# What is an electrocardiogram?

An electrocardiogram (ECG) reflects energetic processes which occur in the heart muscle tissue cells and which are responsible for contractility of the heart muscle fibers.

Consequently, an ECG contains data on the following:

1. biochemical processes in heart cells determining the quality of the heart muscle performance;

2. times of action pulse firing by SA and AV nodes;

3. durations of cardiac cycle phases;

4. amplitudes of heart muscle fiber contractions;

5. anatomical changes in the muscle-valve complex configuration;

6. system processes regulating the cardiac contraction rhythm;

7. influence of pathological processes on the heart muscle contractility performance.

The energy used for the heart muscle contraction can be treated as sine waves changing with the time. Each cardiac cycle shows 10 such time-related change patterns. These change patterns are considered to be “phases” in a cardiac cycle. Following this way, we can say that every phase-related wave pattern has its own maximum and minimum and demonstrates a transition from an energy growing to its attenuation. These points are considered to be “the specific points”. They can be identified with the use of mathematical tools based on an analysis of a mathematical curve that describes repetitive oscillation as a function of time. The above specific points are identified by the first order derivative as follows:

* considering the interval from energy growing to its attenuation, it is the maximum on the derivative curve; *

* considering the interval from attenuation to growing, it is the minimum on the derivative curve;*

* the energy maximum and its minimum correspond to the respective inflection points on the oscillation graph, and in this case the inflection point is zero.*

Therefore, it should be concluded that boundaries of the cardiac cycle phases correspond to the respective maxima and minima on the first order derivative curve, depending on the contraction and relaxation of the heart muscle fibers. These criteria are identical for all ten phases in a cardiac cycle.

**Interpretation of the derivative of a function. The geometrical interpretation of the derivative.**

*Definition: **The physical interpretation of the derivative is that it is treated as a rate of change of a function.*

An example: Figure 1 offers graphs of three functions. Which of them shows the fastest rate of change?

Figure 1. Graphs of functions 1,2 and 3.

To answer this question: it is evident that graph 3 shows the fastest rate of change, i.e., we deal with the greatest velocity.

Slope of tangent line is the next major interpretation of the derivative graph. In other words, it means we can judge how fast y is changing in comparison to x. So, the first order derivative demonstrates us whether a function is increasing or decreasing, and by how much it is increasing or decreasing. This is reflected in the graph of a function by the slope of the tangent line to a point on the graph, which is called the slope of the function.

**Graphical representation of differentiation. Inflection points on ECG curve. Criteria for identification of phase boundaries on ECG curve**

Mathematical differentiation is widely used in analysis of various processes in many areas in science. For this purpose, utilized should be higher order derivatives. When considering an ECG curve differentiation, it should be noted that for this purpose the information obtained from the first order derivative is quite sufficient, since its maxima and minima represent in the most precise manner the changing energy of the contraction of the heart muscle fibers.

Figure 2 below depicts a graph of sin oscillations where you can find one period of oscillation.

Figure 2. Harmonic oscillation graph and the corresponding derivative

The classical physics describes the simple pendulum motion as the above type of the oscillations: the simple pendulum is swinging back and forth and reaching its extreme positions. These extreme positions correspond to energy transformation ranges from energy increase to its decrease. You can find it on the upper graph in Figure 2, when the curve passing through the time axis changes its sign. Each inflection point on the upper curve corresponds to a maximum or a minimum on the derivative curve. The maxima and minima of the function are two kinds of the extrema.

If we differentiate an ECG curve, then the extrema on the derivative curve will represent the boundaries of the cardiac cycle phases showing the energy increase and decrease, and vice versa. It is just the criterion used for the proper identifying of the boundaries of each phase in a cardiac cycle.

**ECG as a sequence of simple harmonic oscillations (sine waves)**

An ECG can be represented as a sequence of simple harmonic oscillations (sine waves) (see Figure 3 below). Each oscillation or wave of the curve corresponds to a phase in a cardiac cycle. The respective boundaries of the waves on the ECG curve are the boundaries of the respective phases within the given cardiac cycle. To identify them, used should be the first order derivative of the ECG curve.

