In silico screening method for non‑responders to cardiac resynchronization therapy in patients with heart failure: a pilot study

Background@#Cardiac resynchronization therapy (CRT) is an effective treatment option for patients with heart failure (HF) and left ventricular (LV) dyssynchrony. However, the problem of some patients not responding to CRT remains unresolved. This study aimed to propose a novel in silico method for CRT simulation. @*Methods@#Three-dimensional heart geometry was constructed from computed tomography images. The finite ele‑ ment method was used to elucidate the electric wave propagation in the heart. The electric excitation and mechani‑ cal contraction were coupled with vascular hemodynamics by the lumped parameter model. The model parameters for three-dimensional (3D) heart and vascular mechanics were estimated by matching computed variables with measured physiological parameters. CRT effects were simulated in a patient with HF and left bundle branch block (LBBB). LV end-diastolic (LVEDV) and end-systolic volumes (LVESV), LV ejection fraction (LVEF), and CRT responsiveness measured from the in silico simulation model were compared with those from clinical observation. A CRT responder was defined as absolute increase in LVEF ≥ 5% or relative increase in LVEF ≥ 15%. @*Results@#A 68-year-old female with nonischemic HF and LBBB was retrospectively included. The in silico CRT simu‑ lation modeling revealed that changes in LVEDV, LVESV, and LVEF by CRT were from 174 to 173 mL, 116 to 104 mL, and 33 to 40%, respectively. Absolute and relative ΔLVEF were 7% and 18%, respectively, signifying a CRT responder.In clinical observation, echocardiography showed that changes in LVEDV, LVESV, and LVEF by CRT were from 162 to 119 mL, 114 to 69 mL, and 29 to 42%, respectively. Absolute and relative ΔLVESV were 13% and 31%, respectively, also signifying a CRT responder. CRT responsiveness from the in silico CRT simulation model was concordant with that in the clinical observation. @*Conclusion@#This in silico CRT simulation method is a feasible technique to screen for CRT non-responders in patients with HF and LBBB.

Toward a grey box approach for cardiovascular physiome

The physiomic approach is now widely used in the diagnosis of cardiovascular diseases. There are two possible methods for cardiovascular physiome: the traditional mathematical model and the machine learning (ML) algorithm. ML is used in almost every area of society for various tasks formerly performed by humans. Specifically, various ML techniques in cardiovascular medicine are being developed and improved at unprecedented speed. The benefits of using ML for various tasks is that the inner working mechanism of the system does not need to be known, which can prove convenient in situations where determining the inner workings of the system can be difficult. The computation speed is also often higher than that of the traditional mathematical models. The limitations with ML are that it inherently leads to an approximation, and special care must be taken in cases where a high accuracy is required. Traditional mathematical models are, however, constructed based on underlying laws either proven or assumed. The results from the mathematical models are accurate as long as the model is. Combining the advantages of both the mathematical models and ML would increase both the accuracy and efficiency of the simulation for many problems. In this review, examples of cardiovascular physiome where approaches of mathematical modeling and ML can be combined are introduced.

Computational analysis of the electromechanical performance of mitral valve cerclage annuloplasty using a patient-specific ventricular model

We aimed to propose a novel computational approach to predict the electromechanical performance of pre- and post-mitral valve cerclage annuloplasty (MVCA). Furthermore, we tested a virtual estimation method to optimize the left ventricular basement tightening scheme using a pre-MVCA computer model. The present model combines the three-dimensional (3D) electromechanics of the ventricles with the vascular hemodynamics implemented in a lumped parameter model. 3D models of pre- and post-MVCA were reconstructed from the computed tomography (CT) images of two patients and simulated by solving the electromechanical-governing equations with the finite element method. Computed results indicate that reduction of the dilated heart chambers volume (reverse remodeling) appears to be dependent on ventricular stress distribution. Reduced ventricular stresses in the basement after MVCA treatment were observed in the patients who showed reverse remodeling of heart during follow up over 6 months. In the case who failed to show reverse remodeling after MVCA, more virtual tightening of the ventricular basement diameter than the actual model can induce stress unloading, aiding in heart recovery. The simulation result that virtual tightening of the ventricular basement resulted in a marked increase of myocardial stress unloading provides in silico evidence for a functional impact of MVCA treatment on cardiac mechanics and post-operative heart recovery. This technique contributes to establishing a pre-operative virtual rehearsal procedure before MVCA treatment by using patient-specific cardiac electromechanical modeling of pre-MVCA.

