Vancomycin: Predictive risk factors for nephrotoxicity and implication for monitoring

The increased use of vancomycin in hospitals has resulted in a standard practice to monitor serum vancomycin levels because of possible nephrotoxicity. However, the routine monitoring of vancomycin serum concentration is under criticism and the cost effectiveness of such routine monitoring is in question because frequent monitoring neither results in increase efficacy nor decrease nephrotoxicity. The purpose of the present study is to determine factors that may place patients at increased risk of developing vancomycin induced nephrotoxicity and for whom monitoring may be most beneficial.^ From September to December 1992, 752 consecutive in patients at The University of Texas M. D. Anderson Cancer Center, Houston, were prospectively evaluated for nephrotoxicity in order to describe predictive risk factors for developing vancomycin related nephrotoxicity. Ninety-five patients (13 percent) developed nephrotoxicity. A total of 299 patients (40 percent) were considered monitored (vancomycin serum levels determined during the course of therapy), and 346 patients (46 percent) were receiving concurrent moderate to highly nephrotoxic drugs.^ Factors that were found to be significantly associated with nephrotoxicity in univariate analysis were: gender, base serum creatinine greater than 1.5mg/dl, monitor, leukemia, concurrent moderate to highly nephrotoxic drugs, and APACHE III scores of 40 or more. Significant factors in the univariate analysis were then entered into a stepwise logistic regression analysis to determine independent predictive risk factors for vancomycin induced nephrotoxicity.^ Factors, with their corresponding odds ratios and 95% confidence limits, selected by stepwise logistic regression analysis to be predictive of vancomycin induced nephrotoxicity were: Concurrent therapy with moderate to highly nephrotoxic drugs (2.89; 1.76-4.74), APACHE III scores of 40 or more (1.98; 1.16-3.38), and male gender (1.98; 1.04-2.71).^ Subgroup (monitor and non-monitor) analysis showed that male (OR = 1.87; 95% CI = 1.01, 3.45) and moderate to highly nephrotoxic drugs (OR = 4.58; 95% CI = 2.11, 9.94) were significant for nephrotoxicity in monitored patients. However, only APACHE III score (OR = 2.67; 95% CI = 1.13,6.29) was significant for nephrotoxicity in non-monitored patients.^ The conclusion drawn from this study is that not every patient receiving vancomycin therapy needs frequent monitoring of vancomycin serum levels. Such routine monitoring may be appropriate in patients with one or more of the identified risk factors and low risk patients do not need to be subjected to the discomfort and added cost of multiple blood sampling. Such prudent selection of patients to monitor may decrease cost to patients and hospital. ^

The missing link between clinical states and biomarkers in mental disorders

Current diagnostic definitions of psychiatric disorders based on collections of symptoms encompass very heterogeneous populations and are thus likely to yield spurious results when exploring biological correlates of mental disturbances. It has been suggested that large studies of biomarkers across diagnostic entities may yield improved clinical information. Such a view is based on the concept of assessment as a collection of symptoms devoid of any clinical judgment and interpretation. Yet, important advances have been made in recent years in clinimetrics, the science of clinical judgment. The current clinical taxonomy in psychiatry, which emphasizes reliability at the cost of clinical validity, does not include effects of comorbid conditions, timing of phenomena, rate of progression of an illness, responses to previous treatments, and other clinical distinctions that demarcate major prognostic and therapeutic differences among patients who otherwise seem to be deceptively similar since they share the same psychiatric diagnosis. Clinimetrics may provide the missing link between clinical states and biomarkers in psychiatry, building pathophysiological bridges from clinical manifestations to their neurobiological counterparts.

The significant effect of endometriosis on physical, mental and social wellbeing: results from an international cross-sectional survey.

