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PubMed2002

Optimal temperature policy for immobilized enzyme packed bed reactor performing reversible Michaelis-Menten kinetics using the disjoint policy.

The optimal temperature policy that maximizes the time-averaged productivity of a continuous immobilized enzyme packed bed reactor is determined. This optimization study takes into consideration the enzyme thermal deactivation with substrate protection during the reactor operation. The general case of reversible Michaelis-Menten kinetics under constant reactor feed flow rate is assumed. The corresponding nonlinear optimization problem is solved using the calculus of variations by applying the disjoint policy. This policy reduces the optimization problem into a differential-algebraic system, DAE. This DAE system defines completely the optimal temperature-time profiles. These profiles depend on the kinetic parameters, feed substrate concentration, operating period, and the residence time and are characterized by increasing form with time. Also, general analytical expressions for the slopes of the temperature and residual enzyme activity profiles are derived. An efficient solution algorithm is developed to solve the DAE system, which results into a one-dimensional optimization problem with simple bounds on the initial feed temperature. The enzymatic isomerization of glucose into fructose is selected as a case study. The computed productivities are very close to that obtained by numerical nonlinear optimization with simpler problem to solve. Moreover, the computed conversion profiles are almost constant over 90% of the operating periods, thus producing a homogeneous product.

Algorithms↗

PubMed1975

Application of modified Rosenbrock's method for optimization of nutrient media used in microorganism culturing.

The Rosenbrock's procedure has been modified for optimization of nutrient medium composition and has been found to be less tedious than the Box-Wilson method, especially for larger numbers of optimized parameters. Its merits are particularly obvious with multiparameter optimization where the gradient method, so far the only one employed in microbiology from a variety of optimization methods (e.g., refs, 9 and 10), becomes impractical because of the excessive number of experiments required. The method suggested is also more stable during optimization than the gradient methods which are very sensitive to the selection of steps in the direction of the gradient and may thus easily shoot out of the optimized region. It is also anticipated that other direct search methods, particularly simplex design, may be easily adapted for optimization of medium composition. It is obvious that direct search methods may find an application in process improvement in antibiotic and related industries.

Culture Media↗

PubMed2003

Geometry optimization with QM/MM, ONIOM, and other combined methods. I. Microiterations and constraints.

Hybrid energy methods such as QM/MM and ONIOM, that combine different levels of theory into one calculation, have been very successful in describing large systems. Geometry optimization methods can take advantage of the partitioning of these calculations into a region treated at a quantum mechanical (QM) level of theory and the larger, remaining region treated by an inexpensive method such as molecular mechanics (MM). A series of microiterations can be employed to fully optimize the MM region for each optimization step in the QM region. Cartesian coordinates are used for the MM region and are chosen so that the internal coordinates of the QM region remain constant during the microiterations. The coordinates of the MM region are augmented to permit rigid body translation and rotation of the QM region. This is essential if any atoms in the MM region are constrained, but it also improves the efficiency of unconstrained optimizations. Because of the microiterations, special care is needed for the optimization step in the QM region so that the system remains in the same local valley during the course of the optimization. The optimization methodology with microiterations, constraints, and step-size control are illustrated by calculations on bacteriorhodopsin and other systems.

Journal Article↗

PubMed1994

Optimization of parameter values for complex pulse sequences by simulated annealing: application to 3D MP-RAGE imaging of the brain.

