COVID-19 and silent hypoxemia in a minimal closed-loop model of the respiratory rhythm generator.

Silent hypoxemia, or "happy hypoxia," is a puzzling phenomenon in which patients who have contracted COVID-19 exhibit very low oxygen saturation ( SaO 2 < 80%) but do not experience discomfort in breathing. The mechanism by which this blunted response to hypoxia occurs is unknown. We have previously shown that a computational model of the respiratory neural network (Diekman et al. in J Neurophysiol 118(4):2194-2215, 2017) can be used to test hypotheses focused on changes in chemosensory inputs to the central pattern generator (CPG). We hypothesize that altered chemosensory function at the level of the carotid bodies and/or the nucleus tractus solitarii are responsible for the blunted response to hypoxia. Here, we use our model to explore this hypothesis by altering the properties of the gain function representing oxygen sensing inputs to the CPG. We then vary other parameters in the model and show that oxygen carrying capacity is the most salient factor for producing silent hypoxemia. We call for clinicians to measure hematocrit as a clinical index of altered physiology in response to COVID-19 infection.

The role of lung ultrasound for detecting atelectasis, consolidation, and/or pneumonia in the adult cardiac surgery population: A scoping review of the literature.

OBJECTIVES: Postoperative pulmonary complications (PPCs) frequently occur after cardiac surgery and may lead to adverse patient outcomes. Traditional diagnostic tools such as auscultation or chest x-ray have inferior diagnostic accuracy compared to the gold standard (chest computed tomography). Lung ultrasound (LUS) is an emerging area of research combating these issues. However, no review has employed a formal search strategy to examine the role of LUS in identifying the specific PPCs of atelectasis, consolidation, and/or pneumonia or investigated the ability of LUS to predict these complications in this cohort. The objective of this study was to collate and present evidence for the use of LUS in the adult cardiac surgery population to specifically identify atelectasis, consolidation, and/or pneumonia. REVIEW METHOD USED: A scoping review of the literature was completed using predefined search terms across six databases which identified 1432 articles. One additional article was included from reviewing reference lists. Six articles met the inclusion criteria, providing sufficient data for the final analysis. DATA SOURCES: Six databases were searched: MEDLINE, Embase, CINAHL, Scopus, CENTRAL, and PEDro. This review was not registered. REVIEW METHODS: The review followed the PRISMA Extension for Scoping Reviews. RESULTS: Several LUS methodologies were reported across studies. Overall, LUS outperformed all other included bedside diagnostic tools, with superior diagnostic accuracy in identifying atelectasis, consolidation, and/or pneumonia. Incidences of PPCs tended to increase with each subsequent timepoint after surgery and were better identified with LUS than all other assessments. A change in diagnosis occurred at a rate of 67% with the inclusion of LUS and transthoracic echocardiography in one study. Pre-established assessment scores were improved by substituting chest x-rays with LUS scans. CONCLUSION: The results of this scoping review support the use of LUS as a diagnostic tool after cardiac surgery; however, they also highlighted a lack of consistent methodologies used. Future research is required to determine the optimal methodology for LUS in diagnosing PPCs in this cohort and to determine whether LUS possesses the ability to predict these complications and guide proactive respiratory supports after extubation.

Tutorial: using NEURON for neuromechanical simulations.

The dynamical properties of the brain and the dynamics of the body strongly influence one another. Their interaction generates complex adaptive behavior. While a wide variety of simulation tools exist for neural dynamics or biomechanics separately, there are few options for integrated brain-body modeling. Here, we provide a tutorial to demonstrate how the widely-used NEURON simulation platform can support integrated neuromechanical modeling. As a first step toward incorporating biomechanics into a NEURON simulation, we provide a framework for integrating inputs from a "periphery" and outputs to that periphery. In other words, "body" dynamics are driven in part by "brain" variables, such as voltages or firing rates, and "brain" dynamics are influenced by "body" variables through sensory feedback. To couple the "brain" and "body" components, we use NEURON's pointer construct to share information between "brain" and "body" modules. This approach allows separate specification of brain and body dynamics and code reuse. Though simple in concept, the use of pointers can be challenging due to a complicated syntax and several different programming options. In this paper, we present five different computational models, with increasing levels of complexity, to demonstrate the concepts of code modularity using pointers and the integration of neural and biomechanical modeling within NEURON. The models include: (1) a neuromuscular model of calcium dynamics and muscle force, (2) a neuromechanical, closed-loop model of a half-center oscillator coupled to a rudimentary motor system, (3) a closed-loop model of neural control for respiration, (4) a pedagogical model of a non-smooth "brain/body" system, and (5) a closed-loop model of feeding behavior in the sea hare Aplysia californica that incorporates biologically-motivated non-smooth dynamics. This tutorial illustrates how NEURON can be integrated with a broad range of neuromechanical models. Code available at: https://github.com/fietkiewicz/PointerBuilder.

