Personalized Radiotherapy Design for Glioblastoma: Integrating Mathematical Tumor Models, Multimodal Scans, and Bayesian Inference.

Glioblastoma (GBM) is a highly invasive brain tumor, whose cells infiltrate surrounding normal brain tissue beyond the lesion outlines visible in the current medical scans. These infiltrative cells are treated mainly by radiotherapy. Existing radiotherapy plans for brain tumors derive from population studies and scarcely account for patient-specific conditions. Here, we provide a Bayesian machine learning framework for the rational design of improved, personalized radiotherapy plans using mathematical modeling and patient multimodal medical scans. Our method, for the first time, integrates complementary information from high-resolution MRI scans and highly specific FET-PET metabolic maps to infer tumor cell density in GBM patients. The Bayesian framework quantifies imaging and modeling uncertainties and predicts patient-specific tumor cell density with credible intervals. The proposed methodology relies only on data acquired at a single time point and, thus, is applicable to standard clinical settings. An initial clinical population study shows that the radiotherapy plans generated from the inferred tumor cell infiltration maps spare more healthy tissue thereby reducing radiation toxicity while yielding comparable accuracy with standard radiotherapy protocols. Moreover, the inferred regions of high tumor cell densities coincide with the tumor radioresistant areas, providing guidance for personalized dose-escalation. The proposed integration of multimodal scans and mathematical modeling provides a robust, non-invasive tool to assist personalized radiotherapy design.

Data driven inference for the repulsive exponent of the Lennard-Jones potential in molecular dynamics simulations.

The Lennard-Jones (LJ) potential is a cornerstone of Molecular Dynamics (MD) simulations and among the most widely used computational kernels in science. The LJ potential models atomistic attraction and repulsion with century old prescribed parameters (q = 6, p = 12, respectively), originally related by a factor of two for simplicity of calculations. We propose the inference of the repulsion exponent through Hierarchical Bayesian uncertainty quantification We use experimental data of the radial distribution function and dimer interaction energies from quantum mechanics simulations. We find that the repulsion exponent p ≈ 6.5 provides an excellent fit for the experimental data of liquid argon, for a range of thermodynamic conditions, as well as for saturated argon vapour. Calibration using the quantum simulation data did not provide a good fit in these cases. However, values p ≈ 12.7 obtained by dimer quantum simulations are preferred for the argon gas while lower values are promoted by experimental data. These results show that the proposed LJ 6-p potential applies to a wider range of thermodynamic conditions, than the classical LJ 6-12 potential. We suggest that calibration of the repulsive exponent in the LJ potential widens the range of applicability and accuracy of MD simulations.

Self-assembly of anionic, ligand-coated nanoparticles in lipid membranes.

Ligand-functionalized nanoparticles (NPs) are a promising platform for imaging and drug delivery applications. A number of recent molecular simulation and theoretical studies explored how these NPs interact with model lipid membranes. However, interactions between ligand-coated NPs leading to possible cooperative effects and association have not been investigated. In this coarse-grained molecular dynamics study, we focus on a specific case of several anionic, ligand-coated NPs embedded in a lipid membrane. Several new effects are observed. Specifically, in the presence of cholesterol in the membrane, NPs tend to form linear clusters, or chains. Analysis of the driving forces for this association reveals an important role of the recently discovered orderphobic effect, although we acknowledge that a combination of factors must be at play. At the same time, we argue that the specific linear shape of the clusters is a result of a subtle balance between the forces that stabilize a NP in the membrane and the forces that drive the NP-NP association processes. These effects, observed for the first time in the NP-membrane systems, have also direct correspondence to similar effects in protein-membrane systems and these links between the two realms should be explored further.

Fusing heterogeneous data for the calibration of molecular dynamics force fields using hierarchical Bayesian models.