A number of pulse sequence techniques, including magnetization-prepared gradient echo (MP-GRE), segmented GRE, and hybrid RARE, employ a relatively large number of variable pulse sequence parameters and acquire the image data during a transient signal evolution. These sequences have recently been proposed and/or used for clinical applications in the brain, spine, liver, and coronary arteries. Thus, the need for a method of deriving optimal pulse sequence parameter values for this class of sequences now exists. Due to the complexity of these sequences, conventional optimization approaches, such as applying differential calculus to signal difference equations, are inadequate. We have developed a general framework for adapting the simulated annealing algorithm to pulse sequence parameter value optimization, and applied this framework to the specific case of optimizing the white matter-gray matter signal difference for a T1-weighted variable flip angle 3D MP-RAGE sequence. Using our algorithm, the values of 35 sequence parameters, including the magnetization-preparation RF pulse flip angle and delay time, 32 flip angles in the variable flip angle gradient-echo acquisition sequence, and the magnetization recovery time, were derived. Optimized 3D MP-RAGE achieved up to a 130% increase in white matter-gray matter signal difference compared with optimized 3D RF-spoiled FLASH with the same total acquisition time. The simulated annealing approach was effective at deriving optimal parameter values for a specific 3D MP-RAGE imaging objective, and may be useful for other imaging objectives and sequences in this general class.

Adipose Tissue↗

PubMed2000

The ability of preoperative serum CA-125 to predict optimal primary tumor cytoreduction in stage III epithelial ovarian carcinoma.

PURPOSE: The aim of this study was to determine the ability of preoperative serum CA-125 to predict optimal primary tumor cytoreduction in patients with Stage III epithelial ovarian carcinoma. METHODS: We performed a retrospective chart review of 100 consecutive patients with Stage III ovarian carcinoma who had a serum CA-125 drawn prior to primary cytoreductive surgery. We used a receiver operating characteristic curve to determine the CA-125 level with the maximal prognostic power in predicting optimal versus suboptimal cytoreduction. RESULTS: The median CA-125 level for the 100 patients was 819 U/ml (range 5.6-26,200 U/ml). Optimal cytoreduction (diameter of largest residual tumor nodule < or =1 cm) was obtained in 45 cases (45%). The probability of performing optimal cytoreduction decreased with increasing CA-125 levels. A preoperative CA-125 level of 500 U/ml was identified as the value with the most predictive power. Optimal cytoreduction was achieved in 33 of the 45 cases (73%) with a CA-125 less than 500 U/ml compared to only 12 of the 55 cases (22%) with a CA-125 greater than 500 U/ml. Using a threshold level of 500 U/ml, the preoperative serum CA-125 level was able to predict optimal versus suboptimal cytoreduction with a sensitivity of 78%, specificity of 73%, positive predictive value of 78%, and negative predictive value of 73%. CONCLUSION: The probability of performing optimal cytoreduction in patients with Stage III ovarian carcinoma and a preoperative CA-125 greater than 500 U/ml was approximately one in five. These patients may be candidates for initial laparoscopic evaluation to obtain a confirmatory tissue diagnosis and to determine resectability.

Adult↗

PubMed2000

Optimal cytoreductive surgery is an independent prognostic indicator in stage IV epithelial ovarian cancer with hepatic metastases.

OBJECTIVES: The aim of this study was to determine the value of optimal cytoreduction in stage IV epithelial ovarian cancer. METHODS: A retrospective review was performed of 37 women with stage IV epithelial ovarian cancer treated by radical surgery. RESULTS: Optimal surgery to less than 2 cm tumor deposits was performed in 16 of the 37 cases (43%) and tumor debulking to less than 1 cm tumor deposits in 6 cases (16.2%). Twenty-three cases (62%) were designated stage IV because of the presence of liver metastases alone. Although no patients died within 2 weeks of surgery, 7 of the 37 cases (22%) failed to survive more than 50 days after primary surgery. The overall median survival was 11 months with overall 2- and 5-year survivals of 23 and 9%, respectively. On multivariate analysis comparing age, histological type, tumor grade, place of surgery, secondary surgical procedure, performance of bowel surgery, presence of liver metastases, and optimal cytoreduction, only optimal surgery and residual tumor deposits of less than 2 cm, or less than 1 cm, remained highly significant (P = 0.0029 and 0.0086, respectively). Even when assessing only the 27 cases who were designated as having stage IV disease because of the presence of liver metastases, by multivariate analysis, only optimal surgery and residual tumor deposits of less than 2 cm, or less than 1 cm, remained significant (P = 0.023 and 0.036, respectively). Site of metastases designating stage IV status was not associated with a reduced likelihood of achieving optimal debulking (P = 0.18). CONCLUSION: Optimal cytoreduction in women with stage IV epithelial ovarian cancer with or without hepatic metastases is associated with a more favorable outcome survival.

