What kind of a pump is the heart?

Notes

1. 1.

   A discrete time linear system can be represented in a state-variable format using an input c : p j  = g 1 p j  − 1 + g 2 c j , where both p and c are scalars and the system gains g 1 and g 2 are constants. When the signal p is not directly measured, but is assessed by a variable v measured with a gain g 3 and noise n:

   $$ {v}_j={g}_3{p}_j+{n}_j. $$

   The Kalman filter is an optimal linear estimator based on an iterative prediction–correction algorithm aimed at extracting an optimal estimate (i.e., filtering out) of a given signal from a series of incomplete, indirect, inaccurate, uncertain, and noisy observations. These measurements ({m j } N j = 1 ) are obtained at diverse instants (j: samples of the discretized time variable). This recursive computational technique delivers statistically optimal estimates (e j ) of the parameter of interest (p), minimizing the mean square error of the estimated parameters that have an assumed Gaussian distribution. A Kalman gain (g K) is calculated at each step. The state and measurement equations of Kalman filter assumed that (1) the N p -dimensional state vector is a linear combination of its previous value, a N c -dimensional input control vector (c j ), and a white process noise (n (P) j ) with zero mean, given covariance, and uncorrelated with the input and (2) any measurement is a linear combination of the signal and zero-mean white measurement noise (n (M) j ) independent of the other noise source and input:

   $$ \begin{array}{l}{p}_j+1=A(j){p}_j+B(j){c}_j+{n}_j^{(P)};\\ {} {v}_j =G(j){p}_j+{n}_j^{(M)}\end{array} $$

   The Kalman filter computes the optimal averaging factor from the previous estimation via iterative refinement to get a small residual r j  = v j  − g 3 e j0, the a priori estimate (e j0) of input p j being used to predict an a posteriori estimate of output v j .

   $$ {e}_j={e}_{j0}+{g}_K{r}_j. $$

2. 2.

   Differential operator associated with the total energy that can be applied to wave-governed problems.

3. 3.

   Five genes encode pore-forming ion channel α subunits (CACNA1C, KCNH2, KCNJ2, KCNQ1, and SCN5A) and 7 genes ion-channel regulators (KCNE1, KCNE2, SCN4B [voltage-gated sodium channel NaV β4 subunit], \( \mathrm{ANKB}\ \left[LQT4;\downarrow {i}_{NaK_{ATP}}\;\mathrm{and}\downarrow {i}_{\mathrm{NaCaX}}\right] \), CAV3 [LQT9; ↑ i Na], AKAP9 [LQT11; ↓ i K;s], and SNTA1 [LQT12; ↑ i Na]).

Abbreviations

Action potential:

Short-duration electrochemical event during which the electrical transmembrane potential of a nodal or muscular cell (in addition to other types of excitable cells, such as neurons and endocrine cells) rapidly rises from a resting potential (depolarization) and falls (repolarization). Action potentials are mainly generated by various categories of voltage-gated ion (calcium, potassium, and sodium) channels located in the plasma membrane, but ion pumps and exchangers are also involved. Any action potential is followed by a refractory period that can be divided into an absolute refractory period, during which another action potential cannot be created, and then a relative refractory period, during which a stimulus that is stronger than a usual signal can trigger a response. The action potential generated at the pacemaker (the sinoatrial node) propagates along the nodal circuit and then myofibers. The shape of the cardiac action potential varies with the cell type (nodal cells in different compartments, i.e., sinoatrial and atrioventricular nodes, the bundle of His, and Purkinje fibers, and cardiomyocytes in diverse layers of the myocardium), more precisely according to its electrochemical features. The entry of calcium ions launches the electromechanical coupling.

Load experienced by the ventricular myocardium that needs to be overcome to expel blood, that is, the resistance against which the ventricle works. It thus depends on the blood arterial pressure, itself depending on the arterial vasomotor tone. It is also the stress developed in the left ventricular wall during ejection.

Increase in ventricular inotropy (myocardial contractility) that results from an increase in afterload (staircase phenomenon). This intrinsic adaptation is observed in denervated heart preparations, but not in myocardial strips, unlike the Bowditch effect. This autoregulatory mechanism was described by G. von Anrep (1889–1955) in a paper published in 1912. This increased inotropy partly compensates for the elevated end-systolic volume and reduced stroke volume caused by an augmented afterload. An elevated coronary perfusion abolishes the Anrep effect in isolated heart preparations.

In cat papillary muscles, in response to an increase in afterload, contractility decreased (antihomeometric autoregulation) during the first few beats and then increased slowly (homeometric autoregulation; Nichols et al. 1988). The fall in left ventricular end-diastolic volume after an elevation in diastolic volume after augmented afterload contrasts with the Frank–Starling law, or heterometric autoregulation (Sarnoff et al. 1960). The homeometric autoregulation is an intrinsic regulation of inotropy in response to influences that depend neither on change in myofiber length, such as the Frank–Starling curve, nor on extrinsic (nervous or hormonal) regulation. In summary, the biphasic contractile response relies on a rapid force response, the Frank–Starling mechanism, that is followed by a slow force response, the Anrep effect.

The positive inotropy after an abrupt increase in systolic pressure may result from recovery from subendocardial ischemia due to reduced coronary flow in the subendocardial ventricular layer (Monroe et al. 1972).

The Anrep effect may be explained by a progressive increase in calcium transients in response to auto- and paracrine signals liberated by myocyte stretch. The myocardial stretch provokes the release of angiotensin-2 that binds to its cognate AT1 receptors and triggers endothelin synthesis and secretion as well as phosphorylation of extracellular signal-regulated kinases ERK1 and ERK2 and of Na+–H+ exchanger NHE1. These chemical events rely on transactivation of the epidermal growth factor receptor (Villa-Abrille et al. 2010).

Valve made up of three quasi-equal semilunar cusps associated with dilations of the aortic root, the sinuses of Valsalva. During diastole, leaflet coaptation prevents flow regurgitation from the aorta to the left ventricle.

Measure of the timing and magnitude of pressure wave reflections from the peripheral circulation and their superimposition on the incident pressure wave.

Intrinsic adaptation, which is like Anrep effect a staircase phenomenon, that associates an increase in myocardial contractility with an increase in cardiac frequency. This frequency-dependent positive inotropy was described by Bowditch (1840–1911).

