Chromo-dynamic multi-component lattice Boltzmann equation scheme for axial symmetry

We validate the chromo-dynamic multi-component lattice Boltzmann equation (MCLBE) simulation for immiscible fluids with a density contrast against analytical results for complex flow geometries, with particular emphasis on the fundamentals of the method, i.e. compliance with inter-facial boundary conditions of continuum hydrodynamics. To achieve the necessary regimes for the chosen validations, we develop, from a three-dimensional, axially-symmetric flow formulation, a novel, two-dimensional, pseudo Cartesian, MCLBE scheme. This requires the inclusion in lattice Boltzmann methodology of a continuously distributed source and a velocity-dependent force density (here, the metric force terms of the cylindrical Navier–Stokes equations). Specifically, we apply our model to the problem of flow past a spherical liquid drop in Re = 0, Ca regime and, also, flow past a lightly deformed drop. The resulting simulation data, once corrected for the simulation’s inter-facial micro-current (using a method we also advance herein, based on freezing the phase field) show good agreement with theory over a small range of density contrasts. In particular, our data extend verified compliance with the kinematic condition from flat (Burgin et al 2019 Phys. Rev. E 100 043310) to the case of curved fluid–fluid interfaces. More generally, our results indicate a route to eliminate the influence of the inter-facial micro-current

Assessing input parameter hyperspace and parameter identifiability in a cardiovascular system model via sensitivity analysis

We aim to clarify our understanding of the process of state-space model input parameter identification, known, within the clinical context, as model personalisation. To do so, we apply reference sensitivity and identifiability techniques to a lumped parameter, single ventricle representation of the systemic circulation, chosen in view of its relative simplicity and prior art. We attempt to quantify the reliability of input parameter identifiability through the lens of 4 clinically relevant measurements and the attendant difficulty in personalising the model. In turn, this that we extend existing methods which combine both parameter influence and orthogonality, to global sensitivities. By examining different parameter sensitivity evaluation methodologies, we investigate the stability of optimal parameter subsets which are commonly used to aid clinical investigations. In order to perform the personalisation process, one must understand the complexity of the high dimensional input parameter hyperspace associated with this class of model. By utilising Sobol indices, we propose a domain-agnostic and intuitive approach. This involves varying the bounds of the input parameter space relative to the model’s base state. These investigations yield a pseudo-mapping of the input hyperspace, cementing our understanding of the role of identifiable input parameters in the state-space model. Our findings suggest a novel global methodology for input parameter identifiability and input hyperspace mapping, providing valuable insights into solving the personalisation process

Personalised parameter estimation of the cardiovascular system: Leveraging data assimilation and sensitivity analysis of the cardiovascular system: Leveraging data assimilation and sensitivity analysis of the cardiovascular system: Leveraging data assimilation and sensitivity analysis

Detailed models of dynamical systems used in the life sciences may include hundreds of state variables and many input parameters, often with physical meanings. Therefore, efficient and unique input parameter identification, from experimental data, is an essential but challenging task for this class of models. This study presents a comprehensive analysis of a nine-dimensional single ventricle lumped-parameter model, representing the systemic circulation. This model is formulated in terms of differential algebraic equations, often found in other areas of the life sciences. We introduce a novel computational algorithm designed to incorporate patient-specific beat-to-beat variability into model investigations, utilising the Unscented Kalman Filter (UKF) for efficient parameter estimation. Our findings demonstrate the exceptional adaptability of the UKF to severe parameter perturbations, representing significant physiological changes. Furthermore, we provide novel insights into the continuous sensitivity of model input parameters, illustrating the robustness and efficacy of UKF. The monitoring of a patient’s physiological state, with minimal delay, becomes feasible, by incorporating patient-specific measurements and leveraging the UKF. The workflow presented in this paper enables prompt identification of pathophysiological conditions and will improve patient care

P83 A pilot study to assess peak systolic velocity as a possible marker of atherosclerotic burden using ultrasound

