Ultrashort echo time magnetic resonance elastography for quantification of the mechanical properties of short T2 tissues via optimal control-based radiofrequency pulses.

The aim of the current study is to demonstrate the feasibility of radiofrequency (RF) pulses generated via an optimal control (OC) algorithm to perform magnetic resonance elastography (MRE) and quantify the mechanical properties of materials with very short transverse relaxation times (T2 < 5 ms) for the first time. OC theory applied to MRE provides RF pulses that bring isochromats from the equilibrium state to a fixed target state, which corresponds to the phase pattern of a conventional MRE acquisition. Such RF pulses applied with a constant gradient allow to simultaneously perform slice selection and motion encoding in the slice direction. Unlike conventional MRE, no additional motion-encoding gradients (MEGs) are needed, enabling shorter echo times. OC pulses were implemented both in turbo spin echo (OC rapid acquisition with refocused echoes [RARE]) and ultrashort echo time (OC UTE) sequences to compare their motion-encoding efficiency with the conventional MEG encoding (classical MEG MRE). MRE experiments were carried out on agar phantoms with very short T2 values and on an ex vivo bovine tendon. Magnitude images, wave field images, phase-to-noise ratio (PNR), and shear storage modulus maps were compared between OC RARE, OC UTE, and classical MEG MRE in samples with different T2 values. Shear storage modulus values of the agar phantoms were in agreement with values found in the literature, and that of the bovine tendon was corroborated with rheometry measurements. Only the OC sequences could encode motion in very short T2 samples, and only OC UTE sequences yielded magnitude images enabling proper visualization of short T2 samples and tissues. The OC UTE sequence produced the best PNRs, demonstrating its ability to perform anatomical and mechanical characterization. Its success warrants in vivo confirmation in further studies.

A model-based strategy for the COVID-19 vaccine roll-out in the Philippines.

COVID-19 has affected millions of people worldwide, causing illness and death, and disrupting daily life while imposing a significant social and economic burden. Vaccination is an important control measure that significantly reduces mortality if properly and efficiently distributed. In this work, an age-structured model of COVID-19 transmission, incorporating an unreported infectious compartment, is developed. Three age groups are considered: young (0-19 years), adult (20-64 years), and elderly (65+ years). The transmission rate and reporting rate are determined for each group by utilizing the number of COVID-19 cases in the National Capital Region in the Philippines. Optimal control theory is employed to identify the best vaccine allocation to different age groups. Further, three different vaccination periods are considered to reflect phases of vaccination priority groups: the first, second, and third account for the inoculation of the elderly, adult and elderly, and all three age groups, respectively. This study could guide in making informed decisions in mitigating a population-structured disease transmission under limited resources.

Resource allocation in a PDE ecosystem model.

The effects of habitat heterogeneity on a diffusing population are investigated here. We formulate a reaction-diffusion system of partial differential equations to analyze the effect of resource allocation in an ecosystem with resource having its own dynamics in space and time. We show a priori estimates to prove the existence of state solutions given a control. We formulate an optimal control problem of our ecosystem model such that the abundance of a single species is maximized while minimizing the cost of inflow resource allocation. In addition, we show the existence and uniqueness of the optimal control as well as the optimal control characterization. We also establish the existence of an optimal intermediate diffusion rate. Moreover, we illustrate several numerical simulations with Dirichlet and Neumann boundary conditions with the space domain in 1D and 2D.

Optimal Shortcuts to Adiabatic Control by Lagrange Mechanics.

We combined an inverse engineering technique based on Lagrange mechanics and optimal control theory to design an optimal trajectory that can transport a cartpole in a fast and stable way. For classical control, we used the relative displacement between the ball and the trolley as the controller to study the anharmonic effect of the cartpole. Under this constraint, we used the time minimization principle in optimal control theory to find the optimal trajectory, and the solution of time minimization is the bang-bang form, which ensures that the pendulum is in a vertical upward position at the initial and the final moments and oscillates in a small angle range.

Longitudinal Predictive Control for Vehicle-Following Collision Avoidance in Autonomous Driving Considering Distance and Acceleration Compensation.