This autoregulatory mechanism results from an increased activity of the voltage-gated CaV1.2 channels, whereas the Na+–K+ ATPase (pump) that removes Na+ brought into the cytosol by the Na+–Ca2+ exchanger to decrease the levels of intracellular calcium does not work efficiently enough with augmented rate of cardiomyocyte activity and the Na+–Ca2+ exchanger has less time to remove Ca2+ from the cytosol. Therefore, Ca2+ ions accumulate in the cytosol.

Inverse of the slope of the relation between the oxygen consumption per beat (VO2) and the pressure–volume area.

Ratio of mechanical work to oxygen consumption (normally ~20–25 %), the remainder of the oxygen used being converted to heat.

Blood volume pumped by each ventricle that crosses any point in the circulatory system per unit of time, that is, the blood flow rate:

$$ CO=SV\times {f}_{\mathrm{C}}, $$

(1)

where SV is the stroke (systolic ejection) volume and f C the cardiac frequency.

Quantity linearly related to the sum of external work and potential energy, that is, the pressure–volume area measured on the pressure–volume curve (Gibbs 1987).

The prefixes myo- and sarco- are commonly used when referring to its components (sarcoplasm and sarcoplasmic reticulum rather than cytoplasm and endoplasmic reticulum, respectively). The sarcoplasm invaginates and forms transverse (T) tubules. The sarcoplasmic reticulum is the main CMC calcium store that contacts T tubules. The sarcomere is the contractile unit. Contraction of sarcomeres in series relies on cross-bridging between actin and myosin filaments. The trigger and fuel of contraction are cytosolic calcium ion and ATP, respectively. ATP is mainly produced in the three pools (subsarcolemmal, interfibrillar, and perinuclear) of mitochondria. Whereas skeletal myocytes have peripheral nuclei, the cardiomyocyte (CMC) possesses a single or several central nuclei. The cardiomyocyte population comprises mono- (~74 %) and multinucleated (bi- [~25 %], tri- [~0.4 %], and tetranucleated [~0.1 %]) cells in normal left ventricles (Olivetti et al. 1996). Mononucleated myocytes constitutes also the main fraction of CMC population of the interventricular septum and right ventricular free wall. Aging, myocardial hypertrophy, and ischemic cardiomyopathy do not change the percentage of mono and multinucleated myocytes in the ventricular myocardium. The existence of multinucleated cells as well as of intercalated discs leads to the concepts of functional (rather than anatomical) syncytium. In a given tiny transmural region, axially aligned cardiomyocytes form a myofiber. Locally, adjoining myofibers are nearly parallel with a given orientation. Transmural myofiber rotation varies from approximately −60° with respect to the circumferential direction at the epicardial surface to about +90° in the subendocardial region. In addition, ventriculomyocytes form a highly branched network with transverse intercalated discs. Ventriculomyocytes are also arranged in myolaminae (sheets), that is, four- to six-cell–thick layers. Myolaminae are separated by perimysial connective tissue with a weak intercellular coupling. A given myolamina at a given wall site has a given lead angle with respect to the endo- or epicardial surface supposed to be locally parallel. The myocardium is thus constituted of an orthotropicmaterial with three structural axes at any point defined by the myofiber direction and myolamina lead angle. At rest, the CMC membrane is hyperpolarized. The arrival of an action potential (electrochemical wave) causes a membrane depolarization caused by an influx of cations (Na+ mainly and Ca2+) that drives contraction via calcium ions (electromechanical or excitation–contraction coupling). Repolarization results form outflux from cytosol of potassium ions. Relaxation is ensured by export from the cytosol to the extracellular medium and intracellular storage organelles of calcium ions. Contraction and relaxation of CMCs are controlled by the autonomous nervous system, the sympathetic component having positive chronotropic, inotropic, and lusitropic effects.

Cord-like tendons that connect papillary muscles to the atrioventricular valves (mitral and tricuspid valves) that then take a parachute-like shape during the contraction of the ventricular myocardium.

Phase of the cardiac (left ventricular) cycle with close ventriculoarterial valves strongly in contact at their coaptation zone to prevent backflow from the corresponding artery. The ventricular myocardium relaxes. Blood flows through open atrioventricular valves. During early distole, blood stored in the atrium enters the ventricle and then blood from veins connected to the atrium directly fills the ventricular cavity.

Adaptation of energy liberation (hence oxygen consumption) by the myocardium contraction according to the length of the myocardial fiber. In skeletal muscles, a contraction with shortening generates more heat than an isometric contraction. However, the Fenn effect differs between the skeletal muscle and myocardium in the magnitude of energy consumption of shortening contraction relative to that of isometric contraction at the same preload, the former being smaller than the latter in the myocardium (Suga 1990).

Also called Maestrini heart law and heterometric regulation, response to an increase in end-diastolic volume due to elevated venous return that suddenly stretches the ventricular wall according to which the heart raises the stroke volume, all other factors remaining constant, or ejects the same stroke volume against an augmented afterload, which, like increased venous return, augments the ventricular volume. The cardiac output is then adjusted to the venous return or afterload.

Ventricular myocardium strips also exhibit the Frank–Starling effect. When the length of the myofiber rises, inotropy rapidly increases, unlike the Anrep effect characterized by a slow response.

The myofiber stretching raises myocardial contraction because it increases the affinity of troponin-C for calcium and promotes actin–myosin cross-bridging.

Phase of the cardiac (left ventricular) cycle during which, both entry and exit valves being closed, the intraventricular pressure soars to become greater than that in the arterial trunk, then enabling a next blood ejection.

Phase of the cardiac (left ventricular) cycle during which, both entry and exit valves being closed, the intraventricular pressure drops to become lower than that in the atrium, then allowing the next ventricular filling with atrial blood.

Left atrioventricular valve. This usually bicuspid valve prevents blood to flow back into the left atrium from the left ventricle. In some patients, additional commissures and indentations of the valve free margin increase the number of valves and valve segments (also called scallops), respectively.

Specialized cardiac cells involved in the generation and transmission of action potentials, hence responsible for the cardiac automatism and intrinsic conduction under the control of the nervous system. Nodal cells of the sinoatrial node, the cardiac natural pacemaker, trigger action potentials that then spread though both atria and reach the atrioventricular node and then bundle of His and its branches and Purkinje fibers to produce successively atrial and ventricular contraction.

Double layered coating of the heart. It is constituted of the outer parietal and inner visceral pericardium, or epicardium, separated by the pericardial cavity that contains a lubrificating fluid.

