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PubMed1989

Species preservations in an optimal harvest model with random prices.

In this paper, we consider an optimal harvest model in which the objective is to maximize the expected return. The unit price of biomass is assumed constant until a random time when the price increases by a given amount. Furthermore, due to obvious environmental protection requirements, it is assumed that the fishery population is bounded from below for all time so as to reduce the danger of species extinction. Clearly, this problem is an optimal control problem in which a random parameter is involved. However, due to its special structure, it is shown that the problem is convertible into a deterministic optimal control problem and hence is solvable by an existing optimal control software package, MISER. The practical implication of several computed results obtained by this approach is discussed. They are also compared with other related results in the literature.

Animals↗

PubMed1990

A mathematical model of cancer chemotherapy with an optimal selection of parameters.

An optimal parameter selection model of cancer chemotherapy is presented which describes the treatment of a tumor over a fixed period of time by the repeated administration of a single drug. The drug is delivered at evenly spaced intervals over the treatment period at doses to be selected by the model. The model constructs a regimen that both minimizes the tumor population at the end of the treatment and satisfies constraints on the drug toxicity and intermediate tumor size. Numerical solutions show that an optimal regimen withholds the bulk of the doses until the end of the treatment period. When a drug used is of either moderate or low effectiveness, an optimal regimen is superior to a schedule that delivers all of the drug at the beginning of the treatment. This study questions whether the current method for the administration of chemotherapy is optimal and suggests that alternative regimens should be considered.

Antineoplastic Agents↗

PubMed1983

Sister-chromatid exchange formation at supra-optimal growth temperatures.

The present research was mainly focused on characterizing the formation of sister-chromatid exchanges at both optimal and supra-optimal growth temperatures. Under these conditions (25, 30 and 35 degrees C) meristem cells of Allium cepa L. exhibited a roughly constant cell-cycle time, and modifications in other cell-cycle parameters were negligible. Second-division chromosomes of cells incubated at 30 and 35 degrees C showed increased SCE yields as compared with those detected in cells maintained at the optimal temperature (25 degrees C). When cells with unifilarly BrdUrd-substituted DNA was damaged by irradiation with visible light, we obtained almost the same SCE yields at the various temperatures tested. We suggest that this production of SCEs could be the result of a reduced number of lesions produced by light (perhaps as a consequence of reduced intracellular free oxygen at high temperature) and/or of an increased efficiency in the repair capacity of the cells at these temperatures. The analysis of SCE formation in undamaged cells incubated at different temperatures during BrdUrd treatment has shown that the optimal growth temperature appears to be the experimental condition in which the cells are able to exhibit the lowest frequency of SCE.

Bromodeoxyuridine↗

PubMed1982

Optimal inputs for parameter determination of inert gas washout from the lung.

The nitrogen washout test will yield more information about the distribution of pulmonary ventilation if a pattern of inspired gas concentrations is utilized other than the standard series of 100% oxygen breaths. The input breathing pattern which yields optimal results will vary with the specific features of the lung being studied but typically includes breaths of air, particularly in the last third of the washout. Using computerized, mathematical techniques, optimal inputs were selected for washout tests of duration 10, 20, 30 and 40 breaths for each of six lung models, ranging from a unicompartmental to a highly non-uniform 'diseased' lung. Knowing these optimal inputs we were able to devise a nominal input which was similar to the optimal inputs for all models. For a 10 breath test this nominal input pattern utilized a breath of air at breath 7. For a 20 breath test, air is utilized at breaths 12, 14, 15, 19; for 30, air at 19, 21, 22, 23, 29 and for a 40-breath test, air at breaths 19, 24, 28, 30, 31, 32 and 39. The 30-breath nominal sequence was compared with the conventional oxygen-only washout and a 31-breath pseudo-random binary (PRB) input. Comparisons were made using computer simulated washouts as well as actual tests on human subjects. The 30-breath nominal input was always superior to the standard washout and was superior to the PRB input for all models except the lung ventilated with vital capacity breaths. We conclude that a significant advantage is gained by substituting the recommended sequences of breaths in studies of the dynamics of gas exchange in the lung.

Humans↗

PubMed1994

Foetal heart rate in early pregnancy by detection of optimally estimated displacements with pulsed Doppler signals.