In response to the widespread adoption of vehicle-following systems in autonomous applications, the demand for collision warning to enable safer functionalities is increasing. This study provides an approach for automated vehicle guidance to follow the preceding vehicles longitudinally and puts emphasis on the performance of collision avoidance. The safety distance model is established, which contains a distance compensation algorithm to deal with the special case on curved roads. By introducing the algorithm of velocity and distance prediction, the collision risks are detected and measured in real time. The objective function is established based on optimal control theory to solve the desired following acceleration. The control system designed with the method of proportion integration differentiation combines throttle percentage and brake pressure as outputs to compensate acceleration. In the Carsim and Simulink co-simulation platform, the control system for longitudinal collision avoidance is simulated and analysed for four typical working conditions: the preceding vehicle drives at a constant speed on straight and curved roads, while the preceding vehicle drives at various speeds on straight and curved roads. The results validate the feasibility and effectiveness of the proposed method, which can be used for the longitudinal control of vehicle-following active collision avoidance.

Optimizing combination therapy in a murine model of HER2+ breast cancer.

Human epidermal growth factor receptor 2 positive (HER2+) breast cancer is frequently treated with drugs that target the HER2 receptor, such as trastuzumab, in combination with chemotherapy, such as doxorubicin. However, an open problem in treatment design is to determine the therapeutic regimen that optimally combines these two treatments to yield optimal tumor control. Working with data quantifying temporal changes in tumor volume due to different trastuzumab and doxorubicin treatment protocols in a murine model of human HER2+ breast cancer, we propose a complete framework for model development, calibration, selection, and treatment optimization to find the optimal treatment protocol. Through different assumptions for the drug-tumor interactions, we propose ten different models to characterize the dynamic relationship between tumor volume and drug availability, as well as the drug-drug interaction. Using a Bayesian framework, each of these models are calibrated to the dataset and the model with the highest Bayesian information criterion weight is selected to represent the biological system. The selected model captures the inhibition of trastuzumab due to pre-treatment with doxorubicin, as well as the increase in doxorubicin efficacy due to pre-treatment with trastuzumab. We then apply optimal control theory (OCT) to this model to identify two optimal treatment protocols. In the first optimized protocol, we fix the maximum dosage for doxorubicin and trastuzumab to be the same as the maximum dose delivered experimentally, while trying to minimize tumor burden. Within this constraint, optimal control theory indicates the optimal regimen is to first deliver two doses of trastuzumab on days 35 and 36, followed by two doses of doxorubicin on days 37 and 38. This protocol predicts an additional 45% reduction in tumor burden compared to that achieved with the experimentally delivered regimen. In the second optimized protocol we fix the tumor control to be the same as that obtained experimentally, and attempt to reduce the doxorubicin dose. Within this constraint, the optimal regimen is the same as the first optimized protocol but uses only 43% of the doxorubicin dose used experimentally. This protocol predicts tumor control equivalent to that achieved experimentally. These results strongly suggest the utility of mathematical modeling and optimal control theory for identifying therapeutic regimens maximizing efficacy and minimizing toxicity.

Connection between Inverse Engineering and Optimal Control in Shortcuts to Adiabaticity.

We consider fast high-fidelity quantum control by using a shortcut to adiabaticity (STA) technique and optimal control theory (OCT). Three specific examples, including expansion of cold atoms from the harmonic trap, atomic transport by moving harmonic trap, and spin dynamics in the presence of dissipation, are explicitly detailed. Using OCT as a qualitative guide, we demonstrate how STA protocols designed from inverse engineering method can approach with very high precision optimal solutions built about physical constraints, by a proper choice of the interpolation function and with a very reduced number of adjustable parameters.

Minimization of Entropy Generation Rate in Hydrogen Iodide Decomposition Reactor Heated by High-Temperature Helium.

