Modeling Of Physiological Systems Research Articles

We are all different: Modeling key individual differences in physiological systems

Mathematical models of whole-body dynamics have advanced our understanding of human integrative systems that regulate physiological processes such as metabolism, temperature, and blood pressure. For most of these whole-body models, baseline parameters describe a 35-year-old young adult man who weighs 70 kg. As such, even among adults those models may not accurately represent half of the population (women), the older population, and those who weigh significantly more than 70 kg. Indeed, sex, age, and weight are known modulators of physiological function. To more accurately simulate a person who does not look like that “baseline person,” or to explain the mechanisms that yield the observed sex or age differences, these factors should be incorporated into mathematical models of physiological systems. Another key modulator is the time of day, because most physiological processes are regulated by the circadian clocks. Thus, ideally, mathematical models of integrative physiological systems should be specific to either a man or woman, of a certain age and weight, and a given time of day. We illustrate the importance of capturing these individual differences, using the blood pressure regulatory system as an example, and explain how that such models can be built.

SECRET: Statistical Emulation for Computational Reverse Engineering and Translation with applications in healthcare

There have been impressive advances in the physical and mathematical modelling of complex physiological systems in the last few decades, with the potential to revolutionise personalised healthcare with patient-specific evidence-based diagnosis, risk assessment and treatment decision support using digital twins. However, practical progress and genuine clinical impact hinge on successful model calibration, parameter estimation and uncertainty quantification, which calls for novel innovative adaptions and methodological extensions of contemporary state-of-the-art inference techniques from Statistics and Machine Learning. In the present study, we focus on two computational fluid-dynamics (CFD) models of the blood systemic and pulmonary circulation. We discuss state-of-the-art emulation techniques based on deep learning and Gaussian processes, which are coupled with established inference techniques based on greedy optimisation, simulated annealing, Markov Chain Monte Carlo, History Matching and rejection sampling for computationally fast inference of unknown parameters of the CFD models from blood flow and pressure data. The inference task was set as a competitive challenge which the participants had to conduct within a limited time frame representative of clinical requirements. The performance of the methods was assessed independently and objectively by the challenge organisers, based on a ground truth that was unknown to the method developers. Our results indicate that for the systemic challenge, in which an idealised case of noise-free data was considered, the relative deviation from the ground-truth in parameter space ranges from 10−5% (highest-performing method) to 3% (lowest-performing method). For the pulmonary challenge, for which noisy data was generated, the performance ranges from 0.9% to 7% deviation for the parameter posterior mean, and from 35% to 570% deviation for the parameter posterior variance.

Time series generative adversarial network for muscle force prognostication using statistical outlier detection

AbstractMachine learning approaches, such as artificial neural networks (ANN), effectively perform various tasks and provide new predictive models for complicated physiological systems. Examples of Robotics applications involving direct human engagement, such as controlling prosthetic arms, athletic training, and investigating muscle physiology. It is now time for automated systems to take over modelling and monitoring tasks. However, there is a problem with the massive amount of time series data collected to build accurate forecasting systems. There may be inconsistencies in forecasting muscle forces due to the enormous amount of data. As a result, anomaly detection techniques play a significant role in detecting anomalous data. Detecting anomalies can help reduce redundancy and free up large storage space for storing relevant time‐series data. This paper employs several anomaly detection techniques, including Isolation Forest (iforest), K‐Nearest Neighbour (KNN), Open Support Vector Machine (OSVM), Histogram, and Local Outlier Factor (LOF). These techniques have been used by Long Short‐Term Memory (LSTM), Auto‐Regressive Integrated Moving Average (ARIMA), and Prophet models. The dataset used in this study contained raw measurements of body movements (kinematics) and the forces generated during walking (kinetics) of 57 healthy people (29 Female, 28 Male) without walking abnormalities or recent leg injuries. To increase the data samples, we used TimeGAN that generates synthetic time series data with temporal dependencies, aiding in training robust predictive models for muscle force prediction. The results are then compared with different evaluation metrics for five different samples. It is found that anomaly detection techniques with LSTM, ARIMA, and Prophet models provided better performance in forecasting muscle forces. The iforest method achieved the best Pearson's Correlation Coefficient (r) of 0.95, which is a competitive score with existing systems that perform between 0.7 and 0.9. The methodology provides a foundation for precision medicine, enhancing prognostic capability over relying solely on population averages.

