Wood
Carbon monoxide. For understanding the risks of CO exposure it's important to note that the body has no sensors for O2 content of blood, only for partial pressure of O2 (in carotid and aortic bodies). So, exposure to CO causes reduction of functional Hb and drop in O2 content but no drop in PO2 in arterial blood.
Swan Ganz catheter. When balloon is inflated, flow (Q) goes to zero. Since Q = P/R this means that P = 0. P is driving pressure which in this case is Pcatheter tip - Pleft atrium = 0. If this deltaP is 0, then Pcatheter tip = Pleft atrium.
This blog is for UNM medical students taking the CV/Pulmonary/Renal block. It is based on notes I took during lectures. Some comments make minor corrections, some are memory tools and mnemonics (red font), some give numerical examples of formulas, some point out high yield concepts, etc. You are welcome to comment on the posts as are the faculty who gave the lectures. If you want to follow the blog by email, enter your email address below. Steve Wood, PhD, block tutor, scwood@salud.unm.edu
Wednesday, March 30, 2011
Tuesday, March 29, 2011
March 29 Lecture
Harkins
Wood
The presence of alveolar dead space is due to alveoli that are ventilated, but not perfused with blood. This acts like anatomical dead space in that the ventilation does no good ("wasted ventilation"). This can occur at the top of the lung during diastole (no blood flows to the top), during continuous pressure ventilation (CPAP), and as a result of blood clots blocking arteries.
The converse is wasted perfusion (shunt) which is blood flowing to regions of the lung that are not ventilated; e.g., bronchospasm, mucous plug, aspirated foreign body.
Paul
Wood
The presence of alveolar dead space is due to alveoli that are ventilated, but not perfused with blood. This acts like anatomical dead space in that the ventilation does no good ("wasted ventilation"). This can occur at the top of the lung during diastole (no blood flows to the top), during continuous pressure ventilation (CPAP), and as a result of blood clots blocking arteries.
The converse is wasted perfusion (shunt) which is blood flowing to regions of the lung that are not ventilated; e.g., bronchospasm, mucous plug, aspirated foreign body.
Paul
Monday, March 28, 2011
March 28 Lecture
Practice questions for the pulmonary physiology lectures this week are available at:
http://www.boom-outahere.com/boardreview/pulmoquestions.html
http://www.boom-outahere.com/boardreview/pulmoquestions.html
Friday, March 25, 2011
March 25 Lecture - Dr, Valenzuela
Valenzuela
Potassium changes are confusing. Hyperkalemia according to the Nernst equation causes hypopolarization. However, the significant effect on the heart is due to the effect on Na channels (decreases conductance) and potassium channels (increases conductance). These effects are summarized in the figure below:
Illustration of a normal action potential (solid line) and the action potential as seen in the setting of hyperkalemia (interrupted line). The phases of the action potential are labeled on the normal action potential. Note the decrease in both the resting membrane potential and the rate of phase 0 of the action potential (Vmax) seen in hyperkalemia. Phase 2 and 3 of the action potential have a greater slope in the setting of hyperkalemia compared with the normal action potential due to hyperkalemia induced increase in K conductance (I kr).
reference: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1413606/
The membrane potential at the onset of phase 0 determines the number of Na channels that are activated during phase 0, so with hypopolarization there are fewer activated Na channels and a reduced rate of depolarization. This decrease in Vmax causes a slowing of impulse conduction through the myocardium and a prolongation of membrane depolarization; as a result, the QRS duration is prolonged.
Beta blockers reduce sympathetic NS stimulation of renin production from juxtaglomerular cells of the afferent arteriole in the kidney, but decreased pressure will still trigger renin release from these cells.
Combo pill - ACEinhibitor + thiazide diuretic stabilizes K levels (blocked aldosterone increases plasma K - thiazide diuretic reduces plasma K)
Potassium changes are confusing. Hyperkalemia according to the Nernst equation causes hypopolarization. However, the significant effect on the heart is due to the effect on Na channels (decreases conductance) and potassium channels (increases conductance). These effects are summarized in the figure below:
Illustration of a normal action potential (solid line) and the action potential as seen in the setting of hyperkalemia (interrupted line). The phases of the action potential are labeled on the normal action potential. Note the decrease in both the resting membrane potential and the rate of phase 0 of the action potential (Vmax) seen in hyperkalemia. Phase 2 and 3 of the action potential have a greater slope in the setting of hyperkalemia compared with the normal action potential due to hyperkalemia induced increase in K conductance (I kr).
reference: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1413606/
The membrane potential at the onset of phase 0 determines the number of Na channels that are activated during phase 0, so with hypopolarization there are fewer activated Na channels and a reduced rate of depolarization. This decrease in Vmax causes a slowing of impulse conduction through the myocardium and a prolongation of membrane depolarization; as a result, the QRS duration is prolonged.
