A Comparison of Mathematical and Statistical Modeling with Longitudinal Data: An Application to Ecological Momentary Assessment of Behavior Change in Individuals with Alcohol Use Disorder.

Ecological momentary assessment (EMA) has been broadly used to collect real-time longitudinal data in behavioral research. Several analytic methods have been applied to EMA data to understand the changes of motivation, behavior, and emotions on a daily or within-day basis. One challenge when utilizing those methods on intensive datasets in the behavioral field is to understand when and why the methods are appropriate to investigate particular research questions. In this manuscript, we compared two widely used methods (generalized estimating equations and generalized linear mixed models) in behavioral research with three other less frequently used methods (Markov models, generalized linear mixed-effects Markov models, and differential equations) in behavioral research but widely used in other fields. The purpose of this manuscript is to illustrate the application of five distinct analytic methods to one dataset of intensive longitudinal data on drinking behavior, highlighting the utility of each method.

Beyond body size-new traits for new heights in trait-based modelling of predator-prey dynamics.

Food webs map feeding interactions among species, providing a valuable tool for understanding and predicting community dynamics. Using species' body sizes is a promising avenue for parameterizing food-web models, but such approaches have not yet been able to fully recover observed community dynamics. Such discrepancies suggest that traits other than body size also play important roles. For example, differences in species' use of microhabitat or non-consumptive effects of intraguild predators may affect dynamics in ways not captured by body size. In Laubmeier et al. (2018), we developed a dynamic food-web model incorporating microhabitat and non-consumptive predator effects in addition to body size, and used simulations to suggest an optimal sampling design of a mesocosm experiment to test the model. Here, we perform the mesocosm experiment to generate empirical time-series of insect herbivore and predator abundance dynamics. We minimize least squares error between the model and time-series to determine parameter values of four alternative models, which differ in terms of including vs excluding microhabitat use and non-consumptive predator-predator effects. We use both statistical and expert-knowledge criteria to compare the models and find including both microhabitat use and non-consumptive predator-predator effects best explains observed aphid and predator population dynamics, followed by the model including microhabitat alone. This ranking suggests that microhabitat plays a larger role in driving population dynamics than non-consumptive predator-predator effects, although both are clearly important. Our results illustrate the importance of additional traits alongside body size in driving trophic interactions. They also point to the need to consider trophic interactions and population dynamics in a wider community context, where non-trophic impacts can dramatically modify the interplay between multiple predators and prey. Overall, we demonstrate the potential for utilizing traits beyond body size to improve trait-based models and the value of iterative cycling between theory, data and experiment to hone current insights into how traits affect food-web dynamics.

Using ultrasonic attenuation in cortical bone to infer distributions on pore size.

In this work we infer the underlying distribution on pore radius in human cortical bone samples using ultrasonic attenuation data. We first discuss how to formulate polydisperse attenuation models using a probabilistic approach and the Waterman Truell model for scattering attenuation. We then compare the Independent Scattering Approximation and the higher-order Waterman Truell models' forward predictions for total attenuation in polydisperse samples. Following this, we formulate an inverse problem under the Prohorov Metric Framework coupled with variational regularization to stabilize this inverse problem. We then use experimental attenuation data taken from human cadaver samples and solve inverse problems resulting in nonparametric estimates of the probability density function on pore radius. We compare these estimates to the "true" microstructure of the bone samples determined via microCT imaging. We find that our methodology allows us to reliably estimate the underlying microstructure of the bone from attenuation data.

Transformation of Cancer Care during and after the COVID Pandemic, a point of no return. The Experience of Italy.

Policymakers everywhere struggle to introduce therapeutic innovation while controlling costs, a particular challenge for the universal Italian National Healthcare System (SSN), which spends only 8.8% of GDP to care for one of the world's oldest populations. Oncology provides a telling example, where innovation has dramatically improved care and survival, transforming cancer into a chronic condition. However, innovation has also increased therapy duration, adverse event management, and service demand. The SSN risks collapse unless centralized cancer planning changes gear, particularly with Covid-19 causing treatment delays, worsening patient prognosis and straining capacity. In view of the 750 billion Euro "Next Generation EU", released by the European Union to relieve Member States hit by the pandemic, the SSN tapped a multidisciplinary research team to identify key strategies for equitable uptake of innovations in treatment and delivery, with emphasis on data-driven technological and managerial advancements - and lessons from Covid-19.

