IFAC-PapersOnLine

The dynamics of gene regulatory networks are governed by intrinsic noise, stemming from the random nature of biochemical reactions, and by extrinsic noise, arising from fluctuations in cellular components and environmental conditions. Together, these sources can compromise the reliability of predictive computational models if not properly accounted for, and capturing both effects within a single framework remains a non-trivial task in computational biology. In this work, we propose an uncertainty quantification framework that addresses these two contributions jointly: intrinsic stochasticity is described through a partial integro-differential equation (PIDE) for the protein probability density function, whereas extrinsic noise is represented as parametric uncertainty in the kinetic parameters. The propagation of the uncertainty is carried out via an intrusive polynomial chaos expansion (PCE), in which the PCE coefficients are obtained from a stochastic Galerkin projection of the PIDE, yielding a coupled deterministic system that is solved with standard numerical methods. We illustrate the approach on a positive autoregulatory gene network with one and two uncertain kinetic parameters. The proposed approach accurately reproduces the mean, variance, and full protein probability density function, including the bimodal distributions, at a substantially lower computational cost.

Muscle regeneration relies on the coordinated activation of muscle stem cells, whose fate decisions are regulated by intracellular gene expression dynamics and intercellular coupling via the Notch-Dll1 signaling pathway. Central components of this regulatory network include the transcriptional repressor Hes1, its target gene Dll1, and the myogenic regulator MyoD. Experimental and theoretical studies have shown that proliferating muscle stem cells exhibit oscillatory dynamics of these molecules, whereas sustained expression is associated with differentiation. Here, we investigate the dynamics of a previously established delay differential equation model of two coupled muscle stem cells. Using linear stability analysis, we systematically characterize how model parameters affect the transition between stable and unstable steady states. In addition, numerical bifurcation analysis is employed to study the influence of intercellular coupling strength and delay on the system dynamics. Our analysis shows that continuous variation of the coupling delay induces repetitive changes in the stability of the steady state. However, this sensitivity towards the coupling delay is confined to a narrow region of parameter space and therefore requires a fine tuning of all other parameters. Beside the identification of parameter sets for in-phase and out-of-phase oscillations, we demonstrate the possibility of coexisting stable in-phase and out-of-phase oscillations, a dynamical feature that has not been reported previously. While oscillation periods are largely determined by intracellular regulatory mechanisms, oscillation amplitudes can be strongly modulated by intercellular coupling. These results provide new insight into how the intracellular network and intercellular communication interact to generate different collective dynamics.

Across metazoa, morphogen gradients differentially regulate gene expression and activate a spatially distinct program to specify body axis development. The Drosophila gap gene network, initiated by maternal morphogen Bicoid, is one of the most well-studied systems. Several regulatory interactions act synergistically to produce distinct gap gene expression patterns along the anterior-posterior (AP) axis of the blastoderm stage Drosophila embryo to ensure the proper segmentation of the larval and, eventually, adult stage fly. Several mathematical models have been proposed to summarize the interconnectivity of gap gene regulatory elements and predict expression in mutant systems. However, these models have not successfully predicted the gap gene expression profile over the entire AP axis. Here, we present an Enhancer Activity-informed Gap GEne Regulatory network (EAGER) model that incorporates enhancer activity-driven differential regulation along the AP axis, which successfully summarizes gap gene expression patterns over the entire AP axis. We validated the predictions of EAGER on Kr mutants and performed a comprehensive parametric sensitivity and identifiability analysis to evaluate the robustness of the EAGER model fits and predictions. We also propose a reduced version of the model, rEAGER, which identifies a minimal set of regulatory interactions and successfully summarizes the gap gene interactions over the entire AP axis. Our results suggest that the expression driven by individual enhancers must be accounted for in models of developmental pattern formation.