Beta blockers reduce sympathetic NS stimulation of renin production from juxtaglomerular cells of the afferent arteriole in the kidney, but decreased pressure will still trigger renin release from these cells.
Combo pill - ACEinhibitor + thiazide diuretic stabilizes K levels (blocked aldosterone increases plasma K - thiazide diuretic reduces plasma K)
Thursday, March 24, 2011
March 24 Lecture Dr. Boivin
Boivin
Hypertension (pulmonary or systemic) can cause edema - not because the arterial pressure is high causing higher capillary pressure but because the increased afterload can increase hypertropy and increased EDV causing increased filling pressure of RV or LV leading to increased venous pressure. The high arterial pressure doesn't result in high capillary pressure because of the protection of the arterioles and pre-capillary sphincters.
Horses have large spleens that contract from sympathetic stimulation during racing. this can cause hematocrit to go from 45 to 65% greatly increasing viscosity of their blood and contributing to pulmonary hypertension/stress fracture.
Hypertension (pulmonary or systemic) can cause edema - not because the arterial pressure is high causing higher capillary pressure but because the increased afterload can increase hypertropy and increased EDV causing increased filling pressure of RV or LV leading to increased venous pressure. The high arterial pressure doesn't result in high capillary pressure because of the protection of the arterioles and pre-capillary sphincters.
Horses have large spleens that contract from sympathetic stimulation during racing. this can cause hematocrit to go from 45 to 65% greatly increasing viscosity of their blood and contributing to pulmonary hypertension/stress fracture.
Wednesday, March 23, 2011
March 23 Lectures
Resta
p. 302 bottom left. ACh not physiologically important except in the few areas of the body where arterioles have parasympathetic innervation (salivary glands, gastrointestinal glands, and in genital erectile tissue.)
Vascular smooth muscle tone - big picture (you can fill in details from today's lectures):
p. 302 bottom left. ACh not physiologically important except in the few areas of the body where arterioles have parasympathetic innervation (salivary glands, gastrointestinal glands, and in genital erectile tissue.)
Vascular smooth muscle tone - big picture (you can fill in details from today's lectures):
"How does NO inhibit platelet aggregation?" NO diffuses across platelet membrane and activates guanyl cyclase which induces formation of cGMP and cAMP which both inhibit aggregation and adhesion of platelets by multiple mechansism including decreasing expression of fibrinogen receptors.
Tuesday, March 22, 2011
March 22 Lectures
Wood
corrected powerpoint with practice questions is up on Sharepoint
p. 249. with increased preload (EDV) ejcection fraction will always increase. Lecturer mis-spoke when he said it may not change. Thanks to student for correcting this. Example:
starting EF = SV/EDV = 50/100 50%. If EDV increases by 20, EF = 70/120 = 58%.
Most books only consider the left ventricle PV loop but it is important to consider the differences between the left and right ventricles. Below is a PV loop for the right ventricle:
Notice how much less work the RV does in stroke work and that the work of the RV is mainly volume work. The isovolumic contraction and relaxation periods are not pronounced in the RV.
Resta
humans have receptors in the circulatory system for pressure (carotid and aortic bodies; cranial nerves IX and X are afferents), volume (chambers of the heart, vena cava, pulm. artery). Volume increase is corrected by SNS and by chambers release of peptide that stimulates sodium secretion by kidneys. ANP is from atrial myocytes. BNP is from ventricular myocytes (called "brain" because it was first isolated from pig brains. In humans, it is produced primarily by the ventricle). BNP pretty good marker for CHF. Volume decrease inhibits above and may trigger thirst receptors via angiotensin II to also help increase volume.
summary figure for renin-angiotensin-aldosterone system (RAAS)
p. 285 beta agonists cause contraction of cardiac muscle but relaxation of smooth muscle. same signal transduction pathway at membrane. In both types of cells cAMP is increased and PKA is activated and intracellular Ca++ is increased. In cardiac muscle this leads to contraction via Troponin C mechanism. Smooth muscle doesn't have Troponin and increased PKA acts to inhibit MLCK and activate MLCP causing relaxation.
http://www.cvphysiology.com/Blood%20Pressure/BP026.htm
corrected powerpoint with practice questions is up on Sharepoint
p. 249. with increased preload (EDV) ejcection fraction will always increase. Lecturer mis-spoke when he said it may not change. Thanks to student for correcting this. Example:
starting EF = SV/EDV = 50/100 50%. If EDV increases by 20, EF = 70/120 = 58%.
