Cardiovascular and Respiratory Bioengineering

By Nenad Filipovic

Cardiovascular and Respiratory Bioengineering focuses on computational tools and modeling techniques in cardiovascular and respiratory systems that help develop bioengineered solutions. The book demonstrates how these technologies can be utilized in order to tackle diseases and medical issues. It provides practical guidance on how a bioengineering or medical problem can be modeled, along with which computational models can be used. Topics include computer modeling of Purkinje fibers with different electrical potential applied, modeling of cardiomyopathies caused by sarcomeric gene mutations, altered sarcomere function, perturbations in intracellular ion homeostasis, impaired myocardial energetics at reduced costs, and more.

The book also discusses blood flow through deformable blood vessels in human aorta, abdominal aortic aneurysm, carotid artery, coronary artery and plaque formation, along with content on stent deployment modeling and stent design and optimization techniques.

• Features practical applications of cardiovascular and respiratory technology to counteract diseases
• Includes detailed steps for the modeling of cardiovascular and respiratory systems
• Explores a range of different modeling methods, including computational modeling, predictive modeling and multi-scale modeling
• Covers biological processes and biomechanics relevant to cardiovascular and respiratory bioengineering

• Language: English
• Publisher: Academic Press
• Release date: May 12, 2022
• ISBN: 9780128242292

Nenad Filipovic

Nenad D. Filipovic is Rector of University of Kragujevac, Serbia, full Professor at Faculty of Engineering and Head of Center for Bioengineering at University of Kragujevac, Serbia. He was Research Associate at Harvard School of Public Health in Boston, US. His research interests are in the area of biomedical engineering, cardiovascular disease, fluid-structure interaction, biomechanics, bioinformatics, biomedical image processing, medical informatics, multi-scale modeling, data mining, software engineering, parallel computing, computational chemistry and bioprocess modeling. He is author and co-author 16 textbooks and 11 monographies, over 300 publications in peer review journals and over 10 software for modeling with finite element method and discrete methods from biofluid mechanics and multiphysics. He also leads a number of national and international projects in EU and US in area of bioengineering and software development. He is Director of Center for Bioengineering at University of Kragujevac and leads joint research projects with Harvard University and University of Texas in area of bio-nano-medicine computer simulation. He also leads a number of national and international projects in area of bioengineering and bioinformatics. He is a Managing Editor for Journal of Serbian Society for Computational Mechanics and member of European Society of Biomechanics (ESB), European Society for Artificial Organs (ESAO) and IEEE member.

Book preview

Preface

This book is intended for pregraduate and postgraduate students as well as for researchers in the domains of bioengineering, biomechanics, biomedical engineering, and medicine.

The book can be useful for researchers in various fields related to bioengineering and other scientific fields, including medical applications. It provides basic information about how a bioengineering (or medical) problem can be modeled, which computational model can be used, and what is the background of the applied computer models.

Different examples in the area of cardiovascular and respiratory systems give readers an overview of typical problems that can be modeled, followed by a complete theoretical background with numerical method behind.

There are different examples of application: electromechanical ventricle modeling, carotid artery disease, stent mechanical testing, ECG simulation for cardiac disease, aorta stenosis, lung tissue, particle deposition, pulmonary acinus, respiratory airways, drug efficacy, tissue engineering, electrospinning, AI, COVID-19, and economic analysis of in silico clinical trials.

This book will not only be useful for lecturers of bioengineering courses at universities, but it will also be very helpful for researchers, medical doctors, and clinical researchers.

In Chapter 1, computational modeling of electromechanical coupling of the left ventricle is presented. Chapter 2 introduces a deep learning approach in the stratification of patients with carotid artery disease. Simulation of stent mechanical testing is described in Chapter 3. Chapter 4 presents a basic numerical and experimental approach for ECG simulation of cardiac hypertrophic conditions. The simulation of carotid artery plaque development and treatment is presented in Chapter 5. Myocardial work and aorta stenosis simulation are described in Chapter 6. Chapter 7 gives numerical and experimental examples for lab-on-a-chip for lung tissue. Chapter 8 provides a review of the chaotic mixing and its role in enhancing particle deposition in the pulmonary acinus. Three-dimensional reconstruction and modeling of the respiratory airways, particle deposition, and drug delivery efficacy are introduced in Chapter 9. In Chapter 10, the basic tissue engineering—electrospinning approach is given. Chapter 11 focuses on the application of numerical methods for the analysis of the respiratory system. Artificial intelligence approach toward analysis of COVID-19 development—personalized and epidemiological model is presented in Chapter 12. Finally, economic analysis of in silico clinical trials is given in Chapter 13.