Adenocarcinoma↗

PubMed1992

Time optimality in the control of human movements.

In a simulation study the control of maximally fast goal directed movements has been analyzed. For a simple linear model it is shown that the presence of a third input block reduces the movement duration. The time optimal size of the third block depends on the ratio of a neuromuscular time constant (first-order lag) and movement time. As a second step a non-linear muscle model was simulated. By an optimization of input parameters it was found that the time optimal input, as expected, switches between maximal agonist and maximal antagonist activation. As for the linear model, a third phase was required for an optimal movement. It was found that the third phase serves to compensate the slowly decaying antagonist force. Also an input similar to experimentally found activation patterns was simulated. This input contains a silent period between the first two bursts and the second and the third burst have submaximal amplitudes. This input led to a near time optimal movement with a duration 9% larger than the minimal duration but with largely reduced muscle forces. This suggests that a criterion is minimized which also takes into account the effort spent. Including gravity in the model indicates optimality of a silent period between the third phase and a final agonist activity to resist gravity. When assuming different dynamics for agonist and antagonist, the optimal switch times for agonist and antagonist no longer coincide, also after the three block pattern some extra activity is required to obtain a cancellation of the slowly decaying force in agonist and antagonist.

Biological Clocks↗

PubMed1995

A variable target intensity-restrained global optimization (VARTIGO) procedure for determining three-dimensional structures of polypeptides from NOESY data: application to gramicidin-S.

A global optimization method for intensity-restrained structure refinement, based on variable target function (VTF) analysis, is illustrated using experimental data on a model peptide, gramicidin-S (GS) dissolved in DMSO. The method (referred to as VARTIGO for variable target intensity-restrained global optimization) involves minimization of a target function in which the range of NOE contacts is gradually increased in successive cycles of optimization in dihedral angle space. Several different starting conformations (including all-trans) have been tested to establish the validity of the method. Not all optimizations were successful, but these were readily identifiable from their large NOE R-factors. We also show that it is possible to simultaneously optimize the rotational correlation time along with the dihedral angles. The structural features of GS thus obtained from the successful optimizations are in excellent agreement with the available experimental data. A comparison is made with structures generated from an intensity-restrained single target function (STF) analysis. The results on GS suggest that VARTIGO refinement is capable of yielding better quality structures. Our work also underscores the need for a simultaneous analysis of different NOE R-factors in judging the quality of optimized structures. The NOESY data on GS in DMSO appear to provide evidence for the presence of two orientations for the ornithine side chain, in fast exchange. The NOESY spectra for this case were analyzed using a relaxation rate matrix which is a weighted average of the relaxation rate matrices for the individual conformations.

Amino Acid Sequence↗

PubMed1993

The relative importance of dispositional optimism and control appraisals in quality of life after coronary artery bypass surgery.

Similar mechanisms have been proposed to explain the stress-buffering effects of both dispositional optimism and perceived control. Yet dispositional optimism as a personal resource should function independently of situational control appraisals. To evaluate the unique and additive contributions to adaptation of control appraisals and optimism, we followed 49 individuals scheduled for coronary artery bypass surgery. One month before surgery dispositional optimism was associated with neither health locus of control nor specific expectancies about the outcomes of surgery. Dispositional optimism, however, was associated with perceived control over the course of the illness and with quality of life appraisals. Although presurgery optimism predicted life quality 8 months after surgery, this was not the case when general and specific control appraisals and specific expectancies were included in the prediction. These findings are discussed as they relate to current conceptions of trait optimism.

Adaptation, Psychological↗

PubMed1996

Individual differences in the perception of optimism and disease severity: a study among individuals with Parkinson's disease.