Most books only consider the left ventricle PV loop but it is important to consider the differences between the left and right ventricles. Below is a PV loop for the right ventricle:
Notice how much less work the RV does in stroke work and that the work of the RV is mainly volume work. The isovolumic contraction and relaxation periods are not pronounced in the RV.
Resta
humans have receptors in the circulatory system for pressure (carotid and aortic bodies; cranial nerves IX and X are afferents), volume (chambers of the heart, vena cava, pulm. artery). Volume increase is corrected by SNS and by chambers release of peptide that stimulates sodium secretion by kidneys. ANP is from atrial myocytes. BNP is from ventricular myocytes (called "brain" because it was first isolated from pig brains. In humans, it is produced primarily by the ventricle). BNP pretty good marker for CHF. Volume decrease inhibits above and may trigger thirst receptors via angiotensin II to also help increase volume.
summary figure for renin-angiotensin-aldosterone system (RAAS)
p. 285 beta agonists cause contraction of cardiac muscle but relaxation of smooth muscle. same signal transduction pathway at membrane. In both types of cells cAMP is increased and PKA is activated and intracellular Ca++ is increased. In cardiac muscle this leads to contraction via Troponin C mechanism. Smooth muscle doesn't have Troponin and increased PKA acts to inhibit MLCK and activate MLCP causing relaxation.
http://www.cvphysiology.com/Blood%20Pressure/BP026.htm
Monday, March 21, 2011
March 21 Lecture
Ramo
The Valsalva maneuver Dr. Ramo described would increase total peripheral resistance from hand grasping and contracting gluts. A pure Valsalva maneuver is exhaling against a closed glottis. If this is done by itself, there is a complex response of heart rate, first falling, then rising. This is shown below for a 10 second Valsalva. The initial rise in aortic pressure and reflex bradycardia is due to compression of thoracic arteries and increased flow from compressed lungs to left atrium. This is followed by a drop and mean pressure due to reduced venous return to heart and reflex tachycardia. http://www.cvphysiology.com/Hemodynamics/H014.htm
The Valsalva maneuver Dr. Ramo described would increase total peripheral resistance from hand grasping and contracting gluts. A pure Valsalva maneuver is exhaling against a closed glottis. If this is done by itself, there is a complex response of heart rate, first falling, then rising. This is shown below for a 10 second Valsalva. The initial rise in aortic pressure and reflex bradycardia is due to compression of thoracic arteries and increased flow from compressed lungs to left atrium. This is followed by a drop and mean pressure due to reduced venous return to heart and reflex tachycardia. http://www.cvphysiology.com/Hemodynamics/H014.htm
Friday, March 18, 2011
Friday, March 18 Lectures
Ramo
LEADS MI CA
I, AVL Lateral Circumflex
II,III, AVF Inferior RCA
V1-V4 Anterior LAD
V5-V6 Antero-Lateral LAD/Circumflex
MCL1* Anterior LAD
V3, V4 RV RCA
* analogous to lead V1
Valenzuela
inotropic versus ionotropic - ionotropic refers to ligand gated ion channels (see Partridge lecture); e.g., nicotinic receptor, GABA receptor.
Inotropic refers to force of contraction of cardiac myocytes. agents that increase intracellular calcium are positive inotropic agents.
Resta
M2 receptors and Autonomic Innervation of the Heart
p. 231, 233, to clarify point raised in lecture: In human hearts there is lots of sympathetic innervation of the ventricle but parasympathetic innervation is sparse. this means the major effect of parasympathetic stimulation is on automaticity but not contractility.