Ventricular muscular pillars that attach to the cusps of the atrioventricular valves via chordae tendineae and contract to prevent valve prolapse during myocardial contraction.

Load associated with the venous return exerted on the myocardium. It corresponds to the venous-filling end-diastolic pressure that stretches the ventricular wall prior to contraction. Preload is assessed by ventricular end-diastolic volume (EDV) and/or pressure (EDP), as stretching of cardiomyocytes before systole cannot be measured. Preload is estimated using the Laplace’s law:

$$ \mathrm{preload}=\frac{ED{\mathrm{P}}_{LV}\cdot ED{\mathrm{R}}_{LV}}{2h}, $$

(2)

where EDPLV and EDRLV are the left ventricular end-diastolic pressure and radius at the ventricle midpoint and h the ventricular wall thickness.

Sum of the two areas of the pressure–volume curve, that is, the external mechanical work per beat that corresponds to the area limited by the diastolic and systolic pressure–volume curves and isovolumic relaxation and contraction lines plus the potential energy, that is, the area between the systolic and diastolic traces bounded by the isovolumic relaxation line.

Valve located between the right ventricle and the pulmonary trunk that prevents backflow into the right ventricle.

Product of systolic pressure and cardiac frequency used as a measure of oxygen consumption.

Blood volume expelled by the ventricle during a single beat. It can be calculated from the following formula:

$$ SV=EDV-ESV, $$

(3)

where EDV and ESV are the end-diastolic and end-systolic volume, respectively.

Phase of the cardiac (left ventricular) cycle with closed atrioventricular valves and open semilunar (ventriculoarterial) valves through which a blood bolus (systolic ejection volume) is expelled in the arterial trunk. The flow rate through the cardiac exit section reaches a peak after an accelerating phase and then decays. During the decelerating phase, the ventriculoarterial leaflets begin to close.

Averaged pressure during the ejection phase.

Right atrioventricular valve that enables blood flow in a single direction between the right atrium and ventricle.

References

• Aggarwal A, Aguilar VS, Lee CH, Ferrari G, Gorman J, Gorman RC, Sacks MS (2013) Patient-specific modeling of heart valves: from image to simulation. In: Ourselin S, Rueckert D, Smith N (eds) Functional imaging and modeling of the heart, vol 7945, Lecture notes in computer science. Springer, Heidelberg, pp 141–149

  CrossRef  Google Scholar 

• Aliev RR, Panfilov AV (1996) A simple two-variable model of cardiac excitation. Chaos 7:293–301

  Google Scholar 

• Anderson RH, Webb S, Brown NA (1999) Clinical anatomy of the atrial septum with reference to its developmental components. Clin Anat 12:362–374

  CrossRef  CAS  PubMed  Google Scholar 

• Anderson RH, Razavi R, Taylor AM (2004) Cardiac anatomy revisited. J Anat 205:159–177

  CrossRef  PubMed  PubMed Central  Google Scholar 

• Arciero JC, Carlson BE, Secomb TW (2008) Theoretical model of metabolic blood flow regulation: roles of ATP release by red blood cells and conducted responses. Am J Physiol Heart Circ Physiol 295:H1562–H1571

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Arora R (2013) How the pulmonary veins “talk” to the sinoatrial node: new insights into an old mystery. Cardiovasc Res 99:380–381

  CrossRef  CAS  PubMed  Google Scholar 

• Azhari H, Weiss JL, Rogers WJ, Siu CO, Zerhouni EA, Shapiro EP (1993) Noninvasive quantification of principal strains in normal canine hearts using tagged MRI images in 3-D. Am J Physiol Heart Circ Physiol 264:205–216

  Google Scholar 

• Bäck M, Gasser TC, Michel JB, Caligiuri G (2013) Biomechanical factors in the biology of aortic wall and aortic valve diseases. Cardiovasc Res 99:232–241

  CrossRef  PubMed  PubMed Central  CAS  Google Scholar 

• Baumgarten CM (2004) Cardiac bioelectricity. Encyclopedia of biomaterials and biomedical engineering. Marcel Dekker, New York

  Google Scholar 

• Baumgartner H, Schima H, Kuhn P (1991) Value and limitations of proximal jet dimensions for the quantitation of valvular regurgitation: an in vitro study using Doppler flow imaging. J Am Soc Echocardiogr 4:57–66

  CrossRef  CAS  PubMed  Google Scholar 

• Beeler GW, Reuter H (1977) Reconstruction of the action potential of ventricular myocardial fibres. J Physiol 268:177–210

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Belhamadia Y, Fortin A, Chamberland É (2004a) Anisotropic mesh adaptation for the solution of the Stefan problem. J Comput Phys 194:233–255

  CrossRef  Google Scholar 

• Belhamadia Y, Fortin A, Chamberland É (2004b) Three-dimensional anisotropic mesh adaptation for phase change problems. J Comput Phys 201:753–770

  CrossRef  Google Scholar 

• Bellhouse BJ (1969) Velocity and pressure distributions in the aortic valve. J Fluid Mech 37:587–600

  CrossRef  Google Scholar 

• Bellhouse BJ, Talbot L (1969) The fluid mechanics of the aortic valve. J Fluid Mech 35:721–735

  CrossRef  Google Scholar 

• Belohlavek M (2012) Vortex formation time: an emerging echocardiographic index of left ventricular filling efficiency? Eur Heart J Cardiovasc Imaging 13:367–369

  CrossRef  PubMed  PubMed Central  Google Scholar 

• Bernus O, Wilders R, Zemlin CW, Verschelde H, Panfilov AV (2002) A computationally efficient electrophysiological model of human ventricular cells. Am J Physiol Heart Circ Physiol 282:H2296–H2308

  CrossRef  CAS  PubMed  Google Scholar 

• Bestel J (2000) Modèle différentiel de la contraction musculaire contrôlée. Application au système cardio-vasculaire. (Model of controlled muscle contraction. Application to the cardiovascular system). Ph.D. thesis, University Paris Dauphine, Paris

  Google Scholar 

• Bestel J, Clément F, Sorine M (2001) A biomechanical model of muscle contraction. In: Niessen WJ, Viergever MA (eds) Medical image computing and computer-assisted intervention (MICCAI’01), vol 2208, Lecture notes in computer science (LNCS). Springer, New York, pp 1159–1161