Nenad Filipovic, Faculty of Engineering, University of Kragujevac, Serbia

Chapter 1: Computational modeling of electromechanical coupling of left ventricle

Nenad Filipovic    Bioengineering Research and Development Center (BioIRC), Kragujevac, Serbia

Abstract

Cardiovascular diseases are the leading cause of death in the world. They reduce the life quality and consume almost a trillion dollars in health-care expenses in Europe and the United States alone. Computational modeling and simulation technologies hold promise as important tools to improve cardiac care and are already in use to elucidate the fundamental mechanisms of cardiac physiology and pathophysiology. In this chapter, detailed computational modeling of electromechanical coupling for the left ventricle is presented.

A computational platform in the SILICOFCM project was developed using state-of-the-art finite element modeling for macro-simulation of fluid-structure interaction with micro-modeling at the molecular level for drug interaction with the cardiac cells.

In this chapter, fluid-solid coupling for the left ventricle was introduced. A nonlinear material model for the heart wall using constitutive curves that include the stress-strain relationship was presented.

A monodomain model of the modified FitzHugh-Nagumo model of the cardiac cell was used. Six electrodes are positioned at the chest to model the precordial leads and the results are compared with real clinical measurements. The inverse ECG method was used to optimize the potential on the heart. A whole heart electrical activity in the torso embedded environment, with spontaneous initiation of activation in the sinoatrial node, incorporating a specialized conduction system with heterogeneous action potential morphologies throughout the heart was presented. Body surface potential maps in a healthy subject during progression of ventricular activation in nine sequences were used.

The results with a parametric and realistic model of the left ventricle where PV (pressure/volume) diagrams depend on the change of Ca² +, elasticity of the wall, and the inlet and outlet velocity profiles have been presented. It directly affects the ejection fraction.

The presented approach with variation of LV geometry and simulations, which include the influence of different parameters on the PV diagrams, is directly interlinked with drug effects on heart function. This work is in continuous progress and it includes the incorporation of different drugs that directly affect the cardiac PV diagrams and ejection fraction (e.g., angiotensin-converting enzyme inhibitors, angiotensin receptor blockers, nitrates, diuretics, calcium channel blockers). A computational platform such as SILICOFCM for sure will open a new avenue for in silico clinical trials as well as a new tool for risk prediction of cardiac disease in specific patients using drug therapy.

Keywords

SILICOFCM; Heart modeling; Finite element; Electromechanical coupling; Drug simulation; In silico clinical trials

1: Introduction

It is very important to use detailed and complex model, with high-resolution anatomically accurate model of whole heart electrical activity, which requires extensive computation times, dedicated software, and even the use of supercomputers (Gibbons Kroeker et al., 2006; Pullan et al., 2005; Trudel et al., 2004).

We recently developed methodology for a real 3D heart model, using a linear elastic and orthotropic material model based on Holzapfel experiments. Using this methodology, we can accurately predict the transport of electrical signals and the displacement field within the heart tissue (Kojic, Milosevic, Simic, Milicevic, et al., 2019).

Muscles in the body are activated by electrical signals transmitted from the nervous system to muscle cells, thus affecting the change of the cell membrane potentials. Additionally, calcium current and concentration inside the cell are the main causes of generating active stress within muscle fibers.

In order to simulate an electrical model of the heart, it requires an adequate model of the transfer between cardiac electrical activity and the ECG signals measured on the torso surface. Also, it requires solving a mathematically inverse problem for which no unique solution exists. Clinical validation in humans is very limited since simultaneous whole heart electrical distribution recordings are inaccessible for both practical and ethical reasons (Trudel et al., 2004).

The rapid development of information technologies, simulation software packages, and medical devices in recent years provides the opportunity for collecting a large amount of clinical information. Creating comprehensive and detailed computational tools has become essential to process specific information from the abundance of available data. From the point of view of physicians, it becomes of paramount importance to distinguish normal phenotypes from the appearance of the phenotype in a specific patient in order to estimate its disease progression, therapeutic responses, and future risks. Recent computational models have significantly improved integrative understanding of the heart muscles behavior in HCM (hypertrophic) and DCM (diluted) cardiomyopathies. The development of novel integrative modeling approaches could be an effective tool in distinguishing the type and severity of symptoms in, for example, multigenic disorder patients and assessing the degree to which normal physical activity is impaired.

