# Application of In Silico Trials for the Investigation of Drug Effects on Cardiomyopathy-Diseased Heart Cycle Properties

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## Abstract

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## 1. Introduction

^{®}), Table 1.

^{2+}transient, which reduces the contractility of the heart muscle [8]. Digoxin can be used in DCM patients, and it increases the intracellular calcium concentration transient [17,18,19], but also myocardial contractility, stroke volume, and blood pressure [9]. It is proven that mavacamten affects the contractility of the heart muscle, and produces a significant decrease in tension during resting [4,20]. The influence of this drug is still under investigation in HCM patients. 2-deoxy adenosine triphosphate (dATP) is proven to be a molecule with a lot of potential in the treatment of DCM [21,22]. dATP has been shown to increase the contractility of heart tissue in heart failure patients [12], and systolic pressure in heart failure [13]. Finally, it was shown in [15] that Entresto

^{®}contributes to the remodelling of the walls of the heart chambers and to changes in the elasticity of blood vessels, which leads to a decrease in the resistance to blood flow. The changes in calcium concentration in the muscle cells, obtained for the aforementioned drugs and presented in Figure 1, represent the basis for further application in in silico clinical trials.

**Figure 1.**Effects of different drugs on calcium transient. (

**a**) Referent calcium transient predictions for HCM [6], disopyramide lowering total calcium transient (purple dashed line) [4] and dATP significantly lowering diastolic calcium concentration, reducing wall stiffness, and increasing contractility (black dashed line) [25]. (

**b**) Calcium transient predictions for DCM without (purple) and with (pink) digoxin, significantly lowering calcium concentration [24].

^{2+}concentrations, velocities, and pressure fields with analysis of the ejection fraction and wall stiffness have been presented, to show that a computational model can mimic, at a macroscopic level, the effects that different drugs can have on the cardiac cycle.

## 2. Materials and Methods

^{3}]. These equations are transformed by using the standard Galerkin method [27,28] in the balance equations of a finite element. The final form of this equation is solved for increments of blood velocity and pressure $\Delta {V}^{(i)}$ and $\Delta {P}^{(i)}$

**K**(details about matrices ${K}_{vp}^{}$ and ${\tilde{K}}_{vv}^{}$ are given elsewhere [27]), and mass matrix $M$, to find the vectors of velocity ${}^{n+1}{V}^{{}^{(i)}}$ and pressure ${}^{n+1}{P}^{{}^{(i)}}$ at the end of the current time step “n + 1”.

## 3. Results

^{2+}concentration, (2) the effect of the Holzapfel scale factor (wall stiffness), and (3) the effect of the inlet and outlet velocities. Finally, we present the effects on ejection fraction of different wall stiffness and inlet/outlet velocity values. Figure 4a shows the pressure distribution inside the HCM case LV model from Figure 3a across the 1.0 s time cycle, while Figure 4b shows the distribution of velocity within the fluid.

^{2+}concentration functions as shown in Figure 5a. Additionally, shifted and wider parabolic Ca

^{2+}concentration profiles are shown in Figure 5b.

^{2+}concentration functions on the PV diagram for the HCM model are shown in Figure 6a, while the effect of shifted and wider parabolic Ca

^{2+}concentration profiles on the PV diagrams are shown in Figure 6b.

^{2+}inlet concentration functions on the PV diagrams are shown in Figure 7a. In the case of a shifted and wider parabolic Ca

^{2+}concentration (Figure 6c), the PV diagrams are shown in Figure 7b. The PV diagrams for 50%, 80%, 120%, and 130% of nominal wall stiffness are shown in Figure 7c (nominal value shown in Figure 4). In Figure 7d, we present the influence of changes in the inlet and outlet velocities on the PV diagrams.

## 4. Discussion

^{2+}concentrations, wall stiffnesses, and inlet and outlet velocities. A quantitative evaluation of the effects of various medicines (digoxin, dATP, disopyramide, and mavacamten) on the cardiac output, encompassing both systolic and diastolic pressures, as well as the ejection fraction, is also provided by the FE simulations.

