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Finding optimal vaccination strategies for pandemic influenza using genetic algorithms.

In the event of pandemic influenza, only limited supplies of vaccine may be available. We use stochastic epidemic simulations, genetic algorithms (GA), and random mutation hill climbing (RMHC) to find optimal vaccine distributions to minimize the number of illnesses or deaths in the population, given limited quantities of vaccine. Due to the non-linearity, complexity and stochasticity of the epidemic process, it is not possible to solve for optimal vaccine distributions mathematically. However, we use GA and RMHC to find near optimal vaccine distributions. We model an influenza pandemic that has age-specific illness attack rates similar to the Asian pandemic in 1957-1958 caused by influenza A(H2N2), as well as a distribution similar to the Hong Kong pandemic in 1968-1969 caused by influenza A(H3N2). We find the optimal vaccine distributions given that the number of doses is limited over the range of 10-90% of the population. While GA and RMHC work well in finding optimal vaccine distributions, GA is significantly more efficient than RMHC. We show that the optimal vaccine distribution found by GA and RMHC is up to 84% more effective than random mass vaccination in the mid range of vaccine availability. GA is generalizable to the optimization of stochastic model parameters for other infectious diseases and population structures.

Adolescent↗

Optimality models of phage life history and parallels in disease evolution.

Optimality models constitute one of the simplest approaches to understanding phenotypic evolution. Yet they have shortcomings that are not easily evaluated in most organisms. Most importantly, the genetic basis of phenotype evolution is almost never understood, and phenotypic selection experiments are rarely possible. Both limitations can be overcome with bacteriophages. However, phages have such elementary life histories that few phenotypes seem appropriate for optimality approaches. Here we develop optimality models of two phage life history traits, lysis time and host range. The lysis time models show that the optimum is less sensitive to differences in host density than suggested by earlier analytical work. Host range evolution is approached from the perspective of whether the virus should avoid particular hosts, and the results match optimal foraging theory: there is an optimal "diet" in which host types are either strictly included or excluded, depending on their infection qualities. Experimental tests of both models are feasible, and phages provide concrete illustrations of many ways that optimality models can guide understanding and explanation. Phage genetic systems already support the perspective that lysis time and host range can evolve readily and evolve without greatly affecting other traits, one of the main tenets of optimality theory. The models can be extended to more general properties of infection, such as the evolution of virulence and tissue tropism.

Animals↗

Optimal conservation strategy in fluctuating environments with species interactions: resource-enhancement of the native species versus extermination of the alien species.

Alien species are often a major threat to native species. We consider optimal conservation strategies for a population whose viability is affected both by an alien species (such as a competitor, a predator, or a pathogen) and by random fluctuations of the environment (e.g. precipitation, temperature). We assume that the survivorship of the native population can be improved by providing resources such as food and shelter, and also by an extermination effort that decreases the abundance of the alien species. These efforts decrease the extinction probability of the native population, but they are accompanied by economic costs. We search for the optimal strategy that minimizes the weighted sum of the extinction probability and the economic costs over a single year. We derive conditions under which investment should be made in both resource-enhancement and extermination, and examine how the optimal effort levels change with parameters. When the optimal strategy includes both types of efforts, the optimal extermination effort level turns out to be independent of the density and economic value of the native species, or the variance of the environmental fluctuation. Furthermore, the optimal resource-enhancement effort is then independent of the density of the alien species. However, the parameter dependencies greatly change if one of the efforts becomes zero. We also examine the situation in which the impact of the alien species is uncertain. The optimal extermination effort increases with the uncertainty of this impact except when the cost of extermination is very high.

Animals↗

Stochastic optimal therapy for enhanced immune response.

