination of bupivacaine, fentanyl, and clonidine for continuous postoperative lumbar epidural analgesia. METHODS: One hundred eighteen patients undergoing knee or hip surgery participated in the study. Postoperative epidural analgesia during 48 h after surgery was optimized under restrictions dictated by side effects. Initially, eight combinations of bupivacaine, fentanyl, and clonidine (expressed as drug concentration in the solution administered) were empirically chosen and investigated. To determine subsequent combinations, an optimization model was applied until three consecutive steps showed no decrease in pain score. For the first time in a clinical investigation, a regression model was applied when the optimization procedure led to combinations associated with unacceptable side effects. RESULTS: The authors analyzed 12 combinations with an allowed bupivacaine concentration range of 0-2.5 mg/ml, a fentanyl concentration range of 0-5 microg/ml, and a clonidine concentration range of 0-5 microg/ml. The best combinations of bupivacaine, fentanyl, and clonidine concentrations were 1.0 mg/ml-1.4 microg/ml-0.5 microg/ml, 0.9 mg/ml-3.0 microg/ml-0.3 microg/ml, 0.6 mg/ml-2.5 microg/ml-0.8 microg/ml, and 1.0 mg/ml-2.4 microg/ml-1.0 microg/ml, respectively, all producing a similarly low pain score. The incidence of side effects was low. The application of the regression model to combinations associated with high incidence of motor block successfully directed the optimization procedure to combinations within the therapeutic range. CONCLUSIONS: The results support further study of the combinations of bupivacaine, fentanyl, and clonidine mentioned above for postoperative analgesia after knee and hip surgery. This novel optimization method may be useful in clinical research.

Adolescent↗

PubMed1987

An optimized computational method for determining the beta dose distribution using a multiple-element thermoluminescent dosimeter system.

This paper describes an optimization method for determining the beta dose distribution in tissue, and it describes the associated testing and verification. The method uses electron transport theory and optimization techniques to analyze the responses of a three-element thermoluminescent dosimeter (TLD) system. Specifically, the method determines the effective beta energy distribution incident on the dosimeter system, and thus the system performs as a beta spectrometer. Electron transport theory provides the mathematical model for performing the optimization calculation. In this calculation, parameters are determined that produce calculated doses for each of the chip/absorber components in the three-element TLD system. The resulting optimized parameters describe an effective incident beta distribution. This method can be used to determine the beta dose specifically at 7 mg X cm-2 or at any depth of interest. The doses at 7 mg X cm-2 in tissue determined by this method are compared to those experimentally determined using an extrapolation chamber. For a great variety of pure beta sources having different incident beta energy distributions, good agreement is found. The results are also compared to those produced by a commonly used empirical algorithm. Although the optimization method produces somewhat better results, the advantage of the optimization method is that its performance is not sensitive to the specific method of calibration.

Algorithms↗

PubMed2000

Hinged external fixation of the elbow: optimal axis alignment to minimize motion resistance.

OBJECTIVE: To establish an optimal single hinge axis position for application of hinged external fixation to the elbow joint. DESIGN: Cadaveric biomechanical investigation. SETTING: A customized motion transducer applied passive elbow motion to six cadaveric upper extremities. The instant rotation axis of the humero-ulnar articulation was determined from three-dimensional kinematic data acquired by an electromagnetic motion tracking system. For each specimen, an optimal fixator hinge position was calculated from these motion data. INTERVENTION: A prototype articulated external fixator was applied to the elbow, first with its hinge aligned along the computed optimal position. Then the fixator was mounted in sixteen distinct off-axis positions. MAIN OUTCOME MEASURE: Additional resistance to joint motion (in terms of energy) corresponding to deliberately introduced amounts of relative malalignment between the optimal elbow axis and the actual fixator hinge axis. RESULTS: Aligning the fixator hinge along the optimized axis position resulted in a minimal amount of energy (0.15 joules) needed to rotate the elbow through a prescribed range of motion. Malpositioning the hinge by ten millimeters caused up to ten times that amount of motion resistance. CONCLUSIONS: An optimal fixator hinge position can be determined to minimize the increase in motion resistance due to fixator application. The severely increased motion resistance associated with small amounts of malalignment between the fixator hinge and the anatomic elbow axis suggests the need for highly accurate fixator hinge application.

Cadaver↗

PubMed1997

Optimization of walking in children.

Previous work demonstrated that adults naturally adopt a walking frequency to optimize physiological cost, symmetry, and stability. Furthermore, the optimal frequency is predictable using the force-driven harmonic oscillator (FDHO) model. However, no studies have established the developmental processes of optimization in children. Thus, the purposes of this study were to examine the predictability of the preferred stride frequency (PSF) and optimization features of 3- to 12-yr-old children using the FDHO model. Forty-five children and nine adults were measured for anthropometric data to calculate the predicted frequency. They later walked at three frequencies (PSF, PSF +25%, and PSF -25%) at a constant speed on a treadmill. The results indicated that the FDHO model was accurate in predicting the preferred frequency of children (prediction error < 0.07 s). We identified three stages of learning in the development of optimization: an early manifestation of sensitivity to resonant frequency, the subsequent development of ability to modulate walking frequency, and the final establishment of an adult optimization form at age seven. Our findings suggest that walking development may be determined by the dynamic cooperation of physiological, neural, and musculoskeletal systems with respect to the environmental context.

Adult↗

PubMedDate not supplied

Violence exposure and optimism predict task-induced changes in blood pressure and pulse rate in a normotensive sample of inner-city black youth.