  Google Scholar 

• Bitbol M, Dantan P, Perrot P, Oddou C (1982) Collapsible tube model for the dynamics of closure of the mitral valve. J Fluid Mech 114:187–211

  CrossRef  Google Scholar 

• Blain G, Meste O, Blain A, Bermon S (2009) Time-frequency analysis of heart rate variability reveals cardiolocomotor coupling during dynamic cycling exercise in humans. Am J Physiol Heart Circ Physiol 296:H1651–H1659

  CrossRef  CAS  PubMed  Google Scholar 

• Bogaert J, Rademakers FE (2001) Regional nonuniformity of normal adult human left ventricle. Am J Physiol Heart Circ Physiol 280(2):H610–H620

  CAS  PubMed  Google Scholar 

• Brookes PS, Yoon Y, Robotham JL, Anders MW, Sheu SS (2004) Calcium, ATP, and ROS: a mitochondrial love-hate triangle. Am J Physiol Cell Physiol 287:817–833

  CrossRef  Google Scholar 

• Burnes J, Taccardi B, Rudy Y (2000) A noninvasive imaging modality for cardiac arrhythmias. Circulation 102:2152–2158

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Carlson BE, Arciero JC, Secomb TW (2008) Theoretical model of blood flow autoregulation: roles of myogenic, shear-dependent, and metabolic responses. Am J Physiol Heart Circ Physiol 295:H1572–H1579

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Chapelle D, Clément F, Génot F, Le Tallec P, Sorine M, Urquiza JM (2001) A physiologically-based model for the active cardiac muscle. In: Katila T, Magnin IE, Clarysse P, Montagnat J, Nenonen J (eds) Functional imaging and modeling of the heart. Springer, Berlin

  Google Scholar 

• Chapelle D, Moireau P, Le Tallec P (2009) Robust filtering for joint state-parameter estimation in distributed mechanical systems. Discrete Cont Dyn Syst, Ser A 23:65–84

  Google Scholar 

• Chapelle D, Gerbeau JF, Sainte-Marie J, Vignon-Clementel IE (2010) A poroelastic model valid in large strains with applications to perfusion in cardiac modeling. Comput Mech 46:91–101

  CrossRef  Google Scholar 

• Chu C, Thai K, Park KW, Wang P, Makwana O, Lovett DH, Simpson PC, Baker AJ (2013) Intraventricular and interventricular cellular heterogeneity of inotropic responses to 1-adrenergic stimulation. Am J Physiol Heart Circ Physiol 304:H946–H953

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Cifelli C, Rose RA, Zhang H, Voigtlaender-Bolz J, Bolz SS, Backx PH, Heximer SP (2008) RGS4 regulates parasympathetic signaling and heart rate control in the sinoatrial node. Circ Res 103:527–535

  CrossRef  CAS  PubMed  Google Scholar 

• Cimrman R, Rohan E (2003) Modelling heart tissue using a composite muscle model with blood perfusion. In: Bathe KJ (ed) Computational fluid and solid mechanics. Elsevier, Amsterdam

  Google Scholar 

• Cohen D, Edelsack EA, Zimmerman JE (1970) Magnetocardiograms taken inside a shielded room with a superconducting point-contact magnetometer. Appl Phys Lett 16:278–280

  CrossRef  Google Scholar 

• Conrad WA, McQueen DM, Yellin EL (1980) Steady pressure flow relations in compressed arteries: possible origin of Korotkoff sounds. Med Biol Eng Comput 18:419–426

  CrossRef  CAS  PubMed  Google Scholar 

• Coron JM, Crépeau E (2003) Exact boundary controllability of a nonlinear KdV equation with critical lengths. INRIA Research Report RR-5000

  Google Scholar 

• d’Alché P (1973) Pourquoi le cœur bat [Why the heart beats]. La Recherche 33:327–336

  Google Scholar 

• Dantan P (1985) Étude numérique et expérimentale de l’écoulement instationnaire d’un fluide visqueux incompressible dans une cavité de dimension variable. Modélisation de l’hémodynamique cardiaque (Unsteady flow of a viscous incompressible fluid through varying-size cavity: a numerical and experimental study. Modeling of heart hemodynamics). Ph.D. Thesis, University Paris VII, Paris

  Google Scholar 

• Delavaud E (2003) Couplage de l’écoulement entre le ventricule gauche et l’aorte [Coupling of the flow between the left ventricle and aorta]. DESS, University Paris VI, Paris

  Google Scholar 

• Delhaas T, Arts T, Prinzen FW, Reneman RS (1993) Relation between regional electrical activation time and subepicardial fiber strain in the canine left ventricle. Pflugers Arch 423:78–87

  CrossRef  CAS  PubMed  Google Scholar 

• Diniz dos Santos N, Gerbeau JF, Bourgat JF (2008) A partitioned fluid–structure algorithm for elastic thin valves with contact. Comput Meth Appl Mech Eng 197:1750–1761

  CrossRef  Google Scholar 

• Djabella K, Sorine M (2006) A reduced differential model of the electrical activity of cardiac Purkinje fibres. IEEE Engineering in Medicine and Biology Society, Conference Proceedings, Raleigh, USA

  Google Scholar 

• Durrer D, van Dam RT, Freud GE, Janse MJ, Meijler FL, Arzbaecher RC (1970) Total excitation of the isolated human heart. Circulation 41:899–912

  CrossRef  CAS  PubMed  Google Scholar 

• Ebbers T, Wigstrom L, Bolger AF, Wranne B, Karlsson M (2002) Noninvasive measurement of time-varying three-dimensional relative pressure fields within the human heart. J Biomech Eng 124:288–293

  CrossRef  CAS  PubMed  Google Scholar 

• Faris OP, Evans FJ, Ennis DB, Helm PA, Taylor JL, Chesnick AS, Guttman MA, Ozturk C, McVeigh ER (2003) Novel technique for cardiac electromechanical mapping with magnetic resonance imaging tagging and an epicardial electrode sock. Ann Biomed Eng 31:430–440

  CrossRef  PubMed  PubMed Central  Google Scholar 

• Fenton F, Karma A (1998) Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation. Chaos 8:20–47

  CrossRef  PubMed  Google Scholar 

• Fogel MA, Weinberg PM, Hubbard A, Haselgrove J (2000) Diastolic biomechanics in normal infants utilizing MRI tissue tagging. Circulation 102:218–224

