Mathematical multi-scale model of the cardiovascular system including mitral valve dynamics. Application to ischemic mitral insufficiency

A variable heart rate multi-compartmental coupled model of the cardiovascular and respiratory systems

Current mathematical models of the cardiovascular system that are based on systems of ordinary differential equations are limited in their ability to mimic important features of measured patient data, such as variable heart rates (HR). Such limitations present a significant obstacle in the use of such models for clinical decision-making, as it is the variations in vital signs such as HR and systolic and diastolic blood pressure that are monitored and recorded in typical critical care bedside monitoring systems. In this paper, novel extensions to well-established multi-compartmental models of the cardiovascular and respiratory systems are proposed that permit the simulation of variable HR. Furthermore, a correction to current models is also proposed to stabilize the respiratory behaviour and enable realistic simulation of vital signs over the longer time scales required for clinical management. The results of the extended model developed here show better agreement with measured bio-signals, and these extensions provide an important first step towards estimating model parameters from patient data, using methods such as neural ordinary differential equations. The approach presented is generalizable to many other similar multi-compartmental models of the cardiovascular and respiratory systems.

Mathematical modeling of antihypertensive therapy

Hypertension is a multifactorial disease arising from complex pathophysiological pathways. Individual characteristics of patients result in different responses to various classes of antihypertensive medications. Therefore, evaluating the efficacy of therapy based on in silico predictions is an important task. This study is a continuation of research on the modular agent-based model of the cardiovascular and renal systems (presented in the previously published article). In the current work, we included in the model equations simulating the response to antihypertensive therapies with different mechanisms of action. For this, we used the pharmacodynamic effects of the angiotensin II receptor blocker losartan, the calcium channel blocker amlodipine, the angiotensin-converting enzyme inhibitor enalapril, the direct renin inhibitor aliskiren, the thiazide diuretic hydrochlorothiazide, and the β-blocker bisoprolol. We fitted therapy parameters based on known clinical trials for all considered medications, and then tested the model's ability to show reasonable dynamics (expected by clinical observations) after treatment with individual drugs and their dual combinations in a group of virtual patients with hypertension. The extended model paves the way for the next step in personalized medicine that is adapting the model parameters to a real patient and predicting his response to antihypertensive therapy. The model is implemented in the BioUML software and is available at https://gitlab.sirius-web.org/virtual-patient/antihypertensive-treatment-modeling.

Cardiovascular Circulatory System and Left Carotid Model: A Fractional Approach to Disease Modeling

Cardiovascular diseases (CVDs) remain the leading cause of death worldwide, according to recent reports from the World Health Organization (WHO). This fact encourages research into the cardiovascular system (CVS) from multiple and different points of view than those given by the medical perspective, highlighting among them the computational and mathematical models that involve experiments much simpler and less expensive to be performed in comparison with in vivo or in vitro heart experiments. However, the CVS is a complex system that needs multidisciplinary knowledge to describe its dynamic models, which help to predict cardiovascular events in patients with heart failure, myocardial or valvular heart disease, so it remains an active area of research. Firstly, this paper presents a novel electrical model of the CVS that extends the classic Windkessel models to the left common carotid artery motivated by the need to have a more complete model from a medical point of view for validation purposes, as well as to describe other cardiovascular phenomena in this area, such as atherosclerosis, one of the main risk factors for CVDs. The model is validated by clinical indices and experimental data obtained from clinical trials performed on a pig. Secondly, as a first step, the goodness of a fractional-order behavior of this model is discussed to characterize different heart diseases through pressure–volume (PV) loops. Unlike other models, it allows us to modify not only the topology, parameters or number of model elements, but also the dynamic by tuning a single parameter, the characteristic differentiation order; consequently, it is expected to provide a valuable insight into this complex system and to support the development of clinical decision systems for CVDs.