^{2+}concentration (Figure 6b and Figure 7b), the calcium concentration rises with the shifted parabolic function, and the muscles are activated later, leading to a delayed isovolumetric contraction. With a wider parabolic Ca

^{2+}concentration, the decrease rate is slower and more blood is ejected during systole.

^{2+}concentration profiles, heart wall stiffness, and the inlet/outlet velocities on heart performance. It was shown that drugs affect one or more heart parameters and properties. As can be seen from Figure 6a and Figure 7a, for triangular, parabolic, and steep time Ca

^{2+}time functions, with calcium concentrations that have the slowest decrease rate (i.e., triangular), muscles are activated for a prolonged period and, as a result, more blood is ejected from the left ventricle. When calcium starts to rise prematurely, which is the case for parabolic functions, the isovolumetric contraction occurs earlier than compared to other Ca

^{2+}concentrations. The results from Figure 6c and Figure 7c show lower pressure during isovolumetric contraction and systole with lower stiffness of the left ventricle wall. In Figure 8c, we show that a similar trend occurs with the two model geometries—the ejection fraction increases with wall stiffness. For the lower outlet velocity, less blood is ejected during systole, and vice versa. Also, the stroke volume during diastole is increased with an increase in the inlet velocity.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Elliott, P.M.; Anastasakis, A.; Borger, M.A.; Borggrefe, M.; Cecchi, F.; Charron, P.; Hagege, A.A.; Lafont, A.; Limongelli, G.; Mahrholdt, H.; et al. 2014 ESC Guidelines on diagnosis and management of hypertrophic cardiomyopathy. Eur. Heart J.
**2014**, 35, 2733–2779. [Google Scholar] [CrossRef] [PubMed] - World Health Organization. Cardiovascular Diseases (CVDS). Available online: https://www.who.int/en/news-room/fact-sheets/detail/cardiovascular-diseases-(cvds) (accessed on 1 February 2023).
- McNally, E.M.; Golbus, J.R.; Puckelwartz, M.J. Genetic mutations and mechanisms in dilated cardiomyopathy. J. Clin. Investig.
**2013**, 123, 19–26. [Google Scholar] [CrossRef] [PubMed] - Mijailovich, S.M.; Prodanovic, M.; Poggesi, C.; Regnier, M.; Geeves, M.A. Computational modeling of the effects of drugs in HCM and DCM cardiomyopathies. Biophys. J.
**2022**, 121, 236a. [Google Scholar] [CrossRef] - Hershberger, R.E.; Morales, A.; Siegfried, J.D. Clinical and genetic issues in dilated cardiomyopathy: A review for genetics professionals. Genet. Med.
**2010**, 12, 655–667. [Google Scholar] [CrossRef] [PubMed] - Mijailovich, S.M.; Prodanovic, M.; Poggesi, C.; Powers, J.D.; Davis, J.; Geeves, M.A.; Regnier, M. The Effect of Variable Troponin C Mutation Thin Filament Incorporation on Cardiac Muscle Twitch Contractions. J. Mol. Cell. Cardiol.
**2021**, 155, 112–124. [Google Scholar] [CrossRef] - Prodanovic, M.; Geeves, M.A.; Poggesi, C.; Regnier, M.; Mijailovich, S.M. Effect of Myosin Isoforms on Cardiac Muscle Twitch of Mice, Rats and Humans. Int. J. Mol. Sci.
