Sensitivity analysis methods in the biomedical sciences

Multi objective optimization and experimental investigation of the stirring performance of a novel micro actuator

Fragmented thrombolytic micro-actuators, a novel vascular recanalization technology, demonstrate potential excellent stirring performance in narrow and curved blood vessels. Optimizing their structural parameters and conducting performance evaluations are key areas of research in this field. This study employs the finite element (FE) method to numerically investigate the effect of critical structural parameters on the stirring performance of a novel scissor-type thrombolytic micro-actuator. A quadratic predictive model for its tip amplitude and stirring force is established using the Response Surface Methodology (RSM). Subsequently, the Non-dominated Sorting Genetic Algorithm III (NSGA-III) is utilized for Multi-Objective Optimization to identify the optimal combination of structural parameters. A micro-actuator prototype is fabricated and experiments on its stirring performance are conducted. The results indicate that the slit beam thickness has the most significant effect on stirring performance. After optimization, the maximum tip amplitude and maximum stirring force of the micro-actuator improve by 61.33% and 80.19%, respectively. This research lays a solid foundation for the miniaturization and clinical application of fragmented thrombolytic micro-actuators.

The Evolution of Systems Biology and Systems Medicine: From Mechanistic Models to Uncertainty Quantification

Understanding interaction mechanisms within cells, tissues, and organisms is crucial for driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating such biological systems. Building on experiments, mechanistic models are widely used to describe small-scale intracellular networks. The development of sequencing techniques and computational tools has recently enabled multiscale models. Combining such larger scale network modeling with mechanistic modeling provides us with an opportunity to reveal previously unknown disease mechanisms and pharmacological interventions. Here, we review systems biology models from mechanistic models to multiscale models that integrate multiple layers of cellular networks and discuss how they can be used to shed light on disease states and even wellness-related states. Additionally, we introduce several methods that increase the certainty and accuracy of model predictions. Thus, combining mechanistic models with emerging mathematical and computational techniques can provide us with increasingly powerful tools to understand disease states and inspire drug discoveries.

Practical parameter identifiability of respiratory mechanics in the extremely preterm infant

The complexity of mathematical models describing respiratory mechanics has grown in recent years, however, parameter identifiability of such models has only been studied in the last decade in the context of observable data. This study investigates parameter identifiability of a nonlinear respiratory mechanics model tuned to the physiology of an extremely preterm infant, using global Morris screening, local deterministic sensitivity analysis and singular value decomposition-based subset selection. The model predicts airflow and dynamic pulmonary volumes and pressures under varying levels of continuous positive airway pressure, and a range of parameters characterizing both surfactant-treated and surfactant-deficient lung. Sensitivity analyses indicated 11 parameters influence model outputs over the range of continuous positive airway pressure and lung health scenarios. The model was adapted to data from a spontaneously breathing 1 kg infant using gradient-based optimization to estimate the parameter subset characterizing the patient's state of health.This article is part of the theme issue 'Uncertainty quantification for healthcare and biological systems (Part 2)'.

Noninvasive estimation of central blood pressure through fluid-structure interaction modeling

Central blood pressure (cBP) is considered a superior indicator of cardiovascular fitness than brachial blood pressure (bBP). Even though bBP is easy to measure noninvasively, it is usually higher than cBP due to pulse wave amplification, characterized by the gradual increase in peak systolic pressure during pulse wave propagation. In this study, we aim to develop an individualized transfer function that can accurately estimate cBP from bBP. We first construct a three-dimensional, patient-specific model of the upper limb arterial system using fluid-structure interaction simulations, incorporating variable material properties and complex boundary conditions. Then, we develop an analytical brachial-aortic transfer function based on novel solutions for compliant vessels. The accuracy of this transfer function is successfully validated against numerical simulation results, which effectively reproduce pulse wave propagation and amplification, with key hemodynamic parameters falling within the range of clinical measurements. Further analysis of the transfer function reveals that cBP is a linear combination of bBP and aortic flow rate in the frequency domain, with the coefficients determined by vessel geometry, material properties, and boundary conditions. Additionally, bBP primarily contributes to the steady component of cBP, while the aortic flow rate is responsible for the pulsatile component. Furthermore, local sensitivity analysis indicates that the lumen radius is the most influential parameter in accurately estimating cBP. Although not directly applicable clinically, the proposed transfer function enhances understanding of the underlying physics-highlighting the importance of aortic flow and lumen radius-and can guide the development of more practical transfer functions.

Role of forelimb morphology in muscle sensorimotor functions during locomotion in the cat

Previous studies established strong links between morphological characteristics of mammalian hindlimb muscles and their sensorimotor functions during locomotion. Less is known about the role of forelimb morphology in motor outputs and generation of sensory signals. Here, we measured morphological characteristics of 46 forelimb muscles from six cats. These characteristics included muscle attachments, physiological cross-sectional area (PCSA) and fascicle length. We also recorded full-body mechanics and EMG activity of forelimb muscles during level overground and treadmill locomotion in seven and 16 adult cats of either sex, respectively. We computed forelimb muscle forces along with force- and length-dependent sensory signals mapped onto corresponding cervical spinal segments. We found that patterns of computed muscle forces and afferent activities were strongly affected by the muscle's moment arm, PCSA and fascicle length. Morphology of the shoulder muscles suggests distinct roles of the forelimbs in lateral force production and movements. Patterns of length-dependent sensory activity of muscles with long fibres (brachioradialis, extensor carpi radialis) closely matched patterns of overall forelimb length, whereas the activity pattern of biceps brachii length afferents matched forelimb orientation. We conclude that cat forelimb muscle morphology contributes substantially to locomotor function, particularly to control lateral stability and turning, rather than propulsion. KEY POINTS: Little is known about the role of forelimb muscle morphology in producing motor outputs and generating somatosensory signals. This information is needed to understand the contributions of forelimbs in locomotor control. We measured morphological characteristics of 46 muscles from cat forelimbs, recorded cat walking mechanics and electromyographic activity, and computed patterns of moment arms, length, velocity, activation, and force of forelimb muscles, as well as length- and force-dependent afferent activity during walking. We demonstrated that moment arms, physiological cross-sectional area and fascicle length of forelimb muscles contribute substantially to muscle force production and proprioceptive activity, to the regulation of locomotor cycle phase transitions and to control of lateral stability. The obtained information can guide the development of biologically accurate neuromechanical models of quadrupedal locomotion for exploring and testing novel methods of treatments of central nervous system pathologies by modulating activities in neural pathways controlling forelimbs/arms.

Examining the Influence of Nondimensionalization on Partial Rank Correlation Coefficient Results when Modeling the Epithelial Mesenchymal Transition

Partial Rank Correlation Coefficient (PRCC) is a powerful type of global sensitivity analysis. Usually performed following Latin Hypercube Sampling (LHS), this analysis can highlight the parameters in a mathematical model producing the observed results, a crucial step when using models to understand real-world phenomena and guide future experiments. Recently, Gasior et al. performed LHS and PRCC when modeling the influence of cell-cell contact and TGF- β signaling on the epithelial mesenchymal transition (Gasior et al. in J Theor Biol 546:111160, 2022). Though their analysis provided insight into how these tumor-level factors can impact intracellular signaling during the transition, their results were potentially impacted by nondimensionalizing the model prior to performing sensitivity analysis. This work seeks to understand the true impact of nondimensionalization on sensitivity analysis by performing LHS and PRCC on both the original model that Gasior et al. proposed and seven different nondimensionalizations. Parameter ranges were kept small to capture shifts in the values that originally produced bistable behavior. By comparing these eight different iterations, this work shows that the issues from performing sensitivity analysis following nondimensionalization are two-fold: (1) nondimensionalization can obscure or exclude important parameters from in-depth analysis and (2) how a model is nondimensionalized can, potentially, change analysis results. Ultimately, this work cautions against using nondimensionalization prior to sensitivity analysis if the subsequent results are meant to guide future experiments.