  CrossRef  CAS  PubMed  Google Scholar 

• Garnaud X, Lesshafft L, Schmid PJ, Huerre P (2013) Modal and transient dynamics of jet flows. Phys Fluids 25:044103

  CrossRef  CAS  Google Scholar 

• Gharib M, Rambod E, Shariff K (1998) A universal time scale for vortex ring formation. J Fluid Mech 360:121–140

  CrossRef  CAS  Google Scholar 

• Gharib M, Rambod E, Kheradvar A, Sahn DJ, Dabiri JO (2006) Optimal vortex formation as an index of cardiac health. Proc Natl Acad Sci U S A 103:6305–6308

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Ghista DN, Chandran KB, Ray G, Reul H (1978) Optimal design of aortic leaflet prosthesis. J Eng Mech 104:97–117

  Google Scholar 

• Gibbs CL (1987) Cardiac energetics and the Fenn effect. Basic Res Cardiol 82:61–68

  PubMed  Google Scholar 

• Goldberger AL, Rigney DR, West BJ (1990) Chaos and fractals in human physiology. Sci Am 262:42–49

  CrossRef  CAS  PubMed  Google Scholar 

• Grande KJ, Kunzelman KS, Cochran RP, David TE, Verrier ED (1993) Porcine aortic leaflet arrangement may contribute to clinical xenograft failure. ASAIO J 39:918–922

  CrossRef  CAS  PubMed  Google Scholar 

• Gray H (1995) Gray’s anatomy: anatomy descriptive and surgical. Barnes and Noble, New York

  Google Scholar 

• Groeger S, Bison G, Knowles PE, Wynands R, Weis A (2006) Laser-pumped cesium magnetometers for high-resolution medical and fundamental research. Sens Actuators A Phys 129:1–5

  CrossRef  CAS  Google Scholar 

• Guccione J, McCulloch A (1991) Theory of heart: biomechanics, biophysics, and non-linear dynamics of cardiac function. In: Glass L, Hunter P, McCulloch A (eds) Finite element modeling of ventricular mechanics. Springer, Berlin

  CrossRef  Google Scholar 

• Gupta S, Matulevicius SA, Ayers CR, Berry JD, Patel PC, Markham DW, Levine BD, Chin KM, de Lemos JA, Peshock RM, Drazner MH (2013) Left atrial maximal volume and left atrial emptying fraction as predictors of cardiovascular events in community-based or population studies. Eur Heart J 34:278–285

  CrossRef  PubMed  Google Scholar 

• Guyenet PG (2006) The sympathetic control of blood pressure. Nat Rev Neurosci 7:335–346

  CrossRef  CAS  PubMed  Google Scholar 

• Guyton AC, Hall JE (2006) Textbook of medical physiology, 7th edn. Elsevier – Saunders, Philadelphia

  Google Scholar 

• Heethaar RM, Pao YC, Ritman EL (1977) Computer aspects of three-dimensional finite element analysis of stresses and strains in the intact hear. Comput Biomed Res 10:271–285

  CrossRef  CAS  PubMed  Google Scholar 

• Henderson Y, Johnson F (1912) Two modes of the closure of the heart valves. Heart 4:69–82

  Google Scholar 

• Hill AV (1938) The heat of shortening and the dynamic constants in muscle. Proc R Soc Lond B 126:136–195

  CrossRef  Google Scholar 

• Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500–544

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Hoffman JI, Spaan JA (1990) Pressure-flow relations in coronary circulation. Physiol Rev 70:331–390

  CAS  PubMed  Google Scholar 

• Hsu EW, Henriquez CS (2001) Myocardial fiber orientation mapping using reduced encoding diffusion tensor imaging. J Cardiovasc Magn Reson 3:339–347

  CrossRef  CAS  PubMed  Google Scholar 

• Hunter PJ, Nash MP, Sands GB (1997) Computational electromechanics of the heart. In: Panfilov AV, Holden AV (eds) Computational biology of the heart. Wiley, Chichester

  Google Scholar 

• Hunter PJ, McCulloch AD, ter Keurs HE (1998) Modelling the mechanical properties of cardiac muscle. Prog Biophys Mol Biol 69:289–331

  CrossRef  CAS  PubMed  Google Scholar 

• Huxley AF (1957) Muscle structure and theories of contraction. Prog Biophys Biophys Chem 7:255–318

  CAS  PubMed  Google Scholar 

• Huyghe JM, Arts T, van Campen DH (1992) Porous medium finite element model of the beating left ventricle. Am J Physiol Heart Circ Physiol 262:1256–1267

  Google Scholar 

• Imholz BP, Wieling W, van Montfrans GA, Wesseling KH (1998) Fifteen years experience with finger arterial pressure monitoring: assessment of the technology. Cardiovasc Res 38:605–616

  CrossRef  CAS  PubMed  Google Scholar 

• Janssen PM (2010) Myocardial contraction-relaxation coupling. Am J Physiol Heart Circ Physiol 299:H1741–H1749

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Jatene MB, Monteiro R, Guimaraes MH, Veronezi SC, Koike MK, Jatene FB, Jatene AD (1999) Aortic valve assessment. Anatomical study of 100 healthy human hearts. Arq Bras Cardiol 73:81–86

  CrossRef  Google Scholar 

• Kilner PJ, Yang GZ, Wilkes AJ, Mohiaddin RH, Firmin DN, Yacoub MH (2000) Asymmetric redirection of flow through the heart. Nature 404:759–761

  CrossRef  CAS  PubMed  Google Scholar 

• Koch H (2004) Recent advances in magnetocardiography. J Electrocardiol 37:117–122

  CrossRef  PubMed  Google Scholar 

• Krejci P, Sainte-Marie J, Sorine M, Urquiza JM (2006) Solutions to muscle fiber equations and their long time behaviour. Nonlinear Anal Real World Appl 7:535558

  CrossRef  Google Scholar 

• Laleg TM, Crépeau E, Papelier Y, Sorine M (2007) Arterial blood pressure analysis based on scattering transform. In: 29th annual international conference of the IEEE engineering in medicine and biology society (IEEE EMBC), Lyon, France

  Google Scholar 

• Lancellotti P, Rosenhek R, Pibarot P, Iung B, Otto CM, Tornos P, Donal E, Prendergast B, Magne J, La Canna G, Piérard LA, Maurer G (2013) ESC working group on valvular heart disease position paper – heart valve clinics: organization, structure, and experiences. Eur Heart J 34:1597–1606