STUDY QUESTION To what extent do the management of endometriosis and the symptoms that remain after treatment affect the quality of life in women with the disease? SUMMARY ANSWER Many women with endometriosis had impaired quality of life and continued to suffer from endometriosis-associated symptoms even though their endometriosis has been managed in tertiary care centres. WHAT IS KNOWN ALREADY The existing literature indicates that quality of life and work productivity is reduced in women with endometriosis. However, most studies have small sample sizes, are treatment related or examine newly diagnosed patients only. STUDY DESIGN, SIZE, DURATION A cross-sectional questionnaire-based survey among 931 women with endometriosis treated in 12 tertiary care centres in 10 countries. PARTICIPANTS/MATERIALS, SETTING, METHODS Women diagnosed with endometriosis who had at least one contact related to endometriosis-associated symptoms during 2008 with a participating centre were enrolled into the study. The study investigated the effect of endometriosis on education, work and social wellbeing, endometriosis-associated symptoms and health-related quality of life, by using questions obtained from the World Endometriosis Research Foundation (WERF) GSWH instrument (designed and validated for the WERF Global Study on Women's Health) and the Short Form 36 version 2 (SF-36v2). MAIN RESULTS AND THE ROLE OF CHANCE Of 3216 women invited to participate in the study, 1450 (45%) provided informed consent and out of these, 931 (931/3216 = 29%) returned the questionnaires. Endometriosis had affected work in 51% of the women and affected relationships in 50% of the women at some time during their life. Dysmenorrhoea was reported by 59%, dyspareunia by 56% and chronic pelvic pain by 60% of women. Quality of life was decreased in all eight dimensions of the SF-36v2 compared with norm-based scores from a general US population (all P < 0.01). Multivariate regression analysis showed that number of co-morbidities, chronic pain and dyspareunia had an independent negative effect on both the physical and mental component of the SF-36v2. LIMITATIONS, REASONS FOR CAUTION The fact that women were enrolled in tertiary care centres could lead to a possible over-representation of women with moderate-to-severe endometriosis, because the participating centres typically treat more complex and referred cases of endometriosis. The response rate was relatively low. Since there was no Institute Review Board approval to do a non-responder investigation on basic characteristics, some uncertainty remains regarding the representativeness of the investigated population. WIDER IMPLICATIONS OF THE FINDINGS This international multicentre survey represents a large group of women with endometriosis, in all phases of the disease, which increases the generalizability of the data. Women still suffer from frequent symptoms, despite tertiary care management, in particular chronic pain and dyspareunia. As a result their quality of life is significantly decreased. A patient-centred approach with extensive collaboration across disciplines, such as pain specialists, psychologists, sexologists and social workers, may be a valuable strategy to improve the long-term care of women with endometriosis. STUDY FUNDING/COMPETING INTEREST(S) The WERF EndoCost study is funded by the World Endometriosis Research Foundation (WERF) through grants received from Bayer Schering Pharma AG, Takeda Italia Farmaceutici SpA, Pfizer Ltd and the European Society of Human Reproduction and Embryology. The sponsors did not have a role in the design and conduct of the study; collection, management, analysis and interpretation of the data; and preparation, review or approval of the manuscript. L.H. is the chief executive and T.D. was a board member of WERF at the time of funding. T.D. holds the Merck-Serono Chair in Reproductive Medicine and Surgery, and the Ferring Chair in Reproductive Medicine at the Katholieke Universiteit Leuven in Belgium and has served as consultant/research collaborator for Merck-Serono, Schering-Plough, Astellas and Arresto.

Strengthening the Reporting of Observational Studies in Epidemiology (STROBE): Explanation and elaboration

Much medical research is observational. The reporting of observational studies is often of insufficient quality. Poor reporting hampers the assessment of the strengths and weaknesses of a study and the generalisability of its results. Taking into account empirical evidence and theoretical considerations, a group of methodologists, researchers, and editors developed the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) recommendations to improve the quality of reporting of observational studies. The STROBE Statement consists of a checklist of 22 items, which relate to the title, abstract, introduction, methods, results and discussion sections of articles. Eighteen items are common to cohort studies, case-control studies and cross-sectional studies and four are specific to each of the three study designs. The STROBE Statement provides guidance to authors about how to improve the reporting of observational studies and facilitates critical appraisal and interpretation of studies by reviewers, journal editors and readers. This explanatory and elaboration document is intended to enhance the use, understanding, and dissemination of the STROBE Statement. The meaning and rationale for each checklist item are presented. For each item, one or several published examples and, where possible, references to relevant empirical studies and methodological literature are provided. Examples of useful flow diagrams are also included. The STROBE Statement, this document, and the associated Web site (http://www.strobe-statement.org/) should be helpful resources to improve reporting of observational research.

