Fiducial Point Location

The presence of ventricular ectopic beats in the heart action of a patient often gives early warning of impending conditions that can be fatal. It is important, therefore, that equipment used to monitor the patient's condition provide indicia of their presence so that timely remedial action can be taken. However, it is equally important that the frequency of false indicia be reduced to a minumum in order that the time of medical attendants may be used efficiently and to prevent the presence of the indicia from being ignored. Unfortunately, however, present monitors leave much to be desired in this regard.

One method of identifying a ventricular ectopic heartbeat is by comparing its ECG wave with a wave that is considered to be normal for the particular patient involved. Any one of the number of empirical formulae can be used for this purpose, but in addition to certain physiological data, many require an input as to the measure of the degree of correlation between the form of the ECG wave for the heartbeat being examined and the form of the ECG wave representing the normal heartbeat. A reliable measurement can be attained only if the waves are effectively aligned, so that the portions of each that correspond to the same part of the heartbeat cycle are in time coincidence. This result can be attained by locating a single point in each heartbeat cycle, known as a fiducial point, that uniquely occurs at the same functional point in any ECG wave and aligning the waves with their points in time coincidence. If the location of the fiducial points is not accurate, the degree of form correlation, even for identical waves, can be far less than the actual 100 percent. In the present state of the art, the location of the fiducial points is unreliable, so that too many ectopic beats are not detected or too many false alarms are given.

In determining whether a particular heartbeat is a ventricular ectopic beat, data relating to the time between it and the previous beat, the average time between beats, and the average deviation of the beats from the average time between them is often used. If, as in the prior art, the fiducial point is not properly located, this data will be inaccurate so as to make the identification of a ventricular ectopic beat unreliable.

In making form correlation, data as to the area of non-overlap between the ECG wave being examined and the ECG wave that is considered normal is often used. In prior methods, correlation has depended on the sum of the absolute differences in the areas of corresponding samples of the wave being examined and the normal wave, so that the correlation changes with amplitude. This makes it difficult to identify the ectopic beat.

In accordance with this invention, the fiducial point is located in such manner that the portions of the cycle of the greatest clinical interest, namely, those that occur when the ventricle is stimulated, have a greater effect on the location of the fiducial point than other portions of the heartbeat cycle. This can be accomplished by locating the fiducial point at the centroid of the ECG wave in accordance with the following expression in which the times t.sub.1 and t.sub.2 respectively occur before and after the QRS wave, T is the time after t.sub.1 at which the centroid occurs, M is the order of the derivative, and n is the power to which it is raised. ##EQU1## If n is an odd integer, the absolute value of dV/dt must be used in the above equation, so that negative derivatives contribute in the same way as positive derivatives. It is possible to use M= .phi.. The program for making the calculation of T is unimportant and, as will be explained in detail, the first derivative for at least the lower frequencies can be derived by a filter coupled between the ECG machine and the means making the computation.

FIG. 1 shows a normal cardiac waveform;

FIG. 2 shows a nearly normal cardiac waveform to be analyzed for a ventricular ectopic beat;

FIG. 3 illustrates the alignment of the cardiac waveforms of FIGS. 1 and 2 by superimposition of fiducial points that are respectively located at the peaks having the greatest amplitude;

FIG. 4 illustrates the alignment of the cardiac waveforms of FIGS. 1 and 2 by superimposing fiducial points that are located at the centroid in accordance with the present invention;

FIG. 5 shows a cardiac waveform differing substantially from the normal cardiac waveform of FIG. 1;

FIG. 6 shows the alignment of the cardiac waveform of FIG. 5 with the normal cardiac waveform of FIG. 1 utilizing the fiducial points located in accordance with this invention;

FIG. 7 is a block diagram of the portions of a monitoring system in which indicia is provided whenever an ECG signal represents an ectopic beat;

FIGS. 8A and 8B together are a flow chart for one computer program that can be used with monitoring systems that provide indicia of the presence of ectopic beats in the ECG waves derived from a patient;

FIG. 9 is a flow chart of one computer program that may be used to determine the location of the fiducial point in accordance with this invention;

FIG. 9A is a QRS waveform used in explaining the operation of FIG. 9;

FIG. 9B is a graph of a filter characteristic shown in FIG. 8A; and

FIG. 10 illustrates a circuit for locating the fiducial point in accordance with this invention.