A Health Risk Assessment of Workers Exposed to Organic Paint Solvents Used in the Korean Shipbuilding Industry

In the shipbuilding industry, during the painting process, workers are exposed to various substances in paint, including organic solvents that can adversely affect their health. Most workplace exposures to organic solvents involve mixtures of organic compounds. Therefore, in this study, the hazard quotient (HQ) and hazard index (HI) were derived using data from the Workplace Environmental Monitoring Program in Korea for six organic solvents (xylene, n-butanol, ethylbenzene, isobutyl alcohol, toluene, and methylisobutyl ketone [MIBK]) commonly used in the steel shipbuilding industry. The non-carcinogenic risk was assessed using Monte Carlo simulations, and sensitivity analysis was performed using the Spearman rank correlation coefficient with the R program. The HI for neurotoxicity and developmental toxicity exceeded 1 in the 25th and 75th percentile, respectively. According to the sensitivity analysis, the HI for neurotoxicity was correlated with the concentration of xylene and its exposure duration, whereas that for developmental toxicity was correlated with the concentration of ethylbenzene and MIBK and their exposure duration. This study investigated the health risks posed by organic solvents among workers involved in the painting process of shipbuilding. Additional research on percutaneous exposure to organic solvents and a detailed process analysis are needed.

The development of drug resistance in metastatic tumours under chemotherapy: An evolutionary perspective

We present a mathematical model of the evolutionary dynamics of a metastatic tumour under chemotherapy, comprising non-local partial differential equations for the phenotype-structured cell populations in the primary tumour and its metastasis. These equations are coupled with a physiologically-based pharmacokinetic model of drug administration and distribution, implementing a realistic delivery schedule. The model is carefully calibrated from the literature, focusing on BRAF-mutated melanoma treated with Dabrafenib as a case study. By means of long-time asymptotic and global sensitivity analyses, as well as numerical simulations, we explore the impact of cell migration from the primary to the metastatic site, physiological aspects of the tumour tissues and drug dose on the development of chemoresistance and treatment efficacy. Our findings provide a possible explanation for empirical evidence indicating that chemotherapy may foster metastatic spread and that metastases may be less impacted by the chemotherapeutic agent.

Sensitivity analysis of models of gas exchange for lung hyperpolarised 129Xe MR

Sensitivity analysis enables the identification of influential parameters and the optimisation of model composition. Such methods have not previously been applied systematically to models describing hyperpolarised 129Xe gas exchange in the lung. Here, we evaluate the current 129Xe gas exchange models to assess their precision for identifying alterations in pulmonary vascular function and lung microstructure. We assess sensitivity using established univariate methods and scatter plots for parameter interactions. We apply them to the model described by Patz et al and the Model of Xenon Exchange (MOXE), examining their ability to measure: i) importance (rank), ii) temporal dependence and iii) interaction effects of each parameter across healthy and diseased ranges. The univariate methods and scatter plot analyses demonstrate consistently similar results for the importance of parameters common to both models evaluated. Alveolar surface area to volume ratio is identified as the parameter to which model signals are most sensitive. The alveolar-capillary barrier thickness is identified as a low-sensitivity parameter for the MOXE model. An acquisition window of at least 200 ms effectively demonstrates model sensitivity to most parameters. Scatter plots reveal interaction effects in both models, impacting output variability and sensitivity. Our sensitivity analysis ranks the parameters within the model described by Patz et al and within the MOXE model. The MOXE model shows low sensitivity to alveolar-capillary barrier thickness, highlighting the need for designing acquisition protocols optimised for the measurement of this parameter. The presence of parameter interaction effects highlights the requirement for care in interpreting model outputs.

Two-step global sensitivity analysis of a non-local integro-differential model for Cancer-on-Chip experiments

The present work focuses on a non-local integro-differential model reproducing Cancer-on-chip experiments where tumor cells, treated with chemotherapy drugs, secrete chemical signals stimulating the immune response. The reliability of the model in reproducing the phenomenon of interest is investigated through a global sensitivity analysis, rather than a local one, to have global information about the role of parameters, and by examining potential non-linear effects in greater detail. Focusing on a region in the parameter space, the effect of 13 model parameters on the in silico outcome is investigated by considering 11 different target outputs, properly selected to monitor the spatial distribution and the dynamics of immune cells along the period of observation. In order to cope with the large number of model parameters to be investigated and the computational cost of each numerical simulation, a two-step global sensitivity analysis is performed. First, the screening Morris method is applied to rank the effect of the 13 model parameters on each target output and it emerges that all the output targets are mainly affected by the same 6 parameters. The extended Fourier Amplitude Sensitivity Test (eFAST) method is then used to quantify the role of these 6 parameters. As a result, the proposed analysis highlights the feasibility of the considered space of parameters, and indicates that the most relevant parameters are those related to the chemical field and cell-substrate adhesion. In turn, it suggests how to possibly improve the model description as well as the calibration procedure, in order to better capture the observed phenomena and, at the same time, reduce the complexity of the simulation algorithm. On one hand, the model could be simplified by neglecting cell-cell alignment effects unless clear empirical evidences of their importance emerge. On the other hand, the best way to increase the accuracy and reliability of our model predictions would be to have experimental data/information to reduce the uncertainty of the more relevant parameters.

Towards verifiable cancer digital twins: tissue level modeling protocol for precision medicine

Cancer exhibits substantial heterogeneity, manifesting as distinct morphological and molecular variations across tumors, which frequently undermines the efficacy of conventional oncological treatments. Developments in multiomics and sequencing technologies have paved the way for unraveling this heterogeneity. Nevertheless, the complexity of the data gathered from these methods cannot be fully interpreted through multimodal data analysis alone. Mathematical modeling plays a crucial role in delineating the underlying mechanisms to explain sources of heterogeneity using patient-specific data. Intra-tumoral diversity necessitates the development of precision oncology therapies utilizing multiphysics, multiscale mathematical models for cancer. This review discusses recent advancements in computational methodologies for precision oncology, highlighting the potential of cancer digital twins to enhance patient-specific decision-making in clinical settings. We review computational efforts in building patient-informed cellular and tissue-level models for cancer and propose a computational framework that utilizes agent-based modeling as an effective conduit to integrate cancer systems models that encode signaling at the cellular scale with digital twin models that predict tissue-level response in a tumor microenvironment customized to patient information. Furthermore, we discuss machine learning approaches to building surrogates for these complex mathematical models. These surrogates can potentially be used to conduct sensitivity analysis, verification, validation, and uncertainty quantification, which is especially important for tumor studies due to their dynamic nature.

Sensitivity-analysis-guided Bayesian parameter estimation for neural mass models: Applications in epilepsy

It is well established that neural mass models (NMMs) can effectively simulate the mesoscopic and macroscopic dynamics of electroencephalography (EEG), including epileptic EEG. However, the use of NMMs to gain insight on the neuronal system by parameter estimation is hampered by their high dimensionality and the lack of knowledge on what NMM parameters can be reliably estimated. In this article, we analyze the parameter sensitivity of the Jansen and Rit NMM (JR NMM) in order to identify the most sensitive JR-NMM parameters for reliable parameter estimation from EEG data. We then propose a Bayesian approach for estimating the JR-NMM states and parameters based on an expectation-maximization algorithm combined with the unscented Kalman smoother (UKS EM). Global sensitivity analysis methods including the Morris method and the Sobol method are used to perform sensitivity analysis. Results from both the Morris and the Sobol method show that the average inhibitory synaptic gain, B, and the reciprocal of the time constant of the average inhibitory postsynaptic potentials, b, have a significant impact on the JR-NMM output along with having the least interaction with other model parameters. The UKS-EM method for estimating the parameters B and b is validated using simulations under varying levels of measurement noise. Finally we apply the UKS-EM algorithm to intracranial EEG data from 16 epileptic patients. Our results, both at individual and group level show that the parameters B and b change significantly between the preseizure and seizure period, and between the seizure and postseizure period, with the transition to seizure characterized by a decrease in the average B, and the high frequency activity in seizure characterized by an increase in b. These results establish a sensitivity analysis guided Bayesian parameter estimation as a powerful tool for reducing the parameter space of high-dimensional NMMs enabling reliable and efficient estimation of the most sensitive NMM parameters, with the potential for online and fast tracking of NMM parameters in applications such as seizure tracking and control.