We propose a hierarchical Bayesian framework to systematically integrate heterogeneous data for the calibration of force fields in Molecular Dynamics (MD) simulations. Our approach enables the fusion of diverse experimental data sets of the physico-chemical properties of a system at different thermodynamic conditions. We demonstrate the value of this framework for the robust calibration of MD force-fields for water using experimental data of its diffusivity, radial distribution function, and density. In order to address the high computational cost associated with the hierarchical Bayesian models, we develop a novel surrogate model based on the empirical interpolation method. Further computational savings are achieved by implementing a highly parallel transitional Markov chain Monte Carlo technique. The present method bypasses possible subjective weightings of the experimental data in identifying MD force-field parameters.

Kapitza Resistance between Few-Layer Graphene and Water: Liquid Layering Effects.

The Kapitza resistance (RK) between few-layer graphene (FLG) and water was studied using molecular dynamics simulations. The RK was found to depend on the number of the layers in the FLG though, surprisingly, not on the water block thickness. This distinct size dependence is attributed to the large difference in the phonon mean free path between the FLG and water. Remarkably, RK is strongly dependent on the layering of water adjacent to the FLG, exhibiting an inverse proportionality relationship to the peak density of the first water layer, which is consistent with better acoustic phonon matching between FLG and water. These findings suggest novel ways to engineer the thermal transport properties of solid-liquid interfaces by controlling and regulating the liquid layering at the interface.

Placental plasticity in monochorionic twins: Impact on birth weight and placental weight.

INTRODUCTION: The knowledge about adaptive mechanisms of monochorionic placentas to fulfill the demands of two instead of one fetus is largely speculative. The aim of our study was to investigate the impact of chorionicity on birth weight and placental weight in twin pregnancies. METHODS: Forty Monochorionic (MC) and 43 dichorionic (DC) twin pregnancies were included in this retrospective study. Individual and total (sum of both twins) birth weights, placental weights ratios between placental and birth weights and observed-to-expected (O/E)-ratios were calculated and analyzed. Additionally, we investigated whether in twin pregnancies placental and birth weights follow the law of allometric metabolic scaling. RESULTS: MC pregnancies showed higher placental O/E-ratios than DC ones (2.25 ± 0.85 versus 1.66 ± 0.61; p < 0.05), whereas the total neonatal birth weight O/E-ratios were not different. In DC twins total placental weights correlated significantly with gestational age (r = 0.74, p < 0.001), but not in MC twins. Analysis of deliveries ≤32 weeks revealed that the placenta to birth weight ratio in MC twins was higher than in matched DC twins (0.49 ± 0.3 versus 0.24 ± 0.03; p = 0.03). Allometric metabolic scaling revealed that dichorionic twin placentas scale with birth weight, while the monochorionic ones do not. DISCUSSION: The weight of MC placentas compared to that of DC is not gestational age dependent in the third trimester. Therefore an early accelerated placental growth pattern has to be postulated which leads to an excess placental mass particularly below 32 weeks of gestation. The monochorionic twins do not follow allometric metabolic scaling principle making them more vulnerable to placental compromise.

Membrane partitioning of anionic, ligand-coated nanoparticles is accompanied by ligand snorkeling, local disordering, and cholesterol depletion.

Intracellular uptake of nanoparticles (NPs) may induce phase transitions, restructuring, stretching, or even complete disruption of the cell membrane. Therefore, NP cytotoxicity assessment requires a thorough understanding of the mechanisms by which these engineered nanostructures interact with the cell membrane. In this study, extensive Coarse-Grained Molecular Dynamics (MD) simulations are performed to investigate the partitioning of an anionic, ligand-decorated NP in model membranes containing dipalmitoylphosphatidylcholine (DPPC) phospholipids and different concentrations of cholesterol. Spontaneous fusion and translocation of the anionic NP is not observed in any of the 10-µs unbiased MD simulations, indicating that longer timescales may be required for such phenomena to occur. This picture is supported by the free energy analysis, revealing a considerable free energy barrier for NP translocation across the lipid bilayer. 5-µs unbiased MD simulations with the NP inserted in the bilayer core reveal that the hydrophobic and hydrophilic ligands of the NP surface rearrange to form optimal contacts with the lipid bilayer, leading to the so-called snorkeling effect. Inside cholesterol-containing bilayers, the NP induces rearrangement of the structure of the lipid bilayer in its vicinity from the liquid-ordered to the liquid phase spanning a distance almost twice its core radius (8-10 nm). Based on the physical insights obtained in this study, we propose a mechanism of cellular anionic NP partitioning, which requires structural rearrangements of both the NP and the bilayer, and conclude that the translocation of anionic NPs through cholesterol-rich membranes must be accompanied by formation of cholesterol-lean regions in the proximity of NPs.