A computationally efficient physiologically comprehensive 3D-0D closed-loop model of the heart and circulation

Computer models of cardiac electro-mechanics (EM) show promise as an effective means for the quantitative analysis of clinical data and, potentially, for predicting therapeutic responses. To realize such advanced applications methodological key challenges must be addressed. Enhanced computational efficiency and robustness is crucial to facilitate, within tractable time frames, model personalization, the simulation of prolonged observation periods under a broad range of conditions, and physiological completeness encompassing therapy-relevant mechanisms is needed to endow models with predictive capabilities beyond the mere replication of observations. Here, we introduce a universal feature-complete cardiac EM modeling framework that builds on a flexible method for coupling a 3D model of bi-ventricular EM to the physiologically comprehensive 0D CircAdapt model representing atrial mechanics and closed-loop circulation. A detailed mathematical description is given and efficiency, robustness, and accuracy of numerical scheme and solver implementation are evaluated. After parameterization and stabilization of the coupled 3D-0D model to a limit cycle under baseline conditions, the model's ability to replicate physiological behaviors is demonstrated, by simulating the transient response to alterations in loading conditions and contractility, as induced by experimental protocols used for assessing systolic and diastolic ventricular properties. Mechanistic completeness and computational efficiency of this novel model render advanced applications geared towards predicting acute outcomes of EM therapies feasible.

A computationally efficient physiologically comprehensive 3D-0D closed-loop model of the heart and circulation

Computer models of cardiac electro-mechanics (EM) show promise as an effective means for the quantitative analysis of clinical data and, potentially, for predicting therapeutic responses. To realize such advanced applications methodological key challenges must be addressed. Enhanced computational efficiency and robustness is crucial to facilitate, within tractable time frames, model personalization, the simulation of prolonged observation periods under a broad range of conditions, and physiological completeness encompassing therapy-relevant mechanisms is needed to endow models with predictive capabilities beyond the mere replication of observations. Here, we introduce a universal feature-complete cardiac EM modeling framework that builds on a flexible method for coupling a 3D model of bi-ventricular EM to the physiologically comprehensive 0D CircAdapt model representing atrial mechanics and closed-loop circulation. A detailed mathematical description is given and efficiency, robustness, and accuracy of numerical scheme and solver implementation are evaluated. After parameterization and stabilization of the coupled 3D-0D model to a limit cycle under baseline conditions, the model's ability to replicate physiological behaviors is demonstrated, by simulating the transient response to alterations in loading conditions and contractility, as induced by experimental protocols used for assessing systolic and diastolic ventricular properties. Mechanistic completeness and computational efficiency of this novel model render advanced applications geared towards predicting acute outcomes of EM therapies feasible.

Thoroughly Calibrated Modular Agent-Based Model of the Human Cardiovascular and Renal Systems for Blood Pressure Regulation in Health and Disease

Here we present a modular agent-based mathematical model of the human cardiovascular and renal systems. It integrates the previous models primarily developed by A. C. Guyton, F. Karaaslan, K. M. Hallow, and Y. V. Solodyannikov. We performed the model calibration to find an equilibrium state within the normal vital sign ranges for a healthy adult. We verified the model's abilities to reproduce equilibrium states with abnormal physiological values related to different combinations of cardiovascular diseases (such as systemic hypertension, chronic heart failure, pulmonary hypertension, etc.). For the model creation and validation, we involved over 200 scientific studies covering known models of the human cardiovascular and renal functions, biosimulation platforms, and clinical measurements of physiological quantities in normal and pathological conditions. We compiled detailed documentation describing all equations, parameters and variables of the model with justification of all formulas and values. The model is implemented in BioUML and available in the web-version of the software.

Computational fluid dynamics investigation of the novel hybrid comprehensive stage II operation

Background

The hybrid comprehensive stage 2 (HCS2) procedure is a novel palliative operation applicable to a select subset of single ventricle patients with adequate native antegrade aortic flow to the upper body. Flow to the descending aorta, through the pulmonary outlet and ductal arch, is influenced by a stented intrapulmonary baffle connecting the branch pulmonary arteries. We used computational fluid dynamics (CFD) to elucidate the hemodynamic characteristics of this reconstruction.

Methods

We used multiscale CFD analysis of a synthetic, patient-derived HCS2 anatomic configuration with unsteady laminar flow conditions and a non-Newtonian blood model to quantify the resultant hemodynamics. The 3-dimensional CFD model was coupled to a 0-dimensional lumped parameter model of the peripheral circulation to determine the required boundary conditions.

Results

For the specific anatomy studied, the intrapulmonary baffle did not obstruct flow from the pulmonary trunk to ductal arch as long as the distance between the anterior pulmonary artery wall and baffle wall exceeded ∼7 mm. Vortex shedding off of the baffle wall did not develop, because of the short distance to the ductal arch. The stented baffle experienced significantly uneven "inward" loading from the systemic side. Pulmonary outlet flow separation distal to the baffle produced a low-speed recirculation region.