Assessing key parameters in simultaneous simulation of rapid kinetics of chlorophyll a fluorescence and trans-thylakoid electric potential difference

Our study attempts to address the following questions: among numerous photosynthetic modules, which parameters notably influence the rapid chlorophyll fluorescence (ChlF) rise, the so-called O-J-I-P transient, in conjunction with the P515 signal, as these two records are easily obtained and widely used in photosynthesis research, and how are these parameters ranked in terms of their importance? These questions might be difficult to answer solely through experimental assays. Therefore, we employed an established photosynthesis model. Firstly, we utilized the model to simulate the measured rapid ChlF rise and P515 kinetics simultaneously. Secondly, we employed the sensitivity analysis (SA) tool by randomly altering model parameters to observe their effects on model output variables. Thirdly, we systematically identified significant parameters for both or one of the kinetics across various scenarios. A novel aspect of our study is the application of the Morris method, a global SA tool, to simultaneously assess the significance of model parameters in shaping both or one of the kinetics. The Morris SA technique enables the quantification of how much a specific parameter affects O-J-I-P transient during particular time intervals (e.g., J, I, and P steps). This allowed us to theoretically analyze which step is more significantly influenced by the parameter. In summary, our study contributes to the field by providing a comprehensive analysis of photosynthesis kinetics and emphasizing the importance of parameter selection in modelling this process. These findings can inform future research efforts aimed at improving photosynthesis models and advancing our understanding of photosynthetic processes.

ROLE OF FORELIMB MORPHOLOGY IN MUSCLE SENSORIMOTOR FUNCTIONS DURING LOCOMOTION IN THE CAT

Previous studies established strong links between morphological characteristics of mammalian hindlimb muscles and their sensorimotor functions during locomotion. Less is known about the role of forelimb morphology in motor outputs and generation of sensory signals. Here, we measured morphological characteristics of 46 forelimb muscles from 6 cats. These characteristics included muscle attachments, physiological cross-sectional area (PCSA), fascicle length, etc. We also recorded full-body mechanics and EMG activity of forelimb muscles during level overground and treadmill locomotion in 7 and 16 adult cats of either sex, respectively. We computed forelimb muscle forces along with force- and length-dependent sensory signals mapped onto corresponding cervical spinal segments. We found that patterns of computed muscle forces and afferent activities were strongly affected by the muscle's moment arm, PCSA, and fascicle length. Morphology of the shoulder muscles suggests distinct roles of the forelimbs in lateral force production and movements. Patterns of length-dependent sensory activity of muscles with long fibers (brachioradialis, extensor carpi radialis) closely matched patterns of overall forelimb length, whereas the activity pattern of biceps brachii matched forelimb orientation. We conclude that cat forelimb muscle morphology contributes substantially to locomotor function, particularly to control lateral stability and turning, rather than propulsion.

Addressing the sources of inter-subject variability in E-field parameters in anodal tDCS stimulation over motor cortical network

Objetive: .Although transcranial direct current stimulation constitutes a non-invasive neuromodulation technique with promising results in a great variety of applications, its clinical implementation is compromised by the high inter-subject variability reported. This study aims to analyze the inter-subject variability in electric fields (E-fields) over regions of the cortical motor network under two electrode montages: the classical C3Fp2 and an alternative P3F3, which confines more the E-field over this region.Approach.Computational models of the head of 98 healthy subjects were developed to simulate the E-field under both montages. E-field parameters such as magnitude, focality and orientation were calculated over three regions of interest (ROI): M1S1, supplementary motor area (SMA) and preSMA. The role of anatomical characteristics as a source of inter-subject variability on E-field parameters and individualized stimulation intensity were addressed using linear mixed-effect models.Main results.P3F3 showed a more confined E-field distribution over M1S1 than C3Fp2; the latter elicited higher E-fields over supplementary motor areas. Both montages showed high inter-subject variability, especially for the normal component over C3Fp2. Skin, bone and CSF ROI volumes showed a negative association with E-field magnitude irrespective of montage. Grey matter volume and montage were the main sources of variability for focality. The curvature of gyri was found to be significantly associated with the variability of normal E-fields.Significance.Computational modeling proves useful in the assessment of E-field variability. Our simulations predict significant differences in E-field magnitude and focality for C3Fp2 and P3F3. However, anatomical characteristics were also found to be significant sources of E-field variability irrespective of electrode montage. The normal E-field component better captured the individual variability and low rate of responder subjects observed in experimental studies.

Convergence, sampling and total order estimator effects on parameter orthogonality in global sensitivity analysis

Dynamical system models typically involve numerous input parameters whose "effects" and orthogonality need to be quantified through sensitivity analysis, to identify inputs contributing the greatest uncertainty. Whilst prior art has compared total-order estimators' role in recovering "true" effects, assessing their ability to recover robust parameter orthogonality for use in identifiability metrics has not been investigated. In this paper, we perform: (i) an assessment using a different class of numerical models representing the cardiovascular system, (ii) a wider evaluation of sampling methodologies and their interactions with estimators, (iii) an investigation of the consequences of permuting estimators and sampling methodologies on input parameter orthogonality, (iv) a study of sample convergence through resampling, and (v) an assessment of whether positive outcomes are sustained when model input dimensionality increases. Our results indicate that Jansen or Janon estimators display efficient convergence with minimum uncertainty when coupled with Sobol and the lattice rule sampling methods, making them prime choices for calculating parameter orthogonality and influence. This study reveals that global sensitivity analysis is convergence driven. Unconverged indices are subject to error and therefore the true influence or orthogonality of the input parameters are not recovered. This investigation importantly clarifies the interactions of the estimator and the sampling methodology by reducing the associated ambiguities, defining novel practices for modelling in the life sciences.

Mechanism-based and data-driven modeling in cell-free synthetic biology

Cell-free systems have emerged as a versatile platform in synthetic biology, finding applications in various areas such as prototyping synthetic circuits, biosensor development, and biomanufacturing. To streamline the prototyping process, cell-free systems often incorporate a modeling step that predicts the outcomes of various experimental scenarios, providing a deeper insight into the underlying mechanisms and functions. There are two recognized approaches for modeling these systems: mechanism-based modeling, which models the underlying reaction mechanisms; and data-driven modeling, which makes predictions based on data without preconceived interactions between system components. In this highlight, we focus on the latest advancements in both modeling approaches for cell-free systems, exploring their potential for the design and optimization of synthetic genetic circuits.

Screening rate constants in the simulation of rapid kinetics of chlorophyll a fluorescence using the Morris method

Chlorophyll a fluorescence, a sensitive and cost-effective probe, is widely used in photosynthetic research. Its rapid phase, occurring within 1 second under intense illumination, displays complex O-J-I-P transients, providing valuable insights into various aspects of photosynthesis. In addition to employing experimental approaches to measure the rapid Fluorescence Induction (FI) kinetics, mathematical modeling serves as a crucial tool for understanding the underlying mechanisms that drive FI dynamics. However, the significant uncertainty and arbitrary nature of selecting model parameters amplify concerns about the effectiveness of modeling tools in aiding photosynthesis research. Therefore, there is a need to gain a deeper understanding of how these models operate and how arbitrary parameter choices may influence their outcomes. In this study, we employed the Morris method, a global Sensitivity Analysis (SA) tool, to assess the significance of rate constants employed in an existing fluorescence model, particularly those linked to the entire electron transport chain, in shaping the rapid FI dynamics. In summary, utilizing the insights gained from the Morris SA allows for targeted refinement of the photosynthesis model, thereby improving our understanding of the complex processes inherent in photosynthetic systems.

Nonlinear compartmental modeling to monitor ovarian follicle population dynamics on the whole lifespan

In this work, we introduce a compartmental model of ovarian follicle development all along lifespan, based on ordinary differential equations. The model predicts the changes in the follicle numbers in different maturation stages with aging. Ovarian follicles may either move forward to the next compartment (unidirectional migration) or degenerate and disappear (death). The migration from the first follicle compartment corresponds to the activation of quiescent follicles, which is responsible for the progressive exhaustion of the follicle reserve (ovarian aging) until cessation of reproductive activity. The model consists of a data-driven layer embedded into a more comprehensive, knowledge-driven layer encompassing the earliest events in follicle development. The data-driven layer is designed according to the most densely sampled experimental dataset available on follicle numbers in the mouse. Its salient feature is the nonlinear formulation of the activation rate, whose formulation includes a feedback term from growing follicles. The knowledge-based, coating layer accounts for cutting-edge studies on the initiation of follicle development around birth. Its salient feature is the co-existence of two follicle subpopulations of different embryonic origins. We then setup a complete estimation strategy, including the study of structural identifiability, the elaboration of a relevant optimization criterion combining different sources of data (the initial dataset on follicle numbers, together with data in conditions of perturbed activation, and data discriminating the subpopulations) with appropriate error models, and a model selection step. We finally illustrate the model potential for experimental design (suggestion of targeted new data acquisition) and in silico experiments.

