Multi-axis fields boost SABRE hyperpolarization.

The inherently low signal-to-noise ratio of NMR and MRI is now being addressed by hyperpolarization methods. For example, iridium-based catalysts that reversibly bind both parahydrogen and ligands in solution can hyperpolarize protons (SABRE) or heteronuclei (X-SABRE) on a wide variety of ligands, using a complex interplay of spin dynamics and chemical exchange processes, with common signal enhancements between 103 and 104. This does not approach obvious theoretical limits, and further enhancement would be valuable in many applications (such as imaging mM concentration species in vivo). Most SABRE/X-SABRE implementations require far lower fields (µT-mT) than standard magnetic resonance (>1T), and this gives an additional degree of freedom: the ability to fully modulate fields in three dimensions. However, this has been underexplored because the standard simplifying theoretical assumptions in magnetic resonance need to be revisited. Here, we take a different approach, an evolutionary strategy algorithm for numerical optimization, multi-axis computer-aided heteronuclear transfer enhancement for SABRE (MACHETE-SABRE). We find nonintuitive but highly efficient multiaxial pulse sequences which experimentally can produce a sevenfold improvement in polarization over continuous excitation. This approach optimizes polarization differently than traditional methods, thus gaining extra efficiency.

Internal feedback in the cortical perception-action loop enables fast and accurate behavior.

Animals move smoothly and reliably in unpredictable environments. Models of sensorimotor control, drawing on control theory, have assumed that sensory information from the environment leads to actions, which then act back on the environment, creating a single, unidirectional perception-action loop. However, the sensorimotor loop contains internal delays in sensory and motor pathways, which can lead to unstable control. We show here that these delays can be compensated by internal feedback signals that flow backward, from motor toward sensory areas. This internal feedback is ubiquitous in neural sensorimotor systems, and we show how internal feedback compensates internal delays. This is accomplished by filtering out self-generated and other predictable changes so that unpredicted, actionable information can be rapidly transmitted toward action by the fastest components, effectively compressing the sensory input to more efficiently use feedforward pathways: Tracts of fast, giant neurons necessarily convey less accurate signals than tracts with many smaller neurons, but they are crucial for fast and accurate behavior. We use a mathematically tractable control model to show that internal feedback has an indispensable role in achieving state estimation, localization of function (how different parts of the cortex control different parts of the body), and attention, all of which are crucial for effective sensorimotor control. This control model can explain anatomical, physiological, and behavioral observations, including motor signals in the visual cortex, heterogeneous kinetics of sensory receptors, and the presence of giant cells in the cortex of humans as well as internal feedback patterns and unexplained heterogeneity in neural systems.

Prevalence and scalable control of localized networks.

The ability to control network dynamics is essential for ensuring desirable functionality of many technological, biological, and social systems. Such systems often consist of a large number of network elements, and controlling large-scale networks remains challenging because the computation and communication requirements increase prohibitively fast with network size. Here, we introduce a notion of network locality that can be exploited to make the control of networks scalable, even when the dynamics are nonlinear. We show that network locality is captured by an information metric and is almost universally observed across real and model networks. In localized networks, the optimal control actions and system responses are both shown to be necessarily concentrated in small neighborhoods induced by the information metric. This allows us to develop localized algorithms for determining network controllability and optimizing the placement of driver nodes. This also allows us to develop a localized algorithm for designing local feedback controllers that approach the performance of the corresponding best global controllers, while incurring a computational cost orders-of-magnitude lower. We validate the locality, performance, and efficiency of the algorithms in Kuramoto oscillator networks, as well as three large empirical networks: synchronization dynamics in the Eastern US power grid, epidemic spreading mediated by the global air-transportation network, and Alzheimer's disease dynamics in a human brain network. Taken together, our results establish that large networks can be controlled with computation and communication costs comparable to those for small networks.

Optimal transport and control of active drops.

Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here, we use optimal control theory to pose the problem of transporting a slender drop of an active fluid and determine the dynamical profile of the active stresses to move it with minimal viscous dissipation. By parametrizing the position and size of the drop using a low-order description based on lubrication theory, we uncover a natural "gather-move-spread" strategy that leads to an optimal bound on the maximum achievable displacement of the drop relative to its size. In the continuum setting, the competition between passive surface tension and active controls generates richer behavior with futile oscillations and complex drop morphologies that trade internal dissipation against the transport cost to select optimal strategies. Our work combines active hydrodynamics and optimal control in a tractable and interpretable framework and begins to pave the way for the spatiotemporal manipulation of active matter.

Optimal Control Costs of Brain State Transitions in Linear Stochastic Systems.

The brain is a system that performs numerous functions by controlling its states. Quantifying the cost of this control is essential as it reveals how the brain can be controlled based on the minimization of the control cost, and which brain regions are most important to the optimal control of transitions. Despite its great potential, the current control paradigm in neuroscience uses a deterministic framework and is therefore unable to consider stochasticity, severely limiting its application to neural data. Here, to resolve this limitation, we propose a novel framework for the evaluation of control costs based on a linear stochastic model. Following our previous work, we quantified the optimal control cost as the minimal Kullback-Leibler divergence between the uncontrolled and controlled processes. In the linear model, we established an analytical expression for minimal cost and showed that we can decompose it into the cost for controlling the mean and covariance of brain activity. To evaluate the utility of our novel framework, we examined the significant brain regions in the optimal control of transitions from the resting state to seven cognitive task states in human whole-brain imaging data of either sex. We found that, in realizing the different transitions, the lower visual areas commonly played a significant role in controlling the means, while the posterior cingulate cortex commonly played a significant role in controlling the covariances.SIGNIFICANCE STATEMENT The brain performs many cognitive functions by controlling its states. Quantifying the cost of this control is essential as it reveals how the brain can be optimally controlled in terms of the cost, and which brain regions are most important to the optimal control of transitions. Here, we built a novel framework to quantify control cost that takes account of stochasticity of neural activity, which is ignored in previous studies. We established the analytical expression of the stochastic control cost, which enables us to compute the cost in high-dimensional neural data. We identified the significant brain regions for the optimal control in cognitive tasks in human whole-brain imaging data.

Force Reserve Predicts Compensation in Reaching Movement with Induced Shoulder Strength Deficit.

Following events such as fatigue or stroke, individuals often move their trunks forward during reaching, leveraging a broader muscle group even when only arm movement would suffice. In previous work, we showed the existence of a 'force reserve' - a phenomenon where individuals, when challenged with a heavy weight, adjusted their motor coordination to preserve approximately 40% of their shoulder's force. Here, we investigated if such reserve can predict hip, shoulder, and elbow movements and torques resulting from an induced shoulder strength deficit. We engaged 20 healthy participants in a reaching task with incrementally heavier dumbbells, analyzing arm and trunk movements via motion capture and joint torques through inverse dynamics. We simulated these movements using an optimal control model of a 3-degree-of-freedom upper body, contrasting three cost functions: traditional sum of squared torques, a force reserve function incorporating a nonlinear penalty, and a normalized torque function. Our results demonstrate a clear increase in trunk movement correlated with heavier dumbbell weights, with participants employing compensatory movements to maintain a shoulder force reserve of approximately 40% of maximum torque. Simulations showed that while traditional and reserve functions accurately predicted trunk compensation, only the reserve function effectively predicted joint torques under heavier weights. These findings suggest that compensatory movements are strategically employed to minimize shoulder effort and distribute load across multiple joints in response to weakness. We discuss the implications of the force reserve cost function in the context of optimal control of human movements and its relevance for understanding of compensatory movements post-stroke.

Enhanced and robust contrast in CEST MRI: Saturation pulse shape design via optimal control.

