Bond Graph Model of Cerebral Circulation: Toward Clinically Feasible Systemic Blood Flow Simulations

An arteriovenous mock circulatory loop and accompanying bond graph model for in vitro study of peripheral intravascular bioartificial organs

BACKGROUND

Silicon nanopore membrane-based implantable bioartificial organs are dependent on arteriovenous implantation of a mechanically robust and biocompatible hemofilter. The hemofilter acts as a low-resistance, high-flow network, with blood flow physiology similar to arteriovenous shunts commonly created for hemodialysis access. A mock circulatory loop (MCL) that mimics shunt physiology is an essential tool for refinement and durability testing of arteriovenous implantable bioartificial organs and silicon blood-interfacing membranes. We sought to develop a compact and cost-effective MCL to replicate flow conditions through an arteriovenous shunt and used data from the MCL and swine to inform a bond graph mathematical model of the physical setup.

METHODS

Flow physiology through bioartificial organ prototypes was obtained in the MCL and during extracorporeal attachment to swine for biologic comparison. The MCL was tested for stability overtime by measuring pressurewave variability over a 48-h period. Data obtained in vitro and extracorporeally informed creation of a bond graph model of the MCL.

RESULTS

The arteriovenous MCL was a cost-effective, portable system that reproduced flow rates and pressures consistent with a pulsatile arteriovenous shunt as measured in swine. MCL performance was stable over prolonged use, providing a cost-effective simulator for enhanced testing of peripherally implanted bioartificial organ prototypes. The corresponding bond graph model recapitulates MCL and animal physiology, offering a tool for further refinement of the MCL system.

Computational fluid dynamic modeling of the lymphatic system: a review of existing models and future directions

Historically, research into the lymphatic system has been overlooked due to both a lack of knowledge and limited recognition of its importance. In the last decade however, lymphatic research has gained substantial momentum and has included the development of a variety of computational models to aid understanding of this complex system. This article reviews existing computational fluid dynamic models of the lymphatics covering each structural component including the initial lymphatics, pre-collecting and collecting vessels, and lymph nodes. This is followed by a summary of limitations and gaps in existing computational models and reasons that development in this field has been hindered to date. Over the next decade, efforts to further characterize lymphatic anatomy and physiology are anticipated to provide key data to further inform and validate lymphatic fluid dynamic models. Development of more comprehensive multiscale- and multi-physics computational models has the potential to significantly enhance the understanding of lymphatic function in both health and disease.

BondGraphs.jl: composable energy-based modelling in systems biology

SUMMARY

BondGraphs.jl is a Julia implementation of bond graphs. Bond graphs provide a modelling framework that describes energy flow through a physical system and by construction enforce thermodynamic constraints. The framework is widely used in engineering and has recently been shown to be a powerful approach for modelling biology. Models are mutable, hierarchical, multiscale, and multiphysics, and BondGraphs.jl is compatible with the Julia modelling ecosystem.

AVAILABILITY AND IMPLEMENTATION

BondGraphs.jl is freely available under the MIT license. Source code and documentation can be found at https://github.com/jedforrest/BondGraphs.jl.

In silico modeling for the hepatic circulation and transport: From the liver organ to lobules

The function of the liver depends critically on its blood supply. Numerous in silico models have been developed to study various aspects of the hepatic circulation, including not only the macro-hemodynamics at the organ level, but also the microcirculation at the lobular level. In addition, computational models of blood flow and bile flow have been used to study the transport, metabolism, and clearance of drugs in pharmacokinetic studies. These in silico models aim to provide insights into the liver organ function under both healthy and diseased states, and to assist quantitative analysis for surgical planning and postsurgery treatment. The purpose of this review is to provide an update on state-of-the-art in silico models of the hepatic circulation and transport processes. We introduce the numerical methods and the physiological background of these models. We also discuss multiscale frameworks that have been proposed for the liver, and their linkage with the large context of systems biology, systems pharmacology, and the Physiome project. This article is categorized under: Metabolic Diseases > Computational Models Metabolic Diseases > Biomedical Engineering Cardiovascular Diseases > Computational Models.