Foetal heart rate (FHR) in the early stage of pregnancy can be optimally estimated by a simple system combining a conventional pulsed Doppler device with a microcomputer (CPU). The input signals for FHR have been obtained as low frequency components of foetal Doppler signals. These components are less than 50 Hz and are directly transferred from the conventional pulsed Doppler device to a microcomputer as radio-frequency signals by a specially designed I/O unit. The low frequency components have been converted into displacement signals by the continuous calculation of an arc-tangent function combined with five channel recordings from the foetal cardiac area, each separated by 2 mm on the same echo line. After selecting the optimal displacement data line, the FHR is measured by the proposed algorithm of non-parametric frequency estimation and/or the conventional autocorrelation method. The algorithm draws attention to the improved frequency selectivity by multiplication with reference signals, whose frequency is automatically optimized by the standard FHR rate determined by the length of pregnancy. The FHR determined from the displacement signals by this algorithm has provided a more optimally controlled selectivity than with the presently used autocorrelation method, especially in those pregnancies of less than 8 weeks gestation. Clinical application of this system allowed a complete determination of foetal heart rate from 6 weeks of gestation by a transvaginal approach and from 7 weeks by transabdominal procedures. In some specific cases, with prominent foetal components, it was possible from 5 weeks 2 days by a vaginal, and 6 weeks by an abdominal procedure.

Algorithms↗

PubMed1991

Optimal spatial displacement for direction selectivity in cat visual cortex neurons.

Responses of single neurons in cat visual cortex were measured in response to sinewave grating stimuli. Firstly, a neuron's spatial frequency tuning was determined, and subsequent stimuli were set at the optimal spatial frequency for that neuron. Then a "jumping grating" stimulus was used: a sinewave grating subjected to a series of abrupt spatial displacements, while remaining stationary for a fixed exposure time between displacements. The amount of direction selectivity elicited by this stimulus was measured as a function of the amount of spatial displacement. Visual cortex neurons generally showed an optimal spatial displacement, corresponding to somewhat less than one quarter of a spatial period of the neuron's optimal spatial frequency (close to, but systematically less than, "quadrature phase"). In a majority of neurons tested, this optimal displacement was not affected by increasing the exposure time between displacements, indicating that the measurements were not a simple consequence of temporal frequency tuning. These results closely parallel recent human psychophysical data obtained from measurements of motion aftereffect or direction discrimination elicited by jumping grating stimuli.

Animals↗

PubMed1996

Bone remodelling adjacent to intramedullary stems: an optimal structures approach.

The internal parameters in bone remodelling theories often are not clearly related to the bony structure which results from the simulations in which they are implemented. For a restricted class of bone remodelling theories, we have previously found a connection between overall structural optimization and the parameters within a continuum-level remodelling rule. In this study, we assess whether a simplified analytical formula based on structural optimization can predict the behaviour of a large-scale finite element bone remodelling simulation. The analytical formula predicts when bone will remain around an intramedullary implant. The predictions of the formula are borne out in the numerical results. This leads to a physical interpretation of one of the two parameters in the remodelling rule used. The results also show some characteristics which are clinically relevant. This study extends earlier results due to Huiskes for internal remodelling around intramedullary implants by using a different, numerically stable remodelling algorithm based on optimization. The study also shows a direct practical application of the optimizing remodelling theory the authors have developed previously.

Biomechanical Phenomena↗

PubMed1987

Individual muscle force estimations using a non-linear optimal design.

In order to estimate individual muscle forces during human movement a mathematically underdetermined system, representing the human musculoskeletal system, was solved using a non-linear optimization algorithm. The load sharing between muscles was made to depend upon the instantaneous contractile conditions of the muscles, a feature not incorporated in comparable non-linear optimal designs reported in the literature. The optimization algorithm was formulated as a convex system which guarantees a unique solution at the global minimum. The strengths and weaknesses of the present optimization algorithm were evaluated and compared to the classical algorithm reported by Crowninshield and Brand (J. Biomech., 14 (1981) 793-801).

Humans↗

PubMed1995

Optimal experimental design and sample size for the statistical evaluation of data from somatic mutation and recombination tests (SMART) in Drosophila.