On the other hand, patient-specific modeling presents many new challenges, including (1) the lack of details regarding physical and biological properties of the human heart; (2) the need for a subject-specific estimation of parameters from limited, noisy data, typically obtained using noninvasive measurements; (3) the need to perform numerous large-scale computations in a clinically useful time frame; and (4) the need to store and share model metadata that can be reused without compromising patient confidentiality. Despite the difficulties, multiscale models of the heart can include a level of detail sufficient to achieve predictions that closely follow observed transient responses providing solid evidence for prospective clinical applications.

However, regardless of the substantial scientific effort by multiple research labs and significant amount of grant support, currently there is only one commercially available software package regarding multiscale and whole heart simulations called the SIMULIA Living heart model (Baillargeon et al., 2014). It includes dynamic, electromechanical simulation, refined heart geometry, a blood flow model, and a complete characterization of cardiac tissues including passive and active characteristics, its fibrous nature, and the electrical pathways. This model is targeted for use in personalized medicine, but active material characterization is based on a phenomenological model introduced by Guccione et al. (Guccione et al., 1993; Guccione & McCulloch, 1993). Therefore, SIMULIA cannot directly and accurately translate the changes in the contractile protein functional characteristics observed in numerous cardiac diseases. These changes are caused by mutations and other abnormalities at the molecular and subcellular level. The limited use of SIMULIA software in a small number of applications in clinical practice is a great example of today's struggles in developing higher-level multiscale human heart models. On the other hand, it is a motivation for developing a new generation of multiscale program packages that can trace the effects of mutations from the molecular to organ scale.

In silico clinical trials are a new paradigm for the development and testing of a new drug and medical device. The SILICOFCM project (H2020 project SILICOFCM, 2018–2022) is the multiscale modeling of familial cardiomyopathy which considers a comprehensive list of patient-specific features as genetic, biological, pharmacologic, clinical, imaging, and cellular aspects. The biomechanics of the heart is a key part of the in silico clinical platform. We have built this platform using state-of-the-art finite element modeling for macro-simulation of the fluid-structure interaction with micro-modeling on the molecular level for drug interaction with the cardiac cells.

2: Method

2.1: Fluid-solid coupling

The blood is considered as an incompressible homogenous viscous fluid. The fundamental laws of physics which include balance of mass and balance of linear momentum are applicable here. These laws are expressed by the continuity equation and the Navier-Stokes equations (Kojic, Milosevic, Simic, Geroski, et al., 2019).

We present here the final form of these equations to emphasize some specifics related to blood flow. The incremental-iterative balance equation of a finite element for a time step ‘n’ and equilibrium iteration ‘i’ has a form

si1_e

  

(1)

where n + 1V(i − 1) n + 1P(i − 1) are the nodal vectors of blood velocity and pressure, with the increments in time step ΔV(i) and ΔP(i) (the index ‘blood’ is used to emphasize that we are considering blood as the fluid); Δt is the time step size and the left upper indices ‘n’ and ‘n + 1’ denote the start and end of time step. Note that the vector n + 1Fext(i − 1) of external forces includes the volumetric and surface forces. In the assembling of these equations, the system of equations of the form (1) is obtained, with the volumetric external forces and the surface forces acting only on the fluid domain boundary (the surface forces among the internal element boundaries cancel).

The solid domain for the left ventricle was defined with a nonlinear finite element equation taking into account the Holzaphel and Hunter model (Kojic, Milosevic, Simic, Geroski, et al., 2019). The balance of linear momentum is derived from the fundamental differential equations of balance of forces acting at an elementary material volume. In dynamic analysis, we include the inertial forces. Then by applying the principle of virtual work

si2_e    (2)

Here the element matrices are M is the mass matrix; Bw is the damping matrix in cases when the material has a viscous resistance; K is the stiffness matrix; and Fext is the external nodal force vector which includes body and surface forces acting on the element.