A Dynamic Fitting Strategy for Physiological Models: A Case Study of a Cardiorespiratory Model for the Simulation of Incremental Aerobic Exercise.

Using mathematical models of physiological systems in medicine has allowed for the development of diagnostic, treatment, and medical educational tools. However, their complexity restricts, in most cases, their application for predictive, preventive, and personalized purposes. Although there are strategies that reduce the complexity of applying models based on fitting techniques, most of them are focused on a single instant of time, neglecting the effect of the system's temporal evolution. The objective of this research was to introduce a dynamic fitting strategy for physiological models with an extensive array of parameters and a constrained amount of experimental data. The proposed strategy focused on obtaining better predictions based on the temporal trends in the system's parameters and being capable of predicting future states. The study utilized a cardiorespiratory model as a case study. Experimental data from a longitudinal study of healthy adult subjects undergoing aerobic exercise were used for fitting and validation. The model predictions obtained in a steady state using the proposed strategy and the traditional single-fit approach were compared. The most successful outcomes were primarily linked to the proposed strategy, exhibiting better overall results regarding accuracy and behavior than the traditional population fitting approach at a single instant in time. The results evidenced the usefulness of the dynamic fitting strategy, highlighting its use for predictive, preventive, and personalized applications.

A General Approach for the Modelling of Negative Feedback Physiological Control Systems.

Mathematical models can improve the understanding of physiological systems behaviour, which is a fundamental topic in the bioengineering field. Having a reliable model enables researchers to carry out in silico experiments, which require less time and resources compared to their in vivo and in vitro counterparts. This work's objective is to capture the characteristics that a nonlinear dynamical mathematical model should exhibit, in order to describe physiological control systems at different scales. The similarities among various negative feedback physiological systems have been investigated and a unique general framework to describe them has been proposed. Within such a framework, both the existence and stability of equilibrium points are investigated. The model here introduced is based on a closed-loop topology, on which the homeostatic process is based. Finally, to validate the model, three paradigmatic examples of physiological control systems are illustrated and discussed: the ultrasensitivity mechanism for achieving homeostasis in biomolecular circuits, the blood glucose regulation, and the neuromuscular reflex arc (also referred to as muscle stretch reflex). The results show that, by a suitable choice of the modelling functions, the dynamic evolution of the systems under study can be described through the proposed general nonlinear model. Furthermore, the analysis of the equilibrium points and dynamics of the above-mentioned systems are consistent with the literature.

CellML 2.0.1

Abstract We present here CellML 2.0.1, an XML-based language for describing and exchanging mathematical models of physiological systems. MathML embedded in CellML documents is used to define the underlying mathematics of models. Models consist of a network of reusable components, each with variables and equations giving relationships between those variables. Models may import other models to create systems of increasing complexity. CellML 2.0.1 is defined by the normative specification presented here, prescribing the CellML syntax and the rules by which it should be used. The normative specification is intended primarily for the developers of software tools which directly consume CellML syntax. Users of CellML models may prefer to browse the informative rendering of the specification (https://cellml.org/specifications/cellml_2.0/) which extends the normative specification with explanations of the rules combined with examples of their usage. This version improves the identification of rule statements and corrects errata present in the CellML 2.0 specification.

A Novel Strategy to Fit and Validate Physiological Models: A Case Study of a Cardiorespiratory Model for Simulation of Incremental Aerobic Exercise.

Applying complex mathematical models of physiological systems is challenging due to the large number of parameters. Identifying these parameters through experimentation is difficult, and although procedures for fitting and validating models are reported, no integrated strategy exists. Additionally, the complexity of optimization is generally neglected when the number of experimental observations is restricted, obtaining multiple solutions or results without physiological justification. This work proposes a fitting and validation strategy for physiological models with many parameters under various populations, stimuli, and experimental conditions. A cardiorespiratory system model is used as a case study, and the strategy, model, computational implementation, and data analysis are described. Using optimized parameter values, model simulations are compared to those obtained using nominal values, with experimental data as a reference. Overall, a reduction in prediction error is achieved compared to that reported for model building. Furthermore, the behavior and accuracy of all the predictions in the steady state were improved. The results validate the fitted model and provide evidence of the proposed strategy's usefulness.

