Adaptive COVID-19 Mitigation Strategies: Tradeoffs between Trigger Thresholds, Response Timing, and Effectiveness

Background. To support proactive decision making during the COVID-19 pandemic, mathematical models have been leveraged to identify surveillance indicator thresholds at which strengthening nonpharmaceutical interventions (NPIs) is necessary to protect health care capacity. Understanding tradeoffs between different adaptive COVID-19 response components is important when designing strategies that balance public preference and public health goals. Methods. We considered 3 components of an adaptive COVID-19 response: 1) the threshold at which to implement the NPI, 2) the time needed to implement the NPI, and 3) the effectiveness of the NPI. Using a compartmental model of SARS-CoV-2 transmission calibrated to Minnesota state data, we evaluated different adaptive policies in terms of the peak number of hospitalizations and the time spent with the NPI in force. Scenarios were compared with a reference strategy, in which an NPI with an 80% contact reduction was triggered when new weekly hospitalizations surpassed 8 per 100,000 population, with a 7-day implementation period. Assumptions were varied in sensitivity analysis. Results. All adaptive response scenarios substantially reduced peak hospitalizations relative to no response. Among adaptive response scenarios, slower NPI implementation resulted in somewhat higher peak hospitalization and a longer time spent under the NPIs than the reference scenario. A stronger NPI response resulted in slightly less time with the NPIs in place and smaller hospitalization peak. A higher trigger threshold resulted in greater peak hospitalizations with little reduction in the length of time under the NPIs. Conclusions. An adaptive NPI response can substantially reduce infection circulation and prevent health care capacity from being exceeded. However, population preferences as well as the feasibility and timeliness of compliance with reenacting NPIs should inform response design.

Highlights

This study uses a mathematical model to compare different adaptive nonpharmaceutical intervention (NPI) strategies for COVID-19 management across 3 dimensions: threshold when the NPI should be implemented, time it takes to implement the NPI, and the effectiveness of the NPI.All adaptive NPI response scenarios considered substantially reduced peak hospitalizations compared with no response.Slower NPI implementation results in a somewhat higher peak hospitalization and longer time spent with the NPI in place but may make an adaptive strategy more feasible by allowing the population sufficient time to prepare for changing restrictions.A stronger, more effective NPI response results in a modest reduction in the time spent under the NPIs and slightly lower peak hospitalizations.A higher threshold for triggering the NPI delays the time at which the NPI starts but results in a higher peak hospitalization and does not substantially reduce the time the NPI remains in force.

High-resolution volumetric imaging constrains compartmental models to explore synaptic integration and temporal processing by cochlear nucleus globular bushy cells

Globular bushy cells (GBCs) of the cochlear nucleus play central roles in the temporal processing of sound. Despite investigation over many decades, fundamental questions remain about their dendrite structure, afferent innervation, and integration of synaptic inputs. Here, we use volume electron microscopy (EM) of the mouse cochlear nucleus to construct synaptic maps that precisely specify convergence ratios and synaptic weights for auditory nerve innervation and accurate surface areas of all postsynaptic compartments. Detailed biophysically based compartmental models can help develop hypotheses regarding how GBCs integrate inputs to yield their recorded responses to sound. We established a pipeline to export a precise reconstruction of auditory nerve axons and their endbulb terminals together with high-resolution dendrite, soma, and axon reconstructions into biophysically detailed compartmental models that could be activated by a standard cochlear transduction model. With these constraints, the models predict auditory nerve input profiles whereby all endbulbs onto a GBC are subthreshold (coincidence detection mode), or one or two inputs are suprathreshold (mixed mode). The models also predict the relative importance of dendrite geometry, soma size, and axon initial segment length in setting action potential threshold and generating heterogeneity in sound-evoked responses, and thereby propose mechanisms by which GBCs may homeostatically adjust their excitability. Volume EM also reveals new dendritic structures and dendrites that lack innervation. This framework defines a pathway from subcellular morphology to synaptic connectivity, and facilitates investigation into the roles of specific cellular features in sound encoding. We also clarify the need for new experimental measurements to provide missing cellular parameters, and predict responses to sound for further in vivo studies, thereby serving as a template for investigation of other neuron classes.

Four-Compartment Diffusion Model of Cortisol Disposition: Comparison With 3 Alternative Models in Current Clinical Use

Context

Estimated rates of cortisol elimination and appearance vary according to the model used to obtain them. Generalizability of current models of cortisol disposition in healthy humans is limited.

Objective

Development and validation of a realistic, mechanistic model of cortisol disposition that accounts for the major factors influencing plasma cortisol concentrations in vivo (Model 4), and comparison to previously described models of cortisol disposition in current clinical use (Models 1-3).

Methods

The 4 models were independently applied to cortisol concentration data obtained for the hydrocortisone bolus experiment (20 mg) in 2 clinical groups: healthy volunteers (HVs, n = 6) and corticosteroid binding globulin (CBG)-deficient (n = 2). Model 4 used Fick's first law of diffusion to model free cortisol flux between vascular and extravascular compartments. Pharmacokinetic parameter solutions for Models 1-4 were optimized by numerical methods, and model-specific parameter solutions were compared by repeated measures analysis of variance. Models and respective parameter solutions were compared by mathematical and simulation analyses, and an assessment tool was used to compare performance characteristics of the four models evaluated herein.

Results

Cortisol half-lives differed significantly between models (all P < .001) with significant model-group interaction (P = .02). In comparative analysis, Model 4 solutions yielded significantly reduced free cortisol half-life, improved fit to experimental data (both P < .01), and superior model performance.

Conclusion

The proposed 4-compartment diffusion model (Model 4) is consistent with relevant experimental observations and met the greatest number of empiric validation criteria. Cortisol half-life solutions obtained using Model 4 were generalizable between HV and CBG-deficient groups and bolus and continuous modes of hydrocortisone infusion.

In vivo kinetics of oleic, linoleic, and α-linolenic acid biohydrogenation in the rumen of dairy cows

Ruminal biohydrogenation (BH) of unsaturated fatty acids (FA) reduces absorption of essential FA and can result in formation of bioactive FA that cause milk fat depression. Rates of biohydrogenation of unsaturated FA are commonly observed using in vitro systems and are not well described in vivo. Seven ruminally cannulated cows were enrolled in a 3 × 3 Latin square design study to quantify biohydrogenation of 18:1n-9, 18:2n-6, and 18:3n-3 using a recently developed in vivo BH assay. All cows were fed a common high corn silage basal diet. Biohydrogenation was quantified using a perturbation model that consisted of a bolus dose of 200 g of an oil enriched in each unsaturated FA (oleic acid, OA = 87% 18:1n-9 sunflower oil; linoleic acid, LA = 70% 18:2n-6 safflower oil; and α-linolenic acid, ALA = 54% 18:3n-3 flaxseed oil) and 12 g of 17:0 as a marker of rumen outflow. Rumen contents were sampled before and after the bolus and enrichment of the bolused FA modeled. Using first-order kinetics to model FA disappearance, the fractional rates of disappearance of 18:1n-9 was 0.597 per hour, 18:2n-6 was 0.618 per hour, and 18:3n-3 was 0.834 per hour, similar to rates previously reported with this approach. Rumen turnover of 17:0 was 0.123 per hour, 0.065 per hour, and 0.106 per hour during the OA, LA, and ALA treatments, respectively. The extents of BH were calculated to be 82.8, 90.4, and 88.6% for 18:1n-9, 18:2n-6, and 18:3n-3, respectively. Finally, compartmental modeling was used to quantify the amount of each unsaturated FA metabolized through trans-10 and trans-11 BH pathways. The recently developed in vivo BH assay was able to predict rates of BH and provide insight into rumen metabolism of individual FA and may be useful to future investigations.

Total-Body PET Multiparametric Imaging of Cancer Using a Voxelwise Strategy of Compartmental Modeling

Quantitative dynamic PET with compartmental modeling has the potential to enable multiparametric imaging and more accurate quantification than static PET imaging. Conventional methods for parametric imaging commonly use a single kinetic model for all image voxels and neglect the heterogeneity of physiologic models, which can work well for single-organ parametric imaging but may significantly compromise total-body parametric imaging on a scanner with a long axial field of view. In this paper, we evaluate the necessity of voxelwise compartmental modeling strategies, including time delay correction (TDC) and model selection, for total-body multiparametric imaging. Methods: Ten subjects (5 patients with metastatic cancer and 5 healthy volunteers) were scanned on a total-body PET/CT system after injection of 370 MBq of 18F-FDG. Dynamic data were acquired for 60 min. Total-body parametric imaging was performed using 2 approaches. One was the conventional method that uses a single irreversible 2-tissue-compartment model with and without TDC. The second approach selects the best kinetic model from 3 candidate models for individual voxels. The differences between the 2 approaches were evaluated for parametric imaging of microkinetic parameters and the 18F-FDG net influx rate, KiResults: TDC had a nonnegligible effect on kinetic quantification of various organs and lesions. The effect was larger in lesions with a higher blood volume. Parametric imaging of Ki with the standard 2-tissue-compartment model introduced vascular-region artifacts, which were overcome by the voxelwise model selection strategy. Conclusion: The time delay and appropriate kinetic model vary in different organs and lesions. Modeling of the time delay of the blood input function and model selection improved total-body multiparametric imaging.