A modeling analysis of whole body potassium regulation on a high-potassium diet: proximal tubule and tubuloglomerular feedback effects

Potassium (K+) is an essential electrolyte that plays a key role in many physiological processes, including mineralcorticoid action, systemic blood-pressure regulation, and hormone secretion and action. Indeed, maintaining K+ balance is critical for normal cell function, as too high or too low K+ levels can have serious and potentially deadly health consequences. K+ homeostasis is achieved by an intricate balance between the intracellular and extracellular fluid as well as balance between K+ intake and excretion. This is achieved via the coordinated actions of regulatory mechanisms such as the gastrointestinal feedforward effect, insulin and aldosterone upregulation of Na+-K+-ATPase uptake, and hormone and electrolyte impacts on renal K+ handling. We recently developed a mathematical model of whole body K+ regulation to unravel the individual impacts of these regulatory mechanisms. In this study, we extend our mathematical model to incorporate recent experimental findings that showed decreased fractional proximal tubule reabsorption under a high-K+ diet. We conducted model simulations and sensitivity analyses to investigate how these renal alterations impact whole body K+ regulation. Model predictions quantify the sensitivity of K+ regulation to various levels of proximal tubule K+ reabsorption adaptation and tubuloglomerular feedback. Our results suggest that the reduced proximal tubule K+ reabsorption under a high-K+ diet could achieve K+ balance in isolation, but the resulting tubuloglomerular feedback reduces filtration rate and thus K+ excretion.NEW & NOTEWORTHY Potassium homeostasis is maintained in the body by a complex system of regulatory mechanisms. This system, when healthy, maintains a small extracellular potassium concentration, despite large fluctuations of dietary potassium. The complexities of the system make this problem well suited for investigation with mathematical modeling. In this study, we extend our mathematical model to consider recent experimental results on renal potassium handling on a high potassium diet and investigate the impacts from a whole body perspective.

Untangling the Molecular Interactions Underlying Intracellular Phase Separation Using Combined Global Sensitivity Analyses

Liquid-liquid phase separation is an intracellular mechanism by which molecules, usually proteins and RNAs, interact and then rapidly demix from the surrounding matrix to form membrane-less compartments necessary for cellular function. Occurring in both the cytoplasm and the nucleus, properties of the resulting droplets depend on a variety of characteristics specific to the molecules involved, such as valency, density, and diffusion within the crowded environment. Capturing these complexities in a biologically relevant model is difficult. To understand the nuanced dynamics between proteins and RNAs as they interact and form droplets, as well as the impact of these interactions on the resulting droplet properties, we turn to sensitivity analysis. In this work, we examine a previously published mathematical model of two RNA species competing for the same protein-binding partner. We use the combined analyses of Morris Method and Sobol' sensitivity analysis to understand the impact of nine molecular parameters, subjected to three different initial conditions, on two observable LLPS outputs: the time of phase separation and the composition of the droplet field. Morris Method is a screening method capable of highlighting the most important parameters impacting a given output, while the variance-based Sobol' analysis can quantify both the importance of a given parameter, as well as the other model parameters it interacts with, to produce the observed phenomena. Combining these two techniques allows Morris Method to identify the most important dynamics and circumvent the large computational expense associated with Sobol', which then provides more nuanced information about parameter relationships. Together, the results of these combined methodologies highlight the complicated protein-RNA relationships underlying both the time of phase separation and the composition of the droplet field. Sobol' sensitivity analysis reveals that observed spatial and temporal dynamics are due, at least in part, to high-level interactions between multiple (3+) parameters. Ultimately, this work discourages using a single measurement to extrapolate the value of any single rate or parameter value, while simultaneously establishing a framework in which to analyze and assess the impact of these small-scale molecular interactions on large-scale droplet properties.

Bacteriophage specificity is impacted by interactions between bacteria

Predators play a central role in shaping community structure, function, and stability. The degree to which bacteriophage predators (viruses that infect bacteria) evolve to be specialists with a single bacterial prey species versus generalists able to consume multiple types of prey has implications for their effect on microbial communities. The presence and abundance of multiple bacterial prey types can alter selection for phage generalists, but less is known about how interactions between prey shape predator specificity in microbial systems. Using a phenomenological mathematical model of phage and bacterial populations, we find that the dominant phage strategy depends on prey ecology. Given a fitness cost for generalism, generalist predators maintain an advantage when prey species compete, while specialists dominate when prey are obligately engaged in cross-feeding interactions. We test these predictions in a synthetic microbial community with interacting strains of Escherichia coli and Salmonella enterica by competing a generalist T5-like phage able to infect both prey against P22vir, an S. enterica-specific phage. Our experimental data conform to our modeling expectations when prey species are competing or obligately mutualistic, although our results suggest that the in vitro cost of generalism is caused by a combination of biological mechanisms not anticipated in our model. Our work demonstrates that interactions between bacteria play a role in shaping ecological selection on predator specificity in obligately lytic bacteriophages and emphasizes the diversity of ways in which fitness trade-offs can manifest.

IMPORTANCE

There is significant natural diversity in how many different types of bacteria a bacteriophage can infect, but the mechanisms driving this diversity are unclear. This study uses a combination of mathematical modeling and an in vitro system consisting of Escherichia coli, Salmonella enterica, a T5-like generalist phage, and the specialist phage P22vir to highlight the connection between bacteriophage specificity and interactions between their potential microbial prey. Mathematical modeling suggests that competing bacteria tend to favor generalist bacteriophage, while bacteria that benefit each other tend to favor specialist bacteriophage. Experimental results support this general finding. The experiments also show that the optimal phage strategy is impacted by phage degradation and bacterial physiology. These findings enhance our understanding of how complex microbial communities shape selection on bacteriophage specificity, which may improve our ability to use phage to manage antibiotic-resistant microbial infections.

Construction of a novel kinetic model for the production process of a CVA6 VLP vaccine in CHO cells

Bioprocess development benefits from kinetic models in many aspects, including scale-up, optimization, and process understanding. However, current models are unable to simulate the production process of a coxsackievirus A6 (CVA6) virus-like particle (VLP) vaccine using Chinese hamster ovary cell culture. In this study, a novel kinetic model was constructed, correlating (1) cell growth, death, and lysis kinetics, (2) metabolism of major metabolites, and (3) CVA6 VLP production. To construct the model, two batches of a laboratory-scale 2 L bioreactor cell culture were prepared and various pH shift strategies were applied to examine the effect of pH shift. The proposed model described the experimental data under various conditions with high accuracy and quantified the effect of pH shift. Next, cell culture performance with various pH shift timings was predicted by the calibrated model. A trade-off relationship was found between product yield and quality. Consequently, multiple objective optimization was performed by integrating desirability methodology with model simulation. Finally, the optimal operating conditions that balanced product yield and quality were predicted. In general, the proposed model improved the process understanding and enabled in silico process development of a CVA6 VLP vaccine.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10616-023-00598-8.

Understanding the Interplay of CAR-NK Cells and Triple-Negative Breast Cancer: Insights from Computational Modeling

Chimeric antigen receptor (CAR)-engineered natural killer (NK) cells have recently emerged as a promising and safe alternative to CAR-T cells for targeting solid tumors. In the case of triple-negative breast cancer (TNBC), traditional cancer treatments and common immunotherapies have shown limited effectiveness. However, CAR-NK cells have been successfully employed to target epidermal growth factor receptor (EGFR) on TNBC cells, thereby enhancing the efficacy of immunotherapy. The effectiveness of CAR-NK-based immunotherapy is influenced by various factors, including the vaccination dose, vaccination pattern, and tumor immunosuppressive factors in the microenvironment. To gain insights into the dynamics and effects of CAR-NK-based immunotherapy, we propose a computational model based on experimental data and immunological theories. This model integrates an individual-based model that describes the interplay between the tumor and the immune system, along with an ordinary differential equation model that captures the variation of inflammatory cytokines. Computational results obtained from the proposed model shed light on the conditions necessary for initiating an effective anti-tumor response. Furthermore, global sensitivity analysis highlights the issue of low persistence of CAR-NK cells in vivo, which poses a significant challenge for the successful clinical application of these cells. Leveraging the model, we identify the optimal vaccination time, vaccination dose, and time interval between injections for maximizing therapeutic outcomes.