FIGS. 1 through 6 illustrate the situation where the degree of correlation between the forms of two ECG waves is determined by the amount of non-overlap between them. It will be understood that actual graphs of the waves need not be used, and that the area of non-overlap can be determined by finding the difference between cotemperal samples of the waves occurring between times of interest when the fiducial points coincide in time.

FIG. 1 shows an ECG wave in a dotted line that is considered to be normal for a given patient, and FIG. 2 shows a wave that would also be considered normal because it is nearly identical to the wave of FIG. 1. The only difference is that the amplitude of the most positive peaks P.sub.1 + of the wave of FIG. 1 is slightly greater than the amplitude of its most negative peak P.sub.1 -, whereas in FIG. 2, the amplitude of the most negative peak P.sub.2 - is slightly greater than the amplitude of its most positive peak P.sub.2 +.

If the dotted line ECG wave of FIG. 1 and the solid line ECG wave of FIG. 2 are mapped by locating the fiducial points at the peaks of greatest amplitude, the peaks P.sub.1 + and P.sub.2 - will be aligned in time, as indicated in FIG. 3. The area of non-overlap shown by the shaded area of FIG. 3 is so large that the wave of FIG. 2 would be considered ectopic. Such a slight difference in peak amplitudes and the resulting false indication of an ectopic beat can be caused by the movement of the patient or of the electrodes, or by the patient's breathing.

If, however, the fiducial points F.sub.1 and F.sub.2 of the waves of FIGS. 1 and 2 are each located at a centroid in accordance with this invention, the area of non-overlap is very small, as shown in FIG. 4, so that the solid line ECG wave of FIG. 2 would be indicated as being normal.

Now consider the solid line ECG wave of FIG. 5 that differs substantially in shape from the normal dotted line ECG wave of FIG. 1. The fiducial point F.sub.5 of the wave of FIG. 5 is located at a centroid, in accordance with this invention. When the waves are mapped, the results are as shown in FIG. 6. The area of non-overlap shown by the shading is so large that the ECG wave of FIG. 5 would be indicated as representing an ectopic beat.

FIG. 7 is a block diagram of the kind of known monitoring systems in which the present invention can be used to advantage. An ECG machine 10 supplies ECG signals indicative of the heartbeat of a patient P to a computer 12. When the beat is not ectopic, the computer 12 provides a signal via a lead 16 to a stylus control means 18 so as to cause the stylus 20 to make a short mark 22 on a tape 24 that is transverse to the direction in which the tape 24 is moved by rollers 26 and 28 and a motor 30. When, however, the beat is ectopic, the computer 12 provides a signal via a lead 32 to the stylus control means 18 so as to cause the stylus 20 to make a long mark 34 on the tape 24.

The detailed operation of a monitoring system, such as shown in FIG. 7, is now explained by reference to FIGS. 8A and 8B. They include a portion of a flow chart applicable to any computer for a program set forth at the end of the specification that may be used to control the computer 12 of FIG. 7 if it is an HP Computer Model 2109 or 2113. The steps of the program that apply to various parts of the flow chart are written adjacent the appropriate blocks. Information flow is indicated by dotted lines and logic flow by solid lines.