Monitoring of emergency and intensive care patients: simple diagnostic aids

This article describes in short sections the use and interpretation of indirect blood pressure measurements, central venous pressure, body temperature, pulse oximetry, end tidal CO2 measurements, pulse and heart rate, urine production and emergency laboratory values. Most of these parameters are directly or indirectly linked to the perfusion of the patient. Optimizing these values are one of the most important goals in emergency and critical care medicine.

Contrasting interannual and multidecadal NAO variability

Decadal and longer timescale variability in the winter North Atlantic Oscillation (NAO) has considerable impact on regional climate, yet it remains unclear what fraction of this variability is potentially predictable. This study takes a new approach to this question by demonstrating clear physical differences between NAO variability on interannual-decadal (<30 year) and multidecadal (>30 year) timescales. It is shown that on the shorter timescale the NAO is dominated by variations in the latitude of the North Atlantic jet and storm track, whereas on the longer timescale it represents changes in their strength instead. NAO variability on the two timescales is associated with different dynamical behaviour in terms of eddy-mean flow interaction, Rossby wave breaking and blocking. The two timescales also exhibit different regional impacts on temperature and precipitation and different relationships to sea surface temperatures. These results are derived from linear regression analysis of the Twentieth Century and NCEP-NCAR reanalyses and of a high-resolution HiGEM General Circulation Model control simulation, with additional analysis of a long sea level pressure reconstruction. Evidence is presented for an influence of the ocean circulation on the longer timescale variability of the NAO, which is particularly clear in the model data. As well as providing new evidence of potential predictability, these findings are shown to have implications for the reconstruction and interpretation of long climate records.

New LA-ICP-MS cryocell and calibration technique for sub-millimeter analysis of ice cores

Ice cores provide a robust reconstruction of past climate. However, development of timescales by annual-layer counting, essential to detailed climate reconstruction and interpretation, on ice cores collected at low-accumulation sites or in regions of compressed ice, is problematic due to closely spaced layers. Ice-core analysis by laser ablation–inductively coupled plasma–mass spectrometry (LA-ICP-MS) provides sub-millimeter-scale sampling resolution (on the order of 100μm in this study) and the low detection limits (ng L–1) necessary to measure the chemical constituents preserved in ice cores. We present a newly developed cryocell that can hold a 1m long section of ice core, and an alternative strategy for calibration. Using ice-core samples from central Greenland, we demonstrate the repeatability of multiple ablation passes, highlight the improved sampling resolution, verify the calibration technique and identify annual layers in the chemical profile in a deep section of an ice core where annual layers have not previously been identified using chemistry. In addition, using sections of cores from the Swiss/Italian Alps we illustrate the relationship between Ca, Na and Fe and particle concentration and conductivity, and validate the LA-ICP-MS Ca profile through a direct comparison with continuous flow analysis results.

Virtopsy: postmortem imaging of the human heart in situ using MSCT and MRI.

The rapid further development of computed tomography (CT) and magnetic resonance imaging (MRI) induced the idea to use these techniques for postmortem documentation of forensic findings. Until now, only a few institutes of forensic medicine have acquired experience in postmortem cross-sectional imaging. Protocols, image interpretation and visualization have to be adapted to the postmortem conditions. Especially, postmortem alterations, such as putrefaction and livores, different temperature of the corpse and the loss of the circulation are a challenge for the imaging process and interpretation. Advantages of postmortem imaging are the higher exposure and resolution available in CT when there is no concern for biologic effects of ionizing radiation, and the lack of cardiac motion artifacts during scanning. CT and MRI may become useful tools for postmortem documentation in forensic medicine. In Bern, 80 human corpses underwent postmortem imaging by CT and MRI prior to traditional autopsy until the month of August 2003. Here, we describe the imaging appearance of postmortem alterations--internal livores, putrefaction, postmortem clotting--and distinguish them from the forensic findings of the heart, such as calcification, endocarditis, myocardial infarction, myocardial scarring, injury and other morphological alterations.