Therapeutic enhancement of humoral immune response to microbial attack is addressed as the stochastic optimal control of a dynamic system. Without therapy, the modeled immune response depends upon the initial concentration of pathogens in a simulated attack. Immune response can be augmented by agents that kill the pathogen directly, that stimulate the production of plasma cells or antibodies, or that enhance organ health. Using a generic mathematical model of immune response to the infection (i.e., of the dynamic state of the system), previous papers demonstrated optimal (open-loop) and neighboring-optimal (closed-loop) control solutions that defeat the pathogen and preserve organ health, given initial conditions that otherwise would be lethal [Optimal Contr. Appl. Methods 23 (2002) 91, Bioinformatics 18 (2002) 1227]. Therapies based on separate and combined application of the agents were derived by minimizing a quadratic cost function that weighted both system response and drug usage, providing implicit control over harmful side effects. Here, we focus on the effects that corrupted or incomplete measurements of the dynamic state may have on neighboring-optimal feedback control. Imperfect measurements degrade the precision of feedback adjustments to therapy; however, optimal state estimation allows the feedback strategy to be implemented with incomplete measurements and minimizes the expected effects of measurement error. Complete observability of the perturbed state for this four state example is provided by measurement of four of the six possible pairs of two variables, either set of three variables, or all four variables. The inclusion of state estimation extends the applicability of optimal control theory for developing new therapeutic protocols to enhance immune response.

Anti-Infective Agents↗

The empirical relationship between longevity and physical stature may be obscured by unobserved genetic diversity in the optimal metabolic rate.

It is hypothesized that an inheritable "optimal" metabolic rate is associated with the lowest attainable mortality risk, greatest attainable height (in youth) and a desirable body weight. Positive deviations from this rate are reflected in overweight and higher mortality, negative deviations in shorter stature (stunting), low body mass index (BMI), and higher mortality. In a heterogeneous population the optimal rate may differ among genotypes, and those with a higher optimal rate are the ones who can translate more energy intake into growth in height such that under optimal net-nutritional intake, they are able to reach a greater final adult height with a lower body mass index than genotypes with a lower optimal rate. Hence, the optimal height and weight - in terms of longevity - may differ substantially among genotypes, so that an empirical estimation of the relationship may be blurred in a heterogeneous society. Conversely, the "true" association (within genotypes) may be stronger than the measured one, which may have some implications for the contribution of the secular increase in human height to the rise in life expectancy or the optimal BMI in persons who experienced stunting in youth.

Adolescent↗

Intensity-modulated radiotherapy of breast cancer using direct aperture optimization.

BACKGROUND AND PURPOSE: To design a clinically reliable and efficient step-and-shoot IMRT delivery technique for the treatment of breast cancer using direct aperture optimization (DAO). Using DAO, segments are created and optimized within the same optimization process. PATIENTS AND METHODS: The DAO technique implemented in the Pinnacle treatment planning system, which is called direct machine parameter optimization (DMPO), was used to generate IMRT plans for twelve breast cancer patients. The prescribed dose was 50 Gy. Two DMPO plans were generated. The first approach uses DMPO only; the second technique combines DMPO with two predefined segments (DMPO(segm)), having shapes identical to the conventional tangential fields. The weight of these predefined segments is optimized simultaneously with DMPO. The DMPO plans were compared with normal two-step (TS) IMRT, creating segments after optimizing the intensity. RESULTS: Dose homogeneity within the target volume was 4.8+/-0.6, 4.3+/-0.5 and 3.8+/-0.5 Gy for the TS, DMPO and DMPO(segm) plans, respectively. Comparing the IMRT plans with an idealized dose distribution obtained using only beamlet optimization, the degradation of the dose distribution was less for the DMPO plans compared with the two-step IMRT approach. Furthermore, this degradation was similar for all patients, while for the two-step IMRT approach it was patient specific. CONCLUSIONS: An efficient step-and-shoot IMRT solution was developed for the treatment of breast cancer using DMPO combined with two predefined segments.

Algorithms↗

Is optimal paddle force applied during paediatric external defibrillation?

INTRODUCTION: Optimal paddle force minimises transthoracic impedance; a factor associated with increased defibrillation success. Optimal force for the defibrillation of children < or =10 kg using paediatric paddles has previously been shown to be 2.9 kgf, and for children >10 kg using adult paddles is 5.1 kgf. We compared defibrillation paddle force applied during simulated paediatric defibrillation with these optimal values. METHODS: 72 medical and nursing staff who would be expected to perform paediatric defibrillation were recruited from a University teaching hospital. Participants, blinded to the nature of the study, were asked to simulate defibrillation of an infant manikin (9 months of age) and a child manikin (6 years of age) using paediatric or adult paddles, respectively, according to guidelines. Paddle force (kgf) was measured at the time of simulated shock and compared with known optimal values. RESULTS: Median paddle force applied to the infant manikin was 2.8 kgf (max 9.6, min 0.6), with only 47% operators attaining optimal force. Median paddle force applied to the child manikin was 3.8 kgf (max 10.2, min 1.0), with only 24% of operators attaining optimal force. CONCLUSION: Defibrillation paddle force applied during paediatric defibrillation often falls below optimal values.