Automated model calibration with parallel MCMC: Applications for a cardiovascular system model

Computational physiological models continue to increase in complexity, however, the task of efficiently calibrating the model to available clinical data remains a significant challenge. One part of this challenge is associated with long calibration times, which present a barrier for the routine application of model-based prediction in clinical practice. Another aspect of this challenge is the limited available data for the unique calibration of complex models. Therefore, to calibrate a patient-specific model, it may be beneficial to verify that task-specific model predictions have acceptable uncertainty, rather than requiring all parameters to be uniquely identified. We have developed a pipeline that reduces the set of fitting parameters to make them structurally identifiable and to improve the efficiency of a subsequent Markov Chain Monte Carlo (MCMC) analysis. MCMC was used to find the optimal parameter values and to determine the confidence interval of a task-specific prediction. This approach was demonstrated on numerical experiments where a lumped parameter model of the cardiovascular system was calibrated to brachial artery cuff pressure, echocardiogram volume measurements, and synthetic cerebral blood flow data that approximates what can be obtained from 4D-flow MRI data. This pipeline provides a cerebral arterial pressure prediction that may be useful for determining the risk of hemorrhagic stroke. For a set of three patients, this pipeline successfully reduced the parameter set of a cardiovascular system model from 12 parameters to 8–10 structurally identifiable parameters. This enabled a significant (>4×) efficiency improvement in determining confidence intervals on predictions of pressure compared to performing a naive MCMC analysis with the full parameter set. This demonstrates the potential that the proposed pipeline has in helping address one of the key challenges preventing clinical application of such models. Additionally, for each patient, the MCMC approach yielded a 95% confidence interval on systolic blood pressure prediction in the middle cerebral artery smaller than ±10 mmHg (±1.3 kPa). The proposed pipeline exploits available high-performance computing parallelism to allow straightforward automation for general models and arbitrary data sets, enabling automated calibration of a parameter set that is specific to the available clinical data with minimal user interaction.

Energy-based advection modelling using bond graphs

Advection, the transport of a substance by the flow of a fluid, is a key process in biological systems. The energy-based bond graph approach to modelling chemical transformation within reaction networks is extended to include transport and thus advection. The approach is illustrated using a simple model of advection via circulating flow and by a simple pharmacokinetic model of anaesthetic gas uptake. This extension provides a physically consistent framework for linking advective flows with the fluxes associated with chemical reactions within the context of physiological systems in general and the human physiome in particular.

A semantics, energy-based approach to automate biomodel composition

Hierarchical modelling is essential to achieving complex, large-scale models. However, not all modelling schemes support hierarchical composition, and correctly mapping points of connection between models requires comprehensive knowledge of each model's components and assumptions. To address these challenges in integrating biosimulation models, we propose an approach to automatically and confidently compose biosimulation models. The approach uses bond graphs to combine aspects of physical and thermodynamics-based modelling with biological semantics. We improved on existing approaches by using semantic annotations to automate the recognition of common components. The approach is illustrated by coupling a model of the Ras-MAPK cascade to a model of the upstream activation of EGFR. Through this methodology, we aim to assist researchers and modellers in readily having access to more comprehensive biological systems models.

Systems analysis of the mechanisms governing the cardiovascular response to changes in posture and in peripheral demand during exercise