Pattern forming mechanisms of color vision.

While our understanding of the way single neurons process chromatic stimuli in the early visual pathway has advanced significantly in recent years, we do not yet know how these cells interact to form stable representations of hue. Drawing on physiological studies, we offer a dynamical model of how the primary visual cortex tunes for color, hinged on intracortical interactions and emergent network effects. After detailing the evolution of network activity through analytical and numerical approaches, we discuss the effects of the model's cortical parameters on the selectivity of the tuning curves. In particular, we explore the role of the model's thresholding nonlinearity in enhancing hue selectivity by expanding the region of stability, allowing for the precise encoding of chromatic stimuli in early vision. Finally, in the absence of a stimulus, the model is capable of explaining hallucinatory color perception via a Turing-like mechanism of biological pattern formation.

A universal description of stochastic oscillators.

Many systems in physics, chemistry, and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example, linear dynamics of a stable focus with fluctuations, limit-cycle systems perturbed by noise, or excitable systems in which random inputs lead to a train of pulses. Despite their diverse origins, the phenomenology of random oscillations can be strikingly similar. Here, we introduce a nonlinear transformation of stochastic oscillators to a complex-valued function [Formula: see text](x) that greatly simplifies and unifies the mathematical description of the oscillator's spontaneous activity, its response to an external time-dependent perturbation, and the correlation statistics of different oscillators that are weakly coupled. The function [Formula: see text] (x) is the eigenfunction of the Kolmogorov backward operator with the least negative (but nonvanishing) eigenvalue λ1 = µ1 + iω1. The resulting power spectrum of the complex-valued function is exactly given by a Lorentz spectrum with peak frequency ω1 and half-width µ1; its susceptibility with respect to a weak external forcing is given by a simple one-pole filter, centered around ω1; and the cross-spectrum between two coupled oscillators can be easily expressed by a combination of the spontaneous power spectra of the uncoupled systems and their susceptibilities. Our approach makes qualitatively different stochastic oscillators comparable, provides simple characteristics for the coherence of the random oscillation, and gives a framework for the description of weakly coupled oscillators.

Fluorescence intensity and fluorescence lifetime measurements of various carbon dots as a function of pH.

Measurement and monitoring of pH are essential in both the industry and academia. It is therefore important to continue developing novel, low-cost pH sensors that provide increased accuracy over long periods of time. Particularly promising are sensors based on materials that show pH-dependent fluorescence intensity (FI) and lifetime (FL). Carbon dots (CDs) are emerging as promising candidates because of their low cost, ease of manufacturing, low toxicity, and negligible photobleaching. However, little has been done to quantify the FI and FL values of CDs. Here we report the characterisation of the pH-dependent FI and FL of four novel solvothermal synthesised CDs. The fifth CD is used as a reference sample and was synthesised following a published synthesis. The precursors for the CDs include disperse blue 1 dye, phloroglucinol, m-phenylenediamine (m-PD), N, and N-dimethylformamide (DMF). The average diameter size of the CDs ranges from 1.5 to 15 nm. An excitation wavelength of 452 nm with a bandwidth of 45 nm was used to quantify the fluorescence in the pH range 5-9. Three CDs show a decreasing trend in FI with pH, while two CDs show an increasing trend. None of the CDs shows strong FL dependence. The FL changes around 0.5 ± 0.2 ns across the tested pH range. We suggest that the differences in the fluorescence trends can be attributed to the precursors chosen for synthesising the CDs.

COVID-19 and silent hypoxemia in a minimal closed-loop model of the respiratory rhythm generator.

Silent hypoxemia, or 'happy hypoxia', is a puzzling phenomenon in which patients who have contracted COVID-19 exhibit very low oxygen saturation (SaO2 < 80%) but do not experience discomfort in breathing. The mechanism by which this blunted response to hypoxia occurs is unknown. We have previously shown that a computational model (Diekman et al., 2017, J. Neurophysiol) of the respiratory neural network can be used to test hypotheses focused on changes in chemosensory inputs to the central pattern generator (CPG). We hypothesize that altered chemosensory function at the level of the carotid bodies and/or the nucleus tractus solitarii are responsible for the blunted response to hypoxia. Here, we use our model to explore this hypothesis by altering the properties of the gain function representing oxygen sensing inputs to the CPG. We then vary other parameters in the model and show that oxygen carrying capacity is the most salient factor for producing silent hypoxemia. We call for clinicians to measure hematocrit as a clinical index of altered physiology in response to COVID-19 infection.