Body Weight↗

Codon optimization of the HIV-1 vpu and vif genes stabilizes their mRNA and allows for highly efficient Rev-independent expression.

Two HIV-1 accessory proteins, Vpu and Vif, are notoriously difficult to express autonomously in the absence of the viral Tat and Rev proteins. We examined whether the codon bias observed in the vpu and vif genes relative to highly expressed human genes contributes to the Rev dependence and low expression level outside the context of the viral genome. The entire vpu gene as well as the 5' half of the vif gene were codon optimized and the resulting open reading frames (ORFs) (vphu and hvif, respectively) were cloned in autonomous expression vectors under the transcriptional control of the CMV promoter. Codon optimization efficiently removed the expression block observed in the native genes and allowed high levels of Rev- and Tat-independent expression of Vpu and Vif. Most of the higher protein levels detected are accounted for by enhanced steady-state levels of the mRNA encoding the optimized species. Nuclear run-on experiments show for the first time that codon optimization has no effect on the rate of transcriptional initiation or elongation of the vphu mRNA. Instead, optimization of the vpu gene was found to stabilize the vphu mRNA in the nucleus and enhance its export to the cytoplasm. This was achieved by allowing the optimized mRNA to use a new CRM I-independent nuclear export pathway. This work provides a better understanding of the molecular mechanisms underlying the process of codon optimization and introduces novel tools to study the biological functions of the Vpu and Vif proteins independently of other viral proteins.

Cell Line↗

Comparison of economically optimized culling recommendations and actual culling decisions of Finnish Ayrshire cows.

Our purpose was to compare culling recommendations obtained from an economic-optimization model with actual culling of Finnish Ayrshire cows. The dynamic-programming (DP) model we used optimizes replacement and breeding decisions to maximize the net revenues from cows currently in a herd and their potential replacements over a 5-year decision horizon. Cows were described in the model by five state variables: parity, stage of lactation, month of calving, milk-production level, and days open (pregnancy status). We performed survival analysis to study the effects of those five factors on culling and to compare the actual culling of cows in December 1993 and June 1994 with the optimized replacement recommendations for the same months and for cows in the same herds. The risk of culling increased as a cow grew older, both in the actual herds and in the DP recommendations for December. In the optimized replacements for June, however, the age of a cow did not play a significant role. A cow that had been in milk > 270 days had a lower risk of culling than cows in earlier stages of lactation. When 305-day milk production increased by 100 kg, the risk of culling decreased by 4% in the actual herds and by 6 and 12% in the DP recommendations for June and December, respectively. When the days open lengthened by a month, the risk of culling was 2.0- and 1.6-times higher in the actual herds and 1.7- and 2.0-times higher in the DP recommendations for June and December, respectively. Month of calving had a different effect in the optimized recommendations compared with the real-life situation: cows calving from January to August had a lower risk of culling than cows calving in the fall in the actual herds, but the optimization model recommended heavier culling for cows calving between January and August. The DP did not account for diseases and did not allow replacements during the first 2 months of lactation and some of the observed differences could be due to this. However, the results suggested that Finnish farmers might not be taking full advantage of the seasonality in milk pricing and production to maximize the profits of their herds--even though their culling decisions are rational and in quite close agreement with the optimized recommendations.

Animals↗

On the optimization of drug release from multi-laminated polymer matrix devices.

