Comparison of methods for intravoxel incoherent motion parameter estimation in the brain from flow-compensated and non-flow-compensated diffusion-encoded data

PURPOSE

Joint analysis of flow-compensated (FC) and non-flow-compensated (NC) diffusion MRI (dMRI) data has been suggested for increased robustness of intravoxel incoherent motion (IVIM) parameter estimation. For this purpose, a set of methods commonly used or previously found useful for IVIM analysis of dMRI data obtained with conventional diffusion encoding were evaluated in healthy human brain.

METHODS

Five methods for joint IVIM analysis of FC and NC dMRI data were compared: (1) direct non-linear least squares fitting, (2) a segmented fitting algorithm with estimation of the diffusion coefficient from higher b-values of NC data, (3) a Bayesian algorithm with uniform prior distributions, (4) a Bayesian algorithm with spatial prior distributions, and (5) a deep learning-based algorithm. Methods were evaluated on brain dMRI data from healthy subjects and simulated data at multiple noise levels. Bipolar diffusion encoding gradients were used with b-values 0-200 s/mm2 and corresponding flow weighting factors 0-2.35 s/mm for NC data and by design 0 for FC data. Data were acquired twice for repeatability analysis.

RESULTS

Measurement repeatability as well as estimation bias and variability were at similar levels or better with the Bayesian algorithm with spatial prior distributions and the deep learning-based algorithm for IVIM parametersD $$ D $$ andf $$ f $$ , and for the Bayesian algorithm only forv d $$ {v}_d $$ , relative to the other methods.

CONCLUSION

A Bayesian algorithm with spatial prior distributions is preferable for joint IVIM analysis of FC and NC dMRI data in the healthy human brain, but deep learning-based algorithms appear promising.

Building Individual Player Performance Profiles According to Pre-Game Expectations and Goal Difference in Soccer

Soccer player performance is influenced by multiple unpredictable factors. During a game, score changes and pre-game expectations affect the effort exerted by players. This study used GPS wearable sensors to track players' energy expenditure in 5-min intervals, alongside recording the goal timings and the win and lose probabilities from betting sites. A mathematical model was developed that considers pre-game expectations (e.g., favorite, non-favorite), endurance, and goal difference (GD) dynamics on player effort. Particle Swarm and Nelder-Mead optimization methods were used to construct these models, both consistently converging to similar cost function values. The model outperformed baselines relying solely on mean and median power per GD. This improvement is underscored by the mean absolute error (MAE) of 396.87±61.42 and root mean squared error (RMSE) of 520.69±88.66 achieved by our model, as opposed to the B1 MAE of 429.04±84.87 and RMSE of 581.34±185.84, and B2 MAE of 421.57±95.96 and RMSE of 613.47±300.11 observed across all players in the dataset. This research offers an enhancement to the current approaches for assessing players' responses to contextual factors, particularly GD. By utilizing wearable data and contextual factors, the proposed methods have the potential to improve decision-making and deepen the understanding of individual player characteristics.

Adsorption performance of nanoplastics in carbon filtration column

Nanoplastics (NPs) are usually formed by the decomposition of large plastics, which will cause water pollution after entering the water body. Carbon filter column is used to adsorb and remove polystyrene nanoparticles (PSNPs). The influence of experimental conditions on adsorption was investigated and fitted by kinetic model. The results show that increasing the height of carbon filter column and decreasing the initial concentration of PSNPs and water flow rate can prolong the breakthrough time of carbon filter column. When the initial concentration of PSNPs is 0.8 mg L-1, the influent flow rate is 4 mL min-1 and the height of carbon filter bed is 8.5 cm, the removal effect is the best, and the depletion point of carbon filter column is extended to 48 h. Adams-Bohart model is suitable for describing the initial stage of adsorption. Thomas and Yoon-Nelson models can well describe the whole dynamic adsorption process of PSNPs, and Yoon-Nelson model can accurately predict the time required for 50% PSNPs to penetrate the carbon column. The adsorption mechanism of NPs by carbon filter column is mainly through the attachment sites and pore retention provided by particles on the surface of activated carbon. This study can provide new technical and theoretical support for the removal of NPs.

The existence and strength of higher order interactions is sensitive to environmental context

One strategy for understanding the dynamics of any complex system, such as a community of competing species, is to study the dynamics of parts of the system in isolation. Ecological communities can be decomposed into single species, and pairs of interacting species. This reductionist strategy assumes that whole-community dynamics are predictable and explainable from knowledge of the dynamics of single species and pairs of species. This assumption will be violated if higher order interactions (HOIs) are strong. Theory predicts that HOIs should be common. But it is difficult to detect HOIs, and to infer their long-term consequences for species coexistence, solely from short-term data. I conducted a protist microcosm experiment to test for HOIs among competing bacterivorous ciliates, and test the sensitivity of HOIs to environmental context. I grew three competing ciliate species in all possible combinations at each of two resource enrichment levels, and used the population dynamic data from the one- and two-species treatments to parameterize a competition model at each enrichment level. I then compared the predictions of the parameterized model to the dynamics of the whole community (three-species treatment). I found that the existence, and thus strength, of HOIs was environment dependent. I found a strong HOI at low enrichment, which enabled the persistence of a species that would otherwise have been competitively excluded. At high enrichment, three-species dynamics could be predicted from a parameterized model of one- and two-species dynamics, provided that the model accounted for nonlinear intraspecific density dependence. The results provide one of the first rigorous demonstrations of the long-term consequences of HOIs for species coexistence, and demonstrate the context dependence of HOIs. HOIs create difficult challenges for predicting and explaining species coexistence in nature.

Dynamic Release Characteristics and Kinetics of a Persulfate Sustained-Release Material

Sustained-release materials are increasingly being used in the delivery of oxidants for in situ chemical oxidation (ISCO) for groundwater remediation. Successful implementation of sustained-release materials depends on a clear understanding of the mechanism and kinetics of sustained release. In this research, a columnar sustained-release material (PS@PW) was prepared with paraffin wax and sodium persulfate (PS), and column experiments were performed to investigate the impacts of the PS@PW diameter and PS/PW mass ratio on PS release. The results demonstrated that a reduction in diameter led to an increase in both the rate and proportion of PS release, as well as a diminished lifespan of release. The release process followed the second-order kinetics, and the release rate constant was positively correlated with the PS@PW diameter. A matrix boundary diffusion model was utilized to determine the PS@PW diffusion coefficient of the PS release process, and the release lifespan of a material with a length of 500 mm and a diameter of 80 mm was predicted to be more than 280 days. In general, this research provided a better understanding of the release characteristics and kinetics of persulfate from a sustained-release system and could lead to the development of columnar PS@PW as a practical oxidant for in situ chemical oxidation of contaminated aquifers.

Modeling the Batch Sedimentation of Calcium Carbonate Particles in Laboratory Experiments-A Systematic Approach

The design of continuous thickeners and clarifiers is commonly based on the solid flux theory. Batch sedimentation experiments conducted with solid concentrations still provide useful information for their application. The construction of models for the velocity of settling allows the estimation of the flux of solids throughout time, which can, in turn, be used to find the area of the units required to achieve a given solid concentration in the clarified stream. This paper addresses the numerical treatment of data obtained from batch sedimentation experiments of calcium carbonate particles. We propose a systematic framework to fit a model that is capable of representing the process features that involve (i) the numerical differentiation of data to generate initial estimates for the instantaneous velocity of settling; (ii) the integration of a differential equation to fit the model for the velocity of settling; and (iii) the assessment of the quality of the fit using common statistical indicators. The model used for demonstration has a theoretical basis combined with an empirical component to account for the effect of the particle concentrations and their state of aggregation. The values of the numerical parameters obtained are related to the characteristic dimensions of the aggregates and their mass-length fractal dimensions.