Inferring pore radius and density from ultrasonic attenuation using physics-based modeling.

This work proposes the use of two physics-based models for wave attenuation to infer the microstructure of cortical bone-like structures. One model for ultrasound attenuation in porous media is based on the independent scattering approximation (ISA) and the other model is based on the Waterman Truell (WT) approximation. The microstructural parameters of interest are pore radius and pore density. Attenuation data are simulated for three-dimensional structures mimicking cortical bone using the finite-difference time domain package SimSonic. These simulated structures have fixed sized pores (monodisperse), allowing fine-tuned control of the microstructural parameters. Structures with pore radii ranging from 50 to 100 µm and densities ranging from 20 to 50 pores/mm3 are generated in which only the attenuation due to scattering is considered. From here, an inverse problem is formulated and solved, calibrating the models to the simulated data and producing estimates of pore radius and density. The estimated microstructural parameters closely match the values used to simulate the data, validating the use of both the ISA and WT approximations to model ultrasonic wave attenuation in heterogeneous structures mimicking cortical bone. Furthermore, this illustrates the effectiveness of both models in inferring pore radius and density solely from ultrasonic attenuation data.

Lethal and sublethal effects of toxicants on bumble bee populations: a modelling approach.

Pollinator decline worldwide is well-documented; globally, chemical pesticides (especially the class of pesticides known as neonicotinoids) have been implicated in hymenopteran decline, but the mechanics and drivers of population trends and dynamics of wild bees is poorly understood. Declines and shifts in community composition of bumble bees (Bombus spp.) have been documented in North America and Europe, with a suite of lethal and sub-lethal effects of pesticides on bumble bee populations documented. We employ a mathematical model parameterized with values taken from the literature that uses differential equations to track bumble bee populations through time in order to attain a better understanding of toxicant effects on a developing colony of bumble bees. We use a delay differential equation (DDE) model, which requires fewer parameter estimations than agent-based models while affording us the ability to explicitly describe the effect of larval incubation and colony history on population outcomes. We explore how both lethal and sublethal effects such as reduced foraging ability may combine to affect population outcomes, and discuss the implications for the protection and conservation of ecosystem services.

Estimation of probability distributions of parameters using aggregate population data: analysis of a CAR T-cell cancer model.

In this effort we explain fundamental formulations for aggregate data inverse problems requiring estimation of probability distribution parameters. We use as a motivating example a class of CAR T-call cancer models in mice. After ascertaining results on model stability and sensitivity with respect to parameters, we carry out first elementary computations on the question how much data is needed for successful estimation of probability distributions.

Modeling Zika Virus Transmission Dynamics: Parameter Estimates, Disease Characteristics, and Prevention.

Because of limited data, much remains uncertain about parameters related to transmission dynamics of Zika virus (ZIKV). Estimating a large number of parameters from the limited information in data may not provide useful knowledge about the ZIKV. Here, we developed a method that utilizes a mathematical model of ZIKV dynamics and the complex-step derivative approximation technique to identify parameters that can be estimated from the available data. Applying our method to epidemic data from the ZIKV outbreaks in French Polynesia and Yap Island, we identified the parameters that can be estimated from these island data. Our results suggest that the parameters that can be estimated from a given data set, as well as the estimated values of those parameters, vary from Island to Island. Our method allowed us to estimate some ZIKV-related parameters with reasonable confidence intervals. We also computed the basic reproduction number to be from 2.03 to 3.20 across islands. Furthermore, using our model, we evaluated potential prevention strategies and found that peak prevalence can be reduced to nearly 10% by reducing mosquito-to-human contact by at least 60% or increasing mosquito death by at least a factor of three of the base case. With these preventions, the final outbreak-size is predicted to be negligible, thereby successfully controlling ZIKV epidemics.