The extent to which individuals with Parkinson's disease (PD) show lability in optimism was explored in the present study. The relationship between optimism and perceived disease severity was examined as well. Twelve individuals diagnosed with PD completed self-report measures for 70 consecutive days. All individuals in this study showed lability in optimism over short time periods; however, 67% of the sample showed no pervasive negative changes in optimism over time. Increased levels of optimism on one day were predictive of decreased perceived disease severity the next day for one-fourth of the sample, after controlling for negative affect. Individual differences in the relationship between optimism and disease severity provided support for the idea that living with chronic illness has no monolithic meaning. More optimistic individuals reported less need for assistance with basic functional abilities than less optimistic individuals. The usefulness of lability in optimism among individuals with PD is discussed.

Activities of Daily Living↗

PubMed2001

Optimization of automatic bolus tracking for timing of the arterial phase of helical liver CT.

The aim of this study was to optimize bolus tracking for timing of the arterial phase of biphasic helical liver CT and to compare optimized bolus tracking to a standard delay. One hundred fifty patients were examined with six protocols: 5- or 10-s delay after triggering at a threshold of 50 or 75 or 100 HU enhancement in the aorta at the origin of the celiac arteries after injection of 120 ml contrast material at 3 ml/s. Optimal arterial enhancement was defined as 20-30% of hepatic enhancement in portal venous phase. Another 50 patients were examined with the optimized protocol and compared to 50 gender- and age-matched patients who underwent a 25-s standard delay. A 10-s delay after the 75-HU threshold resulted in the most patients with an optimal arterial phase (p < 0.01). Thirty-one of 75 patients examined with this protocol showed optimal early liver enhancement. Bolus tracking compared with standard delay revealed only a trend for a difference (p = 0.07). The outcome of automatic bolus tracking differs depending on the protocol used; however, optimal arterial phase imaging was seen in only 41% of patients, indicating only a trend for superior timing compared with a standard delay.

Adolescent↗

PubMed2001

Optimal posture control of a musculo-skeletal arm model.

In this paper maximal performance posture control of the human arm is investigated by means of model simulations. Recent experiments (F.C.T. van der Helm, submitted, 2000) have shown that the reflexive feedback during postural control varies with the bandwidth of the applied force disturbances. This paper focusses on the influence of the frequency content of force disturbances on the reflexive feedback gains by means of optimization. The arm is modelled by a nonlinear musculo-skeletal model with two degrees of freedom and six muscles. To facilitate the optimization of the model parameters, the arm model is linearized. A performance criterion is minimized for stochastic force disturbances in a two-step procedure: (1) optimization of static muscle activations using an additional energy criterion to obtain a unique and energy-efficient solution; antid (2) optimization of reflex gains using an additional control effort criterion to obtain a unique solution. The optimization reveals that for the given task and posture, the shoulder muscles have the largest contribution, whereas the bi-articular muscles have a relatively small contribution to the behaviour. The dynamics at the endpoint level are estimated so that a comparison can be made with the experiments. Compared to the experiments, the intrinsic damping of the model is relatively large (about 150%), whereas the intrinsic stiffness is relatively small (about 60%). These differences can be attributed to unmodelled mechanical effects of crossbridges in Hill-type muscle models. The optimized reflex gains show remarkable similarities with the values found in the experiments, implying that humans can adjust their reflexive feedback gains in an optimal way, weighting the performance and energy. The approach in this paper could be useful in the study of various posture tasks, for example in the prediction of the relation between the control parameters of various musculo-skeletal models and different experimental variables.

Arm↗

PubMed2003

Multicriteria optimization of gluconic acid production using net flow.