**2022**, 23, 1135. [Google Scholar] [CrossRef] - Coppini, R.; Ferrantini, C.; Pioner, J.M.; Santini, L.; Wang, Z.J.; Palandri, C.; Scardigli, M.; Vitale, G.; Sacconi, L.; Stefàno, P.; et al. Electrophysiological and Contractile Effects of Disopyramide in Patients with Obstructive Hypertrophic Cardiomyopathy: A Translational Study. JACC Basic Transl. Sci.
**2019**, 4, 795–813. [Google Scholar] [CrossRef] - Patocka, J.; Nepovimova, E.; Wu, W.; Kuca, K. Digoxin: Pharmacology and toxicology—A review. Environ. Toxicol. Pharmacol.
**2020**, 79, 103400. [Google Scholar] [CrossRef] - Olivotto, I.; Oreziak, A.; Barriales-Villa, R.; Abraham, T.P.; Masri, A.; Garcia-Pavia, P.; Saberi, S.; Lakdawala, N.K.; Wheeler, M.T.; Owens, A.; et al. Mavacamten for treatment of symptomatic obstructive hypertrophic cardiomyopathy (EXPLORER-HCM): A randomised, double-blind, placebo-controlled, phase 3 trial. Lancet
**2020**, 396, 759–769. [Google Scholar] [CrossRef] - Ma, W.; Henze, M.; Anderson, R.L.; Gong, H.; Wong, F.L.; Del Rio, C.L.; Irving, T. The Super-Relaxed State and Length Dependent Activation in Porcine Myocardium. Circ. Res.
**2021**, 129, 617–630. [Google Scholar] [CrossRef] - Moussavi-Harami, F.; Razumova, M.V.; Racca, A.W.; Cheng, Y.; Stempien-Otero, A.; Regnier, M. 2-Deoxy adenosine triphosphate improves contraction in human end-stage heart failure. J. Mol. Cell. Cardiol.
**2015**, 79, 256–263. [Google Scholar] [CrossRef] [PubMed] - Kolwicz, S.C., Jr.; Hall, J.K.; Moussavi-Harami, F.; Chen, X.; Hauschka, S.D.; Chamberlain, J.S.; Regnier, M.; Odom, G.L. Gene Therapy Rescues Cardiac Dysfunction in Duchenne Muscular Dystrophy Mice by Elevating Cardiomyocyte Deoxy-Adenosine Triphosphate. JACC Basic Transl. Sci.
**2019**, 4, 778–791. [Google Scholar] [CrossRef] [PubMed] - McMurray, J.J.V.; Packer, M.; Desai, A.S.; Gong, J.; Lefkowitz, M.P.; Rizkala, A.R.; Rouleau, J.L.; Shi, V.C.; Solomon, S.D.; Swedberg, K.; et al. Angiotensin–Neprilysin Inhibition versus Enalapril in Heart Failure. N. Engl. J. Med.
**2014**, 371, 993–1004. [Google Scholar] [CrossRef] [PubMed] - Romano, G.; Vitale, G.; Ajello, L.; Bellavia, D.; Caccamo, G.; Corrado, E.; Di Gesaro, G.; Falletta, C.; La Franca, E.; Minà, C.; et al. The Effects of Sacubitril/Valsartan on Clinical, Biochemical and Echocardiographic Parameters in Patients with Heart Failure with Reduced Ejection Fraction: The “Hemodynamic Recovery”. J. Clin. Med.
**2019**, 8, 2165. [Google Scholar] [CrossRef] - Sherrid, M.V.; Pearle, G.; Gunsburg, D.Z. Mechanism of Benefit of Negative Inotropes in Obstructive Hypertrophic Cardiomyopathy. Circulation
**1998**, 97, 41–47. [Google Scholar] [CrossRef] - Bers, D.M. Cardiac excitation–contraction coupling. Nature
**2002**, 415, 198–205. [Google Scholar] [CrossRef] - Morgan, J. The effects of digitalis on intracellular calcium transients in mammalian working myocardium as detected with aequorin. J. Mol. Cell. Cardiol.
**1985**, 17, 1065–1075. [Google Scholar] [CrossRef] - Morgan, J.P.; Chesebro, J.H.; Pluth, J.R.; Puga, F.J.; Schaff, H.V. Intracellular calcium transients in human working myocardium as detected with aequorin. J. Am. Coll. Cardiol.
**1984**, 3, 410–418. [Google Scholar] [CrossRef] - Sparrow, A.J.; Watkins, H.; Daniels, M.J.; Redwood, C.; Robinson, P. Mavacamten rescues increased myofilament calcium sensitivity and dysregulation of Ca
^{2+}flux caused by thin filament hypertrophic cardiomyopathy mutations. Am. J. Physiol.-Heart Circ. Physiol.**2020**, 318, H715–H722. [Google Scholar] [CrossRef] - Cheng, Y.; Hogarth, K.A.; O’Sullivan, M.L.; Regnier, M.; Pyle, W.G. 2-Deoxyadenosine triphosphate restores the contractile function of cardiac myofibril from adult dogs with naturally occurring dilated cardiomyopathy. Am. J. Physiol.-Heart Circ. Physiol.