The thermochemical sulfur-iodine cycle is a potential method for hydrogen production, and the hydrogen iodide (HI) decomposition is the key step to determine the efficiency of hydrogen production in the cycle. To further reduce the irreversibility of various transmission processes in the HI decomposition reaction, a one-dimensional plug flow model of HI decomposition tubular reactor is established, and performance optimization with entropy generate rate minimization (EGRM) in the decomposition reaction system as an optimization goal based on finite-time thermodynamics is carried out. The reference reactor is heated counter-currently by high-temperature helium gas, the optimal reactor and the modified reactor are designed based on the reference reactor design parameters. With the EGRM as the optimization goal, the optimal control method is used to solve the optimal configuration of the reactor under the condition that both the reactant inlet state and hydrogen production rate are fixed, and the optimal value of total EGR in the reactor is reduced by 13.3% compared with the reference value. The reference reactor is improved on the basis of the total EGR in the optimal reactor, two modified reactors with increased length are designed under the condition of changing the helium inlet state. The total EGR of the two modified reactors are the same as that of the optimal reactor, which are realized by decreasing the helium inlet temperature and helium inlet flow rate, respectively. The results show that the EGR of heat transfer accounts for a large proportion, and the decrease of total EGR is mainly caused by reducing heat transfer irreversibility. The local total EGR of the optimal reactor distribution is more uniform, which approximately confirms the principle of equipartition of entropy production. The EGR distributions of the modified reactors are similar to that of the reference reactor, but the reactor length increases significantly, bringing a relatively large pressure drop. The research results have certain guiding significance to the optimum design of HI decomposition reactors.

Embodied skillful performance: where the action is.

When someone masters a skill, their performance looks to us like second nature: it looks as if their actions are smoothly performed without explicit, knowledge-driven, online monitoring of their performance. Contemporary computational models in motor control theory, however, are instructionist: that is, they cast skillful performance as a knowledge-driven process. Optimal motor control theory (OMCT), as representative par excellence of such approaches, casts skillful performance as an instruction, instantiated in the brain, that needs to be executed-a motor command. This paper aims to show the limitations of such instructionist approaches to skillful performance. We specifically address the question of whether the assumption of control-theoretic models is warranted. The first section of this paper examines the instructionist assumption, according to which skillful performance consists of the execution of theoretical instructions harnessed in motor representations. The second and third sections characterize the implementation of motor representations as motor commands, with a special focus on formulations from OMCT. The final sections of this paper examine predictive coding and active inference-behavioral modeling frameworks that descend, but are distinct, from OMCT-and argue that the instructionist, control-theoretic assumptions are ill-motivated in light of new developments in active inference.

Disturbances Can Promote and Hinder Coexistence of Competitors in Ongoing Partner Choice Mutualisms.

Ecosystems are under threat from anthropogenic and natural disturbances, yet little is known about how these disturbances alter mutualistic interactions. Many mutualistic interactions are highly context dependent and dynamic due to "ongoing" partner choice, impeding our understanding of how disturbances might influence mutualistic systems. Previously we showed that in the absence of additional known mechanisms of competitive coexistence, mutualistic fungi can coexist in a system where the plant community associates dynamically with two empirically defined arbuscular mycorrhizal fungal types: a cheap kind that provides low nutrient benefits, and an expensive type that provides high nutrient benefits. We built on this framework to ask how disturbances of different types, frequencies, amplitudes, and predictabilities alter ongoing partner choice and thereby influence the coexistence of mutualists. We found that the effects of disturbances depend on the type, amplitude, and predictability of disturbances and, to a lesser extent, on their frequency. Disturbance can disrupt mutualist coexistence by enabling hosts more efficiently to exclude partners that behave as parasites. Disturbance can also promote coexistence by altering the strength and direction of consumer-resource interactions. Predicting the effects of disturbance on the mutualist community therefore requires us to understand better the consumer-resource relationships under various environmental conditions. We show how, through such context-dependent effects, disturbance and ongoing partner choice can together generate relative nonlinearity and investment in future benefit, introducing fluctuation-dependent mechanisms of competitive coexistence. Our findings support a broadening of the conceptual framework regarding disturbances and competition to include fluctuation-dependent mechanisms alongside the spatiotemporal intermediate disturbance hypothesis.