Flow-induced self-sustained oscillations in a straight channel with rigid walls and elastic supports

This work considers the two-dimensional flow field of an incompressible viscous fluid in a parallel-sided channel. In our study, one of the walls is fixed whereas the other one is elastically mounted, and sustained oscillations are induced by the fluid motion. The flow that forces the wall movement is produced as a consequence that one of the ends of the channel is pressurized, whereas the opposite end is at atmospheric pressure. The study aims at reducing the complexity of models for several physiological systems in which fluid-structure interaction produces large deformation of the wall. We report the experimental results of the observed self-sustained oscillations. These oscillations occur at frequencies close to the natural frequency of the system. The vertical motion is accompanied by a slight trend to rotate the moving mass at intervals when the gap height is quite narrow. We propose a simplified analytical model to explore the conditions under which this motion is possible. The analytical approach considers asymptotic solutions of the Navier–Stokes equation with a perturbation technique. The comparison between the experimental pressure measured at the midlength of the channel and the analytical result issued with a model neglecting viscous effects shows a very good agreement. Also, the rotating trend of the moving wall can be explained in terms of the quadratic dependence of the pressure with the streamwise coordinate that is predicted by this simplified model.

CellML 2.0.

We present here CellML 2.0, an XML-based language for describing and exchanging mathematical models of physiological systems. MathML embedded in CellML documents is used to define the underlying mathematics of models. Models consist of a network of reusable components, each with variables and equations giving relationships between those variables. Models may import other models to create systems of increasing complexity. CellML 2.0 is defined by the normative specification presented here, prescribing the CellML syntax and the rules by which it should be used. The normative specification is intended primarily for the developers of software tools which directly consume CellML syntax. Users of CellML models may prefer to browse the informative rendering of the specification (https://cellml.org/specifications/cellml_2.0/) which extends the normative specification with explanations of the rules combined with examples of their usage.

3D Bioprinting and Its Application to Military Medicine.

Traditionally, tissue engineering techniques have largely focused on 2D cell culture models-monolayers of immortalized or primary cells growing on tissue culture plastic. Although these techniques have proven useful in research, they often lack physiological validity, because of the absence of fundamental tissue properties, such as multicellular organization, specialized extracellular matrix structures, and molecular or force gradients essential to proper physiological function. More recent advances in 3D cell culture methods have facilitated the development of more complex physiological models and tissue constructs; however, these often rely on self-organization of cells (bottom-up design), and the range of tissue construct size and complexity generated by these methods remains relatively limited. By borrowing from advances in the additive manufacturing field, 3D bioprinting techniques are enabling top-down design and fabrication of cellular constructs with controlled sizing, spacing, and chemical functionality. The high degree of control over engineered tissue architecture, previously unavailable to researchers, enables the generation of more complex, physiologically relevant 3D tissue constructs. Three main 3D bioprinting techniques are reviewed-extrusion, droplet-based, and laser-assisted bioprinting techniques are among the more robust 3D bioprinting techniques, each with its own strengths and weaknesses. High complexity tissue constructs created through 3D bioprinting are opening up new avenues in tissue engineering, regenerative medicine, and physiological model systems for researchers in the military medicine community. Recent primary literature and reviews were selected to provide a broad overview of the field of 3D bioprinting and illustrate techniques and examples of 3D bioprinting relevant to military medicine. References were selected to illustrate specific examples of advances and potential military medicine applications in the 3D bioprinting field, rather than to serve as a comprehensive review. Three classes of 3D bioprinting techniques were reviewed: extrusion, droplet-based, and laser-assisted bioprinting. Advantages, disadvantages, important considerations, and constraints of each technique were discussed. Examples from the primary literature were given to illustrate the techniques. Relevant applications of 3D bioprinting to military medicine, namely tissue engineering/regenerative medicine and new models of physiological systems, are discussed in the context of advancing military medicine. 3D bioprinting is a rapidly evolving field that provides researchers the ability to build tissue constructs that are more complex and physiologically relevant than traditional 2D culture methods. Advances in bioprinting techniques, bioink formulation, and cell culture methods are being translated into new paradigms in tissue engineering and physiological system modeling, advancing the state of the art, and increasing construct availability to the military medicine research community.