Quantification of MR spectra by deep learning in an idealized setting: Investigation of forms of input, network architectures, optimization by ensembles of networks, and training bias

PURPOSE

The aims of this work are (1) to explore deep learning (DL) architectures, spectroscopic input types, and learning designs toward optimal quantification in MR spectroscopy of simulated pathological spectra; and (2) to demonstrate accuracy and precision of DL predictions in view of inherent bias toward the training distribution.

METHODS

Simulated 1D spectra and 2D spectrograms that mimic an extensive range of pathological in vivo conditions are used to train and test 24 different DL architectures. Active learning through altered training and testing data distributions is probed to optimize quantification performance. Ensembles of networks are explored to improve DL robustness and reduce the variance of estimates. A set of scores compares performances of DL predictions and traditional model fitting (MF).

RESULTS

Ensembles of heterogeneous networks that combine 1D frequency-domain and 2D time-frequency domain spectrograms as input perform best. Dataset augmentation with active learning can improve performance, but gains are limited. MF is more accurate, although DL appears to be more precise at low SNR. However, this overall improved precision originates from a strong bias for cases with high uncertainty toward the dataset the network has been trained with, tending toward its average value.

CONCLUSION

MF mostly performs better compared to the faster DL approach. Potential intrinsic biases on training sets are dangerous in a clinical context that requires the algorithm to be unbiased to outliers (i.e., pathological data). Active learning and ensemble of networks are good strategies to improve prediction performances. However, data quality (sufficient SNR) has proven as a bottleneck for adequate unbiased performance-like in the case of MF.

Parameter estimation for WMTI-Watson model of white matter using encoder-decoder recurrent neural network

PURPOSE

Biophysical modeling of the diffusion MRI (dMRI) signal provides estimates of specific microstructural tissue properties. Although non-linear least squares (NLLS) is the most widespread fitting method, it suffers from local minima and high computational cost. Deep learning approaches are steadily replacing NLLS, but come with the limitation that the model needs to be retrained for each acquisition protocol and noise level. In this study, a novel fitting approach was proposed based on the encoder-decoder recurrent neural network (RNN) to accelerate model estimation with good generalization to various datasets.

METHODS

The white matter tract integrity (WMTI)-Watson model as an implementation of the Standard Model of diffusion in white matter derives its parameters indirectly from the diffusion and kurtosis tensors (DKI). The RNN-based solver, which estimates the WMTI-Watson model from DKI, is therefore more readily translatable to various data, irrespective of acquisition protocols as long as the DKI was pre-computed from the signal. An embedding approach was also used to render the model insensitive to potential differences in distributions between training data and experimental data. The analytical solution, NLLS, RNN-, and a multilayer perceptron (MLP)-based methods were evaluated on synthetic and in vivo datasets of rat and human brain.

RESULTS

The proposed RNN solver showed highly reduced computation time over the analytical solution and NLLS, with similar accuracy but improved robustness, and superior generalizability over MLP.

CONCLUSION

The RNN estimator can be easily applied to various datasets without retraining, which shows great potential for a widespread use.

A tribute to Howard Rachlin and his two-parameter discounting model: Reliable and flexible model fitting

Delay discounting reflects the rate at which a reward loses its subjective value as a function of delay to that reward. Many models have been proposed to measure delay discounting, and many comparisons have been made among these models. We highlight the two-parameter delay discounting model popularized by Howard Rachlin by demonstrating two key practical features of the Rachlin model. The first feature is flexibility; the Rachlin model fits empirical discounting data closely. Second, when compared with other available two-parameter discounting models, the Rachlin model has the advantage that unique best estimates for parameters are easy to obtain across a wide variety of potential discounting patterns. We focus this work on this second feature in the context of maximum likelihood, showing the relative ease with which the Rachlin model can be utilized compared with the extreme care that must be used with other models for discounting data, focusing on two illustrative cases that pass checks for data validity. Both of these features are demonstrated via a reanalysis of discounting data the authors have previously used for model selection purposes.

Multimodal parameter spaces of a complex multi-channel neuron model

One of the most common types of models that helps us to understand neuron behavior is based on the Hodgkin-Huxley ion channel formulation (HH model). A major challenge with inferring parameters in HH models is non-uniqueness: many different sets of ion channel parameter values produce similar outputs for the same input stimulus. Such phenomena result in an objective function that exhibits multiple modes (i.e., multiple local minima). This non-uniqueness of local optimality poses challenges for parameter estimation with many algorithmic optimization techniques. HH models additionally have severe non-linearities resulting in further challenges for inferring parameters in an algorithmic fashion. To address these challenges with a tractable method in high-dimensional parameter spaces, we propose using a particular Markov chain Monte Carlo (MCMC) algorithm, which has the advantage of inferring parameters in a Bayesian framework. The Bayesian approach is designed to be suitable for multimodal solutions to inverse problems. We introduce and demonstrate the method using a three-channel HH model. We then focus on the inference of nine parameters in an eight-channel HH model, which we analyze in detail. We explore how the MCMC algorithm can uncover complex relationships between inferred parameters using five injected current levels. The MCMC method provides as a result a nine-dimensional posterior distribution, which we analyze visually with solution maps or landscapes of the possible parameter sets. The visualized solution maps show new complex structures of the multimodal posteriors, and they allow for selection of locally and globally optimal value sets, and they visually expose parameter sensitivities and regions of higher model robustness. We envision these solution maps as enabling experimentalists to improve the design of future experiments, increase scientific productivity and improve on model structure and ideation when the MCMC algorithm is applied to experimental data.

Effects of Image Dataset Configuration on the Accuracy of Rice Disease Recognition Based on Convolution Neural Network

In recent years, the convolution neural network has been the most widely used deep learning algorithm in the field of plant disease diagnosis and has performed well in classification. However, in practice, there are still some specific issues that have not been paid adequate attention to. For instance, the same pathogen may cause similar or different symptoms when infecting plant leaves, while the same pathogen may cause similar or disparate symptoms on different parts of the plant. Therefore, questions come up naturally: should the images showing different symptoms of the same disease be in one class or two separate classes in the image database? Also, how will the different classification methods affect the results of image recognition? In this study, taking rice leaf blast and neck blast caused by Magnaporthe oryzae, and rice sheath blight caused by Rhizoctonia solani as examples, three experiments were designed to explore how database configuration affects recognition accuracy in recognizing different symptoms of the same disease on the same plant part, similar symptoms of the same disease on different parts, and different symptoms on different parts. The results suggested that when the symptoms of the same disease were the same or similar, no matter whether they were on the same plant part or not, training combined classes of these images can get better performance than training them separately. When the difference between symptoms was obvious, the classification was relatively easy, and both separate training and combined training could achieve relatively high recognition accuracy. The results also, to a certain extent, indicated that the greater the number of images in the training data set, the higher the average classification accuracy.