In silico evaluation of the acute occlusion effect of coronary artery on cardiac electrophysiology and the body surface potential map

Body surface potential map, an electric potential distribution on the body torso surface, enables us to infer the electrical activities of the heart. Therefore, observing electric potential projected to the torso surface can be highly useful for diagnosing heart diseases such as coronary occlusion. The BSPM for the heart of a patient show a higher level of sensitivity than 12-lead ECG. Relevant research has been mostly based on clinical statistics obtained from patients, and, therefore, a simulation for a variety of pathological phenomena of the heart is required. In this study, by using computer simulation, a body surface potential map was implemented according to various occlusion locations (distal, mid, proximal occlusion) in the left anterior descending coronary artery. Electrophysiological characteristics of the body surface during the ST segment period were observed and analyzed based on an ST isointegral map. We developed an integrated system that takes into account the cellular to organ levels, and performed simulation regarding the electrophysiological phenomena of the heart that occur during the first 5 minutes (stage 1) and 10 minutes (stage 2) after commencement of coronary occlusion. Subsequently, we calculated the bipolar angle and amplitude of the ST isointegral map, and observed the correlation between the relevant characteristics and the location of coronary occlusion. In the result, in the ventricle model during the stage 1, a wider area of ischemia led to counterclockwise rotation of the bipolar angle; and, during the stage 2, the amplitude increased when the ischemia area exceeded a certain size.

Spatial reproducibility of complex fractionated atrial electrogram depending on the direction and configuration of bipolar electrodes: an in-silico modeling study

Although 3D-complex fractionated atrial electrogram (CFAE) mapping is useful in radiofrequency catheter ablation for persistent atrial fibrillation (AF), the directions and configuration of the bipolar electrodes may affect the electrogram. This study aimed to compare the spatial reproducibility of CFAE by changing the catheter orientations and electrode distance in an in-silico left atrium (LA). We conducted this study by importing the heart CT image of a patient with AF into a 3D-homogeneous human LA model. Electrogram morphology, CFAE-cycle lengths (CLs) were compared for 16 different orientations of a virtual bipolar conventional catheter (conv-cath: size 3.5 mm, inter-electrode distance 4.75 mm). Additionally, the spatial correlations of CFAE-CLs and the percentage of consistent sites with CFAE-CL<120 ms were analyzed. The results from the conv-cath were compared with that obtained using a mini catheter (mini-cath: size 1 mm, inter-electrode distance 2.5 mm). Depending on the catheter orientation, the electrogram morphology and CFAE-CLs varied (conv-cath: 11.5±0.7% variation, mini-cath: 7.1±1.2% variation), however the mini-cath produced less variation of CFAE-CL than conv-cath (p<0.001). There were moderate spatial correlations among CFAE-CL measured at 16 orientations (conv-cath: r=0.3055±0.2194 vs. mini-cath: 0.6074±0.0733, p<0.001). Additionally, the ratio of consistent CFAE sites was higher for mini catheter than conventional one (38.3±4.6% vs. 22.3±1.4%, p<0.05). Electrograms and CFAE distribution are affected by catheter orientation and electrode configuration in the in-silico LA model. However, there was moderate spatial consistency of CFAE areas, and narrowly spaced bipolar catheters were less influenced by catheter direction than conventional catheters.

Minimal systems analysis of mitochondria-dependent apoptosis induced by cisplatin

Recently, it was reported that the role of mitochondria-reactive oxygen species (ROS) generating pathway in cisplatin-induced apoptosis is remarkable. Since a variety of molecules are involved in the pathway, a comprehensive approach to delineate the biological interactions of the molecules is required. However, quantitative modeling of the mitochondria-ROS generating pathway based on experiment and systemic analysis using the model have not been attempted so far. Thus, we conducted experiments to measure the concentration changes of critical molecules associated with mitochondrial apoptosis in both human mesothelioma H2052 and their ρ0 cells lacking mitochondrial DNA (mtDNA). Based on the experiments, a novel mathematical model that can represent the essential dynamics of the mitochondrial apoptotic pathway induced by cisplatin was developed. The kinetic parameter values of the mathematical model were estimated from the experimental data. Then, we have investigated the dynamical properties of this model and predicted the apoptosis levels for various concentrations of cisplatin beyond the range of experiments. From parametric perturbation analysis, we further found that apoptosis will reach its saturation level beyond a certain critical cisplatin concentration.

