on 26-Dec-2019 (Thu)

Ions (sodium [Na⁺], potassium [K⁺], chloride [Cl^-], and calcium [Ca²⁺]) flow through cardiac membrane channels with pores formed by proteins, with these ion channels encoded by specific genes [3]. The pore-forming protein is called the alpha subunit, which also contains the voltage-dependent sensors and gates. For many ion channels, one or more secondary regulatory subunit proteins are present (usually named beta, gamma, delta, and so on) in association with the alpha subunit, and many ion channel proteins have subunit isoforms adding to their complexity

The dominant channel types in heart cells are Na⁺ channels (I_Na), L-type and T-type Ca²⁺ channels (I_Ca-L, I_Ca-T), and several K⁺ channels (I_K1, I_to1, I_to2, I_Kr, I_Ks). The sodium-potassium pump and the sodium-calcium exchanger are not considered channels because they require energy to drive ions across the membrane against their gradients, however they do generate currents (figure 1).

The resting cardiac cell membrane potential is normally polarized between -80 and -95 mV, with the cell interior negative relative to the extracellular space. The resting membrane potential is determined by the balance of inward (Na⁺ and Ca²⁺) and outward (K⁺) currents and the corresponding equilibrium potentials of these currents

In the heart, the resting membrane potential is generated by the inward rectifier current (I_K1), which is the predominant open channel at rest. Potassium current I_K1 flowing through this channel continues until the interior negative potential is at the same magnitude as the equilibrium potential for potassium. Only small amounts of actual potassium flow are required to maintain this potential. The equilibrium potentials for sodium and calcium are positive (approximately +40 mV and approximately +80 mV, respectively) so that when these channels are open, they tend to depolarize the membrane.

Voltage-sensitive sodium, calcium, and potassium channels play only a small role in the resting state since most of these channels are closed [5,6]. The Na-K-ATPase pump maintains the potassium and sodium gradients by pumping potassium into and sodium out of the cells. The Na-Ca exchanger uses the power of the Na gradient to pump Ca out of the cell

Action potential in fast response tissues —

Tissues that depend upon the opening of voltage-sensitive, kinetically rapid (opening in less than a millisecond) sodium channels to initiate depolarization are called fast response tissues [7].

Fast response tissues include the atria, the specialized infranodal conducting system (bundle of His, fascicles and bundle branches, and terminal Purkinje fibers), and the ventricles (figure 2), while the sinoatrial (SA) and atrioventricular (AV) nodes represent slow response tissues.

It is important to recognize that accessory AV pathways (ie, bypass tracts) associated with Wolff-Parkinson-White syndrome are derived from the atria and are thus also fast response tissues dependent upon sodium current for depolarization.

Phase 0 — Rapid depolarization (phase 0) occurs when the resting cell is brought to threshold, leading sequentially to activation or opening of voltage-dependent sodium channels, rapid sodium entry into the cells down a favorable concentration gradient, and a cell interior positive potential that can approach +45 mV. The marked depolarization initiates voltage-dependent inactivation of the sodium channels. Calcium channels also open during depolarization, but the inward calcium flux is much slower.

Phase 1 — Phase 1 repolarization often inscribes a "notch" and is primarily caused by activation of the transient outward potassium currents (I_to) combined with a corresponding rapid decay of the sodium current. The degree of repolarization in phase 1 is dependent on the density of I_to and varies between cardiac chambers and regions within chambers.

Phase 2 — Following initial repolarization in phase 1, phase 2 represents a plateau that lasts for hundreds of milliseconds and distinguishes the cardiac action potential from nerve and skeletal muscle action potentials, which are significantly shorter. Late inactivating depolarizing calcium and sodium currents are balanced by activating repolarizing potassium currents to maintain the plateau, which is often down-sloping as repolarizing currents begin to dominate.

Phases 3 and 4 — The final rapid repolarizing phase 3 is driven by the decay of the calcium current and progressive activation of repolarizing potassium currents (I_Kr, I_Ks). Terminal repolarization toward the potassium equilibrium potential is dominated in phase 3 by I_K1, which then maintains the resting membrane potential (phase 4).