Introduction: Ischemic heart disease (IHD) has been associated with lower peak systolic velocity (PSV) on penile Doppler measurements [1]. This study establishes whether carotid ultrasound (US) PSV was associated with computational fluid dynamics (CFD) outputs, which in turn may contribute to IHD pathogenesis. Methods: A sample of 57 subjects (with IHD: 27, without IHD: 30) had US velocity profiles (left- common carotid artery) determined between 10e12 equispaced points. Bezier curve fitting was used to fit the profile through the measured velocity points for a normalised diameter. PSV was correlated against CFD results such as wall shear stress (WSS) [2]. Difference in PSV between individuals with/without IHD was studied via t-test. Linear regression was carried out to see if peak systolic velocity was associated with CFD outputs. Any significant associations were analysed within stratified groups (with/without IHD). Results: PSV was significantly lower (p Z 0.042) in subjects with IHD (with IHD: 53.6 17.3 cm/s, without IHD: 62.8 16.1 cm/s). PSV was associated with carotid bulb average pressure drop (p < 0.001), area of average bulb WSS (<1 Pa: p Z 0.016, <2 Pa: p Z 0.006, <3 Pa: p Z 0.001). All the above associations remained significant in individuals with IHD (average bulb pressure drop: p Z 0.001, average bulb WSS (<1 Pa: p Z 0.013, <2 Pa: p Z 0.008, <3 Pa: p Z 0.003). In subjects without IHD, PSV was associated with only average bulb pressure drop (p Z 0.016). Conclusions: This study suggests that further work on PSV and its associations with CFD outputs is required in individuals with and without IHD in various vascular beds

New perspectives on sensitivity and identifiability analysis using the unscented kalman filter

Detailed dynamical systems' models used in the life sciences may include hundreds of state variables and many input parameters, often with physical meaning. Therefore, efficient and unique input parameter identification, from experimental data, is an essential but challenging task for this class of model. To clarify our understating of the process (which within a clinical context amounts to a personalisation), we utilise the computational methods of Unscented Kalman filtration (UKF), sensitivity and orthogonality analysis. We have applied these three techniques to a test-bench model of a single ventricle, coupled, via Ohmic valves, to a Compliance-Resistor-Compliance (CRC) Windkessel electrical analogue model of the systemic circulation, chosen in view of its relative simplicity, interpretability and prior art. Utilising an efficient, novel and real-time implementation of the UKF (Code available at https://github.com/H-Sax/CMSB-2023), we show how, counter-intuitively, input parameters are efficiently recovered from experimental data \emph{even if they are not sensitive parameters in the currently accepted sense}. This result (i) exposes potential limitations in the standard interpretation of what it means for an input parameter to be designated identifiable and (ii) suggests that the concepts of sensitivity and identifiability may have a weaker relationship than commonly thought - at least in the presence of an appropriate data set. We rationalise these observations. Practically, we present results which show the UKF to be an efficient method for assigning personalised input parameters from experimental data in real-time, which enhances the clinical significance of our approach

Chromodynamic multirelaxation-time lattice Boltzmann scheme for fluids with density difference

We develop, after Dellar ( P. J. Dellar, Phys. Rev. E. 65, 036309 (2002), J. Comput. Phys. 190, pp351 (2003)), a multiple-relaxation time (MRT), chromodynamic, multi-component lattice Boltzmann equation (MCLBE) scheme for simulation of isothermal, immiscible fluid flow with a density contrast. It is based on Lishchuk’s method (J. U. Brackbill, D. B. Kothe and C. Zemach, J. Comp. Phys. 100, 335-354 (1992), S. V. Lishchuk, C. M. Care and I. Halliday, Phys. Rev. E. 67(3), 036701(2), (2003)) and the segregation of d’Ortona et al. (U. D’Ortona, D. Salin, M. Cieplak, R. B. Rybka and J. R. Banavar Phys. Rev. E. 51, 3718, (1995)). We focus on fundamental model verifiability but do relate some of our data to that from previous approaches, due to Ba et al. (Y. Ba, H. Liu, Q. Li, Q. Kang and J. Sun, Phys. Rev. E 94, 023310 (2016)) and earlier Liu et al. (H. Liu, A. J. Valocchi and Q. Kang, Phys. Rev. E 85, 046309 (2012)), who pioneered large density difference chromodynamic MCLBE and showed the practical benefits of a MRT collision model. Specifically, we test the extent to which chromodynamic MCLBE MRT schemes comply with the kinematic condition of mutual impenetrability and the continuous traction condition by developing analytical benchmarking flows. We conclude that our data, taken with those of Ba et al., verify the utility of MRT chromodynamic MCLBE

Three-dimensional single framework multi-component lattice Boltzmann equation method for vesicle hydrodynamics

We develop a three dimensional immersed boundary chromodynamic multi-component lattice Boltzmann method capable of simulating vesicles, such as erythrocytes. The presented method is encapsulated in a single framework, where the application of the immersed boundary force in the automatically adaptive interfacial region results in correct vesicle behaviour. We also set-down a methodology for computing the principal curvatures of a surface in a three-dimensional, physical space which is defined solely in terms of its surface normal vectors. The benefits of such a model are its transparent methodology, stability at high levels of deformation, automatic-adaptive interface and potential for the simulation of many erythrocytes. We demonstrate the utility of the model by examining the steady state properties, as well as dynamical behaviour within shear flow. The stability of the method is highlighted through its handling of high deformations, as well as interaction with another vesicle

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