Signals representing heart action are derived from the patient P by the ECG machine 10, as in FIG. 7, and applied to an A/D converter 40. Its output is coupled via an A/D driver 42 and a switch S to a circular buffer 44. The converter 40 and driver 42 are both synchronized by a digital clock 46. Part of the initialization of the system is achieved by carrying out program steps RWAV 28-98 indicated by the block 48 to purge the system of all information signals. One storage position of the circular buffer 44 is then examined by a buffer scan 50. If no QRS wave is present, a decision is made, as indicated by the decision block D.sub.1, to cause the buffer scan 50 to examine the next storage position in the circular buffer 44. The process continues until a QRS wave is detected. The time after initialization at which the first QRS wave occurs is stored in a preliminary fiducial point storage, as indicated by block 52. These functions are controlled by program steps NOPAC 30-56 and RWAV 658-742, so that the buffer scan block 50 in combination with the decision block D.sub.1 constitutes a QRS detector of a known type that sets the time of the preliminary fiducial point at the time of the positive or negative peak having the greatest amplitude in each QRS wave, as illustrated in FIGS. 1 or 2.

After the preliminary fiducial point is stored by the block 52, the ECG wave then in the circular buffer 44 is examined, as indicated in the block 54, to determine the time of the corrected fiducial point with respect to the time of the preliminary fiducial point. This has been done in a number of ways, but if it is to be determined in accordance with the principles of this invention, as indicated by expression (1), it may be accomplished by carrying out the program steps NOPAC 59 and RWAV 745-877 in a manner to be described in detail in connection with FIG. 9.

After initialization, it is essential to identify and store information as to the heartbeat cycle that is to be considered "normal". One heartbeat cycle that can be used for this purpose is the one occurring immediately after the longest interval between any of about ten successive cycles. Block 56 measures the intervals, known as R to R intervals, between successive corrected fiducial points determined by the block 54 in accordance with program steps NOPAC 62-71. Upon operator request, the normal beat request flag is set by means not shown to inform the decision block D.sub.2 that a new normal heartbeat cycle is requested. This causes the block 58 to clear the flag and the block 60 to set the count, to be explained, to zero under control of program step NOPAC 124. The block 62 then sets the maximum interval between heartbeat cycles R.sub.MAX, to be explained, to zero under the control of step NOPAC 124. The count referred to is the count in blocks 60 and 64. With this set to zero, the count in block 64 becomes unity under the control of step NOPAC 129, so that the output of the decision block D.sub.3, that determines if the count has reached ten under the control of steps NOPAC 126-128, is NO. The decision block D.sub.4 determines under the control of steps NOPAC 130-133 whether the R to R interval is greater than R.sub.MAX. R.sub.MAX is initially made equal to zero by block 62, so that the output of D.sub.4 is YES. This, in turn, causes a block 66 to substitute the first R to R interval for R.sub.MAX in accordance with step NOPAC 134. Block 68 stores this heartbeay cycle from the circular buffer 44, as well as information as to the location of its corrected fiducial point, in a snapshot memory 70 under the control of steps NOPAC 136 and RWAV 1341-1352.

If the R to R intervals between the next nine successive heartbeat cycles are less than the first one, the output of the decision block D.sub.4 is negative and the match block 72 successively superimposes each of these cycles from the circular buffer 44 on the normal beat from the snapshot memory 70, which, in this case, was the first cycle, with their corrected fiducial points occurring at the same time. Successive cycles are compared until one of them follows a larger R to R interval, in which event it is stored in the snapshot memory 70. This process continues until the count equals ten or some other arbitrarily selected value, at which point the output of the decision block D.sub.3 is YES. From this point on, unless a new normal beat is requested by activating the normal beat request flag, each successive cycle of of a beat from the circular buffer 44 is matched by the block 72 with the normal cycle stored in the snapshot memory 70 and the correlation (as explained below) is calculated.

In order to prevent the match block 72 from comparing each of the first ten heartbeat cycles with the cycle stored in the snapshot memory 70, the NO output of the decision block D.sub.4 and the output of the store block 68 can be applied so as to activate the buffer scan 50, as indicated by the dash-dot lines 74 and 76. Thus, the match block 72 is not activated until the output of the decision block D.sub.3 is YES, which occurs ten cycles after a new normal beat is requested.