A Flexible and Reproducible Framework for Modelling Renal Tubules

We have developed a new framework for defining renal tubule models utilising a repository of existing models from the literature. The CellML format ( https://cellml.org) is an XML format for encoding mathematical models ‐ typically used for lumped parameter, non‐spatial models of physiological systems. We have previously demonstrated how models of epithelial transport processes can be discovered in public model repositories such as the Physiome Model Repository ( https://models.physiomeproject.org) and reused in building novel models at the epithelial cellular spatial scale.In this work we present a novel Python‐based framework in which we extend our previous work to now look at solute transport and flow in generic tubule segments. The Python code captures the standard equations for flow and solute transport and we link to CellML descriptions of transport mechanisms to define the transport of solutes between the lumen, intracellular space, and interstitial fluid.By linking to models of, for example, epithelial transport proteins encoded in the CellML format we are able to configure the generic tubule segment to represent known physiology of the various nephron segments in the kidney. As the number and variety of suitable models in the model repository grows, we will be able to “automatically” discover and utilize them in this framework.In future work, we will are attempting to utilize clinical data captured in semantic knowledge frameworks, such as openEHR, to guide the discovery and parameterization of the epithelial cellular transport processes based on clinical or experimental observations.Support or Funding InformationWe gratefully acknowledge funding from the Aotearoa Foundation, Medical Technologies Centre of Research Excellence, and the Auckland Bioengineering Institute.

Square-wave protein-film voltammetry: new insights in the enzymatic electrode processes coupled with chemical reactions

Redox mechanisms in which the redox transformation is coupled to other chemical reactions are of significant interest since they are regarded as relevant models for many physiological systems. Protein-film voltammetry, based on surface confined electrochemical processes, is a methodology of exceptional importance, which is designed to provide information on enzyme redox chemistry. In this work, we address some theoretical aspects of surface confined electrode mechanisms under conditions of square-wave voltammetry (SWV). Attention is paid to a collection of specific voltammetric features of a surface electrode reaction coupled with a follow-up (ECrev), preceding (CrevE) and regenerative (EC’) chemical reaction. While presenting a collection of numerically calculated square-wave voltammograms, several intriguing and simple features enabling kinetic characterization of studied mechanisms in time-independent experiments (i.e., voltammetric experiments at a constant scan rate) are addressed. The aim of the work is to help in designing a suitable experimental set-up for studying surface electrode processes, as well as to provide a means for determination of kinetic and/or thermodynamic parameters of both electrode and chemical steps.

Credibility Evidence for Computational Patient Models Used in the Development of Physiological Closed-Loop Controlled Devices for Critical Care Medicine.

Physiological closed-loop controlled medical devices automatically adjust therapy delivered to a patient to adjust a measured physiological variable. In critical care scenarios, these types of devices could automate, for example, fluid resuscitation, drug delivery, mechanical ventilation, and/or anesthesia and sedation. Evidence from simulations using computational models of physiological systems can play a crucial role in the development of physiological closed-loop controlled devices; but the utility of this evidence will depend on the credibility of the computational model used. Computational models of physiological systems can be complex with numerous non-linearities, time-varying properties, and unknown parameters, which leads to challenges in model assessment. Given the wide range of potential uses of computational patient models in the design and evaluation of physiological closed-loop controlled systems, and the varying risks associated with the diverse uses, the specific model as well as the necessary evidence to make a model credible for a use case may vary. In this review, we examine the various uses of computational patient models in the design and evaluation of critical care physiological closed-loop controlled systems (e.g., hemodynamic stability, mechanical ventilation, anesthetic delivery) as well as the types of evidence (e.g., verification, validation, and uncertainty quantification activities) presented to support the model for that use. We then examine and discuss how a credibility assessment framework (American Society of Mechanical Engineers Verification and Validation Subcommittee, V&V 40 Verification and Validation in Computational Modeling of Medical Devices) for medical devices can be applied to computational patient models used to test physiological closed-loop controlled systems.