Estimating in vivo potassium distribution and fluxes with stable potassium isotopes

Extracellular potassium (K⁺) homeostasis is achieved by a concerted effort of multiple organs and tissues. A limitation in studies of K⁺ homeostasis is inadequate techniques to quantify K⁺ fluxes into and out of organs and tissues in vivo. The goal of the present study was to test the feasibility of a novel approach to estimate K⁺ distribution and fluxes in vivo using stable K⁺ isotopes. ⁴¹K was infused as KCl into rats consuming control or K⁺-deficient chow (n = 4 each), ⁴¹K-to-³⁹K ratios in plasma and red blood cells (RBCs) were measured by inductively coupled plasma mass spectrometry, and results were subjected to compartmental modeling. The plasma ⁴¹K/³⁹K increased during ⁴¹K infusion and decreased upon infusion cessation, without altering plasma total K⁺ concentration ([K⁺], i.e., ⁴¹K + ³⁹K). The time course of changes was analyzed with a two-compartmental model of K⁺ distribution and elimination. Model parameters, representing transport into and out of the intracellular pool and renal excretion, were identified in each rat, accurately predicting decreased renal K⁺ excretion in rats fed K⁺-deficient vs. control diet (P < 0.05). To estimate rate constants of K⁺ transport into and out of RBCs, ⁴¹K/³⁹K were subjected to a simple model, indicating no effects of the K⁺-deficient diet. The findings support the feasibility of the novel stable isotope approach to quantify K⁺ fluxes in vivo and sets a foundation for experimental protocols using more complex models to identify heterogeneous intracellular K⁺ pools and to answer questions pertaining to K⁺ homeostatic mechanisms in vivo.

Integrating Risk Assessment and Decision-Making Methods in Analyzing the Dynamics of COVID-19 Epidemics in Davao City, Mindanao Island, Philippines

The COVID-19 pandemic has become a public health crisis in the Philippines and the attention of national and local health authorities is focused on managing the fluctuating COVID-19 cases. This study presents a method that integrates risk management tools into health care decision-making processes to enhance the understanding and utilization of risk-based thinking in public health decision making. The risk assessment consists of the identification of the key risk factors of the COVID-19 contagion via bow-tie diagrams. Second, the safety controls for each risk factor relevant to the Davao City context are taken into account and are identified as barriers in the bow-tie. After which, the prioritization of the identified COVID-19 risks, as well as the effectiveness of the proposed interventions, is performed using the analytic hierarchy process. Consequently, the dynamics of COVID-19 management initiatives were explored using these priorities and a system of ordinary differential equations. Our results show that reducing the number of COVID-19 fatalities should be the top priority of the health authorities. In turn, we predict that the COVID-19 contagion can be controlled and eliminated in Davao city in three-month time after prioritizing the fatalities. In order to reduce the COVID-19 fatalities, health authorities should ensure an adequate number of COVID-ready ICU facilities. The general public, on the other hand, should follow medical and science-based advice and suspected and confirmed COVID-19 patients should strictly follow isolation protocols. Overall, an informed decision-making is necessary to avoid the unwanted consequences of an uncontrolled contagion.

Transmission rates and environmental reservoirs for COVID-19 - a modeling study

The coronavirus disease 2019 (COVID-19) remains a global pandemic at present. Although the human-to-human transmission route for this disease has been well established, its transmission mechanism is not fully understood. In this paper, we propose a mathematical model for COVID-19 which incorporates multiple transmission pathways and which employs time-dependent transmission rates reflecting the impact of disease prevalence and outbreak control. Applying this model to a retrospective study based on publicly reported data in China, we argue that the environmental reservoirs play an important role in the transmission and spread of the coronavirus. This argument is supported by our data fitting and numerical simulation results for the city of Wuhan, for the provinces of Hubei and Guangdong, and for the entire country of China.

Radiomic Analysis of Pharmacokinetic Heterogeneity Within Tumor Based on the Unsupervised Decomposition of Dynamic Contrast-Enhanced MRI for Predicting Histological Characteristics of Breast Cancer

BACKGROUND

Breast tumor heterogeneity is associated with histological characteristics. However, pharmacokinetic (PK) heterogeneity within tumor might merit further exploration.

PURPOSE

To enhance the predictive power of molecular subtypes, Ki-67, and tumor grade by analyzing PK heterogeneity within tumor based on dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI).

STUDY TYPE

Retrospective.

POPULATION

Two hundred and eight biopsy-proven breast cancer patients, randomly divided into a training cohort (N = 144) and a testing cohort (N = 64).

FIELD STRENGTH/SEQUENCE

T₁ -weighted DCE-MRI at 3.0 T.

ASSESSMENT

A convex analysis of mixtures-compartmental modeling decomposition method was used to estimate the PK parameter (i.e., the volume transfer constant K^trans ) in tumor subregions with distinct physiological kinetic patterns, including fast-flow kinetics, slow-flow kinetics, and plasma input. Radiomic features based on the PK parameter were calculated from each tumor subregion.

STATISTICAL TESTS

The training cohort was used to build random forest classifiers based on the optimal features determined by the 5-fold cross-validation method. The performance was assessed on the testing cohort using the area under the receiver operating characteristic curve (AUC). The AUCs derived from the tumor subregion-based PK parameter were compared with those of the original images of the entire tumor using the DeLong test. A P-value of <0.05 was considered statistically significant.

RESULTS

The tumor subregion-based PK parameter, which yielded the highest AUCs of 0.8782, 0.7568, 0.7019, 0.7963, 0.8080, and 0.7375 for luminal A, luminal B, basal-like, human epidermal growth factor receptor 2, Ki-67, and tumor grade, respectively, obtained better diagnostic performance than the original images in the entire tumor (highest AUCs = 0.8612, 0.6191, 0.5593, 0.7704, 0.7494, and 0.6261, respectively). In particular, statistically significant improvement in the diagnostic performance was obtained for luminal B.

DATA CONCLUSION

Radiomic analysis of PK heterogeneity within tumor can enhance the predictive performance of radiomic models compared with that of the entire tumor.

LEVEL OF EVIDENCE

4 TECHNICAL EFFICACY STAGE: 3.

Compartmental and COMSOL Multiphysics 3D Modeling of Drug Diffusion to the Vitreous Following the Administration of a Sustained-Release Drug Delivery System

The purpose of this study was to examine antibiotic drug transport from a hydrogel drug delivery system (DDS) using a computational model and a 3D model of the eye. Hydrogel DDSs loaded with vancomycin (VAN) were synthesized and release behavior was characterized in vitro. Four different compartmental and four COMSOL models of the eye were developed to describe transport into the vitreous originating from a DDS placed topically, in the subconjunctiva, subretinally, and intravitreally. The concentration of the simulated DDS was assumed to be the initial concentration of the hydrogel DDS. The simulation was executed over 1500 and 100 h for the compartmental and COMSOL models, respectively. Based on the MATLAB model, topical, subconjunctival, subretinal and vitreous administration took most (~500 h to least (0 h) amount of time to reach peak concentrations in the vitreous, respectively. All routes successfully achieved therapeutic levels of drug (0.007 mg/mL) in the vitreous. These models predict the relative build-up of drug in the vitreous following DDS administration in four different points of origin in the eye. Our model may eventually be used to explore the minimum loading dose of drug required in our DDS leading to reduced drug use and waste.

Dynamic 18F-FDopa PET Imaging for Newly Diagnosed Gliomas: Is a Semiquantitative Model Sufficient?

Purpose

Dynamic amino acid positron emission tomography (PET) has become essential in neuro-oncology, most notably for its prognostic value in the noninvasive prediction of isocitrate dehydrogenase (IDH) mutations in newly diagnosed gliomas. The 6-[¹⁸F]fluoro-l-DOPA (¹⁸F-FDOPA) kinetic model has an underlying complexity, while previous studies have predominantly used a semiquantitative dynamic analysis. Our study addresses whether a semiquantitative analysis can capture all the relevant information contained in time–activity curves for predicting the presence of IDH mutations compared to the more sophisticated graphical and compartmental models.