This work presents a systematic optimization framework to achieve desired release rates in drug delivery devices using multi-laminated layers. A simple mathematical model is used to describe the transient mass transfer between successive layers, laminated together to form matrices with different initial concentrations, drug diffusivities and thickness. First, an efficient analytical-based optimization approach is investigated to define the optimal nonuniform initial drug distribution for constant diffusivity profile. The results obtained are in a good agreement with relevant work from the literature resorting to advanced optimal control techniques. Then, a formal dynamic optimization approach is employed, to systematically explore the synergistic benefits when all the available controllable parameters are simultaneously optimized, in order to achieve a drug release profile as close to a desired profile as possible for the entire period of operation. The optimization results lead to significantly improved constant release profiles.

Drug Delivery Systems↗

Effect of center of pressure and trunk center of mass optimization methods on the analysis of whole body lifting mechanics.

OBJECTIVE: This study evaluates methods to optimize the trunk center of mass position, the center of pressure position, or both to minimize the difference between horizontal location of the whole body center of mass estimated by the model and center of pressure measured during static postures. DESIGN: Within subjects repeated measures. BACKGROUND: Methods to optimize the trunk center of mass position have been proposed in the past, but have not been fully evaluated nor have accounted for errors in the location of the center of pressure. Accurately determining these locations affects the understanding of the control of balance. METHODS: Six methods were compared using kinematic and force plate data from 22 subjects. Static postures resembling both leg and back lifting techniques were used to optimize the center of mass. A typical lifting movement was used to evaluate the effectiveness of the methods in reducing the difference between external moment and time derivative of the angular momentum. RESULTS: Optimization of the center of pressure had a statistically significant effect on reducing errors (P<0.05), whereas optimization of the trunk center of mass alone had not (P>0.05). CONCLUSIONS: Optimizing the center of pressure was simple and compensated for systematic errors introduced from the model and instrumentation. The addition of the center of mass optimization improved some results but added much complexity to the experimental procedures. RELEVANCE: Reducing errors in determining the relative position of the center of pressure and center of mass enhances the understanding of balance control as this relationship reflects the dynamic stability of the system.

Adult↗

Intraoperative dynamic dose optimization in permanent prostate implants.

PURPOSE: With the advent of intraoperative optimized planning, the treatment of prostate cancer with permanent implants has reached an unprecedented level of dose conformity. However, because of well-documented (and unavoidable) inaccuracies in seed placement into the gland, carrying out a plan results in a large degree of variability relative to the intended dose distribution. This brings forth the need to periodically readjust the plan to allow for the real positions of seeds already implanted. In this paper, an algorithm for performing this task, hereby described as intraoperative dynamic dose optimization (IDDO), is presented and assessed. METHODS AND MATERIALS: The general scheme for performing IDDO consists of three steps: (1) at some point during the implant, coordinates of implanted seeds are identified; (2) seed images are projected onto the reference frame of the ultrasound images for planning; and (3) the plan is reoptimized. Work on the first two steps is reported elsewhere. Here, we focus on the strategy for implementing the reoptimization step. An optimal treatment plan is first obtained based on initial operating room-acquired ultrasound images. We analyze the sensitivity and effect of the IDDO procedure with respect to the total number of reoptimizations performed. Specifically, we consider reoptimizing 2, 3, and 4 times. When two reoptimizations are used, half of the seeds from the initial optimal plan are implanted. The first reoptimization is performed on the remaining possible seed positions, and all the seeds designated in this reoptimized plan are implanted. The second (final) reoptimization is done on the remaining unused seed positions to ensure 100% coverage of the gland and to eliminate possible cold spots in the gland. Similarly, when three reoptimization steps are used, one-third of the seeds from the initial optimized plan, one-half of the seeds from the first reoptimization, and all seeds from the second reoptimization are implanted. The third (final) reoptimization is performed to assist in eliminating possible cold spots. Reoptimizing four times proceeds in a like manner. Fifteen patient cases are used for comparison. Strict dose bounds of 100% and 120% of the prescription dose are imposed on the urethra, and 100% coverage is imposed on the prostate volume. To assist in achieving good conformity, prostate contour points are assigned a target upper dose bound of 150% of the prescription dose. RESULTS: A two-way comparison is performed: (a) initial optimized plan, (b) IDDO plan. Postimplant dose analysis, coverage and conformity measures, as well as actual dose received by urethra and rectum are used to gauge the results. The initial optimized plan consistently provides 93% prescription dose coverage to the gland with average conformity index of 1.32. The urethra dose ranges within 100% to 150%, and the maximum dose delivered to the rectum reaches 91% of the prescription dose. On average, about 50% of the urethra receives more than 120% of the prescription dose, and 19% of the rectum volume receives more than the 78% upper dose limit. For the IDDO plan, 100% postimplant coverage with 1.16 conformity is achieved. Urethra and rectum dose is maintained within the prescribed 100% to 120% range and 78% upper bound, respectively. CONCLUSIONS: With real-time treatment planning, it is possible to dynamically reoptimize treatment plans to account for actual seed positions (as opposed to planned positions) and needle-induced swelling to the gland during implantation. Postimplant analysis shows that the final seed configuration resulting from the IDDO method yields improved dosimetry. The algorithmic design ensures that one can achieve complete coverage while maintaining good conformity, thus sparing excess radiation to external tissue. The study also provides evidence of the possibility of morbidity reduction to urethra and rectum (because of reduced dose delivered to these structures) via the use of IDDO planning. Clinical studies are needed to validate the importance of our approach.

