Question 1. Einthoven triangle Consider Einthoven's triangle of the frontal electrocardiogram (ECG) shown below. The triangle is equilateral and the augmented lead vectors (aVR, aVL, and aVF) bisect the bipolar lead vectors (I, II, and III). All three electrodes RA, LA and LL are at distance d = 50 cm to the heart. (a) Determine the magnitude of the bipolar (I, II, III) and augmented (aVR, aVL, aVF) lead vectors in meters. (b) At the peak of the S wave, the cardiac vector points horizontally from right to left with magnitude 1 mV/m. Find the voltage on lead I, lead II, lead aVF, and lead aVR. Hint: $V(vec{A}) = vec{M} cdot vec{A}$, where V is the voltage along the lead vector $vec{A}$ and $vec{M}$ is the cardiac vector.
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The augmented leads (aVR, aVL, and aVF) are derived from the same points but provide a different view of the heart's electrical activity. The distance from each electrode to the heart is given as d = 50 cm, but for the purpose of calculating vector magnitudes, Show more…
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Vectorcardiography In each of the following questions the heart voltage vector of a patient with different pathologies is given. Determine the electrocardiograph reading that would result in each of the three leads of Einthoven's triangle, and draw a sketch like that in Figure 7. Recall from Example 7 that vector representations of the sides of Einthoven's triangle are $$\begin{array}{c}{\mathbf{I}_{1}=[1,0] \quad \mathbf{I}_{2}=[1 / 2,-\sqrt{3} / 2]} \\ {\mathbf{I}_{3}=[-1 / 2,-\sqrt{3} / 2]}\end{array}$$ $$\begin{array}{l}{\text { (a) Left anterior hemiblock: } \mathbf{h}=[0.3,0.2]} \\ {\text { (b) Left posterior hemiblock: } \mathbf{h}=[-0.3,-0.2]} \\ {\text { (c) Apical ischemia: } \mathbf{h}=[-0.3,0.2]} \\ {\text { (d) Chronic obstructive pulmonary disease: }}\end{array}$$ $$\mathbf{h}=[0.1,-0.0667]$$
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The table below shows the configuration of electrodes for each of the 12 ECG leads. Lead Position of Electrodes Positive Electrode Negative Electrode Earth Standard limb leads LA = left arm; LL = left leg RA = right arm; RL = right leg RA LA Augmented limb leads aVR aVL aVF LA + LL RA + LL As above C RA + LA Chest leads V1 V2 V3 Fourth intercostal space, right of sternum V1 V2 V3 Fourth intercostal space, left of sternum Halfway between V2 and V4 RA + LA + LL Fifth intercostal space, midclavicular line V4 Fifth intercostal space, anterior axillary line V5 Fifth intercostal space, midaxillary line V6 Which leads are unipolar and which are bipolar? pts Enter your answer here B Xzlxz Check Answer MORE
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4. The Hearts Electric Dipole (3p) The ECG records the electrical activity that accompanies the contraction and relaxation of the heart muscle tissue. The human heart has four chambers. During each heartbeat cycle, each chamber pumps in a specific sequence. During the pumping-process specific muscle cells in the heart contract, which leads to charge separation. You can model the heart like an electric dipole that rotates. 4.1 Construct, using an electric field vector for each of the point charges, the net electric field at point P. Use the idealized case where P is the corner of an isosceles triangle as shown in the figure below. Show the electric field vector for each contributing point charge and how you determine the vector sum of those two fields. (2p) 4.2 We can model the movable charges in the body as a solution of Na+ and Cl- ions. At a moment when the electric dipole of the heart is oriented as shown above, the force on the ions in this dipole electric field causes a charge separation. At the location of electrode L, there is an accumulation of _____ ions and at the location of electrode R, there is an accumulation of _____ ions. At this moment: â—‹ VL > VR â—‹ VL < VR (1p) Potential differences that are measured in an ECG are of the order of 1 milli-V.
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