Methods

Thirty-seven tumour time–activity curves from ¹⁸F-FDOPA PET dynamic acquisitions of newly diagnosed gliomas (median age = 58.3 years, range = 20.3–79.9 years, 16 women, 16 IDH-wild type) were analyzed with a semiquantitative model based on classical parameters, with (SQ) or without (Ref SQ) a reference region, or on parameters of a fit function (SQ Fit), a graphical Logan model with input function (Logan) or reference region (Ref Logan), and a two-tissue compartmental model previously reported for ¹⁸F-FDOPA PET imaging of gliomas (2TCM). The overall predictive performance of each model was assessed with an area under the curve (AUC) comparison using multivariate analysis of all the parameters included in the model. Moreover, each extracted parameter was assessed in a univariate analysis by a receiver operating characteristic curve analysis.

Results

The SQ model with an AUC of 0.733 for predicting IDH mutations showed comparable performance to the other models with AUCs of 0.752, 0.814, 0.693, 0.786, and 0.863, respectively corresponding to SQ Fit, Ref SQ, Logan, Ref Logan, and 2TCM (p ≥ 0.10 for the pairwise comparisons with other models). In the univariate analysis, the SQ time-to-peak parameter had the best diagnostic performance (75.7% accuracy) compared to all other individual parameters considered.

Conclusions

The SQ model circumvents the complexities of the ¹⁸F-FDOPA kinetic model and yields similar performance in predicting IDH mutations when compared to the other models, most notably the compartmental model. Our study provides supportive evidence for the routine clinical application of the SQ model for the dynamic analysis of ¹⁸F-FDOPA PET images in newly diagnosed gliomas.

[11C]deschloroclozapine is an improved PET radioligand for quantifying a human muscarinic DREADD expressed in monkey brain

Previous work found that [¹¹C]deschloroclozapine ([¹¹C]DCZ) is superior to [¹¹C]clozapine ([¹¹C]CLZ) for imaging Designer Receptors Exclusively Activated by Designer Drugs (DREADDs). This study used PET to quantitatively and separately measure the signal from transfected receptors, endogenous receptors/targets, and non-displaceable binding in other brain regions to better understand this superiority. A genetically-modified muscarinic type-4 human receptor (hM₄Di) was injected into the right amygdala of a male rhesus macaque. [¹¹C]DCZ and [¹¹C]CLZ PET scans were conducted 2-24 months later. Uptake was quantified relative to the concentration of parent radioligand in arterial plasma at baseline (n = 3 scans/radioligand) and after receptor blockade (n = 3 scans/radioligand). Both radioligands had greater uptake in the transfected region and displaceable uptake in other brain regions. Displaceable uptake was not uniformly distributed, perhaps representing off-target binding to endogenous receptor(s). After correction, [¹¹C]DCZ signal was 19% of that for [¹¹C]CLZ, and background uptake was 10% of that for [¹¹C]CLZ. Despite stronger [¹¹C]CLZ binding, the signal-to-background ratio for [¹¹C]DCZ was almost two-fold greater than for [¹¹C]CLZ. Both radioligands had comparable DREADD selectivity. All reference tissue models underestimated signal-to-background ratio in the transfected region by 40%-50% for both radioligands. Thus, the greater signal-to-background ratio of [¹¹C]DCZ was due to its lower background uptake.

Receptor/Raft Ratio Is a Determinant for LRP6 Phosphorylation and WNT/β-Catenin Signaling

Microdomains or lipid rafts greatly affect the distribution of proteins and peptides in the membrane and play a vital role in the formation and activation of receptor/protein complexes. A prominent example for the decisive impact of lipid rafts on signaling is LRP6, whose localization to the same lipid rafts domain as the kinase CK1γ is crucial for its successful phosphorylation and the subsequent activation of the signalosome, hence WNT/β-catenin signaling. However, according to various experimental measurements, approximately 25 to 35 % of the cell plasma membrane is covered by nanoscopic raft domains with diameters ranging between 10 to 200 nm. Extrapolating/Translating these values to the membrane of a “normal sized” cell yields a raft abundance, that, by far, outnumbers the membrane-associated pathway components of most individual signaling pathway, such as receptor and kinases. To analyze whether and how the quantitative ratio between receptor and rafts affects LRP6 phosphorylation and WNT/β-catenin pathway activation, we present a computational modeling study, that for the first time employs realistic raft numbers in a compartment-based pathway model. Our simulation experiments indicate, that for receptor/raft ratios smaller than 1, i.e., when the number of raft compartments clearly exceeds the number of pathway specific membrane proteins, we observe significant decrease in LRP6 phosphorylation and downstream pathway activity. Our results suggest that pathway specific targeting and sorting mechanism are required to significantly narrow down the receptor/raft ratio and to enable the formation of the LRP6 signalosome, hence signaling.

Effects of inflammation and soluble epoxide hydrolase inhibition on oxylipin composition of very low-density lipoproteins in isolated perfused rat livers

Oxylipins are metabolites of polyunsaturated fatty acids that mediate cardiovascular health by attenuation of inflammation, vascular tone, hemostasis, and thrombosis. Very low-density lipoproteins (VLDL) contain oxylipins, but it is unknown whether the liver regulates their concentrations. In this study, we used a perfused liver model to observe the effect of inflammatory lipopolysaccharide (LPS) challenge and soluble epoxide hydrolase inhibition (sEHi) on VLDL oxylipins. A compartmental model of deuterium-labeled linoleic acid and palmitic acid incorporation into VLDL was also developed to assess the dependence of VLDL oxylipins on fatty acid incorporation rates. LPS decreased the total fatty acid VLDL content by 30% [6%,47%], and decreased final concentration of several oxylipins by a similar amount (13-HOTrE, 35% [4%,55%], -1.3 nM; 9(10)-EpODE, 29% [3%,49%], -2.0 nM; 15(16)-EpODE, 29% [2%,49%], -1.6 nM; AA-derived diols, 32% [5%,52%], -2.4 nM; 19(20)-DiHDPA, 31% [7%,50%], -1.0 nM). However, the EPA-derived epoxide, 17(18)-EpETE, was decreased by 75% [49%,88%], (-0.52 nM) with LPS, double the suppression of other oxylipins. sEHi increased final concentration of DHA epoxide, 16(17)-EpDPE, by 99% [35%,193%], (2.0 nM). Final VLDL-oxylipin concentrations with LPS treatment were not correlated with linoleic acid kinetics, suggesting they were independently regulated under inflammatory conditions. We conclude that the liver regulates oxylipin incorporation into VLDL, and the oxylipin content is altered by LPS challenge and by inhibition of the epoxide hydrolase pathway. This provides evidence for delivery of systemic oxylipin signals by VLDL transport.

A Compartmental Model Describing the Kinetics of β-Carotene and β-Carotene-Derived Retinol in Healthy Older Adults

BACKGROUND

Descriptive and quantitative information on β-carotene whole-body kinetics in humans is limited.

OBJECTIVES

Our objective was to advance the development of a physiologically based, working hypothesis compartmental model describing the metabolism of β-carotene and β-carotene-derived retinol.

METHODS

We used model-based compartmental analysis (Simulation, Analysis and Modeling software) to analyze previously published data on plasma kinetics of [2H8]β-carotene, [2H4]β-carotene-derived retinol, and [2H8]retinyl acetate-derived retinol in healthy, older US adults (3 female, 2 male; 50-68 y); subjects were studied for 56 d after consuming doses of 11 μmol [2H8]β-carotene and, 3 d later, 9 μmol [2H8]retinyl acetate in oil.

RESULTS

We developed a complex model for labeled β-carotene and β-carotene-derived retinol, as well as preformed vitamin A, using simulations to augment observed data during model calibration. The model predicts that mean (range) β-carotene absorption (bioavailability) was 9.5% (5.2-14%) and bioefficacy was 7.3% (3.6-14%). Of the absorbed β-carotene, 41% (25-58%) was packaged intact in chylomicrons and the balance was converted to retinol, with 58% (42-75%) transported as retinyl esters in chylomicrons and 0-2% by retinol-binding protein. Most (95%) chylomicron β-carotene was cleared by the liver. Later data revealed differences in the metabolism of retinyl acetate- versus β-carotene-derived retinol; data required that both β-carotene and derived retinol be recycled from extrahepatic tissues (e.g. adipose) in HDL. Of total bioconversion [73% (47-99%)], 82% occurred in the intestine, 17% in the liver, and 0.83% in other tissues.

CONCLUSIONS

Our model advances knowledge about whole-body β-carotene metabolism in healthy adults, including the kinetics of transport in all lipoprotein species, and suggests hypotheses to be tested in future studies, such as the possibility that retinol derived from hepatic conversion over a long period of time might contribute to plasma retinol homeostasis and total body vitamin A stores.