Minimally sufficient experimental design using identifiability analysis

Mathematical models are increasingly being developed and calibrated in tandem with data collection, empowering scientists to intervene in real time based on quantitative model predictions. Well-designed experiments can help augment the predictive power of a mathematical model but the question of when to collect data to maximize its utility for a model is non-trivial. Here we define data as model-informative if it results in a unique parametrization, assessed through the lens of practical identifiability. The framework we propose identifies an optimal experimental design (how much data to collect and when to collect it) that ensures parameter identifiability (permitting confidence in model predictions), while minimizing experimental time and costs. We demonstrate the power of the method by applying it to a modified version of a classic site-of-action pharmacokinetic/pharmacodynamic model that describes distribution of a drug into the tumor microenvironment (TME), where its efficacy is dependent on the level of target occupancy in the TME. In this context, we identify a minimal set of time points when data needs to be collected that robustly ensures practical identifiability of model parameters. The proposed methodology can be applied broadly to any mathematical model, allowing for the identification of a minimally sufficient experimental design that collects the most informative data.

Determination of acceptable Hounsfield units uncertainties via a sensitivity analysis for an accurate dose calculation in the context of prostate MRI-only radiotherapy

Radiation therapy is moving from CT based to MRI guided planning, particularly for soft tissue anatomy. An important requirement of this new workflow is the generation of synthetic-CT (sCT) from MRI to enable treatment dose calculations. Automatic methods to determine the acceptable range of CT Hounsfield Unit (HU) uncertainties to avoid dose distribution errors is thus a key step toward safe MRI-only radiotherapy. This work has analysed the effects of controlled errors introduced in CT scans on the delivered radiation dose for prostate cancer patients. Spearman correlation coefficient has been computed, and a global sensitivity analysis performed following the Morris screening method. This allows the classification of different error factors according to their impact on the dose at the isocentre. sCT HU estimation errors in the bladder appeared to be the least influential factor, and sCT quality assessment should not only focus on organs surrounding the radiation target, as errors in other soft tissue may significantly impact the dose in the target volume. This methodology links dose and intensity-based metrics, and is the first step to define a threshold of acceptability of HU uncertainties for accurate dose planning.

Estimating global identifiability using conditional mutual information in a Bayesian framework

A novel information-theoretic approach is proposed to assess the global practical identifiability of Bayesian statistical models. Based on the concept of conditional mutual information, an estimate of information gained for each model parameter is used to quantify the identifiability with practical considerations. No assumptions are made about the structure of the statistical model or the prior distribution while constructing the estimator. The estimator has the following notable advantages: first, no controlled experiment or data is required to conduct the practical identifiability analysis; second, unlike popular variance-based global sensitivity analysis methods, different forms of uncertainties, such as model-form, parameter, or measurement can be taken into account; third, the identifiability analysis is global, and therefore independent of a realization of the parameters. If an individual parameter has low identifiability, it can belong to an identifiable subset such that parameters within the subset have a functional relationship and thus have a combined effect on the statistical model. The practical identifiability framework is extended to highlight the dependencies between parameter pairs that emerge a posteriori to find identifiable parameter subsets. The applicability of the proposed approach is demonstrated using a linear Gaussian model and a non-linear methane-air reduced kinetics model. It is shown that by examining the information gained for each model parameter along with its dependencies with other parameters, a subset of parameters that can be estimated with high posterior certainty can be found.

Elementary effects for models with dimensional inputs of arbitrary type and range: Scaling and trajectory generation

The Elementary Effects method is a global sensitivity analysis approach for identifying (un)important parameters in a model. However, it has almost exclusively been used where inputs are dimensionless and take values on [0, 1]. Here, we consider models with dimensional inputs, inputs taking values on arbitrary intervals or discrete inputs. In such cases scaling effects by a function of the input range is essential for correct ranking results. We propose two alternative dimensionless sensitivity indices by normalizing the scaled mean or median of absolute effects. Testing these indices with 9 trajectory generation methods on 4 test functions (including the Penman-Monteith equation for evapotranspiration) reveals that: i) scaled elementary effects are necessary to obtain correct parameter importance rankings; ii) small step-size methods typically produce more accurate rankings; iii) it is beneficial to compute and compare both sensitivity indices; and iv) spread and discrepancy of the simulation points are poor proxies for trajectory generation method performance.

Efficient parameter generation for constrained models using MCMC

Mathematical models of complex systems rely on parameter values to produce a desired behavior. As mathematical and computational models increase in complexity, it becomes correspondingly difficult to find parameter values that satisfy system constraints. We propose a Markov Chain Monte Carlo (MCMC) approach for the problem of constrained model parameter generation by designing a Markov chain that efficiently explores a model's parameter space. We demonstrate the use of our proposed methodology to analyze responses of a newly constructed bistability-constrained model of protein phosphorylation to perturbations in the underlying protein network. Our results suggest that parameter generation for constrained models using MCMC provides powerful tools for modeling-aided analysis of complex natural processes.

Theoretical and computational tools to model multistable gene regulatory networks

The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the use of theoretical modeling to describe genetic and biochemical circuits becomes more widespread, theoreticians with mathematical and physical backgrounds routinely apply concepts from statistical physics, non-linear dynamics, and network theory to biological systems. This review aims at providing a clear overview of the most important methodologies applied in the field while highlighting current and future challenges. It also includes hands-on tutorials to solve and simulate some of the archetypical biological system models used in the field. Furthermore, we provide concrete examples from the existing literature for theoreticians that wish to explore this fast-developing field. Whenever possible, we highlight the similarities and differences between biochemical and regulatory networks and 'classical' systems typically studied in non-equilibrium statistical and quantum mechanics.

Thoracoabdominal asynchrony in a virtual preterm infant: computational modeling and analysis

Thoracoabdominal asynchrony (TAA), the asynchronous volume changes between the rib cage and abdomen during breathing, is associated with respiratory distress, progressive lung volume loss, and chronic lung disease in the newborn infant. Preterm infants are prone to TAA risk factors such as weak intercostal muscles, surfactant deficiency, and a flaccid chest wall. The causes of TAA in this fragile population are not fully understood and, to date, the assessment of TAA has not included a mechanistic modeling framework to explore the role these risk factors play in breathing dynamics and how TAA can be resolved. We present a dynamic compartmental model of pulmonary mechanics that simulates TAA in the preterm infant under various adverse clinical conditions, including high chest wall compliance, applied inspiratory resistive loads, bronchopulmonary dysplasia, anesthesia-induced intercostal muscle deactivation, weakened costal diaphragm, impaired lung compliance, and upper airway obstruction. Sensitivity analyses performed to screen and rank model parameter influence on model TAA and respiratory volume outputs show that risk factors are additive so that maximal TAA occurs in a virtual preterm infant with multiple adverse conditions, and addressing risk factors individually causes incremental changes in TAA. An abruptly obstructed upper airway caused immediate nearly paradoxical breathing and tidal volume reduction despite greater effort. In most simulations, increased TAA occurred together with decreased tidal volume. Simulated indices of TAA are consistent with published experimental studies and clinically observed pathophysiology, motivating further investigation into the use of computational modeling for assessing and managing TAA.NEW & NOTEWORTHY A novel model of thoracoabdominal asynchrony incorporates literature-derived mechanics and simulates the impact of risk factors on a virtual preterm infant. Sensitivity analyses were performed to determine the influence of model parameters on TAA and respiratory volume. Predicted phase angles are consistent with prior experimental and clinical results, and influential parameters are associated with clinical scenarios that significantly alter phase angle, motivating further investigation into the use of computational modeling for assessing and managing thoracoabdominal asynchrony.