In genetic toxicology it is important to know whether chemicals should be regarded as clearly hazardous or whether they can be considered sufficiently safe, which latter would be the case from the genotoxicologist's view if their genotoxic effects are nil or at least significantly below a predefined minimal effect level. A previously presented statistical decision procedure which allows one to make precisely this distinction is now extended to the question of how optimal experimental sample size can be determined in advance for genotoxicity experiments using the somatic mutation and recombination tests (SMART) of Drosophila. Optimally, the statistical tests should have high power to minimise the chance for statistically inconclusive results. Based on the normal test, the statistical principles are explained, and in an application to the wing spot assay, it is shown how the practitioner can proceed to optimise sample size to achieve numerically satisfactory conditions for statistical testing. The somatic genotoxicity assays of Drosophila are in principle based on somatic spots (mutant clones) that are recovered in variable numbers on individual flies. The underlying frequency distributions are expected to be of the Poisson type. However, some care seems indicated with respect to this latter assumption, because pooling of data over individuals, sexes, and experiments, for sample, can (but need not) lead to data which are overdispersed, i.e., the data may show more variability than theoretically expected. It is an undesired effect of overdispersion that in comparisons of pooled totals it can lead to statistical testing which is too liberal, because overall it yields too many seemingly significant results. If individual variability considered alone is not in contradiction with Poisson expectation, however, experimental planning can help to minimise the undesired effects of overdispersion on statistical testing of pooled totals. The rule for the practice is to avoid disproportionate sampling. It is recalled that for optimal power in statistical testing, it is preferable to use equal total numbers of flies in the control and treated series. Statistical tests which are based on Poisson expectations are too liberal if there is overdispersion in the data due to excess individual variability. In this case we propose to use the U test as a non-parametric two-sample test and to adjust the estimated optimal sample size according to (i) the overdispersion observed in a large historical control and (ii) the relative efficiency of the U test in comparison to the t test and related parametric tests.

Animals↗

PubMed1992

Determination of optimal in vitro conditions for caprine alternative complement pathway assay.

Optimal in vitro testing conditions for caprine alternative complement pathway assay were determined. Effects of the following variables were tested: heterologous erythrocytes; pH, ionic strength and Mg2+ ion concentration of the complement diluent; incubation time and temperature. Rabbit erythrocytes were the optimal target cells. The optimal buffer conditions were: pH 8.0, ionic strength 0.06 mmol NaCl and 5mmol Mg2+ ion. Optimal incubation time and temperature were 75 min and 30 degrees C, respectively.

Animals↗

PubMed1993

The optimal current direction for excitation of human cervical motor roots with a double coil magnetic stimulator.

Upper limb muscles can easily be excited using magnetic stimulation with a circular coil over the cervical vertebrae. Double coil magnetic stimulators generate a more focal and directed form of stimulus and may offer an advantage in the more specific stimulation of individual motor roots. The aims of this study were to determine the optimal rostro-caudal locations and orientations of a double coil magnetic stimulator for excitation of the human 5th cervical to 1st thoracic motor roots. Compound muscle action potentials (CMAPs) evoked by magnetic stimuli were recorded from deltoid, brachioradialis, extensor digitorum communis and first dorsal interosseus muscles. Optimal rostro-caudal location was determined with the coil current flowing horizontally towards the midline. Optimal orientation was determined by rotating the coil in increments of 22.5 degrees about the optimal rostro-caudal location. In all subjects with all muscles examined, the best orientation was with the coil current flowing downwards towards the midline at a mean angle between 14.9 degrees and 27.6 degrees to the horizontal. Review of the anatomy of motor roots reveals a short upwardly directed segment within the intervertebral foramen and it is postulated that excitation occurs exclusively within this segment.

Action Potentials↗

PubMed1994

Differentiation of sensorimotor neuronal structures responsible for induction of motor evoked potentials, attenuation in detection of somatosensory stimuli, and induction of sensation of movement by mapping of optimal current directions.