Inducibility of human atrial fibrillation in an in silico model reflecting local acetylcholine distribution and concentration

Vagal nerve activity has been known to play a crucial role in the induction and maintenance of atrial fibrillation (AF). However, it is unclear how the distribution and concentration of local acetylcholine (ACh) promotes AF. In this study, we investigated the effect of the spatial distribution and concentration of ACh on fibrillation patterns in an in silico human atrial model. A human atrial action potential model with an ACh-dependent K+ current (I(KAch)) was used to examine the effect of vagal activation. A simulation of cardiac wave dynamics was performed in a realistic 3D model of the atrium. A model of the ganglionated plexus (GP) and nerve was developed based on the "octopus hypothesis". The pattern of cardiac wave dynamics was examined by applying vagal activation to the GP areas or randomly. AF inducibility in the octopus hypothesis-based GP and nerve model was tested. The effect of the ACh concentration level was also examined. In the single cell simulation, an increase in the ACh concentration shortened APD90 and increased the maximal slope of the restitution curve. In the 3D simulation, a random distribution of vagal activation promoted wavebreaks while ACh secretion limited to the GP areas did not induce a noticeable change in wave dynamics. The octopus hypothesis-based model of the GP and nerve exhibited AF inducibility at higher ACh concentrations. In conclusion, a 3D in silico model of the GP and parasympathetic nerve based on the octopus model exhibited higher AF inducibility with higher ACh concentrations.

The Relationship among Complex Fractionated Electrograms, Wavebreak, Phase Singularity, and Local Dominant Frequency in Fibrillation Wave-Dynamics: a Modeling Comparison Study

Although complex fractionated electrogram (CFE) is known to be a target for catheter ablation of fibrillation, its physiological meaning in fibrillation wave-dynamics remains to be clarified. We evaluated the spatiotemporal relationships among the parameters of fibrillation wave-dynamics by simulation modeling. We generated maps of CFE-cycle length (CFE-CL), local dominant frequency (LDF), wave break (WB), and phase singularity (PS) of fibrillation in 2-dimensional homogeneous bidomain cardiac modeling (1,000 x 1,000 cells ten Tusscher model). We compared spatiotemporal correlations by dichotomizing each maps into 10 x 10 lattice zones. In spatial distribution, WB and PS showed excellent correlation (R = 0.963, P < 0.001). CFE-CL had weak correlations with WB (R = 0.288, P < 0.001), PS (R = 0.313, P < 0.001), and LDF (R = -0.411, P < 0.001). However, LDF did not show correlation with PS or WB. PSs were mostly distributed at the periphery of low CFE-CL area. Virtual ablation (5% of critical mass) of CFE-CL < 100 ms terminated fibrillation at 14.3 sec, and high LDF ablation (5% of critical mass) changed fibrillation to organized tachycardia, respectively. In homogeneous 2D fibrillation modeling, CFE-CL was weakly correlated with WB, PS, and LDF, spatiotemporally. PSs are mostly positioned at the periphery of low CFE-CL areas, and virtual ablation targeting low CFE-CL regions terminated fibrillation successfully.

Computational Quantification of the Cardiac Energy Consumption during Intra-Aortic Balloon Pumping Using a Cardiac Electromechanics Model

To quantify the reduction in workload during intra-aortic balloon pump (IABP) therapy, indirect parameters are used, such as the mean arterial pressure during diastole, product of heart rate and peak systolic pressure, and pressure-volume area. Therefore, we investigated the cardiac energy consumption during IABP therapy using a cardiac electromechanics model. We incorporated an IABP function into a previously developed electromechanical model of the ventricle with a lumped model of the circulatory system and investigated the cardiac energy consumption at different IABP inflation volumes. When the IABP was used at inflation level 5, the cardiac output and stroke volume increased 11%, the ejection fraction increased 21%, the stroke work decreased 1%, the mean arterial pressure increased 10%, and the ATP consumption decreased 12%. These results show that although the ATP consumption is decreased significantly, stroke work is decreased only slightly, which indicates that the IABP helps the failed ventricle to pump blood efficiently.

An Integrative Model of the Cardiovascular System Coupling Heart Cellular Mechanics with Arterial Network Hemodynamics

The current study proposes a model of the cardiovascular system that couples heart cell mechanics with arterial hemodynamics to examine the physiological role of arterial blood pressure (BP) in left ventricular hypertrophy (LVH). We developed a comprehensive multiphysics and multiscale cardiovascular model of the cardiovascular system that simulates physiological events, from membrane excitation and the contraction of a cardiac cell to heart mechanics and arterial blood hemodynamics. Using this model, we delineated the relationship between arterial BP or pulse wave velocity and LVH. Computed results were compared with existing clinical and experimental observations. To investigate the relationship between arterial hemodynamics and LVH, we performed a parametric study based on arterial wall stiffness, which was obtained in the model. Peak cellular stress of the left ventricle and systolic blood pressure (SBP) in the brachial and central arteries also increased; however, further increases were limited for higher arterial stiffness values. Interestingly, when we doubled the value of arterial stiffness from the baseline value, the percentage increase of SBP in the central artery was about 6.7% whereas that of the brachial artery was about 3.4%. It is suggested that SBP in the central artery is more critical for predicting LVH as compared with other blood pressure measurements.