Pharmacokinetic Characterization and External Evaluation of a Quantitative Framework of Sublingual Buprenorphine in Patients with an Opioid Disorder in Puerto Rico

Background: The aim of this analysis was to characterize the pharmacokinetics (PK) of sublingual buprenorphine (BUP) and its metabolites (buprenorphine glucuronide; BUP-g, norbuprenorphine; Nor-BUP, and norbuprenorphine glucuronide; Nor-BUP-g) in opioid use disorder (OUD) patients in Puerto Rico (PR) as a first step of evidence-based BUP dosing strategies in this population. Methods: BUP and metabolites concentrations were measured from 0 to 8 h after the administration of sublingual buprenorphine/naloxone films in 12 stable OUD subjects. Results: PK non-compartmental characteristics showed considerable variability in parameters between the subjects over the 8-h sampling time (t_max = 1.5 ± 0.7 h, C_o = 1.6 ± 1.4 ng/mL, C_max= 7.1 ± 6 ng/mL, and AUC_0–8h = 26.8 ± 17.8 h·ng/mL). Subjects had a significantly higher tendency towards CYP-mediated N-demethylation, with the AUC_0–8h ratios of the molar concentrations of [Nor-BUP + Nor-BUP-g] to BUP being (3.4 ± 1.9) significantly higher compared with BUP-g to BUP (0.19 ± 0.2). A two-compartment population-PK model with linear absorption (k_a = 2.54 h⁻¹), distribution (k₁₂= 2.34 h⁻¹, k₁₄ = 1.29 h⁻¹), metabolism (k₂₄ = 1.28 × 10⁻¹ h⁻¹, k₂₃ = 6.43 × 10⁻² h⁻¹, k₃₅ = 1.23 × 10⁻¹ h⁻¹, k₄₅ = 8.73 × 10⁻¹ h⁻¹), and elimination (k₃₀ = 3.81 × 10⁻³ h⁻¹, k₅₀ = 1.27 × 10⁻¹ h⁻¹) adequately described the time-course of BUP and its metabolites, which has been externally validated using published data. Conclusions: Although limited in sampling time and number of recruited subjects, this study presents specific BUP PK characteristics that evidenced the need for additional PK studies and subsequent modeling of the data for the development of evidence-based dosing approaches in Puerto Rico.

Unifying Long-Term Plasticity Rules for Excitatory Synapses by Modeling Dendrites of Cortical Pyramidal Neurons

A large number of experiments have indicated that precise spike times, firing rates, and synapse locations crucially determine the dynamics of long-term plasticity induction in excitatory synapses. However, it remains unknown how plasticity mechanisms of synapses distributed along dendritic trees cooperate to produce the wide spectrum of outcomes for various plasticity protocols. Here, we propose a four-pathway plasticity framework that is well grounded in experimental evidence and apply it to a biophysically realistic cortical pyramidal neuron model. We show in computer simulations that several seemingly contradictory experimental landmark studies are consistent with one unifying set of mechanisms when considering the effects of signal propagation in dendritic trees with respect to synapse location. Our model identifies specific spatiotemporal contributions of dendritic and axo-somatic spikes as well as of subthreshold activation of synaptic clusters, providing a unified parsimonious explanation not only for rate and timing dependence but also for location dependence of synaptic changes.

•

A phenomenological synaptic plasticity rule is applied to a pyramidal neuron model

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Model reproduces rate-, timing-, and location-dependent plasticity results

•

Active dendrites allow plasticity via dendritic spikes and subthreshold events

•

Cooperative plasticity exists across the dendritic tree and within single branches

Perceptron Learning and Classification in a Modeled Cortical Pyramidal Cell

The perceptron learning algorithm and its multiple-layer extension, the backpropagation algorithm, are the foundations of the present-day machine learning revolution. However, these algorithms utilize a highly simplified mathematical abstraction of a neuron; it is not clear to what extent real biophysical neurons with morphologically-extended non-linear dendritic trees and conductance-based synapses can realize perceptron-like learning. Here we implemented the perceptron learning algorithm in a realistic biophysical model of a layer 5 cortical pyramidal cell with a full complement of non-linear dendritic channels. We tested this biophysical perceptron (BP) on a classification task, where it needed to correctly binarily classify 100, 1,000, or 2,000 patterns, and a generalization task, where it was required to discriminate between two "noisy" patterns. We show that the BP performs these tasks with an accuracy comparable to that of the original perceptron, though the classification capacity of the apical tuft is somewhat limited. We concluded that cortical pyramidal neurons can act as powerful classification devices.

Trafficking of nonesterified fatty acids in insulin resistance and relationship to dysglycemia

In adipose, insulin functions to suppress intracellular lipolysis and secretion of nonesterified fatty acid (NEFA) into plasma. We applied glucose and NEFA minimal models (MM) following a frequently sampled intravenous glucose tolerance test (FSIVGTT) to assess glucose-specific and NEFA-specific insulin resistance. We used total NEFA and individual fatty acids in the NEFA MM, comparing the model parameters in metabolic syndrome (MetSyn) subjects (n = 52) with optimally healthy controls (OptHC; n = 14). Results are reported as mean difference (95% confidence interval). Using the glucose MM, MetSyn subjects had lower [-73% (-82, -57)] sensitivity to insulin (S_i) and higher [138% (44, 293)] acute insulin response to glucose (AIR_g). Using the NEFA MM, MetSyn subjects had lower [-24% (-35, -13)] percent suppression, higher [32% (15, 52)] threshold glucose (g_s), and a higher [81% (12, 192)] affinity constant altering NEFA secretion (ϕ). Comparing fatty acids, percent suppression was lower in myristic acid (MA) than in all other fatty acids, and the stearic acid (SA) response was so unique that it did not fit the NEFA MM. MA and SA percent of total were increased at 50 min after glucose injection, whereas oleic acid (OA) and palmitic acid (PA) were decreased (P < 0.05). We conclude that the NEFA MM, as well as the response of individual NEFA fatty acids after a FSIVGTT, differ between OptHC and MetSyn subjects and that the NEFA MM parameters differ between individual fatty acids.

Assessment of the effect of polymers combination and effervescent component on the drug release of swellable gastro-floating tablet formulation through compartmental modeling-based approach

The aim of this research was to assess the effect of polymer blend and effervescent components on the floating and swelling behaviors of swellable gastro-floating formulation as well as the drug release through a compartmental modeling analysis. Swellable gastro-floating formulation of freely water-soluble drug, metformin HCl as a drug model, was formulated and developed using D-optimal design. Polymer combination between interpolymer complex (IPC) (poly-vinyl acetate-copolymer methacrylate) and hydroxy propyl methyl cellulose (HPMC), and effervescent components were studied and optimized in this work. Several factors affecting the drug release behavior were determined e.g. swelling behavior, erosion behavior, and floating behavior were studied as well as the drug release through compartmental modeling analysis. The results revealed that the hydrophilic polymer was responsible for gas entrapment formed from effervescent reaction, meanwhile IPC contributed on maintaining the swollen matrix integrity through intermolecular polymer interaction. In addition, effervescent components played fundamental role in the formation of porous system as well as inducing burst release effect. Compartmental modeling provided different outlook about the drug release. Presence of IPC at a high proportion (10-15%) of the polymer blend modulated the changes of pattern of the drug release kinetics and mechanism. Finally, compartmental modeling-based approach was more adequate to describe the drug release kinetics and mechanism compared to the monophasic equation model correlating with process understanding of the drug release from swellable gastro-floating formulation.

Extreme Compartmentalization in a Drosophila Amacrine Cell

A neuron is conventionally regarded as a single processing unit. It receives input from one or several presynaptic cells, transforms these signals, and transmits one output signal to its postsynaptic partners. Exceptions exist: amacrine cells in the mammalian retina [1-3] or interneurons in the locust mesothoracic ganglion [4] are thought to represent many electrically isolated microcircuits within one neuron. An extreme case of such an amacrine cell has recently been described in the Drosophila visual system. This cell, called CT1, reaches into two neuropils of the optic lobe, where it visits each of 700 repetitive columns, thereby covering the whole visual field [5, 6]. Due to its unusual morphology, CT1 has been suspected to perform local computations [6, 7], but this has never been proven. Using 2-photon calcium imaging and visual stimulation, we find highly compartmentalized retinotopic response properties in neighboring terminals of CT1, with each terminal acting as an independent functional unit. Model simulations demonstrate that this extreme case of compartmentalization is at the biophysical limit of neural computation.