Kinetic parameters in engineered biomolecular circuits are typically known only within intervals and are not precisely tunable; controller synthesis is therefore naturally posed over sets of gains rather than at a single nominal design. We formulate robust controller tuning under parametric plant uncertainty as a universally quantified set-inversion problem: given a plant-parameter box, compute the controller gains that stabilize every plant in the box. Robust stability is decided by Hurwitz sign conditions, which are bounded over the joint gain-parameter domain using validated range enclosures, yielding machine-checkable certificates of local exponential stability of the deterministic equilibrium. Numerical experiments show that the certified region depends strongly on the range enclosure. For an antithetic integral feedback (AIF) controller acting on a two-species gene-expression cascade, a tensor-product Bernstein enclosure certifies 83.2% of the design plane at bisection tolerance epsilon=0.05 with 324 terminal boxes, whereas four baseline enclosures certify between 50.9% and 58.9% on the same paving. For a fifth-order loop, the certified fraction increases from 34.4% to 73.8%, and the certified and excluded terminal boxes confine the robustly stabilizing area to a window of about 2.1 percentage points. Finally, for a refining variant of the algorithm in which the plant box is refined alongside the design box, the undecided area satisfies |U(epsilon)|=O(epsilon) under a non-degeneracy assumption on the stability boundary.

One goal of Scientific Machine Learning (SciML) is to advance traditional scientific computing frameworks with modern machine learning tools. This includes extending established methods, such as the finite element method, with cardiac function applications due to their complexity and need for very rapid execution times for real time clinical use. In this work, we present an advanced form of the Neural Network Finite Element (NNFE) method specialized for cardiac simulations, termed CARDIAX-NNFE. The NNFE method learns the parameter-to-displacement field map by training over the residual of the hyperelastic material PDE, using the domain represented by finite elements. The implementation is developed in Python using JAX to leverage its automatic differentiation, highly parallel GPU, and JIT-compilation capabilities. To demonstrate CARDIAX-NNFE effectiveness, we trained full cardiac pressure-volume responses using a simplified heart model, spanning the entire cardiac physiological functional range. Results indicated the ability to simulate a family of pressure-volume solutions with average nodal positional error of 0.023 mm and maximal error of 0.054 mm, with a single complete PV loop evaluated in 0.002 seconds. The CARDIAX-NNFE software platform thus provides for a robust platform for cardiac functional simulations. Moreover, it provides the structure for residual-based SciML methods, which can apply to a variety of physics-based biomedical problems that require high execution speed for clinical applications.

Oscillatory and saturating dynamics in regulatory gene networks govern processes such as cell cycle timing, circadian rhythms, and inflammatory signaling, and sparse regression methods such as SINDy offer an interpretable method for recovering their governing equations from time-series data. However, these networks are typically governed by Hill-type nonlinearities that become nearly collinear with polynomial candidates over most bounds of an oscillating curve, and placing them in a shared library produces ill-conditioned regressions and unreliable coefficient estimates. Standard approaches such as ridge regularization, library normalization, and orthogonalization can marginally improve conditioning but cannot remove the structural multicollinearity of these systems, in turn limiting our ability to produce accurate parameter estimates. To address this issue, we propose the Regulation-Informed Sparse Identification of Nonlinear Dynamics (RI-SINDy) method, which removes known regulatory terms from the regression and recovers their coefficients directly from an asymptotic drift-balance condition. Because the time averaged derivative of a bounded trajectory approaches zero, the coefficients of regulatory nonlinearities can be computed independently by constraining them to offset the mean contribution of the remaining terms. We demonstrate that this method effectively reduces library collinearity and improves conditioning numbers by 3-45x, substantially improving coefficient recovery and regression accuracy. We test the RI-SINDy method on experimental Hes1 data and on synthetic Goodwin and NF-{kappa}B models. On Hes1, it achieves the lowest trajectory error among the compared methods (Traditional SINDy, SR3, and Nullcline Reconstruction). On the synthetic systems, it recovers the correct sparse structure with lower trajectory error than SR3 and Nullcline Reconstruction, and in a Goodwin noise sweep it recovers all active terms at noise levels up to 15%, where Traditional SINDy and E-SINDy fail to. In conclusion, the RI-SINDy method provides a robust framework to overcome the issue of multicollinearity for system identification in biological systems.