Optimizing the Timing and Composition of Therapeutic Phage Cocktails: A Control-Theoretic Approach.

Viruses that infect bacteria, i.e., bacteriophage or 'phage,' are increasingly considered as treatment options for the control and clearance of bacterial infections, particularly as compassionate use therapy for multi-drug-resistant infections. In practice, clinical use of phage often involves the application of multiple therapeutic phage, either together or sequentially. However, the selection and timing of therapeutic phage delivery remains largely ad hoc. In this study, we evaluate principles underlying why careful application of multiple phage (i.e., a 'cocktail') might lead to therapeutic success in contrast to the failure of single-strain phage therapy to control an infection. First, we use a nonlinear dynamics model of within-host interactions to show that a combination of fast intra-host phage decay, evolution of phage resistance amongst bacteria, and/or compromised immune response might limit the effectiveness of single-strain phage therapy. To resolve these problems, we combine dynamical modeling of phage, bacteria, and host immune cell populations with control-theoretic principles (via optimal control theory) to devise evolutionarily robust phage cocktails and delivery schedules to control the bacterial populations. Our numerical results suggest that optimal administration of single-strain phage therapy may be sufficient for curative outcomes in immunocompetent patients, but may fail in immunodeficient hosts due to phage resistance. We show that optimized treatment with a two-phage cocktail that includes a counter-resistant phage can restore therapeutic efficacy in immunodeficient hosts.

Modeling the impact of non-pharmaceutical interventions on the dynamics of novel coronavirus with optimal control analysis with a case study.

Coronavirus disease (COVID-19) is the biggest public health challenge the world is facing in recent days. Since there is no effective vaccine and treatment for this virus, therefore, the only way to mitigate this infection is the implementation of non-pharmaceutical interventions such as social-distancing, community lockdown, quarantine, hospitalization or self-isolation and contact-tracing. In this paper, we develop a mathematical model to explore the transmission dynamics and possible control of the COVID-19 pandemic in Pakistan, one of the Asian countries with a high burden of disease with more than 200,000 confirmed infected cases so far. Initially, a mathematical model without optimal control is formulated and some of the basic necessary analysis of the model, including stability results of the disease-free equilibrium is presented. It is found that the model is stable around the disease-free equilibrium both locally and globally when the basic reproduction number is less than unity. Despite the basic analysis of the model, we further consider the confirmed infected COVID-19 cases documented in Pakistan from March 1, till May 28, 2020 and estimate the model parameters using the least square fitting tools from statistics and probability theory. The results show that the model output is in good agreement with the reported COVID-19 infected cases. The approximate value of the basic reproductive number based on the estimated parameters is R 0 ≈ 1.87 . The effect of low (or mild), moderate, and comparatively strict control interventions like social-distancing, quarantine rate, (or contact-tracing of suspected people) and hospitalization (or self-isolation) of testing positive COVID-19 cases are shown graphically. It is observed that the most effective strategy to minimize the disease burden is the implementation of maintaining a strict social-distancing and contact-tracing to quarantine the exposed people. Furthermore, we carried out the global sensitivity analysis of the most crucial parameter known as the basic reproduction number using the Latin Hypercube Sampling (LHS) and the partial rank correlation coefficient (PRCC) techniques. The proposed model is then reformulated by adding the time-dependent control variables u 1(t) for quarantine and u 2(t) for the hospitalization interventions and present the necessary optimality conditions using the optimal control theory and Pontryagin's maximum principle. Finally, the impact of constant and optimal control interventions on infected individuals is compared graphically.

Assessing the potential of quantitative 2D HSQC NMR in 13C enriched living organisms.