Sensitivity analysis of biochemical systems using bond graphs

The sensitivity of systems biology models to parameter variation can give insights into which parameters are most important for physiological function, and also direct efforts to estimate parameters. However, in general, kinetic models of biochemical systems do not remain thermodynamically consistent after perturbing parameters. To address this issue, we analyse the sensitivity of biological reaction networks in the context of a bond graph representation. We find that the parameter sensitivities can themselves be represented as bond graph components, mirroring potential mechanisms for controlling biochemistry. In particular, a sensitivity system is derived which re-expresses parameter variation as additional system inputs. The sensitivity system is then linearized with respect to these new inputs to derive a linear system which can be used to give local sensitivity to parameters in terms of linear system properties such as gain and time constant. This linear system can also be used to find so-called sloppy parameters in biological models. We verify our approach using a model of the Pentose Phosphate Pathway, confirming the reactions and metabolites most essential to maintaining the function of the pathway.

Cost-effectiveness of the combination of immunotherapy and chemotherapy for extensive-stage small-cell lung cancer: a systematic review

BACKGROUND

The combination of immunotherapy and chemotherapy for extensive-stage small-cell lung cancer (ES-SCLC) was primarily carried out with a combination of immune checkpoint inhibitors (ICIs) and platinum-etoposide (EP). It is likely to be more effective in treating ES-SCLC than EP alone, but could result in high healthcare costs. The study aimed to investigate the cost-effectiveness of this combination therapy for ES-SCLC.

METHODS

We searched literature from the following databases: PubMed, Embase, Cochrane Library, and Web of Science for studies on cost-effectiveness of immunotherapy combined with chemotherapy for ES-SCLC. The literature search period was up to April 20, 2023. The quality of the studies was evaluated using the Cochrane Collaboration's tool and Consolidated Health Economic Evaluation Reporting Standards (CHEERS) checklist.

RESULTS

A total of 16 eligible studies were included in the review. All studies met CHEERS recommendations, and all randomized controlled trials (RCTs) in these studies were rated as having low risk of bias using the Cochrane Collaboration's tool. The treatment regimens compared were ICIs plus EP or EP alone. All studies mainly used incremental quality-adjusted life year and incremental cost-effectiveness ratio as outcomes. Most ICIs plus EP treatment regimens were not cost-effective based on corresponding willingness-to-pay thresholds.

CONCLUSIONS

Adebrelimab plus EP and serplulimab plus EP were probably cost-effective for ES-SCLC in China, and serplulimab plus EP was probably cost-effective for ES-SCLC in the U.S. Lowering the price of ICIs and selecting ES-SCLC patients who were sensitive to ICIs could improve the cost-effectiveness of the ICIs-combined treatment.

Increased interleukin-6 is associated with long COVID-19: a systematic review and meta-analysis

BACKGROUND

Coronavirus disease 2019 (COVID-19) can involve persistence, sequelae, and other clinical complications that last weeks to months to evolve into long COVID-19. Exploratory studies have suggested that interleukin-6 (IL-6) is related to COVID-19; however, the correlation between IL-6 and long COVID-19 is unknown. We designed a systematic review and meta-analysis to assess the relationship between IL-6 levels and long COVID-19.

METHODS

Databases were systematically searched for articles with data on long COVID-19 and IL-6 levels published before September 2022. A total of 22 published studies were eligible for inclusion following the PRISMA guidelines. Analysis of data was undertaken by using Cochran's Q test and the Higgins I-squared (I²) statistic for heterogeneity. Random-effect meta-analyses were conducted to pool the IL-6 levels of long COVID-19 patients and to compare the differences in IL-6 levels among the long COVID-19, healthy, non-postacute sequelae of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection (non-PASC), and acute COVID-19 populations. The funnel plot and Egger's test were used to assess potential publication bias. Sensitivity analysis was used to test the stability of the results.

RESULTS

An increase in IL-6 levels was observed after SARS-CoV-2 infection. The pooled estimate of IL-6 revealed a mean value of 20.92 pg/ml (95% CI = 9.30-32.54 pg/ml, I² = 100%, P < 0.01) for long COVID-19 patients. The forest plot showed high levels of IL-6 for long COVID-19 compared with healthy controls (mean difference = 9.75 pg/ml, 95% CI = 5.75-13.75 pg/ml, I² = 100%, P < 0.00001) and PASC category (mean difference = 3.32 pg/ml, 95% CI = 0.22-6.42 pg/ml, I² = 88%, P = 0.04). The symmetry of the funnel plots was not obvious, and Egger's test showed that there was no significant small study effect in all groups.

CONCLUSIONS

This study showed that increased IL-6 correlates with long COVID-19. Such an informative revelation suggests IL-6 as a basic determinant to predict long COVID-19 or at least inform on the "early stage" of long COVID-19.

Tumour growth: An approach to calibrate parameters of a multiphase porous media model based on in vitro observations of Neuroblastoma spheroid growth in a hydrogel microenvironment

To unravel processes that lead to the growth of solid tumours, it is necessary to link knowledge of cancer biology with the physical properties of the tumour and its interaction with the surrounding microenvironment. Our understanding of the underlying mechanisms is however still imprecise. We therefore developed computational physics-based models, which incorporate the interaction of the tumour with its surroundings based on the theory of porous media. However, the experimental validation of such models represents a challenge to its clinical use as a prognostic tool. This study combines a physics-based model with in vitro experiments based on microfluidic devices used to mimic a three-dimensional tumour microenvironment. By conducting a global sensitivity analysis, we identify the most influential input parameters and infer their posterior distribution based on Bayesian calibration. The resulting probability density is in agreement with the scattering of the experimental data and thus validates the proposed workflow. This study demonstrates the huge challenges associated with determining precise parameters with usually only limited data for such complex processes and models, but also demonstrates in general how to indirectly characterise the mechanical properties of neuroblastoma spheroids that cannot feasibly be measured experimentally.

Using sensitivity analyses to understand bistable system behavior

BACKGROUND

Bistable systems, i.e., systems that exhibit two stable steady states, are of particular interest in biology. They can implement binary cellular decision making, e.g., in pathways for cellular differentiation and cell cycle regulation. The onset of cancer, prion diseases, and neurodegenerative diseases are known to be associated with malfunctioning bistable systems. Exploring and characterizing parameter spaces in bistable systems, so that they retain or lose bistability, is part of a lot of therapeutic research such as cancer pharmacology.

RESULTS

We use eigenvalue sensitivity analysis and stable state separation sensitivity analysis to understand bistable system behaviors, and to characterize the most sensitive parameters of a bistable system. While eigenvalue sensitivity analysis is an established technique in engineering disciplines, it has not been frequently used to study biological systems. We demonstrate the utility of these approaches on a published bistable system. We also illustrate scalability and generalizability of these methods to larger bistable systems.

CONCLUSIONS

Eigenvalue sensitivity analysis and separation sensitivity analysis prove to be promising tools to define parameter design rules to make switching decisions between either stable steady state of a bistable system and a corresponding monostable state after bifurcation. These rules were applied to the smallest two-component bistable system and results were validated analytically. We showed that with multiple parameter settings of the same bistable system, we can design switching to a desirable state to retain or lose bistability when the most sensitive parameter is varied according to our parameter perturbation recommendations. We propose eigenvalue and stable state separation sensitivity analyses as a framework to evaluate large and complex bistable systems.

Robust morris screening method (RMSM) for complex physiological models

BACKGROUND AND OBJECTIVES

Morris screening sensitivity analysis (MSM) comes forth as the method needing the minimum number of model simulations to qualify the impact of input parameter variations on outputs of complex, nonlinear and overparametrized models. However, the reliability of MSM indices (mean and standard deviation) and the reproducibility of their results are rarely explored despite the input parameter tuning/identification needs. In fact, these models, such those used in medical applications as digital twins, often lie in this category and need efficient and robust tools to assess both sensitivity and reliability of the outputs to numerous input model parameters.