Conclusions

Hemodynamic patterns in this complex anatomy are generally favorable. Low flow recirculation could be mitigated by preoperative shape optimization. Calculated inward stresses on the pulmonary baffle can be used in the future to study baffle stent deformation, which is expected to be small.

Electro-Mechanical Whole-Heart Digital Twins: A Fully Coupled Multi-Physics Approach

Mathematical models of the human heart are evolving to become a cornerstone of precision medicine and support clinical decision making by providing a powerful tool to understand the mechanisms underlying pathophysiological conditions. In this study, we present a detailed mathematical description of a fully coupled multi-scale model of the human heart, including electrophysiology, mechanics, and a closed-loop model of circulation. State-of-the-art models based on human physiology are used to describe membrane kinetics, excitation-contraction coupling and active tension generation in the atria and the ventricles. Furthermore, we highlight ways to adapt this framework to patient specific measurements to build digital twins. The validity of the model is demonstrated through simulations on a personalized whole heart geometry based on magnetic resonance imaging data of a healthy volunteer. Additionally, the fully coupled model was employed to evaluate the effects of a typical atrial ablation scar on the cardiovascular system. With this work, we provide an adaptable multi-scale model that allows a comprehensive personalization from ion channels to the organ level enabling digital twin modeling.

Application of 0D model of blood flow to study vessel abnormalities in the human systemic circulation: An in-silico study

In this paper, a multi-compartment 0D model of the blood flow is considered to study the vessel abnormalities (stenoses and aneurysms) in the human systemic circulation (SC). In the complete SC, different levels of stenosis and aneurysms are artificially created by decreasing and increasing the vessel diameters respectively and their effects on pressure and flow are studied using sensitivity analysis (SA). Normalized local sensitivity analysis (LSA) is used to study the impact of stenosis and aneurysms on pressure and flow wave pattern. Furthermore, global sensitivity analysis (GSA), Sobol’s method is used to quantify the overall influence of stenoses and aneurysms in the complete SC.

The results of global sensitivity analysis revealed that the impact of both stenoses and aneurysms is strong within the individual structures (arm, legs, carotid bifurcation, aorta), while, aortic stenoses and aneurysms have effect on almost all downstream nodes. Moreover, the study could be useful for medical doctors, teachers and students to observe the hemodynamical changes in the SC with respect to vessel abnormalities, which could further help in making any clinical decision for patients having different levels of vessel abnormalities in any part or structure of the SC.

Extract of Spatholobus suberctus Dunn ameliorates ischemia-induced injury by targeting miR-494

Cerebral stroke is a leading cause of death and permanent disability. The current therapeutic outcome of ischemic stroke (>85% of all strokes) is very poor, thus novel therapeutic drug is urgently needed. In vitro cell model of ischemia was established by oxygen-glucose deprivation (OGD) and in vivo animal model of ischemia was established by middle cerebral artery occlusion (MCAO). The effects of Spatholobus suberctus Dunn extract (SSCE) on OGD-induced cell injury, MCAO-induced neural injury and miR-494 level were all evaluated. The possible target genes were virtually screened utilizing bioinformatics and verified by luciferase assay. Subsequently, the effects of abnormally expressed miR-494 on OGD-induced cell injury and target gene expression were determined. Additionally, whether SSCE affected target gene expression through modulation of miR-494 was studied. Finally, the effects of aberrantly expressed Sox8 on OGD-induced injury and signaling pathways were estimated. SSCE reduced OGD-induced cell injury and ameliorated MCAO-induced neuronal injury, along with down-regulation of miR-494. Then, OGD-induced cell injury was increased by miR-494 overexpression but decreased by miR-494 silence. Sox8 was a target gene of miR-494, and SSCE could up-regulate Sox8 expression via down-regulating miR-494. Afterwards, OGD-induced cell injury was proved to be increased by Sox8 inhibition but reduced by Sox8 overexpression. Finally, OGD-induced inhibition of PI3K/AKT/mTOR and MAPK pathways was further inhibited by Sox8 silence but activated by Sox8 overexpression. SSCE ameliorates ischemia-induced injury both in vitro and in vivo by miR-494-mediated modulation of Sox8, involving activations of PI3K/AKT/mTOR and MAPK pathways.