In vivo Nuclear Magnetic Resonance (NMR) spectroscopy has great potential to interpret the biochemical response of organisms to their environment, thus making it an essential tool in understanding toxic mechanisms. However, magnetic susceptibility distortions lead to 1D NMR spectra of living organisms with lines that are too broad to identify and quantify metabolites, necessitating the use of 2D 1H-13C Heteronuclear Single Quantum Coherence (HSQC) as a primary tool. While quantitative 2D HSQC is well established, to our knowledge it has yet to be applied in vivo. This study represents a simple pilot study that compares two of the most popular quantitative 2D HSQC approaches to determine if quantitative results can be directly obtained in vivo in isotopically enriched Daphnia magna (water flea). The results show the perfect-HSQC experiment performs very well in vivo, but the decoupling scheme used is critical for accurate quantitation. An improved decoupling approach derived using optimal control theory is presented here that improves the accuracy of metabolite concentrations that can be extracted in vivo down to micromolar concentrations. When combined with 2D Electronic Reference To access In vivo Concentrations (ERETIC) protocols, the protocol allows for the direct extraction of in vivo metabolite concentrations without the use of internal standards that can be detrimental to living organisms. Extracting absolute metabolic concentrations in vivo is an important first step and should, for example, be important for the parameterization as well as the validation of metabolic flux models in the future.

Ultrafast (milliseconds), multidimensional RF pulse design with deep learning.

PURPOSE: Some advanced RF pulses, like multidimensional RF pulses, are often long and require substantial computation time because of a number of constraints and requirements, sometimes hampering clinical use. However, the pulses offer opportunities of reduced-FOV imaging, regional flip-angle homogenization, and localized spectroscopy, e.g., of hyperpolarized metabolites. Proposed herein is a novel deep learning approach to ultrafast design of multidimensional RF pulses with intention of real-time pulse updates. METHODS: The proposed neural network considers input maps of the desired excitation region of interest and outputs a single-channel, multidimensional RF pulse. The training library is, e.g., retrieved from a large image database, and the target RF pulses trained upon are calculated with a method of choice. RESULTS: A relatively simple neural network is enough to produce reliable 2D spatial-selective RF pulses of comparable performance to the teaching method. For binary regions of interest, the training library does not need to be vast; hence, reestablishment of the training library is not necessarily cumbersome. The predicted pulses were tested numerically and experimentally at 3 T. CONCLUSION: Relatively effortless training of multidimensional RF pulses, based on non-MRI-related inputs, but working in an MRI setting still, has been demonstrated. The prediction time of a few milliseconds renders real-time updates of advanced RF pulses possible.

Energy-Efficient Patching Strategy for Wireless Sensor Networks.

Wireless sensor networks (WSNs) are vulnerable to computer viruses. To protect WSNs from virus attack, the virus library associated with each sensor node must be updated in a timely way. This article is devoted to developing energy-efficient patching strategies for WSNs. First, we model the original problem as an optimal control problem in which (a) each control stands for a patching strategy, and (b) the objective functional to be optimized stands for the energy efficiency of a patching strategy. Second, we prove that the optimal control problem is solvable. Next, we derive the optimality system for solving the optimal control problem, accompanied with a few examples. Finally, we examine the effects of some factors on the optimal control. The obtained results help improve the security of WSNs.

Entropy Generation Rate Minimization for Methanol Synthesis via a CO2 Hydrogenation Reactor.

The methanol synthesis via CO2 hydrogenation (MSCH) reaction is a useful CO2 utilization strategy, and this synthesis path has also been widely applied commercially for many years. In this work the performance of a MSCH reactor with the minimum entropy generation rate (EGR) as the objective function is optimized by using finite time thermodynamic and optimal control theory. The exterior wall temperature (EWR) is taken as the control variable, and the fixed methanol yield and conservation equations are taken as the constraints in the optimization problem. Compared with the reference reactor with a constant EWR, the total EGR of the optimal reactor decreases by 20.5%, and the EGR caused by the heat transfer decreases by 68.8%. In the optimal reactor, the total EGRs mainly distribute in the first 30% reactor length, and the EGRs caused by the chemical reaction accounts for more than 84% of the total EGRs. The selectivity of CH3OH can be enhanced by increasing the inlet molar flow rate of CO, and the CO2 conversion rate can be enhanced by removing H2O from the reaction system. The results obtained herein are in favor of optimal designs of practical tubular MSCH reactors.

Dynamic preferential allocation to arbuscular mycorrhizal fungi explains fungal succession and coexistence.