Detecting and interpreting higher-order interactions in ecological communities

When species simultaneously compete with two or more species of competitor, higher-order interactions (HOIs) can lead to emergent properties not present when species interact in isolated pairs. To extend ecological theory to multi-competitor communities, ecologists must confront the challenges of measuring and interpreting HOIs in models of competition fit to data from nature. Such efforts are hindered by the fact that different studies use different definitions, and these definitions have unclear relationships to one another. Here, we propose a distinction between 'soft' HOIs, which identify possible interaction modification by competitors, and 'hard' HOIs, which identify interactions uniquely emerging in systems with three or more competitors. We show how these two classes of HOI differ in their motivation and interpretation, as well as the tests one uses to identify them in models fit to data. We then show how to operationalise this structure of definitions by analysing the results of a simulated competition experiment underlain by a consumer resource model. In the course of doing so, we clarify the challenges of interpreting HOIs in nature, and suggest a more precise framing of this research endeavour to catalyse further investigations.

[Kinetics and variation of volatile components of Atractylodis Macrocephalae Rhizoma during hot-air drying]

The present study explored the kinetics and variation of volatile components of Atractylodis Macrocephalae Rhizoma during the hot-air drying process to obtain the optimal process parameters under multiple goals such as drying efficiency and drying quality. The dry basis moisture content and drying rate curves along with the change of drying time of Atractylodis Macrocephalae Rhizoma were investigated at five levels of drying air temperatures(30, 40, 50, 60, and 70 ℃). The relationship between moisture ratio and time in the drying process of Atractylodis Macrocephalae Rhizoma was fitted and verified by Midilli model, Page model, Overhults model, Modified Page model, Logaritmic model, Two terms Exponential model, and Newton model. Meanwhile, the effective diffusion coefficient of moisture(D_(eff)) and activation energy(E_a) in Atractylodis Macrocephalae Rhizoma were calculated under different drying air temperatures. GC-MS was used to determine the volatile components and content changes of the fresh Atractylodis Macrocephalae Rhizoma and dried products at different temperatures. The dry basis moisture content and drying rate of Atractylodis Macrocephalae Rhizoma were closely related to the temperature of the drying medium, and the moisture of the Atractylodis Macrocephalae Rhizoma decreased with the prolonged drying time. As revealed by the drying rate curve, the drying rate increased with the increase in hot air temperature, and the migration of moisture was accelerated. The comparison of the correlation coefficient(R~2), chi-square(χ~2), and root mean standard error(RMSE) of each model indicated that the parameter average of the Midilli model had the highest degree of fit, with R~2=0.999 2, χ~2=8.78×10~(-5), and RMSE=8.20×10~(-3). Besides, the D_(eff) at 30-70 ℃ was in the range of 1.04×10~(-9)-6.28×10~(-9) m~2·s~(-1), and E_a was 37.47 kJ·mol~(-1). The volatile components of fresh Atractylodis Macrocephalae Rhizoma and dried products at different temperatures were determined by GC-MS, and 18, 18, 18, 17, 17, and 18 compounds were identified respectively, which accounted for more than 84.76% of the volatile components. In conclusion, the hot-air drying of Atractylodis Macrocephalae Rhizoma can be model-fitted and verified and the variation law of the moisture and volatile components of Atractylodis Macrocephalae Rhizoma with temperature is obtained. This study is expected to provide new ideas for exploring the drying characteristics and quality of aromatic Chinese medicine.

Thermal Modeling of the Port on a Refining Furnace to Prevent Copper Infiltration and Slag Accretion

Fire refining of blister copper is a singular process at very high temperatures (~1400 K), which means the furnace is exposed to heavy thermal loads. The charge is directly heated by an internal burner. The impurities in the charge oxidize with the flux of hot gases, creating a slag layer on the top of the molten bath. This slag is periodically removed, which implies liquid metal flowing through the furnace port. To address its malfunction, a re-design of the furnace port is presented in this work. Due to the lack of previous technical information, the convective heat transfer coefficient between the slag and the furnace port was characterized through a combination of an experimental test and a three-dimensional transient model. Finally, the original design of the furnace port was analyzed and modifications were proposed, resulting in a reduction of the average temperature of the critical areas up to 300 K. This improvement prevents the anchoring of the accretion layer over the port plates and the steel plate from being attacked by the copper.

A sub+cortical fMRI-based surface parcellation

Both cortical and subcortical structures are organized into a large number of distinct areas reflecting functional and cytoarchitectonic differences. Mapping these areas is of fundamental importance to neuroscience. A central obstacle to this task is the inaccuracy associated with bringing results from individuals into a common space. The vast individual differences in morphology pose a serious problem for volumetric registration. Surface‐based approaches fare substantially better, but have thus far been used only for cortical parcellation, leaving subcortical parcellation in volumetric space. We extend the surface‐based approach to include also the subcortical deep gray‐matter structures, thus achieving a uniform representation across both cortex and subcortex, suitable for use with surface‐based metrics that span these structures, for example, white/gray contrast. Using data from the Enhanced Nathan Klein Institute—Rockland Sample, limited to individuals between 19 and 69 years of age, we generate a functional parcellation of both the cortical and subcortical surfaces. To assess this extended parcellation, we show that (a) our parcellation provides greater homogeneity of functional connectivity patterns than do arbitrary parcellations matching in the number and size of parcels; (b) our parcels align with known cortical and subcortical architecture; and (c) our extended functional parcellation provides an improved fit to the complexity of life‐span (6–85 years) changes in white/gray contrast data compared to arbitrary parcellations matching in the number and size of parcels, supporting its use with surface‐based measures. We provide our extended functional parcellation for the use of the neuroimaging community.

Training data distribution significantly impacts the estimation of tissue microstructure with machine learning

PURPOSE

Supervised machine learning (ML) provides a compelling alternative to traditional model fitting for parameter mapping in quantitative MRI. The aim of this work is to demonstrate and quantify the effect of different training data distributions on the accuracy and precision of parameter estimates when supervised ML is used for fitting.

METHODS

We fit a two- and three-compartment biophysical model to diffusion measurements from in-vivo human brain, as well as simulated diffusion data, using both traditional model fitting and supervised ML. For supervised ML, we train several artificial neural networks, as well as random forest regressors, on different distributions of ground truth parameters. We compare the accuracy and precision of parameter estimates obtained from the different estimation approaches using synthetic test data.

RESULTS

When the distribution of parameter combinations in the training set matches those observed in healthy human data sets, we observe high precision, but inaccurate estimates for atypical parameter combinations. In contrast, when training data is sampled uniformly from the entire plausible parameter space, estimates tend to be more accurate for atypical parameter combinations but may have lower precision for typical parameter combinations.

CONCLUSION

This work highlights that estimation of model parameters using supervised ML depends strongly on the training-set distribution. We show that high precision obtained using ML may mask strong bias, and visual assessment of the parameter maps is not sufficient for evaluating the quality of the estimates.

Computational modelling of social cognition and behaviour-a reinforcement learning primer

Social neuroscience aims to describe the neural systems that underpin social cognition and behaviour. Over the past decade, researchers have begun to combine computational models with neuroimaging to link social computations to the brain. Inspired by approaches from reinforcement learning theory, which describes how decisions are driven by the unexpectedness of outcomes, accounts of the neural basis of prosocial learning, observational learning, mentalizing and impression formation have been developed. Here we provide an introduction for researchers who wish to use these models in their studies. We consider both theoretical and practical issues related to their implementation, with a focus on specific examples from the field.