There are several formulae which can be used to compare beats after they are aligned. As a class, they are called correlation. Several investigators have employed a "cross correlation coefficient": ##EQU2## This formula has rather formidable computational difficulties due to the large number of multiplying operations involved. It yields a number which varies from 0 for a worst case mismatch to 1 if V.sub.1 and V.sub.2 differ only in amplitude.

An attempt to get around the computational difficulties is the absolute area of non-overlap calculation:

this formula is certainly simpler but, unlike cross correlation, it is not dimensionless. That is, if V.sub.1 and V.sub.2 change proportionally, the correlation changes.

This problem is removed in the system described by normalization: ##EQU3##

The formula is now dimensionless and equal to 512 for a worst case mismatch and to 0 for perfect identity. In the system described, the above formula is multiplied by 512 so that integer arithmetic can be used. This latter computation is done in match block 72 in accordance with the steps NOPAC 167-169 and RWAV 1204-1247.

Having correlated the current and normal waves by determining the normalized area of non-overlap A in the matching block 72, there are a number of acceptable ways of determining whether a beat is a ventricular ectopic beat. They generally require inputs as to the time R between the beat being examined and the previous beat, the average time Z between beats, and the average deviation W of the beats from the average time Z between them. A particularly advantageous way of making the determination from these inputs is to substitute them into the following expression: ##EQU4## This is done in decision block D.sub.5 under control of program steps NOPAC 177-319. . It can be seen, for example, that, if the beat being examined follows the previous beat by a time R equal to average time Z between beats, then B= 250, and that if R is less than Z, B is reduced. If B is less than 125, it is arbitrarily assigned a value of 125. If A, the normalized area of non-overlap, is greater than B, the beat is considered to be ectopic and the output of the decision block D.sub.5 is YES. When this occurs, a block 82 outputs a long mark on the tape or other record media under the control of program steps NOPAC 254 and 255 and RWAV 281-292.

If the decision block D.sub.5 concludes that the current beat is not ectopic, so that the output of the block D.sub.5 is NO, a block 78 outputs a short mark on a tape or other record media under the control of program steps NOPAC 371 and 372 and RWAV 281-292. Block 80 updates the normal cycle in the snapshot memory 70 by adding 1/8 of the difference between the normal cycle and the current cycle to the normal cycle, as indicated by

under the control of program steps NOPAC 356 and 357 and RWAV 1296-1314. This makes the normal heartbeat cycle stored in the snapshot memory 70 a running average. After block 82 has produced a long mark or after block 80 has updated the snapshot memory 70, the scan buffer 50 is advanced to the next cycle stored in the circular buffer 44, and the process is repeated.

There are a number of means that can be used in the block 54 of FIG. 8A for determining the location of the fiducial points in accordance with equation (1) so that they are located at the centroid in accordance with this invention. The required integration is performed between an earlier limit occurring prior to the heartbeat cycle and a later limit occurring after it. The process of integration can start at the lower limit and proceed to the higher limit, or it can start at an intermediate point in the cycle and proceed forward to the later limit and backward to the earlier limit at the same time. One way of carrying out the latter method is illustrated by the flow chart of FIG. 9 in which the steps of the program at the end of the specification are indicated near the appropriate blocks. Assume that the QRS portion of a wave representing a heartbeat cycle is as shown by the curve of FIG. 9A and that the samples provided by the A/D converter 40 of FIG. 8A are at times indicated by the vertical lines. The samples are farther apart than normal in order to clarify the drawing and will occur during the portions of the heartbeat cycle other than the QRS portion shown. For this particular wave, the preliminary fiducial point determined by the QRS detector comprised of the blocks 50 and D.sub.1 of FIG. 8A will be at the sample indicated by V(O) because it has the greatest amplitude from the baseline b which is at ground potential.