Transcranial magnetic stimulation (TMS) of the sensorimotor cortex can evoke motor evoked potentials (MEPs), attenuation in detection of somatosensory stimuli (ADSS), and sensation of movement (SOM) referred to the same body part. In this study we tried to differentiate the substrates responsible for these effects. In 6 normal volunteers, TMS was applied with a nearly monopolar Dantec stimulator and a butterfly coil. Optimal scalp location and current direction were determined for induction of MEPs in abductor pollicis brevis (APB), first dorsal interosseous (FDI), and adductor digiti minimi (ADM); SOM in digits 2 and 5 in an ischemically paralyzed hand; and ADSS applied to digits 2 and 5. All 3 muscles' MEPs and SOM and ADSS in both digits were optimally activated from a single scalp position. In all subjects, optimal current directions for MEPs pointed anteriorly; those for ADSS and SOM pointed posteriorly. Optimal current directions showed the same progression in all subjects for MEPs (ADM, FDI, and APB from antero-lateral to antero-medial), ADSS (digit 5 postero-medial, 2 postero-lateral), and SOM (digit 1 through 5 postero-lateral to postero-medial). We conclude that neuronal networks targeting corticospinal neurons responsible for MEPs are different from those leading to SOM and ADSS (which could not be differentiated).

Adult↗

PubMed1990

Lung function analysis and optimization during artificial ventilation. A personal computer-based system.

In an intensive care unit a personal computer (PC) application for lung function analysis has been in use for 5 years. The PC system is applied to measure conventional and new parameters for diagnosis and therapy. The primary goal was to find parameters which could be used as optimization indices in optimal control systems for mechanical ventilation. Another clinical application of the PC system was as an automatic controller that stabilizes end-tidal CO2 concentration. The controller and the next application, the optimizer, could be integrated into an optimal control system. Such a system is described and a simulation trial of the integrated structure has demonstrated the potential.

Humans↗

PubMed1996

Studies on optimal dose and administration schedule of a hematopoietic stimulatory beta-(1,4)-linked mannan.

Several complex carbohydrates have been found to significantly stimulate hematopoiesis. CARN 750, a polydispersed beta-(1,4)-linked acetylated mannan isolated from the Aloe vera plant, has been shown to have activity in wound repair, to function as a antineoplastic, and to activate macrophages. We report, herein, the hematoaugmenting properties of CARN 750 and its optimal dose and timing of administration in an animal model of irradiation-induced myelosuppression. We observed that subcutaneous injections of 1 mg/animal of CARN 750 had equal or greater stimulatory activity for white blood cell (WBC) counts and spleen cellularity as well as on the absolute numbers of neutrophils, lymphocytes, monocytes and platelets than did higher or lower doses of CARN 750 or an optimal dose of granulocyte-colony stimulating factor (G-CSF). Hematopoietic progenitors, measured as interleukin-3-supported colony forming units-culture (CFU-C) and high proliferative potential colony-forming cells (HPP-CFC) assays, were similarly increased by CARN 750 in the spleen but not in the bone marrow. The frequency of splenic HPP-CFCs and absolute number of splenic HPP-CFCs and CFU-Cs were optimally increased by 1 mg/animal of CARN 750. In contrast, bone marrow cellularity, frequency and absolute number of HPP-CFCs and CFU-Cs had as a dosage optimum 2 mg/animal of CARN 750. These parameters were similarly increased by G-CSF. In studies to determine the optimal protocol for the administration of CARN 750 we found that the hematopoietic activity of CARN 750 increased with the frequency of administration. The greatest activity in myelosuppressed mice was observed for all hematopoietic parameters except the platelet number in mice receiving daily administration of 1 mg/animal of CARN 750 with activity equal to or greater than G-CSF.

Animals↗

PubMed1994

An optimal rule for screening subjects for clinical trials in the presence of within-person variability.

In screening subjects for a continuous variable, such as blood pressure (BP), for eligibility for clinical trials, multistage rules are often used to select subjects within a target range. Multiple readings may be taken over successive visits, and the subject must meet eligibility criteria at each visit. We present an optimal rule that minimizes the number of clinic visits needed per eligible subject or the overall number of screening visits needed to achieve a given sample size of eligible subjects. We illustrate these methods with the design of phase I of the Trials of Hypertension Prevention (TOHP), which attempts to identify subjects with mean diastolic BP in the range 80- < 90 mm Hg over three screening visits. The optimal rule requires only 73% of the visits needed with a no-screening rule in which all subjects are examined at each visit, and the average BP at all screening visits is used as a criterion. The optimal rule requires only 36% of visits needed in a more standard approach in which a subject must have an observed mean diastolic BP of 80- < 90 mm Hg on each of three consecutive visits. Alternatively, one may minimize the expected cost of screening per eligible subject when screening visits differ in cost. Examples are given of optimal rules with differing relative costs per visit.