Use of Stable Isotopes to Evaluate Bioefficacy of Provitamin A Carotenoids, Vitamin A Status, and Bioavailability of Iron and Zinc

The ability of nutrition scientists to measure the status, bioavailability, and bioefficacy of micronutrients is affected by lack of access to the parts of the body through which a nutrient may travel before appearing in accessible body compartments (typically blood or urine). Stable isotope-labeled tracers function as safe, nonradioactive tools to follow micronutrients in a quantitative manner because the absorption, distribution, metabolism, and excretion of the tracer are assumed to be similar to the unlabeled vitamin or mineral. The International Atomic Energy Agency (IAEA) supports research on the safe use of stable isotopes in global health and nutrition. This review focuses on IAEA's contributions to vitamin A, iron, and zinc research. These micronutrients are specifically targeted by the WHO because of their importance in health and worldwide prevalence of deficiency. These 3 micronutrients are included in food fortification and biofortification efforts in low- and middle-income regions of the world. Vitamin A isotopic techniques can be used to evaluate the efficacy and effectiveness of interventions. For example, total body retinol stores were estimated by using 13C2-retinol isotope dilution before and after feeding Zambian children maize biofortified with β-carotene to determine if vitamin A reserves were improved by the intervention. Stable isotopes of iron and zinc have been used to determine mineral bioavailability. In Thailand, ferrous sulfate was better absorbed from fish sauce than was ferrous lactate or ferric ammonium citrate, determined with the use of different iron isotopes in each compound. Comparisons of one zinc isotope injected intravenously with another isotope taken orally from a micronutrient powder proved that the powder increased total absorbed zinc from a meal in Pakistani infants. Capacity building by the IAEA with appropriate collaborations in low- and middle-income countries to use stable isotopes has resulted in many advancements in human nutrition.

Human Cortical Pyramidal Neurons: From Spines to Spikes via Models

We present detailed models of pyramidal cells from human neocortex, including models on their excitatory synapses, dendritic spines, dendritic NMDA- and somatic/axonal Na⁺ spikes that provided new insights into signal processing and computational capabilities of these principal cells. Six human layer 2 and layer 3 pyramidal cells (HL2/L3 PCs) were modeled, integrating detailed anatomical and physiological data from both fresh and postmortem tissues from human temporal cortex. The models predicted particularly large AMPA- and NMDA-conductances per synaptic contact (0.88 and 1.31 nS, respectively) and a steep dependence of the NMDA-conductance on voltage. These estimates were based on intracellular recordings from synaptically-connected HL2/L3 pairs, combined with extra-cellular current injections and use of synaptic blockers, and the assumption of five contacts per synaptic connection. A large dataset of high-resolution reconstructed HL2/L3 dendritic spines provided estimates for the EPSPs at the spine head (12.7 ± 4.6 mV), spine base (9.7 ± 5.0 mV), and soma (0.3 ± 0.1 mV), and for the spine neck resistance (50–80 MΩ). Matching the shape and firing pattern of experimental somatic Na⁺-spikes provided estimates for the density of the somatic/axonal excitable membrane ion channels, predicting that 134 ± 28 simultaneously activated HL2/L3-HL2/L3 synapses are required for generating (with 50% probability) a somatic Na⁺ spike. Dendritic NMDA spikes were triggered in the model when 20 ± 10 excitatory spinous synapses were simultaneously activated on individual dendritic branches. The particularly large number of basal dendrites in HL2/L3 PCs and the distinctive cable elongation of their terminals imply that ~25 NMDA-spikes could be generated independently and simultaneously in these cells, as compared to ~14 in L2/3 PCs from the rat somatosensory cortex. These multi-sites non-linear signals, together with the large (~30,000) excitatory synapses/cell, equip human L2/L3 PCs with enhanced computational capabilities. Our study provides the most comprehensive model of any human neuron to-date demonstrating the biophysical and computational distinctiveness of human cortical neurons.

Effective Network Size Predicted From Simulations of Pathogen Outbreaks Through Social Networks Provides a Novel Measure of Structure-Standardized Group Size

The transmission of infectious disease through a population is often modeled assuming that interactions occur randomly in groups, with all individuals potentially interacting with all other individuals at an equal rate. However, it is well known that pairs of individuals vary in their degree of contact. Here, we propose a measure to account for such heterogeneity: effective network size (ENS), which refers to the size of a maximally complete network (i.e., unstructured, where all individuals interact with all others equally) that corresponds to the outbreak characteristics of a given heterogeneous, structured network. We simulated susceptible-infected (SI) and susceptible-infected-recovered (SIR) models on maximally complete networks to produce idealized outbreak duration distributions for a disease on a network of a given size. We also simulated the transmission of these same diseases on random structured networks and then used the resulting outbreak duration distributions to predict the ENS for the group or population. We provide the methods to reproduce these analyses in a public R package, "enss." Outbreak durations of simulations on randomly structured networks were more variable than those on complete networks, but tended to have similar mean durations of disease spread. We then applied our novel metric to empirical primate networks taken from the literature and compared the information represented by our ENSs to that by other established social network metrics. In AICc model comparison frameworks, group size and mean distance proved to be the metrics most consistently associated with ENS for SI simulations, while group size, centralization, and modularity were most consistently associated with ENS for SIR simulations. In all cases, ENS was shown to be associated with at least two other independent metrics, supporting its use as a novel metric. Overall, our study provides a proof of concept for simulation-based approaches toward constructing metrics of ENS, while also revealing the conditions under which this approach is most promising.

T2N as a new tool for robust electrophysiological modeling demonstrated for mature and adult-born dentate granule cells

Compartmental models are the theoretical tool of choice for understanding single neuron computations. However, many models are incomplete, built ad hoc and require tuning for each novel condition rendering them of limited usability. Here, we present T2N, a powerful interface to control NEURON with Matlab and TREES toolbox, which supports generating models stable over a broad range of reconstructed and synthetic morphologies. We illustrate this for a novel, highly detailed active model of dentate granule cells (GCs) replicating a wide palette of experiments from various labs. By implementing known differences in ion channel composition and morphology, our model reproduces data from mouse or rat, mature or adult-born GCs as well as pharmacological interventions and epileptic conditions. This work sets a new benchmark for detailed compartmental modeling. T2N is suitable for creating robust models useful for large-scale networks that could lead to novel predictions. We discuss possible T2N application in degeneracy studies.

Population Pharmacokinetics of Posaconazole Tablets and Monte Carlo Simulations To Determine whether All Patients Should Receive the Same Dose

Posaconazole is extensively used for prophylaxis for invasive fungal infections. The gastro-resistant tablet formulation has allowed the bioavailability issues encountered with the oral suspension to be overcome. However, overexposure is now frequent. This study aimed to (i) describe the pharmacokinetics of posaconazole tablets in a real-life cohort of patients with hematological malignancies and (ii) perform Monte Carlo simulations to assess the possibility that the daily dose can be reduced while keeping a sufficient exposure. Forty-nine consecutive inpatients were prospectively included in the study. Posaconazole trough concentrations (TC) were measured once a week, and biological and demographic data were collected. The concentrations were analyzed by compartmental modeling, and Monte Carlo simulations were performed using estimated parameters to assess the rate of attainment of the target TC after dose reduction. The pharmacokinetics of posaconazole were well described using a one-compartment model with first-order absorption and elimination. The values of the parameters (interindividual variabilities) were as follows: the absorption constant (k_a ) was 0.588 h^-1 (fixed), the volume of distribution (V/F) was 420 liters (28.2%), and clearance (CL/F) was 7.3 liters/h (24.2%) with 31.9% interoccasion variability. Forty-nine percent of the simulated patients had TC at steady state of ≥1.5 μg/ml and maintained a TC above 1 μg/ml after a reduction of the dose to 200 mg daily. A third of these patients eligible for a dose reduction had TC of ≥1.5 μg/ml as soon as 48 h of treatment. Though posaconazole tablets were less impacted by bioavailability issues than the oral suspension, the pharmacokinetics of posaconazole tablets remain highly variable. Simulations showed that approximately half of the patients would benefit from a reduction of the dose from 300 mg to 200 mg while keeping the TC above the minimal recommended target of 0.7 μg/ml, resulting in a 33% savings in the cost of this very expensive drug.

Wiring variations that enable and constrain neural computation in a sensory microcircuit

Neural network function can be shaped by varying the strength of synaptic connections. One way to achieve this is to vary connection structure. To investigate how structural variation among synaptic connections might affect neural computation, we examined primary afferent connections in the Drosophila olfactory system. We used large-scale serial section electron microscopy to reconstruct all the olfactory receptor neuron (ORN) axons that target a left-right pair of glomeruli, as well as all the projection neurons (PNs) postsynaptic to these ORNs. We found three variations in ORN→PN connectivity. First, we found a systematic co-variation in synapse number and PN dendrite size, suggesting total synaptic conductance is tuned to postsynaptic excitability. Second, we discovered that PNs receive more synapses from ipsilateral than contralateral ORNs, providing a structural basis for odor lateralization behavior. Finally, we found evidence of imprecision in ORN→PN connections that can diminish network performance.

