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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.
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Alcoholismo , Evaluación Ecológica Momentánea , Humanos , Conceptos Matemáticos , Modelos Biológicos , Consumo de Bebidas Alcohólicas/psicologíaRESUMEN
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.
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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.
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Hueso Cortical , Ultrasonido , Densidad Ósea , Huesos , Hueso Cortical/diagnóstico por imagen , Porosidad , UltrasonografíaRESUMEN
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.
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Abejas/fisiología , Monitoreo del Ambiente , Sustancias Peligrosas/toxicidad , Agricultura , Animales , Ecosistema , Neonicotinoides/toxicidad , Plaguicidas/toxicidad , PolinizaciónRESUMEN
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.
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Neoplasias Encefálicas/patología , Glioblastoma/patología , Modelos Biológicos , Antineoplásicos/uso terapéutico , Neoplasias Encefálicas/tratamiento farmacológico , Movimiento Celular , Proliferación Celular , Simulación por Computador , Glioblastoma/tratamiento farmacológico , Humanos , Conceptos Matemáticos , Invasividad Neoplásica/patología , Fenotipo , Probabilidad , Análisis Espacio-Temporal , Carga Tumoral/efectos de los fármacosRESUMEN
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 (Ï) 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.
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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.
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We continue our efforts in modeling Daphnia magna, a species of water flea, by proposing a continuously structured population model incorporating density-dependent and density-independent fecundity and mortality rates. We collected new individual-level data to parameterize the individual demographics relating food availability and individual daphnid growth. Our model is fit to experimental data using the generalized least-squares framework, and we use cross-validation and Akaike Information Criteria to select hyper-parameters. We present our confidence intervals on parameter estimates.
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Daphnia/crecimiento & desarrollo , Modelos Biológicos , Animales , Simulación por Computador , Intervalos de Confianza , Daphnia/fisiología , Femenino , Fertilidad , Alimentos , Análisis de los Mínimos Cuadrados , Masculino , Conceptos Matemáticos , Dinámica PoblacionalRESUMEN
We use dynamical systems modeling to help understand how selected intra-personal factors interact to form mechanisms of behavior change in problem drinkers. Our modeling effort illustrates the iterative process of modeling using an individual's clinical data. Due to the lack of previous work in modeling behavior change in individual patients, we build our preliminary model relying on our understandings of the psychological relationships among the variables. This model is refined and the psychological understanding is then enhanced through the iterative modeling process. Our results suggest that this is a promising direction in research in alcohol use disorders as well as other behavioral sciences.
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Consumo de Bebidas Alcohólicas , Alcoholismo/terapia , Toma de Decisiones , Modelos Teóricos , HumanosRESUMEN
Randomized longitudinal clinical trials are the gold standard to evaluate the effectiveness of interventions among different patient treatment groups. However, analysis of such clinical trials becomes difficult in the presence of missing data, especially in the case where the study endpoints become difficult to measure because of subject dropout rates or/and the time to discontinue the assigned interventions are different among the patient groups. Here we report on using a validated mathematical model combined with an inverse problem approach to predict the values for the missing endpoints. A small randomized HIV clinical trial where endpoints for most of patients are missing is used to demonstrate this approach.
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Antiretroviral therapy is able to suppress the viral load to below the detection limit, but it is not able to eradicate HIV reservoirs. Thus, there is a critical need for a novel treatment to eradicate (or reduce) the reservoir in order to eliminate the need for a lifelong adherence to antiretroviral therapy, which is expensive and potentially toxic. In this paper, we investigate the possible pharmacological strategies or combinations of strategies that may be beneficial to reduce or possibly eradicate the latent reservoir. We do this via studies with a validated mathematical model, where the parameter values are obtained with newly acquired clinical data for HIV patients. Our findings indicate that the strategy of reactivating the reservoir combined with enhancement of the killing rate of HIV-specific CD8+ T cells is able to eradicate the reservoir. In addition, our analysis shows that a targeted suppression of the immune system is also a possible strategy to eradicate the reservoir.
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Linfocitos T CD4-Positivos/virología , Linfocitos T CD8-positivos/virología , Infecciones por VIH/inmunología , Infecciones por VIH/terapia , Fármacos Anti-VIH/química , Linfocitos T CD4-Positivos/inmunología , Linfocitos T CD8-positivos/inmunología , Proliferación Celular , Simulación por Computador , VIH-1 , Homeostasis , Humanos , Modelos Biológicos , Carga Viral , Latencia del VirusRESUMEN
Many experimental systems in biology, especially synthetic gene networks, are amenable to perturbations that are controlled by the experimenter. We developed an optimal design algorithm that calculates optimal observation times in conjunction with optimal experimental perturbations in order to maximize the amount of information gained from longitudinal data derived from such experiments. We applied the algorithm to a validated model of a synthetic Brome Mosaic Virus (BMV) gene network and found that optimizing experimental perturbations may substantially decrease uncertainty in estimating BMV model parameters.