Double Two-State Opsin Model With Autonomous Parameter Inference

Optogenetics has a lot of potential to become an effective neuromodulative therapy for clinical applications. Selecting the correct opsin is crucial to have an optimal optogenetic tool. With computational modeling, the neuronal response to the current dynamics of an opsin can be extensively and systematically tested. Unlike electrical stimulation where the effect is directly defined by the applied field, the stimulation in optogenetics is indirect, depending on the selected opsin's non-linear kinetics. With the continuous expansion of opsin possibilities, computational studies are difficult due to the need for an accurate model of the selected opsin first. To this end, we propose a double two-state opsin model as alternative to the conventional three and four state Markov models used for opsin modeling. Furthermore, we provide a fitting procedure, which allows for autonomous model fitting starting from a vast parameter space. With this procedure, we successfully fitted two distinctive opsins (ChR2(H134R) and MerMAID). Both models are able to represent the experimental data with great accuracy and were obtained within an acceptable time frame. This is due to the absence of differential equations in the fitting procedure, with an enormous reduction in computational cost as result. The performance of the proposed model with a fit to ChR2(H134R) was tested, by comparing the neural response in a regular spiking neuron to the response obtained with the non-instantaneous, four state Markov model (4SB), derived by Williams et al. (2013). Finally, a computational speed gain was observed with the proposed model in a regular spiking and sparse Pyramidal-Interneuron-Network-Gamma (sPING) network simulation with respect to the 4SB-model, due to the former having two differential equations less. Consequently, the proposed model allows for computationally efficient optogenetic neurostimulation and with the proposed fitting procedure will be valuable for further research in the field of optogenetics.

Natural enemies have inconsistent impacts on the coexistence of competing species

The role of natural enemies in promoting coexistence of competing species has generated substantial debate. Modern coexistence theory provides a detailed framework to investigate this topic, but there have been remarkably few empirical applications to the impact of natural enemies. We tested experimentally the capacity for a generalist enemy to promote coexistence of competing insect species, and the extent to which any impact can be predicted by trade-offs between reproductive rate and susceptibility to natural enemies. We used experimental mesocosms to conduct a fully factorial pairwise competition experiment for six rainforest Drosophila species, with and without a generalist pupal parasitoid. We then parameterised models of competition and examined the coexistence of each pair of Drosophila species within the framework of modern coexistence theory. We found idiosyncratic impacts of parasitism on pairwise coexistence, mediated through changes in fitness differences, not niche differences. There was no evidence of an overall reproductive rate-susceptibility trade-off. Pairwise reproductive rate-susceptibility relationships were not useful shortcuts for predicting the impact of parasitism on coexistence. Our results exemplify the value of modern coexistence theory in multi-trophic contexts and the importance of contextualising the impact of generalist natural enemies to determine their impact. In the set of species investigated, competition was affected by the higher trophic level, but the overall impact on coexistence cannot be easily predicted just from knowledge of relative susceptibility. Methodologically, our Bayesian approach highlights issues with the separability of model parameters within modern coexistence theory and shows how using the full posterior parameter distribution improves inferences. This method should be widely applicable for understanding species coexistence in a range of systems.

Isothermal Kinetics of Epoxyphosphazene Cure

The influence of epoxycyclophosphazene modifier on the process of epoxy-amine curing was studied by differential scanning calorimetry (DSC). The study revealed that the curing process of epoxyphosphazene binders with 4′4′diaminodiphenylsulfone (DDS) provides more complete curing of the formulations in comparison with ones applying low molecular-weight polyamide curing agent (L-20). The isothermal kinetics of curing was described by means of model fitting and the isoconversional approach (Friedman method). Accurate n-order approximation was obtained for all systems under study. In particular, the 2-order equation fits well with the main part of curing excluding high degrees of conversion. The process of curing could be distinguished into three zones. The transition from zone 2 to zone 3 correlates with gelation. According to the isoconversional analysis by Friedman method, the diffusion-controlled mechanism is found at final stage of curing.

TEMPy2: a Python library with improved 3D electron microscopy density-fitting and validation workflows

Structural determination of molecular complexes by cryo-EM requires large, often complex processing of the image data that are initially obtained. Here, TEMPy2, an update of the TEMPy package to process, optimize and assess cryo-EM maps and the structures fitted to them, is described. New optimization routines, comprehensive automated checks and workflows to perform these tasks are described.

Some Critical Remarks about Mathematical Model Used for the Description of Transport Kinetics in Polymer Inclusion Membrane Systems

Two kinetic models which are applied for the description of metal ion transport in polymer inclusion membrane (PIM) systems are presented and compared. The models were fitted to the real experimental data of Zn(II), Cd(II), Cu(II), and Pb(II) simultaneous transport through PIM with di-(2-ethylhexyl)phosphoric acid (D2EHPA) as a carrier, o-nitrophenyl octyl ether (NPOE) as a plasticizer, and cellulose triacetate (CTA) as a polymer matrix. The selected membrane was composed of 43 wt. % D2EHPA, 19 wt. % NPOE, and 38 wt. % CTA. The results indicated that the calculated initial fluxes (from 2 × 10-11 up to 9 × 10-10 mol/cm2s) are similar to the values observed by other authors in systems operating under similar conditions. It was found that one of the most frequently applied models based on an equation similar to the first-order chemical reaction equation leads to abnormal distribution of residuals. It was also found that application of this model causes some problems with curve fitting and leads to the underestimation of permeability coefficients and initial maximum fluxes. Therefore, a new model has been proposed to describe the transport kinetics in PIM systems. This new model, based on an equation similar to the first-order chemical reaction equation with equilibrium, was successfully applied. The fit of this model to the experimental data is much better and makes it possible to determine more precisely the initial maximum flux as the parameter describing the transport efficiency.

Pyrolysis Kinetic Study and Reaction Mechanism of Epoxy Glass Fiber Reinforced Plastic by Thermogravimetric Analyzer (TG) and TG-FTIR (Fourier-Transform Infrared) Techniques

TG–FTIR combined technology was used to study the degradation process and gas phase products of epoxy glass fiber reinforced plastic (glass fiber reinforced plastic) under the atmospheres of high purity nitrogen. The pyrolysis characteristics of epoxy glass fiber reinforced plastic were measured under different heating rates (5, 10, 15, 20 °C min⁻¹) from 25 to 1000 °C. The thermogravimetric analyzer (TG) and differential thermogravimetric analyzer (DTG) curves show that the initial temperature, terminal temperature, and temperature of maximum weight loss rate in the pyrolysis reaction phase all move towards high temperature, as the heating rate increases. Epoxy glass fiber reinforced plastic has two stages of thermal weightlessness. The temperature range of the first stage of weight loss is 290–460 °C. The second stage is 460–1000 °C. The above two weight loss stages are caused by pyrolysis of the epoxy resin matrix, and the glass fiber will not decompose. The dynamic parameters of glass fiber reinforced plastic were obtained through the Kissinger-Akahira-Sunose (KAS), Flynn–Wall-Ozawa (FWO) and advanced Vyazovkin methods in model-free and the Coats–Redfern (CR) method in model fitting. FTIR spectrum result shows that the main components of the product gas are CO₂, H₂O, carbonyl components, and aromatic components during its pyrolysis.

Clustering and Characterization of the Lactation Curves of Dairy Cows Using K-Medoids Clustering Algorithm

Simple Summary

A lactation curve (LC) provides valuable insights in planning appropriate management strategies related to health, nutrition, and breeding in dairy cows. A clustering based approach on LC patterns analysis is presented. The k-medoids algorithm is adopted for the clustering. This approach generates several clusters which have similar milking characteristics of total milk yield, peak milk yield, and days in milk at peak yield. The LCs of some groups represent characteristics of atypical milking patterns which are not considered much in previous approaches, whereas LCs of the other groups show the typical LC patterns similar to the results of previous methods. This approach could be used as a tool to manage an abnormal herd of cows.