LEADS MI CA
I, AVL Lateral Circumflex
II,III, AVF Inferior RCA
V1-V4 Anterior LAD
V5-V6 Antero-Lateral LAD/Circumflex
MCL1* Anterior LAD
V3, V4 RV RCA
* analogous to lead V1
Valenzuela
inotropic versus ionotropic - ionotropic refers to ligand gated ion channels (see Partridge lecture); e.g., nicotinic receptor, GABA receptor.
Inotropic refers to force of contraction of cardiac myocytes. agents that increase intracellular calcium are positive inotropic agents.
Resta
M2 receptors and Autonomic Innervation of the Heart
p. 231, 233, to clarify point raised in lecture: In human hearts there is lots of sympathetic innervation of the ventricle but parasympathetic innervation is sparse. this means the major effect of parasympathetic stimulation is on automaticity but not contractility.
Thursday, March 17, 2011
March 17 Lectures
Inbar
p. 195; rate of change in electrolyte disturbances often more important than absolute values.
Nernst equation is a bit easier to manage if you use the version
Em = -61 log [K]in/[K]out since K is always higher inside than outside, the math is a bit easier. answer is the same. -61 = RT/ZF. the reason hypothermia doesn't really change resting membrane potential is that T is absolute temperature (not Farenheit or centigrade) so it doesn't change much with hypothermia.
p. 195 & 196 intracellular shifts of potassium important in acidosis, beta blockers, glucose levels.
see Costanzo, p. 277, showing this figure:
p. 195; rate of change in electrolyte disturbances often more important than absolute values.
Nernst equation is a bit easier to manage if you use the version
Em = -61 log [K]in/[K]out since K is always higher inside than outside, the math is a bit easier. answer is the same. -61 = RT/ZF. the reason hypothermia doesn't really change resting membrane potential is that T is absolute temperature (not Farenheit or centigrade) so it doesn't change much with hypothermia.
p. 195 & 196 intracellular shifts of potassium important in acidosis, beta blockers, glucose levels.
see Costanzo, p. 277, showing this figure:
Wednesday, March 16, 2011
March 16 Lectures
Inbar
depolarization is phase 0, not phase 1. check your notes on this.
8.5 x 11 standard EKG paper is 10 seconds of time for rhythm strip. can use this to quickly calculate heart rate; no. of beats in rhythm strip x 60 = BPM.
Krinsky
p. 152; Textbooks definition of Cor Pulmonale: "Cor pulmonale is defined as an alteration in the structure and function of the right ventricle caused by a primary disorder of the respiratory system."
cardiomegaly = increased size or weight (or both)
intercalated disks = gap junctions
p. 152; pressure load leads to hypertrophy; volume load leads to dilation of heart.
findings at autopsy after first and fatal MI: no morphologic or histologic changes (but vessels may look bad); subsequent fatal heart attack reveals morphologic and histologic changes that took days to weeks to develope. Microvascular injury mainly occurs during reperfusion rather than ischemia. This injury is caused by the reintroduction of oxygen and subsequent formation of superoxide radicals.
p. 157; restrictive cardiomyopathy = decrease in compliance of ventricle. compliance = dV/dP. decreased compliance = stiffer ventricle = diastolic heart failure. also see p. 162 - constrictive pericarditis = decreased compliance.
depolarization is phase 0, not phase 1. check your notes on this.
8.5 x 11 standard EKG paper is 10 seconds of time for rhythm strip. can use this to quickly calculate heart rate; no. of beats in rhythm strip x 60 = BPM.
Krinsky
p. 152; Textbooks definition of Cor Pulmonale: "Cor pulmonale is defined as an alteration in the structure and function of the right ventricle caused by a primary disorder of the respiratory system."
cardiomegaly = increased size or weight (or both)
intercalated disks = gap junctions
p. 152; pressure load leads to hypertrophy; volume load leads to dilation of heart.
findings at autopsy after first and fatal MI: no morphologic or histologic changes (but vessels may look bad); subsequent fatal heart attack reveals morphologic and histologic changes that took days to weeks to develope. Microvascular injury mainly occurs during reperfusion rather than ischemia. This injury is caused by the reintroduction of oxygen and subsequent formation of superoxide radicals.
p. 157; restrictive cardiomyopathy = decrease in compliance of ventricle. compliance = dV/dP. decreased compliance = stiffer ventricle = diastolic heart failure. also see p. 162 - constrictive pericarditis = decreased compliance.