Figure 3. ECG as a sequence of harmonic oscillations (sine waves)

**Accurate identification and location of cardiac cycle phases on ECG with the use of the first order derivative (mathematical differentiation of a curve)**

*Cardiac cycle pattern according to the ECG *

Each cardiac cycle consists of 10 phases (see Figure 4 below). The distinguishing feature of each of the phases is that the contraction of strictly specified heart muscle fibers occurs.

Figure 4. Cardiac cycle pattern according to the ECG

The contraction of the muscle fibers requires energy. The energy generation in the heart muscle cells is provided by biochemical reactions. The performance of the phase is determined by the rate of the contraction of the respective muscle fibers. Considering individual intervals from phase to phase, we can observe the rate of energy increasing and decreasing that corresponds to the heart muscle fiber contraction and relaxation. Following this concept, it should be stated that we can find in this case also inflection points of the curve passing through the zero-axis, when considering the energy consumption that is identical to the case with the formation of the ocean waves which also grow and decay. These inflection points can be precisely identified by the first order derivative showing the respective maxima and minima. The same is applicable to ECG curve processing with the use of the first order derivative which also depicts its maxima and minima and according to which the boundaries of each cardiac cycle phase can be identified in the most accurate way (see figure 5 below).

Figure 5. An ECG curve and the respective first order derivative. The local extrema on the derivative can be defined as the boundaries of the respective cardiac cycle phases (the only exception is the R point).

** **

**Identification of the boundaries of phase P-Q responsible for atrioventricular valve closure**

At the beginning of this phase, the atrioventricular valve closing procedure is starting. It corresponds to point Р on the ECG. The procedure is being completed at point Q. Point Р is an inflection point at the trailing edge of the P wave. It is defined as the minimum considering the trailing edge derivative segment (see Figure 6 below).

**Identification of the boundaries of phase S-L responsible for heart muscle pre-load **

The phase is responsible for pre-load or pre-tension of the heart muscle fibers and for applying the increasing load to the ventricular blood volume in order to initiate the aortic valve opening procedure. At the beginning of this phase, at point S, the heart muscle fibers are starting their pre-tensioning. At point L, the pressure in the ventricles reaches the required level to initiate the aortic valve opening procedure and start the rapid ejection of blood into the aorta.

Figure 6 а

Figure 6 b

Figure 6 c

Figure 6 d

Figure 6 e

Figure 6. Examples: identification of boundaries of cardiac cycle phases in practice with the use of the first order derivative of ECG

It should be noted that the notation of point L as the end of the pre-load or pre-tension phase has been introduced for the first time by the cardiac cycle phase analysis concept developers. That has never been done before by classical ECG researchers and interpreters. This phase is of significant value for diagnostics. The concept of the new cardiac cycle phase analysis offers a detailed description of this phase.

Point S corresponds to the respective local maximum on the derivative curve (see Figure 6).

Point L corresponds to another local maximum of the derivative which is located first to the right of point S (s. Figure 6 above).

**Identification of point j **

Pont j is defined as an inflection point of the leading edge of the Rheogram (see Figure 7 below). It can be identified as a local maximum of the first order derivative of the Rheo. It is located on the ECG close to the onset of the T wave.

Figure 7. Point j is defined as a local maximum of the first order derivative of the leading edge segment of the Rheo. On the ECG, it is located close to the onset of the T wave.

**Identification of point Т**

According to the cardiac cycle phase analysis, point T is defined as the end of systole (or the beginning of the diastole). It is identified as the respective local minimum on the T wave trailing edge derivative (see Figure 6 above).

**Use of measured durations of cardiac cycle phases for calculation of basic hemodynamic parameters**

Upon measuring of durations of each cardiac cycle phase and using them in the hemodynamic equations by G. Poyedintsev – O. Voronova, we can non-invasively obtain 7 phase-related volumes of blood in each cardiac cycle as listed below:

SV – stroke volume (ml);

MV – minute volume (l/min);

PV1 – volume of blood entering the ventricle in the early diastole (ml);

PV2 – volume of blood entering the left ventricle in the atrial systole (ml);

PV3 – volume of blood ejected by the ventricle during the rapid ejection phase (ml);

PV4 – volume of blood ejected by the ventricle during the slow ejection phase (ml);

PV5 – volume of blood pumped by the ascending aorta as peristaltic pump in systole.

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