Evidence accumulates about the role of arbuscular mycorrhizal (AM) fungi in shaping plant communities, but little is known about the factors determining the biomass and coexistence of several types of AM fungi in a plant community. Here, using a consumer-resource framework that treats the relationship between plants and fungi as simultaneous, reciprocal exploitation, we investigated what patterns of dynamic preferential plant carbon allocation to empirically-defined fungal types (on-going partner choice) would be optimal for plants, and how these patterns depend on successional dynamics. We found that ruderal AM fungi can dominate under low steady-state nutrient availability, and competitor AM fungi can dominate at higher steady-state nutrient availability; these are conditions characteristic of early and late succession, respectively. We also found that dynamic preferential allocation alone can maintain a diversity of mutualists, suggesting that on-going partner choice is a new coexistence mechanism for mutualists. Our model can therefore explain both mutualist coexistence and successional strategy, providing a powerful tool to derive testable predictions.

Mathematical model and intervention strategies for mitigating tuberculosis in the Philippines.

Tuberculosis (TB) is the sixth leading cause of morbidity and mortality in the Philippines. Although significant progress has been made in the detection and cure of TB under the Directly Observed Treatment Short Course, battling against the disease is still a burdensome task. It demands a concerted effort for specific and effective interventions. In this work, a mathematical TB model fitted to the Philippine data is developed to understand its transmission dynamics. Different control strategies such as distancing, latent case finding, case holding, active case finding controls, and combinations thereof are investigated within the framework of optimal control theory. This study proposes optimal control strategies for reducing the number of high-risk latent and infectious TB patients with minimum intervention implementation costs. Results suggest that distancing control is the most efficient control strategy when a single intervention is utilized. However, full scale employment of the distancing control measure is a daunting task. This burden can be circumvented by the combination of other control interventions. Our noble finding in this study is that enhancing active case finding control instead of case holding control together with distancing and latent case finding control is shown to have significant potential for curtailing the spread of TB in the Philippines.

Ultrashort Broadband Cooperative Pulses for Multidimensional Biomolecular NMR Experiments.

NMR spectroscopy at ultra-high magnetic fields requires improved radiofrequency (rf) pulses to cover the increased spectral bandwidth. Optimized 90° pulse pairs were introduced as Ramsey-type cooperative (Ram-COOP) pulses for biomolecular NMR applications. The Ram-COOP element provides broadband excitation with enhanced sensitivity and reduced artifacts even at magnetic fields >1.0 GHz 1 H Larmor frequency (23 T). A pair of 30 µs Ram-COOP pulses achieves an excitation bandwidth of 100 kHz with a maximum rf field of 20 kHz, more than three-fold improved compared to excitation by rectangular pulses. Ram-COOP pulses exhibit little offset-dependent phase errors and are robust to rf inhomogeneity. The performance of the Ram-COOP element is experimentally confirmed with heteronuclear multidimensional NMR experiments, applied to proteins and nucleic acids. Ram-COOP provides broadband excitation at low rf field strength suitable for application at current magnetic fields and beyond 23 T.

Exploring optimal control strategies in seasonally varying flu-like epidemics.

The impact of optimal control strategies in the context of seasonally varying infectious disease transmission remains a wide open research area. We investigate optimal control strategies for flu-like epidemics using an SIR (susceptible-infectious-recovered) type epidemic model where the transmission rate varies seasonally Specifically, we explore optimal control strategies using time-dependent treatment and vaccination as control functions alone or in combination. Optimal strategies and associated epidemic outcomes are contrasted for epidemics with constant and seasonal transmission rates. Our results show that the epidemic outcomes assessed in terms of the timing and size of seasonal epidemics subject to optimal control strategies are highly sensitive to various parameters including R0, the timing of the introduction of the initial number of infectious individuals into the population, the time at which interventions start, and the strength of the seasonal forcing that modulates the time-dependent transmission rate. Findings highlight the difficult challenge in predicting short-term epidemic impact in the context of seasonally varying infectious disease transmission with some interventions scenarios exhibiting larger epidemic size compared to scenarios without control interventions.