Abstract

The aim of the study was to group the lactation curve (LC) of Holstein cows in several clusters based on their milking characteristics and to investigate physiological differences among the clusters. Milking data of 330 lactations which have a milk yield per day during entire lactation period were used. The data were obtained by refinement from 1332 lactations from 724 cows collected from commercial farms. Based on the similarity measures, clustering was performed using the k-medoids algorithm; the number of clusters was determined to be six, following the elbow method. Significant differences on parity, peak milk yield, DIM at peak milk yield, and average and total milk yield (p < 0.01) were observed among the clusters. Four clusters, which include 82% of data, show typical LC patterns. The other two clusters represent atypical patterns. Comparing to the LCs generated from the previous models, Wood, Wilmink and Dijsktra, it is observed that the prediction errors in the atypical patterns of the two clusters are much larger than those of the other four cases of typical patterns. The presented model can be used as a tool to refine characterization on the typical LC patterns, excluding atypical patterns as exceptional cases.

A flexible framework for simulating and fitting generalized drift-diffusion models

The drift-diffusion model (DDM) is an important decision-making model in cognitive neuroscience. However, innovations in model form have been limited by methodological challenges. Here, we introduce the generalized drift-diffusion model (GDDM) framework for building and fitting DDM extensions, and provide a software package which implements the framework. The GDDM framework augments traditional DDM parameters through arbitrary user-defined functions. Models are solved numerically by directly solving the Fokker-Planck equation using efficient numerical methods, yielding a 100-fold or greater speedup over standard methodology. This speed allows GDDMs to be fit to data using maximum likelihood on the full response time (RT) distribution. We demonstrate fitting of GDDMs within our framework to both animal and human datasets from perceptual decision-making tasks, with better accuracy and fewer parameters than several DDMs implemented using the latest methodology, to test hypothesized decision-making mechanisms. Overall, our framework will allow for decision-making model innovation and novel experimental designs.

Robustness Analysis of the Estimators for the Nonlinear System Identification

The main objective of the system identification is to deliver maximum information about the system dynamics, while still ensuring an acceptable cost of the identification experiment. The focus of such an idea is to design an appropriate experiment so that the departure from normal working conditions during the identification task is minimized. In this paper, the adaptive filtering (AF) scheme for plant model parameter estimation is proposed. The experimental results are obtained using the nonlinear interacting water tanks system. The adaptive filtering is expressed by minimizing the error between the system and the plant model outputs subject to the white noise signal affecting system output. This measurement error is quantified by the comparison of Minimum Error Entropy Renyi (MEER), Least Entropy Like (LEL), Least Squares (LS), and Least Absolute Deviation (LAD) estimators, respectively. The plant model parameters were obtained using sequential quadratic programming (SQP) algorithm. The robustness tests for the double-tank water system parameter estimators are performed using the ellipsoidal confidence regions. The effectiveness analysis for the above-mentioned estimators relies on the total number of iterations and the number of function evaluation comparisons. The main contribution of this paper is the evaluation of different estimation methods for the nonlinear system identification using various excitation signals. The proposed empirical study is illustrated by the numerical examples, and the simulation results are discussed.

Pyrolytic Kinetics of Polystyrene Particle in Nitrogen Atmosphere: Particle Size Effects and Application of Distributed Activation Energy Method

This work was motivated by a study of particle size effects on pyrolysis kinetics and models of polystyrene particle. Micro-size polystyrene particles with four different diameters, 5, 10, 15, and 50 µm, were selected as experimental materials. Activation energies were obtained by isoconversional methods, and pyrolysis model of each particle size and heating rate was examined through different reaction models by the Coats–Redfern method. To identify the controlling model, the Avrami–Eroféev model was identified as the controlling pyrolysis model for polystyrene pyrolysis. Accommodation function effect was employed to modify the Avrami–Eroféev model. The model was then modified to f(α) = nα^{0.39n − 1.15}(1 − α)[−ln(1 − α)]^{1 − 1/n}, by which the polystyrene pyrolysis with different particle sizes can be well explained. It was found that the reaction model cannot be influenced by particle geometric dimension. The reaction rate can be changed because the specific surface area will decrease with particle diameter. To separate each step reaction and identify their distributions to kinetics, distributed activation energy method was introduced to calculate the weight factor and kinetic triplets. Results showed that particle size has big impacts on both first and second step reactions. Smaller size particle can accelerate the process of pyrolysis reaction. Finally, sensitivity analysis was brought to check the sensitivity and weight of each parameter in the model.

Ten simple rules for the computational modeling of behavioral data

Computational modeling of behavior has revolutionized psychology and neuroscience. By fitting models to experimental data we can probe the algorithms underlying behavior, find neural correlates of computational variables and better understand the effects of drugs, illness and interventions. But with great power comes great responsibility. Here, we offer ten simple rules to ensure that computational modeling is used with care and yields meaningful insights. In particular, we present a beginner-friendly, pragmatic and details-oriented introduction on how to relate models to data. What, exactly, can a model tell us about the mind? To answer this, we apply our rules to the simplest modeling techniques most accessible to beginning modelers and illustrate them with examples and code available online. However, most rules apply to more advanced techniques. Our hope is that by following our guidelines, researchers will avoid many pitfalls and unleash the power of computational modeling on their own data.

Global and Multiplexed Dendritic Computations under In Vivo-like Conditions

Dendrites integrate inputs nonlinearly, but it is unclear how these nonlinearities contribute to the overall input-output transformation of single neurons. We developed statistically principled methods using a hierarchical cascade of linear-nonlinear subunits (hLN) to model the dynamically evolving somatic response of neurons receiving complex, in vivo-like spatiotemporal synaptic input patterns. We used the hLN to predict the somatic membrane potential of an in vivo-validated detailed biophysical model of a L2/3 pyramidal cell. Linear input integration with a single global dendritic nonlinearity achieved above 90% prediction accuracy. A novel hLN motif, input multiplexing into parallel processing channels, could improve predictions as much as conventionally used additional layers of local nonlinearities. We obtained similar results in two other cell types. This approach provides a data-driven characterization of a key component of cortical circuit computations: the input-output transformation of neurons during in vivo-like conditions.

An Automated Biomodel Selection System (BMSS) for Gene Circuit Designs

Constructing a complex functional gene circuit composed of different modular biological parts to achieve the desired performance remains challenging without a proper understanding of how the individual module behaves. To address this, mathematical models serve as an important tool toward better interpretation by quantifying the performance of the overall gene circuit, providing insights, and guiding the experimental designs. As different gene circuits might require exclusively different mathematical representations in the form of ordinary differential equations to capture their transient dynamic behaviors, a recurring challenge in model development is the selection of the appropriate model. Here, we developed an automated biomodel selection system (BMSS) which includes a library of pre-established models with intuitive or unintuitive features derived from a vast array of expression profiles. Selection of models is built upon the Akaike information criteria (AIC). We tested the automated platform using characterization data of routinely used inducible systems, constitutive expression systems, and several different logic gate systems (NOT, AND, and OR gates). The BMSS achieved a good agreement for all the different characterization data sets and managed to select the most appropriate model accordingly. To enable exchange and reproducibility of gene circuit design models, the BMSS platform also generates Synthetic Biology Open Language (SBOL)-compliant gene circuit diagrams and Systems Biology Markup Language (SBML) output files. All aspects of the algorithm were programmed in a modular manner to ease the efforts on model extensions or customizations by users. Taken together, the BMSS which is implemented in Python supports users in deriving the best mathematical model candidate in a fast, efficient, and automated way using part/circuit characterization data.