  CrossRef  PubMed  Google Scholar 

• Le TB, Sotiropoulos F (2012) On the three-dimensional vortical structure of early diastolic flow in a patient-specific left ventricle. Eur J Mech B Fluids 35:20–24

  CrossRef  PubMed  PubMed Central  Google Scholar 

• Le TB, Borazjani I, Kang S, Sotiropoulos F (2011) On the structure of vortex rings from inclined nozzles. J Fluid Mech 686:451–483

  CrossRef  Google Scholar 

• Le TB, Sotiropoulos F, Coffey D, Keefe D (2012) Vortex formation and instability in the left ventricle. Phys Fluids 24:091110

  CrossRef  CAS  Google Scholar 

• Lee CSF, Talbot L (1979) A fluid mechanical study on the closure of heart valves. J Fluid Mech 91:41–63

  CrossRef  Google Scholar 

• Lenègre J, Blondeau M, Bourdarias JP, Gerbaux A, Himbert J, Maurice P (1973) Cœur et Circulation [Heart and circulation]. In: Vallery-Radot P, Hamburger J, Lhermitte F (eds) Pathologie Médicale. [Medical pathology], vol 3. Flammarion Médecine Sciences, Paris

  Google Scholar 

• Lundby A, Andersen MN, Steffensen AB, Horn H, Kelstrup CD, Francavilla C, Jensen LJ, Schmitt N, Thomsen MB, Olsen JV (2013) In vivo phosphoproteomics analysis reveals the cardiac targets of -adrenergic receptor signaling. Sci Signal 6:rs11

  CrossRef  PubMed  CAS  Google Scholar 

• Luo CH, Rudy Y (1991) A model of the ventricular cardiac action-potential: depolarization, repolarization, and their interaction. Circ Res 68:1501–1526

  CrossRef  CAS  PubMed  Google Scholar 

• Malik M, Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology et al (1996) Heart rate variability: standards of measurement, physiological interpretation and clinical use. Circulation 93:1043–1065

  CrossRef  Google Scholar 

• McVeigh E, Faris O, Ennis D, Helm P, Evans F (2001) Measurement of ventricular wall motion, epicardial, electrical mapping, and myocardial fiber angles in the same heart. In: Katila T, Magnin IE, Clarysse P, Montagnat J, Nenonen J (eds) Functional imaging and modeling of the heart. Springer, Berlin

  Google Scholar 

• Mesirca P, Marger L, Toyoda F, Rizzetto R, Audoubert M, Dubel S, Torrente AG, Difrancesco ML, Muller JC, Leoni AL, Couette B, Nargeot J, Clapham DE, Wickman K, Mangoni ME (2013) The G-protein-gated K+ channel, IKACh, is required for regulation of pacemaker activity and recovery of resting heart rate after sympathetic stimulation. J General Phys 142:113–126

  CrossRef  CAS  Google Scholar 

• Mirsky I, Parmley WW (1973) Assessment of passive elastic stiffness for isolated heart muscle and the intact heart. Circ Res 33:233–243

  CrossRef  CAS  PubMed  Google Scholar 

• Mitchell CC, Schaeffer DG (2003) A two-current model for the dynamics of cardiac membrane. Bull Math Biol 65:767–793

  CrossRef  CAS  PubMed  Google Scholar 

• Miyake Y, Binder G (1970) Évolution d’un jet pulsant [Evolution of a pulsatile jet]. Comptes Rendus Hebdomadaires Des Séances De l’Académie Des Sciences – Série A 271:615–618

  Google Scholar 

• Moireau P, Chapelle D, Le Tallec P (2008) Joint state and parameter estimation for distributed mechanical systems. Comput Meth Appl Mech Eng 197:659–677

  CrossRef  Google Scholar 

• Momen A, Mascarenhas V, Gahremanpour A, Gao Z, Moradkhan R, Kunselman A, Boehmer JP, Sinoway LI, Leuenberger UA (2009) Coronary blood flow responses to physiological stress in humans. Am J Physiol Heart Circ Physiol 296:H854–H861

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Monroe RG, Gamble WJ, Lafarge CG, Kumar AE, Stark J, Sanders GL, Phornphutkul C, Davis M (1972) The Anrep effect reconsidered. J Clin Invest 51:2573–2583

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Morgagni GB (1740) Dissertationes Tres Anatomicae Posthumae. Anatomical dissertations – works of Valsalva, 2 vols. F. Pitteri, Venice

  Google Scholar 

• Mori H, Tanaka E, Hyodo K, Mohammed MU, Sekka T, Ito K, Shinozaki Y, Tanaka A, Nakazawa H, Abe S, Handa S, Kubota M, Tanioka K, Umetani K, Ando M (1999) Synchrotron microangiography reveals configurational changes and to-and-fro flow in intramyocardial vessels. Am J Physiol Heart Circ Physiol 276:H429–H437

  CAS  Google Scholar 

• Neckyfarow CW, Perlman AB (1976) Deformation of the left ventricle: material and geometric effect. In: Saha S (ed) New England bioengineering conference. Karger, Basel

  Google Scholar 

• Nichols CG, Hanck DA, Jewell BR (1988) The Anrep effect: an intrinsic myocardial mechanism. Can J Physiol Pharmacol 66:924–929

  CrossRef  CAS  PubMed  Google Scholar 

• Novak V, Novak P, Schondorf R (1994) Accuracy of beat-to-beat noninvasive measurement of finger arterial pressure using the Finapres: a spectral analysis approach. J Clin Monit 10:118–126

  CrossRef  CAS  PubMed  Google Scholar 

• O’Rourke MF, Avolio AP, Kelly RP (1992) The arterial pulse. Lea & Febiger, Baltimore

  Google Scholar 

• Olivetti G, Cigola E, Maestri R, Corradi D, Lagrasta C, Gambert SR, Anversa P (1996) Aging, cardiac hypertrophy and ischemic cardiomyopathy do not affect the proportion of mononucleated and multinucleated myocytes in the human heart. J Mol Cell Cardiol 28:1463–1477

  CrossRef  CAS  PubMed  Google Scholar 

• Olsson RA (1981) Local factors regulating cardiac and skeletal muscle blood flow. Annu Rev Physiol 43:385–395

  CrossRef  CAS  PubMed  Google Scholar 

• Olufsen MS (1998) Modeling the arterial system with reference to an anesthesia simulator. Ph.D. thesis, Roskilde University, Roskilde