DOI:http://dx.doi.org/10.7554/eLife.24838.001

Spectral Clustering Predicts Tumor Tissue Heterogeneity Using Dynamic 18F-FDG PET: A Complement to the Standard Compartmental Modeling Approach

In this study, we described and validated an unsupervised segmentation algorithm for the assessment of tumor heterogeneity using dynamic ¹⁸F-FDG PET. The aim of our study was to objectively evaluate the proposed method and make comparisons with compartmental modeling parametric maps and SUV segmentations using simulations of clinically relevant tumor tissue types. Methods: An irreversible 2-tissue-compartmental model was implemented to simulate clinical and preclinical ¹⁸F-FDG PET time-activity curves using population-based arterial input functions (80 clinical and 12 preclinical) and the kinetic parameter values of 3 tumor tissue types. The simulated time-activity curves were corrupted with different levels of noise and used to calculate the tissue-type misclassification errors of spectral clustering (SC), parametric maps, and SUV segmentation. The utility of the inverse noise variance- and Laplacian score-derived frame weighting schemes before SC was also investigated. Finally, the SC scheme with the best results was tested on a dynamic ¹⁸F-FDG measurement of a mouse bearing subcutaneous colon cancer and validated using histology. Results: In the preclinical setup, the inverse noise variance-weighted SC exhibited the lowest misclassification errors (8.09%-28.53%) at all noise levels in contrast to the Laplacian score-weighted SC (16.12%-31.23%), unweighted SC (25.73%-40.03%), parametric maps (28.02%-61.45%), and SUV (45.49%-45.63%) segmentation. The classification efficacy of both weighted SC schemes in the clinical case was comparable to the unweighted SC. When applied to the dynamic ¹⁸F-FDG measurement of colon cancer, the proposed algorithm accurately identified densely vascularized regions from the rest of the tumor. In addition, the segmented regions and clusterwise average time-activity curves showed excellent correlation with the tumor histology. Conclusion: The promising results of SC mark its position as a robust tool for quantification of tumor heterogeneity using dynamic PET studies. Because SC tumor segmentation is based on the intrinsic structure of the underlying data, it can be easily applied to other cancer types as well.

Unique membrane properties and enhanced signal processing in human neocortical neurons

The advanced cognitive capabilities of the human brain are often attributed to our recently evolved neocortex. However, it is not known whether the basic building blocks of the human neocortex, the pyramidal neurons, possess unique biophysical properties that might impact on cortical computations. Here we show that layer 2/3 pyramidal neurons from human temporal cortex (HL2/3 PCs) have a specific membrane capacitance (C_m) of ~0.5 µF/cm², half of the commonly accepted 'universal' value (~1 µF/cm²) for biological membranes. This finding was predicted by fitting in vitro voltage transients to theoretical transients then validated by direct measurement of C_m in nucleated patch experiments. Models of 3D reconstructed HL2/3 PCs demonstrated that such low C_m value significantly enhances both synaptic charge-transfer from dendrites to soma and spike propagation along the axon. This is the first demonstration that human cortical neurons have distinctive membrane properties, suggesting important implications for signal processing in human neocortex.

DOI:http://dx.doi.org/10.7554/eLife.16553.001

Multiple apolipoprotein kinetics measured in human HDL by high-resolution/accurate mass parallel reaction monitoring

Endogenous labeling with stable isotopes is used to study the metabolism of proteins in vivo. However, traditional detection methods such as GC/MS cannot measure tracer enrichment in multiple proteins simultaneously, and multiple reaction monitoring MS cannot measure precisely the low tracer enrichment in slowly turning-over proteins as in HDL. We exploited the versatility of the high-resolution/accurate mass (HR/AM) quadrupole Orbitrap for proteomic analysis of five HDL sizes. We identified 58 proteins in HDL that were shared among three humans and that were organized into five subproteomes according to HDL size. For seven of these proteins, apoA-I, apoA-II, apoA-IV, apoC-III, apoD, apoE, and apoM, we performed parallel reaction monitoring (PRM) to measure trideuterated leucine tracer enrichment between 0.03 to 1.0% in vivo, as required to study their metabolism. The results were suitable for multicompartmental modeling in all except apoD. These apolipoproteins in each HDL size mainly originated directly from the source compartment, presumably the liver and intestine. Flux of apolipoproteins from smaller to larger HDL or the reverse contributed only slightly to apolipoprotein metabolism. These novel findings on HDL apolipoprotein metabolism demonstrate the analytical breadth and scope of the HR/AM-PRM technology to perform metabolic research.

Absorption and Distribution Kinetics of the 13C-Labeled Tomato Carotenoid Phytoene in Healthy Adults

BACKGROUND

Phytoene is a tomato carotenoid that may contribute to the apparent health benefits of tomato consumption. Although phytoene is a less prominent tomato carotenoid than lycopene, it is a major carotenoid in various human tissues. Phytoene distribution to plasma lipoproteins and tissues differs from lycopene, suggesting the kinetics of phytoene and lycopene differ.

OBJECTIVE

The objective of this study was to characterize the kinetic parameters of phytoene absorption, distribution, and excretion in adults, to better understand why biodistribution of phytoene differs from lycopene.

METHODS

Four adults (2 males, 2 females) maintained a controlled phytoene diet (1-5 mg/d) for 42 d. On day 14, each consumed 3.2 mg (13)C-phytoene, produced using tomato cell suspension culture technology. Blood samples were collected at 0, 1-15, 17, 21, and 24 h and 2, 3, 4, 7, 10, 14, 17, 21, and 28 d after (13)C-phytoene consumption. Plasma-unlabeled and plasma-labeled phytoene concentrations were determined using ultra-HPLC-quadrupole time-of-flight-mass spectrometry, and data were fit to a 7-compartment carotenoid kinetic model using WinSAAM 3.0.7 software.

RESULTS

Subjects were compliant with a controlled phytoene diet, consuming a mean ± SE of 2.5 ± 0.6 mg/d, resulting in a plasma unlabeled phytoene concentration of 71 ± 14 nmol/L. A maximal plasma (13)C-phytoene concentration of 55.6 ± 5.9 nM was achieved 19.8 ± 9.2 h after consumption, and the plasma half-life was 2.3 ± 0.2 d. Compared with previous results for lycopene, phytoene bioavailability was nearly double at 58% ± 19%, the clearance rate from chylomicrons was slower, and the rates of deposition into and utilization by the slow turnover tissue compartment were nearly 3 times greater.

CONCLUSIONS

Although only differing from lycopene by 4 double bonds, phytoene exhibits markedly different kinetic characteristics in human plasma, providing insight into metabolic processes contributing to phytoene enrichment in plasma and tissues compared with lycopene. This trial was registered at clinicaltrials.gov as NCT01692340.

Compartmental and noncompartmental modeling of ¹³C-lycopene absorption, isomerization, and distribution kinetics in healthy adults

BACKGROUND

Lycopene, which is a red carotenoid in tomatoes, has been hypothesized to mediate disease-preventive effects associated with tomato consumption. Lycopene is consumed primarily as the all-trans geometric isomer in foods, whereas human plasma and tissues show greater proportions of cis isomers.

OBJECTIVE

With the use of compartmental modeling and stable isotope technology, we determined whether endogenous all-trans-to-cis-lycopene isomerization or isomeric-bioavailability differences underlie the greater proportion of lycopene cis isomers in human tissues than in tomato foods.

DESIGN

Healthy men (n = 4) and women (n = 4) consumed (13)C-lycopene (10.2 mg; 82% all-trans and 18% cis), and plasma was collected over 28 d. Unlabeled and (13)C-labeled total lycopene and lycopene-isomer plasma concentrations, which were measured with the use of high-performance liquid chromatography-mass spectrometry, were fit to a 7-compartment model.

RESULTS

Subjects absorbed a mean ± SEM of 23% ± 6% of the lycopene. The proportion of plasma cis-(13)C-lycopene isomers increased over time, and all-trans had a shorter half-life than that of cis isomers (5.3 ± 0.3 and 8.8 ± 0.6 d, respectively; P < 0.001) and an earlier time to reach maximal plasma concentration than that of cis isomers (28 ± 7 and 48 ± 9 h, respectively). A compartmental model that allowed for interindividual differences in cis- and all-trans-lycopene bioavailability and endogenous trans-to-cis-lycopene isomerization was predictive of plasma (13)C and unlabeled cis- and all-trans-lycopene concentrations. Although the bioavailability of cis (24.5% ± 6%) and all-trans (23.2% ± 8%) isomers did not differ, endogenous isomerization (0.97 ± 0.25 μmol/d in the fast-turnover tissue lycopene pool) drove tissue and plasma isomeric profiles.

CONCLUSION

(13)C-Lycopene combined with physiologic compartmental modeling provides a strategy for following complex in vivo metabolic processes in humans and reveals that postabsorptive trans-to-cis-lycopene isomerization, and not the differential bioavailability of isomers, drives tissue and plasma enrichment of cis-lycopene. This trial was registered at clinicaltrials.gov as NCT01692340.