The blocks of the flow chart of FIG. 9 that are now to be described set up initial conditions for the logic loop L that performs the integration necessary to determine the respective values of the numerator and denominator of equation (1) for each heartbeat cycle. The purpose of these initial conditions will be apparent when the operation of the loop L is considered.

Block 82 sets the initial value of numerator.sup.O to zero in accordance with program steps RWAV 768-770. Following this, the block 84 sets the initial value of the denominator.sup.O equal to the square of the difference between the amplitude of the sample V(O) and the amplitude of the sample V(-1) in accordance with steps RWAV 777-780. The letter D and the numbers in the parenthesis following it in FIG. 9A designate the difference between successive amplitude samples. These differences are the samples of slope to be used in making calculations of the location of the fiducial point in accordance with the equation (1). If there are to be 75 slope samples including the zero.sup.th sample, N varies from 1 to 37. The block 86 sets the initial value of N at one in accordance with steps RWAV 781 and 782.

Turning now to the loop L, block 88 operates in response to steps RWAV 785-792 to compute

for successive values of N from the lowest value of N permitted by the block 86, which is one, until a value of N equal to 38, if there are to be 75 samples in the integration. The output of the block 88 for each value of N is stored in a temporary memory DTMP 4. Block 90 then operates in response to steps RWAV 793-802 to compute

for successive value of N from 1 to 37. The output of the block 90 for each value of N is stored in DTMP 2. A block 92 then calculates the value of the new denominator.sup.N in accordance with steps RWAV 803-812. The new denominator.sup.N is equal to the value of the previous or initial denominator plus the information stored in DTMP 4 plus the information stored in DTMP 2. A block 94 then calculates in accordance with steps RWAV 815-840 the value of the new numerator.sup.N, which is equal to the old numerator plus N times the information in DTMP 4 minus N times the information in DTMP 2. At this time, a block 96 substitutes N+ 1 for N in response to step RWAV 843. If N is less than 38, a decision block D.sub.6 has a negative output that causes a repetition of the calculation just described at a value of N that is one unit larger. The calculations indicated by the above blocks 88, 90, 92, 94 and 96 are repeated for successive values of N from 1 to 37. When, however, N=38, the output of the decision block D.sub.6 is YES and causes a block 98 to compute in accordance with steps RWAV 848-876 the time of occurrence of the corrected fiducial point. This is done by adding to the preliminary fiducial point indicated by the QRS detector a fraction with the same units as N in which the numerator is the numerator provided by the block 94 and the denominator is the denominator provided by the block 92. This information is then supplied to the block 56 of FIG. 8A.

The expressions for the numerator provided by the block 94 is

and the expression for denominator.sup.N provided by the block 92 is

at the time of initialization, numerator.sup.o is made equal to zero by the block 82, and denominator.sup.O is made equal to [V(O)-V(-1)].sup.2 by the block 84. Then N is made equal to 1 by the block 86, so that after block 94 on the first pass