  Google Scholar 

• Omboni S, Parati G, Frattola A, Mutti E, Di Rienzo M, Castiglioni P, Mancia G (1993) Spectral and sequence analysis of finger blood pressure variability. Comparison with analysis of intra-arterial recordings. Hypertension 22:26–33

  CrossRef  CAS  PubMed  Google Scholar 

• Pagel PS, Kehl F, Gare M, Hettrick DA, Kersten JR, Warltier DC (2003) Mechanical function of the left atrium: new insights based on analysis of pressure-volume relations and Doppler echocardiography. Anesthesiology 98:975–994

  CrossRef  PubMed  Google Scholar 

• Panerai RB (1980) A model of cardiac muscle mechanics and energetics. J Biomech 13:929–940

  CrossRef  CAS  PubMed  Google Scholar 

• Pao YC, Ritman EL (1998) Comparative characterization of the infarcted and reperfused ventricular wall muscles by finite element analysis and a myocardial muscle-blood composite model. Comput Biomed Res 31:18–31

  CrossRef  CAS  PubMed  Google Scholar 

• Pao YC, Robb RA, Ritman EL (1976) Plane-strain finite-element analysis of reconstructed diastolic left ventricular cross section. Ann Biomed Eng 4:232–249

  CrossRef  CAS  PubMed  Google Scholar 

• Parker KK, Ingber DE (2007) Extracellular matrix, mechanotransduction and structural hierarchies in heart tissue engineering. Phil Trans Roy Soc London B Biol Sci 362:1267–1279

  CrossRef  CAS  Google Scholar 

• Penaz J (1992) Criteria for set point estimation in the volume clamp method of blood pressure measurement. Physiol Res 41:5–10

  CAS  PubMed  Google Scholar 

• Pioletti DP, Rakotomanana LR (2000) Nonlinear viscoelastic laws for soft biological tissues. Eur J Mech A Solids 19:749–759

  CrossRef  Google Scholar 

• Pironet A, Dauby PC, Paeme S, Kosta S, Chase JG, Desaive T (2013) Simulation of left atrial function using a multi-scale model of the cardiovascular system. PLoS One 8:e65146

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Poh KK, Lee LC, Shen L, Chong E, Tan YL, Chai P, Yeo TC, Wood MJ (2012) Left ventricular fluid dynamics in heart failure: echocardiographic measurement and utilities of vortex formation time. Eur Heart J Cardiovasc Imaging 13:385–393

  CrossRef  PubMed  Google Scholar 

• Poon CS, Merrill CK (1997) Decrease of cardiac chaos in congestive heart failure. Nature 389:492–495

  CrossRef  CAS  PubMed  Google Scholar 

• Prassl AJ, Kickinger F, Ahammer H, Grau V, Schneider JE, Hofer E, Vigmond EJ, Trayanova NA, Plank G (2009) Automatically generated, anatomically accurate meshes for cardiac electrophysiology problems. IEEE Trans Biomed Eng 56:1318–1330

  CrossRef  PubMed  PubMed Central  Google Scholar 

• Risacher F (1995) Étude de la propagation de l’onde de pouls par pléthysmographie d’impédance électrique. (Study of the propagation of pulse waves by electric impedance plethysmography). Ph.D. Thesis, University Claude Bernard, Lyon

  Google Scholar 

• Robinson TF, Factor SM, Sonnenblick EH (1986) The heart as a suction pump. Sci Am 6:62–69

  Google Scholar 

• Rodriguez Muñoz D, Markl M, Moya Mur JL, Barker A, Fernández-Golfín C, Lancellotti P, Zamorano Gómez JL (2013) Intracardiac flow visualization: current status and future directions. Eur Heart J Cardiovasc Imaging 14:1029–1038

  CrossRef  PubMed  PubMed Central  Google Scholar 

• Sainte-Marie J, Chapelle D, Sorine M (2003) Data assimilation for an electro-mechanical model of the myocardium. In: Bathe KJ (ed) Computational fluid and solid mechanics 2003. Elsevier, Amsterdam

  Google Scholar 

• Sainte-Marie J, Chapelle D, Cimrman R, Sorine M (2006) Modeling and estimation of the cardiac electromechanical activity. Comput Struct 84:1743–1759

  CrossRef  Google Scholar 

• Sarnoff SJ, Mitchell JH, Gilmore JP, Remensnyder JP (1960) Homeometric autoregulation in the heart. Circ Res 8:1077–1091

  CrossRef  CAS  PubMed  Google Scholar 

• Scaramucci J (1695) De motu cordis, theorema sexton. Theoremata familiaria viros eruditos consulentia de variis physico medicis lucubrationibus iucta leges mecanicas. Apud Joannem Baptistam Bustum, Urbino, pp 70–81

  Google Scholar 

• Seiler C, Stoller M, Pitt B, Meier P (2013a) The human coronary collateral circulation: development and clinical importance. Eur Heart J 34:2674–2682

  CrossRef  CAS  PubMed  Google Scholar 

• Seiler C, Stoller M, Pitt B, Meier P (2013b) The human coronary collateral circulation: development and clinical importance. Eur Heart J 34:2674–2682

  CrossRef  CAS  PubMed  Google Scholar 

• Shukla P, Sun C, O’Rourke ST (2012) Melatonin inhibits nitric oxide signaling by increasing PDE5 phosphorylation in coronary arteries. Am J Physiol Heart Circ Physiol 303:H1418–H1425

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Sin PY, Galletly DC, Tzeng YC (2010) Influence of breathing frequency on the pattern of respiratory sinus arrhythmia and blood pressure: old questions revisited. Am J Physiol Heart Circ Physiol 298:H1588–H1599

  CrossRef  CAS  PubMed  Google Scholar 

• Smith NP, Mulquiney PJ, Nash MP, Bradley CP, Nickerson DP, Hunter PJ (2002a) Mathematical modelling of the heart: cell to organ. Chaos 13:1613–1621

  CAS  Google Scholar 

• Smith NP, Pullan AJ, Hunter PJ (2002b) An anatomically based model of transient coronary blood flow in the heart. SIAM J Appl Math 62:990–1018

  CrossRef  Google Scholar 

• Staszewsky L, Latini R (2013) What is the atrium trying to tell us? Eur Heart J 34:255–257

  CrossRef  PubMed  Google Scholar 

• Stergiopulos N, Westerhof BE, Westerhof N (1999) Total arterial inertance as the fourth element of the windkessel model. Am J Physiol 276:81–88

