Analyzing electrocardiogram voltage signals
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Analyzing electrocardiogram voltage signals
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[post_content] => Practice Passage (Question 1-5)
*This passage is the property of Khan Academy and has been reformatted into an AAMC-style interface in their entirety by MedLife Mastery. MedLife Mastery does not endorse and is not an affiliate of Khan Academy.
An electrocardiogram (ECG) measures the heart’s electrical activity using a series of probes placed on the skin. In addition to detecting rhythmic electrical activity due to the heart’s beating, an ECG can detect other processes, like spasms, that occur with different frequencies than the heartbeat. The ECG is able to convert data indicating the magnitude of the electrical activity as a function of time into information about specific processes that occur in the heart over different timescales using a mathematical operation known as a Fourier transform.
In a Fourier transform, a time-varying signal is converted into a histogram showing the various frequencies that constitute the signal. As a result, an ECG voltage versus time graph can be replotted as an amplitude versus frequency graph, which indicates the relative presence of various frequencies in the original voltage reading. For example, The Fourier transform of a time series showing an undulating sine wave with frequency
1hz would be a histogram with peaks at 1 hz (Figure 1).
For a more complex signal consisting of many different sine waves superimposed, the Fourier transform shows the relative amounts of various frequencies present in the signal. For example, in the Figure 2, the Fourier transform of the voltage signal V (t) = (1/3) sin(23t) + 1sin(2t) (Figure 2A) produces a bar chart with a higher peak at 1 hz than at 3 hz (Figure 2B). A mathematical theorem guarantees that a valid Fourier transform can be generated for any periodic signal, which equivalently suggest that any periodic ECG signal can be represented as a sum of sine waves with various frequencies and amplitudes.
The raw output of an ECG is a periodic signal indicating the electrical activity arising from a patient’s heart as a function of time, but the shape of this signal is generally NOT purely sinusoidal-instead, it consists of a superposition of many different periodic processes in the body which generally ARE sinusoidal. As a result, the Fourier transform of an ECG signal can be used to indicate the presence or absence of various processes that occur with different characteristic frequencies based on their presence or absence in the Fourier histogram.
Figure 1: A) A sinusoidal output from an ECG and B) its Fourier transform.
Figure 2: A) An ECG signal consisting of two superimposed sinusoids and B) its Fourier transform.
Figure 3: The output of an ECG test for a healthy patient contains many different frequencies and, as a result, is generally not a single sine wave.
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[question] => Suppose a rare genetic mutation doubles the diameters of the electrically conducting cells that transmit electrical activity throughout the heart and body. Which of the following describes the most direct effect this would have on observed ECG voltage fluctuations if all other aspects of the patient (height, weight, composition) remain the same?
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[description] => Reason for the Correct Answer:
he voltage produced by the heart is reduced linearly by the total resistance the current encounters as it passes through the body on the way to the ECG pads via Ohm’s law.
Ohm’s law states that voltage(the signal) is proportional to the current and resistance.
A reduced body resistance results in a stronger ECG signal.
The resistance of a material goes as 1/(its cross-sectional area).
If all conducting channels have twice the diameter, they will have four times the area, reducing resistance (and improving the signal) by a factor of four.
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[each_answer] => A. No direct effect.
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[each_answer] => B. A quadrupling of the amplitude.
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[each_answer] => C. A doubling of the amplitude.
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[each_answer] => D. A doubling of the frequency.
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[question] => Which of the following traits MUST be present in a Fourier transform of Figure 3?
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[description] => Reason for the Correct Answer:
The signal appears to repeat itself every .5 seconds
Since the signal has a well-defined frequency, and it must be a sum of sine waves, there must be a component with a frequency matching that of the signal.
Two of the answer choices have the wrong units
Because the signal repeats every .5 seconds, there must be a 2 hz peak in the Fourier transform.
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[each_answer] => A. A peak at 2 hz
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[each_answer] => B. A peak at .5 hz
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[each_answer] => C. A peak with amplitude 1 V
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[each_answer] => D. A peak with amplitude 2 V
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[question] => Which of the following graphs most likely represents the Fourier transform of an ECG reading that is well-fitted by the function V (t) = 4 sin(2π4t) + sin(2π8t) ?
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[answer] => 4
[description] => Reason for the Correct Answer:
In Figure 2, the presence of two different frequencies in the ECG output led to two pairs of peaks when the Fourier transform was applied.
The x axis locations of peaks correspond to the frequencies (in Hz) of the sine waves from which they were derived with the Fourier transform.
The amplitude of each frequency peak is proportional to the amplitude of that frequency component in the signal.
The correct figure contains a peak at 8 Hz and 4 Hz, and the 4 Hz peak should be taller.
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[each_answer] => A.
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[each_answer] => B.
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[question] => Which of the following most directly determines the MINIMUM frequency that an ECG device can measure?
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[answer] => 3
[description] => Reason for the Correct Answer:
The Fourier transform maps time to frequency, or inverse time.
The longer the measurement period, the smaller the frequency accessible
The limits on ECG amplitude sensitivity would not limit the low frequency resolution preferentially.
If a frequency is so low that 1/frequency is longer than the total acquisition time, then the voltage will not undergo a full cycle at that frequency, making it difficult to observe
The minimum observable frequency is set by the total measurement time.
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[each_answer] => A. The minimum change in voltage that the device can detect
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[each_answer] => B. The minimum time interval between two measurement points on the voltage versus time graph.
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[each_answer] => C. The total time for which the voltage is measured
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[each_answer] => D. The minimum total voltage that the device can detect.
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[question] => Which of the following most directly determines the MAXIMUM frequency that an ECG device can measure?
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[answer] => 1
[description] => Reason for the Correct Answer:
The Fourier transform maps time to frequency, or inverse time.
The shorter the time interval between successive measurements of the voltage, the larger the frequencies that can be accessed
If the voltage varies faster than the time difference between the closest possible readings on the graph, then the ECG will not detect the fluctuation.
The maximum observable frequency is set by the interval between two points on the electrical activity graph.
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[each_answer] => A. The minimum time interval between two measurement points on the voltage versus time graph.
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[each_answer] => B. The minimum change in voltage that the device can detect
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[each_answer] => C. The minimum total voltage that the device can detect.
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[each_answer] => D. The total time for which the voltage is measured
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