About half of the cardiomyopathies are caused by genetic malformations with mutations in sarcomeric proteins (Vikhorev & Vikhoreva, 2018). In addition to significant changes at the level of molecular mechanisms within cardiomyocytes, significant changes are also observed at the macroscopic level in terms of changes in blood pressure, the left ventricular mass index, wall thickness, left ventricular diameter, left ventricular volume, fractional shortening, and ejection fraction. A change in these parameters induces many other physiologically important features and finally on status of suffering patients. Many drugs are created to counteract these changes by reducing the wall thickness, increasing the left ventricular volume, or increasing the ejection fraction.

2.2: Nonlinear material model of the left ventricle

In the heart cycle, we have two repeated regimes: systole and diastole. In the systole regime, the left ventricle (LV) contract and pump blood to the arterial system and the right ventricle (RV) contract and pump blood to the lung. At the same time, the atria expand while the blood comes from the veins to the right atrium and from the lung to the left atrium. In the diastole regime, the atria contract and blood flows from the atria into the ventricles which expand. Expansion is a consequence of the blood loading which enters the ventricles. At the end of diastole, there is maximum deformation and maximum passive stress within the tissue of ventricles. The active stress is generated during systole within the muscle cells and, together with the passive stress, provides the mechanical forces to overcome the resistance to blood flow to the arterial system (from the LV) and to the lung (from the RV). It can be observed that the resistance to blood flow to the arterial system is higher than to the lung. This directly indicates that overall loading is higher on the walls of the LV. That is a reason why it is very important to study processes in the LV. Heart dysfunction and heart failure are often related to the tissue of the left ventricle. Mechanical characteristics of the LV tissue represent one of the fundamental components of heart behavior, and have been under investigation over centuries.

The structural morphology of the left ventricle tissue is very complex. The microstructural composition has been intensively studied and it has been described in the medical and engineering literature (e.g., Sommer et al., 2015a; Holzapfel & Ogden, 2009; McEvoy, Holzapfel, & McGarry, 2018). The outline of the specificities which are most important for our computational modeling has been presented here. In Fig. 1 is shown a schematic representation of the ventricle according to Bovendeerd et al. (1992), indicating that the ventricle can geometrically be approximated by a thick shell. The wall is composed of layers (or sheets) of parallel muscle cells (myocytes) which have a fibrous character and occupy about 70% of the volume. The remaining 30% consist of various interstitial components, where 2%–5% represent the collagen network for lateral connections.

Fig. 1

Fig. 1 Schematic representation of geometry of the left ventricle with material element and local unit vectors of fiber, sheet, and normal directions.

Long muscle cells form fibers where the muscle activation occurs producing active stress along directions of fibers. The material can be considered orthotropic with the orthotropic unit vectors f and s for the fiber and sheet directions, respectively, lying in the tangential plane of the sheet surface. The third direction is defined by the unit vector n normal to the sheet plane, as shown in Fig. 1. As stated above, the fibers have a helicoidal character with the angle ϕ changing over the wall thickness.

2.2.1: Biaxial tests

The mechanical behavior of the ventricle as a thick shell structure is mainly characterized by the mechanical properties of the sheet layers. Due to these circumstances, experimental and theoretical investigations are focused on the kinematics of deformation and constitutive laws of the sheet layers, as outlined in the Introduction. Mechanical investigations are usually performed as biaxial loading and shear on a sample in a sheet plane. In Fig. 2 are shown the average constitutive curves obtained by using samples of 26 human ventricles subjected to biaxial loading in the sheet plane.

Fig. 2

Fig. 2 Average constitutive curves (26 samples) for human left ventricle tissue subjected to biaxial loading for various ratios of sheet strain e 2 and fiber strain e 1 , according to Sommer et al. (2015b).

Tests were performed by loading and unloading into fiber (MFD—according to the notation in Sommer et al. (2015b)) and sheet (CFD) directions up to three levels of maximum stretch (1.05, 1.075,1.1) and maintaining the constant ratios between strain e2 = λ2 − 1 in the sheet direction and fiber strain e1 = λ1 − 1; here λ2 and λ1 are stretches. It can be seen that the constitutive curves are highly nonlinear, with hyperelastic characteristics usual for biological materials. The stress-stretch relationship depends on the stretch level to which the material is stretched before unloading and on the stretch ratio. The material displays a hysteretic character, with hysteresis and therefore the dissipation energy per unit volume is more pronounced at higher level of stretch. In Fig. 3 are shown average constitutive curves with the curves obtained using mean values of the loading and unloading paths. They can be used in our computational procedure and also in applications of the analytical forms of the constitutive laws.