Biochemical Systems Theory (BST) represents nonlinear biochemical rate laws by local power-law approximations in logarithmic concentration coordinates. First-order coefficients are elasticities, whereas higher-order derivatives describe local log-synergism and its variation. Ordinary higher derivatives, however, are not tensorial under nonlinear reparameterizations and can mix biochemical response structure with coordinate artifacts. We formulate a covariant hierarchy, cBST1-cBST3, on a positive operating-point space equipped with a declared reference connection. cBST1 recovers classical elasticities in a flat logarithmic chart, cBST2 is the covariant Hessian of the log-response, and cBST3 is the symmetrized covariant derivative of cBST2. The framework is quantitatively evaluated using three representative rate laws from the curated yeast glycolysis model BIOMD0000000064: glucose transport, glucose phosphorylation, and phosphofructokinase. For 10,000 finite log-concentration perturbations at each of five radii, cBST2 reduced the cBST1 log-rate root-mean-square error by 96.6-98.6% at the largest tested radius, and cBST3 provided a further 68.4-98.1% reduction. The contracted cBST2 and cBST3 terms strongly predicted the corresponding lower-order truncation errors. Under the nonlinear transformation qi = sinh(ui), covariant contractions agreed across coordinates to within a 95th-percentile relative error of 1.2 x 10-13, whereas ordinary higher derivatives showed order-unity coordinate mismatches. Supplementary analytic tests recovered the expected second-, third-, and fourth-order truncation-error scaling. These results show that cBST1-cBST3 are not only coordinate-consistent descriptors but also practical diagnostics of where local power-law approximations require higher-order correction.

Recent models describe drug release from polymeric nanoparticles through an analogy with the quantum tunneling effect, treating the delivery system as a static rectangular potential barrier. In this work, we argue that this analogy is structurally identical to the standard solution of the Schrodinger equation for a rectangular barrier, and that the introduction of a multifractal formalism to describe time evolution -- obtained via a formal Wick rotation (x [->] t) -- lacks direct physical justification. We propose, instead, to treat the barrier height as an effective function of time, Ueff(t) = U0 f(t), with f(t) varying slowly within the barrier region, reflecting the progressive degradation/swelling of the polymeric matrix, under two hypotheses for f(t)-- exponential decay and rational decay (Hill-type). Rather than the thick-barrier WKB approximation, the exact transmission formula is used throughout, which is real-analytic in f(t) and continues smoothly into the resonance (over-barrier) regime once the barrier collapses, avoiding the artificial step-like transitions produced by the WKB approximation used in earlier drafts of this work. Both hypotheses for f(t) predict a finite barrier collapse time, t*, whose dependence on the energy ratio m = U0/E differs qualitatively between them (t* {propto}ln m vs. t* {propto}(m-1)1/n), offering a distinguishable criterion from experimental release data. The model was tested against ex-vivo chicken-skin permeation kinetics of 5-FU digitized from Rata et al. [1] (three systems: NCA-1-5-FU, G-NCA-1-5-FU, G-5-FU). The exact formula substantially improved fit quality relative to the WKB approximation for all three systems. Fits were obtained by global optimization (differential evolution, polished with scipy.optimize.curve_fit for covariance estimates) rather than a single local search, which proved necessary: for G-5-FU and NCA-1-5-FU, the exponential family is well-identified (all parameter uncertainties below 11% and 6% of the estimates, respectively; R2 > 0.999), while the rational (Hill) family remained poorly identified for all three systems despite the improved formula - favoring, by parsimony, the simpler exponential model throughout. Only G-NCA-1-5-FU remained non-identified with m free. A sensitivity check fixing m at the G-5-FU-derived value (m = 1.377) resolves this non-identifiability for G-NCA-1-5-FU at negligible cost in fit quality, consistent with a shared energy ratio for that system; the same constraint applied to NCA-1-5-FU, however, degrades its (already well-identified) fit by a factor of [~]4 in maximum residual; its own energy ratio (m = 1.188 {+/-} 0.007) differs from the shared value by [~]4{sigma}, a formally significant difference, so a single universal m is rejected for the complete set of systems studied. Reference values from the original multifractal study [2-4] and candidate extensions to further aptamer-functionalized nanocarrier systems [5-7] are also discussed. We discuss the implications of this treatment and its limits of validity, and point out paths for further empirical validation.