Strengths, weaknesses, opportunities and threats: A SWOT analysis of the ecosystem services framework

The ecosystem services concept (ES) is becoming a cornerstone of contemporary sustainability thought. Challenges with this concept and its applications are well documented, but have not yet been systematically assessed alongside strengths and external factors that influence uptake. Such an assessment could form the basis for improving ES thinking, further embedding it into environmental decisions and management. The Young Ecosystem Services Specialists (YESS) completed a Strengths–Weaknesses–Opportunities–Threats (SWOT) analysis of ES through YESS member surveys. Strengths include the approach being interdisciplinary, and a useful communication tool. Weaknesses include an incomplete scientific basis, frameworks being inconsistently applied, and accounting for nature's intrinsic value. Opportunities include alignment with existing policies and established methodologies, and increasing environmental awareness. Threats include resistance to change, and difficulty with interdisciplinary collaboration. Consideration of SWOT themes suggested five strategic areas for developing and implementing ES. The ES concept could improve decision-making related to natural resource use, and interpretation of the complexities of human-nature interactions. It is contradictory – valued as a simple means of communicating the importance of conservation, whilst also considered an oversimplification characterised by ambiguous language. Nonetheless, given sufficient funding and political will, the ES framework could facilitate interdisciplinary research, ensuring decision-making that supports sustainable development.

Hole in the Head: a Play, Accompanied by a Conspectus of Knowledge, Both Repressed and Researched, that Directly Influenced the Playwright in Her Development of a New Work

"Hole in the Head" is a play about a woman who wakes up. Maude wakes up in the first act, and in every subsequent scene she undergoes some form of physical or emotional awakening as characters walk in and out of her front door."Hole in the Head" is accompanied by an introduction that attempts to understand the interplay between creativity and academia through an analysis of theatre, feminist and queer theory, and science.

Alessandro Baricco: A Modern Homer / Alessandro Baricco: Omero Modern

Alessandro Baricco is an Italian author, pianist, journalist and music critic, among a wide range of many other talents. His novels have won great critical acclaim in Italy and France and are popular around the world. While generally considered among the postmodern writers, some critics have accused him of being a forerunner in a 1990s movement dubbed letteratura giovanile, that is juvenile literature that is simplistic, targets a young audience and is created for the sole purpose of making money. This criticism is unwarranted. Baricco is a multitalented author who pays strict attention to the quality of his work and weaves plotlines replete with a diverse set of genres, literary devices and symbolism, often inspired by other great writers and thinkers. However, literary critics have yet to acknowledge one of Baricco's strongest and most important influences: Homer, the ancient Greek bard and author of the epic poems, the Iliad and the Odyssey. Taking Baricco's work in a Homeric context can aid in viewing it as valid and important work, worthy of scholarly discussion and interpretation, rather than, as some critics accuse, a one-dimensional story meant only for children. This paper will argue that Baricco's work is Homeric and, in fact, Baricco's implementation of many of Homer's devices, such as his understanding of his audience and use rhythmic language and stereotyped story patterns, has aided Baricco's great success and popularity.

Ethnographic and epidemiologic approaches for the programming of prenatal and birth services in Mesa los Hornos, Mexico

The investigator conducted an action-oriented investigation of pregnancy and birth among the women of Mesa los Hornos, an urban squatter slum in Mexico City. Three aims guided the project: (1) To obtain information for improving prenatal and maternity service utilization; (2) To examine the utility of rapid ethnographic and epidemiologic assessment methodologies; (3) To cultivate community involvement in health development.^ Viewing service utilization as a culturally-bound decision, the study included a qualitative phase to explore women's cognition of pregnancy and birth, their perceived needs during pregnancy, and their criteria of service acceptability. A probability-based community survey delineated parameters of service utilization and pregnancy health events, and probed reasons for decisions to use medical services, lay midwives, or other sources of prenatal and labor and delivery assistance. Qualitative survey of service providers at relevant clinics, hospitals, and practices contributed information on service availability and access, and on coordination among private, social security, and public assistance health service sectors. The ethnographic approach to exploring the rationale for use or non-use of services provided a necessary complement to conventional barrier-based assessment, to inform planning of culturally appropriate interventions.^ Information collection and interpretation was conducted under the aegis of an advisory committee of community residents and service agency representatives; the residents' committee formulated recommendations for action based on findings, and forwarded the mandate to governmental social and urban development offices. Recommendations were designed to inform and develop community participation in health care decision-making.^ Rapid research methods are powerful tools for achieving community-based empowerment toward investigation and resolution of local health problems. But while ethnography works well in synergy with quantitative assessment approaches to strengthen the validity and richness of short-term field work, the author strongly urges caution in application of Rapid Ethnographic Assessments. An ethnographic sensibility is essential to the research enterprise for the development of an active and cooperative community base, the design and use of quantitative instruments, the appropriate use of qualitative techniques, and the interpretation of culturally-oriented information. However, prescribed and standardized Rapid Ethnographic Assessment techniques are counter-productive if used as research short-cuts before locale- and subject-specific cultural understanding is achieved. ^

