Fast Prediction of Femoral Biomechanics Using Supervised Machine Learning and Statistical Shape Modeling

Finite element (FE) analysis is an important computational tool in biomechanics. However, its adoption into clinical practice has been hampered by its computational complexity and required high technical competences for clinicians. In this paper we propose a supervised learning approach to predict the outcome of the FE analysis. We demonstrate our approach on clinical CT and X-ray femur images for FE predictions ( FEP), with features extracted, respectively, from a statistical shape model and from 2D-based morphometric and density information. Using leave-one-out experiments and sensitivity analysis, comprising a database of 89 clinical cases, our method is capable of predicting the distribution of stress values for a walking loading condition with an average correlation coefficient of 0.984 and 0.976, for CT and X-ray images, respectively. These findings suggest that supervised learning approaches have the potential to leverage the clinical integration of mechanical simulations for the treatment of musculoskeletal conditions.

Modeling postglacial vegetation dynamics of temperate forests on the Olympic Peninsula (WA, USA) with special regard to snowpack

Past and future forest composition and distribution in temperate mountain ranges is strongly influenced by temperature and snowpack. We used LANDCLIM, a spatially explicit, dynamic vegetation model, to simulate forest dynamics for the last 16,000 years and compared the simulation results to pollen and macrofossil records at five sites on the Olympic Peninsula (Washington, USA). To address the hydrological effects of climate-driven variations in snowpack on simulated forest dynamics, we added a simple snow accumulation-and-melt module to the vegetation model and compared simulations with and without the module. LANDCLIM produced realistic present-day species composition with respect to elevation and precipitation gradients. Over the last 16,000 years, simulations driven by transient climate data from an atmosphere-ocean general circulation model (AOGCM) and by a chironomid-based temperature reconstruction captured Late-glacial to Late Holocene transitions in forest communities. Overall, the reconstruction-driven vegetation simulations matched observed vegetation changes better than the AOGCM-driven simulations. This study also indicates that forest composition is very sensitive to snowpack-mediated changes in soil moisture. Simulations without the snow module showed a strong effect of snowpack on key bioclimatic variables and species composition at higher elevations. A projected upward shift of the snow line and a decrease in snowpack might lead to drastic changes in mountain forests composition and even a shift to dry meadows due to insufficient moisture availability in shallow alpine soils.

Early Life History and a Modeling Framework for Lobster (Homarus Americanus) Populations in the Gulf of Maine

Beginning in the late 1980s, lobster (Homarus americanus) landings for the state of Maine and the Bay of Fundy increased to levels more than three times their previous 20-year means. Reduced predation may have permitted the expansion of lobsters into previously inhospitable territory, but we argue that in this region the spatial patterns of recruitment and the abundance of lobsters are substantially driven by events governing the earliest life history stages, including the abundance and distribution of planktonic stages and their initial settlement as Young-of-Year (YOY) lobsters. Settlement densities appear to be strongly driven by abundance of the pelagic postlarvae. Postlarvae and YOY show large-scale spatial patterns commensurate with coastal circulation, but also multi-year trends in abundance and abrupt shifts in abundance and spatial patterns that signal strong environmental forcing. The extent of the coastal shelf that defines the initial settlement grounds for lobsters is important to future population modeling. We address one part of this definition by examining patterns of settlement with depth, and discuss a modeling framework for the full life history of lobsters in the Gulf of Maine.