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In the context of inverse or parameter estimation problems we demonstrate the use of statistically based model comparison tests in several examples of practical interest. In these examples we are interested in questions related to information content of a particular given data set and whether the data will support a more complicated model to describe it. In the first example we compare fits for several different models to describe simple decay in a size histogram for aggregates in amyloid fibril formation. In a second example we investigate whether the information content in data sets for the pest Lygus hesperus in cotton fields as it is currently collected is sufficient to support a model in which one distinguishes between nymphs and adults. Finally in a third example with data for patients having undergone an organ transplant, we question whether the data content is sufficient to estimate more than 5 of the fundamental parameters in a particular dynamic model.
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We formulate an optimal design problem for the selection of best states to observe and optimal sampling times and locations for parameter estimation or inverse problems involving complex nonlinear nonlinear partial differential systems. An iterative algorithm for implementation of the resulting methodology is proposed.
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We developed a series of models for the label decay in cell proliferation assays when the intracellular dye carboxyfluorescein succinimidyl ester (CFSE) is used as a staining agent. Data collected from two healthy patients were used to validate the models and to compare the models with the Akiake Information Criteria. The distinguishing features of multiple decay rates in the data are readily characterized and explained via time dependent decay models such as the logistic and Gompertz models.
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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.
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Cadena Alimentaria , Conducta Predatoria , Animales , Tamaño Corporal , Herbivoria , InsectosRESUMEN
The host inflammatory response to HIV invasion is a necessary component of the innate antiviral activity that vaccines and early interventions seek to exploit/enhance. However, the response is dependent on CD4+ T-helper cell 1 (Th1) recruitment and activation. It is this very recruitment of HIV-susceptible target cells that is associated with the initial viral proliferation. Hence, global enhancement of the inflammatory response by T-cells and dendritic cells will likely feed viral propagation. Mucosal entry sites contain inherent pathways, in the form of natural regulatory T-cells (nTreg), that globally dampen the inflammatory response. We created a model of this inflammatory response to virus as well as inherent nTreg-mediated regulation of Th1 recruitment and activation. With simulations using this model we sought to address the net effect of nTreg activation and its specific functions as well as identify mechanisms of the natural inflammatory response that are best targeted to inhibit viral spread without compromising initial antiviral activity. Simulation results provide multiple insights that are relevant to developing intervention strategies that seek to exploit natural immune processes: (i) induction of the regulatory response through nTreg activation expedites viral proliferation due to viral production by nTreg itself and not to reduced Natural Killer (NK) cell activity; (ii) at the same time, induction of the inflammation response through either DC activation or Th1 activation expedites viral proliferation; (iii) within the inflammatory pathway, the NK response is an effective controller of viral proliferation while DC-mediated stimulation of T-cells is a significant driver of viral proliferation; and (iv) nTreg-mediated DC deactivation plays a significant role in slowing viral proliferation by inhibiting T-cell stimulation, making this function an aide to the antiviral immune response.
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Infecciones por VIH/inmunología , Modelos Inmunológicos , Linfocitos T CD4-Positivos/inmunología , Células Dendríticas/inmunología , VIH/fisiología , Infecciones por VIH/transmisión , Infecciones por VIH/virología , Humanos , Inflamación/inmunología , Inflamación/virología , Activación de Linfocitos/inmunología , Linfocitos T Reguladores/inmunología , Replicación Viral/inmunologíaRESUMEN
Advances in fluorescent labeling of cells as measured by flow cytometry have allowed for quantitative studies of proliferating populations of cells. The investigations (Luzyanina et al. in J. Math. Biol. 54:57-89, 2007; J. Math. Biol., 2009; Theor. Biol. Med. Model. 4:1-26, 2007) contain a mathematical model with fluorescence intensity as a structure variable to describe the evolution in time of proliferating cells labeled by carboxyfluorescein succinimidyl ester (CFSE). Here, this model and several extensions/modifications are discussed. Suggestions for improvements are presented and analyzed with respect to statistical significance for better agreement between model solutions and experimental data. These investigations suggest that the new decay/label loss and time dependent effective proliferation and death rates do indeed provide improved fits of the model to data. Statistical models for the observed variability/noise in the data are discussed with implications for uncertainty quantification. The resulting new cell dynamics model should prove useful in proliferation assay tracking and modeling, with numerous applications in the biomedical sciences.
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Proliferación Celular , Fluoresceínas , Colorantes Fluorescentes , Succinimidas , Citometría de Flujo/métodos , Citometría de Flujo/estadística & datos numéricos , Humanos , Técnicas In Vitro , Análisis de los Mínimos Cuadrados , Conceptos Matemáticos , Modelos Biológicos , Modelos EstadísticosRESUMEN
Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher Information Matrix (FIM). A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criteria with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model [13], the standard harmonic oscillator model [13] and a popular glucose regulation model [16, 19, 29].
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We present a general class of cell population models that can be used to track the proliferation of cells which have been labeled with a fluorescent dye. The mathematical models employ fluorescence intensity as a structure variable to describe the evolution in time of the population density of proliferating cells. While cell division is a major component of changes in cellular fluorescence intensity, models developed here also address overall label degradation.