Fast numerical design of spatial-selective rf pulses in MRI using Krotov and quasi-Newton based optimal control methods

The use of increasingly strong magnetic fields in magnetic resonance imaging (MRI) improves sensitivity, susceptibility contrast, and spatial or spectral resolution for functional and localized spectroscopic imaging applications. However, along with these benefits come the challenges of increasing static field (B(0)) and rf field (B(1)) inhomogeneities induced by radial field susceptibility differences and poorer dielectric properties of objects in the scanner. Increasing fields also impose the need for rf irradiation at higher frequencies which may lead to elevated patient energy absorption, eventually posing a safety risk. These reasons have motivated the use of multidimensional rf pulses and parallel rf transmission, and their combination with tailoring of rf pulses for fast and low-power rf performance. For the latter application, analytical and approximate solutions are well-established in linear regimes, however, with increasing nonlinearities and constraints on the rf pulses, numerical iterative methods become attractive. Among such procedures, optimal control methods have recently demonstrated great potential. Here, we present a Krotov-based optimal control approach which as compared to earlier approaches provides very fast, monotonic convergence even without educated initial guesses. This is essential for in vivo MRI applications. The method is compared to a second-order gradient ascent method relying on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method, and a hybrid scheme Krotov-BFGS is also introduced in this study. These optimal control approaches are demonstrated by the design of a 2D spatial selective rf pulse exciting the letters "JCP" in a water phantom.     

Controlling dynamics in diatomic systems

Controlling molecular energetics using laser pulses is exemplified for nuclear motion in two different diatomic systems. The problem of finding the optimized field for maximizing a desired quantum dynamical target is formulated using an iterative method. The method is applied for two diatomic systems, HF and OH. The power spectra of the fields and evolution of populations of different vibrational states during transitions are obtained.     

Upper and lower bounds on the control field and the quality of achieved optimally controlled quantum molecular motion

A large class of problems in optimally controlled quantum or classical molecular dynamics has multiple solutions for the control field amplitude. A denumerably infinite number of solutions may exist depending on the structure of the design cost functional. This fact has been recently proved with the aid of perturbation theory by considering the electric field as the perturbating agent. In carrying out this analysis, an eigenvalue (i.e., a spectral parameter) appears which gives the degree of deviation of the control objective from its desired value. In this work, we develop a scheme to construct upper and lower bounds for the field amplitude and spectral parameter for each member of the denumerably infinite set of control solutions. The bounds can be tightened if desired. The analysis here is primarily restricted to the weak field regime, although the bounds for the strong field nonlinear case are also presented.     

Photochromic Fentanyl Derivatives for Controlled μ-Opioid Receptor Activation

Photoswitchable ligands as biological tools provide an opportunity to explore the kinetics and dynamics of the clinically relevant μ-opioid receptor. These ligands can potentially activate or deactivate the receptor when desired by using light. Spatial and temporal control of biological activity allows for application in a diverse range of biological investigations. Photoswitchable ligands have been developed in this work, modelled on the known agonist fentanyl, with the aim of expanding the current “toolbox” of fentanyl photoswitchable ligands. In doing so, ligands have been developed that change geometry (isomerize) upon exposure to light, with varying photophysical and biochemical properties. This variation in properties could be valuable in further studying the functional significance of the μ-opioid receptor.     

Molecular Property Optimizations with Boundary Conditions through the Best First Search Scheme

There is an increasing interest in applying quantum chemistry to rationally design novel compounds with some desired characteristics. Furthermore, many applications require more than one property to be optimal. In this Concept, several inverse design strategies, based on the discrete best first search scheme, are introduced that allow for the simultaneous optimization of multiple properties or the optimization of the most vital target property with constraints for secondary properties. A detailed assessment of the different optimization techniques is carried out, and special attention is paid to improve the cost efficacy and performance by tuning the process parameters. Our suggested protocol allows for a more successful optimization routine when additional boundary conditions are desired.     

Subnanometer size uncapped quantum dots via electroporation of synthetic vesicles

The very rapid, usually diffusion-controlled, self-aggregation of nascent molecules of semiconductors (MX) or metals (M) in solution represents an experimental challenge for arresting the growth of the particles at a desired size. Unfortunately, the typical remedy used, namely capping of the clusters with a protective coating, alters their intrinsic electronic and optical properties. An additional defect of capping's virtue is that it prevents the observation of further cluster growth—which is especially important in the subnanometer (molecular) size regime, where particle growth is associated with dramatic changes in structure, surface states, and transition energy.