PURPOSE: To employ optimal control for the numerical design of Chemical Exchange Saturation Transfer (CEST) saturation pulses to maximize contrast and stability against B 0 $$ {\mathrm{B}}_0 $$ inhomogeneities. THEORY AND METHODS: We applied an optimal control framework for the design pulse shapes for CEST saturation pulse trains. The cost functional minimized both the pulse energy and the discrepancy between the corresponding CEST spectrum and the target spectrum based on a continuous radiofrequency (RF) pulse. The optimization is subject to hardware limitations. In measurements on a 7 T preclinical scanner, the optimal control pulses were compared to continuous-wave and Gaussian saturation methods. We conducted a comparison of the optimal control pulses with Gaussian, block pulse trains, and adiabatic spin-lock pulses. RESULTS: The optimal control pulse train demonstrated saturation levels comparable to continuous-wave saturation and surpassed Gaussian saturation by up to 50 % in phantom measurements. In phantom measurements at 3 T the optimized pulses not only showcased the highest CEST contrast, but also the highest stability against field inhomogeneities. In contrast, block pulse saturation resulted in severe artifacts. Dynamic Bloch-McConnell simulations were employed to identify the source of these artifacts, and underscore the B 0 $$ {\mathrm{B}}_0 $$ robustness of the optimized pulses. CONCLUSION: In this work, it was shown that a substantial improvement in pulsed saturation CEST imaging can be achieved by using Optimal Control design principles. It is possible to overcome the sensitivity of saturation to B0 inhomogeneities while achieving CEST contrast close to continuous wave saturation.

Modelling optimal ligninolytic activity during plant litter decomposition.

A large fraction of plant litter comprises recalcitrant aromatic compounds (lignin and other phenolics). Quantifying the fate of aromatic compounds is difficult, because oxidative degradation of aromatic carbon (C) is a costly but necessary endeavor for microorganisms, and we do not know when gains from the decomposition of aromatic C outweigh energetic costs. To evaluate these tradeoffs, we developed a litter decomposition model in which the aromatic C decomposition rate is optimized dynamically to maximize microbial growth for the given costs of maintaining ligninolytic activity. We tested model performance against > 200 litter decomposition datasets collected from published literature and assessed the effects of climate and litter chemistry on litter decomposition. The model predicted a time-varying ligninolytic oxidation rate, which was used to calculate the lag time before the decomposition of aromatic C is initiated. Warmer conditions increased decomposition rates, shortened the lag time of aromatic C oxidation, and improved microbial C-use efficiency by decreasing the costs of oxidation. Moreover, a higher initial content of aromatic C promoted an earlier start of aromatic C decomposition under any climate. With this contribution, we highlight the application of eco-evolutionary approaches based on optimized microbial life strategies as an alternative parametrization scheme for litter decomposition models.

Optimal control in a magnetization-prepared rapid acquisition gradient-echo sequence.

This article proposes a numerical framework to determine the optimal magnetization preparation in a three-dimensional magnetization-prepared rapid gradient-echo (MP-RAGE) sequence to obtain the best achievable contrast between target tissues based on differences in their relaxation times. The benefit lies in the adaptation of the algorithm of optimal control, GRAdient Ascent Pulse Engineering (GRAPE), to the optimization of magnetization preparation in a cyclic sequence without full recovery between each cycle. This numerical approach optimizes magnetization preparation of an arbitrary number of radio frequency pulses to enhance contrast, taking into account the establishment of a steady state in the longitudinal component of the magnetization. The optimal control preparation offers an optimized mixed T 1 / T 2 contrast in this traditional T 1 -weighted sequence. To show the versatility of the proposed method, numerical and in vitro results are described. Examples of contrasts acquired on brain regions of a healthy volunteer are presented for potential applications at 3 T.

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.

Robust dual-angle T 1 $$ {T}_1 $$ measurement in magnetization transfer spectroscopy by time-optimal control.