  Google Scholar 

• Suga H (1990) Variable series elasticity accounts for Fenn effects of skeletal and cardiac muscles. Am J Physiol 258:R457–R461

  CAS  PubMed  Google Scholar 

• Sun Y, Beshara M, Lucariello RJ, Chiaramida SA (1997) A comprehensive model for right-left heart interaction under the influence of pericardium and baroreflex. Am J Physiol Heart Circ Physiol 272:H1499–H1515

  CAS  Google Scholar 

• Swanson WM, Clark RE (1974) Dimensions and geometric relationships of the human aortic valve as a function of pressure. Circ Res 35:871–882

  CrossRef  CAS  PubMed  Google Scholar 

• Takahashi E, Asano K (2002) Mitochondrial respiratory control can compensate for intracellular O2 gradients in cardiomyocytes at low PO2. Am J Physiol Heart and Circ Physiol 283:H871–H878

  CrossRef  CAS  Google Scholar 

• Tasu J-P, Mousseaux E, Colin P, Slama MS, Jolivet O, Bittoun J (2002) Estimation of left ventricle performance through temporal pressure variations measured by MR velocity and acceleration mappings. J Magn Reson Imaging 16:246–252

  CrossRef  PubMed  Google Scholar 

• ten Tusscher KH, Noble D, Noble PJ, Panfilov AV (2004) A model for human ventricular tissue. Am J Physiol Heart Circ Physiol 286:H1573–H1589

  CrossRef  PubMed  Google Scholar 

• ter Keurs HEDJ (2012) The interaction of Ca2+ with sarcomeric proteins: role in function and dysfunction of the heart. Am J Physiol Heart Circ Physiol 302:H38–H50

  CrossRef  PubMed  CAS  Google Scholar 

• Timmer SAJ, Knaapen P (2013) Coronary microvascular function, myocardial metabolism, and energetics in hypertrophic cardiomyopathy: insights from positron emission tomography. Eur Heart J Cardiovasc Imaging 14:95–101

  CrossRef  PubMed  Google Scholar 

• Tolkacheva EG, Schaeffer DG, Gauthier DJ, Mitchell CC (2002) Analysis of the Fenton-Karma model through an approximation by a one-dimensional map. Chaos 12:1034–1042

  CrossRef  PubMed  Google Scholar 

• van Steenhoven AA, van Dongen MEH (1979) Model studies of the closing behaviour of the aortic valve. J Fluid Mech 90:21–32

  CrossRef  Google Scholar 

• van Steenhoven AA, Veenstra PC, Reneman RS (1982) The effect of some hemodynamic factors on the behaviour of the aortic valve. J Biomech 15:941–950

  CrossRef  PubMed  Google Scholar 

• Veronda DR, Westmann RA (1970) Mechanical characterization of skin. Finite deformation. J Biomech 3:114–124

  CrossRef  Google Scholar 

• Villa-Abrille MC, Caldiz CI, Ennis IL, Nolly MB, Casarini MJ, Chiappe de Cingolani GE, Cingolani HE, Pérez NG (2010) The Anrep effect requires transactivation of the epidermal growth factor receptor. J Physiol 588:1579–1590

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Vlachopoulos C, Aznaouridis K, O’Rourke MF, Safar ME, Baou K, Stefanadis C (2010) Prediction of cardiovascular events and all-cause mortality with central haemodynamics: a systematic review and meta-analysis. Eur Heart J 31:1865–1871

  CrossRef  PubMed  Google Scholar 

• Watanabe H, Sugiura S, Kafuku H, Hisada T (2004) Multiphysics simulation of left ventricular filling dynamics using fluid-structure interaction finite element method. Biophys J 87:2074–2085

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Weber KT (2000) Fibrosis and hypertensive heart disease. Curr Opin Cardiol 15:264–272

  CrossRef  CAS  PubMed  Google Scholar 

• Westerhof N, Bosman F, De Vries CJ, Noordergraaf A (1969) Analog studies of the human systemic arterial tree. J Biomech 2:121–143

  CrossRef  CAS  PubMed  Google Scholar 

• Whitman GB (1999) Linear and nonlinear waves. Wiley, New York

  Google Scholar 

• Williams B, Lacy PS (2010) Central haemodynamics and clinical outcomes: going beyond brachial blood pressure? Eur Heart J 31:1819–1822

  CrossRef  PubMed  Google Scholar 

• Wu JZ, Herzog W (1999) Modelling concentric contraction of muscle using an improved cross-bridge model. J Biomech 32:837–848

  CrossRef  CAS  PubMed  Google Scholar 

• Yaniv Y, Spurgeon HA, Ziman BD, Lyashkov AE, Lakatta EG (2013) Mechanisms that match ATP supply to demand in cardiac pacemaker cells during high ATP demand. Am J Physiol Heart Circ Physiol 304:H1428–H1438

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Zahalak GI (1981) A distribution-moment approximation for kinetic theories of muscular contraction. Math Biosci 114:55–89

  Google Scholar 

• Zarzoso M, Rysevaite K, Milstein ML, Calvo CJ, Kean AC, Atienza F, Pauza DH, Jalife J, Noujaim SF (2013) Nerves projecting from the intrinsic cardiac ganglia of the pulmonary veins modulate sinoatrial node pacemaker function. Cardiovasc Res 99:566–575

  CrossRef  CAS  PubMed  PubMed Central  Google Scholar 

• Zimmerman JE, Theine P, Harding JT (1970) Design and operation of stable rf-biased superconducting point-contact quantum devices, and a note on the properties of perfectly clean metal contacts. J Appl Phys 41:1572–1580

  CrossRef  Google Scholar 

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1. team INRIA-UPMC-CNRS REO, Laboratoire Jaques-Louis Lions, CNRS UMR 7598, Université Pierre et Marie Curie (Sorbonne Universités), Paris, France

   Marc Thiriet

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1. Division of Cardiovascular Disease Department of Internal Medicine, Health Care Center Bitterfeld, Bitterfeld-Wolfen, Germany

   Peter Lanzer

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Thiriet, M. (2015). Cardiac Pump: An Introduction. In: Lanzer, P. (eds) PanVascular Medicine. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37078-6_25

Is the heart a single or double pump?

Is the heart actually a pump?

Is the heart a mechanical pump?

Is the heart a suction pump?