METHODS

In this study, a new Robust Morris Screening Method (RMSM) is proposed and based on new indices: the absolute median (χ^*) and the median absolute deviation (ρ). The proposed RMSM approach is evaluated on a complex multi-scales neuromuscular electrophysiological model simulating HD-sEMG (high density surface electromyography) signals at the skin surface. The reliability and stability of new RMSM indicators are evaluated at different trajectories within the parameter space and compared to classical MSM results. For this purpose, We propose a new methodology for parameter screening based on the ratio ρ/χ^* as a graphic indicator of (non)linearity and (non)monotonicity of parameter effects.

RESULTS

Firstly, the results demonstrated that the computed elementary effects (EE) of inputs are not normally distributed using MSM indices contrary to the proposed RMSM indices. Secondly, the ranking stability of RMSM indices was earlier obtained from 20 trajectories (T=20), while MSM ranking remained unstable until T = 100. Thirdly, The screening separation between influential and negligible input model parameters was more distinct and interpretable with RMSM than MSM.

CONCLUSION

The proposed RMSM approach ensures a fast, reliable and stable ranking of parameters for complex and overparametrized models compared to classical MSM. this allows a more precise exploration of the model parameter influence space for future application in parameter tuning and identification.

Global sensitivity analysis based on Gaussian-process metamodelling for complex biomechanical problems

Biomechanical models often need to describe very complex systems, organs or diseases, and hence also include a large number of parameters. One of the attractive features of physics-based models is that in those models (most) parameters have a clear physical meaning. Nevertheless, the determination of these parameters is often very elaborate and costly and shows a large scatter within the population. Hence, it is essential to identify the most important parameters (worth the effort) for a particular problem at hand. In order to distinguish parameters which have a significant influence on a specific model output from non-influential parameters, we use sensitivity analysis, in particular the Sobol method as a global variance-based method. However, the Sobol method requires a large number of model evaluations, which is prohibitive for computationally expensive models. We therefore employ Gaussian processes as a metamodel for the underlying full model. Metamodelling introduces further uncertainty, which we also quantify. We demonstrate the approach by applying it to two different problems: nanoparticle-mediated drug delivery in a complex, multiphase tumour-growth model, and arterial growth and remodelling. Even relatively small numbers of evaluations of the full model suffice to identify the influential parameters in both cases and to separate them from non-influential parameters. The approach also allows the quantification of higher-order interaction effects. We thus show that a variance-based global sensitivity analysis is feasible for complex, computationally expensive biomechanical models. Different aspects of sensitivity analysis are covered including a transparent declaration of the uncertainties involved in the estimation process. Such a global sensitivity analysis not only helps to massively reduce costs for experimental determination of parameters but is also highly beneficial for inverse analysis of such complex models.

Vascular refilling coefficient is not a good marker of whole-body capillary hydraulic conductivity in hemodialysis patients: insights from a simulation study

Refilling of the vascular space through absorption of interstitial fluid by micro vessels is a crucial mechanism for maintaining hemodynamic stability during hemodialysis (HD) and allowing excess fluid to be removed from body tissues. The rate of vascular refilling depends on the imbalance between the Starling forces acting across the capillary walls as well as on their hydraulic conductivity and total surface area. Various approaches have been proposed to assess the vascular refilling process during HD, including the so-called refilling coefficient (Kr) that describes the rate of vascular refilling per changes in plasma oncotic pressure, assuming that other Starling forces and the flow of lymph remain constant during HD. Several studies have shown that Kr decreases exponentially during HD, which was attributed to a dialysis-induced decrease in the whole-body capillary hydraulic conductivity (L_pS). Here, we employ a lumped-parameter mathematical model of the cardiovascular system and water and solute transport between the main body fluid compartments to assess the impact of all Starling forces and the flow of lymph on vascular refilling during HD in order to explain the reasons behind the observed intradialytic decrease in Kr. We simulated several HD sessions in a virtual patient with different blood priming procedures, ultrafiltration rates, session durations, and constant or variable levels of L_pS. We show that the intradialytic decrease in Kr is not associated with a possible reduction of L_pS but results from the inherent assumption that plasma oncotic pressure is the only variable Starling force during HD, whereas in fact other Starling forces, in particular the oncotic pressure of the interstitial fluid, have an important impact on the transcapillary fluid exchange during HD. We conclude that Kr is not a good marker of L_pS and should not be used to guide fluid removal during HD or to assess the fluid status of dialysis patients.

Predictive Modelling in Clinical Bioinformatics: Key Concepts for Startups

Clinical bioinformatics is a newly emerging field that applies bioinformatics techniques for facilitating the identification of diseases, discovery of biomarkers, and therapy decision. Mathematical modelling is part of bioinformatics analysis pipelines and a fundamental step to extract clinical insights from genomes, transcriptomes and proteomes of patients. Often, the chosen modelling techniques relies on either statistical, machine learning or deterministic approaches. Research that combines bioinformatics with modelling techniques have been generating innovative biomedical technology, algorithms and models with biotech applications, attracting private investment to develop new business; however, startups that emerge from these technologies have been facing difficulties to implement clinical bioinformatics pipelines, protect their technology and generate profit. In this commentary, we discuss the main concepts that startups should know for enabling a successful application of predictive modelling in clinical bioinformatics. Here we will focus on key modelling concepts, provide some successful examples and briefly discuss the modelling framework choice. We also highlight some aspects to be taken into account for a successful implementation of cost-effective bioinformatics from a business perspective.

Effect of cognitive reserve on amnestic mild cognitive impairment due to Alzheimer’s disease defined by fluorodeoxyglucose-positron emission tomography

This study aimed to investigate the effect of cognitive reserve (CR) on the rate of cognitive decline and cerebral glucose metabolism in amnestic mild cognitive impairment (MCI) using the Study on Diagnosis of Early Alzheimer’s Disease-Japan (SEAD-J) dataset. The patients in SEAD-J underwent cognitive tests and fluorodeoxyglucose-positron emission tomography (FDG-PET). MCI to be studied was classified as amnestic MCI due to Alzheimer’s disease (AD) with neurodegeneration. A total of 57 patients were visually interpreted as having an AD pattern (P1 pattern, Silverman’s classification). The 57 individuals showing the P1 pattern were divided into a high-education group (years of school education ≥13, N = 18) and a low-education group (years of school education ≤12, N = 39). Voxel-based statistical parametric mapping revealed more severe hypometabolism in the high-education group than in the low-education group. Glucose metabolism in the hippocampus and temporoparietal area was inversely associated with the years of school education in the high- and low-education groups (N = 57). General linear mixed model analyses demonstrated that cognitive decline was more rapid in the high-education group during 3-year follow-up. These results suggest that the cerebral glucose metabolism is lower and cognitive function declines faster in patients with high CR of amnestic MCI due to AD defined by FDG-PET.

Differential methods for assessing sensitivity in biological models

Differential sensitivity analysis is indispensable in fitting parameters, understanding uncertainty, and forecasting the results of both thought and lab experiments. Although there are many methods currently available for performing differential sensitivity analysis of biological models, it can be difficult to determine which method is best suited for a particular model. In this paper, we explain a variety of differential sensitivity methods and assess their value in some typical biological models. First, we explain the mathematical basis for three numerical methods: adjoint sensitivity analysis, complex perturbation sensitivity analysis, and forward mode sensitivity analysis. We then carry out four instructive case studies. (a) The CARRGO model for tumor-immune interaction highlights the additional information that differential sensitivity analysis provides beyond traditional naive sensitivity methods, (b) the deterministic SIR model demonstrates the value of using second-order sensitivity in refining model predictions, (c) the stochastic SIR model shows how differential sensitivity can be attacked in stochastic modeling, and (d) a discrete birth-death-migration model illustrates how the complex perturbation method of differential sensitivity can be generalized to a broader range of biological models. Finally, we compare the speed, accuracy, and ease of use of these methods. We find that forward mode automatic differentiation has the quickest computational time, while the complex perturbation method is the simplest to implement and the most generalizable.