Algorithms↗

Optimization and characterization of controlled release multi-particulate beads formulated with a customized cellulose acetate butyrate dispersion.

The objectives of the present investigation were: (1) to model the effect of process and formulation variables viz., coating weight gain, duration of curing, and plasticizer concentration on in-vitro release profile of verapamil HCl from multi-particulate beads formulated with a novel aqueous-based pseudolatex dispersion; (2) to optimize the formulation by response surface methodology (RSM) and artificial neural network (ANN); and (3) to characterize the optimized product by thermal and X-ray analyses. Inert beads (Nupareil) were loaded with verapamil HCl and subsequently coated with a custom designed aqueous-based pseudolatex dispersion of cellulose acetate butyrate (CAB). Experiments were designed and data was collected according to a three factor, three level face centered central composite design. Data was analyzed for modeling and optimizing the release profile using both RSM and ANN. Model fitted the data and explained 90% of variability in response in the case of RSM and at least 70% in the case of ANN. Release profile was optimized for a zero-order model. Optimized formulations were prepared according to the factor combinations dictated by RSM and ANN. In each case, the observed drug release data of the optimized formulations was close to the predicted release pattern. However, the modeling and optimization abilities of RSM as evaluated by the R-squared values, were found to be higher than that of ANN. X-ray and drug content analysis suggested the absence of any degradation of verapamil HCl and excipients incorporated in the formulation.

Algorithms↗

Optimizing selection on multiple identified quantitative trait loci in population with overlapping generations.

A method was developed to model and optimize selection on multiple identified quantitative trait loci (QTLs) and polygenic estimated breeding value, in order to maximize a weighted sum of cumulative response to selection over multiple years in a population with overlapping generations. The model allows for a population with multiple sex-age classes, different number of age class between sires and dams, and varied genetic contribution of the age class. The optimization problem was formulated as a multiple-stage optimal control problem and solved by a forward and backward iteration loop. The practical utility of this method was illustrated in an example of pig breeding population with overlapping generations. The selection response of this method was compared with standard QTL selection and conventional best linear unbiased prediction (BLUP) selection. Simulation results show that optimal selection achieved greater selection response than either standard QTL or conventional BLUP selections. The influence of population structure on optimal selection was significant. Optimal QTL selection and standard QTL selection were more favorable in a population with overlapping generations than discrete generations, and obtained more benefits relative to conventional BLUP selection in a population with overlapping generations. Optimal QTL selection relative to conventional BLUP selection is also more favorable following increase of genetic contribution of two-year-old boars and sows in a population with overlapping generations.

Algorithms↗

Optimal pressure support level for beginning weaning in patients with COPD: measurement of diaphragmatic activity with step-by-step decreasing pressure support level.