The biochemical process industry is often confronted with the challenge of making decisions in an atmosphere of multiple and conflicting objectives. Recent innovations in the field of operations research and systems science have yielded rigorous multicriteria optimization techniques that can be successfully applied to the field of biochemical engineering. These techniques incorporate the expert's experience into the optimization routine and provide valuable information about the zone of possible solutions. This paper presents a multicriteria optimization strategy that generates a Pareto domain, given a set of conflicting objective criteria, and determines the optimal operating region for the production of gluconic acid using the net flow method (NFM). The objective criteria include maximizing the productivity and concentration of gluconic acid, while minimizing the residual substrate. Three optimization strategies are considered. The first two strategies identify the optimal operating region for the process inputs. The results yielded an acceptable compromise between productivity, gluconic acid concentration and residual substrate concentration. Fixing the process inputs representing the batch time, initial substrate concentration and initial biomass equal to their optimal values, the remaining simulations were used to study the sensitivity of the optimum operating region to changes in the oxygen mass transfer coefficient, K(L) a, by utilizing a multi-level K(L) a strategy. The results show that controlling K(L) a during the reaction reduced the production of biomass, which in turn resulted in increased productivity and concentration of gluconic acid above that of a fixed K(L) a.

Journal Article↗

PubMed1990

DESIGN: computerized optimization of experimental design for estimating Kd and Bmax in ligand binding experiments. II. Simultaneous analysis of homologous and heterologous competition curves and analysis blocking and of "multiligand" dose-response surfaces.

We have developed a computer program, DESIGN, for optimization of ligand binding experiments to minimize the "average" uncertainty in all unknown parameters. An earlier report [G. E. Rovati, D. Rodbard, and P. J. Munson (1988) Anal. Biochem. 174, 636-649] described the application of this program to experiments involving a single homologous or heterologous dose-response curve. We now present several advanced features of the program DESIGN, including simultaneous optimization of two or more binding competition curves optimization of a "multiligand" experiment. Multiligand designs are those which use combinations of two (or more) ligands in each reaction tube. Such designs are an important and natural extension of the popular method of "blocking experiments" where an additional ligand is used to suppress one or more classes of sites. Extending the idea of a dose-response curve, the most general multiligand design would result in a "dose-response surface". One can now optimize the design not only for a single binding curve, but also for families of curves and for binding surfaces. The examples presented in this report further demonstrate the power and utility of the program DESIGN and the nature of D-optimal designs in the context of more complex binding experiments. We illustrate D-optimal designs involving one radioligand and two unlabeled ligands; we consider one example of homogeneous and several examples of heterogeneous binding sites. Further, to demonstrate the virtues of the dose-response surface experiment, we have compared the optimal surface design to the equivalent design restricted to traditional dose-response curves. The use of DESIGN in conjunction with multiligand experiments can improve the efficiency of estimation of the binding parameters, potentially resulting in reduction of the number of observations needed to obtain a desired degree of precision in representative cases.

Binding Sites↗

PubMed1987

A dynamic optimization technique for predicting muscle forces in the swing phase of gait.

The muscle force sharing problem was solved for the swing phase of gait using a dynamic optimization algorithm. For comparison purposes the problem was also solved using a typical static optimization algorithm. The objective function for the dynamic optimization algorithm was a combination of the tracking error and the metabolic energy consumption. The latter quantity was taken to be the sum of the total work done by the muscles and the enthalpy change during the contraction. The objective function for the static optimization problem was the sum of the cubes of the muscle stresses. To solve the problem using the static approach, the inverse dynamics problem was first solved in order to determine the resultant joint torques required to generate the given hip, knee and ankle trajectories. To this effect the angular velocities and accelerations were obtained by numerical differentiation using a low-pass digital filter. The dynamic optimization problem was solved using the Fletcher-Reeves conjugate gradient algorithm, and the static optimization problem was solved using the Gradient-restoration algorithm. The results show influence of internal muscle dynamics on muscle control histories vis a vis muscle forces. They also illustrate the strong sensitivity of the results to the differentiation procedure used in the static optimization approach.

Algorithms↗

PubMed1992

Optimization of 3D radiation therapy with both physical and biological end points and constraints.