Tuesday, March 15, 2011
March 15 Lectures
Partridge
cell to cell propagation in cardiac cells uses gap junctions. speed of propagation depends on slope of phase 0 of cell action potential which can be altered by electrolyte imbalance (high K for example) and autonomic drugs. Agents that alter speed of conduction are said to have a "dromotropic" effect.
p. 130 Costanzo is wrong is stating that phase 0 of SA node action potential is due to T-type Ca channels. It is L-type. Here is a nice figure on the SA node action potential:
From http://www.cvphysiology.com/Arrhythmias/A004.htm
Phase 4 starts with funny channels. If. As the membrane potential reaches about -50 mV, another type of channel opens. This channel is called transient or T-type Ca++ channel. As Ca++ enters the cell through these channels down its electrochemical gradient, the inward directed Ca++ currents further depolarize the cell. As the membrane continues to depolarize to about -40 mV, a second Ca++ channel opens. These are the so-called long-lasting, or L-type Ca++ channels.
heart muscle can't cramp. twitches can't summate.
total period of systole is about 300 msec (total conduction time through heart). diastole is about 500 msec. at resting heart rate (ca. 70 bpm). at higher heart rates, period of systole shortens only slightly; diastole period is decreased so filling time decreases and can lead to decreased stroke volume.
Intrinsic firing rate of the SA node (without autonomic tone) is about 100 bpm. The normal autonomic tone is predominantly vagal which lowers the innervated SA node resting rate to about 70 bpm.
Resta
P. 82. Flow path of blood through heart and order of valves: tricuspid then biscuspid (mitral);
Memory tool: "try it before you buy it"
p. 85. LeCesne
For box method, you can also count the big boxes between R waves. Divide 300 by the number of big boxes. There are 5 big boxes per second (25 mm) so 300 big boxes per minute. 1 big box between R waves = 300/1 or 300 bpm. 2 big boxes = 300/2 or 150 bpm, etc.
most books give the normal electrical axis as -30 to + 90 degrees instead of 0 to + 90 degrees. When I and aVF are both positive, axis is in range of 0 to + 90 degrees. When leads I and II are positive, then the axis is within the larger normal range of -30 to + 90 degrees.
Biphasic leads (equally positive and negative) are a great tool because the electrical axis is perpendicular to that lead.
In this ECG, lead aVL is biphasic. The positive perpendicular axis to aVL is +60°. Therefore, the mean electrical axis is +60°, which is normal. It could also be -60° but if that were true, aVF would be negative, not positive.
Timm
aortic regurgitation diastolic (H)ARD
HARD ASS MSD (missed) MRS
If chambers are connected via a septal defect, the direction of shunted blood flow is from higher to lower pressure OR if pressures are equal, from stiffer chamber to more compliant chamber.
Sounds
cell to cell propagation in cardiac cells uses gap junctions. speed of propagation depends on slope of phase 0 of cell action potential which can be altered by electrolyte imbalance (high K for example) and autonomic drugs. Agents that alter speed of conduction are said to have a "dromotropic" effect.
p. 130 Costanzo is wrong is stating that phase 0 of SA node action potential is due to T-type Ca channels. It is L-type. Here is a nice figure on the SA node action potential:
From http://www.cvphysiology.com/Arrhythmias/A004.htm
Phase 4 starts with funny channels. If. As the membrane potential reaches about -50 mV, another type of channel opens. This channel is called transient or T-type Ca++ channel. As Ca++ enters the cell through these channels down its electrochemical gradient, the inward directed Ca++ currents further depolarize the cell. As the membrane continues to depolarize to about -40 mV, a second Ca++ channel opens. These are the so-called long-lasting, or L-type Ca++ channels.
heart muscle can't cramp. twitches can't summate.
total period of systole is about 300 msec (total conduction time through heart). diastole is about 500 msec. at resting heart rate (ca. 70 bpm). at higher heart rates, period of systole shortens only slightly; diastole period is decreased so filling time decreases and can lead to decreased stroke volume.