OBJECTIVE: This investigation examined the association of violence exposure (home and neighborhood) and optimism to task-induced changes in systolic blood pressure (SBP), diastolic blood pressure (DBP), and pulse rate (PR). METHODS: Drawn from a larger investigation, the convenience sample for this study consisted of 172 normotensive black youth (mean age = 11.5 years, standard deviation = 1.3). Violence exposure and optimism were self-reported by participants, and task-induced changes in SBP, DBP, and PR were measured with an automated monitor during two sequentially administered digit-forward and digit-backward tasks. RESULTS: Hierarchical regression analyses revealed that violence exposure was inversely related to task-induced changes in SBP (p = .010) and DBP (p = .005). Optimism was not an independent predictor of blood pressure or PR changes (p-s > .32). The final step of these hierarchical analyses indicated that the effects of violence exposure and optimism interacted to predict task-induced changes in SBP (p = .013) and PR (p = .003). Follow-up regression analyses indicated that violence exposure was inversely related to task-induced changes in SBP among participants high in optimism and was positively associated with PR reactivity in participants low in optimism. CONCLUSIONS: The youth in this study have intact mechanisms for buffering blood pressure responses to violence exposure, especially those who are more optimistic about their future-a person factor whose moderating effects might wane with advancing age.

Attitude↗

PubMed2005

Continuous extremal optimization for Lennard-Jones clusters.

We explore a general-purpose heuristic algorithm for finding high-quality solutions to continuous optimization problems. The method, called continuous extremal optimization (CEO), can be considered as an extension of extremal optimization and consists of two components, one which is responsible for global searching and the other which is responsible for local searching. The CEO's performance proves competitive with some more elaborate stochastic optimization procedures such as simulated annealing, genetic algorithms, and so on. We demonstrate it on a well-known continuous optimization problem: the Lennard-Jones cluster optimization problem.

Journal Article↗

PubMed1989

Optimal stroke volume in left-ventricular ejection.

Previous papers related to the recent concept of matching between the ventricle and arterial load have only dealt with the optimization of arterial load. Thus, stroke volumes predicted by the suggested models for an optimal arterial load have only been analyzed. In this paper, optimal value of stroke volume ejected against a given arterial load was studied, i.e., left-ventricular function was described by an optimization model. In the model, end-diastolic volume (Ved), the linear end-systolic pressure-volume relation, heart rate, and ejection time are given and arterial load is described by the three-element wind-kessel model. The cost function of the model takes into account two optimality criteria for ventricular function: energy economy and efficient response to an increase in Ved. The observed stroke volumes of isolated canine hearts (data from the literature) could be predicted quite accurately by the model. It was concluded that the left-ventricular response to a change in arterial load and Ved can be explained by an optimization model when contractility and heart rate are kept constant. The results also strongly suggest that energy economy and efficiency are essential features of left-ventricular function.

Animals↗

PubMed1993

Computer-optimization of vascular trees.

Arterial branchings closely fulfill several "bifurcation rules" which are deemed to optimize blood flow. The question is whether these local criteria in conjunction with a general optimization principle can explain the overall structure of an arterial tree. We present a model of an arterial vascular tree which is grown on the computer by successively adding terminal vessel segments. Each new terminal segment is connected to the optimum site within the preexisting tree, and the new bifurcation is optimized geometrically. After each step of adding and optimizing, the whole tree is rescaled to meet invariant boundary conditions of pressure and flow at each terminal site. Thus, local geometric optimization is used to induce simultaneously an optimized global structure. The comparison between the model and real coronary arterial trees shows good agreement regarding structural appearance, morphometric parameters, and pressure profiles.

Arteries↗

PubMed2002

Optimization of electromagnetic phased-arrays for hyperthermia via magnetic resonance temperature estimation.

A technique for the optimization of electromagnetic annular phased arrays (APAs) for therapeutic hyperthermia has been developed and implemented. The controllable inputs are the amplitudes and phases of the driving signals of each element of the array. Magnetic resonance imaging (MRI) is used to estimate noninvasively the temperature distribution based on the temperature dependence of the proton resonance frequency (PRF). A parametric model of the dynamics that couple the control inputs to the resultant temperature elevations is developed based on physical considerations. The unknown parameters of this model are estimated during a pretreatment identification phase and can be continuously updated as new measurement data become available. Based on the parametric model, a controller automatically chooses optimal phases and amplitudes of the driving signals of the APA. An advantage of this approach to optimizing the APA is that no a priori information is required, eliminating the need for patient-specific computational modeling and optimization. Additionally, this approach represents a first step toward employing temperature feedback to make the optimization of the APA robust with respect to modeling errors and physiological changes. The ability of the controller to choose therapeutically beneficial driving amplitudes and phases is demonstrated via simulation. Experimental results are presented which demonstrate the ability of the controller to choose optimal phases for the APA using only information from magnetic resonance thermometry (MRT).

Computer Simulation↗

PubMedDate not supplied

Faster algorithms for optimal multiple sequence alignment based on pairwise comparisons.

Multiple Sequence Alignment (MSA) is one of the most fundamental problems in computational molecular biology. The running time of the best known scheme for finding an optimal alignment, based on dynamic programming, increases exponentially with the number of input sequences. Hence, many heuristics were suggested for the problem. We consider a version of the MSA problem where the goal is to find an optimal alignment in which matches are restricted to positions in predefined matching segments. We present several techniques for making the dynamic programming algorithm more efficient, while still finding an optimal solution under these restrictions. We prove that it suffices to find an optimal alignment of the predefined sequence segments, rather than single letters, thereby reducing the input size and thus improving the running time. We also identify "shortcuts" that expedite the dynamic programming scheme. Empirical study shows that, taken together, these observations lead to an improved running time over the basic dynamic programming algorithm by 4 to 12 orders of magnitude, while still obtaining an optimal solution. Under the additional assumption that matches between segments are transitive, we further improve the running time for finding the optimal solution by restricting the search space of the dynamic programming algorithm.

Algorithms↗