Bioengineering and Metabolism Voices

To explore the world where technology fuses with the life sciences, we asked a diverse group of scientists to tell us about bioengineering innovations that impact metabolism and physiology. From miniaturized models of physiological systems to smart drugs with feedback control, we take a journey with them through the frontiers of biomedicine.

Симулятор физиологии человека в условиях энергетического баланса в клетках

For IBM-compatible personal computers, a software simulator (PS) is created, based on simplified mathematical models (UMM) of complex physiological systems (CFS) that provide energy balance in human cells. The differential equations of the previously created and published dynamic model in UMM are replaced by algebraic equations describing the proportional dependences between the variables of the state of the CFS. UMMs describe only the statics of cellular and multicellular CFS. The PS developed in C ++ provides the user (physiologist) with an interface through which different combinations of specified state variables are selected to calculate the mean arterial pressure (SBP). Multidimensional equations contain coefficients characterizing the sensitivity of state variables to changes in the energy status of the organism. By means of numerical values of these coefficients the user can simulate different static physiological regimes of the organism. Examples of such computations are given. PS is a convenient information technology, complementing the traditional empirical methods of human physiology. Problems in programming 2018; 4: 93-100

Parameter subset selection techniques for problems in mathematical biology.

Patient-specific models for diagnostics and treatment planning require reliable parameter estimation and model predictions. Mathematical models of physiological systems are often formulated as systems of nonlinear ordinary differential equations with many parameters and few options for measuring all state variables. Consequently, it can be difficult to determine which parameters can reliably be estimated from available data. This investigation highlights pitfalls associated with practical parameter identifiability and subset selection. The latter refer to the process associated with selecting a subset of parameters that can be identified uniquely by parameter estimation protocols. The methods will be demonstrated using five examples of increasing complexity, as well as with patient-specific model predicting arterial blood pressure. This study demonstrates that methods based on local sensitivities are preferable in terms of computational cost and model fit when good initial parameter values are available, but that global methods should be considered when initial parameter value is not known or poorly understood. For global sensitivity analysis, Morris screening provides results in terms of parameter sensitivity ranking at a much lower computational cost.

Applying a Computational Model Credibility Framework to Physiological Closed-loop Controlled Medical Device Testing.

Physiological closed-loop controlled medical devices are safety-critical systems that combine patient monitors with therapy delivery devices to automatically titrate therapy to meet a patient's current need. Computational models of physiological systems can be used to test these devices and generate pre-clinical evidence of safety and performance before using the devices on patients. The credibility, utility, and acceptability of such model-based test results will depend on, among other factors, the computational model used. We examine how a recently developed risk-informed framework for establishing the credibility of computational models in medical device applications can be applied in the evaluation of physiological closed-loop controlled devices.

Fitting tissue chips and microphysiological systems into the grand scheme of medicine, biology, pharmacology, and toxicology.