PURPOSE: The study objective was to determine an "optimal" individual pressure support (PS) level for beginning weaning with PS ventilation in patients with chronic obstructive pulmonary disease (COPD). MATERIALS AND METHODS: Eleven COPD patients intubated and ventilated for acute respiratory failure and judged ready for weaning were studied. The technique consisted of lowering the PS level from a point that was characteristic for each patient and measurable under controlled mechanical ventilation, after setting the ventilator as recommended for COPD patients judged ready for weaning, that is, peak inflation pressure (PIP). This determination was based mainly on exploring the diaphragm with an electromyographic technique by defining the optimal PS level as the lowest PS level associated with no EMG evidence of diaphragmatic stress. Diaphragmatic electromyographic activity (diEMG) was recorded by a bipolar esophageal electrode (Disa-Denmark), and the high-frequency electrical component/low-frequency ratio (H/L) was calculated. The reference H/L was determined during a few spontaneous ventilatory cycles. Muscle stress was defined as a greater than 20% reduction in H/L compared with the reference value. RESULTS: Optimal PS levels ranged from 4 to 24 cm H2O with a mean of 14+/-6 cm H2O. Two patients with optimal PS level at 4 cm H2O did not require weaning and were quickly extubated. For the nine other patients, optimal PS levels were found to be 70% of PIP; in none was it necessary during weaning to use PS levels higher than individual optimal PS levels. CONCLUSIONS: Optimal PS level established with diEMG monitoring seems to be a useful index for beginning weaning in the PS ventilation mode in COPD patients. The hypothesis of beginning weaning with a PS level equal to 70% of PIP needs to be tested.

Aged↗

Improved optimization for the robust and accurate linear registration and motion correction of brain images.

Linear registration and motion correction are important components of structural and functional brain image analysis. Most modern methods optimize some intensity-based cost function to determine the best registration. To date, little attention has been focused on the optimization method itself, even though the success of most registration methods hinges on the quality of this optimization. This paper examines the optimization process in detail and demonstrates that the commonly used multiresolution local optimization methods can, and do, get trapped in local minima. To address this problem, two approaches are taken: (1) to apodize the cost function and (2) to employ a novel hybrid global-local optimization method. This new optimization method is specifically designed for registering whole brain images. It substantially reduces the likelihood of producing misregistrations due to being trapped by local minima. The increased robustness of the method, compared to other commonly used methods, is demonstrated by a consistency test. In addition, the accuracy of the registration is demonstrated by a series of experiments with motion correction. These motion correction experiments also investigate how the results are affected by different cost functions and interpolation methods.

Acoustic Stimulation↗

Is the breadth of individualized ranges of optimal anxiety (IZOF) equal for all athletes? A graphical method for establishing IZOF.

Recall and direct methods to determine the individual zone of optimal functioning (IZOF) cannot account for potential individual differences in the span of optimal anxiety. Accordingly, an attempt was made to test a graphical technique that could establish the span of optimal anxiety ranges for individuals. State anxiety (STAI; Spielberger, Gorusch, & Lushene, 1970; and CSAI-2; Martens, Burton, Vealey, Bump, & Smith, 1990) was assessed before competitions (10 to 20) in six Spanish golfers during a season. Performance in each match was determined using golf scores and self-ratings. Optimal anxiety ranges were established graphically by plotting individual scores of precompetition anxiety against individual performance values. Optimal ranges were also determined using Hanin's (1986, 1989) direct and recall methods. The efficacy of each method was contrasted by comparing performance between cases in which the golfers possessed optimal or non-optimal anxiety according to each method. More of the golfers performed better when competing within an IZOF established with the graphic procedures than with the other methods.

Adolescent↗

Optimization of a microfluidic mixer for studying protein folding kinetics.

We have applied an optimization method in conjunction with numerical simulations to minimize the mixing time of a microfluidic mixer developed for protein folding studies. The optimization method uses a semideterministic algorithm to find the global minimum of the mixing time by varying the mixer geometry and flow conditions. We describe the minimization problem and constraints and give a brief overview of the optimization algorithm. We present results of the optimization, including the optimized geometry and parameter sensitivities, and we demonstrate the improvement in mixing performance with experiments using microfabricated mixers. The dye-quenching experiments of the original and optimized mixer designs show respective mixing times of 7 and 4 mus, a 40% reduction. The new design also provides more uniform mixing across streamlines that enter the mixer. The optimized mixer is the fastest reported continuous flow mixer for protein folding.

Kinetics↗