Carbon-Based Primary Productivity Modeling With Vertically Resolved Photoacclimation

Net primary production (NPP) is commonly modeled as a function of chlorophyll concentration (Chl), even though it has been long recognized that variability in intracellular chlorophyll content from light acclimation and nutrient stress confounds the relationship between Chl and phytoplankton biomass. It was suggested previously that satellite estimates of backscattering can be related to phytoplankton carbon biomass (C) under conditions of a conserved particle size distribution or a relatively stable relationship between C and total particulate organic carbon. Together, C and Chl can be used to describe physiological state (through variations in Chl:C ratios) and NPP. Here, we fully develop the carbon-based productivity model (CbPM) to include information on the subsurface light field and nitracline depths to parameterize photoacclimation and nutrient stress throughout the water column. This depth-resolved approach produces profiles of biological properties (Chl, C, NPP) that are broadly consistent with observations. The CbPM is validated using regional in situ data sets of irradiance-derived products, phytoplankton chlorophyll: carbon ratios, and measured NPP rates. CbPM-based distributions of global NPP are significantly different in both space and time from previous Chl-based estimates because of the distinction between biomass and physiological influences on global Chl fields. The new model yields annual, areally integrated water column production of similar to 52 Pg C a(-1) for the global oceans.

A LAPLACE TRANSFORM PAIR MODEL TO DETERMINE BREMSSTRAHLUNG SPECTRA FROM ATTENUATION DATA (RADIATION, X-RAY, SPECTRAL MODELING)

Every x-ray attenuation curve inherently contains all the information necessary to extract the complete energy spectrum of a beam. To date, attempts to obtain accurate spectral information from attenuation data have been inadequate.^ This investigation presents a mathematical pair model, grounded in physical reality by the Laplace Transformation, to describe the attenuation of a photon beam and the corresponding bremsstrahlung spectral distribution. In addition the Laplace model has been mathematically extended to include characteristic radiation in a physically meaningful way. A method to determine the fraction of characteristic radiation in any diagnostic x-ray beam was introduced for use with the extended model.^ This work has examined the reconstructive capability of the Laplace pair model for a photon beam range of from 50 kVp to 25 MV, using both theoretical and experimental methods.^ In the diagnostic region, excellent agreement between a wide variety of experimental spectra and those reconstructed with the Laplace model was obtained when the atomic composition of the attenuators was accurately known. The model successfully reproduced a 2 MV spectrum but demonstrated difficulty in accurately reconstructing orthovoltage and 6 MV spectra. The 25 MV spectrum was successfully reconstructed although poor agreement with the spectrum obtained by Levy was found.^ The analysis of errors, performed with diagnostic energy data, demonstrated the relative insensitivity of the model to typical experimental errors and confirmed that the model can be successfully used to theoretically derive accurate spectral information from experimental attenuation data. ^

The Discontinuous Nature of Kriging Interpolation for Digital Terrain Modeling

Kriging is a widely employed method for interpolating and estimating elevations from digital elevation data. Its place of prominence is due to its elegant theoretical foundation and its convenient practical implementation. From an interpolation point of view, kriging is equivalent to a thin-plate spline and is one species among the many in the genus of weighted inverse distance methods, albeit with attractive properties. However, from a statistical point of view, kriging is a best linear unbiased estimator and, consequently, has a place of distinction among all spatial estimators because any other linear estimator that performs as well as kriging (in the least squares sense) must be equivalent to kriging, assuming that the parameters of the semivariogram are known. Therefore, kriging is often held to be the gold standard of digital terrain model elevation estimation. However, I prove that, when used with local support, kriging creates discontinuous digital terrain models, which is to say, surfaces with “rips” and “tears” throughout them. This result is general; it is true for ordinary kriging, kriging with a trend, and other forms. A U.S. Geological Survey (USGS) digital elevation model was analyzed to characterize the distribution of the discontinuities. I show that the magnitude of the discontinuity does not depend on surface gradient but is strongly dependent on the size of the kriging neighborhood.