Blood flows and pressures throughout the human cardiovascular system are regulated in response to various dynamic perturbations, such as changes to peripheral demands in exercise, rapid changes in posture, or loss of blood from hemorrhage, via the coordinated action of the heart, the vasculature, and autonomic reflexes. To assess how the systemic and pulmonary arterial and venous circulation, the heart, and the baroreflex work together to effect the whole-body responses to these perturbations, we integrated an anatomically-based large-vessel arterial tree model with the TriSeg heart model, models capturing nonlinear characteristics of the large and small veins, and baroreflex-mediated regulation of vascular tone and cardiac chronotropy and inotropy. The model was identified by matching data from the Valsalva maneuver (VM), exercise, and head-up tilt (HUT). Thirty-one parameters were optimized using a custom parameter-fitting tool chain, resulting in an unique, high-fidelity whole-body human cardiovascular systems model. Because the model captures the effects of exercise and posture changes, it can be used to simulate numerous clinical assessments, such as HUT, the VM, and cardiopulmonary exercise stress testing. The model can also be applied as a framework for representing and simulating individual patients and pathologies. Moreover, it can serve as a framework for integrating multi-scale organ-level models, such as for the heart or the kidneys, into a whole-body model. Here, the model is used to analyze the relative importance of chronotropic, inotropic, and peripheral vascular contributions to the whole-body cardiovascular response to exercise. It is predicted that in normal physiological conditions chronotropy and inotropy make roughly equal contributions to increasing cardiac output and cardiac power output during exercise. Under upright exercise conditions, the nonlinear pressure-volume relationship of the large veins and sympathetic-mediated venous vasoconstriction are both required to maintain preload to achieve physiological exercise levels. The developed modeling framework is built using the open Modelica modeling language and is freely distributed.

Preclinical modeling of mechanical thrombectomy

Mechanical thrombectomy to treat large vessel occlusions (LVO) causing a stroke is one of the most effective treatments in medicine, with a number needed to treat to improve clinical outcomes as low as 2.6. As the name implies, it is a mechanical solution to a blocked artery and modeling these mechanics preclinically for device design, regulatory clearance and high-fidelity physician training made clinical applications possible. In vitro simulation of LVO is extensively used to characterize device performance in representative vascular anatomies with physiologically accurate hemodynamics. Embolus analogues, validated against clots extracted from patients, provide a realistic simulated use experience. In vitro experimentation produces quantitative results such as particle analysis of distal emboli generated during the procedure, as well as pressure and flow throughout the experiment. Animal modeling, used mostly for regulatory review, allows estimation of device safety. Other than one recent development, nearly all animal modeling does not incorporate the desired target organ, the brain, but rather is performed in the extracranial circulation. Computational modeling of the procedure remains at the earliest stages but represents an enormous opportunity to rapidly characterize and iterate new thrombectomy concepts as well as optimize procedure workflow. No preclinical model is a perfect surrogate; however, models available can answer important questions during device development and have to date been successful in delivering efficacious and safe devices producing excellent clinical outcomes. This review reflects on the developments of preclinical modeling of mechanical thrombectomy with particular focus on clinical translation, as well as articulate existing gaps requiring additional research.

On the Periodicity of Cardiovascular Fluid Dynamics Simulations

Three-dimensional cardiovascular fluid dynamics simulations typically require computation of several cardiac cycles before they reach a periodic solution, rendering them computationally expensive. Furthermore, there is currently no standardized method to determine whether a simulation has yet reached that periodic state. In this work, we propose the use of an asymptotic error measurement to quantify the difference between simulation results and their ideal periodic state using open-loop lumped-parameter modeling. We further show that initial conditions are crucial in reducing computational time and develop an automated framework to generate appropriate initial conditions from a one-dimensional model of blood flow. We demonstrate the performance of our initialization method using six patient-specific models from the Vascular Model Repository. In our examples, our initialization protocol achieves periodic convergence within one or two cardiac cycles, leading to a significant reduction in computational cost compared to standard methods. All computational tools used in this work are implemented in the open-source software platform SimVascular. Automatically generated initial conditions have the potential to significantly reduce computation time in cardiovascular fluid dynamics simulations.