Magnetization transfer spectroscopy relies heavily on the robust determination of T 1 $$ {T}_1 $$ relaxation times of nuclei participating in metabolic exchange. Challenges arise due to the use of surface RF coils for transmission (high B 1 + $$ {B}_1^{+} $$ variation) and the broad resonance band of most X nuclei. These challenges are particularly pronounced when fast T 1 $$ {T}_1 $$ mapping methods, such as the dual-angle method, are employed. Consequently, in this work, we develop resonance offset and B 1 + $$ {B}_1^{+} $$ robust excitation RF pulses for 31P magnetization transfer spectroscopy at 7T through ensemble-based time-optimal control. In our approach, we introduce a cost functional for designing robust pulses, incorporating the full Bloch equations as constraints, which are solved using symmetric operator splitting techniques. The optimal control design of the RF pulses developed demonstrates improved accuracy, desired phase properties, and reduced RF power when applied to dual-angle T 1 $$ {T}_1 $$ mapping, thereby improving the precision of exchange-rate measurements, as demonstrated in a preclinical in vivo study quantifying brain creatine kinase activity.

The optimal momentum of population growth and decline.

About 50 years ago, Keyfitz (1971) asked how much further a growing human population would increase if its fertility rate were immediately to be reduced to replacement level and remain there forever. The reason for demographic momentum is an age-structure inertia due to relatively many potential parents because of past high fertility. Although nobody expects such a miraculous reduction in reproductive behavior, a gradual decline in fertility in rapidly growing populations seems inevitable. As any delay in fertility decline to a stationary level leads to an increase in the momentum, it makes sense to think about the timing and the quantum of the reduction in reproduction. More specifically, we consider an intertemporal trade-off between costly pro- and anti-natalistic measures and the demographic momentum at the end of the planning period. This paper uses the McKendrick-von Foerster partial differential equation of age-structured population dynamics to study a sketched problem in a distributed parameter control framework. Among the results obtained by applying an appropriate extension of Pontryagin's Maximum Principle are the following: (i) monotony of adaptation efforts to net reproduction rate and convex decrease/concave increase (if initial net reproduction rate exceeds 1/is below 1); and (ii) oscillating efforts and reproduction rate if, additionally, the size of the total population does not deviate from a fixed level.

Selectively Probing the Magnetic Resonance Signals of γ-Aminobutyric Acid in Human Brains In Vivo.

BACKGROUND: Gamma-aminobutyric acid (GABA) is an inhibitory neurotransmitter in human brains, playing a role in the pathogenesis of various psychiatric disorders. Current methods have some non-neglectable shortcomings and noninvasive and accurate detection of GABA in human brains is long-term challenge. PURPOSE: To develop a pulse sequence capable of selectively detecting and quantifying the 1 H signal of GABA in human brains based on optimal controlled spin singlet order. STUDY TYPE: Prospective. SUBJECTS/PHANTOM: A phantom of GABA (pH = 7.3 ± 0.1) and 11 healthy subjects (5 females and 6 males, body mass index: 21 ± 3 kg/m2 , age: 25 ± 4 years). FIELD STRENGTH/SEQUENCE: 7 Tesla, 3 Tesla, GABA-targeted magnetic resonance spectroscopy (GABA-MRS-7 T, GABA-MRS-3 T), magnetization prepared two rapid acquisition gradient echoes sequence. ASSESSMENT: By using the developed pulse sequences applied on the phantom and healthy subjects, the signals of GABA were successfully selectively probed. Quantification of the signals yields the concentration of GABA in the dorsal anterior cingulate cortex (dACC) in human brains. STATISTICAL TESTS: Frequency. RESULTS: The 1 H signals of GABA in the phantom and in the human brains of healthy subjects were successfully detected. The concentration of GABA in the dACC of human brains was 3.3 ± 1.5 mM. DATA CONCLUSION: The developed pulse sequences can be used to selectively probe the 1 H MR signals of GABA in human brains in vivo. EVIDENCE LEVEL: 1 TECHNICAL EFFICACY STAGE: 1.