Intrinsic firing rate of the SA node (without autonomic tone) is about 100 bpm. The normal autonomic tone is predominantly vagal which lowers the innervated SA node resting rate to about 70 bpm.
http://www.cvphysiology.com/Arrhythmias/A005.htmResta
P. 82. Flow path of blood through heart and order of valves: tricuspid then biscuspid (mitral);
Memory tool: "try it before you buy it"
p. 85. LeCesne
Leads I, II, and III
memory trick: count the L's
RA - LA = lead I (1 L)
RA - LL = lead II (2 Ls)
LA - LL = lead III (3 Ls)
Fast and Easy way to calculate heart rate (and more accurate with irregular rhythms) = count R waves in rhythm strip and multiply by 6. Standard 8.5 x 11 inch EKG rhythm strip gives 10 seconds of recording. beats in 10 seconds x 6 = BPM.For box method, you can also count the big boxes between R waves. Divide 300 by the number of big boxes. There are 5 big boxes per second (25 mm) so 300 big boxes per minute. 1 big box between R waves = 300/1 or 300 bpm. 2 big boxes = 300/2 or 150 bpm, etc.
most books give the normal electrical axis as -30 to + 90 degrees instead of 0 to + 90 degrees. When I and aVF are both positive, axis is in range of 0 to + 90 degrees. When leads I and II are positive, then the axis is within the larger normal range of -30 to + 90 degrees.
Biphasic leads (equally positive and negative) are a great tool because the electrical axis is perpendicular to that lead.
In this ECG, lead aVL is biphasic. The positive perpendicular axis to aVL is +60°. Therefore, the mean electrical axis is +60°, which is normal. It could also be -60° but if that were true, aVF would be negative, not positive.
Timm
Mneumonic for valve defects (left ventricle)
aortic regurgitation diastolic (H)ARD
aortic stenosis systolic ASS
mitral stenosis diastolic MSD
mitral regurgitation systolic MRS
If chambers are connected via a septal defect, the direction of shunted blood flow is from higher to lower pressure OR if pressures are equal, from stiffer chamber to more compliant chamber.
Sounds
website for heart sounds: http://depts.washington.edu/physdx/heart/tech2.html
Monday, March 14, 2011
March 14 Lectures
Resta
syllabus p. 58: Memory tool for pressure, flow, and resistance relationships.
be able to rearrange for Q =P/R; R = P/Q. used to solve for flow, resistance, and pressure. Pressure is the most tightly regulated of the 3 via pressure receptors (baroreceptors). Drop in P is due to either drop in Q or drop in R (helpful for figuring out different forms of shock (e.g., hemorrhagic vs. anaphylactic).
The figure at top of page is incorrect for mean arterial pressure. It is not 100 mm Hg when blood pressure is 120/80. Because more time is spent is diastole than systole, MAP is calculated as 2/3 Diastolic BP + 1/3 Systolic BP, so for 120/80, MAP would be about 93 mm Hg.
p. 59: blood doping may increase hematocrit too much; i.e., above the optimum hct, and cause reduced oxygen delivery due to reduced blood flow.
(Taken from Williams Hematology by Lichtman et al.
p. 60 If R = 1 for each of the resistance in series and parallel, then for the series resistances:
Rt = 1 + 1 +1 = 3
and for the parallel resistances:
1/Rt = 1/1 + 1/1 + 1/1 = 3 and Rt = 1/3
So, if you add another resistance to the parallel, Rt would = 1/4 (always gets less with added resistance)
syllabus p. 58: Memory tool for pressure, flow, and resistance relationships.
PQR (alphabetical). P=QR
be able to rearrange for Q =P/R; R = P/Q. used to solve for flow, resistance, and pressure. Pressure is the most tightly regulated of the 3 via pressure receptors (baroreceptors). Drop in P is due to either drop in Q or drop in R (helpful for figuring out different forms of shock (e.g., hemorrhagic vs. anaphylactic).
The figure at top of page is incorrect for mean arterial pressure. It is not 100 mm Hg when blood pressure is 120/80. Because more time is spent is diastole than systole, MAP is calculated as 2/3 Diastolic BP + 1/3 Systolic BP, so for 120/80, MAP would be about 93 mm Hg.
p. 59: blood doping may increase hematocrit too much; i.e., above the optimum hct, and cause reduced oxygen delivery due to reduced blood flow.
(Taken from Williams Hematology by Lichtman et al.
p. 60 If R = 1 for each of the resistance in series and parallel, then for the series resistances:
Rt = 1 + 1 +1 = 3
and for the parallel resistances:
1/Rt = 1/1 + 1/1 + 1/1 = 3 and Rt = 1/3
So, if you add another resistance to the parallel, Rt would = 1/4 (always gets less with added resistance)
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