In silico Tools at Early Stage of Pharmaceutical Development: Data Needs and Software Capabilities

In early drug development, the selection of a formulation platform and decisions on formulation strategies have to be made within a short timeframe and often with minimal use of the active pharmaceutical ingredient (API). The current work evaluated the various physicochemical parameters required to improve the prediction accuracy of simulation software for immediate release tablets in early drug development. DDDPlus™ was used in simulating dissolution test profiles of immediate release tablets of ritonavir and all simulations were compared with experimental results. The minimum data requirements to make useful predictions were assessed using the ADMET predictor (part of DDDPlus) and Chemicalize (an online resource). A surfactant model was developed to estimate the solubility enhancement in media containing surfactant and the software's transfer model based on the USP two-tiered dissolution test was assessed. One measured data point was shown to be sufficient to make predictive simulations in DDDPlus. At pH 2.0, the software overestimated drug release while at pH 1.0 and 6.8, simulations were close to the measured values. A surfactant solubility model established with measured data gave good dissolution predictions. The transfer model uses a single-vessel model and was unable to predict the two in vivo environments separately. For weak bases like ritonavir, a minimum of three solubility data points is recommended for in silico predictions in buffered media. A surfactant solubility model is useful when predicting dissolution behavior in surfactant media and in silico predictions need measured solubility data to be predictive.

Time for a Drink? A Mathematical Model of Non-human Primate Alcohol Consumption

We simulate a non-human primate's alcohol drinking pattern in order to better understand temporal patterning of alcoholic drinks that can lead to the excessive intakes associated with alcohol use disorder. A stochastic mathematical model of alcohol consumption pattern is developed, where model parameters are calibrated to an individual monkey's drinking history. The model predicts a time series that simulates a monkey's alcohol intake in time, and we analyze this drinking pattern to understand the variations in day and night drinking, the lengths of drinks (intake in 5 or more consecutive secs), and lengths of bouts (1 or more drinks per 5 min occasion). This time series can predict a lifetime categorical drinking level (light, binge, heavy, or very heavy), thus correlating an individual monkey's parameters with distinct long term drinking classifications.

Catheter segmentation in three-dimensional ultrasound images by feature fusion and model fitting

Ultrasound (US) has been increasingly used during interventions, such as cardiac catheterization. To accurately identify the catheter inside US images, extra training for physicians and sonographers is needed. As a consequence, automated segmentation of the catheter in US images and optimized presentation viewing to the physician can be beneficial to accelerate the efficiency and safety of interventions and improve their outcome. For cardiac catheterization, a three-dimensional (3-D) US image is potentially attractive because of no radiation modality and richer spatial information. However, due to a limited spatial resolution of 3-D cardiac US and complex anatomical structures inside the heart, image-based catheter segmentation is challenging. We propose a cardiac catheter segmentation method in 3-D US data through image processing techniques. Our method first applies a voxel-based classification through newly designed multiscale and multidefinition features, which provide a robust catheter voxel segmentation in 3-D US. Second, a modified catheter model fitting is applied to segment the curved catheter in 3-D US images. The proposed method is validated with extensive experiments, using different in-vitro, ex-vivo, and in-vivo datasets. The proposed method can segment the catheter within an average tip-point error that is smaller than the catheter diameter (1.9 mm) in the volumetric images. Based on automated catheter segmentation and combined with optimal viewing, physicians do not have to interpret US images and can focus on the procedure itself to improve the quality of cardiac intervention.

Machine Learning Based Localization in Large-Scale Wireless Sensor Networks

The rapid proliferation of wireless sensor networks over the past few years has posed some serious technical challenges to researchers. The primary function of a multi-hop wireless sensor network (WSN) is to collect and forward sensor data towards the destination node. However, for many applications, the knowledge of the location of sensor nodes is crucial for meaningful interpretation of the sensor data. Localization refers to the process of estimating the location of sensor nodes in a WSN. Self-localization is required in large wireless sensor networks where these nodes cannot be manually positioned. Traditional methods iteratively localize these nodes by using triangulation. However, the inherent instability in wireless signals introduces an error, however minute it might be, in the estimated position of the target node. This results in the embedded error propagating and magnifying rapidly. Machine learning based localizing algorithms for large wireless sensor networks do not function in an iterative manner. In this paper, we investigate the suitability of some of these algorithms while exploring different trade-offs. Specifically, we first formulate a novel way of defining multiple feature vectors for mapping the localizing problem onto different machine learning models. As opposed to treating the localization as a classification problem, as done in the most of the reported work, we treat it as a regression problem. We have studied the impact of varying network parameters, such as network size, anchor population, transmitted signal power, and wireless channel quality, on the localizing accuracy of these models. We have also studied the impact of deploying the anchor nodes in a grid rather than placing these nodes randomly in the deployment area. Our results have revealed interesting insights while using the multivariate regression model and support vector machine (SVM) regression model with radial basis function (RBF) kernel.

A Comet Assay for DNA Damage and Repair After Exposure to Carbon-Ion Beams or X-rays in Saccharomyces Cerevisiae

Ionizing radiation (IR) can result in serious genomic instability and genotoxicity by causing DNA damage. Carbon ion (CI) beams and X-rays are typical IRs and possess high-linear energy transfer (LET) and low-LET, respectively. In this article, a comet assay that was optimized by decreasing the electrophoresis time (8 minutes) and voltage (0.5 V/cm) was performed to elucidate and quantify the DNA damage induced by CI or X-rays radiation. Two quantitative methods for the comet assay, namely, comet score and olive tail moment, were compared, and the appropriate means and parameter values were selected for the present assay. The dose-effect relationship for CI or X-rays radiation and the DNA repair process were studied in yeast cells. These results showed that the quadratic function fitted the dose-effect relationship after CI or X-rays exposure, and the trend for the models fitted the dose-effect curves for various repair times was precisely described by the cubic function. A kinetics model was also creatively used to describe the process of DNA repair, and equations were calculated within repairable ranges that could be used to roughly evaluate the process and time necessary for DNA repair.

Free Final Time Input Design Problem for Robust Entropy-Like System Parameter Estimation

In this paper, a novel method is proposed to design a free final time input signal, which is then used in the robust system identification process. The solution of the constrained optimal input design problem is based on the minimization of an extra state variable representing the free final time scaling factor, formulated in the Bolza functional form, subject to the D-efficiency constraint as well as the input energy constraint. The objective function used for the model of the system identification provides robustness regarding the outlying data and was constructed using the so-called Entropy-like estimator. The perturbation time interval has a significant impact on the cost of the real-life system identification experiment. The contribution of this work is to examine the economic aspects between the imposed constraints on the input signal design, and the experiment duration while undertaking an identification experiment in the real operating conditions. The methodology is applicable to the general class of systems and was supported by numerical examples. Illustrative examples of the Least Squares, and the Entropy-Like estimators for the system parameter data validation where measurements include additive white noise are compared using ellipsoidal confidence regions.