Fig. 3

Fig. 3 Average constitutive curves for the human left ventricle tissue subjected to biaxial loading, with mean values of the loading and unloading, and for several ratios of sheet strain e 2 and fiber strain e 1 , according to Sommer et al. (2015b) .

Here we add constitutive curves for the left ventricle, according to Stevens et al. (2003). These curves include the stress-strain relationship for the sheet-normal direction which will be used in our computational model (Fig. 4).

Fig. 4

Fig. 4 Constitutive curves obtained by uniaxial tension in the three material directions of the left ventricle tissue, according to Stevens et al. (2003) .

2.2.2: Shear tests

In Sommer et al. (2015b) are reported results of triaxial shear tests. Six modes of shear deformation are generated in planes corresponding to the f-s-n material coordinate system in the undeformed material, with initial unit vectors f0, s0, n0 as shown in Fig. 5. Shear stresses corresponding to each mode are expressed in terms of the ‘amount of shear’ ΔL/L where ΔL is the displacement in direction of the shear stress and L is the sample dimension. This amount of shear represents a part of the usually used engineering shear strain of a continuum. The specimen was loaded in cycles, where loading is increased and then decreased, further followed by loading in the opposite direction. Also, tests were performed with different load levels. Results are shown in Fig. 6 displaying the anisotropic and hysteretic character of the material under shear. The shear stresses are the largest on planes with normal f (FS and FN) and smallest on planes with normal n (NF and NS).

Fig. 5

Fig. 5 Shear modes used in triaxial shear tests ( H2020 project SILICOFCM, 2018–2022 ).

Fig. 6

Fig. 6 Shear constitutive curves, relation between shear stress and amount of shear, for the six planes: (A) FS-FN, (B) SF-SN, and (C) NF-NS according to H2020 project SILICOFCM (2018–2022) .

2.3: Electrophysiology of the left ventricle

Cardiac cells are filled and surrounded by ionic solution, mostly sodium Na +, potassium K +, and calcium Ca² +. These charged atoms move between the inside and the outside of the cell through proteins called ion channels. Cells are connected through gap junctions which form channels that allow ions to flow from one cell to another.

An accurate numerical model is needed for a better understanding of heart behavior in cardiomyopathy, heart failure, cardiac arrhythmia, and other heart diseases. These numerical models usually include drug transport, electrophysiology, and muscle mechanics (Fitzhugh, 1961).

We have presented the heart geometry and seven different regions of the model where we included the: (1) sinoatrial node, (2) atria, (3) atrioventricular node, (4) His bundle, (5) bundle fibers, (6) Purkinje fibers, and (7) ventricular myocardium (Fig. 7).

Fig. 7

Fig. 7 Heart geometry and seven different regions of the model.

In this study, we used the monodomain model of the modified FitzHugh-Nagumo model of the cardiac cell (Nagumo et al., 1962; Sovilj et al., 2013; Wang & Rudy, 2006).

si3_e

  

(3)

where Vm is the membrane potential, R is the recovery variable, a is relating to the excitation threshold, ℯ is relating to the excitability, A is the action potential amplitude, B is the resting membrane potential, and c1, c2, and k are the membrane-specific parameters.

The monodomain model (Sovilj et al., 2013; Wang & Rudy, 2006) with incorporated modified FitzHugh-Nagumo equations is

si4_e

  

(4)

where β is the membrane surface-to-volume ratio, Cm is the membrane capacitance per unit area, σ is the tissue conductivity, Iion is the ionic transmembrane current density per unit area, and Is is the stimulation current density per unit area.

Parameters for the monodomain model with modified FitzHugh-Nahumo equations are presented in Table 1.

Table 1

The 12-Lead ECG became a standard in clinical practice since the American Heart Association published its recommendation in 1954. It consists in recording signals from 10 electrodes respecting the following placement (Fig. 8):

•V1: 4th intercostal space to the right of the sternum;

•V2: 4th intercostal space to the left of the sternum;

•V3: midway between V2 and V4;

•V4: 5th intercostal space at the midclavicular line;

•V5: anterior axillary line at the same level as V4;

•V6: midaxillary line at the same level as V4 and V5;

Fig. 8

Fig. 8 Six electrodes (V1–V6) which are positioned at the chest to model the precordial leads.

Computer simulations were conducted using the fully coupled heart torso monodomain equations including a detailed description of human ventricular cellular electrophysiology. Myocardial and torso conductivities were based on the literature, as presented in Table 1.