and

Fourier analysis of a heartbeat cycle, such as that shown in FIG. 9A, shows that the frequencies involved generally fall between 0.5 and 50 Hz, and that most of the energy lies below 16 Hz. Whereas there is some noise at these lower frequencies in the signals provided by the ECG machine 10 of FIG. 8A, there is also a great deal of noise at the higher frequencies. The high frequency noise can be attenuated by insertion of a filter between the output of the ECG machine 10 and the input of the circular buffer 44 without interfering too much with the information contained in the signal. An analog filter could be inserted between the ECG machine 10 and the A/D converter 40 or, as in FIG. 8A, a digital filter 100 can be connected between the A/D driver 42 and the circular buffer 44 by placing the switch S in the proper position. Of course, differentiation is filtering, but preferably the filter 100 may have a bandpass characteristic passing through the origin of response vs. frequency and having half-power points located at 7 Hz and 16 Hz, as shown in FIG. 9B. This would reduce the effect of noise. Inasmuch as the lower frequencies are effectively differentiated by the filter 100, there is no need of differentiating a second time, as is done in FIG. 9 unless, of course, the second derivative is to be used at low frequencies, i.e., M is to equal 2 in equation (1). Accordingly, if the filter 100 is used and the first derivative at low frequencies is desired, the computer program would have to be changed in ways known to those skilled in the art so as to eliminate the term -V(N-1) from the calculation performed by the block 88 and to eliminate the term -V(-N) from the calculation performed by the block 90. The RWAV and NOPAC programs include both filtering and differentiation. Either could be eliminated but it would be preferable to retain the filtering because of noise consideration. It should be noted, however, that the amplitude V in the remaining terms is different than before because of the presence of the filter 100.

FIG. 10 shows a circuit for calculating the location of the fiducial point of a cardiac waveform so that it will be located at the centroid in accordance with this invention. The ECG signals which represent normal beats, as well as ventricular ectopic beats, are supplied by a source 102 to an A/D converter 104. Its output is applied to a point in a computer 108 corresponding to the input of the A/D driver 42 of FIG. 8A. The output of the converter 104 is also applied to a delay means 106 that delays the signals by an amount d/2 that is equal to half the duration d of the longest QRS wave to be expected, e.g., d=300 ms. The output of the delay means 106 is applied to a converter 110 that restores it to the same shape it had at the output of the ECG source 102. The output of the D/A converter 110 is coupled to a differentiator 112 comprised of a capacitor 114 coupled between the output of the D/A converter 110 and the inverting input of an operational amplifier 116, a resistor 118 connected between the output of the amplifier and its inverting input, and a ground connection for the non-inverting input.

The output of the differentiator 112, (dV/dt), is applied to X and Y inputs of a multiplier 120 so as to produce a signal (dV/dt).sup.2 at its output. The output of the multiplier 120 is coupled to an integrator 122 which is comprised of a resistor 124 connected between the output of the multiplier 120 and the inverting input of an operational amplifier 126, a capacitor 128 connected between the output of the amplifier 126 and its inverting input, a normally closed switch S.sub.1 shunting the capacitor 128, and a ground connection for the non-inverting input of the amplifier 126. As will be explained, the output of the amplifier 126, which is ##EQU5## is connected to an input A of a divider contained within the dotted rectangle 130.

The signal (dV/dt).sup.2 at the output of the multiplier 120 is also applied to the X input of a multiplier 132. Its Y input is connected to the junction of a source 132 of constant current I.sub.1 and one side of a capacitor 136. The other side of the capacitor 136 is connected to a point of negative potential -V, and a normally closed switch S.sub.2 is connected in shunt with the capacitor 136. The capacitance of the capacitor 136 is I,d/2V. The voltage applied to the Y input of the multiplier 132 is proportional to the time after the switch S.sub.2 is opened, so that the output of the multiplier 132 is t(dV/dt).sup.2.

The output of the multiplier 132 is applied to an integrator 138 comprised of a resistor 140 connected between the output of a multiplier 132 and the inverting input of an operational amplifier 142, a capacitor 144 shunted by a normally closed switch S.sub.3 and connected between the output of the amplifier 142 and its inverting input, and a ground connection for the non-inverting input of the amplifier 142. As will be explained, the output of the amplifier 142 is ##EQU6## This signal is applied to the input, B, of the divider 130.

