A deep learning approach for converting prompt gamma images to proton dose distributions: A Monte Carlo simulation study

PurposeIn proton therapy, imaging prompt gamma (PG) rays has the potential to verify proton dose (PD) distribution. Despite the fact that there is a strong correlation between the gamma-ray emission and PD, they are still different in terms of the distribution and the Bragg peak (BP) position. In this work, we investigated the feasibility of using a deep learning approach to convert PG images to PD distributions.MethodsWe designed the Monte Carlo simulations using 20 digital brain phantoms irradiated with a 100-MeV proton pencil beam. Each phantom was used to simulate 200 pairs of PG images and PD distributions. A convolutional neural network based on the U-net architecture was trained to predict PD distributions from PG images.ResultsOur simulation results show that the pseudo PD distributions derived from the corresponding PG images agree well with the simulated ground truths. The mean of the BP position errors from each phantom was less than 0.4 mm. We also found that 2000 pairs of PG images and dose distributions would be sufficient to train the U-net. Moreover, the trained network could be deployed on the unseen data (i.e. different beam sizes, proton energies and real patient CT data).ConclusionsOur simulation study has shown the feasibility of predicting PD distributions from PG images using a deep learning approach, but the reliable prediction of PD distributions requires high-quality PG images. Image-degrading factors such as low counts and limited spatial resolution need to be considered in order to obtain high-quality PG images.     

The mechanical unfolding of ubiquitin through all-atom Monte Carlo simulation with a Go-type potential

The mechanical unfolding of proteins under a stretching force has an important role in living systems and is a logical extension of the more general protein folding problem. Recent advances in experimental methodology have allowed the stretching of single molecules, thus rendering this process ripe for computational study. We use all-atom Monte Carlo simulation with a Gō-type potential to study the mechanical unfolding pathway of ubiquitin. A detailed, robust, well-defined pathway is found, confirming existing results in this vein though using a different model. Additionally, we identify the protein's fundamental stabilizing secondary structure interactions in the presence of a stretching force and show that this fundamental stabilizing role does not persist in the absence of mechanical stress. The apparent success of simulation methods in studying ubiquitin's mechanical unfolding pathway indicates their potential usefulness for future study of the stretching of other proteins and the relationship between protein structure and the response to mechanical deformation.     

On computational efficiency of the hybrid Monte Carlo method applied to the multicanonical ensemble

Abstract

In the present paper, computational efficiency of the hybrid Monte Carlo (HMC) method applied to the multicanonical ensemble is studied; the HMC is an equation of motion guided Monte Carlo method. As in the standard HMC for the canonical ensemble, the multicanonical HMC calculations with high acceptance ratio show better efficiency; about 60% acceptance yields the best performance for the system examined.     

Computer simulation of stochastic processes through model-sampling (Monte Carlo) techniques

A simple Monte Carlo simulation program is outlined which can be used for the investigation of random-walk problems, for example in diffusion, or the movement of tracers in the blood circulation. The results given by the simulation are compared with those predicted by well-established theory, and it is shown how the model can be expanded to deal with drift, and with reflexion from or adsorption at a boundary.     

A Monte Carlo simulation of chemical reactions

A computer-based algorithm to solve complex chemical rate equations is introduced. A simple Monte Carlo sampling method is used to generate chemical reactions in numbers proportional to reaction probabilities, and a second-order Runge-Kutta method is used to calculate time. The method is compared with a closed form mathematical solution for a simple chemical system, and it is compared with a numerical integration of the rate equations for a more complicated system.     

Hydration of uracil and thymine methylderivatives: a Monte Carlo simulation

The simulation performed shows that under methylation of uracil and thymine NH-groups the interaction energy between a base and water (Uwb) is increased. It is also detected that the increase in this energy was observed in the 1st and the 3rd sectors. These conclusions do not confirm the assumption made in the literature on the character of an interaction between methylated bases and water. According to this assumption, when the NH-groups are methylated, the energy of Uwb in these sectors decreases as a result of the van der Waals interactions between a methyl group and water, whose energy compensates the increase in the Uwb energy due to the breaking of an H-bond. Regularity of water molecules near a hydrophobic group under the hydration of polar molecules is detected for the first time.     