In the resting state, the channels can be opened positive to the threshold potential. In comparison, the inactivated channel cannot be activated until it cycles or "recovers" to the resting state. These different states are important clinically, since, for example, some antiarrhythmic drugs (such as the class I antiarrhythmic drugs) preferentially bind to open and inactivated sodium channels

Action potential in slow response tissues — The SA and AV nodes represent slow response tissues, which have different properties from the fast response tissues (table 1). Phase 0 depolarization depends on an inward calcium (not sodium) current via L-type calcium channels [10]. These channels are selective for calcium, have a slower conduction velocity than the sodium channels, and take longer to reactivate.

In some cases, as with tissue damage or changes in the extracellular milieu, fast response tissues can be converted to slow response tissues. In this setting, sodium channels become inactivated and depolarization is dependent upon the slow calcium channels.

The gap junctions are actually active, opening and closing in response to changes in pH, calcium, and, at times, voltage.

In addition to ion flow and gap junction resistance, impulse propagation can also be affected by the orientation of fibers and of the collagen matrix in which the fibers reside

Three distinct mechanisms underlie tachyarrhythmia induction: enhanced automaticity, reentry, and triggered activity

Enhanced automaticity — Enhanced automaticity refers to abnormal phase 4 diastolic depolarization, and occurs when spontaneous depolarization develops during diastole (figure 5). While this is a normal phenomenon in nodal cells, and with subsidiary pacemakers at slower rates in all myocardial cells, enhanced or abnormal automaticity may lead to tachyarrhythmia. A typical example is automatic (ie, focal) atrial tachycardia. Common automaticity stimulants include excess catecholamine or situations causing hypoxia, acidosis, or ischemic related metabolites.

Critical components for reentry include both of the following:

● The presence of fast and slow conduction with varying refractory/recovery periods

● A fixed or functional core about which the circuit moves

Interventions to terminate reentrant arrhythmias differ from other mechanisms and are generally geared to modify the critical components of the reentrant circuit. Blocking Na⁺ or Ca²⁺ channels can slow or block conduction, while blocking K⁺ channels prolongs the action potential and therefore increases refractoriness

Triggered activity — Triggered activity refers to a depolarization that occurs after the initial depolarization wavefront and comes in two forms, either early or late. Secondary depolarizations that occur before the action potential has fully repolarized are early afterdepolarizations (EADs) (figure 5). Those that occur after the action potential has fully repolarized are delayed afterdepolarizations (DADs) (figure 5). Both EADs and DADs depend on the previous action potential to trigger them, hence an afterdepolarization is said to be a triggered arrhythmia. However, it is important to understand that DADs and EADs differ in mechanism.

EADs — EADs are triggered during prolonged action potentials. A prolonged action potential allows a longer window for reopening of L-type Ca²⁺ channels during phase 2 (or occasionally phase 3) of the action potential. L-type Ca²⁺ current depolarizes the membrane before repolarization, triggering an afterdepolarization. Due to L-type Ca²⁺ channel time and voltage dependence, EADs occur at slow stimulation rates or after a ventricular pause when action potential duration (phase 2) is prolonged and they are suppressed with faster heart rates. EADs are thought to initiate the polymorphic ventricular arrhythmias torsades de pointes (TdP) found in inherited and acquired long QT syndrome (LQTS), for example drug-induced LQTS

DADs — DADs, which result from intracellular Ca²⁺ overload, are triggered after the action potential is fully repolarized. Under conditions of Ca²⁺ overload, Ca²⁺ taken back up by the sarcoplasmic reticulum is then transiently re-released into the cytoplasm. This in turn causes a transient rise in cytoplasmic Ca²⁺ activating Ca²⁺-dependent depolarizing membrane current mostly through the Na⁺-Ca²⁺ exchanger. The exchange of three Na⁺ for two Ca²⁺ produces a net inward and transient depolarization or a DAD.

Conditions which enhance cellular Ca ²⁺ loading, such as rapid heart rates, enhance DAD susceptibility

Certain arrhythmogenic substrates are common, such as those induced by ischemia or infarction. In this setting, a certain effect of a drug becomes predominant and predictable, as with class I activity in ischemia, and a drug classification appears accurate. However, the major drug effect may be quite different if a different proarrhythmic substrate exists. Consider, for example, the differences in digitalis action in hypokalemia and hyperkalemia.

Class 0 — Drugs in the newly proposed Class 0 modulate the pacemaker channel HCN4, affecting the pacemaker current I_f [11]. The blocker ivabradine slows heart rate.