We have developed a novel method for the preparation of subnanometer size uncapped quantum dots, which also allows the monitoring of their growth up to several hundreds of nanometer in diameter. The essence of the method is the initial encapsulation of the metal ion (M⁺) in synthetic vesicles (liposomes) and the placement of the anion (X⁻) in the bulk solution. Exposure of the suspension to a rectangular pulse of a high-voltage homogenous electric field E of suitable intensity and duration causes the formation of transient pores in the vesicle's bilayer (electroporation). A fraction of the metal ions that are ejected through the pores react with the anions in the bulk, and the freshly created monomers (MX) adsorb on the exterior surface of the vesicle. On the vesicle surface, the self-aggregation is slowed down to the hour and day timescales which allows for convenient spectral monitoring of the growth of the clusters.

The discussion will focus on the behavior of vesicles in an electric field, the mechanism of electroporation, and our experimental and density functional theoretical findings of previously unobserved, unusual spectroscopic properties of subnanometer size AgBr, CdS, PbS, ZnS and gold quantum dots.     

Feasibility of encoding Shor's algorithm into the motional states of an ion in the anharmonic trap

We demonstrate theoretically that it may be possible to encode states of a multi-qubit system into the progression of quantized motional∕vibrational levels of an ion trapped in a weakly anharmonic potential. Control over such register of quantum information is achieved by applying oscillatory radio-frequency fields shaped optimally for excitation of the desired state-to-state transitions. Anharmonicity of the vibrational spectrum plays a key role in this approach to the control and quantum computation, since it allows resolving different state-to-state transitions and addressing them selectively. Optimal control theory is used to derive pulses for implementing the four-qubit version of Shor's algorithm in a single step. Accuracy of the qubit-state transformations, reached in the numerical simulations, is around 0.999. Very detailed insight is obtained by analysis of the time-evolution of state populations and by spectral analysis of the optimized pulse.     

A method to evaluate economical carrier-mediated transport across the biological membrane by the optimal control principle

We propose an optimal control strategy for carrier-mediated transport across biological membranes in an attempt to evaluate the functions quantitatively and to create an artificial membrane. The transport system was described by the substrate, unloaded and loaded forms of the carrier where the binding sites were facing to the outside and inside of the membrane with the corresponding control inputs. The temporal behavior of the transport was expressed by a linear four-states model employing the conservation law. We assigned the state variables for the concentrations of the loaded and unloaded carriers on both sides of the unit membrane area. Two control inputs were set on each individual state variable so as to describe the producing and converting processes. The cost function to evaluate the performance of the transport involved the temporal static concentration changes in the loaded and unloaded carriers and the control inputs for driving the system. Minimizing this cost function resulted in a smooth and non wasteful transport with the least energy consumption. The relative magnitude of minimizing these quantities was characterized by the weighting coefficients and we defined that the optimal transport state is achieved when this cost function has been minimized. We utilized reported experimental data of Na/glucose cotransport for the initial condition and rate constants. Since transport by the carrier is a recycling process, we set a rigorous terminal condition as the target state for the optimally controlled transport. The optimized system equations and co-state equations were solved numerically as a multiple points boundary value problem. The influences of a given weighting coefficient were observed not only on the time course of its proper variable but extended to those of other variables. The changes in the time course could be explained by the compensatory action of the optimized control input so as to prevent excessive increase or decrease of the materials. Finally we showed the successful simulation of experimental data by the present method. The present method is available for evaluating the function of biological transport and for creating an artificial membrane.     

The effective local potential method: implementation for molecules and relation to approximate optimized effective potential techniques

We have recently formulated a new approach, named the effective local potential (ELP) method, for calculating local exchange-correlation potentials for orbital-dependent functionals based on minimizing the variance of the difference between a given nonlocal potential and its desired local counterpart [V. N. Staroverov et al., J. Chem. Phys. 125, 081104 (2006)]. Here we show that under a mildly simplifying assumption of frozen molecular orbitals, the equation defining the ELP has a unique analytic solution which is identical with the expression arising in the localized Hartree-Fock (LHF) and common energy denominator approximations (CEDA) to the optimized effective potential. The ELP procedure differs from the CEDA and LHF in that it yields the target potential as an expansion in auxiliary basis functions. We report extensive calculations of atomic and molecular properties using the frozen-orbital ELP method and its iterative generalization to prove that ELP results agree with the corresponding LHF and CEDA values, as they should. Finally, we make the case for extending the iterative frozen-orbital ELP method to full orbital relaxation.     