Hypoxic pulmonary vasoconstriction as a regulator of alveolar-capillary oxygen flux: A computational model of ventilation-perfusion matching

The relationship between regional variabilities in airflow (ventilation) and blood flow (perfusion) is a critical determinant of gas exchange efficiency in the lungs. Hypoxic pulmonary vasoconstriction is understood to be the primary active regulator of ventilation-perfusion matching, where upstream arterioles constrict to direct blood flow away from areas that have low oxygen supply. However, it is not understood how the integrated action of hypoxic pulmonary vasoconstriction affects oxygen transport at the system level. In this study we develop, and make functional predictions with a multi-scale multi-physics model of ventilation-perfusion matching governed by the mechanism of hypoxic pulmonary vasoconstriction. Our model consists of (a) morphometrically realistic 2D pulmonary vascular networks to the level of large arterioles and venules; (b) a tileable lumped-parameter model of vascular fluid and wall mechanics that accounts for the influence of alveolar pressure; (c) oxygen transport accounting for oxygen bound to hemoglobin and dissolved in plasma; and (d) a novel empirical model of hypoxic pulmonary vasoconstriction. Our model simulations predict that under the artificial test condition of a uniform ventilation distribution (1) hypoxic pulmonary vasoconstriction matches perfusion to ventilation; (2) hypoxic pulmonary vasoconstriction homogenizes regional alveolar-capillary oxygen flux; and (3) hypoxic pulmonary vasoconstriction increases whole-lobe oxygen uptake by improving ventilation-perfusion matching.

The relationship between regional ventilation (airflow) and perfusion (blood flow) is a major determinant of gas exchange efficiency. Atelactasis and pulmonary vascular occlusive diseases, such as acute pulmonary embolism, are characterized by ventilation-perfusion mismatching and decreased oxygen in the bloodstream. Despite the physiological and medical importance of ventilation-perfusion matching, there are gaps in our knowledge of the regulatory mechanisms that maintain adequate gas exchange under pathological and normal conditions. Hypoxic pulmonary vasoconstriction is understood to be the primary regulator of ventilation-perfusion matching, where upstream arterioles constrict to direct blood flow away from areas that have low oxygen supply, yet it is not understood how this mechanism affects oxygen transport at the system level. In this study we present a computational model of the ventilation-perfusion matching and hypoxic pulmonary vasoconstriction to better understand how physiological regulation at the regional level scales to affect oxygen transport at the system level. Our model simulations predict that this regulatory mechanism improves the spatial overlap of airflow and blood flow, which serves to increase the uptake of oxygen into the bloodstream. This improved understanding of ventilation-perfusion matching may offer insights into the etiology of, and therapeutic interventions for diseases characterized by ventilation-perfusion mismatching.

Hierarchical semantic composition of biosimulation models using bond graphs

Simulating complex biological and physiological systems and predicting their behaviours under different conditions remains challenging. Breaking systems into smaller and more manageable modules can address this challenge, assisting both model development and simulation. Nevertheless, existing computational models in biology and physiology are often not modular and therefore difficult to assemble into larger models. Even when this is possible, the resulting model may not be useful due to inconsistencies either with the laws of physics or the physiological behaviour of the system. Here, we propose a general methodology for composing models, combining the energy-based bond graph approach with semantics-based annotations. This approach improves model composition and ensures that a composite model is physically plausible. As an example, we demonstrate this approach to automated model composition using a model of human arterial circulation. The major benefit is that modellers can spend more time on understanding the behaviour of complex biological and physiological systems and less time wrangling with model composition.

Modelling the leptomeningeal collateral circulation during acute ischaemic stroke

A novel model of the leptomeningeal collateral circulation is created by combining data from multiple sources with statistical scaling laws. The extent of the collateral circulation is varied by defining a collateral vessel probability. Blood flow and pressure are simulated using a one-dimensional steady state blood flow model. The leptomeningeal collateral vessels provide significant flow during a stroke. The pressure drop over an occlusion predicted by the model ranges between 60 and 85 mmHg depending on the extent of the collateral circulation. The linear transport of contrast material was simulated in the circulatory network. The time delay of peak contrast over an occlusion is 3.3 s in the model, and 2.1 s (IQR 0.8-4.0 s) when measured in dynamic CTA data of acute ischaemic stroke patients. Modelling the leptomeningeal collateral circulation could lead to better estimates of infarct volume and patient outcome.