Population model for the decline of Homalodisca vitripennis (Hemiptera: Cicadellidae) over a ten-year period.

The glassy-winged sharpshooter, Homalodisca vitripennis (Germar), is an invasive pest which presents a major economic threat to grape industries in California, because it spreads a disease-causing bacterium, Xylella fastidiosa. In this note we develop a time and temperature dependent mathematical model to analyze aggregate population data for H. vitripennis from a 10-year study consisting of biweekly monitoring of H. vitripennis populations on unsprayed citrus, during which H. vitripennis decreased significantly. This model was fitted to the aggregate H. vitripennis time series data using iterative reweighted weighted least squares (IRWLS) with assumed probability distributions for certain parameter values. Results indicate that the H. vitripennis model fits the phenological and temperature data reasonably well, but the observed population decrease may possibly be attributed to factors other than the abiotic effect of temperature. A key factor responsible for this decline but not analyzed here could be biotic, for example, potentially parasitism of H. vitripennis eggs by Cosmocomoidea ashmeadi. A biological control program targeting H. vitripennis utilizing the mymarid egg parasitoid Cosmocomoidea (formerly Gonatocerus) ashmeadi (Girault) is described.

Analysis of compartments-in-series models of liver metabolism as partial differential equations: the effect of dispersion and number of compartments.

Non-alcoholic fatty liver disease is the most common cause of chronic liver disease. Precipitated by the build up of extra fat in the liver not caused by alcohol, it is still not understood why steatosis occurs where it does in the liver microstructure in non-alcoholic fatty liver disease. It is likely, however, that the location of steatosis is due, at least in part, to metabolic zonation (heterogeneity among liver cells in function and enzyme expression). Recently, there has been an influx of computational and mathematical models in order to investigate the relationship between metabolic zonation and steatosis in non-alcoholic fatty liver disease. Of interest among these models are "compartments-in-series" models. Compartments-in-series models include the spatial distribution of metabolite concentrations via series of compartments that are connected through some representation of blood flow. In this paper, we analyze one such model, focusing specifically at how the number of compartments and inclusion of dispersion in the flow affect simulation results. We find the number of compartments to have a much larger effect than the inclusion of dispersion, however this is likely due to numerical artifacts. Overall, we conclude that considering partial differential equations that are equivalent to compartments-in-series models would be beneficial both in computation and in theoretical analyses.

Correctly modeling plant-insect-herbivore-pesticide interactions as aggregate data.

We consider a population dynamics model in investigating data from controlled experiments with aphids in broccoli patches surrounded by different margin types (bare or weedy ground) and three levels of insecticide spray (no, light, or heavy spray). The experimental data is clearly aggregate in nature. In previous efforts [1], the aggregate nature of the data was ignored. In this paper, we embrace this aspect of the experiment and correctly model the data as aggregate data, comparing the results to the previous approach. We discuss cases in which the approach may provide similar results as well as cases in which there is a clear difference in the resulting fit to the data.

Ecosystem function in predator-prey food webs-confronting dynamic models with empirical data.

Most ecosystem functions and related services involve species interactions across trophic levels, for example, pollination and biological pest control. Despite this, our understanding of ecosystem function in multitrophic communities is poor, and research has been limited to either manipulation in small communities or statistical descriptions in larger ones. Recent advances in food web ecology may allow us to overcome the trade-off between mechanistic insight and ecological realism. Molecular tools now simplify the detection of feeding interactions, and trait-based approaches allow the application of dynamic food web models to real ecosystems. We performed the first test of an allometric food web model's ability to replicate temporally nonaggregated abundance data from the field and to provide mechanistic insight into the function of predation. We aimed to reproduce and explore the drivers of the population dynamics of the aphid herbivore Rhopalosiphum padi observed in ten Swedish barley fields. We used a dynamic food web model, taking observed interactions and abundances of predators and alternative prey as input data, allowing us to examine the role of predation in aphid population control. The inverse problem methods were used for simultaneous model fit optimization and model parameterization. The model captured >70% of the variation in aphid abundance in five of ten fields, supporting the model-embodied hypothesis that body size can be an important determinant of predation in the arthropod community. We further demonstrate how in-depth model analysis can disentangle the likely drivers of function, such as the community's abundance and trait composition. Analysing the variability in model performance revealed knowledge gaps, such as the source of episodic aphid mortality, and general method development needs that, if addressed, would further increase model success and enable stronger inference about ecosystem function. The results demonstrate that confronting dynamic food web models with abundance data from the field is a viable approach to evaluate ecological theory and to aid our understanding of function in real ecosystems. However, to realize the full potential of food web models, in ecosystem function research and beyond, trait-based parameterization must be refined and extended to include more traits than body size.