Compartmental and Data-Based Modeling of Cerebral Hemodynamics: Linear Analysis

Compartmental and data-based modeling of cerebral hemodynamics are alternative approaches that utilize distinct model forms and have been employed in the quantitative study of cerebral hemodynamics. This paper examines the relation between a compartmental equivalent-circuit and a data-based input-output model of dynamic cerebral autoregulation (DCA) and CO2-vasomotor reactivity (DVR). The compartmental model is constructed as an equivalent-circuit utilizing putative first principles and previously proposed hypothesis-based models. The linear input-output dynamics of this compartmental model are compared with data-based estimates of the DCA-DVR process. This comparative study indicates that there are some qualitative similarities between the two-input compartmental model and experimental results.

Mathematical framework for activity-based cancer biomarkers

Advances in nanomedicine are providing sophisticated functions to precisely control the behavior of nanoscale drugs and diagnostics. Strategies that coopt protease activity as molecular triggers are increasingly important in nanoparticle design, yet the pharmacokinetics of these systems are challenging to understand without a quantitative framework to reveal nonintuitive associations. We describe a multicompartment mathematical model to predict strategies for ultrasensitive detection of cancer using synthetic biomarkers, a class of activity-based probes that amplify cancer-derived signals into urine as a noninvasive diagnostic. Using a model formulation made of a PEG core conjugated with protease-cleavable peptides, we explore a vast design space and identify guidelines for increasing sensitivity that depend on critical parameters such as enzyme kinetics, dosage, and probe stability. According to this model, synthetic biomarkers that circulate in stealth but then activate at sites of disease have the theoretical capacity to discriminate tumors as small as 5 mm in diameter-a threshold sensitivity that is otherwise challenging for medical imaging and blood biomarkers to achieve. This model may be adapted to describe the behavior of additional activity-based approaches to allow cross-platform comparisons, and to predict allometric scaling across species.

Spatiotemporal characteristics and pharmacological modulation of multiple gamma oscillations in the CA1 region of the hippocampus

Multiple components of "γ-oscillations" between 30-170 Hz in the CA1 region of the hippocampus have been described, based on their coherence with oscillations in other brain regions and on their cross-frequency coupling with local θ-oscillations. However, it remains unclear whether the different sub-bands are generated by a single broadband oscillator coupled to multiple external inputs, or by separate oscillators that incorporate distinct circuit elements. To distinguish between these possibilities, we used high-density linear array recording electrodes in awake behaving mice to examine the spatiotemporal characteristics of γ-oscillations and their responses to midazolam and atropine. We characterized oscillations using current source density (CSD) analysis, and measured θ-γ phase-amplitude coupling by cross frequency coupling (CFC) analysis. Prominent peaks were present in the CSD signal in the mid- and distal apical dendritic layers at all frequencies, and at stratum pyramidale for γ(slow) (30-45 Hz) and γ(mid) (50-90 Hz), but not γ(fast) (90-170 Hz) oscillations. Differences in the strength and timing of θ-γ(slow) and θ-γ(mid) cross frequency coupling, and a lack of coupling at the soma and mid-apical region for γ(fast) oscillations, indicated that separate circuit components generate the three sub-bands. Midazolam altered CSD amplitudes and cross-frequency coupling in a lamina- and frequency specific manner, providing further evidence for separate generator circuits. Atropine altered CSD amplitudes and θ-γ CFC uniformly at all locations. Simulations using a detailed compartmental model were consistent with γ(slow) and γ(mid) oscillations driven primarily by inputs at the mid-apical dendrites, and γ(fast) at the distal apical dendrite. Our results indicate that multiple distinct local circuits generate γ-oscillations in the CA1 region of the hippocampus, and provide detailed information about their spatiotemporal characteristics.

Midazolam and atropine alter theta oscillations in the hippocampal CA1 region by modulating both the somatic and distal dendritic dipoles

Theta (4-12 Hz) oscillations in the hippocampus play an important role in learning and memory. They are altered by a wide variety of drugs that impair memory, and these effects may underlie or contribute to drug-induced amnesia. However, the network mechanisms linking drug actions with changes in memory formation remain poorly defined. Here, we used a multisite linear electrode array to measure local field potentials simultaneously across the CA1 layers of the hippocampus during active exploration, and employed current source density analysis and computational modeling to investigate how midazolam and atropine-two amnestic drugs that are used clinically and experimentally-change the relative timing and strength of the drivers of θ-oscillations. We found that two dipoles are present, with active inputs that are centered at the soma and the distal apical dendrite and passive return pathways that overlap in the mid-apical dendrite. Both drugs shifted the position of the phase reversal in the local field potential that occurred in the mid-apical dendritic region, but in opposite directions, by changing the strength of the dendritic pole, without altering the somatic pole or relative timing. Computational modeling showed that this constellation of changes, as well as an additional effect on a variably present mid-apical pole, could be produced by simultaneous changes in the active somatic and distal dendritic inputs. These network-level changes, produced by two amnestic drugs that target different types of receptors, may thus serve as a common basis for impaired memory encoding.

LFPy: a tool for biophysical simulation of extracellular potentials generated by detailed model neurons

Electrical extracellular recordings, i.e., recordings of the electrical potentials in the extracellular medium between cells, have been a main work-horse in electrophysiology for almost a century. The high-frequency part of the signal (≳500 Hz), i.e., the multi-unit activity (MUA), contains information about the firing of action potentials in surrounding neurons, while the low-frequency part, the local field potential (LFP), contains information about how these neurons integrate synaptic inputs. As the recorded extracellular signals arise from multiple neural processes, their interpretation is typically ambiguous and difficult. Fortunately, a precise biophysical modeling scheme linking activity at the cellular level and the recorded signal has been established: the extracellular potential can be calculated as a weighted sum of all transmembrane currents in all cells located in the vicinity of the electrode. This computational scheme can considerably aid the modeling and analysis of MUA and LFP signals. Here, we describe LFPy, an open source Python package for numerical simulations of extracellular potentials. LFPy consists of a set of easy-to-use classes for defining cells, synapses and recording electrodes as Python objects, implementing this biophysical modeling scheme. It runs on top of the widely used NEURON simulation environment, which allows for flexible usage of both new and existing cell models. Further, calculation of extracellular potentials using the line-source-method is efficiently implemented. We describe the theoretical framework underlying the extracellular potential calculations and illustrate by examples how LFPy can be used both for simulating LFPs, i.e., synaptic contributions from single cells as well a populations of cells, and MUAs, i.e., extracellular signatures of action potentials.

Chylomicron metabolism in rats: kinetic modeling indicates that the particles remain at endothelial sites for minutes

Chylomicrons labeled in vivo with (14)C-oleic acid (primarily in triglycerides, providing a tracer for lipolysis) and (3)H-retinol (primarily in ester form, providing a tracer for the core lipids) were injected into rats. Radioactivity in tissues was followed at a series of times up to 40 min and the data were analyzed by compartmental modeling. For heart-like tissues it was necessary to allow the chylomicrons to enter into a compartment where lipolysis is rapid and then transfer to a second compartment where lipolysis is slower. The particles remained in these compartments for minutes and when they returned to blood they had reduced affinity for binding in the tissue. In contrast, the data for liver could readily be fitted with a single compartment for native and lipolyzed chylomicrons in blood, and there was no need for a pathway back to blood. A composite model was built from the individual tissue models. This whole-body model could simultaneously fit all data for both fed and fasted rats and allowed estimation of fluxes and residence times in the four compartments; native and lipolyzed chylomicrons ("remnants") in blood, and particles in the tissue compartments where lipolysis is rapid and slow, respectively.

Accelerating compartmental modeling on a graphical processing unit

Compartmental modeling is a widely used tool in neurophysiology but the detail and scope of such models is frequently limited by lack of computational resources. Here we implement compartmental modeling on low cost Graphical Processing Units (GPUs), which significantly increases simulation speed compared to NEURON. Testing two methods for solving the current diffusion equation system revealed which method is more useful for specific neuron morphologies. Regions of applicability were investigated using a range of simulations from a single membrane potential trace simulated in a simple fork morphology to multiple traces on multiple realistic cells. A runtime peak 150-fold faster than the CPU was achieved. This application can be used for statistical analysis and data fitting optimizations of compartmental models and may be used for simultaneously simulating large populations of neurons. Since GPUs are forging ahead and proving to be more cost-effective than CPUs, this may significantly decrease the cost of computation power and open new computational possibilities for laboratories with limited budgets.

Physiologically based pharmacokinetic tissue compartment model selection in drug development and risk assessment

A well-stirred tank (WST) has been the predominant flow-limited tissue compartment model in physiologically based pharmacokinetic (PBPK) modeling. Recently, we developed a two-region asymptotically reduced (TAR) PBPK tissue compartment model through an asymptotic approximation to a two-region vascular-extravascular system to incorporate more biophysical detail than the WST model. To determine the relevance of a flow-limited TAR (F-TAR) approach, 75 structurally diverse drugs were evaluated herein using a priori predicted tissue:plasma partition coefficients along with hybrid and whole-body PBPK of eight rat tissues to determine the impact of model selection on simulation and optimization. Simulations showed that the F-TAR model significantly improved the ability to predict drug exposure, with hybrid and whole-body WST model error approaching 50% for tissues with larger vascular volumes. When optimization was used to fit F-TAR and WST models to pseudo data, WST-optimized drug partition coefficients more appropriately represented curve-fitting parameters rather than biophysically meaningful partition coefficients. Median F-TAR-optimized error ranged from -0.4% to +0.3%, whereas WST-optimized median error ranged from -22.2% to +1.8%. These studies demonstrated that the use of F-TAR represents a more accurate, biophysically realistic PBPK tissue model for predicting tissue exposure to drug and that it should be considered for use in drug development and regulatory review.