A Graph-Based Framework for Multiscale Modeling of Physiological Transport

Trillions of chemical reactions occur in the human body every second, where the generated products are not only consumed locally but also transported to various locations in a systematic manner to sustain homeostasis. Current solutions to model these biological phenomena are restricted in computability and scalability due to the use of continuum approaches in which it is practically impossible to encapsulate the complexity of the physiological processes occurring at diverse scales. Here, we present a discrete modeling framework defined on an interacting graph that offers the flexibility to model multiscale systems by translating the physical space into a metamodel. We discretize the graph-based metamodel into functional units composed of well-mixed volumes with vascular and cellular subdomains; the operators defined over these volumes define the transport dynamics. We predict glucose drift governed by advective-dispersive transport in the vascular subdomains of an islet vasculature and cross-validate the flow and concentration fields with finite-element-based COMSOL simulations. Vascular and cellular subdomains are coupled to model the nutrient exchange occurring in response to the gradient arising out of reaction and perfusion dynamics. The application of our framework for modeling biologically relevant test systems shows how our approach can assimilate both multi-omics data from in vitro-in vivo studies and vascular topology from imaging studies for examining the structure-function relationship of complex vasculatures. The framework can advance simulation of whole-body networks at user-defined levels and is expected to find major use in personalized medicine and drug discovery.

A patient-specific modelling method of blood circulatory system for the numerical simulation of enhanced external counterpulsation

Lumped parameter model (LPM) is a common numerical model for hemodynamic simulation of human's blood circulatory system. The numerical simulation of enhanced external counterpulsation (EECP) is a typical biomechanical simulation process based on the LPM of blood circulatory system. In order to simulate patient-specific hemodynamic effects of EECP and develop best treatment strategy for each individual, this study developed an optimization algorithm to individualize LPM elements. Physiological data from 30 volunteers including approximate aortic pressure, cardiac output, ankle pressure and carotid artery flow were clinically collected as optimization objectives. A closed-loop LPM was established for the simulation of blood circulatory system. Aiming at clinical data, a sensitivity analysis for each element was conducted to identify the significant ones. We improved the traditional simulated annealing algorithm to iteratively optimize the sensitive elements. To verify the accuracy of the patient-specific model, 30 samples of simulated data were compared with clinical measurements. In addition, an EECP experiment was conducted on a volunteer to verify the applicability of the optimized model for the simulation of EECP. For these 30 samples, the optimization results show a slight difference between clinical data and simulated data. The average relative root mean square error is lower than 5%. For the subject of EECP experiment, the relative error of hemodynamic responses during EECP is lower than 10%. This slight error demonstrated a good state of optimization. The optimized modeling algorithm can effectively individualize the LPM for blood circulatory system, which is significant to the numerical simulation of patient-specific hemodynamics.

Personalized Hemodynamic Modeling of the Human Cardiovascular System: A Reduced-Order Computing Model

OBJECTIVE

Personalization of hemodynamic modeling plays a crucial role in functional prediction of the cardiovascular system (CVS). While reduced-order models of one-dimensional (1D) blood vessel models with zero-dimensional (0D) blood vessel and heart models have been widely recognized to be an effective tool for reasonably estimating the hemodynamic functions of the whole CVS, practical personalized models are still lacking. In this paper, we present a novel 0-1D coupled, personalized hemodynamic model of the CVS that can predict both pressure waveforms and flow velocities in arteries.

METHODS

We proposed a methodology by combining the multiscale CVS model with the Levenberg-Marquardt optimization algorithm for effectively solving an inverse problem based on measured blood pressure waveforms. Hemodynamic characteristics including brachial arterial pressure waveforms, artery diameters, stroke volumes, and flow velocities were measured noninvasively for 62 volunteers aged from 20 to 70 years for developing and validating the model.