Ultrasound-responsive droplets for therapy: A review.

The last two decades have seen the development of acoustically activated droplets, also known as phase-change emulsions, from a diagnostic tool to a therapeutic agent. Through bubble effects and triggered drug release, these superheated agents have found potential applications from oncology to neuromodulation. The aim of this review is to summarise the key developments in therapeutic droplet design and use, to discuss the current challenges slowing clinical translation, and to highlight the new frontiers progressing towards clinical implementation. The literature is summarised by addressing the droplet design criteria and by carrying out a multiparametric study of a range of droplet formulations and their associated vaporisation thresholds.

Optimal design for dynamical modeling of pest populations.

We apply SE-optimal design methodology to investigate optimal data collection procedures as a first step in investigating information content in ecoinformatics data sets. To illustrate ideas we use a simple phenomenological citrus red mite population model for pest dynamics. First the optimal sampling distributions for a varying number of data points are determined. We then analyze these optimal distributions by comparing the standard errors of parameter estimates corresponding to each distribution. This allows us to investigate how many data are required to have confidence in model parameter estimates in order to employ dynamical modeling to infer population dynamics. Our results suggest that a field researcher should collect at least 12 data points at the optimal times. Data collected according to this procedure along with dynamical modeling will allow us to estimate population dynamics from presence/absence-based data sets through the development of a scaling relationship. These Likert-type data sets are commonly collected by agricultural pest management consultants and are increasingly being used in ecoinformatics studies. By applying mathematical modeling with the relationship scale from the new data, we can then explore important integrated pest management questions using past and future presence/absence data sets.

The effect of pore size and density on ultrasonic attenuation in porous structures with mono-disperse random pore distribution: A two-dimensional in-silico study.

This work proposes a power law model to describe the attenuation of ultrasonic waves in non-absorbing heterogeneous media with randomly distributed scatterers, mimicking a simplified structure of cortical bone. This paper models the propagation in heterogeneous structures with controlled porosity using a two-dimensional finite-difference time domain numerical simulation in order to measure the frequency dependent attenuation. The paper then fits a phenomenological model to the simulated frequency dependent attenuation by optimizing parameters under an ordinary least squares framework. Local sensitivity analysis is then performed on the resulting parameter estimates in order to determine to which estimates the model is most sensitive. This paper finds that the sensitivity of the model to various parameter estimates depends on the micro-architectural parameters, pore diameter (ϕ) and pore density (ρ). In order to get a sense for how confidently model parameters are able to be estimated, 95% confidence intervals for these estimates are calculated. In doing so, the ability to estimate model-sensitive parameters with a high degree of confidence is established. In the future, being able to accurately estimate model parameters from which micro-architectural ones could be inferred will allow pore density and diameter to be estimated via an inverse problem given real or simulated ultrasonic data to be determined.

Improving the generation and selection of virtual populations in quantitative systems pharmacology models.

