Abstract
The heart is a hollow muscular organ composed of two apposed two-chamber pumps that receives blood from veins, where the driving pressure is relatively low, and then expels it into arteries, where the driving pressure is much higher, each pump being related to the systemic and pulmonary circulation.
The heart has an intrinsic chaotic behavior (in the sense of deterministic chaos and nonlinear dynamics) that enables it to quickly respond to any sudden changes in the environment and adjust to physical activity. It is endowed with automatism that triggers its muscular activity under the control of the nervous system. The latter regulates its excitability (threshold of excitation), or bathmotropy; its action potential emission frequency, or chronotropy; its action potential conduction speed (conductibility), or dromotropy; its muscular contraction force, or inotropy; its diastolic relaxation, or lusitropy; and its distensibility, or tonotropy.
Cardiac functioning depends on several factors, such as (1) ion carriers that determine ion fluxes and intracellular concentrations, especially in the nodal tissue that creates and propagates action potentials and myocytes that undergo contraction–relaxation cycles; (2) sarcomere activity, particularly the cross-bridge cycling rate; (3) extracellular matrix, other categories of associated cells (fibroblasts), capillaries, and nerve endings, that signals to myocytes; (4) wall perfusion responsible for nutrient inputs; and (5) cardiac loads, that is, flow conditions in upstream (veins) and downstream vessels (arteries), the so-called pre- and afterload (or postload).
Functional noninvasive imaging of the heart is aimed at visualizing motions of the blood container and pump as well as its content during the cardiac cycle, using Doppler echography and echocardiographic particle image velocimetry as well as nuclear magnetic resonance imaging with its two derived techniques, diffusion tensor MRI and MR velocimetry.
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Notes
- 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:
$$ \begin{array}{l}{p}_j+1=A(j){p}_j+B(j){c}_j+{n}_j^{(P)};\\ {}\kern0.6em {v}_j\kern1.44em =G(j){p}_j+{n}_j^{(M)}\end{array} $$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.
Differential operator associated with the total energy that can be applied to wave-governed problems.
- 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], \( \mathrm{ANKB}\ \left[\mathrm{LQT}4;\downarrow {i}_{{\mathrm{NaK}}_{\mathrm{ATP}}}\;\mathrm{and}\downarrow {i}_{\mathrm{NaCaX}}\right] \), 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.
- Afterload:
-
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.
- Anrep effect:
-
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).
- Aortic valve:
-
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.
- Augmentation index:
-
Measure of the timing and magnitude of pressure wave reflections from the peripheral circulation and their superimposition on the incident pressure wave.
- Bowditch effect or Treppe effect:
-
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.
- Cardiac contractile efficiency:
-
Inverse of the slope of the relation between the oxygen consumption per beat (VO2) and the pressure–volume area.
- Cardiac mechanical efficiency:
-
Ratio of mechanical work to oxygen consumption (normally ~20–25 %), the remainder of the oxygen used being converted to heat.
- Cardiac output:
-
Blood volume pumped by each ventricle that crosses any point in the circulatory system per unit of time, that is, the blood flow rate:
$$ \mathrm{CO}=\mathrm{SV}\times {f}_{\mathrm{C}}, $$(1)where SV is the stroke (systolic ejection) volume and f C the cardiac frequency.
- Cardiac oxygen consumption per beat:
-
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).
- Cardiomyocyte Cardiac striated myocyte:
-
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.
- Chordae tendineae:
-
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.
- Diastolic filling:
-
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.
- Fenn effect:
-
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).
- Frank–Starling effect:
-
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.
- Isovolumetric contraction:
-
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.
- Isovolumetric relaxation:
-
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.
- Mitral valve:
-
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.
- Nodal cells:
-
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.
- Pericardium:
-
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.
- Papillary muscle:
-
Ventricular muscular pillars that attach to the cusps of the atrioventricular valves via chordae tendineae and contract to prevent valve prolapse during myocardial contraction.
- Preload:
-
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:
$$ \mathrm{preload}=\frac{\mathrm{ED}{\mathrm{P}}_{\mathrm{LV}}\cdot \mathrm{ED}{\mathrm{R}}_{\mathrm{LV}}}{2h}, $$(2)where EDPLV and EDRLV are the left ventricular end-diastolic pressure and radius at the ventricle midpoint and h the ventricular wall thickness.
- Pressure–volume area (PVA):
-
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.
- Pulmonary valve:
-
Valve located between the right ventricle and the pulmonary trunk that prevents backflow into the right ventricle.
- Rate pressure product (RPP):
-
Product of systolic pressure and cardiac frequency used as a measure of oxygen consumption.
- Stroke volume:
-
Blood volume expelled by the ventricle during a single beat. It can be calculated from the following formula:
$$ \mathrm{SV}=\mathrm{EDV}-\mathrm{ESV}, $$(3)where EDV and ESV are the end-diastolic and end-systolic volume, respectively.
- Systolic ejection:
-
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.
- Tension time index (TTI):
-
Averaged pressure during the ejection phase.
- Tricuspid valve:
-
Right atrioventricular valve that enables blood flow in a single direction between the right atrium and ventricle.
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Thiriet, M. (2014). Cardiac Pump. In: Lanzer, P. (eds) PanVascular Medicine. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37393-0_25-1
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