Sensitivity to Control Signals in Triphasic Rhythmic Neural Systems: A Comparative Mechanistic Analysis via Infinitesimal Local Timing Response Curves.

Similar activity patterns may arise from model neural networks with distinct coupling properties and individual unit dynamics. These similar patterns may, however, respond differently to parameter variations and specifically to tuning of inputs that represent control signals. In this work, we analyze the responses resulting from modulation of a localized input in each of three classes of model neural networks that have been recognized in the literature for their capacity to produce robust three-phase rhythms: coupled fast-slow oscillators, near-heteroclinic oscillators, and threshold-linear networks. Triphasic rhythms, in which each phase consists of a prolonged activation of a corresponding subgroup of neurons followed by a fast transition to another phase, represent a fundamental activity pattern observed across a range of central pattern generators underlying behaviors critical to survival, including respiration, locomotion, and feeding. To perform our analysis, we extend the recently developed local timing response curve (lTRC), which allows us to characterize the timing effects due to perturbations, and we complement our lTRC approach with model-specific dynamical systems analysis. Interestingly, we observe disparate effects of similar perturbations across distinct model classes. Thus, this work provides an analytical framework for studying control of oscillations in nonlinear dynamical systems and may help guide model selection in future efforts to study systems exhibiting triphasic rhythmic activity.

Inferring density-dependent population dynamics mechanisms through rate disambiguation for logistic birth-death processes.

Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can manifest in birth processes, death processes, or both. Therefore, we utilize the mean and variance of cell number fluctuations to separately identify birth and death rates from time series that follow stochastic birth-death processes with logistic growth. Our nonparametric method provides a novel perspective on stochastic parameter identifiability, which we validate by analyzing the accuracy in terms of the discretization bin size. We apply our method to the scenario where a homogeneous cell population goes through three stages: (1) grows naturally to its carrying capacity, (2) is treated with a drug that reduces its carrying capacity, and (3) overcomes the drug effect to restore its original carrying capacity. In each stage, we disambiguate whether the dynamics occur through the birth process, death process, or some combination of the two, which contributes to understanding drug resistance mechanisms. In the case of limited sample sizes, we provide an alternative method based on maximum likelihood and solve a constrained nonlinear optimization problem to identify the most likely density dependence parameter for a given cell number time series. Our methods can be applied to other biological systems at different scales to disambiguate density-dependent mechanisms underlying the same net growth rate.

Explicitly Solvable Continuous-time Inference for Partially Observed Markov Processes.

Many natural and engineered systems can be modeled as discrete state Markov processes. Often, only a subset of states are directly observable. Inferring the conditional probability that a system occupies a particular hidden state, given the partial observation, is a problem with broad application. In this paper, we introduce a continuous-time formulation of the sum-product algorithm, which is a well-known discrete-time method for finding the hidden states' conditional probabilities, given a set of finite, discrete-time observations. From our new formulation, we can explicitly solve for the conditional probability of occupying any state, given the transition rates and observations within a finite time window. We apply our algorithm to a realistic model of the cystic fibrosis transmembrane conductance regulator (CFTR) protein for exact inference of the conditional occupancy probability, given a finite time series of partial observations.

Heteroclinic cycling and extinction in May-Leonard models with demographic stochasticity.

May and Leonard (SIAM J Appl Math 29:243-253, 1975) introduced a three-species Lotka-Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete each "cycle", passing closer and closer to unstable fixed points in which one population dominates and the others approach zero. Aperiodic heteroclinic dynamics have subsequently been studied in ecological systems (side-blotched lizards; colicinogenic Escherichia coli), in the immune system, in neural information processing models ("winnerless competition"), and in models of neural central pattern generators. Yet as May and Leonard observed "Biologically, the behavior (produced by the model) is nonsense. Once it is conceded that the variables represent animals, and therefore cannot fall below unity, it is clear that the system will, after a few cycles, converge on some single population, extinguishing the other two." Here, we explore different ways of introducing discrete stochastic dynamics based on May and Leonard's ODE model, with application to ecological population dynamics, and to a neuromotor central pattern generator system. We study examples of several quantitatively distinct asymptotic behaviors, including total extinction of all species, extinction to a single species, and persistent cyclic dominance with finite mean cycle length.