Quantitative systems pharmacology (QSP) models aim to describe mechanistically the pathophysiology of disease and predict the effects of therapies on that disease. For most drug development applications, it is important to predict not only the mean response to an intervention but also the distribution of responses, due to inter-patient variability. Given the necessary complexity of QSP models, and the sparsity of relevant human data, the parameters of QSP models are often not well determined. One approach to overcome these limitations is to develop alternative virtual patients (VPs) and virtual populations (Vpops), which allow for the exploration of parametric uncertainty and reproduce inter-patient variability in response to perturbation. Here we evaluated approaches to improve the efficiency of generating Vpops. We aimed to generate Vpops without sacrificing diversity of the VPs' pathophysiologies and phenotypes. To do this, we built upon a previously published approach (Allen et al., 2016) by (a) incorporating alternative optimization algorithms (genetic algorithm and Metropolis-Hastings) or alternatively (b) augmenting the optimized objective function. Each method improved the baseline algorithm by requiring significantly fewer plausible patients (precursors to VPs) to create a reasonable Vpop.

Estimating intratumoral heterogeneity from spatiotemporal data.

Glioblastoma multiforme (GBM) is a malignant brain cancer with a tendency to both migrate and proliferate. We propose modeling GBM with heterogeneity in cell phenotypes using a random differential equation version of the reaction-diffusion equation, where the parameters describing diffusion (D) and proliferation ([Formula: see text]) are random variables. We investigate the ability to perform the inverse problem to recover the probability distributions of D and [Formula: see text] using the Prohorov metric, for a variety of probability distribution functions. We test the ability to perform the inverse problem for noisy synthetic data. We then examine the predicted effect of treatment, specifically, chemotherapy, when assuming such a heterogeneous population and compare with predictions from a homogeneous cell population model.

From theory to experimental design-Quantifying a trait-based theory of predator-prey dynamics.

Successfully applying theoretical models to natural communities and predicting ecosystem behavior under changing conditions is the backbone of predictive ecology. However, the experiments required to test these models are dictated by practical constraints, and models are often opportunistically validated against data for which they were never intended. Alternatively, we can inform and improve experimental design by an in-depth pre-experimental analysis of the model, generating experiments better targeted at testing the validity of a theory. Here, we describe this process for a specific experiment. Starting from food web ecological theory, we formulate a model and design an experiment to optimally test the validity of the theory, supplementing traditional design considerations with model analysis. The experiment itself will be run and described in a separate paper. The theory we test is that trophic population dynamics are dictated by species traits, and we study this in a community of terrestrial arthropods. We depart from the Allometric Trophic Network (ATN) model and hypothesize that including habitat use, in addition to body mass, is necessary to better model trophic interactions. We therefore formulate new terms which account for micro-habitat use as well as intra- and interspecific interference in the ATN model. We design an experiment and an effective sampling regime to test this model and the underlying assumptions about the traits dominating trophic interactions. We arrive at a detailed sampling protocol to maximize information content in the empirical data obtained from the experiment and, relying on theoretical analysis of the proposed model, explore potential shortcomings of our design. Consequently, since this is a "pre-experimental" exercise aimed at improving the links between hypothesis formulation, model construction, experimental design and data collection, we hasten to publish our findings before analyzing data from the actual experiment, thus setting the stage for strong inference.

THE PROHOROV METRIC FRAMEWORK AND AGGREGATE DATA INVERSE PROBLEMS FOR RANDOM PDEs.

We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades [24, 5, 12, 28, 16]. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other) least squares estimates and estimators for the measure estimation problem with specific application to random PDEs.

Inferring porosity from frequency dependent attenuation in cortical bone mimicking porous media.

Osteoporosis affects porosity in cortical bone. Quantifying levels of osteoporosis by inferring the micro-architectural properties from ultrasonic wave attenuation in cortical bone has yet to be done. In this work we use a phenomenological, power law model to describe the frequency dependent attenuation in non-absorbing porous media mimicking a simplified cortical bone structure. We optimize this model to fit data generated using a finite-difference, time domain (FDTD) numerical simulation. Model parameters are estimated using an ordinary least squares (OLS) formulation of the inverse problem. With these we determine linear, functional relationships between the model parameter estimates and the micro-architectural parameters, pore density and pore diameter. These relationships allow us to infer ranges of porosity from simulated attenuation data. Repeating this process for attenuation data collected from cortical bone samples could allow one to characterize the micro-architectural properties of bone.