Cancer survival rates increase with earlier diagnosis. However, many cancers are diagnosed only after symptoms develop, in the later stages of cancer progression. We need a diagnostic tool that can detect cancer earlier. Circulating tumour cells (CTCs) are cells that detach from the main tumour and can enter the bloodstream. The capture and analysis of CTCs can provide an early indicator of cancer. However, rarity of CTCs in blood makes their efficient capture challenging. Inertial microfluidics can be utilised for a label-free separation of CTCs from white blood cells (WBCs) by manipulating cells in the microchannel based on cell properties, achieving good separation performance. Inertial microfluidic devices mainly rely on size-based separation. However, residual WBC carryover limits complete separation. Here, we show that cell mechanical heterogeneity plays a large role in the separation process and should be considered in the design of these devices. We simulate the migration dynamics of CTCs and WBCs in a straight microchannel using a 3D lattice-Boltzmann-immersed-boundary-finite-element solver. Our results demonstrate that WBC migration behaviour changes depending on the deformability of a CTC. The size and deformability of the cells have been shown to determine the cell-specific heteroclinic orbits leading to different interaction types, these interactions alter WBC migration resulting in more/less WBC carryover. This work highlights that both cell-specific heteroclinic orbits and single cell migration rates should be considered in the design of inertial microfluidics for separation.

Immune checkpoint blockade (ICB) therapy has revolutionized cancer treatment, though it is still effective in only about 20-40% of patients. To increase the efficacy of ICB therapy, combinations of ICB antibodies such as anti-PD1 and anticoagulants (e.g., thrombin inhibitors) have been studied in preclinical mouse models and clinical trials. We developed a Bliss-type analysis to quantify the synergy between anti-PD1 and dabigatran etexilate using published tumor growth data from a mouse model. We then developed a minimal mechanistic computational model to quantitatively study the synergy between anti-PD1 and the thrombin inhibitor dabigatran etexilate in a published study (Metelli et al.) of a preclinical mouse model of colon cancer. Our model included tumor cells, CD8+ T cells, and the pleiotropic cytokine TGF{beta}, whose production in platelets is influenced by thrombin, and described a potential mechanism of interplay among these components in the tumor microenvironment. We performed nonlinear mixed-effects modeling to capture mouse-to-mouse variation in tumor growth under different treatment conditions. The estimated parameter values pointed to several underlying mechanisms of synergy, including increased expansion of CD8+ T cells in the tumor microenvironment in the presence of anti-PD1 and dabigatran etexilate. These predictions can be further validated in future experiments. Thus, the combination of longitudinal tumor growth data, mechanistic population dynamics modeling, and nonlinear mixed-effects modeling can be used to study synergy between ICB and other drugs in controlling tumor growth.

Marker-based optical motion capture remains the gold standard for kinematic analysis across biomechanical research. However, when tracking dynamic movements, severe occlusions often create missing data and noisy signals that require time-consuming manual cleaning. Existing automated methods usually rely on predefined skeleton models or need massive training datasets for machine learning solutions. This study presents the AMP: an automated marker based motion capture processing pipeline. The AMP is a fully analytical approach that uses hierarchical algorithms including 1) rigid-body constraint, 2) Kalman Filter state estimation and 3) kinematic pattern match to label markers and fill data gaps without manual human intervention. First, the algorithm identifies and removes mislabeling markers before any data scrubbing. During the data cleaning process, our hierarchical algorithm uses a translation-based step to track segments even when there are insufficient donor markers to form a full rigid body. To reconstruct missing marker trajectories, the pipeline initially uses Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) interpolation for short marker gaps. However, the PCHIP creates massive spatial errors during long occlusions, the system automatically switches to rigid-body tracking for gaps over 40 ms. Results showed the pipeline drastically reduced processing time compared to manual human expert methods by 73.5%. In addition, the AMP kept spatial errors within 10 mm of the manual ground truth. By using this combined hierarchical approach to match marker processing accuracy, the pipeline provides a fast, general-purpose tool that fully automates data cleaning and saves hours of manual effort.

Multiview data analysis has become increasingly important for integrating heterogeneous information from multiple data sources. Cooperative learning provides a flexible framework for multiview integration by bridging early and late fusion strategies. However, its use of squared loss makes it sensitive to outliers. In this study, we propose robust cooperative learning based on the soft-IPOD framework. The proposed method introduces an observation-specific outlier absorption vector into the cooperative learning objective, thereby reducing the influence of outlying observations while preserving information sharing across views. The resulting optimization problem can be formulated as a weighted Lasso-type problem using an augmented design matrix and can be naturally extended to more than two data views. Numerical simulations and a real-data application to labor onset prediction demonstrate the predictive performance of the proposed method in the presence of outliers.