Scaling of agent-based models to evaluate transmission risks of infectious diseases.

The scaling behaviour of agent-based computational models, to evaluate transmission risks of infectious diseases, is addressed. To this end we use an existing computational code, made available in the public domain by its author, to analyse the system dynamics from a general perspective. The goal being to obtain deeper insight into the system behaviour than can be obtained from considering raw data alone. The data analysis collapses the output data for infection numbers and leads to closed-form expressions for the results. It is found that two parameters are sufficient to summarize the system development and the scaling of the data. One of the parameters characterizes the overall system dynamics. It represents a scaling factor for time when expressed in iteration steps of the computational code. The other parameter identifies the instant when the system adopts its maximum infection rate. The data analysis methodology presented constitutes a means for a quantitative intercomparison of predictions for infection numbers, and infection dynamics, for data produced by different models and can enable a quantitative comparison to real-world data.

Variational and phase response analysis for limit cycles with hard boundaries, with applications to neuromechanical control problems.

Motor systems show an overall robustness, but because they are highly nonlinear, understanding how they achieve robustness is difficult. In many rhythmic systems, robustness against perturbations involves response of both the shape and the timing of the trajectory. This makes the study of robustness even more challenging. To understand how a motor system produces robust behaviors in a variable environment, we consider a neuromechanical model of motor patterns in the feeding apparatus of the marine mollusk Aplysia californica (Shaw et al. in J Comput Neurosci 38(1):25-51, 2015; Lyttle et al. in Biol Cybern 111(1):25-47, 2017). We established in (Wang et al. in SIAM J Appl Dyn Syst 20(2):701-744, 2021. https://doi.org/10.1137/20M1344974 ) the tools for studying combined shape and timing responses of limit cycle systems under sustained perturbations and here apply them to study robustness of the neuromechanical model against increased mechanical load during swallowing. Interestingly, we discover that nonlinear biomechanical properties confer resilience by immediately increasing resistance to applied loads. In contrast, the effect of changed sensory feedback signal is significantly delayed by the firing rates' hard boundary properties. Our analysis suggests that sensory feedback contributes to robustness in swallowing primarily by shifting the timing of neural activation involved in the power stroke of the motor cycle (retraction). This effect enables the system to generate stronger retractor muscle forces to compensate for the increased load, and hence achieve strong robustness. The approaches that we are applying to understanding a neuromechanical model in Aplysia, and the results that we have obtained, are likely to provide insights into the function of other motor systems that encounter changing mechanical loads and hard boundaries, both due to mechanical and neuronal firing properties.

Permissive and nonpermissive channel closings in CFTR revealed by a factor graph inference algorithm.

The closing of the gated ion channel in the cystic fibrosis transmembrane conductance regulator can be categorized as nonpermissive to reopening, which involves the unbinding of ADP or ATP, or permissive, which does not. Identifying the type of closing is of interest as interactions with nucleotides can be affected in mutants or by introducing agonists. However, all closings are electrically silent and difficult to differentiate. For single-channel patch-clamp traces, we show that the type of the closing can be accurately determined by an inference algorithm implemented on a factor graph, which we demonstrate using both simulated and lab-obtained patch-clamp traces.

Cheater suppression and stochastic clearance through quorum sensing.

The evolutionary consequences of quorum sensing in regulating bacterial cooperation are not fully understood. In this study, we reveal unexpected effects of regulating public good production through quorum sensing on bacterial population dynamics, showing that quorum sensing can be a collectively harmful alternative to unregulated production. We analyze a birth-death model of bacterial population dynamics accounting for public good production and the presence of non-producing cheaters. Our model demonstrates that when demographic noise is a factor, the consequences of controlling public good production according to quorum sensing depend on the cost of public good production and the growth rate of populations in the absence of public goods. When public good production is inexpensive, quorum sensing is a destructive alternative to unconditional production, in terms of the mean population extinction time. When costs are higher, quorum sensing becomes a constructive strategy for the producing strain, both stabilizing cooperation and decreasing the risk of population extinction.

Optimised polymer trapped-air lenses for ultrasound focusing in water exploiting Fabry-Pérot resonance.

The concept of employing air volumes trapped inside polymer shells to make a lens for ultrasound focusing in water is investigated. The proposed lenses use evenly-spaced concentric rings, each having an air-filled polymer shell construction, defining concentric water-filled channels. Numerical simulations and experiments have shown that a plane wave can be focused, and that the amplification can be boosted by Fabry-Pérot resonances within the water channels with an appropriate choice of the lens thickness. The effect of the polymer shell thickness and the depth of the channels is discussed, as these factors can affect the geometry and hence the frequency of operation. The result was a lens with a Full Width at Half Maximum value of 0.65 of a wavelength at the focus. Results obtained on a metal-based counterpart are also shown for comparison. An advantage of this polymeric design is that it is easily constructed via additive manufacturing. This study shows that trapped-air lenses made of polymer are suitable for ultrasound focusing in water near 500 kHz.