Monte Carlo simulation of diffusion of adsorbed proteins

We present the results of three-dimensional lattice Monte Carlo simulations of protein diffusion on the liquid-solid interface in a wide temperature range including the most interesting temperatures (from slightly below T(f) and up to T(c), where T(f) and T(c) are the folding and collapse temperatures). For the model under consideration (27 monomers of two types), the temperature dependence of the diffusion coefficient is found to obey the Arrhenius law with the normal value (approximately 10(-2)-10(-3) cm(2)/s) of the preexponential factor. Proteins 2000;39:76-81.     

Simulating proteins at constant pH: An approach combining molecular dynamics and Monte Carlo simulation

For the structure and function of proteins, the pH of the solution is one of the determining parameters. Current molecular dynamics (MD) simulations account for the solution pH only in a limited way by keeping each titratable site in a chosen protonation state. We present an algorithm that generates trajectories at a Boltzmann distributed ensemble of protonation states by a combination of MD and Monte Carlo (MC) simulation. The algorithm is useful for pH-dependent structural studies and to investigate in detail the titration behavior of proteins. The method is tested on the acidic residues of the protein hen egg white lysozyme. It is shown that small structural changes may have a big effect on the pK(A) values of titratable residues.     

Development of a grand canonical-kinetic Monte Carlo scheme for simulation of mixtures

A rejection-free methodology-based kinetic Monte Carlo (kMC) method has been developed in the grand canonical ensemble to simulate fluid mixtures. It comprises two different moves: entropic displacement of a selected molecule (based on the Rosenbluth algorithm) in the volume space of the system, and exchange of molecules with the surroundings (insertion or deletion). These two moves are made sequentially with M displacement moves followed by one exchange. The displacement moves are treated as sub-NVT sequences within a grand canonical ensemble. The procedure for deletion or insertion of a molecule is either, based on the Rosenbluth algorithm, or on a direct comparison, in which the average activity of one component is compared with its specified activity. The components are chosen either with equal probability or with a probability proportional to their density. The implementation of rejection-free kMC is much simpler than the Metropolis importance sampling MC procedure, which requires three different types of move, all of which must be tested for acceptance or rejection. The new scheme has been evaluated by applying it to fluid argon and to an equimolar mixture of methane, ethane and propane.     

Monte Carlo simulation of the enzymatic lysis of yeast

The overall reaction in the enzymatic lysis of yeast takes place in three major steps: (i) the two-layer wall is digested, (ii) the cell bursts under the osmotic pressure difference to release its intracellular material, and (iii) the intracellular material is digested by the enzymes still present in the solution. The first and third steps are continuous processes, adequately described by Michaelis-Menten kinetic models. The second step is a discrete event, statistical in nature. A model of engineering value should effectively bridge the gap between the two continuous processes (first and third steps). In this work, Monte Carlo simulations are used to identify a suitable function that captures the statistical nature of cell rupture and represents the rate of release of intracellular material. It is shown that the two-parameter beta distribution function serves this purpose most effectively. Comparisons with experimental results indicate that the cell rupture ratio is a widely distributed statistical function. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 53: 290-295, 1997.     

Monte Carlo simulation of the water in a channel with charges.

A Monte Carlo simulation of water in a channel with charges suggests the existence of water in immobile, high density, essentially glasslike form near the charges. The channel model has a conical section with an opening through which water molecules can pass, at the narrow end of the cone, and a cylindrical section at the other end. When the charges are placed near the narrow section of the model, the "glass" effectively blocks the channel; with the charges removed, the channel opens. The effect can be determined from the rate of passage of the water molecules through the pore, from the average orientation of the water molecule, and from distortion of the distribution of molecules. In the simulations carried out to date, no external ions have been considered. In addition to the energy, the Helmholtz free energy has been calculated.     