Dehydration Study of Piracetam Co-Crystal Hydrates

A hydrate of co-crystal of piracetam and 3,5-dihydroxybenzoic acid was obtained via crystallization from water. Single-crystal X-ray data show that piracetam/3,5-dihydroxybenzoic acid tetrahydrate (P35TH) crystallizes in the triclinic system with a P1 space group. The physicochemical properties of co-crystal hydrate were characterized using powder X-ray diffractometry, differential scanning calorimetry (DSC), thermogravimetric analyzer (TGA), and FTIR spectroscopy. The dehydration kinetics of P35TH was monitored at various temperatures and heating rates by DSC and TGA. Activation energy of P35TH dehydration was obtained using temperature ramp DSC, isothermal and nonisothermal TGA methods. Kinetic analysis of isothermal TGA data was fitted to various solid-state reaction models. Mechanistic models derived from isothermal dehydration kinetic data are best described as a 2-dimensional diffusion mechanism. A correlation was noted between the dehydration behavior and the bonding environment of the water molecules in the crystal structure. This study is a good demonstration of complexity of co-crystal hydrate and their dehydration behavior.

Taking error into account when fitting models using Approximate Bayesian Computation

Stochastic computer simulations are often the only practical way of answering questions relating to ecological management. However, due to their complexity, such models are difficult to calibrate and evaluate. Approximate Bayesian Computation (ABC) offers an increasingly popular approach to this problem, widely applied across a variety of fields. However, ensuring the accuracy of ABC's estimates has been difficult. Here, we obtain more accurate estimates by incorporating estimation of error into the ABC protocol. We show how this can be done where the data consist of repeated measures of the same quantity and errors may be assumed to be normally distributed and independent. We then derive the correct acceptance probabilities for a probabilistic ABC algorithm, and update the coverage test with which accuracy is assessed. We apply this method, which we call error-calibrated ABC, to a toy example and a realistic 14-parameter simulation model of earthworms that is used in environmental risk assessment. A comparison with exact methods and the diagnostic coverage test show that our approach improves estimation of parameter values and their credible intervals for both models.

Kinetics of HIV-Specific CTL Responses Plays a Minimal Role in Determining HIV Escape Dynamics

Cytotoxic T lymphocytes (CTLs) have been suggested to play an important role in controlling human immunodeficiency virus (HIV-1 or simply HIV) infection. HIV, due to its high mutation rate, can evade recognition of T cell responses by generating escape variants that cannot be recognized by HIV-specific CTLs. Although HIV escape from CTL responses has been well documented, factors contributing to the timing and the rate of viral escape from T cells have not been fully elucidated. Fitness costs associated with escape and magnitude of the epitope-specific T cell response are generally considered to be the key in determining timing of HIV escape. Several previous analyses generally ignored the kinetics of T cell responses in predicting viral escape by either considering constant or maximal T cell response; several studies also considered escape from different T cell responses to be independent. Here, we focus our analysis on data from two patients from a recent study with relatively frequent measurements of both virus sequences and HIV-specific T cell response to determine impact of CTL kinetics on viral escape. In contrast with our expectation, we found that including temporal dynamics of epitope-specific T cell response did not improve the quality of fit of different models to escape data. We also found that for well-sampled escape data, the estimates of the model parameters including T cell killing efficacy did not strongly depend on the underlying model for escapes: models assuming independent, sequential, or concurrent escapes from multiple CTL responses gave similar estimates for CTL killing efficacy. Interestingly, the model assuming sequential escapes (i.e., escapes occurring along a defined pathway) was unable to accurately describe data on escapes occurring rapidly within a short-time window, suggesting that some of model assumptions must be violated for such escapes. Our results thus suggest that the current sparse measurements of temporal CTL dynamics in blood bear little quantitative information to improve predictions of HIV escape kinetics. More frequent measurements using more sensitive techniques and sampling in secondary lymphoid tissues may allow to better understand whether and how CTL kinetics impacts viral escape.

Development of a classification model for non-alcoholic steatohepatitis (NASH) using confocal Raman micro-spectroscopy

Non-alcoholic fatty liver disease (NAFLD) is the most common liver disorder in developed countries [1]. A subset of individuals with NAFLD progress to non-alcoholic steatohepatitis (NASH), an advanced form of NAFLD which predisposes individuals to cirrhosis, liver failure and hepatocellular carcinoma. The current gold standard for NASH diagnosis and staging is based on histological evaluation, which is largely semi-quantitative and subjective. To address the need for an automated and objective approach to NASH detection, we combined Raman micro-spectroscopy and machine learning techniques to develop a classification model based on a well-established NASH mouse model, using spectrum pre-processing, biochemical component analysis (BCA) and logistic regression. By employing a selected pool of biochemical components, we identified biochemical changes specific to NASH and show that the classification model is capable of accurately detecting NASH (AUC=0.85-0.87) in mice. The unique biochemical fingerprint generated in this study may serve as a useful criterion to be leveraged for further validation in clinical samples.

Justification of disintegration testing beyond current FDA criteria using in vitro and in silico models

Drug product performance testing is an important part of quality-by-design approaches, but this process often lacks the underlying mechanistic understanding of the complex interactions between the disintegration and dissolution processes involved. Whereas a recent draft guideline by the US Food and Drug Administration (FDA) has allowed the replacement of dissolution testing with disintegration testing, the mentioned criteria are not globally accepted. This study provides scientific justification for using disintegration testing rather than dissolution testing as a quality control method for certain immediate release (IR) formulations. A mechanistic approach, which is beyond the current FDA criteria, is presented. Dissolution testing via United States Pharmacopeial Convention Apparatus II at various paddle speeds was performed for immediate and extended release formulations of metronidazole. Dissolution profile fitting via DDSolver and dissolution profile predictions via DDDPlus™ were performed. The results showed that Fickian diffusion and drug particle properties (DPP) were responsible for the dissolution of the IR tablets, and that formulation factors (eg, coning) impacted dissolution only at lower rotation speeds. Dissolution was completely formulation controlled if extended release tablets were tested and DPP were not important. To demonstrate that disintegration is the most important dosage form attribute when dissolution is DPP controlled, disintegration, intrinsic dissolution and dissolution testing were performed in conventional and disintegration impacting media (DIM). Tablet disintegration was affected by DIM and model fitting to the Korsmeyer-Peppas equation showed a growing effect of the formulation in DIM. DDDPlus was able to predict tablet dissolution and the intrinsic dissolution profiles in conventional media and DIM. The study showed that disintegration has to occur before DPP-dependent dissolution can happen. The study suggests that disintegration can be used as performance test of rapidly disintegrating tablets beyond the FDA criteria. The scientific criteria and justification is that dissolution has to be DPP dependent, originated from active pharmaceutical ingredient characteristics and formulations factors have to be negligible.

Modelling lactation curve for milk fat to protein ratio in Iranian buffaloes (Bubalus bubalis) using non-linear mixed models

The aim of this study was to compare seven non-linear mathematical models (Brody, Wood, Dhanoa, Sikka, Nelder, Rook and Dijkstra) to examine their efficiency in describing the lactation curves for milk fat to protein ratio (FPR) in Iranian buffaloes. Data were 43 818 test-day records for FPR from the first three lactations of Iranian buffaloes which were collected on 523 dairy herds in the period from 1996 to 2012 by the Animal Breeding Center of Iran. Each model was fitted to monthly FPR records of buffaloes using the non-linear mixed model procedure (PROC NLMIXED) in SAS and the parameters were estimated. The models were tested for goodness of fit using Akaike's information criterion (AIC), Bayesian information criterion (BIC) and log maximum likelihood (-2 Log L). The Nelder and Sikka mixed models provided the best fit of lactation curve for FPR in the first and second lactations of Iranian buffaloes, respectively. However, Wood, Dhanoa and Sikka mixed models provided the best fit of lactation curve for FPR in the third parity buffaloes. Evaluation of first, second and third lactation features showed that all models, except for Dijkstra model in the third lactation, under-predicted test time at which daily FPR was minimum. On the other hand, minimum FPR was over-predicted by all equations. Evaluation of the different models used in this study indicated that non-linear mixed models were sufficient for fitting test-day FPR records of Iranian buffaloes.