Boundary conditions on all interior boundaries in contact with the torso, lungs, and cardiac cavities are zero flux for Vm; therefore, − n ⋅ Γ = 0 where n is the unit outward normal vector on the boundary and Γ is the flux vector through that boundary for the intracellular voltage, equal to Γ = − σ ⋅∂ Vm/∂ n. For the variable Vm, the inward flux on these boundaries is equal to the outward current density J from the torso/chamber volume conductor; therefore, − σ ∂ Vm/∂ n = n ⋅ J.

In the second part, we implement the performance of classical approaches for solving the ECG inverse problem using the epicardial potential formulation. The studied methods are the family of Tikhonov methods and the L regularization-based methods (Van Oosterom, 1999, 2001, 2003; Wang & Rudy, 2006).

ECG measurement was performed on the healthy volunteer in the Clinical Center Kragujevac, University of Kragujevac.

3: Results

The whole heart activation simulations from the lead II ECG signal at various time points on the ECG signal for patients #1 and #2 have been presented in Figs. 9 and 10. A comparison of the simulated ECG on the surface body with real ECG measurement at V1 for patients #1 and #2 has been presented in Figs. 11 and 12.

Fig. 9

Fig. 9 Patient #1: Whole heart activation simulation from the lead II ECG signal at various time points on the ECG signal. There are 1–5 activation sequences corresponding to the ECG signal above. The color bar denotes the mV of the transmembrane potential.

Fig. 10

Fig. 10 Patient #2: Whole heart activation simulation from the lead II ECG signal at various time points on the ECG signal. There are 1–5 activation sequences corresponding to the ECG signal above. The color bar denotes the mV of the transmembrane potential.

Fig. 11

Fig. 11 Patient #1: Comparison of the simulated ECG on the surface body with the real ECG measurement at V1.

Fig. 12

Fig. 12 Patient #2: Comparison of the simulated ECG on the surface body with the real ECG measurement at V1.

The P glyph_sbnd V diagram plots volume along the X-axis and pressure on the Y-axis. The area of the loop is equal to the stroke volume, which refers to the amount of blood pumped out of the left ventricle in one cardiac cycle. The effects of isolated changes in the preload are best demonstrated on the pressure-volume (P glyph_sbnd V) diagram, which relates ventricular volume to the pressure inside the ventricle throughout the cardiac cycle. The maximum right point on the diagram is denoted as the end-diastolic volume (EDV), while the minimum left point is denoted as the end-systolic volume (ESV). Also, as EDV increases, the proportion of blood ejected by the heart increases slightly; this is the ejection fraction (EF) calculated by the equation: (EDV-ESV)/EDV. The reverse is also true. A decrease in the preload will result in a leftward shift down the end-diastolic P glyph_sbnd V line, decreasing EDV, stroke volume, and causing a slight decrease in the ejection fraction (Villars et al., 2004).

A variety of commonly used medications affects the cardiac function. Some of the first-line treatments for heart failure, myocardial ischemia, and hypertension are described. Drugs that decrease the preload and have an influence on the cardiac PV diagrams are as follows (Sheth et al., 2015):

•Angiotensin-converting enzyme (ACE) inhibitors—interrupt the renin-angiotensin-aldosterone system (RAAS). RAAS is a complex system responsible for regulating the body's blood pressure. The kidneys release an enzyme called renin in response to the low blood volume, low salt (sodium) levels, or high potassium levels.

•Angiotensin receptor blockers (ARBs)—interrupt the RAAS.

•Nitrates—cause nitric oxide-induced vasodilation.

•Diuretics—promote the elimination of salt and water, resulting in a decreased overall intravascular volume.

•Calcium channel blockers—block calcium-induced vasoconstriction and decrease cardiac contractility.

The results obtained with a parametric model where PV diagrams depend on the change of Ca² +, elasticity of the wall, and the inlet and outlet velocity profiles have been presented. It directly affects the ejection fraction.

The result of the PAK solver simulation (PAK, 2022) with different LV geometry and corresponding scenarios has been presented. The first part is related to the results obtained from the LV model with a 20% shorter base length. The second part is related to the results obtained from the LV model with a 50% longer base length and 50% thicker lateral wall. Both cases cover three scenarios: (i) influence of Ca² + concentration, (ii) influence of the Holzapfel scale factor (elasticity), and (iii) influence of inlet and outlet