**2016**, 310, H80–H91. [Google Scholar] [CrossRef] - Powers, J.D.; Yuan, C.-C.; McCabe, K.J.; Murray, J.D.; Childers, M.C.; Flint, G.V.; Moussavi-Harami, F.; Mohran, S.; Castillo, R.; Zuzek, C.; et al. Cardiac myosin activation with 2-deoxy-ATP via increased electrostatic interactions with actin. Proc. Natl. Acad. Sci. USA
**2019**, 116, 11502–11507. [Google Scholar] [CrossRef] [PubMed] - Tomasevic, S.; Milosevic, M.; Milicevic, B.; Simic, V.; Prodanovic, M.; Mijailovich, S.M.; Filipovic, N. Computational Modeling on Drugs Effects for Left Ventricle in Cardiomyopathy Disease. Pharmaceutics
**2023**, 15, 793. [Google Scholar] [CrossRef] [PubMed] - Prodanovic, M.; Stojanovic, B.; Prodanovic, D.; Filipovic, N.; Mijailovich, S.M. Computational Modeling of Sarcomere Protein Mutations and Drug Effects on Cardiac Muscle Behavior. In Proceedings of the 2021 IEEE 21st International Conference on Bioinformatics and Bioengineering (BIBE), Kragujevac, Serbia, 25–27 October 2021. [Google Scholar] [CrossRef]
- Davis, J.; Davis, L.C.; Correll, R.N.; Makarewich, C.A.; Schwanekamp, J.A.; Moussavi-Harami, F.; Wang, D.; York, A.J.; Wu, H.; Houser, S.R.; et al. A Tension-Based Model Distinguishes Hypertrophic versus Dilated Cardiomyopathy. Cell
**2016**, 165, 1147–1159. [Google Scholar] [CrossRef] [PubMed] - SILICOFCM. In Silico Trials for Drug Tracing the Effects of Sarcomeric Protein Mutations Leading to Familial Cardiomyopathy. 777204. 2018–2022, H2020 Project. Available online: www.silicofcm.eu (accessed on 23 October 2023).
- Kojić, M.; Filipović, N.; Stojanović, B.; Kojić, N. Computer Modeling in Bioengineering: Theoretical Background, Examples and Software; John Wiley & Sons: Hoboken, NJ, USA, 2008. [Google Scholar]
- Bathe, K. Finite Element Procedures; Prentice-Hall: Englewood Cliffs, NJ, USA, 1996. [Google Scholar]
- Kojić, M.; Milošević, M.; Milićević, B.; Geroski, V.; Simić, V.; Trifunović, D.; Stanković, G.; Filipović, N. Computational model for heart tissue with direct use of experimental constitutive relationships. J. Serbian Soc. Comput. Mech.
**2021**, 15, 1–23. [Google Scholar] [CrossRef] - Sommer, G.; Schriefl, A.J.; Andrä, M.; Sacherer, M.; Viertler, C.; Wolinski, H.; Holzapfel, G.A. Biomechanical properties and microstructure of human ventricular myocardium. Acta Biomater.
**2015**, 24, 172–192. [Google Scholar] [CrossRef] - Sommer, G.; Haspinger, D.C.; Andrä, M.; Sacherer, M.; Viertler, C.; Regitnig, P. Quantification of Shear Deformations and Corresponding Stresses in the Biaxially Tested Human Myocardium. Ann. Biomed. Eng.
**2015**, 43, 2334–2348. [Google Scholar] [CrossRef] - Filipovic, N.; Mijailovic, S.; Tsuda, A.; Kojic, M. An Implicit Algorithm within the Arbitrary Lagrangian–Eulerian Formulation for Solving Incompressible Fluid Flow with Large Boundary Motions. Comput. Methods Appl. Mech. Eng.
**2006**, 195, 6347–6361. [Google Scholar] [CrossRef] - Kojić, M.; Milošević, M.; Ziemys, A. Computational Models in Biomedical Engineering; Elsevier: Amsterdam, The Netherlands, 2023. [Google Scholar] [CrossRef]
- Fung, Y.C.; Fronek, K.; Patitucci, P. Pseudoelasticity of arteries and the choice of its mathematical expression. Am. J. Physiol.-Heart Circ. Physiol.