Moisture Sorption-desorption Characteristics and the Corresponding Thermodynamic Properties of Carvedilol Phosphate

Aims:

Carvedilol phosphate (CDP) is a nonselective beta-blocker used for the treatment of heart failures and hypertension. In this work, moisture sorption–desorption characteristics and thermodynamic properties of CDP have been investigated.

Materials and Methods:

The isotherms were determined using dynamic vapor sorption analyzer at different humidity conditions (0%–90% relative humidity) and three pharmaceutically relevant temperatures (20°C, 30°C, and 40°C). The experimental sorption data determined were fitted to various models, namely, Brunauer–Emmett–Teller; Guggenheim-Anderson-De Boer (GAB); Peleg; and modified GAB. Isosteric heats of sorption were evaluated through the direct use of sorption isotherms by means of the Clausius-Clapeyron equation.

Statistical Analysis Used:

The sorption model parameters were determined from the experimental sorption data using nonlinear regression analysis, and mean relative percentage deviation (P), correlation (Correl), root mean square error, and model efficiency were considered as the criteria to select the best fit model.

Results:

The sorption–desorption isotherms have sigmoidal shape – confirming to Type II isotherms. Based on the statistical data analysis, modified GAB model was found to be more adequate to explain sorption characteristics of CDP. It is noted that the rate of adsorption and desorption is specific to the temperature at which it was being studied. It is observed that isosteric heat of sorption decreased with increasing equilibrium moisture content.

Conclusions:

The calculation of the thermodynamic properties was further used to draw an understanding of the properties of water and energy requirements associated with the sorption behavior. The sorption–desorption data and the set of equations are useful in the simulation of processing, handling, and storage of CDP and further behavior during manufacture and storage of CDP formulations.

On the heterogeneity of human populations as reflected by mortality dynamics

The heterogeneity of populations is used to explain the variability of mortality rates across the lifespan and their deviations from an exponential growth at young and very old ages. A mathematical model that combines the heterogeneity with the assumption that the mortality of each constituent subpopulation increases exponentially with age, has been shown to successfully reproduce the entire mortality pattern across the lifespan and its evolution over time. In this work we aim to show that the heterogeneity is not only a convenient consideration for fitting mortality data but is indeed the actual structure of the population as reflected by the mortality dynamics over age and time. In particular, we show that the model of heterogeneous population fits mortality data better than other commonly used mortality models. This was demonstrated using cohort data taken for the entire lifespan as well as for only old ages. Also, we show that the model can reproduce seemingly contradicting observations in late-life mortality dynamics. Finally, we show that the homogenisation of a population, observed by fitting the model to actual data of consecutive periods, can be associated with the evolution of allele frequencies if the heterogeneity is assumed to reflect the genetic variations within the population.

IN VITRO RELEASE KINETICS MODEL FITTING OF LIPOSOMES: AN INSIGHT

Liposomes are emerging cargoes for bioactive delivery owing to their widely accepted biocompatible and biodegradable nature. It is always a challenge to control the release of payload for effective delivery to the site of interest. Over the couple of decennia, mathematical modeling of release process is a need of time whether the drug remains in the circulation or reaches at the target site. For establishing a better in vitro - in vivo correlation, release kinetics models viz. Peppas, Higuchi, Weibull, Zero Order and First order including mechanistic models like All-or-None, Toroidal, and Biomembrane models etc. are continuously exploited to predict drug release profile. Most of these models rely on the diffusion equations based on the composition of liposomes and conditions of release. Here, we summarized the crucial reports exploring these models and associated interventions to know the underlying physicochemical release phenomenon. Such mathematical model fitting can be a promising approach to deduce release/delivery process to help in designing the safe and efficacious ("Smart") liposomes.

Modelling lactation curve for milk fat to protein ratio in Iranian buffaloes (Bubalus bubalis) using non-linear mixed models

The aim of this study was to compare seven non-linear mathematical models (Brody, Wood, Dhanoa, Sikka, Nelder, Rook and Dijkstra) to examine their efficiency in describing the lactation curves for milk fat to protein ratio (FPR) in Iranian buffaloes. Data were 43 818 test-day records for FPR from the first three lactations of Iranian buffaloes which were collected on 523 dairy herds in the period from 1996 to 2012 by the Animal Breeding Center of Iran. Each model was fitted to monthly FPR records of buffaloes using the non-linear mixed model procedure (PROC NLMIXED) in SAS and the parameters were estimated. The models were tested for goodness of fit using Akaike's information criterion (AIC), Bayesian information criterion (BIC) and log maximum likelihood (-2 Log L). The Nelder and Sikka mixed models provided the best fit of lactation curve for FPR in the first and second lactations of Iranian buffaloes, respectively. However, Wood, Dhanoa and Sikka mixed models provided the best fit of lactation curve for FPR in the third parity buffaloes. Evaluation of first, second and third lactation features showed that all models, except for Dijkstra model in the third lactation, under-predicted test time at which daily FPR was minimum. On the other hand, minimum FPR was over-predicted by all equations. Evaluation of the different models used in this study indicated that non-linear mixed models were sufficient for fitting test-day FPR records of Iranian buffaloes.

An approximation method for improving dynamic network model fitting

There has been a great deal of interest recently in the modeling and simulation of dynamic networks, i.e., networks that change over time. One promising model is the separable temporal exponential-family random graph model (ERGM) of Krivitsky and Handcock, which treats the formation and dissolution of ties in parallel at each time step as independent ERGMs. However, the computational cost of fitting these models can be substantial, particularly for large, sparse networks. Fitting cross-sectional models for observations of a network at a single point in time, while still a non-negligible computational burden, is much easier. This paper examines model fitting when the available data consist of independent measures of cross-sectional network structure and the duration of relationships under the assumption of stationarity. We introduce a simple approximation to the dynamic parameters for sparse networks with relationships of moderate or long duration and show that the approximation method works best in precisely those cases where parameter estimation is most likely to fail-networks with very little change at each time step. We consider a variety of cases: Bernoulli formation and dissolution of ties, independent-tie formation and Bernoulli dissolution, independent-tie formation and dissolution, and dependent-tie formation models.

An integration of competing accounts on children's number line estimation

Children’s estimation patterns in bounded number line estimation (NLE) reveal marked developmental changes. Three different theoretical accounts were proposed to explain these changes: a log-to-linear shift account, a proportion-judgment account and a two-linear account considering familiarity with numbers or the understanding of the place-value structure of the Arabic number system. However, only the first two accounts are considered prominently in the ongoing scientific debate. Therefore, we first present a reanalysis of NLE data of Austrian first-graders contrasting all three accounts. Results indicate that the two-linear account is a reliable alternative to the log-to-linear shift as well as the proportion-judgment account. However, we do not claim the two-liner account to provide an exhaustive explanation for the observed developmental changes. We rather introduce the idea that aspects of all three accounts may complement – instead of exclude – each other. Jointly considering conceptual (i.e., familiarity, place-value) and procedural (i.e., proportion-judgments) aspects will allow for a more comprehensive understanding of children’s development in NLE.