Modeling the survival of T-cell lymphocytes using compound branching processes

Radiotherapy has been a method of choice in cancer treatment for a number of years. Mathematical modeling is an important tool in studying the survival behavior of any cell as well as its radiosensitivity. One particular cell under investigation is the normal T-cell, the radiosensitivity of which may be indicative to the patient's tolerance to radiation doses.^ The model derived is a compound branching process with a random initial population of T-cells that is assumed to have compound distribution. T-cells in any generation are assumed to double or die at random lengths of time. This population is assumed to undergo a random number of generations within a period of time. The model is then used to obtain an estimate for the survival probability of T-cells for the data under investigation. This estimate is derived iteratively by applying the likelihood principle. Further assessment of the validity of the model is performed by simulating a number of subjects under this model.^ This study shows that there is a great deal of variation in T-cells survival from one individual to another. These variations can be observed under normal conditions as well as under radiotherapy. The findings are in agreement with a recent study and show that genetic diversity plays a role in determining the survival of T-cells. ^

Mixture modeling for joint analysis of survival, discrete, and continuous data

Mixture modeling is commonly used to model categorical latent variables that represent subpopulations in which population membership is unknown but can be inferred from the data. In relatively recent years, the potential of finite mixture models has been applied in time-to-event data. However, the commonly used survival mixture model assumes that the effects of the covariates involved in failure times differ across latent classes, but the covariate distribution is homogeneous. The aim of this dissertation is to develop a method to examine time-to-event data in the presence of unobserved heterogeneity under a framework of mixture modeling. A joint model is developed to incorporate the latent survival trajectory along with the observed information for the joint analysis of a time-to-event variable, its discrete and continuous covariates, and a latent class variable. It is assumed that the effects of covariates on survival times and the distribution of covariates vary across different latent classes. The unobservable survival trajectories are identified through estimating the probability that a subject belongs to a particular class based on observed information. We applied this method to a Hodgkin lymphoma study with long-term follow-up and observed four distinct latent classes in terms of long-term survival and distributions of prognostic factors. Our results from simulation studies and from the Hodgkin lymphoma study demonstrated the superiority of our joint model compared with the conventional survival model. This flexible inference method provides more accurate estimation and accommodates unobservable heterogeneity among individuals while taking involved interactions between covariates into consideration.^

Modeling the sensitivity of precipitation oxygen isotopes to the Last Glacial Maximum boundary conditions: A study using Community Atmosphere Model (CAM3.0)

To understand the validity of d18O proxy records as indicators of past temperature change, a series of experiments was conducted using an atmospheric general circulation model fitted with water isotope tracers (Community Atmosphere Model version 3.0, IsoCAM). A pre-industrial simulation was performed as the control experiment, as well as a simulation with all the boundary conditions set to Last Glacial Maximum (LGM) values. Results from the pre-industrial and LGM simulations were compared to experiments in which the influence of individual boundary conditions (greenhouse gases, ice sheet albedo and topography, sea surface temperature (SST), and orbital parameters) were changed each at a time to assess their individual impact. The experiments were designed in order to analyze the spatial variations of the oxygen isotopic composition of precipitation (d18Oprecip) in response to individual climate factors. The change in topography (due to the change in land ice cover) played a significant role in reducing the surface temperature and d18Oprecip over North America. Exposed shelf areas and the ice sheet albedo reduced the Northern Hemisphere surface temperature and d18Oprecip further. A global mean cooling of 4.1 °C was simulated with combined LGM boundary conditions compared to the control simulation, which was in agreement with previous experiments using the fully coupled Community Climate System Model (CCSM3). Large reductions in d18Oprecip over the LGM ice sheets were strongly linked to the temperature decrease over them. The SST and ice sheet topography changes were responsible for most of the changes in the climate and hence the d18Oprecip distribution among the simulations.