rLj-RGD3, a Novel Three-RGD-Motif-Containing Recombinant Protein from Lampetra japonica, Protects PC12 Cells from Injury Induced by Oxygen-Glucose Deprivation and Reperfusion

rLj-RGD3 is a 14.5 kDa recombinant protein with 3 RGD (Arg-Gly-Asp) motifs from the salivary gland secretions of Lampetra japonica, which is a histidine-rich and arginine-rich protein. Previous reports indicated that rLj-RGD3 has typical functions of RGD-toxin protein, such as platelet aggregation suppression tumour metastasis and angiogenesis inhibition. Because histidine and arginine have cerebral ischemia-reperfusion and neuroprotective functions, we investigated whether rLj-RGD3 has such activities and studied the mechanism. The effects of rLj-RGD3 on neuroprotection and antiapoptosis were determined. The expression level of focal adhesion kinase (FAK), p-FAK, Caspase-3, and Bcl-2 after oxygen-glucose deprivation and reperfusion (OGD-R) was examined. The viability of PC12 cells incubated with rLj-RGD3 at high concentrations (16 μmol/L) increased significantly due to its ability to protect the cells from apoptosis after OGD-R-induced injury. Furthermore, rLj-RGD3 attenuated the damage due to OGD-R. Most of the PC12 cells were apoptotic after OGD-R. In contrast, the number of apoptotic PC12 cells was significantly decreased in the group treated with a high-dose of rLj-RGD3. In addition, rLj-RGD3 activated FAK and p-FAK protein. rLj-RGD3 inhibited Caspase-3 and upregulated Bcl-2 protein expression in PC12 cells after OGD-R. The study provides the first evidence for neuroprotective effects of rLj-RGD3 in ischemic injury that may be partly mediated through inhibition of Caspase-3 and upregulation of Bcl-2, FAK, and p-FAK protein expression.

Data assimilation and modelling of patient-specific single-ventricle physiology with and without valve regurgitation

A closed-loop lumped parameter model of blood circulation is considered for single-ventricle shunt physiology. Its parameters are estimated by an inverse problem based on patient-specific haemodynamics measurements. As opposed to a black-box approach, maximizing the number of parameters that are related to physically measurable quantities motivates the present model. Heart chambers are described by a single-fibre mechanics model, and valve function is modelled with smooth opening and closure. A model for valve prolapse leading to valve regurgitation is proposed. The method of data assimilation, in particular the unscented Kalman filter, is used to estimate the model parameters from time-varying clinical measurements. This method takes into account both the uncertainty in prior knowledge related to the parameters and the uncertainty associated with the clinical measurements. Two patient-specific cases - one without regurgitation and one with atrioventricular valve regurgitation - are presented. Pulmonary and systemic circulation parameters are successfully estimated, without assumptions on their relationships. Parameters governing the behaviour of heart chambers and valves are either fixed based on biomechanics, or estimated. Results of the inverse problem are validated qualitatively through clinical measurements or clinical estimates that were not included in the parameter estimation procedure. The model and the estimation method are shown to successfully capture patient-specific clinical observations, even with regurgitation, such as the double peaked nature of valvular flows and anomalies in electrocardiogram readings. Lastly, biomechanical implications of the results are discussed.

E, Cerrolaza M. ANALYSIS OF BLOOD FLOW PASSING THROUGH AORTIC AND MITRAL VALVES USING A COMPUTATIONAL MODEL OF CONCENTRATED PARAMETERS

Blood flow has been extensively studied because of its close relationship with cardiovascular disease. Heart valves blood flow analysis is particularly complex due to the high mobility of its leaflets, a fact that has stimulated the development of computational models aimed to its better understanding. For studying heart valves blood flow, we developed a mathematical model derived from clinical observations based on echocardiographic images, which describe valve leaflets motion and its influence on blood flow. This work presents a concentrated-parameters-based model of heart valves blood flow that takes into consideration five main factors affecting such a flow in the mitral and aortic valves. This model considers factors that are related to blood fluid and valve leaflets characteristics. Considering the main factors involved, it was found that blood flow exhibit an abnormal behavior in response to small variations (less than 10%) in blood pressure gradient or in leaflets stiffness. Likewise, after changing the roughness of the leaflets, the impact is smaller, only slightly affecting blood flow behavior with changes beyond 30%. Moreover, it was observed that the influence of fluid vortices originated behind the valves can be disregarded and the kinetic energy induced by them is almost negligible.