Analytical technologies that can provide quick, precise, and continuous information regarding process performance are necessary for the development of biopharmaceutical manufacturing. Conventional bioprocess monitoring is largely dependent on laboratory-based data and offline sampling, which can restrict process management and cause delays in decision-making. This study develops a machine learning-enabled Raman spectroscopy framework for Process Analytical Technology (PAT) and Real-Time Release Testing (RTRT) applications in bioprocess manufacturing. Five predictive modeling techniques--Partial Least Squares (PLS) regression, Support Vector Regression (SVR), Random Forest, Extreme Gradient Boosting (XGBoost), and Neural Networks--were used to analyze Raman spectral data from an Escherichia coli fermentation dataset. The models were assessed using the coefficient of determination (R{superscript 2}), root mean square error (RMSE), and mean absolute error (MAE) to predict two crucial fermentation parameters: the concentrations of glucose and acetate. The superior performance of PLS regression for glucose prediction and the improved prediction accuracy of XGBoost for acetate concentration demonstrated the importance of selecting modeling techniques based on biological complexity. Explainable artificial intelligence using SHAP analysis was incorporated to improve model transparency by identifying Raman spectral regions contributing to predictions. The suggested architecture shows how Raman spectroscopy and machine learning can be combined to assist automated process monitoring, enhance process comprehension, and hasten the implementation of real-time quality judgments in next-generation biomanufacturing. Graphical Abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=114 SRC="FIGDIR/small/740653v1_ufig1.gif" ALT="Figure 1"> View larger version (51K): org.highwire.dtl.DTLVardef@6a460aorg.highwire.dtl.DTLVardef@11c68e5org.highwire.dtl.DTLVardef@2acf7aorg.highwire.dtl.DTLVardef@9b890a_HPS_FORMAT_FIGEXP M_FIG C_FIG Overall workflow of the Raman spectroscopy-based machine learning framework for PAT and RTRT implementation. Raman spectra collected from E. coli fermentation were preprocessed and analyzed using multiple machine learning algorithms for the prediction of glucose and acetate concentrations. Model performance evaluation and SHAP-based explainable AI analysis enabled the identification of important spectral features for real-time bioprocess monitoring. HighlightsO_LIDeveloped a Raman spectroscopy-based machine learning framework for real-time monitoring of critical bioprocess parameters. C_LIO_LICompared traditional chemometric modeling (PLS regression) with advanced machine learning approaches, including SVR, Random Forest, XGBoost, and neural networks. C_LIO_LIShowed that the biochemical target affects the models performance, with XGBoost improving acetate prediction and PLS offering better glucose prediction. C_LIO_LIIntegrated explainable artificial intelligence to identify Raman spectral regions contributing to bioprocess predictions. C_LIO_LIEstablished a pathway toward interpretable Raman-based Process Analytical Technology (PAT) and Real-Time Release Testing (RTRT) implementation. C_LI

Musculoskeletal simulations are widely used to estimate joint loading, yet most musculoskeletal models estimate knee contact forces as resultant forces or as normal medial and lateral contact forces, without resolving pressure distributions across the articular surfaces. This paper presents a smoothed mesh-based knee contact pressure model that computes continuously differentiable tibiofemoral contact pressures, enabling its direct integration into full-body movement simulations. Built on an elastic foundation formulation, the model introduces smooth approximations ensuring that all contact functions and their derivatives remain continuous throughout the simulation. A systematic sensitivity analysis was performed across five key parameters: mesh resolution, joint damping and three smoothing parameters. Tracking simulations across eight gait trials demonstrated that the nominal configuration achieved mean RMSE values for medial and lateral knee contact forces of 51.6 N and 75.2 N, respectively, with a mean RMSE for joint angles of 1.45{degrees} and (r = 0.97), converging in less than three hours on a standard computer. Mesh resolution was identified as the dominant factor that affected both accuracy and convergence, while damping variations had negligible influence. As a proof of concept, the model was also incorporated into predictive simulations, demonstrating that increasing the weight on the contact pressure term in the cost function leads to reduced tibiofemoral loading, particularly in the lateral compartment. The proposed formulation provides a computationally efficient and numerically robust framework for simulating knee contact mechanics within full-body musculoskeletal models.