Modelling the performance of an integrated fixed-film activated sludge (IFAS) system: a systematic approach to automated calibration

IFAS systems are inherently complex due to the hybrid use of both suspended and attached bacterial colonies for the purpose of pollutant degradation as part of wastewater treatment. This poses challenges when attempting to represent these systems mathematically due to the vast number of parameters involved. Besides becoming convoluted, large effort will be incurred during model calibration. This paper demonstrates a systematic approach to calibration of an IFAS process model that incorporates two sensitivity analyses to identify influential parameters and detect collinearity from a subset of 68 kinetic and stoichiometric parameters, and the use of the Nelder–Mead optimization algorithm to estimate the required values of these parameters. The model considers the removal of three critical pollutants including biochemical oxygen demand (BOD), total nitrogen (TN) and total suspended solids (TSS). Results from the sensitivity analyses identified four parameters that were the primary influence on the model. The model was found to be most sensitive to the two stoichiometric parameters including aerobic heterotrophic yield on soluble substrate whose total effects were responsible for 92.4% of the model’s BOD output sensitivity and 92.8% of the model’s TSS output sensitivity. The anoxic heterotrophic yield on soluble substrate was observed to be responsible for 54.3% of the model’s TN output sensitivity. To a lesser extent the two kinetic parameters, aerobic heterotrophic decay rate and reduction factor for denitrification on nitrite, were responsible for only 8.0% and 13.1% of the model’s BOD and TN output sensitivities respectively. Parameter estimation identified the need for only minor adjustments to default values in order to achieve sufficient accuracy of simulation with deviation from observed data to be only ± 3.6 mg/L, ± 1.3 mg/L, and ± 9.5 mg/L for BOD, TN and TSS respectively. Validation showed the model was limited in its capacity to predict system behaviour under extreme dissolved oxygen stress.

The Spatiotemporal Characteristics of Water Quality and Main Controlling Factors of Algal Blooms in Tai Lake, China

Taking Tai Lake in China as the research area, a 3D water environment mathematical model was built. Combined with the LHS and Morris uncertainty and sensitivity analysis methods, the uncertainty and sensitivity analysis of total phosphorus (TP), total nitrogen (TN), dissolved oxygen (DO), and chlorophyll a (Chl-a) were carried out. The main conclusions are: (1) The performance assessment of the 3D water environment mathematical model is good (R2 and NSE > 0.8) and is suitable for water quality research in large shallow lakes. (2) The time uncertainty study proves that the variation range of Chl-a is much larger than that of the other three water quality parameters and is more severe in summer and autumn. (3) The spatial uncertainty study proves that Chl-a is mainly present in the northwest lake area (heavily polluted area) and the other three water quality indicators are mainly present in the center. (4) The sensitivity results show that the main controlling factors of DO are ters (0.15) and kmsc (0.12); those of TN and TP are tetn (0.58) and tetp (0.24); and those of Chl-a are its own growth rate (0.14), optimal growth temperature (0.12), death rate (0.12), optimal growth light (0.11), and TP uptake rate (0.11). Thus, TP control is still the key treatment method for algal blooms that can be implemented by the Chinese government.

Sensitivity Analysis of a Transmission Interruption Model for the Soil-Transmitted Helminth Infections in Kenya

As the world rallies toward the endgame of soil-transmitted helminths (STH) elimination by the year 2030, there is a need for efficient and robust mathematical models that would enable STH programme managers to target the scarce resources and interventions, increase treatment coverage among specific sub-groups of the population, and develop reliable surveillance systems that meet sensitivity and specificity requirements for the endgame of STH elimination. However, the considerable complexities often associated with STH-transmission models underpin the need for specifying a large number of parameters and inputs, which are often available with considerable degree of uncertainty. Additionally, the model may behave counter-intuitive especially when there are non-linearities in multiple input-output relationships. In this study, we performed a global sensitivity analysis (GSA), based on a variance decomposition method: extended Fourier Amplitude Sensitivity Test (eFAST), to a recently developed STH-transmission model in Kenya (an STH endemic country) to; (1) robustly compute sensitivity index (SI) for each parameter, (2) rank the parameters in order of their importance (from most to least influential), and (3) quantify the influence of each parameter, singly and cumulatively, on the model output. The sensitivity analysis (SA) results demonstrated that the model outcome (STH worm burden elimination in the human host) was significantly sensitive to some key parameter groupings: combined effect of improved water source and sanitation (ϕ), rounds of treatment offered (τ), efficacy of the drug used during treatment (h), proportion of the adult population treated (g_a: akin to community-wide treatment), mortality rate of the mature worms in the human host (μ), and the strength of the -dependence of worm egg production (γ). For STH control programmes to effectively reach the endgame (STH elimination in the entire community), these key parameter groupings need to be targeted since together they contribute to a strategic public health intervention.

A novel nonlocal partial differential equation model of endothelial progenitor cell cluster formation during the early stages of vasculogenesis

The formation of new vascular networks is essential for tissue development and regeneration, in addition to playing a key role in pathological settings such as ischemia and tumour development. Experimental findings in the past two decades have led to the identification of a new mechanism of neovascularisation, known as cluster-based vasculogenesis, during which endothelial progenitor cells (EPCs) mobilised from the bone marrow are capable of bridging distant vascular beds in a variety of hypoxic settings in vivo. This process is characterised by the formation of EPC clusters during its early stages and, while much progress has been made in identifying various mechanisms underlying cluster formation, we are still far from a comprehensive description of such spatio-temporal dynamics. In order to achieve this, we propose a novel mathematical model of the early stages of cluster-based vasculogenesis, comprising of a system of nonlocal partial differential equations including key mechanisms such as endogenous chemotaxis, matrix degradation, cell proliferation and cell-to-cell adhesion. We conduct a linear stability analysis on the system and solve the equations numerically. We then conduct a parametric analysis of the numerical solutions of the one-dimensional problem to investigate the role of underlying dynamics on the speed of cluster formation and the size of clusters, measured via appropriate metrics for the cluster width and compactness. We verify the key results of the parametric analysis with simulations of the two-dimensional problem. Our results, which qualitatively compare with data from in vitro experiments, elucidate the complementary role played by endogenous chemotaxis and matrix degradation in the formation of clusters, suggesting chemotaxis is responsible for the cluster topology while matrix degradation is responsible for the speed of cluster formation. Our results also indicate that the nonlocal cell-to-cell adhesion term in our model, even though it initially causes cells to aggregate, is not sufficient to ensure clusters are stable over long time periods. Consequently, new modelling strategies for cell-to-cell adhesion are required to stabilise in silico clusters. We end the paper with a thorough discussion of promising, fruitful future modelling and experimental research perspectives.

Understanding virtual patients efficiently and rigorously by combining machine learning with dynamical modelling

Individual biological organisms are characterized by daunting heterogeneity, which precludes describing or understanding populations of ‘patients’ with a single mathematical model. Recently, the field of quantitative systems pharmacology (QSP) has adopted the notion of virtual patients (VPs) to cope with this challenge. A typical population of VPs represents the behavior of a heterogeneous patient population with a distribution of parameter values over a mathematical model of fixed structure. Though this notion of VPs is a powerful tool to describe patients’ heterogeneity, the analysis and understanding of these VPs present new challenges to systems pharmacologists. Here, using a model of the hypothalamic–pituitary–adrenal axis, we show that an integrated pipeline that combines machine learning (ML) and bifurcation analysis can be used to effectively and efficiently analyse the behaviors observed in populations of VPs. Compared with local sensitivity analyses, ML allows us to capture and analyse the contributions of simultaneous changes of multiple model parameters. Following up with bifurcation analysis, we are able to provide rigorous mechanistic insight regarding the influences of ML-identified parameters on the dynamical system’s behaviors. In this work, we illustrate the utility of this pipeline and suggest that its wider adoption will facilitate the use of VPs in the practice of systems pharmacology.

An Inverse Problem Approach for Parameter Estimation of Cardiovascular System Models

Left ventricular assist devices (LVADs) are mechanical pumps that help patients with chronic heart failure waiting for a heart transplant. Mathematical models of these devices can be used along cardiovascular system (CVS) models to evaluate the assistance performance under different operating modes. The estimation of the CVS model parameters for a particular patient and numerical simulations allow the implementation of adequate LVAD operation mode. This work presents a method to estimate the parameters of a CVS model using only one hemodynamic variable: the systemic arterial pressure (P_s). Synthetic signals of P_s are used to solve this ill-posed inverse problem partially, and the results show the high accuracy of the proposed method, which achieves 0.5%.Clinical relevance- The measurements of hemodynamic variables using noninvasive techniques avoid many clinical problems arising from invasive measures such as infections.