The particular construction of the divider 130 is unimportant, but in this particular illustration, it is comprised of a resistor 144 connected between the B input of the divider 130 and the inverting input of an operational amplifier 146 having its non-inverting input connected to ground. Also included is a multiplier 148 having its X input connected to the input A of the divider 130 and its Y input connected to the output of the amplifier 146. A resistor 150, having the same value as the resistor 144, is connected between the output of the multiplier 148 and the inverting input of the operational amplifier 146. The signal at the output of the divider 130 is ##EQU7##

The output of the ECG amplifier 102 is also applied to the input of a QRS detector 152 that provides a pulse at some point within the QRS portion of the cardiac waveform. The timing of this pulse cannot be used as the time of a fiducial point because it does not always occur at the same functional point in the cardiac waveform. The pulse at the output of the QRS detector 152 is applied to means (not shown) for opening the swiches S.sub.1, S.sub.2 and S.sub.3 and also to a delay means 154 having a delay of d ms. The delayed pulse at the output of the delay means 154 is applied to means (not shown) to cause an A/D converted 156 to sample the output of the divider 130 and input this information to a point in the computer 108 corresponding to the input to the block 56 of FIG. 8A.

The purpose of introducing the various delays into the circuit is to establish the limits of integration, i.e., t.sub.1 and t.sub.2 of the expression (1). When the switches S.sub.1, S.sub.2 and S.sub.3 are closed, as they normally are, the circuits are inoperative. At the approximate center of the QRS wave, the QRS detector 152 outputs a pulse that opens the switches S.sub.1, S.sub.2 and S.sub.3 and starts the calculation at time t.sub.1. Assuming that the QRS wave will not have a duration greater than d, the fact that the wave at the output of the D/A converter 110 is delayed by d/2 means that the switches open so as to permit calculations to start at some point before the QRS wave begins. The pulse outputted by the QRS detector 152 is delayed by a time d in the delay means 154 before it activates an A/D converter 156 at a time t.sub.2. Thus, the computer 108 has both the ECG waveform and information as to location of the fiducial point and can compute the area of non-overlap or any other correlation calculation or integrative measure of difference between this ECG waveform and any other previous input in a like manner, including a beat designated as normal. When the difference exceeds a predetermined amount, an indication is made to the effect that the heartbeat cycle is ectopic, but if the difference is less than the said predetermined amount, an indication is made to the effect that the heartbeat cycle is not ectopic.

By way of illustration, if the ECG waveform at the output of the D/A converter 110 is as indicated at W.sub.1, the outputs of the differentiator 116, the multiplier 120, and the integrator 122 will be as represented by the waveforms W.sub.2, W.sub.3 and W.sub.4, respectively. The voltage across the capacitor 136 will vary linearly from a value of -V at some time prior to the departure of W.sub.1 from zero to a value of +V at some time after W.sub.1 returns to zero, as indicated by the waveform W.sub.5. W.sub.5 and W.sub.3 are applied to the inputs of the multiplier 140 so as to produce an output as indicated by the waveform W.sub.6. Integration of this output by the integrator 138 produces a parabolic output indicated by the waveform W.sub.7. The division of W.sub.7, at the B input of the divider 130, by W.sub.4, at the A input, yields a value Y, after all calculations have been completed, that represents the difference in time between the preliminary fiducial point determined by the QRS detector 152 and the final fiducial point determined in accordance with this invention. In this particular example, the preliminary fiducial point and the final fiducial point occur at the same time, i.e., at the apex of W.sub.1, so that Y at this point is zero; as indicated by the fact that the parabola W.sub.7 returns to zero. Although not shown, means are provided for closing the switches S.sub.1, S.sub.2 and S.sub.3 in between the waves so as to discharge the capacitors 128, 136 and 144, and set the initial conditions for determining the fiducial point of the next ECG wave.

Whether the timing of the fiducial point of an ECG waveform is made to be in accordance with equation (1) by a computer or by a circuit, it occurs at the proper point so that the R to R intervals are correct. The measure of these intervals appears at the output of the block 56 of FIG. 8A and is used in identifying an ectopic beat, but it can be used by other means for other purposes where its accuracy is also important. ##SPC1## ##SPC2## ##SPC3## ##SPC4## ##SPC5## ##SPC6##