Three species distribution models for the marine diatom Fragilariopsis kerguelensis of the Southern Ocean, links to NetCDF files

Fragilariopsis kerguelensis, a dominant diatom species throughout the Antarctic Circumpolar Current, is coined to be one of the main drivers of the biological silicate pump. Here, we study the distribution of this important species and expected consequences of climate change upon it, using correlative species distribution modeling and publicly available presence-only data. As experience with SDM is scarce for marine phytoplankton, this also serves as a pilot study for this organism group. We used the maximum entropy method to calculate distribution models for the diatom F. kerguelensis based on yearly and monthly environmental data (sea surface temperature, salinity, nitrate and silicate concentrations). Observation data were harvested from GBIF and the Global Diatom Database, and for further analyses also from the Hustedt Diatom Collection (BRM). The models were projected on current yearly and seasonal environmental data to study current distribution and its seasonality. Furthermore, we projected the seasonal model on future environmental data obtained from climate models for the year 2100. Projected on current yearly averaged environmental data, all models showed similar distribution patterns for F. kerguelensis. The monthly model showed seasonality, for example, a shift of the southern distribution boundary toward the north in the winter. Projections on future scenarios resulted in a moderately to negligibly shrinking distribution area and a change in seasonality. We found a substantial bias in the publicly available observation datasets, which could be reduced by additional observation records we obtained from the Hustedt Diatom Collection. Present-day distribution patterns inferred from the models coincided well with background knowledge and previous reports about F. kerguelensis distribution, showing that maximum entropy-based distribution models are suitable to map distribution patterns for oceanic planktonic organisms. Our scenario projections indicate moderate effects of climate change upon the biogeography of F. kerguelensis.

Distribution of biological, anthropogenic, and volcanic constituents in the San Francisco Bay Coastal System

Although conventional sediment parameters (mean grain size, sorting, and skewness) and provenance have typically been used to infer sediment transport pathways, most freshwater, brackish, and marine environments are also characterized by abundant sediment constituents of biological, and possibly anthropogenic and volcanic, origin that can provide additional insight into local sedimentary processes. The biota will be spatially distributed according to its response to environmental parameters such as water temperature, salinity, dissolved oxygen, organic carbon content, grain size, and intensity of currents and tidal flow, whereas the presence of anthropogenic and volcanic constituents will reflect proximity to source areas and whether they are fluvially- or aerially-transported. Because each of these constituents have a unique environmental signature, they are a more precise proxy for that source area than the conventional sedimentary process indicators. This San Francisco Bay Coastal System study demonstrates that by applying a multi-proxy approach, the primary sites of sediment transport can be identified. Many of these sites are far from where the constituents originated, showing that sediment transport is widespread in the region. Although not often used, identifying and interpreting the distribution of naturally-occurring and allochthonous biologic, anthropogenic, and volcanic sediment constituents is a powerful tool to aid in the investigation of sediment transport pathways in other coastal systems.

Investigation of the seasonality of N. pachyderma in the North Atlantic Ocean during Heinrich Stadial 1 using an ecosystem modeling approach

Fossil shells of planktonic foraminifera serve as the prime source of information on past changes in surface ocean conditions. Because the population size of planktonic foraminifera species changes throughout the year, the signal preserved in fossil shells is biased towards the conditions when species production was at its maximum. The amplitude of the potential seasonal bias is a function of the magnitude of the seasonal cycle in production. Here we use a planktonic foraminifera model coupled to an ecosystem model to investigate to what degree seasonal variations in production of the species Neogloboquadrina pachyderma may affect paleoceanographic reconstructions during Heinrich Stadial 1 (~18-15 cal. ka B.P.) in the North Atlantic Ocean. The model implies that during Heinrich Stadial 1 the maximum seasonal production occurred later in the year compared to the Last Glacial Maximum (~21-19 cal. ka B.P.) and the pre-industrial era north of 30 ºN. A diagnosis of the model output indicates that this change reflects the sensitivity of the species to the seasonal cycle of sea-ice cover and food supply, which collectively lead to shifts in the modeled maximum production from the Last Glacial Maximum to Heinrich Stadial 1 by up to six months. Assuming equilibrium oxygen isotopic incorporation in the shells of N. pachyderma, the modeled changes in seasonality would result in an underestimation of the actual magnitude of the meltwater isotopic signal recorded by fossil assemblages of N. pachyderma wherever calcification is likely to take place.