Control of Iron(II)-Tris(2,2'-Bipyridine) Light-Induced Excited-State Trapping via External Electromagnetic Fields.

Light-induced excited spin-state trapping reactions in iron pyridinic complexes allow the iron's low-to-high spin transition in a sub-picosecond timescale. Employing a recently developed model for [Fe(2,2'-bipyridine)3]2+ photochemical spin-crossover reaction in conjunction with quantum wavepacket dynamics, we explore the possibility of controlling the reaction through external electromagnetic fields, aiming at stabilizing the initial metal-to-ligand charge transfer states. We show that simple Gaussian-shaped electromagnetic fields have a minor effect on the population kinetics. However, introducing vibrationally excited initial wavepacket representations allows for maintaining the population trapped in the metal-to-ligand charge transfer states. Using optimal control theory, we propose an electromagnetic field shape that increases the lifetime of metal-to-ligand charge transfer states. These results open the route for controlling the iron photochemistry through the action of external electric fields.

Aß-protein polymerization in Alzheimer disease: Optimal control for nucleation parameter estimation.

In this paper, we are interested in the modeling of Alzheimer's disease from the angle of the amyloid cascade hypothesis, where the pathogenic agent is the Aß protein in its oligomeric form. The formation dynamics of this pathogenic form is modeled by a Becker-Doring type model where APP (Amyloid Precursor Protein) protein, after cleavage by specific enzymes, forms monomeric Aß proteins, which, by polymerization and/or nucleation, lead to the formation of oligomeric Aß. We propose an optimal control problem to estimate the rate of nucleation which seems to be at the base of this amyloid cascade hypothesis and for which no (experimental) measurement exists for the moment.

Optimal Control of Collective Electrotaxis in Epithelial Monolayers.

Epithelial monolayers are some of the best-studied models for collective cell migration due to their abundance in multicellular systems and their tractability. Experimentally, the collective migration of epithelial monolayers can be robustly steered e.g. using electric fields, via a process termed electrotaxis. Theoretically, however, the question of how to design an electric field to achieve a desired spatiotemporal movement pattern is underexplored. In this work, we construct and calibrate an ordinary differential equation model to predict the average velocity of the centre of mass of a cellular monolayer in response to stimulation with an electric field. We use this model, in conjunction with optimal control theory, to derive physically realistic optimal electric field designs to achieve a variety of aims, including maximising the total distance travelled by the monolayer, maximising the monolayer velocity, and keeping the monolayer velocity constant during stimulation. Together, this work is the first to present a unified framework for optimal control of collective monolayer electrotaxis and provides a blueprint to optimally steer collective migration using other external cues.

Optimal Control with RdCVFL for Degenerating Photoreceptors.

Both the rod and cone photoreceptors, along with the retinal pigment epithelium have been experimentally and mathematically shown to work interdependently to maintain vision. Further, the theoredoxin-like rod-derived cone viability factor (RdCVF) and its long form (RdCVFL) have proven to increase photoreceptor survival in experimental results. Aerobic glycolysis is the primary source of energy production for photoreceptors and RdCVF accelerates the intake of glucose into the cones. RdCVFL helps mitigate the negative effects of reactive oxidative species and has shown promise in slowing the death of cones in mouse studies. However, this potential treatment and its effects have never been studied in mathematical models. In this work, we examine an optimal control with the treatment of RdCVFL. We mathematically illustrate the potential this treatment might have for treating degenerative retinal diseases such as retinitis pigmentosa, as well as compare this to the results of an updated control model with RdCVF.

Making Your Own Luck: Weak Vertical Swimming Improves Dispersal Success for Coastal Marine Larvae.