BIOMEDICAL LANGUAGE UNDERSTANDING AND EXTRACTION (BLUE-TEXT): A MINIMAL SYNTACTIC, SEMANTIC METHOD

Clinical text understanding (CTU) is of interest to health informatics because critical clinical information frequently represented as unconstrained text in electronic health records are extensively used by human experts to guide clinical practice, decision making, and to document delivery of care, but are largely unusable by information systems for queries and computations. Recent initiatives advocating for translational research call for generation of technologies that can integrate structured clinical data with unstructured data, provide a unified interface to all data, and contextualize clinical information for reuse in multidisciplinary and collaborative environment envisioned by CTSA program. This implies that technologies for the processing and interpretation of clinical text should be evaluated not only in terms of their validity and reliability in their intended environment, but also in light of their interoperability, and ability to support information integration and contextualization in a distributed and dynamic environment. This vision adds a new layer of information representation requirements that needs to be accounted for when conceptualizing implementation or acquisition of clinical text processing tools and technologies for multidisciplinary research. On the other hand, electronic health records frequently contain unconstrained clinical text with high variability in use of terms and documentation practices, and without commitmentto grammatical or syntactic structure of the language (e.g. Triage notes, physician and nurse notes, chief complaints, etc). This hinders performance of natural language processing technologies which typically rely heavily on the syntax of language and grammatical structure of the text. This document introduces our method to transform unconstrained clinical text found in electronic health information systems to a formal (computationally understandable) representation that is suitable for querying, integration, contextualization and reuse, and is resilient to the grammatical and syntactic irregularities of the clinical text. We present our design rationale, method, and results of evaluation in processing chief complaints and triage notes from 8 different emergency departments in Houston Texas. At the end, we will discuss significance of our contribution in enabling use of clinical text in a practical bio-surveillance setting.

Modeling Techniques for the High-Resolution Interpretation of Cryo-Electron Microscopy Reconstructions