Understanding optimal control results by reducing the complexity

Deciphering control mechanisms from control pulse structures found in closed-loop learning experiments is often complicated due to the complexity of the pulse structure. Simplification of pulse forms is demonstrated by systematically reducing the complexity of the search space, applied on the model-like multi-photon ionization of NaK. Reducing the pulse complexity leads to the exclusion of participating excited states, thereby restricting the involved pathways. The phase function is parameterized by a sinusoidal spectral phase modulation, whose parameters are investigated with respect to the yield and the obtained optimal field. By progressively reducing the number of parameters and thereby the complexity of the phase modulation, control pulses are generated which are more and more reduced to the molecule’s primary dynamical properties. This enables to find optimized control pulses that can be subject to a simple intuitive interpretation.     

Effect of diatomic molecular properties on binary laser pulse optimizations of quantum gate operations

The importance of the ro-vibrational state energies on the ability to produce high fidelity binary shaped laser pulses for quantum logic gates is investigated. The single frequency 2-qubit ACNOT(1) and double frequency 2-qubit NOT(2) quantum gates are used as test cases to examine this behaviour. A range of diatomics is sampled. The laser pulses are optimized using a genetic algorithm for binary (two amplitude and two phase parameter) variation on a discretized frequency spectrum. The resulting trends in the fidelities were attributed to the intrinsic molecular properties and not the choice of method: a discretized frequency spectrum with genetic algorithm optimization. This is verified by using other common laser pulse optimization methods (including iterative optimal control theory), which result in the same qualitative trends in fidelity. The results differ from other studies that used vibrational state energies only. Moreover, appropriate choice of diatomic (relative ro-vibrational state arrangement) is critical for producing high fidelity optimized quantum logic gates. It is also suggested that global phase alignment imposes a significant restriction on obtaining high fidelity regions within the parameter search space. Overall, this indicates a complexity in the ability to provide appropriate binary laser pulse control of diatomics for molecular quantum computing.     

Designing the plasmonic response of shell nanoparticles: spectral representation

A spectral representation formalism in the quasistatic limit is developed to study the optical response of nanoparticles, such as nanospheres, nanospheroids, and concentric nanoshells. A transfer matrix theory is formulated for systems with an arbitrary number of shells. The spectral representation formalism allows us to analyze the optical response in terms of the interacting surface plasmons excited at the interfaces by separating the contributions of the geometry from those of the dielectric properties of each shell and surroundings. Neither numerical nor analytical methods can do this separation. These insights into the physical origin of the optical response of multishelled nanoparticles are very useful for engineering systems with desired properties for applications in different fields ranging from materials science and electronics to medicine and biochemistry.     

PLUMS: a program for the rapid optimization of focused libraries

PLUMS is a new method to perform rational monomer selection for combinatorial chemistry libraries. The algorithm has been developed to optimize focused libraries with specific two-dimensional and/or three-dimensional properties. A preliminary step is the identification of those molecules in the initial virtual library which satisfy the imposed property constraints; we define these molecules as the virtual hits. From the virtual hits, PLUMS generates a starting library, which is the true combinatorial library that includes all the virtual hits. Monomers are then removed in an iterative fashion, thus reducing the size of the library. At each iteration, the worst monomer is removed. Each sublibrary is selected using a global scoring function, which balances effectiveness and efficiency. The iterative process continues until one is left with a library that consists entirely of virtual hits. The optimal library, which is the best compromise between effectiveness and efficiency, can then be selected according to the score. During the iterative process, equivalent solutions may well occur and are taken into account by the algorithm, according to a user-defined parameter. The number of monomers for each substitution site and the size of the library are parameters that can be either optimized or used to constrain the selection. The results obtained on two test libraries are presented. PLUMS was compared with genetic algorithms (GA) and monomer frequency analysis (MFA), which are widely used for monomer selection. For the two test libraries, PLUMS and GA gave equivalent results. MFA is the fastest method, but it can give misleading solutions. Possible advantages and disadvantages of the different methods are discussed.     

