Spatial multi-level interacting particle simulations and information theory-based error quantification

We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution levels, taking advantage of the low sampling cost in a coarse space and by developing local reconstruction strategies from coarse-grained dynamics. Microscopic reconstruction corrects possibly significant errors introduced through coarse-graining, leading to the controlled-error approximation of the sampled stochastic process. In this manner, the proposed multi-level algorithm overcomes known shortcomings of coarse-graining of particle systems with complex interactions such as combined long and short-range particle interactions and/or complex lattice geometries. Specifically, we provide error analysis for the approximation of long-time stationary dynamics in terms of relative entropy and prove that information loss in the multi-level methods is growing linearly in time, which in turn implies that an appropriate observable in the stationary regime is the information loss of the path measures per unit time. We show that this observable can be either estimated a priori, or it can be tracked computationally a posteriori in the course of a simulation. The stationary regime is of critical importance to molecular simulations as it is relevant to long-time sampling, obtaining phase diagrams and in studying metastability properties of high-dimensional complex systems. Finally, the multi-level nature of the method provides flexibility in combining rejection-free and null-event implementations, generating a hierarchy of algorithms with an adjustable number of rejections that includes well-known rejection-free and null-event algorithms.Comment: 34 page

Multilevel coarse graining and nano--pattern discovery in many particle stochastic systems

In this work we propose a hierarchy of Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub - steps efficiently coupling coarse and microscopic state spaces. The method can be designed to sample the exact or controlled-error approximations of the target distribution, providing information on levels of different resolutions, as well as at the microscopic level. In both strategies the method achieves significant reduction of the computational cost compared to conventional Markov Chain Monte Carlo methods. Applications in phase transition and pattern formation problems confirm the efficiency of the proposed methods.Comment: 37 page

The Dosimetric Effects of Photon Energy on the Quality of Volumetric Modulated Arc Therapy for Lung Stereotactic Body Radiation Therapy

Purpose: There is little published data on the optimal energy to use to minimize doses to Organs at Risk (OARs), while maintaining adequate Planning Target Volume (PTV) coverage in lung volumetric-modulated arc therapy (VMAT) stereotactic body radiation therapy (SBRT).Methods: 35 lung lesions in 33 patients were treated at our institution by VMAT SBRT. Dosimetric plans using 6-Megavoltage (6-MV) and 10-Megavoltage (10-MV) energies were generated for each lesion. The median dose was 5000cGy delivered over 3-5 daily fractions. Various dosimetric parameters were recorded for both the 6-MV and 10-MV plans and the patients were stratified according to the tumor to chest wall distance (TCW), the tumor location (central versus peripheral), patient anterior-posterior (AP) diameter, and the diameter of an equivalent sphere encompassing the patient's body over the distance of the PTV (ESD).Results: There was a statistically significant difference between 6-MV and 10-MV with respect to the sum lung dose, which favored 6-MV plans (p=0.04). For those stratified by TCW, there was a difference in conformity index (CI) for patients with peripheral tumors (p=0.04). For the group stratified by AP separation, there was a difference in mean sum lung dose favoring 6-MV (p=0.01). In the group stratified by ESD, there were statistically significant (SS) differences in the volume of lung receiving at least 13Gy (V13), mean sum lung dose, and CI, all favoring 6-MV plans (p=0.05, p<0.01, and p<0.01). For the cohort overall, and within each subgroup, there was a SS difference in the total number of monitor units (MUs), which consistently favored planning with 10-MV.Conclusion: With the exception of thinner patients, for which 6-MV plans was superior with respect to OARs and conformity index, 10-MV should be considered for use in lung VMAT SBRT. 10-MV plans consistently resulted in fewer total MUs. Fewer MUs results in shorter treatment times, with the potential for improved target accuracy due to less intrafractional tumor motion

Genomic Testing in Localized Prostate Cancer Can Identify Subsets of African Americans With Aggressive Disease

BACKGROUND: Personalized genomic classifiers have transformed the management of prostate cancer (PCa) by identifying the most aggressive subsets of PCa. Nevertheless, the performance of genomic classifiers to risk classify African American men is thus far lacking in a prospective setting. METHODS: This is a prospective study of the Decipher genomic classifier for National Comprehensive Cancer Network low- and intermediate-risk PCa. Study-eligible non-African American men were matched to African American men. Diagnostic biopsy specimens were processed to estimate Decipher scores. Samples accrued in NCT02723734, a prospective study, were interrogated to determine the genomic risk of reclassification (GrR) between conventional clinical risk classifiers and the Decipher score. RESULTS: The final analysis included a clinically balanced cohort of 226 patients with complete genomic information (113 African American men and 113 non-African American men). A higher proportion of African American men with National Comprehensive Cancer Network-classified low-risk (18.2%) and favorable intermediate-risk (37.8%) PCa had a higher Decipher score than non-African American men. Self-identified African American men were twice more likely than non-African American men to experience GrR (relative risk [RR] = 2.23, 95% confidence interval [CI] = 1.02 to 4.90; P = .04). In an ancestry-determined race model, we consistently validated a higher risk of reclassification in African American men (RR = 5.26, 95% CI = 1.66 to 16.63; P = .004). Race-stratified analysis of GrR vs non-GrR tumors also revealed molecular differences in these tumor subtypes. CONCLUSIONS: Integration of genomic classifiers with clinically based risk classification can help identify the subset of African American men with localized PCa who harbor high genomic risk of early metastatic disease. It is vital to identify and appropriately risk stratify the subset of African American men with aggressive disease who may benefit from more targeted interventions

Spatial Multi-Level Interacting Particle Simulations and Information Theory-Based Error Quantification

We propose a hierarchy of two-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution levels, taking advantage of the low sampling cost in a coarse space and developing local reconstruction strategies from coarse-grained dynamics. Furthermore, a natural extension to a multilevel kinetic coarse-grained Monte Carlo is presented. Microscopic reconstruction corrects possibly significant errors introduced through coarse-graining, leading to the controlled-error approximation of the sampled stochastic process. In this manner, the proposed algorithm overcomes known shortcomings of coarse-graining of particle systems with complex interactions such as combined long- and short-range particle interactions and/or complex lattice geometries. Specifically, we provide error analysis for the approximation of long-time stationary dynamics in terms of relative entropy, measuring the information loss of the path measures per unit time. We show that this observable either can be estimated a priori, or it can be tracked computationally a posteriori in the course of a simulation. The stationary regime is of critical importance to molecular simulations as it is relevant to long-time sampling, obtaining phase diagrams, and in studying metastability properties of high-dimensional complex systems. Finally, the multilevel nature of the method provides flexibility in combining rejection-free and null-event implementations, generating a hierarchy of algorithms with an adjustable number of rejections that includes well-known rejection-free and null-event algorithms. Read More: http://epubs.siam.org/doi/abs/10.1137/12088706