A new optimization model is described and its clinical usefulness is demonstrated. The optimization technique was developed to allow computer optimization of 3-dimensional radiation therapy plans with biological models of tumor and normal tissue response to radiation as well as with scores based on physical dose. The emphasis was placed on the optimization model, which should describe, as closely as possible, the goal of the radiation treatment, which is eradication of the tumor while sparing normal tissues. Since the statement of the goals may vary from case to case, a technique that allows a variety of objective functions and types of constraints was developed. The optimization algorithm is capable of handling nonlinear and even discrete score (objective) functions and constraints and effectively explores the vast space of feasible solutions in a relatively short time (minutes of MicroVax 3200 CPU time). An example of computer optimization of radiation therapy of a chordoma of the sphenoid bone using x-ray and proton beams is shown and compared with the best plans achieved by an experienced planner. Directions for future development of the algorithm, allowing optimization of beam orientation, are presented.

Chordoma↗

PubMed1994

Tissue heterogeneity effects in treatment plan optimization.

PURPOSE: There is general agreement that tissue density correction factors improve the accuracy of dose calculations. However, there is disagreement over the proper heterogeneity correction algorithm and a lack of clinical experience in using them. Therefore, there has not been widespread implementation of density correction factors into clinical practice. Furthermore, the introduction of optimized conformal therapy leads to new and radically different treatment techniques outside the clinical experience of the physician. It is essential that the effects of tissue density corrections are understood so that these types of treatments can be safely delivered. METHODS AND MATERIALS: In this paper, we investigate the effect of tissue density corrections on optimized conformal type treatment planning in the thorax region. Specifically, we study the effects on treatment plans optimized without type treatment planning in the thorax region. Specifically, we study the effects on treatment plans optimized without tissue density corrections, when those corrections are applied to the resulting dose distributions. These effects are compared for two different conformal techniques. RESULTS: This study indicates that failure to include tissue density correction factors results in an increased dose of approximately 5-15%. This is consistent with published studies using conventional treatment techniques. Additionally, the high-dose region of the dose distribution expands laterally into the uninvolved lung and other normal structures. The use of dose-volume histograms to compare these distributions demonstrates that treatment plans optimized without tissue density corrections lead to an increased dose to uninvolved normal structures. This increase in dose often violates the constraints used to determine the optimal solution. CONCLUSIONS: The neglect of tissue density correction factors can result in a 5-15% increase in the delivered dose. In addition, suboptimal dose distributions are produced. To benefit from the advantages of optimized conformal therapy in the thorax, tissue density correction factors should be used.

Carcinoma↗

PubMed1994

Optimizing the time course of brachytherapy and other accelerated radiotherapeutic protocols.

PURPOSE: It is likely that early-responding tissues, such as tumors, repair sublethal damage more rapidly than do late-responding tissues. This difference can be exploited to design protocols with a significantly improved therapeutic advantage for accelerated radiotherapeutic regimens, including brachytherapy. METHODS AND MATERIALS: The time course of potential protocols is computer optimized, maximizing the therapeutic difference between tumor-control probability (TCP), and normal-tissue complication probability (NTCP). These quantities are evaluated with the linear-quadratic model, using clinically derived parameters. The optimization is performed by individually adjusting doses in different parts of the treatment, maximizing the therapeutic advantage. In the main calculations, half times for damage repair were T1/2(late) = 4 h, T1/2(early) = 0.5 h. Two component (fast/slow) repair processes were also investigated. RESULTS: Protocols determined by optimization have significantly greater therapeutic advantage than continuous low-dose rate (CLDR) protocols of the same overall dose and time. The optimized protocols are either (a) acute-dose/gap/CLDR/gap/acute-dose; or (b) a series of acute doses separated by 3-4 h. As a typical example, results are given for 60 Gy/120 h CLDR brachytherapy, which is assumed to give NTCP = 0.2 and TCP = 0.8. Under our assumptions, optimized regimes, with the same overall time and dose, produce an NTCP of approximately 0.11 and TCP of approximately 0.83, a significant therapeutic gain over CLDR. CONCLUSION: Difference in repair rates between early- and late-responding tissues can be exploited to produce clinically practical protocols that are significantly superior to current regimens. Such optimized protocols produce slightly better tumor control than CLDR with the same overall dose and time, significantly less late damage, and similar early normal-tissue sequellae. Temporal optimization, thus, promises to be a powerful tool in designing better treatment protocols.

Animals↗