The effect of weekend curfews on epidemics: a Monte Carlo simulation

The ongoing COVID-19 pandemic is being responded with various methods, applying vaccines, experimental treatment options, total lockdowns or partial curfews. Weekend curfews are among the methods for reducing the number of infected persons, and this method is practically applied in some countries such as Turkey. In this study, the effect of weekend curfews on reducing the spread of a contagious disease, such as COVID-19, is modeled using a Monte Carlo algorithm with a hybrid lattice model. In the simulation setup, a fictional country with three towns and 26,610 citizens were used as a model. Results indicate that applying a weekend curfew reduces the ratio of ill cases from 0.23 to 0.15. The results also show that applying personal precautions such as social distancing is important for reducing the number of cases and deaths. If the probability of disease spread can be reduced to 0.1, in that case, the death ratio can be minimized down to 0.     

How native proteins aggregate in solution: a dynamic Monte Carlo simulation

Aggregation of native proteins in solution is of fundamental importance with regard to both the processing and the utilization of proteins. In the present work, a dynamic Monte Carlo simulation has been performed to give a molecular insight into the way in which native proteins aggregate in solution and to explore means of suppressing aggregation, using two proteins of different compositions and conformations represented by a two-dimensional (2D) lattice model (HP model). It is shown that the native HP protein with accessible hydrophobic beads on its surface is prone to aggregation. The aggregation of this protein is intensified when the solution conditions favor the partially unfolded conformation as opposed to either the native or fully unfolded conformations. In this case, the partially unfolded proteins form the cores of aggregates, which may also encapsulate the native protein. One way to inhibit protein aggregation is to introduce polymers of appropriate hydrophobicity and chain length into the solution, such that these polymer molecules wrap around the hydrophobic regions of both the unfolded and folded proteins, thereby segregating the protein molecules. Our simulation is consistent with experimental observations reported elsewhere and provides a molecular basis for the behavior of proteins in liquid environments.     

Spacer length in clonal plants and the efficiency of resource capture in heterogeneous environments: A Monte Carlo simulation

A stochastic, spatially explicit simulation model for clonal growth is presented which relates growth patterns to the pattern of resource availability in the environment in both space and time. The effects of two simple growth rules were examined which affect the length of spacers depending on the local environmental conditions. According to one of the rules, shorter spacers were developed in resource-rich microsites than in resource-poor microsites (growth rule G-). If the other rule acted, the spacers were lengthened in resource-rich sites (growth rule G+). The neutral reference, G0, represented a plant of rigid growth form. A wide range of habitat types was used in the tests and characterized by an information theory model. It was found that the effectiveness of resource capture in most habitat types can be explained by spatio-temporal predictability of the environment, measured on the scale of spacer length. Shortening the spacers in resource-rich microsites, as hypothesized by “foraging theory”, reduced the proportion of misplaced ramets. Lengthening the spacers never reduced this proportion. However, the degree of intraclonal competition was significantly reduced by both shortening and lengthening the spacers in response to site quality. There were certain types of environment where plastic modification of spacers had no effect on the efficiency of resource capture when compared to the reference random (non-environment-dependent) search pattern. Such habitats can be identified exactly on the basis of the information content of habitat pattern, measured here by spatio-temporal predictability. This study emphasizes that a wide range of environmental types should be taken into consideration when examining the adaptive nature of a certain growth pattern. Generalizing from experimental results gained in temporally constant environments may strongly bias our view on morphological adaptation.     

Markov chain Monte Carlo for mapping a quantitative trait locus in outbred populations

A Bayesian approach is presented for mapping a quantitative trait locus (QTL) using the 'Fernando and Grossman' multivariate Normal approximation to QTL inheritance. For this model, a Bayesian implementation that includes QTL position is problematic because standard Markov chain Monte Carlo (MCMC) algorithms do not mix, i.e. the QTL position gets stuck in one marker interval. This is because of the dependence of the covariance structure for the QTL effects on the adjacent markers and may be typical of the 'Fernando and Grossman' model. A relatively new MCMC technique, simulated tempering, allows mixing and so makes possible inferences about QTL position based on marginal posterior probabilities. The model was implemented for estimating variance ratios and QTL position using a continuous grid of allowed positions and was applied to simulated data of a standard granddaughter design. The results showed a smooth mixing of QTL position after implementation of the simulated tempering sampler. In this implementation, map distance between QTL and its flanking markers was artificially stretched to reduce the dependence of markers and covariance. The method generalizes easily to more complicated applications and can ultimately contribute to QTL mapping in complex, heterogeneous, human, animal or plant populations.