RESULTS

The estimated arterial stiffness shows a physiologically realistic distribution. The model-fitted individual pressure waves have an averaged mean square error (MSE) of 7.1 mmHg²; simulated blood flow velocity waveforms in carotid artery match ultrasound measurements well, achieving an average correlation coefficient of 0.911.

CONCLUSION

The model is efficient, versatile, and capable of obtaining well-fitting individualized pressure waveforms while reasonably predicting flow waveforms.

SIGNIFICANCE

The proposed methodology of personalized hemodynamic modeling may therefore facilitate individualized patient-specific assessment of both physiological and pathological functions of the CVS.

Optimising mechanical ventilation through model-based methods and automation

Mechanical ventilation (MV) is a core life-support therapy for patients suffering from respiratory failure or acute respiratory distress syndrome (ARDS). Respiratory failure is a secondary outcome of a range of injuries and diseases, and results in almost half of all intensive care unit (ICU) patients receiving some form of MV. Funding the increasing demand for ICU is a major issue and MV, in particular, can double the cost per day due to significant patient variability, over-sedation, and the large amount of clinician time required for patient management. Reducing cost in this area requires both a decrease in the average duration of MV by improving care, and a reduction in clinical workload. Both could be achieved by safely automating all or part of MV care via model-based dynamic systems modelling and control methods are ideally suited to address these problems. This paper presents common lung models, and provides a vision for a more automated future and explores predictive capacity of some current models. This vision includes the use of model-based methods to gain real-time insight to patient condition, improve safety through the forward prediction of outcomes to changes in MV, and develop virtual patients for in-silico design and testing of clinical protocols. Finally, the use of dynamic systems models and system identification to guide therapy for improved personalised control of oxygenation and MV therapy in the ICU will be considered. Such methods are a major part of the future of medicine, which includes greater personalisation and predictive capacity to both optimise care and reduce costs. This review thus presents the state of the art in how dynamic systems and control methods can be applied to transform this core area of ICU medicine.

Functionalized Anatomical Models for Computational Life Sciences

The advent of detailed computational anatomical models has opened new avenues for computational life sciences (CLS). To date, static models representing the anatomical environment have been used in many applications but are insufficient when the dynamics of the body prevents separation of anatomical geometrical variability from physics and physiology. Obvious examples include the assessment of thermal risks in magnetic resonance imaging and planning for radiofrequency and acoustic cancer treatment, where posture and physiology-related changes in shape (e.g., breathing) or tissue behavior (e.g., thermoregulation) affect the impact. Advanced functionalized anatomical models can overcome these limitations and dramatically broaden the applicability of CLS in basic research, the development of novel devices/therapies, and the assessment of their safety and efficacy. Various forms of functionalization are discussed in this paper: (i) shape parametrization (e.g., heartbeat, population variability), (ii) physical property distributions (e.g., image-based inhomogeneity), (iii) physiological dynamics (e.g., tissue and organ behavior), and (iv) integration of simulation/measurement data (e.g., exposure conditions, “validation evidence” supporting model tuning and validation). Although current model functionalization may only represent a small part of the physiology, it already facilitates the next level of realism by (i) driving consistency among anatomy and different functionalization layers and highlighting dependencies, (ii) enabling third-party use of validated functionalization layers as established simulation tools, and (iii) therefore facilitating their application as building blocks in network or multi-scale computational models. Integration in functionalized anatomical models thus leverages and potentiates the value of sub-models and simulation/measurement data toward ever-increasing simulation realism. In our o²S²PARC platform, we propose to expand the concept of functionalized anatomical models to establish an integration and sharing service for heterogeneous computational models, ranging from the molecular to the organ level. The objective of o²S²PARC is to integrate all models developed within the National Institutes of Health SPARC initiative in a unified anatomical and computational environment, to study the role of the peripheral nervous system in controlling organ physiology. The functionalization concept, as outlined for the o²S²PARC platform, could form the basis for many other application areas of CLS. The relationship to other ongoing initiatives, such as the Physiome Project, is also presented.