Activin A prevents neuron-like PC12 cell apoptosis after oxygen-glucose deprivation

In this study, PC12 cells were induced to differentiate into neuron-like cells using nerve growth factor, and were subjected to oxygen-glucose deprivation. Cells were treated with 0, 10, 20, 30, 50, 100 ng/mL exogenous Activin A. The 3-(4,5-dimethyl-2-thiazolyl)-2,5-diphenyl tetrazolium bromide assay and Hoechst 33324 staining showed that the survival percentage of PC12 cells significantly decreased and the rate of apoptosis significantly increased after oxygen-glucose deprivation. Exogenous Activin A significantly increased the survival percentage of PC12 cells in a dose-dependent manner. Reverse transcription-PCR results revealed a significant increase in Activin receptor IIA, Smad3 and Smad4 mRNA levels, which are key sites in the Activin A/Smads signaling pathway, in neuron-like cells subjected to oxygen-glucose deprivation, while mRNA expression of the apoptosis-regulation gene caspase-3 decreased. Our experimental findings indicate that exogenous Activin A plays an anti-apoptotic role and protects neurons by means of activating the Activin A/Smads signaling pathway.

Closed-loop real-time simulation model of hemodynamics and oxygen transport in the cardiovascular system

Background

Computer technology enables realistic simulation of cardiovascular physiology. The increasing number of clinical surgical and medical treatment options imposes a need for better understanding of patient-specific pathology and outcome prediction.

Methods

A distributed lumped parameter real-time closed-loop model with 26 vascular segments, cardiac modelling with time-varying elastance functions and gradually opening and closing valves, the pericardium, intrathoracic pressure, the atrial and ventricular septum, various pathological states and including oxygen transport has been developed.

Results

Model output is pressure, volume, flow and oxygen saturation from every cardiac and vascular compartment. The model produces relevant clinical output and validation of quantitative data in normal physiology and qualitative directions in simulation of pathological states show good agreement with published data.

Conclusion

The results show that it is possible to build a clinically relevant real-time computer simulation model of the normal adult cardiovascular system. It is suggested that understanding qualitative interaction between physiological parameters in health and disease may be improved by using the model, although further model development and validation is needed for quantitative patient-specific outcome prediction.

Challenges and opportunities in cardiovascular health informatics

Cardiovascular health informatics is a rapidly evolving interdisciplinary field concerning the processing, integration/interpretation, storage, transmission, acquisition, and retrieval of information from cardiovascular systems for the early detection, early prediction, early prevention, early diagnosis, and early treatment of cardiovascular diseases (CVDs). Based on the first author's presentation at the first IEEE Life Sciences Grand Challenges Conference, held on October 4-5, 2012, at the National Academy of Sciences, Washington, DC, USA, this paper, focusing on coronary arteriosclerotic disease, will discuss three significant challenges of cardiovascular health informatics, including: 1) to invent unobtrusive and wearable multiparameter sensors with higher sensitivity for the real-time monitoring of physiological states; 2) to develop fast multimodal imaging technologies with higher resolution for the quantification and better understanding of structure, function, metabolism of cardiovascular systems at the different levels; and 3) to develop novel multiscale information fusion models and strategies with higher accuracy for the personalized predication of the CVDs. At the end of this paper, a summary is given to suggest open discussions on these three and more challenges that face the scientific community in this field in the future.

Neuroprotective effects of exogenous activin A on oxygen-glucose deprivation in PC12 cells

Ischemic cerebrovascular disease is one of the most common causes of death in the World. Exogenous activin A (ActA) protects neurons against toxicity and plays a central role in regulating the brain's response to injury. In the present study, we investigated the mechanisms involved in the neuroprotective effects of ActA in a model of hypoxic-ischemic brain disease. We found that ActA could effectively increase the survival rate of PC12 cells and relieve oxygen-glucose deprivation (OGD) damage. To clarify the neuroprotective mechanisms of ActA, the effects of ActA on the ActA/Smad pathway and on the up-regulation of inducible nitric oxide synthase (NOS) and superoxide dismutase (SOD) were investigated using OGD in PC12 cells. The results showed that ActA could increase the expression of activin receptor IIA (ActRIIA), Smad3 and Smad4 and that 50 ng/mL and 100 ng/mL of ActA could reduce NO levels and increase SOD activity by 78.9% and 79.9%, respectively. These results suggested that the neuroprotective effects of ActA in ischemia could be related to the activation of the ActA/Smad signaling pathway and to its anti-oxidant activities.