Planning husbandry tasks and experiments with Drosophila melanogaster requires converting a target date into development times that depend on the rearing temperature. This calculation needs to be done for each cross, genotype, and temperature, and the risk of error grows quickly. Available laboratory management tools let users register stocks, crosses, and track them, but they do not create schedules based on a clear, adjustable thermal model. To fill that gap, we developed DrosoTracker, a self-contained web application that works offline and predicts Drosophila development with a thermal summation model recalibrated through regression on data from Powsner (1935) (T0 = 11.78 {degrees}C, DD = 116.38 {degrees}C{middle dot}days, R{superscript 2} = 0.997). The model offers an optional two-level calibration driven by user observations. A wild-type strain first adjusts the model to the laboratorys own conditions. Then each genotype is calibrated against that reference using a random-effects shrinkage estimator that accounts for measurement error and between-batch variability. The model creates schedules for husbandry tasks, evaluates adult cohort survival with the Kaplan-Meier estimator and the log-rank test, and calculates sample size for lifespan studies using Schoenfelds formula. The quantitative components were checked against independent references, including Rs survival package and manual calculations. Ongoing work is focused on validating the calibrated model using cohorts specifically bred for this purpose. DrosoTracker runs entirely in the browser, stores data locally, and is available in English and Spanish.

Despite the use of technological countermeasures, studies show that the sensory conflict, and thus symptoms of motion sickness such as nausea, cannot be completely prevented while traveling as a car passenger. Accordingly, reliable prediction of motion sickness will represent a possible solution for intelligent vehicles to avoid the abortion of the drive, e.g., through adapted driving strategies or route planning. In previous works, the authors were able to demonstrate an application-oriented parameter set for the popular 6DOF-SVC model to estimate motion sickness incidence (MSI) in passengers with a lowered gaze on a non-driving-related task. In the current study, these parameters were validated and further optimized using five previous conducted motion sickness driving experiments. For the first time, it is also shown that the expected natural MSI fluctuations based on the driving dynamic profile, due to route characteristics or driving style, as well as the variation in experimental determined MSI is approximately 10%. Moreover, findings indicate that the participants appear to have an individual MSI threshold that correlates with their susceptibility to motion sickness, however, this threshold fluctuates too strongly across experiments to be suitable for practical application. As a result, the model can successfully estimate motion sickness risk across the test tracks, however, inaccuracies in the predicted MSI trajectories remain.

Vector flow mapping (VFM) reconstructs left-ventricular (LV) blood velocity from color-Doppler echocardiography by combining the measured beamwise component with physical and regularizing constraints. Analysis of the discrete VFM formulation shows that the inverse problem is intrinsically ill posed: the occurrence of singular modes can be predicted from the geometry of the segmented blood-pool domain, the imposed boundary conditions, and the degree of smoothing. These modes can propagate uncertainty along entire transverse bands of the reconstructed velocity field, yet conventional VFM neither quantifies this uncertainty nor allows for correcting the blood-pool segmentation. We introduce Bayesian VFM (B--VFM), a hierarchical framework that jointly infers radial and transverse velocities, a probabilistic blood-pool mask, their spatially resolved uncertainties, and hyperparameters weighting Doppler and segmentation fidelity, mass conservation, boundary conditions, and smoothness. The discretized posterior admits a closed-form gradient and exact Hessian, enabling computationally efficient, gradient-based MAP estimation, sampling, and direct analysis of ill-posed modes. Posterior inference combines Gibbs sampling of conjugate Gamma-distributed hyperparameters with conditional maximum-a-posteriori estimation and a Laplace approximation for the high-dimensional velocity and mask fields. To accommodate systematic departures from planar mass conservation, B-VFM can learn the covariance of the planar divergence residual from an ensemble of flows and incorporate it as a structured model-discrepancy prior. Independent chains converged reproducibly, while covariance priors learned from flow ensembles illustrated how model discrepancies can be incorporated into the inference. B--VFM was evaluated using Lamb-Chaplygin dipoles under ideal conditions and with Doppler corruption, Doppler voids, and segmentation defects, and using the Hicks-Moffatt family of spherical vortices to assess violations of planar mass conservation. The method produced smooth reconstructions, localized uncertainty near unreliable measurements and regions of model inconsistency, and used flow information to correct segmentation errors. Within the tested vortex family, the data-informed planar divergence prior reduced velocity bias and mask distortion. B--VFM thus provides an uncertainty-aware reconstruction method and a flexible foundation for future VFM formulations incorporating additional priors, observations, and physical models. Future work will evaluate the method using clinical data and more complex three-dimensional benchmark flows.