Subjective Information and Survival in a Simulated Biological System.

Information transmission and storage have gained traction as unifying concepts to characterize biological systems and their chances of survival and evolution at multiple scales. Despite the potential for an information-based mathematical framework to offer new insights into life processes and ways to interact with and control them, the main legacy is that of Shannon's, where a purely syntactic characterization of information scores systems on the basis of their maximum information efficiency. The latter metrics seem not entirely suitable for biological systems, where transmission and storage of different pieces of information (carrying different semantics) can result in different chances of survival. Based on an abstract mathematical model able to capture the parameters and behaviors of a population of single-celled organisms whose survival is correlated to information retrieval from the environment, this paper explores the aforementioned disconnect between classical information theory and biology. In this paper, we present a model, specified as a computational state machine, which is then utilized in a simulation framework constructed specifically to reveal emergence of a "subjective information", i.e., trade-off between a living system's capability to maximize the acquisition of information from the environment, and the maximization of its growth and survival over time. Simulations clearly show that a strategy that maximizes information efficiency results in a lower growth rate with respect to the strategy that gains less information but contains a higher meaning for survival.

Quantitative comparison of the mean-return-time phase and the stochastic asymptotic phase for noisy oscillators.

Seminal work by A. Winfree and J. Guckenheimer showed that a deterministic phase variable can be defined either in terms of Poincaré sections or in terms of the asymptotic (long-time) behaviour of trajectories approaching a stable limit cycle. However, this equivalence between the deterministic notions of phase is broken in the presence of noise. Different notions of phase reduction for a stochastic oscillator can be defined either in terms of mean-return-time sections or as the argument of the slowest decaying complex eigenfunction of the Kolmogorov backwards operator. Although both notions of phase enjoy a solid theoretical foundation, their relationship remains unexplored. Here, we quantitatively compare both notions of stochastic phase. We derive an expression relating both notions of phase and use it to discuss differences (and similarities) between both definitions of stochastic phase for (i) a spiral sink motivated by stochastic models for electroencephalograms, (ii) noisy limit-cycle systems-neuroscience models, and (iii) a stochastic heteroclinic oscillator inspired by a simple motor-control system.

Analytical approach to the mean-return-time phase of isotropic stochastic oscillators.

One notion of phase for stochastic oscillators is based on the mean return-time (MRT): a set of points represents a certain phase if the mean time to return from any point in this set to this set after one rotation is equal to the mean rotation period of the oscillator (irrespective of the starting point). For this so far only algorithmically defined phase, we derive here analytical expressions for the important class of isotropic stochastic oscillators. This allows us to evaluate cases from the literature explicitly and to study the behavior of the MRT phase in the limits of strong noise. We also use the same formalism to show that lines of constant return time variance (instead of constant mean return time) can be defined, and that they in general differ from the MRT isochrons.

A homeostasis criterion for limit cycle systems based on infinitesimal shape response curves.

Homeostasis occurs in a control system when a quantity remains approximately constant as a parameter, representing an external perturbation, varies over some range. Golubitsky and Stewart (J Math Biol 74(1-2):387-407, 2017) developed a notion of infinitesimal homeostasis for equilibrium systems using singularity theory. Rhythmic physiological systems (breathing, locomotion, feeding) maintain homeostasis through control of large-amplitude limit cycles rather than equilibrium points. Here we take an initial step to study (infinitesimal) homeostasis for limit-cycle systems in terms of the average of a quantity taken around the limit cycle. We apply the "infinitesimal shape response curve" (iSRC) introduced by Wang et al. (SIAM J Appl Dyn Syst 82(7):1-43, 2021) to study infinitesimal homeostasis for limit-cycle systems in terms of the mean value of a quantity of interest, averaged around the limit cycle. Using the iSRC, which captures the linearized shape displacement of an oscillator upon a static perturbation, we provide a formula for the derivative of the averaged quantity with respect to the control parameter. Our expression allows one to identify homeostasis points for limit cycle systems in the averaging sense. We demonstrate in the Hodgkin-Huxley model and in a metabolic regulatory network model that the iSRC-based method provides an accurate representation of the sensitivity of averaged quantities.