Microphysiological systems (MPS), which include engineered organoids (EOs), single organ/tissue chips (TCs), and multiple organs interconnected to create miniature in vitro models of human physiological systems, are rapidly becoming effective tools for drug development and the mechanistic understanding of tissue physiology and pathophysiology. The second MPS thematic issue of Experimental Biology and Medicine comprises 15 articles by scientists and engineers from the National Institutes of Health, the IQ Consortium, the Food and Drug Administration, and Environmental Protection Agency, an MPS company, and academia. Topics include the progress, challenges, and future of organs-on-chips, dissemination of TCs into Pharma, children's health protection, liver zonation, liver chips and their coupling to interconnected systems, gastrointestinal MPS, maturation of immature cardiomyocytes in a heart-on-a-chip, coculture of multiple cell types in a human skin construct, use of synthetic hydrogels to create EOs that form neural tissue models, the blood-brain barrier-on-a-chip, MPS models of coupled female reproductive organs, coupling MPS devices to create a body-on-a-chip, and the use of a microformulator to recapitulate endocrine circadian rhythms. While MPS hardware has been relatively stable since the last MPS thematic issue, there have been significant advances in cell sourcing, with increased reliance on human-induced pluripotent stem cells, and in characterization of the genetic and functional cell state in MPS bioreactors. There is growing appreciation of the need to minimize perfusate-to-cell-volume ratios and respect physiological scaling of coupled TCs. Questions asked by drug developers are followed by an analysis of the potential value, costs, and needs of Pharma. Of highest value and lowest switching costs may be the development of MPS disease models to aid in the discovery of disease mechanisms; novel compounds including probes, leads, and clinical candidates; and mechanism of action of drug candidates. Impact statement Microphysiological systems (MPS), which include engineered organoids and both individual and coupled organs-on-chips and tissue chips, are a rapidly growing topic of research that addresses the known limitations of conventional cellular monoculture on flat plastic - a well-perfected set of techniques that produces reliable, statistically significant results that may not adequately represent human biology and disease. As reviewed in this article and the others in this thematic issue, MPS research has made notable progress in the past three years in both cell sourcing and characterization. As the field matures, currently identified challenges are being addressed, and new ones are being recognized. Building upon investments by the Defense Advanced Research Projects Agency, National Institutes of Health, Food and Drug Administration, Defense Threat Reduction Agency, and Environmental Protection Agency of more than $200 million since 2012 and sizable corporate spending, academic and commercial players in the MPS community are demonstrating their ability to meet the translational challenges required to apply MPS technologies to accelerate drug development and advance toxicology.

Interpretation of metabolic memory phenomenon using a physiological systems model: What drives oxidative stress following glucose normalization?

Hyperglycemia is generally associated with oxidative stress, which plays a key role in diabetes-related complications. A complex, quantitative relationship has been established between glucose levels and oxidative stress, both in vitro and in vivo. For example, oxidative stress is known to persist after glucose normalization, a phenomenon described as metabolic memory. Also, uncontrolled glucose levels appear to be more detrimental to patients with diabetes (non-constant glucose levels) vs. patients with high, constant glucose levels. The objective of the current study was to delineate the mechanisms underlying such behaviors, using a mechanistic physiological systems modeling approach that captures and integrates essential underlying pathophysiological processes. The proposed model was based on a system of ordinary differential equations. It describes the interplay between reactive oxygen species production potential (ROS), ROS-induced cell alterations, and subsequent adaptation mechanisms. Model parameters were calibrated using different sources of experimental information, including ROS production in cell cultures exposed to various concentration profiles of constant and oscillating glucose levels. The model adequately reproduced the ROS excess generation after glucose normalization. Such behavior appeared to be driven by positive feedback regulations between ROS and ROS-induced cell alterations. The further oxidative stress-related detrimental effect as induced by unstable glucose levels can be explained by inability of cells to adapt to dynamic environment. Cell adaptation to instable high glucose declines during glucose normalization phases, and further glucose increase promotes similar or higher oxidative stress. In contrast, gradual ROS production potential decrease, driven by adaptation, is observed in cells exposed to constant high glucose.

Modeling Multisystem Physiological Dysregulation.

The purposes of this study were to compare the relative fit of two alternative factor models of allostatic load (AL) and physiological systems, and to test factor invariance across age and sex. Data were from the Midlife in the United States II Biomarker Project, a large (n = 1255) multisite study of adults aged 34 to 84 years (56.8% women). Specifically, 23 biomarkers were included, representing seven physiological systems: metabolic lipids, metabolic glucose, blood pressure, parasympathetic nervous system, sympathetic nervous system, hypothalamic-pituitary-adrenal axis, and inflammation. For factor invariance tests, age was categorized into three groups (≤45, 45-60, and >60 years). A bifactor model where biomarkers simultaneously load onto a common AL factor and seven unique system-specific factors provided the best fit to the biomarker data (comparative fit index = 0.967, root mean square error of approximation = 0.043, standardized root mean square residual = 0.028). Results from the bifactor model were consistent with invariance across age groups and sex. These results support the theory that represents and operationalizes AL as multisystem physiological dysregulation and operationalizing AL as the shared variance across biomarkers. Results also demonstrate that in addition to the variance in biomarkers accounted for by AL, individual physiological systems account for unique variance in system-specific biomarkers. A bifactor model allows researchers greater precision to examine both AL and the unique effects of specific systems.