Moment-closure methods provide a widely used approach for approximating low-order statistics of stochastic biochemical reaction networks, but the resulting closed equations may exhibit physically meaningless dynamics. Here, we systematically investigate the stability of second-order moment-closure approximations for a bursty gene expression model with nonlinear protein degradation. We consider the Gaussian, log-normal, and negative-binomial closures. By analyzing the resulting dynamical systems, we show that the Gaussian closure fails the proposed stability criterion for all parameter values, whereas both the log-normal and negative-binomial closures possess a unique physically accessible fixed point and are stable if and only if kB(1 + 2B) [≥] 1, where B is the mean burst size and k is the dimensionless protein synthesis rate. Moreover, this condition is automatically satisfied when the steady-state mean protein copy number is at least one, suggesting that it is mild in biologically relevant regimes. Numerical comparisons over a broad parameter range further show that the negative-binomial closure is the most accurate, while the Gaussian closure is the least accurate. We further develop higher-order negative-binomial moment-closure schemes and demonstrate that increasing the closure order substantially improves predictive accuracy. These results highlight the importance of considering dynamical stability, in addition to numerical accuracy, when assessing moment-closure approximations.

The chick embryo is a widely used vertebrate model for developmental biology, cardiovascular, and bioengineering research. We present an automated laser speckle contrast imaging (LSCI) platform for non-invasive, longitudinal, label-free imaging of the developing heart and extraembryonic vasculature of the chick embryo through the intact eggshell. The platform can detect blood vessels as small as 70 +/- 17 um in diameter and enable repeated imaging from day 0 to day 8 of incubation without disturbing normal embryonic development. It provides both structural (a map of growing extraembryonic blood vessels) and functional (blood flow dynamics and heart rate) information. Using this system, we generated the first continuous, non-invasive, time-lapse recordings of the early functioning chick heart and its extraembryonic vessels. Longitudinal imaging was performed on 15 embryos from different chicken breeds with eggshell colors white, brown and green. Analysis revealed slight variability in early cardiac and vascular morphogenesis across breeds and shell types and shows its potential for automated developmental staging. Finally, for the first time, the growing vasculature of the yolk sac and the chorioallantoic (CAM) membrane was imaged from day 4 to 8. The heart rate and growth of the extraembryonic blood vessels were quantified automatically during imaging.

Microbial fuel cells (MFCs) have been widely investigated as decentralized bioelectrochemical systems capable of converting organic substrates into electricity. However, their long-term autonomous operation is constrained by substrate depletion in the anode compartment, leading to metabolic starvation of electroactive biofilms and a decline in power output. Conventional MFC design treats substrate crossover through the membrane separator as a parasitic loss that reduces coulombic efficiency. In this work, we propose a conceptual inversion of this paradigm by considering controlled cathodic-to-anodic substrate crossover as a passive mechanism to sustain basal microbial metabolism during periods of substrate scarcity. A transport-reaction framework is developed to quantify the balance between membrane-mediated substrate flux and microbial maintenance demand within the anode biofilm. Based on this balance, a dimensionless maintenance crossover Damkohler number (Dam) is introduced to define three operational regimes: starvation-dominated (Dam >> 1), balanced autonomous (Dam {approx} 1), and crossover-dominated (Dam << 1). The framework integrates membrane transport theory with biofilm kinetics to evaluate the effects of separator properties, substrate gradients, and current-dependent electro-osmotic transport on system stability. Order-of-magnitude analysis indicates that achievable crossover fluxes span several orders of magnitude depending on separator characteristics, suggesting that membrane properties critically influence system behavior. This perspective reframes substrate crossover from a loss mechanism to a potential design variable, offering a conceptual tool for enhancing resilience and guiding separator selection in MFCs intended for long-duration, and low-maintenance operation. HighlightsO_LIControlled crossover can sustain microbial metabolism in MFCs C_LIO_LIIntroduces maintenance crossover Damkohler number (Dam) C_LIO_LIIdentifies regimes for autonomous and starvation operation C_LIO_LILinks membrane properties to long-term system stability C_LIO_LIReframes crossover as a design variable, not only a loss C_LI