**1979**, 237, H620–H631. [Google Scholar] [CrossRef] - Villars, P.S.; Hamlin, S.K.; Shaw, A.D.; Kanusky, J.T. Role of diastole in left ventricular function, I: Biochemical and biomechanical events. Am. J. Crit. Care
**2004**, 13, 394–403, quiz 404-5. [Google Scholar] [CrossRef] - Donea, J.; Huerta, A.; Ponthot, J.-P.; Rodríguez-Ferran, A. Arbitrary Lagrangian-Eulerian Methods. In Encyclopedia of Computational Mechanics, 2nd ed.; John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2017; pp. 1–23. [Google Scholar] [CrossRef]
- Kojic, M.; Milosevic, M.; Filipovic, N. PAK-BIO, Finite Element Program for Bioengineering Problems; Bioengineering Research and Development Center: Kragujevac, Serbia, 2018. [Google Scholar]
- Available online: https://github.com/miljanmilos/CAD-Solid-Field (accessed on 23 October 2023).
- Bayer, J.D.; Blake, R.C.; Plank, G.; Trayanova, N.A. A Novel Rule-Based Algorithm for Assigning Myocardial Fiber Orientation to Computational Heart Models. Ann. Biomed. Eng.
**2012**, 40, 2243–2254. [Google Scholar] [CrossRef] - Wang, K.; Terrar, D.; Gavaghan, D.J.; Mu-u-min, R.; Kohl, P.; Bollensdorff, C. Living cardiac tissue slices: An organotypic pseudo two-dimensional model for cardiac biophysics research. Prog. Biophys. Mol. Biol.
**2014**, 115, 314–327. [Google Scholar] [CrossRef] [PubMed] - Watson, S.A.; Scigliano, M.; Bardi, I.; Ascione, R.; Terracciano, C.M.; Perbellini, F. Preparation of viable adult ventricular myocardial slices from large and small mammals. Nat. Protoc.
**2017**, 12, 2623–2639. [Google Scholar] [CrossRef] [PubMed] - Watson, S.A.; Dendorfer, A.; Thum, T.; Perbellini, F. A practical guide for investigating cardiac physiology using living myocardial slices. Basic Res. Cardiol.
**2020**, 115, 61. [Google Scholar] [CrossRef] - Perbellini, F.; Thum, T. Living myocardial slices: A novel multicellular model for cardiac translational research. Eur. Heart J.
**2019**, 41, 2405–2408. [Google Scholar] [CrossRef] [PubMed] - Meki, M.H.; Miller, J.M.; Mohamed, T.M.A. Heart Slices to Model Cardiac Physiology. Front. Pharmacol.
**2021**, 12, 617922. [Google Scholar] [CrossRef] [PubMed] - Nunez-Toldra, R.; Kirwin, T.; Ferraro, E.; Pitoulis, F.G.; Nicastro, L.; Bardi, I.; Kit-Anan, W.; Gorelik, J.; Simon, A.R.; Terracciano, C.M. Mechanosensitive molecular mechanisms of myocardial fibrosis in living myocardial slices. ESC Heart Fail.
**2022**, 9, 1400–1412. [Google Scholar] [CrossRef] - Amesz, J.H.; Langmuur, S.J.J.; van Schie, M.S.; Taverne, Y.J.H.J. Production of living myocardial slices from circulatory death hearts after ex vivo heart perfusion. JTCVS Tech.
**2022**, 13, 128–130. [Google Scholar] [CrossRef] - Amesz, J.H.; Zhang, L.; Everts, B.R.; De Groot, N.M.S.; Taverne, Y.J.H.J. Living myocardial slices: Advancing arrhythmia research. Front. Physiol.
**2023**, 14, 1076261. [Google Scholar] [CrossRef]