Class I — The class I drugs act by modulating or blocking the sodium channels, thereby inhibiting phase 0 depolarization. They are all at least in part positively charged and presumably interact with specific amino acid residues in the internal pore of the sodium channel.

● The class Ic agents have the slowest binding and dissociation from the binding site.

● The class Ib agents have the most rapid binding and dissociation from the binding site.

● The class Ia agents are intermediate in terms of the speed of binding and dissociation from the binding site.

During faster heart rates, less time exists for the drug to dissociate from the receptor, resulting in an increased number of blocked channels and enhanced blockade. These pharmacologic effects may cause a progressive decrease in impulse conduction velocity and a widening of the QRS complex. This property is known as "use-dependence" and is seen most frequently with the class Ic agents, less frequently with the class Ia drugs, and rarely with the class Ib agents

Class Ia drugs (quinidine, procainamide, and disopyramide) depress phase 0 (sodium-dependent) depolarization, thereby slowing conduction. They also have moderate potassium channel blocking activity (which tends to slow the rate of repolarization and prolong action potential duration [APD])

Class Ia agents also have anticholinergic activity and tend to depress myocardial contractility. At slower heart rates, when use-dependent blockade of the sodium current is not significant, potassium channel blockade may become predominant (reverse use-dependence), leading to prolongation of the APD and QT interval and increased automaticity

One difference between the drugs is that quinidine and procainamide generally decrease vascular resistance, whereas disopyramide increases vascular resistance.

The class Ib drugs (lidocaine and mexiletine) have less prominent sodium channel blocking activity at rest, but effectively block the sodium channel in depolarized tissues.

Class Ic drugs (flecainide and propafenone) primarily block open sodium channels and slow conduction. They dissociate slowly from the sodium channels during diastole, resulting in increased effect at a more rapid rate (use-dependence). This characteristic is the basis for their antiarrhythmic efficacy, especially against supraventricular arrhythmias. Use-dependence may also contribute to the proarrhythmic activity of these drugs, especially in the diseased myocardium, resulting in incessant ventricular tachycardia

Flecainide and propafenone also have potassium channel blocking activity and can increase the APD in ventricular myocytes. Propafenone has significant beta blocking activity.

Class II — Class II drugs act by inhibiting sympathetic activity, primarily by causing beta blockade. They may also have a mild inhibitory effect on the sodium channels.

Sympathetic stimulation has the following potential proarrhythmic actions [ 17]:

● An increase in automaticity due to enhancement of phase 4 spontaneous depolarization (see "Enhanced cardiac automaticity").

● An increase in membrane excitability due to shortening in refractoriness (phases 2 and 3 of the action potential).

● An increase in the rate of impulse conduction through the myocardial membrane, resulting from acceleration of phase 0 upstroke velocity or the rate of membrane depolarization.

● An increase in delayed afterpotentials, especially when the cell is calcium loaded, such as in digoxin toxicity.

By blocking catecholamine and sympathetically mediated actions, beta blockers slow the rate of discharge of the sinus and ectopic pacemakers, and increase the effective refractory period of the AV node. They also slow both antegrade and retrograde conduction in anomalous pathways [18].

Carvedilol is a beta-blocker with unique additional properties. In addition to beta- and alpha-adrenergic blockade, carvedilol can also block potassium (KCNH2, formerly HERG), calcium, and sodium currents and modestly prolong APD. However, when administered chronically, carvedilol increases the number of these channels, which is probably a favorable effect in diseased hearts [19].

The reader is encouraged to pay special attention to the distinctions between the different concepts introduced here. These concepts include the notions of

• a body,
• a configuration of the body,
• a reference configuration of the body,
• the region occupied by the body in some configuration,
• a particle (or material point),
• the location of a particle in some configuration,
• a deformation,
• a motion,
• Eulerian and Lagrangian descriptions of a physical quantity,
• Eulerian and Lagrangian spatial derivatives, and
• Eulerian and Lagrangian time derivatives (including the material time derivative).

For a future or current practitioner of machine learning, it’s important to be able to recognize the signal in the noise so that you can tell world-changing developments from overhyped press releases.

Early chess programs, for instance, only involved hardcoded rules crafted by programmers, and didn’t qualify as machine learning.