Data driven, predictive molecular dynamics for nanoscale flow simulations under uncertainty.

For over five decades, molecular dynamics (MD) simulations have helped to elucidate critical mechanisms in a broad range of physiological systems and technological innovations. MD simulations are synergetic with experiments, relying on measurements to calibrate their parameters and probing "what if scenarios" for systems that are difficult to investigate experimentally. However, in certain systems, such as nanofluidics, the results of experiments and MD simulations differ by several orders of magnitude. This discrepancy may be attributed to the spatiotemporal scales and structural information accessible by experiments and simulations. Furthermore, MD simulations rely on parameters that are often calibrated semiempirically, while the effects of their computational implementation on their predictive capabilities have only been sporadically probed. In this work, we show that experimental and MD investigations can be consolidated through a rigorous uncertainty quantification framework. We employ a Bayesian probabilistic framework for large scale MD simulations of graphitic nanostructures in aqueous environments. We assess the uncertainties in the MD predictions for quantities of interest regarding wetting behavior and hydrophobicity. We focus on three representative systems: water wetting of graphene, the aggregation of fullerenes in aqueous solution, and the water transport across carbon nanotubes. We demonstrate that the dominant mode of calibrating MD potentials in nanoscale fluid mechanics, through single values of water contact angle on graphene, leads to large uncertainties and fallible quantitative predictions. We demonstrate that the use of additional experimental data reduces uncertainty, improves the predictive accuracy of MD models, and consolidates the results of experiments and simulations.

Homogeneous Hydrophobic-Hydrophilic Surface Patterns Enhance Permeation of Nanoparticles through Lipid Membranes.

We employ coarse-grained molecular dynamics simulations to understand why certain interaction patterns on the surface of a nanoparticle promote its translocation through a lipid membrane. We demonstrate that switching from a random, heterogeneous distribution of hydrophobic and hydrophilic areas on the surface of a nanoparticle to even, homogeneous patterns substantially flattens the translocation free-energy profile and dramatically enhances permeation. We then proceed to construct a more detailed coarse-grained model of a nanoparticle with flexible hydrophobic and hydrophilic ligands arranged into striped domains. Molecular dynamics simulations of these nanoparticles show that the terminal groups of the ligands tend to arrange themselves into homogeneous patterns, despite the underlying striped domains. These observations are linked to recent experimental studies.

Angular dependence of surfactant-mediated forces between carbon nanotubes.

We employ dissipative particle dynamics to examine surfactant-mediated forces between two carbon nanotubes. Calculations are performed varying both the distance and the angle between the nanotubes. For small distances, a repulsive region is observed, followed by an overall attractive interval with strong oscillations in the force. Decreasing the angle between the tubes leads to a steady increase in the force, but the relative dependence on the separation distance is preserved. We find that the force scales linearly with the size of the overlap area between the tubes. This allows us to express the angle dependence by a simple equation, whereas the distance dependence is represented by a master curve. For the parallel case, the behavior is significantly different.

Bayesian uncertainty quantification and propagation in molecular dynamics simulations: a high performance computing framework.

We present a Bayesian probabilistic framework for quantifying and propagating the uncertainties in the parameters of force fields employed in molecular dynamics (MD) simulations. We propose a highly parallel implementation of the transitional Markov chain Monte Carlo for populating the posterior probability distribution of the MD force-field parameters. Efficient scheduling algorithms are proposed to handle the MD model runs and to distribute the computations in clusters with heterogeneous architectures. Furthermore, adaptive surrogate models are proposed in order to reduce the computational cost associated with the large number of MD model runs. The effectiveness and computational efficiency of the proposed Bayesian framework is demonstrated in MD simulations of liquid and gaseous argon.