Theoretical Estimation of Cannulation Methods for Left Ventricular Assist Device Support as a Bridge to Recovery

Left ventricular assist device (LVAD) support under cannulation connected from the left atrium to the aorta (LA-AA) is used as a bridge to recovery in heart failure patients because it is non-invasive to ventricular muscle. However, it has serious problems, such as valve stenosis and blood thrombosis due to the low ejection fraction of the ventricle. We theoretically estimated the effect of the in-series cannulation, connected from ascending aorta to descending aorta (AA-DA), on ventricular unloading as an alternative to the LA-AA method. We developed a theoretical model of a LVAD-implanted cardiovascular system that included coronary circulation. Using this model, we compared hemodynamic responses according to various cannulation methods such as LA-AA, AA-DA, and a cannulation connected from the left ventricle to ascending aorta (LV-AA), under continuous and pulsatile LVAD supports. The AA-DA method provided 14% and 18% less left ventricular peak pressure than the LA-AA method under continuous and pulsatile LVAD conditions, respectively. The LA-AA method demonstrated higher coronary flow than AA-DA method. Therefore, the LA-AA method is more advantageous in increasing ventricular unloading whereas the AA-DA method is a better choice to increase coronary perfusion.

Numerical Simulation of the Effect of Sodium Profile on Cardiovascular Response to Hemodialysis

PURPOSE: We developed a numerical model that predicts cardiovascular system response to hemodialysis, focusing on the effect of sodium profile during treatment. MATERIALS and METHODS: The model consists of a 2-compartment solute kinetics model, 3-compartment body fluid model, and 12-lumped-parameter representation of the cardiovascular circulation model connected to set-point models of the arterial baroreflexes. The solute kinetics model includes the dynamics of solutes in the intracellular and extracellular pools and a fluid balance model for the intracellular, interstitial, and plasma volumes. Perturbation due to hemodialysis treatment induces a pressure change in the blood vessels and the arterial baroreceptors then trigger control mechanisms (autoregulation system). These in turn alter heart rate, systemic arterial resistance, and cardiac contractility. The model parameters are based largely on the reported values. RESULTS: We present the results obtained by numerical simulations of cardiovascular response during hemodialysis with 3 different dialysate sodium concentration profiles. In each case, dialysate sodium concentration profile was first calculated using an inverse algorithm according to plasma sodium concentration profiles, and then the percentage changes in each compartment pressure, heart rate, and systolic ventricular compliance and systemic arterial resistance during hemodialysis were determined. A plasma concentration with an upward convex curve profile produced a cardiovascular response more stable than linear or downward convex curves. CONCLUSION: By conducting numerical tests of dialysis/cardivascular models for various treatment profiles and creating a database from the results, it should be possible to estimate an optimal sodium profile for each patient.

Computational Analysis of Tumor Angiogenesis Patterns Using a Two-dimensional Model

Tumor angiogenesis was simulated using a two-dimensional computational model. The equation that governed angiogenesis comprised a tumor angiogenesis factor (TAF) conservation equation in time and space, which was solved numerically using the Galerkin finite element method. The time derivative in the equation was approximated by a forward Euler scheme. A stochastic process model was used to simulate vessel formation and vessel elongation towards a paracrine site, i.e., tumor-secreted basic fibroblast growth factor (bFGF). In this study, we assumed a two-dimensional model that represented a thin (1.0mm) slice of the tumor. The growth of the tumor over time was modeled according to the dynamic value of bFGF secreted within the tumor. The data used for the model were based on a previously reported model of a brain tumor in which four distinct stages (multicellular spherical, first detectable lesion, diagnosis, and death of the virtual patient) were modeled. In our study, computation was not continued beyond the 'diagnosis' time point to avoid the computational complexity of analyzing numerous vascular branches. The numerical solutions revealed that no bFGF remained within the region in which vessels developed, owing to the uptake of bFGF by endothelial cells. Consequently, a sharp declining gradient of bFGF existed near the surface of the tumor. The vascular architecture developed numerous branches close to the tumor surface (the brush-border effect). Asymmetrical tumor growth was associated with a greater degree of branching at the tumor surface.