Essential biological processes are governed by organized, dynamic interactions between multiple biomolecular systems. Complexes are thus formed to enable the biological function and get dissembled as the process is completed. Examples of such processes include the translation of the messenger RNA into protein by the ribosome, the folding of proteins by chaperonins or the entry of viruses in host cells. Understanding these fundamental processes by characterizing the molecular mechanisms that enable then, would allow the (better) design of therapies and drugs. Such molecular mechanisms may be revealed trough the structural elucidation of the biomolecular assemblies at the core of these processes. Various experimental techniques may be applied to investigate the molecular architecture of biomolecular assemblies. High-resolution techniques, such as X-ray crystallography, may solve the atomic structure of the system, but are typically constrained to biomolecules of reduced flexibility and dimensions. In particular, X-ray crystallography requires the sample to form a three dimensional (3D) crystal lattice which is technically di‑cult, if not impossible, to obtain, especially for large, dynamic systems. Often these techniques solve the structure of the different constituent components within the assembly, but encounter difficulties when investigating the entire system. On the other hand, imaging techniques, such as cryo-electron microscopy (cryo-EM), are able to depict large systems in near-native environment, without requiring the formation of crystals. The structures solved by cryo-EM cover a wide range of resolutions, from very low level of detail where only the overall shape of the system is visible, to high-resolution that approach, but not yet reach, atomic level of detail. In this dissertation, several modeling methods are introduced to either integrate cryo-EM datasets with structural data from X-ray crystallography, or to directly interpret the cryo-EM reconstruction. Such computational techniques were developed with the goal of creating an atomic model for the cryo-EM data. The low-resolution reconstructions lack the level of detail to permit a direct atomic interpretation, i.e. one cannot reliably locate the atoms or amino-acid residues within the structure obtained by cryo-EM. Thereby one needs to consider additional information, for example, structural data from other sources such as X-ray crystallography, in order to enable such a high-resolution interpretation. Modeling techniques are thus developed to integrate the structural data from the different biophysical sources, examples including the work described in the manuscript I and II of this dissertation. At intermediate and high-resolution, cryo-EM reconstructions depict consistent 3D folds such as tubular features which in general correspond to alpha-helices. Such features can be annotated and later on used to build the atomic model of the system, see manuscript III as alternative. Three manuscripts are presented as part of the PhD dissertation, each introducing a computational technique that facilitates the interpretation of cryo-EM reconstructions. The first manuscript is an application paper that describes a heuristics to generate the atomic model for the protein envelope of the Rift Valley fever virus. The second manuscript introduces the evolutionary tabu search strategies to enable the integration of multiple component atomic structures with the cryo-EM map of their assembly. Finally, the third manuscript develops further the latter technique and apply it to annotate consistent 3D patterns in intermediate-resolution cryo-EM reconstructions. The first manuscript, titled An assembly model for Rift Valley fever virus, was submitted for publication in the Journal of Molecular Biology. The cryo-EM structure of the Rift Valley fever virus was previously solved at 27Å-resolution by Dr. Freiberg and collaborators. Such reconstruction shows the overall shape of the virus envelope, yet the reduced level of detail prevents the direct atomic interpretation. High-resolution structures are not yet available for the entire virus nor for the two different component glycoproteins that form its envelope. However, homology models may be generated for these glycoproteins based on similar structures that are available at atomic resolutions. The manuscript presents the steps required to identify an atomic model of the entire virus envelope, based on the low-resolution cryo-EM map of the envelope and the homology models of the two glycoproteins. Starting with the results of the exhaustive search to place the two glycoproteins, the model is built iterative by running multiple multi-body refinements to hierarchically generate models for the different regions of the envelope. The generated atomic model is supported by prior knowledge regarding virus biology and contains valuable information about the molecular architecture of the system. It provides the basis for further investigations seeking to reveal different processes in which the virus is involved such as assembly or fusion. The second manuscript was recently published in the of Journal of Structural Biology (doi:10.1016/j.jsb.2009.12.028) under the title Evolutionary tabu search strategies for the simultaneous registration of multiple atomic structures in cryo-EM reconstructions. This manuscript introduces the evolutionary tabu search strategies applied to enable a multi-body registration. This technique is a hybrid approach that combines a genetic algorithm with a tabu search strategy to promote the proper exploration of the high-dimensional search space. Similar to the Rift Valley fever virus, it is common that the structure of a large multi-component assembly is available at low-resolution from cryo-EM, while high-resolution structures are solved for the different components but lack for the entire system. Evolutionary tabu search strategies enable the building of an atomic model for the entire system by considering simultaneously the different components. Such registration indirectly introduces spatial constrains as all components need to be placed within the assembly, enabling the proper docked in the low-resolution map of the entire assembly. Along with the method description, the manuscript covers the validation, presenting the benefit of the technique in both synthetic and experimental test cases. Such approach successfully docked multiple components up to resolutions of 40Å. The third manuscript is entitled Evolutionary Bidirectional Expansion for the Annotation of Alpha Helices in Electron Cryo-Microscopy Reconstructions and was submitted for publication in the Journal of Structural Biology. The modeling approach described in this manuscript applies the evolutionary tabu search strategies in combination with the bidirectional expansion to annotate secondary structure elements in intermediate resolution cryo-EM reconstructions. In particular, secondary structure elements such as alpha helices show consistent patterns in cryo-EM data, and are visible as rod-like patterns of high density. The evolutionary tabu search strategy is applied to identify the placement of the different alpha helices, while the bidirectional expansion characterizes their length and curvature. The manuscript presents the validation of the approach at resolutions ranging between 6 and 14Å, a level of detail where alpha helices are visible. Up to resolution of 12 Å, the method measures sensitivities between 70-100% as estimated in experimental test cases, i.e. 70-100% of the alpha-helices were correctly predicted in an automatic manner in the experimental data. The three manuscripts presented in this PhD dissertation cover different computation methods for the integration and interpretation of cryo-EM reconstructions. The methods were developed in the molecular modeling software Sculptor (http://sculptor.biomachina.org) and are available for the scientific community interested in the multi-resolution modeling of cryo-EM data. The work spans a wide range of resolution covering multi-body refinement and registration at low-resolution along with annotation of consistent patterns at high-resolution. Such methods are essential for the modeling of cryo-EM data, and may be applied in other fields where similar spatial problems are encountered, such as medical imaging.