Dispersive early life stages are common in nature. Although many dispersing organisms ("propagules") are passively moved by outside forces, some improve their chances of successful dispersal through weak movements that exploit the structure of the environment to great effect. The larvae of many coastal marine invertebrates, for instance, swim vertically through the water column to exploit depth-varying currents, food abundance, and predation risk. Several swimming behaviors and their effects on dispersal between habitats are characterized in the literature, yet it remains unclear when and why these behaviors are advantageous. We addressed this gap using a mathematical model of larval dispersal that scored how well behaviors allowed larvae to simultaneously locate habitats, avoid predators, and gather energy. We computed optimal larval behaviors through dynamic programming, and compared those optima against passive floating and three well documented behaviors from the literature. Optimal behaviors often (but not always) resembled the documented ones. However, our model predicted that the behaviors from the literature performed robustly well, if not optimally, across many conditions. Our results shed light on why some larval behaviors are widespread geographically and across species, and underscore the importance of carefully considering the weak movements of otherwise passive propagules when studying dispersal.

Optimal Rotation Age in Fast Growing Plantations: A Dynamical Optimization Problem.

Forest plantations are economically and environmentally relevant, as they play a key role in timber production and carbon capture. It is expected that the future climate change scenario affects forest growth and modify the rotation age for timber production. However, mathematical models on the effect of climate change on the rotation age for timber production remain still limited. We aim to determine the optimal rotation age that maximizes the net economic benefit of timber volume in a negative scenario from the climatic point of view. For this purpose, a bioeconomic optimal control problem was formulated from a system of Ordinary Differential Equations (ODEs) governed by the state variables live biomass volume, intrinsic growth rate, and area affected by fire. Then, four control variables were associated to the system, representing forest management activities, which are felling, thinning, reforestation, and fire prevention. The existence of optimal control solutions was demonstrated, and the solutions of the optimal control problem were also characterized using Pontryagin's Maximum Principle. The solutions of the model were approximated numerically by the Forward-Backward Sweep method. To validate the model, two scenarios were considered: a realistic scenario that represents current forestry activities for the exotic species Pinus radiata D. Don, and a pessimistic scenario, which considers environmental conditions conducive to a higher occurrence of forest fires. The optimal solution that maximizes the net benefit of timber volume consists of a strategy that considers all four control variables simultaneously. For felling and thinning, regardless of the scenario considered, the optimal strategy is to spend on both activities depending on the amount of biomass in the field. Similarly, for reforestation, the optimal strategy is to spend as the forest is harvested. In the case of fire prevention, in the realistic scenario, the optimal strategy consists of reducing the expenses in fire prevention because the incidence of fires is lower, whereas in the pessimistic scenario, the opposite is true. It is concluded that the optimal rotation age that maximizes the net economic benefit of timber volume in P. radiata plantations is 24 and 19 years for the realistic and pessimistic scenarios, respectively. This corroborates that the presence of fires influences the determination of the optimal rotation age, and as a consequence, the net economic benefit.

Modeling of Mouse Experiments Suggests that Optimal Anti-Hormonal Treatment for Breast Cancer is Diet-Dependent.

Estrogen receptor positive breast cancer is frequently treated with anti-hormonal treatment such as aromatase inhibitors (AI). Interestingly, a high body mass index has been shown to have a negative impact on AI efficacy, most likely due to disturbances in steroid metabolism and adipokine production. Here, we propose a mathematical model based on a system of ordinary differential equations to investigate the effect of high-fat diet on tumor growth. We inform the model with data from mouse experiments, where the animals are fed with high-fat or control (normal) diet. By incorporating AI treatment with drug resistance into the model and by solving optimal control problems we found differential responses for control and high-fat diet. To the best of our knowledge, this is the first attempt to model optimal anti-hormonal treatment for breast cancer in the presence of drug resistance. Our results underline the importance of considering high-fat diet and obesity as factors influencing clinical outcomes during anti-hormonal therapies in breast cancer patients.