For a fairly long time, many experts believed that human-level artificial intelligence could be achieved by having programmers handcraft a sufficiently large set of explicit rules for manipulating knowledge. This approach is known as symbolic AI, and it was the dominant paradigm in AI from the 1950s to the late 1980s.

Although symbolic AI proved suitable to solve well-defined, logical problems, such as playing chess, it turned out to be intractable to figure out explicit rules for solving more complex, fuzzy problems, such as image classification, speech recognition, and language translation. A new approach arose to take symbolic AI’s place: machine learning.

Machine learning arises from this question: could a computer go beyond “what we know how to order it to perform” and learn on its own how to perform a specified task? Could a computer surprise us? Rather than programmers crafting data-processing rules by hand, could a computer automatically learn these rules by looking at data?

A machine-learning system is trained rather than explicitly programmed.

if you wished to automate the task of tagging your vacation pictures, you could present a machine-learning system with many examples of pictures already tagged by humans, and the system would learn statistical rules for associating specific pictures to specific tags.

So, to do machine learning, we need three things:

• Input data points—For instance, if the task is speech recognition, these data points could be sound files of people speaking. If the task is image tagging, they could be pictures.
• Examples of the expected output—In a speech-recognition task, these could be human-generated transcripts of sound files. In an image task, expected outputs could be tags such as “dog,” “cat,” and so on.
• A way to measure whether the algorithm is doing a good job—This is necessary in order to determine the distance between the algorithm’s current output and its expected output. The measurement is used as a feedback signal to adjust the way the algorithm works. This adjustment step is what we call learning.

Class III — The class III drugs (eg, amiodarone, dronedarone, ibutilide, dofetilide, sotalol, vernakalant) block the potassium channels to inhibit I_Kr, I_Ks, I_K1, and I_KUR, thereby prolonging repolarization, the APD, and the refractory period

Blockage of ventricular potassium currents is manifested on the surface ECG by prolongation of the QT interval, providing the substrate for torsades de pointes, a polymorphic ventricular tachycardia. Amiodarone and dronedarone are exceptions with very little proarrhythmic activity, perhaps because of a balance of offsetting actions.

Class IV — The class IV drugs are calcium channel blockers. Verapamil has a more pronounced inhibitory effect on the slow response SA and AV nodes than diltiazem.

In this case, we defined the coordinate change by hand. But if instead we tried systematically searching for different possible coordinate changes, and used as feedback the percentage of points being correctly classified, then we would be doing machine learning. Learning, in the context of machine learning, describes an automatic search process for better representations.

All machine-learning algorithms consist of automatically finding such transformations that turn data into more-useful representations for a given task. These operations can be coordinate changes, as you just saw, or linear projections (which may destroy information), translations, nonlinear operations (such as “select all points such that x > 0”), and so on. Machine-learning algorithms aren’t usually creative in finding these transformations; they’re merely searching through a predefined set of operations, called a hypothesis space.

So that’s what machine learning is, technically: searching for useful representations of some input data, within a predefined space of possibilities, using guidance from a feedback signal. This simple idea allows for solving a remarkably broad range of intellectual tasks, from speech recognition to autonomous car driving.

We shall use the term “body” to be a mathematical abstraction of an “object that occurs in nature”. A body \(\mathcal B\) is composed of a set of particles \(p\) (or material points). In a given configuration of the body, each particle is located at some definite point \(\mathbf{y}\) in three-dimensional space. The set of all the points in space, corresponding to the locations of all the particles, is the region \(\mathcal R\) occupied by the body in that configuration. A particular body, composed of a particular set of particles, can adopt different configurations under the action of different stimuli (forces, heating etc.) and therefore occupy different regions of space under different conditions. Note the distinction between the body, a configuration of the body, and the region the body occupies in that configuration; we make these distinctions rigorous in what follows. Similarly note the distinction between a particle and the position in space it occupies in some configuration.

In order to appreciate the difference between a configuration and the region occupied in that configuration, consider the following example: suppose that a body, in a certain configuration, occupies a circular cylindrical region of space. If the object is “twisted” about its axis (as in torsion), it continues to occupy this same (circular cylindrical) region of space. Thus the region occupied by the body has not changed even though we would say that the body is in a different “configuration”.

