Electro-Fluid-Mechanics of the Heart R. Verzicco 1,2,3 1 Università di Roma Tor Vergata, Rome, IT, 2 University of Twente Enschede, NL , 3 GSSI L’Aquila, IT The human heart is a hollow muscular organ that pumps blood throughout the body, to the lungs and to its own tissue. It drives the systemic-, the pulmonary- and the coronary-circulation, to bring oxygen and nutrients to every body cell and to remove the waste products. The heart achieves these fundamental goals by two parallel volumetric pumps, the right and the left, which beat approximately 10 5 times per day to deliver a continuous flow rate of about 5 l/min with an outstanding reliability. This is possible because of the highly cooperative and interconnected dynamics of the heart in which every element is key for the others. In a few words, each heart beat is triggered by specialized pacemaker cells that generate rhythmical electrical impulses propagating along well defined paths and with precise timings thus stimulating a sequence of contractions which pump the blood from atria to ventricles and eventually to the arteries. The resulting hemodynamics yields shear stresses and pressure loads on the myocardium and on the valves, whose opening/closing ensures the correct flow direction across heart chambers: only the synchronized and synergistic action of the electrophysiology, mechanics of the myocardium and hemodynamics allows the heart of an adult human to operate on a power of only 8 W, lifelong. Such a perfect and highly sophisticated mechanism, in which even a minor malfunctioning impairs its pumping efficiency, calls for a complete study considering the whole organ with its interconnected multi-physics dynamics rather than the single heart elements separately. In this talk we will present the results from a multi-physics computational model capable of tackling the electrophysiology, the elasto-mechanics and the fluid dynamics of the heart, including their multi- way coupled interactions. We will show results for physiologic and pathologic conditions as well as comparisons with experiments and clinical data. Figure 1: Isocontours of velocity magnitude over a heartbeat for a `left heart’ made of atrium, ventricle, mitral and aortic valves, fibrous trine, ascending and descending aorta. The phases of the cycle are indicated on the sketch of the electrocardiographic signal at the centre. In these results, any dynamic feature comes as part of the solution and nothing is prescribed. (Adapted from [2]). References: [1] V. Spandan, V. Meschini, R. Ostilla-Mónico, D. Lohse, G. Querzoli, M.D. de Tullio, R. Verzicco, A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes, J. of Comp. Phys., 348, 567-590, (2017). [2] F. Viola, V. Meschini, R. Verzicco, A multi-way coupled computational model for the left-heart: Fluid-Structure-Electrophysiology interaction (FSEI), Eur. J. of Mech. B/Fluids, to appear, (2019). P P Q R S T DIASTOLE DIASTOLE SYSTOLE 1 1.5 2 |u| 0 0.5 a) b) c) d) e) f)

Electro-Fluid-Mechanics of the Heart - ICTAM 2020Electro-Fluid-Mechanics of the Heart R. Verzicco1,2,3 1Università di Roma Tor Vergata, Rome, IT, 2University of Twente Enschede, NL

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Electro-Fluid-MechanicsoftheHeart

R.Verzicco1,2,31UniversitàdiRomaTorVergata,Rome,IT,2UniversityofTwenteEnschede,NL,3GSSIL’Aquila,ITThehumanheartisahollowmuscularorganthatpumpsbloodthroughoutthebody,tothelungsandtoitsowntissue.Itdrivesthesystemic-,thepulmonary-andthecoronary-circulation,tobringoxygenand nutrients to every body cell and to remove the waste products. The heart achieves thesefundamentalgoalsbytwoparallelvolumetricpumps,therightandtheleft,whichbeatapproximately105 timesperday todelivera continuous flowrateofabout5 l/minwithanoutstandingreliability.Thisispossiblebecauseofthehighlycooperativeandinterconnecteddynamicsoftheheartinwhichevery element is key for the others. In a few words, each heart beat is triggered by specializedpacemakercellsthatgeneraterhythmicalelectricalimpulsespropagatingalongwelldefinedpathsandwithprecisetimingsthusstimulatingasequenceofcontractionswhichpumpthebloodfromatriatoventricles and eventually to the arteries. The resulting hemodynamics yields shear stresses andpressureloadsonthemyocardiumandonthevalves,whoseopening/closingensuresthecorrectflowdirection across heart chambers: only the synchronized and synergistic action of theelectrophysiology, mechanics of the myocardium and hemodynamics allows the heart of an adulthumantooperateonapowerofonly8W,lifelong.Suchaperfectandhighlysophisticatedmechanism,inwhichevenaminormalfunctioningimpairsitspumping efficiency, calls for a complete study considering thewhole organwith its interconnectedmulti-physicsdynamicsratherthanthesingleheartelementsseparately.Inthistalkwewillpresenttheresultsfromamulti-physicscomputationalmodelcapableoftacklingtheelectrophysiology,theelasto-mechanicsandthefluiddynamicsoftheheart,includingtheirmulti-way coupled interactions.Wewill showresults forphysiologic andpathologic conditionsaswell ascomparisonswithexperimentsandclinicaldata.

Figure 1: Isocontours of velocitymagnitude over aheartbeat for a `left heart’ made of atrium,ventricle, mitral and aortic valves, fibrous trine,ascendinganddescendingaorta.Thephasesof thecycle are indicated on the sketch of theelectrocardiographic signal at the centre. In theseresults, any dynamic feature comes as part of thesolutionandnothingisprescribed.(Adaptedfrom[2]).

References:[1] V. Spandan, V. Meschini, R. Ostilla-Mónico, D. Lohse, G. Querzoli, M.D. de Tullio, R. Verzicco, Aparallelinteractionpotentialapproachcoupledwiththeimmersedboundarymethodforfullyresolvedsimulationsofdeformableinterfacesandmembranes,J.ofComp.Phys.,348,567-590,(2017).[2] F. Viola, V. Meschini, R. Verzicco, A multi-way coupled computational model for the left-heart:Fluid-Structure-Electrophysiologyinteraction(FSEI),Eur.J.ofMech.B/Fluids,toappear,(2019).

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