Controlling gas-phase reactions for efficient charge reduction electrospray mass spectrometry of intact proteins

Charge reduction electrospray mass spectrometry (CREMS) reduces the charge states of electrospray-generated ions, which concentrates the ions from a protein into fewer peaks spread over a larger m/z range, thereby increasing peak separation and decreasing spectral congestion. An optimized design for a CREMS source is described that provides an order-of-magnitude increase in sensitivity compared to previous designs and provides control over the extent of charge reduction. Either a corona discharge or an alpha-particle source was employed to generate anions that abstract protons from electrosprayed protein cations. These desired ion/ion proton transfer reactions predominated, but some oxidation and ion-attachment reactions also occurred, leading to new peaks or mass-shifted broader peaks while decreasing signal intensity. The species producing these deleterious side-reactions were identified, and conditions were found that prevented their formation. Spectrometer m/z biases were examined because of their effect upon the signal intensity of higher m/z charge-reduced protein ions. The utility of this atmospheric pressure CREMS was demonstrated using a cell lysate fraction from E. coli. The spectral simplification afforded by CREMS reveals more proteins than are observed without charge reduction.     

A new computational method for estimating X-ray spectral distributions

A new computational method is described for estimating the exposure-rate spectral distributions of X-rays from attenuation data measured with various filtrations. The estimation problem of X-ray spectra is formulated as the numerical computation of solving a set of linear equation with an ill-conditional nature. In this paper, the singular-value decomposition technique, which differs from the iterative method, is applied to this singular numerical computation problem. The principle of the analysis method is based on that the response matrix of filtrations can be decomposed into some inherent component matrices. X-ray spectral distributions are then represented in a simple combination of some component curves, so that the estimation process can be systematically constructed. The singularity in its computation is removed by selecting the components of the combination, and a performance index is also presented for the optimal selection. The feasibility of the proposed method is studied in detail in a computer simulation using a hypothetical X-ray spectrum produced by assuming experimental conditions. The application results are also shown about the spectral distribution from a 140 kV constant voltage X-ray source.     

Photolytic control of peptide self-assembly

Herein, we present a methodology that allows for the temporal control of fibrillization of amyloidogenic peptides. This general approach implements a photolabile linker that connects the amyloidogenic peptide to a fibril-inhibitory unit, in this case, a pentamer of amino acids modified with the solubilizing N,N-dimethylethylenediamine (DMDA) units. Upon photolysis, the linker can be dissociated to afford the intact and native amyloidogenic peptide. This methodology should be of value in a variety of studies where spatial and temporal control of supramolecular association processes is desired.     

Coherent control of pump-probe signals of helical structures by adaptive pulse polarizations

The simplification of the pump-probe spectrum of excitons by pure-phase-polarization pulse shaping is investigated by a simulation study. The state of light is manipulated by varying the phases of two perpendicular polarization components of the pump, holding its total spectral and temporal intensity profiles fixed. Genetic and iterative Fourier transform algorithms are used to search for pulse phase functions that optimize the ratio of the signal at two frequencies. New features are extracted from the congested pump-probe spectrum of a helical pentamer by selecting a combination of Liouville space pathways. Tensor components which dominate the optimized spectra are identified.     

Investigation of optimized experimental parameters including laser wavelength for boron measurement in photovoltaic grade silicon using laser-induced breakdown spectroscopy

The quantification of boron and other impurities in photovoltaic grade silicon was investigated using the LIBS technique with attention to the laser wavelength employed, temporal parameters, and the nature of the ambient gas. The laser wavelength was found to have a moderate effect on the performance of the process, while the type of purge gas and temporal parameters had a strong effect on the signal-to-background ratio (SBR) of the boron spectral emission, which was used to determine the boron concentration in silicon. The three parameters are not independent, meaning that for each different purge gas, different optimal temporal parameters are observed. Electron density was also calculated from Stark broadening of the 390.5 nm silicon emission line in order to better understand the different performances observed when using different gases and gating parameters. Calibration curves were made for boron measurement in silicon using certified standards with different purge gases while using the temporal parameters which had been optimized for that gas. By comparing the calibration curves, it was determined that argon is superior to helium or air for use as the analysis chamber purge gas with an UV laser.