Adult↗

PubMed1980

Optimization of the regular frequency of the heart in atrial fibrillation in relation to the cardiac output.

In atrial fibrillation an optimal frequency value has been derived to give the maximum cardiac output. A multiple, non-linear regression analysis of phasic aortic flow velocity in 12 patients with atrial fibrillation yields the parameters: (i) upper limiting frequency, fc; and (ii) 'optimal' frequency of the heart fo = fc/2. fo is defined at maximum cardiac output in resting conditions. An estimate of fc may be obtained from the carotid pulse tracing in a non-invasive way for the individual patient. The maximum cardiac output at fo ranges between 100% and 125% of the cardiac output was measured in the atrial fibrillatory state with irregular excitation of the ventricles. The greater the degree of irregularity of atrial fibrillation, the more expressed was the potential rise in cardiac output at the optimal regularization frequency. In chronic atrial fibrillation a regular excitation of the ventricles could be achieved by pharmacological agents, such as Verapamil or by ventricular pacing, without restitution of normal sinus rhythm. In critically ill patients with atrial fibrillation and the low cardiac output syndrome the heart rate should be adjusted to the individual cardiac output-related optimal frequency.

Aorta↗

PubMed1987

A computer model of evolutionary optimization.

Molecular evolution is viewed as a typical combinatorial optimization problem. We analyse a chemical reaction model which considers RNA replication including correct copying and point mutations together with hydrolytic degradation and the dilution flux of a flow reactor. The corresponding stochastic reaction network is implemented on a computer in order to investigate some basic features of evolutionary optimization dynamics. Characteristic features of real molecular systems are mimicked by folding binary sequences into unknotted two-dimensional structures. Selective values are derived from these molecular 'phenotypes' by an evaluation procedure which assigns numerical values to different elements of the secondary structure. The fitness function obtained thereby contains nontrivial long-range interactions which are typical for real systems. The fitness landscape also reveals quite involved and bizarre local topologies which we consider also representative of polynucleotide replication in actually occurring systems. Optimization operates on an ensemble of sequences via mutation and natural selection. The strategy observed in the simulation experiments is fairly general and resembles closely a heuristic widely applied in operations research areas. Despite the relative smallness of the system--we study 2000 molecules of chain length v = 70 in a typical simulation experiment--features typical for the evolution of real populations are observed as there are error thresholds for replication, evolutionary steps and quasistationary sequence distributions. The relative importance of selectively neutral or almost neutral variants is discussed quantitatively. Four characteristic ensemble properties, entropy of the distribution, ensemble correlation, mean Hamming distance and diversity of the population, are computed and checked for their sensitivity in recording major optimization events during the simulation.

Base Sequence↗

PubMed1993

The reliability of optimization under dose-volume limits.

PURPOSE: An optimization algorithm improves the distribution of dose among discrete points in tissues, but tolerance depends on the distribution of dose across a continuous volume. This report asks whether an exact algorithm can be completed when enough points are taken to accurately model a dose-volume constraint. METHODS AND MATERIALS: Trials were performed using a 3-dimensional model of conformal therapy of lung cancer. Trials were repeated with different limits placed on the fraction of lung which could receive > 20 Gy. Bounds were placed on cord dose and target dose inhomogeneity. A mixed integer algorithm was used to find a feasible set of beam weights which would maximize tumor dose. Tests of feasibility and optimality are introduced to check the solution accuracy. RESULTS: Solutions were optimal for points used to model tissues. An accuracy of 3-4% in a volume condition could be obtained with models of 450-600 points. The error improved to 2% with 800 points to model the lung. Solution times increased six-fold at this level of accuracy. CONCLUSION: The mixed integer method can find optimum weights which respect dose-volume conditions in usually acceptable times. If constraints are violated by an excessive amount, the optimization model should be rerun with more points.

Algorithms↗