**Figure 3.**Left ventricle parametric model with structural mesh. The geometry of the left ventricle models that mimic (

**a**) hypertrophic cardiomyopathy (HCM) and (

**b**) dilated cardiomyopathy (DCM) cases. Geometric parameters of the base and connecting part, along with valves (mitral and aortic), are notated. (

**c**) Diagram of prescribed inlet velocity at the mitral valve cross-section and outlet velocity at the aortic valve cross-section. (

**d**) Helical muscle fibres inside a solid wall.

**Figure 4.**Pressure (

**a**) and velocity (

**b**) fields obtained using FE simulation of LV parametric model with HCM at three different time points.

**Figure 5.**(

**a**) Triangular, parabolic, and steep Ca

^{2+}concentration change diagrams. (

**b**) Shifted and wider parabolic Ca

^{2+}change.

**Figure 6.**Effects of concentration profiles on PV diagrams in the HCM model for (

**a**) triangular, parabolic, and steep Ca

^{2+}concentrations, and (

**b**) shifted and wider parabolic Ca

^{2+}concentrations. Effects of different (

**c**) wall stiffnesses and (

**d**) velocities in HCM model on PV diagrams.

**Figure 7.**PV diagrams for DCM model. (

**a**) Effects of triangular, parabolic, and steep Ca

^{2+}concentration profiles on PV diagrams. (

**b**) Effects of shifted and wider parabolic Ca

^{2+}concentrations on PV diagrams. (

**c**) Effects of fluid velocities on the PV loops in DCM model. (

**c**) Influence of wall stiffness on PV diagrams for 50%, 80%, 120%, and 130% of nominal heart wall stiffness. (

**d**) Influence of the inlet and outlet velocities on the PV diagrams.

**Figure 8.**Dependence of the ejection fraction in DCM and HCM models on (

**a**) inlet velocity, (

**b**) outlet velocity, and (

**c**) wall elasticity (stiffness). Percentages are with respect to the nominal (referent) conditions, (

**d**) calcium concentration functions for different drugs, and (

**e**) corresponding PV diagrams.

Modulation of [Ca^{2+}] Transient | Changes in Kinetic Parameters | Changes in Macroscopic Parameters |
---|---|---|

HCM—Disopyramide, can reduce the contractility of the heart muscle [8] DCM—Digoxin, can increase myocardial contractility, stroke volume, and blood pressure [9] | HCM—Mavacamten, under investigation [10,11] DCM—dATP, increases contractility and systolic pressure in a failing heart [12,13] | HCM—Entresto^{®}, can affect the elasticity and stiffness of the walls of blood vessels and heart chambers, and can reduce resistance to blood flow [14,15]. |

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**MDPI and ACS Style**

Milosevic, M.; Milicevic, B.; Simic, V.; Anic, M.; Kojic, M.; Jakovljevic, D.; Filipovic, N.
Application of In Silico Trials for the Investigation of Drug Effects on Cardiomyopathy-Diseased Heart Cycle Properties. *Appl. Sci.* **2023**, *13*, 11780.
https://doi.org/10.3390/app132111780

**AMA Style**

Milosevic M, Milicevic B, Simic V, Anic M, Kojic M, Jakovljevic D, Filipovic N.
Application of In Silico Trials for the Investigation of Drug Effects on Cardiomyopathy-Diseased Heart Cycle Properties. *Applied Sciences*. 2023; 13(21):11780.
https://doi.org/10.3390/app132111780

**Chicago/Turabian Style**

Milosevic, Miljan, Bogdan Milicevic, Vladimir Simic, Milos Anic, Milos Kojic, Djordje Jakovljevic, and Nenad Filipovic.
2023. "Application of In Silico Trials for the Investigation of Drug Effects on Cardiomyopathy-Diseased Heart Cycle Properties" *Applied Sciences* 13, no. 21: 11780.
https://doi.org/10.3390/app132111780