Tissue-specific compartmental analysis for dynamic contrast-enhanced MR imaging of complex tumors

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) provides a noninvasive method for evaluating tumor vasculature patterns based on contrast accumulation and washout. However, due to limited imaging resolution and tumor tissue heterogeneity, tracer concentrations at many pixels often represent a mixture of more than one distinct compartment. This pixel-wise partial volume effect (PVE) would have profound impact on the accuracy of pharmacokinetics studies using existing compartmental modeling (CM) methods. We, therefore, propose a convex analysis of mixtures (CAM) algorithm to explicitly mitigate PVE by expressing the kinetics in each pixel as a nonnegative combination of underlying compartments and subsequently identifying pure volume pixels at the corners of the clustered pixel time series scatter plot simplex. The algorithm is supported theoretically by a well-grounded mathematical framework and practically by plug-in noise filtering and normalization preprocessing. We demonstrate the principle and feasibility of the CAM-CM approach on realistic synthetic data involving two functional tissue compartments, and compare the accuracy of parameter estimates obtained with and without PVE elimination using CAM or other relevant techniques. Experimental results show that CAM-CM achieves a significant improvement in the accuracy of kinetic parameter estimation. We apply the algorithm to real DCE-MRI breast cancer data and observe improved pharmacokinetic parameter estimation, separating tumor tissue into regions with differential tracer kinetics on a pixel-by-pixel basis and revealing biologically plausible tumor tissue heterogeneity patterns. This method combines the advantages of multivariate clustering, convex geometry analysis, and compartmental modeling approaches. The open-source MATLAB software of CAM-CM is publicly available from the Web.

Dendritic excitability modulates dendritic information processing in a purkinje cell model

Using an electrophysiological compartmental model of a Purkinje cell we quantified the contribution of individual active dendritic currents to processing of synaptic activity from granule cells. We used mutual information as a measure to quantify the information from the total excitatory input current (I_Glu) encoded in each dendritic current. In this context, each active current was considered an information channel. Our analyses showed that most of the information was encoded by the calcium (I_CaP) and calcium activated potassium (I_Kc) currents. Mutual information between I_Glu and I_CaP and I_Kc was sensitive to different levels of excitatory and inhibitory synaptic activity that, at the same time, resulted in the same firing rate at the soma. Since dendritic excitability could be a mechanism to regulate information processing in neurons we quantified the changes in mutual information between I_Glu and all Purkinje cell currents as a function of the density of dendritic Ca (g_CaP) and Kca (g_Kc) conductances. We extended our analysis to determine the window of temporal integration of I_Glu by I_CaP and I_Kc as a function of channel density and synaptic activity. The window of information integration has a stronger dependence on increasing values of g_Kc than on g_CaP, but at high levels of synaptic stimulation information integration is reduced to a few milliseconds. Overall, our results show that different dendritic conductances differentially encode synaptic activity and that dendritic excitability and the level of synaptic activity regulate the flow of information in dendrites.

Dominant ionic mechanisms explored in spiking and bursting using local low-dimensional reductions of a biophysically realistic model neuron

The large number of variables involved in many biophysical models can conceal potentially simple dynamical mechanisms governing the properties of its solutions and the transitions between them as parameters are varied. To address this issue, we extend a novel model reduction method, based on "scales of dominance," to multi-compartment models. We use this method to systematically reduce the dimension of a two-compartment conductance-based model of a crustacean pyloric dilator (PD) neuron that exhibits distinct modes of oscillation--tonic spiking, intermediate bursting and strong bursting. We divide trajectories into intervals dominated by a smaller number of variables, resulting in a locally reduced hybrid model whose dimension varies between two and six in different temporal regimes. The reduced model exhibits the same modes of oscillation as the 16 dimensional model over a comparable parameter range, and requires fewer ad hoc simplifications than a more traditional reduction to a single, globally valid model. The hybrid model highlights low-dimensional organizing structure in the dynamics of the PD neuron, and the dependence of its oscillations on parameters such as the maximal conductances of calcium currents. Our technique could be used to build hybrid low-dimensional models from any large multi-compartment conductance-based model in order to analyze the interactions between different modes of activity.

Global Compartmental Pharmacokinetic Models for Spatiotemporal SPECT and PET Imaging

A new mathematical framework is introduced for combining the linear compartmental models used in pharmacokinetics with the spatiotemporal distributions of activity that are measured in single photon emission computed tomography (SPECT) and PET imaging. This approach is global in the sense that the compartmental differential equations involve only the overall spatially integrated activity in each compartment. The kinetics for the local compartmental activities are not specified by the model and would be determined from data. It is shown that an increase in information about the spatial distribution of the local compartmental activities leads to an increase in the number of identifiable quantities associated with the compartmental matrix. These identifiable quantities, which are important kinetic parameters in applications, are determined by computing the invariants of a symmetry group. This group generates the space of compartmental matrices that are compatible with a given activity distribution, input function, and set of support constraints. An example is provided where all of the compartmental spatial supports have been separated, except that of the vascular compartment. The question of estimating the identifiable parameters from SPECT and PET data is also discussed.

Compartmental analysis of plasma and liver n-3 essential fatty acids in alcohol-dependent men during withdrawal

The mechanism by which chronic ethanol consumption reduces concentrations of long chain polyunsaturated (LCP) fatty acids (FA) in tissues of humans was investigated in alcohol-dependent (AD) men during early withdrawal and to a well-matched control group by fitting the concentration-time curves of d(5)-labeled n-3 FA from plasma and liver, which originated from an oral dose of d(5)-linolenic acid (d(5)-18:3n-3) ethyl ester to a compartmental model. Blood sampled over 168 h and a liver specimen obtained 96 h after isotope administration were analyzed for d(5)-18:3n-3, d(5)-20:5n-3, d(5)-22:5n-3, and d(5)-22:6n-3. Plasma 20:5n-3 and 22:5n-3 were lower in AD subjects, compared with controls (20:5n-3: -50%, 22:5n-3: -34%). Increased amounts of d(5)-18:3n-3 were directed toward synthesis of d(5)-20:5n-3 in AD subjects (P < .05). However, this effect was offset by larger amounts of 20:5n-3 lost from plasma (control: 2.0 vs. AD: 4.2 mg d(-1)). In livers of AD subjects, more d(5)-18:3n-3 and d(5)-22:5n-3 were utilized for synthesis of d(5)-20:5n-3 (+200%) and d(5)-22:6n-3 (+210%), respectively, than was predicted from plasma kinetics. Although, the potential to utilize linolenic acid for synthesis of LCP FA was greater in AD subjects compared with controls, heightened disappearance rates of 20:5n-3 reduced overall plasma concentrations of several endogenous n-3 LCP FA.

Signal transfer in passive dendrites with nonuniform membrane conductance

In recent years it became clear that dendrites possess a host of ion channels that may be distributed nonuniformly over their membrane surface. In cortical pyramids, for example, it was demonstrated that the resting membrane conductance G(m)(x) is higher (the membrane is "leakier") at distal dendritic regions than at more proximal sites. How does this spatial nonuniformity in G(m)(x) affect the input-output function of the neuron? The present study aims at providing basic insights into this question. To this end, we have analytically studied the fundamental effects of membrane non-uniformity in passive cable structures. Keeping the total membrane conductance over a given modeled structure fixed (i.e., a constant number of passive ion channels), the classical case of cables with uniform membrane conductance is contrasted with various nonuniform cases with the following general conclusions. (1) For cylindrical cables with "sealed ends," monotonic increase in G(m)(x) improves voltage transfer from the input location to the soma. The steeper the G(m)(x), the larger the improvement. (2) This effect is further enhanced when the stimulation is distal and consists of a synaptic input rather than a current source. (3) Any nonuniformity in G(m)(x) decreases the electrotonic length, L, of the cylinder. (4) The system time constant tau(0) is larger in the nonuniform case than in the corresponding uniform case. (5) When voltage transients relax with tau(0), the dendritic tree is not isopotential in the nonuniform case, at variance with the uniform case. The effect of membrane nonuniformity on signal transfer in reconstructed dendritic trees and on the I/f relation of the neuron is also considered, and experimental methods for assessing membrane nonuniformity in dendrites are discussed.