More formally, in continuum mechanics a body \(\mathcal B\) is a collection of elements which can be put into one-to-one correspondence with some region \(\mathcal R\) of Euclidean point space. An element \(p \in \mathcal B\) is called a particle (or material point). Thus, given a body \(\mathcal B\), there is necessarily a mapping \(\chi\) that takes particles \(p \in \mathcal B\) into their geometric locations \(y \in \mathcal R\) in three-dimensional Euclidean space:

\(y = \chi(p) \quad \textrm{where} \quad p \in \mathcal B, \mathbf{y} \in \mathcal R.\)

The mapping \(\chi\) is called a configuration of the body \(\mathcal B\); \(\mathbf y\) is the position occupied by the particle \(p\) in the configuration \(\chi\); and \(\mathcal R\) is the region occupied by the body in the configuration \(\chi\). Often, we write \(\mathcal R = \chi \left( \mathcal B \right)\).

First, injections of che- moconvulsants into this region produced bilateral clonic sei- zures at much lower concentrations than required when applied to other brain regions.

Deep learning is a specific subfield of machine learning: a new take on learning representations from data that puts an emphasis on learning successive layers of increasingly meaningful representations. The deep in deep learning isn’t a reference to any kind of deeper understanding achieved by the approach; rather, it stands for this idea of successive layers of representations. How many layers contribute to a model of the data is called the depth of the model. Other appropriate names for the field could have been layered representations learning and hierarchical representations learning. Modern deep learning often involves tens or even hundreds of successive layers of representations—and they’re all learned automatically from exposure to training data. Meanwhile, other approaches to machine learning tend to focus on learning only one or two layers of representations of the data; hence, they’re sometimes called shallow learning.

Deep learning is a specific subfield of machine learning: a new take on learning representations from data that puts an emphasis on learning successive layers of increasingly meaningful representations.

How many layers contribute to a model of the data is called the depth of the model.

In deep learning, these layered representations are (almost always) learned via models called neural networks, structured in literal layers stacked on top of each other. The term neural network is a reference to neurobiology, but although some of the central concepts in deep learning were developed in part by drawing inspiration from our understanding of the brain, deep-learning models are not models of the brain. There’s no evidence that the brain implements anything like the learning mechanisms used in modern deep-learning models.

As you can see in figure 1.6, the network transforms the digit image into representations that are increasingly different from the original image and increasingly informative about the final result. You can think of a deep network as a multistage information-distillation operation, where information goes through successive filters and comes out increasingly purified (that is, useful with regard to some task).

The specification of what a layer does to its input data is stored in the layer’s weights, which in essence are a bunch of numbers. In technical terms, we’d say that the transformation implemented by a layer is parameterized by its weights (see figure 1.7). (Weights are also sometimes called the parameters of a layer.) In this context, learning means finding a set of values for the weights of all layers in a network, such that the network will correctly map example inputs to their associated targets. But here’s the thing: a deep neural network can contain tens of millions of parameters. Finding the correct value for all of them may seem like a daunting task, especially given that modifying the value of one parameter will affect the behavior of all the others!

Learning means finding a set of values for the weights of all layers in a network, such that the network will correctly map example inputs to their associated targets.

To control something, first you need to be able to observe it. To control the output of a neural network, you need to be able to measure how far this output is from what you expected. This is the job of the loss function of the network, also called the objective function. The loss function takes the predictions of the network and the true target (what you wanted the network to output) and computes a distance score, capturing how well the network has done on this specific example (see figure 1.8)

The fundamental trick in deep learning is to use this score as a feedback signal to adjust the value of the weights a little, in a direction that will lower the loss score for the current example (see figure 1.9). This adjustment is the job of the optimizer, which implements what’s called the Backpropagation algorithm: the central algorithm in deep learning.

Initially, the weights of the network are assigned random values, so the network merely implements a series of random transformations. Naturally, its output is far from what it should ideally be, and the loss score is accordingly very high. But with every example the network processes, the weights are adjusted a little in the correct direction, and the loss score decreases. This is the training loop, which, repeated a sufficient number of times (typically tens of iterations over thousands of examples), yields weight values that minimize the loss function. A network with a minimal loss is one for which the outputs are as close as they can be to the targets: a trained network. Once again, it’s a simple mechanism that, once scaled, ends up looking like magic.