The science of dispersing carbon nanotubes with surfactants.

Self-assembled structures adsorbed on carbon nanotubes and other nanofibres offer a plethora of opportunities to endow them with new functions and to integrate them into devices and materials. At the same time they are key to solve the greatest problem in carbon nanotube utilisation--debundling and individualisation. Success will inevitably require an understanding of the underlying structure-function relationship of the adsorbed surfactant layer. Computer simulations are ideally suited to develop this understanding as they enable us to study the structure-function relationship in great detail. Combining the results from mesoscale and atomistic simulations we begin to develop this understanding and derive a number of recommendations for optimal dispersion design.

Surfactant-induced forces between carbon nanotubes.

Dissipative particle dynamics simulations are employed to study surfactant-mediated forces between a pair of perpendicular carbon nanotubes (CNTs) coated by surfactants which form spherical micelles in bulk solution and on the tubes. Two force regimes are observed: at small tube/tube distances the force is attractive, whereas it is repulsive at larger distances. The attractive regime is dominated by a central micelle binding the tubes, while in the repulsive regime the contact region is depleted. The two regimes are separated by a discontinuous transition. The repulsive regime is critical for stabilizing CNT suspensions. Viewing rebundling as a thermally activated process, a connection between the repulsive force and the rebundling rate is established. We find that a larger hydrophilic surfactant headgroup creates a stronger and longer ranged tube/tube force, which reduces the rebundling rate significantly. The longer range originates directly from the further reaching head corona of the adsorbed surfactant layer. The larger magnitude of the force appears to be related to the axial compression force the adsorbed phase can sustain. This compression force appears to be the most critical factor for suspension design.

The differences in surfactant adsorption on carbon nanotubes and their bundles.

Dissipative particle dynamics simulations of a mesoscale model are performed to investigate the concentration dependence of surfactant adsorption on small-diameter carbon nanotubes and their bundles. Adsorption is found to follow fundamentally different mechanisms in the two cases because of the heterogeneity of the bundle surface and the difference in diameter of bundles compared to that of individual tubes. Whereas aggregation dominates adsorption on individual tubes, on bundles it is largely a Langmuir-type process. High adsorption energy sites on the outer surface of bundles, where surfactant molecules can interact with two tubes simultaneously, dominate at low coverage. They also cause adsorption on bundles to become significant well before adsorption on individual tubes starts. The difference in the adsorption mechanisms leads to a crossover point at higher concentrations, where the adsorbed amount per surface area on individual tubes becomes larger than that for the bundles.

Structural forces from directed self-assembly.

We investigate a candidate structure for the bottom-up design of nanocomposite materials. At a pair of crossing carbon nanotubes, surfactants self-assemble into a micelle-like aggregate incorporating the two tubes. The aggregate forms as long as the gap between the tubes is smaller than the core diameter of a bulk micelle. Moreover, the absorbed surfactant aggregate generates an effective force between the tubes. The dependence of this force on the distance between the tubes is complex and includes structural components, such as layering, and a large attractive region at larger distances. This attraction appears to be entropic in nature and to originate from confinement of the surfactant head groups.

Directed self-assembly of surfactants in carbon nanotube materials.

The self-assembly of surfactant molecules on crossing carbon nanotubes has been investigated using a bead-spring model and implicit solvent dissipative particle dynamics simulations. Adsorption is directed to the nanotube crossing by its higher hydrophobic potential which is due to the presence of two surfaces. As a consequence of the tendency of surfactant molecules to self-assemble into micelles, the adsorbed molecules form a "central aggregate" at the crossing, thus, confining the molecules to the immediate vicinity of the crossing. Adsorption on the remaining nanotube surface becomes significant only at higher surfactant concentrations, where the molecules self-assemble to hemimicelles which grow continuously to full micelles upon increase of the (bulk) surfactant concentration. Our results allow two conclusions for the rational design of nanostructured materials: (i) the size of the central aggregate can not be much larger than that of a bulk micelle and (ii) control of the adsorbed structures is conveniently possible via the (bulk) surfactant concentration.